LMFDB - Embedded newform 390.2.bb.b.361.1

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			361.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	390.361
Dual form			390.2.bb.b.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000i q^{5} +(-0.866025 - 0.500000i) q^{6} +(-1.73205 - 1.00000i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(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} +(5.59808 - 3.23205i) 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} +(6.46410 + 3.73205i) q^{19} +(-0.866025 - 0.500000i) q^{20} -2.00000i q^{21} +(-3.23205 + 5.59808i) q^{22} +(-1.86603 - 3.23205i) 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} +(-0.133975 - 0.232051i) q^{29} +(-0.500000 + 0.866025i) q^{30} +1.73205i q^{31} +(0.866025 + 0.500000i) q^{32} +(5.59808 + 3.23205i) q^{33} +4.00000i q^{34} +(-1.00000 + 1.73205i) q^{35} +(0.500000 + 0.866025i) q^{36} +(7.96410 - 4.59808i) q^{37} -7.46410 q^{38} +(-2.50000 + 2.59808i) q^{39} +1.00000 q^{40} +(1.73205 - 1.00000i) q^{41} +(1.00000 + 1.73205i) q^{42} +(-5.96410 + 10.3301i) q^{43} -6.46410i q^{44} +(0.866025 + 0.500000i) q^{45} +(3.23205 + 1.86603i) q^{46} +3.53590i 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} +0.928203 q^{53} +(0.866025 - 0.500000i) q^{54} +(-3.23205 - 5.59808i) q^{55} +(1.00000 - 1.73205i) q^{56} +7.46410i q^{57} +(0.232051 + 0.133975i) q^{58} +(7.33013 + 4.23205i) 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} -6.46410 q^{66} +(-9.92820 + 5.73205i) q^{67} +(-2.00000 - 3.46410i) q^{68} +(1.86603 - 3.23205i) q^{69} -2.00000i q^{70} +(-10.7321 - 6.19615i) q^{71} +(-0.866025 - 0.500000i) q^{72} -2.00000i q^{73} +(-4.59808 + 7.96410i) q^{74} +(-0.500000 - 0.866025i) q^{75} +(6.46410 - 3.73205i) q^{76} -12.9282 q^{77} +(0.866025 - 3.50000i) q^{78} -13.9282 q^{79} +(-0.866025 + 0.500000i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.00000 + 1.73205i) q^{82} -8.92820i q^{83} +(-1.73205 - 1.00000i) q^{84} +(-3.46410 - 2.00000i) q^{85} -11.9282i q^{86} +(0.133975 - 0.232051i) q^{87} +(3.23205 + 5.59808i) q^{88} +(-0.464102 + 0.267949i) q^{89} -1.00000 q^{90} +(1.73205 - 7.00000i) q^{91} -3.73205 q^{92} +(-1.50000 + 0.866025i) q^{93} +(-1.76795 - 3.06218i) q^{94} +(3.73205 - 6.46410i) q^{95} +1.00000i q^{96} +(0.464102 + 0.267949i) q^{97} +(2.59808 + 1.50000i) q^{98} +6.46410i 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	0.135583	−	0.990766i	$-0.456709\pi$
$7$	−1.73205	−	1.00000i	−0.654654	−	0.377964i	−0.790237	+	0.612801i	$0.790043\pi$
$8$			1.00000i			0.353553i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$	5.59808	−	3.23205i	1.68788	−	0.974500i	0.731748	−	0.681575i	$-0.238705\pi$
$11$	5.59808	−	3.23205i	1.68788	−	0.974500i	0.956136	−	0.292925i	$-0.0946285\pi$
$12$	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
$19$	6.46410	+	3.73205i	1.48297	+	0.856191i	0.999813	−	0.0193444i	$-0.00615788\pi$
$19$	6.46410	+	3.73205i	1.48297	+	0.856191i	0.483154	+	0.875536i	$0.339491\pi$
$20$	−0.866025	−	0.500000i	−0.193649	−	0.111803i
$21$		−	2.00000i		−	0.436436i
$22$	−3.23205	+	5.59808i	−0.689076	+	1.19351i
$23$	−1.86603	−	3.23205i	−0.389093	−	0.673929i	0.603235	−	0.797564i	$-0.293878\pi$
$23$	−1.86603	−	3.23205i	−0.389093	−	0.673929i	−0.992328	+	0.123635i	$0.960545\pi$
$24$	−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
$29$	−0.133975	−	0.232051i	−0.0248785	−	0.0430908i	0.853318	−	0.521391i	$-0.174587\pi$
$29$	−0.133975	−	0.232051i	−0.0248785	−	0.0430908i	−0.878197	+	0.478300i	$0.841253\pi$
$30$	−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
$33$	5.59808	+	3.23205i	0.974500	+	0.562628i
$34$			4.00000i			0.685994i
$35$	−1.00000	+	1.73205i	−0.169031	+	0.292770i
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	7.96410	−	4.59808i	1.30929	−	0.755919i	0.327313	−	0.944916i	$-0.393857\pi$
$37$	7.96410	−	4.59808i	1.30929	−	0.755919i	0.981978	+	0.188997i	$0.0605237\pi$
$38$	−7.46410			−1.21084
$39$	−2.50000	+	2.59808i	−0.400320	+	0.416025i
$40$	1.00000			0.158114
$41$	1.73205	−	1.00000i	0.270501	−	0.156174i	−0.358614	−	0.933486i	$-0.616751\pi$
$41$	1.73205	−	1.00000i	0.270501	−	0.156174i	0.629115	+	0.777312i	$0.283417\pi$
$42$	1.00000	+	1.73205i	0.154303	+	0.267261i
$43$	−5.96410	+	10.3301i	−0.909517	+	1.57533i	−0.0947805	+	0.995498i	$0.530215\pi$
$43$	−5.96410	+	10.3301i	−0.909517	+	1.57533i	−0.814736	+	0.579831i	$0.803118\pi$
$44$		−	6.46410i		−	0.974500i
$45$	0.866025	+	0.500000i	0.129099	+	0.0745356i
$46$	3.23205	+	1.86603i	0.476540	+	0.275130i
$47$			3.53590i			0.515764i	0.966176	+	0.257882i	$0.0830245\pi$
$47$			3.53590i			0.515764i	−0.966176	+	0.257882i	$0.916975\pi$
$48$	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
$53$	0.928203			0.127499			0.0637493	−	0.997966i	$-0.479694\pi$
$53$	0.928203			0.127499			0.0637493	+	0.997966i	$0.479694\pi$
$54$	0.866025	−	0.500000i	0.117851	−	0.0680414i
$55$	−3.23205	−	5.59808i	−0.435810	−	0.754844i
$56$	1.00000	−	1.73205i	0.133631	−	0.231455i
$57$			7.46410i			0.988644i
$58$	0.232051	+	0.133975i	0.0304698	+	0.0175917i
$59$	7.33013	+	4.23205i	0.954301	+	0.550966i	0.894414	−	0.447239i	$-0.147593\pi$
$59$	7.33013	+	4.23205i	0.954301	+	0.550966i	0.0598868	+	0.998205i	$0.480926\pi$
$60$		−	1.00000i		−	0.129099i
$61$	5.19615	−	9.00000i	0.665299	−	1.15233i	−0.313905	−	0.949454i	$-0.601637\pi$
$61$	5.19615	−	9.00000i	0.665299	−	1.15233i	0.979204	−	0.202878i	$-0.0650293\pi$
$62$	−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
$66$	−6.46410			−0.795676
$67$	−9.92820	+	5.73205i	−1.21292	+	0.700281i	−0.963395	−	0.268086i	$-0.913609\pi$
$67$	−9.92820	+	5.73205i	−1.21292	+	0.700281i	−0.249528	+	0.968368i	$0.580276\pi$
$68$	−2.00000	−	3.46410i	−0.242536	−	0.420084i
$69$	1.86603	−	3.23205i	0.224643	−	0.389093i
$70$		−	2.00000i		−	0.239046i
$71$	−10.7321	−	6.19615i	−1.27366	−	0.735348i	−0.297985	−	0.954570i	$-0.596315\pi$
$71$	−10.7321	−	6.19615i	−1.27366	−	0.735348i	−0.975675	+	0.219222i	$0.929648\pi$
$72$	−0.866025	−	0.500000i	−0.102062	−	0.0589256i
$73$		−	2.00000i		−	0.234082i	−0.993127	−	0.117041i	$-0.962659\pi$
$73$		−	2.00000i		−	0.234082i	0.993127	−	0.117041i	$-0.0373409\pi$
$74$	−4.59808	+	7.96410i	−0.534516	+	0.925808i
$75$	−0.500000	−	0.866025i	−0.0577350	−	0.100000i
$76$	6.46410	−	3.73205i	0.741483	−	0.428096i
$77$	−12.9282			−1.47331
$78$	0.866025	−	3.50000i	0.0980581	−	0.396297i
$79$	−13.9282			−1.56705			−0.783523	−	0.621363i	$-0.786579\pi$
$79$	−13.9282			−1.56705			−0.783523	+	0.621363i	$0.786579\pi$
$80$	−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
$83$		−	8.92820i		−	0.979998i	−0.871723	−	0.489999i	$-0.836997\pi$
$83$		−	8.92820i		−	0.979998i	0.871723	−	0.489999i	$-0.163003\pi$
$84$	−1.73205	−	1.00000i	−0.188982	−	0.109109i
$85$	−3.46410	−	2.00000i	−0.375735	−	0.216930i
$86$		−	11.9282i		−	1.28625i
$87$	0.133975	−	0.232051i	0.0143636	−	0.0248785i
$88$	3.23205	+	5.59808i	0.344538	+	0.596757i
$89$	−0.464102	+	0.267949i	−0.0491947	+	0.0284026i	−0.524396	−	0.851475i	$-0.675709\pi$
$89$	−0.464102	+	0.267949i	−0.0491947	+	0.0284026i	0.475201	+	0.879877i	$0.342375\pi$
$90$	−1.00000			−0.105409
$91$	1.73205	−	7.00000i	0.181568	−	0.733799i
$92$	−3.73205			−0.389093
$93$	−1.50000	+	0.866025i	−0.155543	+	0.0898027i
$94$	−1.76795	−	3.06218i	−0.182350	−	0.315840i
$95$	3.73205	−	6.46410i	0.382900	−	0.663203i
$96$			1.00000i			0.102062i
$97$	0.464102	+	0.267949i	0.0471224	+	0.0272061i	0.523376	−	0.852102i	$-0.324672\pi$
$97$	0.464102	+	0.267949i	0.0471224	+	0.0272061i	−0.476254	+	0.879308i	$0.658006\pi$
$98$	2.59808	+	1.50000i	0.262445	+	0.151523i
$99$			6.46410i			0.649667i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	−1.46410	−	2.53590i	−0.145684	−	0.252331i	0.783944	−	0.620831i	$-0.213205\pi$
$101$	−1.46410	−	2.53590i	−0.145684	−	0.252331i	−0.929628	+	0.368500i	$0.879871\pi$
$102$	−3.46410	+	2.00000i	−0.342997	+	0.198030i
$103$	−11.8564			−1.16825			−0.584123	−	0.811665i	$-0.698562\pi$
$103$	−11.8564			−1.16825			−0.584123	+	0.811665i	$0.698562\pi$
$104$	−3.46410	+	1.00000i	−0.339683	+	0.0980581i
$105$	−2.00000			−0.195180
$106$	−0.803848	+	0.464102i	−0.0780766	+	0.0450775i
$107$	3.92820	+	6.80385i	0.379754	+	0.657753i	0.991026	−	0.133667i	$-0.0426754\pi$
$107$	3.92820	+	6.80385i	0.379754	+	0.657753i	−0.611273	+	0.791420i	$0.709342\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$			15.8564i			1.51877i	0.650643	+	0.759384i	$0.274500\pi$
$109$			15.8564i			1.51877i	−0.650643	+	0.759384i	$0.725500\pi$
$110$	5.59808	+	3.23205i	0.533756	+	0.308164i
$111$	7.96410	+	4.59808i	0.755919	+	0.436430i
$112$			2.00000i			0.188982i
$113$	−0.401924	+	0.696152i	−0.0378098	+	0.0654885i	−0.884311	−	0.466898i	$-0.845371\pi$
$113$	−0.401924	+	0.696152i	−0.0378098	+	0.0654885i	0.846501	+	0.532387i	$0.178705\pi$
$114$	−3.73205	−	6.46410i	−0.349539	−	0.605419i
$115$	−3.23205	+	1.86603i	−0.301390	+	0.174008i
$116$	−0.267949			−0.0248785
$117$	−3.50000	−	0.866025i	−0.323575	−	0.0800641i
$118$	−8.46410			−0.779184
$119$	−6.92820	+	4.00000i	−0.635107	+	0.366679i
$120$	0.500000	+	0.866025i	0.0456435	+	0.0790569i
$121$	15.3923	−	26.6603i	1.39930	−	2.42366i
$122$			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
$127$	2.46410	+	4.26795i	0.218654	+	0.378719i	0.954397	−	0.298542i	$-0.0965002\pi$
$127$	2.46410	+	4.26795i	0.218654	+	0.378719i	−0.735743	+	0.677261i	$0.763167\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−11.9282			−1.05022
$130$	−2.50000	+	2.59808i	−0.219265	+	0.227866i
$131$	−18.6603			−1.63035			−0.815177	−	0.579212i	$-0.803360\pi$
$131$	−18.6603			−1.63035			−0.815177	+	0.579212i	$0.803360\pi$
$132$	5.59808	−	3.23205i	0.487250	−	0.281314i
$133$	−7.46410	−	12.9282i	−0.647220	−	1.12102i
$134$	5.73205	−	9.92820i	0.495174	−	0.857666i
$135$			1.00000i			0.0860663i
$136$	3.46410	+	2.00000i	0.297044	+	0.171499i
$137$	−2.13397	−	1.23205i	−0.182318	−	0.105261i	0.406063	−	0.913845i	$-0.366901\pi$
$137$	−2.13397	−	1.23205i	−0.182318	−	0.105261i	−0.588381	+	0.808584i	$0.700235\pi$
$138$			3.73205i			0.317693i
$139$	6.46410	−	11.1962i	0.548278	−	0.949645i	−0.450115	−	0.892971i	$-0.648617\pi$
$139$	6.46410	−	11.1962i	0.548278	−	0.949645i	0.998393	−	0.0566745i	$-0.0180497\pi$
$140$	1.00000	+	1.73205i	0.0845154	+	0.146385i
$141$	−3.06218	+	1.76795i	−0.257882	+	0.148888i
$142$	12.3923			1.03994
$143$	16.7942	+	16.1603i	1.40440	+	1.35139i
$144$	1.00000			0.0833333
$145$	−0.232051	+	0.133975i	−0.0192708	+	0.0111260i
$146$	1.00000	+	1.73205i	0.0827606	+	0.143346i
$147$	1.50000	−	2.59808i	0.123718	−	0.214286i
$148$		−	9.19615i		−	0.755919i
$149$	−11.7224	−	6.76795i	−0.960339	−	0.554452i	−0.0640617	−	0.997946i	$-0.520405\pi$
$149$	−11.7224	−	6.76795i	−0.960339	−	0.554452i	−0.896277	+	0.443494i	$0.853739\pi$
$150$	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	$0.861027\pi$
$152$	−3.73205	+	6.46410i	−0.302709	+	0.524308i
$153$	2.00000	+	3.46410i	0.161690	+	0.280056i
$154$	11.1962	−	6.46410i	0.902212	−	0.520892i
$155$	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	$0.563939\pi$
$158$	12.0622	−	6.96410i	0.959615	−	0.554034i
$159$	0.464102	+	0.803848i	0.0368057	+	0.0637493i
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$			7.46410i			0.588254i
$162$	0.866025	+	0.500000i	0.0680414	+	0.0392837i
$163$	13.0359	+	7.52628i	1.02105	+	0.589504i	0.914408	−	0.404794i	$-0.132657\pi$
$163$	13.0359	+	7.52628i	1.02105	+	0.589504i	0.106642	+	0.994297i	$0.465990\pi$
$164$		−	2.00000i		−	0.156174i
$165$	3.23205	−	5.59808i	0.251615	−	0.435810i
$166$	4.46410	+	7.73205i	0.346481	+	0.600124i
$167$	14.1340	−	8.16025i	1.09372	−	0.631459i	0.159155	−	0.987254i	$-0.449123\pi$
$167$	14.1340	−	8.16025i	1.09372	−	0.631459i	0.934564	+	0.355794i	$0.115790\pi$
$168$	2.00000			0.154303
$169$	−11.0000	+	6.92820i	−0.846154	+	0.532939i
$170$	4.00000			0.306786
$171$	−6.46410	+	3.73205i	−0.494322	+	0.285397i
$172$	5.96410	+	10.3301i	0.454758	+	0.787665i
$173$	−5.46410	+	9.46410i	−0.415428	+	0.719542i	−0.995473	−	0.0950419i	$-0.969701\pi$
$173$	−5.46410	+	9.46410i	−0.415428	+	0.719542i	0.580045	+	0.814584i	$0.303035\pi$
$174$			0.267949i			0.0203132i
$175$	1.73205	+	1.00000i	0.130931	+	0.0755929i
$176$	−5.59808	−	3.23205i	−0.421971	−	0.243625i
$177$			8.46410i			0.636201i
$178$	0.267949	−	0.464102i	0.0200836	−	0.0347859i
$179$	9.86603	+	17.0885i	0.737421	+	1.27725i	0.953653	+	0.300909i	$0.0972901\pi$
$179$	9.86603	+	17.0885i	0.737421	+	1.27725i	−0.216231	+	0.976342i	$0.569377\pi$
$180$	0.866025	−	0.500000i	0.0645497	−	0.0372678i
$181$	−2.92820			−0.217652			−0.108826	−	0.994061i	$-0.534709\pi$
$181$	−2.92820			−0.217652			−0.108826	+	0.994061i	$0.534709\pi$
$182$	2.00000	+	6.92820i	0.148250	+	0.513553i
$183$	10.3923			0.768221
$184$	3.23205	−	1.86603i	0.238270	−	0.137565i
$185$	−4.59808	−	7.96410i	−0.338057	−	0.585532i
$186$	0.866025	−	1.50000i	0.0635001	−	0.109985i
$187$		−	25.8564i		−	1.89081i
$188$	3.06218	+	1.76795i	0.223332	+	0.128941i
$189$	1.73205	+	1.00000i	0.125988	+	0.0727393i
$190$			7.46410i			0.541503i
$191$	−10.7321	+	18.5885i	−0.776544	+	1.34501i	0.157379	+	0.987538i	$0.449696\pi$
$191$	−10.7321	+	18.5885i	−0.776544	+	1.34501i	−0.933923	+	0.357475i	$0.883638\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	9.80385	−	5.66025i	0.705696	−	0.407434i	−0.103769	−	0.994601i	$-0.533090\pi$
$193$	9.80385	−	5.66025i	0.705696	−	0.407434i	0.809466	+	0.587167i	$0.199757\pi$
$194$	−0.535898			−0.0384753
$195$	2.59808	+	2.50000i	0.186052	+	0.179029i
$196$	−3.00000			−0.214286
$197$	3.80385	−	2.19615i	0.271013	−	0.156469i	−0.358335	−	0.933593i	$-0.616655\pi$
$197$	3.80385	−	2.19615i	0.271013	−	0.156469i	0.629348	+	0.777124i	$0.283322\pi$
$198$	−3.23205	−	5.59808i	−0.229692	−	0.397838i
$199$	2.53590	−	4.39230i	0.179765	−	0.311362i	−0.762035	−	0.647536i	$-0.775800\pi$
$199$	2.53590	−	4.39230i	0.179765	−	0.311362i	0.941800	+	0.336174i	$0.109133\pi$
$200$		−	1.00000i		−	0.0707107i
$201$	−9.92820	−	5.73205i	−0.700281	−	0.404308i
$202$	2.53590	+	1.46410i	0.178425	+	0.103014i
$203$			0.535898i			0.0376127i
$204$	2.00000	−	3.46410i	0.140028	−	0.242536i
$205$	−1.00000	−	1.73205i	−0.0698430	−	0.120972i
$206$	10.2679	−	5.92820i	0.715402	−	0.413037i
$207$	3.73205			0.259395
$208$	2.50000	−	2.59808i	0.173344	−	0.180144i
$209$	48.2487			3.33743
$210$	1.73205	−	1.00000i	0.119523	−	0.0690066i
$211$	5.66025	+	9.80385i	0.389668	+	0.674925i	0.992405	−	0.123015i	$-0.0392564\pi$
$211$	5.66025	+	9.80385i	0.389668	+	0.674925i	−0.602737	+	0.797940i	$0.705923\pi$
$212$	0.464102	−	0.803848i	0.0318746	−	0.0552085i
$213$		−	12.3923i		−	0.849107i
$214$	−6.80385	−	3.92820i	−0.465101	−	0.268526i
$215$	10.3301	+	5.96410i	0.704509	+	0.406748i
$216$		−	1.00000i		−	0.0680414i
$217$	1.73205	−	3.00000i	0.117579	−	0.203653i
$218$	−7.92820	−	13.7321i	−0.536966	−	0.930052i
$219$	1.73205	−	1.00000i	0.117041	−	0.0675737i
$220$	−6.46410			−0.435810
$221$	14.0000	+	3.46410i	0.941742	+	0.233021i
$222$	−9.19615			−0.617205
$223$	−17.7846	+	10.2679i	−1.19095	+	0.687593i	−0.958521	−	0.285022i	$-0.907999\pi$
$223$	−17.7846	+	10.2679i	−1.19095	+	0.687593i	−0.232424	+	0.972614i	$0.574666\pi$
$224$	−1.00000	−	1.73205i	−0.0668153	−	0.115728i
$225$	0.500000	−	0.866025i	0.0333333	−	0.0577350i
$226$		−	0.803848i		−	0.0534711i
$227$	−14.1962	−	8.19615i	−0.942232	−	0.543998i	−0.0515725	−	0.998669i	$-0.516423\pi$
$227$	−14.1962	−	8.19615i	−0.942232	−	0.543998i	−0.890659	+	0.454672i	$0.849757\pi$
$228$	6.46410	+	3.73205i	0.428096	+	0.247161i
$229$			7.85641i			0.519166i	0.965721	+	0.259583i	$0.0835851\pi$
$229$			7.85641i			0.519166i	−0.965721	+	0.259583i	$0.916415\pi$
$230$	1.86603	−	3.23205i	0.123042	−	0.213115i
$231$	−6.46410	−	11.1962i	−0.425307	−	0.736653i
$232$	0.232051	−	0.133975i	0.0152349	−	0.00879586i
$233$	6.12436			0.401220			0.200610	−	0.979671i	$-0.435708\pi$
$233$	6.12436			0.401220			0.200610	+	0.979671i	$0.435708\pi$
$234$	3.46410	−	1.00000i	0.226455	−	0.0653720i
$235$	3.53590			0.230657
$236$	7.33013	−	4.23205i	0.477151	−	0.275483i
$237$	−6.96410	−	12.0622i	−0.452367	−	0.783523i
$238$	4.00000	−	6.92820i	0.259281	−	0.449089i
$239$			16.3923i			1.06033i	0.847894	+	0.530165i	$0.177870\pi$
$239$			16.3923i			1.06033i	−0.847894	+	0.530165i	$0.822130\pi$
$240$	−0.866025	−	0.500000i	−0.0559017	−	0.0322749i
$241$	15.3564	+	8.86603i	0.989193	+	0.571111i	0.905033	−	0.425341i	$-0.139846\pi$
$241$	15.3564	+	8.86603i	0.989193	+	0.571111i	0.0841601	+	0.996452i	$0.473179\pi$
$242$			30.7846i			1.97891i
$243$	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
$247$	−6.46410	+	26.1244i	−0.411301	+	1.66225i
$248$	−1.73205			−0.109985
$249$	7.73205	−	4.46410i	0.489999	−	0.282901i
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	−7.86603	+	13.6244i	−0.496499	+	0.859962i	−0.999992	−	0.00403776i	$-0.998715\pi$
$251$	−7.86603	+	13.6244i	−0.496499	+	0.859962i	0.503493	+	0.863999i	$0.332048\pi$
$252$		−	2.00000i		−	0.125988i
$253$	−20.8923	−	12.0622i	−1.31349	−	0.758343i
$254$	−4.26795	−	2.46410i	−0.267795	−	0.154611i
$255$		−	4.00000i		−	0.250490i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	2.66987	+	4.62436i	0.166542	+	0.288459i	0.937202	−	0.348787i	$-0.113407\pi$
$257$	2.66987	+	4.62436i	0.166542	+	0.288459i	−0.770660	+	0.637247i	$0.780073\pi$
$258$	10.3301	−	5.96410i	0.643126	−	0.371309i
$259$	−18.3923			−1.14284
$260$	0.866025	−	3.50000i	0.0537086	−	0.217061i
$261$	0.267949			0.0165856
$262$	16.1603	−	9.33013i	0.998384	−	0.576417i
$263$	−3.06218	−	5.30385i	−0.188822	−	0.327049i	0.756036	−	0.654530i	$-0.227134\pi$
$263$	−3.06218	−	5.30385i	−0.188822	−	0.327049i	−0.944858	+	0.327481i	$0.893800\pi$
$264$	−3.23205	+	5.59808i	−0.198919	+	0.344538i
$265$		−	0.928203i		−	0.0570191i
$266$	12.9282	+	7.46410i	0.792679	+	0.457653i
$267$	−0.464102	−	0.267949i	−0.0284026	−	0.0163982i
$268$			11.4641i			0.700281i
$269$	−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
$271$	1.03590	−	0.598076i	0.0629263	−	0.0363305i	−0.468207	−	0.883619i	$-0.655100\pi$
$271$	1.03590	−	0.598076i	0.0629263	−	0.0363305i	0.531133	+	0.847288i	$0.321766\pi$
$272$	−4.00000			−0.242536
$273$	6.92820	−	2.00000i	0.419314	−	0.121046i
$274$	2.46410			0.148862
$275$	−5.59808	+	3.23205i	−0.337577	+	0.194900i
$276$	−1.86603	−	3.23205i	−0.112322	−	0.194547i
$277$	1.96410	−	3.40192i	0.118011	−	0.204402i	−0.800968	−	0.598707i	$-0.795681\pi$
$277$	1.96410	−	3.40192i	0.118011	−	0.204402i	0.918980	+	0.394305i	$0.129015\pi$
$278$			12.9282i			0.775382i
$279$	−1.50000	−	0.866025i	−0.0898027	−	0.0518476i
$280$	−1.73205	−	1.00000i	−0.103510	−	0.0597614i
$281$			8.92820i			0.532612i	0.963889	+	0.266306i	$0.0858032\pi$
$281$			8.92820i			0.532612i	−0.963889	+	0.266306i	$0.914197\pi$
$282$	1.76795	−	3.06218i	0.105280	−	0.182350i
$283$	4.96410	+	8.59808i	0.295085	+	0.511103i	0.975005	−	0.222184i	$-0.0713186\pi$
$283$	4.96410	+	8.59808i	0.295085	+	0.511103i	−0.679920	+	0.733287i	$0.737985\pi$
$284$	−10.7321	+	6.19615i	−0.636830	+	0.367674i
$285$	7.46410			0.442135
$286$	−22.6244	−	5.59808i	−1.33781	−	0.331021i
$287$	−4.00000			−0.236113
$288$	−0.866025	+	0.500000i	−0.0510310	+	0.0294628i
$289$	0.500000	+	0.866025i	0.0294118	+	0.0509427i
$290$	0.133975	−	0.232051i	0.00786726	−	0.0136265i
$291$			0.535898i			0.0314149i
$292$	−1.73205	−	1.00000i	−0.101361	−	0.0585206i
$293$	−27.5885	−	15.9282i	−1.61173	−	0.930536i	−0.988968	−	0.148128i	$-0.952675\pi$
$293$	−27.5885	−	15.9282i	−1.61173	−	0.930536i	−0.622767	−	0.782408i	$-0.713991\pi$
$294$			3.00000i			0.174964i
$295$	4.23205	−	7.33013i	0.246400	−	0.426776i
$296$	4.59808	+	7.96410i	0.267258	+	0.462904i
$297$	−5.59808	+	3.23205i	−0.324833	+	0.187543i
$298$	13.5359			0.784114
$299$	9.33013	−	9.69615i	0.539575	−	0.560743i
$300$	−1.00000			−0.0577350
$301$	20.6603	−	11.9282i	1.19084	−	0.687530i
$302$	−5.19615	−	9.00000i	−0.299005	−	0.517892i
$303$	1.46410	−	2.53590i	0.0841104	−	0.145684i
$304$		−	7.46410i		−	0.428096i
$305$	−9.00000	−	5.19615i	−0.515339	−	0.297531i
$306$	−3.46410	−	2.00000i	−0.198030	−	0.114332i
$307$		−	19.4641i		−	1.11087i	−0.831558	−	0.555437i	$-0.812551\pi$
$307$		−	19.4641i		−	1.11087i	0.831558	−	0.555437i	$-0.187449\pi$
$308$	−6.46410	+	11.1962i	−0.368326	+	0.637960i
$309$	−5.92820	−	10.2679i	−0.337244	−	0.584123i
$310$	−1.50000	+	0.866025i	−0.0851943	+	0.0491869i
$311$	−28.3923			−1.60998			−0.804990	−	0.593288i	$-0.797829\pi$
$311$	−28.3923			−1.60998			−0.804990	+	0.593288i	$0.797829\pi$
$312$	−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
$316$	−6.96410	+	12.0622i	−0.391761	+	0.678551i
$317$		−	14.5359i		−	0.816417i	−0.912889	−	0.408209i	$-0.866154\pi$
$317$		−	14.5359i		−	0.816417i	0.912889	−	0.408209i	$-0.133846\pi$
$318$	−0.803848	−	0.464102i	−0.0450775	−	0.0260255i
$319$	−1.50000	−	0.866025i	−0.0839839	−	0.0484881i
$320$			1.00000i			0.0559017i
$321$	−3.92820	+	6.80385i	−0.219251	+	0.379754i
$322$	−3.73205	−	6.46410i	−0.207979	−	0.360230i
$323$	25.8564	−	14.9282i	1.43869	−	0.830627i
$324$	−1.00000			−0.0555556
$325$	−1.00000	−	3.46410i	−0.0554700	−	0.192154i
$326$	−15.0526			−0.833684
$327$	−13.7321	+	7.92820i	−0.759384	+	0.438431i
$328$	1.00000	+	1.73205i	0.0552158	+	0.0956365i
$329$	3.53590	−	6.12436i	0.194940	−	0.337647i
$330$			6.46410i			0.355837i
$331$	−14.5359	−	8.39230i	−0.798965	−	0.461283i	0.0441440	−	0.999025i	$-0.485944\pi$
$331$	−14.5359	−	8.39230i	−0.798965	−	0.461283i	−0.843109	+	0.537742i	$0.819277\pi$
$332$	−7.73205	−	4.46410i	−0.424351	−	0.244999i
$333$			9.19615i			0.503946i
$334$	−8.16025	+	14.1340i	−0.446509	+	0.773377i
$335$	5.73205	+	9.92820i	0.313175	+	0.542436i
$336$	−1.73205	+	1.00000i	−0.0944911	+	0.0545545i
$337$	9.32051			0.507720			0.253860	−	0.967241i	$-0.418300\pi$
$337$	9.32051			0.507720			0.253860	+	0.967241i	$0.418300\pi$
$338$	6.06218	−	11.5000i	0.329739	−	0.625518i
$339$	−0.803848			−0.0436590
$340$	−3.46410	+	2.00000i	−0.187867	+	0.108465i
$341$	5.59808	+	9.69615i	0.303153	+	0.525076i
$342$	3.73205	−	6.46410i	0.201806	−	0.349539i
$343$			20.0000i			1.07990i
$344$	−10.3301	−	5.96410i	−0.556963	−	0.321563i
$345$	−3.23205	−	1.86603i	−0.174008	−	0.100463i
$346$		−	10.9282i		−	0.587504i
$347$	−0.803848	+	1.39230i	−0.0431528	+	0.0747428i	−0.886795	−	0.462163i	$-0.847074\pi$
$347$	−0.803848	+	1.39230i	−0.0431528	+	0.0747428i	0.843642	+	0.536906i	$0.180407\pi$
$348$	−0.133975	−	0.232051i	−0.00718179	−	0.0124392i
$349$	18.5885	−	10.7321i	0.995017	−	0.574474i	0.0882471	−	0.996099i	$-0.471873\pi$
$349$	18.5885	−	10.7321i	0.995017	−	0.574474i	0.906770	+	0.421625i	$0.138540\pi$
$350$	−2.00000			−0.106904
$351$	−1.00000	−	3.46410i	−0.0533761	−	0.184900i
$352$	6.46410			0.344538
$353$	1.73205	−	1.00000i	0.0921878	−	0.0532246i	−0.453197	−	0.891410i	$-0.649717\pi$
$353$	1.73205	−	1.00000i	0.0921878	−	0.0532246i	0.545385	+	0.838186i	$0.316383\pi$
$354$	−4.23205	−	7.33013i	−0.224931	−	0.389592i
$355$	−6.19615	+	10.7321i	−0.328858	+	0.569598i
$356$			0.535898i			0.0284026i
$357$	−6.92820	−	4.00000i	−0.366679	−	0.211702i
$358$	−17.0885	−	9.86603i	−0.903153	−	0.521436i
$359$		−	5.07180i		−	0.267679i	−0.991003	−	0.133840i	$-0.957269\pi$
$359$		−	5.07180i		−	0.267679i	0.991003	−	0.133840i	$-0.0427307\pi$
$360$	−0.500000	+	0.866025i	−0.0263523	+	0.0456435i
$361$	18.3564	+	31.7942i	0.966127	+	1.67338i
$362$	2.53590	−	1.46410i	0.133284	−	0.0769515i
$363$	30.7846			1.61577
$364$	−5.19615	−	5.00000i	−0.272352	−	0.262071i
$365$	−2.00000			−0.104685
$366$	−9.00000	+	5.19615i	−0.470438	+	0.271607i
$367$	−7.80385	−	13.5167i	−0.407358	−	0.705564i	0.587235	−	0.809416i	$-0.300216\pi$
$367$	−7.80385	−	13.5167i	−0.407358	−	0.705564i	−0.994593	+	0.103852i	$0.966883\pi$
$368$	−1.86603	+	3.23205i	−0.0972733	+	0.168482i
$369$			2.00000i			0.104116i
$370$	7.96410	+	4.59808i	0.414034	+	0.239043i
$371$	−1.60770	−	0.928203i	−0.0834674	−	0.0481899i
$372$			1.73205i			0.0898027i
$373$	7.89230	−	13.6699i	0.408648	−	0.707799i	−0.586090	−	0.810246i	$-0.699334\pi$
$373$	7.89230	−	13.6699i	0.408648	−	0.707799i	0.994739	+	0.102446i	$0.0326670\pi$
$374$	12.9282	+	22.3923i	0.668501	+	1.15788i
$375$	−0.866025	+	0.500000i	−0.0447214	+	0.0258199i
$376$	−3.53590			−0.182350
$377$	0.669873	−	0.696152i	0.0345002	−	0.0358537i
$378$	−2.00000			−0.102869
$379$	24.1244	−	13.9282i	1.23918	−	0.715444i	0.270257	−	0.962788i	$-0.412891\pi$
$379$	24.1244	−	13.9282i	1.23918	−	0.715444i	0.968928	+	0.247344i	$0.0795579\pi$
$380$	−3.73205	−	6.46410i	−0.191450	−	0.331601i
$381$	−2.46410	+	4.26795i	−0.126240	+	0.218654i
$382$		−	21.4641i		−	1.09820i
$383$	21.9904	+	12.6962i	1.12366	+	0.648743i	0.942332	−	0.334680i	$-0.108628\pi$
$383$	21.9904	+	12.6962i	1.12366	+	0.648743i	0.181324	+	0.983423i	$0.441962\pi$
$384$	0.866025	+	0.500000i	0.0441942	+	0.0255155i
$385$			12.9282i			0.658882i
$386$	−5.66025	+	9.80385i	−0.288099	+	0.499003i
$387$	−5.96410	−	10.3301i	−0.303172	−	0.525110i
$388$	0.464102	−	0.267949i	0.0235612	−	0.0136031i
$389$	−23.7321			−1.20326			−0.601631	−	0.798774i	$-0.705482\pi$
$389$	−23.7321			−1.20326			−0.601631	+	0.798774i	$0.705482\pi$
$390$	−3.50000	−	0.866025i	−0.177229	−	0.0438529i
$391$	−14.9282			−0.754952
$392$	2.59808	−	1.50000i	0.131223	−	0.0757614i
$393$	−9.33013	−	16.1603i	−0.470643	−	0.815177i
$394$	−2.19615	+	3.80385i	−0.110641	+	0.191635i
$395$			13.9282i			0.700804i
$396$	5.59808	+	3.23205i	0.281314	+	0.162417i
$397$	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	$0.568260\pi$
$398$			5.07180i			0.254226i
$399$	7.46410	−	12.9282i	0.373672	−	0.647220i
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$	−27.7128	+	16.0000i	−1.38391	+	0.799002i	−0.992620	−	0.121265i	$-0.961305\pi$
$401$	−27.7128	+	16.0000i	−1.38391	+	0.799002i	−0.391292	+	0.920267i	$0.627972\pi$
$402$	11.4641			0.571777
$403$	−6.00000	+	1.73205i	−0.298881	+	0.0862796i
$404$	−2.92820			−0.145684
$405$	−0.866025	+	0.500000i	−0.0430331	+	0.0248452i
$406$	−0.267949	−	0.464102i	−0.0132981	−	0.0230330i
$407$	29.7224	−	51.4808i	1.47329	−	2.55181i
$408$			4.00000i			0.198030i
$409$	3.46410	+	2.00000i	0.171289	+	0.0988936i	0.583193	−	0.812333i	$-0.301803\pi$
$409$	3.46410	+	2.00000i	0.171289	+	0.0988936i	−0.411905	+	0.911227i	$0.635136\pi$
$410$	1.73205	+	1.00000i	0.0855399	+	0.0493865i
$411$		−	2.46410i		−	0.121545i
$412$	−5.92820	+	10.2679i	−0.292062	+	0.505866i
$413$	−8.46410	−	14.6603i	−0.416491	−	0.721384i
$414$	−3.23205	+	1.86603i	−0.158847	+	0.0917101i
$415$	−8.92820			−0.438268
$416$	−0.866025	+	3.50000i	−0.0424604	+	0.171602i
$417$	12.9282			0.633097
$418$	−41.7846	+	24.1244i	−2.04375	+	1.17996i
$419$	−11.1962	−	19.3923i	−0.546968	−	0.947376i	−0.998480	−	0.0551112i	$-0.982449\pi$
$419$	−11.1962	−	19.3923i	−0.546968	−	0.947376i	0.451512	−	0.892265i	$-0.350885\pi$
$420$	−1.00000	+	1.73205i	−0.0487950	+	0.0845154i
$421$		−	4.39230i		−	0.214068i	−0.994255	−	0.107034i	$-0.965865\pi$
$421$		−	4.39230i		−	0.214068i	0.994255	−	0.107034i	$-0.0341353\pi$
$422$	−9.80385	−	5.66025i	−0.477244	−	0.275537i
$423$	−3.06218	−	1.76795i	−0.148888	−	0.0859606i
$424$			0.928203i			0.0450775i
$425$	−2.00000	+	3.46410i	−0.0970143	+	0.168034i
$426$	6.19615	+	10.7321i	0.300205	+	0.519970i
$427$	−18.0000	+	10.3923i	−0.871081	+	0.502919i
$428$	7.85641			0.379754
$429$	−5.59808	+	22.6244i	−0.270278	+	1.09231i
$430$	−11.9282			−0.575229
$431$	24.5885	−	14.1962i	1.18438	−	0.683805i	0.227360	−	0.973811i	$-0.426991\pi$
$431$	24.5885	−	14.1962i	1.18438	−	0.683805i	0.957025	+	0.290006i	$0.0936574\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	−9.66025	+	16.7321i	−0.464242	+	0.804091i	−0.999167	−	0.0408086i	$-0.987007\pi$
$433$	−9.66025	+	16.7321i	−0.464242	+	0.804091i	0.534925	+	0.844900i	$0.320340\pi$
$434$			3.46410i			0.166282i
$435$	−0.232051	−	0.133975i	−0.0111260	−	0.00642359i
$436$	13.7321	+	7.92820i	0.657646	+	0.379692i
$437$		−	27.8564i		−	1.33255i
$438$	−1.00000	+	1.73205i	−0.0477818	+	0.0827606i
$439$	8.92820	+	15.4641i	0.426120	+	0.738061i	0.996524	−	0.0833027i	$-0.0265468\pi$
$439$	8.92820	+	15.4641i	0.426120	+	0.738061i	−0.570404	+	0.821364i	$0.693214\pi$
$440$	5.59808	−	3.23205i	0.266878	−	0.154082i
$441$	3.00000			0.142857
$442$	−13.8564	+	4.00000i	−0.659082	+	0.190261i
$443$	16.3923			0.778822			0.389411	−	0.921064i	$-0.372679\pi$
$443$	16.3923			0.778822			0.389411	+	0.921064i	$0.372679\pi$
$444$	7.96410	−	4.59808i	0.377960	−	0.218215i
$445$	0.267949	+	0.464102i	0.0127020	+	0.0220005i
$446$	10.2679	−	17.7846i	0.486201	−	0.842126i
$447$		−	13.5359i		−	0.640226i
$448$	1.73205	+	1.00000i	0.0818317	+	0.0472456i
$449$	−13.6077	−	7.85641i	−0.642187	−	0.370767i	0.143270	−	0.989684i	$-0.454238\pi$
$449$	−13.6077	−	7.85641i	−0.642187	−	0.370767i	−0.785456	+	0.618917i	$0.787572\pi$
$450$			1.00000i			0.0471405i
$451$	6.46410	−	11.1962i	0.304383	−	0.527206i
$452$	0.401924	+	0.696152i	0.0189049	+	0.0327443i
$453$	−9.00000	+	5.19615i	−0.422857	+	0.244137i
$454$	16.3923			0.769329
$455$	−7.00000	−	1.73205i	−0.328165	−	0.0811998i
$456$	−7.46410			−0.349539
$457$	21.2487	−	12.2679i	0.993973	−	0.573870i	0.0875134	−	0.996163i	$-0.472108\pi$
$457$	21.2487	−	12.2679i	0.993973	−	0.573870i	0.906459	+	0.422293i	$0.138775\pi$
$458$	−3.92820	−	6.80385i	−0.183553	−	0.317923i
$459$	−2.00000	+	3.46410i	−0.0933520	+	0.161690i
$460$			3.73205i			0.174008i
$461$	0.401924	+	0.232051i	0.0187195	+	0.0108077i	0.509331	−	0.860571i	$-0.329893\pi$
$461$	0.401924	+	0.232051i	0.0187195	+	0.0108077i	−0.490611	+	0.871379i	$0.663226\pi$
$462$	11.1962	+	6.46410i	0.520892	+	0.300737i
$463$		−	7.07180i		−	0.328654i	−0.986406	−	0.164327i	$-0.947455\pi$
$463$		−	7.07180i		−	0.328654i	0.986406	−	0.164327i	$-0.0525453\pi$
$464$	−0.133975	+	0.232051i	−0.00621961	+	0.0107727i
$465$	0.866025	+	1.50000i	0.0401610	+	0.0695608i
$466$	−5.30385	+	3.06218i	−0.245696	+	0.141853i
$467$	−15.8564			−0.733747			−0.366873	−	0.930271i	$-0.619572\pi$
$467$	−15.8564			−0.733747			−0.366873	+	0.930271i	$0.619572\pi$
$468$	−2.50000	+	2.59808i	−0.115563	+	0.120096i
$469$	22.9282			1.05873
$470$	−3.06218	+	1.76795i	−0.141248	+	0.0815494i
$471$	−2.50000	−	4.33013i	−0.115194	−	0.199522i
$472$	−4.23205	+	7.33013i	−0.194796	+	0.337396i
$473$			77.1051i			3.54530i
$474$	12.0622	+	6.96410i	0.554034	+	0.319872i
$475$	−6.46410	−	3.73205i	−0.296593	−	0.171238i
$476$			8.00000i			0.366679i
$477$	−0.464102	+	0.803848i	−0.0212498	+	0.0368057i
$478$	−8.19615	−	14.1962i	−0.374883	−	0.649317i
$479$	4.73205	−	2.73205i	0.216213	−	0.124831i	−0.387983	−	0.921667i	$-0.626828\pi$
$479$	4.73205	−	2.73205i	0.216213	−	0.124831i	0.604195	+	0.796836i	$0.293495\pi$
$480$	1.00000			0.0456435
$481$	23.8923	+	22.9904i	1.08940	+	1.04827i
$482$	−17.7321			−0.807673
$483$	−6.46410	+	3.73205i	−0.294127	+	0.169814i
$484$	−15.3923	−	26.6603i	−0.699650	−	1.21183i
$485$	0.267949	−	0.464102i	0.0121669	−	0.0210738i
$486$			1.00000i			0.0453609i
$487$	20.0718	+	11.5885i	0.909540	+	0.525123i	0.880283	−	0.474449i	$-0.157353\pi$
$487$	20.0718	+	11.5885i	0.909540	+	0.525123i	0.0292568	+	0.999572i	$0.490686\pi$
$488$	9.00000	+	5.19615i	0.407411	+	0.235219i
$489$			15.0526i			0.680700i
$490$	1.50000	−	2.59808i	0.0677631	−	0.117369i
$491$	8.66025	+	15.0000i	0.390832	+	0.676941i	0.992559	−	0.121761i	$-0.0388541\pi$
$491$	8.66025	+	15.0000i	0.390832	+	0.676941i	−0.601728	+	0.798701i	$0.705521\pi$
$492$	1.73205	−	1.00000i	0.0780869	−	0.0450835i
$493$	−1.07180			−0.0482713
$494$	−7.46410	−	25.8564i	−0.335826	−	1.16333i
$495$	6.46410			0.290540
$496$	1.50000	−	0.866025i	0.0673520	−	0.0388857i
$497$	12.3923	+	21.4641i	0.555871	+	0.962797i
$498$	−4.46410	+	7.73205i	−0.200041	+	0.346481i
$499$		−	6.53590i		−	0.292587i	−0.989241	−	0.146293i	$-0.953266\pi$
$499$		−	6.53590i		−	0.292587i	0.989241	−	0.146293i	$-0.0467344\pi$
$500$	0.866025	+	0.500000i	0.0387298	+	0.0223607i
$501$	14.1340	+	8.16025i	0.631459	+	0.364573i
$502$		−	15.7321i		−	0.702156i
$503$	15.5885	−	27.0000i	0.695055	−	1.20387i	−0.275107	−	0.961414i	$-0.588713\pi$
$503$	15.5885	−	27.0000i	0.695055	−	1.20387i	0.970162	−	0.242457i	$-0.0779533\pi$
$504$	1.00000	+	1.73205i	0.0445435	+	0.0771517i
$505$	−2.53590	+	1.46410i	−0.112846	+	0.0651517i
$506$	24.1244			1.07246
$507$	−11.5000	−	6.06218i	−0.510733	−	0.269231i
$508$	4.92820			0.218654
$509$	1.20577	−	0.696152i	0.0534449	−	0.0308564i	−0.473039	−	0.881041i	$-0.656843\pi$
$509$	1.20577	−	0.696152i	0.0534449	−	0.0308564i	0.526484	+	0.850185i	$0.323510\pi$
$510$	2.00000	+	3.46410i	0.0885615	+	0.153393i
$511$	−2.00000	+	3.46410i	−0.0884748	+	0.153243i
$512$		−	1.00000i		−	0.0441942i
$513$	−6.46410	−	3.73205i	−0.285397	−	0.164774i
$514$	−4.62436	−	2.66987i	−0.203972	−	0.117763i
$515$			11.8564i			0.522456i
$516$	−5.96410	+	10.3301i	−0.262555	+	0.454758i
$517$	11.4282	+	19.7942i	0.502612	+	0.870549i
$518$	15.9282	−	9.19615i	0.699845	−	0.404056i
$519$	−10.9282			−0.479695
$520$	1.00000	+	3.46410i	0.0438529	+	0.151911i
$521$	−17.3205			−0.758825			−0.379413	−	0.925228i	$-0.623874\pi$
$521$	−17.3205			−0.758825			−0.379413	+	0.925228i	$0.623874\pi$
$522$	−0.232051	+	0.133975i	−0.0101566	+	0.00586391i
$523$	−5.89230	−	10.2058i	−0.257653	−	0.446267i	0.707960	−	0.706252i	$-0.249616\pi$
$523$	−5.89230	−	10.2058i	−0.257653	−	0.446267i	−0.965613	+	0.259985i	$0.916282\pi$
$524$	−9.33013	+	16.1603i	−0.407588	+	0.705964i
$525$			2.00000i			0.0872872i
$526$	5.30385	+	3.06218i	0.231259	+	0.133517i
$527$	6.00000	+	3.46410i	0.261364	+	0.150899i
$528$		−	6.46410i		−	0.281314i
$529$	4.53590	−	7.85641i	0.197213	−	0.341583i
$530$	0.464102	+	0.803848i	0.0201593	+	0.0349169i
$531$	−7.33013	+	4.23205i	−0.318100	+	0.183655i
$532$	−14.9282			−0.647220
$533$	5.19615	+	5.00000i	0.225070	+	0.216574i
$534$	0.535898			0.0231906
$535$	6.80385	−	3.92820i	0.294156	−	0.169831i
$536$	−5.73205	−	9.92820i	−0.247587	−	0.428833i
$537$	−9.86603	+	17.0885i	−0.425750	+	0.737421i
$538$		−	12.0000i		−	0.517357i
$539$	−16.7942	−	9.69615i	−0.723379	−	0.417643i
$540$	0.866025	+	0.500000i	0.0372678	+	0.0215166i
$541$		−	26.9282i		−	1.15773i	−0.815422	−	0.578867i	$-0.803495\pi$
$541$		−	26.9282i		−	1.15773i	0.815422	−	0.578867i	$-0.196505\pi$
$542$	−0.598076	+	1.03590i	−0.0256896	+	0.0444956i
$543$	−1.46410	−	2.53590i	−0.0628306	−	0.108826i
$544$	3.46410	−	2.00000i	0.148522	−	0.0857493i
$545$	15.8564			0.679214
$546$	−5.00000	+	5.19615i	−0.213980	+	0.222375i
$547$	22.9282			0.980339			0.490170	−	0.871627i	$-0.336935\pi$
$547$	22.9282			0.980339			0.490170	+	0.871627i	$0.336935\pi$
$548$	−2.13397	+	1.23205i	−0.0911589	+	0.0526306i
$549$	5.19615	+	9.00000i	0.221766	+	0.384111i
$550$	3.23205	−	5.59808i	0.137815	−	0.238703i
$551$		−	2.00000i		−	0.0852029i
$552$	3.23205	+	1.86603i	0.137565	+	0.0794233i
$553$	24.1244	+	13.9282i	1.02587	+	0.592287i
$554$			3.92820i			0.166893i
$555$	4.59808	−	7.96410i	0.195177	−	0.338057i
$556$	−6.46410	−	11.1962i	−0.274139	−	0.474823i
$557$	15.3397	−	8.85641i	0.649966	−	0.375258i	−0.138477	−	0.990366i	$-0.544221\pi$
$557$	15.3397	−	8.85641i	0.649966	−	0.375258i	0.788443	+	0.615108i	$0.210887\pi$
$558$	1.73205			0.0733236
$559$	−41.7487	−	10.3301i	−1.76578	−	0.436918i
$560$	2.00000			0.0845154
$561$	22.3923	−	12.9282i	0.945404	−	0.545829i
$562$	−4.46410	−	7.73205i	−0.188307	−	0.326157i
$563$	2.33975	−	4.05256i	0.0986085	−	0.170795i	−0.812500	−	0.582961i	$-0.801894\pi$
$563$	2.33975	−	4.05256i	0.0986085	−	0.170795i	0.911109	+	0.412166i	$0.135228\pi$
$564$			3.53590i			0.148888i
$565$	0.696152	+	0.401924i	0.0292874	+	0.0169091i
$566$	−8.59808	−	4.96410i	−0.361404	−	0.208657i
$567$			2.00000i			0.0839921i
$568$	6.19615	−	10.7321i	0.259985	−	0.450307i
$569$	−14.6603	−	25.3923i	−0.614590	−	1.06450i	−0.990456	−	0.137827i	$-0.955988\pi$
$569$	−14.6603	−	25.3923i	−0.614590	−	1.06450i	0.375867	−	0.926674i	$-0.377345\pi$
$570$	−6.46410	+	3.73205i	−0.270751	+	0.156318i
$571$	−17.1769			−0.718832			−0.359416	−	0.933178i	$-0.617024\pi$
$571$	−17.1769			−0.718832			−0.359416	+	0.933178i	$0.617024\pi$
$572$	22.3923	−	6.46410i	0.936269	−	0.270278i
$573$	−21.4641			−0.896676
$574$	3.46410	−	2.00000i	0.144589	−	0.0834784i
$575$	1.86603	+	3.23205i	0.0778186	+	0.134786i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$			10.0000i			0.416305i	0.978096	+	0.208153i	$0.0667451\pi$
$577$			10.0000i			0.416305i	−0.978096	+	0.208153i	$0.933255\pi$
$578$	−0.866025	−	0.500000i	−0.0360219	−	0.0207973i
$579$	9.80385	+	5.66025i	0.407434	+	0.235232i
$580$			0.267949i			0.0111260i
$581$	−8.92820	+	15.4641i	−0.370404	+	0.641559i
$582$	−0.267949	−	0.464102i	−0.0111069	−	0.0192376i
$583$	5.19615	−	3.00000i	0.215203	−	0.124247i
$584$	2.00000			0.0827606
$585$	−0.866025	+	3.50000i	−0.0358057	+	0.144707i
$586$	31.8564			1.31598
$587$	−2.07180	+	1.19615i	−0.0855122	+	0.0493705i	−0.542146	−	0.840284i	$-0.682388\pi$
$587$	−2.07180	+	1.19615i	−0.0855122	+	0.0493705i	0.456634	+	0.889655i	$0.349055\pi$
$588$	−1.50000	−	2.59808i	−0.0618590	−	0.107143i
$589$	−6.46410	+	11.1962i	−0.266349	+	0.461329i
$590$			8.46410i			0.348462i
$591$	3.80385	+	2.19615i	0.156469	+	0.0903376i
$592$	−7.96410	−	4.59808i	−0.327323	−	0.188980i
$593$		−	45.1051i		−	1.85225i	−0.377223	−	0.926123i	$-0.623121\pi$
$593$		−	45.1051i		−	1.85225i	0.377223	−	0.926123i	$-0.376879\pi$
$594$	3.23205	−	5.59808i	0.132613	−	0.229692i
$595$	4.00000	+	6.92820i	0.163984	+	0.284029i
$596$	−11.7224	+	6.76795i	−0.480170	+	0.277226i
$597$	5.07180			0.207575
$598$	−3.23205	+	13.0622i	−0.132168	+	0.534152i
$599$	−10.3923			−0.424618			−0.212309	−	0.977203i	$-0.568098\pi$
$599$	−10.3923			−0.424618			−0.212309	+	0.977203i	$0.568098\pi$
$600$	0.866025	−	0.500000i	0.0353553	−	0.0204124i
$601$	9.89230	+	17.1340i	0.403516	+	0.698909i	0.994147	−	0.108032i	$-0.0344548\pi$
$601$	9.89230	+	17.1340i	0.403516	+	0.698909i	−0.590632	+	0.806941i	$0.701121\pi$
$602$	−11.9282	+	20.6603i	−0.486157	+	0.842049i
$603$		−	11.4641i		−	0.466854i
$604$	9.00000	+	5.19615i	0.366205	+	0.211428i
$605$	−26.6603	−	15.3923i	−1.08389	−	0.625786i
$606$			2.92820i			0.118950i
$607$	9.58846	−	16.6077i	0.389183	−	0.674086i	−0.603156	−	0.797623i	$-0.706091\pi$
$607$	9.58846	−	16.6077i	0.389183	−	0.674086i	0.992340	+	0.123537i	$0.0394239\pi$
$608$	3.73205	+	6.46410i	0.151355	+	0.262154i
$609$	−0.464102	+	0.267949i	−0.0188063	+	0.0108578i
$610$	10.3923			0.420772
$611$	−12.2487	+	3.53590i	−0.495530	+	0.143047i
$612$	4.00000			0.161690
$613$	−33.8205	+	19.5263i	−1.36600	+	0.788659i	−0.990414	−	0.138130i	$-0.955891\pi$
$613$	−33.8205	+	19.5263i	−1.36600	+	0.788659i	−0.375583	+	0.926789i	$0.622558\pi$
$614$	9.73205	+	16.8564i	0.392754	+	0.680269i
$615$	1.00000	−	1.73205i	0.0403239	−	0.0698430i
$616$		−	12.9282i		−	0.520892i
$617$	−19.4545	−	11.2321i	−0.783208	−	0.452185i	0.0543580	−	0.998522i	$-0.482689\pi$
$617$	−19.4545	−	11.2321i	−0.783208	−	0.452185i	−0.837566	+	0.546336i	$0.816022\pi$
$618$	10.2679	+	5.92820i	0.413037	+	0.238467i
$619$			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
$621$	1.86603	+	3.23205i	0.0748810	+	0.129698i
$622$	24.5885	−	14.1962i	0.985907	−	0.569214i
$623$	1.07180			0.0429406
$624$	3.50000	+	0.866025i	0.140112	+	0.0346688i
$625$	1.00000			0.0400000
$626$	24.2487	−	14.0000i	0.969173	−	0.559553i
$627$	24.1244	+	41.7846i	0.963434	+	1.66872i
$628$	−2.50000	+	4.33013i	−0.0997609	+	0.172791i
$629$		−	36.7846i		−	1.46670i
$630$	1.73205	+	1.00000i	0.0690066	+	0.0398410i
$631$	27.2487	+	15.7321i	1.08475	+	0.626283i	0.932175	−	0.362008i	$-0.117909\pi$
$631$	27.2487	+	15.7321i	1.08475	+	0.626283i	0.152579	+	0.988291i	$0.451242\pi$
$632$		−	13.9282i		−	0.554034i
$633$	−5.66025	+	9.80385i	−0.224975	+	0.389668i
$634$	7.26795	+	12.5885i	0.288647	+	0.499952i
$635$	4.26795	−	2.46410i	0.169368	−	0.0977849i
$636$	0.928203			0.0368057
$637$	7.50000	−	7.79423i	0.297161	−	0.308819i
$638$	1.73205			0.0685725
$639$	10.7321	−	6.19615i	0.424553	−	0.245116i
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	−0.0717968	+	0.124356i	−0.00283580	+	0.00491175i	−0.867440	−	0.497542i	$-0.834236\pi$
$641$	−0.0717968	+	0.124356i	−0.00283580	+	0.00491175i	0.864604	+	0.502454i	$0.167569\pi$
$642$		−	7.85641i		−	0.310068i
$643$	−17.7846	−	10.2679i	−0.701357	−	0.404928i	0.106496	−	0.994313i	$-0.466037\pi$
$643$	−17.7846	−	10.2679i	−0.701357	−	0.404928i	−0.807852	+	0.589385i	$0.799370\pi$
$644$	6.46410	+	3.73205i	0.254721	+	0.147063i
$645$			11.9282i			0.469673i
$646$	−14.9282	+	25.8564i	−0.587342	+	1.01731i
$647$	6.66025	+	11.5359i	0.261842	+	0.453523i	0.966731	−	0.255794i	$-0.0823369\pi$
$647$	6.66025	+	11.5359i	0.261842	+	0.453523i	−0.704890	+	0.709317i	$0.749004\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	54.7128			2.14767
$650$	2.59808	+	2.50000i	0.101905	+	0.0980581i
$651$	3.46410			0.135769
$652$	13.0359	−	7.52628i	0.510525	−	0.294752i
$653$	−2.12436	−	3.67949i	−0.0831325	−	0.143990i	0.821461	−	0.570264i	$-0.193159\pi$
$653$	−2.12436	−	3.67949i	−0.0831325	−	0.143990i	−0.904594	+	0.426274i	$0.859826\pi$
$654$	7.92820	−	13.7321i	0.310017	−	0.536966i
$655$			18.6603i			0.729116i
$656$	−1.73205	−	1.00000i	−0.0676252	−	0.0390434i
$657$	1.73205	+	1.00000i	0.0675737	+	0.0390137i
$658$			7.07180i			0.275687i
$659$	0.133975	−	0.232051i	0.00521891	−	0.00903942i	−0.863404	−	0.504513i	$-0.831672\pi$
$659$	0.133975	−	0.232051i	0.00521891	−	0.00903942i	0.868623	+	0.495473i	$0.165005\pi$
$660$	−3.23205	−	5.59808i	−0.125807	−	0.217905i
$661$	−7.51666	+	4.33975i	−0.292364	+	0.168797i	−0.639008	−	0.769200i	$-0.720655\pi$
$661$	−7.51666	+	4.33975i	−0.292364	+	0.168797i	0.346643	+	0.937997i	$0.387321\pi$
$662$	16.7846			0.652352
$663$	4.00000	+	13.8564i	0.155347	+	0.538138i
$664$	8.92820			0.346481
$665$	−12.9282	+	7.46410i	−0.501334	+	0.289445i
$666$	−4.59808	−	7.96410i	−0.178172	−	0.308603i
$667$	−0.500000	+	0.866025i	−0.0193601	+	0.0335326i
$668$		−	16.3205i		−	0.631459i
$669$	−17.7846	−	10.2679i	−0.687593	−	0.396982i
$670$	−9.92820	−	5.73205i	−0.383560	−	0.221448i
$671$		−	67.1769i		−	2.59334i
$672$	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	$-0.378220\pi$
$674$	−8.07180	+	4.66025i	−0.310914	+	0.179506i
$675$	1.00000			0.0384900
$676$	0.500000	+	12.9904i	0.0192308	+	0.499630i
$677$	32.3923			1.24494			0.622469	−	0.782645i	$-0.286130\pi$
$677$	32.3923			1.24494			0.622469	+	0.782645i	$0.286130\pi$
$678$	0.696152	−	0.401924i	0.0267356	−	0.0154358i
$679$	−0.535898	−	0.928203i	−0.0205659	−	0.0356212i
$680$	2.00000	−	3.46410i	0.0766965	−	0.132842i
$681$		−	16.3923i		−	0.628154i
$682$	−9.69615	−	5.59808i	−0.371285	−	0.214361i
$683$	−35.3205	−	20.3923i	−1.35150	−	0.780290i	−0.363042	−	0.931773i	$-0.618262\pi$
$683$	−35.3205	−	20.3923i	−1.35150	−	0.780290i	−0.988460	+	0.151483i	$0.951595\pi$
$684$			7.46410i			0.285397i
$685$	−1.23205	+	2.13397i	−0.0470742	+	0.0815350i
$686$	−10.0000	−	17.3205i	−0.381802	−	0.661300i
$687$	−6.80385	+	3.92820i	−0.259583	+	0.149870i
$688$	11.9282			0.454758
$689$	0.928203	+	3.21539i	0.0353617	+	0.122497i
$690$	3.73205			0.142077
$691$	−23.5359	+	13.5885i	−0.895348	+	0.516929i	−0.875688	−	0.482877i	$-0.839592\pi$
$691$	−23.5359	+	13.5885i	−0.895348	+	0.516929i	−0.0196598	+	0.999807i	$0.506258\pi$
$692$	5.46410	+	9.46410i	0.207714	+	0.359771i
$693$	6.46410	−	11.1962i	0.245551	−	0.425307i
$694$		−	1.60770i		−	0.0610273i
$695$	−11.1962	−	6.46410i	−0.424694	−	0.245197i
$696$	0.232051	+	0.133975i	0.00879586	+	0.00507829i
$697$		−	8.00000i		−	0.303022i
$698$	−10.7321	+	18.5885i	−0.406214	+	0.703583i
$699$	3.06218	+	5.30385i	0.115822	+	0.200610i
$700$	1.73205	−	1.00000i	0.0654654	−	0.0377964i
$701$	−0.267949			−0.0101203			−0.00506015	−	0.999987i	$-0.501611\pi$
$701$	−0.267949			−0.0101203			−0.00506015	+	0.999987i	$0.501611\pi$
$702$	2.59808	+	2.50000i	0.0980581	+	0.0943564i
$703$	68.6410			2.58884
$704$	−5.59808	+	3.23205i	−0.210985	+	0.121812i
$705$	1.76795	+	3.06218i	0.0665848	+	0.115328i
$706$	−1.00000	+	1.73205i	−0.0376355	+	0.0651866i
$707$			5.85641i			0.220253i
$708$	7.33013	+	4.23205i	0.275483	+	0.159050i
$709$	−19.8564	−	11.4641i	−0.745723	−	0.430543i	0.0784234	−	0.996920i	$-0.475011\pi$
$709$	−19.8564	−	11.4641i	−0.745723	−	0.430543i	−0.824146	+	0.566377i	$0.808345\pi$
$710$		−	12.3923i		−	0.465075i
$711$	6.96410	−	12.0622i	0.261174	−	0.452367i
$712$	−0.267949	−	0.464102i	−0.0100418	−	0.0173929i
$713$	5.59808	−	3.23205i	0.209650	−	0.121041i
$714$	8.00000			0.299392
$715$	16.1603	−	16.7942i	0.604359	−	0.628069i
$716$	19.7321			0.737421
$717$	−14.1962	+	8.19615i	−0.530165	+	0.306091i
$718$	2.53590	+	4.39230i	0.0946389	+	0.163919i
$719$	17.3205	−	30.0000i	0.645946	−	1.11881i	−0.338136	−	0.941097i	$-0.609796\pi$
$719$	17.3205	−	30.0000i	0.645946	−	1.11881i	0.984082	−	0.177714i	$-0.0568702\pi$
$720$		−	1.00000i		−	0.0372678i
$721$	20.5359	+	11.8564i	0.764797	+	0.441556i
$722$	−31.7942	−	18.3564i	−1.18326	−	0.683155i
$723$			17.7321i			0.659462i
$724$	−1.46410	+	2.53590i	−0.0544129	+	0.0942459i
$725$	0.133975	+	0.232051i	0.00497569	+	0.00861815i
$726$	−26.6603	+	15.3923i	−0.989455	+	0.571262i
$727$	−31.7128			−1.17616			−0.588082	−	0.808802i	$-0.700117\pi$
$727$	−31.7128			−1.17616			−0.588082	+	0.808802i	$0.700117\pi$
$728$	7.00000	+	1.73205i	0.259437	+	0.0641941i
$729$	1.00000			0.0370370
$730$	1.73205	−	1.00000i	0.0641061	−	0.0370117i
$731$	23.8564	+	41.3205i	0.882361	+	1.52829i
$732$	5.19615	−	9.00000i	0.192055	−	0.332650i
$733$			50.9282i			1.88108i	0.339688	+	0.940538i	$0.389678\pi$
$733$			50.9282i			1.88108i	−0.339688	+	0.940538i	$0.610322\pi$
$734$	13.5167	+	7.80385i	0.498909	+	0.288045i
$735$	−2.59808	−	1.50000i	−0.0958315	−	0.0553283i
$736$		−	3.73205i		−	0.137565i
$737$	−37.0526	+	64.1769i	−1.36485	+	2.36399i
$738$	−1.00000	−	1.73205i	−0.0368105	−	0.0637577i
$739$	−16.7321	+	9.66025i	−0.615498	+	0.355358i	−0.775114	−	0.631821i	$-0.782308\pi$
$739$	−16.7321	+	9.66025i	−0.615498	+	0.355358i	0.159616	+	0.987179i	$0.448974\pi$
$740$	−9.19615			−0.338057
$741$	−25.8564	+	7.46410i	−0.949859	+	0.274201i
$742$	1.85641			0.0681508
$743$	−35.0429	+	20.2321i	−1.28560	+	0.742242i	−0.977866	−	0.209230i	$-0.932904\pi$
$743$	−35.0429	+	20.2321i	−1.28560	+	0.742242i	−0.307734	+	0.951472i	$0.599571\pi$
$744$	−0.866025	−	1.50000i	−0.0317500	−	0.0549927i
$745$	−6.76795	+	11.7224i	−0.247958	+	0.429477i
$746$			15.7846i			0.577916i
$747$	7.73205	+	4.46410i	0.282901	+	0.163333i
$748$	−22.3923	−	12.9282i	−0.818744	−	0.472702i
$749$		−	15.7128i		−	0.574134i
$750$	0.500000	−	0.866025i	0.0182574	−	0.0316228i
$751$	−7.03590	−	12.1865i	−0.256744	−	0.444693i	0.708624	−	0.705586i	$-0.249316\pi$
$751$	−7.03590	−	12.1865i	−0.256744	−	0.444693i	−0.965368	+	0.260893i	$0.915983\pi$
$752$	3.06218	−	1.76795i	0.111666	−	0.0644705i
$753$	−15.7321			−0.573308
$754$	−0.232051	+	0.937822i	−0.00845079	+	0.0341535i
$755$	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	$0.727258\pi$
$758$	−13.9282	+	24.1244i	−0.505895	+	0.876236i
$759$		−	24.1244i		−	0.875659i
$760$	6.46410	+	3.73205i	0.234478	+	0.135376i
$761$	4.39230	+	2.53590i	0.159221	+	0.0919262i	0.577493	−	0.816395i	$-0.304031\pi$
$761$	4.39230	+	2.53590i	0.159221	+	0.0919262i	−0.418272	+	0.908322i	$0.637364\pi$
$762$		−	4.92820i		−	0.178530i
$763$	15.8564	−	27.4641i	0.574040	−	0.994267i
$764$	10.7321	+	18.5885i	0.388272	+	0.672507i
$765$	3.46410	−	2.00000i	0.125245	−	0.0723102i
$766$	−25.3923			−0.917461
$767$	−7.33013	+	29.6244i	−0.264676	+	1.06967i
$768$	−1.00000			−0.0360844
$769$	−10.0359	+	5.79423i	−0.361904	+	0.208945i	−0.669916	−	0.742437i	$-0.733670\pi$
$769$	−10.0359	+	5.79423i	−0.361904	+	0.208945i	0.308012	+	0.951383i	$0.400336\pi$
$770$	−6.46410	−	11.1962i	−0.232950	−	0.403481i

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} +(5.59808 - 3.23205i) 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} +(6.46410 + 3.73205i) q^{19} +(-0.866025 - 0.500000i) q^{20} -2.00000i q^{21} +(-3.23205 + 5.59808i) q^{22} +(-1.86603 - 3.23205i) 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} +(-0.133975 - 0.232051i) q^{29} +(-0.500000 + 0.866025i) q^{30} +1.73205i q^{31} +(0.866025 + 0.500000i) q^{32} +(5.59808 + 3.23205i) q^{33} +4.00000i q^{34} +(-1.00000 + 1.73205i) q^{35} +(0.500000 + 0.866025i) q^{36} +(7.96410 - 4.59808i) q^{37} -7.46410 q^{38} +(-2.50000 + 2.59808i) q^{39} +1.00000 q^{40} +(1.73205 - 1.00000i) q^{41} +(1.00000 + 1.73205i) q^{42} +(-5.96410 + 10.3301i) q^{43} -6.46410i q^{44} +(0.866025 + 0.500000i) q^{45} +(3.23205 + 1.86603i) q^{46} +3.53590i 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} +0.928203 q^{53} +(0.866025 - 0.500000i) q^{54} +(-3.23205 - 5.59808i) q^{55} +(1.00000 - 1.73205i) q^{56} +7.46410i q^{57} +(0.232051 + 0.133975i) q^{58} +(7.33013 + 4.23205i) 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} -6.46410 q^{66} +(-9.92820 + 5.73205i) q^{67} +(-2.00000 - 3.46410i) q^{68} +(1.86603 - 3.23205i) q^{69} -2.00000i q^{70} +(-10.7321 - 6.19615i) q^{71} +(-0.866025 - 0.500000i) q^{72} -2.00000i q^{73} +(-4.59808 + 7.96410i) q^{74} +(-0.500000 - 0.866025i) q^{75} +(6.46410 - 3.73205i) q^{76} -12.9282 q^{77} +(0.866025 - 3.50000i) q^{78} -13.9282 q^{79} +(-0.866025 + 0.500000i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.00000 + 1.73205i) q^{82} -8.92820i q^{83} +(-1.73205 - 1.00000i) q^{84} +(-3.46410 - 2.00000i) q^{85} -11.9282i q^{86} +(0.133975 - 0.232051i) q^{87} +(3.23205 + 5.59808i) q^{88} +(-0.464102 + 0.267949i) q^{89} -1.00000 q^{90} +(1.73205 - 7.00000i) q^{91} -3.73205 q^{92} +(-1.50000 + 0.866025i) q^{93} +(-1.76795 - 3.06218i) q^{94} +(3.73205 - 6.46410i) q^{95} +1.00000i q^{96} +(0.464102 + 0.267949i) q^{97} +(2.59808 + 1.50000i) q^{98} +6.46410i 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

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