LMFDB - Embedded newform 390.2.x.a.49.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(49,390)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(390, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

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

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

chi := DirichletCharacter("390.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.x (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:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} - 8 x^{10} + 34 x^{9} + 8 x^{8} - 134 x^{7} + 98 x^{6} + 154 x^{5} + 104 x^{4} + \cdots + 2197 $ x^12 - 2x^11 - 8x^10 + 34x^9 + 8x^8 - 134x^7 + 98x^6 + 154x^5 + 104x^4 + 190x^3 - 1196x^2 - 338*x + 2197
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.5
Root			$-1.44229 + 0.433312i$ of defining polynomial
Character	$\chi$	$=$	390.49
Dual form			390.2.x.a.199.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.230377 + 2.22417i) q^{5} +(-0.866025 - 0.500000i) q^{6} +(0.432713 - 0.749482i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.230377 + 2.22417i) q^{5} +(-0.866025 - 0.500000i) q^{6} +(0.432713 - 0.749482i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(2.04138 - 0.912572i) q^{10} +(0.151430 - 0.0874279i) q^{11} +1.00000i q^{12} +(1.35486 - 3.34131i) q^{13} -0.865427 q^{14} +(0.912572 + 2.04138i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(7.08339 + 4.08960i) q^{17} -1.00000 q^{18} +(5.20843 + 3.00709i) q^{19} +(-1.81100 - 1.31160i) q^{20} -0.865427i q^{21} +(-0.151430 - 0.0874279i) q^{22} +(2.52211 - 1.45614i) q^{23} +(0.866025 - 0.500000i) q^{24} +(-4.89385 - 1.02479i) q^{25} +(-3.57109 + 0.497314i) q^{26} -1.00000i q^{27} +(0.432713 + 0.749482i) q^{28} +(3.24491 + 5.62035i) q^{29} +(1.31160 - 1.81100i) q^{30} -6.95057i q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.0874279 - 0.151430i) q^{33} -8.17919i q^{34} +(1.56729 + 1.13509i) q^{35} +(0.500000 + 0.866025i) q^{36} +(-0.879573 - 1.52347i) q^{37} -6.01418i q^{38} +(-0.497314 - 3.57109i) q^{39} +(-0.230377 + 2.22417i) q^{40} +(-7.08339 + 4.08960i) q^{41} +(-0.749482 + 0.432713i) q^{42} +(-7.94476 - 4.58691i) q^{43} +0.174856i q^{44} +(1.81100 + 1.31160i) q^{45} +(-2.52211 - 1.45614i) q^{46} -11.9021 q^{47} +(-0.866025 - 0.500000i) q^{48} +(3.12552 + 5.41356i) q^{49} +(1.55943 + 4.75060i) q^{50} +8.17919 q^{51} +(2.21623 + 2.84400i) q^{52} -2.48735i q^{53} +(-0.866025 + 0.500000i) q^{54} +(0.159569 + 0.356946i) q^{55} +(0.432713 - 0.749482i) q^{56} +6.01418 q^{57} +(3.24491 - 5.62035i) q^{58} +(-6.09393 - 3.51833i) q^{59} +(-2.22417 - 0.230377i) q^{60} +(3.98695 - 6.90559i) q^{61} +(-6.01937 + 3.47529i) q^{62} +(-0.432713 - 0.749482i) q^{63} +1.00000 q^{64} +(7.11951 + 3.78319i) q^{65} -0.174856 q^{66} +(1.36766 + 2.36886i) q^{67} +(-7.08339 + 4.08960i) q^{68} +(1.45614 - 2.52211i) q^{69} +(0.199374 - 1.92486i) q^{70} +(12.2677 + 7.08275i) q^{71} +(0.500000 - 0.866025i) q^{72} -12.8706 q^{73} +(-0.879573 + 1.52347i) q^{74} +(-4.75060 + 1.55943i) q^{75} +(-5.20843 + 3.00709i) q^{76} -0.151325i q^{77} +(-2.84400 + 2.21623i) q^{78} +9.48961 q^{79} +(2.04138 - 0.912572i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(7.08339 + 4.08960i) q^{82} +0.139544 q^{83} +(0.749482 + 0.432713i) q^{84} +(-10.7278 + 14.8125i) q^{85} +9.17382i q^{86} +(5.62035 + 3.24491i) q^{87} +(0.151430 - 0.0874279i) q^{88} +(-11.3790 + 6.56966i) q^{89} +(0.230377 - 2.22417i) q^{90} +(-1.91799 - 2.46127i) q^{91} +2.91228i q^{92} +(-3.47529 - 6.01937i) q^{93} +(5.95105 + 10.3075i) q^{94} +(-7.88817 + 10.8917i) q^{95} +1.00000i q^{96} +(-4.32411 + 7.48957i) q^{97} +(3.12552 - 5.41356i) q^{98} -0.174856i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{2} - 6 q^{4} - 2 q^{5} - 2 q^{7} + 12 q^{8} + 6 q^{9}+O(q^{10}) $ 12 * q - 6 * q^2 - 6 * q^4 - 2 * q^5 - 2 * q^7 + 12 * q^8 + 6 * q^9	$ 12 q - 6 q^{2} - 6 q^{4} - 2 q^{5} - 2 q^{7} + 12 q^{8} + 6 q^{9} - 2 q^{10} + 6 q^{11} - 8 q^{13} + 4 q^{14} + 6 q^{15} - 6 q^{16} + 18 q^{17} - 12 q^{18} - 6 q^{19} + 4 q^{20} - 6 q^{22} + 6 q^{23} - 10 q^{25} - 2 q^{26} - 2 q^{28} + 14 q^{29} - 6 q^{30} - 6 q^{32} + 6 q^{33} + 26 q^{35} + 6 q^{36} - 12 q^{37} - 2 q^{39} - 2 q^{40} - 18 q^{41} - 12 q^{42} - 36 q^{43} - 4 q^{45} - 6 q^{46} + 16 q^{47} + 8 q^{49} - 10 q^{50} + 16 q^{51} + 10 q^{52} - 28 q^{55} - 2 q^{56} - 8 q^{57} + 14 q^{58} - 36 q^{59} + 10 q^{61} + 6 q^{62} + 2 q^{63} + 12 q^{64} + 6 q^{65} - 12 q^{66} + 4 q^{67} - 18 q^{68} + 16 q^{69} - 4 q^{70} - 12 q^{71} + 6 q^{72} + 28 q^{73} - 12 q^{74} - 8 q^{75} + 6 q^{76} - 2 q^{78} + 4 q^{79} - 2 q^{80} - 6 q^{81} + 18 q^{82} + 72 q^{83} + 12 q^{84} + 18 q^{85} + 6 q^{87} + 6 q^{88} + 18 q^{89} + 2 q^{90} + 2 q^{91} - 16 q^{93} - 8 q^{94} - 42 q^{95} - 48 q^{97} + 8 q^{98}+O(q^{100}) $ 12 * q - 6 * q^2 - 6 * q^4 - 2 * q^5 - 2 * q^7 + 12 * q^8 + 6 * q^9 - 2 * q^10 + 6 * q^11 - 8 * q^13 + 4 * q^14 + 6 * q^15 - 6 * q^16 + 18 * q^17 - 12 * q^18 - 6 * q^19 + 4 * q^20 - 6 * q^22 + 6 * q^23 - 10 * q^25 - 2 * q^26 - 2 * q^28 + 14 * q^29 - 6 * q^30 - 6 * q^32 + 6 * q^33 + 26 * q^35 + 6 * q^36 - 12 * q^37 - 2 * q^39 - 2 * q^40 - 18 * q^41 - 12 * q^42 - 36 * q^43 - 4 * q^45 - 6 * q^46 + 16 * q^47 + 8 * q^49 - 10 * q^50 + 16 * q^51 + 10 * q^52 - 28 * q^55 - 2 * q^56 - 8 * q^57 + 14 * q^58 - 36 * q^59 + 10 * q^61 + 6 * q^62 + 2 * q^63 + 12 * q^64 + 6 * q^65 - 12 * q^66 + 4 * q^67 - 18 * q^68 + 16 * q^69 - 4 * q^70 - 12 * q^71 + 6 * q^72 + 28 * q^73 - 12 * q^74 - 8 * q^75 + 6 * q^76 - 2 * q^78 + 4 * q^79 - 2 * q^80 - 6 * q^81 + 18 * q^82 + 72 * q^83 + 12 * q^84 + 18 * q^85 + 6 * q^87 + 6 * q^88 + 18 * q^89 + 2 * q^90 + 2 * q^91 - 16 * q^93 - 8 * q^94 - 42 * q^95 - 48 * q^97 + 8 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.230377	+	2.22417i	−0.103028	+	0.994678i
$5$	−0.230377	+	2.22417i	−0.103028	+	0.994678i
$6$	−0.866025	−	0.500000i	−0.353553	−	0.204124i
$7$	0.432713	−	0.749482i	0.163550	−	0.283277i	−0.772589	−	0.634906i	$-0.781039\pi$
$7$	0.432713	−	0.749482i	0.163550	−	0.283277i	0.936140	+	0.351629i	$0.114372\pi$
$8$	1.00000			0.353553
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	2.04138	−	0.912572i	0.645539	−	0.288581i
$11$	0.151430	−	0.0874279i	0.0456577	−	0.0263605i	−0.476997	−	0.878905i	$-0.658275\pi$
$11$	0.151430	−	0.0874279i	0.0456577	−	0.0263605i	0.522655	+	0.852544i	$0.324942\pi$
$12$			1.00000i			0.288675i
$13$	1.35486	−	3.34131i	0.375770	−	0.926713i
$13$	1.35486	−	3.34131i	0.375770	−	0.926713i
$14$	−0.865427			−0.231295
$15$	0.912572	+	2.04138i	0.235625	+	0.527081i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	7.08339	+	4.08960i	1.71797	+	0.991873i	0.922604	+	0.385748i	$0.126057\pi$
$17$	7.08339	+	4.08960i	1.71797	+	0.991873i	0.795370	+	0.606125i	$0.207277\pi$
$18$	−1.00000			−0.235702
$19$	5.20843	+	3.00709i	1.19490	+	0.689873i	0.959413	−	0.282005i	$-0.0909996\pi$
$19$	5.20843	+	3.00709i	1.19490	+	0.689873i	0.235483	+	0.971879i	$0.424333\pi$
$20$	−1.81100	−	1.31160i	−0.404951	−	0.293282i
$21$		−	0.865427i		−	0.188852i
$22$	−0.151430	−	0.0874279i	−0.0322849	−	0.0186397i
$23$	2.52211	−	1.45614i	0.525896	−	0.303626i	−0.213448	−	0.976954i	$-0.568469\pi$
$23$	2.52211	−	1.45614i	0.525896	−	0.303626i	0.739344	+	0.673328i	$0.235136\pi$
$24$	0.866025	−	0.500000i	0.176777	−	0.102062i
$25$	−4.89385	−	1.02479i	−0.978771	−	0.204959i
$26$	−3.57109	+	0.497314i	−0.700348	+	0.0975312i
$27$		−	1.00000i		−	0.192450i
$28$	0.432713	+	0.749482i	0.0817752	+	0.141639i
$29$	3.24491	+	5.62035i	0.602564	+	1.04367i	0.992431	+	0.122801i	$0.0391877\pi$
$29$	3.24491	+	5.62035i	0.602564	+	1.04367i	−0.389867	+	0.920871i	$0.627479\pi$
$30$	1.31160	−	1.81100i	0.239464	−	0.330642i
$31$		−	6.95057i		−	1.24836i	−0.781281	−	0.624180i	$-0.785433\pi$
$31$		−	6.95057i		−	1.24836i	0.781281	−	0.624180i	$-0.214567\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	0.0874279	−	0.151430i	0.0152192	−	0.0263605i
$34$		−	8.17919i		−	1.40272i
$35$	1.56729	+	1.13509i	0.264920	+	0.191865i
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	−0.879573	−	1.52347i	−0.144601	−	0.250456i	0.784623	−	0.619973i	$-0.212856\pi$
$37$	−0.879573	−	1.52347i	−0.144601	−	0.250456i	−0.929224	+	0.369517i	$0.879523\pi$
$38$		−	6.01418i		−	0.975628i
$39$	−0.497314	−	3.57109i	−0.0796339	−	0.571832i
$40$	−0.230377	+	2.22417i	−0.0364258	+	0.351672i
$41$	−7.08339	+	4.08960i	−1.10624	+	0.638688i	−0.937853	−	0.347034i	$-0.887189\pi$
$41$	−7.08339	+	4.08960i	−1.10624	+	0.638688i	−0.168387	+	0.985721i	$0.553856\pi$
$42$	−0.749482	+	0.432713i	−0.115648	+	0.0667691i
$43$	−7.94476	−	4.58691i	−1.21156	−	0.699497i	−0.248465	−	0.968641i	$-0.579926\pi$
$43$	−7.94476	−	4.58691i	−1.21156	−	0.699497i	−0.963100	+	0.269144i	$0.913259\pi$
$44$			0.174856i			0.0263605i
$45$	1.81100	+	1.31160i	0.269968	+	0.195521i
$46$	−2.52211	−	1.45614i	−0.371865	−	0.214696i
$47$	−11.9021			−1.73610			−0.868050	−	0.496478i	$-0.834627\pi$
$47$	−11.9021			−1.73610			−0.868050	+	0.496478i	$0.834627\pi$
$48$	−0.866025	−	0.500000i	−0.125000	−	0.0721688i
$49$	3.12552	+	5.41356i	0.446503	+	0.773365i
$50$	1.55943	+	4.75060i	0.220537	+	0.671836i
$51$	8.17919			1.14532
$52$	2.21623	+	2.84400i	0.307336	+	0.394391i
$53$		−	2.48735i		−	0.341663i	−0.985300	−	0.170832i	$-0.945355\pi$
$53$		−	2.48735i		−	0.341663i	0.985300	−	0.170832i	$-0.0546454\pi$
$54$	−0.866025	+	0.500000i	−0.117851	+	0.0680414i
$55$	0.159569	+	0.356946i	0.0215162	+	0.0481306i
$56$	0.432713	−	0.749482i	0.0578238	−	0.100154i
$57$	6.01418			0.796597
$58$	3.24491	−	5.62035i	0.426077	−	0.737988i
$59$	−6.09393	−	3.51833i	−0.793363	−	0.458048i	0.0477824	−	0.998858i	$-0.484785\pi$
$59$	−6.09393	−	3.51833i	−0.793363	−	0.458048i	−0.841145	+	0.540810i	$0.818118\pi$
$60$	−2.22417	−	0.230377i	−0.287139	−	0.0297415i
$61$	3.98695	−	6.90559i	0.510476	−	0.884171i	−0.489450	−	0.872031i	$-0.662802\pi$
$61$	3.98695	−	6.90559i	0.510476	−	0.884171i	0.999926	−	0.0121394i	$-0.00386418\pi$
$62$	−6.01937	+	3.47529i	−0.764461	+	0.441362i
$63$	−0.432713	−	0.749482i	−0.0545168	−	0.0944258i
$64$	1.00000			0.125000
$65$	7.11951	+	3.78319i	0.883067	+	0.469248i
$66$	−0.174856			−0.0215233
$67$	1.36766	+	2.36886i	0.167086	+	0.289402i	0.937394	−	0.348270i	$-0.113231\pi$
$67$	1.36766	+	2.36886i	0.167086	+	0.289402i	−0.770308	+	0.637672i	$0.779897\pi$
$68$	−7.08339	+	4.08960i	−0.858987	+	0.495936i
$69$	1.45614	−	2.52211i	0.175299	−	0.303626i
$70$	0.199374	−	1.92486i	0.0238298	−	0.230064i
$71$	12.2677	+	7.08275i	1.45591	+	0.840568i	0.998806	−	0.0488476i	$-0.0155549\pi$
$71$	12.2677	+	7.08275i	1.45591	+	0.840568i	0.457100	+	0.889415i	$0.348888\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	−12.8706			−1.50639			−0.753193	−	0.657800i	$-0.771487\pi$
$73$	−12.8706			−1.50639			−0.753193	+	0.657800i	$0.771487\pi$
$74$	−0.879573	+	1.52347i	−0.102248	+	0.177099i
$75$	−4.75060	+	1.55943i	−0.548552	+	0.180067i
$76$	−5.20843	+	3.00709i	−0.597448	+	0.344937i
$77$		−	0.151325i		−	0.0172451i
$78$	−2.84400	+	2.21623i	−0.322019	+	0.250939i
$79$	9.48961			1.06766			0.533832	−	0.845590i	$-0.320751\pi$
$79$	9.48961			1.06766			0.533832	+	0.845590i	$0.320751\pi$
$80$	2.04138	−	0.912572i	0.228233	−	0.102029i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	7.08339	+	4.08960i	0.782229	+	0.451620i
$83$	0.139544			0.0153169			0.00765845	−	0.999971i	$-0.497562\pi$
$83$	0.139544			0.0153169			0.00765845	+	0.999971i	$0.497562\pi$
$84$	0.749482	+	0.432713i	0.0817752	+	0.0472129i
$85$	−10.7278	+	14.8125i	−1.16359	+	1.60664i
$86$			9.17382i			0.989238i
$87$	5.62035	+	3.24491i	0.602564	+	0.347891i
$88$	0.151430	−	0.0874279i	0.0161424	−	0.00931985i
$89$	−11.3790	+	6.56966i	−1.20617	+	0.696382i	−0.961920	−	0.273330i	$-0.911875\pi$
$89$	−11.3790	+	6.56966i	−1.20617	+	0.696382i	−0.244249	+	0.969713i	$0.578541\pi$
$90$	0.230377	−	2.22417i	0.0242839	−	0.234448i
$91$	−1.91799	−	2.46127i	−0.201060	−	0.258011i
$92$			2.91228i			0.303626i
$93$	−3.47529	−	6.01937i	−0.360370	−	0.624180i
$94$	5.95105	+	10.3075i	0.613804	+	1.06314i
$95$	−7.88817	+	10.8917i	−0.809309	+	1.11746i
$96$			1.00000i			0.102062i
$97$	−4.32411	+	7.48957i	−0.439047	+	0.760451i	−0.997616	−	0.0690066i	$-0.978017\pi$
$97$	−4.32411	+	7.48957i	−0.439047	+	0.760451i	0.558570	+	0.829458i	$0.311350\pi$
$98$	3.12552	−	5.41356i	0.315725	−	0.546852i
$99$		−	0.174856i		−	0.0175737i
$100$	3.33442	−	3.72580i	0.333442	−	0.372580i
$101$	−5.28276	−	9.15001i	−0.525654	−	0.910460i	−0.999553	−	0.0298810i	$-0.990487\pi$
$101$	−5.28276	−	9.15001i	−0.525654	−	0.910460i	0.473899	−	0.880579i	$-0.342846\pi$
$102$	−4.08960	−	7.08339i	−0.404930	−	0.701360i
$103$		−	8.93568i		−	0.880459i	−0.897885	−	0.440230i	$-0.854897\pi$
$103$		−	8.93568i		−	0.880459i	0.897885	−	0.440230i	$-0.145103\pi$
$104$	1.35486	−	3.34131i	0.132855	−	0.327642i
$105$	1.92486	+	0.199374i	0.187847	+	0.0194569i
$106$	−2.15410	+	1.24367i	−0.209225	+	0.120796i
$107$	−0.745455	+	0.430389i	−0.0720658	+	0.0416072i	−0.535600	−	0.844472i	$-0.679914\pi$
$107$	−0.745455	+	0.430389i	−0.0720658	+	0.0416072i	0.463534	+	0.886079i	$0.346581\pi$
$108$	0.866025	+	0.500000i	0.0833333	+	0.0481125i
$109$			5.45336i			0.522337i	0.965293	+	0.261168i	$0.0841078\pi$
$109$			5.45336i			0.522337i	−0.965293	+	0.261168i	$0.915892\pi$
$110$	0.229340	−	0.316664i	0.0218667	−	0.0301927i
$111$	−1.52347	−	0.879573i	−0.144601	−	0.0834854i
$112$	−0.865427			−0.0817752
$113$	−10.2036	−	5.89106i	−0.959876	−	0.554184i	−0.0637409	−	0.997966i	$-0.520303\pi$
$113$	−10.2036	−	5.89106i	−0.959876	−	0.554184i	−0.896135	+	0.443782i	$0.853636\pi$
$114$	−3.00709	−	5.20843i	−0.281640	−	0.487814i
$115$	2.65766	+	5.94505i	0.247829	+	0.554379i
$116$	−6.48982			−0.602564
$117$	−2.21623	−	2.84400i	−0.204891	−	0.262928i
$118$			7.03667i			0.647778i
$119$	6.13015	−	3.53925i	0.561950	−	0.324442i
$120$	0.912572	+	2.04138i	0.0833061	+	0.186351i
$121$	−5.48471	+	9.49980i	−0.498610	+	0.863618i
$122$	−7.97389			−0.721922
$123$	−4.08960	+	7.08339i	−0.368746	+	0.638688i
$124$	6.01937	+	3.47529i	0.540555	+	0.312090i
$125$	3.40675	−	10.6487i	0.304709	−	0.952446i
$126$	−0.432713	+	0.749482i	−0.0385492	+	0.0667691i
$127$	6.01228	−	3.47119i	0.533503	−	0.308018i	−0.208939	−	0.977929i	$-0.567001\pi$
$127$	6.01228	−	3.47119i	0.533503	−	0.308018i	0.742442	+	0.669911i	$0.233668\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−9.17382			−0.807710
$130$	−0.283413	−	8.05727i	−0.0248569	−	0.706670i
$131$	2.27133			0.198447			0.0992235	−	0.995065i	$-0.468364\pi$
$131$	2.27133			0.198447			0.0992235	+	0.995065i	$0.468364\pi$
$132$	0.0874279	+	0.151430i	0.00760962	+	0.0131803i
$133$	4.50751	−	2.60241i	0.390851	−	0.225658i
$134$	1.36766	−	2.36886i	0.118148	−	0.204638i
$135$	2.22417	+	0.230377i	0.191426	+	0.0198277i
$136$	7.08339	+	4.08960i	0.607395	+	0.350680i
$137$	3.68809	−	6.38795i	0.315094	−	0.545760i	−0.664363	−	0.747410i	$-0.731297\pi$
$137$	3.68809	−	6.38795i	0.315094	−	0.545760i	0.979458	+	0.201650i	$0.0646305\pi$
$138$	−2.91228			−0.247910
$139$	0.410380	−	0.710798i	0.0348079	−	0.0602891i	−0.848097	−	0.529842i	$-0.822251\pi$
$139$	0.410380	−	0.710798i	0.0348079	−	0.0602891i	0.882905	+	0.469552i	$0.155585\pi$
$140$	−1.76666	+	0.789764i	−0.149310	+	0.0667473i
$141$	−10.3075	+	5.95105i	−0.868050	+	0.501169i
$142$		−	14.1655i		−	1.18874i
$143$	−0.0869582	−	0.624426i	−0.00727181	−	0.0522171i
$144$	−1.00000			−0.0833333
$145$	−13.2482	+	5.92243i	−1.10020	+	0.491831i
$146$	6.43528	+	11.1462i	0.532588	+	0.922469i
$147$	5.41356	+	3.12552i	0.446503	+	0.257788i
$148$	1.75915			0.144601
$149$	−8.90766	−	5.14284i	−0.729744	−	0.421318i	0.0885845	−	0.996069i	$-0.471766\pi$
$149$	−8.90766	−	5.14284i	−0.729744	−	0.421318i	−0.818329	+	0.574751i	$0.805099\pi$
$150$	3.72580	+	3.33442i	0.304211	+	0.272255i
$151$		−	11.7419i		−	0.955544i	−0.878484	−	0.477772i	$-0.841445\pi$
$151$		−	11.7419i		−	0.955544i	0.878484	−	0.477772i	$-0.158555\pi$
$152$	5.20843	+	3.00709i	0.422459	+	0.243907i
$153$	7.08339	−	4.08960i	0.572658	−	0.330624i
$154$	−0.131051	+	0.0756625i	−0.0105604	+	0.00609706i
$155$	15.4592	+	1.60125i	1.24172	+	0.128616i
$156$	3.34131	+	1.35486i	0.267519	+	0.108475i
$157$			6.76034i			0.539534i	0.962926	+	0.269767i	$0.0869467\pi$
$157$			6.76034i			0.539534i	−0.962926	+	0.269767i	$0.913053\pi$
$158$	−4.74480	−	8.21824i	−0.377476	−	0.653808i
$159$	−1.24367	−	2.15410i	−0.0986297	−	0.170832i
$160$	−1.81100	−	1.31160i	−0.143172	−	0.103691i
$161$		−	2.52036i		−	0.198633i
$162$	−0.500000	+	0.866025i	−0.0392837	+	0.0680414i
$163$	−0.713746	+	1.23624i	−0.0559049	+	0.0968301i	−0.892623	−	0.450803i	$-0.851138\pi$
$163$	−0.713746	+	1.23624i	−0.0559049	+	0.0968301i	0.836719	+	0.547633i	$0.184471\pi$
$164$		−	8.17919i		−	0.638688i
$165$	0.316664	+	0.229340i	0.0246522	+	0.0178541i
$166$	−0.0697718	−	0.120848i	−0.00541534	−	0.00937964i
$167$	2.93528	+	5.08406i	0.227139	+	0.393416i	0.956959	−	0.290223i	$-0.0937295\pi$
$167$	2.93528	+	5.08406i	0.227139	+	0.393416i	−0.729820	+	0.683639i	$0.760396\pi$
$168$		−	0.865427i		−	0.0667691i
$169$	−9.32872	−	9.05401i	−0.717594	−	0.696462i
$170$	18.1919	+	1.88430i	1.39526	+	0.144519i
$171$	5.20843	−	3.00709i	0.398298	−	0.229958i
$172$	7.94476	−	4.58691i	0.605782	−	0.349749i
$173$	11.8669	+	6.85138i	0.902226	+	0.520901i	0.877922	−	0.478804i	$-0.158930\pi$
$173$	11.8669	+	6.85138i	0.902226	+	0.520901i	0.0243045	+	0.999705i	$0.492263\pi$
$174$		−	6.48982i		−	0.491992i
$175$	−2.88570	+	3.22441i	−0.218138	+	0.243743i
$176$	−0.151430	−	0.0874279i	−0.0114144	−	0.00659013i
$177$	−7.03667			−0.528908
$178$	11.3790	+	6.56966i	0.852890	+	0.492416i
$179$	−7.09191	−	12.2835i	−0.530074	−	0.918115i	−0.999384	−	0.0350821i	$-0.988831\pi$
$179$	−7.09191	−	12.2835i	−0.530074	−	0.918115i	0.469310	−	0.883033i	$-0.344503\pi$
$180$	−2.04138	+	0.912572i	−0.152155	+	0.0680191i
$181$	13.7728			1.02373			0.511863	−	0.859067i	$-0.328956\pi$
$181$	13.7728			1.02373			0.511863	+	0.859067i	$0.328956\pi$
$182$	−1.17253	+	2.89166i	−0.0869138	+	0.214344i
$183$		−	7.97389i		−	0.589447i
$184$	2.52211	−	1.45614i	0.185932	−	0.107348i
$185$	3.59108	−	1.60535i	0.264021	−	0.118027i
$186$	−3.47529	+	6.01937i	−0.254820	+	0.441362i
$187$	1.43018			0.104585
$188$	5.95105	−	10.3075i	0.434025	−	0.751753i
$189$	−0.749482	−	0.432713i	−0.0545168	−	0.0314753i
$190$	13.3765	+	1.38553i	0.970436	+	0.100517i
$191$	2.78821	−	4.82932i	0.201748	−	0.349437i	−0.747344	−	0.664437i	$-0.768671\pi$
$191$	2.78821	−	4.82932i	0.201748	−	0.349437i	0.949092	+	0.315000i	$0.102005\pi$
$192$	0.866025	−	0.500000i	0.0625000	−	0.0360844i
$193$	−0.110405	−	0.191227i	−0.00794712	−	0.0137648i	0.862024	−	0.506867i	$-0.169196\pi$
$193$	−0.110405	−	0.191227i	−0.00794712	−	0.0137648i	−0.869972	+	0.493102i	$0.835863\pi$
$194$	8.64822			0.620906
$195$	8.05727	−	0.283413i	0.576993	−	0.0202956i
$196$	−6.25104			−0.446503
$197$	0.861905	+	1.49286i	0.0614082	+	0.106362i	0.895095	−	0.445875i	$-0.147108\pi$
$197$	0.861905	+	1.49286i	0.0614082	+	0.106362i	−0.833687	+	0.552237i	$0.813774\pi$
$198$	−0.151430	+	0.0874279i	−0.0107616	+	0.00621323i
$199$	−3.97927	+	6.89229i	−0.282083	+	0.488581i	−0.971898	−	0.235404i	$-0.924359\pi$
$199$	−3.97927	+	6.89229i	−0.282083	+	0.488581i	0.689815	+	0.723986i	$0.257692\pi$
$200$	−4.89385	−	1.02479i	−0.346048	−	0.0724639i
$201$	2.36886	+	1.36766i	0.167086	+	0.0964673i
$202$	−5.28276	+	9.15001i	−0.371694	+	0.643793i
$203$	5.61646			0.394198
$204$	−4.08960	+	7.08339i	−0.286329	+	0.495936i
$205$	−7.46410	−	16.6968i	−0.521315	−	1.16615i
$206$	−7.73853	+	4.46784i	−0.539169	+	0.311289i
$207$		−	2.91228i		−	0.202417i
$208$	−3.57109	+	0.497314i	−0.247610	+	0.0344825i
$209$	1.05161			0.0727416
$210$	−0.789764	−	1.76666i	−0.0544989	−	0.121911i
$211$	2.10991	+	3.65448i	0.145252	+	0.251585i	0.929467	−	0.368905i	$-0.120267\pi$
$211$	2.10991	+	3.65448i	0.145252	+	0.251585i	−0.784215	+	0.620490i	$0.786934\pi$
$212$	2.15410	+	1.24367i	0.147945	+	0.0854158i
$213$	14.1655			0.970604
$214$	0.745455	+	0.430389i	0.0509582	+	0.0294208i
$215$	12.0323	−	16.6138i	0.820599	−	1.13305i
$216$		−	1.00000i		−	0.0680414i
$217$	−5.20933	−	3.00761i	−0.353632	−	0.204170i
$218$	4.72274	−	2.72668i	0.319865	−	0.184674i
$219$	−11.1462	+	6.43528i	−0.753193	+	0.434856i
$220$	−0.388909	−	0.0402827i	−0.0262202	−	0.00271586i
$221$	23.2616	−	18.1270i	1.56474	−	1.21935i
$222$			1.75915i			0.118066i
$223$	3.47638	+	6.02126i	0.232795	+	0.403214i	0.958630	−	0.284656i	$-0.0918794\pi$
$223$	3.47638	+	6.02126i	0.232795	+	0.403214i	−0.725834	+	0.687870i	$0.758546\pi$
$224$	0.432713	+	0.749482i	0.0289119	+	0.0500769i
$225$	−3.33442	+	3.72580i	−0.222295	+	0.248387i
$226$			11.7821i			0.783735i
$227$	1.44823	−	2.50840i	0.0961221	−	0.166488i	−0.813954	−	0.580929i	$-0.802689\pi$
$227$	1.44823	−	2.50840i	0.0961221	−	0.166488i	0.910076	+	0.414441i	$0.136023\pi$
$228$	−3.00709	+	5.20843i	−0.199149	+	0.344937i
$229$			7.88800i			0.521254i	0.965440	+	0.260627i	$0.0839293\pi$
$229$			7.88800i			0.521254i	−0.965440	+	0.260627i	$0.916071\pi$
$230$	3.81974	−	5.27413i	0.251866	−	0.347766i
$231$	−0.0756625	−	0.131051i	−0.00497823	−	0.00862254i
$232$	3.24491	+	5.62035i	0.213039	+	0.368994i
$233$			1.42749i			0.0935181i	0.998906	+	0.0467590i	$0.0148893\pi$
$233$			1.42749i			0.0935181i	−0.998906	+	0.0467590i	$0.985111\pi$
$234$	−1.35486	+	3.34131i	−0.0885699	+	0.218428i
$235$	2.74197	−	26.4723i	0.178866	−	1.72686i
$236$	6.09393	−	3.51833i	0.396681	−	0.229024i
$237$	8.21824	−	4.74480i	0.533832	−	0.308208i
$238$	−6.13015	−	3.53925i	−0.397359	−	0.229415i
$239$		−	10.9084i		−	0.705604i	−0.935698	−	0.352802i	$-0.885229\pi$
$239$		−	10.9084i		−	0.705604i	0.935698	−	0.352802i	$-0.114771\pi$
$240$	1.31160	−	1.81100i	0.0846632	−	0.116899i
$241$	−25.4317	−	14.6830i	−1.63820	−	0.945816i	−0.981452	−	0.191707i	$-0.938598\pi$
$241$	−25.4317	−	14.6830i	−1.63820	−	0.945816i	−0.656749	−	0.754109i	$-0.728069\pi$
$242$	10.9694			0.705141
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	3.98695	+	6.90559i	0.255238	+	0.442085i
$245$	−12.7607	+	5.70452i	−0.815252	+	0.364448i
$246$	8.17919			0.521486
$247$	17.1043	−	13.3288i	1.08832	−	0.848091i
$248$		−	6.95057i		−	0.441362i
$249$	0.120848	−	0.0697718i	0.00765845	−	0.00442161i
$250$	−10.9254	+	2.37400i	−0.690982	+	0.150145i
$251$	8.94708	−	15.4968i	0.564735	−	0.978150i	−0.432339	−	0.901711i	$-0.642312\pi$
$251$	8.94708	−	15.4968i	0.564735	−	0.978150i	0.997074	−	0.0764387i	$-0.0243549\pi$
$252$	0.865427			0.0545168
$253$	0.254615	−	0.441005i	0.0160075	−	0.0277258i
$254$	−6.01228	−	3.47119i	−0.377244	−	0.217802i
$255$	−1.88430	+	18.1919i	−0.117999	+	1.13922i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−10.5472	+	6.08945i	−0.657918	+	0.379849i	−0.791483	−	0.611191i	$-0.790691\pi$
$257$	−10.5472	+	6.08945i	−0.657918	+	0.379849i	0.133565	+	0.991040i	$0.457358\pi$
$258$	4.58691	+	7.94476i	0.285568	+	0.494619i
$259$	−1.52241			−0.0945981
$260$	−6.83610	+	4.27408i	−0.423957	+	0.265067i
$261$	6.48982			0.401710
$262$	−1.13567	−	1.96703i	−0.0701616	−	0.121524i
$263$	−18.3309	+	10.5834i	−1.13033	+	0.652598i	−0.944019	−	0.329892i	$-0.892988\pi$
$263$	−18.3309	+	10.5834i	−1.13033	+	0.652598i	−0.186314	+	0.982490i	$0.559654\pi$
$264$	0.0874279	−	0.151430i	0.00538082	−	0.00931985i
$265$	5.53228	+	0.573027i	0.339845	+	0.0352008i
$266$	−4.50751	−	2.60241i	−0.276373	−	0.159564i
$267$	−6.56966	+	11.3790i	−0.402056	+	0.696382i
$268$	−2.73532			−0.167086
$269$	−6.04371	+	10.4680i	−0.368492	+	0.638246i	−0.989330	−	0.145692i	$-0.953459\pi$
$269$	−6.04371	+	10.4680i	−0.368492	+	0.638246i	0.620838	+	0.783939i	$0.286792\pi$
$270$	−0.912572	−	2.04138i	−0.0555374	−	0.124234i
$271$	−12.7275	+	7.34824i	−0.773142	+	0.446374i	−0.833994	−	0.551773i	$-0.813951\pi$
$271$	−12.7275	+	7.34824i	−0.773142	+	0.446374i	0.0608525	+	0.998147i	$0.480618\pi$
$272$		−	8.17919i		−	0.495936i
$273$	−2.89166	−	1.17253i	−0.175011	−	0.0709648i
$274$	−7.37617			−0.445611
$275$	−0.830670	+	0.272675i	−0.0500913	+	0.0164429i
$276$	1.45614	+	2.52211i	0.0876493	+	0.151813i
$277$	−17.0717	−	9.85638i	−1.02574	−	0.592212i	−0.109980	−	0.993934i	$-0.535079\pi$
$277$	−17.0717	−	9.85638i	−1.02574	−	0.592212i	−0.915762	+	0.401722i	$0.868412\pi$
$278$	−0.820759			−0.0492259
$279$	−6.01937	−	3.47529i	−0.360370	−	0.208060i
$280$	1.56729	+	1.13509i	0.0936633	+	0.0678347i
$281$			9.93073i			0.592418i	0.955123	+	0.296209i	$0.0957225\pi$
$281$			9.93073i			0.592418i	−0.955123	+	0.296209i	$0.904278\pi$
$282$	10.3075	+	5.95105i	0.613804	+	0.354380i
$283$	10.0790	−	5.81912i	0.599135	−	0.345911i	−0.169566	−	0.985519i	$-0.554237\pi$
$283$	10.0790	−	5.81912i	0.599135	−	0.345911i	0.768701	+	0.639608i	$0.220903\pi$
$284$	−12.2677	+	7.08275i	−0.727953	+	0.420284i
$285$	−1.38553	+	13.3765i	−0.0820716	+	0.792358i
$286$	−0.497290	+	0.387521i	−0.0294053	+	0.0229146i
$287$			7.07849i			0.417830i
$288$	0.500000	+	0.866025i	0.0294628	+	0.0510310i
$289$	24.9496	+	43.2139i	1.46762	+	2.54200i
$290$	11.7530	+	8.51202i	0.690163	+	0.499843i
$291$			8.64822i			0.506967i
$292$	6.43528	−	11.1462i	0.376596	−	0.652284i
$293$	6.57636	−	11.3906i	0.384195	−	0.665445i	−0.607462	−	0.794349i	$-0.707812\pi$
$293$	6.57636	−	11.3906i	0.384195	−	0.665445i	0.991657	+	0.128903i	$0.0411457\pi$
$294$		−	6.25104i		−	0.364568i
$295$	9.22927	−	12.7434i	0.537349	−	0.741949i
$296$	−0.879573	−	1.52347i	−0.0511241	−	0.0885496i
$297$	−0.0874279	−	0.151430i	−0.00507308	−	0.00878684i
$298$			10.2857i			0.595834i
$299$	−1.44832	−	10.4000i	−0.0837583	−	0.601448i
$300$	1.02479	−	4.89385i	0.0591665	−	0.282547i
$301$	−6.87561	+	3.96963i	−0.396304	+	0.228806i
$302$	−10.1688	+	5.87096i	−0.585149	+	0.337836i
$303$	−9.15001	−	5.28276i	−0.525654	−	0.303487i
$304$		−	6.01418i		−	0.344937i
$305$	14.4407	+	10.4585i	0.826872	+	0.598854i
$306$	−7.08339	−	4.08960i	−0.404930	−	0.233787i
$307$	−14.8609			−0.848155			−0.424077	−	0.905626i	$-0.639402\pi$
$307$	−14.8609			−0.848155			−0.424077	+	0.905626i	$0.639402\pi$
$308$	0.131051	+	0.0756625i	0.00746734	+	0.00431127i
$309$	−4.46784	−	7.73853i	−0.254167	−	0.440230i
$310$	−6.34290	−	14.1887i	−0.360252	−	0.805865i
$311$	9.17666			0.520361			0.260180	−	0.965560i	$-0.416218\pi$
$311$	9.17666			0.520361			0.260180	+	0.965560i	$0.416218\pi$
$312$	−0.497314	−	3.57109i	−0.0281548	−	0.202173i
$313$			7.43905i			0.420480i	0.977650	+	0.210240i	$0.0674245\pi$
$313$			7.43905i			0.420480i	−0.977650	+	0.210240i	$0.932576\pi$
$314$	5.85463	−	3.38017i	0.330396	−	0.190754i
$315$	1.76666	−	0.789764i	0.0995401	−	0.0444982i
$316$	−4.74480	+	8.21824i	−0.266916	+	0.462312i
$317$	−25.7510			−1.44632			−0.723161	−	0.690679i	$-0.757312\pi$
$317$	−25.7510			−1.44632			−0.723161	+	0.690679i	$0.757312\pi$
$318$	−1.24367	+	2.15410i	−0.0697417	+	0.120796i
$319$	0.982750	+	0.567391i	0.0550235	+	0.0317678i
$320$	−0.230377	+	2.22417i	−0.0128785	+	0.124335i
$321$	−0.430389	+	0.745455i	−0.0240219	+	0.0416072i
$322$	−2.18270	+	1.26018i	−0.121637	+	0.0702272i
$323$	24.5955	+	42.6007i	1.36853	+	2.37037i
$324$	1.00000			0.0555556
$325$	−10.0546	+	14.9634i	−0.557731	+	0.830022i
$326$	1.42749			0.0790614
$327$	2.72668	+	4.72274i	0.150786	+	0.261168i
$328$	−7.08339	+	4.08960i	−0.391115	+	0.225810i
$329$	−5.15020	+	8.92040i	−0.283940	+	0.491798i
$330$	0.0402827	−	0.388909i	0.00221749	−	0.0214087i
$331$	5.63295	+	3.25219i	0.309615	+	0.178756i	0.646754	−	0.762699i	$-0.276126\pi$
$331$	5.63295	+	3.25219i	0.309615	+	0.178756i	−0.337139	+	0.941455i	$0.609459\pi$
$332$	−0.0697718	+	0.120848i	−0.00382922	+	0.00663241i
$333$	−1.75915			−0.0964006
$334$	2.93528	−	5.08406i	0.160612	−	0.278187i
$335$	−5.58382	+	2.49618i	−0.305076	+	0.136381i
$336$	−0.749482	+	0.432713i	−0.0408876	+	0.0236065i
$337$			18.6696i			1.01700i	0.861063	+	0.508498i	$0.169799\pi$
$337$			18.6696i			1.01700i	−0.861063	+	0.508498i	$0.830201\pi$
$338$	−3.17664	+	12.6059i	−0.172786	+	0.685671i
$339$	−11.7821			−0.639917
$340$	−7.46410	−	16.6968i	−0.404798	−	0.905511i
$341$	−0.607674	−	1.05252i	−0.0329074	−	0.0569973i
$342$	−5.20843	−	3.00709i	−0.281640	−	0.162605i
$343$	11.4678			0.619203
$344$	−7.94476	−	4.58691i	−0.428353	−	0.247310i
$345$	5.27413	+	3.81974i	0.283950	+	0.205648i
$346$		−	13.7028i		−	0.736665i
$347$	−24.6009	−	14.2033i	−1.32064	−	0.762474i	−0.336813	−	0.941572i	$-0.609349\pi$
$347$	−24.6009	−	14.2033i	−1.32064	−	0.762474i	−0.983831	+	0.179098i	$0.942682\pi$
$348$	−5.62035	+	3.24491i	−0.301282	+	0.173945i
$349$	1.93797	−	1.11889i	0.103737	−	0.0598926i	−0.447234	−	0.894417i	$-0.647591\pi$
$349$	1.93797	−	1.11889i	0.103737	−	0.0598926i	0.550971	+	0.834524i	$0.314258\pi$
$350$	4.23527	+	0.886885i	0.226385	+	0.0474060i
$351$	−3.34131	−	1.35486i	−0.178346	−	0.0723170i
$352$			0.174856i			0.00931985i
$353$	0.813287	+	1.40866i	0.0432869	+	0.0749751i	0.886857	−	0.462044i	$-0.152884\pi$
$353$	0.813287	+	1.40866i	0.0432869	+	0.0749751i	−0.843570	+	0.537019i	$0.819550\pi$
$354$	3.51833	+	6.09393i	0.186997	+	0.323889i
$355$	−18.5794	+	25.6537i	−0.986093	+	1.36156i
$356$		−	13.1393i		−	0.696382i
$357$	3.53925	−	6.13015i	0.187317	−	0.324442i
$358$	−7.09191	+	12.2835i	−0.374819	+	0.649206i
$359$		−	34.4613i		−	1.81880i	−0.415923	−	0.909400i	$-0.636541\pi$
$359$		−	34.4613i		−	1.81880i	0.415923	−	0.909400i	$-0.363459\pi$
$360$	1.81100	+	1.31160i	0.0954480	+	0.0691272i
$361$	8.58515	+	14.8699i	0.451850	+	0.782627i
$362$	−6.88641	−	11.9276i	−0.361942	−	0.626901i
$363$			10.9694i			0.575746i
$364$	3.09052	−	0.430389i	0.161987	−	0.0225585i
$365$	2.96508	−	28.6263i	0.155199	−	1.49837i
$366$	−6.90559	+	3.98695i	−0.360961	+	0.208401i
$367$	12.6735	−	7.31703i	0.661550	−	0.381946i	−0.131317	−	0.991340i	$-0.541921\pi$
$367$	12.6735	−	7.31703i	0.661550	−	0.381946i	0.792867	+	0.609394i	$0.208587\pi$
$368$	−2.52211	−	1.45614i	−0.131474	−	0.0759065i
$369$			8.17919i			0.425792i
$370$	−3.18581	−	2.30729i	−0.165622	−	0.119950i
$371$	−1.86422	−	1.07631i	−0.0967855	−	0.0558791i
$372$	6.95057			0.360370
$373$	−19.1166	−	11.0370i	−0.989819	−	0.571472i	−0.0845988	−	0.996415i	$-0.526961\pi$
$373$	−19.1166	−	11.0370i	−0.989819	−	0.571472i	−0.905220	+	0.424943i	$0.860294\pi$
$374$	−0.715090	−	1.23857i	−0.0369764	−	0.0640450i
$375$	−2.37400	−	10.9254i	−0.122593	−	0.564185i
$376$	−11.9021			−0.613804
$377$	23.1757	−	3.22747i	1.19361	−	0.166223i
$378$			0.865427i			0.0445128i
$379$	12.0573	−	6.96127i	0.619341	−	0.357577i	−0.157272	−	0.987555i	$-0.550270\pi$
$379$	12.0573	−	6.96127i	0.619341	−	0.357577i	0.776612	+	0.629979i	$0.216936\pi$
$380$	−5.48837	−	12.2772i	−0.281547	−	0.629806i
$381$	3.47119	−	6.01228i	0.177834	−	0.308018i
$382$	−5.57642			−0.285314
$383$	−12.3044	+	21.3119i	−0.628728	+	1.08899i	0.359080	+	0.933307i	$0.383091\pi$
$383$	−12.3044	+	21.3119i	−0.628728	+	1.08899i	−0.987807	+	0.155681i	$0.950243\pi$
$384$	−0.866025	−	0.500000i	−0.0441942	−	0.0255155i
$385$	0.336572	+	0.0348618i	0.0171533	+	0.00177672i
$386$	−0.110405	+	0.191227i	−0.00561946	+	0.00973319i
$387$	−7.94476	+	4.58691i	−0.403855	+	0.233166i
$388$	−4.32411	−	7.48957i	−0.219523	−	0.380226i
$389$	5.60980			0.284428			0.142214	−	0.989836i	$-0.454578\pi$
$389$	5.60980			0.284428			0.142214	+	0.989836i	$0.454578\pi$
$390$	−4.27408	−	6.83610i	−0.216426	−	0.346159i
$391$	23.8201			1.20463
$392$	3.12552	+	5.41356i	0.157863	+	0.273426i
$393$	1.96703	−	1.13567i	0.0992235	−	0.0572867i
$394$	0.861905	−	1.49286i	0.0434222	−	0.0752094i
$395$	−2.18619	+	21.1065i	−0.109999	+	1.06198i
$396$	0.151430	+	0.0874279i	0.00760962	+	0.00439342i
$397$	−1.18438	+	2.05141i	−0.0594424	+	0.102957i	−0.894215	−	0.447637i	$-0.852266\pi$
$397$	−1.18438	+	2.05141i	−0.0594424	+	0.102957i	0.834773	+	0.550595i	$0.185599\pi$
$398$	7.95853			0.398925
$399$	2.60241	−	4.50751i	0.130284	−	0.225658i
$400$	1.55943	+	4.75060i	0.0779714	+	0.237530i
$401$	14.2942	−	8.25276i	0.713818	−	0.412123i	−0.0986548	−	0.995122i	$-0.531454\pi$
$401$	14.2942	−	8.25276i	0.713818	−	0.412123i	0.812473	+	0.582998i	$0.198121\pi$
$402$		−	2.73532i		−	0.136425i
$403$	−23.2240	−	9.41704i	−1.15687	−	0.469096i
$404$	10.5655			0.525654
$405$	2.04138	−	0.912572i	0.101437	−	0.0453461i
$406$	−2.80823	−	4.86400i	−0.139370	−	0.241396i
$407$	−0.266387	−	0.153798i	−0.0132043	−	0.00762351i
$408$	8.17919			0.404930
$409$	28.8448	+	16.6535i	1.42628	+	0.823464i	0.996825	−	0.0796230i	$-0.0253717\pi$
$409$	28.8448	+	16.6535i	1.42628	+	0.823464i	0.429457	+	0.903087i	$0.358705\pi$
$410$	−10.7278	+	14.8125i	−0.529808	+	0.731537i
$411$		−	7.37617i		−	0.363840i
$412$	7.73853	+	4.46784i	0.381250	+	0.220115i
$413$	−5.27385	+	3.04486i	−0.259509	+	0.149828i
$414$	−2.52211	+	1.45614i	−0.123955	+	0.0715654i
$415$	−0.0321476	+	0.310368i	−0.00157806	+	0.0152354i
$416$	2.21623	+	2.84400i	0.108660	+	0.139438i
$417$		−	0.820759i		−	0.0401927i
$418$	−0.525807	−	0.910724i	−0.0257181	−	0.0445450i
$419$	15.1303	+	26.2065i	0.739164	+	1.28027i	0.952872	+	0.303372i	$0.0981126\pi$
$419$	15.1303	+	26.2065i	0.739164	+	1.28027i	−0.213708	+	0.976898i	$0.568554\pi$
$420$	−1.13509	+	1.56729i	−0.0553868	+	0.0764758i
$421$		−	40.2235i		−	1.96038i	−0.198070	−	0.980188i	$-0.563467\pi$
$421$		−	40.2235i		−	1.96038i	0.198070	−	0.980188i	$-0.436533\pi$
$422$	2.10991	−	3.65448i	0.102709	−	0.177897i
$423$	−5.95105	+	10.3075i	−0.289350	+	0.501169i
$424$		−	2.48735i		−	0.120796i
$425$	−30.4741	−	27.2729i	−1.47821	−	1.32293i
$426$	−7.08275	−	12.2677i	−0.343160	−	0.594371i
$427$	−3.45041	−	5.97629i	−0.166977	−	0.289213i
$428$		−	0.860777i		−	0.0416072i
$429$	−0.387521	−	0.497290i	−0.0187097	−	0.0240094i
$430$	−20.4041	−	2.11344i	−0.983974	−	0.101919i
$431$	−28.1980	+	16.2801i	−1.35825	+	0.784185i	−0.989388	−	0.145300i	$-0.953585\pi$
$431$	−28.1980	+	16.2801i	−1.35825	+	0.784185i	−0.368860	+	0.929485i	$0.620252\pi$
$432$	−0.866025	+	0.500000i	−0.0416667	+	0.0240563i
$433$	26.6153	+	15.3663i	1.27905	+	0.738460i	0.976674	−	0.214729i	$-0.0688869\pi$
$433$	26.6153	+	15.3663i	1.27905	+	0.738460i	0.302376	+	0.953189i	$0.402220\pi$
$434$			6.01521i			0.288739i
$435$	−8.51202	+	11.7530i	−0.408120	+	0.563515i
$436$	−4.72274	−	2.72668i	−0.226178	−	0.130584i
$437$	17.5150			0.837854
$438$	11.1462	+	6.43528i	0.532588	+	0.307490i
$439$	3.26422	+	5.65380i	0.155793	+	0.269841i	0.933347	−	0.358974i	$-0.116873\pi$
$439$	3.26422	+	5.65380i	0.155793	+	0.269841i	−0.777555	+	0.628815i	$0.783540\pi$
$440$	0.159569	+	0.356946i	0.00760713	+	0.0170167i
$441$	6.25104			0.297668
$442$	−27.3292	−	11.0816i	−1.29992	−	0.527100i
$443$			30.3111i			1.44012i	0.693911	+	0.720061i	$0.255886\pi$
$443$			30.3111i			1.44012i	−0.693911	+	0.720061i	$0.744114\pi$
$444$	1.52347	−	0.879573i	0.0723005	−	0.0417427i
$445$	−11.9906	−	26.8223i	−0.568407	−	1.27150i
$446$	3.47638	−	6.02126i	0.164611	−	0.285115i
$447$	−10.2857			−0.486496
$448$	0.432713	−	0.749482i	0.0204438	−	0.0354097i
$449$	13.8034	+	7.96938i	0.651421	+	0.376098i	0.789001	−	0.614392i	$-0.210599\pi$
$449$	13.8034	+	7.96938i	0.651421	+	0.376098i	−0.137579	+	0.990491i	$0.543932\pi$
$450$	4.89385	+	1.02479i	0.230698	+	0.0483093i
$451$	−0.715090	+	1.23857i	−0.0336723	+	0.0583221i
$452$	10.2036	−	5.89106i	0.479938	−	0.277092i
$453$	−5.87096	−	10.1688i	−0.275842	−	0.477772i
$454$	−2.89645			−0.135937
$455$	5.91614	−	3.69890i	0.277353	−	0.173407i
$456$	6.01418			0.281640
$457$	9.90436	+	17.1548i	0.463306	+	0.802470i	0.999123	−	0.0418642i	$-0.0133297\pi$
$457$	9.90436	+	17.1548i	0.463306	+	0.802470i	−0.535817	+	0.844334i	$0.679996\pi$
$458$	6.83121	−	3.94400i	0.319202	−	0.184291i
$459$	4.08960	−	7.08339i	0.190886	−	0.330624i
$460$	−6.47740	−	0.670922i	−0.302010	−	0.0312819i
$461$	−11.5898	−	6.69139i	−0.539792	−	0.311649i	0.205202	−	0.978720i	$-0.434215\pi$
$461$	−11.5898	−	6.69139i	−0.539792	−	0.311649i	−0.744995	+	0.667070i	$0.767548\pi$
$462$	−0.0756625	+	0.131051i	−0.00352014	+	0.00609706i
$463$	42.3599			1.96863			0.984316	−	0.176412i	$-0.0564493\pi$
$463$	42.3599			1.96863			0.984316	+	0.176412i	$0.0564493\pi$
$464$	3.24491	−	5.62035i	0.150641	−	0.260918i
$465$	14.1887	−	6.34290i	0.657986	−	0.294145i
$466$	1.23624	−	0.713746i	0.0572679	−	0.0330636i
$467$		−	33.4593i		−	1.54831i	−0.632996	−	0.774155i	$-0.718175\pi$
$467$		−	33.4593i		−	1.54831i	0.632996	−	0.774155i	$-0.281825\pi$
$468$	3.57109	−	0.497314i	0.165074	−	0.0229883i
$469$	2.36722			0.109308
$470$	−24.2966	+	10.8615i	−1.12072	+	0.501005i
$471$	3.38017	+	5.85463i	0.155750	+	0.269767i
$472$	−6.09393	−	3.51833i	−0.280496	−	0.161944i
$473$	−1.60410			−0.0737564
$474$	−8.21824	−	4.74480i	−0.377476	−	0.217936i
$475$	−22.4076	−	20.0538i	−1.02813	−	0.920132i
$476$			7.07849i			0.324442i
$477$	−2.15410	−	1.24367i	−0.0986297	−	0.0569439i
$478$	−9.44692	+	5.45418i	−0.432092	+	0.249469i
$479$	−19.3387	+	11.1652i	−0.883606	+	0.510150i	−0.871846	−	0.489781i	$-0.837077\pi$
$479$	−19.3387	+	11.1652i	−0.883606	+	0.510150i	−0.0117600	+	0.999931i	$0.503743\pi$
$480$	−2.22417	−	0.230377i	−0.101519	−	0.0105152i
$481$	−6.28207	+	0.874847i	−0.286438	+	0.0398896i
$482$			29.3660i			1.33759i
$483$	−1.26018	−	2.18270i	−0.0573403	−	0.0993163i
$484$	−5.48471	−	9.49980i	−0.249305	−	0.431809i
$485$	−15.6619	−	11.3430i	−0.711170	−	0.515058i
$486$			1.00000i			0.0453609i
$487$	−14.3750	+	24.8982i	−0.651392	+	1.12824i	0.331393	+	0.943493i	$0.392481\pi$
$487$	−14.3750	+	24.8982i	−0.651392	+	1.12824i	−0.982785	+	0.184751i	$0.940852\pi$
$488$	3.98695	−	6.90559i	0.180481	−	0.312602i
$489$			1.42749i			0.0645534i
$490$	11.3206	+	8.19884i	0.511413	+	0.370386i
$491$	8.02546	+	13.9005i	0.362184	+	0.627321i	0.988320	−	0.152393i	$-0.0486978\pi$
$491$	8.02546	+	13.9005i	0.362184	+	0.627321i	−0.626136	+	0.779714i	$0.715364\pi$
$492$	−4.08960	−	7.08339i	−0.184373	−	0.319344i
$493$			53.0815i			2.39067i
$494$	−20.0952	−	8.14836i	−0.904127	−	0.366612i
$495$	0.388909	+	0.0402827i	0.0174802	+	0.00181057i
$496$	−6.01937	+	3.47529i	−0.270278	+	0.156045i
$497$	10.6168	−	6.12960i	0.476228	−	0.274950i
$498$	−0.120848	−	0.0697718i	−0.00541534	−	0.00312655i
$499$		−	33.2509i		−	1.48851i	−0.667894	−	0.744256i	$-0.732804\pi$
$499$		−	33.2509i		−	1.48851i	0.667894	−	0.744256i	$-0.267196\pi$
$500$	7.51864	+	8.27466i	0.336244	+	0.370054i
$501$	5.08406	+	2.93528i	0.227139	+	0.131139i
$502$	−17.8942			−0.798656
$503$	−21.7736	−	12.5710i	−0.970838	−	0.560514i	−0.0713466	−	0.997452i	$-0.522730\pi$
$503$	−21.7736	−	12.5710i	−0.970838	−	0.560514i	−0.899492	+	0.436938i	$0.856063\pi$
$504$	−0.432713	−	0.749482i	−0.0192746	−	0.0333846i
$505$	21.5682	−	9.64180i	0.959772	−	0.429055i
$506$	−0.509229			−0.0226380
$507$	−12.6059	−	3.17664i	−0.559848	−	0.141080i
$508$			6.94238i			0.308018i
$509$	22.8809	−	13.2103i	1.01418	−	0.585536i	0.101766	−	0.994808i	$-0.467551\pi$
$509$	22.8809	−	13.2103i	1.01418	−	0.585536i	0.912412	+	0.409272i	$0.134217\pi$
$510$	16.6968	−	7.46410i	0.739347	−	0.330516i
$511$	−5.56927	+	9.64625i	−0.246370	+	0.426725i
$512$	1.00000			0.0441942
$513$	3.00709	−	5.20843i	0.132766	−	0.229958i
$514$	10.5472	+	6.08945i	0.465219	+	0.268594i
$515$	19.8745	+	2.05858i	0.875774	+	0.0907117i
$516$	4.58691	−	7.94476i	0.201927	−	0.349749i
$517$	−1.80233	+	1.04058i	−0.0792664	+	0.0457645i
$518$	0.761206	+	1.31845i	0.0334455	+	0.0579293i
$519$	13.7028			0.601484
$520$	7.11951	+	3.78319i	0.312211	+	0.165904i
$521$	−22.4462			−0.983384			−0.491692	−	0.870769i	$-0.663621\pi$
$521$	−22.4462			−0.983384			−0.491692	+	0.870769i	$0.663621\pi$
$522$	−3.24491	−	5.62035i	−0.142026	−	0.245996i
$523$	25.1815	−	14.5385i	1.10111	−	0.635726i	0.164598	−	0.986361i	$-0.447367\pi$
$523$	25.1815	−	14.5385i	1.10111	−	0.635726i	0.936512	+	0.350635i	$0.114034\pi$
$524$	−1.13567	+	1.96703i	−0.0496118	+	0.0859301i
$525$	−0.886885	+	4.23527i	−0.0387068	+	0.184842i
$526$	18.3309	+	10.5834i	0.799266	+	0.461456i
$527$	28.4250	−	49.2336i	1.23821	−	2.14465i
$528$	−0.174856			−0.00760962
$529$	−7.25931	+	12.5735i	−0.315622	+	0.546674i
$530$	−2.26988	−	5.07761i	−0.0985974	−	0.220557i
$531$	−6.09393	+	3.51833i	−0.264454	+	0.152683i
$532$			5.20483i			0.225658i
$533$	4.06762	+	29.2086i	0.176188	+	1.26517i
$534$	13.1393			0.568594
$535$	−0.785521	−	1.75717i	−0.0339610	−	0.0759690i
$536$	1.36766	+	2.36886i	0.0590739	+	0.102319i
$537$	−12.2835	−	7.09191i	−0.530074	−	0.306038i
$538$	12.0874			0.521126
$539$	0.946592	+	0.546515i	0.0407726	+	0.0235401i
$540$	−1.31160	+	1.81100i	−0.0564421	+	0.0779330i
$541$			8.17282i			0.351377i	0.984446	+	0.175688i	$0.0562151\pi$
$541$			8.17282i			0.351377i	−0.984446	+	0.175688i	$0.943785\pi$
$542$	12.7275	+	7.34824i	0.546694	+	0.315634i
$543$	11.9276	−	6.88641i	0.511863	−	0.295524i
$544$	−7.08339	+	4.08960i	−0.303698	+	0.175340i
$545$	−12.1292	−	1.25633i	−0.519557	−	0.0538152i
$546$	0.430389	+	3.09052i	0.0184189	+	0.132262i
$547$		−	40.7393i		−	1.74188i	−0.491385	−	0.870942i	$-0.663509\pi$
$547$		−	40.7393i		−	1.74188i	0.491385	−	0.870942i	$-0.336491\pi$
$548$	3.68809	+	6.38795i	0.157547	+	0.272880i
$549$	−3.98695	−	6.90559i	−0.170159	−	0.294724i
$550$	0.651479	+	0.583044i	0.0277791	+	0.0248611i
$551$			39.0309i			1.66277i
$552$	1.45614	−	2.52211i	0.0619774	−	0.107348i
$553$	4.10628	−	7.11229i	0.174617	−	0.302445i
$554$			19.7128i			0.837515i
$555$	2.30729	−	3.18581i	0.0979390	−	0.135230i
$556$	0.410380	+	0.710798i	0.0174040	+	0.0301446i
$557$	−0.458421	−	0.794008i	−0.0194239	−	0.0336432i	0.856150	−	0.516727i	$-0.172850\pi$
$557$	−0.458421	−	0.794008i	−0.0194239	−	0.0336432i	−0.875574	+	0.483084i	$0.839517\pi$
$558$			6.95057i			0.294241i
$559$	−26.0903	+	20.3313i	−1.10350	+	0.859922i
$560$	0.199374	−	1.92486i	0.00842511	−	0.0813400i
$561$	1.23857	−	0.715090i	0.0522925	−	0.0301911i
$562$	8.60027	−	4.96537i	0.362780	−	0.209451i
$563$	−10.9632	−	6.32961i	−0.462044	−	0.266761i	0.250859	−	0.968024i	$-0.419287\pi$
$563$	−10.9632	−	6.32961i	−0.462044	−	0.266761i	−0.712903	+	0.701262i	$0.752620\pi$
$564$		−	11.9021i		−	0.501169i
$565$	15.4534	−	21.3374i	0.650129	−	0.897671i
$566$	−10.0790	−	5.81912i	−0.423652	−	0.244596i
$567$	−0.865427			−0.0363445
$568$	12.2677	+	7.08275i	0.514741	+	0.297186i
$569$	12.2559	+	21.2279i	0.513795	+	0.889918i	0.999872	+	0.0160026i	$0.00509402\pi$
$569$	12.2559	+	21.2279i	0.513795	+	0.889918i	−0.486077	+	0.873916i	$0.661573\pi$
$570$	12.2772	−	5.48837i	0.514235	−	0.229882i
$571$	−11.1443			−0.466376			−0.233188	−	0.972432i	$-0.574916\pi$
$571$	−11.1443			−0.466376			−0.233188	+	0.972432i	$0.574916\pi$
$572$	0.584248	+	0.236905i	0.0244286	+	0.00990549i
$573$		−	5.57642i		−	0.232958i
$574$	6.13015	−	3.53925i	0.255868	−	0.147725i
$575$	−13.8351	+	4.54149i	−0.576962	+	0.189393i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	23.8325			0.992161			0.496081	−	0.868276i	$-0.334772\pi$
$577$	23.8325			0.992161			0.496081	+	0.868276i	$0.334772\pi$
$578$	24.9496	−	43.2139i	1.03777	−	1.79746i
$579$	−0.191227	−	0.110405i	−0.00794712	−	0.00458827i
$580$	1.49510	−	14.4344i	0.0620808	−	0.599358i
$581$	0.0603824	−	0.104585i	0.00250508	−	0.00433893i
$582$	7.48957	−	4.32411i	0.310453	−	0.179240i
$583$	−0.217463	−	0.376658i	−0.00900642	−	0.0155996i
$584$	−12.8706			−0.532588
$585$	6.83610	−	4.27408i	0.282638	−	0.176711i
$586$	−13.1527			−0.543334
$587$	18.6811	+	32.3566i	0.771051	+	1.33550i	0.936988	+	0.349362i	$0.113602\pi$
$587$	18.6811	+	32.3566i	0.771051	+	1.33550i	−0.165937	+	0.986136i	$0.553065\pi$
$588$	−5.41356	+	3.12552i	−0.223251	+	0.128894i
$589$	20.9010	−	36.2016i	0.861210	−	1.49166i
$590$	−15.6507	−	1.62109i	−0.644331	−	0.0667391i
$591$	1.49286	+	0.861905i	0.0614082	+	0.0354540i
$592$	−0.879573	+	1.52347i	−0.0361502	+	0.0626140i
$593$	6.46136			0.265336			0.132668	−	0.991161i	$-0.457646\pi$
$593$	6.46136			0.265336			0.132668	+	0.991161i	$0.457646\pi$
$594$	−0.0874279	+	0.151430i	−0.00358721	+	0.00621323i
$595$	6.45963	+	14.4499i	0.264819	+	0.592386i
$596$	8.90766	−	5.14284i	0.364872	−	0.210659i
$597$			7.95853i			0.325721i
$598$	−8.28251	+	6.45428i	−0.338697	+	0.263935i
$599$	−38.5057			−1.57330			−0.786651	−	0.617398i	$-0.788187\pi$
$599$	−38.5057			−1.57330			−0.786651	+	0.617398i	$0.788187\pi$
$600$	−4.75060	+	1.55943i	−0.193942	+	0.0636634i
$601$	−0.371169	−	0.642883i	−0.0151403	−	0.0262237i	0.858356	−	0.513055i	$-0.171486\pi$
$601$	−0.371169	−	0.642883i	−0.0151403	−	0.0262237i	−0.873496	+	0.486831i	$0.838153\pi$
$602$	6.87561	+	3.96963i	0.280229	+	0.161790i
$603$	2.73532			0.111391
$604$	10.1688	+	5.87096i	0.413763	+	0.238886i
$605$	−19.8656	−	14.3875i	−0.807652	−	0.584933i
$606$			10.5655i			0.429195i
$607$	25.5500	+	14.7513i	1.03704	+	0.598736i	0.918994	−	0.394272i	$-0.129003\pi$
$607$	25.5500	+	14.7513i	1.03704	+	0.598736i	0.118047	+	0.993008i	$0.462337\pi$
$608$	−5.20843	+	3.00709i	−0.211230	+	0.121954i
$609$	4.86400	−	2.80823i	0.197099	−	0.113795i
$610$	1.83700	−	17.7353i	0.0743780	−	0.718081i
$611$	−16.1257	+	39.7686i	−0.652374	+	1.60887i
$612$			8.17919i			0.330624i
$613$	−6.86720	−	11.8943i	−0.277364	−	0.480408i	0.693365	−	0.720587i	$-0.256127\pi$
$613$	−6.86720	−	11.8943i	−0.277364	−	0.480408i	−0.970729	+	0.240178i	$0.922794\pi$
$614$	7.43044	+	12.8699i	0.299868	+	0.519387i
$615$	−14.8125	−	10.7278i	−0.597298	−	0.432587i
$616$		−	0.151325i		−	0.00609706i
$617$	21.4394	−	37.1342i	0.863119	−	1.49497i	−0.00578297	−	0.999983i	$-0.501841\pi$
$617$	21.4394	−	37.1342i	0.863119	−	1.49497i	0.868902	−	0.494983i	$-0.164826\pi$
$618$	−4.46784	+	7.73853i	−0.179723	+	0.311289i
$619$		−	30.0054i		−	1.20602i	−0.797734	−	0.603010i	$-0.793968\pi$
$619$		−	30.0054i		−	1.20602i	0.797734	−	0.603010i	$-0.206032\pi$
$620$	−9.11635	+	12.5875i	−0.366121	+	0.505525i
$621$	−1.45614	−	2.52211i	−0.0584329	−	0.101209i
$622$	−4.58833	−	7.94722i	−0.183975	−	0.318655i
$623$			11.3711i			0.455574i
$624$	−2.84400	+	2.21623i	−0.113851	+	0.0887202i
$625$	22.8996	+	10.0304i	0.915984	+	0.401215i
$626$	6.44240	−	3.71952i	0.257490	−	0.148662i
$627$	0.910724	−	0.525807i	0.0363708	−	0.0209987i
$628$	−5.85463	−	3.38017i	−0.233625	−	0.134884i
$629$		−	14.3884i		−	0.573703i
$630$	−1.56729	−	1.13509i	−0.0624422	−	0.0452231i
$631$	7.73137	+	4.46371i	0.307781	+	0.177697i	0.645933	−	0.763394i	$-0.276468\pi$
$631$	7.73137	+	4.46371i	0.307781	+	0.177697i	−0.338152	+	0.941091i	$0.609802\pi$
$632$	9.48961			0.377476
$633$	3.65448	+	2.10991i	0.145252	+	0.0838616i
$634$	12.8755	+	22.3011i	0.511352	+	0.885688i
$635$	6.33542	+	14.1720i	0.251414	+	0.562399i
$636$	2.48735			0.0986297
$637$	22.3230	−	3.10873i	0.884470	−	0.123172i
$638$		−	1.13478i		−	0.0449265i
$639$	12.2677	−	7.08275i	0.485302	−	0.280189i
$640$	2.04138	−	0.912572i	0.0806924	−	0.0360726i
$641$	−11.9079	+	20.6250i	−0.470332	+	0.814639i	−0.999424	−	0.0339254i	$-0.989199\pi$
$641$	−11.9079	+	20.6250i	−0.470332	+	0.814639i	0.529092	+	0.848564i	$0.322532\pi$
$642$	0.860777			0.0339722
$643$	−4.79374	+	8.30300i	−0.189047	+	0.327439i	−0.944933	−	0.327265i	$-0.893873\pi$
$643$	−4.79374	+	8.30300i	−0.189047	+	0.327439i	0.755886	+	0.654703i	$0.227206\pi$
$644$	2.18270	+	1.26018i	0.0860104	+	0.0496581i
$645$	2.11344	−	20.4041i	0.0832165	−	0.803411i
$646$	24.5955	−	42.6007i	0.967699	−	1.67610i
$647$	−39.2219	+	22.6448i	−1.54197	+	0.890259i	−0.543259	+	0.839565i	$0.682810\pi$
$647$	−39.2219	+	22.6448i	−1.54197	+	0.890259i	−0.998714	+	0.0506940i	$0.983857\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	−1.23040			−0.0482975
$650$	17.9860	+	1.22585i	0.705470	+	0.0480819i
$651$	−6.01521			−0.235755
$652$	−0.713746	−	1.23624i	−0.0279524	−	0.0484150i
$653$	8.00988	−	4.62451i	0.313451	−	0.180971i	−0.335019	−	0.942211i	$-0.608743\pi$
$653$	8.00988	−	4.62451i	0.313451	−	0.180971i	0.648470	+	0.761241i	$0.275409\pi$
$654$	2.72668	−	4.72274i	0.106622	−	0.184674i
$655$	−0.523262	+	5.05182i	−0.0204455	+	0.197391i
$656$	7.08339	+	4.08960i	0.276560	+	0.159672i
$657$	−6.43528	+	11.1462i	−0.251064	+	0.434856i
$658$	10.3004			0.401551
$659$	−11.0666	+	19.1679i	−0.431093	+	0.746676i	−0.996968	−	0.0778159i	$-0.975205\pi$
$659$	−11.0666	+	19.1679i	−0.431093	+	0.746676i	0.565874	+	0.824491i	$0.308539\pi$
$660$	−0.356946	+	0.159569i	−0.0138941	+	0.00621120i
$661$	8.75083	−	5.05229i	0.340368	−	0.196511i	−0.320067	−	0.947395i	$-0.603705\pi$
$661$	8.75083	−	5.05229i	0.340368	−	0.196511i	0.660435	+	0.750884i	$0.270372\pi$
$662$		−	6.50437i		−	0.252800i
$663$	11.0816	−	27.3292i	0.430375	−	1.06138i
$664$	0.139544			0.00541534
$665$	4.74978	+	10.6250i	0.184189	+	0.412020i
$666$	0.879573	+	1.52347i	0.0340828	+	0.0590331i
$667$	16.3680	+	9.45008i	0.633772	+	0.365909i
$668$	−5.87057			−0.227139
$669$	6.02126	+	3.47638i	0.232795	+	0.134405i
$670$	4.95366	+	3.58764i	0.191377	+	0.138603i
$671$		−	1.39428i		−	0.0538256i
$672$	0.749482	+	0.432713i	0.0289119	+	0.0166923i
$673$	11.6594	−	6.73157i	0.449437	−	0.259483i	−0.258155	−	0.966103i	$-0.583115\pi$
$673$	11.6594	−	6.73157i	0.449437	−	0.259483i	0.707593	+	0.706621i	$0.249781\pi$
$674$	16.1683	−	9.33479i	0.622781	−	0.359562i
$675$	−1.02479	+	4.89385i	−0.0394444	+	0.188364i
$676$	12.5054	−	3.55190i	0.480975	−	0.136612i
$677$			7.86444i			0.302255i	0.988514	+	0.151127i	$0.0482904\pi$
$677$			7.86444i			0.302255i	−0.988514	+	0.151127i	$0.951710\pi$
$678$	5.89106	+	10.2036i	0.226245	+	0.391868i
$679$	3.74220	+	6.48168i	0.143612	+	0.248744i
$680$	−10.7278	+	14.8125i	−0.411392	+	0.568033i
$681$		−	2.89645i		−	0.110992i
$682$	−0.607674	+	1.05252i	−0.0232690	+	0.0403032i
$683$	9.21246	−	15.9565i	0.352505	−	0.610557i	−0.634183	−	0.773183i	$-0.718663\pi$
$683$	9.21246	−	15.9565i	0.352505	−	0.610557i	0.986688	+	0.162627i	$0.0519966\pi$
$684$			6.01418i			0.229958i
$685$	13.3582	+	9.67456i	0.510392	+	0.369646i
$686$	−5.73390	−	9.93141i	−0.218921	−	0.379183i
$687$	3.94400	+	6.83121i	0.150473	+	0.260627i
$688$			9.17382i			0.349749i
$689$	−8.31100	−	3.37000i	−0.316624	−	0.128387i
$690$	0.670922	−	6.47740i	0.0255416	−	0.246590i
$691$	−20.5618	+	11.8714i	−0.782208	+	0.451608i	−0.837212	−	0.546878i	$-0.815816\pi$
$691$	−20.5618	+	11.8714i	−0.782208	+	0.451608i	0.0550042	+	0.998486i	$0.482483\pi$
$692$	−11.8669	+	6.85138i	−0.451113	+	0.260450i
$693$	−0.131051	−	0.0756625i	−0.00497823	−	0.00287418i
$694$			28.4066i			1.07830i
$695$	1.48639	+	1.07650i	0.0563821	+	0.0408342i
$696$	5.62035	+	3.24491i	0.213039	+	0.122998i
$697$	−66.8992			−2.53399
$698$	−1.93797	−	1.11889i	−0.0733532	−	0.0423505i
$699$	0.713746	+	1.23624i	0.0269963	+	0.0467590i
$700$	−1.34957	−	4.11130i	−0.0510090	−	0.155392i
$701$	−6.52189			−0.246328			−0.123164	−	0.992386i	$-0.539304\pi$
$701$	−6.52189			−0.246328			−0.123164	+	0.992386i	$0.539304\pi$
$702$	0.497314	+	3.57109i	0.0187699	+	0.134782i
$703$		−	10.5798i		−	0.399025i
$704$	0.151430	−	0.0874279i	0.00570722	−	0.00329506i
$705$	−10.8615	−	24.2966i	−0.409069	−	0.915064i
$706$	0.813287	−	1.40866i	0.0306085	−	0.0530154i
$707$	−9.14369			−0.343884
$708$	3.51833	−	6.09393i	0.132227	−	0.229024i
$709$	27.5565	+	15.9098i	1.03491	+	0.597504i	0.918387	−	0.395684i	$-0.129493\pi$
$709$	27.5565	+	15.9098i	1.03491	+	0.597504i	0.116521	+	0.993188i	$0.462826\pi$
$710$	31.5065	+	3.26340i	1.18242	+	0.122473i
$711$	4.74480	−	8.21824i	0.177944	−	0.308208i
$712$	−11.3790	+	6.56966i	−0.426445	+	0.246208i
$713$	−10.1210	−	17.5301i	−0.379035	−	0.656507i
$714$	−7.07849			−0.264906
$715$	1.40886	−	0.0495564i	0.0526884	−	0.00185330i
$716$	14.1838			0.530074
$717$	−5.45418	−	9.44692i	−0.203690	−	0.352802i
$718$	−29.8444	+	17.2307i	−1.11378	+	0.643043i
$719$	11.6970	−	20.2597i	0.436223	−	0.755560i	−0.561172	−	0.827699i	$-0.689649\pi$
$719$	11.6970	−	20.2597i	0.436223	−	0.755560i	0.997395	+	0.0721392i	$0.0229826\pi$
$720$	0.230377	−	2.22417i	0.00858564	−	0.0828899i
$721$	−6.69713	−	3.86659i	−0.249414	−	0.143999i
$722$	8.58515	−	14.8699i	0.319506	−	0.553401i
$723$	−29.3660			−1.09213
$724$	−6.88641	+	11.9276i	−0.255931	+	0.443286i
$725$	−10.1204	−	30.8305i	−0.375862	−	1.14502i
$726$	9.49980	−	5.48471i	0.352571	−	0.203557i
$727$			36.0471i			1.33691i	0.743750	+	0.668457i	$0.233045\pi$
$727$			36.0471i			1.33691i	−0.743750	+	0.668457i	$0.766955\pi$
$728$	−1.91799	−	2.46127i	−0.0710853	−	0.0912208i
$729$	−1.00000			−0.0370370
$730$	−26.2737	+	11.7453i	−0.972432	+	0.434714i
$731$	−37.5172	−	64.9817i	−1.38762	−	2.40344i
$732$	6.90559	+	3.98695i	0.255238	+	0.147362i
$733$	−17.0888			−0.631189			−0.315594	−	0.948894i	$-0.602204\pi$
$733$	−17.0888			−0.631189			−0.315594	+	0.948894i	$0.602204\pi$
$734$	−12.6735	−	7.31703i	−0.467787	−	0.270077i
$735$	−8.19884	+	11.3206i	−0.302419	+	0.417567i
$736$			2.91228i			0.107348i
$737$	0.414209	+	0.239143i	0.0152576	+	0.00880896i
$738$	7.08339	−	4.08960i	0.260743	−	0.150540i
$739$	33.4931	−	19.3373i	1.23206	−	0.711333i	0.264604	−	0.964357i	$-0.414759\pi$
$739$	33.4931	−	19.3373i	1.23206	−	0.711333i	0.967460	+	0.253024i	$0.0814253\pi$
$740$	−0.405267	+	3.91264i	−0.0148979	+	0.143831i
$741$	8.14836	−	20.0952i	0.299337	−	0.738217i
$742$			2.15262i			0.0790250i
$743$	0.225532	+	0.390632i	0.00827395	+	0.0143309i	0.870133	−	0.492817i	$-0.164033\pi$
$743$	0.225532	+	0.390632i	0.00827395	+	0.0143309i	−0.861859	+	0.507148i	$0.830700\pi$
$744$	−3.47529	−	6.01937i	−0.127410	−	0.220681i
$745$	13.4907	−	18.6274i	0.494260	−	0.682453i
$746$			22.0739i			0.808184i
$747$	0.0697718	−	0.120848i	0.00255282	−	0.00442161i
$748$	−0.715090	+	1.23857i	−0.0261463	+	0.0452867i
$749$			0.744940i			0.0272195i
$750$	−8.27466	+	7.51864i	−0.302148	+	0.274542i
$751$	−11.1206	−	19.2614i	−0.405795	−	0.702858i	0.588618	−	0.808411i	$-0.299672\pi$
$751$	−11.1206	−	19.2614i	−0.405795	−	0.702858i	−0.994414	+	0.105553i	$0.966339\pi$
$752$	5.95105	+	10.3075i	0.217012	+	0.375876i
$753$		−	17.8942i		−	0.652100i
$754$	−14.3829	−	18.4570i	−0.523796	−	0.672165i
$755$	26.1160	+	2.70507i	0.950459	+	0.0984475i
$756$	0.749482	−	0.432713i	0.0272584	−	0.0157376i
$757$	7.30326	−	4.21654i	0.265442	−	0.153253i	−0.361373	−	0.932421i	$-0.617692\pi$
$757$	7.30326	−	4.21654i	0.265442	−	0.153253i	0.626814	+	0.779169i	$0.284358\pi$
$758$	−12.0573	−	6.96127i	−0.437940	−	0.252845i
$759$		−	0.509229i		−	0.0184838i
$760$	−7.88817	+	10.8917i	−0.286134	+	0.395082i
$761$	18.3585	+	10.5993i	0.665496	+	0.384224i	0.794368	−	0.607437i	$-0.207802\pi$
$761$	18.3585	+	10.5993i	0.665496	+	0.384224i	−0.128872	+	0.991661i	$0.541136\pi$
$762$	−6.94238			−0.251496
$763$	4.08719	+	2.35974i	0.147966	+	0.0854283i
$764$	2.78821	+	4.82932i	0.100874	+	0.174719i
$765$	7.46410	+	16.6968i	0.269865	+	0.603674i
$766$	24.6089			0.889155
$767$	−20.0123	+	15.5949i	−0.722601	+	0.563099i
$768$

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

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.230377 + 2.22417i) q^{5} +(-0.866025 - 0.500000i) q^{6} +(0.432713 - 0.749482i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.230377 + 2.22417i) q^{5} +(-0.866025 - 0.500000i) q^{6} +(0.432713 - 0.749482i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(2.04138 - 0.912572i) q^{10} +(0.151430 - 0.0874279i) q^{11} +1.00000i q^{12} +(1.35486 - 3.34131i) q^{13} -0.865427 q^{14} +(0.912572 + 2.04138i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(7.08339 + 4.08960i) q^{17} -1.00000 q^{18} +(5.20843 + 3.00709i) q^{19} +(-1.81100 - 1.31160i) q^{20} -0.865427i q^{21} +(-0.151430 - 0.0874279i) q^{22} +(2.52211 - 1.45614i) q^{23} +(0.866025 - 0.500000i) q^{24} +(-4.89385 - 1.02479i) q^{25} +(-3.57109 + 0.497314i) q^{26} -1.00000i q^{27} +(0.432713 + 0.749482i) q^{28} +(3.24491 + 5.62035i) q^{29} +(1.31160 - 1.81100i) q^{30} -6.95057i q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.0874279 - 0.151430i) q^{33} -8.17919i q^{34} +(1.56729 + 1.13509i) q^{35} +(0.500000 + 0.866025i) q^{36} +(-0.879573 - 1.52347i) q^{37} -6.01418i q^{38} +(-0.497314 - 3.57109i) q^{39} +(-0.230377 + 2.22417i) q^{40} +(-7.08339 + 4.08960i) q^{41} +(-0.749482 + 0.432713i) q^{42} +(-7.94476 - 4.58691i) q^{43} +0.174856i q^{44} +(1.81100 + 1.31160i) q^{45} +(-2.52211 - 1.45614i) q^{46} -11.9021 q^{47} +(-0.866025 - 0.500000i) q^{48} +(3.12552 + 5.41356i) q^{49} +(1.55943 + 4.75060i) q^{50} +8.17919 q^{51} +(2.21623 + 2.84400i) q^{52} -2.48735i q^{53} +(-0.866025 + 0.500000i) q^{54} +(0.159569 + 0.356946i) q^{55} +(0.432713 - 0.749482i) q^{56} +6.01418 q^{57} +(3.24491 - 5.62035i) q^{58} +(-6.09393 - 3.51833i) q^{59} +(-2.22417 - 0.230377i) q^{60} +(3.98695 - 6.90559i) q^{61} +(-6.01937 + 3.47529i) q^{62} +(-0.432713 - 0.749482i) q^{63} +1.00000 q^{64} +(7.11951 + 3.78319i) q^{65} -0.174856 q^{66} +(1.36766 + 2.36886i) q^{67} +(-7.08339 + 4.08960i) q^{68} +(1.45614 - 2.52211i) q^{69} +(0.199374 - 1.92486i) q^{70} +(12.2677 + 7.08275i) q^{71} +(0.500000 - 0.866025i) q^{72} -12.8706 q^{73} +(-0.879573 + 1.52347i) q^{74} +(-4.75060 + 1.55943i) q^{75} +(-5.20843 + 3.00709i) q^{76} -0.151325i q^{77} +(-2.84400 + 2.21623i) q^{78} +9.48961 q^{79} +(2.04138 - 0.912572i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(7.08339 + 4.08960i) q^{82} +0.139544 q^{83} +(0.749482 + 0.432713i) q^{84} +(-10.7278 + 14.8125i) q^{85} +9.17382i q^{86} +(5.62035 + 3.24491i) q^{87} +(0.151430 - 0.0874279i) q^{88} +(-11.3790 + 6.56966i) q^{89} +(0.230377 - 2.22417i) q^{90} +(-1.91799 - 2.46127i) q^{91} +2.91228i q^{92} +(-3.47529 - 6.01937i) q^{93} +(5.95105 + 10.3075i) q^{94} +(-7.88817 + 10.8917i) q^{95} +1.00000i q^{96} +(-4.32411 + 7.48957i) q^{97} +(3.12552 - 5.41356i) q^{98} -0.174856i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{2} - 6 q^{4} - 2 q^{5} - 2 q^{7} + 12 q^{8} + 6 q^{9}+O(q^{10}) \) 12 * q - 6 * q^2 - 6 * q^4 - 2 * q^5 - 2 * q^7 + 12 * q^8 + 6 * q^9	\( 12 q - 6 q^{2} - 6 q^{4} - 2 q^{5} - 2 q^{7} + 12 q^{8} + 6 q^{9} - 2 q^{10} + 6 q^{11} - 8 q^{13} + 4 q^{14} + 6 q^{15} - 6 q^{16} + 18 q^{17} - 12 q^{18} - 6 q^{19} + 4 q^{20} - 6 q^{22} + 6 q^{23} - 10 q^{25} - 2 q^{26} - 2 q^{28} + 14 q^{29} - 6 q^{30} - 6 q^{32} + 6 q^{33} + 26 q^{35} + 6 q^{36} - 12 q^{37} - 2 q^{39} - 2 q^{40} - 18 q^{41} - 12 q^{42} - 36 q^{43} - 4 q^{45} - 6 q^{46} + 16 q^{47} + 8 q^{49} - 10 q^{50} + 16 q^{51} + 10 q^{52} - 28 q^{55} - 2 q^{56} - 8 q^{57} + 14 q^{58} - 36 q^{59} + 10 q^{61} + 6 q^{62} + 2 q^{63} + 12 q^{64} + 6 q^{65} - 12 q^{66} + 4 q^{67} - 18 q^{68} + 16 q^{69} - 4 q^{70} - 12 q^{71} + 6 q^{72} + 28 q^{73} - 12 q^{74} - 8 q^{75} + 6 q^{76} - 2 q^{78} + 4 q^{79} - 2 q^{80} - 6 q^{81} + 18 q^{82} + 72 q^{83} + 12 q^{84} + 18 q^{85} + 6 q^{87} + 6 q^{88} + 18 q^{89} + 2 q^{90} + 2 q^{91} - 16 q^{93} - 8 q^{94} - 42 q^{95} - 48 q^{97} + 8 q^{98}+O(q^{100}) \) 12 * q - 6 * q^2 - 6 * q^4 - 2 * q^5 - 2 * q^7 + 12 * q^8 + 6 * q^9 - 2 * q^10 + 6 * q^11 - 8 * q^13 + 4 * q^14 + 6 * q^15 - 6 * q^16 + 18 * q^17 - 12 * q^18 - 6 * q^19 + 4 * q^20 - 6 * q^22 + 6 * q^23 - 10 * q^25 - 2 * q^26 - 2 * q^28 + 14 * q^29 - 6 * q^30 - 6 * q^32 + 6 * q^33 + 26 * q^35 + 6 * q^36 - 12 * q^37 - 2 * q^39 - 2 * q^40 - 18 * q^41 - 12 * q^42 - 36 * q^43 - 4 * q^45 - 6 * q^46 + 16 * q^47 + 8 * q^49 - 10 * q^50 + 16 * q^51 + 10 * q^52 - 28 * q^55 - 2 * q^56 - 8 * q^57 + 14 * q^58 - 36 * q^59 + 10 * q^61 + 6 * q^62 + 2 * q^63 + 12 * q^64 + 6 * q^65 - 12 * q^66 + 4 * q^67 - 18 * q^68 + 16 * q^69 - 4 * q^70 - 12 * q^71 + 6 * q^72 + 28 * q^73 - 12 * q^74 - 8 * q^75 + 6 * q^76 - 2 * q^78 + 4 * q^79 - 2 * q^80 - 6 * q^81 + 18 * q^82 + 72 * q^83 + 12 * q^84 + 18 * q^85 + 6 * q^87 + 6 * q^88 + 18 * q^89 + 2 * q^90 + 2 * q^91 - 16 * q^93 - 8 * q^94 - 42 * q^95 - 48 * q^97 + 8 * q^98

Introduction

L-functions

Modular forms

Varieties

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