LMFDB - Embedded newform 390.2.x.b.199.2

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			199.2
Root			$-1.44229 - 0.433312i$ of defining polynomial
Character	$\chi$	$=$	390.199
Dual form			390.2.x.b.49.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.230377 - 2.22417i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-0.432713 - 0.749482i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(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} +(-1.81100 - 1.31160i) q^{10} +(0.151430 + 0.0874279i) q^{11} +1.00000i q^{12} +(-1.35486 - 3.34131i) q^{13} -0.865427 q^{14} +(-1.31160 + 1.81100i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-7.08339 + 4.08960i) q^{17} +1.00000 q^{18} +(5.20843 - 3.00709i) q^{19} +(-2.04138 + 0.912572i) 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} +(0.912572 + 2.04138i) q^{30} +6.95057i q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.0874279 - 0.151430i) q^{33} +8.17919i q^{34} +(-1.76666 + 0.789764i) 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} +(2.04138 - 0.912572i) q^{45} +(-2.52211 + 1.45614i) q^{46} +11.9021 q^{47} +(0.866025 - 0.500000i) q^{48} +(3.12552 - 5.41356i) q^{49} +(-3.33442 + 3.72580i) q^{50} +8.17919 q^{51} +(-2.21623 + 2.84400i) q^{52} -2.48735i q^{53} +(-0.866025 - 0.500000i) q^{54} +(0.229340 - 0.316664i) 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} +(-7.74377 + 2.24367i) 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} +(3.72580 + 3.33442i) q^{75} +(-5.20843 - 3.00709i) q^{76} -0.151325i q^{77} +(2.84400 + 2.21623i) q^{78} +9.48961 q^{79} +(1.81100 + 1.31160i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-7.08339 + 4.08960i) q^{82} -0.139544 q^{83} +(0.749482 - 0.432713i) q^{84} +(7.46410 + 16.6968i) 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} +(-5.48837 - 12.2772i) 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} + 4 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} + 2 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} - 22 q^{35} + 6 q^{36} + 12 q^{37} - 2 q^{39} - 2 q^{40} - 18 q^{41} + 12 q^{42} + 36 q^{43} - 2 q^{45} - 6 q^{46} - 16 q^{47} + 8 q^{49} - 20 q^{50} + 16 q^{51} - 10 q^{52} + 8 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} - 44 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} + 16 q^{75} + 6 q^{76} + 2 q^{78} + 4 q^{79} - 4 q^{80} - 6 q^{81} - 18 q^{82} - 72 q^{83} + 12 q^{84} + 48 q^{85} - 6 q^{87} - 6 q^{88} + 18 q^{89} + 2 q^{90} + 2 q^{91} + 16 q^{93} - 8 q^{94} + 18 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 + 4 * 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 + 2 * 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 - 22 * q^35 + 6 * q^36 + 12 * q^37 - 2 * q^39 - 2 * q^40 - 18 * q^41 + 12 * q^42 + 36 * q^43 - 2 * q^45 - 6 * q^46 - 16 * q^47 + 8 * q^49 - 20 * q^50 + 16 * q^51 - 10 * q^52 + 8 * 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 - 44 * 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 + 16 * q^75 + 6 * q^76 + 2 * q^78 + 4 * q^79 - 4 * q^80 - 6 * q^81 - 18 * q^82 - 72 * q^83 + 12 * q^84 + 48 * q^85 - 6 * q^87 - 6 * q^88 + 18 * q^89 + 2 * q^90 + 2 * q^91 + 16 * q^93 - 8 * q^94 + 18 * q^95 + 48 * q^97 - 8 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.500000	−	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	$-0.218961\pi$
$7$	−0.432713	−	0.749482i	−0.163550	−	0.283277i	−0.936140	+	0.351629i	$0.885628\pi$
$8$	−1.00000			−0.353553
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−1.81100	−	1.31160i	−0.572688	−	0.414763i
$11$	0.151430	+	0.0874279i	0.0456577	+	0.0263605i	0.522655	−	0.852544i	$-0.324942\pi$
$11$	0.151430	+	0.0874279i	0.0456577	+	0.0263605i	−0.476997	+	0.878905i	$0.658275\pi$
$12$			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
$15$	−1.31160	+	1.81100i	−0.338653	+	0.467598i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−7.08339	+	4.08960i	−1.71797	+	0.991873i	−0.795370	+	0.606125i	$0.792723\pi$
$17$	−7.08339	+	4.08960i	−1.71797	+	0.991873i	−0.922604	+	0.385748i	$0.873943\pi$
$18$	1.00000			0.235702
$19$	5.20843	−	3.00709i	1.19490	−	0.689873i	0.235483	−	0.971879i	$-0.424333\pi$
$19$	5.20843	−	3.00709i	1.19490	−	0.689873i	0.959413	+	0.282005i	$0.0909996\pi$
$20$	−2.04138	+	0.912572i	−0.456465	+	0.204057i
$21$			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	$-0.431531\pi$
$23$	−2.52211	−	1.45614i	−0.525896	−	0.303626i	−0.739344	+	0.673328i	$0.764864\pi$
$24$	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	−0.389867	−	0.920871i	$-0.627479\pi$
$29$	3.24491	−	5.62035i	0.602564	−	1.04367i	0.992431	−	0.122801i	$-0.0391877\pi$
$30$	0.912572	+	2.04138i	0.166612	+	0.372702i
$31$			6.95057i			1.24836i	0.781281	+	0.624180i	$0.214567\pi$
$31$			6.95057i			1.24836i	−0.781281	+	0.624180i	$0.785433\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−0.0874279	−	0.151430i	−0.0152192	−	0.0263605i
$34$			8.17919i			1.40272i
$35$	−1.76666	+	0.789764i	−0.298620	+	0.133495i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	0.879573	−	1.52347i	0.144601	−	0.250456i	−0.784623	−	0.619973i	$-0.787144\pi$
$37$	0.879573	−	1.52347i	0.144601	−	0.250456i	0.929224	+	0.369517i	$0.120477\pi$
$38$		−	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	−0.168387	−	0.985721i	$-0.553856\pi$
$41$	−7.08339	−	4.08960i	−1.10624	−	0.638688i	−0.937853	+	0.347034i	$0.887189\pi$
$42$	0.749482	+	0.432713i	0.115648	+	0.0667691i
$43$	7.94476	−	4.58691i	1.21156	−	0.699497i	0.248465	−	0.968641i	$-0.420074\pi$
$43$	7.94476	−	4.58691i	1.21156	−	0.699497i	0.963100	+	0.269144i	$0.0867407\pi$
$44$		−	0.174856i		−	0.0263605i
$45$	2.04138	−	0.912572i	0.304310	−	0.136038i
$46$	−2.52211	+	1.45614i	−0.371865	+	0.214696i
$47$	11.9021			1.73610			0.868050	−	0.496478i	$-0.165373\pi$
$47$	11.9021			1.73610			0.868050	+	0.496478i	$0.165373\pi$
$48$	0.866025	−	0.500000i	0.125000	−	0.0721688i
$49$	3.12552	−	5.41356i	0.446503	−	0.773365i
$50$	−3.33442	+	3.72580i	−0.471559	+	0.526908i
$51$	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
$55$	0.229340	−	0.316664i	0.0309242	−	0.0426989i
$56$	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	−0.841145	−	0.540810i	$-0.818118\pi$
$59$	−6.09393	+	3.51833i	−0.793363	+	0.458048i	0.0477824	+	0.998858i	$0.484785\pi$
$60$	2.22417	+	0.230377i	0.287139	+	0.0297415i
$61$	3.98695	+	6.90559i	0.510476	+	0.884171i	0.999926	+	0.0121394i	$0.00386418\pi$
$61$	3.98695	+	6.90559i	0.510476	+	0.884171i	−0.489450	+	0.872031i	$0.662802\pi$
$62$	6.01937	+	3.47529i	0.764461	+	0.441362i
$63$	0.432713	−	0.749482i	0.0545168	−	0.0944258i
$64$	1.00000			0.125000
$65$	−7.74377	+	2.24367i	−0.960496	+	0.278293i
$66$	−0.174856			−0.0215233
$67$	−1.36766	+	2.36886i	−0.167086	+	0.289402i	−0.937394	−	0.348270i	$-0.886769\pi$
$67$	−1.36766	+	2.36886i	−0.167086	+	0.289402i	0.770308	+	0.637672i	$0.220103\pi$
$68$	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	0.457100	−	0.889415i	$-0.348888\pi$
$71$	12.2677	−	7.08275i	1.45591	−	0.840568i	0.998806	+	0.0488476i	$0.0155549\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$	12.8706			1.50639			0.753193	−	0.657800i	$-0.228513\pi$
$73$	12.8706			1.50639			0.753193	+	0.657800i	$0.228513\pi$
$74$	−0.879573	−	1.52347i	−0.102248	−	0.177099i
$75$	3.72580	+	3.33442i	0.430219	+	0.385026i
$76$	−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	$0.320751\pi$
$80$	1.81100	+	1.31160i	0.202476	+	0.146641i
$81$	−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	$-0.502438\pi$
$83$	−0.139544			−0.0153169			−0.00765845	+	0.999971i	$0.502438\pi$
$84$	0.749482	−	0.432713i	0.0817752	−	0.0472129i
$85$	7.46410	+	16.6968i	0.809595	+	1.81102i
$86$		−	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	−0.244249	−	0.969713i	$-0.578541\pi$
$89$	−11.3790	−	6.56966i	−1.20617	−	0.696382i	−0.961920	+	0.273330i	$0.911875\pi$
$90$	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
$95$	−5.48837	−	12.2772i	−0.563095	−	1.25961i
$96$		−	1.00000i		−	0.102062i
$97$	4.32411	+	7.48957i	0.439047	+	0.760451i	0.997616	−	0.0690066i	$-0.0219830\pi$
$97$	4.32411	+	7.48957i	0.439047	+	0.760451i	−0.558570	+	0.829458i	$0.688650\pi$
$98$	−3.12552	−	5.41356i	−0.315725	−	0.546852i
$99$			0.174856i			0.0175737i
$100$	1.55943	+	4.75060i	0.155943	+	0.475060i
$101$	−5.28276	+	9.15001i	−0.525654	+	0.910460i	0.473899	+	0.880579i	$0.342846\pi$
$101$	−5.28276	+	9.15001i	−0.525654	+	0.910460i	−0.999553	+	0.0298810i	$0.990487\pi$
$102$	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	$-0.320086\pi$
$107$	0.745455	+	0.430389i	0.0720658	+	0.0416072i	−0.463534	+	0.886079i	$0.653419\pi$
$108$	−0.866025	+	0.500000i	−0.0833333	+	0.0481125i
$109$		−	5.45336i		−	0.522337i	−0.965293	−	0.261168i	$-0.915892\pi$
$109$		−	5.45336i		−	0.522337i	0.965293	−	0.261168i	$-0.0841078\pi$
$110$	−0.159569	−	0.356946i	−0.0152143	−	0.0340335i
$111$	−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	$-0.479697\pi$
$113$	10.2036	−	5.89106i	0.959876	−	0.554184i	0.896135	+	0.443782i	$0.146364\pi$
$114$	−3.00709	+	5.20843i	−0.281640	+	0.487814i
$115$	−3.81974	+	5.27413i	−0.356192	+	0.491815i
$116$	−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
$120$	1.31160	−	1.81100i	0.119732	−	0.165321i
$121$	−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	$-0.432999\pi$
$127$	−6.01228	−	3.47119i	−0.533503	−	0.308018i	−0.742442	+	0.669911i	$0.766332\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−9.17382			−0.807710
$130$	−1.92881	+	7.82814i	−0.169167	+	0.686573i
$131$	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	$-0.268703\pi$
$137$	−3.68809	−	6.38795i	−0.315094	−	0.545760i	−0.979458	+	0.201650i	$0.935370\pi$
$138$	2.91228			0.247910
$139$	0.410380	+	0.710798i	0.0348079	+	0.0602891i	0.882905	−	0.469552i	$-0.155585\pi$
$139$	0.410380	+	0.710798i	0.0348079	+	0.0602891i	−0.848097	+	0.529842i	$0.822251\pi$
$140$	1.56729	+	1.13509i	0.132460	+	0.0959327i
$141$	−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
$145$	−11.7530	−	8.51202i	−0.976037	−	0.706885i
$146$	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	−0.818329	−	0.574751i	$-0.805099\pi$
$149$	−8.90766	+	5.14284i	−0.729744	+	0.421318i	0.0885845	+	0.996069i	$0.471766\pi$
$150$	4.75060	−	1.55943i	0.387885	−	0.127327i
$151$			11.7419i			0.955544i	0.878484	+	0.477772i	$0.158555\pi$
$151$			11.7419i			0.955544i	−0.878484	+	0.477772i	$0.841445\pi$
$152$	−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
$160$	2.04138	−	0.912572i	0.161385	−	0.0721452i
$161$			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	$-0.148862\pi$
$163$	0.713746	+	1.23624i	0.0559049	+	0.0968301i	−0.836719	+	0.547633i	$0.815529\pi$
$164$			8.17919i			0.638688i
$165$	−0.356946	+	0.159569i	−0.0277882	+	0.0124224i
$166$	−0.0697718	+	0.120848i	−0.00541534	+	0.00937964i
$167$	−2.93528	+	5.08406i	−0.227139	+	0.393416i	−0.956959	−	0.290223i	$-0.906271\pi$
$167$	−2.93528	+	5.08406i	−0.227139	+	0.393416i	0.729820	+	0.683639i	$0.239604\pi$
$168$		−	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	$-0.841070\pi$
$173$	−11.8669	+	6.85138i	−0.902226	+	0.520901i	−0.0243045	+	0.999705i	$0.507737\pi$
$174$			6.48982i			0.491992i
$175$	1.34957	+	4.11130i	0.102018	+	0.310785i
$176$	−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	0.469310	+	0.883033i	$0.344503\pi$
$179$	−7.09191	+	12.2835i	−0.530074	+	0.918115i	−0.999384	+	0.0350821i	$0.988831\pi$
$180$	−1.81100	−	1.31160i	−0.134984	−	0.0977606i
$181$	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
$185$	−3.18581	−	2.30729i	−0.234225	−	0.169635i
$186$	−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	0.949092	−	0.315000i	$-0.102005\pi$
$191$	2.78821	+	4.82932i	0.201748	+	0.349437i	−0.747344	+	0.664437i	$0.768671\pi$
$192$	−0.866025	−	0.500000i	−0.0625000	−	0.0360844i
$193$	0.110405	−	0.191227i	0.00794712	−	0.0137648i	−0.862024	−	0.506867i	$-0.830804\pi$
$193$	0.110405	−	0.191227i	0.00794712	−	0.0137648i	0.869972	+	0.493102i	$0.164137\pi$
$194$	8.64822			0.620906
$195$	7.82814	+	1.92881i	0.560584	+	0.138125i
$196$	−6.25104			−0.446503
$197$	−0.861905	+	1.49286i	−0.0614082	+	0.106362i	−0.895095	−	0.445875i	$-0.852892\pi$
$197$	−0.861905	+	1.49286i	−0.0614082	+	0.106362i	0.833687	+	0.552237i	$0.186226\pi$
$198$	0.151430	+	0.0874279i	0.0107616	+	0.00621323i
$199$	−3.97927	−	6.89229i	−0.282083	−	0.488581i	0.689815	−	0.723986i	$-0.257692\pi$
$199$	−3.97927	−	6.89229i	−0.282083	−	0.488581i	−0.971898	+	0.235404i	$0.924359\pi$
$200$	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
$205$	−10.7278	+	14.8125i	−0.749262	+	1.03455i
$206$	−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
$210$	1.13509	−	1.56729i	0.0783287	−	0.108153i
$211$	2.10991	−	3.65448i	0.145252	−	0.251585i	−0.784215	−	0.620490i	$-0.786934\pi$
$211$	2.10991	−	3.65448i	0.145252	−	0.251585i	0.929467	+	0.368905i	$0.120267\pi$
$212$	−2.15410	+	1.24367i	−0.147945	+	0.0854158i
$213$	−14.1655			−0.970604
$214$	0.745455	−	0.430389i	0.0509582	−	0.0294208i
$215$	−8.37177	−	18.7272i	−0.570950	−	1.27718i
$216$			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	$-0.908121\pi$
$223$	−3.47638	+	6.02126i	−0.232795	+	0.403214i	0.725834	+	0.687870i	$0.241454\pi$
$224$	0.432713	−	0.749482i	0.0289119	−	0.0500769i
$225$	−1.55943	−	4.75060i	−0.103962	−	0.316707i
$226$		−	11.7821i		−	0.783735i
$227$	−1.44823	−	2.50840i	−0.0961221	−	0.166488i	0.813954	−	0.580929i	$-0.197311\pi$
$227$	−1.44823	−	2.50840i	−0.0961221	−	0.166488i	−0.910076	+	0.414441i	$0.863977\pi$
$228$	3.00709	+	5.20843i	0.199149	+	0.344937i
$229$		−	7.88800i		−	0.521254i	−0.965440	−	0.260627i	$-0.916071\pi$
$229$		−	7.88800i		−	0.521254i	0.965440	−	0.260627i	$-0.0839293\pi$
$230$	2.65766	+	5.94505i	0.175241	+	0.392005i
$231$	−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	$0.114771\pi$
$239$			10.9084i			0.705604i	−0.935698	+	0.352802i	$0.885229\pi$
$240$	−0.912572	−	2.04138i	−0.0589063	−	0.131770i
$241$	−25.4317	+	14.6830i	−1.63820	+	0.945816i	−0.656749	+	0.754109i	$0.728069\pi$
$241$	−25.4317	+	14.6830i	−1.63820	+	0.945816i	−0.981452	+	0.191707i	$0.938598\pi$
$242$	−10.9694			−0.705141
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	3.98695	−	6.90559i	0.255238	−	0.442085i
$245$	−11.3206	−	8.19884i	−0.723248	−	0.523805i
$246$	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
$250$	7.51864	+	8.27466i	0.475521	+	0.523336i
$251$	8.94708	+	15.4968i	0.564735	+	0.978150i	0.997074	+	0.0764387i	$0.0243549\pi$
$251$	8.94708	+	15.4968i	0.564735	+	0.978150i	−0.432339	+	0.901711i	$0.642312\pi$
$252$	−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	$-0.209309\pi$
$257$	10.5472	+	6.08945i	0.657918	+	0.379849i	−0.133565	+	0.991040i	$0.542642\pi$
$258$	−4.58691	+	7.94476i	−0.285568	+	0.494619i
$259$	−1.52241			−0.0945981
$260$	5.81496	+	5.58446i	0.360629	+	0.346334i
$261$	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	$-0.107012\pi$
$263$	18.3309	+	10.5834i	1.13033	+	0.652598i	0.186314	+	0.982490i	$0.440346\pi$
$264$	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	0.620838	−	0.783939i	$-0.286792\pi$
$269$	−6.04371	−	10.4680i	−0.368492	−	0.638246i	−0.989330	+	0.145692i	$0.953459\pi$
$270$	−1.31160	+	1.81100i	−0.0798212	+	0.110214i
$271$	−12.7275	−	7.34824i	−0.773142	−	0.446374i	0.0608525	−	0.998147i	$-0.480618\pi$
$271$	−12.7275	−	7.34824i	−0.773142	−	0.446374i	−0.833994	+	0.551773i	$0.813951\pi$
$272$		−	8.17919i		−	0.495936i
$273$	2.89166	−	1.17253i	0.175011	−	0.0709648i
$274$	−7.37617			−0.445611
$275$	−0.651479	−	0.583044i	−0.0392856	−	0.0351588i
$276$	1.45614	−	2.52211i	0.0876493	−	0.151813i
$277$	17.0717	−	9.85638i	1.02574	−	0.592212i	0.109980	−	0.993934i	$-0.464921\pi$
$277$	17.0717	−	9.85638i	1.02574	−	0.592212i	0.915762	+	0.401722i	$0.131588\pi$
$278$	0.820759			0.0492259
$279$	−6.01937	+	3.47529i	−0.360370	+	0.208060i
$280$	1.76666	−	0.789764i	0.105578	−	0.0471975i
$281$		−	9.93073i		−	0.592418i	−0.955123	−	0.296209i	$-0.904278\pi$
$281$		−	9.93073i		−	0.592418i	0.955123	−	0.296209i	$-0.0957225\pi$
$282$	−10.3075	+	5.95105i	−0.613804	+	0.354380i
$283$	−10.0790	−	5.81912i	−0.599135	−	0.345911i	0.169566	−	0.985519i	$-0.445763\pi$
$283$	−10.0790	−	5.81912i	−0.599135	−	0.345911i	−0.768701	+	0.639608i	$0.779097\pi$
$284$	−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
$290$	−13.2482	+	5.92243i	−0.777958	+	0.347777i
$291$		−	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	$-0.292188\pi$
$293$	−6.57636	−	11.3906i	−0.384195	−	0.665445i	−0.991657	+	0.128903i	$0.958854\pi$
$294$			6.25104i			0.364568i
$295$	6.42147	+	14.3645i	0.373872	+	0.836332i
$296$	−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
$305$	16.2777	−	7.27675i	0.932059	−	0.416666i
$306$	−7.08339	+	4.08960i	−0.404930	+	0.233787i
$307$	14.8609			0.848155			0.424077	−	0.905626i	$-0.360598\pi$
$307$	14.8609			0.848155			0.424077	+	0.905626i	$0.360598\pi$
$308$	−0.131051	+	0.0756625i	−0.00746734	+	0.00431127i
$309$	−4.46784	+	7.73853i	−0.254167	+	0.440230i
$310$	9.11635	−	12.5875i	0.517774	−	0.714920i
$311$	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
$315$	−1.56729	−	1.13509i	−0.0883066	−	0.0639551i
$316$	−4.74480	−	8.21824i	−0.266916	−	0.462312i
$317$	25.7510			1.44632			0.723161	−	0.690679i	$-0.242688\pi$
$317$	25.7510			1.44632			0.723161	+	0.690679i	$0.242688\pi$
$318$	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
$325$	3.20632	+	17.7403i	0.177855	+	0.984057i
$326$	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	−0.337139	−	0.941455i	$-0.609459\pi$
$331$	5.63295	−	3.25219i	0.309615	−	0.178756i	0.646754	+	0.762699i	$0.276126\pi$
$332$	0.0697718	+	0.120848i	0.00382922	+	0.00663241i
$333$	1.75915			0.0964006
$334$	2.93528	+	5.08406i	0.160612	+	0.278187i
$335$	4.95366	+	3.58764i	0.270647	+	0.196014i
$336$	−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
$340$	10.7278	−	14.8125i	0.581797	−	0.803321i
$341$	−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
$345$	5.94505	−	2.65766i	0.320071	−	0.143084i
$346$			13.7028i			0.736665i
$347$	24.6009	−	14.2033i	1.32064	−	0.762474i	0.336813	−	0.941572i	$-0.390651\pi$
$347$	24.6009	−	14.2033i	1.32064	−	0.762474i	0.983831	+	0.179098i	$0.0573178\pi$
$348$	5.62035	+	3.24491i	0.301282	+	0.173945i
$349$	1.93797	+	1.11889i	0.103737	+	0.0598926i	0.550971	−	0.834524i	$-0.314258\pi$
$349$	1.93797	+	1.11889i	0.103737	+	0.0598926i	−0.447234	+	0.894417i	$0.647591\pi$
$350$	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	$-0.847116\pi$
$353$	−0.813287	+	1.40866i	−0.0432869	+	0.0749751i	0.843570	+	0.537019i	$0.180450\pi$
$354$	3.51833	−	6.09393i	0.186997	−	0.323889i
$355$	−12.9270	−	28.9171i	−0.686096	−	1.53476i
$356$			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	$0.363459\pi$
$359$			34.4613i			1.81880i	−0.415923	+	0.909400i	$0.636541\pi$
$360$	−2.04138	+	0.912572i	−0.107590	+	0.0480968i
$361$	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	$-0.458079\pi$
$367$	−12.6735	−	7.31703i	−0.661550	−	0.381946i	−0.792867	+	0.609394i	$0.791413\pi$
$368$	2.52211	−	1.45614i	0.131474	−	0.0759065i
$369$		−	8.17919i		−	0.425792i
$370$	−3.59108	+	1.60535i	−0.186691	+	0.0834580i
$371$	−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	$-0.473039\pi$
$373$	19.1166	−	11.0370i	0.989819	−	0.571472i	0.905220	+	0.424943i	$0.139706\pi$
$374$	−0.715090	+	1.23857i	−0.0369764	+	0.0640450i
$375$	8.27466	−	7.51864i	0.427302	−	0.388261i
$376$	−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	0.776612	−	0.629979i	$-0.216936\pi$
$379$	12.0573	+	6.96127i	0.619341	+	0.357577i	−0.157272	+	0.987555i	$0.550270\pi$
$380$	−7.88817	+	10.8917i	−0.404655	+	0.558730i
$381$	3.47119	+	6.01228i	0.177834	+	0.308018i
$382$	5.57642			0.285314
$383$	12.3044	+	21.3119i	0.628728	+	1.08899i	0.987807	+	0.155681i	$0.0497573\pi$
$383$	12.3044	+	21.3119i	0.628728	+	1.08899i	−0.359080	+	0.933307i	$0.616909\pi$
$384$	−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	$0.454578\pi$
$390$	5.58446	−	5.81496i	0.282780	−	0.294452i
$391$	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	$-0.147734\pi$
$397$	1.18438	+	2.05141i	0.0594424	+	0.102957i	−0.834773	+	0.550595i	$0.814401\pi$
$398$	−7.95853			−0.398925
$399$	2.60241	+	4.50751i	0.130284	+	0.225658i
$400$	3.33442	−	3.72580i	0.166721	−	0.186290i
$401$	14.2942	+	8.25276i	0.713818	+	0.412123i	0.812473	−	0.582998i	$-0.198121\pi$
$401$	14.2942	+	8.25276i	0.713818	+	0.412123i	−0.0986548	+	0.995122i	$0.531454\pi$
$402$		−	2.73532i		−	0.136425i
$403$	23.2240	−	9.41704i	1.15687	−	0.469096i
$404$	10.5655			0.525654
$405$	1.81100	+	1.31160i	0.0899892	+	0.0651738i
$406$	−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	0.429457	−	0.903087i	$-0.358705\pi$
$409$	28.8448	−	16.6535i	1.42628	−	0.823464i	0.996825	+	0.0796230i	$0.0253717\pi$
$410$	7.46410	+	16.6968i	0.368626	+	0.824596i
$411$			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	−0.213708	−	0.976898i	$-0.568554\pi$
$419$	15.1303	−	26.2065i	0.739164	−	1.28027i	0.952872	−	0.303372i	$-0.0981126\pi$
$420$	−0.789764	−	1.76666i	−0.0385366	−	0.0862042i
$421$			40.2235i			1.96038i	0.198070	+	0.980188i	$0.436533\pi$
$421$			40.2235i			1.96038i	−0.198070	+	0.980188i	$0.563467\pi$
$422$	−2.10991	−	3.65448i	−0.102709	−	0.177897i
$423$	5.95105	+	10.3075i	0.289350	+	0.501169i
$424$			2.48735i			0.120796i
$425$	38.8561	−	12.7549i	1.88480	−	0.618702i
$426$	−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	−0.368860	−	0.929485i	$-0.620252\pi$
$431$	−28.1980	−	16.2801i	−1.35825	−	0.784185i	−0.989388	+	0.145300i	$0.953585\pi$
$432$	0.866025	+	0.500000i	0.0416667	+	0.0240563i
$433$	−26.6153	+	15.3663i	−1.27905	+	0.738460i	−0.976674	−	0.214729i	$-0.931113\pi$
$433$	−26.6153	+	15.3663i	−1.27905	+	0.738460i	−0.302376	+	0.953189i	$0.597780\pi$
$434$		−	6.01521i		−	0.288739i
$435$	5.92243	+	13.2482i	0.283959	+	0.635200i
$436$	−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	−0.777555	−	0.628815i	$-0.783540\pi$
$439$	3.26422	−	5.65380i	0.155793	−	0.269841i	0.933347	+	0.358974i	$0.116873\pi$
$440$	−0.229340	+	0.316664i	−0.0109334	+	0.0150963i
$441$	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
$445$	−17.2335	+	23.7953i	−0.816945	+	1.12800i
$446$	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	−0.137579	−	0.990491i	$-0.543932\pi$
$449$	13.8034	−	7.96938i	0.651421	−	0.376098i	0.789001	+	0.614392i	$0.210599\pi$
$450$	−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
$455$	5.03242	+	4.83294i	0.235924	+	0.226572i
$456$	6.01418			0.281640
$457$	−9.90436	+	17.1548i	−0.463306	+	0.802470i	−0.999123	−	0.0418642i	$-0.986670\pi$
$457$	−9.90436	+	17.1548i	−0.463306	+	0.802470i	0.535817	+	0.844334i	$0.320004\pi$
$458$	−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	−0.744995	−	0.667070i	$-0.767548\pi$
$461$	−11.5898	+	6.69139i	−0.539792	+	0.311649i	0.205202	+	0.978720i	$0.434215\pi$
$462$	0.0756625	+	0.131051i	0.00352014	+	0.00609706i
$463$	−42.3599			−1.96863			−0.984316	−	0.176412i	$-0.943551\pi$
$463$	−42.3599			−1.96863			−0.984316	+	0.176412i	$0.943551\pi$
$464$	3.24491	+	5.62035i	0.150641	+	0.260918i
$465$	−12.5875	−	9.11635i	−0.583730	−	0.422760i
$466$	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
$470$	−21.5547	−	15.6107i	−0.994243	−	0.720070i
$471$	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
$475$	−28.5709	+	9.37868i	−1.31092	+	0.430323i
$476$		−	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	−0.0117600	−	0.999931i	$-0.503743\pi$
$479$	−19.3387	−	11.1652i	−0.883606	−	0.510150i	−0.871846	+	0.489781i	$0.837077\pi$
$480$	−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
$485$	17.6543	−	7.89212i	0.801638	−	0.358363i
$486$		−	1.00000i		−	0.0453609i
$487$	14.3750	+	24.8982i	0.651392	+	1.12824i	0.982785	+	0.184751i	$0.0591479\pi$
$487$	14.3750	+	24.8982i	0.651392	+	1.12824i	−0.331393	+	0.943493i	$0.607519\pi$
$488$	−3.98695	−	6.90559i	−0.180481	−	0.312602i
$489$		−	1.42749i		−	0.0645534i
$490$	−12.7607	+	5.70452i	−0.576470	+	0.257704i
$491$	8.02546	−	13.9005i	0.362184	−	0.627321i	−0.626136	−	0.779714i	$-0.715364\pi$
$491$	8.02546	−	13.9005i	0.362184	−	0.627321i	0.988320	+	0.152393i	$0.0486978\pi$
$492$	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	$0.267196\pi$
$499$			33.2509i			1.48851i	−0.667894	+	0.744256i	$0.732804\pi$
$500$	10.9254	−	2.37400i	0.488598	−	0.106169i
$501$	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	$-0.477270\pi$
$503$	21.7736	−	12.5710i	0.970838	−	0.560514i	0.899492	+	0.436938i	$0.143937\pi$
$504$	−0.432713	+	0.749482i	−0.0192746	+	0.0333846i
$505$	19.1341	+	13.8577i	0.851458	+	0.616660i
$506$	−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	0.912412	−	0.409272i	$-0.134217\pi$
$509$	22.8809	+	13.2103i	1.01418	+	0.585536i	0.101766	+	0.994808i	$0.467551\pi$
$510$	−14.8125	−	10.7278i	−0.655909	−	0.475035i
$511$	−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
$520$	7.74377	−	2.24367i	0.339587	−	0.0983916i
$521$	−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	$-0.552633\pi$
$523$	−25.1815	−	14.5385i	−1.10111	−	0.635726i	−0.936512	+	0.350635i	$0.885966\pi$
$524$	−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
$530$	−3.26239	+	4.50458i	−0.141709	+	0.195666i
$531$	−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
$535$	1.12899	−	1.55887i	0.0488106	−	0.0673956i
$536$	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
$540$	0.912572	+	2.04138i	0.0392708	+	0.0878468i
$541$		−	8.17282i		−	0.351377i	−0.984446	−	0.175688i	$-0.943785\pi$
$541$		−	8.17282i		−	0.351377i	0.984446	−	0.175688i	$-0.0562151\pi$
$542$	−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
$550$	−0.830670	+	0.272675i	−0.0354199	+	0.0116269i
$551$		−	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
$555$	1.60535	+	3.59108i	0.0681432	+	0.152433i
$556$	0.410380	−	0.710798i	0.0174040	−	0.0301446i
$557$	0.458421	−	0.794008i	0.0194239	−	0.0336432i	−0.856150	−	0.516727i	$-0.827150\pi$
$557$	0.458421	−	0.794008i	0.0194239	−	0.0336432i	0.875574	+	0.483084i	$0.160483\pi$
$558$			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	$-0.580713\pi$
$563$	10.9632	−	6.32961i	0.462044	−	0.266761i	0.712903	+	0.701262i	$0.247380\pi$
$564$			11.9021i			0.501169i
$565$	−10.7520	−	24.0517i	−0.452342	−	1.01186i
$566$	−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	−0.486077	−	0.873916i	$-0.661573\pi$
$569$	12.2559	−	21.2279i	0.513795	−	0.889918i	0.999872	−	0.0160026i	$-0.00509402\pi$
$570$	10.8917	+	7.88817i	0.456201	+	0.330399i
$571$	−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
$575$	10.8506	+	9.71078i	0.452501	+	0.404967i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	−23.8325			−0.992161			−0.496081	−	0.868276i	$-0.665228\pi$
$577$	−23.8325			−0.992161			−0.496081	+	0.868276i	$0.665228\pi$
$578$	−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
$585$	−5.81496	−	5.58446i	−0.240419	−	0.230889i
$586$	−13.1527			−0.543334
$587$	−18.6811	+	32.3566i	−0.771051	+	1.33550i	0.165937	+	0.986136i	$0.446935\pi$
$587$	−18.6811	+	32.3566i	−0.771051	+	1.33550i	−0.936988	+	0.349362i	$0.886398\pi$
$588$	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	$-0.542354\pi$
$593$	−6.46136			−0.265336			−0.132668	+	0.991161i	$0.542354\pi$
$594$	−0.0874279	−	0.151430i	−0.00358721	−	0.00621323i
$595$	9.28413	−	12.8191i	0.380612	−	0.525533i
$596$	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	$0.788187\pi$
$600$	−3.72580	−	3.33442i	−0.152105	−	0.136127i
$601$	−0.371169	+	0.642883i	−0.0151403	+	0.0262237i	−0.873496	−	0.486831i	$-0.838153\pi$
$601$	−0.371169	+	0.642883i	−0.0151403	+	0.0262237i	0.858356	+	0.513055i	$0.171486\pi$
$602$	−6.87561	+	3.96963i	−0.280229	+	0.161790i
$603$	−2.73532			−0.111391
$604$	10.1688	−	5.87096i	0.413763	−	0.238886i
$605$	−22.3927	+	10.0104i	−0.910393	+	0.406980i
$606$		−	10.5655i		−	0.429195i
$607$	−25.5500	+	14.7513i	−1.03704	+	0.598736i	−0.918994	−	0.394272i	$-0.870997\pi$
$607$	−25.5500	+	14.7513i	−1.03704	+	0.598736i	−0.118047	+	0.993008i	$0.537663\pi$
$608$	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	$-0.743873\pi$
$613$	6.86720	−	11.8943i	0.277364	−	0.480408i	0.970729	+	0.240178i	$0.0772059\pi$
$614$	7.43044	−	12.8699i	0.299868	−	0.519387i
$615$	16.6968	−	7.46410i	0.673280	−	0.300982i
$616$			0.151325i			0.00609706i
$617$	−21.4394	−	37.1342i	−0.863119	−	1.49497i	−0.868902	−	0.494983i	$-0.835174\pi$
$617$	−21.4394	−	37.1342i	−0.863119	−	1.49497i	0.00578297	−	0.999983i	$-0.498159\pi$
$618$	4.46784	+	7.73853i	0.179723	+	0.311289i
$619$			30.0054i			1.20602i	0.797734	+	0.603010i	$0.206032\pi$
$619$			30.0054i			1.20602i	−0.797734	+	0.603010i	$0.793968\pi$
$620$	−6.34290	−	14.1887i	−0.254737	−	0.569833i
$621$	−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
$630$	−1.76666	+	0.789764i	−0.0703855	+	0.0314650i
$631$	7.73137	−	4.46371i	0.307781	−	0.177697i	−0.338152	−	0.941091i	$-0.609802\pi$
$631$	7.73137	−	4.46371i	0.307781	−	0.177697i	0.645933	+	0.763394i	$0.276468\pi$
$632$	−9.48961			−0.377476
$633$	−3.65448	+	2.10991i	−0.145252	+	0.0838616i
$634$	12.8755	−	22.3011i	0.511352	−	0.885688i
$635$	−9.10560	+	12.5726i	−0.361345	+	0.498930i
$636$	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
$640$	−1.81100	−	1.31160i	−0.0715860	−	0.0518454i
$641$	−11.9079	−	20.6250i	−0.470332	−	0.814639i	0.529092	−	0.848564i	$-0.322532\pi$
$641$	−11.9079	−	20.6250i	−0.470332	−	0.814639i	−0.999424	+	0.0339254i	$0.989199\pi$
$642$	−0.860777			−0.0339722
$643$	4.79374	+	8.30300i	0.189047	+	0.327439i	0.944933	−	0.327265i	$-0.106127\pi$
$643$	4.79374	+	8.30300i	0.189047	+	0.327439i	−0.755886	+	0.654703i	$0.772794\pi$
$644$	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	0.998714	+	0.0506940i	$0.0161433\pi$
$647$	39.2219	+	22.6448i	1.54197	+	0.890259i	0.543259	+	0.839565i	$0.317190\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	−1.23040			−0.0482975
$650$	16.9667	+	6.09341i	0.665490	+	0.239003i
$651$	−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	$-0.391257\pi$
$653$	−8.00988	−	4.62451i	−0.313451	−	0.180971i	−0.648470	+	0.761241i	$0.724591\pi$
$654$	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	0.565874	−	0.824491i	$-0.308539\pi$
$659$	−11.0666	−	19.1679i	−0.431093	−	0.746676i	−0.996968	+	0.0778159i	$0.975205\pi$
$660$	0.316664	+	0.229340i	0.0123261	+	0.00892706i
$661$	8.75083	+	5.05229i	0.340368	+	0.196511i	0.660435	−	0.750884i	$-0.270372\pi$
$661$	8.75083	+	5.05229i	0.340368	+	0.196511i	−0.320067	+	0.947395i	$0.603705\pi$
$662$		−	6.50437i		−	0.252800i
$663$	−11.0816	−	27.3292i	−0.430375	−	1.06138i
$664$	0.139544			0.00541534
$665$	−6.82664	+	9.42594i	−0.264726	+	0.365522i
$666$	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
$670$	5.58382	−	2.49618i	0.215722	−	0.0964358i
$671$			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	$-0.416885\pi$
$673$	−11.6594	−	6.73157i	−0.449437	−	0.259483i	−0.707593	+	0.706621i	$0.750219\pi$
$674$	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
$680$	−7.46410	−	16.6968i	−0.286235	−	0.640293i
$681$			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	$-0.281337\pi$
$683$	−9.21246	−	15.9565i	−0.352505	−	0.610557i	−0.986688	+	0.162627i	$0.948003\pi$
$684$		−	6.01418i		−	0.229958i
$685$	−15.0575	+	6.73129i	−0.575319	+	0.257189i
$686$	−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	0.0550042	−	0.998486i	$-0.482483\pi$
$691$	−20.5618	−	11.8714i	−0.782208	−	0.451608i	−0.837212	+	0.546878i	$0.815816\pi$
$692$	11.8669	+	6.85138i	0.451113	+	0.260450i
$693$	0.131051	−	0.0756625i	0.00497823	−	0.00287418i
$694$		−	28.4066i		−	1.07830i
$695$	1.67548	−	0.749002i	0.0635545	−	0.0284113i
$696$	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
$700$	2.88570	−	3.22441i	0.109069	−	0.121871i
$701$	−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
$705$	−15.6107	+	21.5547i	−0.587935	+	0.811796i
$706$	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	0.116521	−	0.993188i	$-0.462826\pi$
$709$	27.5565	−	15.9098i	1.03491	−	0.597504i	0.918387	+	0.395684i	$0.129493\pi$
$710$	−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
$715$	−1.36880	−	0.337263i	−0.0511900	−	0.0126129i
$716$	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	0.997395	−	0.0721392i	$-0.0229826\pi$
$719$	11.6970	+	20.2597i	0.436223	+	0.755560i	−0.561172	+	0.827699i	$0.689649\pi$
$720$	−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
$725$	−21.6398	+	24.1798i	−0.803682	+	0.898015i
$726$	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
$730$	−23.3086	−	16.8810i	−0.862689	−	0.624794i
$731$	−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	$-0.397796\pi$
$733$	17.0888			0.631189			0.315594	+	0.948894i	$0.397796\pi$
$734$	−12.6735	+	7.31703i	−0.467787	+	0.270077i
$735$	5.70452	+	12.7607i	0.210414	+	0.470686i
$736$		−	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	0.967460	−	0.253024i	$-0.0814253\pi$
$739$	33.4931	+	19.3373i	1.23206	+	0.711333i	0.264604	+	0.964357i	$0.414759\pi$
$740$	−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	$-0.835967\pi$
$743$	−0.225532	+	0.390632i	−0.00827395	+	0.0143309i	0.861859	+	0.507148i	$0.169300\pi$
$744$	−3.47529	+	6.01937i	−0.127410	+	0.220681i
$745$	9.38643	+	20.9969i	0.343892	+	0.769268i
$746$		−	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
$750$	−2.37400	−	10.9254i	−0.0866864	−	0.398939i
$751$	−11.1206	+	19.2614i	−0.405795	+	0.702858i	−0.994414	−	0.105553i	$-0.966339\pi$
$751$	−11.1206	+	19.2614i	−0.405795	+	0.702858i	0.588618	+	0.808411i	$0.299672\pi$
$752$	−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	$-0.382308\pi$
$757$	−7.30326	−	4.21654i	−0.265442	−	0.153253i	−0.626814	+	0.779169i	$0.715642\pi$
$758$	12.0573	−	6.96127i	0.437940	−	0.252845i
$759$			0.509229i			0.0184838i
$760$	5.48837	+	12.2772i	0.199084	+	0.445340i
$761$	18.3585	−	10.5993i	0.665496	−	0.384224i	−0.128872	−	0.991661i	$-0.541136\pi$
$761$	18.3585	−	10.5993i	0.665496	−	0.384224i	0.794368	+	0.607437i	$0.207802\pi$
$762$	6.94238			0.251496
$763$	−4.08719	+	2.35974i	−0.147966	+	0.0854283i
$764$	2.78821	−	4.82932i	0.100874	−	0.174719i
$765$	−10.7278	+	14.8125i	−0.387864	+	0.535547i
$766$	24.6089			0.889155
$767$	20.0123	+	15.5949i	0.722601	+	0.563099i
$768$			1.00000i			0.0360844i
$769$	3.34820	+	1.93308i	0.120739	+	0.0697088i	0.559153	−	0.829064i	$-0.311126\pi$
$769$	3.34820	+	1.93308i	0.120739	+	0.0697088i	−0.438414	+	0.898773i	$0.644460\pi$
$770$	−0.198477	+	0.274049i	−0.00715262	+	0.00987605i
$771$	−6.08945	−	10.5472i	−0.219306	−	0.379849i
$772$	−0.220810			−0.00794712
$773$	16.6218	+	28.7898i	0.597845	+	1.03550i	0.993139	+	0.116944i	$0.0373097\pi$
$773$	16.6218	+	28.7898i	0.597845	+	1.03550i	−0.395293	+	0.918555i	$0.629357\pi$
$774$	7.94476	−	4.58691i	0.285568	−	0.164873i
$775$	7.12291	−	34.0151i	0.255862	−	1.22186i
$776$	−4.32411	−	7.48957i	−0.155226	−	0.268860i
$777$	1.31845	+	0.761206i	0.0472990	+	0.0273081i
$778$	2.80490	−	4.85823i	0.100561	−	0.174176i
$779$	−49.1911			−1.76245
$780$	−2.24367	−	7.74377i	−0.0803364	−	0.277271i
$781$	2.47692			0.0886312
$782$	11.9100	−	20.6288i	0.425902	−	0.737684i
$783$	−5.62035	−	3.24491i	−0.200855	−	0.115964i
$784$	3.12552	+	5.41356i	0.111626	+	0.193341i
$785$	15.0361	+	1.55743i	0.536663	+	0.0555870i
$786$	−1.96703	+	1.13567i	−0.0701616	+	0.0405078i
$787$	−15.9873	−	27.6908i	−0.569886	−	0.987071i	−0.996577	−	0.0826737i	$-0.973654\pi$
$787$	−15.9873	−	27.6908i	−0.569886	−	0.987071i	0.426691	−	0.904398i	$-0.359679\pi$
$788$	1.72381			0.0614082
$789$	−10.5834	−	18.3309i	−0.376778	−	0.652598i
$790$	−17.1857	−	12.4465i	−0.611438	−	0.442828i
$791$	−8.83049	−	5.09828i	−0.313976	−	0.181274i
$792$		−	0.174856i		−	0.00621323i
$793$	17.6720	−	22.6777i	0.627551	−	0.805310i
$794$	2.36876			0.0840643
$795$	4.50458	+	3.26239i	0.159761	+	0.115705i
$796$	−3.97927	+	6.89229i	−0.141041	+	0.244291i
$797$	−31.2464	+	18.0401i	−1.10680	+	0.639014i	−0.938000	−	0.346635i	$-0.887324\pi$
$797$	−31.2464	+	18.0401i	−1.10680	+	0.639014i	−0.168805	+	0.985649i	$0.553991\pi$
$798$	5.20483			0.184249
$799$	−84.3072	+	48.6748i	−2.98257	+	1.72199i
$800$	−1.55943	−	4.75060i	−0.0551341	−	0.167959i
$801$		−	13.1393i		−	0.464255i
$802$	14.2942	−	8.25276i	0.504746	−	0.291415i
$803$	1.94898	+	1.12525i	0.0687782	+	0.0397091i
$804$	−2.36886	−	1.36766i	−0.0835432	−	0.0482337i
$805$	5.60572	+	0.580634i	0.197576	+	0.0204647i
$806$	3.45661	−	24.8211i	0.121754	−	0.874286i
$807$			12.0874i			0.425498i
$808$	5.28276	−	9.15001i	0.185847	−	0.321896i
$809$	12.4162	−	21.5054i	0.436529	−	0.756090i	−0.560890	−	0.827890i	$-0.689541\pi$
$809$	12.4162	−	21.5054i	0.436529	−	0.756090i	0.997419	+	0.0718003i	$0.0228744\pi$
$810$	2.04138	−	0.912572i	0.0717266	−	0.0320645i
$811$		−	21.3899i		−	0.751102i	−0.926802	−	0.375551i	$-0.877453\pi$
$811$		−	21.3899i		−	0.751102i	0.926802	−	0.375551i	$-0.122547\pi$
$812$	2.80823	+	4.86400i	0.0985496	+	0.170693i
$813$	7.34824	+	12.7275i	0.257714	+	0.446374i
$814$		−	0.307597i		−	0.0107813i
$815$	2.91405	−	1.30269i	0.102075	−	0.0456312i
$816$	−4.08960	+	7.08339i	−0.143164	+	0.247968i
$817$	27.5865	−	47.7812i	0.965129	−	1.67165i
$818$		−	33.3071i		−	1.16455i
$819$	−3.09052	−	0.430389i	−0.107991	−	0.0150390i
$820$	18.1919	+	1.88430i	0.635289	+	0.0658025i
$821$	28.4938	+	16.4509i	0.994441	+	0.574141i	0.906599	−	0.421994i	$-0.138670\pi$
$821$	28.4938	+	16.4509i	0.994441	+	0.574141i	0.0878420	+	0.996134i	$0.472003\pi$
$822$	6.38795	+	3.68809i	0.222805	+	0.128637i
$823$	27.5779	−	15.9221i	0.961306	−	0.555010i	0.0647309	−	0.997903i	$-0.479381\pi$
$823$	27.5779	−	15.9221i	0.961306	−	0.555010i	0.896575	+	0.442893i	$0.146048\pi$
$824$			8.93568i			0.311289i
$825$	0.272675	+	0.830670i	0.00949333	+	0.0289202i
$826$	5.27385	−	3.04486i	0.183501	−	0.105944i
$827$	1.91814			0.0667004			0.0333502	−	0.999444i	$-0.489382\pi$
$827$	1.91814			0.0667004			0.0333502	+	0.999444i	$0.489382\pi$
$828$	−2.52211	+	1.45614i	−0.0876493	+	0.0506044i
$829$	−13.2223	+	22.9016i	−0.459228	+	0.795407i	−0.998920	−	0.0464558i	$-0.985207\pi$
$829$	−13.2223	+	22.9016i	−0.459228	+	0.795407i	0.539692	+	0.841863i	$0.318541\pi$
$830$	0.252713	+	0.183025i	0.00877180	+	0.00635288i
$831$	−19.7128			−0.683828
$832$	−1.35486	−	3.34131i	−0.0469713	−	0.115839i
$833$			51.1284i			1.77149i
$834$	−0.710798	−	0.410380i	−0.0246129	−	0.0142103i
$835$	10.6316	+	7.69982i	0.367921	+	0.266463i
$836$	−0.525807	−	0.910724i	−0.0181854	−	0.0314981i
$837$	6.95057			0.240247
$838$	−15.1303	−	26.2065i	−0.522668	−	0.905288i
$839$	25.9126	−	14.9607i	0.894604	−	0.516500i	0.0191582	−	0.999816i	$-0.493901\pi$
$839$	25.9126	−	14.9607i	0.894604	−	0.516500i	0.875446	+	0.483317i	$0.160568\pi$
$840$	−1.92486	−	0.199374i	−0.0664138	−	0.00687907i
$841$	−6.55886	−	11.3603i	−0.226168	−	0.391734i
$842$	34.8346	+	20.1118i	1.20048	+	0.693098i
$843$	−4.96537	+	8.60027i	−0.171016	+	0.296209i
$844$	−4.21983			−0.145252
$845$	17.9885	+	22.8345i	0.618824	+	0.785530i
$846$	11.9021			0.409202
$847$	−4.74662	+	8.22138i	−0.163096	+	0.282490i
$848$	2.15410	+	1.24367i	0.0739723	+	0.0427079i
$849$	5.81912	+	10.0790i	0.199712	+	0.345911i
$850$	8.38199	−	40.0278i	0.287500	−	1.37294i
$851$	−4.43676	+	2.56156i	−0.152090	+	0.0878092i
$852$	7.08275	+	12.2677i	0.242651	+	0.420284i
$853$	−9.19805			−0.314935			−0.157468	−	0.987524i	$-0.550333\pi$
$853$	−9.19805			−0.314935			−0.157468	+	0.987524i	$0.550333\pi$
$854$	−3.45041	−	5.97629i	−0.118071	−	0.204504i
$855$	7.88817	−	10.8917i	0.269770	−	0.372487i
$856$	−0.745455	−	0.430389i	−0.0254791	−	0.0147104i
$857$			13.1946i			0.450720i	0.974276	+	0.225360i	$0.0723559\pi$
$857$			13.1946i			0.450720i	−0.974276	+	0.225360i	$0.927644\pi$
$858$	0.236905	+	0.584248i	0.00808780	+	0.0199459i
$859$	−52.7575			−1.80006			−0.900032	−	0.435824i	$-0.856457\pi$
$859$	−52.7575			−1.80006			−0.900032	+	0.435824i	$0.856457\pi$
$860$	−12.0323	+	16.6138i	−0.410300	+	0.566525i
$861$	3.53925	−	6.13015i	0.120617	−	0.208915i
$862$	−28.1980	+	16.2801i	−0.960426	+	0.554502i
$863$	18.6411			0.634551			0.317276	−	0.948333i	$-0.397232\pi$
$863$	18.6411			0.634551			0.317276	+	0.948333i	$0.397232\pi$
$864$	0.866025	−	0.500000i	0.0294628	−	0.0170103i
$865$	12.5048	+	27.9725i	0.425174	+	0.951092i
$866$			30.7327i			1.04434i
$867$	−43.2139	+	24.9496i	−1.46762	+	0.847332i
$868$	−5.20933	−	3.00761i	−0.176816	−	0.102085i
$869$	1.43701	+	0.829657i	0.0487471	+	0.0281442i
$870$	14.4344	+	1.49510i	0.489374	+	0.0506888i
$871$	9.76808	+	1.36031i	0.330979	+	0.0460924i
$872$			5.45336i			0.184674i
$873$	−4.32411	+	7.48957i	−0.146349	+	0.253484i
$874$	−8.75748	+	15.1684i	−0.296226	+	0.513079i
$875$	9.45512	−	2.05453i	0.319642	−	0.0694557i
$876$			12.8706i			0.434856i
$877$	22.7268	+	39.3640i	0.767429	+	1.32923i	0.938953	+	0.344047i	$0.111798\pi$
$877$	22.7268	+	39.3640i	0.767429	+	1.32923i	−0.171523	+	0.985180i	$0.554869\pi$
$878$	−3.26422	−	5.65380i	−0.110162	−	0.190807i
$879$			13.1527i			0.443630i
$880$	0.159569	+	0.356946i	0.00537905	+	0.0120327i
$881$	10.0027	−	17.3252i	0.337000	−	0.583701i	−0.646867	−	0.762603i	$-0.723921\pi$
$881$	10.0027	−	17.3252i	0.337000	−	0.583701i	0.983867	+	0.178902i	$0.0572545\pi$
$882$	3.12552	−	5.41356i	0.105242	−	0.182284i
$883$		−	29.0388i		−	0.977233i	−0.872499	−	0.488617i	$-0.837502\pi$
$883$		−	29.0388i		−	0.977233i	0.872499	−	0.488617i	$-0.162498\pi$
$884$	4.06762	−	29.2086i	0.136809	−	0.982392i
$885$	1.62109	−	15.6507i	0.0544922	−	0.526094i
$886$	26.2501	+	15.1555i	0.881891	+	0.509160i
$887$	−2.48763	−	1.43623i	−0.0835264	−	0.0482240i	0.457655	−	0.889130i	$-0.348689\pi$
$887$	−2.48763	−	1.43623i	−0.0835264	−	0.0482240i	−0.541181	+	0.840906i	$0.682023\pi$
$888$	1.52347	−	0.879573i	0.0511241	−	0.0295165i
$889$			6.00812i			0.201506i
$890$	11.9906	+	26.8223i	0.401925	+	0.899084i
$891$	−0.151430	+	0.0874279i	−0.00507308	+	0.00292895i
$892$	6.95276			0.232795
$893$	61.9912	−	35.7906i	2.07446	−	1.19769i
$894$	5.14284	−	8.90766i	0.172002	−	0.297917i
$895$	25.6869	+	18.6034i	0.858617	+	0.621845i
$896$	−0.865427			−0.0289119
$897$	6.45428	−	8.28251i	0.215502	−	0.276545i
$898$		−	15.9388i		−	0.531883i
$899$	39.0646	+	22.5540i	1.30288	+	0.752217i
$900$	−3.33442	+	3.72580i	−0.111147	+	0.124193i
$901$	10.1722	+	17.6188i	0.338886	+	0.586968i
$902$	−1.43018			−0.0476198
$903$	3.96963	+	6.87561i	0.132101	+	0.228806i
$904$	−10.2036	+	5.89106i	−0.339367	+	0.195934i
$905$	3.17294	−	30.6331i	0.105472	−	1.01828i
$906$	−5.87096	−	10.1688i	−0.195050	−	0.337836i
$907$	28.9860	+	16.7351i	0.962464	+	0.555679i	0.896931	−	0.442171i	$-0.145792\pi$
$907$	28.9860	+	16.7351i	0.962464	+	0.555679i	0.0655336	+	0.997850i	$0.479125\pi$
$908$	−1.44823	+	2.50840i	−0.0480611	+	0.0832442i
$909$	−10.5655			−0.350436
$910$	6.70166	−	1.94173i	0.222158	−	0.0643679i
$911$	20.7528			0.687570			0.343785	−	0.939048i	$-0.388291\pi$
$911$	20.7528			0.687570			0.343785	+	0.939048i	$0.388291\pi$
$912$	3.00709	−	5.20843i	0.0995746	−	0.172468i
$913$	−0.0211310	−	0.0122000i	−0.000699335	−	0.000403761i
$914$	9.90436	+	17.1548i	0.327607	+	0.567432i
$915$	−17.7353	−	1.83700i	−0.586310	−	0.0607294i
$916$	−6.83121	+	3.94400i	−0.225710	+	0.130313i
$917$	−0.982835	−	1.70232i	−0.0324561	−	0.0562156i
$918$	8.17919			0.269954
$919$	−13.7419	−	23.8017i	−0.453304	−	0.785146i	0.545285	−	0.838251i	$-0.316421\pi$
$919$	−13.7419	−	23.8017i	−0.453304	−	0.785146i	−0.998589	+	0.0531051i	$0.983088\pi$
$920$	3.81974	−	5.27413i	0.125933	−	0.173883i
$921$	−12.8699	−	7.43044i	−0.424077	−	0.244841i
$922$			13.3828i			0.440739i
$923$	−40.2866	−	31.3940i	−1.32605	−	1.03335i
$924$	0.151325			0.00497823
$925$	−5.86574	+	6.55423i	−0.192864	+	0.215502i
$926$	−21.1800	+	36.6848i	−0.696017	+	1.20554i
$927$	7.73853	−	4.46784i	0.254167	−	0.146743i
$928$	6.48982			0.213039
$929$	8.03305	−	4.63788i	0.263556	−	0.152164i	−0.362400	−	0.932023i	$-0.618042\pi$
$929$	8.03305	−	4.63788i	0.263556	−	0.152164i	0.625956	+	0.779859i	$0.284709\pi$
$930$	−14.1887	+	6.34290i	−0.465267	+	0.207992i
$931$		−	37.5948i		−	1.23212i
$932$	1.23624	−	0.713746i	0.0404945	−	0.0233795i
$933$	−7.94722	−	4.58833i	−0.260180	−	0.150215i
$934$	−28.9766	−	16.7296i	−0.948143	−	0.547410i
$935$	−0.329480	+	3.18096i	−0.0107752	+	0.104029i
$936$	−2.21623	+	2.84400i	−0.0724398	+	0.0929590i
$937$			15.0600i			0.491989i	0.969271	+	0.245995i	$0.0791146\pi$
$937$			15.0600i			0.491989i	−0.969271	+	0.245995i	$0.920885\pi$
$938$	1.18361	−	2.05007i	0.0386462	−	0.0669373i
$939$	3.71952	−	6.44240i	0.121382	−	0.210240i
$940$	−24.2966	+	10.8615i	−0.792469	+	0.354264i
$941$		−	19.4194i		−	0.633055i	−0.948583	−	0.316528i	$-0.897483\pi$
$941$		−	19.4194i		−	0.633055i	0.948583	−	0.316528i	$-0.102517\pi$
$942$	−3.38017	−	5.85463i	−0.110132	−	0.190754i
$943$	11.9100	+	20.6288i	0.387844	+	0.671766i
$944$		−	7.03667i		−	0.229024i
$945$	0.789764	+	1.76666i	0.0256910	+	0.0574695i
$946$	0.802048	−	1.38919i	0.0260768	−	0.0451664i
$947$	2.72224	−	4.71506i	0.0884610	−	0.153219i	−0.818400	−	0.574649i	$-0.805138\pi$
$947$	2.72224	−	4.71506i	0.0884610	−	0.153219i	0.906861	+	0.421430i	$0.138472\pi$
$948$			9.48961i			0.308208i
$949$	−17.4378	−	43.0046i	−0.566055	−	1.39599i
$950$	−6.16329	+	29.4325i	−0.199964	+	0.954916i
$951$	−22.3011	−	12.8755i	−0.723161	−	0.417517i
$952$	−6.13015	−	3.53925i	−0.198679	−	0.114708i
$953$	−20.2248	+	11.6768i	−0.655146	+	0.378249i	−0.790425	−	0.612559i	$-0.790140\pi$
$953$	−20.2248	+	11.6768i	−0.655146	+	0.378249i	0.135279	+	0.990808i	$0.456807\pi$
$954$		−	2.48735i		−	0.0805308i
$955$	11.3836	−	5.08888i	0.368363	−	0.164672i
$956$	9.44692	−	5.45418i	0.305535	−	0.176401i
$957$	−1.13478			−0.0366823
$958$	−19.3387	+	11.1652i	−0.624803	+	0.360730i
$959$	−3.19177	+	5.52831i	−0.103068	+	0.178518i
$960$	−1.31160	+	1.81100i	−0.0423316	+	0.0584497i
$961$	−17.3104			−0.558401
$962$	−3.89867	+	5.00301i	−0.125698	+	0.161303i
$963$			0.860777i			0.0277382i
$964$	25.4317	+	14.6830i	0.819101	+	0.472908i
$965$	−0.399886	−	0.289613i	−0.0128728	−	0.00932299i
$966$	−1.26018	−	2.18270i	−0.0405457	−	0.0702272i
$967$	−32.2070			−1.03571			−0.517854	−	0.855469i	$-0.673269\pi$
$967$	−32.2070			−1.03571			−0.517854	+	0.855469i	$0.673269\pi$
$968$	5.48471	+	9.49980i	0.176285	+	0.305335i
$969$	42.6007	−	24.5955i	1.36853	−	0.790123i
$970$	1.99235	−	19.2351i	0.0639705	−	0.617602i
$971$	−15.4181	−	26.7049i	−0.494789	−	0.857000i	0.505193	−	0.863007i	$-0.331421\pi$
$971$	−15.4181	−	26.7049i	−0.494789	−	0.857000i	−0.999982	+	0.00600636i	$0.998088\pi$
$972$	−0.866025	−	0.500000i	−0.0277778	−	0.0160375i
$973$	0.355154	−	0.615144i	0.0113857	−	0.0197206i
$974$	28.7499			0.921207
$975$	6.09341	−	16.9667i	0.195145	−	0.543371i
$976$	−7.97389			−0.255238
$977$	−10.6533	+	18.4521i	−0.340829	+	0.590334i	−0.984587	−	0.174896i	$-0.944041\pi$
$977$	−10.6533	+	18.4521i	−0.340829	+	0.590334i	0.643758	+	0.765230i	$0.277375\pi$
$978$	−1.23624	−	0.713746i	−0.0395307	−	0.0228231i
$979$	−1.14874	−	1.98968i	−0.0367140	−	0.0635905i
$980$	−1.44009	+	13.9034i	−0.0460021	+	0.444127i
$981$	4.72274	−	2.72668i	0.150786	−	0.0870561i
$982$	−8.02546	−	13.9005i	−0.256103	−	0.443583i
$983$	−6.15826			−0.196418			−0.0982090	−	0.995166i	$-0.531311\pi$
$983$	−6.15826			−0.196418			−0.0982090	+	0.995166i	$0.531311\pi$
$984$	−4.08960	−	7.08339i	−0.130372	−	0.225810i
$985$	3.12182	+	2.26094i	0.0994694	+	0.0720397i
$986$	45.9699	+	26.5407i	1.46398	+	0.845229i
$987$			10.3004i			0.327865i
$988$	−2.99093	+	21.4772i	−0.0951542	+	0.683279i
$989$	−26.7167			−0.849542
$990$	0.229340	−	0.316664i	0.00728891	−	0.0100642i
$991$	−2.46451	+	4.26866i	−0.0782877	+	0.135598i	−0.902511	−	0.430666i	$-0.858279\pi$
$991$	−2.46451	+	4.26866i	−0.0782877	+	0.135598i	0.824224	+	0.566265i	$0.191612\pi$
$992$	−6.01937	+	3.47529i	−0.191115	+	0.110340i
$993$	−6.50437			−0.206410
$994$	−10.6168	+	6.12960i	−0.336744	+	0.194419i
$995$	−16.2463	+	7.26273i	−0.515044	+	0.230244i
$996$		−	0.139544i		−	0.00442161i
$997$	20.2628	−	11.6988i	0.641730	−	0.370503i	−0.143550	−	0.989643i	$-0.545852\pi$
$997$	20.2628	−	11.6988i	0.641730	−	0.370503i	0.785281	+	0.619140i	$0.212519\pi$
$998$	28.7961	+	16.6254i	0.911524	+	0.526269i
$999$	−1.52347	−	0.879573i	−0.0482003	−	0.0278285i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.x.b.199.2	yes	12
3.2	odd	2		1170.2.bj.c.199.4		12
5.2	odd	4		1950.2.bc.i.901.5		12
5.3	odd	4		1950.2.bc.j.901.2		12
5.4	even	2		390.2.x.a.199.5	yes	12
13.10	even	6		390.2.x.a.49.5	✓	12
15.14	odd	2		1170.2.bj.d.199.3		12
39.23	odd	6		1170.2.bj.d.829.3		12
65.23	odd	12		1950.2.bc.j.751.2		12
65.49	even	6	inner	390.2.x.b.49.2	yes	12
65.62	odd	12		1950.2.bc.i.751.5		12
195.179	odd	6		1170.2.bj.c.829.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.x.a.49.5	✓	12	13.10	even	6
390.2.x.a.199.5	yes	12	5.4	even	2
390.2.x.b.49.2	yes	12	65.49	even	6	inner
390.2.x.b.199.2	yes	12	1.1	even	1	trivial
1170.2.bj.c.199.4		12	3.2	odd	2
1170.2.bj.c.829.4		12	195.179	odd	6
1170.2.bj.d.199.3		12	15.14	odd	2
1170.2.bj.d.829.3		12	39.23	odd	6
1950.2.bc.i.751.5		12	65.62	odd	12
1950.2.bc.i.901.5		12	5.2	odd	4
1950.2.bc.j.751.2		12	65.23	odd	12
1950.2.bc.j.901.2		12	5.3	odd	4

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} +(-1.81100 - 1.31160i) q^{10} +(0.151430 + 0.0874279i) q^{11} +1.00000i q^{12} +(-1.35486 - 3.34131i) q^{13} -0.865427 q^{14} +(-1.31160 + 1.81100i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-7.08339 + 4.08960i) q^{17} +1.00000 q^{18} +(5.20843 - 3.00709i) q^{19} +(-2.04138 + 0.912572i) 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} +(0.912572 + 2.04138i) q^{30} +6.95057i q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.0874279 - 0.151430i) q^{33} +8.17919i q^{34} +(-1.76666 + 0.789764i) 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} +(2.04138 - 0.912572i) q^{45} +(-2.52211 + 1.45614i) q^{46} +11.9021 q^{47} +(0.866025 - 0.500000i) q^{48} +(3.12552 - 5.41356i) q^{49} +(-3.33442 + 3.72580i) q^{50} +8.17919 q^{51} +(-2.21623 + 2.84400i) q^{52} -2.48735i q^{53} +(-0.866025 - 0.500000i) q^{54} +(0.229340 - 0.316664i) 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} +(-7.74377 + 2.24367i) 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} +(3.72580 + 3.33442i) q^{75} +(-5.20843 - 3.00709i) q^{76} -0.151325i q^{77} +(2.84400 + 2.21623i) q^{78} +9.48961 q^{79} +(1.81100 + 1.31160i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-7.08339 + 4.08960i) q^{82} -0.139544 q^{83} +(0.749482 - 0.432713i) q^{84} +(7.46410 + 16.6968i) 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} +(-5.48837 - 12.2772i) 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	\( 12 q + 6 q^{2} - 6 q^{4} + 2 q^{5} + 2 q^{7} - 12 q^{8} + 6 q^{9} + 4 q^{10} + 6 q^{11} + 8 q^{13} + 4 q^{14} + 6 q^{15} - 6 q^{16} - 18 q^{17} + 12 q^{18} - 6 q^{19} + 2 q^{20} + 6 q^{22} - 6 q^{23} - 10 q^{25} - 2 q^{26} + 2 q^{28} + 14 q^{29} + 6 q^{30} + 6 q^{32} - 6 q^{33} - 22 q^{35} + 6 q^{36} + 12 q^{37} - 2 q^{39} - 2 q^{40} - 18 q^{41} + 12 q^{42} + 36 q^{43} - 2 q^{45} - 6 q^{46} - 16 q^{47} + 8 q^{49} - 20 q^{50} + 16 q^{51} - 10 q^{52} + 8 q^{55} - 2 q^{56} + 8 q^{57} - 14 q^{58} - 36 q^{59} + 10 q^{61} - 6 q^{62} - 2 q^{63} + 12 q^{64} - 44 q^{65} - 12 q^{66} - 4 q^{67} + 18 q^{68} + 16 q^{69} + 4 q^{70} - 12 q^{71} - 6 q^{72} - 28 q^{73} - 12 q^{74} + 16 q^{75} + 6 q^{76} + 2 q^{78} + 4 q^{79} - 4 q^{80} - 6 q^{81} - 18 q^{82} - 72 q^{83} + 12 q^{84} + 48 q^{85} - 6 q^{87} - 6 q^{88} + 18 q^{89} + 2 q^{90} + 2 q^{91} + 16 q^{93} - 8 q^{94} + 18 q^{95} + 48 q^{97} - 8 q^{98}+O(q^{100}) \) 12 * q + 6 * q^2 - 6 * q^4 + 2 * q^5 + 2 * q^7 - 12 * q^8 + 6 * q^9 + 4 * 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 + 2 * 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 - 22 * q^35 + 6 * q^36 + 12 * q^37 - 2 * q^39 - 2 * q^40 - 18 * q^41 + 12 * q^42 + 36 * q^43 - 2 * q^45 - 6 * q^46 - 16 * q^47 + 8 * q^49 - 20 * q^50 + 16 * q^51 - 10 * q^52 + 8 * 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 - 44 * 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 + 16 * q^75 + 6 * q^76 + 2 * q^78 + 4 * q^79 - 4 * q^80 - 6 * q^81 - 18 * q^82 - 72 * q^83 + 12 * q^84 + 48 * q^85 - 6 * q^87 - 6 * q^88 + 18 * q^89 + 2 * q^90 + 2 * q^91 + 16 * q^93 - 8 * q^94 + 18 * q^95 + 48 * q^97 - 8 * q^98

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