LMFDB - Embedded newform 390.2.x.a.49.6

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			49.6
Root			$1.40719 - 0.536449i$ of defining polynomial
Character	$\chi$	$=$	390.49
Dual form			390.2.x.a.199.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.03420 - 0.928463i) q^{5} +(-0.866025 - 0.500000i) q^{6} +(1.40247 - 2.42916i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.03420 - 0.928463i) q^{5} +(-0.866025 - 0.500000i) q^{6} +(1.40247 - 2.42916i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.82117 - 1.29743i) q^{10} +(-0.515171 + 0.297434i) q^{11} +1.00000i q^{12} +(-1.10975 + 3.43052i) q^{13} -2.80495 q^{14} +(1.29743 - 1.82117i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(4.98222 + 2.87649i) q^{17} -1.00000 q^{18} +(-6.59574 - 3.80805i) q^{19} +(-0.213026 + 2.22590i) q^{20} -2.80495i q^{21} +(0.515171 + 0.297434i) q^{22} +(4.02317 - 2.32278i) q^{23} +(0.866025 - 0.500000i) q^{24} +(3.27591 - 3.77735i) q^{25} +(3.52579 - 0.754186i) q^{26} -1.00000i q^{27} +(1.40247 + 2.42916i) q^{28} +(-1.26235 - 2.18645i) q^{29} +(-2.22590 - 0.213026i) q^{30} +6.59309i q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.297434 + 0.515171i) q^{33} -5.75297i q^{34} +(0.597526 - 6.24353i) q^{35} +(0.500000 + 0.866025i) q^{36} +(-5.18679 - 8.98379i) q^{37} +7.61611i q^{38} +(0.754186 + 3.52579i) q^{39} +(2.03420 - 0.928463i) q^{40} +(-4.98222 + 2.87649i) q^{41} +(-2.42916 + 1.40247i) q^{42} +(-3.67593 - 2.12230i) q^{43} -0.594869i q^{44} +(0.213026 - 2.22590i) q^{45} +(-4.02317 - 2.32278i) q^{46} +2.89798 q^{47} +(-0.866025 - 0.500000i) q^{48} +(-0.433868 - 0.751482i) q^{49} +(-4.90924 - 0.948346i) q^{50} +5.75297 q^{51} +(-2.41604 - 2.67633i) q^{52} +13.8960i q^{53} +(-0.866025 + 0.500000i) q^{54} +(-0.771803 + 1.08336i) q^{55} +(1.40247 - 2.42916i) q^{56} -7.61611 q^{57} +(-1.26235 + 2.18645i) q^{58} +(8.40299 + 4.85147i) q^{59} +(0.928463 + 2.03420i) q^{60} +(-3.41309 + 5.91165i) q^{61} +(5.70978 - 3.29654i) q^{62} +(-1.40247 - 2.42916i) q^{63} +1.00000 q^{64} +(0.927657 + 8.00871i) q^{65} +0.594869 q^{66} +(-3.93121 - 6.80906i) q^{67} +(-4.98222 + 2.87649i) q^{68} +(2.32278 - 4.02317i) q^{69} +(-5.70582 + 2.60429i) q^{70} +(-1.11257 - 0.642342i) q^{71} +(0.500000 - 0.866025i) q^{72} +14.5400 q^{73} +(-5.18679 + 8.98379i) q^{74} +(0.948346 - 4.90924i) q^{75} +(6.59574 - 3.80805i) q^{76} +1.66858i q^{77} +(2.67633 - 2.41604i) q^{78} -1.83150 q^{79} +(-1.82117 - 1.29743i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(4.98222 + 2.87649i) q^{82} +4.19184 q^{83} +(2.42916 + 1.40247i) q^{84} +(12.8055 + 1.22553i) q^{85} +4.24460i q^{86} +(-2.18645 - 1.26235i) q^{87} +(-0.515171 + 0.297434i) q^{88} +(-5.24333 + 3.02724i) q^{89} +(-2.03420 + 0.928463i) q^{90} +(6.77687 + 7.50697i) q^{91} +4.64555i q^{92} +(3.29654 + 5.70978i) q^{93} +(-1.44899 - 2.50973i) q^{94} +(-16.9527 - 1.62243i) q^{95} +1.00000i q^{96} +(-8.45318 + 14.6413i) q^{97} +(-0.433868 + 0.751482i) q^{98} +0.594869i 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
$5$	2.03420	−	0.928463i	0.909720	−	0.415221i
$5$	2.03420	−	0.928463i	0.909720	−	0.415221i
$6$	−0.866025	−	0.500000i	−0.353553	−	0.204124i
$7$	1.40247	−	2.42916i	0.530085	−	0.918135i	−0.469299	−	0.883040i	$-0.655493\pi$
$7$	1.40247	−	2.42916i	0.530085	−	0.918135i	0.999384	−	0.0350954i	$-0.0111735\pi$
$8$	1.00000			0.353553
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−1.82117	−	1.29743i	−0.575905	−	0.410285i
$11$	−0.515171	+	0.297434i	−0.155330	+	0.0896798i	−0.575650	−	0.817696i	$-0.695251\pi$
$11$	−0.515171	+	0.297434i	−0.155330	+	0.0896798i	0.420320	+	0.907376i	$0.361918\pi$
$12$			1.00000i			0.288675i
$13$	−1.10975	+	3.43052i	−0.307790	+	0.951454i
$13$	−1.10975	+	3.43052i	−0.307790	+	0.951454i
$14$	−2.80495			−0.749654
$15$	1.29743	−	1.82117i	0.334996	−	0.470224i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	4.98222	+	2.87649i	1.20837	+	0.697650i	0.962402	−	0.271629i	$-0.0875623\pi$
$17$	4.98222	+	2.87649i	1.20837	+	0.697650i	0.245963	+	0.969279i	$0.420896\pi$
$18$	−1.00000			−0.235702
$19$	−6.59574	−	3.80805i	−1.51317	−	0.873628i	−0.999881	−	0.0154099i	$-0.995095\pi$
$19$	−6.59574	−	3.80805i	−1.51317	−	0.873628i	−0.513286	−	0.858218i	$-0.671572\pi$
$20$	−0.213026	+	2.22590i	−0.0476340	+	0.497726i
$21$		−	2.80495i		−	0.612090i
$22$	0.515171	+	0.297434i	0.109835	+	0.0634132i
$23$	4.02317	−	2.32278i	0.838888	−	0.484332i	−0.0179978	−	0.999838i	$-0.505729\pi$
$23$	4.02317	−	2.32278i	0.838888	−	0.484332i	0.856886	+	0.515506i	$0.172396\pi$
$24$	0.866025	−	0.500000i	0.176777	−	0.102062i
$25$	3.27591	−	3.77735i	0.655182	−	0.755471i
$26$	3.52579	−	0.754186i	0.691465	−	0.147908i
$27$		−	1.00000i		−	0.192450i
$28$	1.40247	+	2.42916i	0.265043	+	0.459067i
$29$	−1.26235	−	2.18645i	−0.234412	−	0.406013i	0.724690	−	0.689075i	$-0.241983\pi$
$29$	−1.26235	−	2.18645i	−0.234412	−	0.406013i	−0.959102	+	0.283062i	$0.908650\pi$
$30$	−2.22590	−	0.213026i	−0.406391	−	0.0388930i
$31$			6.59309i			1.18415i	0.805882	+	0.592077i	$0.201692\pi$
$31$			6.59309i			1.18415i	−0.805882	+	0.592077i	$0.798308\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−0.297434	+	0.515171i	−0.0517767	+	0.0896798i
$34$		−	5.75297i		−	0.986626i
$35$	0.597526	−	6.24353i	0.101000	−	1.05535i
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	−5.18679	−	8.98379i	−0.852703	−	1.47693i	−0.878759	−	0.477265i	$-0.841628\pi$
$37$	−5.18679	−	8.98379i	−0.852703	−	1.47693i	0.0260561	−	0.999660i	$-0.491705\pi$
$38$			7.61611i			1.23550i
$39$	0.754186	+	3.52579i	0.120766	+	0.564578i
$40$	2.03420	−	0.928463i	0.321635	−	0.146803i
$41$	−4.98222	+	2.87649i	−0.778092	+	0.449232i	−0.835754	−	0.549105i	$-0.814969\pi$
$41$	−4.98222	+	2.87649i	−0.778092	+	0.449232i	0.0576618	+	0.998336i	$0.481636\pi$
$42$	−2.42916	+	1.40247i	−0.374827	+	0.216406i
$43$	−3.67593	−	2.12230i	−0.560574	−	0.323648i	0.192802	−	0.981238i	$-0.438243\pi$
$43$	−3.67593	−	2.12230i	−0.560574	−	0.323648i	−0.753376	+	0.657590i	$0.771576\pi$
$44$		−	0.594869i		−	0.0896798i
$45$	0.213026	−	2.22590i	0.0317560	−	0.331817i
$46$	−4.02317	−	2.32278i	−0.593184	−	0.342475i
$47$	2.89798			0.422715			0.211357	−	0.977409i	$-0.432212\pi$
$47$	2.89798			0.422715			0.211357	+	0.977409i	$0.432212\pi$
$48$	−0.866025	−	0.500000i	−0.125000	−	0.0721688i
$49$	−0.433868	−	0.751482i	−0.0619812	−	0.107355i
$50$	−4.90924	−	0.948346i	−0.694271	−	0.134116i
$51$	5.75297			0.805577
$52$	−2.41604	−	2.67633i	−0.335044	−	0.371140i
$53$			13.8960i			1.90876i	0.298598	+	0.954379i	$0.403481\pi$
$53$			13.8960i			1.90876i	−0.298598	+	0.954379i	$0.596519\pi$
$54$	−0.866025	+	0.500000i	−0.117851	+	0.0680414i
$55$	−0.771803	+	1.08336i	−0.104070	+	0.146080i
$56$	1.40247	−	2.42916i	0.187414	−	0.324610i
$57$	−7.61611			−1.00878
$58$	−1.26235	+	2.18645i	−0.165754	+	0.287095i
$59$	8.40299	+	4.85147i	1.09398	+	0.631607i	0.934632	−	0.355616i	$-0.115729\pi$
$59$	8.40299	+	4.85147i	1.09398	+	0.631607i	0.159344	+	0.987223i	$0.449062\pi$
$60$	0.928463	+	2.03420i	0.119864	+	0.262614i
$61$	−3.41309	+	5.91165i	−0.437002	+	0.756910i	−0.997457	−	0.0712755i	$-0.977293\pi$
$61$	−3.41309	+	5.91165i	−0.437002	+	0.756910i	0.560455	+	0.828185i	$0.310626\pi$
$62$	5.70978	−	3.29654i	0.725143	−	0.418661i
$63$	−1.40247	−	2.42916i	−0.176695	−	0.306045i
$64$	1.00000			0.125000
$65$	0.927657	+	8.00871i	0.115062	+	0.993358i
$66$	0.594869			0.0732233
$67$	−3.93121	−	6.80906i	−0.480274	−	0.831859i	0.519470	−	0.854489i	$-0.326129\pi$
$67$	−3.93121	−	6.80906i	−0.480274	−	0.831859i	−0.999744	+	0.0226299i	$0.992796\pi$
$68$	−4.98222	+	2.87649i	−0.604183	+	0.348825i
$69$	2.32278	−	4.02317i	0.279629	−	0.484332i
$70$	−5.70582	+	2.60429i	−0.681976	+	0.311272i
$71$	−1.11257	−	0.642342i	−0.132038	−	0.0762320i	0.432526	−	0.901621i	$-0.357622\pi$
$71$	−1.11257	−	0.642342i	−0.132038	−	0.0762320i	−0.564564	+	0.825389i	$0.690956\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	14.5400			1.70178			0.850892	−	0.525341i	$-0.176062\pi$
$73$	14.5400			1.70178			0.850892	+	0.525341i	$0.176062\pi$
$74$	−5.18679	+	8.98379i	−0.602952	+	1.04434i
$75$	0.948346	−	4.90924i	0.109506	−	0.566870i
$76$	6.59574	−	3.80805i	0.756584	−	0.436814i
$77$			1.66858i			0.190152i
$78$	2.67633	−	2.41604i	0.303035	−	0.273563i
$79$	−1.83150			−0.206060			−0.103030	−	0.994678i	$-0.532854\pi$
$79$	−1.83150			−0.206060			−0.103030	+	0.994678i	$0.532854\pi$
$80$	−1.82117	−	1.29743i	−0.203613	−	0.145058i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	4.98222	+	2.87649i	0.550194	+	0.317655i
$83$	4.19184			0.460114			0.230057	−	0.973177i	$-0.426109\pi$
$83$	4.19184			0.460114			0.230057	+	0.973177i	$0.426109\pi$
$84$	2.42916	+	1.40247i	0.265043	+	0.153022i
$85$	12.8055	+	1.22553i	1.38895	+	0.132927i
$86$			4.24460i			0.457707i
$87$	−2.18645	−	1.26235i	−0.234412	−	0.135338i
$88$	−0.515171	+	0.297434i	−0.0549175	+	0.0317066i
$89$	−5.24333	+	3.02724i	−0.555792	+	0.320886i	−0.751455	−	0.659785i	$-0.770647\pi$
$89$	−5.24333	+	3.02724i	−0.555792	+	0.320886i	0.195663	+	0.980671i	$0.437314\pi$
$90$	−2.03420	+	0.928463i	−0.214423	+	0.0978686i
$91$	6.77687	+	7.50697i	0.710409	+	0.786945i
$92$			4.64555i			0.484332i
$93$	3.29654	+	5.70978i	0.341836	+	0.592077i
$94$	−1.44899	−	2.50973i	−0.149452	−	0.258859i
$95$	−16.9527	−	1.62243i	−1.73931	−	0.166457i
$96$			1.00000i			0.102062i
$97$	−8.45318	+	14.6413i	−0.858291	+	1.48660i	0.0152677	+	0.999883i	$0.495140\pi$
$97$	−8.45318	+	14.6413i	−0.858291	+	1.48660i	−0.873558	+	0.486719i	$0.838193\pi$
$98$	−0.433868	+	0.751482i	−0.0438273	+	0.0759111i
$99$			0.594869i			0.0597866i
$100$	1.63333	+	4.72570i	0.163333	+	0.472570i
$101$	2.72360	+	4.71741i	0.271008	+	0.469400i	0.969120	−	0.246589i	$-0.0793096\pi$
$101$	2.72360	+	4.71741i	0.271008	+	0.469400i	−0.698112	+	0.715988i	$0.745976\pi$
$102$	−2.87649	−	4.98222i	−0.284814	−	0.493313i
$103$			13.7529i			1.35511i	0.735471	+	0.677556i	$0.236961\pi$
$103$			13.7529i			1.35511i	−0.735471	+	0.677556i	$0.763039\pi$
$104$	−1.10975	+	3.43052i	−0.108820	+	0.336390i
$105$	−2.60429	−	5.70582i	−0.254153	−	0.556831i
$106$	12.0343	−	6.94798i	1.16887	−	0.674848i
$107$	3.66407	−	2.11545i	0.354219	−	0.204509i	−0.312323	−	0.949976i	$-0.601107\pi$
$107$	3.66407	−	2.11545i	0.354219	−	0.204509i	0.666542	+	0.745468i	$0.267774\pi$
$108$	0.866025	+	0.500000i	0.0833333	+	0.0481125i
$109$			0.447358i			0.0428491i	0.999770	+	0.0214246i	$0.00682017\pi$
$109$			0.447358i			0.0428491i	−0.999770	+	0.0214246i	$0.993180\pi$
$110$	1.32412	+	0.126722i	0.126250	+	0.0120825i
$111$	−8.98379	−	5.18679i	−0.852703	−	0.492308i
$112$	−2.80495			−0.265043
$113$	8.11206	+	4.68350i	0.763119	+	0.440587i	0.830414	−	0.557146i	$-0.188104\pi$
$113$	8.11206	+	4.68350i	0.763119	+	0.440587i	−0.0672956	+	0.997733i	$0.521437\pi$
$114$	3.80805	+	6.59574i	0.356657	+	0.617748i
$115$	6.02730	−	8.46035i	0.562049	−	0.788932i
$116$	2.52469			0.234412
$117$	2.41604	+	2.67633i	0.223363	+	0.247427i
$118$		−	9.70293i		−	0.893227i
$119$	13.9749	−	8.06839i	1.28107	−	0.739628i
$120$	1.29743	−	1.82117i	0.118439	−	0.166249i
$121$	−5.32307	+	9.21982i	−0.483915	+	0.838165i
$122$	6.82619			0.618014
$123$	−2.87649	+	4.98222i	−0.259364	+	0.449232i
$124$	−5.70978	−	3.29654i	−0.512753	−	0.296038i
$125$	3.15672	−	10.7254i	0.282345	−	0.959313i
$126$	−1.40247	+	2.42916i	−0.124942	+	0.216406i
$127$	−5.79190	+	3.34395i	−0.513948	+	0.296728i	−0.734455	−	0.678658i	$-0.762562\pi$
$127$	−5.79190	+	3.34395i	−0.513948	+	0.296728i	0.220507	+	0.975385i	$0.429229\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−4.24460			−0.373716
$130$	6.47192	−	4.80773i	0.567625	−	0.421666i
$131$	−11.6724			−1.01982			−0.509911	−	0.860227i	$-0.670322\pi$
$131$	−11.6724			−1.01982			−0.509911	+	0.860227i	$0.670322\pi$
$132$	−0.297434	−	0.515171i	−0.0258883	−	0.0448399i
$133$	−18.5007	+	10.6814i	−1.60422	+	0.926194i
$134$	−3.93121	+	6.80906i	−0.339605	+	0.588213i
$135$	−0.928463	−	2.03420i	−0.0799094	−	0.175076i
$136$	4.98222	+	2.87649i	0.427222	+	0.246657i
$137$	3.40142	−	5.89144i	0.290603	−	0.503339i	−0.683349	−	0.730092i	$-0.739477\pi$
$137$	3.40142	−	5.89144i	0.290603	−	0.503339i	0.973953	+	0.226752i	$0.0728107\pi$
$138$	−4.64555			−0.395456
$139$	−3.54908	+	6.14719i	−0.301029	+	0.521397i	−0.976369	−	0.216109i	$-0.930663\pi$
$139$	−3.54908	+	6.14719i	−0.301029	+	0.521397i	0.675340	+	0.737506i	$0.263997\pi$
$140$	5.10829	+	3.63924i	0.431729	+	0.307572i
$141$	2.50973	−	1.44899i	0.211357	−	0.122027i
$142$			1.28468i			0.107808i
$143$	−0.448642	−	2.09738i	−0.0375173	−	0.175392i
$144$	−1.00000			−0.0833333
$145$	−4.59790	−	3.27562i	−0.381835	−	0.272026i
$146$	−7.27002	−	12.5920i	−0.601671	−	1.04213i
$147$	−0.751482	−	0.433868i	−0.0619812	−	0.0357848i
$148$	10.3736			0.852703
$149$	−3.02342	−	1.74557i	−0.247688	−	0.143003i	0.371017	−	0.928626i	$-0.379009\pi$
$149$	−3.02342	−	1.74557i	−0.247688	−	0.143003i	−0.618705	+	0.785623i	$0.712342\pi$
$150$	−4.72570	+	1.63333i	−0.385852	+	0.133361i
$151$		−	4.54988i		−	0.370264i	−0.982714	−	0.185132i	$-0.940729\pi$
$151$		−	4.54988i		−	0.370264i	0.982714	−	0.185132i	$-0.0592713\pi$
$152$	−6.59574	−	3.80805i	−0.534985	−	0.308874i
$153$	4.98222	−	2.87649i	0.402789	−	0.232550i
$154$	1.44503	−	0.834288i	0.116444	−	0.0672288i
$155$	6.12144	+	13.4116i	0.491686	+	1.07725i
$156$	−3.43052	−	1.10975i	−0.274661	−	0.0888512i
$157$			11.4957i			0.917460i	0.888576	+	0.458730i	$0.151695\pi$
$157$			11.4957i			0.917460i	−0.888576	+	0.458730i	$0.848305\pi$
$158$	0.915751	+	1.58613i	0.0728532	+	0.126186i
$159$	6.94798	+	12.0343i	0.551011	+	0.954379i
$160$	−0.213026	+	2.22590i	−0.0168411	+	0.175973i
$161$		−	13.0305i		−	1.02695i
$162$	−0.500000	+	0.866025i	−0.0392837	+	0.0680414i
$163$	6.91443	−	11.9762i	0.541580	−	0.938045i	−0.457233	−	0.889347i	$-0.651160\pi$
$163$	6.91443	−	11.9762i	0.541580	−	0.938045i	0.998814	−	0.0486977i	$-0.0155071\pi$
$164$		−	5.75297i		−	0.449232i
$165$	−0.126722	+	1.32412i	−0.00986531	+	0.103082i
$166$	−2.09592	−	3.63024i	−0.162675	−	0.281761i
$167$	−10.7700	−	18.6542i	−0.833409	−	1.44351i	−0.895319	−	0.445425i	$-0.853052\pi$
$167$	−10.7700	−	18.6542i	−0.833409	−	1.44351i	0.0619099	−	0.998082i	$-0.480281\pi$
$168$		−	2.80495i		−	0.216406i
$169$	−10.5369	−	7.61404i	−0.810531	−	0.585696i
$170$	−5.34142	−	11.7027i	−0.409668	−	0.897554i
$171$	−6.59574	+	3.80805i	−0.504389	+	0.291209i
$172$	3.67593	−	2.12230i	0.280287	−	0.161824i
$173$	−11.8342	−	6.83251i	−0.899741	−	0.519466i	−0.0226249	−	0.999744i	$-0.507202\pi$
$173$	−11.8342	−	6.83251i	−0.899741	−	0.519466i	−0.877116	+	0.480278i	$0.840536\pi$
$174$			2.52469i			0.191396i
$175$	−4.58140	−	13.2553i	−0.346321	−	1.00201i
$176$	0.515171	+	0.297434i	0.0388325	+	0.0224200i
$177$	9.70293			0.729317
$178$	5.24333	+	3.02724i	0.393004	+	0.226901i
$179$	5.37886	+	9.31647i	0.402035	+	0.696345i	0.993971	−	0.109639i	$-0.0349696\pi$
$179$	5.37886	+	9.31647i	0.402035	+	0.696345i	−0.591936	+	0.805985i	$0.701636\pi$
$180$	1.82117	+	1.29743i	0.135742	+	0.0967050i
$181$	5.86469			0.435919			0.217959	−	0.975958i	$-0.430060\pi$
$181$	5.86469			0.435919			0.217959	+	0.975958i	$0.430060\pi$
$182$	3.11280	−	9.62243i	0.230736	−	0.713262i
$183$			6.82619i			0.504606i
$184$	4.02317	−	2.32278i	0.296592	−	0.171237i
$185$	−18.8921	−	13.4590i	−1.38897	−	0.989529i
$186$	3.29654	−	5.70978i	0.241714	−	0.418661i
$187$	−3.42226			−0.250261
$188$	−1.44899	+	2.50973i	−0.105679	+	0.183041i
$189$	−2.42916	−	1.40247i	−0.176695	−	0.102015i
$190$	7.07128	+	15.4927i	0.513004	+	1.12396i
$191$	6.91728	−	11.9811i	0.500517	−	0.866921i	−0.499483	−	0.866324i	$-0.666477\pi$
$191$	6.91728	−	11.9811i	0.500517	−	0.866921i	1.00000		0.000597179i	$-0.000190088\pi$
$192$	0.866025	−	0.500000i	0.0625000	−	0.0360844i
$193$	8.50322	+	14.7280i	0.612075	+	1.06014i	0.990890	+	0.134673i	$0.0429983\pi$
$193$	8.50322	+	14.7280i	0.612075	+	1.06014i	−0.378815	+	0.925472i	$0.623668\pi$
$194$	16.9064			1.21381
$195$	4.80773	+	6.47192i	0.344289	+	0.463464i
$196$	0.867736			0.0619812
$197$	3.16487	+	5.48171i	0.225487	+	0.390556i	0.956466	−	0.291845i	$-0.0942692\pi$
$197$	3.16487	+	5.48171i	0.225487	+	0.390556i	−0.730978	+	0.682401i	$0.760936\pi$
$198$	0.515171	−	0.297434i	0.0366116	−	0.0211377i
$199$	8.31782	−	14.4069i	0.589634	−	1.02128i	−0.404646	−	0.914473i	$-0.632605\pi$
$199$	8.31782	−	14.4069i	0.589634	−	1.02128i	0.994280	−	0.106803i	$-0.0340615\pi$
$200$	3.27591	−	3.77735i	0.231642	−	0.267099i
$201$	−6.80906	−	3.93121i	−0.480274	−	0.277286i
$202$	2.72360	−	4.71741i	0.191632	−	0.331916i
$203$	−7.08163			−0.497033
$204$	−2.87649	+	4.98222i	−0.201394	+	0.348825i
$205$	−7.46410	+	10.4771i	−0.521315	+	0.731755i
$206$	11.9104	−	6.87645i	0.829834	−	0.479105i
$207$		−	4.64555i		−	0.322888i
$208$	3.52579	−	0.754186i	0.244470	−	0.0522934i
$209$	4.53058			0.313387
$210$	−3.63924	+	5.10829i	−0.251131	+	0.352506i
$211$	−8.27443	−	14.3317i	−0.569635	−	0.986637i	−0.996602	−	0.0823697i	$-0.973751\pi$
$211$	−8.27443	−	14.3317i	−0.569635	−	0.986637i	0.426967	−	0.904267i	$-0.359582\pi$
$212$	−12.0343	−	6.94798i	−0.826516	−	0.477190i
$213$	−1.28468			−0.0880251
$214$	−3.66407	−	2.11545i	−0.250471	−	0.144609i
$215$	−9.44804	−	0.904208i	−0.644351	−	0.0616665i
$216$		−	1.00000i		−	0.0680414i
$217$	16.0156	+	9.24663i	1.08721	+	0.627702i
$218$	0.387423	−	0.223679i	0.0262396	−	0.0151495i
$219$	12.5920	−	7.27002i	0.850892	−	0.491262i
$220$	−0.552314	−	1.21008i	−0.0372370	−	0.0815836i
$221$	−15.3969	+	13.8994i	−1.03570	+	0.934975i
$222$			10.3736i			0.696229i
$223$	−8.32779	−	14.4242i	−0.557670	−	0.965913i	−0.997690	−	0.0679254i	$-0.978362\pi$
$223$	−8.32779	−	14.4242i	−0.557670	−	0.965913i	0.440020	−	0.897988i	$-0.354971\pi$
$224$	1.40247	+	2.42916i	0.0937068	+	0.162305i
$225$	−1.63333	−	4.72570i	−0.108889	−	0.315047i
$226$		−	9.36701i		−	0.623084i
$227$	−1.51105	+	2.61722i	−0.100292	+	0.173711i	−0.911805	−	0.410624i	$-0.865311\pi$
$227$	−1.51105	+	2.61722i	−0.100292	+	0.173711i	0.811513	+	0.584334i	$0.198644\pi$
$228$	3.80805	−	6.59574i	0.252195	−	0.436814i
$229$		−	16.4472i		−	1.08686i	−0.839453	−	0.543432i	$-0.817125\pi$
$229$		−	16.4472i		−	1.08686i	0.839453	−	0.543432i	$-0.182875\pi$
$230$	−10.3405	−	0.989622i	−0.681834	−	0.0652537i
$231$	0.834288	+	1.44503i	0.0548921	+	0.0950759i
$232$	−1.26235	−	2.18645i	−0.0828771	−	0.143547i
$233$		−	13.8289i		−	0.905959i	−0.891521	−	0.452980i	$-0.850361\pi$
$233$		−	13.8289i		−	0.905959i	0.891521	−	0.452980i	$-0.149639\pi$
$234$	1.10975	−	3.43052i	0.0725467	−	0.224260i
$235$	5.89507	−	2.69067i	0.384552	−	0.175520i
$236$	−8.40299	+	4.85147i	−0.546988	+	0.315804i
$237$	−1.58613	+	0.915751i	−0.103030	+	0.0594844i
$238$	−13.9749	−	8.06839i	−0.905856	−	0.522996i
$239$		−	4.60216i		−	0.297689i	−0.988861	−	0.148845i	$-0.952445\pi$
$239$		−	4.60216i		−	0.297689i	0.988861	−	0.148845i	$-0.0475554\pi$
$240$	−2.22590	−	0.213026i	−0.143681	−	0.0137507i
$241$	5.38108	+	3.10677i	0.346626	+	0.200125i	0.663198	−	0.748444i	$-0.269199\pi$
$241$	5.38108	+	3.10677i	0.346626	+	0.200125i	−0.316572	+	0.948568i	$0.602532\pi$
$242$	10.6461			0.684359
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	−3.41309	−	5.91165i	−0.218501	−	0.378455i
$245$	−1.58030	−	1.12583i	−0.100961	−	0.0719267i
$246$	5.75297			0.366796
$247$	20.3832	−	18.4008i	1.29695	−	1.17082i
$248$			6.59309i			0.418661i
$249$	3.63024	−	2.09592i	0.230057	−	0.132824i
$250$	−10.8669	+	2.62893i	−0.687281	+	0.166268i
$251$	8.19386	−	14.1922i	0.517192	−	0.895802i	−0.482609	−	0.875836i	$-0.660311\pi$
$251$	8.19386	−	14.1922i	0.517192	−	0.895802i	0.999801	−	0.0199663i	$-0.00635591\pi$
$252$	2.80495			0.176695
$253$	−1.38175	+	2.39326i	−0.0868697	+	0.150463i
$254$	5.79190	+	3.34395i	0.363416	+	0.209818i
$255$	11.7027	−	5.34142i	0.732850	−	0.334493i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	7.28269	−	4.20466i	0.454282	−	0.262280i	−0.255355	−	0.966847i	$-0.582192\pi$
$257$	7.28269	−	4.20466i	0.454282	−	0.262280i	0.709637	+	0.704568i	$0.248859\pi$
$258$	2.12230	+	3.67593i	0.132129	+	0.228853i
$259$	−29.0974			−1.80802
$260$	−7.39958	−	3.20098i	−0.458902	−	0.198516i
$261$	−2.52469			−0.156275
$262$	5.83620	+	10.1086i	0.360562	+	0.624511i
$263$	−5.10152	+	2.94536i	−0.314573	+	0.181619i	−0.648971	−	0.760813i	$-0.724800\pi$
$263$	−5.10152	+	2.94536i	−0.314573	+	0.181619i	0.334398	+	0.942432i	$0.391467\pi$
$264$	−0.297434	+	0.515171i	−0.0183058	+	0.0317066i
$265$	12.9019	+	28.2671i	0.792557	+	1.73644i
$266$	18.5007	+	10.6814i	1.13435	+	0.654918i
$267$	−3.02724	+	5.24333i	−0.185264	+	0.320886i
$268$	7.86242			0.480274
$269$	11.4228	−	19.7848i	0.696459	−	1.20630i	−0.273228	−	0.961949i	$-0.588091\pi$
$269$	11.4228	−	19.7848i	0.696459	−	1.20630i	0.969686	−	0.244352i	$-0.0785754\pi$
$270$	−1.29743	+	1.82117i	−0.0789593	+	0.110833i
$271$	−23.2565	+	13.4271i	−1.41273	+	0.815639i	−0.995645	−	0.0932285i	$-0.970281\pi$
$271$	−23.2565	+	13.4271i	−1.41273	+	0.815639i	−0.417084	+	0.908868i	$0.636948\pi$
$272$		−	5.75297i		−	0.348825i
$273$	9.62243	+	3.11280i	0.582376	+	0.188395i
$274$	−6.80285			−0.410975
$275$	−0.564141	+	2.92035i	−0.0340190	+	0.176104i
$276$	2.32278	+	4.02317i	0.139815	+	0.242166i
$277$	−9.20150	−	5.31249i	−0.552865	−	0.319197i	0.197412	−	0.980321i	$-0.436746\pi$
$277$	−9.20150	−	5.31249i	−0.552865	−	0.319197i	−0.750277	+	0.661124i	$0.770080\pi$
$278$	7.09816			0.425719
$279$	5.70978	+	3.29654i	0.341836	+	0.197359i
$280$	0.597526	−	6.24353i	0.0357090	−	0.373122i
$281$			28.3732i			1.69260i	0.532705	+	0.846301i	$0.321176\pi$
$281$			28.3732i			1.69260i	−0.532705	+	0.846301i	$0.678824\pi$
$282$	−2.50973	−	1.44899i	−0.149452	−	0.0862862i
$283$	4.91005	−	2.83482i	0.291872	−	0.168512i	−0.346914	−	0.937897i	$-0.612770\pi$
$283$	4.91005	−	2.83482i	0.291872	−	0.168512i	0.638786	+	0.769385i	$0.279437\pi$
$284$	1.11257	−	0.642342i	0.0660188	−	0.0381160i
$285$	−15.4927	+	7.07128i	−0.917706	+	0.418866i
$286$	−1.59207	+	1.43723i	−0.0941408	+	0.0849850i
$287$			16.1368i			0.952524i
$288$	0.500000	+	0.866025i	0.0294628	+	0.0510310i
$289$	8.04834	+	13.9401i	0.473431	+	0.820007i
$290$	−0.537824	+	5.61971i	−0.0315821	+	0.330001i
$291$			16.9064i			0.991069i
$292$	−7.27002	+	12.5920i	−0.425446	+	0.736894i
$293$	0.829176	−	1.43617i	0.0484410	−	0.0839022i	−0.840788	−	0.541364i	$-0.817908\pi$
$293$	0.829176	−	1.43617i	0.0484410	−	0.0839022i	0.889229	+	0.457462i	$0.151241\pi$
$294$			0.867736i			0.0506074i
$295$	21.5977	+	2.06697i	1.25747	+	0.120344i
$296$	−5.18679	−	8.98379i	−0.301476	−	0.522172i
$297$	0.297434	+	0.515171i	0.0172589	+	0.0298933i
$298$			3.49115i			0.202237i
$299$	3.50361	+	16.3793i	0.202619	+	0.947237i
$300$	3.77735	+	3.27591i	0.218086	+	0.189135i
$301$	−10.3108	+	5.95294i	−0.594304	+	0.343122i
$302$	−3.94031	+	2.27494i	−0.226740	+	0.130908i
$303$	4.71741	+	2.72360i	0.271008	+	0.156467i
$304$			7.61611i			0.436814i
$305$	−1.45415	+	15.1944i	−0.0832645	+	0.870029i
$306$	−4.98222	−	2.87649i	−0.284814	−	0.164438i
$307$	−0.384087			−0.0219210			−0.0109605	−	0.999940i	$-0.503489\pi$
$307$	−0.384087			−0.0219210			−0.0109605	+	0.999940i	$0.503489\pi$
$308$	−1.44503	−	0.834288i	−0.0823382	−	0.0475380i
$309$	6.87645	+	11.9104i	0.391187	+	0.677556i
$310$	8.55410	−	12.0071i	0.485840	−	0.681960i
$311$	−11.6920			−0.662993			−0.331497	−	0.943456i	$-0.607554\pi$
$311$	−11.6920			−0.662993			−0.331497	+	0.943456i	$0.607554\pi$
$312$	0.754186	+	3.52579i	0.0426974	+	0.199609i
$313$			10.5788i			0.597948i	0.954261	+	0.298974i	$0.0966444\pi$
$313$			10.5788i			0.597948i	−0.954261	+	0.298974i	$0.903356\pi$
$314$	9.95560	−	5.74787i	0.561827	−	0.324371i
$315$	−5.10829	−	3.63924i	−0.287820	−	0.205048i
$316$	0.915751	−	1.58613i	0.0515150	−	0.0892266i
$317$	−22.1023			−1.24139			−0.620695	−	0.784052i	$-0.713150\pi$
$317$	−22.1023			−1.24139			−0.620695	+	0.784052i	$0.713150\pi$
$318$	6.94798	−	12.0343i	0.389624	−	0.674848i
$319$	1.30065	+	0.750930i	0.0728224	+	0.0420440i
$320$	2.03420	−	0.928463i	0.113715	−	0.0519027i
$321$	2.11545	−	3.66407i	0.118073	−	0.204509i
$322$	−11.2848	+	6.51527i	−0.628876	+	0.363082i
$323$	−21.9076	−	37.9451i	−1.21897	−	2.11132i
$324$	1.00000			0.0555556
$325$	9.32283	+	15.4300i	0.517138	+	0.855902i
$326$	−13.8289			−0.765910
$327$	0.223679	+	0.387423i	0.0123695	+	0.0214246i
$328$	−4.98222	+	2.87649i	−0.275097	+	0.158827i
$329$	4.06435	−	7.03966i	0.224075	−	0.388109i
$330$	1.21008	−	0.552314i	0.0666127	−	0.0304039i
$331$	−5.28809	−	3.05308i	−0.290660	−	0.167812i	0.347580	−	0.937650i	$-0.387004\pi$
$331$	−5.28809	−	3.05308i	−0.290660	−	0.167812i	−0.638239	+	0.769838i	$0.720337\pi$
$332$	−2.09592	+	3.63024i	−0.115029	+	0.199235i
$333$	−10.3736			−0.568469
$334$	−10.7700	+	18.6542i	−0.589309	+	1.02071i
$335$	−14.3188	−	10.2010i	−0.782321	−	0.557339i
$336$	−2.42916	+	1.40247i	−0.132521	+	0.0765112i
$337$		−	4.29852i		−	0.234155i	−0.993123	−	0.117078i	$-0.962647\pi$
$337$		−	4.29852i		−	0.234155i	0.993123	−	0.117078i	$-0.0373526\pi$
$338$	−1.32550	+	12.9322i	−0.0720979	+	0.703422i
$339$	9.36701			0.508746
$340$	−7.46410	+	10.4771i	−0.404798	+	0.568203i
$341$	−1.96101	−	3.39657i	−0.106195	−	0.183935i
$342$	6.59574	+	3.80805i	0.356657	+	0.205916i
$343$	17.2007			0.928750
$344$	−3.67593	−	2.12230i	−0.198193	−	0.114427i
$345$	0.989622	−	10.3405i	0.0532794	−	0.556715i
$346$			13.6650i			0.734636i
$347$	29.7444	+	17.1730i	1.59677	+	0.921893i	0.992105	+	0.125409i	$0.0400244\pi$
$347$	29.7444	+	17.1730i	1.59677	+	0.921893i	0.604660	+	0.796484i	$0.293309\pi$
$348$	2.18645	−	1.26235i	0.117206	−	0.0676689i
$349$	13.8581	−	8.00099i	0.741808	−	0.428283i	−0.0809181	−	0.996721i	$-0.525785\pi$
$349$	13.8581	−	8.00099i	0.741808	−	0.428283i	0.822726	+	0.568438i	$0.192452\pi$
$350$	−9.18876	+	10.5953i	−0.491160	+	0.566342i
$351$	3.43052	+	1.10975i	0.183107	+	0.0592341i
$352$		−	0.594869i		−	0.0317066i
$353$	−9.69607	−	16.7941i	−0.516070	−	0.893859i	−0.999826	−	0.0186563i	$-0.994061\pi$
$353$	−9.69607	−	16.7941i	−0.516070	−	0.893859i	0.483756	−	0.875203i	$-0.339272\pi$
$354$	−4.85147	−	8.40299i	−0.257853	−	0.446614i
$355$	−2.85958	−	0.273671i	−0.151771	−	0.0145249i
$356$		−	6.05447i		−	0.320886i
$357$	8.06839	−	13.9749i	0.427025	−	0.739628i
$358$	5.37886	−	9.31647i	0.284282	−	0.492391i
$359$			15.8342i			0.835699i	0.908516	+	0.417850i	$0.137216\pi$
$359$			15.8342i			0.835699i	−0.908516	+	0.417850i	$0.862784\pi$
$360$	0.213026	−	2.22590i	0.0112274	−	0.117315i
$361$	19.5026	+	33.7794i	1.02645	+	1.77786i
$362$	−2.93234	−	5.07897i	−0.154121	−	0.266945i
$363$			10.6461i			0.558777i
$364$	−9.88966	+	2.11545i	−0.518359	+	0.110880i
$365$	29.5773	−	13.4999i	1.54815	−	0.706617i
$366$	5.91165	−	3.41309i	0.309007	−	0.178405i
$367$	−13.2440	+	7.64645i	−0.691333	+	0.399141i	−0.804111	−	0.594479i	$-0.797358\pi$
$367$	−13.2440	+	7.64645i	−0.691333	+	0.399141i	0.112778	+	0.993620i	$0.464025\pi$
$368$	−4.02317	−	2.32278i	−0.209722	−	0.121083i
$369$			5.75297i			0.299488i
$370$	−2.20984	+	23.0905i	−0.114884	+	1.20042i
$371$	33.7555	+	19.4887i	1.75250	+	1.01180i
$372$	−6.59309			−0.341836
$373$	−18.7508	−	10.8258i	−0.970881	−	0.560538i	−0.0713760	−	0.997449i	$-0.522739\pi$
$373$	−18.7508	−	10.8258i	−0.970881	−	0.560538i	−0.899505	+	0.436911i	$0.856072\pi$
$374$	1.71113	+	2.96377i	0.0884805	+	0.153253i
$375$	−2.62893	−	10.8669i	−0.135757	−	0.561162i
$376$	2.89798			0.149452
$377$	8.90154	−	1.90409i	0.458453	−	0.0980655i
$378$			2.80495i			0.144271i
$379$	7.81479	−	4.51187i	0.401419	−	0.231759i	−0.285677	−	0.958326i	$-0.592218\pi$
$379$	7.81479	−	4.51187i	0.401419	−	0.231759i	0.687096	+	0.726567i	$0.258885\pi$
$380$	9.88140	−	13.8702i	0.506905	−	0.711528i
$381$	−3.34395	+	5.79190i	−0.171316	+	0.296728i
$382$	−13.8346			−0.707838
$383$	5.03703	−	8.72439i	0.257380	−	0.445795i	−0.708159	−	0.706053i	$-0.750474\pi$
$383$	5.03703	−	8.72439i	0.257380	−	0.445795i	0.965539	+	0.260257i	$0.0838074\pi$
$384$	−0.866025	−	0.500000i	−0.0441942	−	0.0255155i
$385$	1.54921	+	3.39421i	0.0789551	+	0.172985i
$386$	8.50322	−	14.7280i	0.432802	−	0.749636i
$387$	−3.67593	+	2.12230i	−0.186858	+	0.107883i
$388$	−8.45318	−	14.6413i	−0.429145	−	0.743301i
$389$	−24.3591			−1.23505			−0.617527	−	0.786550i	$-0.711865\pi$
$389$	−24.3591			−1.23505			−0.617527	+	0.786550i	$0.711865\pi$
$390$	3.20098	−	7.39958i	0.162088	−	0.374692i
$391$	26.7257			1.35158
$392$	−0.433868	−	0.751482i	−0.0219137	−	0.0379556i
$393$	−10.1086	+	5.83620i	−0.509911	+	0.294397i
$394$	3.16487	−	5.48171i	0.159444	−	0.276165i
$395$	−3.72564	+	1.70048i	−0.187457	+	0.0855606i
$396$	−0.515171	−	0.297434i	−0.0258883	−	0.0149466i
$397$	15.0190	−	26.0137i	0.753784	−	1.30559i	−0.192193	−	0.981357i	$-0.561560\pi$
$397$	15.0190	−	26.0137i	0.753784	−	1.30559i	0.945977	−	0.324234i	$-0.105107\pi$
$398$	−16.6356			−0.833869
$399$	−10.6814	+	18.5007i	−0.534739	+	0.926194i
$400$	−4.90924	−	0.948346i	−0.245462	−	0.0474173i
$401$	2.35786	−	1.36131i	0.117746	−	0.0679807i	−0.439970	−	0.898012i	$-0.645011\pi$
$401$	2.35786	−	1.36131i	0.117746	−	0.0679807i	0.557716	+	0.830032i	$0.311678\pi$
$402$			7.86242i			0.392142i
$403$	−22.6177	−	7.31669i	−1.12667	−	0.364470i
$404$	−5.44720			−0.271008
$405$	−1.82117	−	1.29743i	−0.0904947	−	0.0644700i
$406$	3.54082	+	6.13287i	0.175728	+	0.304369i
$407$	5.34417	+	3.08546i	0.264901	+	0.152941i
$408$	5.75297			0.284814
$409$	−33.1032	−	19.1121i	−1.63685	−	0.945034i	−0.981909	−	0.189352i	$-0.939361\pi$
$409$	−33.1032	−	19.1121i	−1.63685	−	0.945034i	−0.654938	−	0.755683i	$-0.727305\pi$
$410$	12.8055	+	1.22553i	0.632420	+	0.0605246i
$411$		−	6.80285i		−	0.335560i
$412$	−11.9104	−	6.87645i	−0.586781	−	0.338778i
$413$	23.5699	−	13.6081i	1.15980	−	0.669612i
$414$	−4.02317	+	2.32278i	−0.197728	+	0.114158i
$415$	8.52703	−	3.89197i	0.418575	−	0.191049i
$416$	−2.41604	−	2.67633i	−0.118456	−	0.131218i
$417$			7.09816i			0.347598i
$418$	−2.26529	−	3.92360i	−0.110799	−	0.191910i
$419$	14.9365	+	25.8708i	0.729695	+	1.26387i	0.957012	+	0.290048i	$0.0936714\pi$
$419$	14.9365	+	25.8708i	0.729695	+	1.26387i	−0.227317	+	0.973821i	$0.572995\pi$
$420$	6.24353	+	0.597526i	0.304653	+	0.0291563i
$421$		−	14.2033i		−	0.692226i	−0.938193	−	0.346113i	$-0.887501\pi$
$421$		−	14.2033i		−	0.692226i	0.938193	−	0.346113i	$-0.112499\pi$
$422$	−8.27443	+	14.3317i	−0.402793	+	0.697658i
$423$	1.44899	−	2.50973i	0.0704524	−	0.122027i
$424$			13.8960i			0.674848i
$425$	27.1868	−	9.39649i	1.31875	−	0.455797i
$426$	0.642342	+	1.11257i	0.0311216	+	0.0539042i
$427$	9.57355	+	16.5819i	0.463297	+	0.802453i
$428$			4.23091i			0.204509i
$429$	−1.43723	−	1.59207i	−0.0693899	−	0.0768657i
$430$	3.94095	+	8.63435i	0.190050	+	0.416385i
$431$	−8.09901	+	4.67596i	−0.390115	+	0.225233i	−0.682210	−	0.731156i	$-0.738981\pi$
$431$	−8.09901	+	4.67596i	−0.390115	+	0.225233i	0.292095	+	0.956389i	$0.405648\pi$
$432$	−0.866025	+	0.500000i	−0.0416667	+	0.0240563i
$433$	−3.42954	−	1.98005i	−0.164813	−	0.0951549i	0.415325	−	0.909673i	$-0.363668\pi$
$433$	−3.42954	−	1.98005i	−0.164813	−	0.0951549i	−0.580138	+	0.814518i	$0.697001\pi$
$434$		−	18.4933i		−	0.887705i
$435$	−5.61971	−	0.537824i	−0.269444	−	0.0257867i
$436$	−0.387423	−	0.223679i	−0.0185542	−	0.0107123i
$437$	−35.3810			−1.69250
$438$	−12.5920	−	7.27002i	−0.601671	−	0.347375i
$439$	−11.2992	−	19.5708i	−0.539281	−	0.934062i	−0.998943	−	0.0459680i	$-0.985363\pi$
$439$	−11.2992	−	19.5708i	−0.539281	−	0.934062i	0.459662	−	0.888094i	$-0.347971\pi$
$440$	−0.771803	+	1.08336i	−0.0367943	+	0.0516470i
$441$	−0.867736			−0.0413208
$442$	19.7357	+	6.38437i	0.938730	+	0.303673i
$443$		−	29.0428i		−	1.37987i	−0.723873	−	0.689933i	$-0.757640\pi$
$443$		−	29.0428i		−	1.37987i	0.723873	−	0.689933i	$-0.242360\pi$
$444$	8.98379	−	5.18679i	0.426352	−	0.246154i
$445$	−7.85528	+	11.0262i	−0.372376	+	0.522694i
$446$	−8.32779	+	14.4242i	−0.394332	+	0.683004i
$447$	−3.49115			−0.165125
$448$	1.40247	−	2.42916i	0.0662607	−	0.114767i
$449$	23.7886	+	13.7343i	1.12265	+	0.648164i	0.942077	−	0.335397i	$-0.108870\pi$
$449$	23.7886	+	13.7343i	1.12265	+	0.648164i	0.180576	+	0.983561i	$0.442204\pi$
$450$	−3.27591	+	3.77735i	−0.154428	+	0.178066i
$451$	1.71113	−	2.96377i	0.0805740	−	0.139558i
$452$	−8.11206	+	4.68350i	−0.381559	+	0.220293i
$453$	−2.27494	−	3.94031i	−0.106886	−	0.185132i
$454$	3.02210			0.141834
$455$	20.7554	+	8.97859i	0.973030	+	0.420923i
$456$	−7.61611			−0.356657
$457$	2.19087	+	3.79470i	0.102485	+	0.177508i	0.912708	−	0.408613i	$-0.133987\pi$
$457$	2.19087	+	3.79470i	0.102485	+	0.177508i	−0.810223	+	0.586122i	$0.800654\pi$
$458$	−14.2437	+	8.22361i	−0.665565	+	0.384264i
$459$	2.87649	−	4.98222i	0.134263	−	0.232550i
$460$	4.31323	+	9.44997i	0.201105	+	0.440607i
$461$	−21.0593	−	12.1586i	−0.980829	−	0.566282i	−0.0783090	−	0.996929i	$-0.524952\pi$
$461$	−21.0593	−	12.1586i	−0.980829	−	0.566282i	−0.902520	+	0.430647i	$0.858285\pi$
$462$	0.834288	−	1.44503i	0.0388146	−	0.0672288i
$463$	19.0660			0.886071			0.443035	−	0.896504i	$-0.353902\pi$
$463$	19.0660			0.886071			0.443035	+	0.896504i	$0.353902\pi$
$464$	−1.26235	+	2.18645i	−0.0586030	+	0.101503i
$465$	12.0071	+	8.55410i	0.556818	+	0.396687i
$466$	−11.9762	+	6.91443i	−0.554784	+	0.320305i
$467$			10.1176i			0.468188i	0.972214	+	0.234094i	$0.0752123\pi$
$467$			10.1176i			0.468188i	−0.972214	+	0.234094i	$0.924788\pi$
$468$	−3.52579	+	0.754186i	−0.162980	+	0.0348623i
$469$	−22.0537			−1.01834
$470$	−5.27773	−	3.75995i	−0.243443	−	0.173433i
$471$	5.74787	+	9.95560i	0.264848	+	0.458730i
$472$	8.40299	+	4.85147i	0.386779	+	0.223307i
$473$	2.52498			0.116099
$474$	1.58613	+	0.915751i	0.0728532	+	0.0420618i
$475$	−35.9914	+	12.4396i	−1.65140	+	0.570768i
$476$			16.1368i			0.739628i
$477$	12.0343	+	6.94798i	0.551011	+	0.318126i
$478$	−3.98559	+	2.30108i	−0.182297	+	0.105249i
$479$	−24.8215	+	14.3307i	−1.13412	+	0.654786i	−0.944969	−	0.327161i	$-0.893908\pi$
$479$	−24.8215	+	14.3307i	−1.13412	+	0.654786i	−0.189155	+	0.981947i	$0.560575\pi$
$480$	0.928463	+	2.03420i	0.0423784	+	0.0928479i
$481$	36.5751	−	7.82361i	1.66768	−	0.356726i
$482$		−	6.21354i		−	0.283019i
$483$	−6.51527	−	11.2848i	−0.296455	−	0.513475i
$484$	−5.32307	−	9.21982i	−0.241958	−	0.419083i
$485$	−3.60149	+	37.6318i	−0.163535	+	1.70877i
$486$			1.00000i			0.0453609i
$487$	8.71990	−	15.1033i	0.395136	−	0.684396i	−0.597982	−	0.801509i	$-0.704031\pi$
$487$	8.71990	−	15.1033i	0.395136	−	0.684396i	0.993119	+	0.117113i	$0.0373641\pi$
$488$	−3.41309	+	5.91165i	−0.154504	+	0.267608i
$489$		−	13.8289i		−	0.625363i
$490$	−0.184850	+	1.93149i	−0.00835067	+	0.0872559i
$491$	−11.2233	−	19.4394i	−0.506503	−	0.877288i	−0.999972	−	0.00752493i	$-0.997605\pi$
$491$	−11.2233	−	19.4394i	−0.506503	−	0.877288i	0.493469	−	0.869763i	$-0.335729\pi$
$492$	−2.87649	−	4.98222i	−0.129682	−	0.224616i
$493$		−	14.5245i		−	0.654150i
$494$	−26.1272	−	8.45199i	−1.17552	−	0.380273i
$495$	0.552314	+	1.21008i	0.0248247	+	0.0543890i
$496$	5.70978	−	3.29654i	0.256377	−	0.148019i
$497$	−3.12070	+	1.80174i	−0.139983	+	0.0808189i
$498$	−3.63024	−	2.09592i	−0.162675	−	0.0939204i
$499$			10.4136i			0.466177i	0.972456	+	0.233088i	$0.0748832\pi$
$499$			10.4136i			0.466177i	−0.972456	+	0.233088i	$0.925117\pi$
$500$	7.71015	+	8.09652i	0.344808	+	0.362087i
$501$	−18.6542	−	10.7700i	−0.833409	−	0.481169i
$502$	−16.3877			−0.731420
$503$	5.00387	+	2.88899i	0.223112	+	0.128814i	0.607390	−	0.794404i	$-0.292216\pi$
$503$	5.00387	+	2.88899i	0.223112	+	0.128814i	−0.384279	+	0.923217i	$0.625550\pi$
$504$	−1.40247	−	2.42916i	−0.0624712	−	0.108203i
$505$	9.92028	+	7.06738i	0.441447	+	0.314494i
$506$	2.76349			0.122852
$507$	−12.9322	−	1.32550i	−0.574341	−	0.0588677i
$508$		−	6.68791i		−	0.296728i
$509$	−6.18024	+	3.56816i	−0.273934	+	0.158156i	−0.630674	−	0.776048i	$-0.717222\pi$
$509$	−6.18024	+	3.56816i	−0.273934	+	0.158156i	0.356740	+	0.934204i	$0.383888\pi$
$510$	−10.4771	−	7.46410i	−0.463936	−	0.330516i
$511$	20.3920	−	35.3200i	0.902090	−	1.56247i
$512$	1.00000			0.0441942
$513$	−3.80805	+	6.59574i	−0.168130	+	0.291209i
$514$	−7.28269	−	4.20466i	−0.321226	−	0.185460i
$515$	12.7691	+	27.9761i	0.562672	+	1.23277i
$516$	2.12230	−	3.67593i	0.0934290	−	0.161824i
$517$	−1.49296	+	0.861960i	−0.0656603	+	0.0379090i
$518$	14.5487	+	25.1991i	0.639232	+	1.10718i
$519$	−13.6650			−0.599827
$520$	0.927657	+	8.00871i	0.0406805	+	0.351205i
$521$	1.09782			0.0480965			0.0240483	−	0.999711i	$-0.492344\pi$
$521$	1.09782			0.0480965			0.0240483	+	0.999711i	$0.492344\pi$
$522$	1.26235	+	2.18645i	0.0552514	+	0.0956982i
$523$	12.9411	−	7.47153i	0.565873	−	0.326707i	−0.189626	−	0.981856i	$-0.560728\pi$
$523$	12.9411	−	7.47153i	0.565873	−	0.326707i	0.755499	+	0.655149i	$0.227394\pi$
$524$	5.83620	−	10.1086i	0.254956	−	0.441596i
$525$	−10.5953	−	9.18876i	−0.462416	−	0.401031i
$526$	5.10152	+	2.94536i	0.222437	+	0.128424i
$527$	−18.9649	+	32.8482i	−0.826125	+	1.43089i
$528$	0.594869			0.0258883
$529$	−0.709414	+	1.22874i	−0.0308441	+	0.0534235i
$530$	18.0291	−	25.3069i	0.783134	−	1.09926i
$531$	8.40299	−	4.85147i	0.364659	−	0.210536i
$532$		−	21.3628i		−	0.926194i
$533$	−4.33881	−	20.2838i	−0.187935	−	0.878588i
$534$	6.05447			0.262003
$535$	5.48932	−	7.70520i	0.237324	−	0.333125i
$536$	−3.93121	−	6.80906i	−0.169802	−	0.294106i
$537$	9.31647	+	5.37886i	0.402035	+	0.232115i
$538$	−22.8455			−0.984941
$539$	0.447033	+	0.258095i	0.0192551	+	0.0111169i
$540$	2.22590	+	0.213026i	0.0957874	+	0.00916716i
$541$		−	19.3888i		−	0.833589i	−0.909001	−	0.416794i	$-0.863154\pi$
$541$		−	19.3888i		−	0.833589i	0.909001	−	0.416794i	$-0.136846\pi$
$542$	23.2565	+	13.4271i	0.998950	+	0.576744i
$543$	5.07897	−	2.93234i	0.217959	−	0.125839i
$544$	−4.98222	+	2.87649i	−0.213611	+	0.123328i
$545$	0.415355	+	0.910014i	0.0177919	+	0.0389807i
$546$	−2.11545	−	9.88966i	−0.0905330	−	0.423239i
$547$			26.1335i			1.11739i	0.829374	+	0.558693i	$0.188697\pi$
$547$			26.1335i			1.11739i	−0.829374	+	0.558693i	$0.811303\pi$
$548$	3.40142	+	5.89144i	0.145302	+	0.251670i
$549$	3.41309	+	5.91165i	0.145667	+	0.252303i
$550$	2.81117	−	0.971616i	0.119869	−	0.0414298i
$551$			19.2283i			0.819155i
$552$	2.32278	−	4.02317i	0.0988640	−	0.171237i
$553$	−2.56863	+	4.44901i	−0.109229	+	0.189191i
$554$			10.6250i			0.451412i
$555$	−23.0905	−	2.20984i	−0.980139	−	0.0938024i
$556$	−3.54908	−	6.14719i	−0.150514	−	0.260699i
$557$	−17.6927	−	30.6446i	−0.749663	−	1.29846i	−0.947984	−	0.318318i	$-0.896882\pi$
$557$	−17.6927	−	30.6446i	−0.749663	−	1.29846i	0.198321	−	0.980137i	$-0.436451\pi$
$558$		−	6.59309i		−	0.279108i
$559$	11.3600	−	10.2551i	0.480475	−	0.433745i
$560$	−5.70582	+	2.60429i	−0.241115	+	0.110051i
$561$	−2.96377	+	1.71113i	−0.125130	+	0.0722440i
$562$	24.5719	−	14.1866i	1.03650	−	0.598425i
$563$	25.8011	+	14.8963i	1.08739	+	0.627804i	0.932880	−	0.360187i	$-0.117287\pi$
$563$	25.8011	+	14.8963i	1.08739	+	0.627804i	0.154509	+	0.987991i	$0.450621\pi$
$564$			2.89798i			0.122027i
$565$	20.8500	+	1.99541i	0.877166	+	0.0839476i
$566$	−4.91005	−	2.83482i	−0.206385	−	0.119156i
$567$	−2.80495			−0.117797
$568$	−1.11257	−	0.642342i	−0.0466824	−	0.0269521i
$569$	−7.14388	−	12.3736i	−0.299487	−	0.518727i	0.676532	−	0.736414i	$-0.263482\pi$
$569$	−7.14388	−	12.3736i	−0.299487	−	0.518727i	−0.976019	+	0.217687i	$0.930149\pi$
$570$	13.8702	+	9.88140i	0.580960	+	0.413886i
$571$	−37.4439			−1.56698			−0.783490	−	0.621404i	$-0.786562\pi$
$571$	−37.4439			−1.56698			−0.783490	+	0.621404i	$0.786562\pi$
$572$	2.04071	+	0.660156i	0.0853263	+	0.0276025i
$573$		−	13.8346i		−	0.577947i
$574$	13.9749	−	8.06839i	0.583300	−	0.336768i
$575$	4.40559	−	22.8061i	0.183726	−	0.951082i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	47.6052			1.98183			0.990916	−	0.134485i	$-0.0429381\pi$
$577$	47.6052			1.98183			0.990916	+	0.134485i	$0.0429381\pi$
$578$	8.04834	−	13.9401i	0.334767	−	0.579833i
$579$	14.7280	+	8.50322i	0.612075	+	0.353382i
$580$	5.13572	−	2.34408i	0.213249	−	0.0973328i
$581$	5.87895	−	10.1826i	0.243900	−	0.422447i
$582$	14.6413	−	8.45318i	0.606903	−	0.350396i
$583$	−4.13314	−	7.15881i	−0.171177	−	0.296487i
$584$	14.5400			0.601671
$585$	7.39958	+	3.20098i	0.305935	+	0.132344i
$586$	−1.65835			−0.0685059
$587$	18.8016	+	32.5654i	0.776027	+	1.34412i	0.934216	+	0.356709i	$0.116101\pi$
$587$	18.8016	+	32.5654i	0.776027	+	1.34412i	−0.158189	+	0.987409i	$0.550565\pi$
$588$	0.751482	−	0.433868i	0.0309906	−	0.0178924i
$589$	25.1068	−	43.4863i	1.03451	−	1.79182i
$590$	−9.00882	−	19.7377i	−0.370887	−	0.812587i
$591$	5.48171	+	3.16487i	0.225487	+	0.130185i
$592$	−5.18679	+	8.98379i	−0.213176	+	0.369231i
$593$	24.0046			0.985752			0.492876	−	0.870100i	$-0.335946\pi$
$593$	24.0046			0.985752			0.492876	+	0.870100i	$0.335946\pi$
$594$	0.297434	−	0.515171i	0.0122039	−	0.0211377i
$595$	20.9364	−	29.3878i	0.858310	−	1.20478i
$596$	3.02342	−	1.74557i	0.123844	−	0.0715014i
$597$		−	16.6356i		−	0.680851i
$598$	12.4330	−	11.2238i	0.508425	−	0.458977i
$599$	−23.7092			−0.968731			−0.484365	−	0.874866i	$-0.660949\pi$
$599$	−23.7092			−0.968731			−0.484365	+	0.874866i	$0.660949\pi$
$600$	0.948346	−	4.90924i	0.0387161	−	0.200419i
$601$	0.918249	+	1.59045i	0.0374562	+	0.0648760i	0.884146	−	0.467211i	$-0.154741\pi$
$601$	0.918249	+	1.59045i	0.0374562	+	0.0648760i	−0.846690	+	0.532087i	$0.821408\pi$
$602$	10.3108	+	5.95294i	0.420237	+	0.242624i
$603$	−7.86242			−0.320183
$604$	3.94031	+	2.27494i	0.160329	+	0.0925661i
$605$	−2.26790	+	23.6972i	−0.0922032	+	0.963428i
$606$		−	5.44720i		−	0.221277i
$607$	−30.2214	−	17.4483i	−1.22665	−	0.708206i	−0.260321	−	0.965522i	$-0.583828\pi$
$607$	−30.2214	−	17.4483i	−1.22665	−	0.708206i	−0.966327	+	0.257316i	$0.917162\pi$
$608$	6.59574	−	3.80805i	0.267493	−	0.154437i
$609$	−6.13287	+	3.54082i	−0.248517	+	0.143481i
$610$	13.8858	−	6.33786i	0.562220	−	0.256613i
$611$	−3.21604	+	9.94159i	−0.130107	+	0.402194i
$612$			5.75297i			0.232550i
$613$	−4.70575	−	8.15061i	−0.190064	−	0.329200i	0.755207	−	0.655486i	$-0.227536\pi$
$613$	−4.70575	−	8.15061i	−0.190064	−	0.329200i	−0.945271	+	0.326286i	$0.894203\pi$
$614$	0.192044	+	0.332629i	0.00775025	+	0.0134238i
$615$	−1.22553	+	12.8055i	−0.0494181	+	0.516369i
$616$			1.66858i			0.0672288i
$617$	5.47577	−	9.48432i	0.220446	−	0.381824i	−0.734497	−	0.678612i	$-0.762582\pi$
$617$	5.47577	−	9.48432i	0.220446	−	0.381824i	0.954944	+	0.296787i	$0.0959153\pi$
$618$	6.87645	−	11.9104i	0.276611	−	0.479105i
$619$			1.00216i			0.0402803i	0.999797	+	0.0201402i	$0.00641125\pi$
$619$			1.00216i			0.0402803i	−0.999797	+	0.0201402i	$0.993589\pi$
$620$	−14.6755	−	1.40450i	−0.589384	−	0.0564059i
$621$	−2.32278	−	4.02317i	−0.0932098	−	0.161444i
$622$	5.84601	+	10.1256i	0.234404	+	0.405999i
$623$			16.9825i			0.680389i
$624$	2.67633	−	2.41604i	0.107139	−	0.0967190i
$625$	−3.53680	−	24.7486i	−0.141472	−	0.989942i
$626$	9.16150	−	5.28939i	0.366167	−	0.211407i
$627$	3.92360	−	2.26529i	0.156694	−	0.0904671i
$628$	−9.95560	−	5.74787i	−0.397272	−	0.229365i
$629$		−	59.6789i		−	2.37955i
$630$	−0.597526	+	6.24353i	−0.0238060	+	0.248748i
$631$	−33.5167	−	19.3509i	−1.33428	−	0.770346i	−0.348327	−	0.937373i	$-0.613250\pi$
$631$	−33.5167	−	19.3509i	−1.33428	−	0.770346i	−0.985952	+	0.167027i	$0.946583\pi$
$632$	−1.83150			−0.0728532
$633$	−14.3317	−	8.27443i	−0.569635	−	0.328879i
$634$	11.0512	+	19.1412i	0.438898	+	0.760193i
$635$	−8.67712	+	12.1798i	−0.344341	+	0.483341i
$636$	−13.8960			−0.551011
$637$	3.05946	−	0.654435i	0.121220	−	0.0259296i
$638$		−	1.50186i		−	0.0594592i
$639$	−1.11257	+	0.642342i	−0.0440126	+	0.0254107i
$640$	−1.82117	−	1.29743i	−0.0719881	−	0.0512856i
$641$	4.99961	−	8.65957i	0.197473	−	0.342033i	−0.750236	−	0.661170i	$-0.770060\pi$
$641$	4.99961	−	8.65957i	0.197473	−	0.342033i	0.947708	+	0.319138i	$0.103393\pi$
$642$	−4.23091			−0.166981
$643$	−3.38728	+	5.86694i	−0.133581	+	0.231369i	−0.925055	−	0.379834i	$-0.875981\pi$
$643$	−3.38728	+	5.86694i	−0.133581	+	0.231369i	0.791473	+	0.611204i	$0.209314\pi$
$644$	11.2848	+	6.51527i	0.444683	+	0.256738i
$645$	−8.63435	+	3.94095i	−0.339977	+	0.155175i
$646$	−21.9076	+	37.9451i	−0.861944	+	1.49293i
$647$	−14.8850	+	8.59384i	−0.585188	+	0.337859i	−0.763193	−	0.646171i	$-0.776369\pi$
$647$	−14.8850	+	8.59384i	−0.585188	+	0.337859i	0.178004	+	0.984030i	$0.443036\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	−5.77197			−0.226570
$650$	8.70135	−	15.7888i	0.341295	−	0.619288i
$651$	18.4933			0.724808
$652$	6.91443	+	11.9762i	0.270790	+	0.469022i
$653$	21.5401	−	12.4362i	0.842930	−	0.486666i	−0.0153292	−	0.999883i	$-0.504880\pi$
$653$	21.5401	−	12.4362i	0.842930	−	0.486666i	0.858259	+	0.513217i	$0.171546\pi$
$654$	0.223679	−	0.387423i	0.00874654	−	0.0151495i
$655$	−23.7440	+	10.8374i	−0.927753	+	0.423452i
$656$	4.98222	+	2.87649i	0.194523	+	0.112308i
$657$	7.27002	−	12.5920i	0.283631	−	0.491262i
$658$	−8.12870			−0.316890
$659$	−4.12151	+	7.13867i	−0.160551	+	0.278083i	−0.935067	−	0.354472i	$-0.884661\pi$
$659$	−4.12151	+	7.13867i	−0.160551	+	0.278083i	0.774515	+	0.632555i	$0.217994\pi$
$660$	−1.08336	−	0.771803i	−0.0421696	−	0.0300424i
$661$	22.3962	−	12.9305i	0.871112	−	0.502937i	0.00339467	−	0.999994i	$-0.498919\pi$
$661$	22.3962	−	12.9305i	0.871112	−	0.502937i	0.867718	+	0.497057i	$0.165586\pi$
$662$			6.10616i			0.237323i
$663$	−6.38437	+	19.7357i	−0.247948	+	0.766470i
$664$	4.19184			0.162675
$665$	−27.7168	+	38.9053i	−1.07481	+	1.50868i
$666$	5.18679	+	8.98379i	0.200984	+	0.348115i
$667$	−10.1573	−	5.86430i	−0.393291	−	0.227067i
$668$	21.5400			0.833409
$669$	−14.4242	−	8.32779i	−0.557670	−	0.321971i
$670$	−1.67490	+	17.5009i	−0.0647069	+	0.676121i
$671$		−	4.06069i		−	0.156761i
$672$	2.42916	+	1.40247i	0.0937068	+	0.0541016i
$673$	−5.99820	+	3.46306i	−0.231213	+	0.133491i	−0.611132	−	0.791529i	$-0.709285\pi$
$673$	−5.99820	+	3.46306i	−0.231213	+	0.133491i	0.379918	+	0.925020i	$0.375952\pi$
$674$	−3.72263	+	2.14926i	−0.143390	+	0.0827864i
$675$	−3.77735	−	3.27591i	−0.145390	−	0.126090i
$676$	11.8624	−	5.31820i	0.456246	−	0.204546i
$677$		−	4.72639i		−	0.181650i	−0.995867	−	0.0908250i	$-0.971050\pi$
$677$		−	4.72639i		−	0.181650i	0.995867	−	0.0908250i	$-0.0289504\pi$
$678$	−4.68350	−	8.11206i	−0.179869	−	0.311542i
$679$	23.7107	+	41.0682i	0.909935	+	1.57605i
$680$	12.8055	+	1.22553i	0.491069	+	0.0469969i
$681$			3.02210i			0.115807i
$682$	−1.96101	+	3.39657i	−0.0750910	+	0.130061i
$683$	−9.78995	+	16.9567i	−0.374602	+	0.648830i	−0.990267	−	0.139178i	$-0.955554\pi$
$683$	−9.78995	+	16.9567i	−0.374602	+	0.648830i	0.615665	+	0.788008i	$0.288887\pi$
$684$		−	7.61611i		−	0.291209i
$685$	1.44918	−	15.1424i	0.0553703	−	0.578563i
$686$	−8.60034	−	14.8962i	−0.328363	−	0.568741i
$687$	−8.22361	−	14.2437i	−0.313750	−	0.543432i
$688$			4.24460i			0.161824i
$689$	−47.6704	−	15.4211i	−1.81610	−	0.587496i
$690$	−9.44997	+	4.31323i	−0.359754	+	0.164202i
$691$	−10.7079	+	6.18224i	−0.407350	+	0.235183i	−0.689650	−	0.724143i	$-0.742236\pi$
$691$	−10.7079	+	6.18224i	−0.407350	+	0.235183i	0.282301	+	0.959326i	$0.408902\pi$
$692$	11.8342	−	6.83251i	0.449871	−	0.259733i
$693$	1.44503	+	0.834288i	0.0548921	+	0.0316920i
$694$		−	34.3459i		−	1.30375i
$695$	−1.51209	+	15.7998i	−0.0573568	+	0.599320i
$696$	−2.18645	−	1.26235i	−0.0828771	−	0.0478491i
$697$	−33.0967			−1.25363
$698$	−13.8581	−	8.00099i	−0.524538	−	0.302842i
$699$	−6.91443	−	11.9762i	−0.261528	−	0.452980i
$700$	13.7702	+	2.66006i	0.520463	+	0.100541i
$701$	43.7550			1.65260			0.826302	−	0.563227i	$-0.190441\pi$
$701$	43.7550			1.65260			0.826302	+	0.563227i	$0.190441\pi$
$702$	−0.754186	−	3.52579i	−0.0284649	−	0.133072i
$703$			79.0063i			2.97978i
$704$	−0.515171	+	0.297434i	−0.0194163	+	0.0112100i
$705$	3.75995	−	5.27773i	0.141608	−	0.198771i
$706$	−9.69607	+	16.7941i	−0.364916	+	0.632054i
$707$	15.2791			0.574630
$708$	−4.85147	+	8.40299i	−0.182329	+	0.315804i
$709$	16.4104	+	9.47457i	0.616307	+	0.355825i	0.775430	−	0.631434i	$-0.217533\pi$
$709$	16.4104	+	9.47457i	0.616307	+	0.355825i	−0.159123	+	0.987259i	$0.550867\pi$
$710$	1.19278	+	2.61330i	0.0447643	+	0.0980754i
$711$	−0.915751	+	1.58613i	−0.0343434	+	0.0594844i
$712$	−5.24333	+	3.02724i	−0.196502	+	0.113451i
$713$	15.3143	+	26.5251i	0.573524	+	0.993372i
$714$	−16.1368			−0.603904
$715$	−2.85997	−	3.84994i	−0.106957	−	0.143980i
$716$	−10.7577			−0.402035
$717$	−2.30108	−	3.98559i	−0.0859355	−	0.148845i
$718$	13.7129	−	7.91712i	0.511759	−	0.295464i
$719$	−23.5155	+	40.7301i	−0.876981	+	1.51898i	−0.0223436	+	0.999750i	$0.507113\pi$
$719$	−23.5155	+	40.7301i	−0.876981	+	1.51898i	−0.854637	+	0.519225i	$0.826221\pi$
$720$	−2.03420	+	0.928463i	−0.0758100	+	0.0346018i
$721$	33.4079	+	19.2881i	1.24418	+	0.718326i
$722$	19.5026	−	33.7794i	0.725810	−	1.25714i
$723$	6.21354			0.231084
$724$	−2.93234	+	5.07897i	−0.108980	+	0.188758i
$725$	−12.3943	−	2.39428i	−0.460314	−	0.0889214i
$726$	9.21982	−	5.32307i	0.342180	−	0.197557i
$727$		−	4.10440i		−	0.152224i	−0.997099	−	0.0761119i	$-0.975749\pi$
$727$		−	4.10440i		−	0.152224i	0.997099	−	0.0761119i	$-0.0242506\pi$
$728$	6.77687	+	7.50697i	0.251167	+	0.278227i
$729$	−1.00000			−0.0370370
$730$	−26.4799	−	18.8647i	−0.980065	−	0.698216i
$731$	−12.2095	−	21.1475i	−0.451586	−	0.782169i
$732$	−5.91165	−	3.41309i	−0.218501	−	0.126152i
$733$	−24.2968			−0.897421			−0.448711	−	0.893677i	$-0.648117\pi$
$733$	−24.2968			−0.897421			−0.448711	+	0.893677i	$0.648117\pi$
$734$	13.2440	+	7.64645i	0.488847	+	0.282236i
$735$	−1.93149	−	0.184850i	−0.0712442	−	0.00681830i
$736$			4.64555i			0.171237i
$737$	4.05050	+	2.33855i	0.149202	+	0.0861418i
$738$	4.98222	−	2.87649i	0.183398	−	0.105885i
$739$	−35.0414	+	20.2311i	−1.28902	+	0.744215i	−0.978479	−	0.206346i	$-0.933843\pi$
$739$	−35.0414	+	20.2311i	−1.28902	+	0.744215i	−0.310539	+	0.950561i	$0.600509\pi$
$740$	21.1019	−	9.63149i	0.775722	−	0.354061i
$741$	8.45199	−	26.1272i	0.310492	−	0.959806i
$742$		−	38.9775i		−	1.43091i
$743$	−15.7497	−	27.2794i	−0.577802	−	1.00078i	−0.995731	−	0.0923027i	$-0.970577\pi$
$743$	−15.7497	−	27.2794i	−0.577802	−	1.00078i	0.417929	−	0.908480i	$-0.362756\pi$
$744$	3.29654	+	5.70978i	0.120857	+	0.209331i
$745$	−7.77093	−	0.743703i	−0.284705	−	0.0272472i
$746$			21.6516i			0.792721i
$747$	2.09592	−	3.63024i	0.0766857	−	0.132824i
$748$	1.71113	−	2.96377i	0.0625651	−	0.108366i
$749$		−	11.8675i		−	0.433628i
$750$	−8.09652	+	7.71015i	−0.295643	+	0.281535i
$751$	−8.37551	−	14.5068i	−0.305627	−	0.529361i	0.671774	−	0.740756i	$-0.265533\pi$
$751$	−8.37551	−	14.5068i	−0.305627	−	0.529361i	−0.977401	+	0.211395i	$0.932199\pi$
$752$	−1.44899	−	2.50973i	−0.0528393	−	0.0915204i
$753$		−	16.3877i		−	0.597202i
$754$	−6.09976	−	6.75692i	−0.222140	−	0.246072i
$755$	−4.22440	−	9.25536i	−0.153742	−	0.336837i
$756$	2.42916	−	1.40247i	0.0883476	−	0.0510075i
$757$	−23.1908	+	13.3892i	−0.842885	+	0.486640i	−0.858244	−	0.513242i	$-0.828444\pi$
$757$	−23.1908	+	13.3892i	−0.842885	+	0.486640i	0.0153589	+	0.999882i	$0.495111\pi$
$758$	−7.81479	−	4.51187i	−0.283846	−	0.163879i
$759$			2.76349i			0.100308i
$760$	−16.9527	−	1.62243i	−0.614938	−	0.0588516i
$761$	−0.217029	−	0.125302i	−0.00786729	−	0.00454218i	0.496061	−	0.868288i	$-0.334779\pi$
$761$	−0.217029	−	0.125302i	−0.00786729	−	0.00454218i	−0.503928	+	0.863745i	$0.668112\pi$
$762$	6.68791			0.242277
$763$	1.08670	+	0.627408i	0.0393413	+	0.0227137i
$764$	6.91728	+	11.9811i	0.250259	+	0.433461i
$765$	7.46410	−	10.4771i	0.269865	−	0.378802i
$766$	−10.0741			−0.363990
$767$	−25.9683	+	23.4427i	−0.937660	+	0.846466i
$768$			1.00000i			0.0360844i
$769$	17.1777	−	9.91755i	0.619444	−	0.357636i	−0.157209	−	0.987565i	$-0.550250\pi$
$769$	17.1777	−	9.91755i	0.619444	−	0.357636i	0.776652	+	0.629929i	$0.216916\pi$
$770$	2.16487	−	3.03876i	0.0780164	−	0.109509i
$771$	4.20466	−	7.28269i	0.151427	−	0.262280i
$772$	−17.0064			−0.612075
$773$	−18.3185	+	31.7285i	−0.658869	+	1.14120i	0.322039	+	0.946726i	$0.395632\pi$
$773$	−18.3185	+	31.7285i	−0.658869	+	1.14120i	−0.980909	+	0.194469i	$0.937702\pi$
$774$	3.67593	+	2.12230i	0.132129	+	0.0762845i
$775$	24.9044	+	21.5984i	0.894593	+	0.775836i
$776$	−8.45318	+	14.6413i	−0.303452	+	0.525594i
$777$	−25.1991	+	14.5487i	−0.904011	+	0.521931i
$778$	12.1795	+	21.0956i	0.436658	+	0.756313i
$779$	43.8152			1.56984
$780$	−8.00871	+	0.927657i	−0.286758	+	0.0332154i
$781$	0.764218			0.0273459
$782$	−13.3629	−	23.1452i	−0.477855	−	0.827669i
$783$	−2.18645	+	1.26235i	−0.0781373	+	0.0451126i
$784$	−0.433868	+	0.751482i	−0.0154953	+	0.0268386i
$785$	10.6734	+	23.3846i	0.380949	+	0.834632i
$786$	10.1086	+	5.83620i	0.360562	+	0.208170i
$787$	17.9505	−	31.0911i	0.639865	−	1.10828i	−0.345597	−	0.938383i	$-0.612323\pi$
$787$	17.9505	−	31.0911i	0.639865	−	1.10828i	0.985462	−	0.169896i	$-0.0543432\pi$
$788$	−6.32974			−0.225487
$789$	−2.94536	+	5.10152i	−0.104858	+	0.181619i
$790$	3.33548	+	2.37625i	0.118671	+	0.0845433i
$791$	22.7539	−	13.1370i	0.809036	−	0.467097i
$792$			0.594869i			0.0211377i
$793$	−16.4923	−	18.2691i	−0.585660	−	0.648756i
$794$	−30.0381			−1.06601
$795$	25.3069	+	18.0291i	0.897545	+	0.639427i
$796$	8.31782	+	14.4069i	0.294817	+	0.510638i
$797$	4.30187	+	2.48369i	0.152380	+	0.0879767i	0.574251	−	0.818679i	$-0.305293\pi$
$797$	4.30187	+	2.48369i	0.152380	+	0.0879767i	−0.421871	+	0.906656i	$0.638627\pi$
$798$	21.3628			0.756235
$799$	14.4384	+	8.33601i	0.510794	+	0.294907i
$800$	1.63333	+	4.72570i	0.0577469	+	0.167079i
$801$			6.05447i			0.213924i
$802$	−2.35786	−	1.36131i	−0.0832590	−	0.0480696i
$803$	−7.49061	+	4.32471i	−0.264338	+	0.152616i
$804$	6.80906	−	3.93121i	0.240137	−	0.138643i
$805$	−12.0984	−	26.5067i	−0.426412	−	0.934238i
$806$	4.97241	+	23.2458i	0.175146	+	0.818800i
$807$		−	22.8455i		−	0.804201i
$808$	2.72360	+	4.71741i	0.0958159	+	0.165958i
$809$	20.1296	+	34.8656i	0.707720	+	1.22581i	0.965701	+	0.259658i	$0.0836097\pi$
$809$	20.1296	+	34.8656i	0.707720	+	1.22581i	−0.257980	+	0.966150i	$0.583057\pi$
$810$	−0.213026	+	2.22590i	−0.00748496	+	0.0782101i
$811$		−	7.62969i		−	0.267914i	−0.990987	−	0.133957i	$-0.957232\pi$
$811$		−	7.62969i		−	0.267914i	0.990987	−	0.133957i	$-0.0427685\pi$
$812$	3.54082	−	6.13287i	0.124258	−	0.215222i
$813$	−13.4271	+	23.2565i	−0.470910	+	0.815639i
$814$		−	6.17092i		−	0.216291i
$815$	2.94590	−	30.7816i	0.103190	−	1.07823i
$816$	−2.87649	−	4.98222i	−0.100697	−	0.174413i
$817$	16.1637	+	27.9963i	0.565495	+	0.979466i
$818$			38.2243i			1.33648i
$819$	9.88966	−	2.11545i	0.345573	−	0.0739199i
$820$	−5.34142	−	11.7027i	−0.186531	−	0.408675i
$821$	−20.8682	+	12.0483i	−0.728306	+	0.420487i	−0.817802	−	0.575500i	$-0.804808\pi$
$821$	−20.8682	+	12.0483i	−0.728306	+	0.420487i	0.0894964	+	0.995987i	$0.471474\pi$
$822$	−5.89144	+	3.40142i	−0.205487	+	0.118638i
$823$	18.6227	+	10.7518i	0.649145	+	0.374784i	0.788129	−	0.615511i	$-0.211050\pi$
$823$	18.6227	+	10.7518i	0.649145	+	0.374784i	−0.138984	+	0.990295i	$0.544384\pi$
$824$			13.7529i			0.479105i
$825$	0.971616	+	2.81117i	0.0338273	+	0.0978724i
$826$	−23.5699	−	13.6081i	−0.820103	−	0.473487i
$827$	−38.8887			−1.35229			−0.676147	−	0.736767i	$-0.736352\pi$
$827$	−38.8887			−1.35229			−0.676147	+	0.736767i	$0.736352\pi$
$828$	4.02317	+	2.32278i	0.139815	+	0.0807221i
$829$	12.2944	+	21.2945i	0.427001	+	0.739587i	0.996605	−	0.0823320i	$-0.0262368\pi$
$829$	12.2944	+	21.2945i	0.427001	+	0.739587i	−0.569604	+	0.821919i	$0.692903\pi$
$830$	−7.63406	−	5.43864i	−0.264982	−	0.188778i
$831$	−10.6250			−0.368576
$832$	−1.10975	+	3.43052i	−0.0384737	+	0.118932i
$833$		−	4.99206i		−	0.172965i
$834$	6.14719	−	3.54908i	0.212860	−	0.122895i
$835$	−39.2281	−	27.9468i	−1.35754	−	0.967139i
$836$	−2.26529	+	3.92360i	−0.0783468	+	0.135701i
$837$	6.59309			0.227890
$838$	14.9365	−	25.8708i	0.515972	−	0.893690i
$839$	45.1686	+	26.0781i	1.55939	+	0.900316i	0.997315	+	0.0732324i	$0.0233315\pi$
$839$	45.1686	+	26.0781i	1.55939	+	0.900316i	0.562079	+	0.827084i	$0.310002\pi$
$840$	−2.60429	−	5.70582i	−0.0898566	−	0.196869i
$841$	11.3130	−	19.5946i	0.390102	−	0.675677i
$842$	−12.3004	+	7.10165i	−0.423900	+	0.244739i
$843$	14.1866	+	24.5719i	0.488612	+	0.846301i
$844$	16.5489			0.569635
$845$	−28.5035	−	5.70533i	−0.980550	−	0.196269i
$846$	−2.89798			−0.0996348
$847$	14.9309	+	25.8611i	0.513033	+	0.888599i
$848$	12.0343	−	6.94798i	0.413258	−	0.238595i
$849$	2.83482	−	4.91005i	0.0972907	−	0.168512i
$850$	−21.7310	−	18.8462i	−0.745367	−	0.646420i
$851$	−41.7347	−	24.0955i	−1.43065	−	0.825984i
$852$	0.642342	−	1.11257i	0.0220063	−	0.0381160i
$853$	2.06762			0.0707938			0.0353969	−	0.999373i	$-0.488730\pi$
$853$	2.06762			0.0707938			0.0353969	+	0.999373i	$0.488730\pi$
$854$	9.57355	−	16.5819i	0.327600	−	0.567420i
$855$	−9.88140	+	13.8702i	−0.337937	+	0.474352i
$856$	3.66407	−	2.11545i	0.125235	−	0.0723047i
$857$		−	20.1793i		−	0.689310i	−0.938729	−	0.344655i	$-0.887996\pi$
$857$		−	20.1793i		−	0.689310i	0.938729	−	0.344655i	$-0.112004\pi$
$858$	−0.660156	+	2.04071i	−0.0225374	+	0.0696686i
$859$	−34.4160			−1.17426			−0.587129	−	0.809493i	$-0.699742\pi$
$859$	−34.4160			−1.17426			−0.587129	+	0.809493i	$0.699742\pi$
$860$	5.50709	−	7.73014i	0.187790	−	0.263596i
$861$	8.06839	+	13.9749i	0.274970	+	0.476262i
$862$	8.09901	+	4.67596i	0.275853	+	0.159264i
$863$	1.02382			0.0348514			0.0174257	−	0.999848i	$-0.494453\pi$
$863$	1.02382			0.0348514			0.0174257	+	0.999848i	$0.494453\pi$
$864$	0.866025	+	0.500000i	0.0294628	+	0.0170103i
$865$	−30.4169	−	2.91100i	−1.03421	−	0.0989769i
$866$			3.96009i			0.134569i
$867$	13.9401	+	8.04834i	0.473431	+	0.273336i
$868$	−16.0156	+	9.24663i	−0.543606	+	0.313851i
$869$	0.943538	−	0.544752i	0.0320073	−	0.0184794i
$870$	2.34408	+	5.13572i	0.0794719	+	0.174117i
$871$	27.7213	−	5.92973i	0.939299	−	0.200921i
$872$			0.447358i			0.0151495i
$873$	8.45318	+	14.6413i	0.286097	+	0.495534i
$874$	17.6905	+	30.6409i	0.598391	+	1.03644i
$875$	−21.6266	−	22.7103i	−0.731112	−	0.767749i
$876$			14.5400i			0.491262i
$877$	−7.46097	+	12.9228i	−0.251939	+	0.436371i	−0.964060	−	0.265686i	$-0.914402\pi$
$877$	−7.46097	+	12.9228i	−0.251939	+	0.436371i	0.712121	+	0.702057i	$0.247735\pi$
$878$	−11.2992	+	19.5708i	−0.381329	+	0.660481i
$879$		−	1.65835i		−	0.0559348i
$880$	1.32412	+	0.126722i	0.0446360	+	0.00427181i
$881$	21.5282	+	37.2879i	0.725303	+	1.25626i	0.958849	+	0.283916i	$0.0916336\pi$
$881$	21.5282	+	37.2879i	0.725303	+	1.25626i	−0.233546	+	0.972346i	$0.575033\pi$
$882$	0.433868	+	0.751482i	0.0146091	+	0.0253037i
$883$		−	30.1817i		−	1.01569i	−0.861447	−	0.507847i	$-0.830441\pi$
$883$		−	30.1817i		−	1.01569i	0.861447	−	0.507847i	$-0.169559\pi$
$884$	−4.33881	−	20.2838i	−0.145930	−	0.682217i
$885$	19.7377	−	9.00882i	0.663475	−	0.302828i
$886$	−25.1518	+	14.5214i	−0.844992	+	0.487856i
$887$	18.7593	−	10.8307i	0.629877	−	0.363660i	−0.150827	−	0.988560i	$-0.548194\pi$
$887$	18.7593	−	10.8307i	0.629877	−	0.363660i	0.780705	+	0.624900i	$0.214860\pi$
$888$	−8.98379	−	5.18679i	−0.301476	−	0.174057i
$889$			18.7592i			0.629164i
$890$	13.4766	+	1.28976i	0.451738	+	0.0432328i
$891$	0.515171	+	0.297434i	0.0172589	+	0.00996443i
$892$	16.6556			0.557670
$893$	−19.1144	−	11.0357i	−0.639638	−	0.369295i
$894$	1.74557	+	3.02342i	0.0583807	+	0.101118i
$895$	19.5917	+	13.9574i	0.654877	+	0.466546i
$896$	−2.80495			−0.0937068
$897$	11.2238	+	12.4330i	0.374753	+	0.415127i
$898$		−	27.4687i		−	0.916642i
$899$	14.4154	−	8.32276i	0.480782	−	0.277580i
$900$	4.90924	+	0.948346i	0.163641	+	0.0316115i
$901$	−39.9715	+	69.2328i	−1.33165	+	2.30648i
$902$	−3.42226			−0.113949
$903$	−5.95294	+	10.3108i	−0.198101	+	0.343122i
$904$	8.11206	+	4.68350i	0.269803	+	0.155771i
$905$	11.9299	−	5.44515i	0.396564	−	0.181003i
$906$	−2.27494	+	3.94031i	−0.0755799	+	0.130908i
$907$	−2.42051	+	1.39748i	−0.0803717	+	0.0464026i	−0.539647	−	0.841891i	$-0.681442\pi$
$907$	−2.42051	+	1.39748i	−0.0803717	+	0.0464026i	0.459276	+	0.888294i	$0.348109\pi$
$908$	−1.51105	−	2.61722i	−0.0501460	−	0.0868554i
$909$	5.44720			0.180672
$910$	−2.60203	−	22.4640i	−0.0862565	−	0.744675i
$911$	24.2193			0.802422			0.401211	−	0.915986i	$-0.368589\pi$
$911$	24.2193			0.802422			0.401211	+	0.915986i	$0.368589\pi$
$912$	3.80805	+	6.59574i	0.126097	+	0.218407i
$913$	−2.15952	+	1.24680i	−0.0714695	+	0.0412630i
$914$	2.19087	−	3.79470i	0.0724675	−	0.125517i
$915$	6.33786	+	13.8858i	0.209523	+	0.459051i
$916$	14.2437	+	8.22361i	0.470626	+	0.271716i
$917$	−16.3702	+	28.3541i	−0.540593	+	0.936334i
$918$	−5.75297			−0.189876
$919$	−6.54988	+	11.3447i	−0.216061	+	0.374228i	−0.953600	−	0.301076i	$-0.902654\pi$
$919$	−6.54988	+	11.3447i	−0.216061	+	0.374228i	0.737539	+	0.675304i	$0.235988\pi$
$920$	6.02730	−	8.46035i	0.198714	−	0.278929i
$921$	−0.332629	+	0.192044i	−0.0109605	+	0.00632805i
$922$			24.3172i			0.800844i
$923$	3.43824	−	3.10385i	0.113171	−	0.102164i
$924$	−1.66858			−0.0548921
$925$	−50.9264	−	9.83775i	−1.67445	−	0.323463i
$926$	−9.53298	−	16.5116i	−0.313273	−	0.542605i
$927$	11.9104	+	6.87645i	0.391187	+	0.225852i
$928$	2.52469			0.0828771
$929$	24.1564	+	13.9467i	0.792544	+	0.457576i	0.840858	−	0.541257i	$-0.182051\pi$
$929$	24.1564	+	13.9467i	0.792544	+	0.457576i	−0.0483131	+	0.998832i	$0.515385\pi$
$930$	1.40450	−	14.6755i	0.0460552	−	0.481230i
$931$			6.60877i			0.216594i
$932$	11.9762	+	6.91443i	0.392292	+	0.226490i
$933$	−10.1256	+	5.84601i	−0.331497	+	0.191390i
$934$	8.76211	−	5.05881i	0.286705	−	0.165529i
$935$	−6.96155	+	3.17744i	−0.227667	+	0.103914i
$936$	2.41604	+	2.67633i	0.0789707	+	0.0874786i
$937$		−	49.9741i		−	1.63258i	−0.577640	−	0.816292i	$-0.696026\pi$
$937$		−	49.9741i		−	1.63258i	0.577640	−	0.816292i	$-0.303974\pi$
$938$	11.0268	+	19.0991i	0.360039	+	0.623606i
$939$	5.28939	+	9.16150i	0.172613	+	0.298974i
$940$	−0.617345	+	6.45062i	−0.0201356	+	0.210396i
$941$			9.56099i			0.311680i	0.987782	+	0.155840i	$0.0498083\pi$
$941$			9.56099i			0.311680i	−0.987782	+	0.155840i	$0.950192\pi$
$942$	5.74787	−	9.95560i	0.187276	−	0.324371i
$943$	−13.3629	+	23.1452i	−0.435155	+	0.753710i
$944$		−	9.70293i		−	0.315804i
$945$	−6.24353	−	0.597526i	−0.203102	−	0.0194375i
$946$	−1.26249	−	2.18670i	−0.0410471	−	0.0710956i
$947$	22.0817	+	38.2466i	0.717558	+	1.24285i	0.961964	+	0.273175i	$0.0880737\pi$
$947$	22.0817	+	38.2466i	0.717558	+	1.24285i	−0.244406	+	0.969673i	$0.578593\pi$
$948$		−	1.83150i		−	0.0594844i
$949$	−16.1358	+	49.8799i	−0.523791	+	1.61917i
$950$	28.7687	+	24.9497i	0.933381	+	0.809475i
$951$	−19.1412	+	11.0512i	−0.620695	+	0.358359i
$952$	13.9749	−	8.06839i	0.452928	−	0.261498i
$953$	12.8310	+	7.40798i	0.415637	+	0.239968i	0.693209	−	0.720737i	$-0.256196\pi$
$953$	12.8310	+	7.40798i	0.415637	+	0.239968i	−0.277572	+	0.960705i	$0.589530\pi$
$954$		−	13.8960i		−	0.449899i
$955$	2.94712	−	30.7943i	0.0953664	−	0.996481i
$956$	3.98559	+	2.30108i	0.128903	+	0.0744223i
$957$	1.50186			0.0485483
$958$	24.8215	+	14.3307i	0.801946	+	0.463004i
$959$	−9.54082	−	16.5252i	−0.308089	−	0.533626i
$960$	1.29743	−	1.82117i	0.0418745	−	0.0587780i
$961$	−12.4688			−0.402219
$962$	−25.0630	−	27.7632i	−0.808063	−	0.895120i
$963$		−	4.23091i		−	0.136339i
$964$	−5.38108	+	3.10677i	−0.173313	+	0.100062i
$965$	30.9716	+	22.0647i	0.997012	+	0.710289i
$966$	−6.51527	+	11.2848i	−0.209625	+	0.363082i
$967$	−1.88667			−0.0606711			−0.0303356	−	0.999540i	$-0.509658\pi$
$967$	−1.88667			−0.0606711			−0.0303356	+	0.999540i	$0.509658\pi$
$968$	−5.32307	+	9.21982i	−0.171090	+	0.296336i
$969$	−37.9451	−	21.9076i	−1.21897	−	0.703774i
$970$	34.3909	−	15.6969i	1.10422	−	0.503998i
$971$	23.9611	−	41.5018i	0.768947	−	1.33186i	−0.169187	−	0.985584i	$-0.554114\pi$
$971$	23.9611	−	41.5018i	0.768947	−	1.33186i	0.938134	−	0.346271i	$-0.112552\pi$
$972$	0.866025	−	0.500000i	0.0277778	−	0.0160375i
$973$	9.95499	+	17.2425i	0.319142	+	0.552770i
$974$	−17.4398			−0.558807
$975$	15.7888	+	8.70135i	0.505647	+	0.278666i
$976$	6.82619			0.218501
$977$	−16.1581	−	27.9867i	−0.516945	−	0.895374i	−0.999806	−	0.0196777i	$-0.993736\pi$
$977$	−16.1581	−	27.9867i	−0.516945	−	0.895374i	0.482862	−	0.875697i	$-0.339597\pi$
$978$	−11.9762	+	6.91443i	−0.382955	+	0.221099i
$979$	1.80081	−	3.11909i	0.0575541	−	0.0996866i
$980$	1.76515	−	0.805661i	0.0563855	−	0.0257359i
$981$	0.387423	+	0.223679i	0.0123695	+	0.00714152i
$982$	−11.2233	+	19.4394i	−0.358151	+	0.620336i
$983$	20.4850			0.653370			0.326685	−	0.945133i	$-0.394068\pi$
$983$	20.4850			0.653370			0.326685	+	0.945133i	$0.394068\pi$
$984$	−2.87649	+	4.98222i	−0.0916990	+	0.158827i
$985$	11.5275	+	8.21242i	0.367298	+	0.261669i
$986$	−12.5786	+	7.26224i	−0.400583	+	0.231277i
$987$		−	8.12870i		−	0.258739i
$988$	5.74396	+	26.8528i	0.182740	+	0.854302i
$989$	−19.7185			−0.627012
$990$	0.771803	−	1.08336i	0.0245295	−	0.0344314i
$991$	0.834181	+	1.44484i	0.0264986	+	0.0458970i	0.878971	−	0.476876i	$-0.158231\pi$
$991$	0.834181	+	1.44484i	0.0264986	+	0.0458970i	−0.852472	+	0.522773i	$0.824898\pi$
$992$	−5.70978	−	3.29654i	−0.181286	−	0.104665i
$993$	−6.10616			−0.193773
$994$	3.12070	+	1.80174i	0.0989826	+	0.0571476i
$995$	3.54381	−	37.0292i	0.112346	−	1.17391i
$996$			4.19184i			0.132824i
$997$	−2.71512	−	1.56758i	−0.0859887	−	0.0496456i	0.456389	−	0.889780i	$-0.349143\pi$
$997$	−2.71512	−	1.56758i	−0.0859887	−	0.0496456i	−0.542378	+	0.840135i	$0.682476\pi$
$998$	9.01844	−	5.20680i	0.285474	−	0.164818i
$999$	−8.98379	+	5.18679i	−0.284234	+	0.164103i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.x.a.49.6	✓	12
3.2	odd	2		1170.2.bj.d.829.1		12
5.2	odd	4		1950.2.bc.i.751.6		12
5.3	odd	4		1950.2.bc.j.751.1		12
5.4	even	2		390.2.x.b.49.1	yes	12
13.4	even	6		390.2.x.b.199.1	yes	12
15.14	odd	2		1170.2.bj.c.829.6		12
39.17	odd	6		1170.2.bj.c.199.6		12
65.4	even	6	inner	390.2.x.a.199.6	yes	12
65.17	odd	12		1950.2.bc.i.901.6		12
65.43	odd	12		1950.2.bc.j.901.1		12
195.134	odd	6		1170.2.bj.d.199.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.x.a.49.6	✓	12	1.1	even	1	trivial
390.2.x.a.199.6	yes	12	65.4	even	6	inner
390.2.x.b.49.1	yes	12	5.4	even	2
390.2.x.b.199.1	yes	12	13.4	even	6
1170.2.bj.c.199.6		12	39.17	odd	6
1170.2.bj.c.829.6		12	15.14	odd	2
1170.2.bj.d.199.1		12	195.134	odd	6
1170.2.bj.d.829.1		12	3.2	odd	2
1950.2.bc.i.751.6		12	5.2	odd	4
1950.2.bc.i.901.6		12	65.17	odd	12
1950.2.bc.j.751.1		12	5.3	odd	4
1950.2.bc.j.901.1		12	65.43	odd	12

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)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.03420 - 0.928463i) q^{5} +(-0.866025 - 0.500000i) q^{6} +(1.40247 - 2.42916i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.03420 - 0.928463i) q^{5} +(-0.866025 - 0.500000i) q^{6} +(1.40247 - 2.42916i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.82117 - 1.29743i) q^{10} +(-0.515171 + 0.297434i) q^{11} +1.00000i q^{12} +(-1.10975 + 3.43052i) q^{13} -2.80495 q^{14} +(1.29743 - 1.82117i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(4.98222 + 2.87649i) q^{17} -1.00000 q^{18} +(-6.59574 - 3.80805i) q^{19} +(-0.213026 + 2.22590i) q^{20} -2.80495i q^{21} +(0.515171 + 0.297434i) q^{22} +(4.02317 - 2.32278i) q^{23} +(0.866025 - 0.500000i) q^{24} +(3.27591 - 3.77735i) q^{25} +(3.52579 - 0.754186i) q^{26} -1.00000i q^{27} +(1.40247 + 2.42916i) q^{28} +(-1.26235 - 2.18645i) q^{29} +(-2.22590 - 0.213026i) q^{30} +6.59309i q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.297434 + 0.515171i) q^{33} -5.75297i q^{34} +(0.597526 - 6.24353i) q^{35} +(0.500000 + 0.866025i) q^{36} +(-5.18679 - 8.98379i) q^{37} +7.61611i q^{38} +(0.754186 + 3.52579i) q^{39} +(2.03420 - 0.928463i) q^{40} +(-4.98222 + 2.87649i) q^{41} +(-2.42916 + 1.40247i) q^{42} +(-3.67593 - 2.12230i) q^{43} -0.594869i q^{44} +(0.213026 - 2.22590i) q^{45} +(-4.02317 - 2.32278i) q^{46} +2.89798 q^{47} +(-0.866025 - 0.500000i) q^{48} +(-0.433868 - 0.751482i) q^{49} +(-4.90924 - 0.948346i) q^{50} +5.75297 q^{51} +(-2.41604 - 2.67633i) q^{52} +13.8960i q^{53} +(-0.866025 + 0.500000i) q^{54} +(-0.771803 + 1.08336i) q^{55} +(1.40247 - 2.42916i) q^{56} -7.61611 q^{57} +(-1.26235 + 2.18645i) q^{58} +(8.40299 + 4.85147i) q^{59} +(0.928463 + 2.03420i) q^{60} +(-3.41309 + 5.91165i) q^{61} +(5.70978 - 3.29654i) q^{62} +(-1.40247 - 2.42916i) q^{63} +1.00000 q^{64} +(0.927657 + 8.00871i) q^{65} +0.594869 q^{66} +(-3.93121 - 6.80906i) q^{67} +(-4.98222 + 2.87649i) q^{68} +(2.32278 - 4.02317i) q^{69} +(-5.70582 + 2.60429i) q^{70} +(-1.11257 - 0.642342i) q^{71} +(0.500000 - 0.866025i) q^{72} +14.5400 q^{73} +(-5.18679 + 8.98379i) q^{74} +(0.948346 - 4.90924i) q^{75} +(6.59574 - 3.80805i) q^{76} +1.66858i q^{77} +(2.67633 - 2.41604i) q^{78} -1.83150 q^{79} +(-1.82117 - 1.29743i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(4.98222 + 2.87649i) q^{82} +4.19184 q^{83} +(2.42916 + 1.40247i) q^{84} +(12.8055 + 1.22553i) q^{85} +4.24460i q^{86} +(-2.18645 - 1.26235i) q^{87} +(-0.515171 + 0.297434i) q^{88} +(-5.24333 + 3.02724i) q^{89} +(-2.03420 + 0.928463i) q^{90} +(6.77687 + 7.50697i) q^{91} +4.64555i q^{92} +(3.29654 + 5.70978i) q^{93} +(-1.44899 - 2.50973i) q^{94} +(-16.9527 - 1.62243i) q^{95} +1.00000i q^{96} +(-8.45318 + 14.6413i) q^{97} +(-0.433868 + 0.751482i) q^{98} +0.594869i 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

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