LMFDB - Embedded newform 390.2.x.b.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			$-2.39378 + 0.0429626i$ of defining polynomial
Character	$\chi$	$=$	390.49
Dual form			390.2.x.b.199.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.10012 - 0.767774i) q^{5} +(0.866025 + 0.500000i) q^{6} +(0.823063 - 1.42559i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.10012 - 0.767774i) q^{5} +(0.866025 + 0.500000i) q^{6} +(0.823063 - 1.42559i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(1.71497 + 1.43487i) q^{10} +(2.08305 - 1.20265i) q^{11} +1.00000i q^{12} +(-3.59643 - 0.256262i) q^{13} +1.64613 q^{14} +(1.43487 - 1.71497i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.210702 + 0.121649i) q^{17} +1.00000 q^{18} +(3.82681 + 2.20941i) q^{19} +(-0.385150 + 2.20265i) q^{20} -1.64613i q^{21} +(2.08305 + 1.20265i) q^{22} +(-7.46758 + 4.31141i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(3.82105 - 3.22484i) q^{25} +(-1.57629 - 3.24273i) q^{26} -1.00000i q^{27} +(0.823063 + 1.42559i) q^{28} +(0.0221633 + 0.0383880i) q^{29} +(2.20265 + 0.385150i) q^{30} +4.24458i q^{31} +(0.500000 - 0.866025i) q^{32} +(1.20265 - 2.08305i) q^{33} +0.243297i q^{34} +(0.634006 - 3.62584i) q^{35} +(0.500000 + 0.866025i) q^{36} +(4.47415 + 7.74945i) q^{37} +4.41882i q^{38} +(-3.24273 + 1.57629i) q^{39} +(-2.10012 + 0.767774i) q^{40} +(0.210702 - 0.121649i) q^{41} +(1.42559 - 0.823063i) q^{42} +(-5.82728 - 3.36438i) q^{43} +2.40530i q^{44} +(0.385150 - 2.20265i) q^{45} +(-7.46758 - 4.31141i) q^{46} -7.29560 q^{47} +(-0.866025 - 0.500000i) q^{48} +(2.14514 + 3.71548i) q^{49} +(4.70332 + 1.69670i) q^{50} +0.243297 q^{51} +(2.02015 - 2.98647i) q^{52} -2.44613i q^{53} +(0.866025 - 0.500000i) q^{54} +(3.45130 - 4.12502i) q^{55} +(-0.823063 + 1.42559i) q^{56} +4.41882 q^{57} +(-0.0221633 + 0.0383880i) q^{58} +(-8.35669 - 4.82474i) q^{59} +(0.767774 + 2.10012i) q^{60} +(1.31630 - 2.27990i) q^{61} +(-3.67591 + 2.12229i) q^{62} +(-0.823063 - 1.42559i) q^{63} +1.00000 q^{64} +(-7.74971 + 2.22307i) q^{65} +2.40530 q^{66} +(0.937098 + 1.62310i) q^{67} +(-0.210702 + 0.121649i) q^{68} +(-4.31141 + 7.46758i) q^{69} +(3.45707 - 1.26385i) q^{70} +(-6.53035 - 3.77030i) q^{71} +(-0.500000 + 0.866025i) q^{72} +1.70370 q^{73} +(-4.47415 + 7.74945i) q^{74} +(1.69670 - 4.70332i) q^{75} +(-3.82681 + 2.20941i) q^{76} -3.95942i q^{77} +(-2.98647 - 2.02015i) q^{78} +6.79707 q^{79} +(-1.71497 - 1.43487i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.210702 + 0.121649i) q^{82} -17.4986 q^{83} +(1.42559 + 0.823063i) q^{84} +(0.535898 + 0.0937060i) q^{85} -6.72876i q^{86} +(0.0383880 + 0.0221633i) q^{87} +(-2.08305 + 1.20265i) q^{88} +(-8.69772 + 5.02163i) q^{89} +(2.10012 - 0.767774i) q^{90} +(-3.32541 + 4.91611i) q^{91} -8.62281i q^{92} +(2.12229 + 3.67591i) q^{93} +(-3.64780 - 6.31817i) q^{94} +(9.73310 + 1.70191i) q^{95} -1.00000i q^{96} +(8.25647 - 14.3006i) q^{97} +(-2.14514 + 3.71548i) q^{98} -2.40530i 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 $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

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

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
$5$	2.10012	−	0.767774i	0.939204	−	0.343359i
$5$	2.10012	−	0.767774i	0.939204	−	0.343359i
$6$	0.866025	+	0.500000i	0.353553	+	0.204124i
$7$	0.823063	−	1.42559i	0.311088	−	0.538821i	−0.667510	−	0.744601i	$-0.732640\pi$
$7$	0.823063	−	1.42559i	0.311088	−	0.538821i	0.978598	+	0.205780i	$0.0659731\pi$
$8$	−1.00000			−0.353553
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	1.71497	+	1.43487i	0.542322	+	0.453747i
$11$	2.08305	−	1.20265i	0.628063	−	0.362612i	−0.151939	−	0.988390i	$-0.548552\pi$
$11$	2.08305	−	1.20265i	0.628063	−	0.362612i	0.780001	+	0.625778i	$0.215218\pi$
$12$			1.00000i			0.288675i
$13$	−3.59643	−	0.256262i	−0.997471	−	0.0710744i
$13$	−3.59643	−	0.256262i	−0.997471	−	0.0710744i
$14$	1.64613			0.439946
$15$	1.43487	−	1.71497i	0.370483	−	0.442804i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.210702	+	0.121649i	0.0511027	+	0.0295041i	0.525334	−	0.850896i	$-0.323941\pi$
$17$	0.210702	+	0.121649i	0.0511027	+	0.0295041i	−0.474231	+	0.880400i	$0.657274\pi$
$18$	1.00000			0.235702
$19$	3.82681	+	2.20941i	0.877930	+	0.506873i	0.869975	−	0.493095i	$-0.164135\pi$
$19$	3.82681	+	2.20941i	0.877930	+	0.506873i	0.00795483	+	0.999968i	$0.497468\pi$
$20$	−0.385150	+	2.20265i	−0.0861222	+	0.492527i
$21$		−	1.64613i		−	0.359214i
$22$	2.08305	+	1.20265i	0.444107	+	0.256405i
$23$	−7.46758	+	4.31141i	−1.55710	+	0.898991i	−0.559565	+	0.828787i	$0.689032\pi$
$23$	−7.46758	+	4.31141i	−1.55710	+	0.898991i	−0.997533	+	0.0702038i	$0.977635\pi$
$24$	−0.866025	+	0.500000i	−0.176777	+	0.102062i
$25$	3.82105	−	3.22484i	0.764209	−	0.644969i
$26$	−1.57629	−	3.24273i	−0.309135	−	0.635952i
$27$		−	1.00000i		−	0.192450i
$28$	0.823063	+	1.42559i	0.155544	+	0.269411i
$29$	0.0221633	+	0.0383880i	0.00411562	+	0.00712846i	0.868076	−	0.496432i	$-0.165357\pi$
$29$	0.0221633	+	0.0383880i	0.00411562	+	0.00712846i	−0.863960	+	0.503560i	$0.832023\pi$
$30$	2.20265	+	0.385150i	0.402147	+	0.0703185i
$31$			4.24458i			0.762348i	0.924503	+	0.381174i	$0.124480\pi$
$31$			4.24458i			0.762348i	−0.924503	+	0.381174i	$0.875520\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	1.20265	−	2.08305i	0.209354	−	0.362612i
$34$			0.243297i			0.0417251i
$35$	0.634006	−	3.62584i	0.107167	−	0.612878i
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	4.47415	+	7.74945i	0.735545	+	1.27400i	0.954484	+	0.298263i	$0.0964071\pi$
$37$	4.47415	+	7.74945i	0.735545	+	1.27400i	−0.218939	+	0.975739i	$0.570260\pi$
$38$			4.41882i			0.716827i
$39$	−3.24273	+	1.57629i	−0.519253	+	0.252408i
$40$	−2.10012	+	0.767774i	−0.332059	+	0.121396i
$41$	0.210702	−	0.121649i	0.0329061	−	0.0189983i	−0.483457	−	0.875368i	$-0.660619\pi$
$41$	0.210702	−	0.121649i	0.0329061	−	0.0189983i	0.516363	+	0.856370i	$0.327286\pi$
$42$	1.42559	−	0.823063i	0.219973	−	0.127001i
$43$	−5.82728	−	3.36438i	−0.888652	−	0.513063i	−0.0151507	−	0.999885i	$-0.504823\pi$
$43$	−5.82728	−	3.36438i	−0.888652	−	0.513063i	−0.873501	+	0.486822i	$0.838156\pi$
$44$			2.40530i			0.362612i
$45$	0.385150	−	2.20265i	0.0574148	−	0.328351i
$46$	−7.46758	−	4.31141i	−1.10103	−	0.635682i
$47$	−7.29560			−1.06417			−0.532086	−	0.846690i	$-0.678592\pi$
$47$	−7.29560			−1.06417			−0.532086	+	0.846690i	$0.678592\pi$
$48$	−0.866025	−	0.500000i	−0.125000	−	0.0721688i
$49$	2.14514	+	3.71548i	0.306448	+	0.530783i
$50$	4.70332	+	1.69670i	0.665150	+	0.239950i
$51$	0.243297			0.0340684
$52$	2.02015	−	2.98647i	0.280144	−	0.414149i
$53$		−	2.44613i		−	0.336002i	−0.985787	−	0.168001i	$-0.946269\pi$
$53$		−	2.44613i		−	0.336002i	0.985787	−	0.168001i	$-0.0537312\pi$
$54$	0.866025	−	0.500000i	0.117851	−	0.0680414i
$55$	3.45130	−	4.12502i	0.465373	−	0.556218i
$56$	−0.823063	+	1.42559i	−0.109986	+	0.190502i
$57$	4.41882			0.585287
$58$	−0.0221633	+	0.0383880i	−0.00291018	+	0.00504059i
$59$	−8.35669	−	4.82474i	−1.08795	−	0.628127i	−0.154919	−	0.987927i	$-0.549512\pi$
$59$	−8.35669	−	4.82474i	−1.08795	−	0.628127i	−0.933029	+	0.359800i	$0.882845\pi$
$60$	0.767774	+	2.10012i	0.0991192	+	0.271125i
$61$	1.31630	−	2.27990i	0.168535	−	0.291911i	−0.769370	−	0.638804i	$-0.779430\pi$
$61$	1.31630	−	2.27990i	0.168535	−	0.291911i	0.937905	+	0.346892i	$0.112763\pi$
$62$	−3.67591	+	2.12229i	−0.466841	+	0.269531i
$63$	−0.823063	−	1.42559i	−0.103696	−	0.179607i
$64$	1.00000			0.125000
$65$	−7.74971	+	2.22307i	−0.961233	+	0.275737i
$66$	2.40530			0.296072
$67$	0.937098	+	1.62310i	0.114485	+	0.198293i	0.917574	−	0.397566i	$-0.130145\pi$
$67$	0.937098	+	1.62310i	0.114485	+	0.198293i	−0.803089	+	0.595859i	$0.796812\pi$
$68$	−0.210702	+	0.121649i	−0.0255513	+	0.0147521i
$69$	−4.31141	+	7.46758i	−0.519032	+	0.898991i
$70$	3.45707	−	1.26385i	0.413199	−	0.151059i
$71$	−6.53035	−	3.77030i	−0.775010	−	0.447452i	0.0596488	−	0.998219i	$-0.481002\pi$
$71$	−6.53035	−	3.77030i	−0.775010	−	0.447452i	−0.834659	+	0.550767i	$0.814335\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	1.70370			0.199403			0.0997015	−	0.995017i	$-0.468211\pi$
$73$	1.70370			0.199403			0.0997015	+	0.995017i	$0.468211\pi$
$74$	−4.47415	+	7.74945i	−0.520109	+	0.900855i
$75$	1.69670	−	4.70332i	0.195918	−	0.543092i
$76$	−3.82681	+	2.20941i	−0.438965	+	0.253437i
$77$		−	3.95942i		−	0.451218i
$78$	−2.98647	−	2.02015i	−0.338151	−	0.228737i
$79$	6.79707			0.764730			0.382365	−	0.924011i	$-0.375110\pi$
$79$	6.79707			0.764730			0.382365	+	0.924011i	$0.375110\pi$
$80$	−1.71497	−	1.43487i	−0.191740	−	0.160424i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	0.210702	+	0.121649i	0.0232681	+	0.0134338i
$83$	−17.4986			−1.92073			−0.960363	−	0.278754i	$-0.910079\pi$
$83$	−17.4986			−1.92073			−0.960363	+	0.278754i	$0.910079\pi$
$84$	1.42559	+	0.823063i	0.155544	+	0.0898035i
$85$	0.535898	+	0.0937060i	0.0581263	+	0.0101638i
$86$		−	6.72876i		−	0.725581i
$87$	0.0383880	+	0.0221633i	0.00411562	+	0.00237615i
$88$	−2.08305	+	1.20265i	−0.222054	+	0.128203i
$89$	−8.69772	+	5.02163i	−0.921956	+	0.532292i	−0.884259	−	0.466997i	$-0.845336\pi$
$89$	−8.69772	+	5.02163i	−0.921956	+	0.532292i	−0.0376977	+	0.999289i	$0.512002\pi$
$90$	2.10012	−	0.767774i	0.221373	−	0.0809305i
$91$	−3.32541	+	4.91611i	−0.348598	+	0.515348i
$92$		−	8.62281i		−	0.898991i
$93$	2.12229	+	3.67591i	0.220071	+	0.381174i
$94$	−3.64780	−	6.31817i	−0.376242	−	0.651670i
$95$	9.73310	+	1.70191i	0.998595	+	0.174612i
$96$		−	1.00000i		−	0.102062i
$97$	8.25647	−	14.3006i	0.838317	−	1.45201i	−0.0529831	−	0.998595i	$-0.516873\pi$
$97$	8.25647	−	14.3006i	0.838317	−	1.45201i	0.891301	−	0.453413i	$-0.149794\pi$
$98$	−2.14514	+	3.71548i	−0.216691	+	0.375321i
$99$		−	2.40530i		−	0.241741i
$100$	0.882273	+	4.92154i	0.0882273	+	0.492154i
$101$	5.66777	+	9.81687i	0.563964	+	0.976815i	0.997145	+	0.0755077i	$0.0240577\pi$
$101$	5.66777	+	9.81687i	0.563964	+	0.976815i	−0.433181	+	0.901307i	$0.642609\pi$
$102$	0.121649	+	0.210702i	0.0120450	+	0.0208626i
$103$		−	5.98168i		−	0.589392i	−0.955591	−	0.294696i	$-0.904782\pi$
$103$		−	5.98168i		−	0.589392i	0.955591	−	0.294696i	$-0.0952184\pi$
$104$	3.59643	+	0.256262i	0.352659	+	0.0251286i
$105$	−1.26385	−	3.45707i	−0.123339	−	0.337375i
$106$	2.11841	−	1.22307i	0.205758	−	0.118795i
$107$	9.24559	−	5.33795i	0.893805	−	0.516039i	0.0186200	−	0.999827i	$-0.494073\pi$
$107$	9.24559	−	5.33795i	0.893805	−	0.516039i	0.875185	+	0.483788i	$0.160739\pi$
$108$	0.866025	+	0.500000i	0.0833333	+	0.0481125i
$109$		−	9.50683i		−	0.910589i	−0.890341	−	0.455295i	$-0.849534\pi$
$109$		−	9.50683i		−	0.910589i	0.890341	−	0.455295i	$-0.150466\pi$
$110$	5.29802	+	0.926401i	0.505147	+	0.0883288i
$111$	7.74945	+	4.47415i	0.735545	+	0.424667i
$112$	−1.64613			−0.155544
$113$	−3.11433	−	1.79806i	−0.292972	−	0.169147i	0.346310	−	0.938120i	$-0.387435\pi$
$113$	−3.11433	−	1.79806i	−0.292972	−	0.169147i	−0.639281	+	0.768973i	$0.720768\pi$
$114$	2.20941	+	3.82681i	0.206930	+	0.358414i
$115$	−12.3727	+	14.7879i	−1.15376	+	1.37898i
$116$	−0.0443266			−0.00411562
$117$	−2.02015	+	2.98647i	−0.186763	+	0.276099i
$118$		−	9.64947i		−	0.888306i
$119$	0.346841	−	0.200249i	0.0317949	−	0.0183568i
$120$	−1.43487	+	1.71497i	−0.130985	+	0.156555i
$121$	−2.60727	+	4.51593i	−0.237025	+	0.410539i
$122$	2.63260			0.238345
$123$	0.121649	−	0.210702i	0.0109687	−	0.0189983i
$124$	−3.67591	−	2.12229i	−0.330106	−	0.190587i
$125$	5.54872	−	9.70627i	0.496293	−	0.868155i
$126$	0.823063	−	1.42559i	0.0733243	−	0.127001i
$127$	−15.0230	+	8.67351i	−1.33307	+	0.769650i	−0.985769	−	0.168103i	$-0.946236\pi$
$127$	−15.0230	+	8.67351i	−1.33307	+	0.769650i	−0.347303	+	0.937753i	$0.612902\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−6.72876			−0.592435
$130$	−5.80009	−	5.59991i	−0.508701	−	0.491145i
$131$	14.1654			1.23764			0.618818	−	0.785534i	$-0.287612\pi$
$131$	14.1654			1.23764			0.618818	+	0.785534i	$0.287612\pi$
$132$	1.20265	+	2.08305i	0.104677	+	0.181306i
$133$	6.29941	−	3.63697i	0.546228	−	0.315365i
$134$	−0.937098	+	1.62310i	−0.0809530	+	0.140215i
$135$	−0.767774	−	2.10012i	−0.0660795	−	0.180750i
$136$	−0.210702	−	0.121649i	−0.0180675	−	0.0104313i
$137$	3.66709	−	6.35158i	0.313300	−	0.542652i	−0.665774	−	0.746153i	$-0.731899\pi$
$137$	3.66709	−	6.35158i	0.313300	−	0.542652i	0.979075	+	0.203501i	$0.0652320\pi$
$138$	−8.62281			−0.734023
$139$	7.10185	−	12.3008i	0.602371	−	1.04334i	−0.390090	−	0.920777i	$-0.627556\pi$
$139$	7.10185	−	12.3008i	0.602371	−	1.04334i	0.992461	−	0.122561i	$-0.0391107\pi$
$140$	2.82306	+	2.36198i	0.238592	+	0.199624i
$141$	−6.31817	+	3.64780i	−0.532086	+	0.307200i
$142$		−	7.54060i		−	0.632793i
$143$	−7.79974	+	3.79144i	−0.652247	+	0.317056i
$144$	−1.00000			−0.0833333
$145$	0.0760190	+	0.0636031i	0.00631303	+	0.00528195i
$146$	0.851850	+	1.47545i	0.0704996	+	0.122109i
$147$	3.71548	+	2.14514i	0.306448	+	0.176928i
$148$	−8.94829			−0.735545
$149$	−9.61623	−	5.55193i	−0.787792	−	0.454832i	0.0513926	−	0.998679i	$-0.483634\pi$
$149$	−9.61623	−	5.55193i	−0.787792	−	0.454832i	−0.839185	+	0.543847i	$0.816967\pi$
$150$	4.92154	−	0.882273i	0.401842	−	0.0720373i
$151$		−	0.874663i		−	0.0711791i	−0.999366	−	0.0355895i	$-0.988669\pi$
$151$		−	0.874663i		−	0.0711791i	0.999366	−	0.0355895i	$-0.0113309\pi$
$152$	−3.82681	−	2.20941i	−0.310395	−	0.179207i
$153$	0.210702	−	0.121649i	0.0170342	−	0.00983471i
$154$	3.42896	−	1.97971i	0.276313	−	0.159530i
$155$	3.25888	+	8.91414i	0.261759	+	0.716001i
$156$	0.256262	−	3.59643i	0.0205174	−	0.287945i
$157$			15.5085i			1.23771i	0.785504	+	0.618856i	$0.212404\pi$
$157$			15.5085i			1.23771i	−0.785504	+	0.618856i	$0.787596\pi$
$158$	3.39854	+	5.88644i	0.270373	+	0.468300i
$159$	−1.22307	−	2.11841i	−0.0969954	−	0.168001i
$160$	0.385150	−	2.20265i	0.0304488	−	0.174135i
$161$			14.1942i			1.11866i
$162$	0.500000	−	0.866025i	0.0392837	−	0.0680414i
$163$	−10.9464	+	18.9597i	−0.857388	+	1.48504i	0.0170229	+	0.999855i	$0.494581\pi$
$163$	−10.9464	+	18.9597i	−0.857388	+	1.48504i	−0.874411	+	0.485185i	$0.838752\pi$
$164$			0.243297i			0.0189983i
$165$	0.926401	−	5.29802i	0.0721202	−	0.412450i
$166$	−8.74932	−	15.1543i	−0.679079	−	1.17620i
$167$	2.64815	+	4.58673i	0.204920	+	0.354932i	0.950107	−	0.311923i	$-0.100973\pi$
$167$	2.64815	+	4.58673i	0.204920	+	0.354932i	−0.745187	+	0.666855i	$0.767640\pi$
$168$			1.64613i			0.127001i
$169$	12.8687	+	1.84326i	0.989897	+	0.141789i
$170$	0.186797	+	0.510955i	0.0143267	+	0.0391884i
$171$	3.82681	−	2.20941i	0.292643	−	0.168958i
$172$	5.82728	−	3.36438i	0.444326	−	0.256532i
$173$	14.9469	+	8.62958i	1.13639	+	0.656095i	0.945534	−	0.325523i	$-0.105540\pi$
$173$	14.9469	+	8.62958i	1.13639	+	0.656095i	0.190856	+	0.981618i	$0.438874\pi$
$174$			0.0443266i			0.00336039i
$175$	−1.45233	−	8.10148i	−0.109786	−	0.612414i
$176$	−2.08305	−	1.20265i	−0.157016	−	0.0906530i
$177$	−9.64947			−0.725299
$178$	−8.69772	−	5.02163i	−0.651922	−	0.376387i
$179$	−4.17781	−	7.23617i	−0.312264	−	0.540857i	0.666588	−	0.745426i	$-0.267754\pi$
$179$	−4.17781	−	7.23617i	−0.312264	−	0.540857i	−0.978852	+	0.204569i	$0.934421\pi$
$180$	1.71497	+	1.43487i	0.127827	+	0.106949i
$181$	12.7335			0.946476			0.473238	−	0.880935i	$-0.343085\pi$
$181$	12.7335			0.946476			0.473238	+	0.880935i	$0.343085\pi$
$182$	−5.92018	−	0.421840i	−0.438833	−	0.0312689i
$183$		−	2.63260i		−	0.194608i
$184$	7.46758	−	4.31141i	0.550517	−	0.317841i
$185$	15.3461	+	12.8397i	1.12827	+	0.943991i
$186$	−2.12229	+	3.67591i	−0.155614	+	0.269531i
$187$	0.585202			0.0427942
$188$	3.64780	−	6.31817i	0.266043	−	0.460800i
$189$	−1.42559	−	0.823063i	−0.103696	−	0.0598690i
$190$	3.39265	+	9.28007i	0.246129	+	0.673247i
$191$	−0.207632	+	0.359629i	−0.0150237	+	0.0260219i	−0.873440	−	0.486933i	$-0.838116\pi$
$191$	−0.207632	+	0.359629i	−0.0150237	+	0.0260219i	0.858416	+	0.512955i	$0.171449\pi$
$192$	0.866025	−	0.500000i	0.0625000	−	0.0360844i
$193$	12.9918	+	22.5025i	0.935173	+	1.61977i	0.774324	+	0.632789i	$0.218090\pi$
$193$	12.9918	+	22.5025i	0.935173	+	1.61977i	0.160849	+	0.986979i	$0.448577\pi$
$194$	16.5129			1.18556
$195$	−5.59991	+	5.80009i	−0.401018	+	0.415353i
$196$	−4.29027			−0.306448
$197$	7.72121	+	13.3735i	0.550113	+	0.952824i	0.998266	+	0.0588672i	$0.0187488\pi$
$197$	7.72121	+	13.3735i	0.550113	+	0.952824i	−0.448152	+	0.893957i	$0.647918\pi$
$198$	2.08305	−	1.20265i	0.148036	−	0.0854685i
$199$	6.85286	−	11.8695i	0.485787	−	0.841407i	−0.514080	−	0.857742i	$-0.671867\pi$
$199$	6.85286	−	11.8695i	0.485787	−	0.841407i	0.999867	+	0.0163352i	$0.00519988\pi$
$200$	−3.82105	+	3.22484i	−0.270189	+	0.228031i
$201$	1.62310	+	0.937098i	0.114485	+	0.0660978i
$202$	−5.66777	+	9.81687i	−0.398783	+	0.690712i
$203$	0.0729671			0.00512129
$204$	−0.121649	+	0.210702i	−0.00851711	+	0.0147521i
$205$	0.349101	−	0.417249i	0.0243823	−	0.0291419i
$206$	5.18029	−	2.99084i	0.360928	−	0.208382i
$207$			8.62281i			0.599327i
$208$	1.57629	+	3.24273i	0.109296	+	0.224843i
$209$	10.6286			0.735193
$210$	2.36198	−	2.82306i	0.162992	−	0.194810i
$211$	8.05616	+	13.9537i	0.554609	+	0.960611i	0.997934	+	0.0642497i	$0.0204654\pi$
$211$	8.05616	+	13.9537i	0.554609	+	0.960611i	−0.443325	+	0.896361i	$0.646201\pi$
$212$	2.11841	+	1.22307i	0.145493	+	0.0840005i
$213$	−7.54060			−0.516673
$214$	9.24559	+	5.33795i	0.632016	+	0.364894i
$215$	−14.8211	−	2.59159i	−1.01079	−	0.176745i
$216$			1.00000i			0.0680414i
$217$	6.05101	+	3.49355i	0.410769	+	0.237158i
$218$	8.23316	−	4.75342i	0.557620	−	0.321942i
$219$	1.47545	−	0.851850i	0.0997015	−	0.0575627i
$220$	1.84672	+	5.05142i	0.124506	+	0.340567i
$221$	−0.726600	−	0.491496i	−0.0488764	−	0.0330616i
$222$			8.94829i			0.600570i
$223$	−5.55886	−	9.62823i	−0.372249	−	0.644754i	0.617662	−	0.786443i	$-0.288080\pi$
$223$	−5.55886	−	9.62823i	−0.372249	−	0.644754i	−0.989911	+	0.141690i	$0.954747\pi$
$224$	−0.823063	−	1.42559i	−0.0549932	−	0.0952510i
$225$	−0.882273	−	4.92154i	−0.0588182	−	0.328103i
$226$		−	3.59612i		−	0.239210i
$227$	11.0399	−	19.1217i	0.732747	−	1.26915i	−0.222958	−	0.974828i	$-0.571571\pi$
$227$	11.0399	−	19.1217i	0.732747	−	1.26915i	0.955705	−	0.294327i	$-0.0950953\pi$
$228$	−2.20941	+	3.82681i	−0.146322	+	0.253437i
$229$		−	10.3397i		−	0.683266i	−0.939834	−	0.341633i	$-0.889020\pi$
$229$		−	10.3397i		−	0.683266i	0.939834	−	0.341633i	$-0.110980\pi$
$230$	−18.9930	−	3.32108i	−1.25236	−	0.218985i
$231$	−1.97971	−	3.42896i	−0.130255	−	0.225609i
$232$	−0.0221633	−	0.0383880i	−0.00145509	−	0.00252029i
$233$		−	21.8928i		−	1.43425i	−0.696947	−	0.717123i	$-0.745459\pi$
$233$		−	21.8928i		−	1.43425i	0.696947	−	0.717123i	$-0.254541\pi$
$234$	−3.59643	−	0.256262i	−0.235106	−	0.0167524i
$235$	−15.3217	+	5.60137i	−0.999475	+	0.365393i
$236$	8.35669	−	4.82474i	0.543974	−	0.314064i
$237$	5.88644	−	3.39854i	0.382365	−	0.220759i
$238$	0.346841	+	0.200249i	0.0224824	+	0.0129802i
$239$			26.2510i			1.69804i	0.528362	+	0.849019i	$0.322806\pi$
$239$			26.2510i			1.69804i	−0.528362	+	0.849019i	$0.677194\pi$
$240$	−2.20265	−	0.385150i	−0.142180	−	0.0248613i
$241$	22.5952	+	13.0454i	1.45549	+	0.840326i	0.998784	−	0.0492931i	$-0.0156968\pi$
$241$	22.5952	+	13.0454i	1.45549	+	0.840326i	0.456703	+	0.889619i	$0.349030\pi$
$242$	−5.21455			−0.335204
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	1.31630	+	2.27990i	0.0842676	+	0.145956i
$245$	7.35770	+	6.15600i	0.470066	+	0.393292i
$246$	0.243297			0.0155121
$247$	−13.1967	−	8.92666i	−0.839684	−	0.567990i
$248$		−	4.24458i		−	0.269531i
$249$	−15.1543	+	8.74932i	−0.960363	+	0.554466i
$250$	11.1802	−	0.0478026i	0.707100	−	0.00302330i
$251$	−0.312397	+	0.541088i	−0.0197183	+	0.0341532i	−0.875716	−	0.482826i	$-0.839610\pi$
$251$	−0.312397	+	0.541088i	−0.0197183	+	0.0341532i	0.855998	+	0.516979i	$0.172944\pi$
$252$	1.64613			0.103696
$253$	−10.3702	+	17.9617i	−0.651970	+	1.12924i
$254$	−15.0230	−	8.67351i	−0.942624	−	0.544224i
$255$	0.510955	−	0.186797i	0.0319972	−	0.0116977i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	12.0758	−	6.97195i	0.753266	−	0.434898i	−0.0736066	−	0.997287i	$-0.523451\pi$
$257$	12.0758	−	6.97195i	0.753266	−	0.434898i	0.826873	+	0.562389i	$0.190118\pi$
$258$	−3.36438	−	5.82728i	−0.209457	−	0.362791i
$259$	14.7300			0.915278
$260$	1.94962	−	7.82298i	0.120910	−	0.485160i
$261$	0.0443266			0.00274375
$262$	7.08270	+	12.2676i	0.437571	+	0.757894i
$263$	16.8325	−	9.71828i	1.03794	−	0.599255i	0.118690	−	0.992931i	$-0.462130\pi$
$263$	16.8325	−	9.71828i	1.03794	−	0.599255i	0.919249	+	0.393677i	$0.128797\pi$
$264$	−1.20265	+	2.08305i	−0.0740179	+	0.128203i
$265$	−1.87808	−	5.13718i	−0.115369	−	0.315574i
$266$	6.29941	+	3.63697i	0.386242	+	0.222997i
$267$	−5.02163	+	8.69772i	−0.307319	+	0.532292i
$268$	−1.87420			−0.114485
$269$	−1.50069	+	2.59928i	−0.0914989	+	0.158481i	−0.908142	−	0.418662i	$-0.862499\pi$
$269$	−1.50069	+	2.59928i	−0.0914989	+	0.158481i	0.816643	+	0.577143i	$0.195832\pi$
$270$	1.43487	−	1.71497i	0.0873237	−	0.104370i
$271$	−24.6538	+	14.2339i	−1.49761	+	0.864645i	−0.999996	−	0.00275396i	$-0.999123\pi$
$271$	−24.6538	+	14.2339i	−1.49761	+	0.864645i	−0.497613	+	0.867399i	$0.665790\pi$
$272$		−	0.243297i		−	0.0147521i
$273$	−0.421840	+	5.92018i	−0.0255309	+	0.358306i
$274$	7.33417			0.443074
$275$	4.08107	−	11.3129i	0.246098	−	0.682192i
$276$	−4.31141	−	7.46758i	−0.259516	−	0.449495i
$277$	0.738423	+	0.426329i	0.0443676	+	0.0256156i	0.522020	−	0.852933i	$-0.325179\pi$
$277$	0.738423	+	0.426329i	0.0443676	+	0.0256156i	−0.477652	+	0.878549i	$0.658512\pi$
$278$	14.2037			0.851882
$279$	3.67591	+	2.12229i	0.220071	+	0.127058i
$280$	−0.634006	+	3.62584i	−0.0378891	+	0.216685i
$281$		−	15.6851i		−	0.935697i	−0.883809	−	0.467848i	$-0.845029\pi$
$281$		−	15.6851i		−	0.935697i	0.883809	−	0.467848i	$-0.154971\pi$
$282$	−6.31817	−	3.64780i	−0.376242	−	0.217223i
$283$	7.00390	−	4.04370i	0.416339	−	0.240373i	−0.277171	−	0.960821i	$-0.589397\pi$
$283$	7.00390	−	4.04370i	0.416339	−	0.240373i	0.693510	+	0.720447i	$0.256063\pi$
$284$	6.53035	−	3.77030i	0.387505	−	0.223726i
$285$	9.28007	−	3.39265i	0.549704	−	0.200964i
$286$	−7.18335	−	4.85905i	−0.424760	−	0.287322i
$287$		−	0.400498i		−	0.0236406i
$288$	−0.500000	−	0.866025i	−0.0294628	−	0.0510310i
$289$	−8.47040	−	14.6712i	−0.498259	−	0.863010i
$290$	−0.0170724	+	0.0976359i	−0.00100253	+	0.00573338i
$291$		−	16.5129i		−	0.968006i
$292$	−0.851850	+	1.47545i	−0.0498508	+	0.0863440i
$293$	−0.967192	+	1.67523i	−0.0565040	+	0.0978677i	−0.892894	−	0.450267i	$-0.851329\pi$
$293$	−0.967192	+	1.67523i	−0.0565040	+	0.0978677i	0.836390	+	0.548135i	$0.184662\pi$
$294$			4.29027i			0.250214i
$295$	−21.2544	−	3.71650i	−1.23748	−	0.216383i
$296$	−4.47415	−	7.74945i	−0.260054	−	0.450427i
$297$	−1.20265	−	2.08305i	−0.0697847	−	0.120871i
$298$		−	11.1039i		−	0.643229i
$299$	27.9615	−	13.5920i	1.61705	−	0.786047i
$300$	3.22484	+	3.82105i	0.186186	+	0.220608i
$301$	−9.59244	+	5.53820i	−0.552899	+	0.319216i
$302$	0.757480	−	0.437332i	0.0435881	−	0.0251656i
$303$	9.81687	+	5.66777i	0.563964	+	0.325605i
$304$		−	4.41882i		−	0.253437i
$305$	1.01395	−	5.79870i	0.0580585	−	0.332033i
$306$	0.210702	+	0.121649i	0.0120450	+	0.00695419i
$307$	−12.4384			−0.709894			−0.354947	−	0.934886i	$-0.615501\pi$
$307$	−12.4384			−0.709894			−0.354947	+	0.934886i	$0.615501\pi$
$308$	3.42896	+	1.97971i	0.195383	+	0.112804i
$309$	−2.99084	−	5.18029i	−0.170143	−	0.294696i
$310$	−6.09043	+	7.27934i	−0.345913	+	0.413439i
$311$	−18.3700			−1.04167			−0.520835	−	0.853657i	$-0.674379\pi$
$311$	−18.3700			−1.04167			−0.520835	+	0.853657i	$0.674379\pi$
$312$	3.24273	−	1.57629i	0.183584	−	0.0892397i
$313$		−	31.9445i		−	1.80561i	−0.430051	−	0.902804i	$-0.641504\pi$
$313$		−	31.9445i		−	1.80561i	0.430051	−	0.902804i	$-0.358496\pi$
$314$	−13.4307	+	7.75425i	−0.757941	+	0.437597i
$315$	−2.82306	−	2.36198i	−0.159062	−	0.133083i
$316$	−3.39854	+	5.88644i	−0.191183	+	0.331138i
$317$	−23.3625			−1.31217			−0.656083	−	0.754689i	$-0.727788\pi$
$317$	−23.3625			−1.31217			−0.656083	+	0.754689i	$0.727788\pi$
$318$	1.22307	−	2.11841i	0.0685861	−	0.118795i
$319$	0.0923344	+	0.0533093i	0.00516973	+	0.00298475i
$320$	2.10012	−	0.767774i	0.117401	−	0.0429199i
$321$	5.33795	−	9.24559i	0.297935	−	0.516039i
$322$	−12.2926	+	7.09712i	−0.685038	+	0.395507i
$323$	0.537543	+	0.931052i	0.0299097	+	0.0518051i
$324$	1.00000			0.0555556
$325$	−14.5685	+	10.6187i	−0.808117	+	0.589022i
$326$	−21.8928			−1.21253
$327$	−4.75342	−	8.23316i	−0.262865	−	0.455295i
$328$	−0.210702	+	0.121649i	−0.0116341	+	0.00671692i
$329$	−6.00474	+	10.4005i	−0.331052	+	0.573399i
$330$	5.05142	−	1.84672i	0.278072	−	0.101659i
$331$	−18.5879	−	10.7317i	−1.02168	−	0.589868i	−0.107090	−	0.994249i	$-0.534153\pi$
$331$	−18.5879	−	10.7317i	−1.02168	−	0.589868i	−0.914590	+	0.404382i	$0.867487\pi$
$332$	8.74932	−	15.1543i	0.480181	−	0.831698i
$333$	8.94829			0.490363
$334$	−2.64815	+	4.58673i	−0.144900	+	0.250975i
$335$	3.21420	+	2.68924i	0.175610	+	0.146929i
$336$	−1.42559	+	0.823063i	−0.0777721	+	0.0449018i
$337$		−	14.3561i		−	0.782026i	−0.920385	−	0.391013i	$-0.872125\pi$
$337$		−	14.3561i		−	0.782026i	0.920385	−	0.391013i	$-0.127875\pi$
$338$	4.83802	+	12.0662i	0.263154	+	0.656316i
$339$	−3.59612			−0.195314
$340$	−0.349101	+	0.417249i	−0.0189327	+	0.0226285i
$341$	5.10473	+	8.84165i	0.276437	+	0.478802i
$342$	3.82681	+	2.20941i	0.206930	+	0.119471i
$343$	18.5852			1.00351
$344$	5.82728	+	3.36438i	0.314186	+	0.181395i
$345$	−3.32108	+	18.9930i	−0.178801	+	1.02255i
$346$			17.2592i			0.927858i
$347$	−0.576005	−	0.332557i	−0.0309216	−	0.0178526i	0.484460	−	0.874814i	$-0.339016\pi$
$347$	−0.576005	−	0.332557i	−0.0309216	−	0.0178526i	−0.515381	+	0.856961i	$0.672350\pi$
$348$	−0.0383880	+	0.0221633i	−0.00205781	+	0.00118808i
$349$	3.25007	−	1.87643i	0.173972	−	0.100443i	−0.410485	−	0.911867i	$-0.634641\pi$
$349$	3.25007	−	1.87643i	0.173972	−	0.100443i	0.584458	+	0.811424i	$0.301307\pi$
$350$	6.28992	−	5.30850i	0.336210	−	0.283751i
$351$	−0.256262	+	3.59643i	−0.0136783	+	0.191963i
$352$		−	2.40530i		−	0.128203i
$353$	−2.28180	−	3.95219i	−0.121448	−	0.210354i	0.798891	−	0.601476i	$-0.205420\pi$
$353$	−2.28180	−	3.95219i	−0.121448	−	0.210354i	−0.920339	+	0.391122i	$0.872087\pi$
$354$	−4.82474	−	8.35669i	−0.256432	−	0.444153i
$355$	−16.6093	−	2.90426i	−0.881530	−	0.154142i
$356$		−	10.0433i		−	0.532292i
$357$	0.200249	−	0.346841i	0.0105983	−	0.0183568i
$358$	4.17781	−	7.23617i	0.220804	−	0.382444i
$359$			4.75785i			0.251110i	0.992087	+	0.125555i	$0.0400711\pi$
$359$			4.75785i			0.251110i	−0.992087	+	0.125555i	$0.959929\pi$
$360$	−0.385150	+	2.20265i	−0.0202992	+	0.116090i
$361$	0.262979	+	0.455494i	0.0138410	+	0.0239733i
$362$	6.36677	+	11.0276i	0.334630	+	0.579596i
$363$			5.21455i			0.273693i
$364$	−2.59477	−	5.33795i	−0.136003	−	0.279784i
$365$	3.57798	−	1.30806i	0.187280	−	0.0684668i
$366$	2.27990	−	1.31630i	0.119172	−	0.0688042i
$367$	1.29432	−	0.747277i	0.0675630	−	0.0390075i	−0.465838	−	0.884870i	$-0.654247\pi$
$367$	1.29432	−	0.747277i	0.0675630	−	0.0390075i	0.533401	+	0.845863i	$0.320914\pi$
$368$	7.46758	+	4.31141i	0.389274	+	0.224748i
$369$		−	0.243297i		−	0.0126656i
$370$	−3.44644	+	19.7099i	−0.179172	+	1.02467i
$371$	−3.48717	−	2.01332i	−0.181045	−	0.104526i
$372$	−4.24458			−0.220071
$373$	17.8323	+	10.2955i	0.923323	+	0.533081i	0.884694	−	0.466173i	$-0.154368\pi$
$373$	17.8323	+	10.2955i	0.923323	+	0.533081i	0.0386291	+	0.999254i	$0.487701\pi$
$374$	0.292601	+	0.506800i	0.0151300	+	0.0262060i
$375$	−0.0478026	−	11.1802i	−0.00246852	−	0.577345i
$376$	7.29560			0.376242
$377$	−0.0698714	−	0.143739i	−0.00359856	−	0.00740295i
$378$		−	1.64613i		−	0.0846676i
$379$	−18.4173	+	10.6332i	−0.946032	+	0.546192i	−0.891846	−	0.452339i	$-0.850590\pi$
$379$	−18.4173	+	10.6332i	−0.946032	+	0.546192i	−0.0541858	+	0.998531i	$0.517256\pi$
$380$	−6.34045	+	7.57816i	−0.325258	+	0.388751i
$381$	−8.67351	+	15.0230i	−0.444357	+	0.769650i
$382$	−0.415264			−0.0212468
$383$	5.31095	−	9.19884i	0.271377	−	0.470039i	−0.697838	−	0.716256i	$-0.745854\pi$
$383$	5.31095	−	9.19884i	0.271377	−	0.470039i	0.969215	+	0.246217i	$0.0791877\pi$
$384$	0.866025	+	0.500000i	0.0441942	+	0.0255155i
$385$	−3.03994	−	8.31527i	−0.154930	−	0.423786i
$386$	−12.9918	+	22.5025i	−0.661267	+	1.14535i
$387$	−5.82728	+	3.36438i	−0.296217	+	0.171021i
$388$	8.25647	+	14.3006i	0.419159	+	0.726004i
$389$	−37.0443			−1.87822			−0.939111	−	0.343613i	$-0.888349\pi$
$389$	−37.0443			−1.87822			−0.939111	+	0.343613i	$0.888349\pi$
$390$	−7.82298	−	1.94962i	−0.396132	−	0.0987230i
$391$	−2.09791			−0.106096
$392$	−2.14514	−	3.71548i	−0.108346	−	0.187660i
$393$	12.2676	−	7.08270i	0.618818	−	0.357275i
$394$	−7.72121	+	13.3735i	−0.388989	+	0.673749i
$395$	14.2747	−	5.21862i	0.718238	−	0.262577i
$396$	2.08305	+	1.20265i	0.104677	+	0.0604353i
$397$	−0.843593	+	1.46115i	−0.0423387	+	0.0733328i	−0.886418	−	0.462885i	$-0.846814\pi$
$397$	−0.843593	+	1.46115i	−0.0423387	+	0.0733328i	0.844079	+	0.536218i	$0.180148\pi$
$398$	13.7057			0.687006
$399$	3.63697	−	6.29941i	0.182076	−	0.315365i
$400$	−4.70332	−	1.69670i	−0.235166	−	0.0848351i
$401$	17.2949	−	9.98524i	0.863668	−	0.498639i	−0.00157101	−	0.999999i	$-0.500500\pi$
$401$	17.2949	−	9.98524i	0.863668	−	0.498639i	0.865239	+	0.501360i	$0.167167\pi$
$402$			1.87420i			0.0934764i
$403$	1.08772	−	15.2653i	0.0541834	−	0.760420i
$404$	−11.3355			−0.563964
$405$	−1.71497	−	1.43487i	−0.0852178	−	0.0712995i
$406$	0.0364836	+	0.0631914i	0.00181065	+	0.00313614i
$407$	18.6397	+	10.7616i	0.923936	+	0.533435i
$408$	−0.243297			−0.0120450
$409$	10.6603	+	6.15471i	0.527117	+	0.304331i	0.739842	−	0.672781i	$-0.234900\pi$
$409$	10.6603	+	6.15471i	0.527117	+	0.304331i	−0.212725	+	0.977112i	$0.568234\pi$
$410$	0.535898	+	0.0937060i	0.0264661	+	0.00462781i
$411$		−	7.33417i		−	0.361768i
$412$	5.18029	+	2.99084i	0.255214	+	0.147348i
$413$	−13.7562	+	7.94212i	−0.676896	+	0.390806i
$414$	−7.46758	+	4.31141i	−0.367011	+	0.211894i
$415$	−36.7493	+	13.4350i	−1.80395	+	0.659498i
$416$	−2.02015	+	2.98647i	−0.0990458	+	0.146424i
$417$		−	14.2037i		−	0.695559i
$418$	5.31428	+	9.20461i	0.259930	+	0.450212i
$419$	11.0411	+	19.1238i	0.539393	+	0.934256i	0.998937	+	0.0461011i	$0.0146796\pi$
$419$	11.0411	+	19.1238i	0.539393	+	0.934256i	−0.459544	+	0.888155i	$0.651987\pi$
$420$	3.62584	+	0.634006i	0.176923	+	0.0309363i
$421$		−	8.98036i		−	0.437676i	−0.975761	−	0.218838i	$-0.929773\pi$
$421$		−	8.98036i		−	0.437676i	0.975761	−	0.218838i	$-0.0702266\pi$
$422$	−8.05616	+	13.9537i	−0.392168	+	0.679254i
$423$	−3.64780	+	6.31817i	−0.177362	+	0.307200i
$424$			2.44613i			0.118795i
$425$	1.19740	−	0.214655i	0.0580824	−	0.0104123i
$426$	−3.77030	−	6.53035i	−0.182672	−	0.316397i
$427$	−2.16680	−	3.75300i	−0.104859	−	0.181621i
$428$			10.6759i			0.516039i
$429$	−4.85905	+	7.18335i	−0.234597	+	0.346815i
$430$	−5.16617	−	14.1312i	−0.249135	−	0.681469i
$431$	7.16090	−	4.13435i	0.344928	−	0.199145i	−0.317521	−	0.948251i	$-0.602850\pi$
$431$	7.16090	−	4.13435i	0.344928	−	0.199145i	0.662449	+	0.749107i	$0.269517\pi$
$432$	−0.866025	+	0.500000i	−0.0416667	+	0.0240563i
$433$	17.1825	+	9.92035i	0.825740	+	0.476741i	0.852392	−	0.522903i	$-0.175151\pi$
$433$	17.1825	+	9.92035i	0.825740	+	0.476741i	−0.0266515	+	0.999645i	$0.508484\pi$
$434$			6.98710i			0.335392i
$435$	0.0976359	+	0.0170724i	0.00468128	+	0.000818559i
$436$	8.23316	+	4.75342i	0.394297	+	0.227647i
$437$	−38.1027			−1.82270
$438$	1.47545	+	0.851850i	0.0704996	+	0.0407030i
$439$	−14.4415	−	25.0134i	−0.689255	−	1.19382i	−0.972079	−	0.234653i	$-0.924605\pi$
$439$	−14.4415	−	25.0134i	−0.689255	−	1.19382i	0.282824	−	0.959172i	$-0.408729\pi$
$440$	−3.45130	+	4.12502i	−0.164534	+	0.196653i
$441$	4.29027			0.204299
$442$	0.0623479	−	0.875002i	0.00296559	−	0.0416196i
$443$		−	5.76986i		−	0.274134i	−0.990562	−	0.137067i	$-0.956232\pi$
$443$		−	5.76986i		−	0.274134i	0.990562	−	0.137067i	$-0.0437676\pi$
$444$	−7.74945	+	4.47415i	−0.367772	+	0.212334i
$445$	−14.4108	+	17.2239i	−0.683138	+	0.816493i
$446$	5.55886	−	9.62823i	0.263220	−	0.455910i
$447$	−11.1039			−0.525195
$448$	0.823063	−	1.42559i	0.0388861	−	0.0673526i
$449$	−33.9034	−	19.5741i	−1.60000	−	0.923760i	−0.991486	−	0.130217i	$-0.958433\pi$
$449$	−33.9034	−	19.5741i	−1.60000	−	0.923760i	−0.608514	−	0.793543i	$-0.708234\pi$
$450$	3.82105	−	3.22484i	0.180126	−	0.152021i
$451$	0.292601	−	0.506800i	0.0137780	−	0.0238643i
$452$	3.11433	−	1.79806i	0.146486	−	0.0845736i
$453$	−0.437332	−	0.757480i	−0.0205476	−	0.0355895i
$454$	22.0799			1.03626
$455$	−3.20932	+	12.8776i	−0.150455	+	0.603711i
$456$	−4.41882			−0.206930
$457$	−12.2403	−	21.2008i	−0.572575	−	0.991730i	−0.996300	−	0.0859387i	$-0.972611\pi$
$457$	−12.2403	−	21.2008i	−0.572575	−	0.991730i	0.423725	−	0.905791i	$-0.360722\pi$
$458$	8.95443	−	5.16984i	0.418413	−	0.241571i
$459$	0.121649	−	0.210702i	0.00567807	−	0.00983471i
$460$	−6.62037	−	18.1090i	−0.308677	−	0.844336i
$461$	3.02923	+	1.74893i	0.141085	+	0.0814557i	0.568881	−	0.822420i	$-0.307376\pi$
$461$	3.02923	+	1.74893i	0.141085	+	0.0814557i	−0.427796	+	0.903875i	$0.640710\pi$
$462$	1.97971	−	3.42896i	0.0921044	−	0.159530i
$463$	18.3063			0.850767			0.425384	−	0.905013i	$-0.360139\pi$
$463$	18.3063			0.850767			0.425384	+	0.905013i	$0.360139\pi$
$464$	0.0221633	−	0.0383880i	0.00102891	−	0.00178212i
$465$	7.27934	+	6.09043i	0.337571	+	0.282437i
$466$	18.9597	−	10.9464i	0.878292	−	0.507082i
$467$		−	6.46019i		−	0.298942i	−0.988766	−	0.149471i	$-0.952243\pi$
$467$		−	6.46019i		−	0.298942i	0.988766	−	0.149471i	$-0.0477571\pi$
$468$	−1.57629	−	3.24273i	−0.0728639	−	0.149895i
$469$	3.08516			0.142460
$470$	−12.5118	−	10.4683i	−0.577125	−	0.482865i
$471$	7.75425	+	13.4307i	0.357297	+	0.618856i
$472$	8.35669	+	4.82474i	0.384648	+	0.222077i
$473$	−16.1847			−0.744172
$474$	5.88644	+	3.39854i	0.270373	+	0.156100i
$475$	21.7474	−	3.89860i	0.997840	−	0.178880i
$476$			0.400498i			0.0183568i
$477$	−2.11841	−	1.22307i	−0.0969954	−	0.0560003i
$478$	−22.7341	+	13.1255i	−1.03983	+	0.600347i
$479$	26.5980	−	15.3564i	1.21529	−	0.701651i	0.251387	−	0.967887i	$-0.419113\pi$
$479$	26.5980	−	15.3564i	1.21529	−	0.701651i	0.963908	+	0.266236i	$0.0857800\pi$
$480$	−0.767774	−	2.10012i	−0.0350439	−	0.0958571i
$481$	−14.1051	−	29.0169i	−0.643136	−	1.32306i
$482$			26.0907i			1.18840i
$483$	7.09712	+	12.2926i	0.322930	+	0.559331i
$484$	−2.60727	−	4.51593i	−0.118512	−	0.205270i
$485$	6.35996	−	36.3722i	0.288791	−	1.65158i
$486$		−	1.00000i		−	0.0453609i
$487$	6.23335	−	10.7965i	0.282460	−	0.489235i	−0.689530	−	0.724257i	$-0.742183\pi$
$487$	6.23335	−	10.7965i	0.282460	−	0.489235i	0.971990	+	0.235022i	$0.0755162\pi$
$488$	−1.31630	+	2.27990i	−0.0595862	+	0.103206i
$489$			21.8928i			0.990027i
$490$	−1.65240	+	9.44996i	−0.0746478	+	0.426906i
$491$	1.29120	+	2.23642i	0.0582710	+	0.100928i	0.893689	−	0.448686i	$-0.148108\pi$
$491$	1.29120	+	2.23642i	0.0582710	+	0.100928i	−0.835418	+	0.549615i	$0.814775\pi$
$492$	0.121649	+	0.210702i	0.00548434	+	0.00949916i
$493$			0.0107845i			0.000485711i
$494$	1.13238	−	15.8920i	0.0509480	−	0.715014i
$495$	−1.84672	−	5.05142i	−0.0830041	−	0.227045i
$496$	3.67591	−	2.12229i	0.165053	−	0.0952935i
$497$	−10.7498	+	6.20639i	−0.482194	+	0.278395i
$498$	−15.1543	−	8.74932i	−0.679079	−	0.392066i
$499$			20.2443i			0.906261i	0.891444	+	0.453130i	$0.149693\pi$
$499$			20.2443i			0.906261i	−0.891444	+	0.453130i	$0.850307\pi$
$500$	5.63152	+	9.65847i	0.251849	+	0.431940i
$501$	4.58673	+	2.64815i	0.204920	+	0.118311i
$502$	−0.624794			−0.0278859
$503$	−7.33148	−	4.23283i	−0.326894	−	0.188733i	0.327567	−	0.944828i	$-0.393771\pi$
$503$	−7.33148	−	4.23283i	−0.326894	−	0.188733i	−0.654461	+	0.756095i	$0.727105\pi$
$504$	0.823063	+	1.42559i	0.0366621	+	0.0635007i
$505$	19.4402	+	16.2651i	0.865076	+	0.723786i
$506$	−20.7404			−0.922024
$507$	12.0662	−	4.83802i	0.535879	−	0.214864i
$508$		−	17.3470i		−	0.769650i
$509$	−33.4172	+	19.2935i	−1.48119	+	0.855167i	−0.999773	−	0.0213225i	$-0.993212\pi$
$509$	−33.4172	+	19.2935i	−1.48119	+	0.855167i	−0.481421	+	0.876490i	$0.659879\pi$
$510$	0.417249	+	0.349101i	0.0184761	+	0.0154585i
$511$	1.40225	−	2.42877i	0.0620320	−	0.107443i
$512$	−1.00000			−0.0441942
$513$	2.20941	−	3.82681i	0.0975478	−	0.168958i
$514$	12.0758	+	6.97195i	0.532640	+	0.307520i
$515$	−4.59258	−	12.5623i	−0.202373	−	0.553560i
$516$	3.36438	−	5.82728i	0.148109	−	0.256532i
$517$	−15.1971	+	8.77404i	−0.668367	+	0.385882i
$518$	7.36500	+	12.7566i	0.323600	+	0.560491i
$519$	17.2592			0.757593
$520$	7.74971	−	2.22307i	0.339847	−	0.0974879i
$521$	12.5345			0.549148			0.274574	−	0.961566i	$-0.411463\pi$
$521$	12.5345			0.549148			0.274574	+	0.961566i	$0.411463\pi$
$522$	0.0221633	+	0.0383880i	0.000970061	+	0.00168020i
$523$	11.0846	−	6.39970i	0.484696	−	0.279839i	−0.237676	−	0.971345i	$-0.576386\pi$
$523$	11.0846	−	6.39970i	0.484696	−	0.279839i	0.722371	+	0.691505i	$0.243052\pi$
$524$	−7.08270	+	12.2676i	−0.309409	+	0.535912i
$525$	−5.30850	−	6.28992i	−0.231682	−	0.274515i
$526$	16.8325	+	9.71828i	0.733934	+	0.423737i
$527$	−0.516347	+	0.894339i	−0.0224924	+	0.0389580i
$528$	−2.40530			−0.104677
$529$	25.6765	−	44.4729i	1.11637	−	1.93361i
$530$	3.50989	−	4.19505i	0.152460	−	0.182221i
$531$	−8.35669	+	4.82474i	−0.362649	+	0.209376i
$532$			7.27393i			0.315365i
$533$	−0.788948	+	0.383506i	−0.0341731	+	0.0166115i
$534$	−10.0433			−0.434614
$535$	15.3186	−	18.3089i	0.662279	−	0.791562i
$536$	−0.937098	−	1.62310i	−0.0404765	−	0.0701073i
$537$	−7.23617	−	4.17781i	−0.312264	−	0.180286i
$538$	−3.00139			−0.129399
$539$	8.93684	+	5.15969i	0.384937	+	0.222243i
$540$	2.20265	+	0.385150i	0.0947869	+	0.0165742i
$541$		−	24.9605i		−	1.07314i	−0.843857	−	0.536568i	$-0.819720\pi$
$541$		−	24.9605i		−	1.07314i	0.843857	−	0.536568i	$-0.180280\pi$
$542$	−24.6538	−	14.2339i	−1.05897	−	0.611396i
$543$	11.0276	−	6.36677i	0.473238	−	0.273224i
$544$	0.210702	−	0.121649i	0.00903376	−	0.00521564i
$545$	−7.29910	−	19.9655i	−0.312659	−	0.855229i
$546$	−5.33795	+	2.59477i	−0.228443	+	0.111046i
$547$			10.4152i			0.445321i	0.974896	+	0.222660i	$0.0714741\pi$
$547$			10.4152i			0.445321i	−0.974896	+	0.222660i	$0.928526\pi$
$548$	3.66709	+	6.35158i	0.156650	+	0.271326i
$549$	−1.31630	−	2.27990i	−0.0561784	−	0.0973038i
$550$	11.8378	−	2.12213i	0.504764	−	0.0904878i
$551$			0.195871i			0.00834439i
$552$	4.31141	−	7.46758i	0.183506	−	0.317841i
$553$	5.59442	−	9.68981i	0.237899	−	0.412053i
$554$			0.852658i			0.0362260i
$555$	19.7099	+	3.44644i	0.836640	+	0.146293i
$556$	7.10185	+	12.3008i	0.301186	+	0.521669i
$557$	0.697392	+	1.20792i	0.0295495	+	0.0511812i	0.880422	−	0.474191i	$-0.157259\pi$
$557$	0.697392	+	1.20792i	0.0295495	+	0.0511812i	−0.850872	+	0.525372i	$0.823926\pi$
$558$			4.24458i			0.179687i
$559$	20.0953	+	13.5931i	0.849939	+	0.574926i
$560$	−3.45707	+	1.26385i	−0.146088	+	0.0534075i
$561$	0.506800	−	0.292601i	0.0213971	−	0.0123536i
$562$	13.5837	−	7.84257i	0.572995	−	0.330819i
$563$	−14.0404	−	8.10624i	−0.591733	−	0.341637i	0.174049	−	0.984737i	$-0.444315\pi$
$563$	−14.0404	−	8.10624i	−0.591733	−	0.341637i	−0.765782	+	0.643100i	$0.777648\pi$
$564$		−	7.29560i		−	0.307200i
$565$	−7.92099	−	1.38505i	−0.333238	−	0.0582693i
$566$	7.00390	+	4.04370i	0.294396	+	0.169970i
$567$	−1.64613			−0.0691308
$568$	6.53035	+	3.77030i	0.274007	+	0.158198i
$569$	19.6198	+	33.9825i	0.822505	+	1.42462i	0.903811	+	0.427932i	$0.140758\pi$
$569$	19.6198	+	33.9825i	0.822505	+	1.42462i	−0.0813055	+	0.996689i	$0.525909\pi$
$570$	7.57816	+	6.34045i	0.317414	+	0.265572i
$571$	−16.0498			−0.671662			−0.335831	−	0.941922i	$-0.609017\pi$
$571$	−16.0498			−0.671662			−0.335831	+	0.941922i	$0.609017\pi$
$572$	0.616387	−	8.65049i	0.0257724	−	0.361695i
$573$			0.415264i			0.0173479i
$574$	0.346841	−	0.200249i	0.0144769	−	0.00835823i
$575$	−14.6303	+	40.5558i	−0.610127	+	1.69130i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	28.5363			1.18798			0.593992	−	0.804471i	$-0.297551\pi$
$577$	28.5363			1.18798			0.593992	+	0.804471i	$0.297551\pi$
$578$	8.47040	−	14.6712i	0.352322	−	0.610240i
$579$	22.5025	+	12.9918i	0.935173	+	0.539923i
$580$	−0.0930914	+	0.0340328i	−0.00386541	+	0.00141314i
$581$	−14.4025	+	24.9458i	−0.597515	+	1.03493i
$582$	14.3006	−	8.25647i	0.592780	−	0.342242i
$583$	−2.94183	−	5.09541i	−0.121838	−	0.211030i
$584$	−1.70370			−0.0704996
$585$	−1.94962	+	7.82298i	−0.0806070	+	0.323440i
$586$	−1.93438			−0.0799087
$587$	22.5265	+	39.0171i	0.929770	+	1.61041i	0.783704	+	0.621134i	$0.213328\pi$
$587$	22.5265	+	39.0171i	0.929770	+	1.61041i	0.146066	+	0.989275i	$0.453339\pi$
$588$	−3.71548	+	2.14514i	−0.153224	+	0.0884639i
$589$	−9.37800	+	16.2432i	−0.386414	+	0.669289i
$590$	−7.40862	−	20.2651i	−0.305008	−	0.834301i
$591$	13.3735	+	7.72121i	0.550113	+	0.317608i
$592$	4.47415	−	7.74945i	0.183886	−	0.318500i
$593$	37.0634			1.52201			0.761005	−	0.648746i	$-0.224706\pi$
$593$	37.0634			1.52201			0.761005	+	0.648746i	$0.224706\pi$
$594$	1.20265	−	2.08305i	0.0493453	−	0.0854685i
$595$	0.574664	−	0.686844i	0.0235589	−	0.0281578i
$596$	9.61623	−	5.55193i	0.393896	−	0.227416i
$597$		−	13.7057i		−	0.560938i
$598$	25.7518	+	17.4193i	1.05307	+	0.712330i
$599$	18.6309			0.761238			0.380619	−	0.924732i	$-0.375711\pi$
$599$	18.6309			0.761238			0.380619	+	0.924732i	$0.375711\pi$
$600$	−1.69670	+	4.70332i	−0.0692675	+	0.192012i
$601$	9.69008	+	16.7837i	0.395266	+	0.684622i	0.993135	−	0.116972i	$-0.0373189\pi$
$601$	9.69008	+	16.7837i	0.395266	+	0.684622i	−0.597869	+	0.801594i	$0.703986\pi$
$602$	−9.59244	−	5.53820i	−0.390958	−	0.225720i
$603$	1.87420			0.0763232
$604$	0.757480	+	0.437332i	0.0308214	+	0.0177948i
$605$	−2.00839	+	11.4858i	−0.0816525	+	0.466965i
$606$			11.3355i			0.460475i
$607$	30.2066	+	17.4398i	1.22605	+	0.707858i	0.966200	−	0.257792i	$-0.0829949\pi$
$607$	30.2066	+	17.4398i	1.22605	+	0.707858i	0.259846	+	0.965650i	$0.416328\pi$
$608$	3.82681	−	2.20941i	0.155198	−	0.0896034i
$609$	0.0631914	−	0.0364836i	0.00256064	−	0.00147839i
$610$	5.52879	−	2.02124i	0.223854	−	0.0818378i
$611$	26.2381	+	1.86959i	1.06148	+	0.0756354i
$612$			0.243297i			0.00983471i
$613$	−4.07179	−	7.05254i	−0.164458	−	0.284849i	0.772005	−	0.635617i	$-0.219254\pi$
$613$	−4.07179	−	7.05254i	−0.164458	−	0.284849i	−0.936463	+	0.350767i	$0.885921\pi$
$614$	−6.21918	−	10.7719i	−0.250986	−	0.434720i
$615$	0.0937060	−	0.535898i	0.00377859	−	0.0216095i
$616$			3.95942i			0.159530i
$617$	−16.7288	+	28.9752i	−0.673477	+	1.16650i	0.303435	+	0.952852i	$0.401867\pi$
$617$	−16.7288	+	28.9752i	−0.673477	+	1.16650i	−0.976912	+	0.213644i	$0.931467\pi$
$618$	2.99084	−	5.18029i	0.120309	−	0.208382i
$619$			41.1780i			1.65508i	0.561404	+	0.827542i	$0.310261\pi$
$619$			41.1780i			1.65508i	−0.561404	+	0.827542i	$0.689739\pi$
$620$	−9.34931	−	1.63480i	−0.375477	−	0.0656551i
$621$	4.31141	+	7.46758i	0.173011	+	0.299664i
$622$	−9.18502	−	15.9089i	−0.368286	−	0.637890i
$623$			16.5325i			0.662359i
$624$	2.98647	+	2.02015i	0.119555	+	0.0808706i
$625$	4.20078	−	24.6445i	0.168031	−	0.985782i
$626$	27.6647	−	15.9722i	1.10571	−	0.638379i
$627$	9.20461	−	5.31428i	0.367597	−	0.212232i
$628$	−13.4307	−	7.75425i	−0.535945	−	0.309428i
$629$			2.17709i			0.0868065i
$630$	0.634006	−	3.62584i	0.0252594	−	0.144457i
$631$	12.6839	+	7.32307i	0.504939	+	0.291527i	0.730751	−	0.682644i	$-0.239170\pi$
$631$	12.6839	+	7.32307i	0.504939	+	0.291527i	−0.225812	+	0.974171i	$0.572503\pi$
$632$	−6.79707			−0.270373
$633$	13.9537	+	8.05616i	0.554609	+	0.320204i
$634$	−11.6812	−	20.2325i	−0.463921	−	0.803535i
$635$	−24.8908	+	29.7497i	−0.987761	+	1.18058i
$636$	2.44613			0.0969954
$637$	−6.76270	−	13.9122i	−0.267948	−	0.551222i
$638$			0.106619i			0.00422107i
$639$	−6.53035	+	3.77030i	−0.258337	+	0.149151i
$640$	1.71497	+	1.43487i	0.0677903	+	0.0567184i
$641$	23.9793	−	41.5334i	0.947125	−	1.64047i	0.195686	−	0.980667i	$-0.437307\pi$
$641$	23.9793	−	41.5334i	0.947125	−	1.64047i	0.751439	−	0.659803i	$-0.229360\pi$
$642$	10.6759			0.421344
$643$	−1.99884	+	3.46209i	−0.0788265	+	0.136531i	−0.902744	−	0.430178i	$-0.858451\pi$
$643$	−1.99884	+	3.46209i	−0.0788265	+	0.136531i	0.823917	+	0.566710i	$0.191784\pi$
$644$	−12.2926	−	7.09712i	−0.484395	−	0.279666i
$645$	−14.1312	+	5.16617i	−0.556417	+	0.203418i
$646$	−0.537543	+	0.931052i	−0.0211494	+	0.0366318i
$647$	−20.4521	+	11.8080i	−0.804053	+	0.464220i	−0.844886	−	0.534946i	$-0.820332\pi$
$647$	−20.4521	+	11.8080i	−0.804053	+	0.464220i	0.0408333	+	0.999166i	$0.486999\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	−23.2098			−0.911066
$650$	−16.4804	−	7.30736i	−0.646413	−	0.286618i
$651$	6.98710			0.273846
$652$	−10.9464	−	18.9597i	−0.428694	−	0.742520i
$653$	−30.5411	+	17.6329i	−1.19516	+	0.690029i	−0.959473	−	0.281799i	$-0.909069\pi$
$653$	−30.5411	+	17.6329i	−1.19516	+	0.690029i	−0.235692	+	0.971828i	$0.575735\pi$
$654$	4.75342	−	8.23316i	0.185873	−	0.321942i
$655$	29.7491	−	10.8758i	1.16239	−	0.424954i
$656$	−0.210702	−	0.121649i	−0.00822652	−	0.00474958i
$657$	0.851850	−	1.47545i	0.0332338	−	0.0575627i
$658$	−12.0095			−0.468178
$659$	12.6686	−	21.9427i	0.493499	−	0.854765i	−0.506473	−	0.862256i	$-0.669051\pi$
$659$	12.6686	−	21.9427i	0.493499	−	0.854765i	0.999972	+	0.00749088i	$0.00238444\pi$
$660$	4.12502	+	3.45130i	0.160566	+	0.134342i
$661$	4.21373	−	2.43280i	0.163895	−	0.0946248i	−0.415809	−	0.909452i	$-0.636502\pi$
$661$	4.21373	−	2.43280i	0.163895	−	0.0946248i	0.579704	+	0.814827i	$0.303168\pi$
$662$		−	21.4634i		−	0.834199i
$663$	−0.875002	−	0.0623479i	−0.0339823	−	0.00242139i
$664$	17.4986			0.679079
$665$	10.4372	−	12.4746i	0.404736	−	0.483744i
$666$	4.47415	+	7.74945i	0.173370	+	0.300285i
$667$	−0.331012	−	0.191110i	−0.0128168	−	0.00739981i
$668$	−5.29630			−0.204920
$669$	−9.62823	−	5.55886i	−0.372249	−	0.214918i
$670$	−0.721847	+	4.12820i	−0.0278874	+	0.159486i
$671$		−	6.33219i		−	0.244452i
$672$	−1.42559	−	0.823063i	−0.0549932	−	0.0317503i
$673$	6.48493	−	3.74408i	0.249976	−	0.144324i	−0.369777	−	0.929120i	$-0.620566\pi$
$673$	6.48493	−	3.74408i	0.249976	−	0.144324i	0.619753	+	0.784797i	$0.287233\pi$
$674$	12.4327	−	7.17805i	0.478891	−	0.276488i
$675$	−3.22484	−	3.82105i	−0.124124	−	0.147072i
$676$	−8.03064	+	10.2230i	−0.308871	+	0.393191i
$677$			37.4181i			1.43810i	0.694961	+	0.719048i	$0.255422\pi$
$677$			37.4181i			1.43810i	−0.694961	+	0.719048i	$0.744578\pi$
$678$	−1.79806	−	3.11433i	−0.0690541	−	0.119605i
$679$	−13.5912	−	23.5406i	−0.521582	−	0.903406i
$680$	−0.535898	−	0.0937060i	−0.0205508	−	0.00359346i
$681$		−	22.0799i		−	0.846103i
$682$	−5.10473	+	8.84165i	−0.195470	+	0.338564i
$683$	−3.13940	+	5.43761i	−0.120126	+	0.208064i	−0.919817	−	0.392347i	$-0.871663\pi$
$683$	−3.13940	+	5.43761i	−0.120126	+	0.208064i	0.799691	+	0.600411i	$0.204997\pi$
$684$			4.41882i			0.168958i
$685$	2.82476	−	16.1546i	0.107928	−	0.617236i
$686$	9.29260	+	16.0953i	0.354793	+	0.614520i
$687$	−5.16984	−	8.95443i	−0.197242	−	0.341633i
$688$			6.72876i			0.256532i
$689$	−0.626851	+	8.79735i	−0.0238811	+	0.335152i
$690$	−18.1090	+	6.62037i	−0.689397	+	0.252033i
$691$	−9.17461	+	5.29696i	−0.349019	+	0.201506i	−0.664253	−	0.747508i	$-0.731250\pi$
$691$	−9.17461	+	5.29696i	−0.349019	+	0.201506i	0.315234	+	0.949014i	$0.397917\pi$
$692$	−14.9469	+	8.62958i	−0.568195	+	0.328047i
$693$	−3.42896	−	1.97971i	−0.130255	−	0.0752030i
$694$		−	0.665114i		−	0.0252474i
$695$	5.47056	−	31.2858i	0.207510	−	1.18674i
$696$	−0.0383880	−	0.0221633i	−0.00145509	−	0.000840098i
$697$	0.0591936			0.00224212
$698$	3.25007	+	1.87643i	0.123017	+	0.0710239i
$699$	−10.9464	−	18.9597i	−0.414031	−	0.717123i
$700$	7.74225	+	2.79298i	0.292630	+	0.105565i
$701$	−29.6773			−1.12090			−0.560449	−	0.828189i	$-0.689371\pi$
$701$	−29.6773			−1.12090			−0.560449	+	0.828189i	$0.689371\pi$
$702$	−3.24273	+	1.57629i	−0.122389	+	0.0594931i
$703$			39.5409i			1.49131i
$704$	2.08305	−	1.20265i	0.0785078	−	0.0453265i
$705$	−10.4683	+	12.5118i	−0.394258	+	0.471220i
$706$	2.28180	−	3.95219i	0.0858766	−	0.148743i
$707$	18.6597			0.701771
$708$	4.82474	−	8.35669i	0.181325	−	0.314064i
$709$	0.563901	+	0.325568i	0.0211777	+	0.0122270i	0.510551	−	0.859847i	$-0.329441\pi$
$709$	0.563901	+	0.325568i	0.0211777	+	0.0122270i	−0.489374	+	0.872074i	$0.662775\pi$
$710$	−5.78948	−	15.8362i	−0.217275	−	0.594322i
$711$	3.39854	−	5.88644i	0.127455	−	0.220759i
$712$	8.69772	−	5.02163i	0.325961	−	0.188194i
$713$	−18.3001	−	31.6967i	−0.685344	−	1.18705i
$714$	0.400498			0.0149883
$715$	−13.4694	+	13.9509i	−0.503729	+	0.521735i
$716$	8.35561			0.312264
$717$	13.1255	+	22.7341i	0.490181	+	0.849019i
$718$	−4.12042	+	2.37892i	−0.153773	+	0.0887807i
$719$	−3.21203	+	5.56340i	−0.119789	+	0.207480i	−0.919684	−	0.392660i	$-0.871555\pi$
$719$	−3.21203	+	5.56340i	−0.119789	+	0.207480i	0.799895	+	0.600140i	$0.204888\pi$
$720$	−2.10012	+	0.767774i	−0.0782670	+	0.0286133i
$721$	−8.52740	−	4.92330i	−0.317577	−	0.183353i
$722$	−0.262979	+	0.455494i	−0.00978708	+	0.0169517i
$723$	26.0907			0.970325
$724$	−6.36677	+	11.0276i	−0.236619	+	0.409836i
$725$	0.208482	+	0.0752090i	0.00774283	+	0.00279319i
$726$	−4.51593	+	2.60727i	−0.167602	+	0.0967650i
$727$		−	16.3170i		−	0.605165i	−0.953123	−	0.302583i	$-0.902151\pi$
$727$		−	16.3170i		−	0.605165i	0.953123	−	0.302583i	$-0.0978488\pi$
$728$	3.32541	−	4.91611i	0.123248	−	0.182203i
$729$	−1.00000			−0.0370370
$730$	2.92180	+	2.44459i	0.108141	+	0.0904785i
$731$	−0.818545	−	1.41776i	−0.0302750	−	0.0524378i
$732$	2.27990	+	1.31630i	0.0842676	+	0.0486519i
$733$	24.4136			0.901735			0.450868	−	0.892591i	$-0.351115\pi$
$733$	24.4136			0.901735			0.450868	+	0.892591i	$0.351115\pi$
$734$	1.29432	+	0.747277i	0.0477743	+	0.0275825i
$735$	9.44996	+	1.65240i	0.348567	+	0.0609497i
$736$			8.62281i			0.317841i
$737$	3.90404	+	2.25400i	0.143807	+	0.0830271i
$738$	0.210702	−	0.121649i	0.00775603	−	0.00447795i
$739$	4.75775	−	2.74689i	0.175017	−	0.101046i	−0.409932	−	0.912116i	$-0.634448\pi$
$739$	4.75775	−	2.74689i	0.175017	−	0.101046i	0.584949	+	0.811070i	$0.301114\pi$
$740$	−18.7925	+	6.87027i	−0.690827	+	0.252556i
$741$	−15.8920	−	1.13238i	−0.583807	−	0.0415989i
$742$		−	4.02664i		−	0.147823i
$743$	−10.6512	−	18.4484i	−0.390753	−	0.676804i	0.601796	−	0.798650i	$-0.294452\pi$
$743$	−10.6512	−	18.4484i	−0.390753	−	0.676804i	−0.992549	+	0.121845i	$0.961119\pi$
$744$	−2.12229	−	3.67591i	−0.0778068	−	0.134765i
$745$	−24.4579	−	4.27666i	−0.896068	−	0.156685i
$746$			20.5910i			0.753890i
$747$	−8.74932	+	15.1543i	−0.320121	+	0.554466i
$748$	−0.292601	+	0.506800i	−0.0106986	+	0.0185304i
$749$		−	17.5739i		−	0.642135i
$750$	9.65847	−	5.63152i	0.352677	−	0.205634i
$751$	−15.4023	−	26.6776i	−0.562040	−	0.973481i	−0.997318	−	0.0731853i	$-0.976684\pi$
$751$	−15.4023	−	26.6776i	−0.562040	−	0.973481i	0.435279	−	0.900296i	$-0.356650\pi$
$752$	3.64780	+	6.31817i	0.133022	+	0.230400i
$753$			0.624794i			0.0227688i
$754$	0.0895462	−	0.132380i	0.00326108	−	0.00482100i
$755$	−0.671544	−	1.83690i	−0.0244400	−	0.0668517i
$756$	1.42559	−	0.823063i	0.0518481	−	0.0299345i
$757$	−30.4180	+	17.5618i	−1.10556	+	0.638296i	−0.937676	−	0.347511i	$-0.887027\pi$
$757$	−30.4180	+	17.5618i	−1.10556	+	0.638296i	−0.167885	+	0.985807i	$0.553694\pi$
$758$	−18.4173	−	10.6332i	−0.668946	−	0.386216i
$759$			20.7404i			0.752830i
$760$	−9.73310	−	1.70191i	−0.353057	−	0.0617347i
$761$	−25.0686	−	14.4734i	−0.908737	−	0.524659i	−0.0287122	−	0.999588i	$-0.509141\pi$
$761$	−25.0686	−	14.4734i	−0.908737	−	0.524659i	−0.880024	+	0.474928i	$0.842474\pi$
$762$	−17.3470			−0.628416
$763$	−13.5528	−	7.82472i	−0.490645	−	0.283274i
$764$	−0.207632	−	0.359629i	−0.00751187	−	0.0130109i
$765$	0.349101	−	0.417249i	0.0126218	−	0.0150857i
$766$	10.6219			0.383785
$767$	28.8179	+	19.4933i	1.04055	+	0.703864i
$768$			1.00000i			0.0360844i
$769$	−34.3740	+	19.8459i	−1.23956	+	0.715660i	−0.969004	−	0.247045i	$-0.920541\pi$
$769$	−34.3740	+	19.8459i	−1.23956	+	0.715660i	−0.270555	+	0.962704i	$0.587207\pi$
$770$	5.68127	−	6.79030i	0.204739	−	0.244706i
$771$	6.97195	−	12.0758i	0.251089	−	0.434898i
$772$	−25.9837			−0.935173
$773$	−7.16938	+	12.4177i	−0.257865	+	0.446635i	−0.965670	−	0.259773i	$-0.916352\pi$
$773$	−7.16938	+	12.4177i	−0.257865	+	0.446635i	0.707805	+	0.706408i	$0.249686\pi$
$774$	−5.82728	−	3.36438i	−0.209457	−	0.120930i
$775$	13.6881	+	16.2187i	0.491691	+	0.582594i
$776$	−8.25647	+	14.3006i	−0.296390	+	0.513363i
$777$	12.7566	−	7.36500i	0.457639	−	0.264218i
$778$	−18.5222	−	32.0813i	−0.664052	−	1.15017i
$779$	1.07509			0.0385190
$780$	−2.22307	−	7.74971i	−0.0795985	−	0.277484i
$781$	−18.1374			−0.649007
$782$	−1.04895	−	1.81684i	−0.0375105	−	0.0649701i
$783$	0.0383880	−	0.0221633i	0.00137187	−	0.000792052i
$784$	2.14514	−	3.71548i	0.0766120	−	0.132696i
$785$	11.9070	+	32.5698i	0.424980	+	1.16246i
$786$	12.2676	+	7.08270i	0.437571	+	0.252631i
$787$	5.52776	−	9.57437i	0.197043	−	0.341289i	−0.750525	−	0.660842i	$-0.770199\pi$
$787$	5.52776	−	9.57437i	0.197043	−	0.341289i	0.947568	+	0.319553i	$0.103533\pi$
$788$	−15.4424			−0.550113
$789$	9.71828	−	16.8325i	0.345980	−	0.599255i
$790$	11.6568	+	9.75294i	0.414730	+	0.346994i
$791$	−5.12658	+	2.95983i	−0.182280	+	0.105240i
$792$			2.40530i			0.0854685i
$793$	−5.31824	+	7.86219i	−0.188856	+	0.279195i
$794$	−1.68719			−0.0598760
$795$	−4.19505	−	3.50989i	−0.148783	−	0.124483i
$796$	6.85286	+	11.8695i	0.242893	+	0.420704i
$797$	0.453218	+	0.261666i	0.0160538	+	0.00926867i	0.508005	−	0.861354i	$-0.330383\pi$
$797$	0.453218	+	0.261666i	0.0160538	+	0.00926867i	−0.491952	+	0.870623i	$0.663716\pi$
$798$	7.27393			0.257494
$799$	−1.53719	−	0.887500i	−0.0543820	−	0.0313975i
$800$	−0.882273	−	4.92154i	−0.0311931	−	0.174003i
$801$			10.0433i			0.354861i
$802$	17.2949	+	9.98524i	0.610705	+	0.352591i
$803$	3.54889	−	2.04895i	0.125238	−	0.0723059i
$804$	−1.62310	+	0.937098i	−0.0572424	+	0.0330489i
$805$	10.8980	+	29.8097i	0.384103	+	1.05065i
$806$	13.7640	−	6.69067i	0.484817	−	0.235669i
$807$			3.00139i			0.105654i
$808$	−5.66777	−	9.81687i	−0.199391	−	0.345356i
$809$	−24.5608	−	42.5405i	−0.863511	−	1.49564i	−0.868518	−	0.495657i	$-0.834927\pi$
$809$	−24.5608	−	42.5405i	−0.863511	−	1.49564i	0.00500771	−	0.999987i	$-0.498406\pi$
$810$	0.385150	−	2.20265i	0.0135328	−	0.0773932i
$811$			31.5157i			1.10667i	0.832960	+	0.553333i	$0.186644\pi$
$811$			31.5157i			1.10667i	−0.832960	+	0.553333i	$0.813356\pi$
$812$	−0.0364836	+	0.0631914i	−0.00128032	+	0.00221758i
$813$	−14.2339	+	24.6538i	−0.499203	+	0.864645i
$814$			21.5233i			0.754391i
$815$	−8.43202	+	48.2222i	−0.295361	+	1.68915i
$816$	−0.121649	−	0.210702i	−0.00425855	−	0.00737603i
$817$	−14.8666	−	25.7497i	−0.520116	−	0.900868i
$818$			12.3094i			0.430389i
$819$	2.59477	+	5.33795i	0.0906685	+	0.186523i
$820$	0.186797	+	0.510955i	0.00652325	+	0.0178433i
$821$	−13.8449	+	7.99335i	−0.483190	+	0.278970i	−0.721745	−	0.692159i	$-0.756660\pi$
$821$	−13.8449	+	7.99335i	−0.483190	+	0.278970i	0.238555	+	0.971129i	$0.423326\pi$
$822$	6.35158	−	3.66709i	0.221537	−	0.127904i
$823$	21.8287	+	12.6028i	0.760900	+	0.439306i	0.829619	−	0.558330i	$-0.188558\pi$
$823$	21.8287	+	12.6028i	0.760900	+	0.439306i	−0.0687187	+	0.997636i	$0.521891\pi$
$824$			5.98168i			0.208382i
$825$	−2.12213	−	11.8378i	−0.0738830	−	0.412138i
$826$	−13.7562	−	7.94212i	−0.478638	−	0.276342i
$827$	22.0889			0.768106			0.384053	−	0.923311i	$-0.374528\pi$
$827$	22.0889			0.768106			0.384053	+	0.923311i	$0.374528\pi$
$828$	−7.46758	−	4.31141i	−0.259516	−	0.149832i
$829$	−4.72499	−	8.18393i	−0.164106	−	0.284240i	0.772232	−	0.635341i	$-0.219141\pi$
$829$	−4.72499	−	8.18393i	−0.164106	−	0.284240i	−0.936337	+	0.351102i	$0.885807\pi$
$830$	−30.0097	−	25.1083i	−1.04165	−	0.871523i
$831$	0.852658			0.0295784
$832$	−3.59643	−	0.256262i	−0.124684	−	0.00888430i
$833$			1.04381i			0.0361659i
$834$	12.3008	−	7.10185i	0.425941	−	0.245917i
$835$	9.08302	+	7.59952i	0.314331	+	0.262992i
$836$	−5.31428	+	9.20461i	−0.183798	+	0.318348i
$837$	4.24458			0.146714
$838$	−11.0411	+	19.1238i	−0.381409	+	0.660619i
$839$	−10.8542	−	6.26667i	−0.374728	−	0.216350i	0.300794	−	0.953689i	$-0.402748\pi$
$839$	−10.8542	−	6.26667i	−0.374728	−	0.216350i	−0.675522	+	0.737340i	$0.736082\pi$
$840$	1.26385	+	3.45707i	0.0436071	+	0.119280i
$841$	14.4990	−	25.1130i	0.499966	−	0.865967i
$842$	7.77722	−	4.49018i	0.268021	−	0.154742i
$843$	−7.84257	−	13.5837i	−0.270112	−	0.467848i
$844$	−16.1123			−0.554609
$845$	28.4410	−	6.00915i	0.978400	−	0.206721i
$846$	−7.29560			−0.250828
$847$	4.29190	+	7.43379i	0.147471	+	0.255428i
$848$	−2.11841	+	1.22307i	−0.0727465	+	0.0420002i
$849$	4.04370	−	7.00390i	0.138780	−	0.240373i
$850$	0.784596	+	0.929650i	0.0269114	+	0.0318867i
$851$	−66.8220	−	38.5797i	−2.29063	−	1.32250i
$852$	3.77030	−	6.53035i	0.129168	−	0.223726i
$853$	−54.5472			−1.86766			−0.933830	−	0.357718i	$-0.883555\pi$
$853$	−54.5472			−1.86766			−0.933830	+	0.357718i	$0.883555\pi$
$854$	2.16680	−	3.75300i	0.0741463	−	0.128425i
$855$	6.34045	−	7.57816i	0.216839	−	0.259168i
$856$	−9.24559	+	5.33795i	−0.316008	+	0.182447i
$857$			16.1596i			0.552000i	0.961158	+	0.276000i	$0.0890091\pi$
$857$			16.1596i			0.552000i	−0.961158	+	0.276000i	$0.910991\pi$
$858$	−8.65049	−	0.616387i	−0.295323	−	0.0210431i
$859$	8.02338			0.273754			0.136877	−	0.990588i	$-0.456293\pi$
$859$	8.02338			0.273754			0.136877	+	0.990588i	$0.456293\pi$
$860$	9.65493	−	11.5397i	0.329230	−	0.393499i
$861$	−0.200249	−	0.346841i	−0.00682447	−	0.0118203i
$862$	7.16090	+	4.13435i	0.243901	+	0.140816i
$863$	−28.2909			−0.963033			−0.481517	−	0.876437i	$-0.659914\pi$
$863$	−28.2909			−0.963033			−0.481517	+	0.876437i	$0.659914\pi$
$864$	−0.866025	−	0.500000i	−0.0294628	−	0.0170103i
$865$	38.0159	+	6.64737i	1.29258	+	0.226017i
$866$			19.8407i			0.674214i
$867$	−14.6712	−	8.47040i	−0.498259	−	0.287670i
$868$	−6.05101	+	3.49355i	−0.205385	+	0.118579i
$869$	14.1586	−	8.17449i	0.480298	−	0.277300i
$870$	0.0340328	+	0.0930914i	0.00115382	+	0.00315609i
$871$	−2.95427	−	6.07752i	−0.100102	−	0.205929i
$872$			9.50683i			0.321942i
$873$	−8.25647	−	14.3006i	−0.279439	−	0.484003i
$874$	−19.0513	−	32.9979i	−0.644421	−	1.11617i
$875$	−9.27018	−	15.8991i	−0.313389	−	0.537486i
$876$			1.70370i			0.0575627i
$877$	11.3031	−	19.5775i	0.381678	−	0.661085i	−0.609625	−	0.792690i	$-0.708680\pi$
$877$	11.3031	−	19.5775i	0.381678	−	0.661085i	0.991302	+	0.131605i	$0.0420131\pi$
$878$	14.4415	−	25.0134i	0.487377	−	0.844161i
$879$			1.93438i			0.0652451i
$880$	−5.29802	−	0.926401i	−0.178596	−	0.0312290i
$881$	22.1679	+	38.3959i	0.746854	+	1.29359i	0.949324	+	0.314301i	$0.101770\pi$
$881$	22.1679	+	38.3959i	0.746854	+	1.29359i	−0.202470	+	0.979289i	$0.564897\pi$
$882$	2.14514	+	3.71548i	0.0722305	+	0.125107i
$883$		−	3.93200i		−	0.132322i	−0.997809	−	0.0661612i	$-0.978925\pi$
$883$		−	3.93200i		−	0.132322i	0.997809	−	0.0661612i	$-0.0210752\pi$
$884$	0.788948	−	0.383506i	0.0265352	−	0.0128987i
$885$	−20.2651	+	7.40862i	−0.681204	+	0.249038i
$886$	4.99684	−	2.88493i	0.167872	−	0.0969211i
$887$	25.2382	−	14.5713i	0.847416	−	0.489256i	−0.0123622	−	0.999924i	$-0.503935\pi$
$887$	25.2382	−	14.5713i	0.847416	−	0.489256i	0.859778	+	0.510668i	$0.170602\pi$
$888$	−7.74945	−	4.47415i	−0.260054	−	0.150142i
$889$			28.5554i			0.957717i
$890$	−22.1218	−	3.86817i	−0.741523	−	0.129661i
$891$	−2.08305	−	1.20265i	−0.0697847	−	0.0402902i
$892$	11.1177			0.372249
$893$	−27.9189	−	16.1190i	−0.934269	−	0.539401i
$894$	−5.55193	−	9.61623i	−0.185684	−	0.321615i
$895$	−14.3297	−	11.9893i	−0.478988	−	0.400756i
$896$	1.64613			0.0549932
$897$	17.4193	−	25.7518i	0.581615	−	0.859827i
$898$		−	39.1483i		−	1.30639i
$899$	−0.162941	+	0.0940738i	−0.00543437	+	0.00313754i
$900$	4.70332	+	1.69670i	0.156777	+	0.0565567i
$901$	0.297569	−	0.515404i	0.00991344	−	0.0171706i
$902$	0.585202			0.0194851
$903$	−5.53820	+	9.59244i	−0.184300	+	0.319216i
$904$	3.11433	+	1.79806i	0.103581	+	0.0598026i
$905$	26.7420	−	9.77648i	0.888934	−	0.324981i
$906$	0.437332	−	0.757480i	0.0145294	−	0.0251656i
$907$	31.2795	−	18.0592i	1.03862	−	0.599647i	0.119177	−	0.992873i	$-0.461974\pi$
$907$	31.2795	−	18.0592i	1.03862	−	0.599647i	0.919442	+	0.393226i	$0.128641\pi$
$908$	11.0399	+	19.1217i	0.366373	+	0.634577i
$909$	11.3355			0.375976
$910$	−12.7570	+	3.65944i	−0.422890	+	0.121309i
$911$	−16.1738			−0.535863			−0.267931	−	0.963438i	$-0.586340\pi$
$911$	−16.1738			−0.535863			−0.267931	+	0.963438i	$0.586340\pi$
$912$	−2.20941	−	3.82681i	−0.0731609	−	0.126718i
$913$	−36.4505	+	21.0447i	−1.20634	+	0.696478i
$914$	12.2403	−	21.2008i	0.404872	−	0.701259i
$915$	−2.02124	−	5.52879i	−0.0668203	−	0.182776i
$916$	8.95443	+	5.16984i	0.295863	+	0.170816i
$917$	11.6590	−	20.1940i	0.385014	−	0.666865i
$918$	0.243297			0.00803001
$919$	−1.12534	+	1.94914i	−0.0371214	+	0.0642962i	−0.883989	−	0.467507i	$-0.845152\pi$
$919$	−1.12534	+	1.94914i	−0.0371214	+	0.0642962i	0.846868	+	0.531803i	$0.178486\pi$
$920$	12.3727	−	14.7879i	0.407914	−	0.487543i
$921$	−10.7719	+	6.21918i	−0.354947	+	0.204929i
$922$			3.49785i			0.115196i
$923$	22.5198	+	15.2331i	0.741248	+	0.501404i
$924$	3.95942			0.130255
$925$	42.0867	+	15.1826i	1.38380	+	0.499200i
$926$	9.15317	+	15.8537i	0.300792	+	0.520987i
$927$	−5.18029	−	2.99084i	−0.170143	−	0.0982321i
$928$	0.0443266			0.00145509
$929$	23.2193	+	13.4057i	0.761801	+	0.439826i	0.829942	−	0.557850i	$-0.188374\pi$
$929$	23.2193	+	13.4057i	0.761801	+	0.439826i	−0.0681412	+	0.997676i	$0.521707\pi$
$930$	−1.63480	+	9.34931i	−0.0536072	+	0.306576i
$931$			18.9579i			0.621321i
$932$	18.9597	+	10.9464i	0.621046	+	0.358561i
$933$	−15.9089	+	9.18502i	−0.520835	+	0.300704i
$934$	5.59469	−	3.23010i	0.183064	−	0.105692i
$935$	1.22900	−	0.449303i	0.0401925	−	0.0146938i
$936$	2.02015	−	2.98647i	0.0660305	−	0.0976159i
$937$			44.1333i			1.44177i	0.693053	+	0.720887i	$0.256265\pi$
$937$			44.1333i			1.44177i	−0.693053	+	0.720887i	$0.743735\pi$
$938$	1.54258	+	2.67183i	0.0503671	+	0.0872383i
$939$	−15.9722	−	27.6647i	−0.521234	−	0.902804i
$940$	2.80990	−	16.0696i	0.0916489	−	0.524134i
$941$		−	28.3857i		−	0.925348i	−0.886528	−	0.462674i	$-0.846890\pi$
$941$		−	28.3857i		−	0.925348i	0.886528	−	0.462674i	$-0.153110\pi$
$942$	−7.75425	+	13.4307i	−0.252647	+	0.437597i
$943$	−1.04895	+	1.81684i	−0.0341586	+	0.0591645i
$944$			9.64947i			0.314064i
$945$	−3.62584	−	0.634006i	−0.117948	−	0.0206242i
$946$	−8.09234	−	14.0163i	−0.263105	−	0.455710i
$947$	−24.6676	−	42.7256i	−0.801590	−	1.38839i	−0.918569	−	0.395260i	$-0.870654\pi$
$947$	−24.6676	−	42.7256i	−0.801590	−	1.38839i	0.116979	−	0.993134i	$-0.462679\pi$
$948$			6.79707i			0.220759i
$949$	−6.12724	−	0.436594i	−0.198899	−	0.0141724i
$950$	14.2500	+	16.8845i	0.462331	+	0.547806i
$951$	−20.2325	+	11.6812i	−0.656083	+	0.378790i
$952$	−0.346841	+	0.200249i	−0.0112412	+	0.00649011i
$953$	−9.62904	−	5.55933i	−0.311915	−	0.180084i	0.335868	−	0.941909i	$-0.390970\pi$
$953$	−9.62904	−	5.55933i	−0.311915	−	0.180084i	−0.647783	+	0.761825i	$0.724304\pi$
$954$		−	2.44613i		−	0.0791964i
$955$	−0.159939	+	0.914681i	−0.00517551	+	0.0295984i
$956$	−22.7341	−	13.1255i	−0.735272	−	0.424510i
$957$	0.106619			0.00344649
$958$	26.5980	+	15.3564i	0.859343	+	0.496142i
$959$	−6.03648	−	10.4555i	−0.194928	−	0.337626i
$960$	1.43487	−	1.71497i	0.0463104	−	0.0553506i
$961$	12.9836			0.418825
$962$	18.0769	−	26.7238i	0.582821	−	0.861610i
$963$		−	10.6759i		−	0.344026i
$964$	−22.5952	+	13.0454i	−0.727744	+	0.420163i
$965$	44.5614	+	37.2833i	1.43448	+	1.20019i
$966$	−7.09712	+	12.2926i	−0.228346	+	0.395507i
$967$	−55.3514			−1.77998			−0.889990	−	0.455980i	$-0.849289\pi$
$967$	−55.3514			−1.77998			−0.889990	+	0.455980i	$0.849289\pi$
$968$	2.60727	−	4.51593i	0.0838010	−	0.145148i
$969$	0.931052	+	0.537543i	0.0299097	+	0.0172684i
$970$	34.6792	−	12.6782i	1.11348	−	0.407073i
$971$	−26.8248	+	46.4619i	−0.860848	+	1.49103i	0.0102641	+	0.999947i	$0.496733\pi$
$971$	−26.8248	+	46.4619i	−0.860848	+	1.49103i	−0.871112	+	0.491085i	$0.836601\pi$
$972$	0.866025	−	0.500000i	0.0277778	−	0.0160375i
$973$	−11.6905	−	20.2486i	−0.374782	−	0.649141i
$974$	12.4667			0.399459
$975$	−7.30736	+	16.4804i	−0.234023	+	0.527794i
$976$	−2.63260			−0.0842676
$977$	−6.23411	−	10.7978i	−0.199447	−	0.345452i	0.748902	−	0.662680i	$-0.230581\pi$
$977$	−6.23411	−	10.7978i	−0.199447	−	0.345452i	−0.948349	+	0.317228i	$0.897248\pi$
$978$	−18.9597	+	10.9464i	−0.606265	+	0.350027i
$979$	−12.0785	+	20.9206i	−0.386031	+	0.668625i
$980$	−9.01010	+	3.29396i	−0.287817	+	0.105222i
$981$	−8.23316	−	4.75342i	−0.262865	−	0.151765i
$982$	−1.29120	+	2.23642i	−0.0412038	+	0.0713671i
$983$	19.1972			0.612296			0.306148	−	0.951984i	$-0.400960\pi$
$983$	19.1972			0.612296			0.306148	+	0.951984i	$0.400960\pi$
$984$	−0.121649	+	0.210702i	−0.00387802	+	0.00671692i
$985$	26.4833	+	22.1579i	0.843830	+	0.706010i
$986$	−0.00933969	+	0.00539227i	−0.000297436	+	0.000171725i
$987$			12.0095i			0.382266i
$988$	14.3291	−	6.96533i	0.455868	−	0.221597i
$989$	58.0209			1.84496
$990$	3.45130	−	4.12502i	0.109689	−	0.131102i
$991$	−27.4152	−	47.4845i	−0.870872	−	1.50840i	−0.861096	−	0.508443i	$-0.830221\pi$
$991$	−27.4152	−	47.4845i	−0.870872	−	1.50840i	−0.00977694	−	0.999952i	$-0.503112\pi$
$992$	3.67591	+	2.12229i	0.116710	+	0.0673827i
$993$	−21.4634			−0.681120
$994$	−10.7498	−	6.20639i	−0.340962	−	0.196855i
$995$	5.27876	−	30.1889i	0.167348	−	0.957052i
$996$		−	17.4986i		−	0.554466i
$997$	35.4227	+	20.4513i	1.12185	+	0.647700i	0.941872	−	0.335971i	$-0.109064\pi$
$997$	35.4227	+	20.4513i	1.12185	+	0.647700i	0.179977	+	0.983671i	$0.442398\pi$
$998$	−17.5321	+	10.1222i	−0.554969	+	0.320412i
$999$	7.74945	−	4.47415i	0.245182	−	0.141556i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.x.b.49.6	yes	12
3.2	odd	2		1170.2.bj.c.829.1		12
5.2	odd	4		1950.2.bc.i.751.2		12
5.3	odd	4		1950.2.bc.j.751.5		12
5.4	even	2		390.2.x.a.49.1	✓	12
13.4	even	6		390.2.x.a.199.1	yes	12
15.14	odd	2		1170.2.bj.d.829.6		12
39.17	odd	6		1170.2.bj.d.199.6		12
65.4	even	6	inner	390.2.x.b.199.6	yes	12
65.17	odd	12		1950.2.bc.i.901.2		12
65.43	odd	12		1950.2.bc.j.901.5		12
195.134	odd	6		1170.2.bj.c.199.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.x.a.49.1	✓	12	5.4	even	2
390.2.x.a.199.1	yes	12	13.4	even	6
390.2.x.b.49.6	yes	12	1.1	even	1	trivial
390.2.x.b.199.6	yes	12	65.4	even	6	inner
1170.2.bj.c.199.1		12	195.134	odd	6
1170.2.bj.c.829.1		12	3.2	odd	2
1170.2.bj.d.199.6		12	39.17	odd	6
1170.2.bj.d.829.6		12	15.14	odd	2
1950.2.bc.i.751.2		12	5.2	odd	4
1950.2.bc.i.901.2		12	65.17	odd	12
1950.2.bc.j.751.5		12	5.3	odd	4
1950.2.bc.j.901.5		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)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.10012 - 0.767774i) q^{5} +(0.866025 + 0.500000i) q^{6} +(0.823063 - 1.42559i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.10012 - 0.767774i) q^{5} +(0.866025 + 0.500000i) q^{6} +(0.823063 - 1.42559i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(1.71497 + 1.43487i) q^{10} +(2.08305 - 1.20265i) q^{11} +1.00000i q^{12} +(-3.59643 - 0.256262i) q^{13} +1.64613 q^{14} +(1.43487 - 1.71497i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.210702 + 0.121649i) q^{17} +1.00000 q^{18} +(3.82681 + 2.20941i) q^{19} +(-0.385150 + 2.20265i) q^{20} -1.64613i q^{21} +(2.08305 + 1.20265i) q^{22} +(-7.46758 + 4.31141i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(3.82105 - 3.22484i) q^{25} +(-1.57629 - 3.24273i) q^{26} -1.00000i q^{27} +(0.823063 + 1.42559i) q^{28} +(0.0221633 + 0.0383880i) q^{29} +(2.20265 + 0.385150i) q^{30} +4.24458i q^{31} +(0.500000 - 0.866025i) q^{32} +(1.20265 - 2.08305i) q^{33} +0.243297i q^{34} +(0.634006 - 3.62584i) q^{35} +(0.500000 + 0.866025i) q^{36} +(4.47415 + 7.74945i) q^{37} +4.41882i q^{38} +(-3.24273 + 1.57629i) q^{39} +(-2.10012 + 0.767774i) q^{40} +(0.210702 - 0.121649i) q^{41} +(1.42559 - 0.823063i) q^{42} +(-5.82728 - 3.36438i) q^{43} +2.40530i q^{44} +(0.385150 - 2.20265i) q^{45} +(-7.46758 - 4.31141i) q^{46} -7.29560 q^{47} +(-0.866025 - 0.500000i) q^{48} +(2.14514 + 3.71548i) q^{49} +(4.70332 + 1.69670i) q^{50} +0.243297 q^{51} +(2.02015 - 2.98647i) q^{52} -2.44613i q^{53} +(0.866025 - 0.500000i) q^{54} +(3.45130 - 4.12502i) q^{55} +(-0.823063 + 1.42559i) q^{56} +4.41882 q^{57} +(-0.0221633 + 0.0383880i) q^{58} +(-8.35669 - 4.82474i) q^{59} +(0.767774 + 2.10012i) q^{60} +(1.31630 - 2.27990i) q^{61} +(-3.67591 + 2.12229i) q^{62} +(-0.823063 - 1.42559i) q^{63} +1.00000 q^{64} +(-7.74971 + 2.22307i) q^{65} +2.40530 q^{66} +(0.937098 + 1.62310i) q^{67} +(-0.210702 + 0.121649i) q^{68} +(-4.31141 + 7.46758i) q^{69} +(3.45707 - 1.26385i) q^{70} +(-6.53035 - 3.77030i) q^{71} +(-0.500000 + 0.866025i) q^{72} +1.70370 q^{73} +(-4.47415 + 7.74945i) q^{74} +(1.69670 - 4.70332i) q^{75} +(-3.82681 + 2.20941i) q^{76} -3.95942i q^{77} +(-2.98647 - 2.02015i) q^{78} +6.79707 q^{79} +(-1.71497 - 1.43487i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.210702 + 0.121649i) q^{82} -17.4986 q^{83} +(1.42559 + 0.823063i) q^{84} +(0.535898 + 0.0937060i) q^{85} -6.72876i q^{86} +(0.0383880 + 0.0221633i) q^{87} +(-2.08305 + 1.20265i) q^{88} +(-8.69772 + 5.02163i) q^{89} +(2.10012 - 0.767774i) q^{90} +(-3.32541 + 4.91611i) q^{91} -8.62281i q^{92} +(2.12229 + 3.67591i) q^{93} +(-3.64780 - 6.31817i) q^{94} +(9.73310 + 1.70191i) q^{95} -1.00000i q^{96} +(8.25647 - 14.3006i) q^{97} +(-2.14514 + 3.71548i) q^{98} -2.40530i 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more