LMFDB - Embedded newform 390.2.x.a.199.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("390.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.x (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.11416567883$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} - 8 x^{10} + 34 x^{9} + 8 x^{8} - 134 x^{7} + 98 x^{6} + 154 x^{5} + 104 x^{4} + \cdots + 2197 $ x^12 - 2x^11 - 8x^10 + 34x^9 + 8x^8 - 134x^7 + 98x^6 + 154x^5 + 104x^4 + 190x^3 - 1196x^2 - 338*x + 2197
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.1
Root			$-2.39378 - 0.0429626i$ of defining polynomial
Character	$\chi$	$=$	390.199
Dual form			390.2.x.a.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.10012 + 0.767774i) q^{5} +(0.866025 - 0.500000i) q^{6} +(-0.823063 - 1.42559i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(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} +(0.385150 - 2.20265i) q^{10} +(2.08305 + 1.20265i) q^{11} +1.00000i q^{12} +(3.59643 - 0.256262i) q^{13} +1.64613 q^{14} +(2.20265 + 0.385150i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.210702 + 0.121649i) q^{17} -1.00000 q^{18} +(3.82681 - 2.20941i) q^{19} +(1.71497 + 1.43487i) 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} +(-1.43487 + 1.71497i) q^{30} -4.24458i q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.20265 - 2.08305i) q^{33} -0.243297i q^{34} +(2.82306 + 2.36198i) 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} +(-1.71497 - 1.43487i) q^{45} +(-7.46758 + 4.31141i) q^{46} +7.29560 q^{47} +(0.866025 - 0.500000i) q^{48} +(2.14514 - 3.71548i) q^{49} +(0.882273 + 4.92154i) q^{50} +0.243297 q^{51} +(-2.02015 - 2.98647i) q^{52} -2.44613i q^{53} +(0.866025 + 0.500000i) q^{54} +(-5.29802 - 0.926401i) 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} +(-7.35621 + 3.29943i) 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} +(-4.92154 + 0.882273i) q^{75} +(-3.82681 - 2.20941i) q^{76} -3.95942i q^{77} +(2.98647 - 2.02015i) q^{78} +6.79707 q^{79} +(0.385150 - 2.20265i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.210702 + 0.121649i) q^{82} +17.4986 q^{83} +(1.42559 - 0.823063i) q^{84} +(0.349101 - 0.417249i) 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} +(-6.34045 + 7.57816i) 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} - 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 $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−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	$-0.267360\pi$
$7$	−0.823063	−	1.42559i	−0.311088	−	0.538821i	−0.978598	+	0.205780i	$0.934027\pi$
$8$	1.00000			0.353553
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	0.385150	−	2.20265i	0.121795	−	0.696539i
$11$	2.08305	+	1.20265i	0.628063	+	0.362612i	0.780001	−	0.625778i	$-0.215218\pi$
$11$	2.08305	+	1.20265i	0.628063	+	0.362612i	−0.151939	+	0.988390i	$0.548552\pi$
$12$			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
$15$	2.20265	+	0.385150i	0.568721	+	0.0994454i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.210702	+	0.121649i	−0.0511027	+	0.0295041i	−0.525334	−	0.850896i	$-0.676059\pi$
$17$	−0.210702	+	0.121649i	−0.0511027	+	0.0295041i	0.474231	+	0.880400i	$0.342726\pi$
$18$	−1.00000			−0.235702
$19$	3.82681	−	2.20941i	0.877930	−	0.506873i	0.00795483	−	0.999968i	$-0.497468\pi$
$19$	3.82681	−	2.20941i	0.877930	−	0.506873i	0.869975	+	0.493095i	$0.164135\pi$
$20$	1.71497	+	1.43487i	0.383480	+	0.320848i
$21$			1.64613i			0.359214i
$22$	−2.08305	+	1.20265i	−0.444107	+	0.256405i
$23$	7.46758	+	4.31141i	1.55710	+	0.898991i	0.997533	+	0.0702038i	$0.0223650\pi$
$23$	7.46758	+	4.31141i	1.55710	+	0.898991i	0.559565	+	0.828787i	$0.310968\pi$
$24$	−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	−0.863960	−	0.503560i	$-0.832023\pi$
$29$	0.0221633	−	0.0383880i	0.00411562	−	0.00712846i	0.868076	+	0.496432i	$0.165357\pi$
$30$	−1.43487	+	1.71497i	−0.261971	+	0.313110i
$31$		−	4.24458i		−	0.762348i	−0.924503	−	0.381174i	$-0.875520\pi$
$31$		−	4.24458i		−	0.762348i	0.924503	−	0.381174i	$-0.124480\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−1.20265	−	2.08305i	−0.209354	−	0.362612i
$34$		−	0.243297i		−	0.0417251i
$35$	2.82306	+	2.36198i	0.477185	+	0.399248i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	−4.47415	+	7.74945i	−0.735545	+	1.27400i	0.218939	+	0.975739i	$0.429740\pi$
$37$	−4.47415	+	7.74945i	−0.735545	+	1.27400i	−0.954484	+	0.298263i	$0.903593\pi$
$38$			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	0.516363	−	0.856370i	$-0.327286\pi$
$41$	0.210702	+	0.121649i	0.0329061	+	0.0189983i	−0.483457	+	0.875368i	$0.660619\pi$
$42$	−1.42559	−	0.823063i	−0.219973	−	0.127001i
$43$	5.82728	−	3.36438i	0.888652	−	0.513063i	0.0151507	−	0.999885i	$-0.495177\pi$
$43$	5.82728	−	3.36438i	0.888652	−	0.513063i	0.873501	+	0.486822i	$0.161844\pi$
$44$		−	2.40530i		−	0.362612i
$45$	−1.71497	−	1.43487i	−0.255653	−	0.213898i
$46$	−7.46758	+	4.31141i	−1.10103	+	0.635682i
$47$	7.29560			1.06417			0.532086	−	0.846690i	$-0.321408\pi$
$47$	7.29560			1.06417			0.532086	+	0.846690i	$0.321408\pi$
$48$	0.866025	−	0.500000i	0.125000	−	0.0721688i
$49$	2.14514	−	3.71548i	0.306448	−	0.530783i
$50$	0.882273	+	4.92154i	0.124772	+	0.696011i
$51$	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
$55$	−5.29802	−	0.926401i	−0.714385	−	0.124916i
$56$	−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	−0.933029	−	0.359800i	$-0.882845\pi$
$59$	−8.35669	+	4.82474i	−1.08795	+	0.628127i	−0.154919	+	0.987927i	$0.549512\pi$
$60$	−0.767774	−	2.10012i	−0.0991192	−	0.271125i
$61$	1.31630	+	2.27990i	0.168535	+	0.291911i	0.937905	−	0.346892i	$-0.112763\pi$
$61$	1.31630	+	2.27990i	0.168535	+	0.291911i	−0.769370	+	0.638804i	$0.779430\pi$
$62$	3.67591	+	2.12229i	0.466841	+	0.269531i
$63$	0.823063	−	1.42559i	0.103696	−	0.179607i
$64$	1.00000			0.125000
$65$	−7.35621	+	3.29943i	−0.912425	+	0.409244i
$66$	2.40530			0.296072
$67$	−0.937098	+	1.62310i	−0.114485	+	0.198293i	−0.917574	−	0.397566i	$-0.869855\pi$
$67$	−0.937098	+	1.62310i	−0.114485	+	0.198293i	0.803089	+	0.595859i	$0.203188\pi$
$68$	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	−0.834659	−	0.550767i	$-0.814335\pi$
$71$	−6.53035	+	3.77030i	−0.775010	+	0.447452i	0.0596488	+	0.998219i	$0.481002\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$	−1.70370			−0.199403			−0.0997015	−	0.995017i	$-0.531789\pi$
$73$	−1.70370			−0.199403			−0.0997015	+	0.995017i	$0.531789\pi$
$74$	−4.47415	−	7.74945i	−0.520109	−	0.900855i
$75$	−4.92154	+	0.882273i	−0.568291	+	0.101876i
$76$	−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	$0.375110\pi$
$80$	0.385150	−	2.20265i	0.0430611	−	0.246264i
$81$	−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	$-0.0899214\pi$
$83$	17.4986			1.92073			0.960363	+	0.278754i	$0.0899214\pi$
$84$	1.42559	−	0.823063i	0.155544	−	0.0898035i
$85$	0.349101	−	0.417249i	0.0378653	−	0.0452570i
$86$			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	−0.0376977	−	0.999289i	$-0.512002\pi$
$89$	−8.69772	−	5.02163i	−0.921956	−	0.532292i	−0.884259	+	0.466997i	$0.845336\pi$
$90$	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
$95$	−6.34045	+	7.57816i	−0.650516	+	0.777503i
$96$			1.00000i			0.102062i
$97$	−8.25647	−	14.3006i	−0.838317	−	1.45201i	−0.891301	−	0.453413i	$-0.850206\pi$
$97$	−8.25647	−	14.3006i	−0.838317	−	1.45201i	0.0529831	−	0.998595i	$-0.483127\pi$
$98$	2.14514	+	3.71548i	0.216691	+	0.375321i
$99$			2.40530i			0.241741i
$100$	−4.70332	−	1.69670i	−0.470332	−	0.169670i
$101$	5.66777	−	9.81687i	0.563964	−	0.976815i	−0.433181	−	0.901307i	$-0.642609\pi$
$101$	5.66777	−	9.81687i	0.563964	−	0.976815i	0.997145	−	0.0755077i	$-0.0240577\pi$
$102$	−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	$-0.505927\pi$
$107$	−9.24559	−	5.33795i	−0.893805	−	0.516039i	−0.875185	+	0.483788i	$0.839261\pi$
$108$	−0.866025	+	0.500000i	−0.0833333	+	0.0481125i
$109$			9.50683i			0.910589i	0.890341	+	0.455295i	$0.150466\pi$
$109$			9.50683i			0.910589i	−0.890341	+	0.455295i	$0.849534\pi$
$110$	3.45130	−	4.12502i	0.329068	−	0.393305i
$111$	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	$-0.612565\pi$
$113$	3.11433	−	1.79806i	0.292972	−	0.169147i	0.639281	+	0.768973i	$0.279232\pi$
$114$	2.20941	−	3.82681i	0.206930	−	0.358414i
$115$	−18.9930	−	3.32108i	−1.77111	−	0.309692i
$116$	−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
$120$	2.20265	+	0.385150i	0.201073	+	0.0351593i
$121$	−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	$-0.0537642\pi$
$127$	15.0230	+	8.67351i	1.33307	+	0.769650i	0.347303	+	0.937753i	$0.387098\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−6.72876			−0.592435
$130$	0.820711	−	8.02038i	0.0719811	−	0.703434i
$131$	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	$-0.268101\pi$
$137$	−3.66709	−	6.35158i	−0.313300	−	0.542652i	−0.979075	+	0.203501i	$0.934768\pi$
$138$	8.62281			0.734023
$139$	7.10185	+	12.3008i	0.602371	+	1.04334i	0.992461	+	0.122561i	$0.0391107\pi$
$139$	7.10185	+	12.3008i	0.602371	+	1.04334i	−0.390090	+	0.920777i	$0.627556\pi$
$140$	0.634006	−	3.62584i	0.0535833	−	0.306439i
$141$	−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
$145$	−0.0170724	+	0.0976359i	−0.00141779	+	0.00810822i
$146$	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	−0.839185	−	0.543847i	$-0.816967\pi$
$149$	−9.61623	+	5.55193i	−0.787792	+	0.454832i	0.0513926	+	0.998679i	$0.483634\pi$
$150$	1.69670	−	4.70332i	0.138535	−	0.384024i
$151$			0.874663i			0.0711791i	0.999366	+	0.0355895i	$0.0113309\pi$
$151$			0.874663i			0.0711791i	−0.999366	+	0.0355895i	$0.988669\pi$
$152$	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
$160$	1.71497	+	1.43487i	0.135581	+	0.113437i
$161$		−	14.1942i		−	1.11866i
$162$	−0.500000	−	0.866025i	−0.0392837	−	0.0680414i
$163$	10.9464	+	18.9597i	0.857388	+	1.48504i	0.874411	+	0.485185i	$0.161248\pi$
$163$	10.9464	+	18.9597i	0.857388	+	1.48504i	−0.0170229	+	0.999855i	$0.505419\pi$
$164$		−	0.243297i		−	0.0189983i
$165$	4.12502	+	3.45130i	0.321132	+	0.268683i
$166$	−8.74932	+	15.1543i	−0.679079	+	1.17620i
$167$	−2.64815	+	4.58673i	−0.204920	+	0.354932i	−0.950107	−	0.311923i	$-0.899027\pi$
$167$	−2.64815	+	4.58673i	−0.204920	+	0.354932i	0.745187	+	0.666855i	$0.232360\pi$
$168$			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	$-0.894460\pi$
$173$	−14.9469	+	8.62958i	−1.13639	+	0.656095i	−0.190856	+	0.981618i	$0.561126\pi$
$174$		−	0.0443266i		−	0.00336039i
$175$	−7.74225	−	2.79298i	−0.585259	−	0.211130i
$176$	−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	−0.978852	−	0.204569i	$-0.934421\pi$
$179$	−4.17781	+	7.23617i	−0.312264	+	0.540857i	0.666588	+	0.745426i	$0.267754\pi$
$180$	−0.385150	+	2.20265i	−0.0287074	+	0.164176i
$181$	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
$185$	3.44644	−	19.7099i	0.253387	−	1.44910i
$186$	−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	0.858416	−	0.512955i	$-0.171449\pi$
$191$	−0.207632	−	0.359629i	−0.0150237	−	0.0260219i	−0.873440	+	0.486933i	$0.838116\pi$
$192$	−0.866025	−	0.500000i	−0.0625000	−	0.0360844i
$193$	−12.9918	+	22.5025i	−0.935173	+	1.61977i	−0.160849	+	0.986979i	$0.551423\pi$
$193$	−12.9918	+	22.5025i	−0.935173	+	1.61977i	−0.774324	+	0.632789i	$0.781910\pi$
$194$	16.5129			1.18556
$195$	8.02038	+	0.820711i	0.574351	+	0.0587724i
$196$	−4.29027			−0.306448
$197$	−7.72121	+	13.3735i	−0.550113	+	0.952824i	0.448152	+	0.893957i	$0.352082\pi$
$197$	−7.72121	+	13.3735i	−0.550113	+	0.952824i	−0.998266	+	0.0588672i	$0.981251\pi$
$198$	−2.08305	−	1.20265i	−0.148036	−	0.0854685i
$199$	6.85286	+	11.8695i	0.485787	+	0.841407i	0.999867	−	0.0163352i	$-0.00519988\pi$
$199$	6.85286	+	11.8695i	0.485787	+	0.841407i	−0.514080	+	0.857742i	$0.671867\pi$
$200$	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
$205$	−0.535898	−	0.0937060i	−0.0374288	−	0.00654471i
$206$	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
$210$	3.62584	+	0.634006i	0.250206	+	0.0437506i
$211$	8.05616	−	13.9537i	0.554609	−	0.960611i	−0.443325	−	0.896361i	$-0.646201\pi$
$211$	8.05616	−	13.9537i	0.554609	−	0.960611i	0.997934	−	0.0642497i	$-0.0204654\pi$
$212$	−2.11841	+	1.22307i	−0.145493	+	0.0840005i
$213$	7.54060			0.516673
$214$	9.24559	−	5.33795i	0.632016	−	0.364894i
$215$	−9.65493	+	11.5397i	−0.658461	+	0.786998i
$216$		−	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	$-0.711920\pi$
$223$	5.55886	−	9.62823i	0.372249	−	0.644754i	0.989911	+	0.141690i	$0.0452535\pi$
$224$	−0.823063	+	1.42559i	−0.0549932	+	0.0952510i
$225$	4.70332	+	1.69670i	0.313555	+	0.113113i
$226$			3.59612i			0.239210i
$227$	−11.0399	−	19.1217i	−0.732747	−	1.26915i	−0.955705	−	0.294327i	$-0.904905\pi$
$227$	−11.0399	−	19.1217i	−0.732747	−	1.26915i	0.222958	−	0.974828i	$-0.428429\pi$
$228$	2.20941	+	3.82681i	0.146322	+	0.253437i
$229$			10.3397i			0.683266i	0.939834	+	0.341633i	$0.110980\pi$
$229$			10.3397i			0.683266i	−0.939834	+	0.341633i	$0.889020\pi$
$230$	12.3727	−	14.7879i	0.815829	−	0.975085i
$231$	−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	$-0.677194\pi$
$239$		−	26.2510i		−	1.69804i	0.528362	−	0.849019i	$-0.322806\pi$
$240$	−1.43487	+	1.71497i	−0.0926207	+	0.110701i
$241$	22.5952	−	13.0454i	1.45549	−	0.840326i	0.456703	−	0.889619i	$-0.349030\pi$
$241$	22.5952	−	13.0454i	1.45549	−	0.840326i	0.998784	+	0.0492931i	$0.0156968\pi$
$242$	5.21455			0.335204
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	1.31630	−	2.27990i	0.0842676	−	0.145956i
$245$	−1.65240	+	9.44996i	−0.105568	+	0.603736i
$246$	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
$250$	−5.63152	−	9.65847i	−0.356168	−	0.610855i
$251$	−0.312397	−	0.541088i	−0.0197183	−	0.0341532i	0.855998	−	0.516979i	$-0.172944\pi$
$251$	−0.312397	−	0.541088i	−0.0197183	−	0.0341532i	−0.875716	+	0.482826i	$0.839610\pi$
$252$	−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	$-0.476549\pi$
$257$	−12.0758	−	6.97195i	−0.753266	−	0.434898i	−0.826873	+	0.562389i	$0.809882\pi$
$258$	3.36438	−	5.82728i	0.209457	−	0.362791i
$259$	14.7300			0.915278
$260$	6.53549	+	4.72094i	0.405314	+	0.292781i
$261$	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	$-0.537870\pi$
$263$	−16.8325	−	9.71828i	−1.03794	−	0.599255i	−0.919249	+	0.393677i	$0.871203\pi$
$264$	−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	0.816643	−	0.577143i	$-0.195832\pi$
$269$	−1.50069	−	2.59928i	−0.0914989	−	0.158481i	−0.908142	+	0.418662i	$0.862499\pi$
$270$	−2.20265	−	0.385150i	−0.134049	−	0.0234395i
$271$	−24.6538	−	14.2339i	−1.49761	−	0.864645i	−0.497613	−	0.867399i	$-0.665790\pi$
$271$	−24.6538	−	14.2339i	−1.49761	−	0.864645i	−0.999996	+	0.00275396i	$0.999123\pi$
$272$		−	0.243297i		−	0.0147521i
$273$	0.421840	+	5.92018i	0.0255309	+	0.358306i
$274$	7.33417			0.443074
$275$	11.8378	−	2.12213i	0.713845	−	0.127969i
$276$	−4.31141	+	7.46758i	−0.259516	+	0.449495i
$277$	−0.738423	+	0.426329i	−0.0443676	+	0.0256156i	−0.522020	−	0.852933i	$-0.674821\pi$
$277$	−0.738423	+	0.426329i	−0.0443676	+	0.0256156i	0.477652	+	0.878549i	$0.341488\pi$
$278$	−14.2037			−0.851882
$279$	3.67591	−	2.12229i	0.220071	−	0.127058i
$280$	2.82306	+	2.36198i	0.168710	+	0.141155i
$281$			15.6851i			0.935697i	0.883809	+	0.467848i	$0.154971\pi$
$281$			15.6851i			0.935697i	−0.883809	+	0.467848i	$0.845029\pi$
$282$	6.31817	−	3.64780i	0.376242	−	0.217223i
$283$	−7.00390	−	4.04370i	−0.416339	−	0.240373i	0.277171	−	0.960821i	$-0.410603\pi$
$283$	−7.00390	−	4.04370i	−0.416339	−	0.240373i	−0.693510	+	0.720447i	$0.743937\pi$
$284$	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
$290$	−0.0760190	−	0.0636031i	−0.00446399	−	0.00373490i
$291$			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	$-0.148671\pi$
$293$	0.967192	+	1.67523i	0.0565040	+	0.0978677i	−0.836390	+	0.548135i	$0.815338\pi$
$294$		−	4.29027i		−	0.250214i
$295$	13.8458	−	16.5486i	0.806133	−	0.963497i
$296$	−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
$305$	−4.51485	−	3.77745i	−0.258519	−	0.216296i
$306$	0.210702	−	0.121649i	0.0120450	−	0.00695419i
$307$	12.4384			0.709894			0.354947	−	0.934886i	$-0.384499\pi$
$307$	12.4384			0.709894			0.354947	+	0.934886i	$0.384499\pi$
$308$	−3.42896	+	1.97971i	−0.195383	+	0.112804i
$309$	−2.99084	+	5.18029i	−0.170143	+	0.294696i
$310$	−9.34931	−	1.63480i	−0.531005	−	0.0928504i
$311$	−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
$315$	−0.634006	+	3.62584i	−0.0357222	+	0.204293i
$316$	−3.39854	−	5.88644i	−0.191183	−	0.331138i
$317$	23.3625			1.31217			0.656083	−	0.754689i	$-0.272212\pi$
$317$	23.3625			1.31217			0.656083	+	0.754689i	$0.272212\pi$
$318$	−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
$325$	12.9157	−	12.5771i	0.716436	−	0.697653i
$326$	−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	−0.914590	−	0.404382i	$-0.867487\pi$
$331$	−18.5879	+	10.7317i	−1.02168	+	0.589868i	−0.107090	+	0.994249i	$0.534153\pi$
$332$	−8.74932	−	15.1543i	−0.480181	−	0.831698i
$333$	−8.94829			−0.490363
$334$	−2.64815	−	4.58673i	−0.144900	−	0.250975i
$335$	0.721847	−	4.12820i	0.0394387	−	0.225547i
$336$	−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
$340$	−0.535898	−	0.0937060i	−0.0290632	−	0.00508192i
$341$	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
$345$	14.7879	+	12.3727i	0.796154	+	0.666121i
$346$		−	17.2592i		−	0.927858i
$347$	0.576005	−	0.332557i	0.0309216	−	0.0178526i	−0.484460	−	0.874814i	$-0.660984\pi$
$347$	0.576005	−	0.332557i	0.0309216	−	0.0178526i	0.515381	+	0.856961i	$0.327650\pi$
$348$	0.0383880	+	0.0221633i	0.00205781	+	0.00118808i
$349$	3.25007	+	1.87643i	0.173972	+	0.100443i	0.584458	−	0.811424i	$-0.301307\pi$
$349$	3.25007	+	1.87643i	0.173972	+	0.100443i	−0.410485	+	0.911867i	$0.634641\pi$
$350$	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	$-0.794580\pi$
$353$	2.28180	−	3.95219i	0.121448	−	0.210354i	0.920339	+	0.391122i	$0.127913\pi$
$354$	−4.82474	+	8.35669i	−0.256432	+	0.444153i
$355$	10.8198	−	12.9319i	0.574256	−	0.686356i
$356$			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	$-0.959929\pi$
$359$		−	4.75785i		−	0.251110i	0.992087	−	0.125555i	$-0.0400711\pi$
$360$	−1.71497	−	1.43487i	−0.0903871	−	0.0756245i
$361$	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	$-0.345753\pi$
$367$	−1.29432	−	0.747277i	−0.0675630	−	0.0390075i	−0.533401	+	0.845863i	$0.679086\pi$
$368$	−7.46758	+	4.31141i	−0.389274	+	0.224748i
$369$			0.243297i			0.0126656i
$370$	15.3461	+	12.8397i	0.797805	+	0.667503i
$371$	−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	$-0.845632\pi$
$373$	−17.8323	+	10.2955i	−0.923323	+	0.533081i	−0.0386291	+	0.999254i	$0.512299\pi$
$374$	0.292601	−	0.506800i	0.0151300	−	0.0262060i
$375$	9.65847	−	5.63152i	0.498761	−	0.290810i
$376$	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	−0.0541858	−	0.998531i	$-0.517256\pi$
$379$	−18.4173	−	10.6332i	−0.946032	−	0.546192i	−0.891846	+	0.452339i	$0.850590\pi$
$380$	9.73310	+	1.70191i	0.499298	+	0.0873061i
$381$	−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	$-0.254146\pi$
$383$	−5.31095	−	9.19884i	−0.271377	−	0.470039i	−0.969215	+	0.246217i	$0.920812\pi$
$384$	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	$0.888349\pi$
$390$	−4.72094	+	6.53549i	−0.239054	+	0.330938i
$391$	−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	$-0.153186\pi$
$397$	0.843593	+	1.46115i	0.0423387	+	0.0733328i	−0.844079	+	0.536218i	$0.819852\pi$
$398$	−13.7057			−0.687006
$399$	3.63697	+	6.29941i	0.182076	+	0.315365i
$400$	0.882273	+	4.92154i	0.0441136	+	0.246077i
$401$	17.2949	+	9.98524i	0.863668	+	0.498639i	0.865239	−	0.501360i	$-0.167167\pi$
$401$	17.2949	+	9.98524i	0.863668	+	0.498639i	−0.00157101	+	0.999999i	$0.500500\pi$
$402$			1.87420i			0.0934764i
$403$	−1.08772	−	15.2653i	−0.0541834	−	0.760420i
$404$	−11.3355			−0.563964
$405$	0.385150	−	2.20265i	0.0191383	−	0.109450i
$406$	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	−0.212725	−	0.977112i	$-0.568234\pi$
$409$	10.6603	−	6.15471i	0.527117	−	0.304331i	0.739842	+	0.672781i	$0.234900\pi$
$410$	0.349101	−	0.417249i	0.0172409	−	0.0206064i
$411$			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	−0.459544	−	0.888155i	$-0.651987\pi$
$419$	11.0411	−	19.1238i	0.539393	−	0.934256i	0.998937	−	0.0461011i	$-0.0146796\pi$
$420$	−2.36198	+	2.82306i	−0.115253	+	0.137751i
$421$			8.98036i			0.437676i	0.975761	+	0.218838i	$0.0702266\pi$
$421$			8.98036i			0.437676i	−0.975761	+	0.218838i	$0.929773\pi$
$422$	8.05616	+	13.9537i	0.392168	+	0.679254i
$423$	3.64780	+	6.31817i	0.177362	+	0.307200i
$424$		−	2.44613i		−	0.118795i
$425$	−0.412803	+	1.14430i	−0.0200239	+	0.0555069i
$426$	−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	0.662449	−	0.749107i	$-0.269517\pi$
$431$	7.16090	+	4.13435i	0.344928	+	0.199145i	−0.317521	+	0.948251i	$0.602850\pi$
$432$	0.866025	+	0.500000i	0.0416667	+	0.0240563i
$433$	−17.1825	+	9.92035i	−0.825740	+	0.476741i	−0.852392	−	0.522903i	$-0.824849\pi$
$433$	−17.1825	+	9.92035i	−0.825740	+	0.476741i	0.0266515	+	0.999645i	$0.491516\pi$
$434$		−	6.98710i		−	0.335392i
$435$	0.0636031	−	0.0760190i	0.00304953	−	0.00364483i
$436$	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	0.282824	+	0.959172i	$0.408729\pi$
$439$	−14.4415	+	25.0134i	−0.689255	+	1.19382i	−0.972079	+	0.234653i	$0.924605\pi$
$440$	−5.29802	−	0.926401i	−0.252573	−	0.0441644i
$441$	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
$445$	22.1218	+	3.86817i	1.04867	+	0.183369i
$446$	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	−0.608514	+	0.793543i	$0.708234\pi$
$449$	−33.9034	+	19.5741i	−1.60000	+	0.923760i	−0.991486	+	0.130217i	$0.958433\pi$
$450$	−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
$455$	10.7582	+	7.77127i	0.504354	+	0.364323i
$456$	−4.41882			−0.206930
$457$	12.2403	−	21.2008i	0.572575	−	0.991730i	−0.423725	−	0.905791i	$-0.639278\pi$
$457$	12.2403	−	21.2008i	0.572575	−	0.991730i	0.996300	−	0.0859387i	$-0.0273889\pi$
$458$	−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	−0.427796	−	0.903875i	$-0.640710\pi$
$461$	3.02923	−	1.74893i	0.141085	−	0.0814557i	0.568881	+	0.822420i	$0.307376\pi$
$462$	−1.97971	−	3.42896i	−0.0921044	−	0.159530i
$463$	−18.3063			−0.850767			−0.425384	−	0.905013i	$-0.639861\pi$
$463$	−18.3063			−0.850767			−0.425384	+	0.905013i	$0.639861\pi$
$464$	0.0221633	+	0.0383880i	0.00102891	+	0.00178212i
$465$	1.63480	−	9.34931i	0.0758120	−	0.433564i
$466$	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
$470$	2.80990	−	16.0696i	0.129611	−	0.741237i
$471$	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
$475$	7.49742	−	20.7831i	0.344005	−	0.953595i
$476$		−	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	0.963908	−	0.266236i	$-0.0857800\pi$
$479$	26.5980	+	15.3564i	1.21529	+	0.701651i	0.251387	+	0.967887i	$0.419113\pi$
$480$	−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
$485$	28.3193	+	23.6940i	1.28591	+	1.07589i
$486$			1.00000i			0.0453609i
$487$	−6.23335	−	10.7965i	−0.282460	−	0.489235i	0.689530	−	0.724257i	$-0.257817\pi$
$487$	−6.23335	−	10.7965i	−0.282460	−	0.489235i	−0.971990	+	0.235022i	$0.924484\pi$
$488$	1.31630	+	2.27990i	0.0595862	+	0.103206i
$489$		−	21.8928i		−	0.990027i
$490$	−7.35770	−	6.15600i	−0.332387	−	0.278100i
$491$	1.29120	−	2.23642i	0.0582710	−	0.100928i	−0.835418	−	0.549615i	$-0.814775\pi$
$491$	1.29120	−	2.23642i	0.0582710	−	0.100928i	0.893689	+	0.448686i	$0.148108\pi$
$492$	−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	$-0.850307\pi$
$499$		−	20.2443i		−	0.906261i	0.891444	−	0.453130i	$-0.149693\pi$
$500$	11.1802	−	0.0478026i	0.499995	−	0.00213780i
$501$	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	$-0.606229\pi$
$503$	7.33148	−	4.23283i	0.326894	−	0.188733i	0.654461	+	0.756095i	$0.272895\pi$
$504$	0.823063	−	1.42559i	0.0366621	−	0.0635007i
$505$	−4.36589	+	24.9682i	−0.194279	+	1.11107i
$506$	−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	−0.481421	−	0.876490i	$-0.659879\pi$
$509$	−33.4172	−	19.2935i	−1.48119	−	0.855167i	−0.999773	+	0.0213225i	$0.993212\pi$
$510$	0.0937060	−	0.535898i	0.00414937	−	0.0237300i
$511$	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
$520$	−7.35621	+	3.29943i	−0.322591	+	0.144690i
$521$	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	$-0.423614\pi$
$523$	−11.0846	−	6.39970i	−0.484696	−	0.279839i	−0.722371	+	0.691505i	$0.756948\pi$
$524$	−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
$530$	−5.38797	−	0.942128i	−0.234038	−	0.0409234i
$531$	−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
$535$	23.5152	+	4.11182i	1.01665	+	0.177770i
$536$	−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
$540$	1.43487	−	1.71497i	0.0617471	−	0.0738007i
$541$			24.9605i			1.07314i	0.843857	+	0.536568i	$0.180280\pi$
$541$			24.9605i			1.07314i	−0.843857	+	0.536568i	$0.819720\pi$
$542$	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
$550$	−4.08107	+	11.3129i	−0.174017	+	0.482383i
$551$		−	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
$555$	−12.8397	+	15.3461i	−0.545014	+	0.651405i
$556$	7.10185	−	12.3008i	0.301186	−	0.521669i
$557$	−0.697392	+	1.20792i	−0.0295495	+	0.0511812i	−0.880422	−	0.474191i	$-0.842741\pi$
$557$	−0.697392	+	1.20792i	−0.0295495	+	0.0511812i	0.850872	+	0.525372i	$0.176074\pi$
$558$			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	$-0.555685\pi$
$563$	14.0404	−	8.10624i	0.591733	−	0.341637i	0.765782	+	0.643100i	$0.222352\pi$
$564$			7.29560i			0.307200i
$565$	−5.15998	+	6.16725i	−0.217082	+	0.259458i
$566$	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	−0.0813055	−	0.996689i	$-0.525909\pi$
$569$	19.6198	−	33.9825i	0.822505	−	1.42462i	0.903811	−	0.427932i	$-0.140758\pi$
$570$	−1.70191	+	9.73310i	−0.0712851	+	0.407675i
$571$	−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
$575$	42.4376	−	7.60767i	1.76977	−	0.317262i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	−28.5363			−1.18798			−0.593992	−	0.804471i	$-0.702449\pi$
$577$	−28.5363			−1.18798			−0.593992	+	0.804471i	$0.702449\pi$
$578$	−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
$585$	−6.53549	−	4.72094i	−0.270209	−	0.195187i
$586$	−1.93438			−0.0799087
$587$	−22.5265	+	39.0171i	−0.929770	+	1.61041i	−0.146066	+	0.989275i	$0.546661\pi$
$587$	−22.5265	+	39.0171i	−0.929770	+	1.61041i	−0.783704	+	0.621134i	$0.786672\pi$
$588$	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	$-0.775294\pi$
$593$	−37.0634			−1.52201			−0.761005	+	0.648746i	$0.775294\pi$
$594$	1.20265	+	2.08305i	0.0493453	+	0.0854685i
$595$	−0.882156	−	0.154252i	−0.0361649	−	0.00632371i
$596$	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	$0.375711\pi$
$600$	−4.92154	+	0.882273i	−0.200921	+	0.0360186i
$601$	9.69008	−	16.7837i	0.395266	−	0.684622i	−0.597869	−	0.801594i	$-0.703986\pi$
$601$	9.69008	−	16.7837i	0.395266	−	0.684622i	0.993135	+	0.116972i	$0.0373189\pi$
$602$	9.59244	−	5.53820i	0.390958	−	0.225720i
$603$	−1.87420			−0.0763232
$604$	0.757480	−	0.437332i	0.0308214	−	0.0177948i
$605$	8.94282	+	7.48222i	0.363577	+	0.304196i
$606$		−	11.3355i		−	0.460475i
$607$	−30.2066	+	17.4398i	−1.22605	+	0.707858i	−0.966200	−	0.257792i	$-0.917005\pi$
$607$	−30.2066	+	17.4398i	−1.22605	+	0.707858i	−0.259846	+	0.965650i	$0.583672\pi$
$608$	−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	$-0.780746\pi$
$613$	4.07179	−	7.05254i	0.164458	−	0.284849i	0.936463	+	0.350767i	$0.114079\pi$
$614$	−6.21918	+	10.7719i	−0.250986	+	0.434720i
$615$	0.417249	+	0.349101i	0.0168251	+	0.0140771i
$616$		−	3.95942i		−	0.159530i
$617$	16.7288	+	28.9752i	0.673477	+	1.16650i	0.976912	+	0.213644i	$0.0685332\pi$
$617$	16.7288	+	28.9752i	0.673477	+	1.16650i	−0.303435	+	0.952852i	$0.598133\pi$
$618$	−2.99084	−	5.18029i	−0.120309	−	0.208382i
$619$		−	41.1780i		−	1.65508i	−0.561404	−	0.827542i	$-0.689739\pi$
$619$		−	41.1780i		−	1.65508i	0.561404	−	0.827542i	$-0.310261\pi$
$620$	6.09043	−	7.27934i	0.244598	−	0.292345i
$621$	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
$630$	−2.82306	−	2.36198i	−0.112474	−	0.0941036i
$631$	12.6839	−	7.32307i	0.504939	−	0.291527i	−0.225812	−	0.974171i	$-0.572503\pi$
$631$	12.6839	−	7.32307i	0.504939	−	0.291527i	0.730751	+	0.682644i	$0.239170\pi$
$632$	6.79707			0.270373
$633$	−13.9537	+	8.05616i	−0.554609	+	0.320204i
$634$	−11.6812	+	20.2325i	−0.463921	+	0.803535i
$635$	−38.2094	−	6.68121i	−1.51629	−	0.265136i
$636$	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
$640$	0.385150	−	2.20265i	0.0152244	−	0.0870673i
$641$	23.9793	+	41.5334i	0.947125	+	1.64047i	0.751439	+	0.659803i	$0.229360\pi$
$641$	23.9793	+	41.5334i	0.947125	+	1.64047i	0.195686	+	0.980667i	$0.437307\pi$
$642$	−10.6759			−0.421344
$643$	1.99884	+	3.46209i	0.0788265	+	0.136531i	0.902744	−	0.430178i	$-0.141549\pi$
$643$	1.99884	+	3.46209i	0.0788265	+	0.136531i	−0.823917	+	0.566710i	$0.808216\pi$
$644$	−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	$-0.179668\pi$
$647$	20.4521	+	11.8080i	0.804053	+	0.464220i	−0.0408333	+	0.999166i	$0.513001\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	−23.2098			−0.911066
$650$	4.43424	+	17.4739i	0.173925	+	0.685383i
$651$	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	$-0.0909312\pi$
$653$	30.5411	+	17.6329i	1.19516	+	0.690029i	0.235692	+	0.971828i	$0.424265\pi$
$654$	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	0.999972	−	0.00749088i	$-0.00238444\pi$
$659$	12.6686	+	21.9427i	0.493499	+	0.854765i	−0.506473	+	0.862256i	$0.669051\pi$
$660$	0.926401	−	5.29802i	0.0360601	−	0.206225i
$661$	4.21373	+	2.43280i	0.163895	+	0.0946248i	0.579704	−	0.814827i	$-0.303168\pi$
$661$	4.21373	+	2.43280i	0.163895	+	0.0946248i	−0.415809	+	0.909452i	$0.636502\pi$
$662$		−	21.4634i		−	0.834199i
$663$	0.875002	−	0.0623479i	0.0339823	−	0.00242139i
$664$	17.4986			0.679079
$665$	16.0219	+	2.80156i	0.621303	+	0.108640i
$666$	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
$670$	3.21420	+	2.68924i	0.124175	+	0.103894i
$671$			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	$-0.379434\pi$
$673$	−6.48493	−	3.74408i	−0.249976	−	0.144324i	−0.619753	+	0.784797i	$0.712767\pi$
$674$	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
$680$	0.349101	−	0.417249i	0.0133874	−	0.0160008i
$681$			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	$-0.128337\pi$
$683$	3.13940	+	5.43761i	0.120126	+	0.208064i	−0.799691	+	0.600411i	$0.795003\pi$
$684$		−	4.41882i		−	0.168958i
$685$	12.5779	+	10.5236i	0.480577	+	0.402087i
$686$	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	0.315234	−	0.949014i	$-0.397917\pi$
$691$	−9.17461	−	5.29696i	−0.349019	−	0.201506i	−0.664253	+	0.747508i	$0.731250\pi$
$692$	14.9469	+	8.62958i	0.568195	+	0.328047i
$693$	3.42896	−	1.97971i	0.130255	−	0.0752030i
$694$			0.665114i			0.0252474i
$695$	−24.3590	−	20.3805i	−0.923989	−	0.773078i
$696$	−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
$700$	1.45233	+	8.10148i	0.0548930	+	0.306207i
$701$	−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
$705$	16.0696	+	2.80990i	0.605218	+	0.105827i
$706$	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	−0.489374	−	0.872074i	$-0.662775\pi$
$709$	0.563901	−	0.325568i	0.0211777	−	0.0122270i	0.510551	+	0.859847i	$0.329441\pi$
$710$	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
$715$	−19.2914	−	1.97405i	−0.721457	−	0.0738254i
$716$	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	0.799895	−	0.600140i	$-0.204888\pi$
$719$	−3.21203	−	5.56340i	−0.119789	−	0.207480i	−0.919684	+	0.392660i	$0.871555\pi$
$720$	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
$725$	−0.0391081	−	0.218155i	−0.00145244	−	0.00810208i
$726$	−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
$730$	−0.656181	+	3.75265i	−0.0242863	+	0.138892i
$731$	−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	$-0.648885\pi$
$733$	−24.4136			−0.901735			−0.450868	+	0.892591i	$0.648885\pi$
$734$	1.29432	−	0.747277i	0.0477743	−	0.0275825i
$735$	6.15600	−	7.35770i	0.227067	−	0.271393i
$736$		−	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	0.584949	−	0.811070i	$-0.301114\pi$
$739$	4.75775	+	2.74689i	0.175017	+	0.101046i	−0.409932	+	0.912116i	$0.634448\pi$
$740$	−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	$-0.705548\pi$
$743$	10.6512	−	18.4484i	0.390753	−	0.676804i	0.992549	+	0.121845i	$0.0388812\pi$
$744$	−2.12229	+	3.67591i	−0.0778068	+	0.134765i
$745$	15.9326	−	19.0428i	0.583727	−	0.697676i
$746$		−	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
$750$	0.0478026	+	11.1802i	0.00174551	+	0.408245i
$751$	−15.4023	+	26.6776i	−0.562040	+	0.973481i	0.435279	+	0.900296i	$0.356650\pi$
$751$	−15.4023	+	26.6776i	−0.562040	+	0.973481i	−0.997318	+	0.0731853i	$0.976684\pi$
$752$	−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	$-0.112973\pi$
$757$	30.4180	+	17.5618i	1.10556	+	0.638296i	0.167885	+	0.985807i	$0.446306\pi$
$758$	18.4173	−	10.6332i	0.668946	−	0.386216i
$759$		−	20.7404i		−	0.752830i
$760$	−6.34045	+	7.57816i	−0.229992	+	0.274889i
$761$	−25.0686	+	14.4734i	−0.908737	+	0.524659i	−0.880024	−	0.474928i	$-0.842474\pi$
$761$	−25.0686	+	14.4734i	−0.908737	+	0.524659i	−0.0287122	+	0.999588i	$0.509141\pi$
$762$	17.3470			0.628416
$763$	13.5528	−	7.82472i	0.490645	−	0.283274i
$764$	−0.207632	+	0.359629i	−0.00751187	+	0.0130109i
$765$	0.535898	+	0.0937060i	0.0193754	+	0.00338795i
$766$	10.6219			0.383785
$767$	−28.8179	+	19.4933i	−1.04055	+	0.703864i

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} +(0.385150 - 2.20265i) q^{10} +(2.08305 + 1.20265i) q^{11} +1.00000i q^{12} +(3.59643 - 0.256262i) q^{13} +1.64613 q^{14} +(2.20265 + 0.385150i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.210702 + 0.121649i) q^{17} -1.00000 q^{18} +(3.82681 - 2.20941i) q^{19} +(1.71497 + 1.43487i) 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} +(-1.43487 + 1.71497i) q^{30} -4.24458i q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.20265 - 2.08305i) q^{33} -0.243297i q^{34} +(2.82306 + 2.36198i) 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} +(-1.71497 - 1.43487i) q^{45} +(-7.46758 + 4.31141i) q^{46} +7.29560 q^{47} +(0.866025 - 0.500000i) q^{48} +(2.14514 - 3.71548i) q^{49} +(0.882273 + 4.92154i) q^{50} +0.243297 q^{51} +(-2.02015 - 2.98647i) q^{52} -2.44613i q^{53} +(0.866025 + 0.500000i) q^{54} +(-5.29802 - 0.926401i) 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} +(-7.35621 + 3.29943i) 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} +(-4.92154 + 0.882273i) q^{75} +(-3.82681 - 2.20941i) q^{76} -3.95942i q^{77} +(2.98647 - 2.02015i) q^{78} +6.79707 q^{79} +(0.385150 - 2.20265i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.210702 + 0.121649i) q^{82} +17.4986 q^{83} +(1.42559 - 0.823063i) q^{84} +(0.349101 - 0.417249i) 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} +(-6.34045 + 7.57816i) 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	\( 12 q - 6 q^{2} - 6 q^{4} - 2 q^{5} - 2 q^{7} + 12 q^{8} + 6 q^{9} - 2 q^{10} + 6 q^{11} - 8 q^{13} + 4 q^{14} + 6 q^{15} - 6 q^{16} + 18 q^{17} - 12 q^{18} - 6 q^{19} + 4 q^{20} - 6 q^{22} + 6 q^{23} - 10 q^{25} - 2 q^{26} - 2 q^{28} + 14 q^{29} - 6 q^{30} - 6 q^{32} + 6 q^{33} + 26 q^{35} + 6 q^{36} - 12 q^{37} - 2 q^{39} - 2 q^{40} - 18 q^{41} - 12 q^{42} - 36 q^{43} - 4 q^{45} - 6 q^{46} + 16 q^{47} + 8 q^{49} - 10 q^{50} + 16 q^{51} + 10 q^{52} - 28 q^{55} - 2 q^{56} - 8 q^{57} + 14 q^{58} - 36 q^{59} + 10 q^{61} + 6 q^{62} + 2 q^{63} + 12 q^{64} + 6 q^{65} - 12 q^{66} + 4 q^{67} - 18 q^{68} + 16 q^{69} - 4 q^{70} - 12 q^{71} + 6 q^{72} + 28 q^{73} - 12 q^{74} - 8 q^{75} + 6 q^{76} - 2 q^{78} + 4 q^{79} - 2 q^{80} - 6 q^{81} + 18 q^{82} + 72 q^{83} + 12 q^{84} + 18 q^{85} + 6 q^{87} + 6 q^{88} + 18 q^{89} + 2 q^{90} + 2 q^{91} - 16 q^{93} - 8 q^{94} - 42 q^{95} - 48 q^{97} + 8 q^{98}+O(q^{100}) \) 12 * q - 6 * q^2 - 6 * q^4 - 2 * q^5 - 2 * q^7 + 12 * q^8 + 6 * q^9 - 2 * q^10 + 6 * q^11 - 8 * q^13 + 4 * q^14 + 6 * q^15 - 6 * q^16 + 18 * q^17 - 12 * q^18 - 6 * q^19 + 4 * q^20 - 6 * q^22 + 6 * q^23 - 10 * q^25 - 2 * q^26 - 2 * q^28 + 14 * q^29 - 6 * q^30 - 6 * q^32 + 6 * q^33 + 26 * q^35 + 6 * q^36 - 12 * q^37 - 2 * q^39 - 2 * q^40 - 18 * q^41 - 12 * q^42 - 36 * q^43 - 4 * q^45 - 6 * q^46 + 16 * q^47 + 8 * q^49 - 10 * q^50 + 16 * q^51 + 10 * q^52 - 28 * q^55 - 2 * q^56 - 8 * q^57 + 14 * q^58 - 36 * q^59 + 10 * q^61 + 6 * q^62 + 2 * q^63 + 12 * q^64 + 6 * q^65 - 12 * q^66 + 4 * q^67 - 18 * q^68 + 16 * q^69 - 4 * q^70 - 12 * q^71 + 6 * q^72 + 28 * q^73 - 12 * q^74 - 8 * q^75 + 6 * q^76 - 2 * q^78 + 4 * q^79 - 2 * q^80 - 6 * q^81 + 18 * q^82 + 72 * q^83 + 12 * q^84 + 18 * q^85 + 6 * q^87 + 6 * q^88 + 18 * q^89 + 2 * q^90 + 2 * q^91 - 16 * q^93 - 8 * q^94 - 42 * q^95 - 48 * q^97 + 8 * q^98

Introduction

L-functions

Modular forms

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