LMFDB - Embedded newform 1950.2.bc.i.901.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1950,2,Mod(751,1950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1950, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1950.751");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1950.bc (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:	$15.5708283941$
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:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 390)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			901.2
Root			$-2.39378 + 0.0429626i$ of defining polynomial
Character	$\chi$	$=$	1950.901
Dual form			1950.2.bc.i.751.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{6} +(1.42559 - 0.823063i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{6} +(1.42559 - 0.823063i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(2.08305 + 1.20265i) q^{11} -1.00000 q^{12} +(-0.256262 - 3.59643i) q^{13} -1.64613 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-0.121649 - 0.210702i) q^{17} +1.00000i q^{18} +(-3.82681 + 2.20941i) q^{19} +1.64613i q^{21} +(-1.20265 - 2.08305i) q^{22} +(4.31141 - 7.46758i) q^{23} +(0.866025 + 0.500000i) q^{24} +(-1.57629 + 3.24273i) q^{26} +1.00000 q^{27} +(1.42559 + 0.823063i) q^{28} +(-0.0221633 + 0.0383880i) q^{29} -4.24458i q^{31} +(0.866025 - 0.500000i) q^{32} +(-2.08305 + 1.20265i) q^{33} +0.243297i q^{34} +(0.500000 - 0.866025i) q^{36} +(-7.74945 - 4.47415i) q^{37} +4.41882 q^{38} +(3.24273 + 1.57629i) q^{39} +(0.210702 + 0.121649i) q^{41} +(0.823063 - 1.42559i) q^{42} +(-3.36438 - 5.82728i) q^{43} +2.40530i q^{44} +(-7.46758 + 4.31141i) q^{46} +7.29560i q^{47} +(-0.500000 - 0.866025i) q^{48} +(-2.14514 + 3.71548i) q^{49} +0.243297 q^{51} +(2.98647 - 2.02015i) q^{52} -2.44613 q^{53} +(-0.866025 - 0.500000i) q^{54} +(-0.823063 - 1.42559i) q^{56} -4.41882i q^{57} +(0.0383880 - 0.0221633i) q^{58} +(8.35669 - 4.82474i) q^{59} +(1.31630 + 2.27990i) q^{61} +(-2.12229 + 3.67591i) q^{62} +(-1.42559 - 0.823063i) q^{63} -1.00000 q^{64} +2.40530 q^{66} +(-1.62310 - 0.937098i) q^{67} +(0.121649 - 0.210702i) q^{68} +(4.31141 + 7.46758i) q^{69} +(-6.53035 + 3.77030i) q^{71} +(-0.866025 + 0.500000i) q^{72} +1.70370i q^{73} +(4.47415 + 7.74945i) q^{74} +(-3.82681 - 2.20941i) q^{76} +3.95942 q^{77} +(-2.02015 - 2.98647i) q^{78} -6.79707 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-0.121649 - 0.210702i) q^{82} -17.4986i q^{83} +(-1.42559 + 0.823063i) q^{84} +6.72876i q^{86} +(-0.0221633 - 0.0383880i) q^{87} +(1.20265 - 2.08305i) q^{88} +(8.69772 + 5.02163i) q^{89} +(-3.32541 - 4.91611i) q^{91} +8.62281 q^{92} +(3.67591 + 2.12229i) q^{93} +(3.64780 - 6.31817i) q^{94} +1.00000i q^{96} +(14.3006 - 8.25647i) q^{97} +(3.71548 - 2.14514i) q^{98} -2.40530i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{3} + 6 q^{4} + 12 q^{7} - 6 q^{9}+O(q^{10}) $ 12 * q - 6 * q^3 + 6 * q^4 + 12 * q^7 - 6 * q^9	$ 12 q - 6 q^{3} + 6 q^{4} + 12 q^{7} - 6 q^{9} + 6 q^{11} - 12 q^{12} - 4 q^{13} - 4 q^{14} - 6 q^{16} - 8 q^{17} + 6 q^{19} + 6 q^{22} - 16 q^{23} - 2 q^{26} + 12 q^{27} + 12 q^{28} - 14 q^{29} - 6 q^{33} + 6 q^{36} + 6 q^{37} + 8 q^{38} + 2 q^{39} - 18 q^{41} + 2 q^{42} - 10 q^{43} - 6 q^{46} - 6 q^{48} - 8 q^{49} + 16 q^{51} - 2 q^{52} - 2 q^{56} - 6 q^{58} + 36 q^{59} + 10 q^{61} - 16 q^{62} - 12 q^{63} - 12 q^{64} - 12 q^{66} - 24 q^{67} + 8 q^{68} - 16 q^{69} - 12 q^{71} + 12 q^{74} + 6 q^{76} - 24 q^{77} + 10 q^{78} - 4 q^{79} - 6 q^{81} - 8 q^{82} - 12 q^{84} - 14 q^{87} - 6 q^{88} - 18 q^{89} + 2 q^{91} - 32 q^{92} + 6 q^{93} + 8 q^{94} + 24 q^{97} - 24 q^{98}+O(q^{100}) $ 12 * q - 6 * q^3 + 6 * q^4 + 12 * q^7 - 6 * q^9 + 6 * q^11 - 12 * q^12 - 4 * q^13 - 4 * q^14 - 6 * q^16 - 8 * q^17 + 6 * q^19 + 6 * q^22 - 16 * q^23 - 2 * q^26 + 12 * q^27 + 12 * q^28 - 14 * q^29 - 6 * q^33 + 6 * q^36 + 6 * q^37 + 8 * q^38 + 2 * q^39 - 18 * q^41 + 2 * q^42 - 10 * q^43 - 6 * q^46 - 6 * q^48 - 8 * q^49 + 16 * q^51 - 2 * q^52 - 2 * q^56 - 6 * q^58 + 36 * q^59 + 10 * q^61 - 16 * q^62 - 12 * q^63 - 12 * q^64 - 12 * q^66 - 24 * q^67 + 8 * q^68 - 16 * q^69 - 12 * q^71 + 12 * q^74 + 6 * q^76 - 24 * q^77 + 10 * q^78 - 4 * q^79 - 6 * q^81 - 8 * q^82 - 12 * q^84 - 14 * q^87 - 6 * q^88 - 18 * q^89 + 2 * q^91 - 32 * q^92 + 6 * q^93 + 8 * q^94 + 24 * q^97 - 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times$.

$n$	$301$	$1301$	$1327$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	0.866025	−	0.500000i	0.353553	−	0.204124i
$7$	1.42559	−	0.823063i	0.538821	−	0.311088i	−0.205780	−	0.978598i	$-0.565973\pi$
$7$	1.42559	−	0.823063i	0.538821	−	0.311088i	0.744601	+	0.667510i	$0.232640\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	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	$0.548552\pi$
$12$	−1.00000			−0.288675
$13$	−0.256262	−	3.59643i	−0.0710744	−	0.997471i
$13$	−0.256262	−	3.59643i	−0.0710744	−	0.997471i
$14$	−1.64613			−0.439946
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.121649	−	0.210702i	−0.0295041	−	0.0511027i	0.850896	−	0.525334i	$-0.176059\pi$
$17$	−0.121649	−	0.210702i	−0.0295041	−	0.0511027i	−0.880400	+	0.474231i	$0.842726\pi$
$18$			1.00000i			0.235702i
$19$	−3.82681	+	2.20941i	−0.877930	+	0.506873i	−0.869975	−	0.493095i	$-0.835865\pi$
$19$	−3.82681	+	2.20941i	−0.877930	+	0.506873i	−0.00795483	+	0.999968i	$0.502532\pi$
$20$		0			0
$21$			1.64613i			0.359214i
$22$	−1.20265	−	2.08305i	−0.256405	−	0.444107i
$23$	4.31141	−	7.46758i	0.898991	−	1.55710i	0.0702038	−	0.997533i	$-0.477635\pi$
$23$	4.31141	−	7.46758i	0.898991	−	1.55710i	0.828787	−	0.559565i	$-0.189032\pi$
$24$	0.866025	+	0.500000i	0.176777	+	0.102062i
$25$		0			0
$26$	−1.57629	+	3.24273i	−0.309135	+	0.635952i
$27$	1.00000			0.192450
$28$	1.42559	+	0.823063i	0.269411	+	0.155544i
$29$	−0.0221633	+	0.0383880i	−0.00411562	+	0.00712846i	−0.868076	−	0.496432i	$-0.834643\pi$
$29$	−0.0221633	+	0.0383880i	−0.00411562	+	0.00712846i	0.863960	+	0.503560i	$0.167977\pi$
$30$		0			0
$31$		−	4.24458i		−	0.762348i	−0.924503	−	0.381174i	$-0.875520\pi$
$31$		−	4.24458i		−	0.762348i	0.924503	−	0.381174i	$-0.124480\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−2.08305	+	1.20265i	−0.362612	+	0.209354i
$34$			0.243297i			0.0417251i
$35$		0			0
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	−7.74945	−	4.47415i	−1.27400	−	0.735545i	−0.298263	−	0.954484i	$-0.596407\pi$
$37$	−7.74945	−	4.47415i	−1.27400	−	0.735545i	−0.975739	+	0.218939i	$0.929740\pi$
$38$	4.41882			0.716827
$39$	3.24273	+	1.57629i	0.519253	+	0.252408i
$40$		0			0
$41$	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	$0.660619\pi$
$42$	0.823063	−	1.42559i	0.127001	−	0.219973i
$43$	−3.36438	−	5.82728i	−0.513063	−	0.888652i	−0.999885	−	0.0151507i	$-0.995177\pi$
$43$	−3.36438	−	5.82728i	−0.513063	−	0.888652i	0.486822	−	0.873501i	$-0.338156\pi$
$44$			2.40530i			0.362612i
$45$		0			0
$46$	−7.46758	+	4.31141i	−1.10103	+	0.635682i
$47$			7.29560i			1.06417i	0.846690	+	0.532086i	$0.178592\pi$
$47$			7.29560i			1.06417i	−0.846690	+	0.532086i	$0.821408\pi$
$48$	−0.500000	−	0.866025i	−0.0721688	−	0.125000i
$49$	−2.14514	+	3.71548i	−0.306448	+	0.530783i
$50$		0			0
$51$	0.243297			0.0340684
$52$	2.98647	−	2.02015i	0.414149	−	0.280144i
$53$	−2.44613			−0.336002			−0.168001	−	0.985787i	$-0.553731\pi$
$53$	−2.44613			−0.336002			−0.168001	+	0.985787i	$0.553731\pi$
$54$	−0.866025	−	0.500000i	−0.117851	−	0.0680414i
$55$		0			0
$56$	−0.823063	−	1.42559i	−0.109986	−	0.190502i
$57$		−	4.41882i		−	0.585287i
$58$	0.0383880	−	0.0221633i	0.00504059	−	0.00291018i
$59$	8.35669	−	4.82474i	1.08795	−	0.628127i	0.154919	−	0.987927i	$-0.450488\pi$
$59$	8.35669	−	4.82474i	1.08795	−	0.628127i	0.933029	+	0.359800i	$0.117155\pi$
$60$		0			0
$61$	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	$0.779430\pi$
$62$	−2.12229	+	3.67591i	−0.269531	+	0.466841i
$63$	−1.42559	−	0.823063i	−0.179607	−	0.103696i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	2.40530			0.296072
$67$	−1.62310	−	0.937098i	−0.198293	−	0.114485i	0.397566	−	0.917574i	$-0.369855\pi$
$67$	−1.62310	−	0.937098i	−0.198293	−	0.114485i	−0.595859	+	0.803089i	$0.703188\pi$
$68$	0.121649	−	0.210702i	0.0147521	−	0.0255513i
$69$	4.31141	+	7.46758i	0.519032	+	0.898991i
$70$		0			0
$71$	−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	$0.481002\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$			1.70370i			0.199403i	0.995017	+	0.0997015i	$0.0317888\pi$
$73$			1.70370i			0.199403i	−0.995017	+	0.0997015i	$0.968211\pi$
$74$	4.47415	+	7.74945i	0.520109	+	0.900855i
$75$		0			0
$76$	−3.82681	−	2.20941i	−0.438965	−	0.253437i
$77$	3.95942			0.451218
$78$	−2.02015	−	2.98647i	−0.228737	−	0.338151i
$79$	−6.79707			−0.764730			−0.382365	−	0.924011i	$-0.624890\pi$
$79$	−6.79707			−0.764730			−0.382365	+	0.924011i	$0.624890\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−0.121649	−	0.210702i	−0.0134338	−	0.0232681i
$83$		−	17.4986i		−	1.92073i	−0.278754	−	0.960363i	$-0.589921\pi$
$83$		−	17.4986i		−	1.92073i	0.278754	−	0.960363i	$-0.410079\pi$
$84$	−1.42559	+	0.823063i	−0.155544	+	0.0898035i
$85$		0			0
$86$			6.72876i			0.725581i
$87$	−0.0221633	−	0.0383880i	−0.00237615	−	0.00411562i
$88$	1.20265	−	2.08305i	0.128203	−	0.222054i
$89$	8.69772	+	5.02163i	0.921956	+	0.532292i	0.884259	−	0.466997i	$-0.154664\pi$
$89$	8.69772	+	5.02163i	0.921956	+	0.532292i	0.0376977	+	0.999289i	$0.487998\pi$
$90$		0			0
$91$	−3.32541	−	4.91611i	−0.348598	−	0.515348i
$92$	8.62281			0.898991
$93$	3.67591	+	2.12229i	0.381174	+	0.220071i
$94$	3.64780	−	6.31817i	0.376242	−	0.651670i
$95$		0			0
$96$			1.00000i			0.102062i
$97$	14.3006	−	8.25647i	1.45201	−	0.838317i	0.453413	−	0.891301i	$-0.350206\pi$
$97$	14.3006	−	8.25647i	1.45201	−	0.838317i	0.998595	+	0.0529831i	$0.0168729\pi$
$98$	3.71548	−	2.14514i	0.375321	−	0.216691i
$99$		−	2.40530i		−	0.241741i
$100$		0			0
$101$	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	$-0.0240577\pi$
$102$	−0.210702	−	0.121649i	−0.0208626	−	0.0120450i
$103$	−5.98168			−0.589392			−0.294696	−	0.955591i	$-0.595218\pi$
$103$	−5.98168			−0.589392			−0.294696	+	0.955591i	$0.595218\pi$
$104$	−3.59643	+	0.256262i	−0.352659	+	0.0251286i
$105$		0			0
$106$	2.11841	+	1.22307i	0.205758	+	0.118795i
$107$	5.33795	−	9.24559i	0.516039	−	0.893805i	−0.483788	−	0.875185i	$-0.660739\pi$
$107$	5.33795	−	9.24559i	0.516039	−	0.893805i	0.999827	−	0.0186200i	$-0.00592729\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$		−	9.50683i		−	0.910589i	−0.890341	−	0.455295i	$-0.849534\pi$
$109$		−	9.50683i		−	0.910589i	0.890341	−	0.455295i	$-0.150466\pi$
$110$		0			0
$111$	7.74945	−	4.47415i	0.735545	−	0.424667i
$112$			1.64613i			0.155544i
$113$	−1.79806	−	3.11433i	−0.169147	−	0.292972i	0.768973	−	0.639281i	$-0.220768\pi$
$113$	−1.79806	−	3.11433i	−0.169147	−	0.292972i	−0.938120	+	0.346310i	$0.887435\pi$
$114$	−2.20941	+	3.82681i	−0.206930	+	0.358414i
$115$		0			0
$116$	−0.0443266			−0.00411562
$117$	−2.98647	+	2.02015i	−0.276099	+	0.186763i
$118$	−9.64947			−0.888306
$119$	−0.346841	−	0.200249i	−0.0317949	−	0.0183568i
$120$		0			0
$121$	−2.60727	−	4.51593i	−0.237025	−	0.410539i
$122$		−	2.63260i		−	0.238345i
$123$	−0.210702	+	0.121649i	−0.0189983	+	0.0109687i
$124$	3.67591	−	2.12229i	0.330106	−	0.190587i
$125$		0			0
$126$	0.823063	+	1.42559i	0.0733243	+	0.127001i
$127$	−8.67351	+	15.0230i	−0.769650	+	1.33307i	0.168103	+	0.985769i	$0.446236\pi$
$127$	−8.67351	+	15.0230i	−0.769650	+	1.33307i	−0.937753	+	0.347303i	$0.887098\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	6.72876			0.592435
$130$		0			0
$131$	14.1654			1.23764			0.618818	−	0.785534i	$-0.287612\pi$
$131$	14.1654			1.23764			0.618818	+	0.785534i	$0.287612\pi$
$132$	−2.08305	−	1.20265i	−0.181306	−	0.104677i
$133$	−3.63697	+	6.29941i	−0.315365	+	0.546228i
$134$	0.937098	+	1.62310i	0.0809530	+	0.140215i
$135$		0			0
$136$	−0.210702	+	0.121649i	−0.0180675	+	0.0104313i
$137$	6.35158	−	3.66709i	0.542652	−	0.313300i	−0.203501	−	0.979075i	$-0.565232\pi$
$137$	6.35158	−	3.66709i	0.542652	−	0.313300i	0.746153	+	0.665774i	$0.231899\pi$
$138$		−	8.62281i		−	0.734023i
$139$	−7.10185	−	12.3008i	−0.602371	−	1.04334i	−0.992461	−	0.122561i	$-0.960889\pi$
$139$	−7.10185	−	12.3008i	−0.602371	−	1.04334i	0.390090	−	0.920777i	$-0.372444\pi$
$140$		0			0
$141$	−6.31817	−	3.64780i	−0.532086	−	0.307200i
$142$	7.54060			0.632793
$143$	3.79144	−	7.79974i	0.317056	−	0.652247i
$144$	1.00000			0.0833333
$145$		0			0
$146$	0.851850	−	1.47545i	0.0704996	−	0.122109i
$147$	−2.14514	−	3.71548i	−0.176928	−	0.306448i
$148$		−	8.94829i		−	0.735545i
$149$	9.61623	−	5.55193i	0.787792	−	0.454832i	−0.0513926	−	0.998679i	$-0.516366\pi$
$149$	9.61623	−	5.55193i	0.787792	−	0.454832i	0.839185	+	0.543847i	$0.183033\pi$
$150$		0			0
$151$			0.874663i			0.0711791i	0.999366	+	0.0355895i	$0.0113309\pi$
$151$			0.874663i			0.0711791i	−0.999366	+	0.0355895i	$0.988669\pi$
$152$	2.20941	+	3.82681i	0.179207	+	0.310395i
$153$	−0.121649	+	0.210702i	−0.00983471	+	0.0170342i
$154$	−3.42896	−	1.97971i	−0.276313	−	0.159530i
$155$		0			0
$156$	0.256262	+	3.59643i	0.0205174	+	0.287945i
$157$	−15.5085			−1.23771			−0.618856	−	0.785504i	$-0.712404\pi$
$157$	−15.5085			−1.23771			−0.618856	+	0.785504i	$0.712404\pi$
$158$	5.88644	+	3.39854i	0.468300	+	0.270373i
$159$	1.22307	−	2.11841i	0.0969954	−	0.168001i
$160$		0			0
$161$		−	14.1942i		−	1.11866i
$162$	0.866025	−	0.500000i	0.0680414	−	0.0392837i
$163$	18.9597	−	10.9464i	1.48504	−	0.857388i	0.485185	−	0.874411i	$-0.338752\pi$
$163$	18.9597	−	10.9464i	1.48504	−	0.857388i	0.999855	+	0.0170229i	$0.00541883\pi$
$164$			0.243297i			0.0189983i
$165$		0			0
$166$	−8.74932	+	15.1543i	−0.679079	+	1.17620i
$167$	−4.58673	−	2.64815i	−0.354932	−	0.204920i	0.311923	−	0.950107i	$-0.399027\pi$
$167$	−4.58673	−	2.64815i	−0.354932	−	0.204920i	−0.666855	+	0.745187i	$0.732360\pi$
$168$	1.64613			0.127001
$169$	−12.8687	+	1.84326i	−0.989897	+	0.141789i
$170$		0			0
$171$	3.82681	+	2.20941i	0.292643	+	0.168958i
$172$	3.36438	−	5.82728i	0.256532	−	0.444326i
$173$	8.62958	+	14.9469i	0.656095	+	1.13639i	0.981618	+	0.190856i	$0.0611263\pi$
$173$	8.62958	+	14.9469i	0.656095	+	1.13639i	−0.325523	+	0.945534i	$0.605540\pi$
$174$			0.0443266i			0.00336039i
$175$		0			0
$176$	−2.08305	+	1.20265i	−0.157016	+	0.0906530i
$177$			9.64947i			0.725299i
$178$	−5.02163	−	8.69772i	−0.376387	−	0.651922i
$179$	4.17781	−	7.23617i	0.312264	−	0.540857i	−0.666588	−	0.745426i	$-0.732246\pi$
$179$	4.17781	−	7.23617i	0.312264	−	0.540857i	0.978852	+	0.204569i	$0.0655794\pi$
$180$		0			0
$181$	12.7335			0.946476			0.473238	−	0.880935i	$-0.343085\pi$
$181$	12.7335			0.946476			0.473238	+	0.880935i	$0.343085\pi$
$182$	0.421840	+	5.92018i	0.0312689	+	0.438833i
$183$	−2.63260			−0.194608
$184$	−7.46758	−	4.31141i	−0.550517	−	0.317841i
$185$		0			0
$186$	−2.12229	−	3.67591i	−0.155614	−	0.269531i
$187$		−	0.585202i		−	0.0427942i
$188$	−6.31817	+	3.64780i	−0.460800	+	0.266043i
$189$	1.42559	−	0.823063i	0.103696	−	0.0598690i
$190$		0			0
$191$	−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	$0.838116\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	22.5025	+	12.9918i	1.61977	+	0.935173i	0.986979	+	0.160849i	$0.0514232\pi$
$193$	22.5025	+	12.9918i	1.61977	+	0.935173i	0.632789	+	0.774324i	$0.281910\pi$
$194$	−16.5129			−1.18556
$195$		0			0
$196$	−4.29027			−0.306448
$197$	−13.3735	−	7.72121i	−0.952824	−	0.550113i	−0.0588672	−	0.998266i	$-0.518749\pi$
$197$	−13.3735	−	7.72121i	−0.952824	−	0.550113i	−0.893957	+	0.448152i	$0.852082\pi$
$198$	−1.20265	+	2.08305i	−0.0854685	+	0.148036i
$199$	−6.85286	−	11.8695i	−0.485787	−	0.841407i	0.514080	−	0.857742i	$-0.328133\pi$
$199$	−6.85286	−	11.8695i	−0.485787	−	0.841407i	−0.999867	+	0.0163352i	$0.994800\pi$
$200$		0			0
$201$	1.62310	−	0.937098i	0.114485	−	0.0660978i
$202$	−9.81687	+	5.66777i	−0.690712	+	0.398783i
$203$			0.0729671i			0.00512129i
$204$	0.121649	+	0.210702i	0.00851711	+	0.0147521i
$205$		0			0
$206$	5.18029	+	2.99084i	0.360928	+	0.208382i
$207$	−8.62281			−0.599327
$208$	3.24273	+	1.57629i	0.224843	+	0.109296i
$209$	−10.6286			−0.735193
$210$		0			0
$211$	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	$-0.0204654\pi$
$212$	−1.22307	−	2.11841i	−0.0840005	−	0.145493i
$213$		−	7.54060i		−	0.516673i
$214$	−9.24559	+	5.33795i	−0.632016	+	0.364894i
$215$		0			0
$216$		−	1.00000i		−	0.0680414i
$217$	−3.49355	−	6.05101i	−0.237158	−	0.410769i
$218$	−4.75342	+	8.23316i	−0.321942	+	0.557620i
$219$	−1.47545	−	0.851850i	−0.0997015	−	0.0575627i
$220$		0			0
$221$	−0.726600	+	0.491496i	−0.0488764	+	0.0330616i
$222$	−8.94829			−0.600570
$223$	−9.62823	−	5.55886i	−0.644754	−	0.372249i	0.141690	−	0.989911i	$-0.454747\pi$
$223$	−9.62823	−	5.55886i	−0.644754	−	0.372249i	−0.786443	+	0.617662i	$0.788080\pi$
$224$	0.823063	−	1.42559i	0.0549932	−	0.0952510i
$225$		0			0
$226$			3.59612i			0.239210i
$227$	19.1217	−	11.0399i	1.26915	−	0.732747i	0.294327	−	0.955705i	$-0.404905\pi$
$227$	19.1217	−	11.0399i	1.26915	−	0.732747i	0.974828	+	0.222958i	$0.0715713\pi$
$228$	3.82681	−	2.20941i	0.253437	−	0.146322i
$229$		−	10.3397i		−	0.683266i	−0.939834	−	0.341633i	$-0.889020\pi$
$229$		−	10.3397i		−	0.683266i	0.939834	−	0.341633i	$-0.110980\pi$
$230$		0			0
$231$	−1.97971	+	3.42896i	−0.130255	+	0.225609i
$232$	0.0383880	+	0.0221633i	0.00252029	+	0.00145509i
$233$	−21.8928			−1.43425			−0.717123	−	0.696947i	$-0.754541\pi$
$233$	−21.8928			−1.43425			−0.717123	+	0.696947i	$0.754541\pi$
$234$	3.59643	−	0.256262i	0.235106	−	0.0167524i
$235$		0			0
$236$	8.35669	+	4.82474i	0.543974	+	0.314064i
$237$	3.39854	−	5.88644i	0.220759	−	0.382365i
$238$	0.200249	+	0.346841i	0.0129802	+	0.0224824i
$239$			26.2510i			1.69804i	0.528362	+	0.849019i	$0.322806\pi$
$239$			26.2510i			1.69804i	−0.528362	+	0.849019i	$0.677194\pi$
$240$		0			0
$241$	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	$0.0156968\pi$
$242$			5.21455i			0.335204i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−1.31630	+	2.27990i	−0.0842676	+	0.145956i
$245$		0			0
$246$	0.243297			0.0155121
$247$	8.92666	+	13.1967i	0.567990	+	0.839684i
$248$	−4.24458			−0.269531
$249$	15.1543	+	8.74932i	0.960363	+	0.554466i
$250$		0			0
$251$	−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	$0.839610\pi$
$252$		−	1.64613i		−	0.103696i
$253$	17.9617	−	10.3702i	1.12924	−	0.651970i
$254$	15.0230	−	8.67351i	0.942624	−	0.544224i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	6.97195	−	12.0758i	0.434898	−	0.753266i	−0.562389	−	0.826873i	$-0.690118\pi$
$257$	6.97195	−	12.0758i	0.434898	−	0.753266i	0.997287	+	0.0736066i	$0.0234509\pi$
$258$	−5.82728	−	3.36438i	−0.362791	−	0.209457i
$259$	−14.7300			−0.915278
$260$		0			0
$261$	0.0443266			0.00274375
$262$	−12.2676	−	7.08270i	−0.757894	−	0.437571i
$263$	−9.71828	+	16.8325i	−0.599255	+	1.03794i	0.393677	+	0.919249i	$0.371203\pi$
$263$	−9.71828	+	16.8325i	−0.599255	+	1.03794i	−0.992931	+	0.118690i	$0.962130\pi$
$264$	1.20265	+	2.08305i	0.0740179	+	0.128203i
$265$		0			0
$266$	6.29941	−	3.63697i	0.386242	−	0.222997i
$267$	−8.69772	+	5.02163i	−0.532292	+	0.307319i
$268$		−	1.87420i		−	0.114485i
$269$	1.50069	+	2.59928i	0.0914989	+	0.158481i	0.908142	−	0.418662i	$-0.137501\pi$
$269$	1.50069	+	2.59928i	0.0914989	+	0.158481i	−0.816643	+	0.577143i	$0.804168\pi$
$270$		0			0
$271$	−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	$0.999123\pi$
$272$	0.243297			0.0147521
$273$	5.92018	−	0.421840i	0.358306	−	0.0255309i
$274$	−7.33417			−0.443074
$275$		0			0
$276$	−4.31141	+	7.46758i	−0.259516	+	0.449495i
$277$	−0.426329	−	0.738423i	−0.0256156	−	0.0443676i	0.852933	−	0.522020i	$-0.174821\pi$
$277$	−0.426329	−	0.738423i	−0.0256156	−	0.0443676i	−0.878549	+	0.477652i	$0.841488\pi$
$278$			14.2037i			0.851882i
$279$	−3.67591	+	2.12229i	−0.220071	+	0.127058i
$280$		0			0
$281$			15.6851i			0.935697i	0.883809	+	0.467848i	$0.154971\pi$
$281$			15.6851i			0.935697i	−0.883809	+	0.467848i	$0.845029\pi$
$282$	3.64780	+	6.31817i	0.217223	+	0.376242i
$283$	−4.04370	+	7.00390i	−0.240373	+	0.416339i	−0.960821	−	0.277171i	$-0.910603\pi$
$283$	−4.04370	+	7.00390i	−0.240373	+	0.416339i	0.720447	+	0.693510i	$0.243937\pi$
$284$	−6.53035	−	3.77030i	−0.387505	−	0.223726i
$285$		0			0
$286$	−7.18335	+	4.85905i	−0.424760	+	0.287322i
$287$	0.400498			0.0236406
$288$	−0.866025	−	0.500000i	−0.0510310	−	0.0294628i
$289$	8.47040	−	14.6712i	0.498259	−	0.863010i
$290$		0			0
$291$			16.5129i			0.968006i
$292$	−1.47545	+	0.851850i	−0.0863440	+	0.0498508i
$293$	1.67523	−	0.967192i	0.0978677	−	0.0565040i	−0.450267	−	0.892894i	$-0.648671\pi$
$293$	1.67523	−	0.967192i	0.0978677	−	0.0565040i	0.548135	+	0.836390i	$0.315338\pi$
$294$			4.29027i			0.250214i
$295$		0			0
$296$	−4.47415	+	7.74945i	−0.260054	+	0.450427i
$297$	2.08305	+	1.20265i	0.120871	+	0.0697847i
$298$	−11.1039			−0.643229
$299$	−27.9615	−	13.5920i	−1.61705	−	0.786047i
$300$		0			0
$301$	−9.59244	−	5.53820i	−0.552899	−	0.319216i
$302$	0.437332	−	0.757480i	0.0251656	−	0.0435881i
$303$	5.66777	+	9.81687i	0.325605	+	0.563964i
$304$		−	4.41882i		−	0.253437i
$305$		0			0
$306$	0.210702	−	0.121649i	0.0120450	−	0.00695419i
$307$			12.4384i			0.709894i	0.934886	+	0.354947i	$0.115501\pi$
$307$			12.4384i			0.709894i	−0.934886	+	0.354947i	$0.884499\pi$
$308$	1.97971	+	3.42896i	0.112804	+	0.195383i
$309$	2.99084	−	5.18029i	0.170143	−	0.294696i
$310$		0			0
$311$	−18.3700			−1.04167			−0.520835	−	0.853657i	$-0.674379\pi$
$311$	−18.3700			−1.04167			−0.520835	+	0.853657i	$0.674379\pi$
$312$	1.57629	−	3.24273i	0.0892397	−	0.183584i
$313$	−31.9445			−1.80561			−0.902804	−	0.430051i	$-0.858496\pi$
$313$	−31.9445			−1.80561			−0.902804	+	0.430051i	$0.858496\pi$
$314$	13.4307	+	7.75425i	0.757941	+	0.437597i
$315$		0			0
$316$	−3.39854	−	5.88644i	−0.191183	−	0.331138i
$317$			23.3625i			1.31217i	0.754689	+	0.656083i	$0.227788\pi$
$317$			23.3625i			1.31217i	−0.754689	+	0.656083i	$0.772212\pi$
$318$	−2.11841	+	1.22307i	−0.118795	+	0.0685861i
$319$	−0.0923344	+	0.0533093i	−0.00516973	+	0.00298475i
$320$		0			0
$321$	5.33795	+	9.24559i	0.297935	+	0.516039i
$322$	−7.09712	+	12.2926i	−0.395507	+	0.685038i
$323$	0.931052	+	0.537543i	0.0518051	+	0.0299097i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	−21.8928			−1.21253
$327$	8.23316	+	4.75342i	0.455295	+	0.262865i
$328$	0.121649	−	0.210702i	0.00671692	−	0.0116341i
$329$	6.00474	+	10.4005i	0.331052	+	0.573399i
$330$		0			0
$331$	−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	$0.534153\pi$
$332$	15.1543	−	8.74932i	0.831698	−	0.480181i
$333$			8.94829i			0.490363i
$334$	2.64815	+	4.58673i	0.144900	+	0.250975i
$335$		0			0
$336$	−1.42559	−	0.823063i	−0.0777721	−	0.0449018i
$337$	14.3561			0.782026			0.391013	−	0.920385i	$-0.372125\pi$
$337$	14.3561			0.782026			0.391013	+	0.920385i	$0.372125\pi$
$338$	12.0662	+	4.83802i	0.656316	+	0.263154i
$339$	3.59612			0.195314
$340$		0			0
$341$	5.10473	−	8.84165i	0.276437	−	0.478802i
$342$	−2.20941	−	3.82681i	−0.119471	−	0.206930i
$343$			18.5852i			1.00351i
$344$	−5.82728	+	3.36438i	−0.314186	+	0.181395i
$345$		0			0
$346$		−	17.2592i		−	0.927858i
$347$	0.332557	+	0.576005i	0.0178526	+	0.0309216i	0.874814	−	0.484460i	$-0.160984\pi$
$347$	0.332557	+	0.576005i	0.0178526	+	0.0309216i	−0.856961	+	0.515381i	$0.827650\pi$
$348$	0.0221633	−	0.0383880i	0.00118808	−	0.00205781i
$349$	−3.25007	−	1.87643i	−0.173972	−	0.100443i	0.410485	−	0.911867i	$-0.365359\pi$
$349$	−3.25007	−	1.87643i	−0.173972	−	0.100443i	−0.584458	+	0.811424i	$0.698693\pi$
$350$		0			0
$351$	−0.256262	−	3.59643i	−0.0136783	−	0.191963i
$352$	2.40530			0.128203
$353$	−3.95219	−	2.28180i	−0.210354	−	0.121448i	0.391122	−	0.920339i	$-0.372087\pi$
$353$	−3.95219	−	2.28180i	−0.210354	−	0.121448i	−0.601476	+	0.798891i	$0.705420\pi$
$354$	4.82474	−	8.35669i	0.256432	−	0.444153i
$355$		0			0
$356$			10.0433i			0.532292i
$357$	0.346841	−	0.200249i	0.0183568	−	0.0105983i
$358$	−7.23617	+	4.17781i	−0.382444	+	0.220804i
$359$			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			0
$361$	0.262979	−	0.455494i	0.0138410	−	0.0239733i
$362$	−11.0276	−	6.36677i	−0.579596	−	0.334630i
$363$	5.21455			0.273693
$364$	2.59477	−	5.33795i	0.136003	−	0.279784i
$365$		0			0
$366$	2.27990	+	1.31630i	0.119172	+	0.0688042i
$367$	0.747277	−	1.29432i	0.0390075	−	0.0675630i	−0.845863	−	0.533401i	$-0.820914\pi$
$367$	0.747277	−	1.29432i	0.0390075	−	0.0675630i	0.884870	+	0.465838i	$0.154247\pi$
$368$	4.31141	+	7.46758i	0.224748	+	0.389274i
$369$		−	0.243297i		−	0.0126656i
$370$		0			0
$371$	−3.48717	+	2.01332i	−0.181045	+	0.104526i
$372$			4.24458i			0.220071i
$373$	10.2955	+	17.8323i	0.533081	+	0.923323i	0.999254	+	0.0386291i	$0.0122991\pi$
$373$	10.2955	+	17.8323i	0.533081	+	0.923323i	−0.466173	+	0.884694i	$0.654368\pi$
$374$	−0.292601	+	0.506800i	−0.0151300	+	0.0262060i
$375$		0			0
$376$	7.29560			0.376242
$377$	0.143739	+	0.0698714i	0.00740295	+	0.00359856i
$378$	−1.64613			−0.0846676
$379$	18.4173	+	10.6332i	0.946032	+	0.546192i	0.891846	−	0.452339i	$-0.149410\pi$
$379$	18.4173	+	10.6332i	0.946032	+	0.546192i	0.0541858	+	0.998531i	$0.482744\pi$
$380$		0			0
$381$	−8.67351	−	15.0230i	−0.444357	−	0.769650i
$382$			0.415264i			0.0212468i
$383$	−9.19884	+	5.31095i	−0.470039	+	0.271377i	−0.716256	−	0.697838i	$-0.754146\pi$
$383$	−9.19884	+	5.31095i	−0.470039	+	0.271377i	0.246217	+	0.969215i	$0.420812\pi$
$384$	−0.866025	+	0.500000i	−0.0441942	+	0.0255155i
$385$		0			0
$386$	−12.9918	−	22.5025i	−0.661267	−	1.14535i
$387$	−3.36438	+	5.82728i	−0.171021	+	0.296217i
$388$	14.3006	+	8.25647i	0.726004	+	0.419159i
$389$	37.0443			1.87822			0.939111	−	0.343613i	$-0.111651\pi$
$389$	37.0443			1.87822			0.939111	+	0.343613i	$0.111651\pi$
$390$		0			0
$391$	−2.09791			−0.106096
$392$	3.71548	+	2.14514i	0.187660	+	0.108346i
$393$	−7.08270	+	12.2676i	−0.357275	+	0.618818i
$394$	7.72121	+	13.3735i	0.388989	+	0.673749i
$395$		0			0
$396$	2.08305	−	1.20265i	0.104677	−	0.0604353i
$397$	−1.46115	+	0.843593i	−0.0733328	+	0.0423387i	−0.536218	−	0.844079i	$-0.680148\pi$
$397$	−1.46115	+	0.843593i	−0.0733328	+	0.0423387i	0.462885	+	0.886418i	$0.346814\pi$
$398$			13.7057i			0.687006i
$399$	−3.63697	−	6.29941i	−0.182076	−	0.315365i
$400$		0			0
$401$	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	$0.500500\pi$
$402$	−1.87420			−0.0934764
$403$	−15.2653	+	1.08772i	−0.760420	+	0.0541834i
$404$	11.3355			0.563964
$405$		0			0
$406$	0.0364836	−	0.0631914i	0.00181065	−	0.00313614i
$407$	−10.7616	−	18.6397i	−0.533435	−	0.923936i
$408$		−	0.243297i		−	0.0120450i
$409$	−10.6603	+	6.15471i	−0.527117	+	0.304331i	−0.739842	−	0.672781i	$-0.765100\pi$
$409$	−10.6603	+	6.15471i	−0.527117	+	0.304331i	0.212725	+	0.977112i	$0.431766\pi$
$410$		0			0
$411$			7.33417i			0.361768i
$412$	−2.99084	−	5.18029i	−0.147348	−	0.255214i
$413$	7.94212	−	13.7562i	0.390806	−	0.676896i
$414$	7.46758	+	4.31141i	0.367011	+	0.211894i
$415$		0			0
$416$	−2.02015	−	2.98647i	−0.0990458	−	0.146424i
$417$	14.2037			0.695559
$418$	9.20461	+	5.31428i	0.450212	+	0.259930i
$419$	−11.0411	+	19.1238i	−0.539393	+	0.934256i	0.459544	+	0.888155i	$0.348013\pi$
$419$	−11.0411	+	19.1238i	−0.539393	+	0.934256i	−0.998937	+	0.0461011i	$0.985320\pi$
$420$		0			0
$421$			8.98036i			0.437676i	0.975761	+	0.218838i	$0.0702266\pi$
$421$			8.98036i			0.437676i	−0.975761	+	0.218838i	$0.929773\pi$
$422$	−13.9537	+	8.05616i	−0.679254	+	0.392168i
$423$	6.31817	−	3.64780i	0.307200	−	0.177362i
$424$			2.44613i			0.118795i
$425$		0			0
$426$	−3.77030	+	6.53035i	−0.182672	+	0.316397i
$427$	3.75300	+	2.16680i	0.181621	+	0.104859i
$428$	10.6759			0.516039
$429$	4.85905	+	7.18335i	0.234597	+	0.346815i
$430$		0			0
$431$	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	$0.602850\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	9.92035	+	17.1825i	0.476741	+	0.825740i	0.999645	−	0.0266515i	$-0.00848445\pi$
$433$	9.92035	+	17.1825i	0.476741	+	0.825740i	−0.522903	+	0.852392i	$0.675151\pi$
$434$			6.98710i			0.335392i
$435$		0			0
$436$	8.23316	−	4.75342i	0.394297	−	0.227647i
$437$			38.1027i			1.82270i
$438$	0.851850	+	1.47545i	0.0407030	+	0.0704996i
$439$	14.4415	−	25.0134i	0.689255	−	1.19382i	−0.282824	−	0.959172i	$-0.591271\pi$
$439$	14.4415	−	25.0134i	0.689255	−	1.19382i	0.972079	−	0.234653i	$-0.0753953\pi$
$440$		0			0
$441$	4.29027			0.204299
$442$	0.875002	−	0.0623479i	0.0416196	−	0.00296559i
$443$	−5.76986			−0.274134			−0.137067	−	0.990562i	$-0.543768\pi$
$443$	−5.76986			−0.274134			−0.137067	+	0.990562i	$0.543768\pi$
$444$	7.74945	+	4.47415i	0.367772	+	0.212334i
$445$		0			0
$446$	5.55886	+	9.62823i	0.263220	+	0.455910i
$447$			11.1039i			0.525195i
$448$	−1.42559	+	0.823063i	−0.0673526	+	0.0388861i
$449$	33.9034	−	19.5741i	1.60000	−	0.923760i	0.608514	−	0.793543i	$-0.291766\pi$
$449$	33.9034	−	19.5741i	1.60000	−	0.923760i	0.991486	−	0.130217i	$-0.0415674\pi$
$450$		0			0
$451$	0.292601	+	0.506800i	0.0137780	+	0.0238643i
$452$	1.79806	−	3.11433i	0.0845736	−	0.146486i
$453$	−0.757480	−	0.437332i	−0.0355895	−	0.0205476i
$454$	−22.0799			−1.03626
$455$		0			0
$456$	−4.41882			−0.206930
$457$	21.2008	+	12.2403i	0.991730	+	0.572575i	0.905791	−	0.423725i	$-0.139278\pi$
$457$	21.2008	+	12.2403i	0.991730	+	0.572575i	0.0859387	+	0.996300i	$0.472611\pi$
$458$	−5.16984	+	8.95443i	−0.241571	+	0.418413i
$459$	−0.121649	−	0.210702i	−0.00567807	−	0.00983471i
$460$		0			0
$461$	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	$0.307376\pi$
$462$	3.42896	−	1.97971i	0.159530	−	0.0921044i
$463$			18.3063i			0.850767i	0.905013	+	0.425384i	$0.139861\pi$
$463$			18.3063i			0.850767i	−0.905013	+	0.425384i	$0.860139\pi$
$464$	−0.0221633	−	0.0383880i	−0.00102891	−	0.00178212i
$465$		0			0
$466$	18.9597	+	10.9464i	0.878292	+	0.507082i
$467$	6.46019			0.298942			0.149471	−	0.988766i	$-0.452243\pi$
$467$	6.46019			0.298942			0.149471	+	0.988766i	$0.452243\pi$
$468$	−3.24273	−	1.57629i	−0.149895	−	0.0728639i
$469$	−3.08516			−0.142460
$470$		0			0
$471$	7.75425	−	13.4307i	0.357297	−	0.618856i
$472$	−4.82474	−	8.35669i	−0.222077	−	0.384648i
$473$		−	16.1847i		−	0.744172i
$474$	−5.88644	+	3.39854i	−0.270373	+	0.156100i
$475$		0			0
$476$		−	0.400498i		−	0.0183568i
$477$	1.22307	+	2.11841i	0.0560003	+	0.0969954i
$478$	13.1255	−	22.7341i	0.600347	−	1.03983i
$479$	−26.5980	−	15.3564i	−1.21529	−	0.701651i	−0.251387	−	0.967887i	$-0.580887\pi$
$479$	−26.5980	−	15.3564i	−1.21529	−	0.701651i	−0.963908	+	0.266236i	$0.914220\pi$
$480$		0			0
$481$	−14.1051	+	29.0169i	−0.643136	+	1.32306i
$482$	−26.0907			−1.18840
$483$	12.2926	+	7.09712i	0.559331	+	0.322930i
$484$	2.60727	−	4.51593i	0.118512	−	0.205270i
$485$		0			0
$486$			1.00000i			0.0453609i
$487$	10.7965	−	6.23335i	0.489235	−	0.282460i	−0.235022	−	0.971990i	$-0.575516\pi$
$487$	10.7965	−	6.23335i	0.489235	−	0.282460i	0.724257	+	0.689530i	$0.242183\pi$
$488$	2.27990	−	1.31630i	0.103206	−	0.0595862i
$489$			21.8928i			0.990027i
$490$		0			0
$491$	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	$0.148108\pi$
$492$	−0.210702	−	0.121649i	−0.00949916	−	0.00548434i
$493$	0.0107845			0.000485711
$494$	−1.13238	−	15.8920i	−0.0509480	−	0.715014i
$495$		0			0
$496$	3.67591	+	2.12229i	0.165053	+	0.0952935i
$497$	−6.20639	+	10.7498i	−0.278395	+	0.482194i
$498$	−8.74932	−	15.1543i	−0.392066	−	0.679079i
$499$			20.2443i			0.906261i	0.891444	+	0.453130i	$0.149693\pi$
$499$			20.2443i			0.906261i	−0.891444	+	0.453130i	$0.850307\pi$
$500$		0			0
$501$	4.58673	−	2.64815i	0.204920	−	0.118311i
$502$			0.624794i			0.0278859i
$503$	−4.23283	−	7.33148i	−0.188733	−	0.326894i	0.756095	−	0.654461i	$-0.227105\pi$
$503$	−4.23283	−	7.33148i	−0.188733	−	0.326894i	−0.944828	+	0.327567i	$0.893771\pi$
$504$	−0.823063	+	1.42559i	−0.0366621	+	0.0635007i
$505$		0			0
$506$	−20.7404			−0.922024
$507$	4.83802	−	12.0662i	0.214864	−	0.535879i
$508$	−17.3470			−0.769650
$509$	33.4172	+	19.2935i	1.48119	+	0.855167i	0.999773	−	0.0213225i	$-0.00678766\pi$
$509$	33.4172	+	19.2935i	1.48119	+	0.855167i	0.481421	+	0.876490i	$0.340121\pi$
$510$		0			0
$511$	1.40225	+	2.42877i	0.0620320	+	0.107443i
$512$			1.00000i			0.0441942i
$513$	−3.82681	+	2.20941i	−0.168958	+	0.0975478i
$514$	−12.0758	+	6.97195i	−0.532640	+	0.307520i
$515$		0			0
$516$	3.36438	+	5.82728i	0.148109	+	0.256532i
$517$	−8.77404	+	15.1971i	−0.385882	+	0.668367i
$518$	12.7566	+	7.36500i	0.560491	+	0.323600i
$519$	−17.2592			−0.757593
$520$		0			0
$521$	12.5345			0.549148			0.274574	−	0.961566i	$-0.411463\pi$
$521$	12.5345			0.549148			0.274574	+	0.961566i	$0.411463\pi$
$522$	−0.0383880	−	0.0221633i	−0.00168020	−	0.000970061i
$523$	−6.39970	+	11.0846i	−0.279839	+	0.484696i	−0.971345	−	0.237676i	$-0.923614\pi$
$523$	−6.39970	+	11.0846i	−0.279839	+	0.484696i	0.691505	+	0.722371i	$0.256948\pi$
$524$	7.08270	+	12.2676i	0.309409	+	0.535912i
$525$		0			0
$526$	16.8325	−	9.71828i	0.733934	−	0.423737i
$527$	−0.894339	+	0.516347i	−0.0389580	+	0.0224924i
$528$		−	2.40530i		−	0.104677i
$529$	−25.6765	−	44.4729i	−1.11637	−	1.93361i
$530$		0			0
$531$	−8.35669	−	4.82474i	−0.362649	−	0.209376i
$532$	−7.27393			−0.315365
$533$	0.383506	−	0.788948i	0.0166115	−	0.0341731i
$534$	10.0433			0.434614
$535$		0			0
$536$	−0.937098	+	1.62310i	−0.0404765	+	0.0701073i
$537$	4.17781	+	7.23617i	0.180286	+	0.312264i
$538$		−	3.00139i		−	0.129399i
$539$	−8.93684	+	5.15969i	−0.384937	+	0.222243i
$540$		0			0
$541$			24.9605i			1.07314i	0.843857	+	0.536568i	$0.180280\pi$
$541$			24.9605i			1.07314i	−0.843857	+	0.536568i	$0.819720\pi$
$542$	14.2339	+	24.6538i	0.611396	+	1.05897i
$543$	−6.36677	+	11.0276i	−0.273224	+	0.473238i
$544$	−0.210702	−	0.121649i	−0.00903376	−	0.00521564i
$545$		0			0
$546$	−5.33795	−	2.59477i	−0.228443	−	0.111046i
$547$	−10.4152			−0.445321			−0.222660	−	0.974896i	$-0.571474\pi$
$547$	−10.4152			−0.445321			−0.222660	+	0.974896i	$0.571474\pi$
$548$	6.35158	+	3.66709i	0.271326	+	0.156650i
$549$	1.31630	−	2.27990i	0.0561784	−	0.0973038i
$550$		0			0
$551$		−	0.195871i		−	0.00834439i
$552$	7.46758	−	4.31141i	0.317841	−	0.183506i
$553$	−9.68981	+	5.59442i	−0.412053	+	0.237899i
$554$			0.852658i			0.0362260i
$555$		0			0
$556$	7.10185	−	12.3008i	0.301186	−	0.521669i
$557$	−1.20792	−	0.697392i	−0.0511812	−	0.0295495i	0.474191	−	0.880422i	$-0.342741\pi$
$557$	−1.20792	−	0.697392i	−0.0511812	−	0.0295495i	−0.525372	+	0.850872i	$0.676074\pi$
$558$	4.24458			0.179687
$559$	−20.0953	+	13.5931i	−0.849939	+	0.574926i
$560$		0			0
$561$	0.506800	+	0.292601i	0.0213971	+	0.0123536i
$562$	7.84257	−	13.5837i	0.330819	−	0.572995i
$563$	−8.10624	−	14.0404i	−0.341637	−	0.591733i	0.643100	−	0.765782i	$-0.277648\pi$
$563$	−8.10624	−	14.0404i	−0.341637	−	0.591733i	−0.984737	+	0.174049i	$0.944315\pi$
$564$		−	7.29560i		−	0.307200i
$565$		0			0
$566$	7.00390	−	4.04370i	0.294396	−	0.169970i
$567$			1.64613i			0.0691308i
$568$	3.77030	+	6.53035i	0.158198	+	0.274007i
$569$	−19.6198	+	33.9825i	−0.822505	+	1.42462i	0.0813055	+	0.996689i	$0.474091\pi$
$569$	−19.6198	+	33.9825i	−0.822505	+	1.42462i	−0.903811	+	0.427932i	$0.859242\pi$
$570$		0			0
$571$	−16.0498			−0.671662			−0.335831	−	0.941922i	$-0.609017\pi$
$571$	−16.0498			−0.671662			−0.335831	+	0.941922i	$0.609017\pi$
$572$	8.65049	−	0.616387i	0.361695	−	0.0257724i
$573$	0.415264			0.0173479
$574$	−0.346841	−	0.200249i	−0.0144769	−	0.00835823i
$575$		0			0
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$		−	28.5363i		−	1.18798i	−0.804471	−	0.593992i	$-0.797551\pi$
$577$		−	28.5363i		−	1.18798i	0.804471	−	0.593992i	$-0.202449\pi$
$578$	−14.6712	+	8.47040i	−0.610240	+	0.352322i
$579$	−22.5025	+	12.9918i	−0.935173	+	0.539923i
$580$		0			0
$581$	−14.4025	−	24.9458i	−0.597515	−	1.03493i
$582$	8.25647	−	14.3006i	0.342242	−	0.592780i
$583$	−5.09541	−	2.94183i	−0.211030	−	0.121838i
$584$	1.70370			0.0704996
$585$		0			0
$586$	−1.93438			−0.0799087
$587$	−39.0171	−	22.5265i	−1.61041	−	0.929770i	−0.989275	−	0.146066i	$-0.953339\pi$
$587$	−39.0171	−	22.5265i	−1.61041	−	0.929770i	−0.621134	−	0.783704i	$-0.713328\pi$
$588$	2.14514	−	3.71548i	0.0884639	−	0.153224i
$589$	9.37800	+	16.2432i	0.386414	+	0.669289i
$590$		0			0
$591$	13.3735	−	7.72121i	0.550113	−	0.317608i
$592$	7.74945	−	4.47415i	0.318500	−	0.183886i
$593$			37.0634i			1.52201i	0.648746	+	0.761005i	$0.275294\pi$
$593$			37.0634i			1.52201i	−0.648746	+	0.761005i	$0.724706\pi$
$594$	−1.20265	−	2.08305i	−0.0493453	−	0.0854685i
$595$		0			0
$596$	9.61623	+	5.55193i	0.393896	+	0.227416i
$597$	13.7057			0.560938
$598$	17.4193	+	25.7518i	0.712330	+	1.05307i
$599$	−18.6309			−0.761238			−0.380619	−	0.924732i	$-0.624289\pi$
$599$	−18.6309			−0.761238			−0.380619	+	0.924732i	$0.624289\pi$
$600$		0			0
$601$	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	$0.0373189\pi$
$602$	5.53820	+	9.59244i	0.225720	+	0.390958i
$603$			1.87420i			0.0763232i
$604$	−0.757480	+	0.437332i	−0.0308214	+	0.0177948i
$605$		0			0
$606$		−	11.3355i		−	0.460475i
$607$	−17.4398	−	30.2066i	−0.707858	−	1.22605i	−0.965650	−	0.259846i	$-0.916328\pi$
$607$	−17.4398	−	30.2066i	−0.707858	−	1.22605i	0.257792	−	0.966200i	$-0.417005\pi$
$608$	−2.20941	+	3.82681i	−0.0896034	+	0.155198i
$609$	−0.0631914	−	0.0364836i	−0.00256064	−	0.00147839i
$610$		0			0
$611$	26.2381	−	1.86959i	1.06148	−	0.0756354i
$612$	−0.243297			−0.00983471
$613$	−7.05254	−	4.07179i	−0.284849	−	0.164458i	0.350767	−	0.936463i	$-0.385921\pi$
$613$	−7.05254	−	4.07179i	−0.284849	−	0.164458i	−0.635617	+	0.772005i	$0.719254\pi$
$614$	6.21918	−	10.7719i	0.250986	−	0.434720i
$615$		0			0
$616$		−	3.95942i		−	0.159530i
$617$	−28.9752	+	16.7288i	−1.16650	+	0.673477i	−0.952852	−	0.303435i	$-0.901867\pi$
$617$	−28.9752	+	16.7288i	−1.16650	+	0.673477i	−0.213644	+	0.976912i	$0.568533\pi$
$618$	−5.18029	+	2.99084i	−0.208382	+	0.120309i
$619$			41.1780i			1.65508i	0.561404	+	0.827542i	$0.310261\pi$
$619$			41.1780i			1.65508i	−0.561404	+	0.827542i	$0.689739\pi$
$620$		0			0
$621$	4.31141	−	7.46758i	0.173011	−	0.299664i
$622$	15.9089	+	9.18502i	0.637890	+	0.368286i
$623$	16.5325			0.662359
$624$	−2.98647	+	2.02015i	−0.119555	+	0.0808706i
$625$		0			0
$626$	27.6647	+	15.9722i	1.10571	+	0.638379i
$627$	5.31428	−	9.20461i	0.212232	−	0.367597i
$628$	−7.75425	−	13.4307i	−0.309428	−	0.535945i
$629$			2.17709i			0.0868065i
$630$		0			0
$631$	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	$0.239170\pi$
$632$			6.79707i			0.270373i
$633$	8.05616	+	13.9537i	0.320204	+	0.554609i
$634$	11.6812	−	20.2325i	0.463921	−	0.803535i
$635$		0			0
$636$	2.44613			0.0969954
$637$	13.9122	+	6.76270i	0.551222	+	0.267948i
$638$	0.106619			0.00422107
$639$	6.53035	+	3.77030i	0.258337	+	0.149151i
$640$		0			0
$641$	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	$0.437307\pi$
$642$		−	10.6759i		−	0.421344i
$643$	3.46209	−	1.99884i	0.136531	−	0.0788265i	−0.430178	−	0.902744i	$-0.641549\pi$
$643$	3.46209	−	1.99884i	0.136531	−	0.0788265i	0.566710	+	0.823917i	$0.308216\pi$
$644$	12.2926	−	7.09712i	0.484395	−	0.279666i
$645$		0			0
$646$	−0.537543	−	0.931052i	−0.0211494	−	0.0366318i
$647$	−11.8080	+	20.4521i	−0.464220	+	0.804053i	−0.999166	−	0.0408333i	$-0.986999\pi$
$647$	−11.8080	+	20.4521i	−0.464220	+	0.804053i	0.534946	+	0.844886i	$0.320332\pi$
$648$	0.866025	+	0.500000i	0.0340207	+	0.0196419i
$649$	23.2098			0.911066
$650$		0			0
$651$	6.98710			0.273846
$652$	18.9597	+	10.9464i	0.742520	+	0.428694i
$653$	17.6329	−	30.5411i	0.690029	−	1.19516i	−0.281799	−	0.959473i	$-0.590931\pi$
$653$	17.6329	−	30.5411i	0.690029	−	1.19516i	0.971828	−	0.235692i	$-0.0757355\pi$
$654$	−4.75342	−	8.23316i	−0.185873	−	0.321942i
$655$		0			0
$656$	−0.210702	+	0.121649i	−0.00822652	+	0.00474958i
$657$	1.47545	−	0.851850i	0.0575627	−	0.0332338i
$658$		−	12.0095i		−	0.468178i
$659$	−12.6686	−	21.9427i	−0.493499	−	0.854765i	0.506473	−	0.862256i	$-0.330949\pi$
$659$	−12.6686	−	21.9427i	−0.493499	−	0.854765i	−0.999972	+	0.00749088i	$0.997616\pi$
$660$		0			0
$661$	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	$0.636502\pi$
$662$	21.4634			0.834199
$663$	−0.0623479	−	0.875002i	−0.00242139	−	0.0339823i
$664$	−17.4986			−0.679079
$665$		0			0
$666$	4.47415	−	7.74945i	0.173370	−	0.300285i
$667$	0.191110	+	0.331012i	0.00739981	+	0.0128168i
$668$		−	5.29630i		−	0.204920i
$669$	9.62823	−	5.55886i	0.372249	−	0.214918i
$670$		0			0
$671$			6.33219i			0.244452i
$672$	0.823063	+	1.42559i	0.0317503	+	0.0549932i
$673$	−3.74408	+	6.48493i	−0.144324	+	0.249976i	−0.929120	−	0.369777i	$-0.879434\pi$
$673$	−3.74408	+	6.48493i	−0.144324	+	0.249976i	0.784797	+	0.619753i	$0.212767\pi$
$674$	−12.4327	−	7.17805i	−0.478891	−	0.276488i
$675$		0			0
$676$	−8.03064	−	10.2230i	−0.308871	−	0.393191i
$677$	−37.4181			−1.43810			−0.719048	−	0.694961i	$-0.755422\pi$
$677$	−37.4181			−1.43810			−0.719048	+	0.694961i	$0.755422\pi$
$678$	−3.11433	−	1.79806i	−0.119605	−	0.0690541i
$679$	13.5912	−	23.5406i	0.521582	−	0.903406i
$680$		0			0
$681$			22.0799i			0.846103i
$682$	−8.84165	+	5.10473i	−0.338564	+	0.195470i
$683$	5.43761	−	3.13940i	0.208064	−	0.120126i	−0.392347	−	0.919817i	$-0.628337\pi$
$683$	5.43761	−	3.13940i	0.208064	−	0.120126i	0.600411	+	0.799691i	$0.295003\pi$
$684$			4.41882i			0.168958i
$685$		0			0
$686$	9.29260	−	16.0953i	0.354793	−	0.614520i
$687$	8.95443	+	5.16984i	0.341633	+	0.197242i
$688$	6.72876			0.256532
$689$	0.626851	+	8.79735i	0.0238811	+	0.335152i
$690$		0			0
$691$	−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	$0.731250\pi$
$692$	−8.62958	+	14.9469i	−0.328047	+	0.568195i
$693$	−1.97971	−	3.42896i	−0.0752030	−	0.130255i
$694$		−	0.665114i		−	0.0252474i
$695$		0			0
$696$	−0.0383880	+	0.0221633i	−0.00145509	+	0.000840098i
$697$		−	0.0591936i		−	0.00224212i
$698$	1.87643	+	3.25007i	0.0710239	+	0.123017i
$699$	10.9464	−	18.9597i	0.414031	−	0.717123i
$700$		0			0
$701$	−29.6773			−1.12090			−0.560449	−	0.828189i	$-0.689371\pi$
$701$	−29.6773			−1.12090			−0.560449	+	0.828189i	$0.689371\pi$
$702$	−1.57629	+	3.24273i	−0.0594931	+	0.122389i
$703$	39.5409			1.49131
$704$	−2.08305	−	1.20265i	−0.0785078	−	0.0453265i
$705$		0			0
$706$	2.28180	+	3.95219i	0.0858766	+	0.148743i
$707$		−	18.6597i		−	0.701771i
$708$	−8.35669	+	4.82474i	−0.314064	+	0.181325i
$709$	−0.563901	+	0.325568i	−0.0211777	+	0.0122270i	−0.510551	−	0.859847i	$-0.670559\pi$
$709$	−0.563901	+	0.325568i	−0.0211777	+	0.0122270i	0.489374	+	0.872074i	$0.337225\pi$
$710$		0			0
$711$	3.39854	+	5.88644i	0.127455	+	0.220759i
$712$	5.02163	−	8.69772i	0.188194	−	0.325961i
$713$	−31.6967	−	18.3001i	−1.18705	−	0.685344i
$714$	−0.400498			−0.0149883
$715$		0			0
$716$	8.35561			0.312264
$717$	−22.7341	−	13.1255i	−0.849019	−	0.490181i
$718$	2.37892	−	4.12042i	0.0887807	−	0.153773i
$719$	3.21203	+	5.56340i	0.119789	+	0.207480i	0.919684	−	0.392660i	$-0.128445\pi$
$719$	3.21203	+	5.56340i	0.119789	+	0.207480i	−0.799895	+	0.600140i	$0.795112\pi$
$720$		0			0
$721$	−8.52740	+	4.92330i	−0.317577	+	0.183353i
$722$	−0.455494	+	0.262979i	−0.0169517	+	0.00978708i
$723$			26.0907i			0.970325i
$724$	6.36677	+	11.0276i	0.236619	+	0.409836i
$725$		0			0
$726$	−4.51593	−	2.60727i	−0.167602	−	0.0967650i
$727$	16.3170			0.605165			0.302583	−	0.953123i	$-0.402151\pi$
$727$	16.3170			0.605165			0.302583	+	0.953123i	$0.402151\pi$
$728$	−4.91611	+	3.32541i	−0.182203	+	0.123248i
$729$	1.00000			0.0370370
$730$		0			0
$731$	−0.818545	+	1.41776i	−0.0302750	+	0.0524378i
$732$	−1.31630	−	2.27990i	−0.0486519	−	0.0842676i
$733$			24.4136i			0.901735i	0.892591	+	0.450868i	$0.148885\pi$
$733$			24.4136i			0.901735i	−0.892591	+	0.450868i	$0.851115\pi$
$734$	−1.29432	+	0.747277i	−0.0477743	+	0.0275825i
$735$		0			0
$736$		−	8.62281i		−	0.317841i
$737$	−2.25400	−	3.90404i	−0.0830271	−	0.143807i
$738$	−0.121649	+	0.210702i	−0.00447795	+	0.00775603i
$739$	−4.75775	−	2.74689i	−0.175017	−	0.101046i	0.409932	−	0.912116i	$-0.365552\pi$
$739$	−4.75775	−	2.74689i	−0.175017	−	0.101046i	−0.584949	+	0.811070i	$0.698886\pi$
$740$		0			0
$741$	−15.8920	+	1.13238i	−0.583807	+	0.0415989i
$742$	4.02664			0.147823
$743$	−18.4484	−	10.6512i	−0.676804	−	0.390753i	0.121845	−	0.992549i	$-0.461119\pi$
$743$	−18.4484	−	10.6512i	−0.676804	−	0.390753i	−0.798650	+	0.601796i	$0.794452\pi$
$744$	2.12229	−	3.67591i	0.0778068	−	0.134765i
$745$		0			0
$746$		−	20.5910i		−	0.753890i
$747$	−15.1543	+	8.74932i	−0.554466	+	0.320121i
$748$	0.506800	−	0.292601i	0.0185304	−	0.0106986i
$749$		−	17.5739i		−	0.642135i
$750$		0			0
$751$	−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	$0.976684\pi$
$752$	−6.31817	−	3.64780i	−0.230400	−	0.133022i
$753$	0.624794			0.0227688
$754$	−0.0895462	−	0.132380i	−0.00326108	−	0.00482100i
$755$		0			0
$756$	1.42559	+	0.823063i	0.0518481	+	0.0299345i
$757$	−17.5618	+	30.4180i	−0.638296	+	1.10556i	0.347511	+	0.937676i	$0.387027\pi$
$757$	−17.5618	+	30.4180i	−0.638296	+	1.10556i	−0.985807	+	0.167885i	$0.946306\pi$
$758$	−10.6332	−	18.4173i	−0.386216	−	0.668946i
$759$			20.7404i			0.752830i
$760$		0			0
$761$	−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	$0.509141\pi$
$762$			17.3470i			0.628416i
$763$	−7.82472	−	13.5528i	−0.283274	−	0.490645i
$764$	0.207632	−	0.359629i	0.00751187	−	0.0130109i
$765$		0			0
$766$	10.6219			0.383785
$767$	−19.4933	−	28.8179i	−0.703864	−	1.04055i
$768$	1.00000			0.0360844
$769$	34.3740	+	19.8459i	1.23956	+	0.715660i	0.969004	−	0.247045i	$-0.0794594\pi$
$769$	34.3740	+	19.8459i	1.23956	+	0.715660i	0.270555	+	0.962704i	$0.412793\pi$
$770$		0			0
$771$	6.97195	+	12.0758i	0.251089	+	0.434898i
$772$			25.9837i			0.935173i
$773$	12.4177	−	7.16938i	0.446635	−	0.257865i	−0.259773	−	0.965670i	$-0.583648\pi$
$773$	12.4177	−	7.16938i	0.446635	−	0.257865i	0.706408	+	0.707805i	$0.250314\pi$
$774$	5.82728	−	3.36438i	0.209457	−	0.120930i
$775$		0			0
$776$	−8.25647	−	14.3006i	−0.296390	−	0.513363i
$777$	7.36500	−	12.7566i	0.264218	−	0.457639i
$778$	−32.0813	−	18.5222i	−1.15017	−	0.664052i
$779$	−1.07509			−0.0385190
$780$		0			0
$781$	−18.1374			−0.649007
$782$	1.81684	+	1.04895i	0.0649701	+	0.0375105i
$783$	−0.0221633	+	0.0383880i	−0.000792052	+	0.00137187i
$784$	−2.14514	−	3.71548i	−0.0766120	−	0.132696i
$785$		0			0
$786$	12.2676	−	7.08270i	0.437571	−	0.252631i
$787$	9.57437	−	5.52776i	0.341289	−	0.197043i	−0.319553	−	0.947568i	$-0.603533\pi$
$787$	9.57437	−	5.52776i	0.341289	−	0.197043i	0.660842	+	0.750525i	$0.270199\pi$
$788$		−	15.4424i		−	0.550113i
$789$	−9.71828	−	16.8325i	−0.345980	−	0.599255i
$790$		0			0
$791$	−5.12658	−	2.95983i	−0.182280	−	0.105240i
$792$	−2.40530			−0.0854685
$793$	7.86219	−	5.31824i	0.279195	−	0.188856i
$794$	1.68719			0.0598760
$795$		0			0
$796$	6.85286	−	11.8695i	0.242893	−	0.420704i
$797$	−0.261666	−	0.453218i	−0.00926867	−	0.0160538i	0.861354	−	0.508005i	$-0.169617\pi$
$797$	−0.261666	−	0.453218i	−0.00926867	−	0.0160538i	−0.870623	+	0.491952i	$0.836284\pi$
$798$			7.27393i			0.257494i
$799$	1.53719	−	0.887500i	0.0543820	−	0.0313975i
$800$		0			0
$801$		−	10.0433i		−	0.354861i
$802$	−9.98524	−	17.2949i	−0.352591	−	0.610705i
$803$	−2.04895	+	3.54889i	−0.0723059	+	0.125238i
$804$	1.62310	+	0.937098i	0.0572424	+	0.0330489i
$805$		0			0
$806$	13.7640	+	6.69067i	0.484817	+	0.235669i
$807$	−3.00139			−0.105654
$808$	−9.81687	−	5.66777i	−0.345356	−	0.199391i
$809$	24.5608	−	42.5405i	0.863511	−	1.49564i	−0.00500771	−	0.999987i	$-0.501594\pi$
$809$	24.5608	−	42.5405i	0.863511	−	1.49564i	0.868518	−	0.495657i	$-0.165073\pi$
$810$		0			0
$811$		−	31.5157i		−	1.10667i	−0.832960	−	0.553333i	$-0.813356\pi$
$811$		−	31.5157i		−	1.10667i	0.832960	−	0.553333i	$-0.186644\pi$
$812$	−0.0631914	+	0.0364836i	−0.00221758	+	0.00128032i
$813$	24.6538	−	14.2339i	0.864645	−	0.499203i
$814$			21.5233i			0.754391i
$815$		0			0
$816$	−0.121649	+	0.210702i	−0.00425855	+	0.00737603i
$817$	25.7497	+	14.8666i	0.900868	+	0.520116i
$818$	12.3094			0.430389
$819$	−2.59477	+	5.33795i	−0.0906685	+	0.186523i
$820$		0			0
$821$	−13.8449	−	7.99335i	−0.483190	−	0.278970i	0.238555	−	0.971129i	$-0.423326\pi$
$821$	−13.8449	−	7.99335i	−0.483190	−	0.278970i	−0.721745	+	0.692159i	$0.756660\pi$
$822$	3.66709	−	6.35158i	0.127904	−	0.221537i
$823$	12.6028	+	21.8287i	0.439306	+	0.760900i	0.997636	−	0.0687187i	$-0.0218911\pi$
$823$	12.6028	+	21.8287i	0.439306	+	0.760900i	−0.558330	+	0.829619i	$0.688558\pi$
$824$			5.98168i			0.208382i
$825$		0			0
$826$	−13.7562	+	7.94212i	−0.478638	+	0.276342i
$827$		−	22.0889i		−	0.768106i	−0.923311	−	0.384053i	$-0.874528\pi$
$827$		−	22.0889i		−	0.768106i	0.923311	−	0.384053i	$-0.125472\pi$
$828$	−4.31141	−	7.46758i	−0.149832	−	0.259516i
$829$	4.72499	−	8.18393i	0.164106	−	0.284240i	−0.772232	−	0.635341i	$-0.780859\pi$
$829$	4.72499	−	8.18393i	0.164106	−	0.284240i	0.936337	+	0.351102i	$0.114193\pi$
$830$		0			0
$831$	0.852658			0.0295784
$832$	0.256262	+	3.59643i	0.00888430	+	0.124684i
$833$	1.04381			0.0361659
$834$	−12.3008	−	7.10185i	−0.425941	−	0.245917i
$835$		0			0
$836$	−5.31428	−	9.20461i	−0.183798	−	0.318348i
$837$		−	4.24458i		−	0.146714i
$838$	19.1238	−	11.0411i	0.660619	−	0.381409i
$839$	10.8542	−	6.26667i	0.374728	−	0.216350i	−0.300794	−	0.953689i	$-0.597252\pi$
$839$	10.8542	−	6.26667i	0.374728	−	0.216350i	0.675522	+	0.737340i	$0.263918\pi$
$840$		0			0
$841$	14.4990	+	25.1130i	0.499966	+	0.865967i
$842$	4.49018	−	7.77722i	0.154742	−	0.268021i
$843$	−13.5837	−	7.84257i	−0.467848	−	0.270112i
$844$	16.1123			0.554609
$845$		0			0
$846$	−7.29560			−0.250828
$847$	−7.43379	−	4.29190i	−0.255428	−	0.147471i
$848$	1.22307	−	2.11841i	0.0420002	−	0.0727465i
$849$	−4.04370	−	7.00390i	−0.138780	−	0.240373i
$850$		0			0
$851$	−66.8220	+	38.5797i	−2.29063	+	1.32250i
$852$	6.53035	−	3.77030i	0.223726	−	0.129168i
$853$		−	54.5472i		−	1.86766i	−0.357718	−	0.933830i	$-0.616445\pi$
$853$		−	54.5472i		−	1.86766i	0.357718	−	0.933830i	$-0.383555\pi$
$854$	−2.16680	−	3.75300i	−0.0741463	−	0.128425i
$855$		0			0
$856$	−9.24559	−	5.33795i	−0.316008	−	0.182447i
$857$	−16.1596			−0.552000			−0.276000	−	0.961158i	$-0.589009\pi$
$857$	−16.1596			−0.552000			−0.276000	+	0.961158i	$0.589009\pi$
$858$	−0.616387	−	8.65049i	−0.0210431	−	0.295323i
$859$	−8.02338			−0.273754			−0.136877	−	0.990588i	$-0.543707\pi$
$859$	−8.02338			−0.273754			−0.136877	+	0.990588i	$0.543707\pi$
$860$		0			0
$861$	−0.200249	+	0.346841i	−0.00682447	+	0.0118203i
$862$	−4.13435	−	7.16090i	−0.140816	−	0.243901i
$863$		−	28.2909i		−	0.963033i	−0.876437	−	0.481517i	$-0.840086\pi$
$863$		−	28.2909i		−	0.963033i	0.876437	−	0.481517i	$-0.159914\pi$
$864$	0.866025	−	0.500000i	0.0294628	−	0.0170103i
$865$		0			0
$866$		−	19.8407i		−	0.674214i
$867$	8.47040	+	14.6712i	0.287670	+	0.498259i
$868$	3.49355	−	6.05101i	0.118579	−	0.205385i
$869$	−14.1586	−	8.17449i	−0.480298	−	0.277300i
$870$		0			0
$871$	−2.95427	+	6.07752i	−0.100102	+	0.205929i
$872$	−9.50683			−0.321942
$873$	−14.3006	−	8.25647i	−0.484003	−	0.279439i
$874$	19.0513	−	32.9979i	0.644421	−	1.11617i
$875$		0			0
$876$		−	1.70370i		−	0.0575627i
$877$	19.5775	−	11.3031i	0.661085	−	0.381678i	−0.131605	−	0.991302i	$-0.542013\pi$
$877$	19.5775	−	11.3031i	0.661085	−	0.381678i	0.792690	+	0.609625i	$0.208680\pi$
$878$	−25.0134	+	14.4415i	−0.844161	+	0.487377i
$879$			1.93438i			0.0652451i
$880$		0			0
$881$	22.1679	−	38.3959i	0.746854	−	1.29359i	−0.202470	−	0.979289i	$-0.564897\pi$
$881$	22.1679	−	38.3959i	0.746854	−	1.29359i	0.949324	−	0.314301i	$-0.101770\pi$
$882$	−3.71548	−	2.14514i	−0.125107	−	0.0722305i
$883$	−3.93200			−0.132322			−0.0661612	−	0.997809i	$-0.521075\pi$
$883$	−3.93200			−0.132322			−0.0661612	+	0.997809i	$0.521075\pi$
$884$	−0.788948	−	0.383506i	−0.0265352	−	0.0128987i
$885$		0			0
$886$	4.99684	+	2.88493i	0.167872	+	0.0969211i
$887$	14.5713	−	25.2382i	0.489256	−	0.847416i	−0.510668	−	0.859778i	$-0.670602\pi$
$887$	14.5713	−	25.2382i	0.489256	−	0.847416i	0.999924	+	0.0123622i	$0.00393513\pi$
$888$	−4.47415	−	7.74945i	−0.150142	−	0.260054i
$889$			28.5554i			0.957717i
$890$		0			0
$891$	−2.08305	+	1.20265i	−0.0697847	+	0.0402902i
$892$		−	11.1177i		−	0.372249i
$893$	−16.1190	−	27.9189i	−0.539401	−	0.934269i
$894$	5.55193	−	9.61623i	0.185684	−	0.321615i
$895$		0			0
$896$	1.64613			0.0549932
$897$	25.7518	−	17.4193i	0.859827	−	0.581615i
$898$	−39.1483			−1.30639
$899$	0.162941	+	0.0940738i	0.00543437	+	0.00313754i
$900$		0			0
$901$	0.297569	+	0.515404i	0.00991344	+	0.0171706i
$902$		−	0.585202i		−	0.0194851i
$903$	9.59244	−	5.53820i	0.319216	−	0.184300i
$904$	−3.11433	+	1.79806i	−0.103581	+	0.0598026i
$905$		0			0
$906$	0.437332	+	0.757480i	0.0145294	+	0.0251656i
$907$	18.0592	−	31.2795i	0.599647	−	1.03862i	−0.393226	−	0.919442i	$-0.628641\pi$
$907$	18.0592	−	31.2795i	0.599647	−	1.03862i	0.992873	−	0.119177i	$-0.0380257\pi$
$908$	19.1217	+	11.0399i	0.634577	+	0.366373i
$909$	−11.3355			−0.375976
$910$		0			0
$911$	−16.1738			−0.535863			−0.267931	−	0.963438i	$-0.586340\pi$
$911$	−16.1738			−0.535863			−0.267931	+	0.963438i	$0.586340\pi$
$912$	3.82681	+	2.20941i	0.126718	+	0.0731609i
$913$	21.0447	−	36.4505i	0.696478	−	1.20634i
$914$	−12.2403	−	21.2008i	−0.404872	−	0.701259i
$915$		0			0
$916$	8.95443	−	5.16984i	0.295863	−	0.170816i
$917$	20.1940	−	11.6590i	0.666865	−	0.385014i
$918$			0.243297i			0.00803001i
$919$	1.12534	+	1.94914i	0.0371214	+	0.0642962i	0.883989	−	0.467507i	$-0.154848\pi$
$919$	1.12534	+	1.94914i	0.0371214	+	0.0642962i	−0.846868	+	0.531803i	$0.821514\pi$
$920$		0			0
$921$	−10.7719	−	6.21918i	−0.354947	−	0.204929i
$922$	−3.49785			−0.115196
$923$	15.2331	+	22.5198i	0.501404	+	0.741248i
$924$	−3.95942			−0.130255
$925$		0			0
$926$	9.15317	−	15.8537i	0.300792	−	0.520987i
$927$	2.99084	+	5.18029i	0.0982321	+	0.170143i
$928$			0.0443266i			0.00145509i
$929$	−23.2193	+	13.4057i	−0.761801	+	0.439826i	−0.829942	−	0.557850i	$-0.811626\pi$
$929$	−23.2193	+	13.4057i	−0.761801	+	0.439826i	0.0681412	+	0.997676i	$0.478293\pi$
$930$		0			0
$931$		−	18.9579i		−	0.621321i
$932$	−10.9464	−	18.9597i	−0.358561	−	0.621046i
$933$	9.18502	−	15.9089i	0.300704	−	0.520835i
$934$	−5.59469	−	3.23010i	−0.183064	−	0.105692i
$935$		0			0
$936$	2.02015	+	2.98647i	0.0660305	+	0.0976159i
$937$	−44.1333			−1.44177			−0.720887	−	0.693053i	$-0.756265\pi$
$937$	−44.1333			−1.44177			−0.720887	+	0.693053i	$0.756265\pi$
$938$	2.67183	+	1.54258i	0.0872383	+	0.0503671i
$939$	15.9722	−	27.6647i	0.521234	−	0.902804i
$940$		0			0
$941$			28.3857i			0.925348i	0.886528	+	0.462674i	$0.153110\pi$
$941$			28.3857i			0.925348i	−0.886528	+	0.462674i	$0.846890\pi$
$942$	−13.4307	+	7.75425i	−0.437597	+	0.252647i
$943$	1.81684	−	1.04895i	0.0591645	−	0.0341586i
$944$			9.64947i			0.314064i
$945$		0			0
$946$	−8.09234	+	14.0163i	−0.263105	+	0.455710i
$947$	42.7256	+	24.6676i	1.38839	+	0.801590i	0.993134	−	0.116979i	$-0.0373212\pi$
$947$	42.7256	+	24.6676i	1.38839	+	0.801590i	0.395260	+	0.918569i	$0.370654\pi$
$948$	6.79707			0.220759
$949$	6.12724	−	0.436594i	0.198899	−	0.0141724i
$950$		0			0
$951$	−20.2325	−	11.6812i	−0.656083	−	0.378790i
$952$	−0.200249	+	0.346841i	−0.00649011	+	0.0112412i
$953$	−5.55933	−	9.62904i	−0.180084	−	0.311915i	0.761825	−	0.647783i	$-0.224304\pi$
$953$	−5.55933	−	9.62904i	−0.180084	−	0.311915i	−0.941909	+	0.335868i	$0.890970\pi$
$954$		−	2.44613i		−	0.0791964i
$955$		0			0
$956$	−22.7341	+	13.1255i	−0.735272	+	0.424510i
$957$		−	0.106619i		−	0.00344649i
$958$	15.3564	+	26.5980i	0.496142	+	0.859343i
$959$	6.03648	−	10.4555i	0.194928	−	0.337626i
$960$		0			0
$961$	12.9836			0.418825
$962$	26.7238	−	18.0769i	0.861610	−	0.582821i
$963$	−10.6759			−0.344026
$964$	22.5952	+	13.0454i	0.727744	+	0.420163i
$965$		0			0
$966$	−7.09712	−	12.2926i	−0.228346	−	0.395507i
$967$			55.3514i			1.77998i	0.455980	+	0.889990i	$0.349289\pi$
$967$			55.3514i			1.77998i	−0.455980	+	0.889990i	$0.650711\pi$
$968$	−4.51593	+	2.60727i	−0.145148	+	0.0838010i
$969$	−0.931052	+	0.537543i	−0.0299097	+	0.0172684i
$970$		0			0
$971$	−26.8248	−	46.4619i	−0.860848	−	1.49103i	−0.871112	−	0.491085i	$-0.836601\pi$
$971$	−26.8248	−	46.4619i	−0.860848	−	1.49103i	0.0102641	−	0.999947i	$-0.496733\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	−20.2486	−	11.6905i	−0.649141	−	0.374782i
$974$	−12.4667			−0.399459
$975$		0			0
$976$	−2.63260			−0.0842676
$977$	10.7978	+	6.23411i	0.345452	+	0.199447i	0.662680	−	0.748902i	$-0.269419\pi$
$977$	10.7978	+	6.23411i	0.345452	+	0.199447i	−0.317228	+	0.948349i	$0.602752\pi$
$978$	10.9464	−	18.9597i	0.350027	−	0.606265i
$979$	12.0785	+	20.9206i	0.386031	+	0.668625i
$980$		0			0
$981$	−8.23316	+	4.75342i	−0.262865	+	0.151765i
$982$	−2.23642	+	1.29120i	−0.0713671	+	0.0412038i
$983$			19.1972i			0.612296i	0.951984	+	0.306148i	$0.0990403\pi$
$983$			19.1972i			0.612296i	−0.951984	+	0.306148i	$0.900960\pi$
$984$	0.121649	+	0.210702i	0.00387802	+	0.00671692i
$985$		0			0
$986$	−0.00933969	−	0.00539227i	−0.000297436	−	0.000171725i
$987$	−12.0095			−0.382266
$988$	−6.96533	+	14.3291i	−0.221597	+	0.455868i
$989$	−58.0209			−1.84496
$990$		0			0
$991$	−27.4152	+	47.4845i	−0.870872	+	1.50840i	−0.00977694	+	0.999952i	$0.503112\pi$
$991$	−27.4152	+	47.4845i	−0.870872	+	1.50840i	−0.861096	+	0.508443i	$0.830221\pi$
$992$	−2.12229	−	3.67591i	−0.0673827	−	0.116710i
$993$		−	21.4634i		−	0.681120i
$994$	10.7498	−	6.20639i	0.340962	−	0.196855i
$995$		0			0
$996$			17.4986i			0.554466i
$997$	−20.4513	−	35.4227i	−0.647700	−	1.12185i	−0.983671	−	0.179977i	$-0.942398\pi$
$997$	−20.4513	−	35.4227i	−0.647700	−	1.12185i	0.335971	−	0.941872i	$-0.390936\pi$
$998$	10.1222	−	17.5321i	0.320412	−	0.554969i
$999$	−7.74945	−	4.47415i	−0.245182	−	0.141556i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1950.2.bc.i.901.2		12
5.2	odd	4		390.2.x.b.199.6	yes	12
5.3	odd	4		390.2.x.a.199.1	yes	12
5.4	even	2		1950.2.bc.j.901.5		12
13.10	even	6	inner	1950.2.bc.i.751.2		12
15.2	even	4		1170.2.bj.c.199.1		12
15.8	even	4		1170.2.bj.d.199.6		12
65.23	odd	12		390.2.x.b.49.6	yes	12
65.49	even	6		1950.2.bc.j.751.5		12
65.62	odd	12		390.2.x.a.49.1	✓	12
195.23	even	12		1170.2.bj.c.829.1		12
195.62	even	12		1170.2.bj.d.829.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.x.a.49.1	✓	12	65.62	odd	12
390.2.x.a.199.1	yes	12	5.3	odd	4
390.2.x.b.49.6	yes	12	65.23	odd	12
390.2.x.b.199.6	yes	12	5.2	odd	4
1170.2.bj.c.199.1		12	15.2	even	4
1170.2.bj.c.829.1		12	195.23	even	12
1170.2.bj.d.199.6		12	15.8	even	4
1170.2.bj.d.829.6		12	195.62	even	12
1950.2.bc.i.751.2		12	13.10	even	6	inner
1950.2.bc.i.901.2		12	1.1	even	1	trivial
1950.2.bc.j.751.5		12	65.49	even	6
1950.2.bc.j.901.5		12	5.4	even	2

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:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1950.bc (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{6} +(1.42559 - 0.823063i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{6} +(1.42559 - 0.823063i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(2.08305 + 1.20265i) q^{11} -1.00000 q^{12} +(-0.256262 - 3.59643i) q^{13} -1.64613 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-0.121649 - 0.210702i) q^{17} +1.00000i q^{18} +(-3.82681 + 2.20941i) q^{19} +1.64613i q^{21} +(-1.20265 - 2.08305i) q^{22} +(4.31141 - 7.46758i) q^{23} +(0.866025 + 0.500000i) q^{24} +(-1.57629 + 3.24273i) q^{26} +1.00000 q^{27} +(1.42559 + 0.823063i) q^{28} +(-0.0221633 + 0.0383880i) q^{29} -4.24458i q^{31} +(0.866025 - 0.500000i) q^{32} +(-2.08305 + 1.20265i) q^{33} +0.243297i q^{34} +(0.500000 - 0.866025i) q^{36} +(-7.74945 - 4.47415i) q^{37} +4.41882 q^{38} +(3.24273 + 1.57629i) q^{39} +(0.210702 + 0.121649i) q^{41} +(0.823063 - 1.42559i) q^{42} +(-3.36438 - 5.82728i) q^{43} +2.40530i q^{44} +(-7.46758 + 4.31141i) q^{46} +7.29560i q^{47} +(-0.500000 - 0.866025i) q^{48} +(-2.14514 + 3.71548i) q^{49} +0.243297 q^{51} +(2.98647 - 2.02015i) q^{52} -2.44613 q^{53} +(-0.866025 - 0.500000i) q^{54} +(-0.823063 - 1.42559i) q^{56} -4.41882i q^{57} +(0.0383880 - 0.0221633i) q^{58} +(8.35669 - 4.82474i) q^{59} +(1.31630 + 2.27990i) q^{61} +(-2.12229 + 3.67591i) q^{62} +(-1.42559 - 0.823063i) q^{63} -1.00000 q^{64} +2.40530 q^{66} +(-1.62310 - 0.937098i) q^{67} +(0.121649 - 0.210702i) q^{68} +(4.31141 + 7.46758i) q^{69} +(-6.53035 + 3.77030i) q^{71} +(-0.866025 + 0.500000i) q^{72} +1.70370i q^{73} +(4.47415 + 7.74945i) q^{74} +(-3.82681 - 2.20941i) q^{76} +3.95942 q^{77} +(-2.02015 - 2.98647i) q^{78} -6.79707 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-0.121649 - 0.210702i) q^{82} -17.4986i q^{83} +(-1.42559 + 0.823063i) q^{84} +6.72876i q^{86} +(-0.0221633 - 0.0383880i) q^{87} +(1.20265 - 2.08305i) q^{88} +(8.69772 + 5.02163i) q^{89} +(-3.32541 - 4.91611i) q^{91} +8.62281 q^{92} +(3.67591 + 2.12229i) q^{93} +(3.64780 - 6.31817i) q^{94} +1.00000i q^{96} +(14.3006 - 8.25647i) q^{97} +(3.71548 - 2.14514i) q^{98} -2.40530i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{3} + 6 q^{4} + 12 q^{7} - 6 q^{9}+O(q^{10}) \) 12 * q - 6 * q^3 + 6 * q^4 + 12 * q^7 - 6 * q^9	\( 12 q - 6 q^{3} + 6 q^{4} + 12 q^{7} - 6 q^{9} + 6 q^{11} - 12 q^{12} - 4 q^{13} - 4 q^{14} - 6 q^{16} - 8 q^{17} + 6 q^{19} + 6 q^{22} - 16 q^{23} - 2 q^{26} + 12 q^{27} + 12 q^{28} - 14 q^{29} - 6 q^{33} + 6 q^{36} + 6 q^{37} + 8 q^{38} + 2 q^{39} - 18 q^{41} + 2 q^{42} - 10 q^{43} - 6 q^{46} - 6 q^{48} - 8 q^{49} + 16 q^{51} - 2 q^{52} - 2 q^{56} - 6 q^{58} + 36 q^{59} + 10 q^{61} - 16 q^{62} - 12 q^{63} - 12 q^{64} - 12 q^{66} - 24 q^{67} + 8 q^{68} - 16 q^{69} - 12 q^{71} + 12 q^{74} + 6 q^{76} - 24 q^{77} + 10 q^{78} - 4 q^{79} - 6 q^{81} - 8 q^{82} - 12 q^{84} - 14 q^{87} - 6 q^{88} - 18 q^{89} + 2 q^{91} - 32 q^{92} + 6 q^{93} + 8 q^{94} + 24 q^{97} - 24 q^{98}+O(q^{100}) \) 12 * q - 6 * q^3 + 6 * q^4 + 12 * q^7 - 6 * q^9 + 6 * q^11 - 12 * q^12 - 4 * q^13 - 4 * q^14 - 6 * q^16 - 8 * q^17 + 6 * q^19 + 6 * q^22 - 16 * q^23 - 2 * q^26 + 12 * q^27 + 12 * q^28 - 14 * q^29 - 6 * q^33 + 6 * q^36 + 6 * q^37 + 8 * q^38 + 2 * q^39 - 18 * q^41 + 2 * q^42 - 10 * q^43 - 6 * q^46 - 6 * q^48 - 8 * q^49 + 16 * q^51 - 2 * q^52 - 2 * q^56 - 6 * q^58 + 36 * q^59 + 10 * q^61 - 16 * q^62 - 12 * q^63 - 12 * q^64 - 12 * q^66 - 24 * q^67 + 8 * q^68 - 16 * q^69 - 12 * q^71 + 12 * q^74 + 6 * q^76 - 24 * q^77 + 10 * q^78 - 4 * q^79 - 6 * q^81 - 8 * q^82 - 12 * q^84 - 14 * q^87 - 6 * q^88 - 18 * q^89 + 2 * q^91 - 32 * q^92 + 6 * q^93 + 8 * q^94 + 24 * q^97 - 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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