LMFDB - Embedded newform 1950.2.bc.i.751.6

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			751.6
Root			$1.40719 + 0.536449i$ of defining polynomial
Character	$\chi$	$=$	1950.751
Dual form			1950.2.bc.i.901.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{6} +(2.42916 + 1.40247i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(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} +(2.42916 + 1.40247i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.515171 + 0.297434i) q^{11} -1.00000 q^{12} +(3.43052 + 1.10975i) q^{13} +2.80495 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.87649 + 4.98222i) q^{17} +1.00000i q^{18} +(6.59574 + 3.80805i) q^{19} -2.80495i q^{21} +(-0.297434 + 0.515171i) q^{22} +(-2.32278 - 4.02317i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(3.52579 - 0.754186i) q^{26} +1.00000 q^{27} +(2.42916 - 1.40247i) q^{28} +(1.26235 + 2.18645i) q^{29} +6.59309i q^{31} +(-0.866025 - 0.500000i) q^{32} +(0.515171 + 0.297434i) q^{33} +5.75297i q^{34} +(0.500000 + 0.866025i) q^{36} +(8.98379 - 5.18679i) q^{37} +7.61611 q^{38} +(-0.754186 - 3.52579i) q^{39} +(-4.98222 + 2.87649i) q^{41} +(-1.40247 - 2.42916i) q^{42} +(-2.12230 + 3.67593i) q^{43} +0.594869i q^{44} +(-4.02317 - 2.32278i) q^{46} +2.89798i q^{47} +(-0.500000 + 0.866025i) q^{48} +(0.433868 + 0.751482i) q^{49} +5.75297 q^{51} +(2.67633 - 2.41604i) q^{52} +13.8960 q^{53} +(0.866025 - 0.500000i) q^{54} +(1.40247 - 2.42916i) q^{56} -7.61611i q^{57} +(2.18645 + 1.26235i) q^{58} +(-8.40299 - 4.85147i) q^{59} +(-3.41309 + 5.91165i) q^{61} +(3.29654 + 5.70978i) q^{62} +(-2.42916 + 1.40247i) q^{63} -1.00000 q^{64} +0.594869 q^{66} +(6.80906 - 3.93121i) q^{67} +(2.87649 + 4.98222i) q^{68} +(-2.32278 + 4.02317i) q^{69} +(-1.11257 - 0.642342i) q^{71} +(0.866025 + 0.500000i) q^{72} -14.5400i q^{73} +(5.18679 - 8.98379i) q^{74} +(6.59574 - 3.80805i) q^{76} -1.66858 q^{77} +(-2.41604 - 2.67633i) q^{78} +1.83150 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-2.87649 + 4.98222i) q^{82} -4.19184i q^{83} +(-2.42916 - 1.40247i) q^{84} +4.24460i q^{86} +(1.26235 - 2.18645i) q^{87} +(0.297434 + 0.515171i) q^{88} +(5.24333 - 3.02724i) q^{89} +(6.77687 + 7.50697i) q^{91} -4.64555 q^{92} +(5.70978 - 3.29654i) q^{93} +(1.44899 + 2.50973i) q^{94} +1.00000i q^{96} +(-14.6413 - 8.45318i) q^{97} +(0.751482 + 0.433868i) q^{98} -0.594869i 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 $\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times$.

$n$	$301$	$1301$	$1327$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

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
$7$	2.42916	+	1.40247i	0.918135	+	0.530085i	0.883040	−	0.469299i	$-0.155493\pi$
$7$	2.42916	+	1.40247i	0.918135	+	0.530085i	0.0350954	+	0.999384i	$0.488827\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	−0.515171	+	0.297434i	−0.155330	+	0.0896798i	−0.575650	−	0.817696i	$-0.695251\pi$
$11$	−0.515171	+	0.297434i	−0.155330	+	0.0896798i	0.420320	+	0.907376i	$0.361918\pi$
$12$	−1.00000			−0.288675
$13$	3.43052	+	1.10975i	0.951454	+	0.307790i
$13$	3.43052	+	1.10975i	0.951454	+	0.307790i
$14$	2.80495			0.749654
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.87649	+	4.98222i	−0.697650	+	1.20837i	0.271629	+	0.962402i	$0.412438\pi$
$17$	−2.87649	+	4.98222i	−0.697650	+	1.20837i	−0.969279	+	0.245963i	$0.920896\pi$
$18$			1.00000i			0.235702i
$19$	6.59574	+	3.80805i	1.51317	+	0.873628i	0.999881	+	0.0154099i	$0.00490533\pi$
$19$	6.59574	+	3.80805i	1.51317	+	0.873628i	0.513286	+	0.858218i	$0.328428\pi$
$20$		0			0
$21$		−	2.80495i		−	0.612090i
$22$	−0.297434	+	0.515171i	−0.0634132	+	0.109835i
$23$	−2.32278	−	4.02317i	−0.484332	−	0.838888i	0.515506	−	0.856886i	$-0.327604\pi$
$23$	−2.32278	−	4.02317i	−0.484332	−	0.838888i	−0.999838	+	0.0179978i	$0.994271\pi$
$24$	−0.866025	+	0.500000i	−0.176777	+	0.102062i
$25$		0			0
$26$	3.52579	−	0.754186i	0.691465	−	0.147908i
$27$	1.00000			0.192450
$28$	2.42916	−	1.40247i	0.459067	−	0.265043i
$29$	1.26235	+	2.18645i	0.234412	+	0.406013i	0.959102	−	0.283062i	$-0.0913502\pi$
$29$	1.26235	+	2.18645i	0.234412	+	0.406013i	−0.724690	+	0.689075i	$0.758017\pi$
$30$		0			0
$31$			6.59309i			1.18415i	0.805882	+	0.592077i	$0.201692\pi$
$31$			6.59309i			1.18415i	−0.805882	+	0.592077i	$0.798308\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	0.515171	+	0.297434i	0.0896798	+	0.0517767i
$34$			5.75297i			0.986626i
$35$		0			0
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	8.98379	−	5.18679i	1.47693	−	0.852703i	0.477265	−	0.878759i	$-0.341628\pi$
$37$	8.98379	−	5.18679i	1.47693	−	0.852703i	0.999660	+	0.0260561i	$0.00829487\pi$
$38$	7.61611			1.23550
$39$	−0.754186	−	3.52579i	−0.120766	−	0.564578i
$40$		0			0
$41$	−4.98222	+	2.87649i	−0.778092	+	0.449232i	−0.835754	−	0.549105i	$-0.814969\pi$
$41$	−4.98222	+	2.87649i	−0.778092	+	0.449232i	0.0576618	+	0.998336i	$0.481636\pi$
$42$	−1.40247	−	2.42916i	−0.216406	−	0.374827i
$43$	−2.12230	+	3.67593i	−0.323648	+	0.560574i	−0.981238	−	0.192802i	$-0.938243\pi$
$43$	−2.12230	+	3.67593i	−0.323648	+	0.560574i	0.657590	+	0.753376i	$0.271576\pi$
$44$			0.594869i			0.0896798i
$45$		0			0
$46$	−4.02317	−	2.32278i	−0.593184	−	0.342475i
$47$			2.89798i			0.422715i	0.977409	+	0.211357i	$0.0677884\pi$
$47$			2.89798i			0.422715i	−0.977409	+	0.211357i	$0.932212\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	0.433868	+	0.751482i	0.0619812	+	0.107355i
$50$		0			0
$51$	5.75297			0.805577
$52$	2.67633	−	2.41604i	0.371140	−	0.335044i
$53$	13.8960			1.90876			0.954379	−	0.298598i	$-0.0965189\pi$
$53$	13.8960			1.90876			0.954379	+	0.298598i	$0.0965189\pi$
$54$	0.866025	−	0.500000i	0.117851	−	0.0680414i
$55$		0			0
$56$	1.40247	−	2.42916i	0.187414	−	0.324610i
$57$		−	7.61611i		−	1.00878i
$58$	2.18645	+	1.26235i	0.287095	+	0.165754i
$59$	−8.40299	−	4.85147i	−1.09398	−	0.631607i	−0.159344	−	0.987223i	$-0.550938\pi$
$59$	−8.40299	−	4.85147i	−1.09398	−	0.631607i	−0.934632	+	0.355616i	$0.884271\pi$
$60$		0			0
$61$	−3.41309	+	5.91165i	−0.437002	+	0.756910i	−0.997457	−	0.0712755i	$-0.977293\pi$
$61$	−3.41309	+	5.91165i	−0.437002	+	0.756910i	0.560455	+	0.828185i	$0.310626\pi$
$62$	3.29654	+	5.70978i	0.418661	+	0.725143i
$63$	−2.42916	+	1.40247i	−0.306045	+	0.176695i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	0.594869			0.0732233
$67$	6.80906	−	3.93121i	0.831859	−	0.480274i	−0.0226299	−	0.999744i	$-0.507204\pi$
$67$	6.80906	−	3.93121i	0.831859	−	0.480274i	0.854489	+	0.519470i	$0.173871\pi$
$68$	2.87649	+	4.98222i	0.348825	+	0.604183i
$69$	−2.32278	+	4.02317i	−0.279629	+	0.484332i
$70$		0			0
$71$	−1.11257	−	0.642342i	−0.132038	−	0.0762320i	0.432526	−	0.901621i	$-0.357622\pi$
$71$	−1.11257	−	0.642342i	−0.132038	−	0.0762320i	−0.564564	+	0.825389i	$0.690956\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$		−	14.5400i		−	1.70178i	−0.525341	−	0.850892i	$-0.676062\pi$
$73$		−	14.5400i		−	1.70178i	0.525341	−	0.850892i	$-0.323938\pi$
$74$	5.18679	−	8.98379i	0.602952	−	1.04434i
$75$		0			0
$76$	6.59574	−	3.80805i	0.756584	−	0.436814i
$77$	−1.66858			−0.190152
$78$	−2.41604	−	2.67633i	−0.273563	−	0.303035i
$79$	1.83150			0.206060			0.103030	−	0.994678i	$-0.467146\pi$
$79$	1.83150			0.206060			0.103030	+	0.994678i	$0.467146\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−2.87649	+	4.98222i	−0.317655	+	0.550194i
$83$		−	4.19184i		−	0.460114i	−0.973177	−	0.230057i	$-0.926109\pi$
$83$		−	4.19184i		−	0.460114i	0.973177	−	0.230057i	$-0.0738913\pi$
$84$	−2.42916	−	1.40247i	−0.265043	−	0.153022i
$85$		0			0
$86$			4.24460i			0.457707i
$87$	1.26235	−	2.18645i	0.135338	−	0.234412i
$88$	0.297434	+	0.515171i	0.0317066	+	0.0549175i
$89$	5.24333	−	3.02724i	0.555792	−	0.320886i	−0.195663	−	0.980671i	$-0.562686\pi$
$89$	5.24333	−	3.02724i	0.555792	−	0.320886i	0.751455	+	0.659785i	$0.229353\pi$
$90$		0			0
$91$	6.77687	+	7.50697i	0.710409	+	0.786945i
$92$	−4.64555			−0.484332
$93$	5.70978	−	3.29654i	0.592077	−	0.341836i
$94$	1.44899	+	2.50973i	0.149452	+	0.258859i
$95$		0			0
$96$			1.00000i			0.102062i
$97$	−14.6413	−	8.45318i	−1.48660	−	0.858291i	−0.486719	−	0.873558i	$-0.661807\pi$
$97$	−14.6413	−	8.45318i	−1.48660	−	0.858291i	−0.999883	+	0.0152677i	$0.995140\pi$
$98$	0.751482	+	0.433868i	0.0759111	+	0.0438273i
$99$		−	0.594869i		−	0.0597866i
$100$		0			0
$101$	2.72360	+	4.71741i	0.271008	+	0.469400i	0.969120	−	0.246589i	$-0.0793096\pi$
$101$	2.72360	+	4.71741i	0.271008	+	0.469400i	−0.698112	+	0.715988i	$0.745976\pi$
$102$	4.98222	−	2.87649i	0.493313	−	0.284814i
$103$	13.7529			1.35511			0.677556	−	0.735471i	$-0.263039\pi$
$103$	13.7529			1.35511			0.677556	+	0.735471i	$0.263039\pi$
$104$	1.10975	−	3.43052i	0.108820	−	0.336390i
$105$		0			0
$106$	12.0343	−	6.94798i	1.16887	−	0.674848i
$107$	2.11545	+	3.66407i	0.204509	+	0.354219i	0.949976	−	0.312323i	$-0.101107\pi$
$107$	2.11545	+	3.66407i	0.204509	+	0.354219i	−0.745468	+	0.666542i	$0.767774\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$		−	0.447358i		−	0.0428491i	−0.999770	−	0.0214246i	$-0.993180\pi$
$109$		−	0.447358i		−	0.0428491i	0.999770	−	0.0214246i	$-0.00682017\pi$
$110$		0			0
$111$	−8.98379	−	5.18679i	−0.852703	−	0.492308i
$112$		−	2.80495i		−	0.265043i
$113$	4.68350	−	8.11206i	0.440587	−	0.763119i	−0.557146	−	0.830414i	$-0.688104\pi$
$113$	4.68350	−	8.11206i	0.440587	−	0.763119i	0.997733	+	0.0672956i	$0.0214371\pi$
$114$	−3.80805	−	6.59574i	−0.356657	−	0.617748i
$115$		0			0
$116$	2.52469			0.234412
$117$	−2.67633	+	2.41604i	−0.247427	+	0.223363i
$118$	−9.70293			−0.893227
$119$	−13.9749	+	8.06839i	−1.28107	+	0.739628i
$120$		0			0
$121$	−5.32307	+	9.21982i	−0.483915	+	0.838165i
$122$			6.82619i			0.618014i
$123$	4.98222	+	2.87649i	0.449232	+	0.259364i
$124$	5.70978	+	3.29654i	0.512753	+	0.296038i
$125$		0			0
$126$	−1.40247	+	2.42916i	−0.124942	+	0.216406i
$127$	−3.34395	−	5.79190i	−0.296728	−	0.513948i	0.678658	−	0.734455i	$-0.262562\pi$
$127$	−3.34395	−	5.79190i	−0.296728	−	0.513948i	−0.975385	+	0.220507i	$0.929229\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	4.24460			0.373716
$130$		0			0
$131$	−11.6724			−1.01982			−0.509911	−	0.860227i	$-0.670322\pi$
$131$	−11.6724			−1.01982			−0.509911	+	0.860227i	$0.670322\pi$
$132$	0.515171	−	0.297434i	0.0448399	−	0.0258883i
$133$	10.6814	+	18.5007i	0.926194	+	1.60422i
$134$	3.93121	−	6.80906i	0.339605	−	0.588213i
$135$		0			0
$136$	4.98222	+	2.87649i	0.427222	+	0.246657i
$137$	5.89144	+	3.40142i	0.503339	+	0.290603i	0.730092	−	0.683349i	$-0.239477\pi$
$137$	5.89144	+	3.40142i	0.503339	+	0.290603i	−0.226752	+	0.973953i	$0.572811\pi$
$138$			4.64555i			0.395456i
$139$	3.54908	−	6.14719i	0.301029	−	0.521397i	−0.675340	−	0.737506i	$-0.736003\pi$
$139$	3.54908	−	6.14719i	0.301029	−	0.521397i	0.976369	+	0.216109i	$0.0693366\pi$
$140$		0			0
$141$	2.50973	−	1.44899i	0.211357	−	0.122027i
$142$	−1.28468			−0.107808
$143$	−2.09738	+	0.448642i	−0.175392	+	0.0375173i
$144$	1.00000			0.0833333
$145$		0			0
$146$	−7.27002	−	12.5920i	−0.601671	−	1.04213i
$147$	0.433868	−	0.751482i	0.0357848	−	0.0619812i
$148$		−	10.3736i		−	0.852703i
$149$	3.02342	+	1.74557i	0.247688	+	0.143003i	0.618705	−	0.785623i	$-0.287658\pi$
$149$	3.02342	+	1.74557i	0.247688	+	0.143003i	−0.371017	+	0.928626i	$0.620991\pi$
$150$		0			0
$151$		−	4.54988i		−	0.370264i	−0.982714	−	0.185132i	$-0.940729\pi$
$151$		−	4.54988i		−	0.370264i	0.982714	−	0.185132i	$-0.0592713\pi$
$152$	3.80805	−	6.59574i	0.308874	−	0.534985i
$153$	−2.87649	−	4.98222i	−0.232550	−	0.402789i
$154$	−1.44503	+	0.834288i	−0.116444	+	0.0672288i
$155$		0			0
$156$	−3.43052	−	1.10975i	−0.274661	−	0.0888512i
$157$	−11.4957			−0.917460			−0.458730	−	0.888576i	$-0.651695\pi$
$157$	−11.4957			−0.917460			−0.458730	+	0.888576i	$0.651695\pi$
$158$	1.58613	−	0.915751i	0.126186	−	0.0728532i
$159$	−6.94798	−	12.0343i	−0.551011	−	0.954379i
$160$		0			0
$161$		−	13.0305i		−	1.02695i
$162$	−0.866025	−	0.500000i	−0.0680414	−	0.0392837i
$163$	−11.9762	−	6.91443i	−0.938045	−	0.541580i	−0.0486977	−	0.998814i	$-0.515507\pi$
$163$	−11.9762	−	6.91443i	−0.938045	−	0.541580i	−0.889347	+	0.457233i	$0.848840\pi$
$164$			5.75297i			0.449232i
$165$		0			0
$166$	−2.09592	−	3.63024i	−0.162675	−	0.281761i
$167$	18.6542	−	10.7700i	1.44351	−	0.833409i	0.445425	−	0.895319i	$-0.353052\pi$
$167$	18.6542	−	10.7700i	1.44351	−	0.833409i	0.998082	+	0.0619099i	$0.0197191\pi$
$168$	−2.80495			−0.216406
$169$	10.5369	+	7.61404i	0.810531	+	0.585696i
$170$		0			0
$171$	−6.59574	+	3.80805i	−0.504389	+	0.291209i
$172$	2.12230	+	3.67593i	0.161824	+	0.280287i
$173$	−6.83251	+	11.8342i	−0.519466	+	0.899741i	0.480278	+	0.877116i	$0.340536\pi$
$173$	−6.83251	+	11.8342i	−0.519466	+	0.899741i	−0.999744	+	0.0226249i	$0.992798\pi$
$174$		−	2.52469i		−	0.191396i
$175$		0			0
$176$	0.515171	+	0.297434i	0.0388325	+	0.0224200i
$177$			9.70293i			0.729317i
$178$	3.02724	−	5.24333i	0.226901	−	0.393004i
$179$	−5.37886	−	9.31647i	−0.402035	−	0.696345i	0.591936	−	0.805985i	$-0.298364\pi$
$179$	−5.37886	−	9.31647i	−0.402035	−	0.696345i	−0.993971	+	0.109639i	$0.965030\pi$
$180$		0			0
$181$	5.86469			0.435919			0.217959	−	0.975958i	$-0.430060\pi$
$181$	5.86469			0.435919			0.217959	+	0.975958i	$0.430060\pi$
$182$	9.62243	+	3.11280i	0.713262	+	0.230736i
$183$	6.82619			0.504606
$184$	−4.02317	+	2.32278i	−0.296592	+	0.171237i
$185$		0			0
$186$	3.29654	−	5.70978i	0.241714	−	0.418661i
$187$		−	3.42226i		−	0.250261i
$188$	2.50973	+	1.44899i	0.183041	+	0.105679i
$189$	2.42916	+	1.40247i	0.176695	+	0.102015i
$190$		0			0
$191$	6.91728	−	11.9811i	0.500517	−	0.866921i	−0.499483	−	0.866324i	$-0.666477\pi$
$191$	6.91728	−	11.9811i	0.500517	−	0.866921i	1.00000		0.000597179i	$-0.000190088\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	14.7280	−	8.50322i	1.06014	−	0.612075i	0.134673	−	0.990890i	$-0.457002\pi$
$193$	14.7280	−	8.50322i	1.06014	−	0.612075i	0.925472	+	0.378815i	$0.123668\pi$
$194$	−16.9064			−1.21381
$195$		0			0
$196$	0.867736			0.0619812
$197$	−5.48171	+	3.16487i	−0.390556	+	0.225487i	−0.682401	−	0.730978i	$-0.739064\pi$
$197$	−5.48171	+	3.16487i	−0.390556	+	0.225487i	0.291845	+	0.956466i	$0.405731\pi$
$198$	−0.297434	−	0.515171i	−0.0211377	−	0.0366116i
$199$	−8.31782	+	14.4069i	−0.589634	+	1.02128i	0.404646	+	0.914473i	$0.367395\pi$
$199$	−8.31782	+	14.4069i	−0.589634	+	1.02128i	−0.994280	+	0.106803i	$0.965939\pi$
$200$		0			0
$201$	−6.80906	−	3.93121i	−0.480274	−	0.277286i
$202$	4.71741	+	2.72360i	0.331916	+	0.191632i
$203$			7.08163i			0.497033i
$204$	2.87649	−	4.98222i	0.201394	−	0.348825i
$205$		0			0
$206$	11.9104	−	6.87645i	0.829834	−	0.479105i
$207$	4.64555			0.322888
$208$	−0.754186	−	3.52579i	−0.0522934	−	0.244470i
$209$	−4.53058			−0.313387
$210$		0			0
$211$	−8.27443	−	14.3317i	−0.569635	−	0.986637i	−0.996602	−	0.0823697i	$-0.973751\pi$
$211$	−8.27443	−	14.3317i	−0.569635	−	0.986637i	0.426967	−	0.904267i	$-0.359582\pi$
$212$	6.94798	−	12.0343i	0.477190	−	0.826516i
$213$			1.28468i			0.0880251i
$214$	3.66407	+	2.11545i	0.250471	+	0.144609i
$215$		0			0
$216$		−	1.00000i		−	0.0680414i
$217$	−9.24663	+	16.0156i	−0.627702	+	1.08721i
$218$	−0.223679	−	0.387423i	−0.0151495	−	0.0262396i
$219$	−12.5920	+	7.27002i	−0.850892	+	0.491262i
$220$		0			0
$221$	−15.3969	+	13.8994i	−1.03570	+	0.934975i
$222$	−10.3736			−0.696229
$223$	−14.4242	+	8.32779i	−0.965913	+	0.557670i	−0.897988	−	0.440020i	$-0.854971\pi$
$223$	−14.4242	+	8.32779i	−0.965913	+	0.557670i	−0.0679254	+	0.997690i	$0.521638\pi$
$224$	−1.40247	−	2.42916i	−0.0937068	−	0.162305i
$225$		0			0
$226$		−	9.36701i		−	0.623084i
$227$	−2.61722	−	1.51105i	−0.173711	−	0.100292i	0.410624	−	0.911805i	$-0.365311\pi$
$227$	−2.61722	−	1.51105i	−0.173711	−	0.100292i	−0.584334	+	0.811513i	$0.698644\pi$
$228$	−6.59574	−	3.80805i	−0.436814	−	0.252195i
$229$			16.4472i			1.08686i	0.839453	+	0.543432i	$0.182875\pi$
$229$			16.4472i			1.08686i	−0.839453	+	0.543432i	$0.817125\pi$
$230$		0			0
$231$	0.834288	+	1.44503i	0.0548921	+	0.0950759i
$232$	2.18645	−	1.26235i	0.143547	−	0.0828771i
$233$	−13.8289			−0.905959			−0.452980	−	0.891521i	$-0.649639\pi$
$233$	−13.8289			−0.905959			−0.452980	+	0.891521i	$0.649639\pi$
$234$	−1.10975	+	3.43052i	−0.0725467	+	0.224260i
$235$		0			0
$236$	−8.40299	+	4.85147i	−0.546988	+	0.315804i
$237$	−0.915751	−	1.58613i	−0.0594844	−	0.103030i
$238$	−8.06839	+	13.9749i	−0.522996	+	0.905856i
$239$			4.60216i			0.297689i	0.988861	+	0.148845i	$0.0475554\pi$
$239$			4.60216i			0.297689i	−0.988861	+	0.148845i	$0.952445\pi$
$240$		0			0
$241$	5.38108	+	3.10677i	0.346626	+	0.200125i	0.663198	−	0.748444i	$-0.269199\pi$
$241$	5.38108	+	3.10677i	0.346626	+	0.200125i	−0.316572	+	0.948568i	$0.602532\pi$
$242$			10.6461i			0.684359i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	3.41309	+	5.91165i	0.218501	+	0.378455i
$245$		0			0
$246$	5.75297			0.366796
$247$	18.4008	+	20.3832i	1.17082	+	1.29695i
$248$	6.59309			0.418661
$249$	−3.63024	+	2.09592i	−0.230057	+	0.132824i
$250$		0			0
$251$	8.19386	−	14.1922i	0.517192	−	0.895802i	−0.482609	−	0.875836i	$-0.660311\pi$
$251$	8.19386	−	14.1922i	0.517192	−	0.895802i	0.999801	−	0.0199663i	$-0.00635591\pi$
$252$			2.80495i			0.176695i
$253$	2.39326	+	1.38175i	0.150463	+	0.0868697i
$254$	−5.79190	−	3.34395i	−0.363416	−	0.209818i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	4.20466	+	7.28269i	0.262280	+	0.454282i	0.966847	−	0.255355i	$-0.0821924\pi$
$257$	4.20466	+	7.28269i	0.262280	+	0.454282i	−0.704568	+	0.709637i	$0.748859\pi$
$258$	3.67593	−	2.12230i	0.228853	−	0.132129i
$259$	29.0974			1.80802
$260$		0			0
$261$	−2.52469			−0.156275
$262$	−10.1086	+	5.83620i	−0.624511	+	0.360562i
$263$	2.94536	+	5.10152i	0.181619	+	0.314573i	0.942432	−	0.334398i	$-0.108533\pi$
$263$	2.94536	+	5.10152i	0.181619	+	0.314573i	−0.760813	+	0.648971i	$0.775200\pi$
$264$	0.297434	−	0.515171i	0.0183058	−	0.0317066i
$265$		0			0
$266$	18.5007	+	10.6814i	1.13435	+	0.654918i
$267$	−5.24333	−	3.02724i	−0.320886	−	0.185264i
$268$		−	7.86242i		−	0.480274i
$269$	−11.4228	+	19.7848i	−0.696459	+	1.20630i	0.273228	+	0.961949i	$0.411909\pi$
$269$	−11.4228	+	19.7848i	−0.696459	+	1.20630i	−0.969686	+	0.244352i	$0.921425\pi$
$270$		0			0
$271$	−23.2565	+	13.4271i	−1.41273	+	0.815639i	−0.995645	−	0.0932285i	$-0.970281\pi$
$271$	−23.2565	+	13.4271i	−1.41273	+	0.815639i	−0.417084	+	0.908868i	$0.636948\pi$
$272$	5.75297			0.348825
$273$	3.11280	−	9.62243i	0.188395	−	0.582376i
$274$	6.80285			0.410975
$275$		0			0
$276$	2.32278	+	4.02317i	0.139815	+	0.242166i
$277$	5.31249	−	9.20150i	0.319197	−	0.552865i	−0.661124	−	0.750277i	$-0.729920\pi$
$277$	5.31249	−	9.20150i	0.319197	−	0.552865i	0.980321	+	0.197412i	$0.0632537\pi$
$278$		−	7.09816i		−	0.425719i
$279$	−5.70978	−	3.29654i	−0.341836	−	0.197359i
$280$		0			0
$281$			28.3732i			1.69260i	0.532705	+	0.846301i	$0.321176\pi$
$281$			28.3732i			1.69260i	−0.532705	+	0.846301i	$0.678824\pi$
$282$	1.44899	−	2.50973i	0.0862862	−	0.149452i
$283$	−2.83482	−	4.91005i	−0.168512	−	0.291872i	0.769385	−	0.638786i	$-0.220563\pi$
$283$	−2.83482	−	4.91005i	−0.168512	−	0.291872i	−0.937897	+	0.346914i	$0.887230\pi$
$284$	−1.11257	+	0.642342i	−0.0660188	+	0.0381160i
$285$		0			0
$286$	−1.59207	+	1.43723i	−0.0941408	+	0.0849850i
$287$	−16.1368			−0.952524
$288$	0.866025	−	0.500000i	0.0510310	−	0.0294628i
$289$	−8.04834	−	13.9401i	−0.473431	−	0.820007i
$290$		0			0
$291$			16.9064i			0.991069i
$292$	−12.5920	−	7.27002i	−0.736894	−	0.425446i
$293$	−1.43617	−	0.829176i	−0.0839022	−	0.0484410i	0.457462	−	0.889229i	$-0.348759\pi$
$293$	−1.43617	−	0.829176i	−0.0839022	−	0.0484410i	−0.541364	+	0.840788i	$0.682092\pi$
$294$		−	0.867736i		−	0.0506074i
$295$		0			0
$296$	−5.18679	−	8.98379i	−0.301476	−	0.522172i
$297$	−0.515171	+	0.297434i	−0.0298933	+	0.0172589i
$298$	3.49115			0.202237
$299$	−3.50361	−	16.3793i	−0.202619	−	0.947237i
$300$		0			0
$301$	−10.3108	+	5.95294i	−0.594304	+	0.343122i
$302$	−2.27494	−	3.94031i	−0.130908	−	0.226740i
$303$	2.72360	−	4.71741i	0.156467	−	0.271008i
$304$		−	7.61611i		−	0.436814i
$305$		0			0
$306$	−4.98222	−	2.87649i	−0.284814	−	0.164438i
$307$		−	0.384087i		−	0.0219210i	−0.999940	−	0.0109605i	$-0.996511\pi$
$307$		−	0.384087i		−	0.0219210i	0.999940	−	0.0109605i	$-0.00348891\pi$
$308$	−0.834288	+	1.44503i	−0.0475380	+	0.0823382i
$309$	−6.87645	−	11.9104i	−0.391187	−	0.677556i
$310$		0			0
$311$	−11.6920			−0.662993			−0.331497	−	0.943456i	$-0.607554\pi$
$311$	−11.6920			−0.662993			−0.331497	+	0.943456i	$0.607554\pi$
$312$	−3.52579	+	0.754186i	−0.199609	+	0.0426974i
$313$	10.5788			0.597948			0.298974	−	0.954261i	$-0.403356\pi$
$313$	10.5788			0.597948			0.298974	+	0.954261i	$0.403356\pi$
$314$	−9.95560	+	5.74787i	−0.561827	+	0.324371i
$315$		0			0
$316$	0.915751	−	1.58613i	0.0515150	−	0.0892266i
$317$		−	22.1023i		−	1.24139i	−0.784052	−	0.620695i	$-0.786850\pi$
$317$		−	22.1023i		−	1.24139i	0.784052	−	0.620695i	$-0.213150\pi$
$318$	−12.0343	−	6.94798i	−0.674848	−	0.389624i
$319$	−1.30065	−	0.750930i	−0.0728224	−	0.0420440i
$320$		0			0
$321$	2.11545	−	3.66407i	0.118073	−	0.204509i
$322$	−6.51527	−	11.2848i	−0.363082	−	0.628876i
$323$	−37.9451	+	21.9076i	−2.11132	+	1.21897i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	−13.8289			−0.765910
$327$	−0.387423	+	0.223679i	−0.0214246	+	0.0123695i
$328$	2.87649	+	4.98222i	0.158827	+	0.275097i
$329$	−4.06435	+	7.03966i	−0.224075	+	0.388109i
$330$		0			0
$331$	−5.28809	−	3.05308i	−0.290660	−	0.167812i	0.347580	−	0.937650i	$-0.387004\pi$
$331$	−5.28809	−	3.05308i	−0.290660	−	0.167812i	−0.638239	+	0.769838i	$0.720337\pi$
$332$	−3.63024	−	2.09592i	−0.199235	−	0.115029i
$333$			10.3736i			0.568469i
$334$	10.7700	−	18.6542i	0.589309	−	1.02071i
$335$		0			0
$336$	−2.42916	+	1.40247i	−0.132521	+	0.0765112i
$337$	4.29852			0.234155			0.117078	−	0.993123i	$-0.462647\pi$
$337$	4.29852			0.234155			0.117078	+	0.993123i	$0.462647\pi$
$338$	12.9322	+	1.32550i	0.703422	+	0.0720979i
$339$	−9.36701			−0.508746
$340$		0			0
$341$	−1.96101	−	3.39657i	−0.106195	−	0.183935i
$342$	−3.80805	+	6.59574i	−0.205916	+	0.356657i
$343$		−	17.2007i		−	0.928750i
$344$	3.67593	+	2.12230i	0.198193	+	0.114427i
$345$		0			0
$346$			13.6650i			0.734636i
$347$	−17.1730	+	29.7444i	−0.921893	+	1.59677i	−0.125409	+	0.992105i	$0.540024\pi$
$347$	−17.1730	+	29.7444i	−0.921893	+	1.59677i	−0.796484	+	0.604660i	$0.793309\pi$
$348$	−1.26235	−	2.18645i	−0.0676689	−	0.117206i
$349$	−13.8581	+	8.00099i	−0.741808	+	0.428283i	−0.822726	−	0.568438i	$-0.807548\pi$
$349$	−13.8581	+	8.00099i	−0.741808	+	0.428283i	0.0809181	+	0.996721i	$0.474215\pi$
$350$		0			0
$351$	3.43052	+	1.10975i	0.183107	+	0.0592341i
$352$	0.594869			0.0317066
$353$	−16.7941	+	9.69607i	−0.893859	+	0.516070i	−0.875203	−	0.483756i	$-0.839272\pi$
$353$	−16.7941	+	9.69607i	−0.893859	+	0.516070i	−0.0186563	+	0.999826i	$0.505939\pi$
$354$	4.85147	+	8.40299i	0.257853	+	0.446614i
$355$		0			0
$356$		−	6.05447i		−	0.320886i
$357$	13.9749	+	8.06839i	0.739628	+	0.427025i
$358$	−9.31647	−	5.37886i	−0.492391	−	0.284282i
$359$		−	15.8342i		−	0.835699i	−0.908516	−	0.417850i	$-0.862784\pi$
$359$		−	15.8342i		−	0.835699i	0.908516	−	0.417850i	$-0.137216\pi$
$360$		0			0
$361$	19.5026	+	33.7794i	1.02645	+	1.77786i
$362$	5.07897	−	2.93234i	0.266945	−	0.154121i
$363$	10.6461			0.558777
$364$	9.88966	−	2.11545i	0.518359	−	0.110880i
$365$		0			0
$366$	5.91165	−	3.41309i	0.309007	−	0.178405i
$367$	−7.64645	−	13.2440i	−0.399141	−	0.691333i	0.594479	−	0.804111i	$-0.297358\pi$
$367$	−7.64645	−	13.2440i	−0.399141	−	0.691333i	−0.993620	+	0.112778i	$0.964025\pi$
$368$	−2.32278	+	4.02317i	−0.121083	+	0.209722i
$369$		−	5.75297i		−	0.299488i
$370$		0			0
$371$	33.7555	+	19.4887i	1.75250	+	1.01180i
$372$		−	6.59309i		−	0.341836i
$373$	−10.8258	+	18.7508i	−0.560538	+	0.970881i	0.436911	+	0.899505i	$0.356072\pi$
$373$	−10.8258	+	18.7508i	−0.560538	+	0.970881i	−0.997449	+	0.0713760i	$0.977261\pi$
$374$	−1.71113	−	2.96377i	−0.0884805	−	0.153253i
$375$		0			0
$376$	2.89798			0.149452
$377$	1.90409	+	8.90154i	0.0980655	+	0.458453i
$378$	2.80495			0.144271
$379$	−7.81479	+	4.51187i	−0.401419	+	0.231759i	−0.687096	−	0.726567i	$-0.741115\pi$
$379$	−7.81479	+	4.51187i	−0.401419	+	0.231759i	0.285677	+	0.958326i	$0.407782\pi$
$380$		0			0
$381$	−3.34395	+	5.79190i	−0.171316	+	0.296728i
$382$		−	13.8346i		−	0.707838i
$383$	−8.72439	−	5.03703i	−0.445795	−	0.257380i	0.260257	−	0.965539i	$-0.416193\pi$
$383$	−8.72439	−	5.03703i	−0.445795	−	0.257380i	−0.706053	+	0.708159i	$0.749526\pi$
$384$	0.866025	+	0.500000i	0.0441942	+	0.0255155i
$385$		0			0
$386$	8.50322	−	14.7280i	0.432802	−	0.749636i
$387$	−2.12230	−	3.67593i	−0.107883	−	0.186858i
$388$	−14.6413	+	8.45318i	−0.743301	+	0.429145i
$389$	24.3591			1.23505			0.617527	−	0.786550i	$-0.288135\pi$
$389$	24.3591			1.23505			0.617527	+	0.786550i	$0.288135\pi$
$390$		0			0
$391$	26.7257			1.35158
$392$	0.751482	−	0.433868i	0.0379556	−	0.0219137i
$393$	5.83620	+	10.1086i	0.294397	+	0.509911i
$394$	−3.16487	+	5.48171i	−0.159444	+	0.276165i
$395$		0			0
$396$	−0.515171	−	0.297434i	−0.0258883	−	0.0149466i
$397$	26.0137	+	15.0190i	1.30559	+	0.753784i	0.981357	−	0.192193i	$-0.0615601\pi$
$397$	26.0137	+	15.0190i	1.30559	+	0.753784i	0.324234	+	0.945977i	$0.394893\pi$
$398$			16.6356i			0.833869i
$399$	10.6814	−	18.5007i	0.534739	−	0.926194i
$400$		0			0
$401$	2.35786	−	1.36131i	0.117746	−	0.0679807i	−0.439970	−	0.898012i	$-0.645011\pi$
$401$	2.35786	−	1.36131i	0.117746	−	0.0679807i	0.557716	+	0.830032i	$0.311678\pi$
$402$	−7.86242			−0.392142
$403$	−7.31669	+	22.6177i	−0.364470	+	1.12667i
$404$	5.44720			0.271008
$405$		0			0
$406$	3.54082	+	6.13287i	0.175728	+	0.304369i
$407$	−3.08546	+	5.34417i	−0.152941	+	0.264901i
$408$		−	5.75297i		−	0.284814i
$409$	33.1032	+	19.1121i	1.63685	+	0.945034i	0.981909	+	0.189352i	$0.0606386\pi$
$409$	33.1032	+	19.1121i	1.63685	+	0.945034i	0.654938	+	0.755683i	$0.272695\pi$
$410$		0			0
$411$		−	6.80285i		−	0.335560i
$412$	6.87645	−	11.9104i	0.338778	−	0.586781i
$413$	−13.6081	−	23.5699i	−0.669612	−	1.15980i
$414$	4.02317	−	2.32278i	0.197728	−	0.114158i
$415$		0			0
$416$	−2.41604	−	2.67633i	−0.118456	−	0.131218i
$417$	−7.09816			−0.347598
$418$	−3.92360	+	2.26529i	−0.191910	+	0.110799i
$419$	−14.9365	−	25.8708i	−0.729695	−	1.26387i	−0.957012	−	0.290048i	$-0.906329\pi$
$419$	−14.9365	−	25.8708i	−0.729695	−	1.26387i	0.227317	−	0.973821i	$-0.427005\pi$
$420$		0			0
$421$		−	14.2033i		−	0.692226i	−0.938193	−	0.346113i	$-0.887501\pi$
$421$		−	14.2033i		−	0.692226i	0.938193	−	0.346113i	$-0.112499\pi$
$422$	−14.3317	−	8.27443i	−0.697658	−	0.402793i
$423$	−2.50973	−	1.44899i	−0.122027	−	0.0704524i
$424$		−	13.8960i		−	0.674848i
$425$		0			0
$426$	0.642342	+	1.11257i	0.0311216	+	0.0539042i
$427$	−16.5819	+	9.57355i	−0.802453	+	0.463297i
$428$	4.23091			0.204509
$429$	1.43723	+	1.59207i	0.0693899	+	0.0768657i
$430$		0			0
$431$	−8.09901	+	4.67596i	−0.390115	+	0.225233i	−0.682210	−	0.731156i	$-0.738981\pi$
$431$	−8.09901	+	4.67596i	−0.390115	+	0.225233i	0.292095	+	0.956389i	$0.405648\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	−1.98005	+	3.42954i	−0.0951549	+	0.164813i	−0.909673	−	0.415325i	$-0.863668\pi$
$433$	−1.98005	+	3.42954i	−0.0951549	+	0.164813i	0.814518	+	0.580138i	$0.197001\pi$
$434$			18.4933i			0.887705i
$435$		0			0
$436$	−0.387423	−	0.223679i	−0.0185542	−	0.0107123i
$437$		−	35.3810i		−	1.69250i
$438$	−7.27002	+	12.5920i	−0.347375	+	0.601671i
$439$	11.2992	+	19.5708i	0.539281	+	0.934062i	0.998943	+	0.0459680i	$0.0146372\pi$
$439$	11.2992	+	19.5708i	0.539281	+	0.934062i	−0.459662	+	0.888094i	$0.652029\pi$
$440$		0			0
$441$	−0.867736			−0.0413208
$442$	−6.38437	+	19.7357i	−0.303673	+	0.938730i
$443$	−29.0428			−1.37987			−0.689933	−	0.723873i	$-0.742360\pi$
$443$	−29.0428			−1.37987			−0.689933	+	0.723873i	$0.742360\pi$
$444$	−8.98379	+	5.18679i	−0.426352	+	0.246154i
$445$		0			0
$446$	−8.32779	+	14.4242i	−0.394332	+	0.683004i
$447$		−	3.49115i		−	0.165125i
$448$	−2.42916	−	1.40247i	−0.114767	−	0.0662607i
$449$	−23.7886	−	13.7343i	−1.12265	−	0.648164i	−0.180576	−	0.983561i	$-0.557796\pi$
$449$	−23.7886	−	13.7343i	−1.12265	−	0.648164i	−0.942077	+	0.335397i	$0.891130\pi$
$450$		0			0
$451$	1.71113	−	2.96377i	0.0805740	−	0.139558i
$452$	−4.68350	−	8.11206i	−0.220293	−	0.381559i
$453$	−3.94031	+	2.27494i	−0.185132	+	0.106886i
$454$	−3.02210			−0.141834
$455$		0			0
$456$	−7.61611			−0.356657
$457$	−3.79470	+	2.19087i	−0.177508	+	0.102485i	−0.586122	−	0.810223i	$-0.699346\pi$
$457$	−3.79470	+	2.19087i	−0.177508	+	0.102485i	0.408613	+	0.912708i	$0.366013\pi$
$458$	8.22361	+	14.2437i	0.384264	+	0.665565i
$459$	−2.87649	+	4.98222i	−0.134263	+	0.232550i
$460$		0			0
$461$	−21.0593	−	12.1586i	−0.980829	−	0.566282i	−0.0783090	−	0.996929i	$-0.524952\pi$
$461$	−21.0593	−	12.1586i	−0.980829	−	0.566282i	−0.902520	+	0.430647i	$0.858285\pi$
$462$	1.44503	+	0.834288i	0.0672288	+	0.0388146i
$463$		−	19.0660i		−	0.886071i	−0.896504	−	0.443035i	$-0.853902\pi$
$463$		−	19.0660i		−	0.886071i	0.896504	−	0.443035i	$-0.146098\pi$
$464$	1.26235	−	2.18645i	0.0586030	−	0.101503i
$465$		0			0
$466$	−11.9762	+	6.91443i	−0.554784	+	0.320305i
$467$	−10.1176			−0.468188			−0.234094	−	0.972214i	$-0.575212\pi$
$467$	−10.1176			−0.468188			−0.234094	+	0.972214i	$0.575212\pi$
$468$	0.754186	+	3.52579i	0.0348623	+	0.162980i
$469$	22.0537			1.01834
$470$		0			0
$471$	5.74787	+	9.95560i	0.264848	+	0.458730i
$472$	−4.85147	+	8.40299i	−0.223307	+	0.386779i
$473$		−	2.52498i		−	0.116099i
$474$	−1.58613	−	0.915751i	−0.0728532	−	0.0420618i
$475$		0			0
$476$			16.1368i			0.739628i
$477$	−6.94798	+	12.0343i	−0.318126	+	0.551011i
$478$	2.30108	+	3.98559i	0.105249	+	0.182297i
$479$	24.8215	−	14.3307i	1.13412	−	0.654786i	0.189155	−	0.981947i	$-0.439425\pi$
$479$	24.8215	−	14.3307i	1.13412	−	0.654786i	0.944969	+	0.327161i	$0.106092\pi$
$480$		0			0
$481$	36.5751	−	7.82361i	1.66768	−	0.356726i
$482$	6.21354			0.283019
$483$	−11.2848	+	6.51527i	−0.513475	+	0.296455i
$484$	5.32307	+	9.21982i	0.241958	+	0.419083i
$485$		0			0
$486$			1.00000i			0.0453609i
$487$	15.1033	+	8.71990i	0.684396	+	0.395136i	0.801509	−	0.597982i	$-0.204031\pi$
$487$	15.1033	+	8.71990i	0.684396	+	0.395136i	−0.117113	+	0.993119i	$0.537364\pi$
$488$	5.91165	+	3.41309i	0.267608	+	0.154504i
$489$			13.8289i			0.625363i
$490$		0			0
$491$	−11.2233	−	19.4394i	−0.506503	−	0.877288i	−0.999972	−	0.00752493i	$-0.997605\pi$
$491$	−11.2233	−	19.4394i	−0.506503	−	0.877288i	0.493469	−	0.869763i	$-0.335729\pi$
$492$	4.98222	−	2.87649i	0.224616	−	0.129682i
$493$	−14.5245			−0.654150
$494$	26.1272	+	8.45199i	1.17552	+	0.380273i
$495$		0			0
$496$	5.70978	−	3.29654i	0.256377	−	0.148019i
$497$	−1.80174	−	3.12070i	−0.0808189	−	0.139983i
$498$	−2.09592	+	3.63024i	−0.0939204	+	0.162675i
$499$		−	10.4136i		−	0.466177i	−0.972456	−	0.233088i	$-0.925117\pi$
$499$		−	10.4136i		−	0.466177i	0.972456	−	0.233088i	$-0.0748832\pi$
$500$		0			0
$501$	−18.6542	−	10.7700i	−0.833409	−	0.481169i
$502$		−	16.3877i		−	0.731420i
$503$	2.88899	−	5.00387i	0.128814	−	0.223112i	−0.794404	−	0.607390i	$-0.792216\pi$
$503$	2.88899	−	5.00387i	0.128814	−	0.223112i	0.923217	+	0.384279i	$0.125550\pi$
$504$	1.40247	+	2.42916i	0.0624712	+	0.108203i
$505$		0			0
$506$	2.76349			0.122852
$507$	1.32550	−	12.9322i	0.0588677	−	0.574341i
$508$	−6.68791			−0.296728
$509$	6.18024	−	3.56816i	0.273934	−	0.158156i	−0.356740	−	0.934204i	$-0.616112\pi$
$509$	6.18024	−	3.56816i	0.273934	−	0.158156i	0.630674	+	0.776048i	$0.282778\pi$
$510$		0			0
$511$	20.3920	−	35.3200i	0.902090	−	1.56247i
$512$			1.00000i			0.0441942i
$513$	6.59574	+	3.80805i	0.291209	+	0.168130i
$514$	7.28269	+	4.20466i	0.321226	+	0.185460i
$515$		0			0
$516$	2.12230	−	3.67593i	0.0934290	−	0.161824i
$517$	−0.861960	−	1.49296i	−0.0379090	−	0.0656603i
$518$	25.1991	−	14.5487i	1.10718	−	0.639232i
$519$	13.6650			0.599827
$520$		0			0
$521$	1.09782			0.0480965			0.0240483	−	0.999711i	$-0.492344\pi$
$521$	1.09782			0.0480965			0.0240483	+	0.999711i	$0.492344\pi$
$522$	−2.18645	+	1.26235i	−0.0956982	+	0.0552514i
$523$	−7.47153	−	12.9411i	−0.326707	−	0.565873i	0.655149	−	0.755499i	$-0.272606\pi$
$523$	−7.47153	−	12.9411i	−0.326707	−	0.565873i	−0.981856	+	0.189626i	$0.939272\pi$
$524$	−5.83620	+	10.1086i	−0.254956	+	0.441596i
$525$		0			0
$526$	5.10152	+	2.94536i	0.222437	+	0.128424i
$527$	−32.8482	−	18.9649i	−1.43089	−	0.826125i
$528$		−	0.594869i		−	0.0258883i
$529$	0.709414	−	1.22874i	0.0308441	−	0.0534235i
$530$		0			0
$531$	8.40299	−	4.85147i	0.364659	−	0.210536i
$532$	21.3628			0.926194
$533$	−20.2838	+	4.33881i	−0.878588	+	0.187935i
$534$	−6.05447			−0.262003
$535$		0			0
$536$	−3.93121	−	6.80906i	−0.169802	−	0.294106i
$537$	−5.37886	+	9.31647i	−0.232115	+	0.402035i
$538$			22.8455i			0.984941i
$539$	−0.447033	−	0.258095i	−0.0192551	−	0.0111169i
$540$		0			0
$541$		−	19.3888i		−	0.833589i	−0.909001	−	0.416794i	$-0.863154\pi$
$541$		−	19.3888i		−	0.833589i	0.909001	−	0.416794i	$-0.136846\pi$
$542$	−13.4271	+	23.2565i	−0.576744	+	0.998950i
$543$	−2.93234	−	5.07897i	−0.125839	−	0.217959i
$544$	4.98222	−	2.87649i	0.213611	−	0.123328i
$545$		0			0
$546$	−2.11545	−	9.88966i	−0.0905330	−	0.423239i
$547$	−26.1335			−1.11739			−0.558693	−	0.829374i	$-0.688697\pi$
$547$	−26.1335			−1.11739			−0.558693	+	0.829374i	$0.688697\pi$
$548$	5.89144	−	3.40142i	0.251670	−	0.145302i
$549$	−3.41309	−	5.91165i	−0.145667	−	0.252303i
$550$		0			0
$551$			19.2283i			0.819155i
$552$	4.02317	+	2.32278i	0.171237	+	0.0988640i
$553$	4.44901	+	2.56863i	0.189191	+	0.109229i
$554$		−	10.6250i		−	0.451412i
$555$		0			0
$556$	−3.54908	−	6.14719i	−0.150514	−	0.260699i
$557$	30.6446	−	17.6927i	1.29846	−	0.749663i	0.318318	−	0.947984i	$-0.396882\pi$
$557$	30.6446	−	17.6927i	1.29846	−	0.749663i	0.980137	+	0.198321i	$0.0635487\pi$
$558$	−6.59309			−0.279108
$559$	−11.3600	+	10.2551i	−0.480475	+	0.433745i
$560$		0			0
$561$	−2.96377	+	1.71113i	−0.125130	+	0.0722440i
$562$	14.1866	+	24.5719i	0.598425	+	1.03650i
$563$	14.8963	−	25.8011i	0.627804	−	1.08739i	−0.360187	−	0.932880i	$-0.617287\pi$
$563$	14.8963	−	25.8011i	0.627804	−	1.08739i	0.987991	−	0.154509i	$-0.0493794\pi$
$564$		−	2.89798i		−	0.122027i
$565$		0			0
$566$	−4.91005	−	2.83482i	−0.206385	−	0.119156i
$567$		−	2.80495i		−	0.117797i
$568$	−0.642342	+	1.11257i	−0.0269521	+	0.0466824i
$569$	7.14388	+	12.3736i	0.299487	+	0.518727i	0.976019	−	0.217687i	$-0.0698511\pi$
$569$	7.14388	+	12.3736i	0.299487	+	0.518727i	−0.676532	+	0.736414i	$0.736518\pi$
$570$		0			0
$571$	−37.4439			−1.56698			−0.783490	−	0.621404i	$-0.786562\pi$
$571$	−37.4439			−1.56698			−0.783490	+	0.621404i	$0.786562\pi$
$572$	−0.660156	+	2.04071i	−0.0276025	+	0.0853263i
$573$	−13.8346			−0.577947
$574$	−13.9749	+	8.06839i	−0.583300	+	0.336768i
$575$		0			0
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$			47.6052i			1.98183i	0.134485	+	0.990916i	$0.457062\pi$
$577$			47.6052i			1.98183i	−0.134485	+	0.990916i	$0.542938\pi$
$578$	−13.9401	−	8.04834i	−0.579833	−	0.334767i
$579$	−14.7280	−	8.50322i	−0.612075	−	0.353382i
$580$		0			0
$581$	5.87895	−	10.1826i	0.243900	−	0.422447i
$582$	8.45318	+	14.6413i	0.350396	+	0.606903i
$583$	−7.15881	+	4.13314i	−0.296487	+	0.171177i
$584$	−14.5400			−0.601671
$585$		0			0
$586$	−1.65835			−0.0685059
$587$	−32.5654	+	18.8016i	−1.34412	+	0.776027i	−0.987409	−	0.158189i	$-0.949435\pi$
$587$	−32.5654	+	18.8016i	−1.34412	+	0.776027i	−0.356709	+	0.934216i	$0.616101\pi$
$588$	−0.433868	−	0.751482i	−0.0178924	−	0.0309906i
$589$	−25.1068	+	43.4863i	−1.03451	+	1.79182i
$590$		0			0
$591$	5.48171	+	3.16487i	0.225487	+	0.130185i
$592$	−8.98379	−	5.18679i	−0.369231	−	0.213176i
$593$		−	24.0046i		−	0.985752i	−0.870100	−	0.492876i	$-0.835946\pi$
$593$		−	24.0046i		−	0.985752i	0.870100	−	0.492876i	$-0.164054\pi$
$594$	−0.297434	+	0.515171i	−0.0122039	+	0.0211377i
$595$		0			0
$596$	3.02342	−	1.74557i	0.123844	−	0.0715014i
$597$	16.6356			0.680851
$598$	−11.2238	−	12.4330i	−0.458977	−	0.508425i
$599$	23.7092			0.968731			0.484365	−	0.874866i	$-0.339051\pi$
$599$	23.7092			0.968731			0.484365	+	0.874866i	$0.339051\pi$
$600$		0			0
$601$	0.918249	+	1.59045i	0.0374562	+	0.0648760i	0.884146	−	0.467211i	$-0.154741\pi$
$601$	0.918249	+	1.59045i	0.0374562	+	0.0648760i	−0.846690	+	0.532087i	$0.821408\pi$
$602$	−5.95294	+	10.3108i	−0.242624	+	0.420237i
$603$			7.86242i			0.320183i
$604$	−3.94031	−	2.27494i	−0.160329	−	0.0925661i
$605$		0			0
$606$		−	5.44720i		−	0.221277i
$607$	17.4483	−	30.2214i	0.708206	−	1.22665i	−0.257316	−	0.966327i	$-0.582838\pi$
$607$	17.4483	−	30.2214i	0.708206	−	1.22665i	0.965522	−	0.260321i	$-0.0838284\pi$
$608$	−3.80805	−	6.59574i	−0.154437	−	0.267493i
$609$	6.13287	−	3.54082i	0.248517	−	0.143481i
$610$		0			0
$611$	−3.21604	+	9.94159i	−0.130107	+	0.402194i
$612$	−5.75297			−0.232550
$613$	−8.15061	+	4.70575i	−0.329200	+	0.190064i	−0.655486	−	0.755207i	$-0.727536\pi$
$613$	−8.15061	+	4.70575i	−0.329200	+	0.190064i	0.326286	+	0.945271i	$0.394203\pi$
$614$	−0.192044	−	0.332629i	−0.00775025	−	0.0134238i
$615$		0			0
$616$			1.66858i			0.0672288i
$617$	9.48432	+	5.47577i	0.381824	+	0.220446i	0.678612	−	0.734497i	$-0.262582\pi$
$617$	9.48432	+	5.47577i	0.381824	+	0.220446i	−0.296787	+	0.954944i	$0.595915\pi$
$618$	−11.9104	−	6.87645i	−0.479105	−	0.276611i
$619$		−	1.00216i		−	0.0402803i	−0.999797	−	0.0201402i	$-0.993589\pi$
$619$		−	1.00216i		−	0.0402803i	0.999797	−	0.0201402i	$-0.00641125\pi$
$620$		0			0
$621$	−2.32278	−	4.02317i	−0.0932098	−	0.161444i
$622$	−10.1256	+	5.84601i	−0.405999	+	0.234404i
$623$	16.9825			0.680389
$624$	−2.67633	+	2.41604i	−0.107139	+	0.0967190i
$625$		0			0
$626$	9.16150	−	5.28939i	0.366167	−	0.211407i
$627$	2.26529	+	3.92360i	0.0904671	+	0.156694i
$628$	−5.74787	+	9.95560i	−0.229365	+	0.397272i
$629$			59.6789i			2.37955i
$630$		0			0
$631$	−33.5167	−	19.3509i	−1.33428	−	0.770346i	−0.348327	−	0.937373i	$-0.613250\pi$
$631$	−33.5167	−	19.3509i	−1.33428	−	0.770346i	−0.985952	+	0.167027i	$0.946583\pi$
$632$		−	1.83150i		−	0.0728532i
$633$	−8.27443	+	14.3317i	−0.328879	+	0.569635i
$634$	−11.0512	−	19.1412i	−0.438898	−	0.760193i
$635$		0			0
$636$	−13.8960			−0.551011
$637$	0.654435	+	3.05946i	0.0259296	+	0.121220i
$638$	−1.50186			−0.0594592
$639$	1.11257	−	0.642342i	0.0440126	−	0.0254107i
$640$		0			0
$641$	4.99961	−	8.65957i	0.197473	−	0.342033i	−0.750236	−	0.661170i	$-0.770060\pi$
$641$	4.99961	−	8.65957i	0.197473	−	0.342033i	0.947708	+	0.319138i	$0.103393\pi$
$642$		−	4.23091i		−	0.166981i
$643$	5.86694	+	3.38728i	0.231369	+	0.133581i	0.611204	−	0.791473i	$-0.290686\pi$
$643$	5.86694	+	3.38728i	0.231369	+	0.133581i	−0.379834	+	0.925055i	$0.624019\pi$
$644$	−11.2848	−	6.51527i	−0.444683	−	0.256738i
$645$		0			0
$646$	−21.9076	+	37.9451i	−0.861944	+	1.49293i
$647$	−8.59384	−	14.8850i	−0.337859	−	0.585188i	0.646171	−	0.763193i	$-0.276369\pi$
$647$	−8.59384	−	14.8850i	−0.337859	−	0.585188i	−0.984030	+	0.178004i	$0.943036\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$	5.77197			0.226570
$650$		0			0
$651$	18.4933			0.724808
$652$	−11.9762	+	6.91443i	−0.469022	+	0.270790i
$653$	−12.4362	−	21.5401i	−0.486666	−	0.842930i	0.513217	−	0.858259i	$-0.328454\pi$
$653$	−12.4362	−	21.5401i	−0.486666	−	0.842930i	−0.999883	+	0.0153292i	$0.995120\pi$
$654$	−0.223679	+	0.387423i	−0.00874654	+	0.0151495i
$655$		0			0
$656$	4.98222	+	2.87649i	0.194523	+	0.112308i
$657$	12.5920	+	7.27002i	0.491262	+	0.283631i
$658$			8.12870i			0.316890i
$659$	4.12151	−	7.13867i	0.160551	−	0.278083i	−0.774515	−	0.632555i	$-0.782006\pi$
$659$	4.12151	−	7.13867i	0.160551	−	0.278083i	0.935067	+	0.354472i	$0.115339\pi$
$660$		0			0
$661$	22.3962	−	12.9305i	0.871112	−	0.502937i	0.00339467	−	0.999994i	$-0.498919\pi$
$661$	22.3962	−	12.9305i	0.871112	−	0.502937i	0.867718	+	0.497057i	$0.165586\pi$
$662$	−6.10616			−0.237323
$663$	19.7357	+	6.38437i	0.766470	+	0.247948i
$664$	−4.19184			−0.162675
$665$		0			0
$666$	5.18679	+	8.98379i	0.200984	+	0.348115i
$667$	5.86430	−	10.1573i	0.227067	−	0.393291i
$668$		−	21.5400i		−	0.833409i
$669$	14.4242	+	8.32779i	0.557670	+	0.321971i
$670$		0			0
$671$		−	4.06069i		−	0.156761i
$672$	−1.40247	+	2.42916i	−0.0541016	+	0.0937068i
$673$	3.46306	+	5.99820i	0.133491	+	0.231213i	0.925020	−	0.379918i	$-0.124048\pi$
$673$	3.46306	+	5.99820i	0.133491	+	0.231213i	−0.791529	+	0.611132i	$0.790715\pi$
$674$	3.72263	−	2.14926i	0.143390	−	0.0827864i
$675$		0			0
$676$	11.8624	−	5.31820i	0.456246	−	0.204546i
$677$	4.72639			0.181650			0.0908250	−	0.995867i	$-0.471050\pi$
$677$	4.72639			0.181650			0.0908250	+	0.995867i	$0.471050\pi$
$678$	−8.11206	+	4.68350i	−0.311542	+	0.179869i
$679$	−23.7107	−	41.0682i	−0.909935	−	1.57605i
$680$		0			0
$681$			3.02210i			0.115807i
$682$	−3.39657	−	1.96101i	−0.130061	−	0.0750910i
$683$	16.9567	+	9.78995i	0.648830	+	0.374602i	0.788008	−	0.615665i	$-0.211113\pi$
$683$	16.9567	+	9.78995i	0.648830	+	0.374602i	−0.139178	+	0.990267i	$0.544446\pi$
$684$			7.61611i			0.291209i
$685$		0			0
$686$	−8.60034	−	14.8962i	−0.328363	−	0.568741i
$687$	14.2437	−	8.22361i	0.543432	−	0.313750i
$688$	4.24460			0.161824
$689$	47.6704	+	15.4211i	1.81610	+	0.587496i
$690$		0			0
$691$	−10.7079	+	6.18224i	−0.407350	+	0.235183i	−0.689650	−	0.724143i	$-0.742236\pi$
$691$	−10.7079	+	6.18224i	−0.407350	+	0.235183i	0.282301	+	0.959326i	$0.408902\pi$
$692$	6.83251	+	11.8342i	0.259733	+	0.449871i
$693$	0.834288	−	1.44503i	0.0316920	−	0.0548921i
$694$			34.3459i			1.30375i
$695$		0			0
$696$	−2.18645	−	1.26235i	−0.0828771	−	0.0478491i
$697$		−	33.0967i		−	1.25363i
$698$	−8.00099	+	13.8581i	−0.302842	+	0.524538i
$699$	6.91443	+	11.9762i	0.261528	+	0.452980i
$700$		0			0
$701$	43.7550			1.65260			0.826302	−	0.563227i	$-0.190441\pi$
$701$	43.7550			1.65260			0.826302	+	0.563227i	$0.190441\pi$
$702$	3.52579	−	0.754186i	0.133072	−	0.0284649i
$703$	79.0063			2.97978
$704$	0.515171	−	0.297434i	0.0194163	−	0.0112100i
$705$		0			0
$706$	−9.69607	+	16.7941i	−0.364916	+	0.632054i
$707$			15.2791i			0.574630i
$708$	8.40299	+	4.85147i	0.315804	+	0.182329i
$709$	−16.4104	−	9.47457i	−0.616307	−	0.355825i	0.159123	−	0.987259i	$-0.449133\pi$
$709$	−16.4104	−	9.47457i	−0.616307	−	0.355825i	−0.775430	+	0.631434i	$0.782467\pi$
$710$		0			0
$711$	−0.915751	+	1.58613i	−0.0343434	+	0.0594844i
$712$	−3.02724	−	5.24333i	−0.113451	−	0.196502i
$713$	26.5251	−	15.3143i	0.993372	−	0.573524i
$714$	16.1368			0.603904
$715$		0			0
$716$	−10.7577			−0.402035
$717$	3.98559	−	2.30108i	0.148845	−	0.0859355i
$718$	−7.91712	−	13.7129i	−0.295464	−	0.511759i
$719$	23.5155	−	40.7301i	0.876981	−	1.51898i	0.0223436	−	0.999750i	$-0.492887\pi$
$719$	23.5155	−	40.7301i	0.876981	−	1.51898i	0.854637	−	0.519225i	$-0.173779\pi$
$720$		0			0
$721$	33.4079	+	19.2881i	1.24418	+	0.718326i
$722$	33.7794	+	19.5026i	1.25714	+	0.725810i
$723$		−	6.21354i		−	0.231084i
$724$	2.93234	−	5.07897i	0.108980	−	0.188758i
$725$		0			0
$726$	9.21982	−	5.32307i	0.342180	−	0.197557i
$727$	4.10440			0.152224			0.0761119	−	0.997099i	$-0.475749\pi$
$727$	4.10440			0.152224			0.0761119	+	0.997099i	$0.475749\pi$
$728$	7.50697	−	6.77687i	0.278227	−	0.251167i
$729$	1.00000			0.0370370
$730$		0			0
$731$	−12.2095	−	21.1475i	−0.451586	−	0.782169i
$732$	3.41309	−	5.91165i	0.126152	−	0.218501i
$733$			24.2968i			0.897421i	0.893677	+	0.448711i	$0.148117\pi$
$733$			24.2968i			0.897421i	−0.893677	+	0.448711i	$0.851883\pi$
$734$	−13.2440	−	7.64645i	−0.488847	−	0.282236i
$735$		0			0
$736$			4.64555i			0.171237i
$737$	−2.33855	+	4.05050i	−0.0861418	+	0.149202i
$738$	−2.87649	−	4.98222i	−0.105885	−	0.183398i
$739$	35.0414	−	20.2311i	1.28902	−	0.744215i	0.310539	−	0.950561i	$-0.399491\pi$
$739$	35.0414	−	20.2311i	1.28902	−	0.744215i	0.978479	+	0.206346i	$0.0661572\pi$
$740$		0			0
$741$	8.45199	−	26.1272i	0.310492	−	0.959806i
$742$	38.9775			1.43091
$743$	−27.2794	+	15.7497i	−1.00078	+	0.577802i	−0.908480	−	0.417929i	$-0.862756\pi$
$743$	−27.2794	+	15.7497i	−1.00078	+	0.577802i	−0.0923027	+	0.995731i	$0.529423\pi$
$744$	−3.29654	−	5.70978i	−0.120857	−	0.209331i
$745$		0			0
$746$			21.6516i			0.792721i
$747$	3.63024	+	2.09592i	0.132824	+	0.0766857i
$748$	−2.96377	−	1.71113i	−0.108366	−	0.0625651i
$749$			11.8675i			0.433628i
$750$		0			0
$751$	−8.37551	−	14.5068i	−0.305627	−	0.529361i	0.671774	−	0.740756i	$-0.265533\pi$
$751$	−8.37551	−	14.5068i	−0.305627	−	0.529361i	−0.977401	+	0.211395i	$0.932199\pi$
$752$	2.50973	−	1.44899i	0.0915204	−	0.0528393i
$753$	−16.3877			−0.597202
$754$	6.09976	+	6.75692i	0.222140	+	0.246072i
$755$		0			0
$756$	2.42916	−	1.40247i	0.0883476	−	0.0510075i
$757$	−13.3892	−	23.1908i	−0.486640	−	0.842885i	0.513242	−	0.858244i	$-0.328444\pi$
$757$	−13.3892	−	23.1908i	−0.486640	−	0.842885i	−0.999882	+	0.0153589i	$0.995111\pi$
$758$	−4.51187	+	7.81479i	−0.163879	+	0.283846i
$759$		−	2.76349i		−	0.100308i
$760$		0			0
$761$	−0.217029	−	0.125302i	−0.00786729	−	0.00454218i	0.496061	−	0.868288i	$-0.334779\pi$
$761$	−0.217029	−	0.125302i	−0.00786729	−	0.00454218i	−0.503928	+	0.863745i	$0.668112\pi$
$762$			6.68791i			0.242277i
$763$	0.627408	−	1.08670i	0.0227137	−	0.0393413i
$764$	−6.91728	−	11.9811i	−0.250259	−	0.433461i
$765$		0			0
$766$	−10.0741			−0.363990
$767$	−23.4427	−	25.9683i	−0.846466	−	0.937660i
$768$	1.00000			0.0360844
$769$	−17.1777	+	9.91755i	−0.619444	+	0.357636i	−0.776652	−	0.629929i	$-0.783084\pi$
$769$	−17.1777	+	9.91755i	−0.619444	+	0.357636i	0.157209	+	0.987565i	$0.449750\pi$
$770$		0			0
$771$	4.20466	−	7.28269i	0.151427	−	0.262280i
$772$		−	17.0064i		−	0.612075i
$773$	31.7285	+	18.3185i	1.14120	+	0.658869i	0.946726	−	0.322039i	$-0.104368\pi$
$773$	31.7285	+	18.3185i	1.14120	+	0.658869i	0.194469	+	0.980909i	$0.437702\pi$
$774$	−3.67593	−	2.12230i	−0.132129	−	0.0762845i
$775$		0			0
$776$	−8.45318	+	14.6413i	−0.303452	+	0.525594i
$777$	−14.5487	−	25.1991i	−0.521931	−	0.904011i
$778$	21.0956	−	12.1795i	0.756313	−	0.436658i
$779$	−43.8152			−1.56984
$780$		0			0
$781$	0.764218			0.0273459
$782$	23.1452	−	13.3629i	0.827669	−	0.477855i
$783$	1.26235	+	2.18645i	0.0451126	+	0.0781373i
$784$	0.433868	−	0.751482i	0.0154953	−	0.0268386i
$785$		0			0
$786$	10.1086	+	5.83620i	0.360562	+	0.208170i
$787$	31.0911	+	17.9505i	1.10828	+	0.639865i	0.938383	−	0.345597i	$-0.112323\pi$
$787$	31.0911	+	17.9505i	1.10828	+	0.639865i	0.169896	+	0.985462i	$0.445657\pi$
$788$			6.32974i			0.225487i
$789$	2.94536	−	5.10152i	0.104858	−	0.181619i
$790$		0			0
$791$	22.7539	−	13.1370i	0.809036	−	0.467097i
$792$	−0.594869			−0.0211377
$793$	−18.2691	+	16.4923i	−0.648756	+	0.585660i
$794$	30.0381			1.06601
$795$		0			0
$796$	8.31782	+	14.4069i	0.294817	+	0.510638i
$797$	−2.48369	+	4.30187i	−0.0879767	+	0.152380i	−0.906656	−	0.421871i	$-0.861373\pi$
$797$	−2.48369	+	4.30187i	−0.0879767	+	0.152380i	0.818679	+	0.574251i	$0.194707\pi$
$798$		−	21.3628i		−	0.756235i
$799$	−14.4384	−	8.33601i	−0.510794	−	0.294907i
$800$		0			0
$801$			6.05447i			0.213924i
$802$	1.36131	−	2.35786i	0.0480696	−	0.0832590i
$803$	4.32471	+	7.49061i	0.152616	+	0.264338i
$804$	−6.80906	+	3.93121i	−0.240137	+	0.138643i
$805$		0			0
$806$	4.97241	+	23.2458i	0.175146	+	0.818800i
$807$	22.8455			0.804201
$808$	4.71741	−	2.72360i	0.165958	−	0.0958159i
$809$	−20.1296	−	34.8656i	−0.707720	−	1.22581i	−0.965701	−	0.259658i	$-0.916390\pi$
$809$	−20.1296	−	34.8656i	−0.707720	−	1.22581i	0.257980	−	0.966150i	$-0.416943\pi$
$810$		0			0
$811$		−	7.62969i		−	0.267914i	−0.990987	−	0.133957i	$-0.957232\pi$
$811$		−	7.62969i		−	0.267914i	0.990987	−	0.133957i	$-0.0427685\pi$
$812$	6.13287	+	3.54082i	0.215222	+	0.124258i
$813$	23.2565	+	13.4271i	0.815639	+	0.470910i
$814$			6.17092i			0.216291i
$815$		0			0
$816$	−2.87649	−	4.98222i	−0.100697	−	0.174413i
$817$	−27.9963	+	16.1637i	−0.979466	+	0.565495i
$818$	38.2243			1.33648
$819$	−9.88966	+	2.11545i	−0.345573	+	0.0739199i
$820$		0			0
$821$	−20.8682	+	12.0483i	−0.728306	+	0.420487i	−0.817802	−	0.575500i	$-0.804808\pi$
$821$	−20.8682	+	12.0483i	−0.728306	+	0.420487i	0.0894964	+	0.995987i	$0.471474\pi$
$822$	−3.40142	−	5.89144i	−0.118638	−	0.205487i
$823$	10.7518	−	18.6227i	0.374784	−	0.649145i	−0.615511	−	0.788129i	$-0.711050\pi$
$823$	10.7518	−	18.6227i	0.374784	−	0.649145i	0.990295	+	0.138984i	$0.0443835\pi$
$824$		−	13.7529i		−	0.479105i
$825$		0			0
$826$	−23.5699	−	13.6081i	−0.820103	−	0.473487i
$827$		−	38.8887i		−	1.35229i	−0.736767	−	0.676147i	$-0.763648\pi$
$827$		−	38.8887i		−	1.35229i	0.736767	−	0.676147i	$-0.236352\pi$
$828$	2.32278	−	4.02317i	0.0807221	−	0.139815i
$829$	−12.2944	−	21.2945i	−0.427001	−	0.739587i	0.569604	−	0.821919i	$-0.307097\pi$
$829$	−12.2944	−	21.2945i	−0.427001	−	0.739587i	−0.996605	+	0.0823320i	$0.973763\pi$
$830$		0			0
$831$	−10.6250			−0.368576
$832$	−3.43052	−	1.10975i	−0.118932	−	0.0384737i
$833$	−4.99206			−0.172965
$834$	−6.14719	+	3.54908i	−0.212860	+	0.122895i
$835$		0			0
$836$	−2.26529	+	3.92360i	−0.0783468	+	0.135701i
$837$			6.59309i			0.227890i
$838$	−25.8708	−	14.9365i	−0.893690	−	0.515972i
$839$	−45.1686	−	26.0781i	−1.55939	−	0.900316i	−0.997315	−	0.0732324i	$-0.976669\pi$
$839$	−45.1686	−	26.0781i	−1.55939	−	0.900316i	−0.562079	−	0.827084i	$-0.689998\pi$
$840$		0			0
$841$	11.3130	−	19.5946i	0.390102	−	0.675677i
$842$	−7.10165	−	12.3004i	−0.244739	−	0.423900i
$843$	24.5719	−	14.1866i	0.846301	−	0.488612i
$844$	−16.5489			−0.569635
$845$		0			0
$846$	−2.89798			−0.0996348
$847$	−25.8611	+	14.9309i	−0.888599	+	0.513033i
$848$	−6.94798	−	12.0343i	−0.238595	−	0.413258i
$849$	−2.83482	+	4.91005i	−0.0972907	+	0.168512i
$850$		0			0
$851$	−41.7347	−	24.0955i	−1.43065	−	0.825984i
$852$	1.11257	+	0.642342i	0.0381160	+	0.0220063i
$853$		−	2.06762i		−	0.0707938i	−0.999373	−	0.0353969i	$-0.988730\pi$
$853$		−	2.06762i		−	0.0707938i	0.999373	−	0.0353969i	$-0.0112695\pi$
$854$	−9.57355	+	16.5819i	−0.327600	+	0.567420i
$855$		0			0
$856$	3.66407	−	2.11545i	0.125235	−	0.0723047i
$857$	20.1793			0.689310			0.344655	−	0.938729i	$-0.387996\pi$
$857$	20.1793			0.689310			0.344655	+	0.938729i	$0.387996\pi$
$858$	2.04071	+	0.660156i	0.0696686	+	0.0225374i
$859$	34.4160			1.17426			0.587129	−	0.809493i	$-0.300258\pi$
$859$	34.4160			1.17426			0.587129	+	0.809493i	$0.300258\pi$
$860$		0			0
$861$	8.06839	+	13.9749i	0.274970	+	0.476262i
$862$	−4.67596	+	8.09901i	−0.159264	+	0.275853i
$863$		−	1.02382i		−	0.0348514i	−0.999848	−	0.0174257i	$-0.994453\pi$
$863$		−	1.02382i		−	0.0348514i	0.999848	−	0.0174257i	$-0.00554705\pi$
$864$	−0.866025	−	0.500000i	−0.0294628	−	0.0170103i
$865$		0			0
$866$			3.96009i			0.134569i
$867$	−8.04834	+	13.9401i	−0.273336	+	0.473431i
$868$	9.24663	+	16.0156i	0.313851	+	0.543606i
$869$	−0.943538	+	0.544752i	−0.0320073	+	0.0184794i
$870$		0			0
$871$	27.7213	−	5.92973i	0.939299	−	0.200921i
$872$	−0.447358			−0.0151495
$873$	14.6413	−	8.45318i	0.495534	−	0.286097i
$874$	−17.6905	−	30.6409i	−0.598391	−	1.03644i
$875$		0			0
$876$			14.5400i			0.491262i
$877$	−12.9228	−	7.46097i	−0.436371	−	0.251939i	0.265686	−	0.964060i	$-0.414402\pi$
$877$	−12.9228	−	7.46097i	−0.436371	−	0.251939i	−0.702057	+	0.712121i	$0.747735\pi$
$878$	19.5708	+	11.2992i	0.660481	+	0.381329i
$879$			1.65835i			0.0559348i
$880$		0			0
$881$	21.5282	+	37.2879i	0.725303	+	1.25626i	0.958849	+	0.283916i	$0.0916336\pi$
$881$	21.5282	+	37.2879i	0.725303	+	1.25626i	−0.233546	+	0.972346i	$0.575033\pi$
$882$	−0.751482	+	0.433868i	−0.0253037	+	0.0146091i
$883$	−30.1817			−1.01569			−0.507847	−	0.861447i	$-0.669559\pi$
$883$	−30.1817			−1.01569			−0.507847	+	0.861447i	$0.669559\pi$
$884$	4.33881	+	20.2838i	0.145930	+	0.682217i
$885$		0			0
$886$	−25.1518	+	14.5214i	−0.844992	+	0.487856i
$887$	10.8307	+	18.7593i	0.363660	+	0.629877i	0.988560	−	0.150827i	$-0.0481937\pi$
$887$	10.8307	+	18.7593i	0.363660	+	0.629877i	−0.624900	+	0.780705i	$0.714860\pi$
$888$	−5.18679	+	8.98379i	−0.174057	+	0.301476i
$889$		−	18.7592i		−	0.629164i
$890$		0			0
$891$	0.515171	+	0.297434i	0.0172589	+	0.00996443i
$892$			16.6556i			0.557670i
$893$	−11.0357	+	19.1144i	−0.369295	+	0.639638i
$894$	−1.74557	−	3.02342i	−0.0583807	−	0.101118i
$895$		0			0
$896$	−2.80495			−0.0937068
$897$	−12.4330	+	11.2238i	−0.415127	+	0.374753i
$898$	−27.4687			−0.916642
$899$	−14.4154	+	8.32276i	−0.480782	+	0.277580i
$900$		0			0
$901$	−39.9715	+	69.2328i	−1.33165	+	2.30648i
$902$		−	3.42226i		−	0.113949i
$903$	10.3108	+	5.95294i	0.343122	+	0.198101i
$904$	−8.11206	−	4.68350i	−0.269803	−	0.155771i
$905$		0			0
$906$	−2.27494	+	3.94031i	−0.0755799	+	0.130908i
$907$	−1.39748	−	2.42051i	−0.0464026	−	0.0803717i	0.841891	−	0.539647i	$-0.181442\pi$
$907$	−1.39748	−	2.42051i	−0.0464026	−	0.0803717i	−0.888294	+	0.459276i	$0.848109\pi$
$908$	−2.61722	+	1.51105i	−0.0868554	+	0.0501460i
$909$	−5.44720			−0.180672
$910$		0			0
$911$	24.2193			0.802422			0.401211	−	0.915986i	$-0.368589\pi$
$911$	24.2193			0.802422			0.401211	+	0.915986i	$0.368589\pi$
$912$	−6.59574	+	3.80805i	−0.218407	+	0.126097i
$913$	1.24680	+	2.15952i	0.0412630	+	0.0714695i
$914$	−2.19087	+	3.79470i	−0.0724675	+	0.125517i
$915$		0			0
$916$	14.2437	+	8.22361i	0.470626	+	0.271716i
$917$	−28.3541	−	16.3702i	−0.936334	−	0.540593i
$918$			5.75297i			0.189876i
$919$	6.54988	−	11.3447i	0.216061	−	0.374228i	−0.737539	−	0.675304i	$-0.764012\pi$
$919$	6.54988	−	11.3447i	0.216061	−	0.374228i	0.953600	+	0.301076i	$0.0973458\pi$
$920$		0			0
$921$	−0.332629	+	0.192044i	−0.0109605	+	0.00632805i
$922$	−24.3172			−0.800844
$923$	−3.10385	−	3.43824i	−0.102164	−	0.113171i
$924$	1.66858			0.0548921
$925$		0			0
$926$	−9.53298	−	16.5116i	−0.313273	−	0.542605i
$927$	−6.87645	+	11.9104i	−0.225852	+	0.391187i
$928$		−	2.52469i		−	0.0828771i
$929$	−24.1564	−	13.9467i	−0.792544	−	0.457576i	0.0483131	−	0.998832i	$-0.484615\pi$
$929$	−24.1564	−	13.9467i	−0.792544	−	0.457576i	−0.840858	+	0.541257i	$0.817949\pi$
$930$		0			0
$931$			6.60877i			0.216594i
$932$	−6.91443	+	11.9762i	−0.226490	+	0.392292i
$933$	5.84601	+	10.1256i	0.191390	+	0.331497i
$934$	−8.76211	+	5.05881i	−0.286705	+	0.165529i
$935$		0			0
$936$	2.41604	+	2.67633i	0.0789707	+	0.0874786i
$937$	49.9741			1.63258			0.816292	−	0.577640i	$-0.196026\pi$
$937$	49.9741			1.63258			0.816292	+	0.577640i	$0.196026\pi$
$938$	19.0991	−	11.0268i	0.623606	−	0.360039i
$939$	−5.28939	−	9.16150i	−0.172613	−	0.298974i
$940$		0			0
$941$			9.56099i			0.311680i	0.987782	+	0.155840i	$0.0498083\pi$
$941$			9.56099i			0.311680i	−0.987782	+	0.155840i	$0.950192\pi$
$942$	9.95560	+	5.74787i	0.324371	+	0.187276i
$943$	23.1452	+	13.3629i	0.753710	+	0.435155i
$944$			9.70293i			0.315804i
$945$		0			0
$946$	−1.26249	−	2.18670i	−0.0410471	−	0.0710956i
$947$	−38.2466	+	22.0817i	−1.24285	+	0.717558i	−0.969673	−	0.244406i	$-0.921407\pi$
$947$	−38.2466	+	22.0817i	−1.24285	+	0.717558i	−0.273175	+	0.961964i	$0.588074\pi$
$948$	−1.83150			−0.0594844
$949$	16.1358	−	49.8799i	0.523791	−	1.61917i
$950$		0			0
$951$	−19.1412	+	11.0512i	−0.620695	+	0.358359i
$952$	8.06839	+	13.9749i	0.261498	+	0.452928i
$953$	7.40798	−	12.8310i	0.239968	−	0.415637i	−0.720737	−	0.693209i	$-0.756196\pi$
$953$	7.40798	−	12.8310i	0.239968	−	0.415637i	0.960705	+	0.277572i	$0.0895297\pi$
$954$			13.8960i			0.449899i
$955$		0			0
$956$	3.98559	+	2.30108i	0.128903	+	0.0744223i
$957$			1.50186i			0.0485483i
$958$	14.3307	−	24.8215i	0.463004	−	0.801946i
$959$	9.54082	+	16.5252i	0.308089	+	0.533626i
$960$		0			0
$961$	−12.4688			−0.402219
$962$	27.7632	−	25.0630i	0.895120	−	0.808063i
$963$	−4.23091			−0.136339
$964$	5.38108	−	3.10677i	0.173313	−	0.100062i
$965$		0			0
$966$	−6.51527	+	11.2848i	−0.209625	+	0.363082i
$967$		−	1.88667i		−	0.0606711i	−0.999540	−	0.0303356i	$-0.990342\pi$
$967$		−	1.88667i		−	0.0606711i	0.999540	−	0.0303356i	$-0.00965759\pi$
$968$	9.21982	+	5.32307i	0.296336	+	0.171090i
$969$	37.9451	+	21.9076i	1.21897	+	0.703774i
$970$		0			0
$971$	23.9611	−	41.5018i	0.768947	−	1.33186i	−0.169187	−	0.985584i	$-0.554114\pi$
$971$	23.9611	−	41.5018i	0.768947	−	1.33186i	0.938134	−	0.346271i	$-0.112552\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	17.2425	−	9.95499i	0.552770	−	0.319142i
$974$	17.4398			0.558807
$975$		0			0
$976$	6.82619			0.218501
$977$	27.9867	−	16.1581i	0.895374	−	0.516945i	0.0196777	−	0.999806i	$-0.493736\pi$
$977$	27.9867	−	16.1581i	0.895374	−	0.516945i	0.875697	+	0.482862i	$0.160403\pi$
$978$	6.91443	+	11.9762i	0.221099	+	0.382955i
$979$	−1.80081	+	3.11909i	−0.0575541	+	0.0996866i
$980$		0			0
$981$	0.387423	+	0.223679i	0.0123695	+	0.00714152i
$982$	−19.4394	−	11.2233i	−0.620336	−	0.358151i
$983$		−	20.4850i		−	0.653370i	−0.945133	−	0.326685i	$-0.894068\pi$
$983$		−	20.4850i		−	0.653370i	0.945133	−	0.326685i	$-0.105932\pi$
$984$	2.87649	−	4.98222i	0.0916990	−	0.158827i
$985$		0			0
$986$	−12.5786	+	7.26224i	−0.400583	+	0.231277i
$987$	8.12870			0.258739
$988$	26.8528	−	5.74396i	0.854302	−	0.182740i
$989$	19.7185			0.627012
$990$		0			0
$991$	0.834181	+	1.44484i	0.0264986	+	0.0458970i	0.878971	−	0.476876i	$-0.158231\pi$
$991$	0.834181	+	1.44484i	0.0264986	+	0.0458970i	−0.852472	+	0.522773i	$0.824898\pi$
$992$	3.29654	−	5.70978i	0.104665	−	0.181286i
$993$			6.10616i			0.193773i
$994$	−3.12070	−	1.80174i	−0.0989826	−	0.0571476i
$995$		0			0
$996$			4.19184i			0.132824i
$997$	1.56758	−	2.71512i	0.0496456	−	0.0859887i	−0.840135	−	0.542378i	$-0.817524\pi$
$997$	1.56758	−	2.71512i	0.0496456	−	0.0859887i	0.889780	+	0.456389i	$0.150857\pi$
$998$	−5.20680	−	9.01844i	−0.164818	−	0.285474i
$999$	8.98379	−	5.18679i	0.284234	−	0.164103i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.x.a.49.6	✓	12	5.3	odd	4
390.2.x.a.199.6	yes	12	65.17	odd	12
390.2.x.b.49.1	yes	12	5.2	odd	4
390.2.x.b.199.1	yes	12	65.43	odd	12
1170.2.bj.c.199.6		12	195.173	even	12
1170.2.bj.c.829.6		12	15.2	even	4
1170.2.bj.d.199.1		12	195.17	even	12
1170.2.bj.d.829.1		12	15.8	even	4
1950.2.bc.i.751.6		12	1.1	even	1	trivial
1950.2.bc.i.901.6		12	13.4	even	6	inner
1950.2.bc.j.751.1		12	5.4	even	2
1950.2.bc.j.901.1		12	65.4	even	6

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)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{6} +(2.42916 + 1.40247i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(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} +(2.42916 + 1.40247i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.515171 + 0.297434i) q^{11} -1.00000 q^{12} +(3.43052 + 1.10975i) q^{13} +2.80495 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.87649 + 4.98222i) q^{17} +1.00000i q^{18} +(6.59574 + 3.80805i) q^{19} -2.80495i q^{21} +(-0.297434 + 0.515171i) q^{22} +(-2.32278 - 4.02317i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(3.52579 - 0.754186i) q^{26} +1.00000 q^{27} +(2.42916 - 1.40247i) q^{28} +(1.26235 + 2.18645i) q^{29} +6.59309i q^{31} +(-0.866025 - 0.500000i) q^{32} +(0.515171 + 0.297434i) q^{33} +5.75297i q^{34} +(0.500000 + 0.866025i) q^{36} +(8.98379 - 5.18679i) q^{37} +7.61611 q^{38} +(-0.754186 - 3.52579i) q^{39} +(-4.98222 + 2.87649i) q^{41} +(-1.40247 - 2.42916i) q^{42} +(-2.12230 + 3.67593i) q^{43} +0.594869i q^{44} +(-4.02317 - 2.32278i) q^{46} +2.89798i q^{47} +(-0.500000 + 0.866025i) q^{48} +(0.433868 + 0.751482i) q^{49} +5.75297 q^{51} +(2.67633 - 2.41604i) q^{52} +13.8960 q^{53} +(0.866025 - 0.500000i) q^{54} +(1.40247 - 2.42916i) q^{56} -7.61611i q^{57} +(2.18645 + 1.26235i) q^{58} +(-8.40299 - 4.85147i) q^{59} +(-3.41309 + 5.91165i) q^{61} +(3.29654 + 5.70978i) q^{62} +(-2.42916 + 1.40247i) q^{63} -1.00000 q^{64} +0.594869 q^{66} +(6.80906 - 3.93121i) q^{67} +(2.87649 + 4.98222i) q^{68} +(-2.32278 + 4.02317i) q^{69} +(-1.11257 - 0.642342i) q^{71} +(0.866025 + 0.500000i) q^{72} -14.5400i q^{73} +(5.18679 - 8.98379i) q^{74} +(6.59574 - 3.80805i) q^{76} -1.66858 q^{77} +(-2.41604 - 2.67633i) q^{78} +1.83150 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-2.87649 + 4.98222i) q^{82} -4.19184i q^{83} +(-2.42916 - 1.40247i) q^{84} +4.24460i q^{86} +(1.26235 - 2.18645i) q^{87} +(0.297434 + 0.515171i) q^{88} +(5.24333 - 3.02724i) q^{89} +(6.77687 + 7.50697i) q^{91} -4.64555 q^{92} +(5.70978 - 3.29654i) q^{93} +(1.44899 + 2.50973i) q^{94} +1.00000i q^{96} +(-14.6413 - 8.45318i) q^{97} +(0.751482 + 0.433868i) q^{98} -0.594869i 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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