LMFDB - Embedded newform 1950.2.bc.i.901.6

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			901.6
Root			$1.40719 - 0.536449i$ of defining polynomial
Character	$\chi$	$=$	1950.901
Dual form			1950.2.bc.i.751.6

$q$-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 $\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times$.

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

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
$7$	2.42916	−	1.40247i	0.918135	−	0.530085i	0.0350954	−	0.999384i	$-0.488827\pi$
$7$	2.42916	−	1.40247i	0.918135	−	0.530085i	0.883040	+	0.469299i	$0.155493\pi$
$8$			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	0.420320	−	0.907376i	$-0.361918\pi$
$11$	−0.515171	−	0.297434i	−0.155330	−	0.0896798i	−0.575650	+	0.817696i	$0.695251\pi$
$12$	−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	−0.969279	−	0.245963i	$-0.920896\pi$
$17$	−2.87649	−	4.98222i	−0.697650	−	1.20837i	0.271629	−	0.962402i	$-0.412438\pi$
$18$		−	1.00000i		−	0.235702i
$19$	6.59574	−	3.80805i	1.51317	−	0.873628i	0.513286	−	0.858218i	$-0.328428\pi$
$19$	6.59574	−	3.80805i	1.51317	−	0.873628i	0.999881	−	0.0154099i	$-0.00490533\pi$
$20$		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	−0.999838	−	0.0179978i	$-0.994271\pi$
$23$	−2.32278	+	4.02317i	−0.484332	+	0.838888i	0.515506	+	0.856886i	$0.327604\pi$
$24$	−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	−0.724690	−	0.689075i	$-0.758017\pi$
$29$	1.26235	−	2.18645i	0.234412	−	0.406013i	0.959102	+	0.283062i	$0.0913502\pi$
$30$		0			0
$31$		−	6.59309i		−	1.18415i	−0.805882	−	0.592077i	$-0.798308\pi$
$31$		−	6.59309i		−	1.18415i	0.805882	−	0.592077i	$-0.201692\pi$
$32$	−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	0.999660	−	0.0260561i	$-0.00829487\pi$
$37$	8.98379	+	5.18679i	1.47693	+	0.852703i	0.477265	+	0.878759i	$0.341628\pi$
$38$	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	0.0576618	−	0.998336i	$-0.481636\pi$
$41$	−4.98222	−	2.87649i	−0.778092	−	0.449232i	−0.835754	+	0.549105i	$0.814969\pi$
$42$	−1.40247	+	2.42916i	−0.216406	+	0.374827i
$43$	−2.12230	−	3.67593i	−0.323648	−	0.560574i	0.657590	−	0.753376i	$-0.271576\pi$
$43$	−2.12230	−	3.67593i	−0.323648	−	0.560574i	−0.981238	+	0.192802i	$0.938243\pi$
$44$		−	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	$-0.932212\pi$
$47$		−	2.89798i		−	0.422715i	0.977409	−	0.211357i	$-0.0677884\pi$
$48$	−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	−0.934632	−	0.355616i	$-0.884271\pi$
$59$	−8.40299	+	4.85147i	−1.09398	+	0.631607i	−0.159344	+	0.987223i	$0.550938\pi$
$60$		0			0
$61$	−3.41309	−	5.91165i	−0.437002	−	0.756910i	0.560455	−	0.828185i	$-0.310626\pi$
$61$	−3.41309	−	5.91165i	−0.437002	−	0.756910i	−0.997457	+	0.0712755i	$0.977293\pi$
$62$	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	0.854489	−	0.519470i	$-0.173871\pi$
$67$	6.80906	+	3.93121i	0.831859	+	0.480274i	−0.0226299	+	0.999744i	$0.507204\pi$
$68$	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	−0.564564	−	0.825389i	$-0.690956\pi$
$71$	−1.11257	+	0.642342i	−0.132038	+	0.0762320i	0.432526	+	0.901621i	$0.357622\pi$
$72$	0.866025	−	0.500000i	0.102062	−	0.0589256i
$73$			14.5400i			1.70178i	0.525341	+	0.850892i	$0.323938\pi$
$73$			14.5400i			1.70178i	−0.525341	+	0.850892i	$0.676062\pi$
$74$	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	$0.0738913\pi$
$83$			4.19184i			0.460114i	−0.973177	+	0.230057i	$0.926109\pi$
$84$	−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	0.751455	−	0.659785i	$-0.229353\pi$
$89$	5.24333	+	3.02724i	0.555792	+	0.320886i	−0.195663	+	0.980671i	$0.562686\pi$
$90$		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	−0.999883	−	0.0152677i	$-0.995140\pi$
$97$	−14.6413	+	8.45318i	−1.48660	+	0.858291i	−0.486719	+	0.873558i	$0.661807\pi$
$98$	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	−0.698112	−	0.715988i	$-0.745976\pi$
$101$	2.72360	−	4.71741i	0.271008	−	0.469400i	0.969120	+	0.246589i	$0.0793096\pi$
$102$	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	−0.745468	−	0.666542i	$-0.767774\pi$
$107$	2.11545	−	3.66407i	0.204509	−	0.354219i	0.949976	+	0.312323i	$0.101107\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$			0.447358i			0.0428491i	0.999770	+	0.0214246i	$0.00682017\pi$
$109$			0.447358i			0.0428491i	−0.999770	+	0.0214246i	$0.993180\pi$
$110$		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	0.997733	−	0.0672956i	$-0.0214371\pi$
$113$	4.68350	+	8.11206i	0.440587	+	0.763119i	−0.557146	+	0.830414i	$0.688104\pi$
$114$	−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	−0.975385	−	0.220507i	$-0.929229\pi$
$127$	−3.34395	+	5.79190i	−0.296728	+	0.513948i	0.678658	+	0.734455i	$0.262562\pi$
$128$	−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	−0.226752	−	0.973953i	$-0.572811\pi$
$137$	5.89144	−	3.40142i	0.503339	−	0.290603i	0.730092	+	0.683349i	$0.239477\pi$
$138$		−	4.64555i		−	0.395456i
$139$	3.54908	+	6.14719i	0.301029	+	0.521397i	0.976369	−	0.216109i	$-0.0693366\pi$
$139$	3.54908	+	6.14719i	0.301029	+	0.521397i	−0.675340	+	0.737506i	$0.736003\pi$
$140$		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	−0.371017	−	0.928626i	$-0.620991\pi$
$149$	3.02342	−	1.74557i	0.247688	−	0.143003i	0.618705	+	0.785623i	$0.287658\pi$
$150$		0			0
$151$			4.54988i			0.370264i	0.982714	+	0.185132i	$0.0592713\pi$
$151$			4.54988i			0.370264i	−0.982714	+	0.185132i	$0.940729\pi$
$152$	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	−0.889347	−	0.457233i	$-0.848840\pi$
$163$	−11.9762	+	6.91443i	−0.938045	+	0.541580i	−0.0486977	+	0.998814i	$0.515507\pi$
$164$		−	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	0.998082	−	0.0619099i	$-0.0197191\pi$
$167$	18.6542	+	10.7700i	1.44351	+	0.833409i	0.445425	+	0.895319i	$0.353052\pi$
$168$	−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	−0.999744	−	0.0226249i	$-0.992798\pi$
$173$	−6.83251	−	11.8342i	−0.519466	−	0.899741i	0.480278	−	0.877116i	$-0.340536\pi$
$174$			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	−0.993971	−	0.109639i	$-0.965030\pi$
$179$	−5.37886	+	9.31647i	−0.402035	+	0.696345i	0.591936	+	0.805985i	$0.298364\pi$
$180$		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	1.00000		0.000597179i	$0.000190088\pi$
$191$	6.91728	+	11.9811i	0.500517	+	0.866921i	−0.499483	+	0.866324i	$0.666477\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	14.7280	+	8.50322i	1.06014	+	0.612075i	0.925472	−	0.378815i	$-0.123668\pi$
$193$	14.7280	+	8.50322i	1.06014	+	0.612075i	0.134673	+	0.990890i	$0.457002\pi$
$194$	−16.9064			−1.21381
$195$		0			0
$196$	0.867736			0.0619812
$197$	−5.48171	−	3.16487i	−0.390556	−	0.225487i	0.291845	−	0.956466i	$-0.405731\pi$
$197$	−5.48171	−	3.16487i	−0.390556	−	0.225487i	−0.682401	+	0.730978i	$0.739064\pi$
$198$	−0.297434	+	0.515171i	−0.0211377	+	0.0366116i
$199$	−8.31782	−	14.4069i	−0.589634	−	1.02128i	−0.994280	−	0.106803i	$-0.965939\pi$
$199$	−8.31782	−	14.4069i	−0.589634	−	1.02128i	0.404646	−	0.914473i	$-0.367395\pi$
$200$		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	0.426967	+	0.904267i	$0.359582\pi$
$211$	−8.27443	+	14.3317i	−0.569635	+	0.986637i	−0.996602	+	0.0823697i	$0.973751\pi$
$212$	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	−0.0679254	−	0.997690i	$-0.521638\pi$
$223$	−14.4242	−	8.32779i	−0.965913	−	0.557670i	−0.897988	+	0.440020i	$0.854971\pi$
$224$	−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	−0.584334	−	0.811513i	$-0.698644\pi$
$227$	−2.61722	+	1.51105i	−0.173711	+	0.100292i	0.410624	+	0.911805i	$0.365311\pi$
$228$	−6.59574	+	3.80805i	−0.436814	+	0.252195i
$229$		−	16.4472i		−	1.08686i	−0.839453	−	0.543432i	$-0.817125\pi$
$229$		−	16.4472i		−	1.08686i	0.839453	−	0.543432i	$-0.182875\pi$
$230$		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	$-0.952445\pi$
$239$		−	4.60216i		−	0.297689i	0.988861	−	0.148845i	$-0.0475554\pi$
$240$		0			0
$241$	5.38108	−	3.10677i	0.346626	−	0.200125i	−0.316572	−	0.948568i	$-0.602532\pi$
$241$	5.38108	−	3.10677i	0.346626	−	0.200125i	0.663198	+	0.748444i	$0.269199\pi$
$242$		−	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	0.999801	+	0.0199663i	$0.00635591\pi$
$251$	8.19386	+	14.1922i	0.517192	+	0.895802i	−0.482609	+	0.875836i	$0.660311\pi$
$252$		−	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	−0.704568	−	0.709637i	$-0.748859\pi$
$257$	4.20466	−	7.28269i	0.262280	−	0.454282i	0.966847	+	0.255355i	$0.0821924\pi$
$258$	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	−0.760813	−	0.648971i	$-0.775200\pi$
$263$	2.94536	−	5.10152i	0.181619	−	0.314573i	0.942432	+	0.334398i	$0.108533\pi$
$264$	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	−0.969686	−	0.244352i	$-0.921425\pi$
$269$	−11.4228	−	19.7848i	−0.696459	−	1.20630i	0.273228	−	0.961949i	$-0.411909\pi$
$270$		0			0
$271$	−23.2565	−	13.4271i	−1.41273	−	0.815639i	−0.417084	−	0.908868i	$-0.636948\pi$
$271$	−23.2565	−	13.4271i	−1.41273	−	0.815639i	−0.995645	+	0.0932285i	$0.970281\pi$
$272$	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	0.980321	−	0.197412i	$-0.0632537\pi$
$277$	5.31249	+	9.20150i	0.319197	+	0.552865i	−0.661124	+	0.750277i	$0.729920\pi$
$278$			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	$-0.678824\pi$
$281$		−	28.3732i		−	1.69260i	0.532705	−	0.846301i	$-0.321176\pi$
$282$	1.44899	+	2.50973i	0.0862862	+	0.149452i
$283$	−2.83482	+	4.91005i	−0.168512	+	0.291872i	−0.937897	−	0.346914i	$-0.887230\pi$
$283$	−2.83482	+	4.91005i	−0.168512	+	0.291872i	0.769385	+	0.638786i	$0.220563\pi$
$284$	−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	−0.541364	−	0.840788i	$-0.682092\pi$
$293$	−1.43617	+	0.829176i	−0.0839022	+	0.0484410i	0.457462	+	0.889229i	$0.348759\pi$
$294$			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	$0.00348891\pi$
$307$			0.384087i			0.0219210i	−0.999940	+	0.0109605i	$0.996511\pi$
$308$	−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	$0.213150\pi$
$317$			22.1023i			1.24139i	−0.784052	+	0.620695i	$0.786850\pi$
$318$	−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	−0.638239	−	0.769838i	$-0.720337\pi$
$331$	−5.28809	+	3.05308i	−0.290660	+	0.167812i	0.347580	+	0.937650i	$0.387004\pi$
$332$	−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	−0.796484	−	0.604660i	$-0.793309\pi$
$347$	−17.1730	−	29.7444i	−0.921893	−	1.59677i	−0.125409	−	0.992105i	$-0.540024\pi$
$348$	−1.26235	+	2.18645i	−0.0676689	+	0.117206i
$349$	−13.8581	−	8.00099i	−0.741808	−	0.428283i	0.0809181	−	0.996721i	$-0.474215\pi$
$349$	−13.8581	−	8.00099i	−0.741808	−	0.428283i	−0.822726	+	0.568438i	$0.807548\pi$
$350$		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	−0.0186563	−	0.999826i	$-0.505939\pi$
$353$	−16.7941	−	9.69607i	−0.893859	−	0.516070i	−0.875203	+	0.483756i	$0.839272\pi$
$354$	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	$0.137216\pi$
$359$			15.8342i			0.835699i	−0.908516	+	0.417850i	$0.862784\pi$
$360$		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	−0.993620	−	0.112778i	$-0.964025\pi$
$367$	−7.64645	+	13.2440i	−0.399141	+	0.691333i	0.594479	+	0.804111i	$0.297358\pi$
$368$	−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	−0.997449	−	0.0713760i	$-0.977261\pi$
$373$	−10.8258	−	18.7508i	−0.560538	−	0.970881i	0.436911	−	0.899505i	$-0.356072\pi$
$374$	−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	0.285677	−	0.958326i	$-0.407782\pi$
$379$	−7.81479	−	4.51187i	−0.401419	−	0.231759i	−0.687096	+	0.726567i	$0.741115\pi$
$380$		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	−0.706053	−	0.708159i	$-0.749526\pi$
$383$	−8.72439	+	5.03703i	−0.445795	+	0.257380i	0.260257	+	0.965539i	$0.416193\pi$
$384$	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	0.324234	−	0.945977i	$-0.394893\pi$
$397$	26.0137	−	15.0190i	1.30559	−	0.753784i	0.981357	+	0.192193i	$0.0615601\pi$
$398$		−	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	0.557716	−	0.830032i	$-0.311678\pi$
$401$	2.35786	+	1.36131i	0.117746	+	0.0679807i	−0.439970	+	0.898012i	$0.645011\pi$
$402$	−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	0.654938	−	0.755683i	$-0.272695\pi$
$409$	33.1032	−	19.1121i	1.63685	−	0.945034i	0.981909	−	0.189352i	$-0.0606386\pi$
$410$		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	0.227317	+	0.973821i	$0.427005\pi$
$419$	−14.9365	+	25.8708i	−0.729695	+	1.26387i	−0.957012	+	0.290048i	$0.906329\pi$
$420$		0			0
$421$			14.2033i			0.692226i	0.938193	+	0.346113i	$0.112499\pi$
$421$			14.2033i			0.692226i	−0.938193	+	0.346113i	$0.887501\pi$
$422$	−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	0.292095	−	0.956389i	$-0.405648\pi$
$431$	−8.09901	−	4.67596i	−0.390115	−	0.225233i	−0.682210	+	0.731156i	$0.738981\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	−1.98005	−	3.42954i	−0.0951549	−	0.164813i	0.814518	−	0.580138i	$-0.197001\pi$
$433$	−1.98005	−	3.42954i	−0.0951549	−	0.164813i	−0.909673	+	0.415325i	$0.863668\pi$
$434$		−	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	−0.459662	−	0.888094i	$-0.652029\pi$
$439$	11.2992	−	19.5708i	0.539281	−	0.934062i	0.998943	−	0.0459680i	$-0.0146372\pi$
$440$		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	−0.942077	−	0.335397i	$-0.891130\pi$
$449$	−23.7886	+	13.7343i	−1.12265	+	0.648164i	−0.180576	+	0.983561i	$0.557796\pi$
$450$		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	0.408613	−	0.912708i	$-0.366013\pi$
$457$	−3.79470	−	2.19087i	−0.177508	−	0.102485i	−0.586122	+	0.810223i	$0.699346\pi$
$458$	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	−0.902520	−	0.430647i	$-0.858285\pi$
$461$	−21.0593	+	12.1586i	−0.980829	+	0.566282i	−0.0783090	+	0.996929i	$0.524952\pi$
$462$	1.44503	−	0.834288i	0.0672288	−	0.0388146i
$463$			19.0660i			0.886071i	0.896504	+	0.443035i	$0.146098\pi$
$463$			19.0660i			0.886071i	−0.896504	+	0.443035i	$0.853902\pi$
$464$	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	0.944969	−	0.327161i	$-0.106092\pi$
$479$	24.8215	+	14.3307i	1.13412	+	0.654786i	0.189155	+	0.981947i	$0.439425\pi$
$480$		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	−0.117113	−	0.993119i	$-0.537364\pi$
$487$	15.1033	−	8.71990i	0.684396	−	0.395136i	0.801509	+	0.597982i	$0.204031\pi$
$488$	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	0.493469	+	0.869763i	$0.335729\pi$
$491$	−11.2233	+	19.4394i	−0.506503	+	0.877288i	−0.999972	+	0.00752493i	$0.997605\pi$
$492$	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	$0.0748832\pi$
$499$			10.4136i			0.466177i	−0.972456	+	0.233088i	$0.925117\pi$
$500$		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	0.923217	−	0.384279i	$-0.125550\pi$
$503$	2.88899	+	5.00387i	0.128814	+	0.223112i	−0.794404	+	0.607390i	$0.792216\pi$
$504$	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	0.630674	−	0.776048i	$-0.282778\pi$
$509$	6.18024	+	3.56816i	0.273934	+	0.158156i	−0.356740	+	0.934204i	$0.616112\pi$
$510$		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	−0.981856	−	0.189626i	$-0.939272\pi$
$523$	−7.47153	+	12.9411i	−0.326707	+	0.565873i	0.655149	+	0.755499i	$0.272606\pi$
$524$	−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	$0.136846\pi$
$541$			19.3888i			0.833589i	−0.909001	+	0.416794i	$0.863154\pi$
$542$	−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	0.980137	−	0.198321i	$-0.0635487\pi$
$557$	30.6446	+	17.6927i	1.29846	+	0.749663i	0.318318	+	0.947984i	$0.396882\pi$
$558$	−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	0.987991	+	0.154509i	$0.0493794\pi$
$563$	14.8963	+	25.8011i	0.627804	+	1.08739i	−0.360187	+	0.932880i	$0.617287\pi$
$564$			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	−0.676532	−	0.736414i	$-0.736518\pi$
$569$	7.14388	−	12.3736i	0.299487	−	0.518727i	0.976019	+	0.217687i	$0.0698511\pi$
$570$		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	$-0.542938\pi$
$577$		−	47.6052i		−	1.98183i	0.134485	−	0.990916i	$-0.457062\pi$
$578$	−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	−0.356709	−	0.934216i	$-0.616101\pi$
$587$	−32.5654	−	18.8016i	−1.34412	−	0.776027i	−0.987409	+	0.158189i	$0.949435\pi$
$588$	−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	$0.164054\pi$
$593$			24.0046i			0.985752i	−0.870100	+	0.492876i	$0.835946\pi$
$594$	−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	−0.846690	−	0.532087i	$-0.821408\pi$
$601$	0.918249	−	1.59045i	0.0374562	−	0.0648760i	0.884146	+	0.467211i	$0.154741\pi$
$602$	−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	0.965522	+	0.260321i	$0.0838284\pi$
$607$	17.4483	+	30.2214i	0.708206	+	1.22665i	−0.257316	+	0.966327i	$0.582838\pi$
$608$	−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	0.326286	−	0.945271i	$-0.394203\pi$
$613$	−8.15061	−	4.70575i	−0.329200	−	0.190064i	−0.655486	+	0.755207i	$0.727536\pi$
$614$	−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	−0.296787	−	0.954944i	$-0.595915\pi$
$617$	9.48432	−	5.47577i	0.381824	−	0.220446i	0.678612	+	0.734497i	$0.262582\pi$
$618$	−11.9104	+	6.87645i	−0.479105	+	0.276611i
$619$			1.00216i			0.0402803i	0.999797	+	0.0201402i	$0.00641125\pi$
$619$			1.00216i			0.0402803i	−0.999797	+	0.0201402i	$0.993589\pi$
$620$		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	−0.985952	−	0.167027i	$-0.946583\pi$
$631$	−33.5167	+	19.3509i	−1.33428	+	0.770346i	−0.348327	+	0.937373i	$0.613250\pi$
$632$			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	0.947708	−	0.319138i	$-0.103393\pi$
$641$	4.99961	+	8.65957i	0.197473	+	0.342033i	−0.750236	+	0.661170i	$0.770060\pi$
$642$			4.23091i			0.166981i
$643$	5.86694	−	3.38728i	0.231369	−	0.133581i	−0.379834	−	0.925055i	$-0.624019\pi$
$643$	5.86694	−	3.38728i	0.231369	−	0.133581i	0.611204	+	0.791473i	$0.290686\pi$
$644$	−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	−0.984030	−	0.178004i	$-0.943036\pi$
$647$	−8.59384	+	14.8850i	−0.337859	+	0.585188i	0.646171	+	0.763193i	$0.276369\pi$
$648$	−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	−0.999883	−	0.0153292i	$-0.995120\pi$
$653$	−12.4362	+	21.5401i	−0.486666	+	0.842930i	0.513217	+	0.858259i	$0.328454\pi$
$654$	−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	0.935067	−	0.354472i	$-0.115339\pi$
$659$	4.12151	+	7.13867i	0.160551	+	0.278083i	−0.774515	+	0.632555i	$0.782006\pi$
$660$		0			0
$661$	22.3962	+	12.9305i	0.871112	+	0.502937i	0.867718	−	0.497057i	$-0.165586\pi$
$661$	22.3962	+	12.9305i	0.871112	+	0.502937i	0.00339467	+	0.999994i	$0.498919\pi$
$662$	−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	−0.791529	−	0.611132i	$-0.790715\pi$
$673$	3.46306	−	5.99820i	0.133491	−	0.231213i	0.925020	+	0.379918i	$0.124048\pi$
$674$	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	−0.139178	−	0.990267i	$-0.544446\pi$
$683$	16.9567	−	9.78995i	0.648830	−	0.374602i	0.788008	+	0.615665i	$0.211113\pi$
$684$		−	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	0.282301	−	0.959326i	$-0.408902\pi$
$691$	−10.7079	−	6.18224i	−0.407350	−	0.235183i	−0.689650	+	0.724143i	$0.742236\pi$
$692$	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	−0.775430	−	0.631434i	$-0.782467\pi$
$709$	−16.4104	+	9.47457i	−0.616307	+	0.355825i	0.159123	+	0.987259i	$0.449133\pi$
$710$		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	0.854637	+	0.519225i	$0.173779\pi$
$719$	23.5155	+	40.7301i	0.876981	+	1.51898i	0.0223436	+	0.999750i	$0.492887\pi$
$720$		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	$-0.851883\pi$
$733$		−	24.2968i		−	0.897421i	0.893677	−	0.448711i	$-0.148117\pi$
$734$	−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	0.978479	−	0.206346i	$-0.0661572\pi$
$739$	35.0414	+	20.2311i	1.28902	+	0.744215i	0.310539	+	0.950561i	$0.399491\pi$
$740$		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	−0.0923027	−	0.995731i	$-0.529423\pi$
$743$	−27.2794	−	15.7497i	−1.00078	−	0.577802i	−0.908480	+	0.417929i	$0.862756\pi$
$744$	−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	−0.977401	−	0.211395i	$-0.932199\pi$
$751$	−8.37551	+	14.5068i	−0.305627	+	0.529361i	0.671774	+	0.740756i	$0.265533\pi$
$752$	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	−0.999882	−	0.0153589i	$-0.995111\pi$
$757$	−13.3892	+	23.1908i	−0.486640	+	0.842885i	0.513242	+	0.858244i	$0.328444\pi$
$758$	−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	−0.503928	−	0.863745i	$-0.668112\pi$
$761$	−0.217029	+	0.125302i	−0.00786729	+	0.00454218i	0.496061	+	0.868288i	$0.334779\pi$
$762$		−	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	0.157209	−	0.987565i	$-0.449750\pi$
$769$	−17.1777	−	9.91755i	−0.619444	−	0.357636i	−0.776652	+	0.629929i	$0.783084\pi$
$770$		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	0.194469	−	0.980909i	$-0.437702\pi$
$773$	31.7285	−	18.3185i	1.14120	−	0.658869i	0.946726	+	0.322039i	$0.104368\pi$
$774$	−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	0.169896	−	0.985462i	$-0.445657\pi$
$787$	31.0911	−	17.9505i	1.10828	−	0.639865i	0.938383	+	0.345597i	$0.112323\pi$
$788$		−	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	0.818679	−	0.574251i	$-0.194707\pi$
$797$	−2.48369	−	4.30187i	−0.0879767	−	0.152380i	−0.906656	+	0.421871i	$0.861373\pi$
$798$			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	0.257980	+	0.966150i	$0.416943\pi$
$809$	−20.1296	+	34.8656i	−0.707720	+	1.22581i	−0.965701	+	0.259658i	$0.916390\pi$
$810$		0			0
$811$			7.62969i			0.267914i	0.990987	+	0.133957i	$0.0427685\pi$
$811$			7.62969i			0.267914i	−0.990987	+	0.133957i	$0.957232\pi$
$812$	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	0.0894964	−	0.995987i	$-0.471474\pi$
$821$	−20.8682	−	12.0483i	−0.728306	−	0.420487i	−0.817802	+	0.575500i	$0.804808\pi$
$822$	−3.40142	+	5.89144i	−0.118638	+	0.205487i
$823$	10.7518	+	18.6227i	0.374784	+	0.649145i	0.990295	−	0.138984i	$-0.0443835\pi$
$823$	10.7518	+	18.6227i	0.374784	+	0.649145i	−0.615511	+	0.788129i	$0.711050\pi$
$824$			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	$0.236352\pi$
$827$			38.8887i			1.35229i	−0.736767	+	0.676147i	$0.763648\pi$
$828$	2.32278	+	4.02317i	0.0807221	+	0.139815i
$829$	−12.2944	+	21.2945i	−0.427001	+	0.739587i	−0.996605	−	0.0823320i	$-0.973763\pi$
$829$	−12.2944	+	21.2945i	−0.427001	+	0.739587i	0.569604	+	0.821919i	$0.307097\pi$
$830$		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	−0.562079	+	0.827084i	$0.689998\pi$
$839$	−45.1686	+	26.0781i	−1.55939	+	0.900316i	−0.997315	+	0.0732324i	$0.976669\pi$
$840$		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	$0.0112695\pi$
$853$			2.06762i			0.0707938i	−0.999373	+	0.0353969i	$0.988730\pi$
$854$	−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	$0.00554705\pi$
$863$			1.02382i			0.0348514i	−0.999848	+	0.0174257i	$0.994453\pi$
$864$	−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	−0.702057	−	0.712121i	$-0.747735\pi$
$877$	−12.9228	+	7.46097i	−0.436371	+	0.251939i	0.265686	+	0.964060i	$0.414402\pi$
$878$	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	−0.233546	−	0.972346i	$-0.575033\pi$
$881$	21.5282	−	37.2879i	0.725303	−	1.25626i	0.958849	−	0.283916i	$-0.0916336\pi$
$882$	−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	−0.624900	−	0.780705i	$-0.714860\pi$
$887$	10.8307	−	18.7593i	0.363660	−	0.629877i	0.988560	+	0.150827i	$0.0481937\pi$
$888$	−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	−0.888294	−	0.459276i	$-0.848109\pi$
$907$	−1.39748	+	2.42051i	−0.0464026	+	0.0803717i	0.841891	+	0.539647i	$0.181442\pi$
$908$	−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	0.953600	−	0.301076i	$-0.0973458\pi$
$919$	6.54988	+	11.3447i	0.216061	+	0.374228i	−0.737539	+	0.675304i	$0.764012\pi$
$920$		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	−0.840858	−	0.541257i	$-0.817949\pi$
$929$	−24.1564	+	13.9467i	−0.792544	+	0.457576i	0.0483131	+	0.998832i	$0.484615\pi$
$930$		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	$-0.950192\pi$
$941$		−	9.56099i		−	0.311680i	0.987782	−	0.155840i	$-0.0498083\pi$
$942$	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	−0.273175	−	0.961964i	$-0.588074\pi$
$947$	−38.2466	−	22.0817i	−1.24285	−	0.717558i	−0.969673	+	0.244406i	$0.921407\pi$
$948$	−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	0.960705	−	0.277572i	$-0.0895297\pi$
$953$	7.40798	+	12.8310i	0.239968	+	0.415637i	−0.720737	+	0.693209i	$0.756196\pi$
$954$		−	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	$0.00965759\pi$
$967$			1.88667i			0.0606711i	−0.999540	+	0.0303356i	$0.990342\pi$
$968$	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	0.938134	+	0.346271i	$0.112552\pi$
$971$	23.9611	+	41.5018i	0.768947	+	1.33186i	−0.169187	+	0.985584i	$0.554114\pi$
$972$	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	0.875697	−	0.482862i	$-0.160403\pi$
$977$	27.9867	+	16.1581i	0.895374	+	0.516945i	0.0196777	+	0.999806i	$0.493736\pi$
$978$	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	$0.105932\pi$
$983$			20.4850i			0.653370i	−0.945133	+	0.326685i	$0.894068\pi$
$984$	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	−0.852472	−	0.522773i	$-0.824898\pi$
$991$	0.834181	−	1.44484i	0.0264986	−	0.0458970i	0.878971	+	0.476876i	$0.158231\pi$
$992$	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	0.889780	−	0.456389i	$-0.150857\pi$
$997$	1.56758	+	2.71512i	0.0496456	+	0.0859887i	−0.840135	+	0.542378i	$0.817524\pi$
$998$	−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.901.6		12
5.2	odd	4		390.2.x.a.199.6	yes	12
5.3	odd	4		390.2.x.b.199.1	yes	12
5.4	even	2		1950.2.bc.j.901.1		12
13.10	even	6	inner	1950.2.bc.i.751.6		12
15.2	even	4		1170.2.bj.d.199.1		12
15.8	even	4		1170.2.bj.c.199.6		12
65.23	odd	12		390.2.x.a.49.6	✓	12
65.49	even	6		1950.2.bc.j.751.1		12
65.62	odd	12		390.2.x.b.49.1	yes	12
195.23	even	12		1170.2.bj.d.829.1		12
195.62	even	12		1170.2.bj.c.829.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.x.a.49.6	✓	12	65.23	odd	12
390.2.x.a.199.6	yes	12	5.2	odd	4
390.2.x.b.49.1	yes	12	65.62	odd	12
390.2.x.b.199.1	yes	12	5.3	odd	4
1170.2.bj.c.199.6		12	15.8	even	4
1170.2.bj.c.829.6		12	195.62	even	12
1170.2.bj.d.199.1		12	15.2	even	4
1170.2.bj.d.829.1		12	195.23	even	12
1950.2.bc.i.751.6		12	13.10	even	6	inner
1950.2.bc.i.901.6		12	1.1	even	1	trivial
1950.2.bc.j.751.1		12	65.49	even	6
1950.2.bc.j.901.1		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)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{6} +(2.42916 - 1.40247i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(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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