LMFDB - Embedded newform 729.2.e.s.406.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(82,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("729.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.e (of order $9$, degree $6$, not 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:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
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} + 18x^{10} + 105x^{8} + 266x^{6} + 306x^{4} + 132x^{2} + 1 $ x^12 + 18x^10 + 105x^8 + 266x^6 + 306x^4 + 132*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			406.2
Root			$1.91182i$ of defining polynomial
Character	$\chi$	$=$	729.406
Dual form			729.2.e.s.325.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.88278 + 1.57984i) q^{2} +(0.701665 + 3.97934i) q^{4} +(-2.89450 - 1.05351i) q^{5} +(-0.461673 + 2.61828i) q^{7} +(-2.50784 + 4.34371i) q^{8} +O(q^{10})$	\(q+(1.88278 + 1.57984i) q^{2} +(0.701665 + 3.97934i) q^{4} +(-2.89450 - 1.05351i) q^{5} +(-0.461673 + 2.61828i) q^{7} +(-2.50784 + 4.34371i) q^{8} +(-3.78532 - 6.55636i) q^{10} +(-3.22722 + 1.17461i) q^{11} +(-2.56162 + 2.14945i) q^{13} +(-5.00567 + 4.20026i) q^{14} +(-3.98997 + 1.45223i) q^{16} +(1.28641 + 2.22813i) q^{17} +(1.04838 - 1.81585i) q^{19} +(2.16131 - 12.2574i) q^{20} +(-7.93184 - 2.88695i) q^{22} +(-0.0928052 - 0.526325i) q^{23} +(3.43802 + 2.88484i) q^{25} -8.21874 q^{26} -10.7430 q^{28} +(-1.93878 - 1.62683i) q^{29} +(1.33964 + 7.59750i) q^{31} +(-0.380097 - 0.138344i) q^{32} +(-1.09805 + 6.22738i) q^{34} +(4.09470 - 7.09222i) q^{35} +(5.14783 + 8.91631i) q^{37} +(4.84261 - 1.76257i) q^{38} +(11.8351 - 9.93082i) q^{40} +(3.74213 - 3.14002i) q^{41} +(-2.57616 + 0.937645i) q^{43} +(-6.93862 - 12.0180i) q^{44} +(0.656775 - 1.13757i) q^{46} +(0.982501 - 5.57204i) q^{47} +(-0.0643792 - 0.0234321i) q^{49} +(1.91544 + 10.8630i) q^{50} +(-10.3508 - 8.68536i) q^{52} -6.42657 q^{53} +10.5787 q^{55} +(-10.2152 - 8.57159i) q^{56} +(-1.08016 - 6.12590i) q^{58} +(1.55514 + 0.566026i) q^{59} +(2.49571 - 14.1539i) q^{61} +(-9.48056 + 16.4208i) q^{62} +(3.74896 + 6.49338i) q^{64} +(9.67908 - 3.52290i) q^{65} +(-4.50356 + 3.77894i) q^{67} +(-7.96384 + 6.68246i) q^{68} +(18.9140 - 6.88411i) q^{70} +(7.40813 + 12.8313i) q^{71} +(-0.940699 + 1.62934i) q^{73} +(-4.39409 + 24.9201i) q^{74} +(7.96150 + 2.89775i) q^{76} +(-1.58554 - 8.99205i) q^{77} +(13.1710 + 11.0518i) q^{79} +13.0789 q^{80} +12.0063 q^{82} +(-3.04027 - 2.55109i) q^{83} +(-1.37615 - 7.80456i) q^{85} +(-6.33165 - 2.30453i) q^{86} +(2.99119 - 16.9639i) q^{88} +(2.54940 - 4.41569i) q^{89} +(-4.44523 - 7.69937i) q^{91} +(2.02931 - 0.738607i) q^{92} +(10.6527 - 8.93871i) q^{94} +(-4.94756 + 4.15150i) q^{95} +(9.99070 - 3.63632i) q^{97} +(-0.0841927 - 0.145826i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} - 3 q^{4} - 12 q^{5} - 3 q^{7} + 6 q^{8}+O(q^{10}) $ 12 * q + 3 * q^2 - 3 * q^4 - 12 * q^5 - 3 * q^7 + 6 * q^8	$ 12 q + 3 q^{2} - 3 q^{4} - 12 q^{5} - 3 q^{7} + 6 q^{8} - 6 q^{10} + 3 q^{11} + 6 q^{13} + 6 q^{14} + 27 q^{16} - 9 q^{17} - 12 q^{19} - 39 q^{20} - 39 q^{22} - 21 q^{23} + 6 q^{25} - 48 q^{26} + 6 q^{28} - 6 q^{29} + 6 q^{31} - 27 q^{32} - 18 q^{34} + 30 q^{35} - 3 q^{37} - 3 q^{38} + 33 q^{40} + 15 q^{41} - 30 q^{43} - 33 q^{44} + 3 q^{46} + 21 q^{47} - 3 q^{49} - 6 q^{50} + 18 q^{53} + 30 q^{55} - 15 q^{56} - 3 q^{58} - 30 q^{59} - 30 q^{61} - 30 q^{62} - 6 q^{64} + 12 q^{65} - 39 q^{67} - 18 q^{68} + 51 q^{70} - 12 q^{73} - 57 q^{74} + 57 q^{76} + 24 q^{77} + 15 q^{79} + 42 q^{80} - 42 q^{82} + 21 q^{83} + 54 q^{85} + 60 q^{86} + 12 q^{88} - 9 q^{89} - 18 q^{91} + 15 q^{92} + 33 q^{94} - 42 q^{95} - 12 q^{97} + 18 q^{98}+O(q^{100}) $ 12 * q + 3 * q^2 - 3 * q^4 - 12 * q^5 - 3 * q^7 + 6 * q^8 - 6 * q^10 + 3 * q^11 + 6 * q^13 + 6 * q^14 + 27 * q^16 - 9 * q^17 - 12 * q^19 - 39 * q^20 - 39 * q^22 - 21 * q^23 + 6 * q^25 - 48 * q^26 + 6 * q^28 - 6 * q^29 + 6 * q^31 - 27 * q^32 - 18 * q^34 + 30 * q^35 - 3 * q^37 - 3 * q^38 + 33 * q^40 + 15 * q^41 - 30 * q^43 - 33 * q^44 + 3 * q^46 + 21 * q^47 - 3 * q^49 - 6 * q^50 + 18 * q^53 + 30 * q^55 - 15 * q^56 - 3 * q^58 - 30 * q^59 - 30 * q^61 - 30 * q^62 - 6 * q^64 + 12 * q^65 - 39 * q^67 - 18 * q^68 + 51 * q^70 - 12 * q^73 - 57 * q^74 + 57 * q^76 + 24 * q^77 + 15 * q^79 + 42 * q^80 - 42 * q^82 + 21 * q^83 + 54 * q^85 + 60 * q^86 + 12 * q^88 - 9 * q^89 - 18 * q^91 + 15 * q^92 + 33 * q^94 - 42 * q^95 - 12 * q^97 + 18 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{9}\right)$

Coefficient data

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

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

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

$2$	1.88278	+	1.57984i	1.33132	+	1.11711i	0.983766	+	0.179454i	$0.0574333\pi$
$2$	1.88278	+	1.57984i	1.33132	+	1.11711i	0.347557	+	0.937659i	$0.387011\pi$
$3$		0			0
$3$		0			0
$4$	0.701665	+	3.97934i	0.350833	+	1.98967i
$5$	−2.89450	−	1.05351i	−1.29446	−	0.471145i	−0.399271	−	0.916833i	$-0.630737\pi$
$5$	−2.89450	−	1.05351i	−1.29446	−	0.471145i	−0.895188	+	0.445688i	$0.852959\pi$
$6$		0			0
$7$	−0.461673	+	2.61828i	−0.174496	+	0.989615i	0.764228	+	0.644946i	$0.223120\pi$
$7$	−0.461673	+	2.61828i	−0.174496	+	0.989615i	−0.938724	+	0.344669i	$0.887991\pi$
$8$	−2.50784	+	4.34371i	−0.886656	+	1.53573i
$9$		0			0
$10$	−3.78532	−	6.55636i	−1.19702	−	2.07330i
$11$	−3.22722	+	1.17461i	−0.973045	+	0.354159i	−0.779132	−	0.626859i	$-0.784340\pi$
$11$	−3.22722	+	1.17461i	−0.973045	+	0.354159i	−0.193912	+	0.981019i	$0.562118\pi$
$12$		0			0
$13$	−2.56162	+	2.14945i	−0.710465	+	0.596151i	−0.924730	−	0.380625i	$-0.875709\pi$
$13$	−2.56162	+	2.14945i	−0.710465	+	0.596151i	0.214264	+	0.976776i	$0.431265\pi$
$14$	−5.00567	+	4.20026i	−1.33782	+	1.12257i
$15$		0			0
$16$	−3.98997	+	1.45223i	−0.997491	+	0.363057i
$17$	1.28641	+	2.22813i	0.312000	+	0.540400i	0.978795	−	0.204841i	$-0.0656678\pi$
$17$	1.28641	+	2.22813i	0.312000	+	0.540400i	−0.666795	+	0.745241i	$0.732334\pi$
$18$		0			0
$19$	1.04838	−	1.81585i	0.240515	−	0.416585i	−0.720346	−	0.693615i	$-0.756017\pi$
$19$	1.04838	−	1.81585i	0.240515	−	0.416585i	0.960861	+	0.277030i	$0.0893503\pi$
$20$	2.16131	−	12.2574i	0.483284	−	2.74084i
$21$		0			0
$22$	−7.93184	−	2.88695i	−1.69107	−	0.615500i
$23$	−0.0928052	−	0.526325i	−0.0193512	−	0.109746i	0.973602	−	0.228252i	$-0.0733009\pi$
$23$	−0.0928052	−	0.526325i	−0.0193512	−	0.109746i	−0.992953	+	0.118505i	$0.962190\pi$
$24$		0			0
$25$	3.43802	+	2.88484i	0.687605	+	0.576969i
$26$	−8.21874			−1.61183
$27$		0			0
$28$	−10.7430			−2.03023
$29$	−1.93878	−	1.62683i	−0.360022	−	0.302094i	0.444778	−	0.895641i	$-0.353283\pi$
$29$	−1.93878	−	1.62683i	−0.360022	−	0.302094i	−0.804799	+	0.593547i	$0.797727\pi$
$30$		0			0
$31$	1.33964	+	7.59750i	0.240607	+	1.36455i	0.830477	+	0.557053i	$0.188068\pi$
$31$	1.33964	+	7.59750i	0.240607	+	1.36455i	−0.589870	+	0.807498i	$0.700821\pi$
$32$	−0.380097	−	0.138344i	−0.0671922	−	0.0244560i
$33$		0			0
$34$	−1.09805	+	6.22738i	−0.188315	+	1.06799i
$35$	4.09470	−	7.09222i	0.692130	−	1.19880i
$36$		0			0
$37$	5.14783	+	8.91631i	0.846298	+	1.46583i	0.884489	+	0.466561i	$0.154507\pi$
$37$	5.14783	+	8.91631i	0.846298	+	1.46583i	−0.0381907	+	0.999270i	$0.512159\pi$
$38$	4.84261	−	1.76257i	0.785576	−	0.285926i
$39$		0			0
$40$	11.8351	−	9.93082i	1.87129	−	1.57020i
$41$	3.74213	−	3.14002i	0.584423	−	0.490389i	−0.301973	−	0.953316i	$-0.597645\pi$
$41$	3.74213	−	3.14002i	0.584423	−	0.490389i	0.886396	+	0.462927i	$0.153201\pi$
$42$		0			0
$43$	−2.57616	+	0.937645i	−0.392860	+	0.142990i	−0.530894	−	0.847438i	$-0.678144\pi$
$43$	−2.57616	+	0.937645i	−0.392860	+	0.142990i	0.138034	+	0.990427i	$0.455922\pi$
$44$	−6.93862	−	12.0180i	−1.04604	−	1.81179i
$45$		0			0
$46$	0.656775	−	1.13757i	0.0968363	−	0.167725i
$47$	0.982501	−	5.57204i	0.143312	−	0.812765i	−0.825394	−	0.564557i	$-0.809047\pi$
$47$	0.982501	−	5.57204i	0.143312	−	0.812765i	0.968707	−	0.248208i	$-0.0798418\pi$
$48$		0			0
$49$	−0.0643792	−	0.0234321i	−0.00919703	−	0.00334745i
$50$	1.91544	+	10.8630i	0.270885	+	1.53626i
$51$		0			0
$52$	−10.3508	−	8.68536i	−1.43540	−	1.20444i
$53$	−6.42657			−0.882758			−0.441379	−	0.897321i	$-0.645511\pi$
$53$	−6.42657			−0.882758			−0.441379	+	0.897321i	$0.645511\pi$
$54$		0			0
$55$	10.5787			1.42643
$56$	−10.2152	−	8.57159i	−1.36507	−	1.14543i
$57$		0			0
$58$	−1.08016	−	6.12590i	−0.141832	−	0.804370i
$59$	1.55514	+	0.566026i	0.202463	+	0.0736903i	0.441261	−	0.897379i	$-0.354531\pi$
$59$	1.55514	+	0.566026i	0.202463	+	0.0736903i	−0.238798	+	0.971069i	$0.576754\pi$
$60$		0			0
$61$	2.49571	−	14.1539i	0.319543	−	1.81222i	−0.225993	−	0.974129i	$-0.572563\pi$
$61$	2.49571	−	14.1539i	0.319543	−	1.81222i	0.545536	−	0.838087i	$-0.316326\pi$
$62$	−9.48056	+	16.4208i	−1.20403	+	2.08544i
$63$		0			0
$64$	3.74896	+	6.49338i	0.468620	+	0.811673i
$65$	9.67908	−	3.52290i	1.20054	−	0.436962i
$66$		0			0
$67$	−4.50356	+	3.77894i	−0.550198	+	0.461671i	−0.875008	−	0.484109i	$-0.839144\pi$
$67$	−4.50356	+	3.77894i	−0.550198	+	0.461671i	0.324810	+	0.945779i	$0.394700\pi$
$68$	−7.96384	+	6.68246i	−0.965758	+	0.810367i
$69$		0			0
$70$	18.9140	−	6.88411i	2.26065	−	0.822809i
$71$	7.40813	+	12.8313i	0.879184	+	1.52279i	0.852238	+	0.523154i	$0.175245\pi$
$71$	7.40813	+	12.8313i	0.879184	+	1.52279i	0.0269456	+	0.999637i	$0.491422\pi$
$72$		0			0
$73$	−0.940699	+	1.62934i	−0.110101	+	0.190700i	−0.915811	−	0.401610i	$-0.868451\pi$
$73$	−0.940699	+	1.62934i	−0.110101	+	0.190700i	0.805710	+	0.592310i	$0.201784\pi$
$74$	−4.39409	+	24.9201i	−0.510803	+	2.89691i
$75$		0			0
$76$	7.96150	+	2.89775i	0.913247	+	0.332395i
$77$	−1.58554	−	8.99205i	−0.180689	−	1.02474i
$78$		0			0
$79$	13.1710	+	11.0518i	1.48185	+	1.24342i	0.904181	+	0.427150i	$0.140482\pi$
$79$	13.1710	+	11.0518i	1.48185	+	1.24342i	0.577670	+	0.816271i	$0.303962\pi$
$80$	13.0789			1.46227
$81$		0			0
$82$	12.0063			1.32588
$83$	−3.04027	−	2.55109i	−0.333712	−	0.280018i	0.460498	−	0.887661i	$-0.347671\pi$
$83$	−3.04027	−	2.55109i	−0.333712	−	0.280018i	−0.794211	+	0.607643i	$0.792115\pi$
$84$		0			0
$85$	−1.37615	−	7.80456i	−0.149265	−	0.846523i
$86$	−6.33165	−	2.30453i	−0.682760	−	0.248504i
$87$		0			0
$88$	2.99119	−	16.9639i	0.318862	−	1.80835i
$89$	2.54940	−	4.41569i	0.270236	−	0.468062i	−0.698686	−	0.715428i	$-0.746232\pi$
$89$	2.54940	−	4.41569i	0.270236	−	0.468062i	0.968922	+	0.247366i	$0.0795651\pi$
$90$		0			0
$91$	−4.44523	−	7.69937i	−0.465987	−	0.807113i
$92$	2.02931	−	0.738607i	0.211570	−	0.0770051i
$93$		0			0
$94$	10.6527	−	8.93871i	1.09875	−	0.921957i
$95$	−4.94756	+	4.15150i	−0.507609	+	0.425935i
$96$		0			0
$97$	9.99070	−	3.63632i	1.01440	−	0.369212i	0.219280	−	0.975662i	$-0.429629\pi$
$97$	9.99070	−	3.63632i	1.01440	−	0.369212i	0.795122	+	0.606450i	$0.207407\pi$
$98$	−0.0841927	−	0.145826i	−0.00850475	−	0.0147307i
$99$		0			0
$100$	−9.06744	+	15.7053i	−0.906744	+	1.57053i
$101$	−0.982517	+	5.57213i	−0.0977641	+	0.554448i	0.896101	+	0.443850i	$0.146388\pi$
$101$	−0.982517	+	5.57213i	−0.0977641	+	0.554448i	−0.993865	+	0.110598i	$0.964723\pi$
$102$		0			0
$103$	−9.74512	−	3.54693i	−0.960215	−	0.349490i	−0.186097	−	0.982531i	$-0.559584\pi$
$103$	−9.74512	−	3.54693i	−0.960215	−	0.349490i	−0.774118	+	0.633042i	$0.781806\pi$
$104$	−2.91247	−	16.5174i	−0.285591	−	1.61967i
$105$		0			0
$106$	−12.0998	−	10.1529i	−1.17524	−	0.986140i
$107$	14.2457			1.37719			0.688594	−	0.725147i	$-0.258228\pi$
$107$	14.2457			1.37719			0.688594	+	0.725147i	$0.258228\pi$
$108$		0			0
$109$	5.76064			0.551769			0.275884	−	0.961191i	$-0.411029\pi$
$109$	5.76064			0.551769			0.275884	+	0.961191i	$0.411029\pi$
$110$	19.9173	+	16.7126i	1.89904	+	1.59348i
$111$		0			0
$112$	−1.96028	−	11.1173i	−0.185229	−	1.05048i
$113$	−10.7282	−	3.90474i	−1.00922	−	0.367327i	−0.216088	−	0.976374i	$-0.569330\pi$
$113$	−10.7282	−	3.90474i	−1.00922	−	0.367327i	−0.793134	+	0.609047i	$0.791552\pi$
$114$		0			0
$115$	−0.285865	+	1.62122i	−0.0266570	+	0.151179i
$116$	5.11333	−	8.85654i	0.474761	−	0.822309i
$117$		0			0
$118$	2.03376	+	3.52257i	0.187223	+	0.324279i
$119$	−6.42775	+	2.33951i	−0.589231	+	0.214462i
$120$		0			0
$121$	0.608773	−	0.510821i	0.0553430	−	0.0464383i
$122$	27.0596	−	22.7057i	2.44987	−	2.05568i
$123$		0			0
$124$	−29.2931	+	10.6618i	−2.63059	+	0.957458i
$125$	0.788517	+	1.36575i	0.0705271	+	0.122157i
$126$		0			0
$127$	−1.29510	+	2.24317i	−0.114921	+	0.199049i	−0.917748	−	0.397163i	$-0.869995\pi$
$127$	−1.29510	+	2.24317i	−0.114921	+	0.199049i	0.802827	+	0.596212i	$0.203328\pi$
$128$	−3.34052	+	18.9450i	−0.295263	+	1.67452i
$129$		0			0
$130$	23.7891	+	8.65854i	2.08645	+	0.759404i
$131$	0.765960	+	4.34397i	0.0669222	+	0.379535i	0.999812	+	0.0193735i	$0.00616717\pi$
$131$	0.765960	+	4.34397i	0.0669222	+	0.379535i	−0.932890	+	0.360161i	$0.882722\pi$
$132$		0			0
$133$	4.27039	+	3.58328i	0.370290	+	0.310710i
$134$	−14.4493			−1.24823
$135$		0			0
$136$	−12.9044			−1.10655
$137$	−13.9173	−	11.6780i	−1.18903	−	0.997716i	−0.999876	−	0.0157685i	$-0.994981\pi$
$137$	−13.9173	−	11.6780i	−1.18903	−	0.997716i	−0.189156	−	0.981947i	$-0.560575\pi$
$138$		0			0
$139$	0.339993	+	1.92820i	0.0288379	+	0.163548i	0.995826	−	0.0912747i	$-0.0290941\pi$
$139$	0.339993	+	1.92820i	0.0288379	+	0.163548i	−0.966988	+	0.254822i	$0.917983\pi$
$140$	31.0955	+	11.3178i	2.62805	+	0.956531i
$141$		0			0
$142$	−6.32344	+	35.8620i	−0.530652	+	3.00948i
$143$	5.74214	−	9.94568i	0.480182	−	0.831700i
$144$		0			0
$145$	3.89791	+	6.75138i	0.323704	+	0.560671i
$146$	−4.34521	+	1.58153i	−0.359613	+	0.130888i
$147$		0			0
$148$	−31.8690	+	26.7412i	−2.61961	+	2.19812i
$149$	−5.60376	+	4.70211i	−0.459078	+	0.385212i	−0.842792	−	0.538240i	$-0.819089\pi$
$149$	−5.60376	+	4.70211i	−0.459078	+	0.385212i	0.383714	+	0.923452i	$0.374645\pi$
$150$		0			0
$151$	−4.55844	+	1.65913i	−0.370960	+	0.135018i	−0.520771	−	0.853696i	$-0.674356\pi$
$151$	−4.55844	+	1.65913i	−0.370960	+	0.135018i	0.149811	+	0.988715i	$0.452133\pi$
$152$	5.25835	+	9.10773i	0.426508	+	0.738734i
$153$		0			0
$154$	11.2208	−	19.4349i	0.904194	−	1.56611i
$155$	4.12646	−	23.4023i	0.331445	−	1.87972i
$156$		0			0
$157$	−1.38765	−	0.505062i	−0.110746	−	0.0403083i	0.286053	−	0.958214i	$-0.407657\pi$
$157$	−1.38765	−	0.505062i	−0.110746	−	0.0403083i	−0.396799	+	0.917906i	$0.629879\pi$
$158$	7.33802	+	41.6160i	0.583782	+	3.31079i
$159$		0			0
$160$	0.954443	+	0.800873i	0.0754554	+	0.0633146i
$161$	1.42091			0.111983
$162$		0			0
$163$	−17.2536			−1.35141			−0.675703	−	0.737174i	$-0.736160\pi$
$163$	−17.2536			−1.35141			−0.675703	+	0.737174i	$0.736160\pi$
$164$	15.1209	+	12.6880i	1.18075	+	0.990765i
$165$		0			0
$166$	−1.69384	−	9.60625i	−0.131468	−	0.745589i
$167$	6.42784	+	2.33954i	0.497401	+	0.181039i	0.578525	−	0.815665i	$-0.303629\pi$
$167$	6.42784	+	2.33954i	0.497401	+	0.181039i	−0.0811236	+	0.996704i	$0.525851\pi$
$168$		0			0
$169$	−0.315685	+	1.79034i	−0.0242835	+	0.137718i
$170$	9.73894	−	16.8683i	0.746942	−	1.29374i
$171$		0			0
$172$	−5.53881	−	9.59350i	−0.422330	−	0.731497i
$173$	−22.5220	+	8.19733i	−1.71231	+	0.623231i	−0.997130	−	0.0757055i	$-0.975879\pi$
$173$	−22.5220	+	8.19733i	−1.71231	+	0.623231i	−0.715184	+	0.698937i	$0.753657\pi$
$174$		0			0
$175$	−9.14056	+	7.66984i	−0.690961	+	0.579785i
$176$	11.1707	−	9.37334i	0.842024	−	0.706542i
$177$		0			0
$178$	11.7760	−	4.28612i	0.882649	−	0.321258i
$179$	−10.2861	−	17.8161i	−0.768820	−	1.33163i	−0.938203	−	0.346084i	$-0.887511\pi$
$179$	−10.2861	−	17.8161i	−0.768820	−	1.33163i	0.169384	−	0.985550i	$-0.445822\pi$
$180$		0			0
$181$	7.73507	−	13.3975i	0.574943	−	0.995830i	−0.421105	−	0.907012i	$-0.638358\pi$
$181$	7.73507	−	13.3975i	0.574943	−	0.995830i	0.996048	−	0.0888184i	$-0.0283091\pi$
$182$	3.79437	−	21.5189i	0.281257	−	1.59509i
$183$		0			0
$184$	2.51894	+	0.916820i	0.185699	+	0.0675888i
$185$	−5.50697	−	31.2316i	−0.404880	−	2.29619i
$186$		0			0
$187$	−6.76872	−	5.67963i	−0.494978	−	0.415336i
$188$	22.8624			1.66741
$189$		0			0
$190$	−15.8738			−1.15161
$191$	8.38884	+	7.03907i	0.606995	+	0.509329i	0.893685	−	0.448694i	$-0.148111\pi$
$191$	8.38884	+	7.03907i	0.606995	+	0.509329i	−0.286691	+	0.958023i	$0.592555\pi$
$192$		0			0
$193$	0.198801	+	1.12746i	0.0143100	+	0.0811562i	0.991126	−	0.132923i	$-0.0424362\pi$
$193$	0.198801	+	1.12746i	0.0143100	+	0.0811562i	−0.976816	+	0.214079i	$0.931325\pi$
$194$	24.5550	+	8.93730i	1.76295	+	0.641661i
$195$		0			0
$196$	0.0480717	−	0.272628i	0.00343370	−	0.0194735i
$197$	−2.52097	+	4.36645i	−0.179612	+	0.311097i	−0.941748	−	0.336320i	$-0.890818\pi$
$197$	−2.52097	+	4.36645i	−0.179612	+	0.311097i	0.762136	+	0.647417i	$0.224151\pi$
$198$		0			0
$199$	−6.86291	−	11.8869i	−0.486499	−	0.842640i	0.513381	−	0.858161i	$-0.328393\pi$
$199$	−6.86291	−	11.8869i	−0.486499	−	0.842640i	−0.999880	+	0.0155206i	$0.995059\pi$
$200$	−21.1529	+	7.69904i	−1.49574	+	0.544404i
$201$		0			0
$202$	−10.6529	+	8.93886i	−0.749536	+	0.628936i
$203$	5.15456	−	4.32519i	0.361779	−	0.303569i
$204$		0			0
$205$	−14.1397	+	5.14641i	−0.987556	+	0.359441i
$206$	−12.7443	−	22.0738i	−0.887938	−	1.53795i
$207$		0			0
$208$	7.09927	−	12.2963i	0.492246	−	0.852595i
$209$	−1.25044	+	7.09160i	−0.0864948	+	0.490536i
$210$		0			0
$211$	5.48323	+	1.99573i	0.377481	+	0.137392i	0.523791	−	0.851847i	$-0.324517\pi$
$211$	5.48323	+	1.99573i	0.377481	+	0.137392i	−0.146310	+	0.989239i	$0.546740\pi$
$212$	−4.50930	−	25.5735i	−0.309700	−	1.75640i
$213$		0			0
$214$	26.8215	+	22.5059i	1.83348	+	1.53847i
$215$	8.44451			0.575911
$216$		0			0
$217$	−20.5108			−1.39237
$218$	10.8460	+	9.10086i	0.734583	+	0.616388i
$219$		0			0
$220$	7.42269	+	42.0961i	0.500437	+	2.83812i
$221$	−8.08454	−	2.94253i	−0.543825	−	0.197936i
$222$		0			0
$223$	1.51572	−	8.59607i	0.101500	−	0.575635i	−0.891061	−	0.453884i	$-0.850038\pi$
$223$	1.51572	−	8.59607i	0.101500	−	0.575635i	0.992561	−	0.121751i	$-0.0388510\pi$
$224$	0.537703	−	0.931329i	0.0359268	−	0.0622270i
$225$		0			0
$226$	−14.0299	−	24.3005i	−0.933256	−	1.61645i
$227$	22.8181	−	8.30511i	1.51449	−	0.551230i	0.554726	−	0.832033i	$-0.312823\pi$
$227$	22.8181	−	8.30511i	1.51449	−	0.551230i	0.959765	+	0.280804i	$0.0906010\pi$
$228$		0			0
$229$	13.9048	−	11.6675i	0.918855	−	0.771011i	−0.0549279	−	0.998490i	$-0.517493\pi$
$229$	13.9048	−	11.6675i	0.918855	−	0.771011i	0.973783	+	0.227479i	$0.0730485\pi$
$230$	−3.09948	+	2.60077i	−0.204374	+	0.171490i
$231$		0			0
$232$	11.9286	−	4.34166i	0.783151	−	0.285044i
$233$	5.26900	+	9.12617i	0.345183	+	0.597875i	0.985387	−	0.170330i	$-0.0544834\pi$
$233$	5.26900	+	9.12617i	0.345183	+	0.597875i	−0.640204	+	0.768205i	$0.721150\pi$
$234$		0			0
$235$	−8.71406	+	15.0932i	−0.568442	+	0.984571i
$236$	−1.16122	+	6.58561i	−0.0755890	+	0.428687i
$237$		0			0
$238$	−15.7981	−	5.75002i	−1.02404	−	0.372718i
$239$	1.65601	+	9.39172i	0.107119	+	0.607500i	0.990353	+	0.138568i	$0.0442499\pi$
$239$	1.65601	+	9.39172i	0.107119	+	0.607500i	−0.883234	+	0.468932i	$0.844639\pi$
$240$		0			0
$241$	−5.39087	−	4.52348i	−0.347256	−	0.291383i	0.452431	−	0.891799i	$-0.350557\pi$
$241$	−5.39087	−	4.52348i	−0.347256	−	0.291383i	−0.799687	+	0.600417i	$0.795001\pi$
$242$	1.95320			0.125556
$243$		0			0
$244$	58.0742			3.71782
$245$	0.161660	+	0.135649i	0.0103281	+	0.00866627i
$246$		0			0
$247$	1.21753	+	6.90496i	0.0774697	+	0.439352i
$248$	−36.3609	−	13.2343i	−2.30892	−	0.840379i
$249$		0			0
$250$	−0.673063	+	3.81713i	−0.0425683	+	0.241417i
$251$	−7.79350	+	13.4987i	−0.491921	+	0.852033i	−0.999957	−	0.00930331i	$-0.997039\pi$
$251$	−7.79350	+	13.4987i	−0.491921	+	0.852033i	0.508035	+	0.861336i	$0.330372\pi$
$252$		0			0
$253$	0.917731	+	1.58956i	0.0576973	+	0.0999346i
$254$	−5.98223	+	2.17735i	−0.375358	+	0.136619i
$255$		0			0
$256$	−24.7320	+	20.7526i	−1.54575	+	1.29704i
$257$	9.33791	−	7.83544i	0.582483	−	0.488761i	−0.303279	−	0.952902i	$-0.598081\pi$
$257$	9.33791	−	7.83544i	0.582483	−	0.488761i	0.885761	+	0.464141i	$0.153637\pi$
$258$		0			0
$259$	−25.7220	+	9.36203i	−1.59828	+	0.581728i
$260$	20.8103	+	36.0445i	1.29060	+	2.23538i
$261$		0			0
$262$	−5.42064	+	9.38882i	−0.334888	+	0.580043i
$263$	−1.19637	+	6.78496i	−0.0737715	+	0.418379i	0.925448	+	0.378875i	$0.123689\pi$
$263$	−1.19637	+	6.78496i	−0.0737715	+	0.418379i	−0.999219	+	0.0395040i	$0.987422\pi$
$264$		0			0
$265$	18.6017	+	6.77047i	1.14269	+	0.415907i
$266$	2.37919	+	13.4930i	0.145877	+	0.827311i
$267$		0			0
$268$	−18.1977	−	15.2697i	−1.11160	−	0.932743i
$269$	7.05875			0.430380			0.215190	−	0.976572i	$-0.430963\pi$
$269$	7.05875			0.430380			0.215190	+	0.976572i	$0.430963\pi$
$270$		0			0
$271$	23.7575			1.44316			0.721581	−	0.692330i	$-0.243416\pi$
$271$	23.7575			1.44316			0.721581	+	0.692330i	$0.243416\pi$
$272$	−8.36848	−	7.02199i	−0.507413	−	0.425770i
$273$		0			0
$274$	−7.75380	−	43.9740i	−0.468424	−	2.65656i
$275$	−14.4838	−	5.27169i	−0.873409	−	0.317895i
$276$		0			0
$277$	−0.0181399	+	0.102877i	−0.00108992	+	0.00618126i	−0.985348	−	0.170557i	$-0.945443\pi$
$277$	−0.0181399	+	0.102877i	−0.00108992	+	0.00618126i	0.984258	+	0.176738i	$0.0565545\pi$
$278$	−2.40611	+	4.16750i	−0.144309	+	0.249950i
$279$		0			0
$280$	20.5377	+	35.5723i	1.22736	+	2.12585i
$281$	−7.66056	+	2.78822i	−0.456991	+	0.166331i	−0.560250	−	0.828323i	$-0.689295\pi$
$281$	−7.66056	+	2.78822i	−0.456991	+	0.166331i	0.103260	+	0.994654i	$0.467073\pi$
$282$		0			0
$283$	18.0909	−	15.1801i	1.07539	−	0.902361i	0.0798620	−	0.996806i	$-0.474552\pi$
$283$	18.0909	−	15.1801i	1.07539	−	0.902361i	0.995530	+	0.0944449i	$0.0301076\pi$
$284$	−45.8619	+	38.4827i	−2.72141	+	2.28353i
$285$		0			0
$286$	26.5237	−	9.65384i	1.56838	−	0.570844i
$287$	6.49380	+	11.2476i	0.383317	+	0.663925i
$288$		0			0
$289$	5.19030	−	8.98987i	0.305312	−	0.528816i
$290$	−3.32718	+	18.8694i	−0.195379	+	1.10805i
$291$		0			0
$292$	−7.14375	−	2.60011i	−0.418056	−	0.152160i
$293$	3.75527	+	21.2972i	0.219385	+	1.24420i	0.873132	+	0.487483i	$0.162085\pi$
$293$	3.75527	+	21.2972i	0.219385	+	1.24420i	−0.653747	+	0.756713i	$0.726804\pi$
$294$		0			0
$295$	−3.90505	−	3.27673i	−0.227361	−	0.190778i
$296$	−51.6398			−3.00150
$297$		0			0
$298$	−17.9792			−1.04151
$299$	1.36904	+	1.14876i	0.0791737	+	0.0664347i
$300$		0			0
$301$	−1.26567	−	7.17798i	−0.0729521	−	0.413732i
$302$	−11.2037	−	4.07780i	−0.644699	−	0.234651i
$303$		0			0
$304$	−1.54598	+	8.76767i	−0.0886678	+	0.502860i
$305$	−22.1351	+	38.3391i	−1.26745	+	2.19529i
$306$		0			0
$307$	−8.17997	−	14.1681i	−0.466855	−	0.808617i	0.532428	−	0.846475i	$-0.321280\pi$
$307$	−8.17997	−	14.1681i	−0.466855	−	0.808617i	−0.999283	+	0.0378581i	$0.987946\pi$
$308$	34.6699	−	12.6188i	1.97550	−	0.719024i
$309$		0			0
$310$	44.7410	−	37.5421i	2.54112	−	2.13225i
$311$	5.94057	−	4.98473i	0.336859	−	0.282658i	−0.458629	−	0.888628i	$-0.651659\pi$
$311$	5.94057	−	4.98473i	0.336859	−	0.282658i	0.795488	+	0.605970i	$0.207215\pi$
$312$		0			0
$313$	−14.4882	+	5.27329i	−0.818923	+	0.298064i	−0.717305	−	0.696760i	$-0.754624\pi$
$313$	−14.4882	+	5.27329i	−0.818923	+	0.298064i	−0.101619	+	0.994823i	$0.532402\pi$
$314$	−1.81471	−	3.14317i	−0.102410	−	0.177380i
$315$		0			0
$316$	−34.7371	+	60.1664i	−1.95412	+	3.38463i
$317$	−1.49966	+	8.50500i	−0.0842294	+	0.477689i	0.913291	+	0.407308i	$0.133532\pi$
$317$	−1.49966	+	8.50500i	−0.0842294	+	0.477689i	−0.997520	+	0.0703805i	$0.977579\pi$
$318$		0			0
$319$	8.16776	+	2.97282i	0.457307	+	0.166446i
$320$	−4.01050	−	22.7447i	−0.224194	−	1.27147i
$321$		0			0
$322$	2.67525	+	2.24480i	0.149086	+	0.125098i
$323$	5.39459			0.300163
$324$		0			0
$325$	−15.0077			−0.832480
$326$	−32.4847	−	27.2579i	−1.79916	−	1.50967i
$327$		0			0
$328$	4.25467	+	24.1294i	0.234925	+	1.33232i
$329$	14.1355	+	5.14492i	0.779318	+	0.283648i
$330$		0			0
$331$	3.56752	−	20.2324i	0.196089	−	1.11207i	−0.714772	−	0.699358i	$-0.753469\pi$
$331$	3.56752	−	20.2324i	0.196089	−	1.11207i	0.910860	−	0.412715i	$-0.135420\pi$
$332$	8.01839	−	13.8883i	0.440066	−	0.762217i
$333$		0			0
$334$	8.40609	+	14.5598i	0.459961	+	0.796675i
$335$	17.0167	−	6.19358i	0.929723	−	0.338391i
$336$		0			0
$337$	12.2400	−	10.2706i	0.666756	−	0.559475i	−0.245347	−	0.969435i	$-0.578902\pi$
$337$	12.2400	−	10.2706i	0.666756	−	0.559475i	0.912103	+	0.409961i	$0.134458\pi$
$338$	−3.42281	+	2.87208i	−0.186176	+	0.156220i
$339$		0			0
$340$	30.0914	−	10.9524i	1.63194	−	0.593976i
$341$	−13.2475	−	22.9453i	−0.717390	−	1.24256i
$342$		0			0
$343$	−9.21426	+	15.9596i	−0.497523	+	0.861736i
$344$	2.38774	−	13.5415i	0.128738	−	0.730111i
$345$		0			0
$346$	−55.3543	−	20.1473i	−2.97586	−	1.08313i
$347$	1.70249	+	9.65533i	0.0913947	+	0.518325i	0.995793	+	0.0916351i	$0.0292093\pi$
$347$	1.70249	+	9.65533i	0.0913947	+	0.518325i	−0.904398	+	0.426690i	$0.859680\pi$
$348$		0			0
$349$	−7.22761	−	6.06468i	−0.386885	−	0.324635i	0.428513	−	0.903536i	$-0.359038\pi$
$349$	−7.22761	−	6.06468i	−0.386885	−	0.324635i	−0.815398	+	0.578900i	$0.803482\pi$
$350$	−29.3267			−1.56758
$351$		0			0
$352$	1.38916			0.0740424
$353$	2.59319	+	2.17594i	0.138021	+	0.115814i	0.709185	−	0.705023i	$-0.249063\pi$
$353$	2.59319	+	2.17594i	0.138021	+	0.115814i	−0.571163	+	0.820836i	$0.693508\pi$
$354$		0			0
$355$	−7.92496	−	44.9447i	−0.420613	−	2.38541i
$356$	19.3604	+	7.04659i	1.02610	+	0.373469i
$357$		0			0
$358$	8.78003	−	49.7940i	0.464039	−	2.63170i
$359$	17.6137	−	30.5078i	0.929614	−	1.61014i	0.145646	−	0.989337i	$-0.453474\pi$
$359$	17.6137	−	30.5078i	0.929614	−	1.61014i	0.783968	−	0.620801i	$-0.213193\pi$
$360$		0			0
$361$	7.30179	+	12.6471i	0.384305	+	0.665636i
$362$	35.7293	−	13.0044i	1.87789	−	0.683496i
$363$		0			0
$364$	27.5194	−	23.0915i	1.44241	−	1.21032i
$365$	4.43938	−	3.72508i	0.232368	−	0.194980i
$366$		0			0
$367$	29.6430	−	10.7892i	1.54735	−	0.563190i	0.579558	−	0.814931i	$-0.303225\pi$
$367$	29.6430	−	10.7892i	1.54735	−	0.563190i	0.967795	+	0.251741i	$0.0810031\pi$
$368$	1.13463	+	1.96524i	0.0591469	+	0.102445i
$369$		0			0
$370$	38.9724	−	67.5021i	2.02608	−	3.50927i
$371$	2.96697	−	16.8265i	0.154038	−	0.873591i
$372$		0			0
$373$	−13.5713	−	4.93956i	−0.702697	−	0.255761i	−0.0341350	−	0.999417i	$-0.510868\pi$
$373$	−13.5713	−	4.93956i	−0.702697	−	0.255761i	−0.668562	+	0.743656i	$0.733090\pi$
$374$	−3.77109	−	21.3869i	−0.194999	−	1.10589i
$375$		0			0
$376$	21.7394	+	18.2415i	1.12112	+	0.940733i
$377$	8.46320			0.435877
$378$		0			0
$379$	1.00099			0.0514176			0.0257088	−	0.999669i	$-0.491816\pi$
$379$	1.00099			0.0514176			0.0257088	+	0.999669i	$0.491816\pi$
$380$	−19.9918	−	16.7751i	−1.02556	−	0.860543i
$381$		0			0
$382$	4.67372	+	26.5060i	0.239128	+	1.35616i
$383$	3.86903	+	1.40821i	0.197698	+	0.0719563i	0.438972	−	0.898501i	$-0.355343\pi$
$383$	3.86903	+	1.40821i	0.197698	+	0.0719563i	−0.241273	+	0.970457i	$0.577565\pi$
$384$		0			0
$385$	−4.88388	+	27.6979i	−0.248906	+	1.41161i
$386$	−1.40690	+	2.43683i	−0.0716094	+	0.124031i
$387$		0			0
$388$	21.4803	+	37.2049i	1.09050	+	1.88879i
$389$	−14.5840	+	5.30812i	−0.739436	+	0.269133i	−0.684153	−	0.729338i	$-0.739828\pi$
$389$	−14.5840	+	5.30812i	−0.739436	+	0.269133i	−0.0552823	+	0.998471i	$0.517606\pi$
$390$		0			0
$391$	1.05333	−	0.883850i	0.0532693	−	0.0446982i
$392$	0.263235	−	0.220880i	0.0132954	−	0.0111561i
$393$		0			0
$394$	−11.6447	+	4.23833i	−0.586652	+	0.213524i
$395$	−26.4802	−	45.8651i	−1.33237	−	2.30772i
$396$		0			0
$397$	0.774463	−	1.34141i	0.0388692	−	0.0673234i	−0.845936	−	0.533284i	$-0.820958\pi$
$397$	0.774463	−	1.34141i	0.0388692	−	0.0673234i	0.884806	+	0.465960i	$0.154291\pi$
$398$	5.85805	−	33.2226i	0.293637	−	1.66530i
$399$		0			0
$400$	−17.9070	−	6.51763i	−0.895352	−	0.325882i
$401$	−1.38005	−	7.82664i	−0.0689163	−	0.390844i	−0.999682	−	0.0252269i	$-0.991969\pi$
$401$	−1.38005	−	7.82664i	−0.0689163	−	0.390844i	0.930765	−	0.365617i	$-0.119142\pi$
$402$		0			0
$403$	−19.7621	−	16.5824i	−0.984422	−	0.826028i
$404$	−22.8628			−1.13747
$405$		0			0
$406$	16.5380			0.820766
$407$	−27.0864	−	22.7282i	−1.34262	−	1.12660i
$408$		0			0
$409$	4.59393	+	26.0535i	0.227155	+	1.28826i	0.858522	+	0.512777i	$0.171383\pi$
$409$	4.59393	+	26.0535i	0.227155	+	1.28826i	−0.631366	+	0.775485i	$0.717506\pi$
$410$	−34.7523	−	12.6488i	−1.71629	−	0.624680i
$411$		0			0
$412$	7.27665	−	41.2679i	0.358495	−	2.03312i
$413$	−2.19998	+	3.81048i	−0.108254	+	0.187501i
$414$		0			0
$415$	6.11245	+	10.5871i	0.300048	+	0.519699i
$416$	1.27103	−	0.462616i	0.0623172	−	0.0226816i
$417$		0			0
$418$	−13.5579	+	11.3764i	−0.663137	+	0.556438i
$419$	−29.3701	+	24.6445i	−1.43483	+	1.20396i	−0.492035	+	0.870576i	$0.663747\pi$
$419$	−29.3701	+	24.6445i	−1.43483	+	1.20396i	−0.942791	+	0.333386i	$0.891809\pi$
$420$		0			0
$421$	−6.90157	+	2.51197i	−0.336362	+	0.122426i	−0.504679	−	0.863307i	$-0.668389\pi$
$421$	−6.90157	+	2.51197i	−0.336362	+	0.122426i	0.168317	+	0.985733i	$0.446167\pi$
$422$	7.17076	+	12.4201i	0.349067	+	0.604602i
$423$		0			0
$424$	16.1168	−	27.9152i	0.782702	−	1.35568i
$425$	−2.00509	+	11.3714i	−0.0972612	+	0.551596i
$426$		0			0
$427$	35.9065	+	13.0689i	1.73764	+	0.632449i
$428$	9.99574	+	56.6887i	0.483162	+	2.74015i
$429$		0			0
$430$	15.8991	+	13.3409i	0.766724	+	0.643358i
$431$	15.8463			0.763289			0.381644	−	0.924309i	$-0.375358\pi$
$431$	15.8463			0.763289			0.381644	+	0.924309i	$0.375358\pi$
$432$		0			0
$433$	−23.8507			−1.14619			−0.573097	−	0.819488i	$-0.694258\pi$
$433$	−23.8507			−1.14619			−0.573097	+	0.819488i	$0.694258\pi$
$434$	−38.6173	−	32.4037i	−1.85369	−	1.55543i
$435$		0			0
$436$	4.04204	+	22.9235i	0.193579	+	1.09784i
$437$	−1.05302	−	0.383269i	−0.0503729	−	0.0183342i
$438$		0			0
$439$	−3.72822	+	21.1438i	−0.177938	+	1.00914i	0.756760	+	0.653693i	$0.226781\pi$
$439$	−3.72822	+	21.1438i	−0.177938	+	1.00914i	−0.934698	+	0.355443i	$0.884330\pi$
$440$	−26.5296	+	45.9507i	−1.26475	+	2.19061i
$441$		0			0
$442$	−10.5727	−	18.3124i	−0.502890	−	0.871031i
$443$	29.6453	−	10.7900i	1.40849	−	0.512649i	0.477806	−	0.878466i	$-0.341432\pi$
$443$	29.6453	−	10.7900i	1.40849	−	0.512649i	0.930687	+	0.365816i	$0.119210\pi$
$444$		0			0
$445$	−12.0312	+	10.0954i	−0.570334	+	0.478567i
$446$	16.4341	−	13.7899i	0.778179	−	0.652970i
$447$		0			0
$448$	−18.7323	+	6.81799i	−0.885016	+	0.322120i
$449$	10.3949	+	18.0045i	0.490565	+	0.849684i	0.999941	−	0.0108605i	$-0.00345708\pi$
$449$	10.3949	+	18.0045i	0.490565	+	0.849684i	−0.509376	+	0.860544i	$0.670124\pi$
$450$		0			0
$451$	−8.38839	+	14.5291i	−0.394994	+	0.684149i
$452$	8.01070	−	45.4309i	0.376791	−	2.13689i
$453$		0			0
$454$	56.0821	+	20.4122i	2.63206	+	0.957993i
$455$	4.75535	+	26.9689i	0.222934	+	1.26432i
$456$		0			0
$457$	−13.3504	−	11.2023i	−0.624506	−	0.524023i	0.274710	−	0.961527i	$-0.411418\pi$
$457$	−13.3504	−	11.2023i	−0.624506	−	0.524023i	−0.899216	+	0.437504i	$0.855863\pi$
$458$	44.6124			2.08460
$459$		0			0
$460$	−6.65196			−0.310149
$461$	23.7508	+	19.9293i	1.10619	+	0.928199i	0.997825	−	0.0659123i	$-0.0209957\pi$
$461$	23.7508	+	19.9293i	1.10619	+	0.928199i	0.108360	+	0.994112i	$0.465440\pi$
$462$		0			0
$463$	1.12662	+	6.38938i	0.0523585	+	0.296940i	0.999731	−	0.0231935i	$-0.00738338\pi$
$463$	1.12662	+	6.38938i	0.0523585	+	0.296940i	−0.947372	+	0.320133i	$0.896272\pi$
$464$	10.0982	+	3.67544i	0.468796	+	0.170628i
$465$		0			0
$466$	−4.49752	+	25.5067i	−0.208343	+	1.18157i
$467$	0.971950	−	1.68347i	0.0449765	−	0.0779016i	−0.842661	−	0.538445i	$-0.819012\pi$
$467$	0.971950	−	1.68347i	0.0449765	−	0.0779016i	0.887637	+	0.460543i	$0.152345\pi$
$468$		0			0
$469$	−7.81513	−	13.5362i	−0.360869	−	0.625044i
$470$	−40.2514	+	14.6503i	−1.85666	+	0.675768i
$471$		0			0
$472$	−6.35871	+	5.33559i	−0.292683	+	0.245590i
$473$	7.21247	−	6.05198i	0.331630	−	0.278270i
$474$		0			0
$475$	8.84280	−	3.21852i	0.405736	−	0.147676i
$476$	−13.8198	−	23.9367i	−0.633431	−	1.09713i
$477$		0			0
$478$	−11.7195	+	20.2987i	−0.536036	+	0.928442i
$479$	−0.230846	+	1.30919i	−0.0105476	+	0.0598186i	−0.989627	−	0.143659i	$-0.954113\pi$
$479$	−0.230846	+	1.30919i	−0.0105476	+	0.0598186i	0.979080	+	0.203477i	$0.0652243\pi$
$480$		0			0
$481$	−32.3520	−	11.7752i	−1.47512	−	0.536901i
$482$	−3.00345	−	17.0334i	−0.136803	−	0.775849i
$483$		0			0
$484$	2.45988	+	2.06409i	0.111813	+	0.0938222i
$485$	−32.7490			−1.48705
$486$		0			0
$487$	21.2040			0.960844			0.480422	−	0.877037i	$-0.340484\pi$
$487$	21.2040			0.960844			0.480422	+	0.877037i	$0.340484\pi$
$488$	55.2214	+	46.3363i	2.49976	+	2.09754i
$489$		0			0
$490$	0.0900663	+	0.510792i	0.00406878	+	0.0230752i
$491$	25.3812	+	9.23801i	1.14544	+	0.416906i	0.843875	−	0.536540i	$-0.180269\pi$
$491$	25.3812	+	9.23801i	1.14544	+	0.416906i	0.301564	+	0.953446i	$0.402491\pi$
$492$		0			0
$493$	1.13072	−	6.41260i	0.0509248	−	0.288809i
$494$	−8.61638	+	14.9240i	−0.387669	+	0.671463i
$495$		0			0
$496$	−16.3784	−	28.3683i	−0.735414	−	1.27377i
$497$	−37.0159	+	13.4727i	−1.66039	+	0.604333i
$498$		0			0
$499$	11.5205	−	9.66683i	0.515727	−	0.432747i	−0.347412	−	0.937713i	$-0.612939\pi$
$499$	11.5205	−	9.66683i	0.515727	−	0.432747i	0.863139	+	0.504966i	$0.168495\pi$
$500$	−4.88152	+	4.09608i	−0.218308	+	0.183182i
$501$		0			0
$502$	−35.9992	+	13.1026i	−1.60672	+	0.584800i
$503$	2.30325	+	3.98934i	0.102697	+	0.177876i	0.912795	−	0.408418i	$-0.133920\pi$
$503$	2.30325	+	3.98934i	0.102697	+	0.177876i	−0.810098	+	0.586294i	$0.800586\pi$
$504$		0			0
$505$	8.71420	−	15.0934i	0.387777	−	0.671649i
$506$	−0.783358	+	4.44265i	−0.0348245	+	0.197500i
$507$		0			0
$508$	−9.83508	−	3.57968i	−0.436361	−	0.158822i
$509$	−5.17414	−	29.3440i	−0.229340	−	1.30065i	−0.854213	−	0.519923i	$-0.825961\pi$
$509$	−5.17414	−	29.3440i	−0.229340	−	1.30065i	0.624874	−	0.780726i	$-0.285151\pi$
$510$		0			0
$511$	−3.83176	−	3.21523i	−0.169507	−	0.142233i
$512$	−40.8760			−1.80648
$513$		0			0
$514$	29.9599			1.32147
$515$	24.4705	+	20.5332i	1.07830	+	0.904801i
$516$		0			0
$517$	3.37424	+	19.1363i	0.148399	+	0.841613i
$518$	−63.2192	−	23.0099i	−2.77769	−	1.01100i
$519$		0			0
$520$	−8.97116	+	50.8780i	−0.393411	+	2.23115i
$521$	−5.88104	+	10.1863i	−0.257653	+	0.446268i	−0.965613	−	0.259985i	$-0.916283\pi$
$521$	−5.88104	+	10.1863i	−0.257653	+	0.446268i	0.707960	+	0.706253i	$0.249616\pi$
$522$		0			0
$523$	−14.6926	−	25.4484i	−0.642464	−	1.11278i	−0.984881	−	0.173232i	$-0.944579\pi$
$523$	−14.6926	−	25.4484i	−0.642464	−	1.11278i	0.342417	−	0.939548i	$-0.388754\pi$
$524$	−16.7487	+	6.09603i	−0.731670	+	0.266306i
$525$		0			0
$526$	−12.9716	+	10.8845i	−0.565590	+	0.474587i
$527$	−15.2048	+	12.7584i	−0.662334	+	0.555764i
$528$		0			0
$529$	21.3445	−	7.76877i	0.928023	−	0.337773i
$530$	24.3266	+	42.1350i	1.05668	+	1.83023i
$531$		0			0
$532$	−11.2627	+	19.5076i	−0.488301	+	0.845761i
$533$	−2.83659	+	16.0871i	−0.122866	+	0.696809i
$534$		0			0
$535$	−41.2343	−	15.0081i	−1.78271	−	0.648855i
$536$	−5.12038	−	29.0391i	−0.221167	−	1.25430i
$537$		0			0
$538$	13.2901	+	11.1517i	0.572975	+	0.480783i
$539$	0.235290			0.0101347
$540$		0			0
$541$	−22.9116			−0.985046			−0.492523	−	0.870300i	$-0.663925\pi$
$541$	−22.9116			−0.985046			−0.492523	+	0.870300i	$0.663925\pi$
$542$	44.7300	+	37.5329i	1.92132	+	1.61218i
$543$		0			0
$544$	−0.180712	−	1.02487i	−0.00774797	−	0.0439409i
$545$	−16.6742	−	6.06890i	−0.714243	−	0.259963i
$546$		0			0
$547$	−2.38900	+	13.5487i	−0.102146	+	0.579300i	0.890176	+	0.455618i	$0.150582\pi$
$547$	−2.38900	+	13.5487i	−0.102146	+	0.579300i	−0.992322	+	0.123682i	$0.960530\pi$
$548$	36.7053	−	63.5755i	1.56797	−	2.71581i
$549$		0			0
$550$	−18.9414	−	32.8075i	−0.807665	−	1.39892i
$551$	−4.98665	+	1.81499i	−0.212439	+	0.0773213i
$552$		0			0
$553$	−35.0172	+	29.3830i	−1.48908	+	1.24949i
$554$	−0.196682	+	0.165036i	−0.00835621	+	0.00701169i
$555$		0			0
$556$	−7.43440	+	2.70590i	−0.315289	+	0.114756i
$557$	10.9520	+	18.9695i	0.464053	+	0.803763i	0.999158	−	0.0410224i	$-0.0130615\pi$
$557$	10.9520	+	18.9695i	0.464053	+	0.803763i	−0.535106	+	0.844785i	$0.679728\pi$
$558$		0			0
$559$	4.58371	−	7.93922i	0.193870	−	0.335793i
$560$	−6.03817	+	34.2442i	−0.255159	+	1.44708i
$561$		0			0
$562$	−18.8280	−	6.85285i	−0.794213	−	0.289070i
$563$	−2.52978	−	14.3471i	−0.106618	−	0.604658i	−0.990562	−	0.137066i	$-0.956233\pi$
$563$	−2.52978	−	14.3471i	−0.106618	−	0.604658i	0.883944	−	0.467592i	$-0.154878\pi$
$564$		0			0
$565$	26.9390	+	22.6045i	1.13333	+	0.950980i
$566$	58.0431			2.43973
$567$		0			0
$568$	−74.3137			−3.11813
$569$	17.1265	+	14.3708i	0.717979	+	0.602456i	0.926825	−	0.375492i	$-0.122526\pi$
$569$	17.1265	+	14.3708i	0.717979	+	0.602456i	−0.208846	+	0.977948i	$0.566971\pi$
$570$		0			0
$571$	−2.67872	−	15.1918i	−0.112101	−	0.635756i	−0.988145	−	0.153525i	$-0.950937\pi$
$571$	−2.67872	−	15.1918i	−0.112101	−	0.635756i	0.876044	−	0.482232i	$-0.160174\pi$
$572$	43.6063	+	15.8714i	1.82327	+	0.663617i
$573$		0			0
$574$	−5.54299	+	31.4359i	−0.231360	+	1.31211i
$575$	1.19930	−	2.07724i	0.0500142	−	0.0866271i
$576$		0			0
$577$	−16.4040	−	28.4126i	−0.682909	−	1.18283i	−0.974089	−	0.226165i	$-0.927381\pi$
$577$	−16.4040	−	28.4126i	−0.682909	−	1.18283i	0.291180	−	0.956668i	$-0.405952\pi$
$578$	23.9747	−	8.72608i	0.997216	−	0.362957i
$579$		0			0
$580$	−24.1310	+	20.2483i	−1.00199	+	0.840766i
$581$	8.08305	−	6.78249i	0.335342	−	0.281385i
$582$		0			0
$583$	20.7400	−	7.54874i	0.858963	−	0.312637i
$584$	−4.71825	−	8.17225i	−0.195242	−	0.338170i
$585$		0			0
$586$	−26.5758	+	46.0306i	−1.09784	+	1.90151i
$587$	−5.25012	+	29.7749i	−0.216696	+	1.22894i	0.661244	+	0.750171i	$0.270029\pi$
$587$	−5.25012	+	29.7749i	−0.216696	+	1.22894i	−0.877939	+	0.478772i	$0.841082\pi$
$588$		0			0
$589$	15.2004	+	5.53248i	0.626321	+	0.227962i
$590$	−2.17564	−	12.3387i	−0.0895698	−	0.507975i
$591$		0			0
$592$	−33.4882	−	28.0999i	−1.37636	−	1.15490i
$593$	−41.1023			−1.68787			−0.843935	−	0.536446i	$-0.819766\pi$
$593$	−41.1023			−1.68787			−0.843935	+	0.536446i	$0.819766\pi$
$594$		0			0
$595$	21.0698			0.863778
$596$	−22.6433	−	19.0000i	−0.927505	−	0.778269i
$597$		0			0
$598$	0.762742	+	4.32573i	0.0311908	+	0.176892i
$599$	34.3463	+	12.5010i	1.40335	+	0.510778i	0.929171	−	0.369651i	$-0.120523\pi$
$599$	34.3463	+	12.5010i	1.40335	+	0.510778i	0.474179	+	0.880428i	$0.342745\pi$
$600$		0			0
$601$	0.685182	−	3.88586i	0.0279491	−	0.158507i	−0.967639	−	0.252339i	$-0.918800\pi$
$601$	0.685182	−	3.88586i	0.0279491	−	0.158507i	0.995588	+	0.0938312i	$0.0299114\pi$
$602$	8.95706	−	15.5141i	0.365062	−	0.632307i
$603$		0			0
$604$	−9.80076	−	16.9754i	−0.398787	−	0.690720i
$605$	−2.30025	+	0.837222i	−0.0935184	+	0.0340379i
$606$		0			0
$607$	7.66927	−	6.43528i	0.311286	−	0.261200i	−0.473737	−	0.880666i	$-0.657095\pi$
$607$	7.66927	−	6.43528i	0.311286	−	0.261200i	0.785023	+	0.619466i	$0.212651\pi$
$608$	−0.649698	+	0.545162i	−0.0263487	+	0.0221092i
$609$		0			0
$610$	−102.245	+	37.2141i	−4.13978	+	1.50676i
$611$	9.46005	+	16.3853i	0.382712	+	0.662877i
$612$		0			0
$613$	9.37838	−	16.2438i	0.378789	−	0.656082i	−0.612097	−	0.790783i	$-0.709674\pi$
$613$	9.37838	−	16.2438i	0.378789	−	0.656082i	0.990886	+	0.134700i	$0.0430072\pi$
$614$	6.98227	−	39.5984i	0.281781	−	1.59806i
$615$		0			0
$616$	43.0351	+	15.6635i	1.73394	+	0.631101i
$617$	3.99566	+	22.6605i	0.160859	+	0.912277i	0.953232	+	0.302240i	$0.0977344\pi$
$617$	3.99566	+	22.6605i	0.160859	+	0.912277i	−0.792373	+	0.610037i	$0.791155\pi$
$618$		0			0
$619$	5.67947	+	4.76564i	0.228277	+	0.191547i	0.749751	−	0.661720i	$-0.230173\pi$
$619$	5.67947	+	4.76564i	0.228277	+	0.191547i	−0.521474	+	0.853267i	$0.674618\pi$
$620$	96.0211			3.85630
$621$		0			0
$622$	19.0598			0.764229
$623$	10.3845	+	8.71363i	0.416046	+	0.349104i
$624$		0			0
$625$	−4.74021	−	26.8831i	−0.189608	−	1.07532i
$626$	−35.6090	−	12.9606i	−1.42322	−	0.518011i
$627$		0			0
$628$	1.03615	−	5.87630i	0.0413469	−	0.234490i
$629$	−13.2444	+	22.9400i	−0.528090	+	0.914679i
$630$		0			0
$631$	15.4962	+	26.8402i	0.616894	+	1.06849i	0.990049	+	0.140723i	$0.0449426\pi$
$631$	15.4962	+	26.8402i	0.616894	+	1.06849i	−0.373155	+	0.927769i	$0.621724\pi$
$632$	−81.0363	+	29.4948i	−3.22345	+	1.17324i
$633$		0			0
$634$	−16.2600	+	13.6438i	−0.645769	+	0.541864i
$635$	6.11187	−	5.12847i	0.242542	−	0.203517i
$636$		0			0
$637$	0.215281	−	0.0783560i	0.00852975	−	0.00310458i
$638$	10.6815	+	18.5009i	0.422884	+	0.732457i
$639$		0			0
$640$	29.6279	−	51.3171i	1.17115	−	2.02849i
$641$	6.13779	−	34.8091i	0.242428	−	1.37488i	−0.583962	−	0.811781i	$-0.698498\pi$
$641$	6.13779	−	34.8091i	0.242428	−	1.37488i	0.826390	−	0.563098i	$-0.190390\pi$
$642$		0			0
$643$	18.5128	+	6.73812i	0.730075	+	0.265725i	0.680196	−	0.733030i	$-0.261894\pi$
$643$	18.5128	+	6.73812i	0.730075	+	0.265725i	0.0498782	+	0.998755i	$0.484117\pi$
$644$	0.997002	+	5.65428i	0.0392874	+	0.222810i
$645$		0			0
$646$	10.1568	+	8.52257i	0.399614	+	0.335316i
$647$	−46.8317			−1.84114			−0.920572	−	0.390572i	$-0.872277\pi$
$647$	−46.8317			−1.84114			−0.920572	+	0.390572i	$0.872277\pi$
$648$		0			0
$649$	−5.68366			−0.223103
$650$	−28.2562	−	23.7098i	−1.10830	−	0.929974i
$651$		0			0
$652$	−12.1063	−	68.6580i	−0.474117	−	2.68885i
$653$	16.2818	+	5.92609i	0.637156	+	0.231906i	0.640343	−	0.768089i	$-0.278792\pi$
$653$	16.2818	+	5.92609i	0.637156	+	0.231906i	−0.00318720	+	0.999995i	$0.501015\pi$
$654$		0			0
$655$	2.35936	−	13.3806i	0.0921877	−	0.522822i
$656$	−10.3709	+	17.9630i	−0.404918	+	0.701338i
$657$		0			0
$658$	18.4859	+	32.0186i	0.720657	+	1.24821i
$659$	41.0967	−	14.9580i	1.60090	−	0.582680i	0.621289	−	0.783582i	$-0.286609\pi$
$659$	41.0967	−	14.9580i	1.60090	−	0.582680i	0.979611	+	0.200902i	$0.0643872\pi$
$660$		0			0
$661$	−6.96094	+	5.84092i	−0.270749	+	0.227185i	−0.768046	−	0.640395i	$-0.778771\pi$
$661$	−6.96094	+	5.84092i	−0.270749	+	0.227185i	0.497297	+	0.867581i	$0.334326\pi$
$662$	38.6807	−	32.4570i	1.50337	−	1.26148i
$663$		0			0
$664$	18.7057	−	6.80831i	0.725921	−	0.264214i
$665$	−8.58561	−	14.8707i	−0.332936	−	0.576661i
$666$		0			0
$667$	−0.676311	+	1.17140i	−0.0261868	+	0.0453570i
$668$	−4.79965	+	27.2201i	−0.185704	+	1.05318i
$669$		0			0
$670$	41.8235	+	15.2225i	1.61578	+	0.588097i
$671$	8.57111	+	48.6092i	0.330884	+	1.87654i
$672$		0			0
$673$	5.74279	+	4.81878i	0.221368	+	0.185750i	0.746727	−	0.665131i	$-0.231624\pi$
$673$	5.74279	+	4.81878i	0.221368	+	0.185750i	−0.525358	+	0.850881i	$0.676069\pi$
$674$	39.2711			1.51266
$675$		0			0
$676$	−7.34587			−0.282534
$677$	−11.7684	−	9.87486i	−0.452296	−	0.379522i	0.387991	−	0.921663i	$-0.373169\pi$
$677$	−11.7684	−	9.87486i	−0.452296	−	0.379522i	−0.840287	+	0.542142i	$0.817614\pi$
$678$		0			0
$679$	4.90845	+	27.8372i	0.188369	+	1.06829i
$680$	37.3519	+	13.5950i	1.43238	+	0.521344i
$681$		0			0
$682$	11.3078	−	64.1296i	0.432997	−	2.45565i
$683$	3.31079	−	5.73445i	0.126684	−	0.219423i	−0.795706	−	0.605683i	$-0.792900\pi$
$683$	3.31079	−	5.73445i	0.126684	−	0.219423i	0.922390	+	0.386260i	$0.126233\pi$
$684$		0			0
$685$	27.9806	+	48.4639i	1.06908	+	1.85171i
$686$	−42.5619	+	15.4913i	−1.62502	+	0.591459i
$687$		0			0
$688$	8.91711	−	7.48234i	0.339962	−	0.285262i
$689$	16.4624	−	13.8136i	0.627169	−	0.526257i
$690$		0			0
$691$	17.5317	−	6.38102i	0.666938	−	0.242745i	0.0137089	−	0.999906i	$-0.495636\pi$
$691$	17.5317	−	6.38102i	0.666938	−	0.242745i	0.653229	+	0.757161i	$0.273414\pi$
$692$	−48.4228	−	83.8708i	−1.84076	−	3.18829i
$693$		0			0
$694$	−12.0484	+	20.8685i	−0.457352	+	0.792157i
$695$	1.04727	−	5.93936i	0.0397252	−	0.225293i
$696$		0			0
$697$	11.8103	+	4.29859i	0.447346	+	0.162821i
$698$	−4.02676	−	22.8369i	−0.152415	−	0.864389i
$699$		0			0
$700$	−36.9345	−	30.9917i	−1.39599	−	1.17138i
$701$	−24.8903			−0.940092			−0.470046	−	0.882642i	$-0.655763\pi$
$701$	−24.8903			−0.940092			−0.470046	+	0.882642i	$0.655763\pi$
$702$		0			0
$703$	21.5876			0.814190
$704$	−19.7259	−	16.5520i	−0.743449	−	0.623828i
$705$		0			0
$706$	1.44476	+	8.19362i	0.0543741	+	0.308371i
$707$	−14.1358	−	5.14500i	−0.531630	−	0.193498i
$708$		0			0
$709$	−4.54589	+	25.7810i	−0.170725	+	0.968227i	0.772239	+	0.635332i	$0.219137\pi$
$709$	−4.54589	+	25.7810i	−0.170725	+	0.968227i	−0.942964	+	0.332895i	$0.891974\pi$
$710$	56.0843	−	97.1409i	2.10481	−	3.64563i
$711$		0			0
$712$	12.7870	+	22.1477i	0.479212	+	0.830020i
$713$	3.87442	−	1.41018i	0.145098	−	0.0528115i
$714$		0			0
$715$	−27.0985	+	22.7384i	−1.01343	+	0.850367i
$716$	63.6788	−	53.4328i	2.37979	−	1.99688i
$717$		0			0
$718$	81.3599	−	29.6126i	3.03632	−	1.10513i
$719$	10.5145	+	18.2117i	0.392125	+	0.679181i	0.992730	−	0.120365i	$-0.0384066\pi$
$719$	10.5145	+	18.2117i	0.392125	+	0.679181i	−0.600604	+	0.799546i	$0.705073\pi$
$720$		0			0
$721$	13.7859	−	23.8779i	0.513414	−	0.889259i
$722$	−6.23267	+	35.3472i	−0.231956	+	1.31549i
$723$		0			0
$724$	58.7408	+	21.3799i	2.18308	+	0.794577i
$725$	−1.97242	−	11.1861i	−0.0732538	−	0.415443i
$726$		0			0
$727$	31.7109	+	26.6086i	1.17609	+	0.986859i	0.999997	+	0.00248653i	$0.000791488\pi$
$727$	31.7109	+	26.6086i	1.17609	+	0.986859i	0.176096	+	0.984373i	$0.443653\pi$
$728$	44.5918			1.65268
$729$		0			0
$730$	14.2434			0.527171
$731$	−5.40318	−	4.53381i	−0.199844	−	0.167689i
$732$		0			0
$733$	5.83922	+	33.1158i	0.215676	+	1.22316i	0.879729	+	0.475476i	$0.157724\pi$
$733$	5.83922	+	33.1158i	0.215676	+	1.22316i	−0.664052	+	0.747686i	$0.731165\pi$
$734$	72.8563	+	26.5175i	2.68917	+	0.978779i
$735$		0			0
$736$	−0.0375388	+	0.212893i	−0.00138370	+	0.00784735i
$737$	10.0952	−	17.4854i	0.371862	−	0.644084i
$738$		0			0
$739$	6.47268	+	11.2110i	0.238101	+	0.412403i	0.960169	−	0.279418i	$-0.0901417\pi$
$739$	6.47268	+	11.2110i	0.238101	+	0.412403i	−0.722068	+	0.691822i	$0.756808\pi$
$740$	120.417	−	43.8282i	4.42662	−	1.61116i
$741$		0			0
$742$	32.1693	−	26.9933i	1.18097	−	0.990955i
$743$	0.0673577	−	0.0565198i	0.00247111	−	0.00207351i	−0.641551	−	0.767080i	$-0.721709\pi$
$743$	0.0673577	−	0.0565198i	0.00247111	−	0.00207351i	0.644022	+	0.765007i	$0.277264\pi$
$744$		0			0
$745$	21.1738	−	7.70664i	0.775749	−	0.282349i
$746$	−17.7481	−	30.7406i	−0.649803	−	1.12549i
$747$		0			0
$748$	17.8518	−	30.9202i	0.652727	−	1.13056i
$749$	−6.57687	+	37.2993i	−0.240314	+	1.36289i
$750$		0			0
$751$	−46.8869	−	17.0654i	−1.71093	−	0.622727i	−0.713935	−	0.700212i	$-0.753089\pi$
$751$	−46.8869	−	17.0654i	−1.71093	−	0.622727i	−0.996993	+	0.0774854i	$0.975311\pi$
$752$	4.17173	+	23.6591i	0.152127	+	0.862757i
$753$		0			0
$754$	15.9343	+	13.3705i	0.580293	+	0.486924i
$755$	14.9423			0.543806
$756$		0			0
$757$	−11.8679			−0.431348			−0.215674	−	0.976465i	$-0.569195\pi$
$757$	−11.8679			−0.431348			−0.215674	+	0.976465i	$0.569195\pi$
$758$	1.88465	+	1.58141i	0.0684534	+	0.0574392i
$759$		0			0
$760$	−5.62519	−	31.9021i	−0.204047	−	1.15721i
$761$	3.56172	+	1.29636i	0.129112	+	0.0469930i	0.405768	−	0.913976i	$-0.367004\pi$
$761$	3.56172	+	1.29636i	0.129112	+	0.0469930i	−0.276656	+	0.960969i	$0.589226\pi$
$762$		0			0
$763$	−2.65953	+	15.0829i	−0.0962814	+	0.546039i
$764$	−22.1247	+	38.3211i	−0.800444	+	1.38641i
$765$		0			0
$766$	5.05978	+	8.76379i	0.182817	+	0.316649i
$767$	−5.20033	+	1.89277i	−0.187773	+	0.0683438i
$768$		0			0
$769$	4.80272	−	4.02996i	0.173190	−	0.145324i	−0.552072	−	0.833796i	$-0.686163\pi$
$769$	4.80272	−	4.02996i	0.173190	−	0.145324i	0.725263	+	0.688472i	$0.241718\pi$
$770$	−52.9534	+	44.4332i	−1.90831	+	1.60126i
$771$		0			0
$772$	−4.34705	+	1.58220i	−0.156454	+	0.0569445i
$773$	−0.647678	−	1.12181i	−0.0232954	−	0.0403487i	0.854143	−	0.520039i	$-0.174082\pi$
$773$	−0.647678	−	1.12181i	−0.0232954	−	0.0403487i	−0.877438	+	0.479690i	$0.840749\pi$
$774$		0			0
$775$	−17.3119	+	29.9850i	−0.621861	+	1.07709i
$776$	−9.25998	+	52.5160i	−0.332414	+	1.88521i
$777$		0			0
$778$	−35.8443	−	13.0463i	−1.28508	−	0.467731i
$779$	−1.77863	−	10.0871i	−0.0637259	−	0.361408i
$780$		0			0
$781$	−38.9795	−	32.7077i	−1.39480	−	1.17037i
$782$	3.37953			0.120852
$783$		0			0
$784$	0.290900			0.0103893
$785$	3.48446	+	2.92380i	0.124366	+	0.104355i
$786$		0			0
$787$	−2.15189	−	12.2040i	−0.0767065	−	0.435024i	−0.998840	−	0.0481523i	$-0.984667\pi$
$787$	−2.15189	−	12.2040i	−0.0767065	−	0.435024i	0.922134	−	0.386872i	$-0.126444\pi$
$788$	−19.1445	−	6.96802i	−0.681994	−	0.248226i
$789$		0			0
$790$	22.6030	−	128.188i	0.804180	−	4.56073i
$791$	15.1766	−	26.2866i	0.539618	−	0.934645i
$792$		0			0
$793$	24.0300	+	41.6212i	0.853331	+	1.47801i
$794$	3.57735	−	1.30205i	0.126955	−	0.0462080i
$795$		0			0
$796$	42.4866	−	35.6505i	1.50590	−	1.26360i
$797$	−18.6782	+	15.6729i	−0.661617	+	0.555163i	−0.910571	−	0.413353i	$-0.864358\pi$
$797$	−18.6782	+	15.6729i	−0.661617	+	0.555163i	0.248954	+	0.968515i	$0.419913\pi$
$798$		0			0
$799$	13.6791	−	4.97879i	0.483932	−	0.176137i
$800$	−0.907681	−	1.57215i	−0.0320914	−	0.0555839i
$801$		0			0
$802$	9.76649	−	16.9161i	0.344867	−	0.597327i
$803$	1.12200	−	6.36320i	0.0395947	−	0.224552i
$804$		0			0
$805$	−4.11282	−	1.49694i	−0.144958	−	0.0527604i
$806$	−11.0102	−	62.4419i	−0.387817	−	2.19942i
$807$		0			0
$808$	−21.7397	−	18.2418i	−0.764800	−	0.641744i
$809$	−24.1156			−0.847861			−0.423930	−	0.905695i	$-0.639350\pi$
$809$	−24.1156			−0.847861			−0.423930	+	0.905695i	$0.639350\pi$
$810$		0			0
$811$	48.1121			1.68944			0.844721	−	0.535206i	$-0.179766\pi$
$811$	48.1121			1.68944			0.844721	+	0.535206i	$0.179766\pi$
$812$	20.8282	+	17.4769i	0.730926	+	0.613320i
$813$		0			0
$814$	−15.0908	−	85.5842i	−0.528933	−	2.99973i
$815$	49.9405	+	18.1769i	1.74934	+	0.636708i
$816$		0			0
$817$	−0.998174	+	5.66093i	−0.0349217	+	0.198051i
$818$	−32.5109	+	56.3105i	−1.13672	+	1.96885i
$819$		0			0
$820$	−30.4006	−	52.6554i	−1.06164	−	1.83881i
$821$	−15.9173	+	5.79342i	−0.555517	+	0.202192i	−0.604496	−	0.796608i	$-0.706626\pi$
$821$	−15.9173	+	5.79342i	−0.555517	+	0.202192i	0.0489789	+	0.998800i	$0.484403\pi$
$822$		0			0
$823$	8.85236	−	7.42801i	0.308574	−	0.258924i	−0.475328	−	0.879808i	$-0.657671\pi$
$823$	8.85236	−	7.42801i	0.308574	−	0.258924i	0.783902	+	0.620884i	$0.213226\pi$
$824$	39.8461	−	33.4348i	1.38810	−	1.16476i
$825$		0			0
$826$	−10.1620	+	3.69867i	−0.353581	+	0.128693i
$827$	−5.11869	−	8.86582i	−0.177994	−	0.308295i	0.763199	−	0.646163i	$-0.223627\pi$
$827$	−5.11869	−	8.86582i	−0.177994	−	0.308295i	−0.941193	+	0.337868i	$0.890294\pi$
$828$		0			0
$829$	−4.67622	+	8.09945i	−0.162412	+	0.281306i	−0.935733	−	0.352709i	$-0.885261\pi$
$829$	−4.67622	+	8.09945i	−0.162412	+	0.281306i	0.773321	+	0.634014i	$0.218594\pi$
$830$	−5.21747	+	29.5898i	−0.181101	+	1.02708i
$831$		0			0
$832$	−23.5606	−	8.57537i	−0.816818	−	0.297297i
$833$	−0.0306083	−	0.173588i	−0.00106051	−	0.00601448i
$834$		0			0
$835$	−16.1406	−	13.5436i	−0.558570	−	0.468696i
$836$	−29.0973			−1.00635
$837$		0			0
$838$	−94.2316			−3.25518
$839$	−9.07388	−	7.61389i	−0.313265	−	0.262861i	0.472575	−	0.881291i	$-0.343325\pi$
$839$	−9.07388	−	7.61389i	−0.313265	−	0.262861i	−0.785840	+	0.618430i	$0.787769\pi$
$840$		0			0
$841$	−3.92351	−	22.2513i	−0.135293	−	0.767287i
$842$	−16.9626	−	6.17388i	−0.584570	−	0.212766i
$843$		0			0
$844$	−4.09431	+	23.2200i	−0.140932	+	0.799265i
$845$	2.79989	−	4.84956i	0.0963193	−	0.166830i
$846$		0			0
$847$	1.05642	+	1.82977i	0.0362989	+	0.0628715i
$848$	25.6418	−	9.33286i	0.880543	−	0.320492i
$849$		0			0
$850$	−21.7401	+	18.2421i	−0.745681	+	0.625701i
$851$	4.21513	−	3.53691i	0.144493	−	0.121244i
$852$		0			0
$853$	35.0236	−	12.7475i	1.19918	−	0.436467i	0.336244	−	0.941775i	$-0.390843\pi$
$853$	35.0236	−	12.7475i	1.19918	−	0.436467i	0.862939	+	0.505308i	$0.168621\pi$
$854$	46.9572	+	81.3322i	1.60684	+	2.78313i
$855$		0			0
$856$	−35.7261	+	61.8793i	−1.22109	+	2.11499i
$857$	−7.19456	+	40.8024i	−0.245762	+	1.39378i	0.572955	+	0.819586i	$0.305797\pi$
$857$	−7.19456	+	40.8024i	−0.245762	+	1.39378i	−0.818717	+	0.574197i	$0.805314\pi$
$858$		0			0
$859$	8.70015	+	3.16660i	0.296845	+	0.108043i	0.486150	−	0.873876i	$-0.338401\pi$
$859$	8.70015	+	3.16660i	0.296845	+	0.108043i	−0.189304	+	0.981918i	$0.560623\pi$
$860$	5.92522	+	33.6036i	0.202048	+	1.14587i
$861$		0			0
$862$	29.8350	+	25.0345i	1.01618	+	0.852680i
$863$	51.4748			1.75222			0.876110	−	0.482110i	$-0.160130\pi$
$863$	51.4748			1.75222			0.876110	+	0.482110i	$0.160130\pi$
$864$		0			0
$865$	73.8258			2.51015
$866$	−44.9056	−	37.6803i	−1.52595	−	1.28043i
$867$		0			0
$868$	−14.3917	−	81.6196i	−0.488487	−	2.77035i
$869$	−55.4872	−	20.1957i	−1.88228	−	0.685092i
$870$		0			0
$871$	3.41376	−	19.3604i	0.115671	−	0.656002i
$872$	−14.4468	+	25.0225i	−0.489229	+	0.847370i
$873$		0			0
$874$	−1.37710	−	2.38521i	−0.0465812	−	0.0806810i
$875$	−3.93995	+	1.43403i	−0.133195	+	0.0484789i
$876$		0			0
$877$	−19.0738	+	16.0048i	−0.644075	+	0.540443i	−0.905267	−	0.424844i	$-0.860329\pi$
$877$	−19.0738	+	16.0048i	−0.644075	+	0.540443i	0.261191	+	0.965287i	$0.415885\pi$
$878$	−40.4231	+	33.9190i	−1.36421	+	1.14471i
$879$		0			0
$880$	−42.2085	+	15.3627i	−1.42285	+	0.517875i
$881$	0.716807	+	1.24155i	0.0241498	+	0.0418287i	0.877848	−	0.478940i	$-0.158979\pi$
$881$	0.716807	+	1.24155i	0.0241498	+	0.0418287i	−0.853698	+	0.520769i	$0.825645\pi$
$882$		0			0
$883$	−13.1023	+	22.6939i	−0.440928	+	0.763709i	−0.997759	−	0.0669168i	$-0.978684\pi$
$883$	−13.1023	+	22.6939i	−0.440928	+	0.763709i	0.556831	+	0.830626i	$0.312017\pi$
$884$	6.03670	−	34.2358i	0.203036	−	1.15148i
$885$		0			0
$886$	72.8620	+	26.5196i	2.44785	+	0.890944i
$887$	7.53157	+	42.7136i	0.252885	+	1.43418i	0.801443	+	0.598071i	$0.204066\pi$
$887$	7.53157	+	42.7136i	0.252885	+	1.43418i	−0.548558	+	0.836113i	$0.684823\pi$
$888$		0			0
$889$	−5.27534	−	4.42653i	−0.176929	−	0.148461i
$890$	−38.6011			−1.29391
$891$		0			0
$892$	35.2702			1.18093
$893$	−9.08795	−	7.62570i	−0.304117	−	0.255184i
$894$		0			0
$895$	11.0037	+	62.4051i	0.367813	+	2.08597i
$896$	−48.0611	−	17.4928i	−1.60561	−	0.584393i
$897$		0			0
$898$	−8.87288	+	50.3206i	−0.296092	+	1.67922i
$899$	9.76254	−	16.9092i	0.325599	−	0.563954i
$900$		0			0
$901$	−8.26720	−	14.3192i	−0.275420	−	0.477042i
$902$	−38.7471	+	14.1028i	−1.29014	+	0.469571i
$903$		0			0
$904$	43.8656	−	36.8076i	1.45895	−	1.22420i
$905$	−36.5036	+	30.6302i	−1.21342	+	1.01818i
$906$		0			0
$907$	−22.4321	+	8.16463i	−0.744846	+	0.271102i	−0.686436	−	0.727191i	$-0.740826\pi$
$907$	−22.4321	+	8.16463i	−0.744846	+	0.271102i	−0.0584110	+	0.998293i	$0.518603\pi$
$908$	49.0595	+	84.9736i	1.62810	+	2.81995i
$909$		0			0
$910$	−33.6532	+	58.2891i	−1.11559	+	1.93227i
$911$	0.750251	−	4.25488i	0.0248569	−	0.140971i	−0.969854	−	0.243688i	$-0.921643\pi$
$911$	0.750251	−	4.25488i	0.0248569	−	0.140971i	0.994711	+	0.102718i	$0.0327538\pi$
$912$		0			0
$913$	12.8082	+	4.66179i	0.423888	+	0.154283i
$914$	−7.43799	−	42.1830i	−0.246027	−	1.39529i
$915$		0			0
$916$	56.1855	+	47.1453i	1.85642	+	1.55772i
$917$	−11.7273			−0.387271
$918$		0			0
$919$	3.56151			0.117483			0.0587417	−	0.998273i	$-0.481291\pi$
$919$	3.56151			0.117483			0.0587417	+	0.998273i	$0.481291\pi$
$920$	−6.32520	−	5.30747i	−0.208536	−	0.174982i
$921$		0			0
$922$	13.2324	+	75.0448i	0.435786	+	2.47147i
$923$	−46.5570	−	16.9454i	−1.53244	−	0.557764i
$924$		0			0
$925$	−8.02379	+	45.5051i	−0.263820	+	1.49620i
$926$	−7.97301	+	13.8097i	−0.262009	+	0.453813i
$927$		0			0
$928$	0.511861	+	0.886570i	0.0168027	+	0.0291031i
$929$	31.3160	−	11.3981i	1.02744	−	0.373959i	0.227337	−	0.973816i	$-0.426998\pi$
$929$	31.3160	−	11.3981i	1.02744	−	0.373959i	0.800107	+	0.599857i	$0.204776\pi$
$930$		0			0
$931$	−0.110043	+	0.0923372i	−0.00360652	+	0.00302623i
$932$	−32.6191	+	27.3707i	−1.06847	+	0.896556i
$933$		0			0
$934$	4.48957	−	1.63407i	0.146903	−	0.0534684i
$935$	13.6085	+	23.5706i	0.445045	+	0.770841i
$936$		0			0
$937$	−13.0297	+	22.5681i	−0.425661	+	0.737267i	−0.996482	−	0.0838079i	$-0.973292\pi$
$937$	−13.0297	+	22.5681i	−0.425661	+	0.737267i	0.570821	+	0.821075i	$0.306625\pi$
$938$	6.67085	−	37.8323i	0.217811	−	1.23527i
$939$		0			0
$940$	−66.1753	−	24.0858i	−2.15840	−	0.785594i
$941$	−4.16644	−	23.6290i	−0.135822	−	0.770285i	−0.974284	−	0.225324i	$-0.927656\pi$
$941$	−4.16644	−	23.6290i	−0.135822	−	0.770285i	0.838462	−	0.544960i	$-0.183455\pi$
$942$		0			0
$943$	−1.99996	−	1.67817i	−0.0651277	−	0.0546486i
$944$	−7.02697			−0.228708
$945$		0			0
$946$	23.1406			0.752366
$947$	22.8930	+	19.2095i	0.743922	+	0.624225i	0.933888	−	0.357566i	$-0.116393\pi$
$947$	22.8930	+	19.2095i	0.743922	+	0.624225i	−0.189966	+	0.981791i	$0.560838\pi$
$948$		0			0
$949$	−1.09248	−	6.19573i	−0.0354632	−	0.201122i
$950$	21.7337	+	7.91044i	0.705136	+	0.256648i
$951$		0			0
$952$	5.95763	−	33.7874i	0.193088	−	1.09506i
$953$	5.09669	−	8.82773i	0.165098	−	0.285958i	−0.771592	−	0.636118i	$-0.780539\pi$
$953$	5.09669	−	8.82773i	0.165098	−	0.285958i	0.936690	+	0.350159i	$0.113873\pi$
$954$		0			0
$955$	−16.8657	−	29.2123i	−0.545763	−	0.945289i
$956$	−36.2109	+	13.1797i	−1.17114	+	0.426261i
$957$		0			0
$958$	−2.50295	+	2.10022i	−0.0808665	+	0.0678550i
$959$	37.0013	−	31.0478i	1.19484	−	1.00259i
$960$		0			0
$961$	−26.7969	+	9.75326i	−0.864415	+	0.314621i
$962$	−42.3087	−	73.2808i	−1.36409	−	2.36267i
$963$		0			0
$964$	14.2179	−	24.6261i	0.457927	−	0.793152i
$965$	0.612360	−	3.47287i	0.0197126	−	0.111796i
$966$		0			0
$967$	17.6348	+	6.41856i	0.567098	+	0.206407i	0.609627	−	0.792688i	$-0.291319\pi$
$967$	17.6348	+	6.41856i	0.567098	+	0.206407i	−0.0425289	+	0.999095i	$0.513541\pi$
$968$	0.692152	+	3.92539i	0.0222466	+	0.126167i
$969$		0			0
$970$	−61.6590	−	51.7380i	−1.97975	−	1.66121i
$971$	−51.9535			−1.66727			−0.833633	−	0.552319i	$-0.813743\pi$
$971$	−51.9535			−1.66727			−0.833633	+	0.552319i	$0.813743\pi$
$972$		0			0
$973$	−5.20552			−0.166881
$974$	39.9223	+	33.4988i	1.27919	+	1.07337i
$975$		0			0
$976$	10.5969	+	60.0978i	0.339197	+	1.92368i
$977$	−30.6190	−	11.1444i	−0.979589	−	0.356541i	−0.197909	−	0.980220i	$-0.563415\pi$
$977$	−30.6190	−	11.1444i	−0.979589	−	0.356541i	−0.781681	+	0.623679i	$0.785637\pi$
$978$		0			0
$979$	−3.04075	+	17.2450i	−0.0971829	+	0.551152i
$980$	−0.426361	+	0.738479i	−0.0136196	+	0.0235898i
$981$		0			0
$982$	33.1926	+	57.4913i	1.05922	+	1.83462i
$983$	−32.9639	+	11.9979i	−1.05139	+	0.382673i	−0.809185	−	0.587553i	$-0.800091\pi$
$983$	−32.9639	+	11.9979i	−1.05139	+	0.382673i	−0.242200	+	0.970226i	$0.577869\pi$
$984$		0			0
$985$	11.8971	−	9.98283i	0.379072	−	0.318079i
$986$	12.2597	−	10.2872i	0.390430	−	0.327610i
$987$		0			0
$988$	−26.6229	+	9.68995i	−0.846988	+	0.308278i
$989$	0.732587	+	1.26888i	0.0232949	+	0.0403479i
$990$		0			0
$991$	27.3818	−	47.4266i	0.869810	−	1.50656i	0.00762014	−	0.999971i	$-0.497574\pi$
$991$	27.3818	−	47.4266i	0.869810	−	1.50656i	0.862190	−	0.506585i	$-0.169092\pi$
$992$	0.541873	−	3.07312i	0.0172045	−	0.0975715i
$993$		0			0
$994$	−90.9773	−	33.1130i	−2.88563	−	1.05028i
$995$	7.34169	+	41.6368i	0.232747	+	1.31998i
$996$		0			0
$997$	38.5551	+	32.3515i	1.22105	+	1.02458i	0.998769	+	0.0496011i	$0.0157950\pi$
$997$	38.5551	+	32.3515i	1.22105	+	1.02458i	0.222282	+	0.974982i	$0.428649\pi$
$998$	36.9625			1.17003
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.e.s.406.2		12
3.2	odd	2		729.2.e.l.406.1		12
9.2	odd	6		729.2.e.k.649.1		12
9.4	even	3		729.2.e.j.163.1		12
9.5	odd	6		729.2.e.u.163.2		12
9.7	even	3		729.2.e.t.649.2		12
27.2	odd	18		729.2.c.a.244.6		12
27.4	even	9		729.2.e.t.82.2		12
27.5	odd	18		729.2.e.l.325.1		12
27.7	even	9		729.2.a.b.1.6	✓	6
27.11	odd	18		729.2.c.a.487.6		12
27.13	even	9		729.2.e.j.568.1		12
27.14	odd	18		729.2.e.u.568.2		12
27.16	even	9		729.2.c.d.487.1		12
27.20	odd	18		729.2.a.e.1.1	yes	6
27.22	even	9	inner	729.2.e.s.325.2		12
27.23	odd	18		729.2.e.k.82.1		12
27.25	even	9		729.2.c.d.244.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
729.2.a.b.1.6	✓	6	27.7	even	9
729.2.a.e.1.1	yes	6	27.20	odd	18
729.2.c.a.244.6		12	27.2	odd	18
729.2.c.a.487.6		12	27.11	odd	18
729.2.c.d.244.1		12	27.25	even	9
729.2.c.d.487.1		12	27.16	even	9
729.2.e.j.163.1		12	9.4	even	3
729.2.e.j.568.1		12	27.13	even	9
729.2.e.k.82.1		12	27.23	odd	18
729.2.e.k.649.1		12	9.2	odd	6
729.2.e.l.325.1		12	27.5	odd	18
729.2.e.l.406.1		12	3.2	odd	2
729.2.e.s.325.2		12	27.22	even	9	inner
729.2.e.s.406.2		12	1.1	even	1	trivial
729.2.e.t.82.2		12	27.4	even	9
729.2.e.t.649.2		12	9.7	even	3
729.2.e.u.163.2		12	9.5	odd	6
729.2.e.u.568.2		12	27.14	odd	18

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:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.88278 + 1.57984i) q^{2} +(0.701665 + 3.97934i) q^{4} +(-2.89450 - 1.05351i) q^{5} +(-0.461673 + 2.61828i) q^{7} +(-2.50784 + 4.34371i) q^{8} +O(q^{10})\)	\(q+(1.88278 + 1.57984i) q^{2} +(0.701665 + 3.97934i) q^{4} +(-2.89450 - 1.05351i) q^{5} +(-0.461673 + 2.61828i) q^{7} +(-2.50784 + 4.34371i) q^{8} +(-3.78532 - 6.55636i) q^{10} +(-3.22722 + 1.17461i) q^{11} +(-2.56162 + 2.14945i) q^{13} +(-5.00567 + 4.20026i) q^{14} +(-3.98997 + 1.45223i) q^{16} +(1.28641 + 2.22813i) q^{17} +(1.04838 - 1.81585i) q^{19} +(2.16131 - 12.2574i) q^{20} +(-7.93184 - 2.88695i) q^{22} +(-0.0928052 - 0.526325i) q^{23} +(3.43802 + 2.88484i) q^{25} -8.21874 q^{26} -10.7430 q^{28} +(-1.93878 - 1.62683i) q^{29} +(1.33964 + 7.59750i) q^{31} +(-0.380097 - 0.138344i) q^{32} +(-1.09805 + 6.22738i) q^{34} +(4.09470 - 7.09222i) q^{35} +(5.14783 + 8.91631i) q^{37} +(4.84261 - 1.76257i) q^{38} +(11.8351 - 9.93082i) q^{40} +(3.74213 - 3.14002i) q^{41} +(-2.57616 + 0.937645i) q^{43} +(-6.93862 - 12.0180i) q^{44} +(0.656775 - 1.13757i) q^{46} +(0.982501 - 5.57204i) q^{47} +(-0.0643792 - 0.0234321i) q^{49} +(1.91544 + 10.8630i) q^{50} +(-10.3508 - 8.68536i) q^{52} -6.42657 q^{53} +10.5787 q^{55} +(-10.2152 - 8.57159i) q^{56} +(-1.08016 - 6.12590i) q^{58} +(1.55514 + 0.566026i) q^{59} +(2.49571 - 14.1539i) q^{61} +(-9.48056 + 16.4208i) q^{62} +(3.74896 + 6.49338i) q^{64} +(9.67908 - 3.52290i) q^{65} +(-4.50356 + 3.77894i) q^{67} +(-7.96384 + 6.68246i) q^{68} +(18.9140 - 6.88411i) q^{70} +(7.40813 + 12.8313i) q^{71} +(-0.940699 + 1.62934i) q^{73} +(-4.39409 + 24.9201i) q^{74} +(7.96150 + 2.89775i) q^{76} +(-1.58554 - 8.99205i) q^{77} +(13.1710 + 11.0518i) q^{79} +13.0789 q^{80} +12.0063 q^{82} +(-3.04027 - 2.55109i) q^{83} +(-1.37615 - 7.80456i) q^{85} +(-6.33165 - 2.30453i) q^{86} +(2.99119 - 16.9639i) q^{88} +(2.54940 - 4.41569i) q^{89} +(-4.44523 - 7.69937i) q^{91} +(2.02931 - 0.738607i) q^{92} +(10.6527 - 8.93871i) q^{94} +(-4.94756 + 4.15150i) q^{95} +(9.99070 - 3.63632i) q^{97} +(-0.0841927 - 0.145826i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} - 3 q^{4} - 12 q^{5} - 3 q^{7} + 6 q^{8}+O(q^{10}) \) 12 * q + 3 * q^2 - 3 * q^4 - 12 * q^5 - 3 * q^7 + 6 * q^8	\( 12 q + 3 q^{2} - 3 q^{4} - 12 q^{5} - 3 q^{7} + 6 q^{8} - 6 q^{10} + 3 q^{11} + 6 q^{13} + 6 q^{14} + 27 q^{16} - 9 q^{17} - 12 q^{19} - 39 q^{20} - 39 q^{22} - 21 q^{23} + 6 q^{25} - 48 q^{26} + 6 q^{28} - 6 q^{29} + 6 q^{31} - 27 q^{32} - 18 q^{34} + 30 q^{35} - 3 q^{37} - 3 q^{38} + 33 q^{40} + 15 q^{41} - 30 q^{43} - 33 q^{44} + 3 q^{46} + 21 q^{47} - 3 q^{49} - 6 q^{50} + 18 q^{53} + 30 q^{55} - 15 q^{56} - 3 q^{58} - 30 q^{59} - 30 q^{61} - 30 q^{62} - 6 q^{64} + 12 q^{65} - 39 q^{67} - 18 q^{68} + 51 q^{70} - 12 q^{73} - 57 q^{74} + 57 q^{76} + 24 q^{77} + 15 q^{79} + 42 q^{80} - 42 q^{82} + 21 q^{83} + 54 q^{85} + 60 q^{86} + 12 q^{88} - 9 q^{89} - 18 q^{91} + 15 q^{92} + 33 q^{94} - 42 q^{95} - 12 q^{97} + 18 q^{98}+O(q^{100}) \) 12 * q + 3 * q^2 - 3 * q^4 - 12 * q^5 - 3 * q^7 + 6 * q^8 - 6 * q^10 + 3 * q^11 + 6 * q^13 + 6 * q^14 + 27 * q^16 - 9 * q^17 - 12 * q^19 - 39 * q^20 - 39 * q^22 - 21 * q^23 + 6 * q^25 - 48 * q^26 + 6 * q^28 - 6 * q^29 + 6 * q^31 - 27 * q^32 - 18 * q^34 + 30 * q^35 - 3 * q^37 - 3 * q^38 + 33 * q^40 + 15 * q^41 - 30 * q^43 - 33 * q^44 + 3 * q^46 + 21 * q^47 - 3 * q^49 - 6 * q^50 + 18 * q^53 + 30 * q^55 - 15 * q^56 - 3 * q^58 - 30 * q^59 - 30 * q^61 - 30 * q^62 - 6 * q^64 + 12 * q^65 - 39 * q^67 - 18 * q^68 + 51 * q^70 - 12 * q^73 - 57 * q^74 + 57 * q^76 + 24 * q^77 + 15 * q^79 + 42 * q^80 - 42 * q^82 + 21 * q^83 + 54 * q^85 + 60 * q^86 + 12 * q^88 - 9 * q^89 - 18 * q^91 + 15 * q^92 + 33 * q^94 - 42 * q^95 - 12 * q^97 + 18 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more