LMFDB - Embedded newform 729.2.g.d.55.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(28,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([44]))

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

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

chi := DirichletCharacter("729.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.g (of order $27$, degree $18$, 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:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	no (minimal twist has level 81)
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			55.5
Character	$\chi$	$=$	729.55
Dual form			729.2.g.d.676.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.280212 - 0.649604i) q^{2} +(1.02902 + 1.09069i) q^{4} +(-0.199739 - 3.42939i) q^{5} +(2.63236 + 0.623881i) q^{7} +(2.32646 - 0.846761i) q^{8} +O(q^{10})$	\(q+(0.280212 - 0.649604i) q^{2} +(1.02902 + 1.09069i) q^{4} +(-0.199739 - 3.42939i) q^{5} +(2.63236 + 0.623881i) q^{7} +(2.32646 - 0.846761i) q^{8} +(-2.28372 - 0.831205i) q^{10} +(-1.23441 - 0.811885i) q^{11} +(5.51427 + 0.644526i) q^{13} +(1.14289 - 1.53517i) q^{14} +(-0.0725347 + 1.24537i) q^{16} +(-3.86594 + 3.24391i) q^{17} +(-3.94119 - 3.30705i) q^{19} +(3.53488 - 3.74676i) q^{20} +(-0.873300 + 0.574378i) q^{22} +(1.68752 - 0.399950i) q^{23} +(-6.75465 + 0.789506i) q^{25} +(1.96385 - 3.40149i) q^{26} +(2.02828 + 3.51309i) q^{28} +(1.28309 + 1.72349i) q^{29} +(1.09167 - 3.64642i) q^{31} +(5.21352 + 2.61833i) q^{32} +(1.02397 + 3.42031i) q^{34} +(1.61375 - 9.15202i) q^{35} +(-0.891723 - 5.05721i) q^{37} +(-3.25264 + 1.63354i) q^{38} +(-3.36856 - 7.80920i) q^{40} +(-1.78715 - 4.14308i) q^{41} +(0.736775 - 0.370022i) q^{43} +(-0.384712 - 2.18181i) q^{44} +(0.213054 - 1.20829i) q^{46} +(1.92513 + 6.43037i) q^{47} +(0.284673 + 0.142968i) q^{49} +(-1.37987 + 4.60908i) q^{50} +(4.97130 + 6.67762i) q^{52} +(2.58797 + 4.48249i) q^{53} +(-2.53771 + 4.39545i) q^{55} +(6.65235 - 0.777549i) q^{56} +(1.47912 - 0.350558i) q^{58} +(2.95286 - 1.94213i) q^{59} +(3.71901 - 3.94192i) q^{61} +(-2.06283 - 1.73092i) q^{62} +(1.25051 - 1.04930i) q^{64} +(1.10892 - 19.0394i) q^{65} +(-3.91063 + 5.25288i) q^{67} +(-7.51622 - 0.878520i) q^{68} +(-5.49299 - 3.61280i) q^{70} +(3.30039 + 1.20125i) q^{71} +(0.668031 - 0.243143i) q^{73} +(-3.53506 - 0.837823i) q^{74} +(-0.448570 - 7.70164i) q^{76} +(-2.74290 - 2.90730i) q^{77} +(-6.21626 + 14.4109i) q^{79} +4.28536 q^{80} -3.19214 q^{82} +(2.35107 - 5.45040i) q^{83} +(11.8968 + 12.6099i) q^{85} +(-0.0339149 - 0.582297i) q^{86} +(-3.55928 - 0.843564i) q^{88} +(-3.78422 + 1.37734i) q^{89} +(14.1135 + 5.13688i) q^{91} +(2.17271 + 1.42901i) q^{92} +(4.71663 + 0.551295i) q^{94} +(-10.5540 + 14.1764i) q^{95} +(0.700141 - 12.0210i) q^{97} +(0.172641 - 0.144863i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8}+O(q^{10}) $ 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8	$ 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} + 45 q^{20} + 9 q^{22} - 45 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28} + 36 q^{29} + 9 q^{31} - 99 q^{32} + 9 q^{34} + 9 q^{35} - 18 q^{37} + 18 q^{38} + 9 q^{40} + 27 q^{41} + 9 q^{43} + 54 q^{44} - 18 q^{46} - 99 q^{47} + 9 q^{49} + 126 q^{50} - 27 q^{52} + 45 q^{53} - 9 q^{55} - 225 q^{56} + 9 q^{58} + 72 q^{59} + 9 q^{61} + 81 q^{62} - 18 q^{64} - 81 q^{65} - 45 q^{67} + 117 q^{68} - 99 q^{70} - 90 q^{71} - 18 q^{73} + 81 q^{74} - 153 q^{76} + 81 q^{77} - 99 q^{79} - 288 q^{80} - 36 q^{82} + 45 q^{83} - 99 q^{85} + 81 q^{86} - 153 q^{88} - 81 q^{89} - 18 q^{91} + 207 q^{92} - 99 q^{94} - 171 q^{95} - 45 q^{97} + 81 q^{98}+O(q^{100}) $ 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8 - 18 * q^10 + 9 * q^11 + 9 * q^13 + 9 * q^14 + 9 * q^16 - 18 * q^17 - 18 * q^19 + 45 * q^20 + 9 * q^22 - 45 * q^23 + 9 * q^25 + 45 * q^26 - 9 * q^28 + 36 * q^29 + 9 * q^31 - 99 * q^32 + 9 * q^34 + 9 * q^35 - 18 * q^37 + 18 * q^38 + 9 * q^40 + 27 * q^41 + 9 * q^43 + 54 * q^44 - 18 * q^46 - 99 * q^47 + 9 * q^49 + 126 * q^50 - 27 * q^52 + 45 * q^53 - 9 * q^55 - 225 * q^56 + 9 * q^58 + 72 * q^59 + 9 * q^61 + 81 * q^62 - 18 * q^64 - 81 * q^65 - 45 * q^67 + 117 * q^68 - 99 * q^70 - 90 * q^71 - 18 * q^73 + 81 * q^74 - 153 * q^76 + 81 * q^77 - 99 * q^79 - 288 * q^80 - 36 * q^82 + 45 * q^83 - 99 * q^85 + 81 * q^86 - 153 * q^88 - 81 * q^89 - 18 * q^91 + 207 * q^92 - 99 * q^94 - 171 * q^95 - 45 * q^97 + 81 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{17}{27}\right)$

Coefficient data

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

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

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

$2$	0.280212	−	0.649604i	0.198140	−	0.459339i	−0.789959	−	0.613159i	$-0.789898\pi$
$2$	0.280212	−	0.649604i	0.198140	−	0.459339i	0.988099	+	0.153820i	$0.0491576\pi$
$3$		0			0
$3$		0			0
$4$	1.02902	+	1.09069i	0.514508	+	0.545347i
$5$	−0.199739	−	3.42939i	−0.0893262	−	1.53367i	−0.683867	−	0.729606i	$-0.739703\pi$
$5$	−0.199739	−	3.42939i	−0.0893262	−	1.53367i	0.594541	−	0.804065i	$-0.297334\pi$
$6$		0			0
$7$	2.63236	+	0.623881i	0.994939	+	0.235805i	0.695668	−	0.718363i	$-0.255108\pi$
$7$	2.63236	+	0.623881i	0.994939	+	0.235805i	0.299271	+	0.954168i	$0.403257\pi$
$8$	2.32646	−	0.846761i	0.822527	−	0.299375i
$9$		0			0
$10$	−2.28372	−	0.831205i	−0.722174	−	0.262850i
$11$	−1.23441	−	0.811885i	−0.372189	−	0.244793i	0.349610	−	0.936895i	$-0.386314\pi$
$11$	−1.23441	−	0.811885i	−0.372189	−	0.244793i	−0.721799	+	0.692103i	$0.756684\pi$
$12$		0			0
$13$	5.51427	+	0.644526i	1.52938	+	0.178759i	0.838779	−	0.544472i	$-0.183270\pi$
$13$	5.51427	+	0.644526i	1.52938	+	0.178759i	0.690606	+	0.723232i	$0.257344\pi$
$14$	1.14289	−	1.53517i	0.305451	−	0.410292i
$15$		0			0
$16$	−0.0725347	+	1.24537i	−0.0181337	+	0.311343i
$17$	−3.86594	+	3.24391i	−0.937627	+	0.786763i	−0.977171	−	0.212455i	$-0.931854\pi$
$17$	−3.86594	+	3.24391i	−0.937627	+	0.786763i	0.0395437	+	0.999218i	$0.487410\pi$
$18$		0			0
$19$	−3.94119	−	3.30705i	−0.904171	−	0.758690i	0.0668301	−	0.997764i	$-0.478711\pi$
$19$	−3.94119	−	3.30705i	−0.904171	−	0.758690i	−0.971001	+	0.239075i	$0.923156\pi$
$20$	3.53488	−	3.74676i	0.790424	−	0.837801i
$21$		0			0
$22$	−0.873300	+	0.574378i	−0.186188	+	0.122458i
$23$	1.68752	−	0.399950i	0.351872	−	0.0833953i	−0.0508787	−	0.998705i	$-0.516202\pi$
$23$	1.68752	−	0.399950i	0.351872	−	0.0833953i	0.402751	+	0.915310i	$0.368054\pi$
$24$		0			0
$25$	−6.75465	+	0.789506i	−1.35093	+	0.157901i
$26$	1.96385	−	3.40149i	0.385143	−	0.667087i
$27$		0			0
$28$	2.02828	+	3.51309i	0.383309	+	0.663911i
$29$	1.28309	+	1.72349i	0.238264	+	0.320044i	0.905131	−	0.425133i	$-0.139773\pi$
$29$	1.28309	+	1.72349i	0.238264	+	0.320044i	−0.666867	+	0.745176i	$0.732365\pi$
$30$		0			0
$31$	1.09167	−	3.64642i	0.196069	−	0.654916i	−0.802252	−	0.596986i	$-0.796365\pi$
$31$	1.09167	−	3.64642i	0.196069	−	0.654916i	0.998321	−	0.0579300i	$-0.0184500\pi$
$32$	5.21352	+	2.61833i	0.921629	+	0.462859i
$33$		0			0
$34$	1.02397	+	3.42031i	0.175610	+	0.586578i
$35$	1.61375	−	9.15202i	0.272773	−	1.54697i
$36$		0			0
$37$	−0.891723	−	5.05721i	−0.146598	−	0.831401i	−0.966070	−	0.258281i	$-0.916844\pi$
$37$	−0.891723	−	5.05721i	−0.146598	−	0.831401i	0.819472	−	0.573120i	$-0.194267\pi$
$38$	−3.25264	+	1.63354i	−0.527648	+	0.264995i
$39$		0			0
$40$	−3.36856	−	7.80920i	−0.532616	−	1.23474i
$41$	−1.78715	−	4.14308i	−0.279106	−	0.647040i	0.719782	−	0.694201i	$-0.244242\pi$
$41$	−1.78715	−	4.14308i	−0.279106	−	0.647040i	−0.998887	+	0.0471609i	$0.984983\pi$
$42$		0			0
$43$	0.736775	−	0.370022i	0.112357	−	0.0564279i	−0.391733	−	0.920079i	$-0.628124\pi$
$43$	0.736775	−	0.370022i	0.112357	−	0.0564279i	0.504090	+	0.863651i	$0.331828\pi$
$44$	−0.384712	−	2.18181i	−0.0579975	−	0.328920i
$45$		0			0
$46$	0.213054	−	1.20829i	0.0314131	−	0.178153i
$47$	1.92513	+	6.43037i	0.280808	+	0.937966i	0.975748	+	0.218897i	$0.0702460\pi$
$47$	1.92513	+	6.43037i	0.280808	+	0.937966i	−0.694939	+	0.719068i	$0.744569\pi$
$48$		0			0
$49$	0.284673	+	0.142968i	0.0406675	+	0.0204240i
$50$	−1.37987	+	4.60908i	−0.195143	+	0.651822i
$51$		0			0
$52$	4.97130	+	6.67762i	0.689395	+	0.926019i
$53$	2.58797	+	4.48249i	0.355485	+	0.615717i	0.987201	−	0.159482i	$-0.0509825\pi$
$53$	2.58797	+	4.48249i	0.355485	+	0.615717i	−0.631716	+	0.775200i	$0.717649\pi$
$54$		0			0
$55$	−2.53771	+	4.39545i	−0.342185	+	0.592682i
$56$	6.65235	−	0.777549i	0.888958	−	0.103904i
$57$		0			0
$58$	1.47912	−	0.350558i	0.194218	−	0.0460305i
$59$	2.95286	−	1.94213i	0.384430	−	0.252843i	−0.342554	−	0.939498i	$-0.611292\pi$
$59$	2.95286	−	1.94213i	0.384430	−	0.252843i	0.726984	+	0.686655i	$0.240922\pi$
$60$		0			0
$61$	3.71901	−	3.94192i	0.476170	−	0.504711i	−0.444109	−	0.895973i	$-0.646480\pi$
$61$	3.71901	−	3.94192i	0.476170	−	0.504711i	0.920280	+	0.391262i	$0.127961\pi$
$62$	−2.06283	−	1.73092i	−0.261980	−	0.219827i
$63$		0			0
$64$	1.25051	−	1.04930i	0.156314	−	0.131163i
$65$	1.10892	−	19.0394i	0.137544	−	2.36154i
$66$		0			0
$67$	−3.91063	+	5.25288i	−0.477759	+	0.641742i	−0.974028	−	0.226427i	$-0.927295\pi$
$67$	−3.91063	+	5.25288i	−0.477759	+	0.641742i	0.496269	+	0.868169i	$0.334703\pi$
$68$	−7.51622	−	0.878520i	−0.911476	−	0.106536i
$69$		0			0
$70$	−5.49299	−	3.61280i	−0.656538	−	0.431812i
$71$	3.30039	+	1.20125i	0.391685	+	0.142562i	0.530352	−	0.847777i	$-0.322060\pi$
$71$	3.30039	+	1.20125i	0.391685	+	0.142562i	−0.138667	+	0.990339i	$0.544282\pi$
$72$		0			0
$73$	0.668031	−	0.243143i	0.0781871	−	0.0284578i	−0.302630	−	0.953108i	$-0.597865\pi$
$73$	0.668031	−	0.243143i	0.0781871	−	0.0284578i	0.380818	+	0.924650i	$0.375643\pi$
$74$	−3.53506	−	0.837823i	−0.410942	−	0.0973950i
$75$		0			0
$76$	−0.448570	−	7.70164i	−0.0514545	−	0.883439i
$77$	−2.74290	−	2.90730i	−0.312582	−	0.331318i
$78$		0			0
$79$	−6.21626	+	14.4109i	−0.699384	+	1.62135i	0.0814970	+	0.996674i	$0.474030\pi$
$79$	−6.21626	+	14.4109i	−0.699384	+	1.62135i	−0.780881	+	0.624680i	$0.785229\pi$
$80$	4.28536			0.479118
$81$		0			0
$82$	−3.19214			−0.352513
$83$	2.35107	−	5.45040i	0.258064	−	0.598259i	−0.739094	−	0.673603i	$-0.764746\pi$
$83$	2.35107	−	5.45040i	0.258064	−	0.598259i	0.997158	+	0.0753432i	$0.0240052\pi$
$84$		0			0
$85$	11.8968	+	12.6099i	1.29039	+	1.36773i
$86$	−0.0339149	−	0.582297i	−0.00365714	−	0.0627907i
$87$		0			0
$88$	−3.55928	−	0.843564i	−0.379420	−	0.0899242i
$89$	−3.78422	+	1.37734i	−0.401127	+	0.145998i	−0.534702	−	0.845040i	$-0.679576\pi$
$89$	−3.78422	+	1.37734i	−0.401127	+	0.145998i	0.133576	+	0.991039i	$0.457354\pi$
$90$		0			0
$91$	14.1135	+	5.13688i	1.47949	+	0.538491i
$92$	2.17271	+	1.42901i	0.226521	+	0.148985i
$93$		0			0
$94$	4.71663	+	0.551295i	0.486484	+	0.0568618i
$95$	−10.5540	+	14.1764i	−1.08281	+	1.45447i
$96$		0			0
$97$	0.700141	−	12.0210i	0.0710886	−	1.22054i	−0.754511	−	0.656287i	$-0.772126\pi$
$97$	0.700141	−	12.0210i	0.0710886	−	1.22054i	0.825600	−	0.564256i	$-0.190837\pi$
$98$	0.172641	−	0.144863i	0.0174394	−	0.0146334i
$99$		0			0
$100$	−7.81176	−	6.55484i	−0.781176	−	0.655484i
$101$	−11.5496	+	12.2419i	−1.14923	+	1.21811i	−0.176967	+	0.984217i	$0.556629\pi$
$101$	−11.5496	+	12.2419i	−1.14923	+	1.21811i	−0.972262	+	0.233895i	$0.924853\pi$
$102$		0			0
$103$	−14.5318	+	9.55771i	−1.43186	+	0.941749i	−0.432668	+	0.901554i	$0.642428\pi$
$103$	−14.5318	+	9.55771i	−1.43186	+	0.941749i	−0.999192	+	0.0401953i	$0.987202\pi$
$104$	13.3745	−	3.16981i	1.31148	−	0.310825i
$105$		0			0
$106$	3.63702	−	0.425107i	0.353259	−	0.0412900i
$107$	−3.74462	+	6.48587i	−0.362006	+	0.627013i	−0.988291	−	0.152581i	$-0.951241\pi$
$107$	−3.74462	+	6.48587i	−0.362006	+	0.627013i	0.626285	+	0.779594i	$0.284575\pi$
$108$		0			0
$109$	−1.69921	−	2.94312i	−0.162755	−	0.281899i	0.773101	−	0.634283i	$-0.218705\pi$
$109$	−1.69921	−	2.94312i	−0.162755	−	0.281899i	−0.935856	+	0.352384i	$0.885371\pi$
$110$	2.14420	+	2.88016i	0.204442	+	0.274613i
$111$		0			0
$112$	−0.967902	+	3.23302i	−0.0914581	+	0.305491i
$113$	−1.83608	−	0.922116i	−0.172724	−	0.0867454i	0.360336	−	0.932822i	$-0.382662\pi$
$113$	−1.83608	−	0.922116i	−0.172724	−	0.0867454i	−0.533061	+	0.846077i	$0.678958\pi$
$114$		0			0
$115$	−1.70865	−	5.70729i	−0.159332	−	0.532207i
$116$	−0.559478	+	3.17296i	−0.0519462	+	0.294602i
$117$		0			0
$118$	−0.434187	−	2.46240i	−0.0399701	−	0.226682i
$119$	−12.2004	+	6.12725i	−1.11840	+	0.561684i
$120$		0			0
$121$	−3.49226	−	8.09598i	−0.317479	−	0.735998i
$122$	−1.51858	−	3.52045i	−0.137485	−	0.318727i
$123$		0			0
$124$	5.10047	−	2.56155i	0.458036	−	0.230034i
$125$	1.07411	+	6.09158i	0.0960713	+	0.544847i
$126$		0			0
$127$	−1.46076	+	8.28439i	−0.129622	+	0.735121i	0.848833	+	0.528661i	$0.177306\pi$
$127$	−1.46076	+	8.28439i	−0.129622	+	0.735121i	−0.978455	+	0.206460i	$0.933806\pi$
$128$	3.01524	+	10.0716i	0.266512	+	0.890212i
$129$		0			0
$130$	−12.0573	−	6.05541i	−1.05750	−	0.531094i
$131$	−3.07600	+	10.2746i	−0.268752	+	0.897693i	0.711958	+	0.702222i	$0.247809\pi$
$131$	−3.07600	+	10.2746i	−0.268752	+	0.897693i	−0.980710	+	0.195471i	$0.937377\pi$
$132$		0			0
$133$	−8.31143	−	11.1642i	−0.720692	−	0.968058i
$134$	2.31649	+	4.01228i	0.200114	+	0.346608i
$135$		0			0
$136$	−6.24712	+	10.8203i	−0.535686	+	0.927835i
$137$	−10.5960	+	1.23850i	−0.905281	+	0.105812i	−0.555978	−	0.831197i	$-0.687656\pi$
$137$	−10.5960	+	1.23850i	−0.905281	+	0.105812i	−0.349304	+	0.937010i	$0.613582\pi$
$138$		0			0
$139$	2.74202	−	0.649870i	0.232575	−	0.0551213i	−0.112676	−	0.993632i	$-0.535942\pi$
$139$	2.74202	−	0.649870i	0.232575	−	0.0551213i	0.345251	+	0.938511i	$0.387794\pi$
$140$	11.6426	−	7.65748i	0.983982	−	0.647175i
$141$		0			0
$142$	1.70514	−	1.80735i	0.143092	−	0.151669i
$143$	−6.28360	−	5.27257i	−0.525461	−	0.440914i
$144$		0			0
$145$	5.65423	−	4.74447i	0.469559	−	0.394006i
$146$	0.0292432	−	0.502087i	0.00242019	−	0.0415530i
$147$		0			0
$148$	4.59827	−	6.17655i	0.377976	−	0.507710i
$149$	0.682167	+	0.0797339i	0.0558853	+	0.00653206i	0.143990	−	0.989579i	$-0.454007\pi$
$149$	0.682167	+	0.0797339i	0.0558853	+	0.00653206i	−0.0881043	+	0.996111i	$0.528081\pi$
$150$		0			0
$151$	−0.419776	−	0.276091i	−0.0341609	−	0.0224680i	0.532314	−	0.846547i	$-0.321323\pi$
$151$	−0.419776	−	0.276091i	−0.0341609	−	0.0224680i	−0.566475	+	0.824079i	$0.691693\pi$
$152$	−11.9693	−	4.35647i	−0.970838	−	0.353356i
$153$		0			0
$154$	−2.65719	+	0.967136i	−0.214122	+	0.0779341i
$155$	−12.7231	−	3.01542i	−1.02194	−	0.242204i
$156$		0			0
$157$	0.737588	+	12.6639i	0.0588660	+	1.01069i	0.890389	+	0.455200i	$0.150432\pi$
$157$	0.737588	+	12.6639i	0.0588660	+	1.01069i	−0.831523	+	0.555490i	$0.812531\pi$
$158$	7.61951	+	8.07621i	0.606176	+	0.642509i
$159$		0			0
$160$	7.93793	−	18.4022i	0.627549	−	1.45482i
$161$	4.69169			0.369757
$162$		0			0
$163$	13.8238			1.08276			0.541382	−	0.840777i	$-0.317901\pi$
$163$	13.8238			1.08276			0.541382	+	0.840777i	$0.317901\pi$
$164$	2.67982	−	6.21253i	0.209259	−	0.485117i
$165$		0			0
$166$	−2.88180	−	3.05453i	−0.223671	−	0.237078i
$167$	−0.161181	−	2.76737i	−0.0124726	−	0.214145i	−0.998786	−	0.0492633i	$-0.984313\pi$
$167$	−0.161181	−	2.76737i	−0.0124726	−	0.214145i	0.986313	−	0.164882i	$-0.0527244\pi$
$168$		0			0
$169$	17.3422	+	4.11018i	1.33402	+	0.316168i
$170$	11.5250	−	4.19477i	0.883931	−	0.321725i
$171$		0			0
$172$	1.16174	+	0.422837i	0.0885815	+	0.0322410i
$173$	17.3443	+	11.4075i	1.31866	+	0.867299i	0.996835	−	0.0794991i	$-0.0253321\pi$
$173$	17.3443	+	11.4075i	1.31866	+	0.867299i	0.321829	+	0.946798i	$0.395702\pi$
$174$		0			0
$175$	−18.2732	−	2.13584i	−1.38133	−	0.161454i
$176$	1.10064	−	1.47841i	0.0829636	−	0.111439i
$177$		0			0
$178$	−0.165655	+	2.84419i	−0.0124164	+	0.213181i
$179$	−10.8498	+	9.10407i	−0.810953	+	0.680470i	−0.950835	−	0.309698i	$-0.899772\pi$
$179$	−10.8498	+	9.10407i	−0.810953	+	0.680470i	0.139882	+	0.990168i	$0.455328\pi$
$180$		0			0
$181$	−0.124097	−	0.104130i	−0.00922404	−	0.00773989i	0.638164	−	0.769901i	$-0.279694\pi$
$181$	−0.124097	−	0.104130i	−0.00922404	−	0.00773989i	−0.647388	+	0.762161i	$0.724139\pi$
$182$	7.29169	−	7.72874i	0.540496	−	0.572892i
$183$		0			0
$184$	3.58728	−	2.35939i	0.264458	−	0.173937i
$185$	−17.1651	+	4.06819i	−1.26200	+	0.299100i
$186$		0			0
$187$	7.40583	−	0.865618i	0.541568	−	0.0633002i
$188$	−5.03258	+	8.71668i	−0.367038	+	0.635729i
$189$		0			0
$190$	6.25172	+	10.8283i	0.453548	+	0.785568i
$191$	13.9010	+	18.6723i	1.00584	+	1.35108i	0.935411	+	0.353562i	$0.115030\pi$
$191$	13.9010	+	18.6723i	1.00584	+	1.35108i	0.0704300	+	0.997517i	$0.477563\pi$
$192$		0			0
$193$	−3.07901	+	10.2846i	−0.221632	+	0.740303i	0.772774	+	0.634681i	$0.218869\pi$
$193$	−3.07901	+	10.2846i	−0.221632	+	0.740303i	−0.994406	+	0.105622i	$0.966317\pi$
$194$	−7.61267	−	3.82323i	−0.546558	−	0.274492i
$195$		0			0
$196$	0.136999	+	0.457608i	0.00978562	+	0.0326863i
$197$	−1.18741	+	6.73411i	−0.0845992	+	0.479786i	0.912843	+	0.408310i	$0.133882\pi$
$197$	−1.18741	+	6.73411i	−0.0845992	+	0.479786i	−0.997442	+	0.0714755i	$0.977229\pi$
$198$		0			0
$199$	1.86766	+	10.5920i	0.132395	+	0.750848i	0.976639	+	0.214889i	$0.0689389\pi$
$199$	1.86766	+	10.5920i	0.132395	+	0.750848i	−0.844244	+	0.535959i	$0.819950\pi$
$200$	−15.0459	+	7.55633i	−1.06390	+	0.534313i
$201$		0			0
$202$	4.71603	+	10.9330i	0.331819	+	0.769242i
$203$	2.30230	+	5.33734i	0.161590	+	0.374608i
$204$		0			0
$205$	−13.8513	+	6.95637i	−0.967415	+	0.485854i
$206$	2.13675	+	12.1181i	0.148874	+	0.844307i
$207$		0			0
$208$	−1.20265	+	6.82057i	−0.0833888	+	0.472922i
$209$	2.18010	+	7.28205i	0.150801	+	0.503710i
$210$		0			0
$211$	7.77699	+	3.90575i	0.535390	+	0.268883i	0.695884	−	0.718154i	$-0.255013\pi$
$211$	7.77699	+	3.90575i	0.535390	+	0.268883i	−0.160495	+	0.987037i	$0.551309\pi$
$212$	−2.22596	+	7.43524i	−0.152880	+	0.510654i
$213$		0			0
$214$	3.16396	+	4.24994i	0.216284	+	0.290520i
$215$	−1.41612	−	2.45278i	−0.0965783	−	0.167279i
$216$		0			0
$217$	5.14859	−	8.91762i	0.349509	−	0.605368i
$218$	−2.38800	+	0.279117i	−0.161736	+	0.0189042i
$219$		0			0
$220$	−7.40544	+	1.75512i	−0.499274	+	0.118330i
$221$	−23.4086	+	15.3961i	−1.57463	+	1.03565i
$222$		0			0
$223$	−5.40580	+	5.72981i	−0.361999	+	0.383696i	−0.882617	−	0.470093i	$-0.844220\pi$
$223$	−5.40580	+	5.72981i	−0.361999	+	0.383696i	0.520618	+	0.853790i	$0.325702\pi$
$224$	12.0903	+	10.1450i	0.807820	+	0.677842i
$225$		0			0
$226$	−1.11350	+	0.934340i	−0.0740691	+	0.0621514i
$227$	1.11147	−	19.0833i	0.0737712	−	1.26660i	−0.734833	−	0.678248i	$-0.762739\pi$
$227$	1.11147	−	19.0833i	0.0737712	−	1.26660i	0.808604	−	0.588354i	$-0.200224\pi$
$228$		0			0
$229$	16.1357	−	21.6740i	1.06628	−	1.43226i	0.171808	−	0.985130i	$-0.445039\pi$
$229$	16.1357	−	21.6740i	1.06628	−	1.43226i	0.894469	−	0.447129i	$-0.147554\pi$
$230$	−4.18626	−	0.489303i	−0.276034	−	0.0322637i
$231$		0			0
$232$	4.44443	+	2.92315i	0.291791	+	0.191914i
$233$	−17.0044	−	6.18909i	−1.11400	−	0.405461i	−0.281538	−	0.959550i	$-0.590844\pi$
$233$	−17.0044	−	6.18909i	−1.11400	−	0.405461i	−0.832457	+	0.554089i	$0.813067\pi$
$234$		0			0
$235$	21.6677	−	7.88641i	1.41345	−	0.514453i
$236$	5.15681	+	1.22219i	0.335680	+	0.0795576i
$237$		0			0
$238$	0.561601	+	9.64232i	0.0364032	+	0.625019i
$239$	7.27252	+	7.70842i	0.470420	+	0.498616i	0.918524	−	0.395365i	$-0.129382\pi$
$239$	7.27252	+	7.70842i	0.470420	+	0.498616i	−0.448104	+	0.893982i	$0.647900\pi$
$240$		0			0
$241$	−6.68400	+	15.4952i	−0.430554	+	0.998137i	0.555470	+	0.831536i	$0.312538\pi$
$241$	−6.68400	+	15.4952i	−0.430554	+	0.998137i	−0.986024	+	0.166600i	$0.946721\pi$
$242$	−6.23775			−0.400978
$243$		0			0
$244$	8.12635			0.520236
$245$	0.433433	−	1.00481i	0.0276910	−	0.0641951i
$246$		0			0
$247$	−19.6013	−	20.7762i	−1.24720	−	1.32196i
$248$	−0.547931	−	9.40761i	−0.0347937	−	0.597384i
$249$		0			0
$250$	4.25809	+	1.00919i	0.269305	+	0.0638265i
$251$	−17.5886	+	6.40174i	−1.11018	+	0.404074i	−0.831061	−	0.556181i	$-0.812266\pi$
$251$	−17.5886	+	6.40174i	−1.11018	+	0.404074i	−0.279123	+	0.960255i	$0.590044\pi$
$252$		0			0
$253$	−2.40781	−	0.876370i	−0.151378	−	0.0550969i
$254$	4.97225	+	3.27030i	0.311987	+	0.205197i
$255$		0			0
$256$	10.6302	+	1.24250i	0.664389	+	0.0776560i
$257$	17.2527	−	23.1744i	1.07620	−	1.44558i	0.190282	−	0.981729i	$-0.439060\pi$
$257$	17.2527	−	23.1744i	1.07620	−	1.44558i	0.885913	−	0.463852i	$-0.153533\pi$
$258$		0			0
$259$	0.807762	−	13.8687i	0.0501919	−	0.861762i
$260$	21.9072	−	18.3823i	1.35863	−	1.14002i
$261$		0			0
$262$	5.81246	+	4.87724i	0.359095	+	0.301317i
$263$	16.4777	−	17.4653i	1.01606	−	1.07696i	0.0190354	−	0.999819i	$-0.493940\pi$
$263$	16.4777	−	17.4653i	1.01606	−	1.07696i	0.997020	−	0.0771375i	$-0.0245780\pi$
$264$		0			0
$265$	14.8553	−	9.77048i	0.912554	−	0.600196i
$266$	−9.58126	+	2.27080i	−0.587465	+	0.139232i
$267$		0			0
$268$	−9.75339	+	1.14001i	−0.595783	+	0.0696370i
$269$	12.8618	−	22.2774i	0.784200	−	1.35827i	−0.145276	−	0.989391i	$-0.546407\pi$
$269$	12.8618	−	22.2774i	0.784200	−	1.35827i	0.929476	−	0.368883i	$-0.120260\pi$
$270$		0			0
$271$	−5.12617	−	8.87880i	−0.311393	−	0.539348i	0.667271	−	0.744815i	$-0.267462\pi$
$271$	−5.12617	−	8.87880i	−0.311393	−	0.539348i	−0.978664	+	0.205466i	$0.934129\pi$
$272$	−3.75945	−	5.04982i	−0.227950	−	0.306190i
$273$		0			0
$274$	−2.16460	+	7.23027i	−0.130768	+	0.436797i
$275$	8.97901	+	4.50943i	0.541454	+	0.271929i
$276$		0			0
$277$	1.70105	+	5.68189i	0.102206	+	0.341392i	0.993762	−	0.111518i	$-0.0355713\pi$
$277$	1.70105	+	5.68189i	0.102206	+	0.341392i	−0.891557	+	0.452909i	$0.850386\pi$
$278$	0.346187	−	1.96333i	0.0207629	−	0.117752i
$279$		0			0
$280$	−3.99526	−	22.6582i	−0.238762	−	1.35409i
$281$	−18.5579	+	9.32011i	−1.10707	+	0.555991i	−0.905868	−	0.423559i	$-0.860781\pi$
$281$	−18.5579	+	9.32011i	−1.10707	+	0.555991i	−0.201201	+	0.979550i	$0.564484\pi$
$282$		0			0
$283$	4.65687	+	10.7958i	0.276822	+	0.641747i	0.998737	−	0.0502352i	$-0.0159971\pi$
$283$	4.65687	+	10.7958i	0.276822	+	0.641747i	−0.721915	+	0.691982i	$0.756738\pi$
$284$	2.08597	+	4.83582i	0.123780	+	0.286953i
$285$		0			0
$286$	−5.18582	+	2.60442i	−0.306644	+	0.154002i
$287$	−2.11963	−	12.0210i	−0.125118	−	0.709580i
$288$		0			0
$289$	1.47052	−	8.33972i	0.0865011	−	0.490572i
$290$	−1.49764	−	5.00247i	−0.0879445	−	0.293755i
$291$		0			0
$292$	0.952610	+	0.478419i	0.0557473	+	0.0279973i
$293$	7.76918	−	25.9509i	0.453880	−	1.51607i	−0.358833	−	0.933402i	$-0.616825\pi$
$293$	7.76918	−	25.9509i	0.453880	−	1.51607i	0.812713	−	0.582664i	$-0.197989\pi$
$294$		0			0
$295$	−7.25012	−	9.73860i	−0.422118	−	0.567003i
$296$	−6.35680	−	11.0103i	−0.369482	−	0.639961i
$297$		0			0
$298$	0.242947	−	0.420796i	0.0140735	−	0.0243761i
$299$	9.56323	−	1.11778i	0.553056	−	0.0646430i
$300$		0			0
$301$	2.17031	−	0.514373i	0.125095	−	0.0296480i
$302$	−0.296976	+	0.195324i	−0.0170891	+	0.0112396i
$303$		0			0
$304$	4.40438	−	4.66837i	0.252609	−	0.267749i
$305$	−14.2612	−	11.9666i	−0.816596	−	0.685205i
$306$		0			0
$307$	−18.6794	+	15.6739i	−1.06609	+	0.894557i	−0.994693	−	0.102891i	$-0.967191\pi$
$307$	−18.6794	+	15.6739i	−1.06609	+	0.894557i	−0.0713990	+	0.997448i	$0.522746\pi$
$308$	0.348489	−	5.98332i	0.0198570	−	0.340932i
$309$		0			0
$310$	−5.52397	+	7.41999i	−0.313741	+	0.421427i
$311$	16.8492	+	1.96939i	0.955431	+	0.111674i	0.579499	−	0.814973i	$-0.303248\pi$
$311$	16.8492	+	1.96939i	0.955431	+	0.111674i	0.375933	+	0.926647i	$0.377322\pi$
$312$		0			0
$313$	−9.74474	−	6.40922i	−0.550805	−	0.362270i	0.243394	−	0.969927i	$-0.421739\pi$
$313$	−9.74474	−	6.40922i	−0.550805	−	0.362270i	−0.794199	+	0.607657i	$0.792109\pi$
$314$	8.43320	+	3.06943i	0.475913	+	0.173218i
$315$		0			0
$316$	−22.1145	+	8.04903i	−1.24404	+	0.452793i
$317$	−26.9412	−	6.38518i	−1.51317	−	0.358628i	−0.611567	−	0.791193i	$-0.709460\pi$
$317$	−26.9412	−	6.38518i	−1.51317	−	0.358628i	−0.901603	+	0.432565i	$0.857608\pi$
$318$		0			0
$319$	−0.184586	−	3.16921i	−0.0103348	−	0.177442i
$320$	−3.84825	−	4.07891i	−0.215124	−	0.228018i
$321$		0			0
$322$	1.31467	−	3.04774i	0.0732634	−	0.169844i
$323$	25.9641			1.44468
$324$		0			0
$325$	−37.7559			−2.09432
$326$	3.87359	−	8.97999i	0.214538	−	0.497356i
$327$		0			0
$328$	−7.66592	−	8.12540i	−0.423279	−	0.448650i
$329$	1.05584	+	18.1281i	0.0582104	+	0.999435i
$330$		0			0
$331$	−18.1435	−	4.30008i	−0.997254	−	0.236354i	−0.300592	−	0.953753i	$-0.597184\pi$
$331$	−18.1435	−	4.30008i	−0.997254	−	0.236354i	−0.696662	+	0.717399i	$0.745332\pi$
$332$	8.36402	−	3.04425i	0.459035	−	0.167075i
$333$		0			0
$334$	−1.84286	−	0.670745i	−0.100837	−	0.0367016i
$335$	18.7953	+	12.3619i	1.02690	+	0.675401i
$336$		0			0
$337$	−30.0243	−	3.50934i	−1.63553	−	0.191166i	−0.751874	−	0.659307i	$-0.770850\pi$
$337$	−30.0243	−	3.50934i	−1.63553	−	0.191166i	−0.883654	+	0.468141i	$0.844924\pi$
$338$	7.52948	−	10.1139i	0.409550	−	0.550121i
$339$		0			0
$340$	−1.51151	+	25.9516i	−0.0819729	+	1.40742i
$341$	−4.30804	+	3.61487i	−0.233293	+	0.195756i
$342$		0			0
$343$	−13.8464	−	11.6185i	−0.747635	−	0.627341i
$344$	1.40076	−	1.48471i	0.0755237	−	0.0800504i
$345$		0			0
$346$	12.2705	−	8.07041i	0.659664	−	0.433868i
$347$	2.99908	−	0.710794i	0.160999	−	0.0381574i	−0.149326	−	0.988788i	$-0.547710\pi$
$347$	2.99908	−	0.710794i	0.160999	−	0.0381574i	0.310325	+	0.950631i	$0.399562\pi$
$348$		0			0
$349$	8.91783	−	1.04234i	0.477360	−	0.0557954i	0.125989	−	0.992032i	$-0.459790\pi$
$349$	8.91783	−	1.04234i	0.477360	−	0.0557954i	0.351371	+	0.936236i	$0.385715\pi$
$350$	−6.50782	+	11.2719i	−0.347858	+	0.602507i
$351$		0			0
$352$	−4.30985	−	7.46487i	−0.229716	−	0.397879i
$353$	−19.9372	−	26.7803i	−1.06115	−	1.42537i	−0.898653	−	0.438661i	$-0.855453\pi$
$353$	−19.9372	−	26.7803i	−1.06115	−	1.42537i	−0.162496	−	0.986709i	$-0.551954\pi$
$354$		0			0
$355$	3.46032	−	11.5583i	0.183655	−	0.613450i
$356$	−5.39629	−	2.71012i	−0.286003	−	0.143636i
$357$		0			0
$358$	2.87379	+	9.59914i	0.151885	+	0.507330i
$359$	0.100805	−	0.571693i	0.00532028	−	0.0301728i	−0.982032	−	0.188714i	$-0.939568\pi$
$359$	0.100805	−	0.571693i	0.00532028	−	0.0301728i	0.987352	+	0.158541i	$0.0506791\pi$
$360$		0			0
$361$	1.29708	+	7.35609i	0.0682672	+	0.387162i
$362$	−0.102416	+	0.0514354i	−0.00538288	+	0.00270338i
$363$		0			0
$364$	8.92022	+	20.6794i	0.467547	+	1.08390i
$365$	−0.967266	−	2.24238i	−0.0506290	−	0.117371i
$366$		0			0
$367$	22.7281	−	11.4145i	1.18640	−	0.595830i	0.257539	−	0.966268i	$-0.417089\pi$
$367$	22.7281	−	11.4145i	1.18640	−	0.595830i	0.928857	+	0.370438i	$0.120792\pi$
$368$	0.375682	+	2.13060i	0.0195838	+	0.111065i
$369$		0			0
$370$	−2.16714	+	12.2904i	−0.112664	+	0.638950i
$371$	4.01592	+	13.4141i	0.208496	+	0.696426i
$372$		0			0
$373$	10.3498	+	5.19788i	0.535894	+	0.269136i	0.696097	−	0.717948i	$-0.254919\pi$
$373$	10.3498	+	5.19788i	0.535894	+	0.269136i	−0.160203	+	0.987084i	$0.551215\pi$
$374$	1.51289	−	5.05341i	0.0782298	−	0.261306i
$375$		0			0
$376$	9.92371	+	13.3299i	0.511776	+	0.687435i
$377$	5.96447	+	10.3308i	0.307186	+	0.532062i
$378$		0			0
$379$	9.18651	−	15.9115i	0.471880	−	0.817319i	−0.527603	−	0.849491i	$-0.676909\pi$
$379$	9.18651	−	15.9115i	0.471880	−	0.817319i	0.999482	+	0.0321718i	$0.0102424\pi$
$380$	−26.3224	+	3.07664i	−1.35031	+	0.157829i
$381$		0			0
$382$	16.0248	−	3.79795i	0.819900	−	0.194320i
$383$	22.3046	−	14.6700i	1.13971	−	0.749601i	0.168005	−	0.985786i	$-0.446267\pi$
$383$	22.3046	−	14.6700i	1.13971	−	0.749601i	0.971708	+	0.236185i	$0.0758971\pi$
$384$		0			0
$385$	−9.42241	+	9.98718i	−0.480211	+	0.508994i
$386$	5.81815	+	4.88201i	0.296136	+	0.248488i
$387$		0			0
$388$	13.8316	−	11.6061i	0.702196	−	0.589212i
$389$	0.184258	−	3.16359i	0.00934226	−	0.160400i	−0.990410	−	0.138157i	$-0.955882\pi$
$389$	0.184258	−	3.16359i	0.00934226	−	0.160400i	0.999753	−	0.0222433i	$-0.00708084\pi$
$390$		0			0
$391$	−5.22645	+	7.02034i	−0.264313	+	0.355034i
$392$	0.783339	+	0.0915592i	0.0395646	+	0.00462444i
$393$		0			0
$394$	4.04178	+	2.65832i	0.203622	+	0.133924i
$395$	50.6623	+	18.4396i	2.54910	+	0.927795i
$396$		0			0
$397$	3.81860	−	1.38986i	0.191650	−	0.0697550i	−0.244412	−	0.969671i	$-0.578595\pi$
$397$	3.81860	−	1.38986i	0.191650	−	0.0697550i	0.436062	+	0.899916i	$0.356373\pi$
$398$	7.40395	+	1.75477i	0.371127	+	0.0879586i
$399$		0			0
$400$	−0.493282	−	8.46932i	−0.0246641	−	0.423466i
$401$	−14.6488	−	15.5269i	−0.731528	−	0.775374i	0.249680	−	0.968328i	$-0.419675\pi$
$401$	−14.6488	−	15.5269i	−0.731528	−	0.775374i	−0.981208	+	0.192954i	$0.938193\pi$
$402$		0			0
$403$	8.36996	−	19.4037i	0.416937	−	0.966569i
$404$	−25.2369			−1.25558
$405$		0			0
$406$	4.11229			0.204089
$407$	−3.00512	+	6.96666i	−0.148958	+	0.345324i
$408$		0			0
$409$	15.2295	+	16.1423i	0.753051	+	0.798188i	0.984635	−	0.174628i	$-0.0558721\pi$
$409$	15.2295	+	16.1423i	0.753051	+	0.798188i	−0.231583	+	0.972815i	$0.574391\pi$
$410$	0.637596	+	10.9471i	0.0314886	+	0.540638i
$411$		0			0
$412$	−25.3780	−	6.01469i	−1.25028	−	0.296323i
$413$	8.98466	−	3.27015i	0.442106	−	0.160913i
$414$		0			0
$415$	−19.1612	−	6.97410i	−0.940585	−	0.342345i
$416$	27.0612	+	17.7984i	1.32678	+	0.872640i
$417$		0			0
$418$	5.34134	+	0.624313i	0.261253	+	0.0305362i
$419$	−15.2277	+	20.4544i	−0.743923	+	0.999262i	0.255549	+	0.966796i	$0.417744\pi$
$419$	−15.2277	+	20.4544i	−0.743923	+	0.999262i	−0.999473	+	0.0324665i	$0.989664\pi$
$420$		0			0
$421$	−1.08117	+	18.5631i	−0.0526932	+	0.904708i	0.863594	+	0.504187i	$0.168208\pi$
$421$	−1.08117	+	18.5631i	−0.0526932	+	0.904708i	−0.916288	+	0.400521i	$0.868829\pi$
$422$	4.71639	−	3.95752i	0.229590	−	0.192649i
$423$		0			0
$424$	9.81639	+	8.23693i	0.476726	+	0.400021i
$425$	23.5520	−	24.9636i	1.14244	−	1.21091i
$426$		0			0
$427$	12.2491	−	8.05634i	0.592774	−	0.389874i
$428$	−10.9274	+	2.58984i	−0.528195	+	0.125184i
$429$		0			0
$430$	−1.99015	+	0.232615i	−0.0959736	+	0.0112177i
$431$	3.46440	−	6.00052i	0.166874	−	0.289035i	−0.770445	−	0.637507i	$-0.779966\pi$
$431$	3.46440	−	6.00052i	0.166874	−	0.289035i	0.937319	+	0.348472i	$0.113299\pi$
$432$		0			0
$433$	−12.4509	−	21.5656i	−0.598352	−	1.03638i	−0.993064	−	0.117571i	$-0.962489\pi$
$433$	−12.4509	−	21.5656i	−0.598352	−	1.03638i	0.394713	−	0.918805i	$-0.370844\pi$
$434$	−4.35023	−	5.84337i	−0.208817	−	0.280491i
$435$		0			0
$436$	1.46152	−	4.88183i	0.0699943	−	0.233797i
$437$	−7.97349	−	4.00444i	−0.381424	−	0.191558i
$438$		0			0
$439$	2.33380	+	7.79545i	0.111386	+	0.372057i	0.995447	−	0.0953156i	$-0.0303860\pi$
$439$	2.33380	+	7.79545i	0.111386	+	0.372057i	−0.884061	+	0.467372i	$0.845201\pi$
$440$	−2.18199	+	12.3747i	−0.104022	+	0.589938i
$441$		0			0
$442$	3.44199	+	19.5205i	0.163719	+	0.928495i
$443$	22.5679	−	11.3340i	1.07223	−	0.538495i	0.177052	−	0.984201i	$-0.443344\pi$
$443$	22.5679	−	11.3340i	1.07223	−	0.538495i	0.895179	+	0.445707i	$0.147048\pi$
$444$		0			0
$445$	5.47932	+	12.7025i	0.259744	+	0.602155i
$446$	2.20734	+	5.11718i	0.104520	+	0.242306i
$447$		0			0
$448$	3.94644	−	1.98197i	0.186452	−	0.0936395i
$449$	−6.85970	−	38.9033i	−0.323729	−	1.83596i	−0.518458	−	0.855103i	$-0.673494\pi$
$449$	−6.85970	−	38.9033i	−0.323729	−	1.83596i	0.194728	−	0.980857i	$-0.437617\pi$
$450$		0			0
$451$	−1.15762	+	6.56522i	−0.0545104	+	0.309144i
$452$	−0.883615	−	2.95148i	−0.0415618	−	0.138826i
$453$		0			0
$454$	−12.0851	−	6.06938i	−0.567183	−	0.284850i
$455$	14.7974	−	49.4266i	0.693711	−	2.31716i
$456$		0			0
$457$	12.4537	+	16.7283i	0.582561	+	0.782515i	0.991508	−	0.130043i	$-0.0415116\pi$
$457$	12.4537	+	16.7283i	0.582561	+	0.782515i	−0.408948	+	0.912558i	$0.634104\pi$
$458$	−9.55811	−	16.5551i	−0.446621	−	0.773570i
$459$		0			0
$460$	4.46668	−	7.73651i	0.208260	−	0.360717i
$461$	−16.8916	+	1.97435i	−0.786722	+	0.0919546i	−0.499961	−	0.866048i	$-0.666653\pi$
$461$	−16.8916	+	1.97435i	−0.786722	+	0.0919546i	−0.286761	+	0.958002i	$0.592578\pi$
$462$		0			0
$463$	9.18958	−	2.17797i	0.427076	−	0.101219i	−0.0114562	−	0.999934i	$-0.503647\pi$
$463$	9.18958	−	2.17797i	0.427076	−	0.101219i	0.438532	+	0.898716i	$0.355499\pi$
$464$	−2.23945	+	1.47291i	−0.103964	+	0.0683781i
$465$		0			0
$466$	−8.78529	+	9.31186i	−0.406971	+	0.431364i
$467$	23.3985	+	19.6337i	1.08275	+	0.908538i	0.996147	−	0.0877046i	$-0.0279532\pi$
$467$	23.3985	+	19.6337i	1.08275	+	0.908538i	0.0866068	+	0.996243i	$0.472398\pi$
$468$		0			0
$469$	−13.5714	+	11.3877i	−0.626667	+	0.525836i
$470$	0.948511	−	16.2853i	0.0437516	−	0.751185i
$471$		0			0
$472$	5.22519	−	7.01864i	0.240509	−	0.323059i
$473$	−1.20990	−	0.141417i	−0.0556312	−	0.00650236i
$474$		0			0
$475$	29.2323	+	19.2264i	1.34127	+	0.882167i
$476$	−19.2373	−	7.00181i	−0.881741	−	0.320928i
$477$		0			0
$478$	7.04526	−	2.56427i	0.322243	−	0.117287i
$479$	−12.1086	−	2.86979i	−0.553256	−	0.131124i	−0.0555278	−	0.998457i	$-0.517684\pi$
$479$	−12.1086	−	2.86979i	−0.553256	−	0.131124i	−0.497728	+	0.867333i	$0.665832\pi$
$480$		0			0
$481$	−1.65770	−	28.4616i	−0.0755846	−	1.29774i
$482$	8.19284	+	8.68390i	0.373174	+	0.395541i
$483$		0			0
$484$	5.23664	−	12.1399i	0.238029	−	0.551813i
$485$	−41.3645			−1.87826
$486$		0			0
$487$	13.2205			0.599077			0.299538	−	0.954084i	$-0.403167\pi$
$487$	13.2205			0.599077			0.299538	+	0.954084i	$0.403167\pi$
$488$	5.31425	−	12.3198i	0.240565	−	0.557692i
$489$		0			0
$490$	−0.531276	−	0.563120i	−0.0240006	−	0.0254392i
$491$	1.05439	+	18.1031i	0.0475839	+	0.816984i	0.934700	+	0.355437i	$0.115668\pi$
$491$	1.05439	+	18.1031i	0.0475839	+	0.816984i	−0.887116	+	0.461546i	$0.847295\pi$
$492$		0			0
$493$	−10.5512	−	2.50067i	−0.475201	−	0.112625i
$494$	−18.9888	+	6.91136i	−0.854347	+	0.310957i
$495$		0			0
$496$	4.46196	+	1.62402i	0.200348	+	0.0729207i
$497$	7.93840	+	5.22117i	0.356086	+	0.234201i
$498$		0			0
$499$	9.44851	+	1.10437i	0.422974	+	0.0494385i	0.324917	−	0.945742i	$-0.394663\pi$
$499$	9.44851	+	1.10437i	0.422974	+	0.0494385i	0.0980561	+	0.995181i	$0.468738\pi$
$500$	−5.53877	+	7.43986i	−0.247701	+	0.332721i
$501$		0			0
$502$	−0.769947	+	13.2195i	−0.0343644	+	0.590014i
$503$	13.1149	−	11.0047i	0.584766	−	0.490677i	−0.301743	−	0.953389i	$-0.597568\pi$
$503$	13.1149	−	11.0047i	0.584766	−	0.490677i	0.886508	+	0.462713i	$0.153124\pi$
$504$		0			0
$505$	44.2891	+	37.1630i	1.97084	+	1.65373i
$506$	−1.24399	+	1.31855i	−0.0553021	+	0.0586168i
$507$		0			0
$508$	−10.5389	+	6.93154i	−0.467588	+	0.307537i
$509$	28.1253	−	6.66581i	1.24663	−	0.295457i	0.446228	−	0.894919i	$-0.352767\pi$
$509$	28.1253	−	6.66581i	1.24663	−	0.295457i	0.800403	+	0.599462i	$0.204619\pi$
$510$		0			0
$511$	1.91019	−	0.223269i	0.0845019	−	0.00987686i
$512$	−6.72742	+	11.6522i	−0.297313	+	0.514961i
$513$		0			0
$514$	−10.2198	−	17.7012i	−0.450775	−	0.780765i
$515$	35.6797	+	47.9262i	1.57224	+	2.11188i
$516$		0			0
$517$	2.84432	−	9.50070i	0.125093	−	0.417840i
$518$	−8.78284	−	4.41091i	−0.385896	−	0.193804i
$519$		0			0
$520$	−13.5419	−	45.2332i	−0.593853	−	1.98361i
$521$	0.716780	−	4.06506i	0.0314027	−	0.178093i	−0.965072	−	0.261984i	$-0.915623\pi$
$521$	0.716780	−	4.06506i	0.0314027	−	0.178093i	0.996475	+	0.0838901i	$0.0267345\pi$
$522$		0			0
$523$	0.273945	+	1.55362i	0.0119788	+	0.0679351i	0.990211	−	0.139577i	$-0.0445744\pi$
$523$	0.273945	+	1.55362i	0.0119788	+	0.0679351i	−0.978232	+	0.207512i	$0.933463\pi$
$524$	−14.3717	+	7.21772i	−0.627829	+	0.315308i
$525$		0			0
$526$	−6.72829	−	15.5979i	−0.293367	−	0.680102i
$527$	7.60832	+	17.6381i	0.331424	+	0.768327i
$528$		0			0
$529$	−17.8658	+	8.97253i	−0.776773	+	0.390110i
$530$	−2.18431	−	12.3879i	−0.0948806	−	0.538094i
$531$		0			0
$532$	3.62411	−	20.5534i	0.157125	−	0.891102i
$533$	−7.18451	−	23.9979i	−0.311195	−	1.03947i
$534$		0			0
$535$	22.9906	+	11.5463i	0.993968	+	0.499190i
$536$	−4.64997	+	15.5320i	−0.200848	+	0.670879i
$537$		0			0
$538$	−10.8674	−	14.5975i	−0.468528	−	0.629342i
$539$	−0.235330	−	0.407603i	−0.0101364	−	0.0175567i
$540$		0			0
$541$	−5.71173	+	9.89300i	−0.245566	+	0.425333i	−0.962291	−	0.272023i	$-0.912307\pi$
$541$	−5.71173	+	9.89300i	−0.245566	+	0.425333i	0.716724	+	0.697357i	$0.245641\pi$
$542$	−7.20411	+	0.842040i	−0.309443	+	0.0361687i
$543$		0			0
$544$	−28.6487	+	6.78988i	−1.22830	+	0.291113i
$545$	−9.75370	+	6.41511i	−0.417803	+	0.274793i
$546$		0			0
$547$	5.56896	−	5.90275i	0.238111	−	0.252383i	−0.597288	−	0.802027i	$-0.703755\pi$
$547$	5.56896	−	5.90275i	0.238111	−	0.252383i	0.835399	+	0.549644i	$0.185236\pi$
$548$	−12.2543	−	10.2826i	−0.523479	−	0.439251i
$549$		0			0
$550$	5.44536	−	4.56920i	0.232191	−	0.194831i
$551$	0.642764	−	11.0358i	0.0273827	−	0.470142i
$552$		0			0
$553$	−25.3541	+	34.0565i	−1.07817	+	1.44823i
$554$	4.16763	+	0.487126i	0.177066	+	0.0206960i
$555$		0			0
$556$	3.53039	+	2.32197i	0.149722	+	0.0984737i
$557$	11.2047	+	4.07820i	0.474760	+	0.172799i	0.568308	−	0.822816i	$-0.307598\pi$
$557$	11.2047	+	4.07820i	0.474760	+	0.172799i	−0.0935472	+	0.995615i	$0.529821\pi$
$558$		0			0
$559$	4.30127	−	1.56553i	0.181924	−	0.0662151i
$560$	11.2806	+	2.67355i	0.476693	+	0.112978i
$561$		0			0
$562$	0.854247	+	14.6669i	0.0360342	+	0.618684i
$563$	−13.8990	−	14.7321i	−0.585772	−	0.620882i	0.364912	−	0.931042i	$-0.381099\pi$
$563$	−13.8990	−	14.7321i	−0.585772	−	0.620882i	−0.950684	+	0.310160i	$0.899617\pi$
$564$		0			0
$565$	−2.79556	+	6.48084i	−0.117610	+	0.272651i
$566$	8.31793			0.349629
$567$		0			0
$568$	8.69539			0.364851
$569$	−5.79341	+	13.4306i	−0.242872	+	0.563042i	−0.995431	−	0.0954837i	$-0.969560\pi$
$569$	−5.79341	+	13.4306i	−0.242872	+	0.563042i	0.752559	+	0.658525i	$0.228819\pi$
$570$		0			0
$571$	−15.8385	−	16.7878i	−0.662820	−	0.702548i	0.305519	−	0.952186i	$-0.401170\pi$
$571$	−15.8385	−	16.7878i	−0.662820	−	0.702548i	−0.968339	+	0.249638i	$0.919688\pi$
$572$	−0.715173	−	12.2790i	−0.0299029	−	0.513413i
$573$		0			0
$574$	−8.40286	−	1.99151i	−0.350729	−	0.0831242i
$575$	−11.0829	+	4.03383i	−0.462187	+	0.168222i
$576$		0			0
$577$	−28.1182	−	10.2342i	−1.17057	−	0.426054i	−0.317711	−	0.948188i	$-0.602914\pi$
$577$	−28.1182	−	10.2342i	−1.17057	−	0.426054i	−0.852864	+	0.522133i	$0.825136\pi$
$578$	−5.00546	−	3.29214i	−0.208200	−	0.136935i
$579$		0			0
$580$	10.9931	+	1.28490i	0.456462	+	0.0533528i
$581$	9.58928	−	12.8806i	0.397830	−	0.534379i
$582$		0			0
$583$	0.444651	−	7.63437i	0.0184156	−	0.316183i
$584$	1.34826	−	1.13132i	0.0557914	−	0.0468146i
$585$		0			0
$586$	−14.6808	−	12.3186i	−0.606457	−	0.508877i
$587$	−0.218618	+	0.231722i	−0.00902333	+	0.00956417i	−0.731870	−	0.681445i	$-0.761352\pi$
$587$	−0.218618	+	0.231722i	−0.00902333	+	0.00956417i	0.722846	+	0.691009i	$0.242833\pi$
$588$		0			0
$589$	−16.3614	+	10.7610i	−0.674158	+	0.443401i
$590$	−8.35780	+	1.98084i	−0.344085	+	0.0815497i
$591$		0			0
$592$	6.36279	−	0.743704i	0.261509	−	0.0305660i
$593$	15.7701	−	27.3146i	0.647601	−	1.12168i	−0.336093	−	0.941829i	$-0.609106\pi$
$593$	15.7701	−	27.3146i	0.647601	−	1.12168i	0.983694	−	0.179849i	$-0.0575609\pi$
$594$		0			0
$595$	23.4496	+	40.6160i	0.961341	+	1.66509i
$596$	0.614996	+	0.826084i	0.0251912	+	0.0338377i
$597$		0			0
$598$	1.95361	−	6.52553i	0.0798892	−	0.266849i
$599$	−19.1667	−	9.62585i	−0.783128	−	0.393302i	0.0118577	−	0.999930i	$-0.496225\pi$
$599$	−19.1667	−	9.62585i	−0.783128	−	0.393302i	−0.794986	+	0.606628i	$0.792522\pi$
$600$		0			0
$601$	−0.117808	−	0.393505i	−0.00480548	−	0.0160514i	0.955553	−	0.294819i	$-0.0952593\pi$
$601$	−0.117808	−	0.393505i	−0.00480548	−	0.0160514i	−0.960359	+	0.278767i	$0.910074\pi$
$602$	0.274008	−	1.55397i	0.0111677	−	0.0633353i
$603$		0			0
$604$	−0.130826	−	0.741950i	−0.00532323	−	0.0301895i
$605$	−27.0667	+	13.5934i	−1.10042	+	0.552652i
$606$		0			0
$607$	−15.2602	−	35.3770i	−0.619391	−	1.43591i	−0.882113	−	0.471037i	$-0.843880\pi$
$607$	−15.2602	−	35.3770i	−0.619391	−	1.43591i	0.262723	−	0.964871i	$-0.415380\pi$
$608$	−11.8885	−	27.5607i	−0.482143	−	1.11773i
$609$		0			0
$610$	−11.7697	+	5.91097i	−0.476541	+	0.239328i
$611$	6.47113	+	36.6996i	0.261794	+	1.48471i
$612$		0			0
$613$	7.63138	−	43.2797i	0.308228	−	1.74805i	−0.299677	−	0.954041i	$-0.596879\pi$
$613$	7.63138	−	43.2797i	0.308228	−	1.74805i	0.607905	−	0.794010i	$-0.292010\pi$
$614$	4.94763	+	16.5262i	0.199670	+	0.666945i
$615$		0			0
$616$	−8.84302	−	4.44113i	−0.356295	−	0.178938i
$617$	−9.84265	+	32.8767i	−0.396250	+	1.32357i	0.494541	+	0.869154i	$0.335336\pi$
$617$	−9.84265	+	32.8767i	−0.396250	+	1.32357i	−0.890791	+	0.454413i	$0.849849\pi$
$618$		0			0
$619$	−3.30757	−	4.44283i	−0.132942	−	0.178573i	0.730667	−	0.682734i	$-0.239209\pi$
$619$	−3.30757	−	4.44283i	−0.132942	−	0.178573i	−0.863610	+	0.504161i	$0.831802\pi$
$620$	−9.80334	−	16.9799i	−0.393711	−	0.681928i
$621$		0			0
$622$	6.00067	−	10.3935i	0.240605	−	0.416740i
$623$	−10.8207	+	1.26476i	−0.433524	+	0.0506717i
$624$		0			0
$625$	−12.4107	+	2.94140i	−0.496429	+	0.117656i
$626$	−6.89404	+	4.53428i	−0.275541	+	0.181226i
$627$		0			0
$628$	−13.0535	+	13.8359i	−0.520889	+	0.552111i
$629$	19.8525	+	16.6582i	0.791569	+	0.664206i
$630$		0			0
$631$	−19.4299	+	16.3036i	−0.773492	+	0.649037i	−0.941601	−	0.336732i	$-0.890678\pi$
$631$	−19.4299	+	16.3036i	−0.773492	+	0.649037i	0.168109	+	0.985768i	$0.446234\pi$
$632$	−2.25926	+	38.7900i	−0.0898686	+	1.54298i
$633$		0			0
$634$	−11.6971	+	15.7119i	−0.464550	+	0.624000i
$635$	28.7022	+	3.35481i	1.13901	+	0.133131i
$636$		0			0
$637$	1.47762	+	0.971844i	0.0585453	+	0.0385059i
$638$	−2.11046	−	0.768143i	−0.0835537	−	0.0304111i
$639$		0			0
$640$	33.9372	−	12.3521i	1.34149	−	0.488261i
$641$	20.5525	+	4.87103i	0.811775	+	0.192394i	0.615482	−	0.788151i	$-0.288961\pi$
$641$	20.5525	+	4.87103i	0.811775	+	0.192394i	0.196293	+	0.980545i	$0.437110\pi$
$642$		0			0
$643$	0.929279	+	15.9551i	0.0366472	+	0.629208i	0.965764	+	0.259422i	$0.0835320\pi$
$643$	0.929279	+	15.9551i	0.0366472	+	0.629208i	−0.929117	+	0.369786i	$0.879431\pi$
$644$	4.82782	+	5.11720i	0.190243	+	0.201646i
$645$		0			0
$646$	7.27546	−	16.8664i	0.286249	−	0.663600i
$647$	−34.6617			−1.36269			−0.681346	−	0.731961i	$-0.738605\pi$
$647$	−34.6617			−1.36269			−0.681346	+	0.731961i	$0.738605\pi$
$648$		0			0
$649$	−5.22183			−0.204975
$650$	−10.5796	+	24.5263i	−0.414967	+	0.962002i
$651$		0			0
$652$	14.2249	+	15.0775i	0.557091	+	0.590482i
$653$	1.25553	+	21.5566i	0.0491326	+	0.843574i	0.929395	+	0.369087i	$0.120329\pi$
$653$	1.25553	+	21.5566i	0.0491326	+	0.843574i	−0.880262	+	0.474487i	$0.842634\pi$
$654$		0			0
$655$	35.8499	+	8.49659i	1.40077	+	0.331989i
$656$	5.28930	−	1.92515i	0.206512	−	0.0751644i
$657$		0			0
$658$	12.0719	+	4.39383i	0.470613	+	0.171289i
$659$	−6.74382	−	4.43548i	−0.262702	−	0.172782i	0.411325	−	0.911489i	$-0.365066\pi$
$659$	−6.74382	−	4.43548i	−0.262702	−	0.172782i	−0.674027	+	0.738707i	$0.735437\pi$
$660$		0			0
$661$	34.1129	+	3.98723i	1.32684	+	0.155085i	0.749818	−	0.661644i	$-0.230141\pi$
$661$	34.1129	+	3.98723i	1.32684	+	0.155085i	0.577021	+	0.816729i	$0.304215\pi$
$662$	−7.87735	+	10.5811i	−0.306162	+	0.411247i
$663$		0			0
$664$	0.854484	−	14.6709i	0.0331604	−	0.569342i
$665$	−36.6263	+	30.7331i	−1.42031	+	1.19178i
$666$		0			0
$667$	2.85455	+	2.39525i	0.110529	+	0.0927445i
$668$	2.85250	−	3.02347i	0.110366	−	0.116982i
$669$		0			0
$670$	13.2970	−	8.74556i	0.513707	−	0.337870i
$671$	−7.79117	+	1.84654i	−0.300775	+	0.0712850i
$672$		0			0
$673$	−1.85004	+	0.216238i	−0.0713137	+	0.00833538i	−0.151675	−	0.988430i	$-0.548467\pi$
$673$	−1.85004	+	0.216238i	−0.0713137	+	0.00833538i	0.0803612	+	0.996766i	$0.474393\pi$
$674$	−10.6928	+	18.5205i	−0.411873	+	0.713385i
$675$		0			0
$676$	13.3625	+	23.1445i	0.513942	+	0.890173i
$677$	−8.56411	−	11.5036i	−0.329146	−	0.442119i	0.606488	−	0.795093i	$-0.292578\pi$
$677$	−8.56411	−	11.5036i	−0.329146	−	0.442119i	−0.935633	+	0.352974i	$0.885171\pi$
$678$		0			0
$679$	9.34268	−	31.2067i	0.358539	−	1.19760i
$680$	38.3550	+	19.2626i	1.47085	+	0.738686i
$681$		0			0
$682$	1.14107	+	3.81145i	0.0436939	+	0.145948i
$683$	−4.45517	+	25.2665i	−0.170472	+	0.966797i	0.772768	+	0.634688i	$0.218871\pi$
$683$	−4.45517	+	25.2665i	−0.170472	+	0.966797i	−0.943241	+	0.332109i	$0.892240\pi$
$684$		0			0
$685$	6.36375	+	36.0906i	0.243147	+	1.37895i
$686$	−11.4274	+	5.73903i	−0.436298	+	0.219117i
$687$		0			0
$688$	0.407374	+	0.944399i	0.0155310	+	0.0360049i
$689$	11.3817	+	26.3857i	0.433607	+	1.00521i
$690$		0			0
$691$	39.6143	−	19.8951i	1.50700	−	0.756844i	0.512217	−	0.858856i	$-0.328825\pi$
$691$	39.6143	−	19.8951i	1.50700	−	0.756844i	0.994783	+	0.102013i	$0.0325282\pi$
$692$	5.40546	+	30.6559i	0.205485	+	1.16536i
$693$		0			0
$694$	0.378642	−	2.14738i	0.0143730	−	0.0815136i
$695$	−2.77635	−	9.27365i	−0.105313	−	0.351770i
$696$		0			0
$697$	20.3487	+	10.2195i	0.770764	+	0.387092i
$698$	1.82177	−	6.08513i	0.0689550	−	0.230326i
$699$		0			0
$700$	−16.4739	−	22.1283i	−0.622656	−	0.836372i
$701$	5.89393	+	10.2086i	0.222611	+	0.385573i	0.955600	−	0.294667i	$-0.0952088\pi$
$701$	5.89393	+	10.2086i	0.222611	+	0.385573i	−0.732989	+	0.680240i	$0.761875\pi$
$702$		0			0
$703$	−13.2100	+	22.8804i	−0.498225	+	0.862951i
$704$	−2.39556	+	0.280001i	−0.0902860	+	0.0105529i
$705$		0			0
$706$	−22.9832	+	5.44712i	−0.864984	+	0.205005i
$707$	−38.0402	+	25.0194i	−1.43065	+	0.940953i
$708$		0			0
$709$	23.3502	−	24.7498i	0.876935	−	0.929497i	−0.121069	−	0.992644i	$-0.538632\pi$
$709$	23.3502	−	24.7498i	0.876935	−	0.929497i	0.998004	+	0.0631469i	$0.0201137\pi$
$710$	−6.53868	−	5.48661i	−0.245392	−	0.205909i
$711$		0			0
$712$	−7.63755	+	6.40867i	−0.286229	+	0.240175i
$713$	0.383825	−	6.59002i	0.0143744	−	0.246798i
$714$		0			0
$715$	−16.8266	+	22.6021i	−0.629280	+	0.845270i
$716$	−21.0944	−	2.46558i	−0.788334	−	0.0921431i
$717$		0			0
$718$	−0.343127	−	0.225678i	−0.0128054	−	0.00842224i
$719$	22.1565	+	8.06429i	0.826297	+	0.300747i	0.720338	−	0.693623i	$-0.243987\pi$
$719$	22.1565	+	8.06429i	0.826297	+	0.300747i	0.105959	+	0.994371i	$0.466209\pi$
$720$		0			0
$721$	−44.2158	+	16.0932i	−1.64668	+	0.599343i
$722$	5.14200	+	1.21868i	0.191365	+	0.0453544i
$723$		0			0
$724$	−0.0141242	−	0.242503i	−0.000524921	−	0.00901254i
$725$	−10.0275	−	10.6286i	−0.372413	−	0.394735i
$726$		0			0
$727$	3.53009	−	8.18366i	0.130924	−	0.303515i	−0.840127	−	0.542390i	$-0.817519\pi$
$727$	3.53009	−	8.18366i	0.130924	−	0.303515i	0.971050	+	0.238875i	$0.0767786\pi$
$728$	37.1841			1.37813
$729$		0			0
$730$	−1.72769			−0.0639448
$731$	−1.64801	+	3.82051i	−0.0609538	+	0.141307i
$732$		0			0
$733$	−16.4513	−	17.4374i	−0.607643	−	0.644063i	0.348381	−	0.937353i	$-0.386731\pi$
$733$	−16.4513	−	17.4374i	−0.607643	−	0.644063i	−0.956024	+	0.293290i	$0.905250\pi$
$734$	−1.04621	−	17.9627i	−0.0386163	−	0.663016i
$735$		0			0
$736$	9.84512	+	2.33334i	0.362896	+	0.0860079i
$737$	9.09205	−	3.30924i	0.334910	−	0.121897i
$738$		0			0
$739$	26.2622	+	9.55867i	0.966071	+	0.351621i	0.776410	−	0.630228i	$-0.217039\pi$
$739$	26.2622	+	9.55867i	0.966071	+	0.351621i	0.189662	+	0.981850i	$0.439261\pi$
$740$	−22.1003	−	14.5356i	−0.812423	−	0.534339i
$741$		0			0
$742$	9.83917	+	1.15003i	0.361207	+	0.0422191i
$743$	23.4200	−	31.4585i	0.859195	−	1.15410i	−0.127552	−	0.991832i	$-0.540712\pi$
$743$	23.4200	−	31.4585i	0.859195	−	1.15410i	0.986747	−	0.162267i	$-0.0518806\pi$
$744$		0			0
$745$	0.137183	−	2.35535i	0.00502601	−	0.0862932i
$746$	6.27670	−	5.26678i	0.229806	−	0.192830i
$747$		0			0
$748$	8.56485	+	7.18676i	0.313162	+	0.262774i
$749$	−13.9036	+	14.7370i	−0.508027	+	0.538477i
$750$		0			0
$751$	−22.5946	+	14.8607i	−0.824489	+	0.542275i	−0.890203	−	0.455564i	$-0.849438\pi$
$751$	−22.5946	+	14.8607i	−0.824489	+	0.542275i	0.0657145	+	0.997838i	$0.479067\pi$
$752$	−8.14784	+	1.93107i	−0.297121	+	0.0704190i
$753$		0			0
$754$	8.38222	−	0.979741i	0.305262	−	0.0356801i
$755$	−0.862979	+	1.49472i	−0.0314070	+	0.0543986i
$756$		0			0
$757$	−10.2471	−	17.7485i	−0.372437	−	0.645080i	0.617503	−	0.786569i	$-0.288144\pi$
$757$	−10.2471	−	17.7485i	−0.372437	−	0.645080i	−0.989940	+	0.141489i	$0.954811\pi$
$758$	−7.76201	−	10.4262i	−0.281929	−	0.378696i
$759$		0			0
$760$	−12.5493	+	41.9176i	−0.455211	+	1.52051i
$761$	13.4726	+	6.76622i	0.488383	+	0.245275i	0.675910	−	0.736984i	$-0.263751\pi$
$761$	13.4726	+	6.76622i	0.488383	+	0.245275i	−0.187527	+	0.982259i	$0.560047\pi$
$762$		0			0
$763$	−2.63678	−	8.80745i	−0.0954577	−	0.318851i
$764$	−6.06139	+	34.3758i	−0.219293	+	1.24367i
$765$		0			0
$766$	−3.27966	−	18.5999i	−0.118499	−	0.672041i
$767$	17.5346	−	8.80623i	0.633139	−	0.317974i
$768$		0			0
$769$	5.36914	+	12.4471i	0.193616	+	0.448852i	0.987175	−	0.159641i	$-0.0510336\pi$
$769$	5.36914	+	12.4471i	0.193616	+	0.448852i	−0.793559	+	0.608493i	$0.791774\pi$
$770$	3.84744	+	8.91936i	0.138652	+	0.321431i
$771$		0			0
$772$	−14.3857	+	7.22479i	−0.517754	+	0.260026i
$773$	0.729570	+	4.13760i	0.0262408	+	0.148819i	0.995113	−	0.0987422i	$-0.0314819\pi$
$773$	0.729570	+	4.13760i	0.0262408	+	0.148819i	−0.968872	+	0.247561i	$0.920371\pi$
$774$		0			0
$775$	−4.49496	+	25.4922i	−0.161464	+	0.915705i
$776$	−8.55003	−	28.5591i	−0.306928	−	1.02521i
$777$		0			0
$778$	−2.00345	−	1.00617i	−0.0718271	−	0.0360729i
$779$	−6.65787	+	22.2388i	−0.238543	+	0.796789i
$780$		0			0
$781$	−3.09877	−	4.16237i	−0.110883	−	0.148941i
$782$	3.09593	+	5.36230i	0.110710	+	0.191755i
$783$		0			0
$784$	−0.198697	+	0.344153i	−0.00709632	+	0.0122912i
$785$	43.2822	−	5.05896i	1.54481	−	0.180562i
$786$		0			0
$787$	−9.48954	+	2.24906i	−0.338266	+	0.0801704i	−0.396238	−	0.918148i	$-0.629685\pi$
$787$	−9.48954	+	2.24906i	−0.338266	+	0.0801704i	0.0579725	+	0.998318i	$0.481536\pi$
$788$	−8.56672	+	5.63442i	−0.305177	+	0.200718i
$789$		0			0
$790$	26.1746	−	27.7434i	0.931250	−	0.987067i
$791$	−4.25795	−	3.57284i	−0.151395	−	0.127036i
$792$		0			0
$793$	23.0483	−	19.3398i	0.818470	−	0.686778i
$794$	0.167160	−	2.87003i	0.00593230	−	0.101854i
$795$		0			0
$796$	−9.63080	+	12.9364i	−0.341355	+	0.458519i
$797$	−10.1126	−	1.18199i	−0.358207	−	0.0418684i	−0.0649135	−	0.997891i	$-0.520677\pi$
$797$	−10.1126	−	1.18199i	−0.358207	−	0.0418684i	−0.293293	+	0.956023i	$0.594751\pi$
$798$		0			0
$799$	−28.3019	−	18.6145i	−1.00125	−	0.658532i
$800$	−37.2827	−	13.5698i	−1.31814	−	0.479765i
$801$		0			0
$802$	−14.1911	+	5.16513i	−0.501105	+	0.182387i
$803$	−1.02203	−	0.242225i	−0.0360666	−	0.00854795i
$804$		0			0
$805$	−0.937115	−	16.0896i	−0.0330290	−	0.567085i
$806$	−10.2594	−	10.8743i	−0.361371	−	0.383031i
$807$		0			0
$808$	−16.5037	+	38.2599i	−0.580599	+	1.34598i
$809$	20.1073			0.706936			0.353468	−	0.935447i	$-0.385002\pi$
$809$	20.1073			0.706936			0.353468	+	0.935447i	$0.385002\pi$
$810$		0			0
$811$	−0.159394			−0.00559707			−0.00279854	−	0.999996i	$-0.500891\pi$
$811$	−0.159394			−0.00559707			−0.00279854	+	0.999996i	$0.500891\pi$
$812$	−3.45230	+	8.00332i	−0.121152	+	0.280861i
$813$		0			0
$814$	3.68350	+	3.90428i	0.129106	+	0.136845i
$815$	−2.76116	−	47.4073i	−0.0967192	−	1.66060i
$816$		0			0
$817$	−4.12745	−	0.978225i	−0.144401	−	0.0342238i
$818$	14.7536	−	5.36988i	0.515848	−	0.187753i
$819$		0			0
$820$	−21.8405	−	7.94928i	−0.762702	−	0.277601i
$821$	3.96387	+	2.60708i	0.138340	+	0.0909876i	0.616793	−	0.787126i	$-0.288432\pi$
$821$	3.96387	+	2.60708i	0.138340	+	0.0909876i	−0.478453	+	0.878113i	$0.658802\pi$
$822$		0			0
$823$	−26.3661	−	3.08176i	−0.919065	−	0.107423i	−0.356612	−	0.934253i	$-0.616068\pi$
$823$	−26.3661	−	3.08176i	−0.919065	−	0.107423i	−0.562453	+	0.826829i	$0.690142\pi$
$824$	−25.7145	+	34.5405i	−0.895806	+	1.20328i
$825$		0			0
$826$	0.393306	−	6.75280i	0.0136849	−	0.234960i
$827$	5.34609	−	4.48590i	0.185902	−	0.155990i	−0.545087	−	0.838379i	$-0.683504\pi$
$827$	5.34609	−	4.48590i	0.185902	−	0.155990i	0.730989	+	0.682389i	$0.239059\pi$
$828$		0			0
$829$	28.3490	+	23.7877i	0.984603	+	0.826180i	0.984777	−	0.173820i	$-0.0556111\pi$
$829$	28.3490	+	23.7877i	0.984603	+	0.826180i	−0.000174449		1.00000i	$0.500056\pi$
$830$	−9.89958	+	10.4929i	−0.343620	+	0.364215i
$831$		0			0
$832$	7.57196	−	4.98016i	0.262511	−	0.172656i
$833$	−1.56430	+	0.370746i	−0.0541998	+	0.0128456i
$834$		0			0
$835$	−9.45820	+	1.10551i	−0.327315	+	0.0382576i
$836$	−5.69913	+	9.87118i	−0.197109	+	0.341402i
$837$		0			0
$838$	9.02026	+	15.6236i	0.311600	+	0.539707i
$839$	−4.60126	−	6.18056i	−0.158853	−	0.213377i	0.715570	−	0.698541i	$-0.246167\pi$
$839$	−4.60126	−	6.18056i	−0.158853	−	0.213377i	−0.874423	+	0.485165i	$0.838760\pi$
$840$		0			0
$841$	6.99320	−	23.3589i	0.241145	−	0.805480i
$842$	11.7557	+	5.90392i	0.405127	+	0.203463i
$843$		0			0
$844$	3.74267	+	12.5014i	0.128828	+	0.430316i
$845$	10.6315	−	60.2943i	0.365735	−	2.07419i
$846$		0			0
$847$	−4.14197	−	23.4903i	−0.142320	−	0.807136i
$848$	−5.77008	+	2.89784i	−0.198145	+	0.0995124i
$849$		0			0
$850$	−9.61693	−	22.2945i	−0.329858	−	0.764697i
$851$	−3.52743	−	8.17751i	−0.120919	−	0.280321i
$852$		0			0
$853$	−30.4520	+	15.2936i	−1.04266	+	0.523642i	−0.885842	−	0.463987i	$-0.846419\pi$
$853$	−30.4520	+	15.2936i	−1.04266	+	0.523642i	−0.156814	+	0.987628i	$0.550122\pi$
$854$	−1.80110	−	10.2145i	−0.0616322	−	0.349534i
$855$		0			0
$856$	−3.21971	+	18.2599i	−0.110048	+	0.624110i
$857$	11.3616	+	37.9504i	0.388105	+	1.29636i	0.899464	+	0.436994i	$0.143957\pi$
$857$	11.3616	+	37.9504i	0.388105	+	1.29636i	−0.511359	+	0.859367i	$0.670858\pi$
$858$		0			0
$859$	−48.8321	−	24.5244i	−1.66613	−	0.836762i	−0.995478	−	0.0949905i	$-0.969718\pi$
$859$	−48.8321	−	24.5244i	−1.66613	−	0.836762i	−0.670652	−	0.741772i	$-0.733986\pi$
$860$	1.21803	−	4.06851i	0.0415345	−	0.138735i
$861$		0			0
$862$	−2.92720	−	3.93191i	−0.0997007	−	0.133921i
$863$	−0.634182	−	1.09844i	−0.0215878	−	0.0373912i	0.855030	−	0.518579i	$-0.173539\pi$
$863$	−0.634182	−	1.09844i	−0.0215878	−	0.0373912i	−0.876617	+	0.481188i	$0.840205\pi$
$864$		0			0
$865$	35.6566	−	61.7590i	1.21236	−	2.09987i
$866$	−17.4980	+	2.04522i	−0.594605	+	0.0694994i
$867$		0			0
$868$	15.0244	−	3.56085i	0.509961	−	0.120863i
$869$	19.3734	−	12.7421i	0.657198	−	0.432246i
$870$		0			0
$871$	−24.9499	+	26.4453i	−0.845394	+	0.896066i
$872$	−6.44525	−	5.40821i	−0.218264	−	0.183145i
$873$		0			0
$874$	−4.83556	+	4.05752i	−0.163565	+	0.137248i
$875$	−0.972976	+	16.7054i	−0.0328926	+	0.564744i
$876$		0			0
$877$	26.1912	−	35.1809i	0.884415	−	1.18798i	−0.0968475	−	0.995299i	$-0.530876\pi$
$877$	26.1912	−	35.1809i	0.884415	−	1.18798i	0.981262	−	0.192676i	$-0.0617167\pi$
$878$	5.71791	+	0.668328i	0.192970	+	0.0225550i
$879$		0			0
$880$	−5.28989	−	3.47922i	−0.178322	−	0.117284i
$881$	−25.7921	−	9.38756i	−0.868959	−	0.316275i	−0.131213	−	0.991354i	$-0.541887\pi$
$881$	−25.7921	−	9.38756i	−0.868959	−	0.316275i	−0.737745	+	0.675079i	$0.764109\pi$
$882$		0			0
$883$	−19.1938	+	6.98597i	−0.645923	+	0.235097i	−0.644147	−	0.764902i	$-0.722787\pi$
$883$	−19.1938	+	6.98597i	−0.645923	+	0.235097i	−0.00177579	+	0.999998i	$0.500565\pi$
$884$	−40.8803	−	9.68880i	−1.37495	−	0.325870i
$885$		0			0
$886$	−1.03883	−	17.8361i	−0.0349003	−	0.599215i
$887$	25.9661	+	27.5225i	0.871857	+	0.924114i	0.997690	−	0.0679372i	$-0.0216418\pi$
$887$	25.9661	+	27.5225i	0.871857	+	0.924114i	−0.125833	+	0.992051i	$0.540160\pi$
$888$		0			0
$889$	−9.01373	+	20.8962i	−0.302311	+	0.700835i
$890$	9.78695			0.328059
$891$		0			0
$892$	−11.8121			−0.395499
$893$	13.6783	−	31.7098i	0.457726	−	1.06113i
$894$		0			0
$895$	33.3886	+	35.3898i	1.11606	+	1.18295i
$896$	1.65372	+	28.3932i	0.0552469	+	0.948552i
$897$		0			0
$898$	−27.1939	−	6.44507i	−0.907472	−	0.215075i
$899$	7.68526	−	2.79721i	0.256318	−	0.0932921i
$900$		0			0
$901$	−24.5457	−	8.93390i	−0.817735	−	0.297631i
$902$	3.94041	+	2.59165i	0.131201	+	0.0862924i
$903$		0			0
$904$	−5.05238	−	0.590539i	−0.168040	−	0.0196410i
$905$	−0.332314	+	0.446375i	−0.0110465	+	0.0148380i
$906$		0			0
$907$	0.480226	−	8.24516i	0.0159456	−	0.273776i	−0.980906	−	0.194484i	$-0.937697\pi$
$907$	0.480226	−	8.24516i	0.0159456	−	0.273776i	0.996851	−	0.0792924i	$-0.0252661\pi$
$908$	21.9578	−	18.4247i	0.728694	−	0.611447i
$909$		0			0
$910$	−27.9613	−	23.4623i	−0.926909	−	0.777769i
$911$	−23.1114	+	24.4967i	−0.765716	+	0.811611i	−0.986509	−	0.163709i	$-0.947654\pi$
$911$	−23.1114	+	24.4967i	−0.765716	+	0.811611i	0.220793	+	0.975321i	$0.429136\pi$
$912$		0			0
$913$	−7.32729	+	4.81924i	−0.242498	+	0.159493i
$914$	14.3564	−	3.40253i	0.474868	−	0.112546i
$915$		0			0
$916$	40.2436	−	4.70381i	1.32969	−	0.155418i
$917$	−14.5073	+	25.1273i	−0.479072	+	0.829777i
$918$		0			0
$919$	−13.1853	−	22.8376i	−0.434943	−	0.753343i	0.562348	−	0.826901i	$-0.309898\pi$
$919$	−13.1853	−	22.8376i	−0.434943	−	0.753343i	−0.997291	+	0.0735573i	$0.976565\pi$
$920$	−8.80781	−	11.8309i	−0.290385	−	0.390054i
$921$		0			0
$922$	−3.45069	+	11.5261i	−0.113642	+	0.379592i
$923$	17.4250	+	8.75119i	0.573552	+	0.288049i
$924$		0			0
$925$	10.0160	+	33.4557i	0.329323	+	1.10002i
$926$	1.16021	−	6.57988i	0.0381269	−	0.216228i
$927$		0			0
$928$	2.17675	+	12.3450i	0.0714554	+	0.405244i
$929$	47.0551	−	23.6319i	1.54383	−	0.775339i	0.545787	−	0.837924i	$-0.316231\pi$
$929$	47.0551	−	23.6319i	1.54383	−	0.775339i	0.998040	+	0.0625852i	$0.0199345\pi$
$930$		0			0
$931$	−0.649147	−	1.50489i	−0.0212749	−	0.0493208i
$932$	−10.7474	−	24.9153i	−0.352043	−	0.816127i
$933$		0			0
$934$	19.3106	−	9.69817i	0.631863	−	0.317334i
$935$	−4.44778	−	25.2246i	−0.145458	−	0.824933i
$936$		0			0
$937$	1.27631	−	7.23831i	0.0416952	−	0.236465i	−0.956837	−	0.290625i	$-0.906137\pi$
$937$	1.27631	−	7.23831i	0.0416952	−	0.236465i	0.998532	+	0.0541595i	$0.0172479\pi$
$938$	3.59465	+	12.0070i	0.117370	+	0.392042i
$939$		0			0
$940$	30.8981	+	15.5176i	1.00779	+	0.506129i
$941$	−7.48541	+	25.0030i	−0.244017	+	0.815075i	0.744973	+	0.667095i	$0.232462\pi$
$941$	−7.48541	+	25.0030i	−0.244017	+	0.815075i	−0.988990	+	0.147980i	$0.952723\pi$
$942$		0			0
$943$	−4.67287	−	6.27676i	−0.152170	−	0.204399i
$944$	2.20449	+	3.81828i	0.0717499	+	0.124274i
$945$		0			0
$946$	−0.430893	+	0.746328i	−0.0140095	+	0.0242652i
$947$	−9.41332	+	1.10026i	−0.305892	+	0.0357536i	−0.267654	−	0.963515i	$-0.586248\pi$
$947$	−9.41332	+	1.10026i	−0.305892	+	0.0357536i	−0.0382377	+	0.999269i	$0.512174\pi$
$948$		0			0
$949$	3.84042	−	0.910196i	0.124665	−	0.0295462i
$950$	20.6808	−	13.6020i	0.670973	−	0.441306i
$951$		0			0
$952$	−23.1953	+	24.5856i	−0.751763	+	0.796823i
$953$	−39.9630	−	33.5329i	−1.29453	−	1.08624i	−0.991063	−	0.133395i	$-0.957412\pi$
$953$	−39.9630	−	33.5329i	−1.29453	−	1.08624i	−0.303464	−	0.952843i	$-0.598143\pi$
$954$		0			0
$955$	61.2580	−	51.4016i	1.98226	−	1.66332i
$956$	−0.923984	+	15.8642i	−0.0298838	+	0.513085i
$957$		0			0
$958$	−5.25720	+	7.06164i	−0.169852	+	0.228151i
$959$	−28.6653	−	3.35049i	−0.925651	−	0.108193i
$960$		0			0
$961$	13.7955	+	9.07344i	0.445016	+	0.292692i
$962$	−18.9533	−	6.89842i	−0.611078	−	0.222414i
$963$		0			0
$964$	−23.7785	+	8.65468i	−0.765855	+	0.278748i
$965$	35.8850	+	8.50491i	1.15518	+	0.273783i
$966$		0			0
$967$	−0.262735	−	4.51099i	−0.00844899	−	0.145064i	−0.999894	−	0.0145407i	$-0.995371\pi$
$967$	−0.262735	−	4.51099i	−0.00844899	−	0.145064i	0.991445	−	0.130523i	$-0.0416656\pi$
$968$	−14.9800	−	15.8778i	−0.481474	−	0.510333i
$969$		0			0
$970$	−11.5908	+	26.8705i	−0.372158	+	0.862760i
$971$	12.4268			0.398796			0.199398	−	0.979919i	$-0.436101\pi$
$971$	12.4268			0.398796			0.199398	+	0.979919i	$0.436101\pi$
$972$		0			0
$973$	7.62342			0.244396
$974$	3.70453	−	8.58807i	0.118701	−	0.275180i
$975$		0			0
$976$	4.63940	+	4.91748i	0.148504	+	0.157405i
$977$	−1.09442	−	18.7905i	−0.0350136	−	0.601161i	−0.969489	−	0.245134i	$-0.921168\pi$
$977$	−1.09442	−	18.7905i	−0.0350136	−	0.601161i	0.934476	−	0.356027i	$-0.115869\pi$
$978$		0			0
$979$	5.78953	+	1.37214i	0.185034	+	0.0438539i
$980$	1.54195	−	0.561225i	0.0492559	−	0.0179277i
$981$		0			0
$982$	12.0553	+	4.38778i	0.384701	+	0.140020i
$983$	−9.56215	−	6.28913i	−0.304985	−	0.200592i	0.387786	−	0.921749i	$-0.373240\pi$
$983$	−9.56215	−	6.28913i	−0.304985	−	0.200592i	−0.692771	+	0.721158i	$0.743610\pi$
$984$		0			0
$985$	23.3311	+	2.72701i	0.743391	+	0.0868899i
$986$	−4.58101	+	6.15336i	−0.145889	+	0.195963i
$987$		0			0
$988$	2.49038	−	42.7581i	0.0792294	−	1.36032i
$989$	1.09533	−	0.919094i	0.0348296	−	0.0292255i
$990$		0			0
$991$	−22.6012	−	18.9647i	−0.717951	−	0.602432i	0.208867	−	0.977944i	$-0.433022\pi$
$991$	−22.6012	−	18.9647i	−0.717951	−	0.602432i	−0.926818	+	0.375512i	$0.877467\pi$
$992$	15.2389	−	16.1523i	0.483837	−	0.512837i
$993$		0			0
$994$	5.61612	−	3.69378i	0.178133	−	0.117160i
$995$	35.9512	−	8.52058i	1.13973	−	0.270121i
$996$		0			0
$997$	−44.1770	+	5.16356i	−1.39910	+	0.163531i	−0.781964	−	0.623324i	$-0.785782\pi$
$997$	−44.1770	+	5.16356i	−1.39910	+	0.163531i	−0.617137	+	0.786856i	$0.711708\pi$
$998$	3.36499	−	5.82833i	0.106517	−	0.184493i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.g.d.55.5		144
3.2	odd	2		729.2.g.a.55.4		144
9.2	odd	6		243.2.g.a.19.5		144
9.4	even	3		729.2.g.c.541.5		144
9.5	odd	6		729.2.g.b.541.4		144
9.7	even	3		81.2.g.a.61.4	yes	144
81.4	even	27		729.2.g.c.190.5		144
81.23	odd	54		243.2.g.a.64.5		144
81.29	odd	54		6561.2.a.d.1.26		72
81.31	even	27	inner	729.2.g.d.676.5		144
81.50	odd	54		729.2.g.a.676.4		144
81.52	even	27		6561.2.a.c.1.47		72
81.58	even	27		81.2.g.a.4.4	✓	144
81.77	odd	54		729.2.g.b.190.4		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.4.4	✓	144	81.58	even	27
81.2.g.a.61.4	yes	144	9.7	even	3
243.2.g.a.19.5		144	9.2	odd	6
243.2.g.a.64.5		144	81.23	odd	54
729.2.g.a.55.4		144	3.2	odd	2
729.2.g.a.676.4		144	81.50	odd	54
729.2.g.b.190.4		144	81.77	odd	54
729.2.g.b.541.4		144	9.5	odd	6
729.2.g.c.190.5		144	81.4	even	27
729.2.g.c.541.5		144	9.4	even	3
729.2.g.d.55.5		144	1.1	even	1	trivial
729.2.g.d.676.5		144	81.31	even	27	inner
6561.2.a.c.1.47		72	81.52	even	27
6561.2.a.d.1.26		72	81.29	odd	54

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.g (of order \(27\), degree \(18\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.280212 - 0.649604i) q^{2} +(1.02902 + 1.09069i) q^{4} +(-0.199739 - 3.42939i) q^{5} +(2.63236 + 0.623881i) q^{7} +(2.32646 - 0.846761i) q^{8} +O(q^{10})\)	\(q+(0.280212 - 0.649604i) q^{2} +(1.02902 + 1.09069i) q^{4} +(-0.199739 - 3.42939i) q^{5} +(2.63236 + 0.623881i) q^{7} +(2.32646 - 0.846761i) q^{8} +(-2.28372 - 0.831205i) q^{10} +(-1.23441 - 0.811885i) q^{11} +(5.51427 + 0.644526i) q^{13} +(1.14289 - 1.53517i) q^{14} +(-0.0725347 + 1.24537i) q^{16} +(-3.86594 + 3.24391i) q^{17} +(-3.94119 - 3.30705i) q^{19} +(3.53488 - 3.74676i) q^{20} +(-0.873300 + 0.574378i) q^{22} +(1.68752 - 0.399950i) q^{23} +(-6.75465 + 0.789506i) q^{25} +(1.96385 - 3.40149i) q^{26} +(2.02828 + 3.51309i) q^{28} +(1.28309 + 1.72349i) q^{29} +(1.09167 - 3.64642i) q^{31} +(5.21352 + 2.61833i) q^{32} +(1.02397 + 3.42031i) q^{34} +(1.61375 - 9.15202i) q^{35} +(-0.891723 - 5.05721i) q^{37} +(-3.25264 + 1.63354i) q^{38} +(-3.36856 - 7.80920i) q^{40} +(-1.78715 - 4.14308i) q^{41} +(0.736775 - 0.370022i) q^{43} +(-0.384712 - 2.18181i) q^{44} +(0.213054 - 1.20829i) q^{46} +(1.92513 + 6.43037i) q^{47} +(0.284673 + 0.142968i) q^{49} +(-1.37987 + 4.60908i) q^{50} +(4.97130 + 6.67762i) q^{52} +(2.58797 + 4.48249i) q^{53} +(-2.53771 + 4.39545i) q^{55} +(6.65235 - 0.777549i) q^{56} +(1.47912 - 0.350558i) q^{58} +(2.95286 - 1.94213i) q^{59} +(3.71901 - 3.94192i) q^{61} +(-2.06283 - 1.73092i) q^{62} +(1.25051 - 1.04930i) q^{64} +(1.10892 - 19.0394i) q^{65} +(-3.91063 + 5.25288i) q^{67} +(-7.51622 - 0.878520i) q^{68} +(-5.49299 - 3.61280i) q^{70} +(3.30039 + 1.20125i) q^{71} +(0.668031 - 0.243143i) q^{73} +(-3.53506 - 0.837823i) q^{74} +(-0.448570 - 7.70164i) q^{76} +(-2.74290 - 2.90730i) q^{77} +(-6.21626 + 14.4109i) q^{79} +4.28536 q^{80} -3.19214 q^{82} +(2.35107 - 5.45040i) q^{83} +(11.8968 + 12.6099i) q^{85} +(-0.0339149 - 0.582297i) q^{86} +(-3.55928 - 0.843564i) q^{88} +(-3.78422 + 1.37734i) q^{89} +(14.1135 + 5.13688i) q^{91} +(2.17271 + 1.42901i) q^{92} +(4.71663 + 0.551295i) q^{94} +(-10.5540 + 14.1764i) q^{95} +(0.700141 - 12.0210i) q^{97} +(0.172641 - 0.144863i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8}+O(q^{10}) \) 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8	\( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} + 45 q^{20} + 9 q^{22} - 45 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28} + 36 q^{29} + 9 q^{31} - 99 q^{32} + 9 q^{34} + 9 q^{35} - 18 q^{37} + 18 q^{38} + 9 q^{40} + 27 q^{41} + 9 q^{43} + 54 q^{44} - 18 q^{46} - 99 q^{47} + 9 q^{49} + 126 q^{50} - 27 q^{52} + 45 q^{53} - 9 q^{55} - 225 q^{56} + 9 q^{58} + 72 q^{59} + 9 q^{61} + 81 q^{62} - 18 q^{64} - 81 q^{65} - 45 q^{67} + 117 q^{68} - 99 q^{70} - 90 q^{71} - 18 q^{73} + 81 q^{74} - 153 q^{76} + 81 q^{77} - 99 q^{79} - 288 q^{80} - 36 q^{82} + 45 q^{83} - 99 q^{85} + 81 q^{86} - 153 q^{88} - 81 q^{89} - 18 q^{91} + 207 q^{92} - 99 q^{94} - 171 q^{95} - 45 q^{97} + 81 q^{98}+O(q^{100}) \) 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8 - 18 * q^10 + 9 * q^11 + 9 * q^13 + 9 * q^14 + 9 * q^16 - 18 * q^17 - 18 * q^19 + 45 * q^20 + 9 * q^22 - 45 * q^23 + 9 * q^25 + 45 * q^26 - 9 * q^28 + 36 * q^29 + 9 * q^31 - 99 * q^32 + 9 * q^34 + 9 * q^35 - 18 * q^37 + 18 * q^38 + 9 * q^40 + 27 * q^41 + 9 * q^43 + 54 * q^44 - 18 * q^46 - 99 * q^47 + 9 * q^49 + 126 * q^50 - 27 * q^52 + 45 * q^53 - 9 * q^55 - 225 * q^56 + 9 * q^58 + 72 * q^59 + 9 * q^61 + 81 * q^62 - 18 * q^64 - 81 * q^65 - 45 * q^67 + 117 * q^68 - 99 * q^70 - 90 * q^71 - 18 * q^73 + 81 * q^74 - 153 * q^76 + 81 * q^77 - 99 * q^79 - 288 * q^80 - 36 * q^82 + 45 * q^83 - 99 * q^85 + 81 * q^86 - 153 * q^88 - 81 * q^89 - 18 * q^91 + 207 * q^92 - 99 * q^94 - 171 * q^95 - 45 * q^97 + 81 * q^98

Introduction

L-functions

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Database

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