LMFDB - Embedded newform 729.2.g.a.676.4

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			676.4
Character	$\chi$	$=$	729.676
Dual form			729.2.g.a.55.4

$q$-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 $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{10}{27}\right)$

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	$-0.210102\pi$
$2$	−0.280212	−	0.649604i	−0.198140	−	0.459339i	−0.988099	+	0.153820i	$0.950842\pi$
$3$		0			0
$3$		0			0
$4$	1.02902	−	1.09069i	0.514508	−	0.545347i
$5$	0.199739	−	3.42939i	0.0893262	−	1.53367i	−0.594541	−	0.804065i	$-0.702666\pi$
$5$	0.199739	−	3.42939i	0.0893262	−	1.53367i	0.683867	−	0.729606i	$-0.260297\pi$
$6$		0			0
$7$	2.63236	−	0.623881i	0.994939	−	0.235805i	0.299271	−	0.954168i	$-0.403257\pi$
$7$	2.63236	−	0.623881i	0.994939	−	0.235805i	0.695668	+	0.718363i	$0.255108\pi$
$8$	−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	$-0.613686\pi$
$11$	1.23441	−	0.811885i	0.372189	−	0.244793i	0.721799	+	0.692103i	$0.243316\pi$
$12$		0			0
$13$	5.51427	−	0.644526i	1.52938	−	0.178759i	0.690606	−	0.723232i	$-0.257344\pi$
$13$	5.51427	−	0.644526i	1.52938	−	0.178759i	0.838779	+	0.544472i	$0.183270\pi$
$14$	−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	$-0.0681460\pi$
$17$	3.86594	+	3.24391i	0.937627	+	0.786763i	−0.0395437	+	0.999218i	$0.512590\pi$
$18$		0			0
$19$	−3.94119	+	3.30705i	−0.904171	+	0.758690i	−0.971001	−	0.239075i	$-0.923156\pi$
$19$	−3.94119	+	3.30705i	−0.904171	+	0.758690i	0.0668301	+	0.997764i	$0.478711\pi$
$20$	−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	$-0.483798\pi$
$23$	−1.68752	−	0.399950i	−0.351872	−	0.0833953i	−0.402751	+	0.915310i	$0.631946\pi$
$24$		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	$-0.860227\pi$
$29$	−1.28309	+	1.72349i	−0.238264	+	0.320044i	0.666867	+	0.745176i	$0.267635\pi$
$30$		0			0
$31$	1.09167	+	3.64642i	0.196069	+	0.654916i	0.998321	+	0.0579300i	$0.0184500\pi$
$31$	1.09167	+	3.64642i	0.196069	+	0.654916i	−0.802252	+	0.596986i	$0.796365\pi$
$32$	−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	0.819472	+	0.573120i	$0.194267\pi$
$37$	−0.891723	+	5.05721i	−0.146598	+	0.831401i	−0.966070	+	0.258281i	$0.916844\pi$
$38$	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	$-0.755758\pi$
$41$	1.78715	−	4.14308i	0.279106	−	0.647040i	0.998887	+	0.0471609i	$0.0150173\pi$
$42$		0			0
$43$	0.736775	+	0.370022i	0.112357	+	0.0564279i	0.504090	−	0.863651i	$-0.331828\pi$
$43$	0.736775	+	0.370022i	0.112357	+	0.0564279i	−0.391733	+	0.920079i	$0.628124\pi$
$44$	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	0.694939	+	0.719068i	$0.255431\pi$
$47$	−1.92513	+	6.43037i	−0.280808	+	0.937966i	−0.975748	+	0.218897i	$0.929754\pi$
$48$		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	$-0.949017\pi$
$53$	−2.58797	+	4.48249i	−0.355485	+	0.615717i	0.631716	+	0.775200i	$0.282351\pi$
$54$		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	$-0.388708\pi$
$59$	−2.95286	−	1.94213i	−0.384430	−	0.252843i	−0.726984	+	0.686655i	$0.759078\pi$
$60$		0			0
$61$	3.71901	+	3.94192i	0.476170	+	0.504711i	0.920280	−	0.391262i	$-0.127961\pi$
$61$	3.71901	+	3.94192i	0.476170	+	0.504711i	−0.444109	+	0.895973i	$0.646480\pi$
$62$	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	0.496269	−	0.868169i	$-0.334703\pi$
$67$	−3.91063	−	5.25288i	−0.477759	−	0.641742i	−0.974028	+	0.226427i	$0.927295\pi$
$68$	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	$-0.677940\pi$
$71$	−3.30039	+	1.20125i	−0.391685	+	0.142562i	0.138667	+	0.990339i	$0.455718\pi$
$72$		0			0
$73$	0.668031	+	0.243143i	0.0781871	+	0.0284578i	0.380818	−	0.924650i	$-0.375643\pi$
$73$	0.668031	+	0.243143i	0.0781871	+	0.0284578i	−0.302630	+	0.953108i	$0.597865\pi$
$74$	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	−0.780881	−	0.624680i	$-0.785229\pi$
$79$	−6.21626	−	14.4109i	−0.699384	−	1.62135i	0.0814970	−	0.996674i	$-0.474030\pi$
$80$	−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	$-0.235254\pi$
$83$	−2.35107	−	5.45040i	−0.258064	−	0.598259i	−0.997158	+	0.0753432i	$0.975995\pi$
$84$		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	$-0.320424\pi$
$89$	3.78422	+	1.37734i	0.401127	+	0.145998i	−0.133576	+	0.991039i	$0.542646\pi$
$90$		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	0.825600	+	0.564256i	$0.190837\pi$
$97$	0.700141	+	12.0210i	0.0710886	+	1.22054i	−0.754511	+	0.656287i	$0.772126\pi$
$98$	−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	0.972262	+	0.233895i	$0.0751471\pi$
$101$	11.5496	+	12.2419i	1.14923	+	1.21811i	0.176967	+	0.984217i	$0.443371\pi$
$102$		0			0
$103$	−14.5318	−	9.55771i	−1.43186	−	0.941749i	−0.999192	−	0.0401953i	$-0.987202\pi$
$103$	−14.5318	−	9.55771i	−1.43186	−	0.941749i	−0.432668	−	0.901554i	$-0.642428\pi$
$104$	−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	$-0.0487586\pi$
$107$	3.74462	+	6.48587i	0.362006	+	0.627013i	−0.626285	+	0.779594i	$0.715425\pi$
$108$		0			0
$109$	−1.69921	+	2.94312i	−0.162755	+	0.281899i	−0.935856	−	0.352384i	$-0.885371\pi$
$109$	−1.69921	+	2.94312i	−0.162755	+	0.281899i	0.773101	+	0.634283i	$0.218705\pi$
$110$	−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	$-0.617338\pi$
$113$	1.83608	−	0.922116i	0.172724	−	0.0867454i	0.533061	+	0.846077i	$0.321042\pi$
$114$		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	−0.978455	−	0.206460i	$-0.933806\pi$
$127$	−1.46076	−	8.28439i	−0.129622	−	0.735121i	0.848833	−	0.528661i	$-0.177306\pi$
$128$	−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	0.980710	+	0.195471i	$0.0626235\pi$
$131$	3.07600	+	10.2746i	0.268752	+	0.897693i	−0.711958	+	0.702222i	$0.752191\pi$
$132$		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	$-0.312344\pi$
$137$	10.5960	+	1.23850i	0.905281	+	0.105812i	0.349304	+	0.937010i	$0.386418\pi$
$138$		0			0
$139$	2.74202	+	0.649870i	0.232575	+	0.0551213i	0.345251	−	0.938511i	$-0.387794\pi$
$139$	2.74202	+	0.649870i	0.232575	+	0.0551213i	−0.112676	+	0.993632i	$0.535942\pi$
$140$	−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	$-0.545993\pi$
$149$	−0.682167	+	0.0797339i	−0.0558853	+	0.00653206i	0.0881043	+	0.996111i	$0.471919\pi$
$150$		0			0
$151$	−0.419776	+	0.276091i	−0.0341609	+	0.0224680i	−0.566475	−	0.824079i	$-0.691693\pi$
$151$	−0.419776	+	0.276091i	−0.0341609	+	0.0224680i	0.532314	+	0.846547i	$0.321323\pi$
$152$	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	−0.831523	−	0.555490i	$-0.812531\pi$
$157$	0.737588	−	12.6639i	0.0588660	−	1.01069i	0.890389	−	0.455200i	$-0.150432\pi$
$158$	−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	−0.986313	−	0.164882i	$-0.947276\pi$
$167$	0.161181	−	2.76737i	0.0124726	−	0.214145i	0.998786	−	0.0492633i	$-0.0156873\pi$
$168$		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	$-0.974668\pi$
$173$	−17.3443	+	11.4075i	−1.31866	+	0.867299i	−0.321829	+	0.946798i	$0.604298\pi$
$174$		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	$-0.100228\pi$
$179$	10.8498	+	9.10407i	0.810953	+	0.680470i	−0.139882	+	0.990168i	$0.544672\pi$
$180$		0			0
$181$	−0.124097	+	0.104130i	−0.00922404	+	0.00773989i	−0.647388	−	0.762161i	$-0.724139\pi$
$181$	−0.124097	+	0.104130i	−0.00922404	+	0.00773989i	0.638164	+	0.769901i	$0.279694\pi$
$182$	−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	−0.0704300	+	0.997517i	$0.522437\pi$
$191$	−13.9010	+	18.6723i	−1.00584	+	1.35108i	−0.935411	+	0.353562i	$0.884970\pi$
$192$		0			0
$193$	−3.07901	−	10.2846i	−0.221632	−	0.740303i	−0.994406	−	0.105622i	$-0.966317\pi$
$193$	−3.07901	−	10.2846i	−0.221632	−	0.740303i	0.772774	−	0.634681i	$-0.218869\pi$
$194$	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	0.997442	+	0.0714755i	$0.0227708\pi$
$197$	1.18741	+	6.73411i	0.0845992	+	0.479786i	−0.912843	+	0.408310i	$0.866118\pi$
$198$		0			0
$199$	1.86766	−	10.5920i	0.132395	−	0.750848i	−0.844244	−	0.535959i	$-0.819950\pi$
$199$	1.86766	−	10.5920i	0.132395	−	0.750848i	0.976639	−	0.214889i	$-0.0689389\pi$
$200$	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	−0.160495	−	0.987037i	$-0.551309\pi$
$211$	7.77699	−	3.90575i	0.535390	−	0.268883i	0.695884	+	0.718154i	$0.255013\pi$
$212$	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	0.520618	−	0.853790i	$-0.325702\pi$
$223$	−5.40580	−	5.72981i	−0.361999	−	0.383696i	−0.882617	+	0.470093i	$0.844220\pi$
$224$	−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	−0.808604	−	0.588354i	$-0.799776\pi$
$227$	−1.11147	−	19.0833i	−0.0737712	−	1.26660i	0.734833	−	0.678248i	$-0.237261\pi$
$228$		0			0
$229$	16.1357	+	21.6740i	1.06628	+	1.43226i	0.894469	+	0.447129i	$0.147554\pi$
$229$	16.1357	+	21.6740i	1.06628	+	1.43226i	0.171808	+	0.985130i	$0.445039\pi$
$230$	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	$-0.409156\pi$
$233$	17.0044	−	6.18909i	1.11400	−	0.405461i	0.832457	+	0.554089i	$0.186933\pi$
$234$		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	$-0.870618\pi$
$239$	−7.27252	+	7.70842i	−0.470420	+	0.498616i	0.448104	+	0.893982i	$0.352100\pi$
$240$		0			0
$241$	−6.68400	−	15.4952i	−0.430554	−	0.998137i	−0.986024	−	0.166600i	$-0.946721\pi$
$241$	−6.68400	−	15.4952i	−0.430554	−	0.998137i	0.555470	−	0.831536i	$-0.312538\pi$
$242$	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	$-0.187734\pi$
$251$	17.5886	+	6.40174i	1.11018	+	0.404074i	0.279123	+	0.960255i	$0.409956\pi$
$252$		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	−0.885913	−	0.463852i	$-0.846467\pi$
$257$	−17.2527	−	23.1744i	−1.07620	−	1.44558i	−0.190282	−	0.981729i	$-0.560940\pi$
$258$		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	−0.997020	−	0.0771375i	$-0.975422\pi$
$263$	−16.4777	−	17.4653i	−1.01606	−	1.07696i	−0.0190354	−	0.999819i	$-0.506060\pi$
$264$		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	−0.929476	−	0.368883i	$-0.879740\pi$
$269$	−12.8618	−	22.2774i	−0.784200	−	1.35827i	0.145276	−	0.989391i	$-0.453593\pi$
$270$		0			0
$271$	−5.12617	+	8.87880i	−0.311393	+	0.539348i	−0.978664	−	0.205466i	$-0.934129\pi$
$271$	−5.12617	+	8.87880i	−0.311393	+	0.539348i	0.667271	+	0.744815i	$0.267462\pi$
$272$	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	−0.891557	−	0.452909i	$-0.850386\pi$
$277$	1.70105	−	5.68189i	0.102206	−	0.341392i	0.993762	+	0.111518i	$0.0355713\pi$
$278$	−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	$-0.139219\pi$
$281$	18.5579	+	9.32011i	1.10707	+	0.555991i	0.201201	+	0.979550i	$0.435516\pi$
$282$		0			0
$283$	4.65687	−	10.7958i	0.276822	−	0.641747i	−0.721915	−	0.691982i	$-0.756738\pi$
$283$	4.65687	−	10.7958i	0.276822	−	0.641747i	0.998737	+	0.0502352i	$0.0159971\pi$
$284$	−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	−0.812713	−	0.582664i	$-0.802011\pi$
$293$	−7.76918	−	25.9509i	−0.453880	−	1.51607i	0.358833	−	0.933402i	$-0.383175\pi$
$294$		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	−0.0713990	−	0.997448i	$-0.522746\pi$
$307$	−18.6794	−	15.6739i	−1.06609	−	0.894557i	−0.994693	+	0.102891i	$0.967191\pi$
$308$	−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	$-0.696752\pi$
$311$	−16.8492	+	1.96939i	−0.955431	+	0.111674i	−0.375933	+	0.926647i	$0.622678\pi$
$312$		0			0
$313$	−9.74474	+	6.40922i	−0.550805	+	0.362270i	−0.794199	−	0.607657i	$-0.792109\pi$
$313$	−9.74474	+	6.40922i	−0.550805	+	0.362270i	0.243394	+	0.969927i	$0.421739\pi$
$314$	−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	$-0.290540\pi$
$317$	26.9412	−	6.38518i	1.51317	−	0.358628i	0.901603	+	0.432565i	$0.142392\pi$
$318$		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	−0.696662	−	0.717399i	$-0.745332\pi$
$331$	−18.1435	+	4.30008i	−0.997254	+	0.236354i	−0.300592	+	0.953753i	$0.597184\pi$
$332$	−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	−0.883654	−	0.468141i	$-0.844924\pi$
$337$	−30.0243	+	3.50934i	−1.63553	+	0.191166i	−0.751874	+	0.659307i	$0.770850\pi$
$338$	−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	$-0.452290\pi$
$347$	−2.99908	−	0.710794i	−0.160999	−	0.0381574i	−0.310325	+	0.950631i	$0.600438\pi$
$348$		0			0
$349$	8.91783	+	1.04234i	0.477360	+	0.0557954i	0.351371	−	0.936236i	$-0.385715\pi$
$349$	8.91783	+	1.04234i	0.477360	+	0.0557954i	0.125989	+	0.992032i	$0.459790\pi$
$350$	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	0.162496	−	0.986709i	$-0.448046\pi$
$353$	19.9372	−	26.7803i	1.06115	−	1.42537i	0.898653	−	0.438661i	$-0.144547\pi$
$354$		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	$-0.0604320\pi$
$359$	−0.100805	−	0.571693i	−0.00532028	−	0.0301728i	−0.987352	+	0.158541i	$0.949321\pi$
$360$		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	0.928857	−	0.370438i	$-0.120792\pi$
$367$	22.7281	+	11.4145i	1.18640	+	0.595830i	0.257539	+	0.966268i	$0.417089\pi$
$368$	−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	−0.160203	−	0.987084i	$-0.551215\pi$
$373$	10.3498	−	5.19788i	0.535894	−	0.269136i	0.696097	+	0.717948i	$0.254919\pi$
$374$	−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	0.999482	−	0.0321718i	$-0.0102424\pi$
$379$	9.18651	+	15.9115i	0.471880	+	0.817319i	−0.527603	+	0.849491i	$0.676909\pi$
$380$	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	$-0.553733\pi$
$383$	−22.3046	−	14.6700i	−1.13971	−	0.749601i	−0.971708	+	0.236185i	$0.924103\pi$
$384$		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	−0.999753	−	0.0222433i	$-0.992919\pi$
$389$	−0.184258	−	3.16359i	−0.00934226	−	0.160400i	0.990410	−	0.138157i	$-0.0441179\pi$
$390$		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	0.436062	−	0.899916i	$-0.356373\pi$
$397$	3.81860	+	1.38986i	0.191650	+	0.0697550i	−0.244412	+	0.969671i	$0.578595\pi$
$398$	−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	$-0.580325\pi$
$401$	14.6488	−	15.5269i	0.731528	−	0.775374i	0.981208	+	0.192954i	$0.0618068\pi$
$402$		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	−0.231583	−	0.972815i	$-0.574391\pi$
$409$	15.2295	−	16.1423i	0.753051	−	0.798188i	0.984635	+	0.174628i	$0.0558721\pi$
$410$	−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	0.999473	+	0.0324665i	$0.0103362\pi$
$419$	15.2277	+	20.4544i	0.743923	+	0.999262i	−0.255549	+	0.966796i	$0.582256\pi$
$420$		0			0
$421$	−1.08117	−	18.5631i	−0.0526932	−	0.904708i	−0.916288	−	0.400521i	$-0.868829\pi$
$421$	−1.08117	−	18.5631i	−0.0526932	−	0.904708i	0.863594	−	0.504187i	$-0.168208\pi$
$422$	−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	$-0.220034\pi$
$431$	−3.46440	−	6.00052i	−0.166874	−	0.289035i	−0.937319	+	0.348472i	$0.886701\pi$
$432$		0			0
$433$	−12.4509	+	21.5656i	−0.598352	+	1.03638i	0.394713	+	0.918805i	$0.370844\pi$
$433$	−12.4509	+	21.5656i	−0.598352	+	1.03638i	−0.993064	+	0.117571i	$0.962489\pi$
$434$	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	−0.884061	−	0.467372i	$-0.845201\pi$
$439$	2.33380	−	7.79545i	0.111386	−	0.372057i	0.995447	+	0.0953156i	$0.0303860\pi$
$440$	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	$-0.556656\pi$
$443$	−22.5679	−	11.3340i	−1.07223	−	0.538495i	−0.895179	+	0.445707i	$0.852952\pi$
$444$		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	−0.194728	−	0.980857i	$-0.562383\pi$
$449$	6.85970	−	38.9033i	0.323729	−	1.83596i	0.518458	−	0.855103i	$-0.326506\pi$
$450$		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	−0.408948	−	0.912558i	$-0.634104\pi$
$457$	12.4537	−	16.7283i	0.582561	−	0.782515i	0.991508	+	0.130043i	$0.0415116\pi$
$458$	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	$-0.333347\pi$
$461$	16.8916	+	1.97435i	0.786722	+	0.0919546i	0.286761	+	0.958002i	$0.407422\pi$
$462$		0			0
$463$	9.18958	+	2.17797i	0.427076	+	0.101219i	0.438532	−	0.898716i	$-0.355499\pi$
$463$	9.18958	+	2.17797i	0.427076	+	0.101219i	−0.0114562	+	0.999934i	$0.503647\pi$
$464$	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	$-0.972047\pi$
$467$	−23.3985	+	19.6337i	−1.08275	+	0.908538i	−0.0866068	+	0.996243i	$0.527602\pi$
$468$		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	$-0.482316\pi$
$479$	12.1086	−	2.86979i	0.553256	−	0.131124i	0.497728	+	0.867333i	$0.334168\pi$
$480$		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	0.887116	+	0.461546i	$0.152705\pi$
$491$	−1.05439	+	18.1031i	−0.0475839	+	0.816984i	−0.934700	+	0.355437i	$0.884332\pi$
$492$		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	0.0980561	−	0.995181i	$-0.468738\pi$
$499$	9.44851	−	1.10437i	0.422974	−	0.0494385i	0.324917	+	0.945742i	$0.394663\pi$
$500$	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	$-0.402432\pi$
$503$	−13.1149	−	11.0047i	−0.584766	−	0.490677i	−0.886508	+	0.462713i	$0.846876\pi$
$504$		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	$-0.647233\pi$
$509$	−28.1253	−	6.66581i	−1.24663	−	0.295457i	−0.800403	+	0.599462i	$0.795381\pi$
$510$		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	$-0.0843766\pi$
$521$	−0.716780	−	4.06506i	−0.0314027	−	0.178093i	−0.996475	+	0.0838901i	$0.973266\pi$
$522$		0			0
$523$	0.273945	−	1.55362i	0.0119788	−	0.0679351i	−0.978232	−	0.207512i	$-0.933463\pi$
$523$	0.273945	−	1.55362i	0.0119788	−	0.0679351i	0.990211	+	0.139577i	$0.0445744\pi$
$524$	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	0.716724	−	0.697357i	$-0.245641\pi$
$541$	−5.71173	−	9.89300i	−0.245566	−	0.425333i	−0.962291	+	0.272023i	$0.912307\pi$
$542$	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	0.835399	−	0.549644i	$-0.185236\pi$
$547$	5.56896	+	5.90275i	0.238111	+	0.252383i	−0.597288	+	0.802027i	$0.703755\pi$
$548$	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	$-0.692402\pi$
$557$	−11.2047	+	4.07820i	−0.474760	+	0.172799i	0.0935472	+	0.995615i	$0.470179\pi$
$558$		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	$-0.618901\pi$
$563$	13.8990	−	14.7321i	0.585772	−	0.620882i	0.950684	+	0.310160i	$0.100383\pi$
$564$		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	$-0.0304398\pi$
$569$	5.79341	+	13.4306i	0.242872	+	0.563042i	−0.752559	+	0.658525i	$0.771181\pi$
$570$		0			0
$571$	−15.8385	+	16.7878i	−0.662820	+	0.702548i	−0.968339	−	0.249638i	$-0.919688\pi$
$571$	−15.8385	+	16.7878i	−0.662820	+	0.702548i	0.305519	+	0.952186i	$0.401170\pi$
$572$	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	−0.852864	−	0.522133i	$-0.825136\pi$
$577$	−28.1182	+	10.2342i	−1.17057	+	0.426054i	−0.317711	+	0.948188i	$0.602914\pi$
$578$	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	$-0.238648\pi$
$587$	0.218618	+	0.231722i	0.00902333	+	0.00956417i	−0.722846	+	0.691009i	$0.757167\pi$
$588$		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	−0.983694	−	0.179849i	$-0.942439\pi$
$593$	−15.7701	−	27.3146i	−0.647601	−	1.12168i	0.336093	−	0.941829i	$-0.390894\pi$
$594$		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	$-0.503775\pi$
$599$	19.1667	−	9.62585i	0.783128	−	0.393302i	0.794986	+	0.606628i	$0.207478\pi$
$600$		0			0
$601$	−0.117808	+	0.393505i	−0.00480548	+	0.0160514i	−0.960359	−	0.278767i	$-0.910074\pi$
$601$	−0.117808	+	0.393505i	−0.00480548	+	0.0160514i	0.955553	+	0.294819i	$0.0952593\pi$
$602$	−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	0.262723	+	0.964871i	$0.415380\pi$
$607$	−15.2602	+	35.3770i	−0.619391	+	1.43591i	−0.882113	+	0.471037i	$0.843880\pi$
$608$	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	0.607905	+	0.794010i	$0.292010\pi$
$613$	7.63138	+	43.2797i	0.308228	+	1.74805i	−0.299677	+	0.954041i	$0.596879\pi$
$614$	−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	0.890791	+	0.454413i	$0.150151\pi$
$617$	9.84265	+	32.8767i	0.396250	+	1.32357i	−0.494541	+	0.869154i	$0.664664\pi$
$618$		0			0
$619$	−3.30757	+	4.44283i	−0.132942	+	0.178573i	−0.863610	−	0.504161i	$-0.831802\pi$
$619$	−3.30757	+	4.44283i	−0.132942	+	0.178573i	0.730667	+	0.682734i	$0.239209\pi$
$620$	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	0.168109	−	0.985768i	$-0.446234\pi$
$631$	−19.4299	−	16.3036i	−0.773492	−	0.649037i	−0.941601	+	0.336732i	$0.890678\pi$
$632$	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	$-0.711039\pi$
$641$	−20.5525	+	4.87103i	−0.811775	+	0.192394i	−0.196293	+	0.980545i	$0.562890\pi$
$642$		0			0
$643$	0.929279	−	15.9551i	0.0366472	−	0.629208i	−0.929117	−	0.369786i	$-0.879431\pi$
$643$	0.929279	−	15.9551i	0.0366472	−	0.629208i	0.965764	−	0.259422i	$-0.0835320\pi$
$644$	−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	$-0.261395\pi$
$647$	34.6617			1.36269			0.681346	+	0.731961i	$0.261395\pi$
$648$		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	0.880262	+	0.474487i	$0.157366\pi$
$653$	−1.25553	+	21.5566i	−0.0491326	+	0.843574i	−0.929395	+	0.369087i	$0.879671\pi$
$654$		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	$-0.634934\pi$
$659$	6.74382	−	4.43548i	0.262702	−	0.172782i	0.674027	+	0.738707i	$0.264563\pi$
$660$		0			0
$661$	34.1129	−	3.98723i	1.32684	−	0.155085i	0.577021	−	0.816729i	$-0.304215\pi$
$661$	34.1129	−	3.98723i	1.32684	−	0.155085i	0.749818	+	0.661644i	$0.230141\pi$
$662$	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	0.0803612	−	0.996766i	$-0.474393\pi$
$673$	−1.85004	−	0.216238i	−0.0713137	−	0.00833538i	−0.151675	+	0.988430i	$0.548467\pi$
$674$	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	$-0.707422\pi$
$677$	8.56411	−	11.5036i	0.329146	−	0.442119i	0.935633	+	0.352974i	$0.114829\pi$
$678$		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	0.943241	+	0.332109i	$0.107760\pi$
$683$	4.45517	+	25.2665i	0.170472	+	0.966797i	−0.772768	+	0.634688i	$0.781129\pi$
$684$		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	0.994783	−	0.102013i	$-0.0325282\pi$
$691$	39.6143	+	19.8951i	1.50700	+	0.756844i	0.512217	+	0.858856i	$0.328825\pi$
$692$	−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	$-0.904791\pi$
$701$	−5.89393	+	10.2086i	−0.222611	+	0.385573i	0.732989	+	0.680240i	$0.238125\pi$
$702$		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	0.998004	−	0.0631469i	$-0.0201137\pi$
$709$	23.3502	+	24.7498i	0.876935	+	0.929497i	−0.121069	+	0.992644i	$0.538632\pi$
$710$	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	$-0.756013\pi$
$719$	−22.1565	+	8.06429i	−0.826297	+	0.300747i	−0.105959	+	0.994371i	$0.533791\pi$
$720$		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	0.971050	−	0.238875i	$-0.0767786\pi$
$727$	3.53009	+	8.18366i	0.130924	+	0.303515i	−0.840127	+	0.542390i	$0.817519\pi$
$728$	−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	−0.956024	−	0.293290i	$-0.905250\pi$
$733$	−16.4513	+	17.4374i	−0.607643	+	0.644063i	0.348381	+	0.937353i	$0.386731\pi$
$734$	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	0.189662	−	0.981850i	$-0.439261\pi$
$739$	26.2622	−	9.55867i	0.966071	−	0.351621i	0.776410	+	0.630228i	$0.217039\pi$
$740$	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	−0.986747	−	0.162267i	$-0.948119\pi$
$743$	−23.4200	−	31.4585i	−0.859195	−	1.15410i	0.127552	−	0.991832i	$-0.459288\pi$
$744$		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	0.0657145	−	0.997838i	$-0.479067\pi$
$751$	−22.5946	−	14.8607i	−0.824489	−	0.542275i	−0.890203	+	0.455564i	$0.849438\pi$
$752$	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	−0.989940	−	0.141489i	$-0.954811\pi$
$757$	−10.2471	+	17.7485i	−0.372437	+	0.645080i	0.617503	+	0.786569i	$0.288144\pi$
$758$	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	$-0.736249\pi$
$761$	−13.4726	+	6.76622i	−0.488383	+	0.245275i	0.187527	+	0.982259i	$0.439953\pi$
$762$		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	−0.793559	−	0.608493i	$-0.791774\pi$
$769$	5.36914	−	12.4471i	0.193616	−	0.448852i	0.987175	+	0.159641i	$0.0510336\pi$
$770$	−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	$-0.968518\pi$
$773$	−0.729570	+	4.13760i	−0.0262408	+	0.148819i	0.968872	+	0.247561i	$0.0796292\pi$
$774$		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	0.0579725	−	0.998318i	$-0.481536\pi$
$787$	−9.48954	−	2.24906i	−0.338266	−	0.0801704i	−0.396238	+	0.918148i	$0.629685\pi$
$788$	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	$-0.479323\pi$
$797$	10.1126	−	1.18199i	0.358207	−	0.0418684i	0.293293	+	0.956023i	$0.405249\pi$
$798$		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	$-0.614998\pi$
$809$	−20.1073			−0.706936			−0.353468	+	0.935447i	$0.614998\pi$
$810$		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	$-0.711568\pi$
$821$	−3.96387	+	2.60708i	−0.138340	+	0.0909876i	0.478453	+	0.878113i	$0.341198\pi$
$822$		0			0
$823$	−26.3661	+	3.08176i	−0.919065	+	0.107423i	−0.562453	−	0.826829i	$-0.690142\pi$
$823$	−26.3661	+	3.08176i	−0.919065	+	0.107423i	−0.356612	+	0.934253i	$0.616068\pi$
$824$	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	$-0.316496\pi$
$827$	−5.34609	−	4.48590i	−0.185902	−	0.155990i	−0.730989	+	0.682389i	$0.760941\pi$
$828$		0			0
$829$	28.3490	−	23.7877i	0.984603	−	0.826180i	−0.000174449	−	1.00000i	$-0.500056\pi$
$829$	28.3490	−	23.7877i	0.984603	−	0.826180i	0.984777	+	0.173820i	$0.0556111\pi$
$830$	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	$-0.753833\pi$
$839$	4.60126	−	6.18056i	0.158853	−	0.213377i	0.874423	+	0.485165i	$0.161240\pi$
$840$		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	−0.156814	−	0.987628i	$-0.550122\pi$
$853$	−30.4520	−	15.2936i	−1.04266	−	0.523642i	−0.885842	+	0.463987i	$0.846419\pi$
$854$	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	0.511359	+	0.859367i	$0.329142\pi$
$857$	−11.3616	+	37.9504i	−0.388105	+	1.29636i	−0.899464	+	0.436994i	$0.856043\pi$
$858$		0			0
$859$	−48.8321	+	24.5244i	−1.66613	+	0.836762i	−0.670652	+	0.741772i	$0.733986\pi$
$859$	−48.8321	+	24.5244i	−1.66613	+	0.836762i	−0.995478	+	0.0949905i	$0.969718\pi$
$860$	−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	$-0.826461\pi$
$863$	0.634182	−	1.09844i	0.0215878	−	0.0373912i	0.876617	+	0.481188i	$0.159795\pi$
$864$		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	0.981262	+	0.192676i	$0.0617167\pi$
$877$	26.1912	+	35.1809i	0.884415	+	1.18798i	−0.0968475	+	0.995299i	$0.530876\pi$
$878$	−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	$-0.458113\pi$
$881$	25.7921	−	9.38756i	0.868959	−	0.316275i	0.737745	+	0.675079i	$0.235891\pi$
$882$		0			0
$883$	−19.1938	−	6.98597i	−0.645923	−	0.235097i	−0.00177579	−	0.999998i	$-0.500565\pi$
$883$	−19.1938	−	6.98597i	−0.645923	−	0.235097i	−0.644147	+	0.764902i	$0.722787\pi$
$884$	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	$-0.978358\pi$
$887$	−25.9661	+	27.5225i	−0.871857	+	0.924114i	0.125833	+	0.992051i	$0.459840\pi$
$888$		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	0.996851	+	0.0792924i	$0.0252661\pi$
$907$	0.480226	+	8.24516i	0.0159456	+	0.273776i	−0.980906	+	0.194484i	$0.937697\pi$
$908$	−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	$-0.0523459\pi$
$911$	23.1114	+	24.4967i	0.765716	+	0.811611i	−0.220793	+	0.975321i	$0.570864\pi$
$912$		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	−0.997291	−	0.0735573i	$-0.976565\pi$
$919$	−13.1853	+	22.8376i	−0.434943	+	0.753343i	0.562348	+	0.826901i	$0.309898\pi$
$920$	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	$-0.683769\pi$
$929$	−47.0551	−	23.6319i	−1.54383	−	0.775339i	−0.998040	+	0.0625852i	$0.980065\pi$
$930$		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	0.998532	−	0.0541595i	$-0.0172479\pi$
$937$	1.27631	+	7.23831i	0.0416952	+	0.236465i	−0.956837	+	0.290625i	$0.906137\pi$
$938$	−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	0.988990	+	0.147980i	$0.0472771\pi$
$941$	7.48541	+	25.0030i	0.244017	+	0.815075i	−0.744973	+	0.667095i	$0.767538\pi$
$942$		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	$-0.413752\pi$
$947$	9.41332	+	1.10026i	0.305892	+	0.0357536i	0.0382377	+	0.999269i	$0.487826\pi$
$948$		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	0.303464	−	0.952843i	$-0.401857\pi$
$953$	39.9630	−	33.5329i	1.29453	−	1.08624i	0.991063	−	0.133395i	$-0.0425878\pi$
$954$		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	0.991445	+	0.130523i	$0.0416656\pi$
$967$	−0.262735	+	4.51099i	−0.00844899	+	0.145064i	−0.999894	+	0.0145407i	$0.995371\pi$
$968$	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	$-0.563899\pi$
$971$	−12.4268			−0.398796			−0.199398	+	0.979919i	$0.563899\pi$
$972$		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	−0.934476	−	0.356027i	$-0.884131\pi$
$977$	1.09442	−	18.7905i	0.0350136	−	0.601161i	0.969489	−	0.245134i	$-0.0788319\pi$
$978$		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	$-0.626760\pi$
$983$	9.56215	−	6.28913i	0.304985	−	0.200592i	0.692771	+	0.721158i	$0.256390\pi$
$984$		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	−0.926818	−	0.375512i	$-0.877467\pi$
$991$	−22.6012	+	18.9647i	−0.717951	+	0.602432i	0.208867	+	0.977944i	$0.433022\pi$
$992$	−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	−0.617137	−	0.786856i	$-0.711708\pi$
$997$	−44.1770	−	5.16356i	−1.39910	−	0.163531i	−0.781964	+	0.623324i	$0.785782\pi$
$998$	−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.a.676.4		144
3.2	odd	2		729.2.g.d.676.5		144
9.2	odd	6		729.2.g.c.190.5		144
9.4	even	3		243.2.g.a.64.5		144
9.5	odd	6		81.2.g.a.4.4	✓	144
9.7	even	3		729.2.g.b.190.4		144
81.7	even	27		243.2.g.a.19.5		144
81.14	odd	54		6561.2.a.c.1.47		72
81.20	odd	54		729.2.g.c.541.5		144
81.34	even	27	inner	729.2.g.a.55.4		144
81.47	odd	54		729.2.g.d.55.5		144
81.61	even	27		729.2.g.b.541.4		144
81.67	even	27		6561.2.a.d.1.26		72
81.74	odd	54		81.2.g.a.61.4	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.4.4	✓	144	9.5	odd	6
81.2.g.a.61.4	yes	144	81.74	odd	54
243.2.g.a.19.5		144	81.7	even	27
243.2.g.a.64.5		144	9.4	even	3
729.2.g.a.55.4		144	81.34	even	27	inner
729.2.g.a.676.4		144	1.1	even	1	trivial
729.2.g.b.190.4		144	9.7	even	3
729.2.g.b.541.4		144	81.61	even	27
729.2.g.c.190.5		144	9.2	odd	6
729.2.g.c.541.5		144	81.20	odd	54
729.2.g.d.55.5		144	81.47	odd	54
729.2.g.d.676.5		144	3.2	odd	2
6561.2.a.c.1.47		72	81.14	odd	54
6561.2.a.d.1.26		72	81.67	even	27

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

Modular forms

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Database

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