LMFDB - Embedded newform 405.2.r.a.287.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [405,2,Mod(8,405)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("405.8"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(405, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([2, 27])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	405.r (of order $36$, degree $12$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.23394128186$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			287.1
Character	$\chi$	$=$	405.287
Dual form			405.2.r.a.278.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.237511 + 2.71476i) q^{2} +(-5.34392 - 0.942278i) q^{4} +(-0.428650 - 2.19460i) q^{5} +(0.907744 - 1.29639i) q^{7} +(2.41667 - 9.01913i) q^{8} +(6.05963 - 0.642443i) q^{10} +(-0.162954 + 0.447712i) q^{11} +(2.76700 - 0.242081i) q^{13} +(3.30380 + 2.77222i) q^{14} +(13.7126 + 4.99098i) q^{16} +(-0.898665 - 3.35386i) q^{17} +(1.97319 - 1.13922i) q^{19} +(0.222753 + 12.1317i) q^{20} +(-1.17673 - 0.548719i) q^{22} +(0.329603 - 0.230790i) q^{23} +(-4.63252 + 1.88143i) q^{25} +7.56924i q^{26} +(-6.07248 + 6.07248i) q^{28} +(4.29568 - 3.60450i) q^{29} +(0.908475 - 5.15222i) q^{31} +(-8.91403 + 19.1162i) q^{32} +(9.31839 - 1.64308i) q^{34} +(-3.23417 - 1.43643i) q^{35} +(1.44483 - 0.387140i) q^{37} +(2.62407 + 5.62733i) q^{38} +(-20.8293 - 1.43756i) q^{40} +(4.99389 - 5.95149i) q^{41} +(-1.07467 + 0.501128i) q^{43} +(1.29268 - 2.23899i) q^{44} +(0.548257 + 0.949609i) q^{46} +(-9.92230 - 6.94767i) q^{47} +(1.53751 + 4.22426i) q^{49} +(-4.00736 - 13.0231i) q^{50} +(-15.0147 - 1.31362i) q^{52} +(-0.274270 - 0.274270i) q^{53} +(1.05240 + 0.165706i) q^{55} +(-9.49862 - 11.3200i) q^{56} +(8.76510 + 12.5179i) q^{58} +(-3.33385 + 1.21342i) q^{59} +(-1.59716 - 9.05792i) q^{61} +(13.7713 + 3.69001i) q^{62} +(-24.5036 - 14.1471i) q^{64} +(-1.71734 - 5.96868i) q^{65} +(1.15101 + 13.1561i) q^{67} +(1.64212 + 18.7696i) q^{68} +(4.66773 - 8.43883i) q^{70} +(13.8198 + 7.97886i) q^{71} +(-7.73957 - 2.07381i) q^{73} +(0.707832 + 4.01431i) q^{74} +(-11.6180 + 4.22862i) q^{76} +(0.432491 + 0.617661i) q^{77} +(2.85683 + 3.40464i) q^{79} +(5.07529 - 32.2331i) q^{80} +(14.9708 + 14.9708i) q^{82} +(2.90211 + 0.253902i) q^{83} +(-6.97517 + 3.40984i) q^{85} +(-1.10520 - 3.03651i) q^{86} +(3.64417 + 2.55168i) q^{88} +(3.50126 + 6.06435i) q^{89} +(2.19789 - 3.80686i) q^{91} +(-1.97884 + 0.922748i) q^{92} +(21.2179 - 25.2866i) q^{94} +(-3.34594 - 3.84203i) q^{95} +(-3.19969 - 6.86175i) q^{97} +(-11.8331 + 3.17066i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35}+ \cdots - 324 q^{98}+O(q^{100}) $ 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8 - 6 * q^10 + 36 * q^11 - 12 * q^13 - 24 * q^16 + 18 * q^17 - 36 * q^20 - 12 * q^22 + 36 * q^23 - 30 * q^25 - 24 * q^28 - 24 * q^31 + 48 * q^32 - 36 * q^35 - 6 * q^37 - 12 * q^38 - 36 * q^40 - 24 * q^41 - 12 * q^43 - 12 * q^46 + 6 * q^47 - 36 * q^50 + 12 * q^52 - 24 * q^55 - 180 * q^56 - 12 * q^58 - 60 * q^61 + 18 * q^62 + 84 * q^65 + 24 * q^67 + 60 * q^68 - 12 * q^70 + 36 * q^71 - 6 * q^73 - 72 * q^76 - 132 * q^77 - 24 * q^82 - 48 * q^83 - 12 * q^85 - 12 * q^86 - 48 * q^88 - 12 * q^91 - 258 * q^92 - 18 * q^95 + 24 * q^97 - 324 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{18}\right)$

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 $

$2$	−0.237511	+	2.71476i	−0.167946	+	1.91963i	0.182786	+	0.983153i	$0.441488\pi$
$2$	−0.237511	+	2.71476i	−0.167946	+	1.91963i	−0.350732	+	0.936476i	$0.614067\pi$
$3$		0			0
$3$		0			0
$4$	−5.34392	−	0.942278i	−2.67196	−	0.471139i
$5$	−0.428650	−	2.19460i	−0.191698	−	0.981454i
$5$	−0.428650	−	2.19460i	−0.191698	−	0.981454i
$6$		0			0
$7$	0.907744	−	1.29639i	0.343095	−	0.489990i	−0.610109	−	0.792317i	$-0.708874\pi$
$7$	0.907744	−	1.29639i	0.343095	−	0.489990i	0.953204	+	0.302327i	$0.0977634\pi$
$8$	2.41667	−	9.01913i	0.854422	−	3.18874i
$9$		0			0
$10$	6.05963	−	0.642443i	1.91622	−	0.203158i
$11$	−0.162954	+	0.447712i	−0.0491325	+	0.134990i	−0.961832	−	0.273642i	$-0.911772\pi$
$11$	−0.162954	+	0.447712i	−0.0491325	+	0.134990i	0.912699	+	0.408632i	$0.133994\pi$
$12$		0			0
$13$	2.76700	−	0.242081i	0.767427	−	0.0671411i	0.303282	−	0.952901i	$-0.401917\pi$
$13$	2.76700	−	0.242081i	0.767427	−	0.0671411i	0.464144	+	0.885760i	$0.346362\pi$
$14$	3.30380	+	2.77222i	0.882978	+	0.740907i
$15$		0			0
$16$	13.7126	+	4.99098i	3.42815	+	1.24775i
$17$	−0.898665	−	3.35386i	−0.217958	−	0.813431i	−0.985104	−	0.171959i	$-0.944990\pi$
$17$	−0.898665	−	3.35386i	−0.217958	−	0.813431i	0.767146	−	0.641473i	$-0.221676\pi$
$18$		0			0
$19$	1.97319	−	1.13922i	0.452681	−	0.261356i	−0.256281	−	0.966602i	$-0.582497\pi$
$19$	1.97319	−	1.13922i	0.452681	−	0.261356i	0.708962	+	0.705247i	$0.249164\pi$
$20$	0.222753	+	12.1317i	0.0498090	+	2.71272i
$21$		0			0
$22$	−1.17673	−	0.548719i	−0.250880	−	0.116987i
$23$	0.329603	−	0.230790i	0.0687269	−	0.0481231i	−0.538708	−	0.842493i	$-0.681087\pi$
$23$	0.329603	−	0.230790i	0.0687269	−	0.0481231i	0.607435	+	0.794369i	$0.292199\pi$
$24$		0			0
$25$	−4.63252	+	1.88143i	−0.926504	+	0.376286i
$26$			7.56924i			1.48445i
$27$		0			0
$28$	−6.07248	+	6.07248i	−1.14759	+	1.14759i
$29$	4.29568	−	3.60450i	0.797687	−	0.669339i	−0.149948	−	0.988694i	$-0.547911\pi$
$29$	4.29568	−	3.60450i	0.797687	−	0.669339i	0.947635	+	0.319355i	$0.103466\pi$
$30$		0			0
$31$	0.908475	−	5.15222i	0.163167	−	0.925366i	−0.787767	−	0.615973i	$-0.788763\pi$
$31$	0.908475	−	5.15222i	0.163167	−	0.925366i	0.950934	−	0.309393i	$-0.100126\pi$
$32$	−8.91403	+	19.1162i	−1.57579	+	3.37930i
$33$		0			0
$34$	9.31839	−	1.64308i	1.59809	−	0.281787i
$35$	−3.23417	−	1.43643i	−0.546674	−	0.242802i
$36$		0			0
$37$	1.44483	−	0.387140i	0.237528	−	0.0636454i	−0.138091	−	0.990420i	$-0.544097\pi$
$37$	1.44483	−	0.387140i	0.237528	−	0.0636454i	0.375619	+	0.926774i	$0.377430\pi$
$38$	2.62407	+	5.62733i	0.425680	+	0.912873i
$39$		0			0
$40$	−20.8293	−	1.43756i	−3.29340	−	0.227299i
$41$	4.99389	−	5.95149i	0.779915	−	0.929467i	−0.219015	−	0.975722i	$-0.570284\pi$
$41$	4.99389	−	5.95149i	0.779915	−	0.929467i	0.998930	+	0.0462550i	$0.0147287\pi$
$42$		0			0
$43$	−1.07467	+	0.501128i	−0.163886	+	0.0764213i	−0.502830	−	0.864385i	$-0.667708\pi$
$43$	−1.07467	+	0.501128i	−0.163886	+	0.0764213i	0.338944	+	0.940806i	$0.389930\pi$
$44$	1.29268	−	2.23899i	0.194879	−	0.337541i
$45$		0			0
$46$	0.548257	+	0.949609i	0.0808361	+	0.140012i
$47$	−9.92230	−	6.94767i	−1.44732	−	1.01342i	−0.992422	−	0.122876i	$-0.960788\pi$
$47$	−9.92230	−	6.94767i	−1.44732	−	1.01342i	−0.454894	−	0.890546i	$-0.650323\pi$
$48$		0			0
$49$	1.53751	+	4.22426i	0.219644	+	0.603466i
$50$	−4.00736	−	13.0231i	−0.566727	−	1.84174i
$51$		0			0
$52$	−15.0147	−	1.31362i	−2.08217	−	0.182166i
$53$	−0.274270	−	0.274270i	−0.0376738	−	0.0376738i	0.688019	−	0.725693i	$-0.258481\pi$
$53$	−0.274270	−	0.274270i	−0.0376738	−	0.0376738i	−0.725693	+	0.688019i	$0.758481\pi$
$54$		0			0
$55$	1.05240	+	0.165706i	0.141905	+	0.0223439i
$56$	−9.49862	−	11.3200i	−1.26931	−	1.51270i
$57$		0			0
$58$	8.76510	+	12.5179i	1.15091	+	1.64368i
$59$	−3.33385	+	1.21342i	−0.434031	+	0.157974i	−0.549790	−	0.835303i	$-0.685292\pi$
$59$	−3.33385	+	1.21342i	−0.434031	+	0.157974i	0.115759	+	0.993277i	$0.463070\pi$
$60$		0			0
$61$	−1.59716	−	9.05792i	−0.204495	−	1.15975i	−0.898233	−	0.439520i	$-0.855149\pi$
$61$	−1.59716	−	9.05792i	−0.204495	−	1.15975i	0.693738	−	0.720228i	$-0.255963\pi$
$62$	13.7713	+	3.69001i	1.74896	+	0.468631i
$63$		0			0
$64$	−24.5036	−	14.1471i	−3.06294	−	1.76839i
$65$	−1.71734	−	5.96868i	−0.213010	−	0.740323i
$66$		0			0
$67$	1.15101	+	13.1561i	0.140618	+	1.60727i	0.659012	+	0.752132i	$0.270975\pi$
$67$	1.15101	+	13.1561i	0.140618	+	1.60727i	−0.518394	+	0.855142i	$0.673470\pi$
$68$	1.64212	+	18.7696i	0.199137	+	2.27614i
$69$		0			0
$70$	4.66773	−	8.43883i	0.557901	−	1.00863i
$71$	13.8198	+	7.97886i	1.64011	+	0.946916i	0.980794	+	0.195047i	$0.0624860\pi$
$71$	13.8198	+	7.97886i	1.64011	+	0.946916i	0.659313	+	0.751869i	$0.270847\pi$
$72$		0			0
$73$	−7.73957	−	2.07381i	−0.905849	−	0.242721i	−0.224322	−	0.974515i	$-0.572017\pi$
$73$	−7.73957	−	2.07381i	−0.905849	−	0.242721i	−0.681526	+	0.731794i	$0.738683\pi$
$74$	0.707832	+	4.01431i	0.0822838	+	0.466655i
$75$		0			0
$76$	−11.6180	+	4.22862i	−1.33268	+	0.485056i
$77$	0.432491	+	0.617661i	0.0492869	+	0.0703890i
$78$		0			0
$79$	2.85683	+	3.40464i	0.321418	+	0.383051i	0.902425	−	0.430848i	$-0.141785\pi$
$79$	2.85683	+	3.40464i	0.321418	+	0.383051i	−0.581006	+	0.813899i	$0.697341\pi$
$80$	5.07529	−	32.2331i	0.567434	−	3.60377i
$81$		0			0
$82$	14.9708	+	14.9708i	1.65325	+	1.65325i
$83$	2.90211	+	0.253902i	0.318548	+	0.0278694i	0.245309	−	0.969445i	$-0.421111\pi$
$83$	2.90211	+	0.253902i	0.318548	+	0.0278694i	0.0732395	+	0.997314i	$0.476666\pi$
$84$		0			0
$85$	−6.97517	+	3.40984i	−0.756563	+	0.369849i
$86$	−1.10520	−	3.03651i	−0.119177	−	0.327435i
$87$		0			0
$88$	3.64417	+	2.55168i	0.388470	+	0.272010i
$89$	3.50126	+	6.06435i	0.371132	+	0.642820i	0.989740	−	0.142880i	$-0.0456363\pi$
$89$	3.50126	+	6.06435i	0.371132	+	0.642820i	−0.618608	+	0.785700i	$0.712303\pi$
$90$		0			0
$91$	2.19789	−	3.80686i	0.230402	−	0.399068i
$92$	−1.97884	+	0.922748i	−0.206308	+	0.0962031i
$93$		0			0
$94$	21.2179	−	25.2866i	2.18846	−	2.60811i
$95$	−3.34594	−	3.84203i	−0.343287	−	0.394184i
$96$		0			0
$97$	−3.19969	−	6.86175i	−0.324879	−	0.696705i	0.674247	−	0.738506i	$-0.264468\pi$
$97$	−3.19969	−	6.86175i	−0.324879	−	0.696705i	−0.999126	+	0.0418007i	$0.986691\pi$
$98$	−11.8331	+	3.17066i	−1.19532	+	0.320285i
$99$		0			0
$100$	26.5286	−	5.68909i	2.65286	−	0.568909i
$101$	−5.72678	+	1.00979i	−0.569836	+	0.100477i	−0.451140	−	0.892453i	$-0.648983\pi$
$101$	−5.72678	+	1.00979i	−0.569836	+	0.100477i	−0.118696	+	0.992931i	$0.537871\pi$
$102$		0			0
$103$	−1.89098	+	4.05522i	−0.186324	+	0.399573i	−0.977175	−	0.212436i	$-0.931860\pi$
$103$	−1.89098	+	4.05522i	−0.186324	+	0.399573i	0.790851	+	0.612009i	$0.209638\pi$
$104$	4.50356	−	25.5409i	0.441610	−	2.50450i
$105$		0			0
$106$	0.809720	−	0.679435i	0.0786469	−	0.0659926i
$107$	0.577939	−	0.577939i	0.0558714	−	0.0558714i	−0.678619	−	0.734490i	$-0.737421\pi$
$107$	0.577939	−	0.577939i	0.0558714	−	0.0558714i	0.734490	+	0.678619i	$0.237421\pi$
$108$		0			0
$109$		−	8.45996i		−	0.810317i	−0.914246	−	0.405159i	$-0.867216\pi$
$109$		−	8.45996i		−	0.810317i	0.914246	−	0.405159i	$-0.132784\pi$
$110$	−0.699811	+	2.81766i	−0.0667243	+	0.268653i
$111$		0			0
$112$	18.9178	−	13.2464i	1.78757	−	1.25167i
$113$	−1.97616	−	0.921497i	−0.185901	−	0.0866871i	0.327439	−	0.944872i	$-0.393814\pi$
$113$	−1.97616	−	0.921497i	−0.185901	−	0.0866871i	−0.513340	+	0.858185i	$0.671592\pi$
$114$		0			0
$115$	−0.647776	−	0.624417i	−0.0604054	−	0.0582272i
$116$	−26.3522	+	15.2145i	−2.44674	+	1.41263i
$117$		0			0
$118$	−2.50233	−	9.33883i	−0.230358	−	0.859709i
$119$	−5.16368	−	1.87943i	−0.473354	−	0.172287i
$120$		0			0
$121$	8.25260	+	6.92475i	0.750236	+	0.629523i
$122$	24.9695	−	2.18454i	2.26063	−	0.197779i
$123$		0			0
$124$	−9.70964	+	26.6770i	−0.871952	+	2.39567i
$125$	6.11471	+	9.36004i	0.546916	+	0.837187i
$126$		0			0
$127$	0.923874	−	3.44795i	0.0819806	−	0.305956i	−0.912745	−	0.408530i	$-0.866041\pi$
$127$	0.923874	−	3.44795i	0.0819806	−	0.305956i	0.994725	+	0.102575i	$0.0327081\pi$
$128$	20.0298	−	28.6056i	1.77040	−	2.52840i
$129$		0			0
$130$	16.6114	−	3.24456i	1.45692	−	0.284566i
$131$	3.02885	+	0.534068i	0.264632	+	0.0466617i	0.304390	−	0.952548i	$-0.401548\pi$
$131$	3.02885	+	0.534068i	0.264632	+	0.0466617i	−0.0397579	+	0.999209i	$0.512659\pi$
$132$		0			0
$133$	0.314273	−	3.59215i	0.0272509	−	0.311479i
$134$	−35.9891			−3.10899
$135$		0			0
$136$	−32.4207			−2.78005
$137$	0.181036	−	2.06926i	0.0154670	−	0.176788i	−0.984532	−	0.175206i	$-0.943941\pi$
$137$	0.181036	−	2.06926i	0.0154670	−	0.176788i	0.999999	−	0.00158226i	$-0.000503650\pi$
$138$		0			0
$139$	−15.2015	−	2.68044i	−1.28938	−	0.227352i	−0.513420	−	0.858137i	$-0.671622\pi$
$139$	−15.2015	−	2.68044i	−1.28938	−	0.227352i	−0.775957	+	0.630785i	$0.782733\pi$
$140$	15.9296	+	10.7237i	1.34630	+	0.906316i
$141$		0			0
$142$	−24.9431	+	35.6224i	−2.09318	+	2.98937i
$143$	−0.342511	+	1.27827i	−0.0286422	+	0.106894i
$144$		0			0
$145$	−9.75177	−	7.88221i	−0.809841	−	0.654582i
$146$	7.46815	−	20.5186i	0.618068	−	1.69813i
$147$		0			0
$148$	−8.08583	+	0.707419i	−0.664651	+	0.0581495i
$149$	12.0609	+	10.1203i	0.988065	+	0.829085i	0.985286	−	0.170911i	$-0.0546712\pi$
$149$	12.0609	+	10.1203i	0.988065	+	0.829085i	0.00277827	+	0.999996i	$0.499116\pi$
$150$		0			0
$151$	−1.00956	−	0.367451i	−0.0821571	−	0.0299027i	0.300615	−	0.953746i	$-0.402808\pi$
$151$	−1.00956	−	0.367451i	−0.0821571	−	0.0299027i	−0.382772	+	0.923843i	$0.625030\pi$
$152$	−5.50625	−	20.5496i	−0.446616	−	1.66679i
$153$		0			0
$154$	−1.77953	+	1.02741i	−0.143398	+	0.0827910i
$155$	−11.6965	+	0.214762i	−0.939483	+	0.0172501i
$156$		0			0
$157$	−15.6022	−	7.27543i	−1.24519	−	0.580643i	−0.315481	−	0.948932i	$-0.602166\pi$
$157$	−15.6022	−	7.27543i	−1.24519	−	0.580643i	−0.929711	+	0.368289i	$0.879944\pi$
$158$	−9.92131	+	6.94698i	−0.789297	+	0.552672i
$159$		0			0
$160$	45.7734	+	11.3685i	3.61870	+	0.898762i
$161$		−	0.636793i		−	0.0501863i
$162$		0			0
$163$	2.47310	−	2.47310i	0.193708	−	0.193708i	−0.603588	−	0.797296i	$-0.706263\pi$
$163$	2.47310	−	2.47310i	0.193708	−	0.193708i	0.797296	+	0.603588i	$0.206263\pi$
$164$	−32.2949	+	27.0987i	−2.52181	+	2.11605i
$165$		0			0
$166$	−1.37857	+	7.81825i	−0.106998	+	0.606814i
$167$	−2.78431	+	5.97097i	−0.215456	+	0.462048i	−0.984097	−	0.177634i	$-0.943156\pi$
$167$	−2.78431	+	5.97097i	−0.215456	+	0.462048i	0.768640	+	0.639681i	$0.220934\pi$
$168$		0			0
$169$	−5.20483	+	0.917752i	−0.400372	+	0.0705963i
$170$	−7.60024	−	19.7458i	−0.582912	−	1.51443i
$171$		0			0
$172$	6.21517	−	1.66535i	0.473902	−	0.126982i
$173$	−4.51859	−	9.69016i	−0.343542	−	0.736729i	0.656300	−	0.754500i	$-0.272121\pi$
$173$	−4.51859	−	9.69016i	−0.343542	−	0.736729i	−0.999842	+	0.0177714i	$0.994343\pi$
$174$		0			0
$175$	−1.76607	+	7.71342i	−0.133502	+	0.583080i
$176$	−4.46905	+	5.32601i	−0.336867	+	0.401463i
$177$		0			0
$178$	−17.2949	+	8.06473i	−1.29631	+	0.604477i
$179$	−3.31311	+	5.73847i	−0.247633	+	0.428913i	−0.962869	−	0.269970i	$-0.912986\pi$
$179$	−3.31311	+	5.73847i	−0.247633	+	0.428913i	0.715235	+	0.698884i	$0.246319\pi$
$180$		0			0
$181$	−4.36897	−	7.56727i	−0.324743	−	0.562471i	0.656717	−	0.754137i	$-0.271944\pi$
$181$	−4.36897	−	7.56727i	−0.324743	−	0.562471i	−0.981460	+	0.191666i	$0.938611\pi$
$182$	9.81271	+	6.87094i	0.727367	+	0.509308i
$183$		0			0
$184$	−1.28499	−	3.53048i	−0.0947306	−	0.260270i
$185$	−1.46894	−	3.00487i	−0.107999	−	0.220922i
$186$		0			0
$187$	1.64801	+	0.144182i	0.120514	+	0.0105436i
$188$	46.4773	+	46.4773i	3.38971	+	3.38971i
$189$		0			0
$190$	11.2249	−	8.17092i	0.814341	−	0.592781i
$191$	12.9658	+	15.4521i	0.938176	+	1.11807i	0.992826	+	0.119569i	$0.0381512\pi$
$191$	12.9658	+	15.4521i	0.938176	+	1.11807i	−0.0546500	+	0.998506i	$0.517404\pi$
$192$		0			0
$193$	10.7709	+	15.3824i	0.775303	+	1.10725i	0.991399	+	0.130875i	$0.0417788\pi$
$193$	10.7709	+	15.3824i	0.775303	+	1.10725i	−0.216096	+	0.976372i	$0.569332\pi$
$194$	19.3880	−	7.05665i	1.39198	−	0.506638i
$195$		0			0
$196$	−4.23588	−	24.0229i	−0.302563	−	1.71592i
$197$	4.84019	+	1.29693i	0.344849	+	0.0924021i	0.427087	−	0.904211i	$-0.359540\pi$
$197$	4.84019	+	1.29693i	0.344849	+	0.0924021i	−0.0822373	+	0.996613i	$0.526207\pi$
$198$		0			0
$199$	14.4356	+	8.33443i	1.02332	+	0.590812i	0.915063	−	0.403312i	$-0.132141\pi$
$199$	14.4356	+	8.33443i	1.02332	+	0.590812i	0.108253	+	0.994123i	$0.465474\pi$
$200$	5.77360	+	46.3281i	0.408255	+	3.27589i
$201$		0			0
$202$	−1.38116	−	15.7867i	−0.0971779	−	1.11075i
$203$	−0.773474	−	8.84085i	−0.0542872	−	0.620506i
$204$		0			0
$205$	−15.2018	−	8.40848i	−1.06174	−	0.587274i
$206$	−10.5599	−	6.09673i	−0.735740	−	0.424779i
$207$		0			0
$208$	39.1510	+	10.4905i	2.71463	+	0.727384i
$209$	0.188505	+	1.06906i	0.0130391	+	0.0739486i
$210$		0			0
$211$	9.81899	−	3.57382i	0.675967	−	0.246032i	0.0188522	−	0.999822i	$-0.493999\pi$
$211$	9.81899	−	3.57382i	0.675967	−	0.246032i	0.657115	+	0.753790i	$0.271777\pi$
$212$	1.20724	+	1.72411i	0.0829134	+	0.118413i
$213$		0			0
$214$	1.43170	+	1.70623i	0.0978690	+	0.116636i
$215$	1.56043	+	2.14367i	0.106421	+	0.146197i
$216$		0			0
$217$	−5.85464	−	5.85464i	−0.397439	−	0.397439i
$218$	22.9668	+	2.00934i	1.55551	+	0.136089i
$219$		0			0
$220$	−5.46780	−	1.87717i	−0.368639	−	0.126559i
$221$	−3.29851	−	9.06258i	−0.221882	−	0.609615i
$222$		0			0
$223$	19.2158	+	13.4550i	1.28678	+	0.901015i	0.998403	−	0.0565006i	$-0.0179943\pi$
$223$	19.2158	+	13.4550i	1.28678	+	0.901015i	0.288381	+	0.957516i	$0.406883\pi$
$224$	16.6904	+	28.9087i	1.11518	+	1.93154i
$225$		0			0
$226$	2.97101	−	5.14593i	0.197628	−	0.342302i
$227$	−18.1424	+	8.45994i	−1.20415	+	0.561506i	−0.917963	−	0.396667i	$-0.870167\pi$
$227$	−18.1424	+	8.45994i	−1.20415	+	0.561506i	−0.286191	+	0.958173i	$0.592389\pi$
$228$		0			0
$229$	−14.1827	+	16.9023i	−0.937218	+	1.11693i	0.0557370	+	0.998445i	$0.482249\pi$
$229$	−14.1827	+	16.9023i	−0.937218	+	1.11693i	−0.992955	+	0.118488i	$0.962195\pi$
$230$	1.84900	−	1.61025i	0.121919	−	0.106177i
$231$		0			0
$232$	−22.1282	−	47.4542i	−1.45279	−	3.11552i
$233$	−18.0369	+	4.83296i	−1.18163	+	0.316618i	−0.795574	−	0.605856i	$-0.792831\pi$
$233$	−18.0369	+	4.83296i	−1.18163	+	0.316618i	−0.386059	+	0.922474i	$0.626164\pi$
$234$		0			0
$235$	−10.9941	+	24.7536i	−0.717179	+	1.61474i
$236$	18.9592	−	3.34302i	1.23414	−	0.217612i
$237$		0			0
$238$	6.32863	−	13.5718i	0.410224	−	0.879729i
$239$	−3.38846	+	19.2169i	−0.219181	+	1.24304i	0.654320	+	0.756218i	$0.272955\pi$
$239$	−3.38846	+	19.2169i	−0.219181	+	1.24304i	−0.873502	+	0.486821i	$0.838156\pi$
$240$		0			0
$241$	−3.76991	+	3.16333i	−0.242841	+	0.203768i	−0.756082	−	0.654476i	$-0.772889\pi$
$241$	−3.76991	+	3.16333i	−0.242841	+	0.203768i	0.513241	+	0.858244i	$0.328445\pi$
$242$	−20.7592	+	20.7592i	−1.33445	+	1.33445i
$243$		0			0
$244$			49.9098i			3.19515i
$245$	8.61150	−	5.18494i	0.550169	−	0.331253i
$246$		0			0
$247$	5.18403	−	3.62990i	0.329852	−	0.230965i
$248$	−44.2731	−	20.6449i	−2.81134	−	1.31095i
$249$		0			0
$250$	−26.8626	+	14.3769i	−1.69894	+	0.909274i
$251$	18.1080	−	10.4546i	1.14297	−	0.659892i	0.195803	−	0.980643i	$-0.437269\pi$
$251$	18.1080	−	10.4546i	1.14297	−	0.659892i	0.947163	+	0.320752i	$0.103935\pi$
$252$		0			0
$253$	0.0496176	+	0.185175i	0.00311943	+	0.0116419i
$254$	9.14093	+	3.32703i	0.573553	+	0.208756i
$255$		0			0
$256$	29.5507	+	24.7960i	1.84692	+	1.54975i
$257$	−14.5430	+	1.27235i	−0.907166	+	0.0793667i	−0.531180	−	0.847259i	$-0.678251\pi$
$257$	−14.5430	+	1.27235i	−0.907166	+	0.0793667i	−0.375986	+	0.926626i	$0.622696\pi$
$258$		0			0
$259$	0.809647	−	2.22449i	0.0503090	−	0.138223i
$260$	3.55320	+	33.5144i	0.220360	+	2.07847i
$261$		0			0
$262$	−2.16925	+	8.09576i	−0.134017	+	0.500158i
$263$	−17.5612	+	25.0799i	−1.08287	+	1.54650i	−0.271067	+	0.962561i	$0.587376\pi$
$263$	−17.5612	+	25.0799i	−1.08287	+	1.54650i	−0.811801	+	0.583935i	$0.801512\pi$
$264$		0			0
$265$	−0.484346	+	0.719477i	−0.0297531	+	0.0441971i
$266$	9.67721	+	1.70635i	0.593348	+	0.104623i
$267$		0			0
$268$	6.24580	−	71.3898i	0.381523	−	4.36083i
$269$	23.6912			1.44448			0.722239	−	0.691643i	$-0.243113\pi$
$269$	23.6912			1.44448			0.722239	+	0.691643i	$0.243113\pi$
$270$		0			0
$271$	20.1164			1.22198			0.610991	−	0.791638i	$-0.290771\pi$
$271$	20.1164			1.22198			0.610991	+	0.791638i	$0.290771\pi$
$272$	4.41603	−	50.4755i	0.267761	−	3.06052i
$273$		0			0
$274$	5.57454	+	0.982943i	0.336771	+	0.0593817i
$275$	−0.0874520	−	2.38062i	−0.00527355	−	0.143557i
$276$		0			0
$277$	8.72217	−	12.4565i	0.524064	−	0.748441i	−0.466644	−	0.884445i	$-0.654537\pi$
$277$	8.72217	−	12.4565i	0.524064	−	0.748441i	0.990708	+	0.136004i	$0.0434260\pi$
$278$	10.8873	−	40.6320i	0.652977	−	2.43694i
$279$		0			0
$280$	−20.7713	+	25.6980i	−1.24132	+	1.53575i
$281$	8.16607	−	22.4361i	0.487147	−	1.33842i	−0.416106	−	0.909316i	$-0.636606\pi$
$281$	8.16607	−	22.4361i	0.487147	−	1.33842i	0.903253	−	0.429108i	$-0.141172\pi$
$282$		0			0
$283$	−0.284217	+	0.0248657i	−0.0168949	+	0.00147811i	−0.0956001	−	0.995420i	$-0.530477\pi$
$283$	−0.284217	+	0.0248657i	−0.0168949	+	0.00147811i	0.0787051	+	0.996898i	$0.474921\pi$
$284$	−66.3335	−	55.6605i	−3.93617	−	3.30284i
$285$		0			0
$286$	−3.38884	−	1.23344i	−0.200387	−	0.0729347i
$287$	−3.18229	−	11.8765i	−0.187845	−	0.701046i
$288$		0			0
$289$	4.28164	−	2.47200i	0.251861	−	0.145412i
$290$	23.7145	−	24.6017i	1.39256	−	1.44466i
$291$		0			0
$292$	39.4056	+	18.3751i	2.30604	+	1.07532i
$293$	12.7347	−	8.91694i	0.743969	−	0.520933i	−0.139041	−	0.990287i	$-0.544402\pi$
$293$	12.7347	−	8.91694i	0.743969	−	0.520933i	0.883010	+	0.469354i	$0.155513\pi$
$294$		0			0
$295$	4.09203	+	6.79633i	0.238247	+	0.395698i
$296$		−	13.9667i		−	0.811796i
$297$		0			0
$298$	−30.3387	+	30.3387i	−1.75748	+	1.75748i
$299$	0.856140	−	0.718387i	0.0495119	−	0.0415454i
$300$		0			0
$301$	−0.325869	+	1.84809i	−0.0187828	+	0.106522i
$302$	1.23733	−	2.65345i	0.0712001	−	0.152689i
$303$		0			0
$304$	32.7435	−	5.77355i	1.87797	−	0.331136i
$305$	−19.1939	+	7.38779i	−1.09904	+	0.423024i
$306$		0			0
$307$	−10.1671	+	2.72426i	−0.580267	+	0.155482i	−0.537001	−	0.843582i	$-0.680443\pi$
$307$	−10.1671	+	2.72426i	−0.580267	+	0.155482i	−0.0432656	+	0.999064i	$0.513776\pi$
$308$	−1.72919	−	3.70826i	−0.0985297	−	0.211298i
$309$		0			0
$310$	2.19501	−	31.8042i	0.124668	−	1.80636i
$311$	−2.06659	+	2.46287i	−0.117186	+	0.139657i	−0.821448	−	0.570283i	$-0.806833\pi$
$311$	−2.06659	+	2.46287i	−0.117186	+	0.139657i	0.704262	+	0.709940i	$0.251278\pi$
$312$		0			0
$313$	22.0403	−	10.2775i	1.24579	−	0.580921i	0.315911	−	0.948789i	$-0.397690\pi$
$313$	22.0403	−	10.2775i	1.24579	−	0.580921i	0.929878	+	0.367868i	$0.119912\pi$
$314$	23.4568	−	40.6283i	1.32374	−	2.29279i
$315$		0			0
$316$	−12.0586	−	20.8860i	−0.678347	−	1.17493i
$317$	−17.0133	−	11.9128i	−0.955562	−	0.669092i	−0.0118742	−	0.999929i	$-0.503780\pi$
$317$	−17.0133	−	11.9128i	−0.955562	−	0.669092i	−0.943688	+	0.330838i	$0.892669\pi$
$318$		0			0
$319$	0.913782	+	2.51060i	0.0511620	+	0.140566i
$320$	−20.5438	+	59.8396i	−1.14843	+	3.34514i
$321$		0			0
$322$	1.72874	+	0.151246i	0.0963391	+	0.00842858i
$323$	−5.59403	−	5.59403i	−0.311260	−	0.311260i
$324$		0			0
$325$	−12.3627	+	6.32735i	−0.685759	+	0.350978i
$326$	6.12650	+	7.30128i	0.339315	+	0.404380i
$327$		0			0
$328$	−41.6087	−	59.4234i	−2.29746	−	3.28111i
$329$	−18.0138	+	6.55649i	−0.993134	+	0.361471i
$330$		0			0
$331$	1.03458	+	5.86738i	0.0568655	+	0.322500i	0.999949	−	0.0100545i	$-0.00320050\pi$
$331$	1.03458	+	5.86738i	0.0568655	+	0.322500i	−0.943084	+	0.332555i	$0.892089\pi$
$332$	−15.2694	−	4.09143i	−0.838018	−	0.224546i
$333$		0			0
$334$	−15.5485	−	8.97692i	−0.850775	−	0.491195i
$335$	28.3790	−	8.16537i	1.55051	−	0.446122i
$336$		0			0
$337$	−0.971978	−	11.1098i	−0.0529470	−	0.605187i	−0.975600	−	0.219556i	$-0.929539\pi$
$337$	−0.971978	−	11.1098i	−0.0529470	−	0.605187i	0.922653	−	0.385631i	$-0.126016\pi$
$338$	−1.25528	−	14.3479i	−0.0682780	−	0.780421i
$339$		0			0
$340$	40.4878	−	11.6494i	2.19576	−	0.631776i
$341$	2.15867	+	1.24631i	0.116899	+	0.0674915i
$342$		0			0
$343$	17.5727	+	4.70859i	0.948837	+	0.254240i
$344$	1.92261	+	10.9037i	0.103660	+	0.587887i
$345$		0			0
$346$	27.3797	−	9.96540i	1.47194	−	0.535743i
$347$	13.6142	+	19.4431i	0.730851	+	1.04376i	0.996813	+	0.0797793i	$0.0254216\pi$
$347$	13.6142	+	19.4431i	0.730851	+	1.04376i	−0.265962	+	0.963984i	$0.585690\pi$
$348$		0			0
$349$	4.82633	+	5.75179i	0.258347	+	0.307886i	0.879591	−	0.475731i	$-0.157817\pi$
$349$	4.82633	+	5.75179i	0.258347	+	0.307886i	−0.621243	+	0.783618i	$0.713372\pi$
$350$	−20.5207	−	6.62649i	−1.09688	−	0.354201i
$351$		0			0
$352$	−7.10598	−	7.10598i	−0.378750	−	0.378750i
$353$	5.16281	+	0.451688i	0.274789	+	0.0240409i	0.223717	−	0.974654i	$-0.428181\pi$
$353$	5.16281	+	0.451688i	0.274789	+	0.0240409i	0.0510716	+	0.998695i	$0.483736\pi$
$354$		0			0
$355$	11.5865	−	33.7490i	0.614949	−	1.79121i
$356$	−12.9961	−	35.7066i	−0.688793	−	1.89244i
$357$		0			0
$358$	−14.7917	−	10.3573i	−0.781765	−	0.547398i
$359$	6.82697	+	11.8247i	0.360314	+	0.624082i	0.988012	−	0.154375i	$-0.0493363\pi$
$359$	6.82697	+	11.8247i	0.360314	+	0.624082i	−0.627699	+	0.778457i	$0.716003\pi$
$360$		0			0
$361$	−6.90435	+	11.9587i	−0.363387	+	0.629404i
$362$	21.5810	−	10.0634i	1.13427	−	0.528921i
$363$		0			0
$364$	−15.3325	+	18.2725i	−0.803641	+	0.957742i
$365$	−1.23361	+	17.8742i	−0.0645703	+	0.935578i
$366$		0			0
$367$	9.11448	+	19.5461i	0.475772	+	1.02030i	0.986981	+	0.160840i	$0.0514203\pi$
$367$	9.11448	+	19.5461i	0.475772	+	1.02030i	−0.511208	+	0.859457i	$0.670802\pi$
$368$	5.67159	−	1.51970i	0.295652	−	0.0792197i
$369$		0			0
$370$	8.50639	−	3.27414i	0.442226	−	0.170215i
$371$	−0.604528	+	0.106595i	−0.0313855	+	0.00553411i
$372$		0			0
$373$	−5.59299	+	11.9942i	−0.289594	+	0.621037i	−0.996250	−	0.0865206i	$-0.972425\pi$
$373$	−5.59299	+	11.9942i	−0.289594	+	0.621037i	0.706656	+	0.707557i	$0.250203\pi$
$374$	−0.782840	+	4.43971i	−0.0404797	+	0.229572i
$375$		0			0
$376$	−86.6408	+	72.7003i	−4.46816	+	3.74923i
$377$	11.0135	−	11.0135i	0.567226	−	0.567226i
$378$		0			0
$379$		−	27.4089i		−	1.40790i	−0.710249	−	0.703951i	$-0.751417\pi$
$379$		−	27.4089i		−	1.40790i	0.710249	−	0.703951i	$-0.248583\pi$
$380$	14.2602	+	23.6843i	0.731533	+	1.21498i
$381$		0			0
$382$	−45.0283	+	31.5292i	−2.30385	+	1.61317i
$383$	32.7469	+	15.2701i	1.67329	+	0.780267i	0.999131	+	0.0416793i	$0.0132708\pi$
$383$	32.7469	+	15.2701i	1.67329	+	0.780267i	0.674157	+	0.738588i	$0.264507\pi$
$384$		0			0
$385$	1.17013	−	1.21390i	0.0596353	−	0.0618663i
$386$	−44.3177	+	25.5869i	−2.25571	+	1.30234i
$387$		0			0
$388$	10.6332	+	39.6836i	0.539819	+	2.01463i
$389$	−17.3733	−	6.32335i	−0.880860	−	0.320607i	−0.138303	−	0.990390i	$-0.544165\pi$
$389$	−17.3733	−	6.32335i	−0.880860	−	0.320607i	−0.742557	+	0.669783i	$0.766387\pi$
$390$		0			0
$391$	−1.07024	−	0.898039i	−0.0541244	−	0.0454158i
$392$	41.8148	−	3.65832i	2.11197	−	0.184773i
$393$		0			0
$394$	−4.67045	+	12.8320i	−0.235294	+	0.646464i
$395$	6.24723	−	7.72899i	0.314332	−	0.388888i
$396$		0			0
$397$	7.80671	−	29.1350i	0.391807	−	1.46224i	−0.435343	−	0.900265i	$-0.643373\pi$
$397$	7.80671	−	29.1350i	0.391807	−	1.46224i	0.827151	−	0.561980i	$-0.189960\pi$
$398$	−26.0546	+	37.2099i	−1.30600	+	1.86516i
$399$		0			0
$400$	−72.9141	+	2.67849i	−3.64571	+	0.133925i
$401$	−34.2820	−	6.04485i	−1.71196	−	0.301865i	−0.770115	−	0.637905i	$-0.779801\pi$
$401$	−34.2820	−	6.04485i	−1.71196	−	0.301865i	−0.941848	+	0.336040i	$0.890912\pi$
$402$		0			0
$403$	1.26649	−	14.4761i	0.0630886	−	0.721106i
$404$	31.5550			1.56992
$405$		0			0
$406$	24.1845			1.20026
$407$	−0.0621128	+	0.709953i	−0.00307882	+	0.0351911i
$408$		0			0
$409$	21.8207	+	3.84758i	1.07897	+	0.190251i	0.684758	−	0.728771i	$-0.259908\pi$
$409$	21.8207	+	3.84758i	1.07897	+	0.190251i	0.394208	+	0.919021i	$0.371019\pi$
$410$	26.4376	−	39.2721i	1.30566	−	1.93951i
$411$		0			0
$412$	13.9264	−	19.8890i	0.686105	−	0.979859i
$413$	−1.45321	+	5.42346i	−0.0715079	+	0.266871i
$414$		0			0
$415$	−0.686778	−	6.47780i	−0.0337126	−	0.317983i
$416$	−20.0374	+	55.0524i	−0.982415	+	2.69916i
$417$		0			0
$418$	−2.94703	+	0.257831i	−0.144144	+	0.0126109i
$419$	−3.82900	−	3.21291i	−0.187059	−	0.156961i	0.544449	−	0.838794i	$-0.316739\pi$
$419$	−3.82900	−	3.21291i	−0.187059	−	0.156961i	−0.731508	+	0.681833i	$0.761183\pi$
$420$		0			0
$421$	12.3825	+	4.50685i	0.603485	+	0.219651i	0.625650	−	0.780104i	$-0.284834\pi$
$421$	12.3825	+	4.50685i	0.603485	+	0.219651i	−0.0221653	+	0.999754i	$0.507056\pi$
$422$	7.36996	+	27.5051i	0.358764	+	1.33893i
$423$		0			0
$424$	−3.13649	+	1.81086i	−0.152322	+	0.0879429i
$425$	10.4731	+	13.8461i	0.508022	+	0.671632i
$426$		0			0
$427$	−13.1924	−	6.15173i	−0.638426	−	0.297703i
$428$	−3.63304	+	2.54388i	−0.175609	+	0.122963i
$429$		0			0
$430$	−6.19017	+	3.72707i	−0.298516	+	0.179735i
$431$		−	14.5168i		−	0.699251i	−0.936890	−	0.349625i	$-0.886309\pi$
$431$		−	14.5168i		−	0.699251i	0.936890	−	0.349625i	$-0.113691\pi$
$432$		0			0
$433$	−16.6348	+	16.6348i	−0.799416	+	0.799416i	−0.983003	−	0.183587i	$-0.941229\pi$
$433$	−16.6348	+	16.6348i	−0.799416	+	0.799416i	0.183587	+	0.983003i	$0.441229\pi$
$434$	17.2845	−	14.5034i	0.829683	−	0.696187i
$435$		0			0
$436$	−7.97163	+	45.2094i	−0.381772	+	2.16514i
$437$	0.387448	−	0.830884i	0.0185341	−	0.0397466i
$438$		0			0
$439$	21.2894	−	3.75390i	1.01609	−	0.179164i	0.359287	−	0.933227i	$-0.383020\pi$
$439$	21.2894	−	3.75390i	1.01609	−	0.179164i	0.656801	+	0.754064i	$0.271909\pi$
$440$	4.03783	−	9.09127i	0.192496	−	0.433409i
$441$		0			0
$442$	25.3862	−	6.80221i	1.20750	−	0.323548i
$443$	5.07285	+	10.8788i	0.241018	+	0.516866i	0.989190	−	0.146640i	$-0.0468458\pi$
$443$	5.07285	+	10.8788i	0.241018	+	0.516866i	−0.748172	+	0.663505i	$0.769068\pi$
$444$		0			0
$445$	11.8080	−	10.2833i	0.559753	−	0.487477i
$446$	−41.0912	+	48.9706i	−1.94572	+	2.31882i
$447$		0			0
$448$	−40.5832	+	18.9243i	−1.91738	+	0.894087i
$449$	15.1373	−	26.2186i	0.714374	−	1.23733i	−0.248826	−	0.968548i	$-0.580045\pi$
$449$	15.1373	−	26.2186i	0.714374	−	1.23733i	0.963200	−	0.268784i	$-0.0866218\pi$
$450$		0			0
$451$	1.85078	+	3.20565i	0.0871499	+	0.150948i
$452$	9.69212	+	6.78649i	0.455879	+	0.319210i
$453$		0			0
$454$	−18.6577	−	51.2617i	−0.875651	−	2.40583i
$455$	−9.29666	−	3.19168i	−0.435834	−	0.149628i
$456$		0			0
$457$	41.4537	+	3.62673i	1.93912	+	0.169651i	0.989579	−	0.143990i	$-0.0459935\pi$
$457$	41.4537	+	3.62673i	1.93912	+	0.169651i	0.949541	+	0.313642i	$0.101549\pi$
$458$	−42.5171	−	42.5171i	−1.98670	−	1.98670i
$459$		0			0
$460$	2.87329	+	3.94722i	0.133968	+	0.184040i
$461$	11.0916	+	13.2184i	0.516586	+	0.615643i	0.959770	−	0.280788i	$-0.0905957\pi$
$461$	11.0916	+	13.2184i	0.516586	+	0.615643i	−0.443184	+	0.896431i	$0.646151\pi$
$462$		0			0
$463$	9.45428	+	13.5021i	0.439378	+	0.627496i	0.976374	−	0.216088i	$-0.0693299\pi$
$463$	9.45428	+	13.5021i	0.439378	+	0.627496i	−0.536996	+	0.843585i	$0.680441\pi$
$464$	76.8950	−	27.9875i	3.56976	−	1.29929i
$465$		0			0
$466$	−8.83640	−	50.1137i	−0.409338	−	2.32147i
$467$	−3.84448	−	1.03012i	−0.177901	−	0.0476685i	0.168769	−	0.985656i	$-0.446021\pi$
$467$	−3.84448	−	1.03012i	−0.177901	−	0.0476685i	−0.346670	+	0.937987i	$0.612688\pi$
$468$		0			0
$469$	18.1003	+	10.4502i	0.835795	+	0.482546i
$470$	−64.5889	−	35.7258i	−2.97926	−	1.64791i
$471$		0			0
$472$	2.88720	+	33.0009i	0.132894	+	1.51899i
$473$	−0.0492391	−	0.562805i	−0.00226402	−	0.0258778i
$474$		0			0
$475$	−6.99748	+	8.98989i	−0.321066	+	0.412484i
$476$	25.8234	+	14.9091i	1.18361	+	0.683359i
$477$		0			0
$478$	−51.3646	−	13.7631i	−2.34936	−	0.629510i
$479$	−0.246236	−	1.39648i	−0.0112508	−	0.0638066i	0.978665	−	0.205460i	$-0.0658692\pi$
$479$	−0.246236	−	1.39648i	−0.0112508	−	0.0638066i	−0.989916	+	0.141654i	$0.954758\pi$
$480$		0			0
$481$	3.90411	−	1.42098i	0.178012	−	0.0647911i
$482$	−7.69230	−	10.9857i	−0.350375	−	0.500387i
$483$		0			0
$484$	−37.5762	−	44.7816i	−1.70801	−	2.03553i
$485$	−13.6872	+	9.96332i	−0.621505	+	0.452411i
$486$		0			0
$487$	−5.92999	−	5.92999i	−0.268714	−	0.268714i	0.559868	−	0.828582i	$-0.310852\pi$
$487$	−5.92999	−	5.92999i	−0.268714	−	0.268714i	−0.828582	+	0.559868i	$0.810852\pi$
$488$	−85.5544	−	7.48504i	−3.87286	−	0.338832i
$489$		0			0
$490$	12.0306	+	24.6097i	0.543485	+	1.11175i
$491$	9.16760	+	25.1878i	0.413728	+	1.13671i	0.955193	+	0.295985i	$0.0956479\pi$
$491$	9.16760	+	25.1878i	0.413728	+	1.13671i	−0.541464	+	0.840724i	$0.682130\pi$
$492$		0			0
$493$	−15.9494	−	11.1679i	−0.718324	−	0.502976i
$494$	8.62305	+	14.9356i	0.387969	+	0.671983i
$495$		0			0
$496$	38.1722	−	66.1162i	1.71398	−	2.96871i
$497$	22.8886	−	10.6731i	1.02669	−	0.478754i
$498$		0			0
$499$	−7.19594	+	8.57579i	−0.322134	+	0.383905i	−0.902672	−	0.430328i	$-0.858398\pi$
$499$	−7.19594	+	8.57579i	−0.322134	+	0.383905i	0.580538	+	0.814233i	$0.302842\pi$
$500$	−23.8568	−	55.7811i	−1.06691	−	2.49460i
$501$		0			0
$502$	24.0811	+	51.6420i	1.07479	+	2.30490i
$503$	−12.8521	+	3.44372i	−0.573049	+	0.153548i	−0.533694	−	0.845677i	$-0.679197\pi$
$503$	−12.8521	+	3.44372i	−0.573049	+	0.153548i	−0.0393543	+	0.999225i	$0.512530\pi$
$504$		0			0
$505$	4.67086	+	12.1351i	0.207851	+	0.540006i
$506$	−0.514493	+	0.0907189i	−0.0228720	+	0.00403295i
$507$		0			0
$508$	−8.18603	+	17.5550i	−0.363197	+	0.778877i
$509$	−1.12261	+	6.36664i	−0.0497588	+	0.282196i	−0.999527	−	0.0307584i	$-0.990208\pi$
$509$	−1.12261	+	6.36664i	−0.0497588	+	0.282196i	0.949768	+	0.312955i	$0.101319\pi$
$510$		0			0
$511$	−9.71403	+	8.15104i	−0.429723	+	0.360581i
$512$	−24.9482	+	24.9482i	−1.10257	+	1.10257i
$513$		0			0
$514$		−	39.7830i		−	1.75475i
$515$	9.71015	+	2.41167i	0.427881	+	0.106271i
$516$		0			0
$517$	4.72744	−	3.31019i	0.207912	−	0.145582i
$518$	5.84666	+	2.72634i	0.256887	+	0.119789i
$519$		0			0
$520$	−57.9825	+	1.06463i	−2.54270	+	0.0466872i
$521$	6.34977	−	3.66604i	0.278188	−	0.160612i	−0.354415	−	0.935088i	$-0.615320\pi$
$521$	6.34977	−	3.66604i	0.278188	−	0.160612i	0.632603	+	0.774476i	$0.281987\pi$
$522$		0			0
$523$	−3.37240	−	12.5860i	−0.147465	−	0.550346i	−0.999633	−	0.0270787i	$-0.991380\pi$
$523$	−3.37240	−	12.5860i	−0.147465	−	0.550346i	0.852168	−	0.523268i	$-0.175287\pi$
$524$	−15.6827	−	5.70803i	−0.685101	−	0.249356i
$525$		0			0
$526$	−63.9152	−	53.6312i	−2.78683	−	2.33843i
$527$	−18.0963	+	1.58322i	−0.788285	+	0.0689660i
$528$		0			0
$529$	−7.81109	+	21.4608i	−0.339613	+	0.933078i
$530$	−1.83817	−	1.48577i	−0.0798452	−	0.0645377i
$531$		0			0
$532$	−5.06425	+	18.9001i	−0.219563	+	0.819421i
$533$	12.3773	−	17.6767i	0.536122	−	0.765662i
$534$		0			0
$535$	−1.51608	−	1.02061i	−0.0655457	−	0.0441248i
$536$	121.438	+	21.4128i	5.24534	+	0.924894i
$537$		0			0
$538$	−5.62693	+	64.3161i	−0.242594	+	2.77286i
$539$	−2.14180			−0.0922537
$540$		0			0
$541$	−19.4815			−0.837576			−0.418788	−	0.908084i	$-0.637545\pi$
$541$	−19.4815			−0.837576			−0.418788	+	0.908084i	$0.637545\pi$
$542$	−4.77786	+	54.6112i	−0.205227	+	2.34575i
$543$		0			0
$544$	72.1238	+	12.7174i	3.09228	+	0.545253i
$545$	−18.5662	+	3.62636i	−0.795289	+	0.155336i
$546$		0			0
$547$	−8.23625	+	11.7626i	−0.352157	+	0.502932i	−0.955678	−	0.294415i	$-0.904875\pi$
$547$	−8.23625	+	11.7626i	−0.352157	+	0.502932i	0.603521	+	0.797347i	$0.293764\pi$
$548$	−2.91726	+	10.8874i	−0.124619	+	0.465085i
$549$		0			0
$550$	6.48360	+	0.328013i	0.276462	+	0.0139865i
$551$	4.36986	−	12.0061i	0.186162	−	0.511477i
$552$		0			0
$553$	7.00702	−	0.613034i	0.297969	−	0.0260689i
$554$	31.7450	+	26.6372i	1.34871	+	1.13171i
$555$		0			0
$556$	78.7101	+	28.6481i	3.33805	+	1.21495i
$557$	−5.99902	−	22.3886i	−0.254187	−	0.948637i	−0.968541	−	0.248853i	$-0.919946\pi$
$557$	−5.99902	−	22.3886i	−0.254187	−	0.948637i	0.714355	−	0.699784i	$-0.246720\pi$
$558$		0			0
$559$	−2.85230	+	1.64678i	−0.120640	+	0.0696513i
$560$	−37.1797	−	35.8389i	−1.57113	−	1.51447i
$561$		0			0
$562$	58.9691	+	27.4978i	2.48746	+	1.15992i
$563$	24.6767	−	17.2788i	1.04000	−	0.728214i	0.0768099	−	0.997046i	$-0.475527\pi$
$563$	24.6767	−	17.2788i	1.04000	−	0.728214i	0.963187	+	0.268832i	$0.0866377\pi$
$564$		0			0
$565$	−1.17523	+	4.73187i	−0.0494425	+	0.199071i
$566$		−	0.777487i		−	0.0326802i
$567$		0			0
$568$	105.360	−	105.360i	4.42082	−	4.42082i
$569$	14.2448	−	11.9528i	0.597173	−	0.501088i	−0.293362	−	0.956001i	$-0.594774\pi$
$569$	14.2448	−	11.9528i	0.597173	−	0.501088i	0.890536	+	0.454913i	$0.150330\pi$
$570$		0			0
$571$	6.82003	−	38.6783i	0.285409	−	1.61864i	−0.418410	−	0.908258i	$-0.637412\pi$
$571$	6.82003	−	38.6783i	0.285409	−	1.61864i	0.703819	−	0.710379i	$-0.251476\pi$
$572$	3.03483	−	6.50822i	0.126893	−	0.272122i
$573$		0			0
$574$	32.9977	−	5.81838i	1.37730	−	0.242854i
$575$	−1.09268	+	1.68926i	−0.0455677	+	0.0704472i
$576$		0			0
$577$	−42.2673	+	11.3255i	−1.75961	+	0.471486i	−0.986634	−	0.162950i	$-0.947899\pi$
$577$	−42.2673	+	11.3255i	−1.75961	+	0.471486i	−0.772975	+	0.634436i	$0.781232\pi$
$578$	5.69397	+	12.2108i	0.236838	+	0.507901i
$579$		0			0
$580$	44.6855	+	51.3108i	1.85546	+	2.13057i
$581$	2.96353	−	3.53180i	0.122948	−	0.146524i
$582$		0			0
$583$	0.167487	−	0.0781006i	0.00693661	−	0.00323460i
$584$	−37.4080	+	64.7925i	−1.54795	+	2.68113i
$585$		0			0
$586$	21.1828	+	36.6896i	0.875051	+	1.51563i
$587$	16.5731	+	11.6046i	0.684046	+	0.478974i	0.863210	−	0.504845i	$-0.168450\pi$
$587$	16.5731	+	11.6046i	0.684046	+	0.478974i	−0.179164	+	0.983819i	$0.557339\pi$
$588$		0			0
$589$	−4.07693	−	11.2013i	−0.167987	−	0.461540i
$590$	−19.4223	+	9.49470i	−0.799605	+	0.390891i
$591$		0			0
$592$	21.7446	+	1.90240i	0.893696	+	0.0781883i
$593$	−2.27116	−	2.27116i	−0.0932652	−	0.0932652i	0.658935	−	0.752200i	$-0.271007\pi$
$593$	−2.27116	−	2.27116i	−0.0932652	−	0.0932652i	−0.752200	+	0.658935i	$0.771007\pi$
$594$		0			0
$595$	−1.91117	+	12.1378i	−0.0783504	+	0.497602i
$596$	−54.9162	−	65.4466i	−2.24946	−	2.68080i
$597$		0			0
$598$	1.74691	+	2.49484i	0.0714364	+	0.102022i
$599$	11.3910	−	4.14598i	0.465423	−	0.169400i	−0.0986548	−	0.995122i	$-0.531454\pi$
$599$	11.3910	−	4.14598i	0.465423	−	0.169400i	0.564078	+	0.825722i	$0.309232\pi$
$600$		0			0
$601$	2.78962	+	15.8207i	0.113791	+	0.645340i	0.987342	+	0.158607i	$0.0507003\pi$
$601$	2.78962	+	15.8207i	0.113791	+	0.645340i	−0.873551	+	0.486733i	$0.838189\pi$
$602$	−4.93974	−	1.32360i	−0.201329	−	0.0539459i
$603$		0			0
$604$	5.04879	+	2.91492i	0.205432	+	0.118606i
$605$	11.6596	−	21.0794i	0.474029	−	0.857000i
$606$		0			0
$607$	−1.10665	−	12.6491i	−0.0449177	−	0.513412i	−0.985011	−	0.172494i	$-0.944818\pi$
$607$	−1.10665	−	12.6491i	−0.0449177	−	0.513412i	0.940093	−	0.340918i	$-0.110738\pi$
$608$	4.18852	+	47.8750i	0.169867	+	1.94159i
$609$		0			0
$610$	−15.4974	−	53.8615i	−0.627470	−	2.18079i
$611$	−29.1369	−	16.8222i	−1.17875	−	0.680552i
$612$		0			0
$613$	−11.7830	−	3.15725i	−0.475912	−	0.127520i	0.0128866	−	0.999917i	$-0.495898\pi$
$613$	−11.7830	−	3.15725i	−0.475912	−	0.127520i	−0.488798	+	0.872397i	$0.662565\pi$
$614$	−4.98094	−	28.2483i	−0.201014	−	1.14001i
$615$		0			0
$616$	6.61595	−	2.40801i	0.266564	−	0.0970215i
$617$	−5.34672	−	7.63591i	−0.215251	−	0.307410i	0.696977	−	0.717094i	$-0.254528\pi$
$617$	−5.34672	−	7.63591i	−0.215251	−	0.307410i	−0.912228	+	0.409684i	$0.865639\pi$
$618$		0			0
$619$	−10.1944	−	12.1492i	−0.409748	−	0.488319i	0.521218	−	0.853423i	$-0.325478\pi$
$619$	−10.1944	−	12.1492i	−0.409748	−	0.488319i	−0.930967	+	0.365104i	$0.881033\pi$
$620$	62.7074	+	9.87365i	2.51839	+	0.396535i
$621$		0			0
$622$	−6.19528	−	6.19528i	−0.248408	−	0.248408i
$623$	11.0400	+	0.965877i	0.442309	+	0.0386971i
$624$		0			0
$625$	17.9204	−	17.4315i	0.716818	−	0.697260i
$626$	22.6663	+	62.2751i	0.905927	+	2.48901i
$627$		0			0
$628$	76.5215	+	53.5809i	3.05354	+	2.13811i
$629$	−2.59683	−	4.49784i	−0.103542	−	0.179341i
$630$		0			0
$631$	−12.2239	+	21.1724i	−0.486626	+	0.842861i	−0.999882	−	0.0153745i	$-0.995106\pi$
$631$	−12.2239	+	21.1724i	−0.486626	+	0.842861i	0.513256	+	0.858236i	$0.328439\pi$
$632$	37.6109	−	17.5382i	1.49608	−	0.697634i
$633$		0			0
$634$	36.3814	−	43.3577i	1.44489	−	1.72195i
$635$	−7.96287	−	0.549570i	−0.315997	−	0.0218090i
$636$		0			0
$637$	5.27689	+	11.3163i	0.209078	+	0.448369i
$638$	−7.03271	+	1.88441i	−0.278428	+	0.0746045i
$639$		0			0
$640$	−71.3635	−	31.6956i	−2.82089	−	1.25288i
$641$	5.87001	−	1.03504i	0.231852	−	0.0408817i	−0.0565151	−	0.998402i	$-0.517999\pi$
$641$	5.87001	−	1.03504i	0.231852	−	0.0408817i	0.288367	+	0.957520i	$0.406888\pi$
$642$		0			0
$643$	−13.5999	+	29.1651i	−0.536328	+	1.15016i	0.432320	+	0.901720i	$0.357695\pi$
$643$	−13.5999	+	29.1651i	−0.536328	+	1.15016i	−0.968648	+	0.248438i	$0.920083\pi$
$644$	−0.600036	+	3.40297i	−0.0236447	+	0.134096i
$645$		0			0
$646$	16.5151	−	13.8578i	0.649779	−	0.545229i
$647$	−5.43613	+	5.43613i	−0.213717	+	0.213717i	−0.805844	−	0.592128i	$-0.798288\pi$
$647$	−5.43613	+	5.43613i	−0.213717	+	0.213717i	0.592128	+	0.805844i	$0.298288\pi$
$648$		0			0
$649$		−	1.69034i		−	0.0663516i
$650$	−14.2410	−	35.0647i	−0.558578	−	1.37535i
$651$		0			0
$652$	−15.5464	+	10.8857i	−0.608844	+	0.426317i
$653$	−14.5983	−	6.80729i	−0.571275	−	0.266390i	0.115443	−	0.993314i	$-0.463171\pi$
$653$	−14.5983	−	6.80729i	−0.571275	−	0.266390i	−0.686717	+	0.726924i	$0.740949\pi$
$654$		0			0
$655$	−0.126253	−	6.87603i	−0.00493310	−	0.268669i
$656$	98.1831	−	56.6861i	3.83341	−	2.21322i
$657$		0			0
$658$	−13.5209	−	50.4605i	−0.527098	−	1.96716i
$659$	−31.0994	−	11.3193i	−1.21146	−	0.440936i	−0.344250	−	0.938878i	$-0.611867\pi$
$659$	−31.0994	−	11.3193i	−1.21146	−	0.440936i	−0.867210	+	0.497942i	$0.834089\pi$
$660$		0			0
$661$	22.7885	+	19.1218i	0.886369	+	0.743752i	0.967478	−	0.252954i	$-0.0814020\pi$
$661$	22.7885	+	19.1218i	0.886369	+	0.743752i	−0.0811098	+	0.996705i	$0.525846\pi$
$662$	−16.1743	+	1.41507i	−0.628631	+	0.0549981i
$663$		0			0
$664$	9.30342	−	25.5609i	0.361043	−	0.991957i
$665$	−8.01804	+	0.850075i	−0.310926	+	0.0329645i
$666$		0			0
$667$	0.583983	−	2.17945i	0.0226119	−	0.0843888i
$668$	20.5054	−	29.2848i	0.793379	−	1.13306i
$669$		0			0
$670$	15.4267	+	78.9816i	0.595987	+	3.05133i
$671$	4.31561	+	0.760958i	0.166602	+	0.0293764i
$672$		0			0
$673$	3.02767	−	34.6064i	0.116708	−	1.33398i	−0.681598	−	0.731727i	$-0.738715\pi$
$673$	3.02767	−	34.6064i	0.116708	−	1.33398i	0.798306	−	0.602252i	$-0.205730\pi$
$674$	30.3912			1.17063
$675$		0			0
$676$	28.6790			1.10304
$677$	−1.51507	+	17.3173i	−0.0582289	+	0.665560i	0.909854	+	0.414929i	$0.136194\pi$
$677$	−1.51507	+	17.3173i	−0.0582289	+	0.665560i	−0.968083	+	0.250631i	$0.919362\pi$
$678$		0			0
$679$	−11.8000	−	2.08066i	−0.452843	−	0.0798485i
$680$	13.8971	+	71.1504i	0.532931	+	2.72849i
$681$		0			0
$682$	−3.89615	+	5.56428i	−0.149191	+	0.213067i
$683$	2.94108	−	10.9763i	0.112537	−	0.419995i	−0.886554	−	0.462626i	$-0.846907\pi$
$683$	2.94108	−	10.9763i	0.112537	−	0.419995i	0.999091	+	0.0426308i	$0.0135739\pi$
$684$		0			0
$685$	−4.61879	+	0.489685i	−0.176475	+	0.0187099i
$686$	−16.9564	+	46.5874i	−0.647400	+	1.77872i
$687$		0			0
$688$	−17.2377	+	1.50810i	−0.657181	+	0.0574959i
$689$	−0.825299	−	0.692508i	−0.0314414	−	0.0263824i
$690$		0			0
$691$	−22.0909	−	8.04044i	−0.840378	−	0.305873i	−0.114267	−	0.993450i	$-0.536452\pi$
$691$	−22.0909	−	8.04044i	−0.840378	−	0.305873i	−0.726111	+	0.687577i	$0.758674\pi$
$692$	15.0162	+	56.0412i	0.570830	+	2.13037i
$693$		0			0
$694$	−56.0171	+	32.3415i	−2.12638	+	1.22767i
$695$	0.633652	+	34.5102i	0.0240358	+	1.30905i
$696$		0			0
$697$	−24.4483	−	11.4004i	−0.926046	−	0.431822i
$698$	−16.7611	+	11.7362i	−0.634416	+	0.444223i
$699$		0			0
$700$	16.7059	−	39.5558i	0.631424	−	1.49507i
$701$			44.6039i			1.68467i	0.538956	+	0.842334i	$0.318819\pi$
$701$			44.6039i			1.68467i	−0.538956	+	0.842334i	$0.681181\pi$
$702$		0			0
$703$	2.40988	−	2.40988i	0.0908903	−	0.0908903i
$704$	10.3268	−	8.66522i	0.389206	−	0.326583i
$705$		0			0
$706$	−2.45245	+	13.9085i	−0.0922992	+	0.523455i
$707$	−3.88937	+	8.34079i	−0.146275	+	0.313688i
$708$		0			0
$709$	−36.4781	+	6.43207i	−1.36996	+	0.241562i	−0.809744	−	0.586783i	$-0.800394\pi$
$709$	−36.4781	+	6.43207i	−1.36996	+	0.241562i	−0.560219	+	0.828344i	$0.689283\pi$
$710$	88.8687	+	39.4705i	3.33518	+	1.48130i
$711$		0			0
$712$	63.1566	−	16.9228i	2.36689	−	0.634207i
$713$	−0.889647	−	1.90785i	−0.0333175	−	0.0714497i
$714$		0			0
$715$	2.95210	+	0.203744i	0.110402	+	0.00761958i
$716$	23.1122	−	27.5441i	0.863744	−	1.02937i
$717$		0			0
$718$	−33.7227	+	15.7251i	−1.25852	+	0.586857i
$719$	−19.2483	+	33.3390i	−0.717839	+	1.24333i	0.244016	+	0.969771i	$0.421535\pi$
$719$	−19.2483	+	33.3390i	−0.717839	+	1.24333i	−0.961854	+	0.273562i	$0.911798\pi$
$720$		0			0
$721$	3.54064	+	6.13256i	0.131860	+	0.228389i
$722$	−30.8251	−	21.5840i	−1.14719	−	0.803273i
$723$		0			0
$724$	16.2169	+	44.5557i	0.602698	+	1.65590i
$725$	−13.1182	+	24.7799i	−0.487197	+	0.920304i
$726$		0			0
$727$	−25.9897	−	2.27381i	−0.963906	−	0.0843308i	−0.405676	−	0.914017i	$-0.632964\pi$
$727$	−25.9897	−	2.27381i	−0.963906	−	0.0843308i	−0.558230	+	0.829686i	$0.688519\pi$
$728$	−29.0230	−	29.0230i	−1.07566	−	1.07566i
$729$		0			0
$730$	−48.2312	−	7.59429i	−1.78512	−	0.281077i
$731$	2.64649	+	3.15396i	0.0978838	+	0.116653i
$732$		0			0
$733$	−27.9576	−	39.9276i	−1.03264	−	1.47476i	−0.873083	−	0.487571i	$-0.837883\pi$
$733$	−27.9576	−	39.9276i	−1.03264	−	1.47476i	−0.159555	−	0.987189i	$-0.551006\pi$
$734$	−55.2278	+	20.1013i	−2.03849	+	0.741951i
$735$		0			0
$736$	1.47374	+	8.35802i	0.0543230	+	0.308081i
$737$	−6.07772	−	1.62852i	−0.223876	−	0.0599873i
$738$		0			0
$739$	−11.7531	−	6.78566i	−0.432345	−	0.249614i	0.268000	−	0.963419i	$-0.413637\pi$
$739$	−11.7531	−	6.78566i	−0.432345	−	0.249614i	−0.700345	+	0.713804i	$0.746971\pi$
$740$	5.01849	+	17.4419i	0.184483	+	0.641178i
$741$		0			0
$742$	−0.145797	−	1.66647i	−0.00535238	−	0.0611780i
$743$	−0.108282	−	1.23767i	−0.00397247	−	0.0454055i	0.993950	−	0.109836i	$-0.0350325\pi$
$743$	−0.108282	−	1.23767i	−0.00397247	−	0.0454055i	−0.997922	+	0.0644303i	$0.979477\pi$
$744$		0			0
$745$	17.0400	−	30.8068i	0.624298	−	1.12867i
$746$	−31.2331	−	18.0324i	−1.14352	−	0.660214i
$747$		0			0
$748$	−8.67096	−	2.32338i	−0.317042	−	0.0849511i
$749$	−0.224615	−	1.27386i	−0.00820726	−	0.0465457i
$750$		0			0
$751$	−8.15950	+	2.96982i	−0.297745	+	0.108370i	−0.486573	−	0.873640i	$-0.661753\pi$
$751$	−8.15950	+	2.96982i	−0.297745	+	0.108370i	0.188828	+	0.982010i	$0.439531\pi$
$752$	−101.385	−	144.793i	−3.69713	−	5.28005i
$753$		0			0
$754$	27.2833	+	32.5150i	0.993601	+	1.18413i
$755$	−0.373658	+	2.37309i	−0.0135988	+	0.0863657i
$756$		0			0
$757$	29.4262	+	29.4262i	1.06951	+	1.06951i	0.997396	+	0.0721170i	$0.0229755\pi$
$757$	29.4262	+	29.4262i	1.06951	+	1.06951i	0.0721170	+	0.997396i	$0.477025\pi$
$758$	74.4088	+	6.50993i	2.70265	+	0.236451i
$759$		0			0
$760$	−42.7378	+	20.8926i	−1.55026	+	0.757854i
$761$	−14.0169	−	38.5111i	−0.508112	−	1.39603i	−0.883183	−	0.469029i	$-0.844604\pi$
$761$	−14.0169	−	38.5111i	−0.508112	−	1.39603i	0.375071	−	0.926996i	$-0.377618\pi$
$762$		0			0
$763$	−10.9674	−	7.67948i	−0.397048	−	0.278016i
$764$	−54.7283	−	94.7922i	−1.98000	−	3.42946i
$765$		0			0
$766$	−49.2326	+	85.2733i	−1.77884	+	3.08105i
$767$	−8.93101	+	4.16460i	−0.322480	+	0.150375i
$768$		0			0
$769$	3.94057	−	4.69619i	0.142100	−	0.169349i	−0.690300	−	0.723523i	$-0.742521\pi$
$769$	3.94057	−	4.69619i	0.142100	−	0.169349i	0.832401	+	0.554174i	$0.186966\pi$
$770$	3.01754	+	3.46494i	0.108745	+	0.124868i
$771$		0			0
$772$	−43.0641	−	92.3513i	−1.54991	−	3.32380i
$773$	9.19044	−	2.46257i	0.330557	−	0.0885726i	−0.0897234	−	0.995967i	$-0.528598\pi$
$773$	9.19044	−	2.46257i	0.330557	−	0.0885726i	0.420281	+	0.907394i	$0.361932\pi$
$774$		0			0
$775$	5.48501	+	25.5770i	0.197027	+	0.918752i
$776$	−69.6196	+	12.2758i	−2.49920	+	0.440676i
$777$		0			0
$778$	21.2928	−	45.6625i	0.763382	−	1.63708i
$779$	3.07383	−	17.4326i	0.110132	−	0.624587i
$780$		0			0
$781$	−5.82422	+	4.88710i	−0.208407	+	0.174874i
$782$	2.69216	−	2.69216i	0.0962714	−	0.0962714i
$783$		0			0
$784$			65.5994i			2.34283i
$785$	−9.27875	+	37.3592i	−0.331173	+	1.33341i
$786$		0			0
$787$	−6.94038	+	4.85971i	−0.247398	+	0.173230i	−0.690698	−	0.723143i	$-0.742697\pi$
$787$	−6.94038	+	4.85971i	−0.247398	+	0.173230i	0.443300	+	0.896373i	$0.353808\pi$
$788$	−24.6435	−	11.4915i	−0.877890	−	0.409367i
$789$		0			0
$790$	19.4986	+	18.7955i	0.693729	+	0.668713i
$791$	−2.98847	+	1.72539i	−0.106258	+	0.0613479i
$792$		0			0
$793$	−6.61207	−	24.6766i	−0.234802	−	0.876291i
$794$	77.2406	+	28.1133i	2.74116	+	0.997702i
$795$		0			0
$796$	−69.2896	−	58.1409i	−2.45591	−	2.06075i
$797$	28.1786	−	2.46530i	0.998136	−	0.0873256i	0.423638	−	0.905832i	$-0.360753\pi$
$797$	28.1786	−	2.46530i	0.998136	−	0.0873256i	0.574498	+	0.818506i	$0.305197\pi$
$798$		0			0
$799$	−14.3847	+	39.5216i	−0.508894	+	1.39818i
$800$	5.32863	−	105.327i	0.188395	−	3.72388i
$801$		0			0
$802$	24.5527	−	91.6319i	0.866986	−	3.23564i
$803$	2.18967	−	3.12717i	0.0772716	−	0.110355i
$804$		0			0
$805$	−1.39751	+	0.272962i	−0.0492556	+	0.00962063i
$806$	38.9984	+	6.87647i	1.37366	+	0.242213i
$807$		0			0
$808$	−4.73234	+	54.0909i	−0.166483	+	1.90291i
$809$	−2.28591			−0.0803683			−0.0401841	−	0.999192i	$-0.512794\pi$
$809$	−2.28591			−0.0803683			−0.0401841	+	0.999192i	$0.512794\pi$
$810$		0			0
$811$	21.6606			0.760605			0.380303	−	0.924862i	$-0.375820\pi$
$811$	21.6606			0.760605			0.380303	+	0.924862i	$0.375820\pi$
$812$	−4.19715	+	47.9736i	−0.147291	+	1.68354i
$813$		0			0
$814$	−1.91260	−	0.337243i	−0.0670367	−	0.0118204i
$815$	−6.48756	−	4.36737i	−0.227249	−	0.152982i
$816$		0			0
$817$	−1.54964	+	2.21311i	−0.0542150	+	0.0774270i
$818$	−15.6279	+	58.3243i	−0.546418	+	2.03926i
$819$		0			0
$820$	73.3139	+	59.2585i	2.56023	+	2.06940i
$821$	−7.91413	+	21.7439i	−0.276205	+	0.758867i	0.721579	+	0.692332i	$0.243417\pi$
$821$	−7.91413	+	21.7439i	−0.276205	+	0.758867i	−0.997784	+	0.0665351i	$0.978806\pi$
$822$		0			0
$823$	−6.50574	+	0.569178i	−0.226776	+	0.0198403i	−0.199977	−	0.979801i	$-0.564087\pi$
$823$	−6.50574	+	0.569178i	−0.226776	+	0.0198403i	−0.0267986	+	0.999641i	$0.508531\pi$
$824$	32.0047	+	26.8552i	1.11494	+	0.935544i
$825$		0			0
$826$	−14.3783	−	5.23326i	−0.500284	−	0.182088i
$827$	−2.39679	−	8.94494i	−0.0833445	−	0.311046i	0.911651	−	0.410965i	$-0.134808\pi$
$827$	−2.39679	−	8.94494i	−0.0833445	−	0.311046i	−0.994996	+	0.0999193i	$0.968142\pi$
$828$		0			0
$829$	−2.45210	+	1.41572i	−0.0851648	+	0.0491699i	−0.541978	−	0.840393i	$-0.682324\pi$
$829$	−2.45210	+	1.41572i	−0.0851648	+	0.0491699i	0.456813	+	0.889563i	$0.348991\pi$
$830$	17.7488	−	0.325891i	0.616071	−	0.0113118i
$831$		0			0
$832$	−71.2260	−	33.2132i	−2.46932	−	1.15146i
$833$	12.7859	−	8.95278i	0.443005	−	0.310195i
$834$		0			0
$835$	14.2974	+	3.55098i	0.494781	+	0.122887i
$836$		−	5.89061i		−	0.203731i
$837$		0			0
$838$	9.63173	−	9.63173i	0.332723	−	0.332723i
$839$	−32.4518	+	27.2303i	−1.12036	+	0.940095i	−0.998623	−	0.0524668i	$-0.983292\pi$
$839$	−32.4518	+	27.2303i	−1.12036	+	0.940095i	−0.121739	+	0.992562i	$0.538847\pi$
$840$		0			0
$841$	0.424617	−	2.40812i	0.0146420	−	0.0830387i
$842$	−15.1760	+	32.5451i	−0.523000	+	1.12158i
$843$		0			0
$844$	−55.8394	+	9.84600i	−1.92207	+	0.338913i
$845$	4.24515	+	11.0291i	0.146038	+	0.379413i
$846$		0			0
$847$	16.4684	−	4.41271i	0.565862	−	0.151622i
$848$	−2.39208	−	5.12983i	−0.0821443	−	0.176159i
$849$		0			0
$850$	−40.0763	+	25.1435i	−1.37460	+	0.862415i
$851$	0.386871	−	0.461054i	0.0132618	−	0.0158047i
$852$		0			0
$853$	30.1905	−	14.0780i	1.03370	−	0.482023i	0.169691	−	0.985497i	$-0.445723\pi$
$853$	30.1905	−	14.0780i	1.03370	−	0.482023i	0.864010	+	0.503474i	$0.167945\pi$
$854$	19.8339	−	34.3532i	0.678701	−	1.17554i
$855$		0			0
$856$	−3.81582	−	6.60919i	−0.130422	−	0.225897i
$857$	25.1791	+	17.6306i	0.860100	+	0.602249i	0.918224	−	0.396061i	$-0.129623\pi$
$857$	25.1791	+	17.6306i	0.860100	+	0.602249i	−0.0581240	+	0.998309i	$0.518512\pi$
$858$		0			0
$859$	−17.6716	−	48.5522i	−0.602946	−	1.65658i	−0.745272	−	0.666760i	$-0.767680\pi$
$859$	−17.6716	−	48.5522i	−0.602946	−	1.65658i	0.142326	−	0.989820i	$-0.454542\pi$
$860$	−6.31891	−	12.9259i	−0.215473	−	0.440771i
$861$		0			0
$862$	39.4098	+	3.44791i	1.34230	+	0.117436i
$863$	−31.9076	−	31.9076i	−1.08615	−	1.08615i	−0.995921	−	0.0902264i	$-0.971241\pi$
$863$	−31.9076	−	31.9076i	−1.08615	−	1.08615i	−0.0902264	−	0.995921i	$-0.528759\pi$
$864$		0			0
$865$	−19.3291	+	14.0702i	−0.657209	+	0.478401i
$866$	−41.2086	−	49.1104i	−1.40032	−	1.66884i
$867$		0			0
$868$	25.7700	+	36.8034i	0.874692	+	1.24919i
$869$	−1.98983	+	0.724239i	−0.0675003	+	0.0245681i
$870$		0			0
$871$	6.36968	+	36.1243i	0.215829	+	1.22402i
$872$	−76.3015	−	20.4449i	−2.58390	−	0.692353i
$873$		0			0
$874$	2.16363	+	1.24917i	0.0731860	+	0.0422539i
$875$	17.6849	+	0.569453i	0.597858	+	0.0192510i
$876$		0			0
$877$	3.42618	+	39.1615i	0.115694	+	1.32239i	0.802982	+	0.596003i	$0.203245\pi$
$877$	3.42618	+	39.1615i	0.115694	+	1.32239i	−0.687288	+	0.726385i	$0.741199\pi$
$878$	5.13448	+	58.6873i	0.173280	+	1.98060i
$879$		0			0
$880$	13.6041	+	7.52478i	0.458594	+	0.253660i
$881$	34.0163	+	19.6393i	1.14604	+	0.661666i	0.947919	−	0.318512i	$-0.103183\pi$
$881$	34.0163	+	19.6393i	1.14604	+	0.661666i	0.198120	+	0.980178i	$0.436516\pi$
$882$		0			0
$883$	17.3273	+	4.64284i	0.583111	+	0.156244i	0.538303	−	0.842752i	$-0.319066\pi$
$883$	17.3273	+	4.64284i	0.583111	+	0.156244i	0.0448081	+	0.998996i	$0.485732\pi$
$884$	9.08751	+	51.5378i	0.305646	+	1.73340i
$885$		0			0
$886$	−30.7381	+	11.1878i	−1.03267	+	0.375860i
$887$	9.98188	+	14.2556i	0.335159	+	0.478656i	0.950990	−	0.309222i	$-0.100069\pi$
$887$	9.98188	+	14.2556i	0.335159	+	0.478656i	−0.615831	+	0.787878i	$0.711180\pi$
$888$		0			0
$889$	−3.63125	−	4.32756i	−0.121788	−	0.145142i
$890$	25.1123	+	34.4983i	0.841766	+	1.15639i
$891$		0			0
$892$	−90.0092	−	90.0092i	−3.01373	−	3.01373i
$893$	−27.4935	−	2.40537i	−0.920036	−	0.0804927i
$894$		0			0
$895$	14.0138	+	4.81114i	0.468430	+	0.160819i
$896$	−18.9021	−	51.9330i	−0.631474	−	1.73496i
$897$		0			0
$898$	67.5821	+	47.3215i	2.25524	+	1.57914i
$899$	−14.6687	−	25.4069i	−0.489227	−	0.847367i
$900$		0			0
$901$	−0.673386	+	1.16634i	−0.0224337	+	0.0388564i
$902$	−9.14216	+	4.26306i	−0.304401	+	0.141944i
$903$		0			0
$904$	−13.0868	+	15.5963i	−0.435261	+	0.518724i
$905$	−14.7344	+	12.8318i	−0.489787	+	0.426545i
$906$		0			0
$907$	−8.34207	−	17.8896i	−0.276994	−	0.594015i	0.717763	−	0.696288i	$-0.245166\pi$
$907$	−8.34207	−	17.8896i	−0.276994	−	0.594015i	−0.994756	+	0.102273i	$0.967389\pi$
$908$	104.923	−	28.1141i	3.48200	−	0.932999i
$909$		0			0
$910$	10.8727	−	24.4802i	0.360427	−	0.811510i
$911$	−29.7171	+	5.23993i	−0.984571	+	0.173606i	−0.642681	−	0.766134i	$-0.722178\pi$
$911$	−29.7171	+	5.23993i	−0.984571	+	0.173606i	−0.341890	+	0.939740i	$0.611067\pi$
$912$		0			0
$913$	−0.586586	+	1.25794i	−0.0194132	+	0.0416317i
$914$	−19.6914	+	111.676i	−0.651334	+	3.69390i
$915$		0			0
$916$	91.7178	−	76.9604i	3.03044	−	2.54284i
$917$	3.44178	−	3.44178i	0.113658	−	0.113658i
$918$		0			0
$919$		−	5.90514i		−	0.194793i	−0.995246	−	0.0973964i	$-0.968949\pi$
$919$		−	5.90514i		−	0.194793i	0.995246	−	0.0973964i	$-0.0310515\pi$
$920$	−7.19716	+	4.33337i	−0.237283	+	0.142867i
$921$		0			0
$922$	−38.5192	+	26.9715i	−1.26856	+	0.888258i
$923$	40.1708	+	18.7320i	1.32224	+	0.616570i
$924$		0			0
$925$	−5.96481	+	4.51177i	−0.196122	+	0.148346i
$926$	−38.9006	+	22.4592i	−1.27835	+	0.738057i
$927$		0			0
$928$	30.6126	+	114.248i	1.00491	+	3.75036i
$929$	−6.36097	−	2.31520i	−0.208697	−	0.0759593i	0.235557	−	0.971861i	$-0.424309\pi$
$929$	−6.36097	−	2.31520i	−0.208697	−	0.0759593i	−0.444253	+	0.895901i	$0.646531\pi$
$930$		0			0
$931$	7.84617	+	6.58371i	0.257148	+	0.215773i
$932$	100.942	−	8.83124i	3.30645	−	0.289277i
$933$		0			0
$934$	3.70965	−	10.1922i	0.121383	−	0.333498i
$935$	−0.389997	−	3.67852i	−0.0127543	−	0.120300i
$936$		0			0
$937$	−1.63137	+	6.08835i	−0.0532945	+	0.198898i	−0.987440	−	0.157995i	$-0.949497\pi$
$937$	−1.63137	+	6.08835i	−0.0532945	+	0.198898i	0.934145	+	0.356892i	$0.116164\pi$
$938$	−32.6689	+	46.6560i	−1.06668	+	1.52337i
$939$		0			0
$940$	82.0766	−	121.922i	2.67704	−	3.97664i
$941$	−26.7793	−	4.72192i	−0.872981	−	0.153930i	−0.280831	−	0.959757i	$-0.590610\pi$
$941$	−26.7793	−	4.72192i	−0.872981	−	0.153930i	−0.592151	+	0.805827i	$0.701721\pi$
$942$		0			0
$943$	0.272455	−	3.11417i	0.00887234	−	0.101411i
$944$	−51.7720			−1.68504
$945$		0			0
$946$	1.53958			0.0500560
$947$	4.20583	−	48.0728i	0.136671	−	1.56216i	−0.549985	−	0.835174i	$-0.685367\pi$
$947$	4.20583	−	48.0728i	0.136671	−	1.56216i	0.686656	−	0.726982i	$-0.259078\pi$
$948$		0			0
$949$	−21.9174	−	3.86463i	−0.711469	−	0.125451i
$950$	−22.7435	−	21.1317i	−0.737895	−	0.685603i
$951$		0			0
$952$	−29.4297	+	42.0300i	−0.953822	+	1.36220i
$953$	5.07394	−	18.9362i	0.164361	−	0.613404i	−0.833760	−	0.552128i	$-0.813816\pi$
$953$	5.07394	−	18.9362i	0.164361	−	0.613404i	0.998121	−	0.0612767i	$-0.0195172\pi$
$954$		0			0
$955$	28.3533	−	35.0784i	0.917492	−	1.13511i
$956$	36.2153	−	99.5008i	1.17129	−	3.21809i
$957$		0			0
$958$	3.84959	−	0.336795i	0.124375	−	0.0108814i
$959$	−2.51823	−	2.11305i	−0.0813180	−	0.0682339i
$960$		0			0
$961$	3.41043	+	1.24130i	0.110014	+	0.0400418i
$962$	2.93036	+	10.9362i	0.0944785	+	0.352599i
$963$		0			0
$964$	23.1268	−	13.3523i	0.744865	−	0.430048i
$965$	29.1412	−	30.2314i	0.938088	−	0.973182i
$966$		0			0
$967$	−3.93769	−	1.83617i	−0.126628	−	0.0590474i	0.358272	−	0.933617i	$-0.383366\pi$
$967$	−3.93769	−	1.83617i	−0.126628	−	0.0590474i	−0.484900	+	0.874570i	$0.661144\pi$
$968$	82.3990	−	57.6964i	2.64841	−	1.85443i
$969$		0			0
$970$	−23.7972	−	39.5240i	−0.764082	−	1.26904i
$971$		−	17.3753i		−	0.557601i	−0.960349	−	0.278800i	$-0.910063\pi$
$971$		−	17.3753i		−	0.557601i	0.960349	−	0.278800i	$-0.0899367\pi$
$972$		0			0
$973$	−17.2740	+	17.2740i	−0.553779	+	0.553779i
$974$	17.5070	−	14.6901i	0.560960	−	0.470701i
$975$		0			0
$976$	23.3068	−	132.179i	0.746031	−	4.23095i
$977$	10.2242	−	21.9259i	0.327101	−	0.701470i	−0.672140	−	0.740424i	$-0.734625\pi$
$977$	10.2242	−	21.9259i	0.327101	−	0.701470i	0.999241	+	0.0389538i	$0.0124025\pi$
$978$		0			0
$979$	−3.28563	+	0.579345i	−0.105009	+	0.0185159i
$980$	−50.9048	+	19.5935i	−1.62610	+	0.625890i
$981$		0			0
$982$	−70.5563	+	18.9055i	−2.25154	+	0.603299i
$983$	10.2662	+	22.0159i	0.327441	+	0.702199i	0.999258	−	0.0385180i	$-0.0122637\pi$
$983$	10.2662	+	22.0159i	0.327441	+	0.702199i	−0.671817	+	0.740717i	$0.734486\pi$
$984$		0			0
$985$	0.771481	−	11.1782i	0.0245814	−	0.356167i
$986$	34.1063	−	40.6463i	1.08617	−	1.29444i
$987$		0			0
$988$	−31.1234	+	14.5131i	−0.990168	+	0.461723i
$989$	−0.238560	+	0.413197i	−0.00758575	+	0.0131389i
$990$		0			0
$991$	−18.0498	−	31.2632i	−0.573372	−	0.993110i	−0.996216	−	0.0869073i	$-0.972302\pi$
$991$	−18.0498	−	31.2632i	−0.573372	−	0.993110i	0.422844	−	0.906202i	$-0.361032\pi$
$992$	90.3927	+	63.2936i	2.86997	+	2.00957i
$993$		0			0
$994$	23.5387	+	64.6720i	0.746602	+	2.05127i
$995$	12.1029	−	35.2530i	0.383687	−	1.11760i
$996$		0			0
$997$	19.8840	+	1.73962i	0.629732	+	0.0550944i	0.397554	−	0.917579i	$-0.369859\pi$
$997$	19.8840	+	1.73962i	0.629732	+	0.0550944i	0.232178	+	0.972673i	$0.425415\pi$
$998$	−21.5721	−	21.5721i	−0.682854	−	0.682854i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.2.r.a.287.1		192
3.2	odd	2		135.2.q.a.32.16	✓	192
5.3	odd	4	inner	405.2.r.a.368.16		192
15.2	even	4		675.2.ba.b.518.16		192
15.8	even	4		135.2.q.a.113.1	yes	192
15.14	odd	2		675.2.ba.b.32.1		192
27.11	odd	18	inner	405.2.r.a.197.16		192
27.16	even	9		135.2.q.a.92.1	yes	192
135.38	even	36	inner	405.2.r.a.278.1		192
135.43	odd	36		135.2.q.a.38.16	yes	192
135.97	odd	36		675.2.ba.b.443.1		192
135.124	even	18		675.2.ba.b.632.16		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.32.16	✓	192	3.2	odd	2
135.2.q.a.38.16	yes	192	135.43	odd	36
135.2.q.a.92.1	yes	192	27.16	even	9
135.2.q.a.113.1	yes	192	15.8	even	4
405.2.r.a.197.16		192	27.11	odd	18	inner
405.2.r.a.278.1		192	135.38	even	36	inner
405.2.r.a.287.1		192	1.1	even	1	trivial
405.2.r.a.368.16		192	5.3	odd	4	inner
675.2.ba.b.32.1		192	15.14	odd	2
675.2.ba.b.443.1		192	135.97	odd	36
675.2.ba.b.518.16		192	15.2	even	4
675.2.ba.b.632.16		192	135.124	even	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	405.r (of order \(36\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.237511 + 2.71476i) q^{2} +(-5.34392 - 0.942278i) q^{4} +(-0.428650 - 2.19460i) q^{5} +(0.907744 - 1.29639i) q^{7} +(2.41667 - 9.01913i) q^{8} +(6.05963 - 0.642443i) q^{10} +(-0.162954 + 0.447712i) q^{11} +(2.76700 - 0.242081i) q^{13} +(3.30380 + 2.77222i) q^{14} +(13.7126 + 4.99098i) q^{16} +(-0.898665 - 3.35386i) q^{17} +(1.97319 - 1.13922i) q^{19} +(0.222753 + 12.1317i) q^{20} +(-1.17673 - 0.548719i) q^{22} +(0.329603 - 0.230790i) q^{23} +(-4.63252 + 1.88143i) q^{25} +7.56924i q^{26} +(-6.07248 + 6.07248i) q^{28} +(4.29568 - 3.60450i) q^{29} +(0.908475 - 5.15222i) q^{31} +(-8.91403 + 19.1162i) q^{32} +(9.31839 - 1.64308i) q^{34} +(-3.23417 - 1.43643i) q^{35} +(1.44483 - 0.387140i) q^{37} +(2.62407 + 5.62733i) q^{38} +(-20.8293 - 1.43756i) q^{40} +(4.99389 - 5.95149i) q^{41} +(-1.07467 + 0.501128i) q^{43} +(1.29268 - 2.23899i) q^{44} +(0.548257 + 0.949609i) q^{46} +(-9.92230 - 6.94767i) q^{47} +(1.53751 + 4.22426i) q^{49} +(-4.00736 - 13.0231i) q^{50} +(-15.0147 - 1.31362i) q^{52} +(-0.274270 - 0.274270i) q^{53} +(1.05240 + 0.165706i) q^{55} +(-9.49862 - 11.3200i) q^{56} +(8.76510 + 12.5179i) q^{58} +(-3.33385 + 1.21342i) q^{59} +(-1.59716 - 9.05792i) q^{61} +(13.7713 + 3.69001i) q^{62} +(-24.5036 - 14.1471i) q^{64} +(-1.71734 - 5.96868i) q^{65} +(1.15101 + 13.1561i) q^{67} +(1.64212 + 18.7696i) q^{68} +(4.66773 - 8.43883i) q^{70} +(13.8198 + 7.97886i) q^{71} +(-7.73957 - 2.07381i) q^{73} +(0.707832 + 4.01431i) q^{74} +(-11.6180 + 4.22862i) q^{76} +(0.432491 + 0.617661i) q^{77} +(2.85683 + 3.40464i) q^{79} +(5.07529 - 32.2331i) q^{80} +(14.9708 + 14.9708i) q^{82} +(2.90211 + 0.253902i) q^{83} +(-6.97517 + 3.40984i) q^{85} +(-1.10520 - 3.03651i) q^{86} +(3.64417 + 2.55168i) q^{88} +(3.50126 + 6.06435i) q^{89} +(2.19789 - 3.80686i) q^{91} +(-1.97884 + 0.922748i) q^{92} +(21.2179 - 25.2866i) q^{94} +(-3.34594 - 3.84203i) q^{95} +(-3.19969 - 6.86175i) q^{97} +(-11.8331 + 3.17066i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35}+ \cdots - 324 q^{98}+O(q^{100}) \) 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8 - 6 * q^10 + 36 * q^11 - 12 * q^13 - 24 * q^16 + 18 * q^17 - 36 * q^20 - 12 * q^22 + 36 * q^23 - 30 * q^25 - 24 * q^28 - 24 * q^31 + 48 * q^32 - 36 * q^35 - 6 * q^37 - 12 * q^38 - 36 * q^40 - 24 * q^41 - 12 * q^43 - 12 * q^46 + 6 * q^47 - 36 * q^50 + 12 * q^52 - 24 * q^55 - 180 * q^56 - 12 * q^58 - 60 * q^61 + 18 * q^62 + 84 * q^65 + 24 * q^67 + 60 * q^68 - 12 * q^70 + 36 * q^71 - 6 * q^73 - 72 * q^76 - 132 * q^77 - 24 * q^82 - 48 * q^83 - 12 * q^85 - 12 * q^86 - 48 * q^88 - 12 * q^91 - 258 * q^92 - 18 * q^95 + 24 * q^97 - 324 * q^98

Introduction

L-functions

Modular forms

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Database

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