LMFDB - Embedded newform 405.2.r.a.368.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,2,Mod(8,405)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			368.16
Character	$\chi$	$=$	405.368
Dual form			405.2.r.a.197.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.71476 + 0.237511i) q^{2} +(5.34392 + 0.942278i) q^{4} +(-1.08230 - 1.95669i) q^{5} +(-1.29639 - 0.907744i) q^{7} +(9.01913 + 2.41667i) q^{8} +O(q^{10})$	\(q+(2.71476 + 0.237511i) q^{2} +(5.34392 + 0.942278i) q^{4} +(-1.08230 - 1.95669i) q^{5} +(-1.29639 - 0.907744i) q^{7} +(9.01913 + 2.41667i) q^{8} +(-2.47344 - 5.56901i) q^{10} +(-0.162954 + 0.447712i) q^{11} +(0.242081 + 2.76700i) q^{13} +(-3.30380 - 2.77222i) q^{14} +(13.7126 + 4.99098i) q^{16} +(-3.35386 + 0.898665i) q^{17} +(-1.97319 + 1.13922i) q^{19} +(-3.93995 - 11.4762i) q^{20} +(-0.548719 + 1.17673i) q^{22} +(0.230790 + 0.329603i) q^{23} +(-2.65727 + 4.23543i) q^{25} +7.56924i q^{26} +(-6.07248 - 6.07248i) q^{28} +(-4.29568 + 3.60450i) q^{29} +(0.908475 - 5.15222i) q^{31} +(19.1162 + 8.91403i) q^{32} +(-9.31839 + 1.64308i) q^{34} +(-0.373094 + 3.51909i) q^{35} +(-0.387140 - 1.44483i) q^{37} +(-5.62733 + 2.62407i) q^{38} +(-5.03269 - 20.2632i) q^{40} +(4.99389 - 5.95149i) q^{41} +(-0.501128 - 1.07467i) q^{43} +(-1.29268 + 2.23899i) q^{44} +(0.548257 + 0.949609i) q^{46} +(-6.94767 + 9.92230i) q^{47} +(-1.53751 - 4.22426i) q^{49} +(-8.21984 + 10.8671i) q^{50} +(-1.31362 + 15.0147i) q^{52} +(0.274270 - 0.274270i) q^{53} +(1.05240 - 0.165706i) q^{55} +(-9.49862 - 11.3200i) q^{56} +(-12.5179 + 8.76510i) q^{58} +(3.33385 - 1.21342i) q^{59} +(-1.59716 - 9.05792i) q^{61} +(3.69001 - 13.7713i) q^{62} +(24.5036 + 14.1471i) q^{64} +(5.15215 - 3.46838i) q^{65} +(13.1561 - 1.15101i) q^{67} +(-18.7696 + 1.64212i) q^{68} +(-1.84869 + 9.46488i) q^{70} +(13.8198 + 7.97886i) q^{71} +(2.07381 - 7.73957i) q^{73} +(-0.707832 - 4.01431i) q^{74} +(-11.6180 + 4.22862i) q^{76} +(0.617661 - 0.432491i) q^{77} +(-2.85683 - 3.40464i) q^{79} +(-5.07529 - 32.2331i) q^{80} +(14.9708 - 14.9708i) q^{82} +(-0.253902 + 2.90211i) q^{83} +(5.38828 + 5.58985i) q^{85} +(-1.10520 - 3.03651i) q^{86} +(-2.55168 + 3.64417i) q^{88} +(-3.50126 - 6.06435i) q^{89} +(2.19789 - 3.80686i) q^{91} +(0.922748 + 1.97884i) q^{92} +(-21.2179 + 25.2866i) q^{94} +(4.36468 + 2.62795i) q^{95} +(-6.86175 + 3.19969i) q^{97} +(-3.17066 - 11.8331i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) $ 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{18}\right)$

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 $

$2$	2.71476	+	0.237511i	1.91963	+	0.167946i	0.983153	−	0.182786i	$-0.0585116\pi$
$2$	2.71476	+	0.237511i	1.91963	+	0.167946i	0.936476	+	0.350732i	$0.114067\pi$
$3$		0			0
$3$		0			0
$4$	5.34392	+	0.942278i	2.67196	+	0.471139i
$5$	−1.08230	−	1.95669i	−0.484017	−	0.875059i
$5$	−1.08230	−	1.95669i	−0.484017	−	0.875059i
$6$		0			0
$7$	−1.29639	−	0.907744i	−0.489990	−	0.343095i	0.302327	−	0.953204i	$-0.402237\pi$
$7$	−1.29639	−	0.907744i	−0.489990	−	0.343095i	−0.792317	+	0.610109i	$0.791126\pi$
$8$	9.01913	+	2.41667i	3.18874	+	0.854422i
$9$		0			0
$10$	−2.47344	−	5.56901i	−0.782171	−	1.76108i
$11$	−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
$13$	0.242081	+	2.76700i	0.0671411	+	0.767427i	0.952901	+	0.303282i	$0.0980826\pi$
$13$	0.242081	+	2.76700i	0.0671411	+	0.767427i	−0.885760	+	0.464144i	$0.846362\pi$
$14$	−3.30380	−	2.77222i	−0.882978	−	0.740907i
$15$		0			0
$16$	13.7126	+	4.99098i	3.42815	+	1.24775i
$17$	−3.35386	+	0.898665i	−0.813431	+	0.217958i	−0.641473	−	0.767146i	$-0.721676\pi$
$17$	−3.35386	+	0.898665i	−0.813431	+	0.217958i	−0.171959	+	0.985104i	$0.555010\pi$
$18$		0			0
$19$	−1.97319	+	1.13922i	−0.452681	+	0.261356i	−0.708962	−	0.705247i	$-0.750836\pi$
$19$	−1.97319	+	1.13922i	−0.452681	+	0.261356i	0.256281	+	0.966602i	$0.417503\pi$
$20$	−3.93995	−	11.4762i	−0.881001	−	2.56616i
$21$		0			0
$22$	−0.548719	+	1.17673i	−0.116987	+	0.250880i
$23$	0.230790	+	0.329603i	0.0481231	+	0.0687269i	0.842493	−	0.538708i	$-0.181087\pi$
$23$	0.230790	+	0.329603i	0.0481231	+	0.0687269i	−0.794369	+	0.607435i	$0.792199\pi$
$24$		0			0
$25$	−2.65727	+	4.23543i	−0.531455	+	0.847087i
$26$			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	−0.947635	−	0.319355i	$-0.896534\pi$
$29$	−4.29568	+	3.60450i	−0.797687	+	0.669339i	0.149948	+	0.988694i	$0.452089\pi$
$30$		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	$-0.100126\pi$
$32$	19.1162	+	8.91403i	3.37930	+	1.57579i
$33$		0			0
$34$	−9.31839	+	1.64308i	−1.59809	+	0.281787i
$35$	−0.373094	+	3.51909i	−0.0630645	+	0.594834i
$36$		0			0
$37$	−0.387140	−	1.44483i	−0.0636454	−	0.237528i	0.926774	−	0.375619i	$-0.122570\pi$
$37$	−0.387140	−	1.44483i	−0.0636454	−	0.237528i	−0.990420	+	0.138091i	$0.955903\pi$
$38$	−5.62733	+	2.62407i	−0.912873	+	0.425680i
$39$		0			0
$40$	−5.03269	−	20.2632i	−0.795738	−	3.20389i
$41$	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
$43$	−0.501128	−	1.07467i	−0.0764213	−	0.163886i	0.864385	−	0.502830i	$-0.167708\pi$
$43$	−0.501128	−	1.07467i	−0.0764213	−	0.163886i	−0.940806	+	0.338944i	$0.889930\pi$
$44$	−1.29268	+	2.23899i	−0.194879	+	0.337541i
$45$		0			0
$46$	0.548257	+	0.949609i	0.0808361	+	0.140012i
$47$	−6.94767	+	9.92230i	−1.01342	+	1.44732i	−0.122876	+	0.992422i	$0.539212\pi$
$47$	−6.94767	+	9.92230i	−1.01342	+	1.44732i	−0.890546	+	0.454894i	$0.849677\pi$
$48$		0			0
$49$	−1.53751	−	4.22426i	−0.219644	−	0.603466i
$50$	−8.21984	+	10.8671i	−1.16246	+	1.53684i
$51$		0			0
$52$	−1.31362	+	15.0147i	−0.182166	+	2.08217i
$53$	0.274270	−	0.274270i	0.0376738	−	0.0376738i	−0.688019	−	0.725693i	$-0.741519\pi$
$53$	0.274270	−	0.274270i	0.0376738	−	0.0376738i	0.725693	+	0.688019i	$0.241519\pi$
$54$		0			0
$55$	1.05240	−	0.165706i	0.141905	−	0.0223439i
$56$	−9.49862	−	11.3200i	−1.26931	−	1.51270i
$57$		0			0
$58$	−12.5179	+	8.76510i	−1.64368	+	1.15091i
$59$	3.33385	−	1.21342i	0.434031	−	0.157974i	−0.115759	−	0.993277i	$-0.536930\pi$
$59$	3.33385	−	1.21342i	0.434031	−	0.157974i	0.549790	+	0.835303i	$0.314708\pi$
$60$		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	$-0.255963\pi$
$62$	3.69001	−	13.7713i	0.468631	−	1.74896i
$63$		0			0
$64$	24.5036	+	14.1471i	3.06294	+	1.76839i
$65$	5.15215	−	3.46838i	0.639046	−	0.430200i
$66$		0			0
$67$	13.1561	−	1.15101i	1.60727	−	0.140618i	0.752132	−	0.659012i	$-0.229025\pi$
$67$	13.1561	−	1.15101i	1.60727	−	0.140618i	0.855142	+	0.518394i	$0.173470\pi$
$68$	−18.7696	+	1.64212i	−2.27614	+	0.199137i
$69$		0			0
$70$	−1.84869	+	9.46488i	−0.220960	+	1.13127i
$71$	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
$73$	2.07381	−	7.73957i	0.242721	−	0.905849i	−0.731794	−	0.681526i	$-0.761317\pi$
$73$	2.07381	−	7.73957i	0.242721	−	0.905849i	0.974515	−	0.224322i	$-0.0720168\pi$
$74$	−0.707832	−	4.01431i	−0.0822838	−	0.466655i
$75$		0			0
$76$	−11.6180	+	4.22862i	−1.33268	+	0.485056i
$77$	0.617661	−	0.432491i	0.0703890	−	0.0492869i
$78$		0			0
$79$	−2.85683	−	3.40464i	−0.321418	−	0.383051i	0.581006	−	0.813899i	$-0.302659\pi$
$79$	−2.85683	−	3.40464i	−0.321418	−	0.383051i	−0.902425	+	0.430848i	$0.858215\pi$
$80$	−5.07529	−	32.2331i	−0.567434	−	3.60377i
$81$		0			0
$82$	14.9708	−	14.9708i	1.65325	−	1.65325i
$83$	−0.253902	+	2.90211i	−0.0278694	+	0.318548i	0.969445	+	0.245309i	$0.0788893\pi$
$83$	−0.253902	+	2.90211i	−0.0278694	+	0.318548i	−0.997314	+	0.0732395i	$0.976666\pi$
$84$		0			0
$85$	5.38828	+	5.58985i	0.584441	+	0.606304i
$86$	−1.10520	−	3.03651i	−0.119177	−	0.327435i
$87$		0			0
$88$	−2.55168	+	3.64417i	−0.272010	+	0.388470i
$89$	−3.50126	−	6.06435i	−0.371132	−	0.642820i	0.618608	−	0.785700i	$-0.287697\pi$
$89$	−3.50126	−	6.06435i	−0.371132	−	0.642820i	−0.989740	+	0.142880i	$0.954364\pi$
$90$		0			0
$91$	2.19789	−	3.80686i	0.230402	−	0.399068i
$92$	0.922748	+	1.97884i	0.0962031	+	0.206308i
$93$		0			0
$94$	−21.2179	+	25.2866i	−2.18846	+	2.60811i
$95$	4.36468	+	2.62795i	0.447807	+	0.269622i
$96$		0			0
$97$	−6.86175	+	3.19969i	−0.696705	+	0.324879i	−0.738506	−	0.674247i	$-0.764468\pi$
$97$	−6.86175	+	3.19969i	−0.696705	+	0.324879i	0.0418007	+	0.999126i	$0.486691\pi$
$98$	−3.17066	−	11.8331i	−0.320285	−	1.19532i
$99$		0			0
$100$	−18.1912	+	20.1299i	−1.81912	+	2.01299i
$101$	−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
$103$	−4.05522	−	1.89098i	−0.399573	−	0.186324i	0.212436	−	0.977175i	$-0.431860\pi$
$103$	−4.05522	−	1.89098i	−0.399573	−	0.186324i	−0.612009	+	0.790851i	$0.709638\pi$
$104$	−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	$-0.262579\pi$
$107$	−0.577939	−	0.577939i	−0.0558714	−	0.0558714i	−0.734490	+	0.678619i	$0.762579\pi$
$108$		0			0
$109$			8.45996i			0.810317i	0.914246	+	0.405159i	$0.132784\pi$
$109$			8.45996i			0.810317i	−0.914246	+	0.405159i	$0.867216\pi$
$110$	2.89637	−	0.199898i	0.276158	−	0.0190595i
$111$		0			0
$112$	−13.2464	−	18.9178i	−1.25167	−	1.78757i
$113$	0.921497	−	1.97616i	0.0866871	−	0.185901i	−0.858185	−	0.513340i	$-0.828408\pi$
$113$	0.921497	−	1.97616i	0.0866871	−	0.185901i	0.944872	+	0.327439i	$0.106186\pi$
$114$		0			0
$115$	0.395147	−	0.808313i	0.0368477	−	0.0753756i
$116$	−26.3522	+	15.2145i	−2.44674	+	1.41263i
$117$		0			0
$118$	9.33883	−	2.50233i	0.859709	−	0.230358i
$119$	5.16368	+	1.87943i	0.473354	+	0.172287i
$120$		0			0
$121$	8.25260	+	6.92475i	0.750236	+	0.629523i
$122$	−2.18454	−	24.9695i	−0.197779	−	2.26063i
$123$		0			0
$124$	9.70964	−	26.6770i	0.871952	−	2.39567i
$125$	11.1634	+	0.615475i	0.998484	+	0.0550498i
$126$		0			0
$127$	−3.44795	−	0.923874i	−0.305956	−	0.0819806i	0.102575	−	0.994725i	$-0.467292\pi$
$127$	−3.44795	−	0.923874i	−0.305956	−	0.0819806i	−0.408530	+	0.912745i	$0.633959\pi$
$128$	28.6056	+	20.0298i	2.52840	+	1.77040i
$129$		0			0
$130$	14.8107	−	8.19215i	1.29898	−	0.718499i
$131$	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
$133$	3.59215	+	0.314273i	0.311479	+	0.0272509i
$134$	35.9891			3.10899
$135$		0			0
$136$	−32.4207			−2.78005
$137$	−2.06926	−	0.181036i	−0.176788	−	0.0154670i	−0.00158226	−	0.999999i	$-0.500504\pi$
$137$	−2.06926	−	0.181036i	−0.176788	−	0.0154670i	−0.175206	+	0.984532i	$0.556059\pi$
$138$		0			0
$139$	15.2015	+	2.68044i	1.28938	+	0.227352i	0.775957	−	0.630785i	$-0.217267\pi$
$139$	15.2015	+	2.68044i	1.28938	+	0.227352i	0.513420	+	0.858137i	$0.328378\pi$
$140$	−5.30974	+	18.4542i	−0.448755	+	1.55966i
$141$		0			0
$142$	35.6224	+	24.9431i	2.98937	+	2.09318i
$143$	−1.27827	−	0.342511i	−0.106894	−	0.0286422i
$144$		0			0
$145$	11.7021	+	4.50418i	0.971805	+	0.374051i
$146$	7.46815	−	20.5186i	0.618068	−	1.69813i
$147$		0			0
$148$	−0.707419	−	8.08583i	−0.0581495	−	0.664651i
$149$	−12.0609	−	10.1203i	−0.988065	−	0.829085i	−0.00277827	−	0.999996i	$-0.500884\pi$
$149$	−12.0609	−	10.1203i	−0.988065	−	0.829085i	−0.985286	+	0.170911i	$0.945329\pi$
$150$		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	$0.625030\pi$
$152$	−20.5496	+	5.50625i	−1.66679	+	0.446616i
$153$		0			0
$154$	1.77953	−	1.02741i	0.143398	−	0.0827910i
$155$	−11.0645	+	3.79862i	−0.888725	+	0.305112i
$156$		0			0
$157$	−7.27543	+	15.6022i	−0.580643	+	1.24519i	0.368289	+	0.929711i	$0.379944\pi$
$157$	−7.27543	+	15.6022i	−0.580643	+	1.24519i	−0.948932	+	0.315481i	$0.897834\pi$
$158$	−6.94698	−	9.92131i	−0.552672	−	0.789297i
$159$		0			0
$160$	−3.24737	−	47.0521i	−0.256727	−	3.71979i
$161$		−	0.636793i		−	0.0501863i
$162$		0			0
$163$	2.47310	+	2.47310i	0.193708	+	0.193708i	0.797296	−	0.603588i	$-0.206263\pi$
$163$	2.47310	+	2.47310i	0.193708	+	0.193708i	−0.603588	+	0.797296i	$0.706263\pi$
$164$	32.2949	−	27.0987i	2.52181	−	2.11605i
$165$		0			0
$166$	−1.37857	+	7.81825i	−0.106998	+	0.606814i
$167$	5.97097	+	2.78431i	0.462048	+	0.215456i	0.639681	−	0.768640i	$-0.279066\pi$
$167$	5.97097	+	2.78431i	0.462048	+	0.215456i	−0.177634	+	0.984097i	$0.556844\pi$
$168$		0			0
$169$	5.20483	−	0.917752i	0.400372	−	0.0705963i
$170$	13.3003	+	16.4549i	1.02008	+	1.26203i
$171$		0			0
$172$	−1.66535	−	6.21517i	−0.126982	−	0.473902i
$173$	9.69016	−	4.51859i	0.736729	−	0.343542i	−0.0177714	−	0.999842i	$-0.505657\pi$
$173$	9.69016	−	4.51859i	0.736729	−	0.343542i	0.754500	+	0.656300i	$0.227879\pi$
$174$		0			0
$175$	7.28956	−	3.07866i	0.551039	−	0.232725i
$176$	−4.46905	+	5.32601i	−0.336867	+	0.401463i
$177$		0			0
$178$	−8.06473	−	17.2949i	−0.604477	−	1.29631i
$179$	3.31311	−	5.73847i	0.247633	−	0.428913i	−0.715235	−	0.698884i	$-0.753681\pi$
$179$	3.31311	−	5.73847i	0.247633	−	0.428913i	0.962869	+	0.269970i	$0.0870139\pi$
$180$		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	$0.938611\pi$
$182$	6.87094	−	9.81271i	0.509308	−	0.727367i
$183$		0			0
$184$	1.28499	+	3.53048i	0.0947306	+	0.260270i
$185$	−2.40808	+	2.32124i	−0.177045	+	0.170661i
$186$		0			0
$187$	0.144182	−	1.64801i	0.0105436	−	0.120514i
$188$	−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
$193$	−15.3824	+	10.7709i	−1.10725	+	0.775303i	−0.976372	−	0.216096i	$-0.930668\pi$
$193$	−15.3824	+	10.7709i	−1.10725	+	0.775303i	−0.130875	+	0.991399i	$0.541779\pi$
$194$	−19.3880	+	7.05665i	−1.39198	+	0.506638i
$195$		0			0
$196$	−4.23588	−	24.0229i	−0.302563	−	1.71592i
$197$	1.29693	−	4.84019i	0.0924021	−	0.344849i	−0.904211	−	0.427087i	$-0.859540\pi$
$197$	1.29693	−	4.84019i	0.0924021	−	0.344849i	0.996613	+	0.0822373i	$0.0262066\pi$
$198$		0			0
$199$	−14.4356	−	8.33443i	−1.02332	−	0.590812i	−0.108253	−	0.994123i	$-0.534526\pi$
$199$	−14.4356	−	8.33443i	−1.02332	−	0.590812i	−0.915063	+	0.403312i	$0.867859\pi$
$200$	−34.2020	+	31.7782i	−2.41844	+	2.24706i
$201$		0			0
$202$	−15.7867	+	1.38116i	−1.11075	+	0.0971779i
$203$	8.84085	−	0.773474i	0.620506	−	0.0542872i
$204$		0			0
$205$	−17.0501	−	3.33023i	−1.19083	−	0.232594i
$206$	−10.5599	−	6.09673i	−0.735740	−	0.424779i
$207$		0			0
$208$	−10.4905	+	39.1510i	−0.727384	+	2.71463i
$209$	−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	$0.271777\pi$
$212$	1.72411	−	1.20724i	0.118413	−	0.0829134i
$213$		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
$218$	−2.00934	+	22.9668i	−0.136089	+	1.55551i
$219$		0			0
$220$	5.78008	+	0.106130i	0.389693	+	0.00715525i
$221$	−3.29851	−	9.06258i	−0.221882	−	0.609615i
$222$		0			0
$223$	−13.4550	+	19.2158i	−0.901015	+	1.28678i	0.0565006	+	0.998403i	$0.482006\pi$
$223$	−13.4550	+	19.2158i	−0.901015	+	1.28678i	−0.957516	+	0.288381i	$0.906883\pi$
$224$	−16.6904	−	28.9087i	−1.11518	−	1.93154i
$225$		0			0
$226$	2.97101	−	5.14593i	0.197628	−	0.342302i
$227$	8.45994	+	18.1424i	0.561506	+	1.20415i	0.958173	+	0.286191i	$0.0923891\pi$
$227$	8.45994	+	18.1424i	0.561506	+	1.20415i	−0.396667	+	0.917963i	$0.629833\pi$
$228$		0			0
$229$	14.1827	−	16.9023i	0.937218	−	1.11693i	−0.0557370	−	0.998445i	$-0.517751\pi$
$229$	14.1827	−	16.9023i	0.937218	−	1.11693i	0.992955	−	0.118488i	$-0.0378047\pi$
$230$	1.26472	−	2.10053i	0.0833929	−	0.138505i
$231$		0			0
$232$	−47.4542	+	22.1282i	−3.11552	+	1.45279i
$233$	−4.83296	−	18.0369i	−0.316618	−	1.18163i	−0.922474	−	0.386059i	$-0.873836\pi$
$233$	−4.83296	−	18.0369i	−0.316618	−	1.18163i	0.605856	−	0.795574i	$-0.292831\pi$
$234$		0			0
$235$	26.9343	+	2.85558i	1.75700	+	0.186277i
$236$	18.9592	−	3.34302i	1.23414	−	0.217612i
$237$		0			0
$238$	13.5718	+	6.32863i	0.879729	+	0.410224i
$239$	3.38846	−	19.2169i	0.219181	−	1.24304i	−0.654320	−	0.756218i	$-0.727045\pi$
$239$	3.38846	−	19.2169i	0.219181	−	1.24304i	0.873502	−	0.486821i	$-0.161844\pi$
$240$		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
$245$	−6.60154	+	7.58032i	−0.421757	+	0.484289i
$246$		0			0
$247$	−3.62990	−	5.18403i	−0.230965	−	0.329852i
$248$	20.6449	−	44.2731i	1.31095	−	2.81134i
$249$		0			0
$250$	30.1598	+	4.32230i	1.90747	+	0.273366i
$251$	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
$253$	−0.185175	+	0.0496176i	−0.0116419	+	0.00311943i
$254$	−9.14093	−	3.32703i	−0.573553	−	0.208756i
$255$		0			0
$256$	29.5507	+	24.7960i	1.84692	+	1.54975i
$257$	1.27235	+	14.5430i	0.0793667	+	0.907166i	0.926626	+	0.375986i	$0.122696\pi$
$257$	1.27235	+	14.5430i	0.0793667	+	0.907166i	−0.847259	+	0.531180i	$0.821749\pi$
$258$		0			0
$259$	−0.809647	+	2.22449i	−0.0503090	+	0.138223i
$260$	30.8009	−	13.6800i	1.91019	−	0.848399i
$261$		0			0
$262$	8.09576	+	2.16925i	0.500158	+	0.134017i
$263$	−25.0799	−	17.5612i	−1.54650	−	1.08287i	−0.962561	−	0.271067i	$-0.912624\pi$
$263$	−25.0799	−	17.5612i	−1.54650	−	1.08287i	−0.583935	−	0.811801i	$-0.698488\pi$
$264$		0			0
$265$	−0.833501	−	0.239820i	−0.0512016	−	0.0147320i
$266$	9.67721	+	1.70635i	0.593348	+	0.104623i
$267$		0			0
$268$	71.3898	+	6.24580i	4.36083	+	0.381523i
$269$	−23.6912			−1.44448			−0.722239	−	0.691643i	$-0.756887\pi$
$269$	−23.6912			−1.44448			−0.722239	+	0.691643i	$0.756887\pi$
$270$		0			0
$271$	20.1164			1.22198			0.610991	−	0.791638i	$-0.290771\pi$
$271$	20.1164			1.22198			0.610991	+	0.791638i	$0.290771\pi$
$272$	−50.4755	−	4.41603i	−3.06052	−	0.267761i
$273$		0			0
$274$	−5.57454	−	0.982943i	−0.336771	−	0.0593817i
$275$	−1.46324	−	1.87988i	−0.0882368	−	0.113361i
$276$		0			0
$277$	−12.4565	−	8.72217i	−0.748441	−	0.524064i	0.136004	−	0.990708i	$-0.456574\pi$
$277$	−12.4565	−	8.72217i	−0.748441	−	0.524064i	−0.884445	+	0.466644i	$0.845463\pi$
$278$	40.6320	+	10.8873i	2.43694	+	0.652977i
$279$		0			0
$280$	−11.8695	+	30.8375i	−0.709336	+	1.84289i
$281$	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
$283$	−0.0248657	−	0.284217i	−0.00147811	−	0.0168949i	0.995420	−	0.0956001i	$-0.0304770\pi$
$283$	−0.0248657	−	0.284217i	−0.00147811	−	0.0168949i	−0.996898	+	0.0787051i	$0.974921\pi$
$284$	66.3335	+	55.6605i	3.93617	+	3.30284i
$285$		0			0
$286$	−3.38884	−	1.23344i	−0.200387	−	0.0729347i
$287$	−11.8765	+	3.18229i	−0.701046	+	0.187845i
$288$		0			0
$289$	−4.28164	+	2.47200i	−0.251861	+	0.145412i
$290$	30.6986	+	15.0072i	1.80268	+	0.881250i
$291$		0			0
$292$	18.3751	−	39.4056i	1.07532	−	2.30604i
$293$	8.91694	+	12.7347i	0.520933	+	0.743969i	0.990287	−	0.139041i	$-0.0444019\pi$
$293$	8.91694	+	12.7347i	0.520933	+	0.743969i	−0.469354	+	0.883010i	$0.655513\pi$
$294$		0			0
$295$	−5.98250	−	5.21003i	−0.348315	−	0.303340i
$296$		−	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
$302$	−2.65345	−	1.23733i	−0.152689	−	0.0712001i
$303$		0			0
$304$	−32.7435	+	5.77355i	−1.87797	+	0.331136i
$305$	−15.9949	+	12.9285i	−0.915868	+	0.740283i
$306$		0			0
$307$	2.72426	+	10.1671i	0.155482	+	0.580267i	0.999064	+	0.0432656i	$0.0137762\pi$
$307$	2.72426	+	10.1671i	0.155482	+	0.580267i	−0.843582	+	0.537001i	$0.819557\pi$
$308$	3.70826	−	1.72919i	0.211298	−	0.0985297i
$309$		0			0
$310$	−30.9398	+	7.68440i	−1.75726	+	0.436445i
$311$	−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
$313$	10.2775	+	22.0403i	0.580921	+	1.24579i	0.948789	+	0.315911i	$0.102310\pi$
$313$	10.2775	+	22.0403i	0.580921	+	1.24579i	−0.367868	+	0.929878i	$0.619912\pi$
$314$	−23.4568	+	40.6283i	−1.32374	+	2.29279i
$315$		0			0
$316$	−12.0586	−	20.8860i	−0.678347	−	1.17493i
$317$	−11.9128	+	17.0133i	−0.669092	+	0.955562i	0.330838	+	0.943688i	$0.392669\pi$
$317$	−11.9128	+	17.0133i	−0.669092	+	0.955562i	−0.999929	+	0.0118742i	$0.996220\pi$
$318$		0			0
$319$	−0.913782	−	2.51060i	−0.0511620	−	0.140566i
$320$	1.16148	−	63.2573i	0.0649289	−	3.53619i
$321$		0			0
$322$	0.151246	−	1.72874i	0.00842858	−	0.0963391i
$323$	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
$328$	59.4234	−	41.6087i	3.28111	−	2.29746i
$329$	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	$0.892089\pi$
$332$	−4.09143	+	15.2694i	−0.224546	+	0.838018i
$333$		0			0
$334$	15.5485	+	8.97692i	0.850775	+	0.491195i
$335$	−16.4910	−	24.4967i	−0.900998	−	1.33840i
$336$		0			0
$337$	−11.1098	+	0.971978i	−0.605187	+	0.0529470i	−0.385631	−	0.922653i	$-0.626016\pi$
$337$	−11.1098	+	0.971978i	−0.605187	+	0.0529470i	−0.219556	+	0.975600i	$0.570461\pi$
$338$	14.3479	−	1.25528i	0.780421	−	0.0682780i
$339$		0			0
$340$	23.5273	+	34.9490i	1.27595	+	1.89537i
$341$	2.15867	+	1.24631i	0.116899	+	0.0674915i
$342$		0			0
$343$	−4.70859	+	17.5727i	−0.254240	+	0.948837i
$344$	−1.92261	−	10.9037i	−0.103660	−	0.587887i
$345$		0			0
$346$	27.3797	−	9.96540i	1.47194	−	0.535743i
$347$	19.4431	−	13.6142i	1.04376	−	0.730851i	0.0797793	−	0.996813i	$-0.474578\pi$
$347$	19.4431	−	13.6142i	1.04376	−	0.730851i	0.963984	+	0.265962i	$0.0856896\pi$
$348$		0			0
$349$	−4.82633	−	5.75179i	−0.258347	−	0.307886i	0.621243	−	0.783618i	$-0.286628\pi$
$349$	−4.82633	−	5.75179i	−0.258347	−	0.307886i	−0.879591	+	0.475731i	$0.842183\pi$
$350$	20.5207	−	6.62649i	1.09688	−	0.354201i
$351$		0			0
$352$	−7.10598	+	7.10598i	−0.378750	+	0.378750i
$353$	−0.451688	+	5.16281i	−0.0240409	+	0.274789i	0.974654	+	0.223717i	$0.0718192\pi$
$353$	−0.451688	+	5.16281i	−0.0240409	+	0.274789i	−0.998695	+	0.0510716i	$0.983736\pi$
$354$		0			0
$355$	0.655066	−	35.6765i	0.0347673	−	1.89351i
$356$	−12.9961	−	35.7066i	−0.688793	−	1.89244i
$357$		0			0
$358$	10.3573	−	14.7917i	0.547398	−	0.781765i
$359$	−6.82697	−	11.8247i	−0.360314	−	0.624082i	0.627699	−	0.778457i	$-0.283997\pi$
$359$	−6.82697	−	11.8247i	−0.360314	−	0.624082i	−0.988012	+	0.154375i	$0.950664\pi$
$360$		0			0
$361$	−6.90435	+	11.9587i	−0.363387	+	0.629404i
$362$	−10.0634	−	21.5810i	−0.528921	−	1.13427i
$363$		0			0
$364$	15.3325	−	18.2725i	0.803641	−	0.957742i
$365$	−17.3884	+	4.31869i	−0.910152	+	0.226051i
$366$		0			0
$367$	19.5461	−	9.11448i	1.02030	−	0.475772i	0.160840	−	0.986981i	$-0.448580\pi$
$367$	19.5461	−	9.11448i	1.02030	−	0.475772i	0.859457	+	0.511208i	$0.170802\pi$
$368$	1.51970	+	5.67159i	0.0792197	+	0.295652i
$369$		0			0
$370$	−7.08869	+	5.72968i	−0.368523	+	0.297872i
$371$	−0.604528	+	0.106595i	−0.0313855	+	0.00553411i
$372$		0			0
$373$	−11.9942	−	5.59299i	−0.621037	−	0.289594i	0.0865206	−	0.996250i	$-0.472425\pi$
$373$	−11.9942	−	5.59299i	−0.621037	−	0.289594i	−0.707557	+	0.706656i	$0.750203\pi$
$374$	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	$0.248583\pi$
$379$			27.4089i			1.40790i	−0.710249	+	0.703951i	$0.751417\pi$
$380$	20.8483	+	18.1563i	1.06949	+	0.931398i
$381$		0			0
$382$	31.5292	+	45.0283i	1.61317	+	2.30385i
$383$	−15.2701	+	32.7469i	−0.780267	+	1.67329i	−0.0416793	+	0.999131i	$0.513271\pi$
$383$	−15.2701	+	32.7469i	−0.780267	+	1.67329i	−0.738588	+	0.674157i	$0.764507\pi$
$384$		0			0
$385$	−1.51474	−	0.740488i	−0.0771984	−	0.0377388i
$386$	−44.3177	+	25.5869i	−2.25571	+	1.30234i
$387$		0			0
$388$	−39.6836	+	10.6332i	−2.01463	+	0.539819i
$389$	17.3733	+	6.32335i	0.880860	+	0.320607i	0.742557	−	0.669783i	$-0.233613\pi$
$389$	17.3733	+	6.32335i	0.880860	+	0.320607i	0.138303	+	0.990390i	$0.455835\pi$
$390$		0			0
$391$	−1.07024	−	0.898039i	−0.0541244	−	0.0454158i
$392$	−3.65832	−	41.8148i	−0.184773	−	2.11197i
$393$		0			0
$394$	4.67045	−	12.8320i	0.235294	−	0.646464i
$395$	−3.56989	+	9.27475i	−0.179620	+	0.466663i
$396$		0			0
$397$	−29.1350	−	7.80671i	−1.46224	−	0.391807i	−0.561980	−	0.827151i	$-0.689960\pi$
$397$	−29.1350	−	7.80671i	−1.46224	−	0.391807i	−0.900265	+	0.435343i	$0.856627\pi$
$398$	−37.2099	−	26.0546i	−1.86516	−	1.30600i
$399$		0			0
$400$	−57.5772	+	44.8165i	−2.87886	+	2.24082i
$401$	−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
$403$	14.4761	+	1.26649i	0.721106	+	0.0630886i
$404$	−31.5550			−1.56992
$405$		0			0
$406$	24.1845			1.20026
$407$	0.709953	+	0.0621128i	0.0351911	+	0.00307882i
$408$		0			0
$409$	−21.8207	−	3.84758i	−1.07897	−	0.190251i	−0.394208	−	0.919021i	$-0.628981\pi$
$409$	−21.8207	−	3.84758i	−1.07897	−	0.190251i	−0.684758	+	0.728771i	$0.740092\pi$
$410$	−45.4960	−	13.0904i	−2.24689	−	0.646488i
$411$		0			0
$412$	−19.8890	−	13.9264i	−0.979859	−	0.686105i
$413$	−5.42346	−	1.45321i	−0.266871	−	0.0715079i
$414$		0			0
$415$	5.95333	−	2.64413i	0.292238	−	0.129795i
$416$	−20.0374	+	55.0524i	−0.982415	+	2.69916i
$417$		0			0
$418$	−0.257831	−	2.94703i	−0.0126109	−	0.144144i
$419$	3.82900	+	3.21291i	0.187059	+	0.156961i	0.731508	−	0.681833i	$-0.238817\pi$
$419$	3.82900	+	3.21291i	0.187059	+	0.156961i	−0.544449	+	0.838794i	$0.683261\pi$
$420$		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	$0.507056\pi$
$422$	27.5051	−	7.36996i	1.33893	−	0.358764i
$423$		0			0
$424$	3.13649	−	1.81086i	0.152322	−	0.0879429i
$425$	5.10590	−	16.5931i	0.247672	−	0.804882i
$426$		0			0
$427$	−6.15173	+	13.1924i	−0.297703	+	0.638426i
$428$	−2.54388	−	3.63304i	−0.122963	−	0.175609i
$429$		0			0
$430$	−4.74535	+	5.44893i	−0.228841	+	0.262771i
$431$		−	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	0.183587	−	0.983003i	$-0.441229\pi$
$433$	−16.6348	−	16.6348i	−0.799416	−	0.799416i	−0.983003	+	0.183587i	$0.941229\pi$
$434$	−17.2845	+	14.5034i	−0.829683	+	0.696187i
$435$		0			0
$436$	−7.97163	+	45.2094i	−0.381772	+	2.16514i
$437$	−0.830884	−	0.387448i	−0.0397466	−	0.0185341i
$438$		0			0
$439$	−21.2894	+	3.75390i	−1.01609	+	0.179164i	−0.656801	−	0.754064i	$-0.728091\pi$
$439$	−21.2894	+	3.75390i	−1.01609	+	0.179164i	−0.359287	+	0.933227i	$0.616980\pi$
$440$	9.89218	+	1.04877i	0.471591	+	0.0499982i
$441$		0			0
$442$	−6.80221	−	25.3862i	−0.323548	−	1.20750i
$443$	−10.8788	+	5.07285i	−0.516866	+	0.241018i	−0.663505	−	0.748172i	$-0.730932\pi$
$443$	−10.8788	+	5.07285i	−0.516866	+	0.241018i	0.146640	+	0.989190i	$0.453154\pi$
$444$		0			0
$445$	−8.07667	+	13.4143i	−0.382871	+	0.635898i
$446$	−41.0912	+	48.9706i	−1.94572	+	2.31882i
$447$		0			0
$448$	−18.9243	−	40.5832i	−0.894087	−	1.91738i
$449$	−15.1373	+	26.2186i	−0.714374	+	1.23733i	0.248826	+	0.968548i	$0.419955\pi$
$449$	−15.1373	+	26.2186i	−0.714374	+	1.23733i	−0.963200	+	0.268784i	$0.913378\pi$
$450$		0			0
$451$	1.85078	+	3.20565i	0.0871499	+	0.150948i
$452$	6.78649	−	9.69212i	0.319210	−	0.455879i
$453$		0			0
$454$	18.6577	+	51.2617i	0.875651	+	2.40583i
$455$	−9.82762	−	0.180448i	−0.460726	−	0.00845951i
$456$		0			0
$457$	3.62673	−	41.4537i	0.169651	−	1.93912i	−0.143990	−	0.989579i	$-0.545993\pi$
$457$	3.62673	−	41.4537i	0.169651	−	1.93912i	0.313642	−	0.949541i	$-0.398451\pi$
$458$	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
$463$	−13.5021	+	9.45428i	−0.627496	+	0.439378i	−0.843585	−	0.536996i	$-0.819559\pi$
$463$	−13.5021	+	9.45428i	−0.627496	+	0.439378i	0.216088	+	0.976374i	$0.430670\pi$
$464$	−76.8950	+	27.9875i	−3.56976	+	1.29929i
$465$		0			0
$466$	−8.83640	−	50.1137i	−0.409338	−	2.32147i
$467$	−1.03012	+	3.84448i	−0.0476685	+	0.177901i	−0.985656	−	0.168769i	$-0.946021\pi$
$467$	−1.03012	+	3.84448i	−0.0476685	+	0.177901i	0.937987	+	0.346670i	$0.112688\pi$
$468$		0			0
$469$	−18.1003	−	10.4502i	−0.835795	−	0.482546i
$470$	72.4420	+	14.1494i	3.34150	+	0.652664i
$471$		0			0
$472$	33.0009	−	2.88720i	1.51899	−	0.132894i
$473$	0.562805	−	0.0492391i	0.0258778	−	0.00226402i
$474$		0			0
$475$	0.418210	−	11.3845i	0.0191888	−	0.522359i
$476$	25.8234	+	14.9091i	1.18361	+	0.683359i
$477$		0			0
$478$	13.7631	−	51.3646i	0.629510	−	2.34936i
$479$	0.246236	+	1.39648i	0.0112508	+	0.0638066i	0.989916	−	0.141654i	$-0.0452420\pi$
$479$	0.246236	+	1.39648i	0.0112508	+	0.0638066i	−0.978665	+	0.205460i	$0.934131\pi$
$480$		0			0
$481$	3.90411	−	1.42098i	0.178012	−	0.0647911i
$482$	−10.9857	+	7.69230i	−0.500387	+	0.350375i
$483$		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	−0.828582	−	0.559868i	$-0.810852\pi$
$487$	−5.92999	+	5.92999i	−0.268714	+	0.268714i	0.559868	+	0.828582i	$0.310852\pi$
$488$	7.48504	−	85.5544i	0.338832	−	3.87286i
$489$		0			0
$490$	−19.7220	+	19.0109i	−0.890951	+	0.858823i
$491$	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
$493$	11.1679	−	15.9494i	0.502976	−	0.718324i
$494$	−8.62305	−	14.9356i	−0.387969	−	0.671983i
$495$		0			0
$496$	38.1722	−	66.1162i	1.71398	−	2.96871i
$497$	−10.6731	−	22.8886i	−0.478754	−	1.02669i
$498$		0			0
$499$	7.19594	−	8.57579i	0.322134	−	0.383905i	−0.580538	−	0.814233i	$-0.697158\pi$
$499$	7.19594	−	8.57579i	0.322134	−	0.383905i	0.902672	+	0.430328i	$0.141602\pi$
$500$	59.0763	+	13.8081i	2.64197	+	0.617515i
$501$		0			0
$502$	51.6420	−	24.0811i	2.30490	−	1.07479i
$503$	−3.44372	−	12.8521i	−0.153548	−	0.573049i	−0.999225	−	0.0393543i	$-0.987470\pi$
$503$	−3.44372	−	12.8521i	−0.153548	−	0.573049i	0.845677	−	0.533694i	$-0.179197\pi$
$504$		0			0
$505$	8.17391	+	10.1127i	0.363734	+	0.450007i
$506$	−0.514493	+	0.0907189i	−0.0228720	+	0.00403295i
$507$		0			0
$508$	−17.5550	−	8.18603i	−0.778877	−	0.363197i
$509$	1.12261	−	6.36664i	0.0497588	−	0.282196i	−0.949768	−	0.312955i	$-0.898681\pi$
$509$	1.12261	−	6.36664i	0.0497588	−	0.282196i	0.999527	+	0.0307584i	$0.00979226\pi$
$510$		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
$515$	0.688883	+	9.98142i	0.0303558	+	0.439834i
$516$		0			0
$517$	−3.31019	−	4.72744i	−0.145582	−	0.207912i
$518$	−2.72634	+	5.84666i	−0.119789	+	0.256887i
$519$		0			0
$520$	54.8499	−	18.8308i	2.40533	−	0.825784i
$521$	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
$523$	12.5860	−	3.37240i	0.550346	−	0.147465i	0.0270787	−	0.999633i	$-0.491380\pi$
$523$	12.5860	−	3.37240i	0.550346	−	0.147465i	0.523268	+	0.852168i	$0.324713\pi$
$524$	15.6827	+	5.70803i	0.685101	+	0.249356i
$525$		0			0
$526$	−63.9152	−	53.6312i	−2.78683	−	2.33843i
$527$	1.58322	+	18.0963i	0.0689660	+	0.788285i
$528$		0			0
$529$	7.81109	−	21.4608i	0.339613	−	0.933078i
$530$	−2.20580	−	0.849021i	−0.0958139	−	0.0368791i
$531$		0			0
$532$	18.9001	+	5.06425i	0.819421	+	0.219563i
$533$	17.6767	+	12.3773i	0.765662	+	0.536122i
$534$		0			0
$535$	−0.505347	+	1.75635i	−0.0218480	+	0.0759335i
$536$	121.438	+	21.4128i	5.24534	+	0.924894i
$537$		0			0
$538$	−64.3161	−	5.62693i	−2.77286	−	0.242594i
$539$	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	$0.637545\pi$
$542$	54.6112	+	4.77786i	2.34575	+	0.205227i
$543$		0			0
$544$	−72.1238	−	12.7174i	−3.09228	−	0.545253i
$545$	16.5535	−	9.15618i	0.709075	−	0.392207i
$546$		0			0
$547$	11.7626	+	8.23625i	0.502932	+	0.352157i	0.797347	−	0.603521i	$-0.206236\pi$
$547$	11.7626	+	8.23625i	0.502932	+	0.352157i	−0.294415	+	0.955678i	$0.595125\pi$
$548$	−10.8874	−	2.91726i	−0.465085	−	0.124619i
$549$		0			0
$550$	−3.52587	−	5.45096i	−0.150344	−	0.232430i
$551$	4.36986	−	12.0061i	0.186162	−	0.511477i
$552$		0			0
$553$	0.613034	+	7.00702i	0.0260689	+	0.297969i
$554$	−31.7450	−	26.6372i	−1.34871	−	1.13171i
$555$		0			0
$556$	78.7101	+	28.6481i	3.33805	+	1.21495i
$557$	−22.3886	+	5.99902i	−0.948637	+	0.254187i	−0.699784	−	0.714355i	$-0.746720\pi$
$557$	−22.3886	+	5.99902i	−0.948637	+	0.254187i	−0.248853	+	0.968541i	$0.580054\pi$
$558$		0			0
$559$	2.85230	−	1.64678i	0.120640	−	0.0696513i
$560$	−22.6798	+	46.3938i	−0.958397	+	1.96049i
$561$		0			0
$562$	27.4978	−	58.9691i	1.15992	−	2.48746i
$563$	17.2788	+	24.6767i	0.728214	+	1.04000i	0.997046	+	0.0768099i	$0.0244735\pi$
$563$	17.2788	+	24.6767i	0.728214	+	1.04000i	−0.268832	+	0.963187i	$0.586638\pi$
$564$		0			0
$565$	−4.86406	+	0.335700i	−0.204632	+	0.0141230i
$566$		−	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	−0.890536	−	0.454913i	$-0.849670\pi$
$569$	−14.2448	+	11.9528i	−0.597173	+	0.501088i	0.293362	+	0.956001i	$0.405226\pi$
$570$		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	$-0.251476\pi$
$572$	−6.50822	−	3.03483i	−0.272122	−	0.126893i
$573$		0			0
$574$	−32.9977	+	5.81838i	−1.37730	+	0.242854i
$575$	−2.00928	+	0.101652i	−0.0837929	+	0.00423918i
$576$		0			0
$577$	11.3255	+	42.2673i	0.471486	+	1.75961i	0.634436	+	0.772975i	$0.281232\pi$
$577$	11.3255	+	42.2673i	0.471486	+	1.75961i	−0.162950	+	0.986634i	$0.552101\pi$
$578$	−12.2108	+	5.69397i	−0.507901	+	0.236838i
$579$		0			0
$580$	58.2908	+	35.0966i	2.42039	+	1.45731i
$581$	2.96353	−	3.53180i	0.122948	−	0.146524i
$582$		0			0
$583$	0.0781006	+	0.167487i	0.00323460	+	0.00693661i
$584$	37.4080	−	64.7925i	1.54795	−	2.68113i
$585$		0			0
$586$	21.1828	+	36.6896i	0.875051	+	1.51563i
$587$	11.6046	−	16.5731i	0.478974	−	0.684046i	−0.504845	−	0.863210i	$-0.668450\pi$
$587$	11.6046	−	16.5731i	0.478974	−	0.684046i	0.983819	+	0.179164i	$0.0573394\pi$
$588$		0			0
$589$	4.07693	+	11.2013i	0.167987	+	0.461540i
$590$	−15.0037	−	15.5649i	−0.617691	−	0.640798i
$591$		0			0
$592$	1.90240	−	21.7446i	0.0781883	−	0.893696i
$593$	2.27116	−	2.27116i	0.0932652	−	0.0932652i	−0.658935	−	0.752200i	$-0.728993\pi$
$593$	2.27116	−	2.27116i	0.0932652	−	0.0932652i	0.752200	+	0.658935i	$0.228993\pi$
$594$		0			0
$595$	−1.91117	−	12.1378i	−0.0783504	−	0.497602i
$596$	−54.9162	−	65.4466i	−2.24946	−	2.68080i
$597$		0			0
$598$	−2.49484	+	1.74691i	−0.102022	+	0.0714364i
$599$	−11.3910	+	4.14598i	−0.465423	+	0.169400i	−0.564078	−	0.825722i	$-0.690768\pi$
$599$	−11.3910	+	4.14598i	−0.465423	+	0.169400i	0.0986548	+	0.995122i	$0.468546\pi$
$600$		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	$0.838189\pi$
$602$	−1.32360	+	4.93974i	−0.0539459	+	0.201329i
$603$		0			0
$604$	−5.04879	−	2.91492i	−0.205432	−	0.118606i
$605$	4.61785	−	23.6424i	0.187742	−	0.961200i
$606$		0			0
$607$	−12.6491	+	1.10665i	−0.513412	+	0.0449177i	−0.340918	−	0.940093i	$-0.610738\pi$
$607$	−12.6491	+	1.10665i	−0.513412	+	0.0449177i	−0.172494	+	0.985011i	$0.555182\pi$
$608$	−47.8750	+	4.18852i	−1.94159	+	0.169867i
$609$		0			0
$610$	−46.4932	+	31.2988i	−1.88245	+	1.26725i
$611$	−29.1369	−	16.8222i	−1.17875	−	0.680552i
$612$		0			0
$613$	3.15725	−	11.7830i	0.127520	−	0.475912i	−0.872397	−	0.488798i	$-0.837435\pi$
$613$	3.15725	−	11.7830i	0.127520	−	0.475912i	0.999917	+	0.0128866i	$0.00410204\pi$
$614$	4.98094	+	28.2483i	0.201014	+	1.14001i
$615$		0			0
$616$	6.61595	−	2.40801i	0.266564	−	0.0970215i
$617$	−7.63591	+	5.34672i	−0.307410	+	0.215251i	−0.717094	−	0.696977i	$-0.754528\pi$
$617$	−7.63591	+	5.34672i	−0.307410	+	0.215251i	0.409684	+	0.912228i	$0.365639\pi$
$618$		0			0
$619$	10.1944	+	12.1492i	0.409748	+	0.488319i	0.930967	−	0.365104i	$-0.118967\pi$
$619$	10.1944	+	12.1492i	0.409748	+	0.488319i	−0.521218	+	0.853423i	$0.674522\pi$
$620$	−62.7074	+	9.87365i	−2.51839	+	0.396535i
$621$		0			0
$622$	−6.19528	+	6.19528i	−0.248408	+	0.248408i
$623$	−0.965877	+	11.0400i	−0.0386971	+	0.442309i
$624$		0			0
$625$	−10.8778	−	22.5094i	−0.435111	−	0.900377i
$626$	22.6663	+	62.2751i	0.905927	+	2.48901i
$627$		0			0
$628$	−53.5809	+	76.5215i	−2.13811	+	3.05354i
$629$	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	$0.328439\pi$
$632$	−17.5382	−	37.6109i	−0.697634	−	1.49608i
$633$		0			0
$634$	−36.3814	+	43.3577i	−1.44489	+	1.72195i
$635$	1.92396	+	7.74647i	0.0763500	+	0.307409i
$636$		0			0
$637$	11.3163	−	5.27689i	0.448369	−	0.209078i
$638$	−1.88441	−	7.03271i	−0.0746045	−	0.278428i
$639$		0			0
$640$	8.23251	−	77.6504i	0.325419	−	3.06940i
$641$	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
$643$	−29.1651	−	13.5999i	−1.15016	−	0.536328i	−0.248438	−	0.968648i	$-0.579917\pi$
$643$	−29.1651	−	13.5999i	−1.15016	−	0.536328i	−0.901720	+	0.432320i	$0.857695\pi$
$644$	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	$-0.201712\pi$
$647$	5.43613	+	5.43613i	0.213717	+	0.213717i	−0.592128	+	0.805844i	$0.701712\pi$
$648$		0			0
$649$			1.69034i			0.0663516i
$650$	−32.0590	−	20.1136i	−1.25746	−	0.788919i
$651$		0			0
$652$	10.8857	+	15.5464i	0.426317	+	0.608844i
$653$	6.80729	−	14.5983i	0.266390	−	0.571275i	−0.726924	−	0.686717i	$-0.759051\pi$
$653$	6.80729	−	14.5983i	0.266390	−	0.571275i	0.993314	+	0.115443i	$0.0368287\pi$
$654$		0			0
$655$	−2.23310	−	6.50454i	−0.0872545	−	0.254153i
$656$	98.1831	−	56.6861i	3.83341	−	2.21322i
$657$		0			0
$658$	50.4605	−	13.5209i	1.96716	−	0.527098i
$659$	31.0994	+	11.3193i	1.21146	+	0.440936i	0.867210	−	0.497942i	$-0.165911\pi$
$659$	31.0994	+	11.3193i	1.21146	+	0.440936i	0.344250	+	0.938878i	$0.388133\pi$
$660$		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	$0.525846\pi$
$662$	1.41507	+	16.1743i	0.0549981	+	0.628631i
$663$		0			0
$664$	−9.30342	+	25.5609i	−0.361043	+	0.991957i
$665$	−3.27284	−	7.36887i	−0.126915	−	0.285752i
$666$		0			0
$667$	−2.17945	−	0.583983i	−0.0843888	−	0.0226119i
$668$	29.2848	+	20.5054i	1.13306	+	0.793379i
$669$		0			0
$670$	−38.9509	−	70.4196i	−1.50480	−	2.72055i
$671$	4.31561	+	0.760958i	0.166602	+	0.0293764i
$672$		0			0
$673$	34.6064	+	3.02767i	1.33398	+	0.116708i	0.731727	−	0.681598i	$-0.238715\pi$
$673$	34.6064	+	3.02767i	1.33398	+	0.116708i	0.602252	+	0.798306i	$0.294270\pi$
$674$	−30.3912			−1.17063
$675$		0			0
$676$	28.6790			1.10304
$677$	17.3173	+	1.51507i	0.665560	+	0.0582289i	0.414929	−	0.909854i	$-0.363806\pi$
$677$	17.3173	+	1.51507i	0.665560	+	0.0582289i	0.250631	+	0.968083i	$0.419362\pi$
$678$		0			0
$679$	11.8000	+	2.08066i	0.452843	+	0.0798485i
$680$	35.0888	+	63.4373i	1.34559	+	2.43271i
$681$		0			0
$682$	5.56428	+	3.89615i	0.213067	+	0.149191i
$683$	10.9763	+	2.94108i	0.419995	+	0.112537i	0.462626	−	0.886554i	$-0.346907\pi$
$683$	10.9763	+	2.94108i	0.419995	+	0.112537i	−0.0426308	+	0.999091i	$0.513574\pi$
$684$		0			0
$685$	1.88531	+	4.24483i	0.0720341	+	0.162187i
$686$	−16.9564	+	46.5874i	−0.647400	+	1.77872i
$687$		0			0
$688$	−1.50810	−	17.2377i	−0.0574959	−	0.657181i
$689$	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	$0.758674\pi$
$692$	56.0412	−	15.0162i	2.13037	−	0.570830i
$693$		0			0
$694$	56.0171	−	32.3415i	2.12638	−	1.22767i
$695$	−11.2078	−	32.6457i	−0.425134	−	1.23832i
$696$		0			0
$697$	−11.4004	+	24.4483i	−0.431822	+	0.926046i
$698$	−11.7362	−	16.7611i	−0.444223	−	0.634416i
$699$		0			0
$700$	41.8558	−	9.58333i	1.58200	−	0.362216i
$701$			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
$707$	8.34079	+	3.88937i	0.313688	+	0.146275i
$708$		0			0
$709$	36.4781	−	6.43207i	1.36996	−	0.241562i	0.560219	−	0.828344i	$-0.310717\pi$
$709$	36.4781	−	6.43207i	1.36996	−	0.241562i	0.809744	+	0.586783i	$0.199606\pi$
$710$	10.2519	−	96.6978i	0.384748	−	3.62900i
$711$		0			0
$712$	−16.9228	−	63.1566i	−0.634207	−	2.36689i
$713$	1.90785	−	0.889647i	0.0714497	−	0.0333175i
$714$		0			0
$715$	0.713275	+	2.87187i	0.0266750	+	0.107402i
$716$	23.1122	−	27.5441i	0.863744	−	1.02937i
$717$		0			0
$718$	−15.7251	−	33.7227i	−0.586857	−	1.25852i
$719$	19.2483	−	33.3390i	0.717839	−	1.24333i	−0.244016	−	0.969771i	$-0.578465\pi$
$719$	19.2483	−	33.3390i	0.717839	−	1.24333i	0.961854	−	0.273562i	$-0.0882018\pi$
$720$		0			0
$721$	3.54064	+	6.13256i	0.131860	+	0.228389i
$722$	−21.5840	+	30.8251i	−0.803273	+	1.14719i
$723$		0			0
$724$	−16.2169	−	44.5557i	−0.602698	−	1.65590i
$725$	−3.85183	−	27.7722i	−0.143053	−	1.03143i
$726$		0			0
$727$	−2.27381	+	25.9897i	−0.0843308	+	0.963906i	0.829686	+	0.558230i	$0.188519\pi$
$727$	−2.27381	+	25.9897i	−0.0843308	+	0.963906i	−0.914017	+	0.405676i	$0.867036\pi$
$728$	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
$733$	39.9276	−	27.9576i	1.47476	−	1.03264i	0.487571	−	0.873083i	$-0.337883\pi$
$733$	39.9276	−	27.9576i	1.47476	−	1.03264i	0.987189	−	0.159555i	$-0.0510060\pi$
$734$	55.2278	−	20.1013i	2.03849	−	0.741951i
$735$		0			0
$736$	1.47374	+	8.35802i	0.0543230	+	0.308081i
$737$	−1.62852	+	6.07772i	−0.0599873	+	0.223876i
$738$		0			0
$739$	11.7531	+	6.78566i	0.432345	+	0.249614i	0.700345	−	0.713804i	$-0.253029\pi$
$739$	11.7531	+	6.78566i	0.432345	+	0.249614i	−0.268000	+	0.963419i	$0.586363\pi$
$740$	−15.0558	+	10.1355i	−0.553464	+	0.372587i
$741$		0			0
$742$	−1.66647	+	0.145797i	−0.0611780	+	0.00535238i
$743$	1.23767	−	0.108282i	0.0454055	−	0.00397247i	−0.0644303	−	0.997922i	$-0.520523\pi$
$743$	1.23767	−	0.108282i	0.0454055	−	0.00397247i	0.109836	+	0.993950i	$0.464967\pi$
$744$		0			0
$745$	−6.74882	+	34.5525i	−0.247257	+	1.26591i
$746$	−31.2331	−	18.0324i	−1.14352	−	0.660214i
$747$		0			0
$748$	2.32338	−	8.67096i	0.0849511	−	0.317042i
$749$	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	$0.439531\pi$
$752$	−144.793	+	101.385i	−5.28005	+	3.69713i
$753$		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	0.0721170	−	0.997396i	$-0.477025\pi$
$757$	29.4262	−	29.4262i	1.06951	−	1.06951i	0.997396	−	0.0721170i	$-0.0229755\pi$
$758$	−6.50993	+	74.4088i	−0.236451	+	2.70265i
$759$		0			0
$760$	33.0147	+	34.2498i	1.19757	+	1.24237i
$761$	−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
$763$	7.67948	−	10.9674i	0.278016	−	0.397048i
$764$	54.7283	+	94.7922i	1.98000	+	3.42946i
$765$		0			0
$766$	−49.2326	+	85.2733i	−1.77884	+	3.08105i
$767$	4.16460	+	8.93101i	0.150375	+	0.322480i
$768$		0			0
$769$	−3.94057	+	4.69619i	−0.142100	+	0.169349i	−0.832401	−	0.554174i	$-0.813034\pi$
$769$	−3.94057	+	4.69619i	−0.142100	+	0.169349i	0.690300	+	0.723523i	$0.257479\pi$
$770$	−3.93629	−	2.37002i	−0.141854	−	0.0854096i
$771$		0			0
$772$	−92.3513	+	43.0641i	−3.32380	+	1.54991i
$773$	2.46257	+	9.19044i	0.0885726	+	0.330557i	0.995967	−	0.0897234i	$-0.0285983\pi$
$773$	2.46257	+	9.19044i	0.0885726	+	0.330557i	−0.907394	+	0.420281i	$0.861932\pi$
$774$		0			0
$775$	19.4078	+	17.5386i	0.697149	+	0.630007i
$776$	−69.6196	+	12.2758i	−2.49920	+	0.440676i
$777$		0			0
$778$	45.6625	+	21.2928i	1.63708	+	0.763382i
$779$	−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
$785$	38.4029	−	2.65043i	1.37066	−	0.0945980i
$786$		0			0
$787$	4.85971	+	6.94038i	0.173230	+	0.247398i	0.896373	−	0.443300i	$-0.146192\pi$
$787$	4.85971	+	6.94038i	0.173230	+	0.247398i	−0.723143	+	0.690698i	$0.757303\pi$
$788$	11.4915	−	24.6435i	0.409367	−	0.877890i
$789$		0			0
$790$	−11.8943	+	24.3309i	−0.423179	+	0.865654i
$791$	−2.98847	+	1.72539i	−0.106258	+	0.0613479i
$792$		0			0
$793$	24.6766	−	6.61207i	0.876291	−	0.234802i
$794$	−77.2406	−	28.1133i	−2.74116	−	0.997702i
$795$		0			0
$796$	−69.2896	−	58.1409i	−2.45591	−	2.06075i
$797$	−2.46530	−	28.1786i	−0.0873256	−	0.998136i	−0.905832	−	0.423638i	$-0.860753\pi$
$797$	−2.46530	−	28.1786i	−0.0873256	−	0.998136i	0.818506	−	0.574498i	$-0.194803\pi$
$798$		0			0
$799$	14.3847	−	39.5216i	0.508894	−	1.39818i
$800$	−88.5517	+	57.2783i	−3.13078	+	2.02510i
$801$		0			0
$802$	−91.6319	−	24.5527i	−3.23564	−	0.866986i
$803$	3.12717	+	2.18967i	0.110355	+	0.0772716i
$804$		0			0
$805$	−1.24601	+	0.689198i	−0.0439160	+	0.0242910i
$806$	38.9984	+	6.87647i	1.37366	+	0.242213i
$807$		0			0
$808$	−54.0909	−	4.73234i	−1.90291	−	0.166483i
$809$	2.28591			0.0803683			0.0401841	−	0.999192i	$-0.487206\pi$
$809$	2.28591			0.0803683			0.0401841	+	0.999192i	$0.487206\pi$
$810$		0			0
$811$	21.6606			0.760605			0.380303	−	0.924862i	$-0.375820\pi$
$811$	21.6606			0.760605			0.380303	+	0.924862i	$0.375820\pi$
$812$	47.9736	+	4.19715i	1.68354	+	0.147291i
$813$		0			0
$814$	1.91260	+	0.337243i	0.0670367	+	0.0118204i
$815$	2.16247	−	7.51572i	0.0757480	−	0.263264i
$816$		0			0
$817$	2.21311	+	1.54964i	0.0774270	+	0.0542150i
$818$	−58.3243	−	15.6279i	−2.03926	−	0.546418i
$819$		0			0
$820$	−87.9763	−	33.8624i	−3.07227	−	1.18253i
$821$	−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
$823$	−0.569178	−	6.50574i	−0.0198403	−	0.226776i	−0.999641	−	0.0267986i	$-0.991469\pi$
$823$	−0.569178	−	6.50574i	−0.0198403	−	0.226776i	0.979801	−	0.199977i	$-0.0640868\pi$
$824$	−32.0047	−	26.8552i	−1.11494	−	0.935544i
$825$		0			0
$826$	−14.3783	−	5.23326i	−0.500284	−	0.182088i
$827$	−8.94494	+	2.39679i	−0.311046	+	0.0833445i	−0.410965	−	0.911651i	$-0.634808\pi$
$827$	−8.94494	+	2.39679i	−0.311046	+	0.0833445i	0.0999193	+	0.994996i	$0.468142\pi$
$828$		0			0
$829$	2.45210	−	1.41572i	0.0851648	−	0.0491699i	−0.456813	−	0.889563i	$-0.651009\pi$
$829$	2.45210	−	1.41572i	0.0851648	−	0.0491699i	0.541978	+	0.840393i	$0.317676\pi$
$830$	16.7899	−	5.76422i	0.582786	−	0.200079i
$831$		0			0
$832$	−33.2132	+	71.2260i	−1.15146	+	2.46932i
$833$	8.95278	+	12.7859i	0.310195	+	0.443005i
$834$		0			0
$835$	−1.01432	−	14.6968i	−0.0351020	−	0.508603i
$836$		−	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	0.121739	−	0.992562i	$-0.461153\pi$
$839$	32.4518	−	27.2303i	1.12036	−	0.940095i	0.998623	+	0.0524668i	$0.0167084\pi$
$840$		0			0
$841$	0.424617	−	2.40812i	0.0146420	−	0.0830387i
$842$	32.5451	+	15.1760i	1.12158	+	0.523000i
$843$		0			0
$844$	55.8394	−	9.84600i	1.92207	−	0.338913i
$845$	−7.42892	−	9.19097i	−0.255563	−	0.316179i
$846$		0			0
$847$	−4.41271	−	16.4684i	−0.151622	−	0.565862i
$848$	5.12983	−	2.39208i	0.176159	−	0.0821443i
$849$		0			0
$850$	17.8024	−	43.8335i	0.610616	−	1.50348i
$851$	0.386871	−	0.461054i	0.0132618	−	0.0158047i
$852$		0			0
$853$	14.0780	+	30.1905i	0.482023	+	1.03370i	0.985497	+	0.169691i	$0.0542771\pi$
$853$	14.0780	+	30.1905i	0.482023	+	1.03370i	−0.503474	+	0.864010i	$0.667945\pi$
$854$	−19.8339	+	34.3532i	−0.678701	+	1.17554i
$855$		0			0
$856$	−3.81582	−	6.60919i	−0.130422	−	0.225897i
$857$	17.6306	−	25.1791i	0.602249	−	0.860100i	−0.396061	−	0.918224i	$-0.629623\pi$
$857$	17.6306	−	25.1791i	0.602249	−	0.860100i	0.998309	+	0.0581240i	$0.0185119\pi$
$858$		0			0
$859$	17.6716	+	48.5522i	0.602946	+	1.65658i	0.745272	+	0.666760i	$0.232320\pi$
$859$	17.6716	+	48.5522i	0.602946	+	1.65658i	−0.142326	+	0.989820i	$0.545458\pi$
$860$	−10.3588	+	9.98522i	−0.353231	+	0.340493i
$861$		0			0
$862$	3.44791	−	39.4098i	0.117436	−	1.34230i
$863$	31.9076	−	31.9076i	1.08615	−	1.08615i	0.0902264	−	0.995921i	$-0.471241\pi$
$863$	31.9076	−	31.9076i	1.08615	−	1.08615i	0.995921	−	0.0902264i	$-0.0287591\pi$
$864$		0			0
$865$	−19.3291	−	14.0702i	−0.657209	−	0.478401i
$866$	−41.2086	−	49.1104i	−1.40032	−	1.66884i
$867$		0			0
$868$	−36.8034	+	25.7700i	−1.24919	+	0.874692i
$869$	1.98983	−	0.724239i	0.0675003	−	0.0245681i
$870$		0			0
$871$	6.36968	+	36.1243i	0.215829	+	1.22402i
$872$	−20.4449	+	76.3015i	−0.692353	+	2.58390i
$873$		0			0
$874$	−2.16363	−	1.24917i	−0.0731860	−	0.0422539i
$875$	−13.9134	−	10.9314i	−0.470360	−	0.369549i
$876$		0			0
$877$	39.1615	−	3.42618i	1.32239	−	0.115694i	0.596003	−	0.802982i	$-0.296755\pi$
$877$	39.1615	−	3.42618i	1.32239	−	0.115694i	0.726385	+	0.687288i	$0.241199\pi$
$878$	−58.6873	+	5.13448i	−1.98060	+	0.173280i
$879$		0			0
$880$	15.2582	+	2.98024i	0.514353	+	0.100464i
$881$	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
$883$	−4.64284	+	17.3273i	−0.156244	+	0.583111i	0.842752	+	0.538303i	$0.180934\pi$
$883$	−4.64284	+	17.3273i	−0.156244	+	0.583111i	−0.998996	+	0.0448081i	$0.985732\pi$
$884$	−9.08751	−	51.5378i	−0.305646	−	1.73340i
$885$		0			0
$886$	−30.7381	+	11.1878i	−1.03267	+	0.375860i
$887$	14.2556	−	9.98188i	0.478656	−	0.335159i	−0.309222	−	0.950990i	$-0.600069\pi$
$887$	14.2556	−	9.98188i	0.478656	−	0.335159i	0.787878	+	0.615831i	$0.211180\pi$
$888$		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
$893$	2.40537	−	27.4935i	0.0804927	−	0.920036i
$894$		0			0
$895$	−14.8142	−	0.272007i	−0.495183	−	0.00909219i
$896$	−18.9021	−	51.9330i	−0.631474	−	1.73496i
$897$		0			0
$898$	−47.3215	+	67.5821i	−1.57914	+	2.25524i
$899$	14.6687	+	25.4069i	0.489227	+	0.847367i
$900$		0			0
$901$	−0.673386	+	1.16634i	−0.0224337	+	0.0388564i
$902$	4.26306	+	9.14216i	0.141944	+	0.304401i
$903$		0			0
$904$	13.0868	−	15.5963i	0.435261	−	0.518724i
$905$	−10.0783	+	16.7387i	−0.335014	+	0.556415i
$906$		0			0
$907$	−17.8896	+	8.34207i	−0.594015	+	0.276994i	−0.696288	−	0.717763i	$-0.745166\pi$
$907$	−17.8896	+	8.34207i	−0.594015	+	0.276994i	0.102273	+	0.994756i	$0.467389\pi$
$908$	28.1141	+	104.923i	0.932999	+	3.48200i
$909$		0			0
$910$	−26.6368	−	2.82404i	−0.883002	−	0.0936161i
$911$	−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
$913$	−1.25794	−	0.586586i	−0.0416317	−	0.0194132i
$914$	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	$0.0310515\pi$
$919$			5.90514i			0.194793i	−0.995246	+	0.0973964i	$0.968949\pi$
$920$	5.51731	−	6.33534i	0.181900	−	0.208870i
$921$		0			0
$922$	26.9715	+	38.5192i	0.888258	+	1.26856i
$923$	−18.7320	+	40.1708i	−0.616570	+	1.32224i
$924$		0			0
$925$	7.14820	+	2.19959i	0.235031	+	0.0723222i
$926$	−38.9006	+	22.4592i	−1.27835	+	0.738057i
$927$		0			0
$928$	−114.248	+	30.6126i	−3.75036	+	1.00491i
$929$	6.36097	+	2.31520i	0.208697	+	0.0759593i	0.444253	−	0.895901i	$-0.353469\pi$
$929$	6.36097	+	2.31520i	0.208697	+	0.0759593i	−0.235557	+	0.971861i	$0.575691\pi$
$930$		0			0
$931$	7.84617	+	6.58371i	0.257148	+	0.215773i
$932$	−8.83124	−	100.942i	−0.289277	−	3.30645i
$933$		0			0
$934$	−3.70965	+	10.1922i	−0.121383	+	0.333498i
$935$	−3.38069	+	1.50151i	−0.110560	+	0.0491046i
$936$		0			0
$937$	6.08835	+	1.63137i	0.198898	+	0.0532945i	0.356892	−	0.934145i	$-0.383836\pi$
$937$	6.08835	+	1.63137i	0.198898	+	0.0532945i	−0.157995	+	0.987440i	$0.550503\pi$
$938$	−46.6560	−	32.6689i	−1.52337	−	1.06668i
$939$		0			0
$940$	141.244	+	40.6396i	4.60687	+	1.32552i
$941$	−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
$943$	3.11417	+	0.272455i	0.101411	+	0.00887234i
$944$	51.7720			1.68504
$945$		0			0
$946$	1.53958			0.0500560
$947$	−48.0728	−	4.20583i	−1.56216	−	0.136671i	−0.726982	−	0.686656i	$-0.759078\pi$
$947$	−48.0728	−	4.20583i	−1.56216	−	0.136671i	−0.835174	+	0.549985i	$0.814633\pi$
$948$		0			0
$949$	21.9174	+	3.86463i	0.711469	+	0.125451i
$950$	3.83930	−	30.8070i	0.124563	−	0.999512i
$951$		0			0
$952$	42.0300	+	29.4297i	1.36220	+	0.953822i
$953$	18.9362	+	5.07394i	0.613404	+	0.164361i	0.552128	−	0.833760i	$-0.313816\pi$
$953$	18.9362	+	5.07394i	0.613404	+	0.164361i	0.0612767	+	0.998121i	$0.480483\pi$
$954$		0			0
$955$	16.2021	−	42.0939i	0.524287	−	1.36213i
$956$	36.2153	−	99.5008i	1.17129	−	3.21809i
$957$		0			0
$958$	0.336795	+	3.84959i	0.0108814	+	0.124375i
$959$	2.51823	+	2.11305i	0.0813180	+	0.0682339i
$960$		0			0
$961$	3.41043	+	1.24130i	0.110014	+	0.0400418i
$962$	10.9362	−	2.93036i	0.352599	−	0.0944785i
$963$		0			0
$964$	−23.1268	+	13.3523i	−0.744865	+	0.430048i
$965$	37.7235	+	18.4413i	1.21436	+	0.593646i
$966$		0			0
$967$	−1.83617	+	3.93769i	−0.0590474	+	0.126628i	−0.933617	−	0.358272i	$-0.883366\pi$
$967$	−1.83617	+	3.93769i	−0.0590474	+	0.126628i	0.874570	+	0.484900i	$0.161144\pi$
$968$	57.6964	+	82.3990i	1.85443	+	2.64841i
$969$		0			0
$970$	34.7912	+	30.2989i	1.11708	+	0.972840i
$971$		−	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
$977$	−21.9259	−	10.2242i	−0.701470	−	0.327101i	0.0389538	−	0.999241i	$-0.487597\pi$
$977$	−21.9259	−	10.2242i	−0.701470	−	0.327101i	−0.740424	+	0.672140i	$0.765375\pi$
$978$		0			0
$979$	3.28563	−	0.579345i	0.105009	−	0.0185159i
$980$	−42.4209	+	34.2882i	−1.35508	+	1.09530i
$981$		0			0
$982$	18.9055	+	70.5563i	0.603299	+	2.25154i
$983$	−22.0159	+	10.2662i	−0.702199	+	0.327441i	−0.740717	−	0.671817i	$-0.765514\pi$
$983$	−22.0159	+	10.2662i	−0.702199	+	0.327441i	0.0385180	+	0.999258i	$0.487736\pi$
$984$		0			0
$985$	−10.8744	+	2.70083i	−0.346488	+	0.0860557i
$986$	34.1063	−	40.6463i	1.08617	−	1.29444i
$987$		0			0
$988$	−14.5131	−	31.1234i	−0.461723	−	0.990168i
$989$	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	$-0.361032\pi$
$992$	63.2936	−	90.3927i	2.00957	−	2.86997i
$993$		0			0
$994$	−23.5387	−	64.6720i	−0.746602	−	2.05127i
$995$	−0.684258	+	37.2664i	−0.0216924	+	1.18142i
$996$		0			0
$997$	1.73962	−	19.8840i	0.0550944	−	0.629732i	−0.917579	−	0.397554i	$-0.869859\pi$
$997$	1.73962	−	19.8840i	0.0550944	−	0.629732i	0.972673	−	0.232178i	$-0.0745853\pi$
$998$	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.368.16		192
3.2	odd	2		135.2.q.a.113.1	yes	192
5.2	odd	4	inner	405.2.r.a.287.1		192
15.2	even	4		135.2.q.a.32.16	✓	192
15.8	even	4		675.2.ba.b.32.1		192
15.14	odd	2		675.2.ba.b.518.16		192
27.11	odd	18	inner	405.2.r.a.278.1		192
27.16	even	9		135.2.q.a.38.16	yes	192
135.43	odd	36		675.2.ba.b.632.16		192
135.92	even	36	inner	405.2.r.a.197.16		192
135.97	odd	36		135.2.q.a.92.1	yes	192
135.124	even	18		675.2.ba.b.443.1		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.32.16	✓	192	15.2	even	4
135.2.q.a.38.16	yes	192	27.16	even	9
135.2.q.a.92.1	yes	192	135.97	odd	36
135.2.q.a.113.1	yes	192	3.2	odd	2
405.2.r.a.197.16		192	135.92	even	36	inner
405.2.r.a.278.1		192	27.11	odd	18	inner
405.2.r.a.287.1		192	5.2	odd	4	inner
405.2.r.a.368.16		192	1.1	even	1	trivial
675.2.ba.b.32.1		192	15.8	even	4
675.2.ba.b.443.1		192	135.124	even	18
675.2.ba.b.518.16		192	15.14	odd	2
675.2.ba.b.632.16		192	135.43	odd	36

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

\(f(q)\)	\(=\)	\(q+(2.71476 + 0.237511i) q^{2} +(5.34392 + 0.942278i) q^{4} +(-1.08230 - 1.95669i) q^{5} +(-1.29639 - 0.907744i) q^{7} +(9.01913 + 2.41667i) q^{8} +O(q^{10})\)	\(q+(2.71476 + 0.237511i) q^{2} +(5.34392 + 0.942278i) q^{4} +(-1.08230 - 1.95669i) q^{5} +(-1.29639 - 0.907744i) q^{7} +(9.01913 + 2.41667i) q^{8} +(-2.47344 - 5.56901i) q^{10} +(-0.162954 + 0.447712i) q^{11} +(0.242081 + 2.76700i) q^{13} +(-3.30380 - 2.77222i) q^{14} +(13.7126 + 4.99098i) q^{16} +(-3.35386 + 0.898665i) q^{17} +(-1.97319 + 1.13922i) q^{19} +(-3.93995 - 11.4762i) q^{20} +(-0.548719 + 1.17673i) q^{22} +(0.230790 + 0.329603i) q^{23} +(-2.65727 + 4.23543i) q^{25} +7.56924i q^{26} +(-6.07248 - 6.07248i) q^{28} +(-4.29568 + 3.60450i) q^{29} +(0.908475 - 5.15222i) q^{31} +(19.1162 + 8.91403i) q^{32} +(-9.31839 + 1.64308i) q^{34} +(-0.373094 + 3.51909i) q^{35} +(-0.387140 - 1.44483i) q^{37} +(-5.62733 + 2.62407i) q^{38} +(-5.03269 - 20.2632i) q^{40} +(4.99389 - 5.95149i) q^{41} +(-0.501128 - 1.07467i) q^{43} +(-1.29268 + 2.23899i) q^{44} +(0.548257 + 0.949609i) q^{46} +(-6.94767 + 9.92230i) q^{47} +(-1.53751 - 4.22426i) q^{49} +(-8.21984 + 10.8671i) q^{50} +(-1.31362 + 15.0147i) q^{52} +(0.274270 - 0.274270i) q^{53} +(1.05240 - 0.165706i) q^{55} +(-9.49862 - 11.3200i) q^{56} +(-12.5179 + 8.76510i) q^{58} +(3.33385 - 1.21342i) q^{59} +(-1.59716 - 9.05792i) q^{61} +(3.69001 - 13.7713i) q^{62} +(24.5036 + 14.1471i) q^{64} +(5.15215 - 3.46838i) q^{65} +(13.1561 - 1.15101i) q^{67} +(-18.7696 + 1.64212i) q^{68} +(-1.84869 + 9.46488i) q^{70} +(13.8198 + 7.97886i) q^{71} +(2.07381 - 7.73957i) q^{73} +(-0.707832 - 4.01431i) q^{74} +(-11.6180 + 4.22862i) q^{76} +(0.617661 - 0.432491i) q^{77} +(-2.85683 - 3.40464i) q^{79} +(-5.07529 - 32.2331i) q^{80} +(14.9708 - 14.9708i) q^{82} +(-0.253902 + 2.90211i) q^{83} +(5.38828 + 5.58985i) q^{85} +(-1.10520 - 3.03651i) q^{86} +(-2.55168 + 3.64417i) q^{88} +(-3.50126 - 6.06435i) q^{89} +(2.19789 - 3.80686i) q^{91} +(0.922748 + 1.97884i) q^{92} +(-21.2179 + 25.2866i) q^{94} +(4.36468 + 2.62795i) q^{95} +(-6.86175 + 3.19969i) q^{97} +(-3.17066 - 11.8331i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) \) 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8	\( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35} - 6 q^{37} - 12 q^{38} - 36 q^{40} - 24 q^{41} - 12 q^{43} - 12 q^{46} + 6 q^{47} - 36 q^{50} + 12 q^{52} - 24 q^{55} - 180 q^{56} - 12 q^{58} - 60 q^{61} + 18 q^{62} + 84 q^{65} + 24 q^{67} + 60 q^{68} - 12 q^{70} + 36 q^{71} - 6 q^{73} - 72 q^{76} - 132 q^{77} - 24 q^{82} - 48 q^{83} - 12 q^{85} - 12 q^{86} - 48 q^{88} - 12 q^{91} - 258 q^{92} - 18 q^{95} + 24 q^{97} - 324 q^{98}+O(q^{100}) \) 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

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more