LMFDB - Embedded newform 270.2.m.b.17.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [270,2,Mod(17,270)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(270, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 3]))

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

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

chi := DirichletCharacter("270.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 270 = 2 \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	270.m (of order $12$, degree $4$, 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:	$2.15596085457$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	16.0.9349208943630483456.9
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 48 x^{14} - 196 x^{13} + 642 x^{12} - 1668 x^{11} + 3580 x^{10} - 6328 x^{9} + \cdots + 25 $ x^16 - 8x^15 + 48x^14 - 196x^13 + 642x^12 - 1668x^11 + 3580x^10 - 6328x^9 + 9297x^8 - 11276x^7 + 11224x^6 - 9024x^5 + 5736x^4 - 2780x^3 + 972x^2 - 220*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			17.3
Root			$0.500000 + 2.00333i$ of defining polynomial
Character	$\chi$	$=$	270.17
Dual form			270.2.m.b.143.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 + 0.258819i) q^{2} +(0.866025 + 0.500000i) q^{4} +(0.139908 + 2.23169i) q^{5} +(-0.622279 + 2.32238i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(0.965926 + 0.258819i) q^{2} +(0.866025 + 0.500000i) q^{4} +(0.139908 + 2.23169i) q^{5} +(-0.622279 + 2.32238i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.442462 + 2.19185i) q^{10} +(-0.991757 + 0.572591i) q^{11} +(-0.640322 - 2.38971i) q^{13} +(-1.20215 + 2.08219i) q^{14} +(0.500000 + 0.866025i) q^{16} +(4.99855 - 4.99855i) q^{17} +2.78390i q^{19} +(-0.994679 + 2.00265i) q^{20} +(-1.10616 + 0.296395i) q^{22} +(5.95746 - 1.59630i) q^{23} +(-4.96085 + 0.624462i) q^{25} -2.47401i q^{26} +(-1.70010 + 1.70010i) q^{28} +(-0.672250 - 1.16437i) q^{29} +(1.25223 - 2.16892i) q^{31} +(0.258819 + 0.965926i) q^{32} +(6.12195 - 3.53451i) q^{34} +(-5.26988 - 1.06381i) q^{35} +(-8.16761 - 8.16761i) q^{37} +(-0.720527 + 2.68904i) q^{38} +(-1.47911 + 1.67697i) q^{40} +(1.70826 + 0.986264i) q^{41} +(8.68498 + 2.32713i) q^{43} -1.14518 q^{44} +6.16761 q^{46} +(-11.9118 - 3.19175i) q^{47} +(1.05598 + 0.609669i) q^{49} +(-4.95344 - 0.680779i) q^{50} +(0.640322 - 2.38971i) q^{52} +(-1.84828 - 1.84828i) q^{53} +(-1.41660 - 2.13318i) q^{55} +(-2.08219 + 1.20215i) q^{56} +(-0.347982 - 1.29869i) q^{58} +(-1.31456 + 2.27688i) q^{59} +(-3.54275 - 6.13623i) q^{61} +(1.77092 - 1.77092i) q^{62} +1.00000i q^{64} +(5.24351 - 1.76334i) q^{65} +(0.0545285 - 0.0146109i) q^{67} +(6.82815 - 1.82960i) q^{68} +(-4.81498 - 2.39151i) q^{70} +9.10005i q^{71} +(7.82779 - 7.82779i) q^{73} +(-5.77537 - 10.0032i) q^{74} +(-1.39195 + 2.41093i) q^{76} +(-0.712623 - 2.65955i) q^{77} +(-8.46375 + 4.88655i) q^{79} +(-1.86274 + 1.23701i) q^{80} +(1.39479 + 1.39479i) q^{82} +(-0.724794 + 2.70497i) q^{83} +(11.8545 + 10.4559i) q^{85} +(7.78674 + 4.49568i) q^{86} +(-1.10616 - 0.296395i) q^{88} +4.87832 q^{89} +5.94827 q^{91} +(5.95746 + 1.59630i) q^{92} +(-10.6798 - 6.16599i) q^{94} +(-6.21280 + 0.389491i) q^{95} +(2.08981 - 7.79929i) q^{97} +(0.862203 + 0.862203i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{5} + 8 q^{7}+O(q^{10}) $ 16 * q + 12 * q^5 + 8 * q^7	$ 16 q + 12 q^{5} + 8 q^{7} - 8 q^{10} + 8 q^{16} + 12 q^{20} + 8 q^{22} + 24 q^{23} - 16 q^{25} - 16 q^{28} - 8 q^{31} - 24 q^{38} - 4 q^{40} - 24 q^{41} - 32 q^{46} - 48 q^{47} - 24 q^{50} + 24 q^{55} - 24 q^{56} + 16 q^{58} - 24 q^{61} - 16 q^{67} + 24 q^{68} + 16 q^{70} + 16 q^{73} + 16 q^{76} + 72 q^{77} - 16 q^{82} - 48 q^{83} - 4 q^{85} + 48 q^{86} + 8 q^{88} + 24 q^{92} - 84 q^{95} - 48 q^{97}+O(q^{100}) $ 16 * q + 12 * q^5 + 8 * q^7 - 8 * q^10 + 8 * q^16 + 12 * q^20 + 8 * q^22 + 24 * q^23 - 16 * q^25 - 16 * q^28 - 8 * q^31 - 24 * q^38 - 4 * q^40 - 24 * q^41 - 32 * q^46 - 48 * q^47 - 24 * q^50 + 24 * q^55 - 24 * q^56 + 16 * q^58 - 24 * q^61 - 16 * q^67 + 24 * q^68 + 16 * q^70 + 16 * q^73 + 16 * q^76 + 72 * q^77 - 16 * q^82 - 48 * q^83 - 4 * q^85 + 48 * q^86 + 8 * q^88 + 24 * q^92 - 84 * q^95 - 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/270\mathbb{Z}\right)^\times$.

$n$	$191$	$217$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$3$		0			0
$3$		0			0
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	0.139908	+	2.23169i	0.0625688	+	0.998041i
$5$	0.139908	+	2.23169i	0.0625688	+	0.998041i
$6$		0			0
$7$	−0.622279	+	2.32238i	−0.235199	+	0.877776i	0.742860	+	0.669447i	$0.233469\pi$
$7$	−0.622279	+	2.32238i	−0.235199	+	0.877776i	−0.978059	+	0.208328i	$0.933198\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		0			0
$10$	−0.442462	+	2.19185i	−0.139919	+	0.693125i
$11$	−0.991757	+	0.572591i	−0.299026	+	0.172643i	−0.642005	−	0.766700i	$-0.721897\pi$
$11$	−0.991757	+	0.572591i	−0.299026	+	0.172643i	0.342979	+	0.939343i	$0.388564\pi$
$12$		0			0
$13$	−0.640322	−	2.38971i	−0.177593	−	0.662788i	−0.996095	−	0.0882838i	$-0.971862\pi$
$13$	−0.640322	−	2.38971i	−0.177593	−	0.662788i	0.818502	−	0.574504i	$-0.194805\pi$
$14$	−1.20215	+	2.08219i	−0.321288	+	0.556487i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	4.99855	−	4.99855i	1.21233	−	1.21233i	0.242068	−	0.970259i	$-0.422174\pi$
$17$	4.99855	−	4.99855i	1.21233	−	1.21233i	0.970259	−	0.242068i	$-0.0778258\pi$
$18$		0			0
$19$			2.78390i			0.638671i	0.947642	+	0.319336i	$0.103460\pi$
$19$			2.78390i			0.638671i	−0.947642	+	0.319336i	$0.896540\pi$
$20$	−0.994679	+	2.00265i	−0.222417	+	0.447806i
$21$		0			0
$22$	−1.10616	+	0.296395i	−0.235834	+	0.0631917i
$23$	5.95746	−	1.59630i	1.24222	−	0.332851i	0.422891	−	0.906181i	$-0.361015\pi$
$23$	5.95746	−	1.59630i	1.24222	−	0.332851i	0.819325	+	0.573330i	$0.194349\pi$
$24$		0			0
$25$	−4.96085	+	0.624462i	−0.992170	+	0.124892i
$26$		−	2.47401i		−	0.485194i
$27$		0			0
$28$	−1.70010	+	1.70010i	−0.321288	+	0.321288i
$29$	−0.672250	−	1.16437i	−0.124834	−	0.216218i	0.796834	−	0.604198i	$-0.206506\pi$
$29$	−0.672250	−	1.16437i	−0.124834	−	0.216218i	−0.921668	+	0.387980i	$0.873173\pi$
$30$		0			0
$31$	1.25223	−	2.16892i	0.224907	−	0.389550i	−0.731385	−	0.681965i	$-0.761126\pi$
$31$	1.25223	−	2.16892i	0.224907	−	0.389550i	0.956292	+	0.292415i	$0.0944589\pi$
$32$	0.258819	+	0.965926i	0.0457532	+	0.170753i
$33$		0			0
$34$	6.12195	−	3.53451i	1.04991	−	0.606164i
$35$	−5.26988	−	1.06381i	−0.890772	−	0.179817i
$36$		0			0
$37$	−8.16761	−	8.16761i	−1.34275	−	1.34275i	−0.893314	−	0.449434i	$-0.851626\pi$
$37$	−8.16761	−	8.16761i	−1.34275	−	1.34275i	−0.449434	−	0.893314i	$-0.648374\pi$
$38$	−0.720527	+	2.68904i	−0.116885	+	0.436221i
$39$		0			0
$40$	−1.47911	+	1.67697i	−0.233868	+	0.265152i
$41$	1.70826	+	0.986264i	0.266785	+	0.154029i	0.627426	−	0.778676i	$-0.284109\pi$
$41$	1.70826	+	0.986264i	0.266785	+	0.154029i	−0.360641	+	0.932705i	$0.617442\pi$
$42$		0			0
$43$	8.68498	+	2.32713i	1.32445	+	0.354885i	0.850642	−	0.525745i	$-0.176213\pi$
$43$	8.68498	+	2.32713i	1.32445	+	0.354885i	0.473805	+	0.880630i	$0.342880\pi$
$44$	−1.14518			−0.172643
$45$		0			0
$46$	6.16761			0.909365
$47$	−11.9118	−	3.19175i	−1.73751	−	0.465565i	−0.755621	−	0.655010i	$-0.772665\pi$
$47$	−11.9118	−	3.19175i	−1.73751	−	0.465565i	−0.981891	+	0.189445i	$0.939331\pi$
$48$		0			0
$49$	1.05598	+	0.609669i	0.150854	+	0.0870956i
$50$	−4.95344	−	0.680779i	−0.700522	−	0.0962767i
$51$		0			0
$52$	0.640322	−	2.38971i	0.0887967	−	0.331394i
$53$	−1.84828	−	1.84828i	−0.253881	−	0.253881i	0.568679	−	0.822560i	$-0.307455\pi$
$53$	−1.84828	−	1.84828i	−0.253881	−	0.253881i	−0.822560	+	0.568679i	$0.807455\pi$
$54$		0			0
$55$	−1.41660	−	2.13318i	−0.191014	−	0.287638i
$56$	−2.08219	+	1.20215i	−0.278244	+	0.160644i
$57$		0			0
$58$	−0.347982	−	1.29869i	−0.0456923	−	0.170526i
$59$	−1.31456	+	2.27688i	−0.171141	+	0.296424i	−0.938819	−	0.344411i	$-0.888079\pi$
$59$	−1.31456	+	2.27688i	−0.171141	+	0.296424i	0.767678	+	0.640835i	$0.221412\pi$
$60$		0			0
$61$	−3.54275	−	6.13623i	−0.453603	−	0.785664i	0.545004	−	0.838434i	$-0.316528\pi$
$61$	−3.54275	−	6.13623i	−0.453603	−	0.785664i	−0.998607	+	0.0527700i	$0.983195\pi$
$62$	1.77092	−	1.77092i	0.224907	−	0.224907i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	5.24351	−	1.76334i	0.650377	−	0.218715i
$66$		0			0
$67$	0.0545285	−	0.0146109i	0.00666172	−	0.00178500i	−0.255487	−	0.966813i	$-0.582236\pi$
$67$	0.0545285	−	0.0146109i	0.00666172	−	0.00178500i	0.262148	+	0.965028i	$0.415569\pi$
$68$	6.82815	−	1.82960i	0.828035	−	0.221871i
$69$		0			0
$70$	−4.81498	−	2.39151i	−0.575500	−	0.285840i
$71$			9.10005i			1.07998i	0.841672	+	0.539989i	$0.181571\pi$
$71$			9.10005i			1.07998i	−0.841672	+	0.539989i	$0.818429\pi$
$72$		0			0
$73$	7.82779	−	7.82779i	0.916174	−	0.916174i	−0.0805747	−	0.996749i	$-0.525676\pi$
$73$	7.82779	−	7.82779i	0.916174	−	0.916174i	0.996749	+	0.0805747i	$0.0256756\pi$
$74$	−5.77537	−	10.0032i	−0.671374	−	1.16285i
$75$		0			0
$76$	−1.39195	+	2.41093i	−0.159668	+	0.276553i
$77$	−0.712623	−	2.65955i	−0.0812109	−	0.303083i
$78$		0			0
$79$	−8.46375	+	4.88655i	−0.952246	+	0.549779i	−0.893778	−	0.448510i	$-0.851955\pi$
$79$	−8.46375	+	4.88655i	−0.952246	+	0.549779i	−0.0584679	+	0.998289i	$0.518622\pi$
$80$	−1.86274	+	1.23701i	−0.208261	+	0.138302i
$81$		0			0
$82$	1.39479	+	1.39479i	0.154029	+	0.154029i
$83$	−0.724794	+	2.70497i	−0.0795565	+	0.296909i	−0.994228	−	0.107290i	$-0.965783\pi$
$83$	−0.724794	+	2.70497i	−0.0795565	+	0.296909i	0.914671	+	0.404198i	$0.132449\pi$
$84$		0			0
$85$	11.8545	+	10.4559i	1.28581	+	1.13410i
$86$	7.78674	+	4.49568i	0.839666	+	0.484781i
$87$		0			0
$88$	−1.10616	−	0.296395i	−0.117917	−	0.0315958i
$89$	4.87832			0.517100			0.258550	−	0.965998i	$-0.416755\pi$
$89$	4.87832			0.517100			0.258550	+	0.965998i	$0.416755\pi$
$90$		0			0
$91$	5.94827			0.623549
$92$	5.95746	+	1.59630i	0.621108	+	0.166425i
$93$		0			0
$94$	−10.6798	−	6.16599i	−1.10154	−	0.635974i
$95$	−6.21280	+	0.389491i	−0.637420	+	0.0399609i
$96$		0			0
$97$	2.08981	−	7.79929i	0.212188	−	0.791898i	−0.774949	−	0.632024i	$-0.782225\pi$
$97$	2.08981	−	7.79929i	0.212188	−	0.791898i	0.987137	−	0.159874i	$-0.0511088\pi$
$98$	0.862203	+	0.862203i	0.0870956	+	0.0870956i
$99$		0			0
$100$	−4.60845	−	1.93963i	−0.460845	−	0.193963i
$101$	0.631074	−	0.364351i	0.0627942	−	0.0362543i	−0.468274	−	0.883583i	$-0.655124\pi$
$101$	0.631074	−	0.364351i	0.0627942	−	0.0362543i	0.531068	+	0.847329i	$0.321791\pi$
$102$		0			0
$103$	0.353393	+	1.31888i	0.0348209	+	0.129953i	0.981148	−	0.193256i	$-0.0619048\pi$
$103$	0.353393	+	1.31888i	0.0348209	+	0.129953i	−0.946327	+	0.323209i	$0.895238\pi$
$104$	1.23701	−	2.14256i	0.121299	−	0.210095i
$105$		0			0
$106$	−1.30693	−	2.26367i	−0.126940	−	0.219867i
$107$	0.399208	−	0.399208i	0.0385929	−	0.0385929i	−0.687547	−	0.726140i	$-0.741312\pi$
$107$	0.399208	−	0.399208i	0.0385929	−	0.0385929i	0.726140	+	0.687547i	$0.241312\pi$
$108$		0			0
$109$			13.5974i			1.30239i	0.758909	+	0.651196i	$0.225732\pi$
$109$			13.5974i			1.30239i	−0.758909	+	0.651196i	$0.774268\pi$
$110$	−0.816222	−	2.42714i	−0.0778237	−	0.231419i
$111$		0			0
$112$	−2.32238	+	0.622279i	−0.219444	+	0.0587998i
$113$	−4.94392	+	1.32472i	−0.465084	+	0.124619i	−0.483749	−	0.875207i	$-0.660725\pi$
$113$	−4.94392	+	1.32472i	−0.465084	+	0.124619i	0.0186645	+	0.999826i	$0.494059\pi$
$114$		0			0
$115$	4.39593	+	13.0718i	0.409922	+	1.21896i
$116$		−	1.34450i		−	0.124834i
$117$		0			0
$118$	−1.85906	+	1.85906i	−0.171141	+	0.171141i
$119$	8.49803	+	14.7190i	0.779013	+	1.34929i
$120$		0			0
$121$	−4.84428	+	8.39054i	−0.440389	+	0.762776i
$122$	−1.83386	−	6.84408i	−0.166030	−	0.619633i
$123$		0			0
$124$	2.16892	−	1.25223i	0.194775	−	0.112453i
$125$	−2.08767	−	10.9837i	−0.186727	−	0.982412i
$126$		0			0
$127$	−4.88817	−	4.88817i	−0.433755	−	0.433755i	0.456149	−	0.889904i	$-0.349228\pi$
$127$	−4.88817	−	4.88817i	−0.433755	−	0.433755i	−0.889904	+	0.456149i	$0.849228\pi$
$128$	−0.258819	+	0.965926i	−0.0228766	+	0.0853766i
$129$		0			0
$130$	5.52123	−	0.346135i	0.484244	−	0.0303580i
$131$	−4.98351	−	2.87723i	−0.435412	−	0.251385i	0.266238	−	0.963907i	$-0.414219\pi$
$131$	−4.98351	−	2.87723i	−0.435412	−	0.251385i	−0.701649	+	0.712522i	$0.747553\pi$
$132$		0			0
$133$	−6.46527	−	1.73236i	−0.560610	−	0.150215i
$134$	0.0564521			0.00487672
$135$		0			0
$136$	7.06902			0.606164
$137$	10.0458	+	2.69177i	0.858272	+	0.229973i	0.661010	−	0.750377i	$-0.270128\pi$
$137$	10.0458	+	2.69177i	0.858272	+	0.229973i	0.197262	+	0.980351i	$0.436795\pi$
$138$		0			0
$139$	−2.19537	−	1.26750i	−0.186209	−	0.107508i	0.403998	−	0.914760i	$-0.367620\pi$
$139$	−2.19537	−	1.26750i	−0.186209	−	0.107508i	−0.590207	+	0.807252i	$0.700954\pi$
$140$	−4.03194	−	3.55623i	−0.340761	−	0.300556i
$141$		0			0
$142$	−2.35527	+	8.78997i	−0.197650	+	0.737638i
$143$	2.00337	+	2.00337i	0.167531	+	0.167531i
$144$		0			0
$145$	2.50446	−	1.66316i	0.207984	−	0.138118i
$146$	9.58705	−	5.53509i	0.793430	−	0.458087i
$147$		0			0
$148$	−2.98955	−	11.1572i	−0.245740	−	0.917114i
$149$	−6.49294	+	11.2461i	−0.531922	+	0.921316i	0.467384	+	0.884055i	$0.345197\pi$
$149$	−6.49294	+	11.2461i	−0.531922	+	0.921316i	−0.999306	+	0.0372613i	$0.988137\pi$
$150$		0			0
$151$	1.58502	+	2.74534i	0.128987	+	0.223412i	0.923284	−	0.384117i	$-0.125494\pi$
$151$	1.58502	+	2.74534i	0.128987	+	0.223412i	−0.794297	+	0.607529i	$0.792161\pi$
$152$	−1.96852	+	1.96852i	−0.159668	+	0.159668i
$153$		0			0
$154$		−	2.75336i		−	0.221872i
$155$	5.01556	+	2.49113i	0.402859	+	0.200093i
$156$		0			0
$157$	10.3186	−	2.76487i	0.823515	−	0.220660i	0.177633	−	0.984097i	$-0.443156\pi$
$157$	10.3186	−	2.76487i	0.823515	−	0.220660i	0.645883	+	0.763437i	$0.276489\pi$
$158$	−9.44008	+	2.52946i	−0.751013	+	0.201233i
$159$		0			0
$160$	−2.11943	+	0.712744i	−0.167556	+	0.0563473i
$161$			14.8288i			1.16867i
$162$		0			0
$163$	−15.7354	+	15.7354i	−1.23249	+	1.23249i	−0.269490	+	0.963003i	$0.586855\pi$
$163$	−15.7354	+	15.7354i	−1.23249	+	1.23249i	−0.963003	+	0.269490i	$0.913145\pi$
$164$	0.986264	+	1.70826i	0.0770143	+	0.133393i
$165$		0			0
$166$	−1.40019	+	2.42521i	−0.108676	+	0.188233i
$167$	1.05230	+	3.92724i	0.0814295	+	0.303899i	0.994614	−	0.103647i	$-0.0330512\pi$
$167$	1.05230	+	3.92724i	0.0814295	+	0.303899i	−0.913185	+	0.407546i	$0.866385\pi$
$168$		0			0
$169$	5.95761	−	3.43963i	0.458277	−	0.264587i
$170$	8.74443	+	13.1678i	0.670667	+	1.00992i
$171$		0			0
$172$	6.35785	+	6.35785i	0.484781	+	0.484781i
$173$	1.44105	−	5.37809i	0.109561	−	0.408889i	−0.889261	−	0.457400i	$-0.848781\pi$
$173$	1.44105	−	5.37809i	0.109561	−	0.408889i	0.998823	+	0.0485110i	$0.0154476\pi$
$174$		0			0
$175$	1.63680	−	11.9096i	0.123730	−	0.900278i
$176$	−0.991757	−	0.572591i	−0.0747565	−	0.0431607i
$177$		0			0
$178$	4.71209	+	1.26260i	0.353186	+	0.0946359i
$179$	0.310192			0.0231848			0.0115924	−	0.999933i	$-0.496310\pi$
$179$	0.310192			0.0231848			0.0115924	+	0.999933i	$0.496310\pi$
$180$		0			0
$181$	3.07416			0.228501			0.114250	−	0.993452i	$-0.463553\pi$
$181$	3.07416			0.228501			0.114250	+	0.993452i	$0.463553\pi$
$182$	5.74559	+	1.53953i	0.425892	+	0.114117i
$183$		0			0
$184$	5.34131	+	3.08381i	0.393767	+	0.227341i
$185$	17.0848	−	19.3703i	1.25610	−	1.42413i
$186$		0			0
$187$	−2.09522	+	7.81948i	−0.153218	+	0.571817i
$188$	−8.72003	−	8.72003i	−0.635974	−	0.635974i
$189$		0			0
$190$	−6.10191	−	1.23177i	−0.442679	−	0.0893622i
$191$	12.3541	−	7.13262i	0.893909	−	0.516098i	0.0186896	−	0.999825i	$-0.494051\pi$
$191$	12.3541	−	7.13262i	0.893909	−	0.516098i	0.875219	+	0.483727i	$0.160717\pi$
$192$		0			0
$193$	−2.48506	−	9.27437i	−0.178879	−	0.667584i	−0.995858	−	0.0909176i	$-0.971020\pi$
$193$	−2.48506	−	9.27437i	−0.178879	−	0.667584i	0.816980	−	0.576666i	$-0.195647\pi$
$194$	4.03721	−	6.99265i	0.289855	−	0.502043i
$195$		0			0
$196$	0.609669	+	1.05598i	0.0435478	+	0.0754270i
$197$	−4.62495	+	4.62495i	−0.329514	+	0.329514i	−0.852402	−	0.522887i	$-0.824855\pi$
$197$	−4.62495	+	4.62495i	−0.329514	+	0.329514i	0.522887	+	0.852402i	$0.324855\pi$
$198$		0			0
$199$			4.07227i			0.288675i	0.989528	+	0.144338i	$0.0461051\pi$
$199$			4.07227i			0.288675i	−0.989528	+	0.144338i	$0.953895\pi$
$200$	−3.94941	−	3.06629i	−0.279266	−	0.216819i
$201$		0			0
$202$	0.703872	−	0.188602i	0.0495243	−	0.0132700i
$203$	3.12243	−	0.836654i	0.219152	−	0.0587216i
$204$		0			0
$205$	−1.96203	+	3.95029i	−0.137034	+	0.275900i
$206$			1.36541i			0.0951324i
$207$		0			0
$208$	1.74939	−	1.74939i	0.121299	−	0.121299i
$209$	−1.59404	−	2.76096i	−0.110262	−	0.190979i
$210$		0			0
$211$	−7.58800	+	13.1428i	−0.522379	+	0.904788i	0.477282	+	0.878750i	$0.341622\pi$
$211$	−7.58800	+	13.1428i	−0.522379	+	0.904788i	−0.999661	+	0.0260371i	$0.991711\pi$
$212$	−0.676517	−	2.52480i	−0.0464634	−	0.173404i
$213$		0			0
$214$	0.488928	−	0.282283i	0.0334224	−	0.0192964i
$215$	−3.97833	+	19.7077i	−0.271320	+	1.34406i
$216$		0			0
$217$	4.25782	+	4.25782i	0.289040	+	0.289040i
$218$	−3.51926	+	13.1341i	−0.238354	+	0.889551i
$219$		0			0
$220$	−0.160220	−	2.55569i	−0.0108021	−	0.172305i
$221$	−15.1458	−	8.74443i	−1.01882	−	0.588214i
$222$		0			0
$223$	8.21978	+	2.20248i	0.550437	+	0.147489i	0.523309	−	0.852143i	$-0.324697\pi$
$223$	8.21978	+	2.20248i	0.550437	+	0.147489i	0.0271279	+	0.999632i	$0.491364\pi$
$224$	−2.40430			−0.160644
$225$		0			0
$226$	−5.11832			−0.340465
$227$	−19.6687	−	5.27021i	−1.30546	−	0.349796i	−0.461946	−	0.886908i	$-0.652849\pi$
$227$	−19.6687	−	5.27021i	−1.30546	−	0.349796i	−0.843511	+	0.537112i	$0.819515\pi$
$228$		0			0
$229$	−12.2032	−	7.04551i	−0.806409	−	0.465580i	0.0392983	−	0.999228i	$-0.487488\pi$
$229$	−12.2032	−	7.04551i	−0.806409	−	0.465580i	−0.845707	+	0.533647i	$0.820821\pi$
$230$	0.862899	+	13.7642i	0.0568979	+	0.907583i
$231$		0			0
$232$	0.347982	−	1.29869i	0.0228461	−	0.0852630i
$233$	−0.643009	−	0.643009i	−0.0421249	−	0.0421249i	0.685731	−	0.727855i	$-0.259483\pi$
$233$	−0.643009	−	0.643009i	−0.0421249	−	0.0421249i	−0.727855	+	0.685731i	$0.759483\pi$
$234$		0			0
$235$	5.45644	−	27.0299i	0.355939	−	1.76324i
$236$	−2.27688	+	1.31456i	−0.148212	+	0.0855703i
$237$		0			0
$238$	4.39890	+	16.4169i	0.285139	+	1.06415i
$239$	5.34131	−	9.25142i	0.345501	−	0.598425i	−0.639944	−	0.768422i	$-0.721042\pi$
$239$	5.34131	−	9.25142i	0.345501	−	0.598425i	0.985445	+	0.169997i	$0.0543758\pi$
$240$		0			0
$241$	−10.5666	−	18.3019i	−0.680654	−	1.17893i	−0.974782	−	0.223161i	$-0.928362\pi$
$241$	−10.5666	−	18.3019i	−0.680654	−	1.17893i	0.294127	−	0.955766i	$-0.404971\pi$
$242$	−6.85084	+	6.85084i	−0.440389	+	0.440389i
$243$		0			0
$244$		−	7.08551i		−	0.453603i
$245$	−1.21285	+	2.44191i	−0.0774862	+	0.156008i
$246$		0			0
$247$	6.65274	−	1.78260i	0.423303	−	0.113424i
$248$	2.41912	−	0.648201i	0.153614	−	0.0411608i
$249$		0			0
$250$	0.826260	−	11.1498i	0.0522573	−	0.705173i
$251$		−	24.6952i		−	1.55874i	−0.626561	−	0.779372i	$-0.715538\pi$
$251$		−	24.6952i		−	1.55874i	0.626561	−	0.779372i	$-0.284462\pi$
$252$		0			0
$253$	−4.99433	+	4.99433i	−0.313991	+	0.313991i
$254$	−3.45646	−	5.98676i	−0.216877	−	0.375643i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	1.36020	+	5.07632i	0.0848467	+	0.316652i	0.995285	−	0.0969925i	$-0.0309223\pi$
$257$	1.36020	+	5.07632i	0.0848467	+	0.316652i	−0.910438	+	0.413645i	$0.864256\pi$
$258$		0			0
$259$	24.0508	−	13.8857i	1.49444	−	0.862818i
$260$	5.42268	+	1.09466i	0.336300	+	0.0678878i
$261$		0			0
$262$	−4.06902	−	4.06902i	−0.251385	−	0.251385i
$263$	3.86551	−	14.4263i	0.238358	−	0.889563i	−0.738249	−	0.674529i	$-0.764347\pi$
$263$	3.86551	−	14.4263i	0.238358	−	0.889563i	0.976606	−	0.215034i	$-0.0689864\pi$
$264$		0			0
$265$	3.86619	−	4.38337i	0.237498	−	0.269268i
$266$	−5.79660	−	3.34667i	−0.355413	−	0.205198i
$267$		0			0
$268$	0.0545285	+	0.0146109i	0.00333086	+	0.000892501i
$269$	−20.0071			−1.21985			−0.609927	−	0.792457i	$-0.708801\pi$
$269$	−20.0071			−1.21985			−0.609927	+	0.792457i	$0.708801\pi$
$270$		0			0
$271$	−3.02714			−0.183886			−0.0919428	−	0.995764i	$-0.529308\pi$
$271$	−3.02714			−0.183886			−0.0919428	+	0.995764i	$0.529308\pi$
$272$	6.82815	+	1.82960i	0.414018	+	0.110936i
$273$		0			0
$274$	9.00683	+	5.20010i	0.544123	+	0.314149i
$275$	4.56240	−	3.45986i	0.275123	−	0.208637i
$276$		0			0
$277$	−0.723941	+	2.70178i	−0.0434974	+	0.162334i	−0.984258	−	0.176736i	$-0.943446\pi$
$277$	−0.723941	+	2.70178i	−0.0434974	+	0.162334i	0.940761	+	0.339071i	$0.110113\pi$
$278$	−1.79251	−	1.79251i	−0.107508	−	0.107508i
$279$		0			0
$280$	−2.97414	−	4.47860i	−0.177739	−	0.267647i
$281$	−13.0998	+	7.56319i	−0.781470	+	0.451182i	−0.836951	−	0.547278i	$-0.815664\pi$
$281$	−13.0998	+	7.56319i	−0.781470	+	0.451182i	0.0554808	+	0.998460i	$0.482331\pi$
$282$		0			0
$283$	−6.22154	−	23.2191i	−0.369832	−	1.38023i	−0.860750	−	0.509027i	$-0.830005\pi$
$283$	−6.22154	−	23.2191i	−0.369832	−	1.38023i	0.490918	−	0.871206i	$-0.336661\pi$
$284$	−4.55002	+	7.88087i	−0.269994	+	0.467644i
$285$		0			0
$286$	1.41660	+	2.45362i	0.0837653	+	0.145086i
$287$	−3.35349	+	3.35349i	−0.197950	+	0.197950i
$288$		0			0
$289$		−	32.9711i		−	1.93948i
$290$	2.84958	−	0.958284i	0.167333	−	0.0562724i
$291$		0			0
$292$	10.6930	−	2.86517i	0.625758	−	0.167671i
$293$	−14.5851	+	3.90805i	−0.852068	+	0.228311i	−0.658318	−	0.752740i	$-0.728732\pi$
$293$	−14.5851	+	3.90805i	−0.852068	+	0.228311i	−0.193750	+	0.981051i	$0.562065\pi$
$294$		0			0
$295$	−5.26519	−	2.61512i	−0.306551	−	0.152258i
$296$		−	11.5507i		−	0.671374i
$297$		0			0
$298$	−9.18240	+	9.18240i	−0.531922	+	0.531922i
$299$	−7.62938	−	13.2145i	−0.441219	−	0.764213i
$300$		0			0
$301$	−10.8090	+	18.7217i	−0.623018	+	1.07910i
$302$	0.820468	+	3.06203i	0.0472126	+	0.176200i
$303$		0			0
$304$	−2.41093	+	1.39195i	−0.138276	+	0.0798339i
$305$	13.1985	−	8.76483i	0.755743	−	0.501872i
$306$		0			0
$307$	8.29531	+	8.29531i	0.473438	+	0.473438i	0.903025	−	0.429587i	$-0.141341\pi$
$307$	8.29531	+	8.29531i	0.473438	+	0.473438i	−0.429587	+	0.903025i	$0.641341\pi$
$308$	0.712623	−	2.65955i	0.0406055	−	0.151542i
$309$		0			0
$310$	4.19990	+	3.70437i	0.238538	+	0.210394i
$311$	−10.8857	−	6.28488i	−0.617274	−	0.356383i	0.158533	−	0.987354i	$-0.449324\pi$
$311$	−10.8857	−	6.28488i	−0.617274	−	0.356383i	−0.775807	+	0.630971i	$0.782657\pi$
$312$		0			0
$313$	11.5304	+	3.08956i	0.651737	+	0.174632i	0.569514	−	0.821982i	$-0.307131\pi$
$313$	11.5304	+	3.08956i	0.651737	+	0.174632i	0.0822229	+	0.996614i	$0.473798\pi$
$314$	10.6826			0.602855
$315$		0			0
$316$	−9.77309			−0.549779
$317$	1.87547	+	0.502531i	0.105337	+	0.0282249i	0.311102	−	0.950376i	$-0.399302\pi$
$317$	1.87547	+	0.502531i	0.105337	+	0.0282249i	−0.205766	+	0.978601i	$0.565968\pi$
$318$		0			0
$319$	1.33342	+	0.769849i	0.0746570	+	0.0431033i
$320$	−2.23169	+	0.139908i	−0.124755	+	0.00782110i
$321$		0			0
$322$	−3.83797	+	14.3235i	−0.213882	+	0.798218i
$323$	13.9155	+	13.9155i	0.774279	+	0.774279i
$324$		0			0
$325$	4.66883	+	11.4552i	0.258980	+	0.635418i
$326$	−19.2719	+	11.1266i	−1.06737	+	0.616247i
$327$		0			0
$328$	0.510528	+	1.90532i	0.0281892	+	0.105203i
$329$	14.8249	−	25.6775i	0.817323	−	1.41565i
$330$		0			0
$331$	−10.9811	−	19.0198i	−0.603575	−	1.04542i	−0.992275	−	0.124058i	$-0.960409\pi$
$331$	−10.9811	−	19.0198i	−0.603575	−	1.04542i	0.388700	−	0.921364i	$-0.372924\pi$
$332$	−1.98017	+	1.98017i	−0.108676	+	0.108676i
$333$		0			0
$334$			4.06578i			0.222470i
$335$	0.0402359	+	0.119646i	0.00219832	+	0.00653698i
$336$		0			0
$337$	−25.8842	+	6.93565i	−1.41000	+	0.377809i	−0.881926	−	0.471388i	$-0.843753\pi$
$337$	−25.8842	+	6.93565i	−1.41000	+	0.377809i	−0.528076	+	0.849197i	$0.677086\pi$
$338$	6.64485	−	1.78048i	0.361432	−	0.0968454i
$339$		0			0
$340$	5.03840	+	14.9823i	0.273246	+	0.812530i
$341$			2.86806i			0.155314i
$342$		0			0
$343$	−13.9737	+	13.9737i	−0.754508	+	0.754508i
$344$	4.49568	+	7.78674i	0.242391	+	0.419833i
$345$		0			0
$346$	2.78390	−	4.82186i	0.149664	−	0.259225i
$347$	7.78712	+	29.0619i	0.418035	+	1.56013i	0.778679	+	0.627423i	$0.215890\pi$
$347$	7.78712	+	29.0619i	0.418035	+	1.56013i	−0.360644	+	0.932704i	$0.617443\pi$
$348$		0			0
$349$	−22.2846	+	12.8660i	−1.19287	+	0.688702i	−0.958956	−	0.283556i	$-0.908486\pi$
$349$	−22.2846	+	12.8660i	−1.19287	+	0.688702i	−0.233911	+	0.972258i	$0.575152\pi$
$350$	4.66344	−	11.0801i	0.249272	−	0.592257i
$351$		0			0
$352$	−0.809767	−	0.809767i	−0.0431607	−	0.0431607i
$353$	4.03627	−	15.0636i	0.214829	−	0.801752i	−0.771398	−	0.636353i	$-0.780442\pi$
$353$	4.03627	−	15.0636i	0.214829	−	0.801752i	0.986227	−	0.165399i	$-0.0528912\pi$
$354$		0			0
$355$	−20.3085	+	1.27317i	−1.07786	+	0.0675728i
$356$	4.22474	+	2.43916i	0.223911	+	0.129275i
$357$		0			0
$358$	0.299622	+	0.0802835i	0.0158355	+	0.00424312i
$359$	22.9830			1.21300			0.606498	−	0.795085i	$-0.292574\pi$
$359$	22.9830			1.21300			0.606498	+	0.795085i	$0.292574\pi$
$360$		0			0
$361$	11.2499			0.592099
$362$	2.96941	+	0.795652i	0.156069	+	0.0418185i
$363$		0			0
$364$	5.15136	+	2.97414i	0.270004	+	0.155887i
$365$	18.5644	+	16.3740i	0.971703	+	0.857055i
$366$		0			0
$367$	−0.901720	+	3.36526i	−0.0470694	+	0.175665i	−0.985459	−	0.169914i	$-0.945651\pi$
$367$	−0.901720	+	3.36526i	−0.0470694	+	0.175665i	0.938389	+	0.345580i	$0.112318\pi$
$368$	4.36116	+	4.36116i	0.227341	+	0.227341i
$369$		0			0
$370$	21.5161	−	14.2884i	1.11857	−	0.742817i
$371$	5.44254	−	3.14225i	0.282563	−	0.163138i
$372$		0			0
$373$	5.91894	+	22.0898i	0.306471	+	1.14377i	0.931671	+	0.363302i	$0.118351\pi$
$373$	5.91894	+	22.0898i	0.306471	+	1.14377i	−0.625200	+	0.780464i	$0.714983\pi$
$374$	−4.04766	+	7.01076i	−0.209300	+	0.362518i
$375$		0			0
$376$	−6.16599	−	10.6798i	−0.317987	−	0.550769i
$377$	−2.35206	+	2.35206i	−0.121137	+	0.121137i
$378$		0			0
$379$			36.3113i			1.86519i	0.360927	+	0.932594i	$0.382460\pi$
$379$			36.3113i			1.86519i	−0.360927	+	0.932594i	$0.617540\pi$
$380$	−5.57519	−	2.76909i	−0.286001	−	0.142051i
$381$		0			0
$382$	13.7792	−	3.69212i	0.705003	−	0.188905i
$383$	−16.0342	+	4.29635i	−0.819308	+	0.219533i	−0.644044	−	0.764988i	$-0.722745\pi$
$383$	−16.0342	+	4.29635i	−0.819308	+	0.219533i	−0.175264	+	0.984521i	$0.556078\pi$
$384$		0			0
$385$	5.83557	−	1.96244i	0.297408	−	0.100015i
$386$		−	9.60153i		−	0.488705i
$387$		0			0
$388$	5.70947	−	5.70947i	0.289855	−	0.289855i
$389$	11.7878	+	20.4171i	0.597667	+	1.03519i	0.993164	+	0.116723i	$0.0372390\pi$
$389$	11.7878	+	20.4171i	0.597667	+	1.03519i	−0.395497	+	0.918467i	$0.629428\pi$
$390$		0			0
$391$	21.7995	−	37.7578i	1.10245	−	1.90950i
$392$	0.315588	+	1.17779i	0.0159396	+	0.0594874i
$393$		0			0
$394$	−5.66439	+	3.27034i	−0.285368	+	0.164757i
$395$	−12.0894	−	18.2048i	−0.608283	−	0.915981i
$396$		0			0
$397$	27.6509	+	27.6509i	1.38776	+	1.38776i	0.830011	+	0.557748i	$0.188334\pi$
$397$	27.6509	+	27.6509i	1.38776	+	1.38776i	0.557748	+	0.830011i	$0.311666\pi$
$398$	−1.05398	+	3.93351i	−0.0528312	+	0.197169i
$399$		0			0
$400$	−3.02123	−	3.98399i	−0.151061	−	0.199200i
$401$	26.4658	+	15.2801i	1.32164	+	0.763050i	0.983990	−	0.178222i	$-0.0570344\pi$
$401$	26.4658	+	15.2801i	1.32164	+	0.763050i	0.337651	+	0.941272i	$0.390368\pi$
$402$		0			0
$403$	−5.98494	−	1.60366i	−0.298131	−	0.0798840i
$404$	0.728702			0.0362543
$405$		0			0
$406$	3.23258			0.160430
$407$	12.7770	+	3.42359i	0.633332	+	0.169701i
$408$		0			0
$409$	−2.43668	−	1.40682i	−0.120486	−	0.0695626i	0.438546	−	0.898709i	$-0.355494\pi$
$409$	−2.43668	−	1.40682i	−0.120486	−	0.0695626i	−0.559032	+	0.829146i	$0.688827\pi$
$410$	−2.91759	+	3.30787i	−0.144089	+	0.163364i
$411$		0			0
$412$	−0.353393	+	1.31888i	−0.0174104	+	0.0649766i
$413$	−4.46974	−	4.46974i	−0.219942	−	0.219942i
$414$		0			0
$415$	−6.13805	−	1.23907i	−0.301305	−	0.0608234i
$416$	2.14256	−	1.23701i	0.105048	−	0.0606493i
$417$		0			0
$418$	−0.825136	−	3.07945i	−0.0403587	−	0.150621i
$419$	2.23812	−	3.87654i	0.109339	−	0.189381i	−0.806163	−	0.591693i	$-0.798460\pi$
$419$	2.23812	−	3.87654i	0.109339	−	0.189381i	0.915503	+	0.402311i	$0.131793\pi$
$420$		0			0
$421$	2.85177	+	4.93941i	0.138987	+	0.240732i	0.927113	−	0.374781i	$-0.122282\pi$
$421$	2.85177	+	4.93941i	0.138987	+	0.240732i	−0.788127	+	0.615513i	$0.788949\pi$
$422$	−10.7310	+	10.7310i	−0.522379	+	0.522379i
$423$		0			0
$424$		−	2.61386i		−	0.126940i
$425$	−21.6757	+	27.9185i	−1.05142	+	1.35425i
$426$		0			0
$427$	16.4552	−	4.40916i	0.796324	−	0.213374i
$428$	0.545328	−	0.146120i	0.0263594	−	0.00706299i
$429$		0			0
$430$	−8.94351	+	18.0065i	−0.431295	+	0.868353i
$431$		−	28.4120i		−	1.36856i	−0.729221	−	0.684278i	$-0.760117\pi$
$431$		−	28.4120i		−	1.36856i	0.729221	−	0.684278i	$-0.239883\pi$
$432$		0			0
$433$	20.2290	−	20.2290i	0.972142	−	0.972142i	−0.0274806	−	0.999622i	$-0.508748\pi$
$433$	20.2290	−	20.2290i	0.972142	−	0.972142i	0.999622	+	0.0274806i	$0.00874844\pi$
$434$	3.01073	+	5.21475i	0.144520	+	0.250316i
$435$		0			0
$436$	−6.79869	+	11.7757i	−0.325598	+	0.563952i
$437$	4.44393	+	16.5850i	0.212582	+	0.793368i
$438$		0			0
$439$	12.4785	−	7.20447i	0.595567	−	0.343851i	−0.171729	−	0.985144i	$-0.554935\pi$
$439$	12.4785	−	7.20447i	0.595567	−	0.343851i	0.767296	+	0.641293i	$0.221602\pi$
$440$	0.506700	−	2.51007i	0.0241560	−	0.119663i
$441$		0			0
$442$	−12.3665	−	12.3665i	−0.588214	−	0.588214i
$443$	−6.94511	+	25.9195i	−0.329972	+	1.23147i	0.579246	+	0.815153i	$0.303347\pi$
$443$	−6.94511	+	25.9195i	−0.329972	+	1.23147i	−0.909218	+	0.416320i	$0.863320\pi$
$444$		0			0
$445$	0.682516	+	10.8869i	0.0323543	+	0.516087i
$446$	7.36965	+	4.25487i	0.348963	+	0.201474i
$447$		0			0
$448$	−2.32238	−	0.622279i	−0.109722	−	0.0293999i
$449$	1.72288			0.0813077			0.0406538	−	0.999173i	$-0.487056\pi$
$449$	1.72288			0.0813077			0.0406538	+	0.999173i	$0.487056\pi$
$450$		0			0
$451$	−2.25891			−0.106368
$452$	−4.94392	−	1.32472i	−0.232542	−	0.0623095i
$453$		0			0
$454$	−17.6345	−	10.1813i	−0.827626	−	0.477830i
$455$	0.832211	+	13.2747i	0.0390147	+	0.622327i
$456$		0			0
$457$	−3.30155	+	12.3215i	−0.154440	+	0.576377i	0.844713	+	0.535220i	$0.179771\pi$
$457$	−3.30155	+	12.3215i	−0.154440	+	0.576377i	−0.999153	+	0.0411576i	$0.986895\pi$
$458$	−9.96386	−	9.96386i	−0.465580	−	0.465580i
$459$		0			0
$460$	−2.72894	+	13.5185i	−0.127237	+	0.630304i
$461$	−8.72418	+	5.03691i	−0.406326	+	0.234592i	−0.689210	−	0.724562i	$-0.742042\pi$
$461$	−8.72418	+	5.03691i	−0.406326	+	0.234592i	0.282884	+	0.959154i	$0.408709\pi$
$462$		0			0
$463$	9.90706	+	36.9737i	0.460420	+	1.71831i	0.671644	+	0.740874i	$0.265588\pi$
$463$	9.90706	+	36.9737i	0.460420	+	1.71831i	−0.211224	+	0.977438i	$0.567745\pi$
$464$	0.672250	−	1.16437i	0.0312084	−	0.0540546i
$465$		0			0
$466$	−0.454676	−	0.787522i	−0.0210625	−	0.0364813i
$467$	14.5094	−	14.5094i	0.671413	−	0.671413i	−0.286629	−	0.958042i	$-0.592535\pi$
$467$	14.5094	−	14.5094i	0.671413	−	0.671413i	0.958042	+	0.286629i	$0.0925347\pi$
$468$		0			0
$469$			0.135728i			0.00626733i
$470$	12.2664	−	24.6967i	0.565806	−	1.13917i
$471$		0			0
$472$	−2.53953	+	0.680464i	−0.116891	+	0.0313209i
$473$	−9.94589	+	2.66499i	−0.457313	+	0.122537i
$474$		0			0
$475$	−1.73844	−	13.8105i	−0.0797652	−	0.633671i
$476$			16.9961i			0.779013i
$477$		0			0
$478$	7.55375	−	7.55375i	0.345501	−	0.345501i
$479$	−2.27813	−	3.94584i	−0.104091	−	0.180290i	0.809276	−	0.587429i	$-0.199860\pi$
$479$	−2.27813	−	3.94584i	−0.104091	−	0.180290i	−0.913366	+	0.407139i	$0.866527\pi$
$480$		0			0
$481$	−14.2884	+	24.7482i	−0.651493	+	1.12842i
$482$	−5.46967	−	20.4131i	−0.249137	−	0.929791i
$483$		0			0
$484$	−8.39054	+	4.84428i	−0.381388	+	0.220194i
$485$	17.6979	+	3.57262i	0.803622	+	0.162225i
$486$		0			0
$487$	−18.4889	−	18.4889i	−0.837814	−	0.837814i	0.150757	−	0.988571i	$-0.451829\pi$
$487$	−18.4889	−	18.4889i	−0.837814	−	0.837814i	−0.988571	+	0.150757i	$0.951829\pi$
$488$	1.83386	−	6.84408i	0.0830151	−	0.309817i
$489$		0			0
$490$	−1.80354	+	2.04480i	−0.0814755	+	0.0923744i
$491$	0.730071	+	0.421507i	0.0329476	+	0.0190223i	0.516383	−	0.856358i	$-0.327278\pi$
$491$	0.730071	+	0.421507i	0.0329476	+	0.0190223i	−0.483436	+	0.875380i	$0.660611\pi$
$492$		0			0
$493$	−9.18045	−	2.45989i	−0.413467	−	0.110788i
$494$	6.88742			0.309880
$495$		0			0
$496$	2.50446			0.112453
$497$	−21.1337	−	5.66277i	−0.947978	−	0.254010i
$498$		0			0
$499$	−8.45869	−	4.88363i	−0.378663	−	0.218621i	0.298573	−	0.954387i	$-0.403489\pi$
$499$	−8.45869	−	4.88363i	−0.378663	−	0.218621i	−0.677236	+	0.735765i	$0.736823\pi$
$500$	3.68388	−	10.5560i	0.164748	−	0.472078i
$501$		0			0
$502$	6.39158	−	23.8537i	0.285270	−	1.06464i
$503$	−22.3161	−	22.3161i	−0.995025	−	0.995025i	0.00496279	−	0.999988i	$-0.498420\pi$
$503$	−22.3161	−	22.3161i	−0.995025	−	0.995025i	−0.999988	+	0.00496279i	$0.998420\pi$
$504$		0			0
$505$	0.901410	+	1.35738i	0.0401122	+	0.0604028i
$506$	−6.11678	+	3.53152i	−0.271924	+	0.156995i
$507$		0			0
$508$	−1.78919	−	6.67736i	−0.0793826	−	0.296260i
$509$	−3.83647	+	6.64497i	−0.170049	+	0.294533i	−0.938437	−	0.345451i	$-0.887726\pi$
$509$	−3.83647	+	6.64497i	−0.170049	+	0.294533i	0.768388	+	0.639984i	$0.221059\pi$
$510$		0			0
$511$	13.3080	+	23.0501i	0.588712	+	1.01968i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$			5.25539i			0.231805i
$515$	−2.89389	+	0.973185i	−0.127520	+	0.0428837i
$516$		0			0
$517$	13.6412	−	3.65514i	0.599938	−	0.160753i
$518$	26.8252	−	7.18779i	1.17863	−	0.315813i
$519$		0			0
$520$	4.95459	+	2.46085i	0.217273	+	0.107915i
$521$			23.2333i			1.01787i	0.860805	+	0.508934i	$0.169960\pi$
$521$			23.2333i			1.01787i	−0.860805	+	0.508934i	$0.830040\pi$
$522$		0			0
$523$	−3.86103	+	3.86103i	−0.168831	+	0.168831i	−0.786465	−	0.617634i	$-0.788091\pi$
$523$	−3.86103	+	3.86103i	−0.168831	+	0.168831i	0.617634	+	0.786465i	$0.288091\pi$
$524$	−2.87723	−	4.98351i	−0.125693	−	0.217706i
$525$		0			0
$526$	7.46760	−	12.9343i	0.325603	−	0.563960i
$527$	−4.58215	−	17.1008i	−0.199602	−	0.744923i
$528$		0			0
$529$	13.0246	−	7.51973i	0.566285	−	0.326945i
$530$	4.86895	−	3.23336i	0.211494	−	0.140448i
$531$		0			0
$532$	−4.73291	−	4.73291i	−0.205198	−	0.205198i
$533$	1.26305	−	4.71378i	0.0547089	−	0.204176i
$534$		0			0
$535$	0.946759	+	0.835055i	0.0409320	+	0.0361026i
$536$	0.0488889	+	0.0282260i	0.00211168	+	0.00121918i
$537$		0			0
$538$	−19.3254	−	5.17822i	−0.833176	−	0.223249i
$539$	−1.39637			−0.0601457
$540$		0			0
$541$	−21.3692			−0.918732			−0.459366	−	0.888247i	$-0.651923\pi$
$541$	−21.3692			−0.918732			−0.459366	+	0.888247i	$0.651923\pi$
$542$	−2.92399	−	0.783481i	−0.125596	−	0.0336534i
$543$		0			0
$544$	6.12195	+	3.53451i	0.262477	+	0.151541i
$545$	−30.3451	+	1.90238i	−1.29984	+	0.0814891i
$546$		0			0
$547$	7.10984	−	26.5343i	0.303995	−	1.13452i	−0.629812	−	0.776747i	$-0.716868\pi$
$547$	7.10984	−	26.5343i	0.303995	−	1.13452i	0.933807	−	0.357777i	$-0.116465\pi$
$548$	7.35405	+	7.35405i	0.314149	+	0.314149i
$549$		0			0
$550$	5.30242	−	2.16113i	0.226096	−	0.0921508i
$551$	3.24150	−	1.87148i	0.138092	−	0.0797277i
$552$		0			0
$553$	−6.08159	−	22.6968i	−0.258615	−	0.965166i
$554$	−1.39855	+	2.42235i	−0.0594185	+	0.102916i
$555$		0			0
$556$	−1.26750	−	2.19537i	−0.0537539	−	0.0931045i
$557$	13.7347	−	13.7347i	0.581958	−	0.581958i	−0.353483	−	0.935441i	$-0.615003\pi$
$557$	13.7347	−	13.7347i	0.581958	−	0.581958i	0.935441	+	0.353483i	$0.115003\pi$
$558$		0			0
$559$		−	22.2447i		−	0.940852i
$560$	−1.71365	−	5.09575i	−0.0724149	−	0.215335i
$561$		0			0
$562$	−14.6110	+	3.91500i	−0.616326	+	0.165144i
$563$	14.3759	−	3.85201i	0.605872	−	0.162343i	0.0571749	−	0.998364i	$-0.481791\pi$
$563$	14.3759	−	3.85201i	0.605872	−	0.162343i	0.548697	+	0.836021i	$0.315124\pi$
$564$		0			0
$565$	−3.64805	−	10.8479i	−0.153475	−	0.456376i
$566$		−	24.0382i		−	1.01040i
$567$		0			0
$568$	−6.43471	+	6.43471i	−0.269994	+	0.269994i
$569$	−14.7082	−	25.4753i	−0.616599	−	1.06798i	−0.990102	−	0.140351i	$-0.955177\pi$
$569$	−14.7082	−	25.4753i	−0.616599	−	1.06798i	0.373503	−	0.927629i	$-0.378157\pi$
$570$		0			0
$571$	15.2909	−	26.4847i	0.639906	−	1.10835i	−0.345548	−	0.938401i	$-0.612307\pi$
$571$	15.2909	−	26.4847i	0.639906	−	1.10835i	0.985453	−	0.169948i	$-0.0543599\pi$
$572$	0.733286	+	2.73666i	0.0306602	+	0.114426i
$573$		0			0
$574$	−4.10717	+	2.37128i	−0.171430	+	0.0989751i
$575$	−28.5572	+	11.6392i	−1.19092	+	0.485388i
$576$		0			0
$577$	−2.75877	−	2.75877i	−0.114849	−	0.114849i	0.647347	−	0.762196i	$-0.275879\pi$
$577$	−2.75877	−	2.75877i	−0.114849	−	0.114849i	−0.762196	+	0.647347i	$0.775879\pi$
$578$	8.53354	−	31.8476i	0.354949	−	1.32469i
$579$		0			0
$580$	3.00050	−	0.188106i	0.124589	−	0.00781069i
$581$	−5.83093	−	3.36649i	−0.241908	−	0.139665i
$582$		0			0
$583$	2.89135	+	0.774736i	0.119748	+	0.0320863i
$584$	11.0702			0.458087
$585$		0			0
$586$	−15.0996			−0.623757
$587$	15.5484	+	4.16617i	0.641750	+	0.171956i	0.564996	−	0.825094i	$-0.308878\pi$
$587$	15.5484	+	4.16617i	0.641750	+	0.171956i	0.0767539	+	0.997050i	$0.475544\pi$
$588$		0			0
$589$	6.03808	+	3.48608i	0.248795	+	0.143642i
$590$	−4.40894	−	3.88875i	−0.181513	−	0.160097i
$591$		0			0
$592$	2.98955	−	11.1572i	0.122870	−	0.458557i
$593$	31.4829	+	31.4829i	1.29285	+	1.29285i	0.933018	+	0.359830i	$0.117165\pi$
$593$	31.4829	+	31.4829i	1.29285	+	1.29285i	0.359830	+	0.933018i	$0.382835\pi$
$594$		0			0
$595$	−31.6593	+	21.0242i	−1.29790	+	0.861910i
$596$	−11.2461	+	6.49294i	−0.460658	+	0.265961i
$597$		0			0
$598$	−3.94926	−	14.7388i	−0.161497	−	0.602716i
$599$	0.0708577	−	0.122729i	0.00289517	−	0.00501457i	−0.864574	−	0.502505i	$-0.832412\pi$
$599$	0.0708577	−	0.122729i	0.00289517	−	0.00501457i	0.867469	+	0.497491i	$0.165745\pi$
$600$		0			0
$601$	21.9425	+	38.0055i	0.895052	+	1.55028i	0.833740	+	0.552157i	$0.186195\pi$
$601$	21.9425	+	38.0055i	0.895052	+	1.55028i	0.0613115	+	0.998119i	$0.480472\pi$
$602$	−15.2862	+	15.2862i	−0.623018	+	0.623018i
$603$		0			0
$604$			3.17004i			0.128987i
$605$	−19.4028	−	9.63701i	−0.788836	−	0.391800i
$606$		0			0
$607$	−32.2841	+	8.65049i	−1.31037	+	0.351113i	−0.845362	−	0.534194i	$-0.820615\pi$
$607$	−32.2841	+	8.65049i	−1.31037	+	0.351113i	−0.465008	+	0.885306i	$0.653949\pi$
$608$	−2.68904	+	0.720527i	−0.109055	+	0.0292212i
$609$		0			0
$610$	15.0173	−	5.05015i	0.608031	−	0.204475i
$611$			30.5095i			1.23428i
$612$		0			0
$613$	6.75021	−	6.75021i	0.272638	−	0.272638i	−0.557523	−	0.830161i	$-0.688248\pi$
$613$	6.75021	−	6.75021i	0.272638	−	0.272638i	0.830161	+	0.557523i	$0.188248\pi$
$614$	5.86567	+	10.1596i	0.236719	+	0.410010i
$615$		0			0
$616$	1.37668	−	2.38448i	0.0554681	−	0.0960736i
$617$	−8.53953	−	31.8700i	−0.343789	−	1.28304i	−0.894021	−	0.448025i	$-0.852128\pi$
$617$	−8.53953	−	31.8700i	−0.343789	−	1.28304i	0.550232	−	0.835012i	$-0.314539\pi$
$618$		0			0
$619$	13.2360	−	7.64183i	0.532001	−	0.307151i	−0.209830	−	0.977738i	$-0.567291\pi$
$619$	13.2360	−	7.64183i	0.532001	−	0.307151i	0.741831	+	0.670587i	$0.233958\pi$
$620$	3.09803	+	4.66516i	0.124420	+	0.187357i
$621$		0			0
$622$	−8.88817	−	8.88817i	−0.356383	−	0.356383i
$623$	−3.03567	+	11.3293i	−0.121622	+	0.453898i
$624$		0			0
$625$	24.2201	−	6.19573i	0.968804	−	0.247829i
$626$	10.3379	+	5.96858i	0.413185	+	0.238552i
$627$		0			0
$628$	10.3186	+	2.76487i	0.411758	+	0.110330i
$629$	−81.6525			−3.25570
$630$		0			0
$631$	10.8347			0.431321			0.215660	−	0.976468i	$-0.430810\pi$
$631$	10.8347			0.431321			0.215660	+	0.976468i	$0.430810\pi$
$632$	−9.44008	−	2.52946i	−0.375506	−	0.100617i
$633$		0			0
$634$	1.68150	+	0.970815i	0.0667809	+	0.0385560i
$635$	10.2250	−	11.5928i	0.405765	−	0.460044i
$636$		0			0
$637$	0.780770	−	2.91387i	0.0309352	−	0.115452i
$638$	1.08873	+	1.08873i	0.0431033	+	0.0431033i
$639$		0			0
$640$	−2.19185	−	0.442462i	−0.0866407	−	0.0174899i
$641$	23.0771	−	13.3236i	0.911491	−	0.526250i	0.0305804	−	0.999532i	$-0.490264\pi$
$641$	23.0771	−	13.3236i	0.911491	−	0.526250i	0.880911	+	0.473283i	$0.156931\pi$
$642$		0			0
$643$	−3.67008	−	13.6969i	−0.144734	−	0.540153i	−0.999767	−	0.0215806i	$-0.993130\pi$
$643$	−3.67008	−	13.6969i	−0.144734	−	0.540153i	0.855033	−	0.518573i	$-0.173537\pi$
$644$	−7.41440	+	12.8421i	−0.292168	+	0.506050i
$645$		0			0
$646$	9.83974	+	17.0429i	0.387139	+	0.670545i
$647$	22.3507	−	22.3507i	0.878698	−	0.878698i	−0.114702	−	0.993400i	$-0.536591\pi$
$647$	22.3507	−	22.3507i	0.878698	−	0.878698i	0.993400	+	0.114702i	$0.0365912\pi$
$648$		0			0
$649$		−	3.01081i		−	0.118185i
$650$	1.54493	+	12.2732i	0.0605971	+	0.481395i
$651$		0			0
$652$	−21.4950	+	5.75956i	−0.841809	+	0.225562i
$653$	−24.6425	+	6.60293i	−0.964334	+	0.258393i	−0.706434	−	0.707779i	$-0.749697\pi$
$653$	−24.6425	+	6.60293i	−0.964334	+	0.258393i	−0.257900	+	0.966172i	$0.583031\pi$
$654$		0			0
$655$	5.72385	−	11.5242i	0.223649	−	0.450287i
$656$			1.97253i			0.0770143i
$657$		0			0
$658$	20.9656	−	20.9656i	0.817323	−	0.817323i
$659$	10.2346	+	17.7269i	0.398684	+	0.690540i	0.993564	−	0.113274i	$-0.0361338\pi$
$659$	10.2346	+	17.7269i	0.398684	+	0.690540i	−0.594880	+	0.803814i	$0.702800\pi$
$660$		0			0
$661$	−0.883223	+	1.52979i	−0.0343534	+	0.0595018i	−0.882691	−	0.469954i	$-0.844271\pi$
$661$	−0.883223	+	1.52979i	−0.0343534	+	0.0595018i	0.848338	+	0.529456i	$0.177604\pi$
$662$	−5.68423	−	21.2138i	−0.220924	−	0.824499i
$663$		0			0
$664$	−2.42521	+	1.40019i	−0.0941163	+	0.0543381i
$665$	2.96155	−	14.6708i	0.114844	−	0.568911i
$666$		0			0
$667$	−5.86358	−	5.86358i	−0.227039	−	0.227039i
$668$	−1.05230	+	3.92724i	−0.0407148	+	0.151950i
$669$		0			0
$670$	0.00789810	+	0.125983i	0.000305130	+	0.00486716i
$671$	7.02711	+	4.05710i	0.271278	+	0.156623i
$672$		0			0
$673$	−13.4819	−	3.61246i	−0.519688	−	0.139250i	−0.0105656	−	0.999944i	$-0.503363\pi$
$673$	−13.4819	−	3.61246i	−0.519688	−	0.139250i	−0.509122	+	0.860694i	$0.670030\pi$
$674$	−26.7973			−1.03219
$675$		0			0
$676$	6.87925			0.264587
$677$	1.70954	+	0.458071i	0.0657031	+	0.0176051i	0.291521	−	0.956564i	$-0.405839\pi$
$677$	1.70954	+	0.458071i	0.0657031	+	0.0176051i	−0.225818	+	0.974170i	$0.572505\pi$
$678$		0			0
$679$	16.8124	+	9.70666i	0.645202	+	0.372508i
$680$	0.989013	+	15.7758i	0.0379269	+	0.604976i
$681$		0			0
$682$	−0.742309	+	2.77034i	−0.0284245	+	0.106082i
$683$	22.8964	+	22.8964i	0.876105	+	0.876105i	0.993129	−	0.117024i	$-0.0373354\pi$
$683$	22.8964	+	22.8964i	0.876105	+	0.876105i	−0.117024	+	0.993129i	$0.537335\pi$
$684$		0			0
$685$	−4.60169	+	22.7957i	−0.175822	+	0.870980i
$686$	−17.1142	+	9.88088i	−0.653423	+	0.377254i
$687$		0			0
$688$	2.32713	+	8.68498i	0.0887211	+	0.331112i
$689$	−3.23336	+	5.60035i	−0.123181	+	0.213356i
$690$		0			0
$691$	11.3908	+	19.7295i	0.433327	+	0.750545i	0.997157	−	0.0753461i	$-0.0240062\pi$
$691$	11.3908	+	19.7295i	0.433327	+	0.750545i	−0.563830	+	0.825891i	$0.690673\pi$
$692$	3.93703	−	3.93703i	0.149664	−	0.149664i
$693$		0			0
$694$			30.0871i			1.14209i
$695$	2.52151	−	5.07672i	0.0956463	−	0.192571i
$696$		0			0
$697$	13.4687	−	3.60893i	0.510164	−	0.136698i
$698$	−24.8552	+	6.65994i	−0.940784	+	0.252082i
$699$		0			0
$700$	7.37228	−	9.49558i	0.278646	−	0.358899i
$701$			26.0321i			0.983220i	0.870816	+	0.491610i	$0.163591\pi$
$701$			26.0321i			0.983220i	−0.870816	+	0.491610i	$0.836409\pi$
$702$		0			0
$703$	22.7379	−	22.7379i	0.857574	−	0.857574i
$704$	−0.572591	−	0.991757i	−0.0215804	−	0.0373783i
$705$		0			0
$706$	7.79747	−	13.5056i	0.293462	−	0.508291i
$707$	0.453456	+	1.69232i	0.0170540	+	0.0636462i
$708$		0			0
$709$	−2.58254	+	1.49103i	−0.0969892	+	0.0559968i	−0.547710	−	0.836668i	$-0.684500\pi$
$709$	−2.58254	+	1.49103i	−0.0969892	+	0.0559968i	0.450721	+	0.892665i	$0.351167\pi$
$710$	−19.9460	−	4.02643i	−0.748559	−	0.151109i
$711$		0			0
$712$	3.44949	+	3.44949i	0.129275	+	0.129275i
$713$	3.99786	−	14.9202i	0.149721	−	0.558766i
$714$		0			0
$715$	−4.19062	+	4.75119i	−0.156720	+	0.177685i
$716$	0.268634	+	0.155096i	0.0100393	+	0.00579621i
$717$		0			0
$718$	22.1999	+	5.94843i	0.828491	+	0.221994i
$719$	7.38853			0.275546			0.137773	−	0.990464i	$-0.456006\pi$
$719$	7.38853			0.275546			0.137773	+	0.990464i	$0.456006\pi$
$720$		0			0
$721$	−3.28285			−0.122260
$722$	10.8665	+	2.91168i	0.404411	+	0.108362i
$723$		0			0
$724$	2.66230	+	1.53708i	0.0989437	+	0.0571252i
$725$	4.06204	+	5.35648i	0.150860	+	0.198935i
$726$		0			0
$727$	−5.57881	+	20.8204i	−0.206906	+	0.772185i	0.781954	+	0.623337i	$0.214223\pi$
$727$	−5.57881	+	20.8204i	−0.206906	+	0.772185i	−0.988860	+	0.148849i	$0.952443\pi$
$728$	4.20607	+	4.20607i	0.155887	+	0.155887i
$729$		0			0
$730$	13.6939	+	20.6209i	0.506833	+	0.763213i
$731$	55.0446	−	31.7800i	2.03590	−	1.17543i
$732$		0			0
$733$	−1.74734	−	6.52116i	−0.0645395	−	0.240865i	0.926119	−	0.377232i	$-0.123124\pi$
$733$	−1.74734	−	6.52116i	−0.0645395	−	0.240865i	−0.990658	+	0.136367i	$0.956457\pi$
$734$	−1.74199	+	3.01721i	−0.0642980	+	0.111367i
$735$		0			0
$736$	3.08381	+	5.34131i	0.113671	+	0.196883i
$737$	−0.0457130	+	0.0457130i	−0.00168386	+	0.00168386i
$738$		0			0
$739$		−	12.8637i		−	0.473200i	−0.971607	−	0.236600i	$-0.923967\pi$
$739$		−	12.8637i		−	0.473200i	0.971607	−	0.236600i	$-0.0760331\pi$
$740$	24.4810	−	8.23273i	0.899941	−	0.302641i
$741$		0			0
$742$	6.07037	−	1.62655i	0.222850	−	0.0597125i
$743$	32.7401	−	8.77270i	1.20112	−	0.321839i	0.397848	−	0.917452i	$-0.369757\pi$
$743$	32.7401	−	8.77270i	1.20112	−	0.321839i	0.803272	+	0.595613i	$0.203091\pi$
$744$		0			0
$745$	−26.0062	−	12.9168i	−0.952792	−	0.473234i
$746$			22.8690i			0.837295i
$747$		0			0
$748$	−5.72426	+	5.72426i	−0.209300	+	0.209300i
$749$	0.678692	+	1.17553i	0.0247989	+	0.0429529i
$750$		0			0
$751$	6.70415	−	11.6119i	0.244638	−	0.423725i	−0.717392	−	0.696670i	$-0.754664\pi$
$751$	6.70415	−	11.6119i	0.244638	−	0.423725i	0.962030	+	0.272945i	$0.0879975\pi$
$752$	−3.19175	−	11.9118i	−0.116391	−	0.434378i
$753$		0			0
$754$	−2.88067	+	1.66316i	−0.104908	+	0.0605686i
$755$	−5.90498	+	3.92137i	−0.214904	+	0.142713i
$756$		0			0
$757$	−1.11492	−	1.11492i	−0.0405223	−	0.0405223i	0.686555	−	0.727078i	$-0.259122\pi$
$757$	−1.11492	−	1.11492i	−0.0405223	−	0.0405223i	−0.727078	+	0.686555i	$0.759122\pi$
$758$	−9.39806	+	35.0741i	−0.341353	+	1.27395i
$759$		0			0
$760$	−4.66853	−	4.11770i	−0.169345	−	0.149365i
$761$	29.7531	+	17.1780i	1.07855	+	0.622702i	0.930505	−	0.366279i	$-0.119368\pi$
$761$	29.7531	+	17.1780i	1.07855	+	0.622702i	0.148046	+	0.988981i	$0.452702\pi$
$762$		0			0
$763$	−31.5782	−	8.46136i	−1.14321	−	0.306322i
$764$	14.2652			0.516098
$765$		0			0
$766$	−16.5998			−0.599775
$767$	6.28282	+	1.68348i	0.226860	+	0.0607869i
$768$		0			0
$769$	14.4890	+	8.36522i	0.522486	+	0.301658i	0.737951	−	0.674854i	$-0.235793\pi$
$769$	14.4890	+	8.36522i	0.522486	+	0.301658i	−0.215465	+	0.976512i	$0.569127\pi$
$770$	6.14465	−	0.385218i	0.221438	−	0.0138823i
$771$		0			0
$772$	2.48506	−	9.27437i	0.0894393	−	0.333792i
$773$	−5.20827	−	5.20827i	−0.187328	−	0.187328i	0.607212	−	0.794540i	$-0.292288\pi$
$773$	−5.20827	−	5.20827i	−0.187328	−	0.187328i	−0.794540	+	0.607212i	$0.792288\pi$
$774$		0			0
$775$	−4.85771	+	11.5417i	−0.174494	+	0.414589i
$776$	6.99265	−	4.03721i	0.251022	−	0.144927i
$777$		0			0
$778$	6.10184	+	22.7724i	0.218761	+	0.816429i
$779$	−2.74567	+	4.75563i	−0.0983737	+	0.170388i
$780$		0			0
$781$	−5.21061	−	9.02504i	−0.186450	−	0.322941i
$782$	30.8291	−	30.8291i	1.10245	−	1.10245i
$783$		0			0
$784$			1.21934i			0.0435478i
$785$	7.61397	+	22.6411i	0.271754	+	0.808095i
$786$		0			0
$787$	−44.6815	+	11.9724i	−1.59272	+	0.426769i	−0.942834	−	0.333262i	$-0.891851\pi$
$787$	−44.6815	+	11.9724i	−1.59272	+	0.426769i	−0.649888	+	0.760030i	$0.725184\pi$
$788$	−6.31780	+	1.69285i	−0.225062	+	0.0603053i
$789$		0			0
$790$	−6.96571	−	20.7134i	−0.247829	−	0.736950i
$791$		−	12.3060i		−	0.437550i
$792$		0			0
$793$	−12.3953	+	12.3953i	−0.440171	+	0.440171i
$794$	19.5521	+	33.8653i	0.693879	+	1.20183i
$795$		0			0
$796$	−2.03613	+	3.52669i	−0.0721688	+	0.125000i
$797$	−13.3339	−	49.7628i	−0.472311	−	1.76269i	−0.631434	−	0.775430i	$-0.717533\pi$
$797$	−13.3339	−	49.7628i	−0.472311	−	1.76269i	0.159123	−	0.987259i	$-0.449134\pi$
$798$		0			0
$799$	−75.4958	+	43.5875i	−2.67085	+	1.54202i
$800$	−1.88715	−	4.63019i	−0.0667207	−	0.163702i
$801$		0			0
$802$	21.6093	+	21.6093i	0.763050	+	0.763050i
$803$	−3.28114	+	12.2454i	−0.115789	+	0.432131i
$804$		0			0
$805$	−33.0932	+	2.07467i	−1.16638	+	0.0731224i
$806$	−5.36595	−	3.09803i	−0.189008	−	0.109124i
$807$		0			0
$808$	0.703872	+	0.188602i	0.0247621	+	0.00663499i
$809$	18.0260			0.633762			0.316881	−	0.948465i	$-0.397364\pi$
$809$	18.0260			0.633762			0.316881	+	0.948465i	$0.397364\pi$
$810$		0			0
$811$	46.7969			1.64326			0.821630	−	0.570021i	$-0.193065\pi$
$811$	46.7969			1.64326			0.821630	+	0.570021i	$0.193065\pi$
$812$	3.12243	+	0.836654i	0.109576	+	0.0293608i
$813$		0			0
$814$	11.4555	+	6.61386i	0.401517	+	0.231816i
$815$	−37.3180	−	32.9150i	−1.30719	−	1.15296i
$816$		0			0
$817$	−6.47852	+	24.1782i	−0.226655	+	0.845886i
$818$	−1.98954	−	1.98954i	−0.0695626	−	0.0695626i
$819$		0			0
$820$	−3.67431	+	2.44003i	−0.128313	+	0.0852096i
$821$	−5.91006	+	3.41218i	−0.206263	+	0.119086i	−0.599573	−	0.800320i	$-0.704663\pi$
$821$	−5.91006	+	3.41218i	−0.206263	+	0.119086i	0.393311	+	0.919406i	$0.371330\pi$
$822$		0			0
$823$	5.27529	+	19.6876i	0.183885	+	0.686268i	0.994866	+	0.101196i	$0.0322670\pi$
$823$	5.27529	+	19.6876i	0.183885	+	0.686268i	−0.810982	+	0.585072i	$0.801066\pi$
$824$	−0.682703	+	1.18248i	−0.0237831	+	0.0411935i
$825$		0			0
$826$	−3.16059	−	5.47430i	−0.109971	−	0.190475i
$827$	−29.8425	+	29.8425i	−1.03773	+	1.03773i	−0.0384654	+	0.999260i	$0.512247\pi$
$827$	−29.8425	+	29.8425i	−1.03773	+	1.03773i	−0.999260	+	0.0384654i	$0.987753\pi$
$828$		0			0
$829$		−	20.4152i		−	0.709050i	−0.935047	−	0.354525i	$-0.884643\pi$
$829$		−	20.4152i		−	0.709050i	0.935047	−	0.354525i	$-0.115357\pi$
$830$	−5.60820	−	2.78549i	−0.194664	−	0.0966857i
$831$		0			0
$832$	2.38971	−	0.640322i	0.0828484	−	0.0221992i
$833$	8.32583	−	2.23090i	0.288473	−	0.0772961i
$834$		0			0
$835$	−8.61715	+	2.89786i	−0.298209	+	0.100285i
$836$		−	3.18808i		−	0.110262i
$837$		0			0
$838$	3.16518	−	3.16518i	0.109339	−	0.109339i
$839$	−9.70261	−	16.8054i	−0.334971	−	0.580187i	0.648508	−	0.761208i	$-0.275393\pi$
$839$	−9.70261	−	16.8054i	−0.334971	−	0.580187i	−0.983479	+	0.181021i	$0.942060\pi$
$840$		0			0
$841$	13.5962	−	23.5492i	0.468833	−	0.812043i
$842$	1.47618	+	5.50919i	0.0508726	+	0.189859i
$843$		0			0
$844$	−13.1428	+	7.58800i	−0.452394	+	0.261190i
$845$	8.50968	+	12.8143i	0.292742	+	0.440825i
$846$		0			0
$847$	−16.4715	−	16.4715i	−0.565967	−	0.565967i
$848$	0.676517	−	2.52480i	0.0232317	−	0.0867018i
$849$		0			0
$850$	−28.1629	+	21.3571i	−0.965981	+	0.732543i
$851$	−61.6961	−	35.6203i	−2.11492	−	1.22105i
$852$		0			0
$853$	−0.496213	−	0.132960i	−0.0169900	−	0.00455246i	0.250314	−	0.968165i	$-0.419466\pi$
$853$	−0.496213	−	0.132960i	−0.0169900	−	0.00455246i	−0.267304	+	0.963612i	$0.586133\pi$
$854$	17.0357			0.582949
$855$		0			0
$856$	0.564565			0.0192964
$857$	43.0427	+	11.5332i	1.47031	+	0.393968i	0.903037	−	0.429562i	$-0.141332\pi$
$857$	43.0427	+	11.5332i	1.47031	+	0.393968i	0.567272	+	0.823530i	$0.307999\pi$
$858$		0			0
$859$	25.5432	+	14.7474i	0.871522	+	0.503174i	0.867854	−	0.496820i	$-0.165499\pi$
$859$	25.5432	+	14.7474i	0.871522	+	0.503174i	0.00366859	+	0.999993i	$0.498832\pi$
$860$	−13.2992	+	15.0782i	−0.453499	+	0.514164i
$861$		0			0
$862$	7.35356	−	27.4438i	0.250463	−	0.934741i
$863$	6.17951	+	6.17951i	0.210353	+	0.210353i	0.804417	−	0.594064i	$-0.202478\pi$
$863$	6.17951	+	6.17951i	0.210353	+	0.210353i	−0.594064	+	0.804417i	$0.702478\pi$
$864$		0			0
$865$	12.2038	+	2.46354i	0.414943	+	0.0837630i
$866$	24.7753	−	14.3040i	0.841899	−	0.486071i
$867$		0			0
$868$	1.55847	+	5.81629i	0.0528979	+	0.197418i
$869$	5.59599	−	9.69254i	0.189831	−	0.328797i
$870$		0			0
$871$	−0.0698316	−	0.120952i	−0.00236615	−	0.00409830i
$872$	−9.61480	+	9.61480i	−0.325598	+	0.325598i
$873$		0			0
$874$			17.1700i			0.580785i
$875$	26.8074	+	1.98658i	0.906255	+	0.0671586i
$876$		0			0
$877$	20.0896	−	5.38298i	0.678376	−	0.181770i	0.0968513	−	0.995299i	$-0.469123\pi$
$877$	20.0896	−	5.38298i	0.678376	−	0.181770i	0.581525	+	0.813528i	$0.302456\pi$
$878$	13.9180	−	3.72931i	0.469709	−	0.125858i
$879$		0			0
$880$	1.13909	−	2.29340i	0.0383987	−	0.0773106i
$881$		−	28.3087i		−	0.953745i	−0.878972	−	0.476873i	$-0.841770\pi$
$881$		−	28.3087i		−	0.953745i	0.878972	−	0.476873i	$-0.158230\pi$
$882$		0			0
$883$	15.1647	−	15.1647i	0.510333	−	0.510333i	−0.404295	−	0.914629i	$-0.632483\pi$
$883$	15.1647	−	15.1647i	0.510333	−	0.510333i	0.914629	+	0.404295i	$0.132483\pi$
$884$	−8.74443	−	15.1458i	−0.294107	−	0.509408i
$885$		0			0
$886$	−13.4169	+	23.2388i	−0.450750	+	0.780723i
$887$	12.4339	+	46.4040i	0.417490	+	1.55809i	0.779796	+	0.626034i	$0.215323\pi$
$887$	12.4339	+	46.4040i	0.417490	+	1.55809i	−0.362306	+	0.932059i	$0.618011\pi$
$888$		0			0
$889$	14.3940	−	8.31036i	0.482758	−	0.278721i
$890$	−2.15847	+	10.6926i	−0.0723521	+	0.358415i
$891$		0			0
$892$	6.01730	+	6.01730i	0.201474	+	0.201474i
$893$	8.88553	−	33.1613i	0.297343	−	1.10970i
$894$		0			0
$895$	0.0433983	+	0.692251i	0.00145065	+	0.0231394i
$896$	−2.08219	−	1.20215i	−0.0695609	−	0.0401610i
$897$		0			0
$898$	1.66417	+	0.445914i	0.0555342	+	0.0148803i
$899$	−3.36724			−0.112304
$900$		0			0
$901$	−18.4774			−0.615573
$902$	−2.18194	−	0.584648i	−0.0726505	−	0.0194666i
$903$		0			0
$904$	−4.43259	−	2.55916i	−0.147426	−	0.0851164i
$905$	0.430100	+	6.86057i	0.0142970	+	0.228053i
$906$		0			0
$907$	9.66001	−	36.0516i	0.320755	−	1.19707i	−0.597755	−	0.801679i	$-0.703941\pi$
$907$	9.66001	−	36.0516i	0.320755	−	1.19707i	0.918511	−	0.395396i	$-0.129393\pi$
$908$	−14.3985	−	14.3985i	−0.477830	−	0.477830i
$909$		0			0
$910$	−2.63189	+	13.0378i	−0.0872462	+	0.432197i
$911$	−46.5957	+	26.9020i	−1.54378	+	0.891304i	−0.545189	+	0.838313i	$0.683542\pi$
$911$	−46.5957	+	26.9020i	−1.54378	+	0.891304i	−0.998595	+	0.0529906i	$0.983125\pi$
$912$		0			0
$913$	−0.830022	−	3.09768i	−0.0274697	−	0.102518i
$914$	−6.37810	+	11.0472i	−0.210969	+	0.365409i
$915$		0			0
$916$	−7.04551	−	12.2032i	−0.232790	−	0.403204i
$917$	9.78315	−	9.78315i	0.323068	−	0.323068i
$918$		0			0
$919$		−	23.1668i		−	0.764203i	−0.924120	−	0.382101i	$-0.875201\pi$
$919$		−	23.1668i		−	0.764203i	0.924120	−	0.382101i	$-0.124799\pi$
$920$	−6.13480	+	12.3516i	−0.202258	+	0.407220i
$921$		0			0
$922$	−9.73056	+	2.60729i	−0.320459	+	0.0858667i
$923$	21.7465	−	5.82696i	0.715795	−	0.191797i
$924$		0			0
$925$	45.6187	+	35.4180i	1.49993	+	1.16454i
$926$			38.2779i			1.25789i
$927$		0			0
$928$	0.950705	−	0.950705i	0.0312084	−	0.0312084i
$929$	6.78350	+	11.7494i	0.222559	+	0.385484i	0.955584	−	0.294717i	$-0.0952255\pi$
$929$	6.78350	+	11.7494i	0.222559	+	0.385484i	−0.733025	+	0.680202i	$0.761892\pi$
$930$		0			0
$931$	−1.69726	+	2.93974i	−0.0556255	+	0.0963462i
$932$	−0.235358	−	0.878367i	−0.00770940	−	0.0287719i
$933$		0			0
$934$	17.7703	−	10.2597i	0.581461	−	0.335706i
$935$	−17.7438	−	3.58188i	−0.580283	−	0.117140i
$936$		0			0
$937$	−6.94086	−	6.94086i	−0.226748	−	0.226748i	0.584585	−	0.811333i	$-0.301258\pi$
$937$	−6.94086	−	6.94086i	−0.226748	−	0.226748i	−0.811333	+	0.584585i	$0.801258\pi$
$938$	−0.0351289	+	0.131103i	−0.00114700	+	0.00428066i
$939$		0			0
$940$	18.2404	−	20.6804i	0.594935	−	0.674520i
$941$	14.5976	+	8.42791i	0.475867	+	0.274742i	0.718693	−	0.695328i	$-0.244741\pi$
$941$	14.5976	+	8.42791i	0.475867	+	0.274742i	−0.242825	+	0.970070i	$0.578074\pi$
$942$		0			0
$943$	11.7513	+	3.14874i	0.382673	+	0.102537i
$944$	−2.62911			−0.0855703
$945$		0			0
$946$	−10.2967			−0.334776
$947$	−37.0498	−	9.92745i	−1.20396	−	0.322599i	−0.399568	−	0.916704i	$-0.630840\pi$
$947$	−37.0498	−	9.92745i	−1.20396	−	0.322599i	−0.804388	+	0.594105i	$0.797506\pi$
$948$		0			0
$949$	−23.7185	−	13.6939i	−0.769935	−	0.444522i
$950$	1.89522	−	13.7899i	0.0614892	−	0.447403i
$951$		0			0
$952$	−4.39890	+	16.4169i	−0.142569	+	0.532076i
$953$	−18.8861	−	18.8861i	−0.611780	−	0.611780i	0.331630	−	0.943410i	$-0.392402\pi$
$953$	−18.8861	−	18.8861i	−0.611780	−	0.611780i	−0.943410	+	0.331630i	$0.892402\pi$
$954$		0			0
$955$	17.6462	+	26.5725i	0.571018	+	0.859865i
$956$	9.25142	−	5.34131i	0.299212	−	0.172750i
$957$		0			0
$958$	−1.17925	−	4.40102i	−0.0380998	−	0.142190i
$959$	−12.5026	+	21.6551i	−0.403730	+	0.699281i
$960$		0			0
$961$	12.3638	+	21.4148i	0.398834	+	0.690800i
$962$	−20.2068	+	20.2068i	−0.651493	+	0.651493i
$963$		0			0
$964$		−	21.1332i		−	0.680654i
$965$	20.3498	−	6.84343i	0.655084	−	0.220298i
$966$		0			0
$967$	30.9494	−	8.29288i	0.995267	−	0.266681i	0.275805	−	0.961213i	$-0.411055\pi$
$967$	30.9494	−	8.29288i	0.995267	−	0.266681i	0.719461	+	0.694533i	$0.244389\pi$
$968$	−9.35843	+	2.50758i	−0.300791	+	0.0805968i
$969$		0			0
$970$	16.1702	+	8.03146i	0.519195	+	0.257875i
$971$			29.2201i			0.937716i	0.883274	+	0.468858i	$0.155334\pi$
$971$			29.2201i			0.937716i	−0.883274	+	0.468858i	$0.844666\pi$
$972$		0			0
$973$	4.30974	−	4.30974i	0.138164	−	0.138164i
$974$	−13.0737	−	22.6442i	−0.418907	−	0.725568i
$975$		0			0
$976$	3.54275	−	6.13623i	0.113401	−	0.196416i
$977$	10.1124	+	37.7399i	0.323523	+	1.20741i	0.915788	+	0.401662i	$0.131567\pi$
$977$	10.1124	+	37.7399i	0.323523	+	1.20741i	−0.592265	+	0.805743i	$0.701766\pi$
$978$		0			0
$979$	−4.83811	+	2.79328i	−0.154627	+	0.0892737i
$980$	−2.27132	+	1.50833i	−0.0725545	+	0.0481819i
$981$		0			0
$982$	0.596101	+	0.596101i	0.0190223	+	0.0190223i
$983$	−2.96514	+	11.0660i	−0.0945732	+	0.352952i	−0.996954	−	0.0779867i	$-0.975151\pi$
$983$	−2.96514	+	11.0660i	−0.0945732	+	0.352952i	0.902381	+	0.430939i	$0.141818\pi$
$984$		0			0
$985$	−10.9685	−	9.67438i	−0.349486	−	0.308251i
$986$	−8.23096	−	4.75215i	−0.262127	−	0.151339i
$987$		0			0
$988$	6.65274	+	1.78260i	0.211652	+	0.0567119i
$989$	55.4552			1.76337
$990$		0			0
$991$	−26.7986			−0.851286			−0.425643	−	0.904891i	$-0.639952\pi$
$991$	−26.7986			−0.851286			−0.425643	+	0.904891i	$0.639952\pi$
$992$	2.41912	+	0.648201i	0.0768071	+	0.0205804i
$993$		0			0
$994$	−18.9480	−	10.9396i	−0.600994	−	0.346984i
$995$	−9.08802	+	0.569743i	−0.288110	+	0.0180621i
$996$		0			0
$997$	14.2233	−	53.0819i	0.450455	−	1.68112i	−0.250661	−	0.968075i	$-0.580648\pi$
$997$	14.2233	−	53.0819i	0.450455	−	1.68112i	0.701116	−	0.713047i	$-0.252685\pi$
$998$	−6.90650	−	6.90650i	−0.218621	−	0.218621i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	270.2.m.b.17.3		16
3.2	odd	2		90.2.l.b.77.2	yes	16
5.2	odd	4		1350.2.q.h.1043.2		16
5.3	odd	4	inner	270.2.m.b.233.4		16
5.4	even	2		1350.2.q.h.557.1		16
9.2	odd	6	inner	270.2.m.b.197.4		16
9.4	even	3		810.2.f.c.647.3		16
9.5	odd	6		810.2.f.c.647.6		16
9.7	even	3		90.2.l.b.47.2	yes	16
12.11	even	2		720.2.cu.b.257.1		16
15.2	even	4		450.2.p.h.293.3		16
15.8	even	4		90.2.l.b.23.2	✓	16
15.14	odd	2		450.2.p.h.257.3		16
36.7	odd	6		720.2.cu.b.497.2		16
45.2	even	12		1350.2.q.h.143.1		16
45.7	odd	12		450.2.p.h.443.3		16
45.13	odd	12		810.2.f.c.323.6		16
45.23	even	12		810.2.f.c.323.3		16
45.29	odd	6		1350.2.q.h.1007.2		16
45.34	even	6		450.2.p.h.407.3		16
45.38	even	12	inner	270.2.m.b.143.3		16
45.43	odd	12		90.2.l.b.83.2	yes	16
60.23	odd	4		720.2.cu.b.113.2		16
180.43	even	12		720.2.cu.b.353.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.l.b.23.2	✓	16	15.8	even	4
90.2.l.b.47.2	yes	16	9.7	even	3
90.2.l.b.77.2	yes	16	3.2	odd	2
90.2.l.b.83.2	yes	16	45.43	odd	12
270.2.m.b.17.3		16	1.1	even	1	trivial
270.2.m.b.143.3		16	45.38	even	12	inner
270.2.m.b.197.4		16	9.2	odd	6	inner
270.2.m.b.233.4		16	5.3	odd	4	inner
450.2.p.h.257.3		16	15.14	odd	2
450.2.p.h.293.3		16	15.2	even	4
450.2.p.h.407.3		16	45.34	even	6
450.2.p.h.443.3		16	45.7	odd	12
720.2.cu.b.113.2		16	60.23	odd	4
720.2.cu.b.257.1		16	12.11	even	2
720.2.cu.b.353.1		16	180.43	even	12
720.2.cu.b.497.2		16	36.7	odd	6
810.2.f.c.323.3		16	45.23	even	12
810.2.f.c.323.6		16	45.13	odd	12
810.2.f.c.647.3		16	9.4	even	3
810.2.f.c.647.6		16	9.5	odd	6
1350.2.q.h.143.1		16	45.2	even	12
1350.2.q.h.557.1		16	5.4	even	2
1350.2.q.h.1007.2		16	45.29	odd	6
1350.2.q.h.1043.2		16	5.2	odd	4

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:	\( N \)	\(=\)	\( 270 = 2 \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	270.m (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 + 0.258819i) q^{2} +(0.866025 + 0.500000i) q^{4} +(0.139908 + 2.23169i) q^{5} +(-0.622279 + 2.32238i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.965926 + 0.258819i) q^{2} +(0.866025 + 0.500000i) q^{4} +(0.139908 + 2.23169i) q^{5} +(-0.622279 + 2.32238i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.442462 + 2.19185i) q^{10} +(-0.991757 + 0.572591i) q^{11} +(-0.640322 - 2.38971i) q^{13} +(-1.20215 + 2.08219i) q^{14} +(0.500000 + 0.866025i) q^{16} +(4.99855 - 4.99855i) q^{17} +2.78390i q^{19} +(-0.994679 + 2.00265i) q^{20} +(-1.10616 + 0.296395i) q^{22} +(5.95746 - 1.59630i) q^{23} +(-4.96085 + 0.624462i) q^{25} -2.47401i q^{26} +(-1.70010 + 1.70010i) q^{28} +(-0.672250 - 1.16437i) q^{29} +(1.25223 - 2.16892i) q^{31} +(0.258819 + 0.965926i) q^{32} +(6.12195 - 3.53451i) q^{34} +(-5.26988 - 1.06381i) q^{35} +(-8.16761 - 8.16761i) q^{37} +(-0.720527 + 2.68904i) q^{38} +(-1.47911 + 1.67697i) q^{40} +(1.70826 + 0.986264i) q^{41} +(8.68498 + 2.32713i) q^{43} -1.14518 q^{44} +6.16761 q^{46} +(-11.9118 - 3.19175i) q^{47} +(1.05598 + 0.609669i) q^{49} +(-4.95344 - 0.680779i) q^{50} +(0.640322 - 2.38971i) q^{52} +(-1.84828 - 1.84828i) q^{53} +(-1.41660 - 2.13318i) q^{55} +(-2.08219 + 1.20215i) q^{56} +(-0.347982 - 1.29869i) q^{58} +(-1.31456 + 2.27688i) q^{59} +(-3.54275 - 6.13623i) q^{61} +(1.77092 - 1.77092i) q^{62} +1.00000i q^{64} +(5.24351 - 1.76334i) q^{65} +(0.0545285 - 0.0146109i) q^{67} +(6.82815 - 1.82960i) q^{68} +(-4.81498 - 2.39151i) q^{70} +9.10005i q^{71} +(7.82779 - 7.82779i) q^{73} +(-5.77537 - 10.0032i) q^{74} +(-1.39195 + 2.41093i) q^{76} +(-0.712623 - 2.65955i) q^{77} +(-8.46375 + 4.88655i) q^{79} +(-1.86274 + 1.23701i) q^{80} +(1.39479 + 1.39479i) q^{82} +(-0.724794 + 2.70497i) q^{83} +(11.8545 + 10.4559i) q^{85} +(7.78674 + 4.49568i) q^{86} +(-1.10616 - 0.296395i) q^{88} +4.87832 q^{89} +5.94827 q^{91} +(5.95746 + 1.59630i) q^{92} +(-10.6798 - 6.16599i) q^{94} +(-6.21280 + 0.389491i) q^{95} +(2.08981 - 7.79929i) q^{97} +(0.862203 + 0.862203i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{5} + 8 q^{7}+O(q^{10}) \) 16 * q + 12 * q^5 + 8 * q^7	\( 16 q + 12 q^{5} + 8 q^{7} - 8 q^{10} + 8 q^{16} + 12 q^{20} + 8 q^{22} + 24 q^{23} - 16 q^{25} - 16 q^{28} - 8 q^{31} - 24 q^{38} - 4 q^{40} - 24 q^{41} - 32 q^{46} - 48 q^{47} - 24 q^{50} + 24 q^{55} - 24 q^{56} + 16 q^{58} - 24 q^{61} - 16 q^{67} + 24 q^{68} + 16 q^{70} + 16 q^{73} + 16 q^{76} + 72 q^{77} - 16 q^{82} - 48 q^{83} - 4 q^{85} + 48 q^{86} + 8 q^{88} + 24 q^{92} - 84 q^{95} - 48 q^{97}+O(q^{100}) \) 16 * q + 12 * q^5 + 8 * q^7 - 8 * q^10 + 8 * q^16 + 12 * q^20 + 8 * q^22 + 24 * q^23 - 16 * q^25 - 16 * q^28 - 8 * q^31 - 24 * q^38 - 4 * q^40 - 24 * q^41 - 32 * q^46 - 48 * q^47 - 24 * q^50 + 24 * q^55 - 24 * q^56 + 16 * q^58 - 24 * q^61 - 16 * q^67 + 24 * q^68 + 16 * q^70 + 16 * q^73 + 16 * q^76 + 72 * q^77 - 16 * q^82 - 48 * q^83 - 4 * q^85 + 48 * q^86 + 8 * q^88 + 24 * q^92 - 84 * q^95 - 48 * q^97

Introduction

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