LMFDB - Embedded newform 675.2.r.a.46.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(46,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 18]))

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

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

chi := DirichletCharacter("675.46");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.r (of order $15$, degree $8$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 225)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			46.16
Character	$\chi$	$=$	675.46
Dual form			675.2.r.a.631.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.220390 + 0.244767i) q^{2} +(0.197717 - 1.88116i) q^{4} +(-2.09765 + 0.774498i) q^{5} +(-1.22023 + 2.11349i) q^{7} +(1.03695 - 0.753387i) q^{8} +(-0.651873 - 0.342746i) q^{10} +(-1.13179 - 1.25698i) q^{11} +(-1.44915 + 1.60944i) q^{13} +(-0.786239 + 0.167120i) q^{14} +(-3.28743 - 0.698765i) q^{16} +(3.09482 - 2.24852i) q^{17} +(-4.15077 + 3.01571i) q^{19} +(1.04221 + 4.09915i) q^{20} +(0.0582329 - 0.554049i) q^{22} +(-8.53438 + 1.81404i) q^{23} +(3.80031 - 3.24926i) q^{25} -0.713316 q^{26} +(3.73455 + 2.71331i) q^{28} +(-5.29950 + 2.35949i) q^{29} +(-6.49762 - 2.89293i) q^{31} +(-1.83522 - 3.17869i) q^{32} +(1.23243 + 0.261961i) q^{34} +(0.922715 - 5.37844i) q^{35} +(2.56039 + 7.88008i) q^{37} +(-1.65293 - 0.351342i) q^{38} +(-1.59166 + 2.38346i) q^{40} +(-2.89941 + 3.22012i) q^{41} +(-3.28981 + 5.69811i) q^{43} +(-2.58834 + 1.88054i) q^{44} +(-2.32491 - 1.68914i) q^{46} +(7.27748 - 3.24014i) q^{47} +(0.522100 + 0.904304i) q^{49} +(1.63286 + 0.214089i) q^{50} +(2.74109 + 3.04429i) q^{52} +(2.04603 + 1.48652i) q^{53} +(3.34762 + 1.76013i) q^{55} +(0.326967 + 3.11088i) q^{56} +(-1.74548 - 0.777139i) q^{58} +(0.645013 - 0.716360i) q^{59} +(-5.83429 - 6.47963i) q^{61} +(-0.723913 - 2.22798i) q^{62} +(-1.70356 + 5.24301i) q^{64} +(1.79330 - 4.49841i) q^{65} +(3.08866 + 1.37516i) q^{67} +(-3.61791 - 6.26641i) q^{68} +(1.51982 - 0.959501i) q^{70} +(0.529305 + 0.384563i) q^{71} +(3.37004 - 10.3719i) q^{73} +(-1.36450 + 2.36339i) q^{74} +(4.85234 + 8.40450i) q^{76} +(4.03764 - 0.858227i) q^{77} +(5.75281 - 2.56132i) q^{79} +(7.43708 - 1.08034i) q^{80} -1.42718 q^{82} +(-1.49547 - 14.2285i) q^{83} +(-4.75039 + 7.11355i) q^{85} +(-2.11975 + 0.450567i) q^{86} +(-2.12059 - 0.450746i) q^{88} +(2.96245 - 9.11749i) q^{89} +(-1.63326 - 5.02664i) q^{91} +(1.72509 + 16.4132i) q^{92} +(2.39696 + 1.06720i) q^{94} +(6.37122 - 9.54068i) q^{95} +(-1.40779 + 0.626788i) q^{97} +(-0.106279 + 0.327092i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8} - 20 q^{10} + 11 q^{11} - 3 q^{13} - q^{14} + 23 q^{16} + 24 q^{17} - 12 q^{19} - q^{20} - 11 q^{22} - q^{23} - 16 q^{25} + 136 q^{26} + 4 q^{28}+ \cdots - 146 q^{98}+O(q^{100}) $ 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8 - 20 * q^10 + 11 * q^11 - 3 * q^13 - q^14 + 23 * q^16 + 24 * q^17 - 12 * q^19 - q^20 - 11 * q^22 - q^23 - 16 * q^25 + 136 * q^26 + 4 * q^28 + 15 * q^29 + 3 * q^31 - 12 * q^32 + q^34 - 14 * q^35 - 24 * q^37 - 55 * q^38 + q^40 + 19 * q^41 - 8 * q^43 - 4 * q^44 - 20 * q^46 + 10 * q^47 - 72 * q^49 + 3 * q^50 - 25 * q^52 + 12 * q^53 - 20 * q^55 + 60 * q^56 - 23 * q^58 + 30 * q^59 - 3 * q^61 + 44 * q^62 - 44 * q^64 - 51 * q^65 - 12 * q^67 + 156 * q^68 - 16 * q^70 - 42 * q^71 - 12 * q^73 - 90 * q^74 - 8 * q^76 - 31 * q^77 - 15 * q^79 - 298 * q^80 + 8 * q^82 - 59 * q^83 - 11 * q^85 - 9 * q^86 - 23 * q^88 - 106 * q^89 + 30 * q^91 - 11 * q^92 + 25 * q^94 - 7 * q^95 - 21 * q^97 - 146 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.220390	+	0.244767i	0.155839	+	0.173077i	0.816008	−	0.578040i	$-0.196182\pi$
$2$	0.220390	+	0.244767i	0.155839	+	0.173077i	−0.660169	+	0.751117i	$0.729516\pi$
$3$		0			0
$3$		0			0
$4$	0.197717	−	1.88116i	0.0988587	−	0.940578i
$5$	−2.09765	+	0.774498i	−0.938099	+	0.346366i
$5$	−2.09765	+	0.774498i	−0.938099	+	0.346366i
$6$		0			0
$7$	−1.22023	+	2.11349i	−0.461202	+	0.798825i	−0.999021	−	0.0442351i	$-0.985915\pi$
$7$	−1.22023	+	2.11349i	−0.461202	+	0.798825i	0.537819	+	0.843060i	$0.319248\pi$
$8$	1.03695	−	0.753387i	0.366616	−	0.266362i
$9$		0			0
$10$	−0.651873	−	0.342746i	−0.206140	−	0.108386i
$11$	−1.13179	−	1.25698i	−0.341246	−	0.378992i	0.547956	−	0.836507i	$-0.315406\pi$
$11$	−1.13179	−	1.25698i	−0.341246	−	0.378992i	−0.889202	+	0.457515i	$0.848740\pi$
$12$		0			0
$13$	−1.44915	+	1.60944i	−0.401921	+	0.446379i	−0.909798	−	0.415051i	$-0.863764\pi$
$13$	−1.44915	+	1.60944i	−0.401921	+	0.446379i	0.507877	+	0.861430i	$0.330430\pi$
$14$	−0.786239	+	0.167120i	−0.210131	+	0.0446648i
$15$		0			0
$16$	−3.28743	−	0.698765i	−0.821857	−	0.174691i
$17$	3.09482	−	2.24852i	0.750604	−	0.545346i	−0.145410	−	0.989372i	$-0.546450\pi$
$17$	3.09482	−	2.24852i	0.750604	−	0.545346i	0.896014	+	0.444025i	$0.146450\pi$
$18$		0			0
$19$	−4.15077	+	3.01571i	−0.952252	+	0.691851i	−0.951338	−	0.308148i	$-0.900291\pi$
$19$	−4.15077	+	3.01571i	−0.952252	+	0.691851i	−0.000913382		1.00000i	$0.500291\pi$
$20$	1.04221	+	4.09915i	0.233045	+	0.916597i
$21$		0			0
$22$	0.0582329	−	0.554049i	0.0124153	−	0.118124i
$23$	−8.53438	+	1.81404i	−1.77954	+	0.378253i	−0.976133	−	0.217175i	$-0.930316\pi$
$23$	−8.53438	+	1.81404i	−1.77954	+	0.378253i	−0.803409	+	0.595428i	$0.796982\pi$
$24$		0			0
$25$	3.80031	−	3.24926i	0.760061	−	0.649852i
$26$	−0.713316			−0.139893
$27$		0			0
$28$	3.73455	+	2.71331i	0.705763	+	0.512767i
$29$	−5.29950	+	2.35949i	−0.984093	+	0.438147i	−0.834744	−	0.550638i	$-0.814384\pi$
$29$	−5.29950	+	2.35949i	−0.984093	+	0.438147i	−0.149349	+	0.988785i	$0.547718\pi$
$30$		0			0
$31$	−6.49762	−	2.89293i	−1.16701	−	0.519585i	−0.270545	−	0.962707i	$-0.587204\pi$
$31$	−6.49762	−	2.89293i	−1.16701	−	0.519585i	−0.896461	+	0.443123i	$0.853871\pi$
$32$	−1.83522	−	3.17869i	−0.324424	−	0.561918i
$33$		0			0
$34$	1.23243	+	0.261961i	0.211360	+	0.0449260i
$35$	0.922715	−	5.37844i	0.155967	−	0.909122i
$36$		0			0
$37$	2.56039	+	7.88008i	0.420926	+	1.29548i	0.906842	+	0.421472i	$0.138486\pi$
$37$	2.56039	+	7.88008i	0.420926	+	1.29548i	−0.485916	+	0.874006i	$0.661514\pi$
$38$	−1.65293	−	0.351342i	−0.268141	−	0.0569952i
$39$		0			0
$40$	−1.59166	+	2.38346i	−0.251664	+	0.376858i
$41$	−2.89941	+	3.22012i	−0.452812	+	0.502898i	−0.925718	−	0.378214i	$-0.876538\pi$
$41$	−2.89941	+	3.22012i	−0.452812	+	0.502898i	0.472906	+	0.881113i	$0.343205\pi$
$42$		0			0
$43$	−3.28981	+	5.69811i	−0.501691	+	0.868954i	0.498307	+	0.867001i	$0.333955\pi$
$43$	−3.28981	+	5.69811i	−0.501691	+	0.868954i	−0.999998	+	0.00195353i	$0.999378\pi$
$44$	−2.58834	+	1.88054i	−0.390207	+	0.283502i
$45$		0			0
$46$	−2.32491	−	1.68914i	−0.342789	−	0.249051i
$47$	7.27748	−	3.24014i	1.06153	−	0.472623i	0.199719	−	0.979853i	$-0.435997\pi$
$47$	7.27748	−	3.24014i	1.06153	−	0.472623i	0.861811	+	0.507230i	$0.169330\pi$
$48$		0			0
$49$	0.522100	+	0.904304i	0.0745857	+	0.129186i
$50$	1.63286	+	0.214089i	0.230921	+	0.0302767i
$51$		0			0
$52$	2.74109	+	3.04429i	0.380120	+	0.422166i
$53$	2.04603	+	1.48652i	0.281043	+	0.204190i	0.719372	−	0.694625i	$-0.244430\pi$
$53$	2.04603	+	1.48652i	0.281043	+	0.204190i	−0.438329	+	0.898815i	$0.644430\pi$
$54$		0			0
$55$	3.34762	+	1.76013i	0.451393	+	0.237336i
$56$	0.326967	+	3.11088i	0.0436928	+	0.415709i
$57$		0			0
$58$	−1.74548	−	0.777139i	−0.229193	−	0.102043i
$59$	0.645013	−	0.716360i	0.0839736	−	0.0932621i	−0.699694	−	0.714443i	$-0.746680\pi$
$59$	0.645013	−	0.716360i	0.0839736	−	0.0932621i	0.783667	+	0.621181i	$0.213347\pi$
$60$		0			0
$61$	−5.83429	−	6.47963i	−0.747004	−	0.829632i	0.243095	−	0.970002i	$-0.421837\pi$
$61$	−5.83429	−	6.47963i	−0.747004	−	0.829632i	−0.990099	+	0.140371i	$0.955171\pi$
$62$	−0.723913	−	2.22798i	−0.0919371	−	0.282953i
$63$		0			0
$64$	−1.70356	+	5.24301i	−0.212945	+	0.655376i
$65$	1.79330	−	4.49841i	0.222432	−	0.557959i
$66$		0			0
$67$	3.08866	+	1.37516i	0.377339	+	0.168002i	0.586638	−	0.809850i	$-0.300451\pi$
$67$	3.08866	+	1.37516i	0.377339	+	0.168002i	−0.209298	+	0.977852i	$0.567118\pi$
$68$	−3.61791	−	6.26641i	−0.438737	−	0.759914i
$69$		0			0
$70$	1.51982	−	0.959501i	0.181654	−	0.114682i
$71$	0.529305	+	0.384563i	0.0628170	+	0.0456392i	0.618751	−	0.785587i	$-0.287639\pi$
$71$	0.529305	+	0.384563i	0.0628170	+	0.0456392i	−0.555934	+	0.831227i	$0.687639\pi$
$72$		0			0
$73$	3.37004	−	10.3719i	0.394434	−	1.21394i	−0.534968	−	0.844872i	$-0.679676\pi$
$73$	3.37004	−	10.3719i	0.394434	−	1.21394i	0.929402	−	0.369070i	$-0.120324\pi$
$74$	−1.36450	+	2.36339i	−0.158620	+	0.274738i
$75$		0			0
$76$	4.85234	+	8.40450i	0.556602	+	0.964062i
$77$	4.03764	−	0.858227i	0.460132	−	0.0978041i
$78$		0			0
$79$	5.75281	−	2.56132i	0.647242	−	0.288171i	−0.0567394	−	0.998389i	$-0.518070\pi$
$79$	5.75281	−	2.56132i	0.647242	−	0.288171i	0.703982	+	0.710218i	$0.251404\pi$
$80$	7.43708	−	1.08034i	0.831491	−	0.120786i
$81$		0			0
$82$	−1.42718			−0.157606
$83$	−1.49547	−	14.2285i	−0.164150	−	1.56178i	−0.697936	−	0.716160i	$-0.745898\pi$
$83$	−1.49547	−	14.2285i	−0.164150	−	1.56178i	0.533786	−	0.845620i	$-0.320769\pi$
$84$		0			0
$85$	−4.75039	+	7.11355i	−0.515252	+	0.771573i
$86$	−2.11975	+	0.450567i	−0.228579	+	0.0485859i
$87$		0			0
$88$	−2.12059	−	0.450746i	−0.226056	−	0.0480496i
$89$	2.96245	−	9.11749i	0.314019	−	0.966452i	−0.662137	−	0.749383i	$-0.730350\pi$
$89$	2.96245	−	9.11749i	0.314019	−	0.966452i	0.976156	−	0.217069i	$-0.0696496\pi$
$90$		0			0
$91$	−1.63326	−	5.02664i	−0.171212	−	0.526935i
$92$	1.72509	+	16.4132i	0.179853	+	1.71119i
$93$		0			0
$94$	2.39696	+	1.06720i	0.247228	+	0.110073i
$95$	6.37122	−	9.54068i	0.653673	−	0.978853i
$96$		0			0
$97$	−1.40779	+	0.626788i	−0.142939	+	0.0636407i	−0.476960	−	0.878925i	$-0.658261\pi$
$97$	−1.40779	+	0.626788i	−0.142939	+	0.0636407i	0.334020	+	0.942566i	$0.391595\pi$
$98$	−0.106279	+	0.327092i	−0.0107358	+	0.0330413i
$99$		0			0
$100$	−5.36097	−	7.79140i	−0.536097	−	0.779140i
$101$	−4.44731	+	7.70297i	−0.442524	+	0.766474i	−0.997876	−	0.0651410i	$-0.979250\pi$
$101$	−4.44731	+	7.70297i	−0.442524	+	0.766474i	0.555352	+	0.831616i	$0.312584\pi$
$102$		0			0
$103$	1.03592	−	9.85609i	0.102072	−	0.971150i	−0.816887	−	0.576797i	$-0.804302\pi$
$103$	1.03592	−	9.85609i	0.102072	−	0.971150i	0.918959	−	0.394353i	$-0.129031\pi$
$104$	−0.290159	+	2.76067i	−0.0284524	+	0.270706i
$105$		0			0
$106$	0.0870699	+	0.828415i	0.00845698	+	0.0804628i
$107$	−0.789838			−0.0763565			−0.0381783	−	0.999271i	$-0.512155\pi$
$107$	−0.789838			−0.0763565			−0.0381783	+	0.999271i	$0.512155\pi$
$108$		0			0
$109$	−5.37002	−	16.5272i	−0.514354	−	1.58302i	−0.784454	−	0.620187i	$-0.787057\pi$
$109$	−5.37002	−	16.5272i	−0.514354	−	1.58302i	0.270100	−	0.962832i	$-0.412943\pi$
$110$	0.306957	+	1.20730i	0.0292672	+	0.115112i
$111$		0			0
$112$	5.48824	−	6.09531i	0.518590	−	0.575952i
$113$	−1.45439	+	1.61527i	−0.136818	+	0.151951i	−0.807660	−	0.589649i	$-0.799266\pi$
$113$	−1.45439	+	1.61527i	−0.136818	+	0.151951i	0.670842	+	0.741600i	$0.265933\pi$
$114$		0			0
$115$	16.4972	−	10.4151i	1.53837	−	0.971212i
$116$	3.39077	+	10.4357i	0.314825	+	0.968931i
$117$		0			0
$118$	0.317496			0.0292279
$119$	0.975849	+	9.28458i	0.0894559	+	0.851116i
$120$		0			0
$121$	0.850765	−	8.09449i	0.0773423	−	0.735862i
$122$	0.300187	−	2.85609i	0.0271776	−	0.258578i
$123$		0			0
$124$	−6.72673	+	11.6510i	−0.604079	+	1.04629i
$125$	−5.45518	+	9.75915i	−0.487926	+	0.872885i
$126$		0			0
$127$	−4.55776	+	14.0274i	−0.404436	+	1.24473i	0.516929	+	0.856028i	$0.327075\pi$
$127$	−4.55776	+	14.0274i	−0.404436	+	1.24473i	−0.921365	+	0.388698i	$0.872925\pi$
$128$	−8.36498	+	3.72433i	−0.739367	+	0.329187i
$129$		0			0
$130$	1.49629	−	0.552462i	0.131233	−	0.0484541i
$131$	1.92662	+	0.857787i	0.168330	+	0.0749452i	0.489172	−	0.872188i	$-0.337299\pi$
$131$	1.92662	+	0.857787i	0.168330	+	0.0749452i	−0.320842	+	0.947133i	$0.603966\pi$
$132$		0			0
$133$	−1.30881	−	12.4525i	−0.113488	−	1.07977i
$134$	0.344114	+	1.05907i	0.0297269	+	0.0914900i
$135$		0			0
$136$	1.51516	−	4.66319i	0.129924	−	0.399866i
$137$	4.51172	+	0.958996i	0.385463	+	0.0819326i	0.396567	−	0.918006i	$-0.370201\pi$
$137$	4.51172	+	0.958996i	0.385463	+	0.0819326i	−0.0111045	+	0.999938i	$0.503535\pi$
$138$		0			0
$139$	3.91514	−	0.832189i	0.332078	−	0.0705853i	−0.0388554	−	0.999245i	$-0.512371\pi$
$139$	3.91514	−	0.832189i	0.332078	−	0.0705853i	0.370933	+	0.928660i	$0.379038\pi$
$140$	−9.93524	−	2.79918i	−0.839681	−	0.236574i
$141$		0			0
$142$	0.0225249	+	0.214310i	0.00189025	+	0.0179845i
$143$	3.66315			0.306328
$144$		0			0
$145$	9.28911	−	9.05385i	0.771418	−	0.751882i
$146$	3.28143	−	1.46099i	0.271573	−	0.120912i
$147$		0			0
$148$	15.3299	−	3.25847i	1.26011	−	0.267844i
$149$	6.88364	+	11.9228i	0.563929	+	0.976755i	0.997148	+	0.0754658i	$0.0240444\pi$
$149$	6.88364	+	11.9228i	0.563929	+	0.976755i	−0.433219	+	0.901289i	$0.642622\pi$
$150$		0			0
$151$	−10.1492	+	17.5789i	−0.825931	+	1.43055i	0.0752750	+	0.997163i	$0.476017\pi$
$151$	−10.1492	+	17.5789i	−0.825931	+	1.43055i	−0.901206	+	0.433391i	$0.857317\pi$
$152$	−2.03213	+	6.25427i	−0.164828	+	0.507288i
$153$		0			0
$154$	1.09992	+	0.799139i	0.0886341	+	0.0643965i
$155$	15.8703	+	1.03597i	1.27473	+	0.0832108i
$156$		0			0
$157$	−4.22601	−	7.31966i	−0.337272	−	0.584172i	0.646647	−	0.762790i	$-0.276171\pi$
$157$	−4.22601	−	7.31966i	−0.337272	−	0.584172i	−0.983919	+	0.178618i	$0.942838\pi$
$158$	1.89479	+	0.843614i	0.150741	+	0.0671143i
$159$		0			0
$160$	6.31154	+	5.24642i	0.498971	+	0.414766i
$161$	6.57991	−	20.2509i	0.518570	−	1.59599i
$162$		0			0
$163$	2.21761	+	6.82510i	0.173696	+	0.534583i	0.999572	−	0.0292704i	$-0.00931840\pi$
$163$	2.21761	+	6.82510i	0.173696	+	0.534583i	−0.825875	+	0.563853i	$0.809318\pi$
$164$	5.48428	+	6.09091i	0.428250	+	0.475620i
$165$		0			0
$166$	3.15308	−	3.50186i	0.244727	−	0.271797i
$167$	5.53430	+	2.46403i	0.428257	+	0.190672i	0.609534	−	0.792760i	$-0.291357\pi$
$167$	5.53430	+	2.46403i	0.428257	+	0.190672i	−0.181277	+	0.983432i	$0.558023\pi$
$168$		0			0
$169$	0.868597	+	8.26415i	0.0668152	+	0.635704i
$170$	−2.78810	+	0.405011i	−0.213838	+	0.0310629i
$171$		0			0
$172$	10.0686	+	7.31525i	0.767722	+	0.557783i
$173$	13.0611	+	14.5058i	0.993017	+	1.10286i	0.994696	+	0.102858i	$0.0327987\pi$
$173$	13.0611	+	14.5058i	0.993017	+	1.10286i	−0.00167954	+	0.999999i	$0.500535\pi$
$174$		0			0
$175$	2.23005	+	11.9967i	0.168576	+	0.906869i
$176$	2.84234	+	4.92307i	0.214249	+	0.371090i
$177$		0			0
$178$	2.88456	−	1.28429i	0.216207	−	0.0962614i
$179$	3.88878	+	2.82536i	0.290661	+	0.211178i	0.723554	−	0.690268i	$-0.242507\pi$
$179$	3.88878	+	2.82536i	0.290661	+	0.211178i	−0.432893	+	0.901445i	$0.642507\pi$
$180$		0			0
$181$	4.50290	−	3.27155i	0.334698	−	0.243172i	−0.407724	−	0.913105i	$-0.633677\pi$
$181$	4.50290	−	3.27155i	0.334698	−	0.243172i	0.742421	+	0.669933i	$0.233677\pi$
$182$	0.870406	−	1.50759i	0.0645188	−	0.111750i
$183$		0			0
$184$	−7.48303	+	8.31075i	−0.551656	+	0.612677i
$185$	−11.4739	−	14.5467i	−0.843580	−	1.06949i
$186$		0			0
$187$	−6.32901	−	1.34527i	−0.462823	−	0.0983761i
$188$	−4.65633	−	14.3307i	−0.339598	−	1.04517i
$189$		0			0
$190$	3.73940	−	0.543200i	0.271284	−	0.0394079i
$191$	−23.1633	−	4.92352i	−1.67604	−	0.356254i	−0.730791	−	0.682601i	$-0.760849\pi$
$191$	−23.1633	−	4.92352i	−1.67604	−	0.356254i	−0.945250	+	0.326347i	$0.894182\pi$
$192$		0			0
$193$	−0.637107	−	1.10350i	−0.0458600	−	0.0794318i	0.842184	−	0.539190i	$-0.181269\pi$
$193$	−0.637107	−	1.10350i	−0.0458600	−	0.0794318i	−0.888044	+	0.459758i	$0.847936\pi$
$194$	−0.463679	−	0.206443i	−0.0332902	−	0.0148218i
$195$		0			0
$196$	1.80436	−	0.803355i	0.128883	−	0.0573825i
$197$	7.96236	+	5.78499i	0.567295	+	0.412164i	0.834122	−	0.551581i	$-0.185975\pi$
$197$	7.96236	+	5.78499i	0.567295	+	0.412164i	−0.266827	+	0.963745i	$0.585975\pi$
$198$		0			0
$199$	−18.5853			−1.31747			−0.658737	−	0.752373i	$-0.728909\pi$
$199$	−18.5853			−1.31747			−0.658737	+	0.752373i	$0.728909\pi$
$200$	1.49277	−	6.23241i	0.105555	−	0.440698i
$201$		0			0
$202$	−2.86558	+	0.609098i	−0.201621	+	0.0428560i
$203$	1.47982	−	14.0796i	0.103863	−	0.988192i
$204$		0			0
$205$	3.58798	−	9.00028i	0.250595	−	0.628607i
$206$	2.64076	−	1.91862i	0.183990	−	0.133677i
$207$		0			0
$208$	5.88859	−	4.27831i	0.408300	−	0.296647i
$209$	8.48846	+	1.80428i	0.587159	+	0.124804i
$210$		0			0
$211$	−2.15974	+	0.459067i	−0.148683	+	0.0316035i	−0.281652	−	0.959517i	$-0.590882\pi$
$211$	−2.15974	+	0.459067i	−0.148683	+	0.0316035i	0.132969	+	0.991120i	$0.457549\pi$
$212$	3.20092	−	3.55498i	0.219840	−	0.244157i
$213$		0			0
$214$	−0.174072	−	0.193327i	−0.0118993	−	0.0132155i
$215$	2.48770	−	14.5006i	0.169660	−	0.988934i
$216$		0			0
$217$	14.0427	−	10.2026i	0.953283	−	0.692600i
$218$	2.86183	−	4.95683i	0.193827	−	0.335719i
$219$		0			0
$220$	3.97297	−	5.94939i	0.267857	−	0.401107i
$221$	−0.865993	+	8.23937i	−0.0582530	+	0.554240i
$222$		0			0
$223$	−17.5445	−	19.4851i	−1.17486	−	1.30482i	−0.943278	−	0.332003i	$-0.892275\pi$
$223$	−17.5445	−	19.4851i	−1.17486	−	1.30482i	−0.231585	−	0.972815i	$-0.574391\pi$
$224$	8.95752			0.598499
$225$		0			0
$226$	−0.715897			−0.0476208
$227$	4.96062	+	5.50933i	0.329248	+	0.365667i	0.884927	−	0.465730i	$-0.154208\pi$
$227$	4.96062	+	5.50933i	0.329248	+	0.365667i	−0.555679	+	0.831397i	$0.687542\pi$
$228$		0			0
$229$	−2.13178	+	20.2826i	−0.140872	+	1.34031i	0.664387	+	0.747388i	$0.268693\pi$
$229$	−2.13178	+	20.2826i	−0.140872	+	1.34031i	−0.805260	+	0.592922i	$0.797974\pi$
$230$	6.18509	+	1.74260i	0.407833	+	0.114904i
$231$		0			0
$232$	−3.71770	+	6.43924i	−0.244079	+	0.422757i
$233$	−6.14372	+	4.46367i	−0.402488	+	0.292425i	−0.770554	−	0.637375i	$-0.780020\pi$
$233$	−6.14372	+	4.46367i	−0.402488	+	0.292425i	0.368065	+	0.929800i	$0.380020\pi$
$234$		0			0
$235$	−12.7562	+	12.4331i	−0.832120	+	0.811045i
$236$	−1.22005	−	1.35501i	−0.0794187	−	0.0882034i
$237$		0			0
$238$	−2.05750	+	2.28508i	−0.133368	+	0.148120i
$239$	15.8639	−	3.37198i	1.02615	−	0.218115i	0.336062	−	0.941840i	$-0.390905\pi$
$239$	15.8639	−	3.37198i	1.02615	−	0.218115i	0.690089	+	0.723725i	$0.257571\pi$
$240$		0			0
$241$	14.3594	+	3.05219i	0.924972	+	0.196609i	0.645689	−	0.763600i	$-0.276570\pi$
$241$	14.3594	+	3.05219i	0.924972	+	0.196609i	0.279282	+	0.960209i	$0.409903\pi$
$242$	2.16877	−	1.57570i	0.139414	−	0.101290i
$243$		0			0
$244$	−13.3427	+	9.69406i	−0.854181	+	0.620599i
$245$	−1.79557	−	1.49255i	−0.114715	−	0.0953556i
$246$		0			0
$247$	1.16147	−	11.0506i	0.0739024	−	0.703135i
$248$	−8.91718	+	1.89540i	−0.566241	+	0.120358i
$249$		0			0
$250$	−3.59099	+	0.815563i	−0.227114	+	0.0515808i
$251$	−17.7351			−1.11943			−0.559716	−	0.828685i	$-0.689090\pi$
$251$	−17.7351			−1.11943			−0.559716	+	0.828685i	$0.689090\pi$
$252$		0			0
$253$	11.9393	+	8.67440i	0.750617	+	0.545355i
$254$	−4.43792	+	1.97589i	−0.278460	+	0.123978i
$255$		0			0
$256$	7.31728	+	3.25786i	0.457330	+	0.203616i
$257$	3.02034	+	5.23139i	0.188404	+	0.326325i	0.944718	−	0.327883i	$-0.106335\pi$
$257$	3.02034	+	5.23139i	0.188404	+	0.326325i	−0.756314	+	0.654208i	$0.773002\pi$
$258$		0			0
$259$	−19.7787	−	4.20410i	−1.22899	−	0.261230i
$260$	−8.10765	−	4.26289i	−0.502815	−	0.264373i
$261$		0			0
$262$	0.214649	+	0.660622i	0.0132611	+	0.0408133i
$263$	−9.90415	−	2.10519i	−0.610716	−	0.129812i	−0.107837	−	0.994169i	$-0.534392\pi$
$263$	−9.90415	−	2.10519i	−0.610716	−	0.129812i	−0.502879	+	0.864357i	$0.667726\pi$
$264$		0			0
$265$	−5.44317	−	1.53357i	−0.334371	−	0.0942066i
$266$	2.75951	−	3.06475i	0.169196	−	0.187912i
$267$		0			0
$268$	3.19757	−	5.53835i	0.195323	−	0.338309i
$269$	−21.9237	+	15.9285i	−1.33671	+	0.971177i	−0.337153	+	0.941450i	$0.609464\pi$
$269$	−21.9237	+	15.9285i	−1.33671	+	0.971177i	−0.999558	+	0.0297274i	$0.990536\pi$
$270$		0			0
$271$	−8.50805	−	6.18146i	−0.516827	−	0.375497i	0.298580	−	0.954385i	$-0.403487\pi$
$271$	−8.50805	−	6.18146i	−0.516827	−	0.375497i	−0.815407	+	0.578888i	$0.803487\pi$
$272$	−11.7452	+	5.22930i	−0.712157	+	0.317073i
$273$		0			0
$274$	0.759606	+	1.31568i	0.0458895	+	0.0794829i
$275$	−8.38537	−	1.09943i	−0.505657	−	0.0662980i
$276$		0			0
$277$	10.8806	+	12.0841i	0.653753	+	0.726066i	0.975314	−	0.220823i	$-0.0708743\pi$
$277$	10.8806	+	12.0841i	0.653753	+	0.726066i	−0.321561	+	0.946889i	$0.604208\pi$
$278$	1.06655	+	0.774893i	0.0639674	+	0.0464750i
$279$		0			0
$280$	−3.09524	−	6.27232i	−0.184976	−	0.374843i
$281$	−1.58707	−	15.0999i	−0.0946766	−	0.900787i	−0.934028	−	0.357199i	$-0.883732\pi$
$281$	−1.58707	−	15.0999i	−0.0946766	−	0.900787i	0.839352	−	0.543589i	$-0.182935\pi$
$282$		0			0
$283$	−1.72853	−	0.769590i	−0.102750	−	0.0457474i	0.354718	−	0.934973i	$-0.384577\pi$
$283$	−1.72853	−	0.769590i	−0.102750	−	0.0457474i	−0.457468	+	0.889226i	$0.651244\pi$
$284$	0.828075	−	0.919670i	0.0491372	−	0.0545724i
$285$		0			0
$286$	0.807321	+	0.896621i	0.0477379	+	0.0530183i
$287$	−3.26777	−	10.0571i	−0.192890	−	0.593655i
$288$		0			0
$289$	−0.731209	+	2.25043i	−0.0430123	+	0.132378i
$290$	4.26331	+	0.278296i	0.250350	+	0.0163421i
$291$		0			0
$292$	−18.8449	−	8.39028i	−1.10281	−	0.491004i
$293$	3.67099	+	6.35834i	0.214462	+	0.371458i	0.953106	−	0.302637i	$-0.0978670\pi$
$293$	3.67099	+	6.35834i	0.214462	+	0.371458i	−0.738644	+	0.674095i	$0.764534\pi$
$294$		0			0
$295$	−0.798195	+	2.00224i	−0.0464727	+	0.116575i
$296$	8.59174	+	6.24227i	0.499385	+	0.362824i
$297$		0			0
$298$	−1.40123	+	4.31255i	−0.0811713	+	0.249820i
$299$	9.44799	−	16.3644i	0.546391	−	0.946377i
$300$		0			0
$301$	−8.02861	−	13.9060i	−0.462761	−	0.801526i
$302$	−6.53953	+	1.39002i	−0.376308	+	0.0799867i
$303$		0			0
$304$	15.7526	−	7.01352i	0.903475	−	0.402253i
$305$	17.2568	+	9.07338i	0.988120	+	0.519540i
$306$		0			0
$307$	4.38216			0.250103			0.125051	−	0.992150i	$-0.460090\pi$
$307$	4.38216			0.250103			0.125051	+	0.992150i	$0.460090\pi$
$308$	−0.816147	−	7.76512i	−0.0465043	−	0.442459i
$309$		0			0
$310$	3.24408	+	4.11285i	0.184251	+	0.233594i
$311$	−17.4478	+	3.70864i	−0.989373	+	0.210298i	−0.674049	−	0.738686i	$-0.735447\pi$
$311$	−17.4478	+	3.70864i	−0.989373	+	0.210298i	−0.315324	+	0.948984i	$0.602113\pi$
$312$		0			0
$313$	−15.9454	−	3.38931i	−0.901290	−	0.191575i	−0.266113	−	0.963942i	$-0.585739\pi$
$313$	−15.9454	−	3.38931i	−0.901290	−	0.191575i	−0.635177	+	0.772367i	$0.719073\pi$
$314$	0.860246	−	2.64756i	0.0485465	−	0.149411i
$315$		0			0
$316$	−3.68081	−	11.3284i	−0.207061	−	0.637270i
$317$	−2.20283	−	20.9585i	−0.123723	−	1.17715i	−0.863519	−	0.504317i	$-0.831744\pi$
$317$	−2.20283	−	20.9585i	−0.123723	−	1.17715i	0.739796	−	0.672832i	$-0.234922\pi$
$318$		0			0
$319$	8.96373	+	3.99091i	0.501872	+	0.223448i
$320$	−0.487227	−	12.3174i	−0.0272368	−	0.688565i
$321$		0			0
$322$	6.40690	−	2.85254i	0.357043	−	0.158966i
$323$	−6.06501	+	18.6662i	−0.337466	+	1.03861i
$324$		0			0
$325$	−0.277714	+	10.8250i	−0.0154048	+	0.600464i
$326$	−1.18182	+	2.04698i	−0.0654551	+	0.113372i
$327$		0			0
$328$	−0.580540	+	5.52347i	−0.0320550	+	0.304983i
$329$	−2.03215	+	19.3346i	−0.112036	+	1.06595i
$330$		0			0
$331$	1.89347	+	18.0152i	0.104075	+	0.990204i	0.914561	+	0.404447i	$0.132536\pi$
$331$	1.89347	+	18.0152i	0.104075	+	0.990204i	−0.810487	+	0.585757i	$0.800797\pi$
$332$	−27.0617			−1.48520
$333$		0			0
$334$	0.616588	+	1.89766i	0.0337382	+	0.103835i
$335$	−7.54399	−	0.492449i	−0.412172	−	0.0269053i
$336$		0			0
$337$	−2.47620	+	2.75010i	−0.134887	+	0.149807i	−0.806804	−	0.590819i	$-0.798805\pi$
$337$	−2.47620	+	2.75010i	−0.134887	+	0.149807i	0.671917	+	0.740627i	$0.265471\pi$
$338$	−1.83137	+	2.03394i	−0.0996131	+	0.110632i
$339$		0			0
$340$	12.4425	+	10.3427i	0.674787	+	0.560911i
$341$	3.71757	+	11.4415i	0.201318	+	0.619593i
$342$		0			0
$343$	−19.6315			−1.06000
$344$	0.881524	+	8.38714i	0.0475286	+	0.452204i
$345$		0			0
$346$	−0.672022	+	6.39386i	−0.0361281	+	0.343736i
$347$	−2.69542	+	25.6452i	−0.144698	+	1.37671i	0.645457	+	0.763797i	$0.276667\pi$
$347$	−2.69542	+	25.6452i	−0.144698	+	1.37671i	−0.790154	+	0.612908i	$0.790000\pi$
$348$		0			0
$349$	15.6853	−	27.1678i	0.839616	−	1.45426i	−0.0506002	−	0.998719i	$-0.516113\pi$
$349$	15.6853	−	27.1678i	0.839616	−	1.45426i	0.890216	−	0.455538i	$-0.150553\pi$
$350$	−2.44493	+	3.18980i	−0.130687	+	0.170502i
$351$		0			0
$352$	−1.91846	+	5.90442i	−0.102254	+	0.314707i
$353$	0.0915256	−	0.0407498i	0.00487142	−	0.00216889i	−0.404299	−	0.914627i	$-0.632485\pi$
$353$	0.0915256	−	0.0407498i	0.00487142	−	0.00216889i	0.409171	+	0.912458i	$0.365818\pi$
$354$		0			0
$355$	−1.40814	−	0.396734i	−0.0747364	−	0.0210564i
$356$	−16.5657	−	7.37552i	−0.877979	−	0.390902i
$357$		0			0
$358$	0.165490	+	1.57453i	0.00874639	+	0.0832164i
$359$	−4.79343	−	14.7527i	−0.252988	−	0.778616i	−0.994219	−	0.107367i	$-0.965758\pi$
$359$	−4.79343	−	14.7527i	−0.252988	−	0.778616i	0.741232	−	0.671249i	$-0.234242\pi$
$360$		0			0
$361$	2.26305	−	6.96496i	0.119108	−	0.366577i
$362$	1.79316	+	0.381148i	0.0942464	+	0.0200327i
$363$		0			0
$364$	−9.77882	+	2.07855i	−0.512549	+	0.108946i
$365$	0.963851	+	24.3668i	0.0504503	+	1.27542i
$366$		0			0
$367$	1.34951	+	12.8397i	0.0704439	+	0.670229i	0.971583	+	0.236699i	$0.0760655\pi$
$367$	1.34951	+	12.8397i	0.0704439	+	0.670229i	−0.901139	+	0.433530i	$0.857268\pi$
$368$	29.3238			1.52861
$369$		0			0
$370$	1.03182	−	6.01438i	0.0536416	−	0.312673i
$371$	−5.63837	+	2.51036i	−0.292730	+	0.130332i
$372$		0			0
$373$	0.226521	−	0.0481486i	0.0117288	−	0.00249304i	−0.202044	−	0.979377i	$-0.564758\pi$
$373$	0.226521	−	0.0481486i	0.0117288	−	0.00249304i	0.213772	+	0.976884i	$0.431425\pi$
$374$	−1.06557	−	1.84562i	−0.0550993	−	0.0954347i
$375$		0			0
$376$	5.10529	−	8.84261i	0.263285	−	0.456023i
$377$	3.88230	−	11.9485i	0.199949	−	0.615379i
$378$		0			0
$379$	4.51376	+	3.27944i	0.231856	+	0.168453i	0.697647	−	0.716441i	$-0.254230\pi$
$379$	4.51376	+	3.27944i	0.231856	+	0.168453i	−0.465791	+	0.884895i	$0.654230\pi$
$380$	−16.6878	−	13.8716i	−0.856066	−	0.711598i
$381$		0			0
$382$	−3.89984	−	6.75473i	−0.199533	−	0.345602i
$383$	12.2595	+	5.45829i	0.626433	+	0.278906i	0.695300	−	0.718720i	$-0.255272\pi$
$383$	12.2595	+	5.45829i	0.626433	+	0.278906i	−0.0688668	+	0.997626i	$0.521938\pi$
$384$		0			0
$385$	−7.80488	+	4.92741i	−0.397774	+	0.251124i
$386$	0.129690	−	0.399143i	0.00660102	−	0.0203159i
$387$		0			0
$388$	0.900742	+	2.77220i	0.0457282	+	0.140737i
$389$	−22.7699	−	25.2885i	−1.15448	−	1.28218i	−0.953097	−	0.302664i	$-0.902124\pi$
$389$	−22.7699	−	25.2885i	−1.15448	−	1.28218i	−0.201380	−	0.979513i	$-0.564543\pi$
$390$		0			0
$391$	−22.3335	+	24.8038i	−1.12945	+	1.25438i
$392$	1.22268	+	0.544373i	0.0617547	+	0.0274950i
$393$		0			0
$394$	0.338843	+	3.22388i	0.0170707	+	0.162417i
$395$	−10.0837	+	9.82830i	−0.507365	+	0.494515i
$396$		0			0
$397$	22.7816	+	16.5518i	1.14338	+	0.830711i	0.987586	−	0.157079i	$-0.0502078\pi$
$397$	22.7816	+	16.5518i	1.14338	+	0.830711i	0.155790	+	0.987790i	$0.450208\pi$
$398$	−4.09600	−	4.54907i	−0.205314	−	0.228024i
$399$		0			0
$400$	−14.7637	+	8.02619i	−0.738185	+	0.401309i
$401$	6.50887	+	11.2737i	0.325037	+	0.562981i	0.981520	−	0.191360i	$-0.0612898\pi$
$401$	6.50887	+	11.2737i	0.325037	+	0.562981i	−0.656483	+	0.754341i	$0.727956\pi$
$402$		0			0
$403$	14.0720	−	6.26526i	0.700976	−	0.312095i
$404$	13.6112	+	9.88910i	0.677181	+	0.492001i
$405$		0			0
$406$	3.77236	−	2.74078i	0.187219	−	0.136023i
$407$	7.00725	−	12.1369i	0.347337	−	0.601605i
$408$		0			0
$409$	22.3589	−	24.8320i	1.10557	−	1.22786i	0.134037	−	0.990976i	$-0.457206\pi$
$409$	22.3589	−	24.8320i	1.10557	−	1.22786i	0.971537	−	0.236888i	$-0.0761275\pi$
$410$	2.99373	−	1.10535i	0.147850	−	0.0545892i
$411$		0			0
$412$	−18.3360	−	3.89744i	−0.903351	−	0.192013i
$413$	0.726959	+	2.23735i	0.0357713	+	0.110093i
$414$		0			0
$415$	14.1569	+	28.6882i	0.694936	+	1.40825i
$416$	7.77542	+	1.65272i	0.381221	+	0.0810311i
$417$		0			0
$418$	1.42914	+	2.47534i	0.0699015	+	0.121073i
$419$	−36.0676	−	16.0583i	−1.76202	−	0.784501i	−0.988593	−	0.150615i	$-0.951875\pi$
$419$	−36.0676	−	16.0583i	−1.76202	−	0.784501i	−0.773426	−	0.633886i	$-0.781459\pi$
$420$		0			0
$421$	2.40676	−	1.07156i	0.117298	−	0.0522246i	−0.347248	−	0.937773i	$-0.612884\pi$
$421$	2.40676	−	1.07156i	0.117298	−	0.0522246i	0.464547	+	0.885549i	$0.346217\pi$
$422$	−0.588349	−	0.427460i	−0.0286404	−	0.0208084i
$423$		0			0
$424$	3.24155			0.157424
$425$	4.45525	−	18.6009i	0.216111	−	0.902278i
$426$		0			0
$427$	20.8138	−	4.42411i	1.00725	−	0.214098i
$428$	−0.156165	+	1.48581i	−0.00754851	+	0.0718192i
$429$		0			0
$430$	4.09754	−	2.58688i	0.197601	−	0.124750i
$431$	−27.7928	+	20.1926i	−1.33873	+	0.972644i	−0.339240	+	0.940700i	$0.610170\pi$
$431$	−27.7928	+	20.1926i	−1.33873	+	0.972644i	−0.999490	+	0.0319446i	$0.989830\pi$
$432$		0			0
$433$	−22.0022	+	15.9856i	−1.05736	+	0.768217i	−0.973598	−	0.228269i	$-0.926694\pi$
$433$	−22.0022	+	15.9856i	−1.05736	+	0.768217i	−0.0837621	+	0.996486i	$0.526694\pi$
$434$	5.59215	+	1.18865i	0.268432	+	0.0570569i
$435$		0			0
$436$	−32.1520	+	6.83412i	−1.53980	+	0.327295i
$437$	29.9536	−	33.2669i	1.43288	−	1.59137i
$438$		0			0
$439$	−10.0470	−	11.1583i	−0.479515	−	0.532556i	0.454044	−	0.890979i	$-0.349981\pi$
$439$	−10.0470	−	11.1583i	−0.479515	−	0.532556i	−0.933559	+	0.358424i	$0.883314\pi$
$440$	4.79737	−	0.696885i	0.228706	−	0.0332227i
$441$		0			0
$442$	−2.20759	+	1.60390i	−0.105004	+	0.0762900i
$443$	−5.24719	+	9.08840i	−0.249301	+	0.431803i	−0.963332	−	0.268312i	$-0.913534\pi$
$443$	−5.24719	+	9.08840i	−0.249301	+	0.431803i	0.714031	+	0.700114i	$0.246868\pi$
$444$		0			0
$445$	0.847277	+	21.4197i	0.0401648	+	1.01539i
$446$	0.902700	−	8.58862i	0.0427441	−	0.406683i
$447$		0			0
$448$	−9.00233	−	9.99810i	−0.425320	−	0.472366i
$449$	−19.5039			−0.920444			−0.460222	−	0.887804i	$-0.652230\pi$
$449$	−19.5039			−0.920444			−0.460222	+	0.887804i	$0.652230\pi$
$450$		0			0
$451$	7.32912			0.345115
$452$	2.75101	+	3.05530i	0.129397	+	0.143709i
$453$		0			0
$454$	−0.255235	+	2.42840i	−0.0119788	+	0.113970i
$455$	7.31913	+	9.27921i	0.343126	+	0.435016i
$456$		0			0
$457$	−6.38012	+	11.0507i	−0.298449	+	0.516929i	−0.975781	−	0.218748i	$-0.929803\pi$
$457$	−6.38012	+	11.0507i	−0.298449	+	0.516929i	0.677332	+	0.735677i	$0.263136\pi$
$458$	−5.43434	+	3.94828i	−0.253930	+	0.184491i
$459$		0			0
$460$	−16.3306	−	33.0931i	−0.761419	−	1.54297i
$461$	9.42808	+	10.4709i	0.439109	+	0.487680i	0.921556	−	0.388245i	$-0.126919\pi$
$461$	9.42808	+	10.4709i	0.439109	+	0.487680i	−0.482447	+	0.875925i	$0.660252\pi$
$462$		0			0
$463$	20.2556	−	22.4961i	0.941356	−	1.04548i	−0.0575325	−	0.998344i	$-0.518323\pi$
$463$	20.2556	−	22.4961i	0.941356	−	1.04548i	0.998888	−	0.0471380i	$-0.0150100\pi$
$464$	19.0705	−	4.05355i	0.885325	−	0.188182i
$465$		0			0
$466$	−2.44657	−	0.520035i	−0.113335	−	0.0240902i
$467$	0.459190	−	0.333621i	0.0212488	−	0.0154382i	−0.577110	−	0.816666i	$-0.695820\pi$
$467$	0.459190	−	0.333621i	0.0212488	−	0.0154382i	0.598359	+	0.801228i	$0.295820\pi$
$468$		0			0
$469$	−6.67524	+	4.84985i	−0.308234	+	0.223945i
$470$	−5.85454	−	0.382166i	−0.270050	−	0.0176280i
$471$		0			0
$472$	0.129149	−	1.22877i	0.00594457	−	0.0565588i
$473$	10.8857	−	2.31384i	0.500527	−	0.106390i
$474$		0			0
$475$	−5.97537	+	24.9475i	−0.274169	+	1.14467i
$476$	17.6587			0.809384
$477$		0			0
$478$	4.32159	+	3.13982i	0.197665	+	0.143612i
$479$	−8.30395	+	3.69716i	−0.379417	+	0.168927i	−0.587579	−	0.809167i	$-0.699919\pi$
$479$	−8.30395	+	3.69716i	−0.379417	+	0.168927i	0.208161	+	0.978094i	$0.433252\pi$
$480$		0			0
$481$	−16.3929	−	7.29860i	−0.747453	−	0.332787i
$482$	2.41759	+	4.18739i	0.110118	+	0.190730i
$483$		0			0
$484$	−15.0588	−	3.20084i	−0.684490	−	0.145493i
$485$	2.46761	−	2.40511i	0.112048	−	0.109211i
$486$		0			0
$487$	−9.84622	−	30.3036i	−0.446175	−	1.37319i	−0.881190	−	0.472762i	$-0.843257\pi$
$487$	−9.84622	−	30.3036i	−0.446175	−	1.37319i	0.435015	−	0.900423i	$-0.356743\pi$
$488$	−10.9315	−	2.32357i	−0.494847	−	0.105183i
$489$		0			0
$490$	−0.0303963	−	0.768439i	−0.00137317	−	0.0347145i
$491$	28.2390	−	31.3625i	1.27441	−	1.41537i	0.410388	−	0.911911i	$-0.365393\pi$
$491$	28.2390	−	31.3625i	1.27441	−	1.41537i	0.864018	−	0.503461i	$-0.167940\pi$
$492$		0			0
$493$	−11.0957	+	19.2182i	−0.499723	+	0.865546i
$494$	2.96081	−	2.15115i	0.133213	−	0.0967850i
$495$		0			0
$496$	19.3390	+	14.0506i	0.868346	+	0.630890i
$497$	−1.45864	+	0.649429i	−0.0654290	+	0.0291309i
$498$		0			0
$499$	9.50928	+	16.4706i	0.425694	+	0.737323i	0.996485	−	0.0837721i	$-0.0266968\pi$
$499$	9.50928	+	16.4706i	0.425694	+	0.737323i	−0.570791	+	0.821095i	$0.693363\pi$
$500$	17.2799	+	12.1916i	0.772780	+	0.545225i
$501$		0			0
$502$	−3.90864	−	4.34098i	−0.174451	−	0.193747i
$503$	−8.48894	−	6.16758i	−0.378503	−	0.274999i	0.382225	−	0.924069i	$-0.375158\pi$
$503$	−8.48894	−	6.16758i	−0.378503	−	0.274999i	−0.760728	+	0.649071i	$0.775158\pi$
$504$		0			0
$505$	3.36299	−	19.6026i	0.149651	−	0.872305i
$506$	0.508084	+	4.83410i	0.0225871	+	0.214902i
$507$		0			0
$508$	25.4865	+	11.3473i	1.13078	+	0.503456i
$509$	18.4464	−	20.4868i	0.817624	−	0.908063i	−0.179508	−	0.983757i	$-0.557450\pi$
$509$	18.4464	−	20.4868i	0.817624	−	0.908063i	0.997131	+	0.0756936i	$0.0241171\pi$
$510$		0			0
$511$	17.8088	+	19.7786i	0.787814	+	0.874956i
$512$	6.47433	+	19.9259i	0.286128	+	0.880611i
$513$		0			0
$514$	−0.614821	+	1.89222i	−0.0271186	+	0.0834624i
$515$	5.46053	+	21.4770i	0.240620	+	0.946389i
$516$		0			0
$517$	−12.3093	−	5.48047i	−0.541364	−	0.241031i
$518$	−3.33000	−	5.76773i	−0.146312	−	0.253420i
$519$		0			0
$520$	−1.52948	−	6.01567i	−0.0670723	−	0.263804i
$521$	−24.6933	−	17.9407i	−1.08183	−	0.785998i	−0.103831	−	0.994595i	$-0.533110\pi$
$521$	−24.6933	−	17.9407i	−1.08183	−	0.785998i	−0.978002	+	0.208597i	$0.933110\pi$
$522$		0			0
$523$	−4.73750	+	14.5805i	−0.207156	+	0.637562i	0.792461	+	0.609922i	$0.208799\pi$
$523$	−4.73750	+	14.5805i	−0.207156	+	0.637562i	−0.999618	+	0.0276401i	$0.991201\pi$
$524$	1.99456	−	3.45467i	0.0871326	−	0.150918i
$525$		0			0
$526$	−1.66749	−	2.88818i	−0.0727060	−	0.125930i
$527$	−26.6138	+	5.65693i	−1.15931	+	0.246420i
$528$		0			0
$529$	48.5334	−	21.6084i	2.11015	−	0.939498i
$530$	−0.824249	−	1.67029i	−0.0358031	−	0.0725529i
$531$		0			0
$532$	−23.6838			−1.02682
$533$	−0.980923	−	9.33285i	−0.0424885	−	0.404251i
$534$		0			0
$535$	1.65681	−	0.611728i	0.0716300	−	0.0264473i
$536$	4.23880	−	0.900985i	0.183088	−	0.0389166i
$537$		0			0
$538$	−8.73053	−	1.85573i	−0.376400	−	0.0800063i
$539$	0.545782	−	1.67975i	0.0235085	−	0.0723518i
$540$		0			0
$541$	0.320574	+	0.986626i	0.0137826	+	0.0424184i	0.957711	−	0.287731i	$-0.0929009\pi$
$541$	0.320574	+	0.986626i	0.0137826	+	0.0424184i	−0.943929	+	0.330149i	$0.892901\pi$
$542$	−0.362065	−	3.44482i	−0.0155520	−	0.147968i
$543$		0			0
$544$	−12.8270	−	5.71096i	−0.549954	−	0.244855i
$545$	24.0647	+	30.5093i	1.03082	+	1.30687i
$546$		0			0
$547$	−25.9691	+	11.5622i	−1.11036	+	0.494364i	−0.878190	−	0.478311i	$-0.841249\pi$
$547$	−25.9691	+	11.5622i	−1.11036	+	0.494364i	−0.232169	+	0.972675i	$0.574582\pi$
$548$	2.69607	−	8.29764i	0.115170	−	0.354458i
$549$		0			0
$550$	−1.57894	−	2.29477i	−0.0673264	−	0.0978492i
$551$	14.8815	−	25.7755i	0.633972	−	1.09807i
$552$		0			0
$553$	−1.60640	+	15.2839i	−0.0683112	+	0.649938i
$554$	−0.559831	+	5.32644i	−0.0237850	+	0.226299i
$555$		0			0
$556$	−0.791385	−	7.52953i	−0.0335622	−	0.319323i
$557$	−23.9335			−1.01409			−0.507047	−	0.861919i	$-0.669263\pi$
$557$	−23.9335			−1.01409			−0.507047	+	0.861919i	$0.669263\pi$
$558$		0			0
$559$	−4.40336	−	13.5522i	−0.186242	−	0.573195i
$560$	−6.79162	+	17.0365i	−0.286998	+	0.719922i
$561$		0			0
$562$	3.34620	−	3.71633i	0.141151	−	0.156764i
$563$	−2.36392	+	2.62540i	−0.0996272	+	0.110647i	−0.790896	−	0.611950i	$-0.790385\pi$
$563$	−2.36392	+	2.62540i	−0.0996272	+	0.110647i	0.691269	+	0.722597i	$0.257052\pi$
$564$		0			0
$565$	1.79979	−	4.51469i	0.0757178	−	0.189935i
$566$	−0.192579	−	0.592697i	−0.00809470	−	0.0249129i
$567$		0			0
$568$	0.838586			0.0351863
$569$	−1.93022	−	18.3648i	−0.0809189	−	0.769892i	−0.957460	−	0.288565i	$-0.906822\pi$
$569$	−1.93022	−	18.3648i	−0.0809189	−	0.769892i	0.876541	−	0.481326i	$-0.159845\pi$
$570$		0			0
$571$	2.82412	−	26.8697i	0.118186	−	1.12446i	−0.761255	−	0.648453i	$-0.775416\pi$
$571$	2.82412	−	26.8697i	0.118186	−	1.12446i	0.879440	−	0.476009i	$-0.157917\pi$
$572$	0.724269	−	6.89096i	0.0302832	−	0.288125i
$573$		0			0
$574$	1.74148	−	3.01633i	0.0726880	−	0.125899i
$575$	−26.5390	+	34.6243i	−1.10675	+	1.44393i
$576$		0			0
$577$	4.52246	−	13.9187i	0.188273	−	0.579444i	−0.811717	−	0.584051i	$-0.801467\pi$
$577$	4.52246	−	13.9187i	0.188273	−	0.579444i	0.999989	+	0.00460768i	$0.00146668\pi$
$578$	−0.711983	+	0.316995i	−0.0296146	+	0.0131853i
$579$		0			0
$580$	−15.1951	−	19.2644i	−0.630942	−	0.799909i
$581$	31.8966	+	14.2013i	1.32329	+	0.589169i
$582$		0			0
$583$	−0.447138	−	4.25423i	−0.0185186	−	0.176192i
$584$	−4.31951	−	13.2941i	−0.178743	−	0.550113i
$585$		0			0
$586$	−0.747267	+	2.29985i	−0.0308693	+	0.0950060i
$587$	−29.1470	−	6.19538i	−1.20302	−	0.255711i	−0.437560	−	0.899189i	$-0.644157\pi$
$587$	−29.1470	−	6.19538i	−1.20302	−	0.255711i	−0.765464	+	0.643479i	$0.777491\pi$
$588$		0			0
$589$	35.6943	−	7.58706i	1.47076	−	0.312620i
$590$	−0.665996	+	0.245900i	−0.0274186	+	0.0101235i
$591$		0			0
$592$	−2.91079	−	27.6943i	−0.119633	−	1.13823i
$593$	−15.3217			−0.629186			−0.314593	−	0.949227i	$-0.601868\pi$
$593$	−15.3217			−0.629186			−0.314593	+	0.949227i	$0.601868\pi$
$594$		0			0
$595$	−9.23788	−	18.7200i	−0.378716	−	0.767447i
$596$	23.7897	−	10.5918i	0.974463	−	0.433859i
$597$		0			0
$598$	6.08771	−	1.29398i	0.248945	−	0.0529149i
$599$	14.5795	+	25.2524i	0.595702	+	1.03179i	0.993447	+	0.114290i	$0.0364594\pi$
$599$	14.5795	+	25.2524i	0.595702	+	1.03179i	−0.397745	+	0.917496i	$0.630207\pi$
$600$		0			0
$601$	−5.97136	+	10.3427i	−0.243577	+	0.421888i	−0.961731	−	0.273997i	$-0.911654\pi$
$601$	−5.97136	+	10.3427i	−0.243577	+	0.421888i	0.718154	+	0.695885i	$0.244987\pi$
$602$	1.63430	−	5.02987i	0.0666093	−	0.205002i
$603$		0			0
$604$	31.0621	+	22.5679i	1.26390	+	0.918275i
$605$	4.48455	+	17.6383i	0.182323	+	0.717101i
$606$		0			0
$607$	11.8537	+	20.5312i	0.481127	+	0.833336i	0.999765	−	0.0216578i	$-0.00689442\pi$
$607$	11.8537	+	20.5312i	0.481127	+	0.833336i	−0.518639	+	0.854993i	$0.673561\pi$
$608$	17.2036	+	7.65953i	0.697697	+	0.310635i
$609$		0			0
$610$	1.58235	+	6.22358i	0.0640673	+	0.251985i
$611$	−5.33132	+	16.4081i	−0.215682	+	0.663801i
$612$		0			0
$613$	10.4855	+	32.2710i	0.423505	+	1.30341i	0.904419	+	0.426646i	$0.140305\pi$
$613$	10.4855	+	32.2710i	0.423505	+	1.30341i	−0.480914	+	0.876768i	$0.659695\pi$
$614$	0.965781	+	1.07261i	0.0389758	+	0.0432870i
$615$		0			0
$616$	3.54025	−	3.93184i	0.142641	−	0.158418i
$617$	−9.30742	−	4.14393i	−0.374703	−	0.166828i	0.210740	−	0.977542i	$-0.432413\pi$
$617$	−9.30742	−	4.14393i	−0.374703	−	0.166828i	−0.585443	+	0.810714i	$0.699079\pi$
$618$		0			0
$619$	0.692019	+	6.58412i	0.0278146	+	0.264638i	0.999587	+	0.0287199i	$0.00914307\pi$
$619$	0.692019	+	6.58412i	0.0278146	+	0.264638i	−0.971773	+	0.235918i	$0.924190\pi$
$620$	5.08665	−	29.6497i	0.204285	−	1.19076i
$621$		0			0
$622$	−4.75307	−	3.45330i	−0.190581	−	0.138465i
$623$	15.6549	+	17.3865i	0.627199	+	0.696576i
$624$		0			0
$625$	3.88465	−	24.6963i	0.155386	−	0.987854i
$626$	−2.68462	−	4.64989i	−0.107299	−	0.185847i
$627$		0			0
$628$	−14.6050	+	6.50255i	−0.582802	+	0.259480i
$629$	25.6425	+	18.6303i	1.02243	+	0.742841i
$630$		0			0
$631$	18.8353	−	13.6847i	0.749823	−	0.544778i	−0.145949	−	0.989292i	$-0.546623\pi$
$631$	18.8353	−	13.6847i	0.749823	−	0.544778i	0.895772	+	0.444514i	$0.146623\pi$
$632$	4.03570	−	6.99004i	0.160532	−	0.278049i
$633$		0			0
$634$	4.64449	−	5.15822i	0.184456	−	0.204859i
$635$	−1.30355	−	32.9545i	−0.0517296	−	1.30776i
$636$		0			0
$637$	−2.21202	−	0.470180i	−0.0876436	−	0.0186292i
$638$	0.998668	+	3.07358i	0.0395376	+	0.121684i
$639$		0			0
$640$	14.6624	−	14.2910i	0.579581	−	0.564902i
$641$	24.4184	+	5.19029i	0.964468	+	0.205004i	0.663123	−	0.748511i	$-0.269231\pi$
$641$	24.4184	+	5.19029i	0.964468	+	0.205004i	0.301346	+	0.953515i	$0.402564\pi$
$642$		0			0
$643$	4.76373	+	8.25102i	0.187863	+	0.325388i	0.944538	−	0.328403i	$-0.106511\pi$
$643$	4.76373	+	8.25102i	0.187863	+	0.325388i	−0.756674	+	0.653792i	$0.773177\pi$
$644$	−36.7941	−	16.3818i	−1.44989	−	0.645533i
$645$		0			0
$646$	−5.90553	+	2.62931i	−0.232350	+	0.103449i
$647$	38.6632	+	28.0905i	1.52001	+	1.10435i	0.961483	+	0.274863i	$0.0886326\pi$
$647$	38.6632	+	28.0905i	1.52001	+	1.10435i	0.558525	+	0.829487i	$0.311367\pi$
$648$		0			0
$649$	−1.63046			−0.0640013
$650$	−2.71082	+	2.31775i	−0.106327	+	0.0909095i
$651$		0			0
$652$	13.2775	−	2.82222i	0.519988	−	0.110527i
$653$	−1.42666	+	13.5738i	−0.0558295	+	0.531182i	0.930488	+	0.366323i	$0.119384\pi$
$653$	−1.42666	+	13.5738i	−0.0558295	+	0.531182i	−0.986317	+	0.164859i	$0.947283\pi$
$654$		0			0
$655$	−4.70574	−	0.307176i	−0.183868	−	0.0120024i
$656$	11.7817	−	8.55991i	0.459998	−	0.334208i
$657$		0			0
$658$	−5.18035	+	3.76374i	−0.201951	+	0.146726i
$659$	−7.11906	−	1.51320i	−0.277319	−	0.0589460i	0.0671526	−	0.997743i	$-0.478609\pi$
$659$	−7.11906	−	1.51320i	−0.277319	−	0.0589460i	−0.344472	+	0.938797i	$0.611942\pi$
$660$		0			0
$661$	21.3346	−	4.53482i	0.829821	−	0.176384i	0.226630	−	0.973981i	$-0.427229\pi$
$661$	21.3346	−	4.53482i	0.829821	−	0.176384i	0.603191	+	0.797597i	$0.293896\pi$
$662$	−3.99223	+	4.43382i	−0.155162	+	0.172325i
$663$		0			0
$664$	−12.2703	−	13.6275i	−0.476179	−	0.528851i
$665$	12.3898	+	25.1073i	0.480457	+	0.973619i
$666$		0			0
$667$	40.9478	−	29.7503i	1.58550	−	1.15194i
$668$	5.72945	−	9.92369i	0.221679	−	0.383959i
$669$		0			0
$670$	−1.54208	−	1.95505i	−0.0595758	−	0.0755303i
$671$	−1.54158	+	14.6671i	−0.0595119	+	0.566218i
$672$		0			0
$673$	32.4377	+	36.0257i	1.25038	+	1.38869i	0.890048	+	0.455868i	$0.150671\pi$
$673$	32.4377	+	36.0257i	1.25038	+	1.38869i	0.360335	+	0.932823i	$0.382662\pi$
$674$	−1.21886			−0.0469488
$675$		0			0
$676$	15.7179			0.604534
$677$	6.61758	+	7.34956i	0.254334	+	0.282467i	0.856768	−	0.515702i	$-0.172469\pi$
$677$	6.61758	+	7.34956i	0.254334	+	0.282467i	−0.602434	+	0.798169i	$0.705802\pi$
$678$		0			0
$679$	0.393108	−	3.74017i	0.0150861	−	0.143535i
$680$	0.433345	+	10.9553i	0.0166180	+	0.420115i
$681$		0			0
$682$	−1.98120	+	3.43153i	−0.0758639	+	0.131400i
$683$	−22.0510	+	16.0210i	−0.843757	+	0.613026i	−0.923418	−	0.383796i	$-0.874616\pi$
$683$	−22.0510	+	16.0210i	−0.843757	+	0.613026i	0.0796603	+	0.996822i	$0.474616\pi$
$684$		0			0
$685$	−10.2068	+	1.48268i	−0.389981	+	0.0566502i
$686$	−4.32657	−	4.80515i	−0.165189	−	0.183461i
$687$		0			0
$688$	14.7966	−	16.4333i	0.564117	−	0.626515i
$689$	−5.35747	+	1.13876i	−0.204103	+	0.0433835i
$690$		0			0
$691$	0.729910	+	0.155147i	0.0277671	+	0.00590208i	0.221774	−	0.975098i	$-0.428815\pi$
$691$	0.729910	+	0.155147i	0.0277671	+	0.00590208i	−0.194007	+	0.981000i	$0.562149\pi$
$692$	29.8701	−	21.7019i	1.13549	−	0.824982i
$693$		0			0
$694$	−6.87115	+	4.99218i	−0.260825	+	0.189501i
$695$	−7.56808	+	4.77791i	−0.287074	+	0.181237i
$696$		0			0
$697$	−1.73265	+	16.4851i	−0.0656288	+	0.624417i
$698$	10.1067	−	2.14824i	0.382543	−	0.0813120i
$699$		0			0
$700$	23.0087	−	1.82311i	0.869646	−	0.0689071i
$701$	14.0062			0.529006			0.264503	−	0.964385i	$-0.414792\pi$
$701$	14.0062			0.529006			0.264503	+	0.964385i	$0.414792\pi$
$702$		0			0
$703$	−34.3916	−	24.9870i	−1.29711	−	0.942402i
$704$	8.51839	−	3.79263i	0.321049	−	0.142940i
$705$		0			0
$706$	0.0301455	+	0.0134217i	0.00113454	+	0.000505131i
$707$	−10.8534	−	18.7987i	−0.408186	−	0.706999i
$708$		0			0
$709$	−24.2191	−	5.14793i	−0.909567	−	0.193334i	−0.270711	−	0.962661i	$-0.587259\pi$
$709$	−24.2191	−	5.14793i	−0.909567	−	0.193334i	−0.638856	+	0.769326i	$0.720592\pi$
$710$	−0.213232	−	0.432103i	−0.00800247	−	0.0162165i
$711$		0			0
$712$	−3.79708	−	11.6862i	−0.142302	−	0.437960i
$713$	60.7010	+	12.9024i	2.27327	+	0.483199i
$714$		0			0
$715$	−7.68403	+	2.83710i	−0.287366	+	0.106102i
$716$	6.08383	−	6.75678i	0.227363	−	0.252513i
$717$		0			0
$718$	2.55455	−	4.42461i	0.0953349	−	0.165125i
$719$	−7.88850	+	5.73133i	−0.294192	+	0.213743i	−0.725084	−	0.688661i	$-0.758199\pi$
$719$	−7.88850	+	5.73133i	−0.294192	+	0.213743i	0.430892	+	0.902403i	$0.358199\pi$
$720$		0			0
$721$	19.5667	+	14.2161i	0.728703	+	0.529434i
$722$	2.20355	−	0.981083i	0.0820076	−	0.0365121i
$723$		0			0
$724$	−5.26399	−	9.11749i	−0.195634	−	0.338849i
$725$	−12.4731	+	26.1862i	−0.463241	+	0.972533i
$726$		0			0
$727$	−1.50130	−	1.66737i	−0.0556802	−	0.0618392i	0.714661	−	0.699471i	$-0.246581\pi$
$727$	−1.50130	−	1.66737i	−0.0556802	−	0.0618392i	−0.770341	+	0.637632i	$0.779914\pi$
$728$	−5.48061	−	3.98189i	−0.203125	−	0.147579i
$729$		0			0
$730$	−5.75178	+	5.60611i	−0.212883	+	0.207491i
$731$	2.63095	+	25.0318i	0.0973093	+	0.925836i
$732$		0			0
$733$	6.55459	+	2.91829i	0.242099	+	0.107790i	0.524200	−	0.851595i	$-0.324364\pi$
$733$	6.55459	+	2.91829i	0.242099	+	0.107790i	−0.282100	+	0.959385i	$0.591031\pi$
$734$	−2.84533	+	3.16006i	−0.105023	+	0.116640i
$735$		0			0
$736$	21.4287	+	23.7990i	0.789873	+	0.877243i
$737$	−1.76716	−	5.43875i	−0.0650941	−	0.200339i
$738$		0			0
$739$	3.95764	−	12.1804i	0.145584	−	0.448062i	−0.851502	−	0.524352i	$-0.824308\pi$
$739$	3.95764	−	12.1804i	0.145584	−	0.448062i	0.997086	+	0.0762903i	$0.0243076\pi$
$740$	−29.6331	+	18.7081i	−1.08934	+	0.687724i
$741$		0			0
$742$	−1.85709	−	0.826832i	−0.0681761	−	0.0303539i
$743$	1.45630	+	2.52238i	0.0534264	+	0.0925372i	0.891502	−	0.453017i	$-0.149652\pi$
$743$	1.45630	+	2.52238i	0.0534264	+	0.0925372i	−0.838075	+	0.545554i	$0.816319\pi$
$744$		0			0
$745$	−23.6737	−	19.6786i	−0.867337	−	0.720967i
$746$	0.0617081	+	0.0448336i	0.00225929	+	0.00164147i
$747$		0			0
$748$	−3.78202	+	11.6399i	−0.138284	+	0.425596i
$749$	0.963780	−	1.66932i	0.0352158	−	0.0609955i
$750$		0			0
$751$	−17.2581	−	29.8919i	−0.629757	−	1.09077i	−0.987600	−	0.156989i	$-0.949821\pi$
$751$	−17.2581	−	29.8919i	−0.629757	−	1.09077i	0.357843	−	0.933782i	$-0.383512\pi$
$752$	−26.1883	+	5.56649i	−0.954989	+	0.202989i
$753$		0			0
$754$	3.78022	−	1.68306i	0.137668	−	0.0612935i
$755$	7.67467	−	44.7351i	0.279310	−	1.62808i
$756$		0			0
$757$	4.55628			0.165601			0.0828005	−	0.996566i	$-0.473614\pi$
$757$	4.55628			0.165601			0.0828005	+	0.996566i	$0.473614\pi$
$758$	0.192086	+	1.82758i	0.00697687	+	0.0663805i
$759$		0			0
$760$	−0.581202	−	14.6932i	−0.0210824	−	0.532977i
$761$	25.2562	−	5.36838i	0.915538	−	0.194604i	0.274031	−	0.961721i	$-0.411643\pi$
$761$	25.2562	−	5.36838i	0.915538	−	0.194604i	0.641507	+	0.767117i	$0.278310\pi$
$762$		0			0
$763$	41.4828	+	8.81743i	1.50178	+	0.319212i
$764$	−13.8417	+	42.6004i	−0.500775	+	1.54123i
$765$		0			0
$766$	1.36586	+	4.20369i	0.0493505	+	0.151885i
$767$	0.218220	+	2.07622i	0.00787946	+	0.0749680i
$768$		0			0
$769$	30.0274	+	13.3690i	1.08281	+	0.482100i	0.869019	−	0.494779i	$-0.164751\pi$
$769$	30.0274	+	13.3690i	1.08281	+	0.482100i	0.213795	+	0.976879i	$0.431418\pi$
$770$	−2.92618	−	0.824431i	−0.105452	−	0.0297104i
$771$		0			0
$772$	−2.20182	+	0.980316i	−0.0792454	+	0.0352823i
$773$	11.0693	−	34.0677i	0.398134	−	1.22533i	−0.528360	−	0.849020i	$-0.677193\pi$
$773$	11.0693	−	34.0677i	0.398134	−	1.22533i	0.926494	−	0.376310i	$-0.122807\pi$
$774$		0			0
$775$	−34.0928	+	10.1184i	−1.22465	+	0.363465i
$776$	−0.987590	+	1.71056i	−0.0354524	+	0.0614054i
$777$		0			0
$778$	1.17156	−	11.1466i	0.0420024	−	0.399626i
$779$	2.32383	−	22.1097i	0.0832598	−	0.792164i
$780$		0			0
$781$	−0.115674	−	1.10057i	−0.00413915	−	0.0393814i
$782$	−10.9932			−0.393117
$783$		0			0
$784$	−1.08447	−	3.33766i	−0.0387311	−	0.119202i
$785$	14.5338	+	12.0811i	0.518732	+	0.431192i
$786$		0			0
$787$	−1.79034	+	1.98837i	−0.0638187	+	0.0708778i	−0.774209	−	0.632930i	$-0.781852\pi$
$787$	−1.79034	+	1.98837i	−0.0638187	+	0.0708778i	0.710390	+	0.703808i	$0.248519\pi$
$788$	12.4568	−	13.8346i	0.443754	−	0.492839i
$789$		0			0
$790$	−4.62799	−	0.302101i	−0.164656	−	0.0107483i
$791$	−1.63917	−	5.04484i	−0.0582820	−	0.179374i
$792$		0			0
$793$	18.8833			0.670567
$794$	0.969486	+	9.22404i	0.0344058	+	0.327349i
$795$		0			0
$796$	−3.67463	+	34.9618i	−0.130244	+	1.23919i
$797$	−3.84156	+	36.5500i	−0.136075	+	1.29467i	0.686968	+	0.726687i	$0.258941\pi$
$797$	−3.84156	+	36.5500i	−0.136075	+	1.29467i	−0.823043	+	0.567979i	$0.807726\pi$
$798$		0			0
$799$	15.2370	−	26.3912i	0.539045	−	0.933654i
$800$	−17.3028	−	6.11690i	−0.611746	−	0.216265i
$801$		0			0
$802$	−1.32495	+	4.07776i	−0.0467854	+	0.143991i
$803$	−16.8514	+	7.50274i	−0.594674	+	0.264766i
$804$		0			0
$805$	1.88189	+	47.5755i	0.0663279	+	1.67682i
$806$	4.63485	+	2.06357i	0.163256	+	0.0726861i
$807$		0			0
$808$	1.19169	+	11.3381i	0.0419233	+	0.398874i
$809$	−15.1395	−	46.5946i	−0.532276	−	1.63818i	−0.749462	−	0.662048i	$-0.769688\pi$
$809$	−15.1395	−	46.5946i	−0.532276	−	1.63818i	0.217186	−	0.976130i	$-0.430312\pi$
$810$		0			0
$811$	8.75261	−	26.9378i	0.307346	−	0.945913i	−0.671446	−	0.741054i	$-0.734326\pi$
$811$	8.75261	−	26.9378i	0.307346	−	0.945913i	0.978791	−	0.204859i	$-0.0656736\pi$
$812$	−26.1933	−	5.56755i	−0.919204	−	0.195383i
$813$		0			0
$814$	4.51505	−	0.959703i	0.158252	−	0.0336376i
$815$	−9.93780	−	12.5992i	−0.348106	−	0.441329i
$816$		0			0
$817$	−3.52863	−	33.5727i	−0.123451	−	1.17456i
$818$	11.0057			0.384806
$819$		0			0
$820$	−16.2215	−	8.52906i	−0.566480	−	0.297848i
$821$	−9.47344	+	4.21785i	−0.330625	+	0.147204i	−0.565335	−	0.824862i	$-0.691253\pi$
$821$	−9.47344	+	4.21785i	−0.330625	+	0.147204i	0.234709	+	0.972066i	$0.424586\pi$
$822$		0			0
$823$	−22.4338	+	4.76845i	−0.781992	+	0.166218i	−0.581575	−	0.813493i	$-0.697563\pi$
$823$	−22.4338	+	4.76845i	−0.781992	+	0.166218i	−0.200418	+	0.979711i	$0.564230\pi$
$824$	−6.35126	−	11.0007i	−0.221257	−	0.383228i
$825$		0			0
$826$	−0.387416	+	0.671025i	−0.0134799	+	0.0233479i
$827$	−3.87041	+	11.9119i	−0.134587	+	0.414218i	−0.995526	−	0.0944920i	$-0.969877\pi$
$827$	−3.87041	+	11.9119i	−0.134587	+	0.414218i	0.860938	+	0.508710i	$0.169877\pi$
$828$		0			0
$829$	8.58869	+	6.24005i	0.298297	+	0.216726i	0.726859	−	0.686787i	$-0.240979\pi$
$829$	8.58869	+	6.24005i	0.298297	+	0.216726i	−0.428561	+	0.903513i	$0.640979\pi$
$830$	−3.90190	+	9.78774i	−0.135437	+	0.339737i
$831$		0			0
$832$	−5.96961	−	10.3397i	−0.206959	−	0.358463i
$833$	3.64915	+	1.62471i	0.126436	+	0.0562928i
$834$		0			0
$835$	−13.5174	−	0.882376i	−0.467790	−	0.0305359i
$836$	5.07244	−	15.6114i	0.175434	−	0.539930i
$837$		0			0
$838$	−4.01837	−	12.3673i	−0.138812	−	0.427220i
$839$	4.12762	+	4.58418i	0.142501	+	0.158264i	0.810170	−	0.586195i	$-0.199375\pi$
$839$	4.12762	+	4.58418i	0.142501	+	0.158264i	−0.667669	+	0.744458i	$0.732708\pi$
$840$		0			0
$841$	3.11276	−	3.45707i	0.107337	−	0.119209i
$842$	0.792708	+	0.352936i	0.0273185	+	0.0121630i
$843$		0			0
$844$	0.436558	+	4.15357i	0.0150269	+	0.142972i
$845$	−8.22258	−	16.6626i	−0.282865	−	0.573211i
$846$		0			0
$847$	16.0695	+	11.6752i	0.552155	+	0.401164i
$848$	−5.68743	−	6.31654i	−0.195307	−	0.216911i
$849$		0			0
$850$	5.53479	−	3.00895i	0.189842	−	0.103206i
$851$	−36.1461	−	62.6070i	−1.23907	−	2.14614i
$852$		0			0
$853$	−25.0320	+	11.1450i	−0.857079	+	0.381596i	−0.787748	−	0.615998i	$-0.788753\pi$
$853$	−25.0320	+	11.1450i	−0.857079	+	0.381596i	−0.0693309	+	0.997594i	$0.522086\pi$
$854$	5.67002	+	4.11951i	0.194024	+	0.140967i
$855$		0			0
$856$	−0.819021	+	0.595053i	−0.0279935	+	0.0203385i
$857$	16.4638	−	28.5161i	0.562392	−	0.974092i	−0.434895	−	0.900481i	$-0.643214\pi$
$857$	16.4638	−	28.5161i	0.562392	−	0.974092i	0.997287	−	0.0736109i	$-0.0234523\pi$
$858$		0			0
$859$	−30.8351	+	34.2459i	−1.05208	+	1.16845i	−0.0667547	+	0.997769i	$0.521264\pi$
$859$	−30.8351	+	34.2459i	−1.05208	+	1.16845i	−0.985326	+	0.170684i	$0.945402\pi$
$860$	−26.7861	−	7.54678i	−0.913397	−	0.257343i
$861$		0			0
$862$	−11.0677	−	2.35252i	−0.376968	−	0.0801271i
$863$	−1.06714	−	3.28433i	−0.0363260	−	0.111800i	0.931249	−	0.364383i	$-0.118720\pi$
$863$	−1.06714	−	3.28433i	−0.0363260	−	0.111800i	−0.967575	+	0.252583i	$0.918720\pi$
$864$		0			0
$865$	−38.6324	−	20.3124i	−1.31354	−	0.690642i
$866$	−8.76181	−	1.86238i	−0.297738	−	0.0632863i
$867$		0			0
$868$	−16.4163	−	28.4338i	−0.557204	−	0.965106i
$869$	−9.73047	−	4.33228i	−0.330083	−	0.146963i
$870$		0			0
$871$	−6.68915	+	2.97820i	−0.226653	+	0.100913i
$872$	−18.0198	−	13.0922i	−0.610227	−	0.443356i
$873$		0			0
$874$	14.7441			0.498727
$875$	−13.9693	−	23.4378i	−0.472250	−	0.792344i
$876$		0			0
$877$	−55.9211	+	11.8864i	−1.88832	+	0.401375i	−0.998491	−	0.0549146i	$-0.982511\pi$
$877$	−55.9211	+	11.8864i	−1.88832	+	0.401375i	−0.889831	+	0.456290i	$0.849178\pi$
$878$	0.516938	−	4.91834i	0.0174458	−	0.165986i
$879$		0			0
$880$	−9.77515	−	8.12552i	−0.329520	−	0.273911i
$881$	25.5288	−	18.5478i	0.860089	−	0.624891i	−0.0678204	−	0.997698i	$-0.521604\pi$
$881$	25.5288	−	18.5478i	0.860089	−	0.624891i	0.927909	+	0.372807i	$0.121604\pi$
$882$		0			0
$883$	−32.6810	+	23.7441i	−1.09980	+	0.799053i	−0.981028	−	0.193868i	$-0.937897\pi$
$883$	−32.6810	+	23.7441i	−1.09980	+	0.799053i	−0.118775	+	0.992921i	$0.537897\pi$
$884$	15.3283	+	3.25813i	0.515547	+	0.109583i
$885$		0			0
$886$	−3.38097	+	0.718647i	−0.113586	+	0.0241434i
$887$	7.80917	−	8.67297i	0.262206	−	0.291210i	−0.597638	−	0.801766i	$-0.703894\pi$
$887$	7.80917	−	8.67297i	0.262206	−	0.291210i	0.859844	+	0.510556i	$0.170561\pi$
$888$		0			0
$889$	−24.0852	−	26.7493i	−0.807792	−	0.897144i
$890$	−5.05612	+	4.92807i	−0.169482	+	0.165189i
$891$		0			0
$892$	−40.1233	+	29.1513i	−1.34343	+	0.976058i
$893$	−20.4358	+	35.3959i	−0.683858	+	1.18448i
$894$		0			0
$895$	−10.3456	−	2.91478i	−0.345814	−	0.0974305i
$896$	2.33582	−	22.2239i	0.0780343	−	0.742447i
$897$		0			0
$898$	−4.29845	−	4.77391i	−0.143441	−	0.159307i
$899$	41.2600			1.37610
$900$		0			0
$901$	9.67456			0.322306
$902$	1.61526	+	1.79393i	0.0537823	+	0.0597313i
$903$		0			0
$904$	−0.291209	+	2.77067i	−0.00968546	+	0.0921510i
$905$	−6.91171	+	10.3501i	−0.229753	+	0.344048i
$906$		0			0
$907$	−15.1100	+	26.1713i	−0.501720	+	0.869005i	0.498278	+	0.867017i	$0.333966\pi$
$907$	−15.1100	+	26.1713i	−0.501720	+	0.869005i	−0.999998	+	0.00198753i	$0.999367\pi$
$908$	11.3447	−	8.24241i	0.376487	−	0.273534i
$909$		0			0
$910$	−0.658187	+	3.83652i	−0.0218187	+	0.127180i
$911$	37.2219	+	41.3391i	1.23322	+	1.36963i	0.905217	+	0.424949i	$0.139708\pi$
$911$	37.2219	+	41.3391i	1.23322	+	1.36963i	0.328000	+	0.944678i	$0.393625\pi$
$912$		0			0
$913$	−16.1923	+	17.9834i	−0.535887	+	0.595163i
$914$	−4.11096	+	0.873811i	−0.135978	+	0.0289031i
$915$		0			0
$916$	37.7332	+	8.02044i	1.24674	+	0.265003i
$917$	−4.16384	+	3.02521i	−0.137502	+	0.0999011i
$918$		0			0
$919$	−45.6386	+	33.1584i	−1.50548	+	1.09379i	−0.537345	+	0.843363i	$0.680573\pi$
$919$	−45.6386	+	33.1584i	−1.50548	+	1.09379i	−0.968134	+	0.250432i	$0.919427\pi$
$920$	9.26016	−	23.2287i	0.305298	−	0.765827i
$921$		0			0
$922$	−0.485095	+	4.61537i	−0.0159758	+	0.151999i
$923$	−1.38597	+	0.294597i	−0.0456198	+	0.00969679i
$924$		0			0
$925$	35.3347	+	21.6273i	1.16180	+	0.711102i
$926$	9.97042			0.327648
$927$		0			0
$928$	17.2258	+	12.5153i	0.565466	+	0.410835i
$929$	12.4179	−	5.52882i	0.407419	−	0.181395i	−0.192786	−	0.981241i	$-0.561752\pi$
$929$	12.4179	−	5.52882i	0.407419	−	0.181395i	0.600205	+	0.799846i	$0.295086\pi$
$930$		0			0
$931$	−4.89424	−	2.17905i	−0.160402	−	0.0714156i
$932$	7.18214	+	12.4398i	0.235259	+	0.407480i
$933$		0			0
$934$	0.182860	+	0.0388682i	0.00598338	+	0.00127181i
$935$	14.3180	−	2.07989i	0.468248	−	0.0680196i
$936$		0			0
$937$	−5.39097	−	16.5917i	−0.176115	−	0.542027i	0.823567	−	0.567218i	$-0.191980\pi$
$937$	−5.39097	−	16.5917i	−0.176115	−	0.542027i	−0.999683	+	0.0251916i	$0.991980\pi$
$938$	−2.65824	−	0.565026i	−0.0867946	−	0.0184488i
$939$		0			0
$940$	20.8665	+	26.4545i	0.680589	+	0.862852i
$941$	−32.8128	+	36.4424i	−1.06967	+	1.18799i	−0.0882513	+	0.996098i	$0.528128\pi$
$941$	−32.8128	+	36.4424i	−1.06967	+	1.18799i	−0.981417	+	0.191888i	$0.938539\pi$
$942$		0			0
$943$	18.9032	−	32.7414i	0.615574	−	1.06621i
$944$	−2.62100	+	1.90427i	−0.0853063	+	0.0619787i
$945$		0			0
$946$	2.96546	+	2.15453i	0.0964153	+	0.0700498i
$947$	−34.3978	+	15.3149i	−1.11778	+	0.497667i	−0.880629	−	0.473806i	$-0.842880\pi$
$947$	−34.3978	+	15.3149i	−1.11778	+	0.497667i	−0.237150	+	0.971473i	$0.576213\pi$
$948$		0			0
$949$	11.8093	+	20.4543i	0.383347	+	0.663976i
$950$	−7.42326	+	4.03560i	−0.240842	+	0.130932i
$951$		0			0
$952$	8.00678	+	8.89243i	0.259501	+	0.288205i
$953$	24.9618	+	18.1358i	0.808594	+	0.587478i	0.913423	−	0.407013i	$-0.133430\pi$
$953$	24.9618	+	18.1358i	0.808594	+	0.587478i	−0.104829	+	0.994490i	$0.533430\pi$
$954$		0			0
$955$	52.4020	−	7.61212i	1.69569	−	0.246322i
$956$	−3.20664	−	30.5092i	−0.103710	−	0.986737i
$957$		0			0
$958$	−2.73505	−	1.21772i	−0.0883654	−	0.0393428i
$959$	−7.53215	+	8.36530i	−0.243226	+	0.270130i
$960$		0			0
$961$	13.1070	+	14.5567i	0.422805	+	0.469573i
$962$	−1.82637	−	5.62099i	−0.0588845	−	0.181228i
$963$		0			0
$964$	8.58075	−	26.4088i	0.276367	−	0.850571i
$965$	2.19109	+	1.82133i	0.0705337	+	0.0586306i
$966$		0			0
$967$	26.3223	+	11.7195i	0.846469	+	0.376872i	0.783688	−	0.621155i	$-0.213336\pi$
$967$	26.3223	+	11.7195i	0.846469	+	0.376872i	0.0627812	+	0.998027i	$0.480003\pi$
$968$	−5.21608	−	9.03451i	−0.167651	−	0.290380i
$969$		0			0
$970$	1.13253	+	0.0739280i	0.0363633	+	0.00237369i
$971$	−0.696107	−	0.505751i	−0.0223391	−	0.0162303i	0.576560	−	0.817055i	$-0.304395\pi$
$971$	−0.696107	−	0.505751i	−0.0223391	−	0.0162303i	−0.598899	+	0.800825i	$0.704395\pi$
$972$		0			0
$973$	−3.01853	+	9.29008i	−0.0967696	+	0.297826i
$974$	5.24732	−	9.08862i	0.168135	−	0.291218i
$975$		0			0
$976$	14.6521	+	25.3781i	0.469001	+	0.812334i
$977$	−48.2956	+	10.2656i	−1.54511	+	0.328424i	−0.900078	−	0.435728i	$-0.856491\pi$
$977$	−48.2956	+	10.2656i	−1.54511	+	0.328424i	−0.645036	+	0.764152i	$0.723158\pi$
$978$		0			0
$979$	−14.8133	+	6.59531i	−0.473436	+	0.210787i
$980$	−3.16274	+	3.08264i	−0.101030	+	0.0984712i
$981$		0			0
$982$	13.9001			0.443570
$983$	5.03462	+	47.9012i	0.160579	+	1.52781i	0.717097	+	0.696974i	$0.245471\pi$
$983$	5.03462	+	47.9012i	0.160579	+	1.52781i	−0.556517	+	0.830836i	$0.687863\pi$
$984$		0			0
$985$	−21.1827	−	5.96808i	−0.674938	−	0.190159i
$986$	−7.14937	+	1.51965i	−0.227682	+	0.0483954i
$987$		0			0
$988$	−20.5583	−	4.36980i	−0.654047	−	0.139022i
$989$	17.7399	−	54.5977i	0.564095	−	1.73611i
$990$		0			0
$991$	6.36275	+	19.5825i	0.202120	+	0.622060i	0.999819	+	0.0190053i	$0.00604994\pi$
$991$	6.36275	+	19.5825i	0.202120	+	0.622060i	−0.797700	+	0.603055i	$0.793950\pi$
$992$	2.72883	+	25.9631i	0.0866404	+	0.824328i
$993$		0			0
$994$	−0.480429	−	0.213901i	−0.0152383	−	0.00678451i
$995$	38.9855	−	14.3943i	1.23592	−	0.456329i
$996$		0			0
$997$	52.1722	−	23.2285i	1.65231	−	0.735655i	0.652553	−	0.757743i	$-0.273698\pi$
$997$	52.1722	−	23.2285i	1.65231	−	0.735655i	0.999756	+	0.0220883i	$0.00703148\pi$
$998$	−1.93571	+	5.95750i	−0.0612738	+	0.188581i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.r.a.46.16		224
3.2	odd	2		225.2.q.a.196.13	yes	224
9.4	even	3	inner	675.2.r.a.496.13		224
9.5	odd	6		225.2.q.a.121.16	yes	224
25.6	even	5	inner	675.2.r.a.181.13		224
75.56	odd	10		225.2.q.a.106.16	yes	224
225.31	even	15	inner	675.2.r.a.631.16		224
225.131	odd	30		225.2.q.a.31.13	✓	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.31.13	✓	224	225.131	odd	30
225.2.q.a.106.16	yes	224	75.56	odd	10
225.2.q.a.121.16	yes	224	9.5	odd	6
225.2.q.a.196.13	yes	224	3.2	odd	2
675.2.r.a.46.16		224	1.1	even	1	trivial
675.2.r.a.181.13		224	25.6	even	5	inner
675.2.r.a.496.13		224	9.4	even	3	inner
675.2.r.a.631.16		224	225.31	even	15	inner

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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.r (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.220390 + 0.244767i) q^{2} +(0.197717 - 1.88116i) q^{4} +(-2.09765 + 0.774498i) q^{5} +(-1.22023 + 2.11349i) q^{7} +(1.03695 - 0.753387i) q^{8} +(-0.651873 - 0.342746i) q^{10} +(-1.13179 - 1.25698i) q^{11} +(-1.44915 + 1.60944i) q^{13} +(-0.786239 + 0.167120i) q^{14} +(-3.28743 - 0.698765i) q^{16} +(3.09482 - 2.24852i) q^{17} +(-4.15077 + 3.01571i) q^{19} +(1.04221 + 4.09915i) q^{20} +(0.0582329 - 0.554049i) q^{22} +(-8.53438 + 1.81404i) q^{23} +(3.80031 - 3.24926i) q^{25} -0.713316 q^{26} +(3.73455 + 2.71331i) q^{28} +(-5.29950 + 2.35949i) q^{29} +(-6.49762 - 2.89293i) q^{31} +(-1.83522 - 3.17869i) q^{32} +(1.23243 + 0.261961i) q^{34} +(0.922715 - 5.37844i) q^{35} +(2.56039 + 7.88008i) q^{37} +(-1.65293 - 0.351342i) q^{38} +(-1.59166 + 2.38346i) q^{40} +(-2.89941 + 3.22012i) q^{41} +(-3.28981 + 5.69811i) q^{43} +(-2.58834 + 1.88054i) q^{44} +(-2.32491 - 1.68914i) q^{46} +(7.27748 - 3.24014i) q^{47} +(0.522100 + 0.904304i) q^{49} +(1.63286 + 0.214089i) q^{50} +(2.74109 + 3.04429i) q^{52} +(2.04603 + 1.48652i) q^{53} +(3.34762 + 1.76013i) q^{55} +(0.326967 + 3.11088i) q^{56} +(-1.74548 - 0.777139i) q^{58} +(0.645013 - 0.716360i) q^{59} +(-5.83429 - 6.47963i) q^{61} +(-0.723913 - 2.22798i) q^{62} +(-1.70356 + 5.24301i) q^{64} +(1.79330 - 4.49841i) q^{65} +(3.08866 + 1.37516i) q^{67} +(-3.61791 - 6.26641i) q^{68} +(1.51982 - 0.959501i) q^{70} +(0.529305 + 0.384563i) q^{71} +(3.37004 - 10.3719i) q^{73} +(-1.36450 + 2.36339i) q^{74} +(4.85234 + 8.40450i) q^{76} +(4.03764 - 0.858227i) q^{77} +(5.75281 - 2.56132i) q^{79} +(7.43708 - 1.08034i) q^{80} -1.42718 q^{82} +(-1.49547 - 14.2285i) q^{83} +(-4.75039 + 7.11355i) q^{85} +(-2.11975 + 0.450567i) q^{86} +(-2.12059 - 0.450746i) q^{88} +(2.96245 - 9.11749i) q^{89} +(-1.63326 - 5.02664i) q^{91} +(1.72509 + 16.4132i) q^{92} +(2.39696 + 1.06720i) q^{94} +(6.37122 - 9.54068i) q^{95} +(-1.40779 + 0.626788i) q^{97} +(-0.106279 + 0.327092i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8} - 20 q^{10} + 11 q^{11} - 3 q^{13} - q^{14} + 23 q^{16} + 24 q^{17} - 12 q^{19} - q^{20} - 11 q^{22} - q^{23} - 16 q^{25} + 136 q^{26} + 4 q^{28}+ \cdots - 146 q^{98}+O(q^{100}) \) 224 * q + 3 * q^2 + 23 * q^4 + 8 * q^5 - 8 * q^7 + 20 * q^8 - 20 * q^10 + 11 * q^11 - 3 * q^13 - q^14 + 23 * q^16 + 24 * q^17 - 12 * q^19 - q^20 - 11 * q^22 - q^23 - 16 * q^25 + 136 * q^26 + 4 * q^28 + 15 * q^29 + 3 * q^31 - 12 * q^32 + q^34 - 14 * q^35 - 24 * q^37 - 55 * q^38 + q^40 + 19 * q^41 - 8 * q^43 - 4 * q^44 - 20 * q^46 + 10 * q^47 - 72 * q^49 + 3 * q^50 - 25 * q^52 + 12 * q^53 - 20 * q^55 + 60 * q^56 - 23 * q^58 + 30 * q^59 - 3 * q^61 + 44 * q^62 - 44 * q^64 - 51 * q^65 - 12 * q^67 + 156 * q^68 - 16 * q^70 - 42 * q^71 - 12 * q^73 - 90 * q^74 - 8 * q^76 - 31 * q^77 - 15 * q^79 - 298 * q^80 + 8 * q^82 - 59 * q^83 - 11 * q^85 - 9 * q^86 - 23 * q^88 - 106 * q^89 + 30 * q^91 - 11 * q^92 + 25 * q^94 - 7 * q^95 - 21 * q^97 - 146 * q^98

Introduction

L-functions

Modular forms

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