LMFDB - Embedded newform 441.2.bg.a.278.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(17,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([21, 25]))

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

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

chi := DirichletCharacter("441.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.bg (of order $42$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$18$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			278.8
Character	$\chi$	$=$	441.278
Dual form			441.2.bg.a.395.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.568908 + 0.223280i) q^{2} +(-1.19230 + 1.10629i) q^{4} +(2.30954 - 1.57462i) q^{5} +(0.0953467 - 2.64403i) q^{7} +(0.961636 - 1.99686i) q^{8} +O(q^{10})$	\(q+(-0.568908 + 0.223280i) q^{2} +(-1.19230 + 1.10629i) q^{4} +(2.30954 - 1.57462i) q^{5} +(0.0953467 - 2.64403i) q^{7} +(0.961636 - 1.99686i) q^{8} +(-0.962336 + 1.41149i) q^{10} +(-0.355186 + 2.35651i) q^{11} +(-2.96799 - 2.36690i) q^{13} +(0.536116 + 1.52550i) q^{14} +(0.141871 - 1.89314i) q^{16} +(2.98520 - 0.920812i) q^{17} +(-5.52972 - 3.19259i) q^{19} +(-1.01168 + 4.43246i) q^{20} +(-0.324092 - 1.41994i) q^{22} +(2.41439 - 7.82724i) q^{23} +(1.02786 - 2.61894i) q^{25} +(2.21699 + 0.683852i) q^{26} +(2.81140 + 3.25797i) q^{28} +(8.18266 + 1.86764i) q^{29} +(3.00894 - 1.73721i) q^{31} +(1.64855 + 5.34446i) q^{32} +(-1.49270 + 1.19039i) q^{34} +(-3.94314 - 6.25665i) q^{35} +(5.29640 + 4.91434i) q^{37} +(3.85874 + 0.581612i) q^{38} +(-0.923353 - 6.12604i) q^{40} +(-2.49594 - 1.20198i) q^{41} +(8.98188 - 4.32545i) q^{43} +(-2.18350 - 3.20261i) q^{44} +(0.374103 + 4.99206i) q^{46} +(-1.52269 - 3.87975i) q^{47} +(-6.98182 - 0.504199i) q^{49} +1.71944i q^{50} +(6.15723 - 0.461421i) q^{52} +(-0.503602 - 0.542754i) q^{53} +(2.89028 + 6.00174i) q^{55} +(-5.18807 - 2.73299i) q^{56} +(-5.07218 + 0.764509i) q^{58} +(-2.77969 - 1.89516i) q^{59} +(-8.06655 + 8.69368i) q^{61} +(-1.32392 + 1.66015i) q^{62} +(0.236150 + 0.296123i) q^{64} +(-10.5817 - 0.792987i) q^{65} +(-1.63319 - 2.82877i) q^{67} +(-2.54057 + 4.40039i) q^{68} +(3.64026 + 2.67903i) q^{70} +(-4.32106 + 0.986253i) q^{71} +(-8.43376 - 3.31001i) q^{73} +(-4.11044 - 1.61323i) q^{74} +(10.1250 - 2.31097i) q^{76} +(6.19681 + 1.16381i) q^{77} +(-5.27084 + 9.12936i) q^{79} +(-2.65332 - 4.59569i) q^{80} +(1.68834 + 0.126523i) q^{82} +(6.22852 + 7.81031i) q^{83} +(5.44452 - 6.82721i) q^{85} +(-4.14407 + 4.46625i) q^{86} +(4.36405 + 2.97536i) q^{88} +(11.8511 - 1.78627i) q^{89} +(-6.54114 + 7.62180i) q^{91} +(5.78056 + 12.0035i) q^{92} +(1.73254 + 1.86723i) q^{94} +(-17.7983 + 1.33379i) q^{95} +3.74135i q^{97} +(4.08459 - 1.27206i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 16 q^{4} + 2 q^{7}+O(q^{10}) $ 216 * q - 16 * q^4 + 2 * q^7	$ 216 q - 16 q^{4} + 2 q^{7} + 12 q^{10} + 12 q^{16} - 6 q^{19} + 44 q^{22} + 26 q^{25} + 84 q^{28} - 6 q^{31} - 112 q^{34} + 60 q^{37} - 304 q^{40} + 20 q^{43} - 20 q^{46} - 86 q^{49} - 168 q^{52} - 84 q^{55} - 120 q^{58} - 2 q^{61} + 32 q^{64} + 22 q^{67} - 136 q^{70} - 6 q^{73} + 84 q^{76} + 2 q^{79} - 104 q^{82} + 96 q^{85} - 12 q^{88} + 58 q^{91} + 52 q^{94}+O(q^{100}) $ 216 * q - 16 * q^4 + 2 * q^7 + 12 * q^10 + 12 * q^16 - 6 * q^19 + 44 * q^22 + 26 * q^25 + 84 * q^28 - 6 * q^31 - 112 * q^34 + 60 * q^37 - 304 * q^40 + 20 * q^43 - 20 * q^46 - 86 * q^49 - 168 * q^52 - 84 * q^55 - 120 * q^58 - 2 * q^61 + 32 * q^64 + 22 * q^67 - 136 * q^70 - 6 * q^73 + 84 * q^76 + 2 * q^79 - 104 * q^82 + 96 * q^85 - 12 * q^88 + 58 * q^91 + 52 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{41}{42}\right)$	$-1$

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 $

$2$	−0.568908	+	0.223280i	−0.402278	+	0.157883i	−0.557850	−	0.829942i	$-0.688373\pi$
$2$	−0.568908	+	0.223280i	−0.402278	+	0.157883i	0.155571	+	0.987825i	$0.450278\pi$
$3$		0			0
$3$		0			0
$4$	−1.19230	+	1.10629i	−0.596151	+	0.553147i
$5$	2.30954	−	1.57462i	1.03286	−	0.704192i	0.0767049	−	0.997054i	$-0.475560\pi$
$5$	2.30954	−	1.57462i	1.03286	−	0.704192i	0.956155	+	0.292862i	$0.0946077\pi$
$6$		0			0
$7$	0.0953467	−	2.64403i	0.0360377	−	0.999350i
$7$	0.0953467	−	2.64403i	0.0360377	−	0.999350i
$8$	0.961636	−	1.99686i	0.339990	−	0.705996i
$9$		0			0
$10$	−0.962336	+	1.41149i	−0.304317	+	0.446352i
$11$	−0.355186	+	2.35651i	−0.107093	+	0.710513i	0.869264	+	0.494348i	$0.164593\pi$
$11$	−0.355186	+	2.35651i	−0.107093	+	0.710513i	−0.976357	+	0.216165i	$0.930645\pi$
$12$		0			0
$13$	−2.96799	−	2.36690i	−0.823173	−	0.656459i	0.118512	−	0.992953i	$-0.462187\pi$
$13$	−2.96799	−	2.36690i	−0.823173	−	0.656459i	−0.941686	+	0.336494i	$0.890759\pi$
$14$	0.536116	+	1.52550i	0.143283	+	0.407707i
$15$		0			0
$16$	0.141871	−	1.89314i	0.0354679	−	0.473286i
$17$	2.98520	−	0.920812i	0.724017	−	0.223330i	0.0892236	−	0.996012i	$-0.471561\pi$
$17$	2.98520	−	0.920812i	0.724017	−	0.223330i	0.634793	+	0.772682i	$0.281085\pi$
$18$		0			0
$19$	−5.52972	−	3.19259i	−1.26861	−	0.732430i	−0.293881	−	0.955842i	$-0.594947\pi$
$19$	−5.52972	−	3.19259i	−1.26861	−	0.732430i	−0.974724	+	0.223412i	$0.928280\pi$
$20$	−1.01168	+	4.43246i	−0.226218	+	0.991128i
$21$		0			0
$22$	−0.324092	−	1.41994i	−0.0690967	−	0.302732i
$23$	2.41439	−	7.82724i	0.503434	−	1.63209i	−0.245462	−	0.969406i	$-0.578940\pi$
$23$	2.41439	−	7.82724i	0.503434	−	1.63209i	0.748896	−	0.662687i	$-0.230584\pi$
$24$		0			0
$25$	1.02786	−	2.61894i	0.205572	−	0.523789i
$26$	2.21699	+	0.683852i	0.434788	+	0.134114i
$27$		0			0
$28$	2.81140	+	3.25797i	0.531304	+	0.615698i
$29$	8.18266	+	1.86764i	1.51948	+	0.346812i	0.899190	−	0.437559i	$-0.144157\pi$
$29$	8.18266	+	1.86764i	1.51948	+	0.346812i	0.620293	+	0.784371i	$0.287014\pi$
$30$		0			0
$31$	3.00894	−	1.73721i	0.540422	−	0.312013i	−0.204828	−	0.978798i	$-0.565664\pi$
$31$	3.00894	−	1.73721i	0.540422	−	0.312013i	0.745250	+	0.666785i	$0.232330\pi$
$32$	1.64855	+	5.34446i	0.291425	+	0.944776i
$33$		0			0
$34$	−1.49270	+	1.19039i	−0.255996	+	0.204150i
$35$	−3.94314	−	6.25665i	−0.666512	−	1.05757i
$36$		0			0
$37$	5.29640	+	4.91434i	0.870723	+	0.807913i	0.982586	−	0.185811i	$-0.0594911\pi$
$37$	5.29640	+	4.91434i	0.870723	+	0.807913i	−0.111862	+	0.993724i	$0.535682\pi$
$38$	3.85874	+	0.581612i	0.625970	+	0.0943499i
$39$		0			0
$40$	−0.923353	−	6.12604i	−0.145995	−	0.968613i
$41$	−2.49594	−	1.20198i	−0.389801	−	0.187718i	0.228710	−	0.973495i	$-0.426549\pi$
$41$	−2.49594	−	1.20198i	−0.389801	−	0.187718i	−0.618510	+	0.785777i	$0.712264\pi$
$42$		0			0
$43$	8.98188	−	4.32545i	1.36972	−	0.659624i	0.402942	−	0.915226i	$-0.367988\pi$
$43$	8.98188	−	4.32545i	1.36972	−	0.659624i	0.966782	+	0.255601i	$0.0822735\pi$
$44$	−2.18350	−	3.20261i	−0.329175	−	0.482811i
$45$		0			0
$46$	0.374103	+	4.99206i	0.0551585	+	0.736039i
$47$	−1.52269	−	3.87975i	−0.222107	−	0.565920i	0.775772	−	0.631013i	$-0.217361\pi$
$47$	−1.52269	−	3.87975i	−0.222107	−	0.565920i	−0.997879	+	0.0650934i	$0.979265\pi$
$48$		0			0
$49$	−6.98182	−	0.504199i	−0.997403	−	0.0720285i
$50$			1.71944i			0.243165i
$51$		0			0
$52$	6.15723	−	0.461421i	0.853854	−	0.0639875i
$53$	−0.503602	−	0.542754i	−0.0691751	−	0.0745530i	0.697516	−	0.716569i	$-0.254289\pi$
$53$	−0.503602	−	0.542754i	−0.0691751	−	0.0745530i	−0.766691	+	0.642016i	$0.778098\pi$
$54$		0			0
$55$	2.89028	+	6.00174i	0.389726	+	0.809274i
$56$	−5.18807	−	2.73299i	−0.693285	−	0.365211i
$57$		0			0
$58$	−5.07218	+	0.764509i	−0.666011	+	0.100385i
$59$	−2.77969	−	1.89516i	−0.361884	−	0.246729i	0.368704	−	0.929547i	$-0.379802\pi$
$59$	−2.77969	−	1.89516i	−0.361884	−	0.246729i	−0.730588	+	0.682818i	$0.760754\pi$
$60$		0			0
$61$	−8.06655	+	8.69368i	−1.03282	+	1.11311i	−0.0393222	+	0.999227i	$0.512520\pi$
$61$	−8.06655	+	8.69368i	−1.03282	+	1.11311i	−0.993494	+	0.113885i	$0.963671\pi$
$62$	−1.32392	+	1.66015i	−0.168139	+	0.210839i
$63$		0			0
$64$	0.236150	+	0.296123i	0.0295187	+	0.0370153i
$65$	−10.5817	−	0.792987i	−1.31250	−	0.0983579i
$66$		0			0
$67$	−1.63319	−	2.82877i	−0.199526	−	0.345589i	0.748849	−	0.662741i	$-0.230607\pi$
$67$	−1.63319	−	2.82877i	−0.199526	−	0.345589i	−0.948375	+	0.317152i	$0.897274\pi$
$68$	−2.54057	+	4.40039i	−0.308089	+	0.533626i
$69$		0			0
$70$	3.64026	+	2.67903i	0.435095	+	0.320205i
$71$	−4.32106	+	0.986253i	−0.512815	+	0.117047i	−0.471095	−	0.882083i	$-0.656141\pi$
$71$	−4.32106	+	0.986253i	−0.512815	+	0.117047i	−0.0417204	+	0.999129i	$0.513284\pi$
$72$		0			0
$73$	−8.43376	−	3.31001i	−0.987097	−	0.387407i	−0.183786	−	0.982966i	$-0.558835\pi$
$73$	−8.43376	−	3.31001i	−0.987097	−	0.387407i	−0.803311	+	0.595559i	$0.796930\pi$
$74$	−4.11044	−	1.61323i	−0.477829	−	0.187534i
$75$		0			0
$76$	10.1250	−	2.31097i	1.16142	−	0.265087i
$77$	6.19681	+	1.16381i	0.706192	+	0.132628i
$78$		0			0
$79$	−5.27084	+	9.12936i	−0.593016	+	1.02713i	0.400808	+	0.916162i	$0.368730\pi$
$79$	−5.27084	+	9.12936i	−0.593016	+	1.02713i	−0.993824	+	0.110971i	$0.964604\pi$
$80$	−2.65332	−	4.59569i	−0.296651	−	0.513814i
$81$		0			0
$82$	1.68834	+	0.126523i	0.186446	+	0.0139722i
$83$	6.22852	+	7.81031i	0.683669	+	0.857293i	0.995686	−	0.0927830i	$-0.0295763\pi$
$83$	6.22852	+	7.81031i	0.683669	+	0.857293i	−0.312018	+	0.950076i	$0.601005\pi$
$84$		0			0
$85$	5.44452	−	6.82721i	0.590541	−	0.740515i
$86$	−4.14407	+	4.46625i	−0.446867	+	0.481608i
$87$		0			0
$88$	4.36405	+	2.97536i	0.465209	+	0.317174i
$89$	11.8511	−	1.78627i	1.25622	−	0.189345i	0.512998	−	0.858390i	$-0.328535\pi$
$89$	11.8511	−	1.78627i	1.25622	−	0.189345i	0.743222	+	0.669045i	$0.233297\pi$
$90$		0			0
$91$	−6.54114	+	7.62180i	−0.685698	+	0.798981i
$92$	5.78056	+	12.0035i	0.602665	+	1.25145i
$93$		0			0
$94$	1.73254	+	1.86723i	0.178698	+	0.192591i
$95$	−17.7983	+	1.33379i	−1.82606	+	0.136844i
$96$		0			0
$97$			3.74135i			0.379877i	0.981796	+	0.189938i	$0.0608289\pi$
$97$			3.74135i			0.379877i	−0.981796	+	0.189938i	$0.939171\pi$
$98$	4.08459	−	1.27206i	0.412606	−	0.128497i
$99$		0			0
$100$	1.67180	+	4.25969i	0.167180	+	0.425969i
$101$	0.997657	+	13.3128i	0.0992706	+	1.32467i	0.795105	+	0.606472i	$0.207416\pi$
$101$	0.997657	+	13.3128i	0.0992706	+	1.32467i	−0.695834	+	0.718202i	$0.744965\pi$
$102$		0			0
$103$	−6.25546	−	9.17507i	−0.616369	−	0.904047i	0.383441	−	0.923565i	$-0.374739\pi$
$103$	−6.25546	−	9.17507i	−0.616369	−	0.904047i	−0.999809	+	0.0195185i	$0.993787\pi$
$104$	−7.58049	+	3.65057i	−0.743328	+	0.357968i
$105$		0			0
$106$	0.407689	+	0.196333i	0.0395982	+	0.0190695i
$107$	0.909514	+	6.03423i	0.0879261	+	0.583351i	0.988797	+	0.149265i	$0.0476907\pi$
$107$	0.909514	+	6.03423i	0.0879261	+	0.583351i	−0.900871	+	0.434086i	$0.857071\pi$
$108$		0			0
$109$	11.1749	+	1.68435i	1.07036	+	0.161331i	0.660508	−	0.750819i	$-0.270341\pi$
$109$	11.1749	+	1.68435i	1.07036	+	0.161331i	0.409856	+	0.912150i	$0.365579\pi$
$110$	−2.98437	−	2.76909i	−0.284549	−	0.264023i
$111$		0			0
$112$	−4.99201	−	0.555618i	−0.471700	−	0.0525009i
$113$	−0.325037	+	0.259208i	−0.0305769	+	0.0243843i	−0.638659	−	0.769490i	$-0.720511\pi$
$113$	−0.325037	+	0.259208i	−0.0305769	+	0.0243843i	0.608082	+	0.793874i	$0.291939\pi$
$114$		0			0
$115$	−6.74881	−	21.8791i	−0.629330	−	2.04024i
$116$	−11.8224	+	6.82564i	−1.09768	+	0.633745i
$117$		0			0
$118$	2.00454	+	0.457522i	0.184532	+	0.0421183i
$119$	−2.15003	−	7.98076i	−0.197093	−	0.731595i
$120$		0			0
$121$	5.08434	+	1.56831i	0.462212	+	0.142574i
$122$	2.64800	−	6.74700i	0.239739	−	0.610844i
$123$		0			0
$124$	−1.66570	+	5.40006i	−0.149584	+	0.484939i
$125$	1.36005	+	5.95878i	0.121647	+	0.532970i
$126$		0			0
$127$	−4.30837	+	18.8762i	−0.382306	+	1.67499i	0.307932	+	0.951408i	$0.400363\pi$
$127$	−4.30837	+	18.8762i	−0.382306	+	1.67499i	−0.690238	+	0.723583i	$0.742494\pi$
$128$	−9.88772	−	5.70868i	−0.873959	−	0.504580i
$129$		0			0
$130$	6.19705	−	1.91154i	0.543518	−	0.167653i
$131$	1.62385	−	21.6688i	0.141876	−	1.89321i	−0.242678	−	0.970107i	$-0.578026\pi$
$131$	1.62385	−	21.6688i	0.141876	−	1.89321i	0.384555	−	0.923102i	$-0.374355\pi$
$132$		0			0
$133$	−8.96854	+	14.3164i	−0.777671	+	1.24139i
$134$	1.56074	+	1.24465i	0.134827	+	0.107521i
$135$		0			0
$136$	1.03194	−	6.84650i	0.0884885	−	0.587083i
$137$	1.44583	−	2.12064i	0.123526	−	0.181179i	−0.759495	−	0.650513i	$-0.774554\pi$
$137$	1.44583	−	2.12064i	0.123526	−	0.181179i	0.883020	+	0.469335i	$0.155506\pi$
$138$		0			0
$139$	−2.52220	+	5.23739i	−0.213930	+	0.444230i	−0.980126	−	0.198377i	$-0.936433\pi$
$139$	−2.52220	+	5.23739i	−0.213930	+	0.444230i	0.766196	+	0.642607i	$0.222147\pi$
$140$	11.6231	+	3.09753i	0.982332	+	0.261789i
$141$		0			0
$142$	2.23807	−	1.52589i	0.187815	−	0.128050i
$143$	6.63180	−	6.15341i	0.554579	−	0.514574i
$144$		0			0
$145$	21.8390	−	8.57119i	1.81363	−	0.711799i
$146$	5.53709			0.458253
$147$		0			0
$148$	−11.7516			−0.965977
$149$	−4.13806	+	1.62407i	−0.339003	+	0.133049i	−0.528735	−	0.848787i	$-0.677333\pi$
$149$	−4.13806	+	1.62407i	−0.339003	+	0.133049i	0.189732	+	0.981836i	$0.439238\pi$
$150$		0			0
$151$	−7.68138	+	7.12727i	−0.625101	+	0.580009i	−0.927800	−	0.373077i	$-0.878303\pi$
$151$	−7.68138	+	7.12727i	−0.625101	+	0.580009i	0.302699	+	0.953086i	$0.402112\pi$
$152$	−11.6927	+	7.97196i	−0.948405	+	0.646612i
$153$		0			0
$154$	−3.78527	+	0.721523i	−0.305026	+	0.0581420i
$155$	4.21383	−	8.75011i	0.338463	−	0.702826i
$156$		0			0
$157$	6.49697	−	9.52930i	0.518514	−	0.760521i	−0.474277	−	0.880376i	$-0.657291\pi$
$157$	6.49697	−	9.52930i	0.518514	−	0.760521i	0.992791	+	0.119855i	$0.0382429\pi$
$158$	0.960219	−	6.37064i	0.0763909	−	0.506821i
$159$		0			0
$160$	12.2229	+	9.74743i	0.966304	+	0.770602i
$161$	−20.4653	−	7.13002i	−1.61289	−	0.561924i
$162$		0			0
$163$	0.476350	−	6.35645i	0.0373106	−	0.497875i	−0.946977	−	0.321302i	$-0.895880\pi$
$163$	0.476350	−	6.35645i	0.0373106	−	0.497875i	0.984287	−	0.176574i	$-0.0565013\pi$
$164$	4.30566	−	1.32812i	0.336216	−	0.103709i
$165$		0			0
$166$	−5.28734	−	3.05264i	−0.410377	−	0.236931i
$167$	−3.32556	+	14.5702i	−0.257340	+	1.12748i	0.666743	+	0.745288i	$0.267688\pi$
$167$	−3.32556	+	14.5702i	−0.257340	+	1.12748i	−0.924083	+	0.382192i	$0.875169\pi$
$168$		0			0
$169$	0.314019	+	1.37581i	0.0241553	+	0.105831i
$170$	−1.57305	+	5.09970i	−0.120647	+	0.391129i
$171$		0			0
$172$	−5.92390	+	15.0938i	−0.451693	+	1.15089i
$173$	3.91986	+	1.20912i	0.298021	+	0.0919274i	0.440160	−	0.897919i	$-0.354922\pi$
$173$	3.91986	+	1.20912i	0.298021	+	0.0919274i	−0.142139	+	0.989847i	$0.545398\pi$
$174$		0			0
$175$	−6.82657	−	2.96740i	−0.516040	−	0.224314i
$176$	4.41081	+	1.00674i	0.332478	+	0.0758858i
$177$		0			0
$178$	−6.34337	+	3.66235i	−0.475456	+	0.274504i
$179$	3.04420	+	9.86906i	0.227534	+	0.737648i	0.995293	+	0.0969091i	$0.0308956\pi$
$179$	3.04420	+	9.86906i	0.227534	+	0.737648i	−0.767759	+	0.640739i	$0.778628\pi$
$180$		0			0
$181$	13.1115	−	10.4561i	0.974573	−	0.777196i	−0.000290678	−	1.00000i	$-0.500093\pi$
$181$	13.1115	−	10.4561i	0.974573	−	0.777196i	0.974863	+	0.222804i	$0.0715211\pi$
$182$	2.01951	−	5.79660i	0.149696	−	0.429673i
$183$		0			0
$184$	−13.3081	−	12.3481i	−0.981089	−	0.910317i
$185$	19.9705	+	3.01007i	1.46826	+	0.221305i
$186$		0			0
$187$	1.10960	+	7.36170i	0.0811418	+	0.538341i
$188$	6.10765	+	2.94129i	0.445446	+	0.214516i
$189$		0			0
$190$	9.82775	−	4.73280i	0.712980	−	0.343353i
$191$	−2.12421	−	3.11564i	−0.153702	−	0.225440i	0.741663	−	0.670773i	$-0.234038\pi$
$191$	−2.12421	−	3.11564i	−0.153702	−	0.225440i	−0.895365	+	0.445333i	$0.853085\pi$
$192$		0			0
$193$	−0.671898	−	8.96585i	−0.0483643	−	0.645376i	−0.967733	−	0.251979i	$-0.918919\pi$
$193$	−0.671898	−	8.96585i	−0.0483643	−	0.645376i	0.919369	−	0.393397i	$-0.128700\pi$
$194$	−0.835369	−	2.12848i	−0.0599760	−	0.152816i
$195$		0			0
$196$	8.88223	−	7.12279i	0.634445	−	0.508771i
$197$			24.7868i			1.76599i	0.469384	+	0.882994i	$0.344476\pi$
$197$			24.7868i			1.76599i	−0.469384	+	0.882994i	$0.655524\pi$
$198$		0			0
$199$	6.43723	−	0.482404i	0.456323	−	0.0341967i	0.155414	−	0.987849i	$-0.450329\pi$
$199$	6.43723	−	0.482404i	0.456323	−	0.0341967i	0.300909	+	0.953653i	$0.402710\pi$
$200$	−4.24123	−	4.57096i	−0.299900	−	0.323216i
$201$		0			0
$202$	−3.54006	−	7.35100i	−0.249077	−	0.517215i
$203$	5.71829	−	21.4572i	0.401345	−	1.50600i
$204$		0			0
$205$	−7.65715	+	1.15413i	−0.534799	+	0.0806079i
$206$	5.60739	+	3.82305i	0.390685	+	0.266365i
$207$		0			0
$208$	−4.90195	+	5.28304i	−0.339889	+	0.366313i
$209$	9.48743	−	11.8969i	0.656259	−	0.822923i
$210$		0			0
$211$	−9.74313	−	12.2175i	−0.670745	−	0.841087i	0.323721	−	0.946153i	$-0.395066\pi$
$211$	−9.74313	−	12.2175i	−0.670745	−	0.841087i	−0.994465	+	0.105065i	$0.966495\pi$
$212$	1.20089	+	0.0899943i	0.0824775	+	0.00618084i
$213$		0			0
$214$	−1.86475	−	3.22984i	−0.127472	−	0.220788i
$215$	13.9331	−	24.1329i	0.950230	−	1.64585i
$216$		0			0
$217$	−4.30636	−	8.12138i	−0.292334	−	0.551315i
$218$	−6.73358	+	1.53690i	−0.456056	+	0.104092i
$219$		0			0
$220$	−10.0858	−	3.95838i	−0.679983	−	0.266874i
$221$	−11.0395	−	4.33269i	−0.742598	−	0.291448i
$222$		0			0
$223$	−2.26598	+	0.517194i	−0.151741	+	0.0346339i	−0.297717	−	0.954654i	$-0.596225\pi$
$223$	−2.26598	+	0.517194i	−0.151741	+	0.0346339i	0.145976	+	0.989288i	$0.453368\pi$
$224$	14.2881	−	3.84924i	0.954664	−	0.257188i
$225$		0			0
$226$	0.127040	−	0.220040i	0.00845058	−	0.0146368i
$227$	6.15258	+	10.6566i	0.408361	+	0.707302i	0.994706	−	0.102759i	$-0.0327672\pi$
$227$	6.15258	+	10.6566i	0.408361	+	0.707302i	−0.586345	+	0.810061i	$0.699434\pi$
$228$		0			0
$229$	−5.76042	−	0.431684i	−0.380659	−	0.0285265i	−0.116973	−	0.993135i	$-0.537319\pi$
$229$	−5.76042	−	0.431684i	−0.380659	−	0.0285265i	−0.263686	+	0.964609i	$0.584938\pi$
$230$	8.72461	+	10.9403i	0.575284	+	0.721383i
$231$		0			0
$232$	11.5982	−	14.5436i	0.761456	−	0.954836i
$233$	−4.48540	+	4.83411i	−0.293848	+	0.316693i	−0.862670	−	0.505768i	$-0.831209\pi$
$233$	−4.48540	+	4.83411i	−0.293848	+	0.316693i	0.568821	+	0.822461i	$0.307400\pi$
$234$		0			0
$235$	−9.62586	−	6.56280i	−0.627922	−	0.428110i
$236$	5.41083	−	0.815551i	0.352215	−	0.0530879i
$237$		0			0
$238$	3.00511	+	4.06026i	0.194792	+	0.263187i
$239$	−1.49317	−	3.10061i	−0.0965853	−	0.200562i	0.847078	−	0.531469i	$-0.178360\pi$
$239$	−1.49317	−	3.10061i	−0.0965853	−	0.200562i	−0.943663	+	0.330907i	$0.892645\pi$
$240$		0			0
$241$	9.39452	+	10.1249i	0.605155	+	0.652201i	0.959101	−	0.283064i	$-0.0913510\pi$
$241$	9.39452	+	10.1249i	0.605155	+	0.652201i	−0.353946	+	0.935266i	$0.615160\pi$
$242$	−3.24269	+	0.243006i	−0.208448	+	0.0156210i
$243$		0			0
$244$		−	19.2895i		−	1.23488i
$245$	−16.9187	+	9.82924i	−1.08090	+	0.627967i
$246$		0			0
$247$	8.85566	+	22.5639i	0.563472	+	1.43570i
$248$	−0.575461	−	7.67900i	−0.0365418	−	0.487617i
$249$		0			0
$250$	−2.10422	−	3.08633i	−0.133083	−	0.195196i
$251$	2.90508	−	1.39901i	0.183367	−	0.0883049i	−0.339948	−	0.940444i	$-0.610409\pi$
$251$	2.90508	−	1.39901i	0.183367	−	0.0883049i	0.523315	+	0.852139i	$0.324695\pi$
$252$		0			0
$253$	17.5874	+	8.46964i	1.10571	+	0.532482i
$254$	−1.76361	−	11.7008i	−0.110659	−	0.734172i
$255$		0			0
$256$	6.15078	+	0.927081i	0.384424	+	0.0579426i
$257$	13.8489	+	12.8499i	0.863871	+	0.801555i	0.981492	−	0.191503i	$-0.0613363\pi$
$257$	13.8489	+	12.8499i	0.863871	+	0.801555i	−0.117621	+	0.993059i	$0.537527\pi$
$258$		0			0
$259$	13.4987	−	13.5353i	0.838767	−	0.841042i
$260$	13.4938	−	10.7610i	0.836852	−	0.667367i
$261$		0			0
$262$	3.91438	+	12.6901i	0.241831	+	0.783997i
$263$	25.5040	−	14.7247i	1.57264	−	0.907965i	0.576797	−	0.816887i	$-0.304302\pi$
$263$	25.5040	−	14.7247i	1.57264	−	0.907965i	0.995844	−	0.0910776i	$-0.0290311\pi$
$264$		0			0
$265$	−2.01772	−	0.460532i	−0.123948	−	0.0282903i
$266$	1.90572	−	10.1472i	0.116847	−	0.622164i
$267$		0			0
$268$	5.07671	+	1.56596i	0.310109	+	0.0956560i
$269$	9.65058	−	24.5893i	0.588406	−	1.49923i	−0.257703	−	0.966224i	$-0.582965\pi$
$269$	9.65058	−	24.5893i	0.588406	−	1.49923i	0.846109	−	0.533010i	$-0.178939\pi$
$270$		0			0
$271$	−0.761616	+	2.46910i	−0.0462649	+	0.149987i	−0.975758	−	0.218852i	$-0.929769\pi$
$271$	−0.761616	+	2.46910i	−0.0462649	+	0.149987i	0.929493	+	0.368840i	$0.120245\pi$
$272$	−1.31971	−	5.78204i	−0.0800194	−	0.350588i
$273$		0			0
$274$	−0.349047	+	1.52927i	−0.0210867	+	0.0923868i
$275$	5.80647	+	3.35237i	0.350144	+	0.202155i
$276$		0			0
$277$	9.27993	−	2.86248i	0.557577	−	0.171990i	−0.00314320	−	0.999995i	$-0.501001\pi$
$277$	9.27993	−	2.86248i	0.557577	−	0.171990i	0.560720	+	0.828005i	$0.310524\pi$
$278$	0.265492	−	3.54275i	0.0159232	−	0.212480i
$279$		0			0
$280$	−16.2855	+	1.85728i	−0.973245	+	0.110994i
$281$	16.1573	+	12.8850i	0.963863	+	0.768655i	0.972881	−	0.231304i	$-0.0742993\pi$
$281$	16.1573	+	12.8850i	0.963863	+	0.768655i	−0.00901855	+	0.999959i	$0.502871\pi$
$282$		0			0
$283$	0.766715	−	5.08682i	0.0455765	−	0.302380i	−0.954416	−	0.298480i	$-0.903520\pi$
$283$	0.766715	−	5.08682i	0.0455765	−	0.302380i	0.999992	−	0.00390027i	$-0.00124150\pi$
$284$	4.06092	−	5.95627i	0.240971	−	0.353440i
$285$		0			0
$286$	−2.39895	+	4.98147i	−0.141853	+	0.294560i
$287$	−3.41606	+	6.48475i	−0.201644	+	0.382782i
$288$		0			0
$289$	−5.98255	+	4.07883i	−0.351914	+	0.239931i
$290$	−10.5106	+	9.75243i	−0.617205	+	0.572683i
$291$		0			0
$292$	13.7174	−	5.38369i	0.802752	−	0.315057i
$293$	−23.2876			−1.36048			−0.680238	−	0.732991i	$-0.738124\pi$
$293$	−23.2876			−1.36048			−0.680238	+	0.732991i	$0.738124\pi$
$294$		0			0
$295$	−9.40397			−0.547520
$296$	14.9065	−	5.85035i	0.866420	−	0.340045i
$297$		0			0
$298$	1.99155	−	1.84789i	0.115367	−	0.107045i
$299$	−25.6922	+	17.5166i	−1.48582	+	1.01301i
$300$		0			0
$301$	−10.5802	−	24.1608i	−0.609834	−	1.39261i
$302$	2.77862	−	5.76986i	0.159891	−	0.332018i
$303$		0			0
$304$	−6.82853	+	10.0156i	−0.391643	+	0.574435i
$305$	−4.94082	+	32.7802i	−0.282910	+	1.87699i
$306$		0			0
$307$	−8.07903	−	6.44281i	−0.461094	−	0.367710i	0.365219	−	0.930922i	$-0.380994\pi$
$307$	−8.07903	−	6.44281i	−0.461094	−	0.367710i	−0.826313	+	0.563211i	$0.809566\pi$
$308$	−8.67599	+	5.46789i	−0.494360	+	0.311562i
$309$		0			0
$310$	−0.443558	+	5.91887i	−0.0251924	+	0.336169i
$311$	1.80833	−	0.557795i	0.102541	−	0.0316297i	−0.243060	−	0.970011i	$-0.578151\pi$
$311$	1.80833	−	0.557795i	0.102541	−	0.0316297i	0.345601	+	0.938382i	$0.387675\pi$
$312$		0			0
$313$	−21.9225	−	12.6570i	−1.23913	−	0.715413i	−0.270215	−	0.962800i	$-0.587095\pi$
$313$	−21.9225	−	12.6570i	−1.23913	−	0.715413i	−0.968917	+	0.247387i	$0.920428\pi$
$314$	−1.56847	+	6.87193i	−0.0885141	+	0.387805i
$315$		0			0
$316$	−3.81533	−	16.7161i	−0.214629	−	0.940352i
$317$	−0.837254	+	2.71431i	−0.0470249	+	0.152451i	−0.976040	−	0.217590i	$-0.930180\pi$
$317$	−0.837254	+	2.71431i	−0.0470249	+	0.152451i	0.929015	+	0.370041i	$0.120656\pi$
$318$		0			0
$319$	−7.30747	+	18.6191i	−0.409140	+	1.04247i
$320$	1.01168	+	0.312062i	0.0565546	+	0.0174448i
$321$		0			0
$322$	13.2348	−	0.513165i	0.737549	−	0.0285976i
$323$	−19.4471	−	4.43867i	−1.08207	−	0.246974i
$324$		0			0
$325$	−9.24945	+	5.34017i	−0.513067	+	0.296219i
$326$	1.14827	+	3.72259i	0.0635966	+	0.206175i
$327$		0			0
$328$	−4.80038	+	3.82817i	−0.265056	+	0.211375i
$329$	−10.4034	+	3.65612i	−0.573557	+	0.201569i
$330$		0			0
$331$	7.16952	+	6.65235i	0.394073	+	0.365646i	0.852178	−	0.523252i	$-0.175281\pi$
$331$	7.16952	+	6.65235i	0.394073	+	0.365646i	−0.458105	+	0.888898i	$0.651472\pi$
$332$	−16.0668	−	2.42168i	−0.881779	−	0.132907i
$333$		0			0
$334$	−1.36130	−	9.03166i	−0.0744872	−	0.494190i
$335$	−8.22616	−	3.96151i	−0.449443	−	0.216440i
$336$		0			0
$337$	1.92190	−	0.925541i	0.104693	−	0.0504174i	−0.380804	−	0.924656i	$-0.624353\pi$
$337$	1.92190	−	0.925541i	0.104693	−	0.0504174i	0.485497	+	0.874238i	$0.338639\pi$
$338$	−0.485837	−	0.712592i	−0.0264260	−	0.0387599i
$339$		0			0
$340$	1.06140	+	14.1633i	0.0575622	+	0.768115i
$341$	3.02502	+	7.70762i	0.163814	+	0.417391i
$342$		0			0
$343$	−1.99881	+	18.4121i	−0.107926	+	0.994159i
$344$		−	22.0950i		−	1.19129i
$345$		0			0
$346$	−2.50001	+	0.187350i	−0.134401	+	0.0100720i
$347$	18.9046	+	20.3743i	1.01485	+	1.09375i	0.995578	+	0.0939348i	$0.0299445\pi$
$347$	18.9046	+	20.3743i	1.01485	+	1.09375i	0.0192725	+	0.999814i	$0.493865\pi$
$348$		0			0
$349$	12.8147	+	26.6100i	0.685955	+	1.42440i	0.894807	+	0.446452i	$0.147313\pi$
$349$	12.8147	+	26.6100i	0.685955	+	1.42440i	−0.208853	+	0.977947i	$0.566973\pi$
$350$	4.54625	+	0.163943i	0.243007	+	0.00876310i
$351$		0			0
$352$	−13.1798	+	1.98653i	−0.702485	+	0.105883i
$353$	10.8537	+	7.39996i	0.577687	+	0.393860i	0.816620	−	0.577176i	$-0.195845\pi$
$353$	10.8537	+	7.39996i	0.577687	+	0.393860i	−0.238933	+	0.971036i	$0.576798\pi$
$354$		0			0
$355$	−8.42670	+	9.08182i	−0.447243	+	0.482013i
$356$	−12.1540	+	15.2406i	−0.644161	+	0.807752i
$357$		0			0
$358$	−3.93543	−	4.93487i	−0.207994	−	0.260816i
$359$	−17.2207	−	1.29051i	−0.908871	−	0.0681105i	−0.387916	−	0.921695i	$-0.626805\pi$
$359$	−17.2207	−	1.29051i	−0.908871	−	0.0681105i	−0.520955	+	0.853584i	$0.674424\pi$
$360$		0			0
$361$	10.8852	+	18.8538i	0.572906	+	0.992303i
$362$	−5.12461	+	8.87609i	−0.269344	+	0.466517i
$363$		0			0
$364$	−0.632940	−	16.3239i	−0.0331751	−	0.855605i
$365$	−24.6901	+	5.63536i	−1.29234	+	0.294968i
$366$		0			0
$367$	−2.22898	−	0.874809i	−0.116352	−	0.0456647i	0.306451	−	0.951886i	$-0.400858\pi$
$367$	−2.22898	−	0.874809i	−0.116352	−	0.0456647i	−0.422803	+	0.906222i	$0.638954\pi$
$368$	−14.4756	−	5.68124i	−0.754591	−	0.296155i
$369$		0			0
$370$	−12.0335	+	2.74656i	−0.625590	+	0.142787i
$371$	−1.48308	+	1.27979i	−0.0769975	+	0.0664434i
$372$		0			0
$373$	5.26798	−	9.12442i	0.272766	−	0.472444i	−0.696803	−	0.717262i	$-0.745395\pi$
$373$	5.26798	−	9.12442i	0.272766	−	0.472444i	0.969569	+	0.244818i	$0.0787282\pi$
$374$	−2.27498	−	3.94037i	−0.117636	−	0.203752i
$375$		0			0
$376$	−9.21159	−	0.690313i	−0.475051	−	0.0356002i
$377$	−19.8656	−	24.9107i	−1.02313	−	1.28296i
$378$		0			0
$379$	−2.36405	+	2.96442i	−0.121433	+	0.152272i	−0.838832	−	0.544390i	$-0.816761\pi$
$379$	−2.36405	+	2.96442i	−0.121433	+	0.152272i	0.717399	+	0.696663i	$0.245332\pi$
$380$	19.7453	−	21.2804i	1.01291	−	1.09166i
$381$		0			0
$382$	1.90414	+	1.29822i	0.0974241	+	0.0664226i
$383$	24.3620	−	3.67198i	1.24484	−	0.187629i	0.506608	−	0.862176i	$-0.330899\pi$
$383$	24.3620	−	3.67198i	1.24484	−	0.187629i	0.738232	+	0.674547i	$0.235661\pi$
$384$		0			0
$385$	16.1444	−	7.06976i	0.822793	−	0.360308i
$386$	2.38414	+	4.95072i	0.121350	+	0.251985i
$387$		0			0
$388$	−4.13904	−	4.46082i	−0.210128	−	0.226464i
$389$	9.28049	−	0.695476i	0.470539	−	0.0352621i	0.162649	−	0.986684i	$-0.447996\pi$
$389$	9.28049	−	0.695476i	0.470539	−	0.0352621i	0.307890	+	0.951422i	$0.400377\pi$
$390$		0			0
$391$		−	25.5891i		−	1.29409i
$392$	−7.72078	+	13.4568i	−0.389958	+	0.679673i
$393$		0			0
$394$	−5.53440	−	14.1014i	−0.278819	−	0.710419i
$395$	2.20204	+	29.3842i	0.110797	+	1.47848i
$396$		0			0
$397$	12.1166	+	17.7717i	0.608112	+	0.891937i	0.999601	−	0.0282461i	$-0.00899219\pi$
$397$	12.1166	+	17.7717i	0.608112	+	0.891937i	−0.391489	+	0.920183i	$0.628040\pi$
$398$	−3.55448	+	1.71175i	−0.178170	+	0.0858021i
$399$		0			0
$400$	−4.81221	−	2.31744i	−0.240611	−	0.115872i
$401$	3.39335	+	22.5134i	0.169456	+	1.12426i	0.898235	+	0.439516i	$0.144850\pi$
$401$	3.39335	+	22.5134i	0.169456	+	1.12426i	−0.728779	+	0.684749i	$0.759912\pi$
$402$		0			0
$403$	−13.0423	−	1.96581i	−0.649684	−	0.0979242i
$404$	−15.9174	−	14.7692i	−0.791920	−	0.734794i
$405$		0			0
$406$	1.53777	+	13.4839i	0.0763183	+	0.669196i
$407$	−13.4619	+	10.7355i	−0.667281	+	0.532139i
$408$		0			0
$409$	9.28497	+	30.1011i	0.459112	+	1.48841i	0.828957	+	0.559312i	$0.188935\pi$
$409$	9.28497	+	30.1011i	0.459112	+	1.48841i	−0.369845	+	0.929094i	$0.620589\pi$
$410$	4.09852	−	2.36628i	0.202411	−	0.116862i
$411$		0			0
$412$	17.6087	+	4.01908i	0.867520	+	0.198006i
$413$	−5.27590	+	7.16889i	−0.259610	+	0.352758i
$414$		0			0
$415$	26.6833	+	8.23071i	1.30983	+	0.404030i
$416$	7.75690	−	19.7643i	0.380313	−	0.969023i
$417$		0			0
$418$	−2.74114	+	8.88657i	−0.134074	+	0.434656i
$419$	−8.17719	−	35.8266i	−0.399482	−	1.75024i	−0.629445	−	0.777045i	$-0.716718\pi$
$419$	−8.17719	−	35.8266i	−0.399482	−	1.75024i	0.229963	−	0.973199i	$-0.426140\pi$
$420$		0			0
$421$	1.91314	−	8.38202i	0.0932408	−	0.408515i	−0.906670	−	0.421840i	$-0.861385\pi$
$421$	1.91314	−	8.38202i	0.0932408	−	0.408515i	0.999911	+	0.0133251i	$0.00424165\pi$
$422$	8.27086	+	4.77518i	0.402619	+	0.232452i
$423$		0			0
$424$	−1.56808	+	0.483690i	−0.0761529	+	0.0234901i
$425$	0.656811	−	8.76453i	0.0318600	−	0.425142i
$426$		0			0
$427$	22.2172	+	22.1571i	1.07517	+	1.07226i
$428$	−7.76005	−	6.18844i	−0.375096	−	0.299129i
$429$		0			0
$430$	−2.53827	+	16.8403i	−0.122406	+	0.812114i
$431$	18.1310	−	26.5933i	0.873339	−	1.28095i	−0.0853083	−	0.996355i	$-0.527188\pi$
$431$	18.1310	−	26.5933i	0.873339	−	1.28095i	0.958647	−	0.284598i	$-0.0918601\pi$
$432$		0			0
$433$	5.06241	−	10.5122i	0.243284	−	0.505184i	−0.743194	−	0.669076i	$-0.766690\pi$
$433$	5.06241	−	10.5122i	0.243284	−	0.505184i	0.986478	+	0.163891i	$0.0524046\pi$
$434$	4.26326	+	3.65879i	0.204643	+	0.175628i
$435$		0			0
$436$	−15.1873	+	10.3545i	−0.727339	+	0.495891i
$437$	−38.3400	+	35.5744i	−1.83405	+	1.70175i
$438$		0			0
$439$	11.7316	−	4.60431i	0.559919	−	0.219752i	−0.0684676	−	0.997653i	$-0.521811\pi$
$439$	11.7316	−	4.60431i	0.559919	−	0.219752i	0.628386	+	0.777901i	$0.283716\pi$
$440$	14.7640			0.703847
$441$		0			0
$442$	7.24787			0.344746
$443$	−13.3936	+	5.25659i	−0.636348	+	0.249748i	−0.661511	−	0.749935i	$-0.730085\pi$
$443$	−13.3936	+	5.25659i	−0.636348	+	0.249748i	0.0251633	+	0.999683i	$0.491989\pi$
$444$		0			0
$445$	24.5581	−	22.7865i	1.16416	−	1.08019i
$446$	1.17365	−	0.800183i	0.0555740	−	0.0378897i
$447$		0			0
$448$	0.805474	−	0.596154i	0.0380551	−	0.0281656i
$449$	8.39188	−	17.4259i	0.396037	−	0.822380i	−0.603647	−	0.797252i	$-0.706286\pi$
$449$	8.39188	−	17.4259i	0.396037	−	0.822380i	0.999684	−	0.0251283i	$-0.00799941\pi$
$450$		0			0
$451$	3.71900	−	5.45477i	0.175121	−	0.256855i
$452$	0.100781	−	0.668641i	0.00474036	−	0.0314502i
$453$		0			0
$454$	−5.87964	−	4.68886i	−0.275945	−	0.220059i
$455$	−3.10561	+	27.9027i	−0.145593	+	1.30810i
$456$		0			0
$457$	2.55635	−	34.1121i	0.119581	−	1.59569i	−0.538419	−	0.842677i	$-0.680978\pi$
$457$	2.55635	−	34.1121i	0.119581	−	1.59569i	0.658000	−	0.753018i	$-0.271403\pi$
$458$	3.37353	−	1.04060i	0.157635	−	0.0486239i
$459$		0			0
$460$	32.2514	+	18.6203i	1.50373	+	0.868177i
$461$	2.13925	−	9.37267i	0.0996348	−	0.436529i	−0.900364	−	0.435137i	$-0.856700\pi$
$461$	2.13925	−	9.37267i	0.0996348	−	0.436529i	0.999999	−	0.00139152i	$-0.000442934\pi$
$462$		0			0
$463$	4.14177	+	18.1463i	0.192484	+	0.843330i	0.975266	+	0.221033i	$0.0709429\pi$
$463$	4.14177	+	18.1463i	0.192484	+	0.843330i	−0.782782	+	0.622296i	$0.786200\pi$
$464$	4.69660	−	15.2260i	0.218034	−	0.706849i
$465$		0			0
$466$	1.47242	−	3.75166i	0.0682085	−	0.173792i
$467$	−10.9618	−	3.38127i	−0.507252	−	0.156466i	0.0305574	−	0.999533i	$-0.490272\pi$
$467$	−10.9618	−	3.38127i	−0.507252	−	0.156466i	−0.537809	+	0.843067i	$0.680748\pi$
$468$		0			0
$469$	−7.63508	+	4.04849i	−0.352555	+	0.186942i
$470$	6.94156	+	1.58437i	0.320190	+	0.0730814i
$471$		0			0
$472$	−6.45741	+	3.72819i	−0.297226	+	0.171604i
$473$	7.00270	+	22.7022i	0.321984	+	1.04385i
$474$		0			0
$475$	−14.0450	+	11.2005i	−0.644428	+	0.513914i
$476$	11.3925	+	7.13691i	0.522177	+	0.327120i
$477$		0			0
$478$	1.54178	+	1.43056i	0.0705194	+	0.0654324i
$479$	−33.4701	−	5.04481i	−1.52929	−	0.230503i	−0.670142	−	0.742233i	$-0.733767\pi$
$479$	−33.4701	−	5.04481i	−1.52929	−	0.230503i	−0.859147	+	0.511729i	$0.829005\pi$
$480$		0			0
$481$	−4.08795	−	27.1218i	−0.186394	−	1.23665i
$482$	−7.60530	−	3.66252i	−0.346412	−	0.166823i
$483$		0			0
$484$	−7.79708	+	3.75487i	−0.354413	+	0.170676i
$485$	5.89121	+	8.64082i	0.267506	+	0.392360i
$486$		0			0
$487$	1.45316	+	19.3911i	0.0658489	+	0.878692i	0.928129	+	0.372260i	$0.121417\pi$
$487$	1.45316	+	19.3911i	0.0658489	+	0.878692i	−0.862280	+	0.506433i	$0.830964\pi$
$488$	9.60295	+	24.4679i	0.434705	+	1.10761i
$489$		0			0
$490$	7.43053	−	9.36954i	0.335677	−	0.423273i
$491$			13.0886i			0.590679i	0.955392	+	0.295340i	$0.0954328\pi$
$491$			13.0886i			0.590679i	−0.955392	+	0.295340i	$0.904567\pi$
$492$		0			0
$493$	26.1466	−	1.95942i	1.17758	−	0.0882477i
$494$	−10.0761	−	10.8595i	−0.453345	−	0.488590i
$495$		0			0
$496$	−2.86191	−	5.94282i	−0.128504	−	0.266840i
$497$	2.19569	+	11.5191i	0.0984900	+	0.516700i
$498$		0			0
$499$	−10.3061	+	1.55340i	−0.461365	+	0.0695396i	−0.375612	−	0.926777i	$-0.622568\pi$
$499$	−10.3061	+	1.55340i	−0.461365	+	0.0695396i	−0.0857528	+	0.996316i	$0.527330\pi$
$500$	−8.21376	−	5.60005i	−0.367331	−	0.250442i
$501$		0			0
$502$	−1.34035	+	1.44456i	−0.0598228	+	0.0644736i
$503$	3.11566	−	3.90692i	0.138921	−	0.174201i	−0.707504	−	0.706709i	$-0.750179\pi$
$503$	3.11566	−	3.90692i	0.138921	−	0.174201i	0.846425	+	0.532508i	$0.178750\pi$
$504$		0			0
$505$	23.2668	+	29.1756i	1.03536	+	1.29830i
$506$	−11.8967	−	0.891534i	−0.528873	−	0.0396335i
$507$		0			0
$508$	−15.7458	−	27.2724i	−0.698605	−	1.21002i
$509$	0.772687	−	1.33833i	0.0342487	−	0.0593205i	−0.848393	−	0.529367i	$-0.822429\pi$
$509$	0.772687	−	1.33833i	0.0342487	−	0.0593205i	0.882642	+	0.470046i	$0.155763\pi$
$510$		0			0
$511$	−9.55590	+	21.9835i	−0.422728	+	0.972494i
$512$	18.5560	−	4.23528i	0.820066	−	0.187175i
$513$		0			0
$514$	−10.7479	−	4.21823i	−0.474068	−	0.186058i
$515$	−28.8945	−	11.3403i	−1.27324	−	0.499712i
$516$		0			0
$517$	9.68350	−	2.21020i	0.425880	−	0.0972043i
$518$	−4.65734	+	10.7143i	−0.204632	+	0.470760i
$519$		0			0
$520$	−11.7592	+	20.3675i	−0.515675	+	0.893176i
$521$	−15.6375	−	27.0849i	−0.685090	−	1.18661i	−0.973409	−	0.229076i	$-0.926430\pi$
$521$	−15.6375	−	27.0849i	−0.685090	−	1.18661i	0.288319	−	0.957534i	$-0.406904\pi$
$522$		0			0
$523$	3.05590	+	0.229008i	0.133625	+	0.0100138i	0.141375	−	0.989956i	$-0.454848\pi$
$523$	3.05590	+	0.229008i	0.133625	+	0.0100138i	−0.00774962	+	0.999970i	$0.502467\pi$
$524$	22.0359	+	27.6322i	0.962644	+	1.20712i
$525$		0			0
$526$	−11.2217	+	14.0715i	−0.489288	+	0.613547i
$527$	7.38264	−	7.95659i	0.321593	−	0.346595i
$528$		0			0
$529$	−36.4330	−	24.8396i	−1.58404	−	1.07998i
$530$	1.25073	−	0.188516i	0.0543280	−	0.00818863i
$531$		0			0
$532$	−5.14490	−	26.9913i	−0.223060	−	1.17022i
$533$	4.56297	+	9.47511i	0.197644	+	0.410413i
$534$		0			0
$535$	11.6022	+	12.5042i	0.501606	+	0.540603i
$536$	−7.21918	+	0.541003i	−0.311821	+	0.0233678i
$537$		0			0
$538$			16.1438i			0.696009i
$539$	3.66799	−	16.2736i	0.157992	−	0.700954i
$540$		0			0
$541$	−13.4069	−	34.1603i	−0.576408	−	1.46866i	−0.860290	−	0.509805i	$-0.829717\pi$
$541$	−13.4069	−	34.1603i	−0.576408	−	1.46866i	0.283881	−	0.958859i	$-0.408378\pi$
$542$	−0.118011	−	1.57474i	−0.00506899	−	0.0676410i
$543$		0			0
$544$	9.84248	+	14.4363i	0.421993	+	0.618950i
$545$	28.4612	−	13.7062i	1.21914	−	0.587109i
$546$		0			0
$547$	−33.1589	−	15.9685i	−1.41777	−	0.682763i	−0.441092	−	0.897462i	$-0.645409\pi$
$547$	−33.1589	−	15.9685i	−1.41777	−	0.682763i	−0.976680	+	0.214699i	$0.931123\pi$
$548$	0.622190	+	4.12796i	0.0265786	+	0.176338i
$549$		0			0
$550$	−4.05186	−	0.610720i	−0.172772	−	0.0260412i
$551$	−39.2853	−	36.4514i	−1.67361	−	1.55288i
$552$		0			0
$553$	23.6358	+	14.8067i	1.00510	+	0.629646i
$554$	−4.64029	+	3.70051i	−0.197147	+	0.157219i
$555$		0			0
$556$	−2.78688	−	9.03484i	−0.118190	−	0.383163i
$557$	33.1476	−	19.1378i	1.40451	−	0.810894i	0.409659	−	0.912239i	$-0.365648\pi$
$557$	33.1476	−	19.1378i	1.40451	−	0.810894i	0.994851	+	0.101344i	$0.0323143\pi$
$558$		0			0
$559$	−36.8960	−	8.42128i	−1.56054	−	0.356182i
$560$	−12.4041	+	6.57729i	−0.524171	+	0.277941i
$561$		0			0
$562$	−12.0690	−	3.72278i	−0.509098	−	0.157036i
$563$	−4.75307	+	12.1106i	−0.200318	+	0.510402i	−0.995368	−	0.0961425i	$-0.969350\pi$
$563$	−4.75307	+	12.1106i	−0.200318	+	0.510402i	0.795050	+	0.606544i	$0.207445\pi$
$564$		0			0
$565$	−0.342533	+	1.11046i	−0.0144105	+	0.0467175i
$566$	0.699594	+	3.06512i	0.0294061	+	0.128837i
$567$		0			0
$568$	−2.18588	+	9.57696i	−0.0917174	+	0.401840i
$569$	22.4059	+	12.9361i	0.939305	+	0.542308i	0.889742	−	0.456463i	$-0.150884\pi$
$569$	22.4059	+	12.9361i	0.939305	+	0.542308i	0.0495625	+	0.998771i	$0.484217\pi$
$570$		0			0
$571$	37.0368	−	11.4243i	1.54994	−	0.478093i	0.602525	−	0.798100i	$-0.294161\pi$
$571$	37.0368	−	11.4243i	1.54994	−	0.478093i	0.947415	+	0.320006i	$0.103685\pi$
$572$	−1.09962	+	14.6734i	−0.0459775	+	0.613527i
$573$		0			0
$574$	0.495510	−	4.45196i	0.0206822	−	0.185821i
$575$	−18.0175	−	14.3684i	−0.751380	−	0.599206i
$576$		0			0
$577$	−0.910238	+	6.03904i	−0.0378937	+	0.251408i	−0.999755	−	0.0221289i	$-0.992956\pi$
$577$	−0.910238	+	6.03904i	−0.0378937	+	0.251408i	0.961861	+	0.273537i	$0.0881937\pi$
$578$	2.49279	−	3.65626i	0.103687	−	0.152080i
$579$		0			0
$580$	−16.5565	+	34.3799i	−0.687470	+	1.42755i
$581$	21.2446	−	15.7237i	0.881374	−	0.652330i
$582$		0			0
$583$	1.45788	−	0.993963i	0.0603790	−	0.0411657i
$584$	−14.7198	+	13.6580i	−0.609111	+	0.565172i
$585$		0			0
$586$	13.2485	−	5.19965i	0.547290	−	0.214796i
$587$	8.51684			0.351528			0.175764	−	0.984432i	$-0.443760\pi$
$587$	8.51684			0.351528			0.175764	+	0.984432i	$0.443760\pi$
$588$		0			0
$589$	−22.1848			−0.914109
$590$	5.34999	−	2.09972i	0.220256	−	0.0864439i
$591$		0			0
$592$	10.0550	−	9.32964i	0.413256	−	0.383446i
$593$	−26.0237	+	17.7427i	−1.06867	+	0.728605i	−0.964000	−	0.265903i	$-0.914330\pi$
$593$	−26.0237	+	17.7427i	−1.06867	+	0.728605i	−0.104667	+	0.994507i	$0.533378\pi$
$594$		0			0
$595$	−17.5322	−	15.0464i	−0.718752	−	0.616844i
$596$	3.13711	−	6.51429i	0.128501	−	0.266836i
$597$		0			0
$598$	10.7054	−	15.7019i	0.437775	−	0.642097i
$599$	4.66133	−	30.9259i	0.190457	−	1.26360i	−0.665441	−	0.746451i	$-0.731756\pi$
$599$	4.66133	−	30.9259i	0.190457	−	1.26360i	0.855897	−	0.517146i	$-0.173006\pi$
$600$		0			0
$601$	−8.61014	−	6.86636i	−0.351215	−	0.280084i	0.431951	−	0.901897i	$-0.357825\pi$
$601$	−8.61014	−	6.86636i	−0.351215	−	0.280084i	−0.783166	+	0.621812i	$0.786397\pi$
$602$	11.4138	+	11.3829i	0.465191	+	0.463933i
$603$		0			0
$604$	1.27365	−	16.9957i	0.0518242	−	0.691546i
$605$	14.2120	−	4.38382i	0.577800	−	0.178228i
$606$		0			0
$607$	23.6262	+	13.6406i	0.958956	+	0.553654i	0.895852	−	0.444353i	$-0.146566\pi$
$607$	23.6262	+	13.6406i	0.958956	+	0.553654i	0.0631048	+	0.998007i	$0.479900\pi$
$608$	7.94664	−	34.8165i	0.322279	−	1.41200i
$609$		0			0
$610$	−4.50828	−	19.7521i	−0.182535	−	0.799738i
$611$	−4.66363	+	15.1191i	−0.188670	+	0.611655i
$612$		0			0
$613$	1.53110	−	3.90117i	0.0618404	−	0.157567i	−0.896614	−	0.442814i	$-0.853980\pi$
$613$	1.53110	−	3.90117i	0.0618404	−	0.157567i	0.958454	+	0.285247i	$0.0920756\pi$
$614$	6.03477	+	1.86148i	0.243543	+	0.0751232i
$615$		0			0
$616$	8.28304	−	11.2550i	0.333733	−	0.453477i
$617$	−23.7804	−	5.42771i	−0.957361	−	0.218511i	−0.284828	−	0.958579i	$-0.591936\pi$
$617$	−23.7804	−	5.42771i	−0.957361	−	0.218511i	−0.672533	+	0.740067i	$0.734794\pi$
$618$		0			0
$619$	11.2869	−	6.51647i	0.453657	−	0.261919i	−0.255716	−	0.966752i	$-0.582311\pi$
$619$	11.2869	−	6.51647i	0.453657	−	0.261919i	0.709374	+	0.704833i	$0.248978\pi$
$620$	4.65604	+	15.0945i	0.186991	+	0.606210i
$621$		0			0
$622$	−0.904227	+	0.721097i	−0.0362562	+	0.0289133i
$623$	−3.59300	−	31.5051i	−0.143950	−	1.26223i
$624$		0			0
$625$	22.8359	+	21.1886i	0.913434	+	0.847543i
$626$	15.2979	+	2.30579i	0.611427	+	0.0921578i
$627$		0			0
$628$	2.79587	+	18.5494i	0.111567	+	0.740200i
$629$	20.3360	+	9.79330i	0.810849	+	0.390484i
$630$		0			0
$631$	−36.0077	+	17.3404i	−1.43344	+	0.690310i	−0.979635	−	0.200788i	$-0.935650\pi$
$631$	−36.0077	+	17.3404i	−1.43344	+	0.690310i	−0.453810	+	0.891099i	$0.649935\pi$
$632$	13.1614	+	19.3042i	0.523533	+	0.767882i
$633$		0			0
$634$	−0.129731	−	1.73113i	−0.00515226	−	0.0687521i
$635$	19.7725	+	50.3794i	0.784647	+	1.99925i
$636$		0			0
$637$	19.5286	+	18.0217i	0.773752	+	0.714046i
$638$		−	12.2242i		−	0.483960i
$639$		0			0
$640$	−31.8251	+	2.38496i	−1.25800	+	0.0942739i
$641$	8.37354	+	9.02453i	0.330735	+	0.356447i	0.876424	−	0.481540i	$-0.159923\pi$
$641$	8.37354	+	9.02453i	0.330735	+	0.356447i	−0.545689	+	0.837988i	$0.683732\pi$
$642$		0			0
$643$	8.45630	+	17.5597i	0.333484	+	0.692486i	0.998523	−	0.0543217i	$-0.0172997\pi$
$643$	8.45630	+	17.5597i	0.333484	+	0.692486i	−0.665040	+	0.746808i	$0.731585\pi$
$644$	32.2887	−	14.1395i	1.27235	−	0.557174i
$645$		0			0
$646$	12.0547	−	1.81695i	0.474284	−	0.0714869i
$647$	9.75819	+	6.65302i	0.383634	+	0.261557i	0.739746	−	0.672886i	$-0.234946\pi$
$647$	9.75819	+	6.65302i	0.383634	+	0.261557i	−0.356112	+	0.934443i	$0.615898\pi$
$648$		0			0
$649$	5.45326	−	5.87722i	0.214059	−	0.230701i
$650$	4.06973	−	5.10328i	0.159628	−	0.200167i
$651$		0			0
$652$	6.46415	+	8.10579i	0.253156	+	0.317447i
$653$	33.2661	+	2.49295i	1.30180	+	0.0975566i	0.707517	−	0.706697i	$-0.249816\pi$
$653$	33.2661	+	2.49295i	1.30180	+	0.0975566i	0.594286	+	0.804253i	$0.297435\pi$
$654$		0			0
$655$	−30.3697	−	52.6019i	−1.18664	−	2.05533i
$656$	−2.62963	+	4.55465i	−0.102670	+	0.177829i
$657$		0			0
$658$	5.10222	−	4.40286i	0.198905	−	0.171641i
$659$	6.03998	−	1.37859i	0.235284	−	0.0537021i	−0.103253	−	0.994655i	$-0.532925\pi$
$659$	6.03998	−	1.37859i	0.235284	−	0.0537021i	0.338537	+	0.940953i	$0.390068\pi$
$660$		0			0
$661$	−2.24012	−	0.879184i	−0.0871307	−	0.0341963i	0.321375	−	0.946952i	$-0.395855\pi$
$661$	−2.24012	−	0.879184i	−0.0871307	−	0.0341963i	−0.408506	+	0.912756i	$0.633950\pi$
$662$	−5.56413	−	2.18376i	−0.216256	−	0.0848743i
$663$		0			0
$664$	21.5857	−	4.92679i	0.837686	−	0.191196i
$665$	1.82959	+	47.1863i	0.0709486	+	1.82981i
$666$		0			0
$667$	34.3746	−	59.5385i	1.33099	−	2.30534i
$668$	−12.1539	−	21.0512i	−0.470249	−	0.814495i
$669$		0			0
$670$	5.56445	+	0.416998i	0.214973	+	0.0161100i
$671$	−17.6216	−	22.0968i	−0.680273	−	0.853036i
$672$		0			0
$673$	−18.0133	+	22.5879i	−0.694360	+	0.870700i	−0.996588	−	0.0825354i	$-0.973698\pi$
$673$	−18.0133	+	22.5879i	−0.694360	+	0.870700i	0.302228	+	0.953236i	$0.402270\pi$
$674$	−0.886732	+	0.955669i	−0.0341556	+	0.0368110i
$675$		0			0
$676$	−1.89645	−	1.29298i	−0.0729404	−	0.0497299i
$677$	42.8377	−	6.45674i	1.64639	−	0.248153i	0.740618	−	0.671926i	$-0.234533\pi$
$677$	42.8377	−	6.45674i	1.64639	−	0.248153i	0.905768	+	0.423773i	$0.139295\pi$
$678$		0			0
$679$	9.89226	+	0.356726i	0.379630	+	0.0136899i
$680$	−8.39732	−	17.4372i	−0.322023	−	0.668687i
$681$		0			0
$682$	−3.44191	−	3.70950i	−0.131798	−	0.142044i
$683$	28.6509	−	2.14709i	1.09630	−	0.0821560i	0.485720	−	0.874114i	$-0.338557\pi$
$683$	28.6509	−	2.14709i	1.09630	−	0.0821560i	0.610575	+	0.791958i	$0.290938\pi$
$684$		0			0
$685$		−	7.17435i		−	0.274118i
$686$	−2.97391	−	10.9211i	−0.113544	−	0.416968i
$687$		0			0
$688$	−6.91441	−	17.6176i	−0.263610	−	0.671666i
$689$	0.210046	+	2.80286i	0.00800210	+	0.106781i
$690$		0			0
$691$	−0.648065	−	0.950537i	−0.0246536	−	0.0361601i	0.813714	−	0.581265i	$-0.197442\pi$
$691$	−0.648065	−	0.950537i	−0.0246536	−	0.0361601i	−0.838368	+	0.545105i	$0.816490\pi$
$692$	−6.01129	+	2.89489i	−0.228515	+	0.110047i
$693$		0			0
$694$	−15.3041	−	7.37008i	−0.580937	−	0.279764i
$695$	2.42178	+	16.0675i	0.0918635	+	0.609475i
$696$		0			0
$697$	−8.55768	−	1.28986i	−0.324145	−	0.0488570i
$698$	−13.2318	−	12.2774i	−0.500833	−	0.464705i
$699$		0			0
$700$	11.4221	−	4.01416i	0.431717	−	0.151721i
$701$	3.83572	−	3.05888i	0.144873	−	0.115532i	−0.548371	−	0.836235i	$-0.684752\pi$
$701$	3.83572	−	3.05888i	0.144873	−	0.115532i	0.693245	+	0.720702i	$0.256181\pi$
$702$		0			0
$703$	−13.5982	−	44.0842i	−0.512865	−	1.66267i
$704$	−0.781692	+	0.451310i	−0.0294611	+	0.0170094i
$705$		0			0
$706$	−7.82704	−	1.78647i	−0.294575	−	0.0672347i
$707$	35.2946	−	1.36851i	1.32739	−	0.0514680i
$708$		0			0
$709$	−42.0232	−	12.9624i	−1.57822	−	0.486815i	−0.622875	−	0.782322i	$-0.714035\pi$
$709$	−42.0232	−	12.9624i	−1.57822	−	0.486815i	−0.955341	+	0.295507i	$0.904512\pi$
$710$	2.76623	−	7.04823i	0.103815	−	0.264515i
$711$		0			0
$712$	7.82956	−	25.3828i	0.293425	−	0.951261i
$713$	−6.33285	−	27.7460i	−0.237167	−	1.03910i
$714$		0			0
$715$	5.62714	−	24.6541i	0.210443	−	0.922012i
$716$	−14.5477	−	8.39911i	−0.543673	−	0.313890i
$717$		0			0
$718$	10.0851	−	3.11084i	0.376373	−	0.116096i
$719$	−2.00621	+	26.7709i	−0.0748188	+	0.998388i	0.825852	+	0.563886i	$0.190694\pi$
$719$	−2.00621	+	26.7709i	−0.0748188	+	0.998388i	−0.900671	+	0.434501i	$0.856925\pi$
$720$		0			0
$721$	−24.8556	+	15.6648i	−0.925672	+	0.583389i
$722$	−10.4023	−	8.29560i	−0.387135	−	0.308730i
$723$		0			0
$724$	−4.06538	+	26.9720i	−0.151089	+	1.00241i
$725$	13.3019	−	19.5103i	0.494019	−	0.724593i
$726$		0			0
$727$	7.19562	−	14.9419i	0.266871	−	0.554163i	−0.723869	−	0.689937i	$-0.757638\pi$
$727$	7.19562	−	14.9419i	0.266871	−	0.554163i	0.990740	+	0.135775i	$0.0433523\pi$
$728$	8.92945	+	20.3911i	0.330948	+	0.755745i
$729$		0			0
$730$	12.7881	−	8.71881i	0.473311	−	0.322698i
$731$	22.8298	−	21.1829i	0.844390	−	0.783479i
$732$		0			0
$733$	−22.0506	+	8.65424i	−0.814459	+	0.319652i	−0.735756	−	0.677246i	$-0.763173\pi$
$733$	−22.0506	+	8.65424i	−0.814459	+	0.319652i	−0.0787029	+	0.996898i	$0.525078\pi$
$734$	1.46341			0.0540154
$735$		0			0
$736$	45.8126			1.68868
$737$	7.24610	−	2.84388i	0.266913	−	0.104756i
$738$		0			0
$739$	−27.1206	+	25.1642i	−0.997647	+	0.925681i	−0.997235	−	0.0743189i	$-0.976322\pi$
$739$	−27.1206	+	25.1642i	−0.997647	+	0.925681i	−0.000412314		1.00000i	$0.500131\pi$
$740$	−27.1409	+	18.5043i	−0.997719	+	0.680233i
$741$		0			0
$742$	0.557982	−	1.05922i	0.0204842	−	0.0388853i
$743$	−13.3347	+	27.6899i	−0.489204	+	1.01584i	0.499549	+	0.866286i	$0.333499\pi$
$743$	−13.3347	+	27.6899i	−0.489204	+	1.01584i	−0.988753	+	0.149557i	$0.952215\pi$
$744$		0			0
$745$	−6.99973	+	10.2667i	−0.256450	+	0.376144i
$746$	−0.959699	+	6.36718i	−0.0351371	+	0.233119i
$747$		0			0
$748$	−9.46718	−	7.54982i	−0.346154	−	0.276049i
$749$	16.0414	−	1.82944i	0.586141	−	0.0668463i
$750$		0			0
$751$	−2.96210	+	39.5264i	−0.108088	+	1.44234i	0.634671	+	0.772782i	$0.281135\pi$
$751$	−2.96210	+	39.5264i	−0.108088	+	1.44234i	−0.742760	+	0.669558i	$0.766484\pi$
$752$	−7.56095	+	2.33224i	−0.275720	+	0.0850482i
$753$		0			0
$754$	16.8637	+	9.73628i	0.614141	+	0.354574i
$755$	−6.51772	+	28.5560i	−0.237204	+	1.03926i
$756$		0			0
$757$	11.6607	+	51.0888i	0.423814	+	1.85685i	0.509412	+	0.860523i	$0.329863\pi$
$757$	11.6607	+	51.0888i	0.423814	+	1.85685i	−0.0855975	+	0.996330i	$0.527280\pi$
$758$	0.683030	−	2.21433i	0.0248088	−	0.0804280i
$759$		0			0
$760$	−14.4520	+	36.8232i	−0.524231	+	1.33572i
$761$	−23.6151	−	7.28430i	−0.856047	−	0.264055i	−0.164491	−	0.986379i	$-0.552598\pi$
$761$	−23.6151	−	7.28430i	−0.856047	−	0.264055i	−0.691556	+	0.722323i	$0.743074\pi$
$762$		0			0
$763$	5.51897	−	29.3863i	0.199800	−	1.06385i
$764$	5.97951	+	1.36478i	0.216331	+	0.0493762i
$765$		0			0
$766$	−13.0398	+	7.52856i	−0.471149	+	0.272018i
$767$	3.76445	+	12.2041i	0.135926	+	0.440663i
$768$		0			0
$769$	−6.59012	+	5.25545i	−0.237646	+	0.189516i	−0.735070	−	0.677991i	$-0.762851\pi$
$769$	−6.59012	+	5.25545i	−0.237646	+	0.189516i	0.497424	+	0.867507i	$0.334279\pi$
$770$	−7.60612	+	7.62675i	−0.274106	+	0.274849i
$771$		0			0
$772$	10.7200	+	9.94669i	0.385820	+	0.357989i
$773$	−46.9211	−	7.07222i	−1.68764	−	0.254370i	−0.766116	−	0.642702i	$-0.777813\pi$
$773$	−46.9211	−	7.07222i	−1.68764	−	0.254370i	−0.921520	+	0.388332i	$0.873051\pi$
$774$		0			0
$775$	−1.45689	−	9.66586i	−0.0523332	−	0.347208i
$776$	7.47095	+	3.59782i	0.268192	+	0.129154i
$777$		0			0
$778$	−5.12445	+	2.46781i	−0.183721	+	0.0884752i
$779$	9.96443	+	14.6151i	0.357013	+	0.523642i
$780$		0			0
$781$	−0.789332	−	10.5329i	−0.0282445	−	0.376897i
$782$	5.71352	+	14.5578i	0.204315	+	0.520586i
$783$		0			0
$784$	−1.94504	+	13.1460i	−0.0694658	+	0.469502i
$785$		−	32.2386i		−	1.15064i
$786$		0			0
$787$	42.5877	−	3.19151i	1.51809	−	0.113765i	0.710577	−	0.703619i	$-0.248434\pi$
$787$	42.5877	−	3.19151i	1.51809	−	0.113765i	0.807510	+	0.589854i	$0.200815\pi$
$788$	−27.4215	−	29.5534i	−0.976851	−	1.05280i
$789$		0			0
$790$	−7.81367	−	16.2252i	−0.277998	−	0.577268i
$791$	0.654364	+	0.884123i	0.0232665	+	0.0314358i
$792$		0			0
$793$	44.5185	−	6.71009i	1.58090	−	0.238282i
$794$	−10.8613	−	7.40508i	−0.385452	−	0.262797i
$795$		0			0
$796$	−7.14144	+	7.69664i	−0.253122	+	0.272800i
$797$	20.2618	−	25.4075i	0.717711	−	0.899981i	−0.280495	−	0.959856i	$-0.590499\pi$
$797$	20.2618	−	25.4075i	0.717711	−	0.899981i	0.998206	+	0.0598743i	$0.0190700\pi$
$798$		0			0
$799$	−8.11805	−	10.1797i	−0.287196	−	0.360133i
$800$	15.6913	+	1.17590i	0.554772	+	0.0415744i
$801$		0			0
$802$	−6.95728	−	12.0504i	−0.245670	−	0.425513i
$803$	10.7956	−	18.6985i	0.380969	−	0.659857i
$804$		0			0
$805$	−58.4926	+	15.7580i	−2.06159	+	0.555396i
$806$	7.85880	−	1.79372i	0.276814	−	0.0631811i
$807$		0			0
$808$	27.5432	+	10.8099i	0.968966	+	0.380291i
$809$	−18.6189	−	7.30737i	−0.654605	−	0.256914i	0.0147106	−	0.999892i	$-0.495317\pi$
$809$	−18.6189	−	7.30737i	−0.654605	−	0.256914i	−0.669316	+	0.742978i	$0.733413\pi$
$810$		0			0
$811$	−26.4713	+	6.04190i	−0.929533	+	0.212160i	−0.660375	−	0.750936i	$-0.729603\pi$
$811$	−26.4713	+	6.04190i	−0.929533	+	0.212160i	−0.269158	+	0.963096i	$0.586745\pi$
$812$	16.9200	+	31.9095i	0.593776	+	1.11980i
$813$		0			0
$814$	5.26155	−	9.11327i	0.184417	−	0.319420i
$815$	−8.90884	−	15.4306i	−0.312063	−	0.540509i
$816$		0			0
$817$	−63.4767	−	4.75692i	−2.22077	−	0.166424i
$818$	−12.0033	−	15.0516i	−0.419684	−	0.526268i
$819$		0			0
$820$	7.85283	−	9.84714i	0.274233	−	0.343877i
$821$	−9.85662	+	10.6229i	−0.343998	+	0.370742i	−0.881226	−	0.472695i	$-0.843281\pi$
$821$	−9.85662	+	10.6229i	−0.343998	+	0.370742i	0.537228	+	0.843437i	$0.319472\pi$
$822$		0			0
$823$	−28.5534	−	19.4673i	−0.995307	−	0.678589i	−0.0479774	−	0.998848i	$-0.515278\pi$
$823$	−28.5534	−	19.4673i	−0.995307	−	0.678589i	−0.947330	+	0.320259i	$0.896230\pi$
$824$	−24.3368	+	3.66818i	−0.847813	+	0.127787i
$825$		0			0
$826$	1.40083	−	5.25643i	0.0487411	−	0.182895i
$827$	−17.3011	−	35.9261i	−0.601617	−	1.24927i	−0.950097	−	0.311955i	$-0.899016\pi$
$827$	−17.3011	−	35.9261i	−0.601617	−	1.24927i	0.348480	−	0.937316i	$-0.386698\pi$
$828$		0			0
$829$	−3.86949	−	4.17032i	−0.134393	−	0.144841i	0.662269	−	0.749266i	$-0.269594\pi$
$829$	−3.86949	−	4.17032i	−0.134393	−	0.144841i	−0.796662	+	0.604425i	$0.793403\pi$
$830$	−17.0181	+	1.27533i	−0.590707	+	0.0442673i
$831$		0			0
$832$		−	1.43783i		−	0.0498479i
$833$	−21.3064	+	4.92380i	−0.738222	+	0.170600i
$834$		0			0
$835$	15.2621	+	38.8871i	0.528166	+	1.34574i
$836$	1.84955	+	24.6805i	0.0639681	+	0.853594i
$837$		0			0
$838$	12.6514	+	18.5562i	0.437036	+	0.641014i
$839$	4.87042	−	2.34547i	0.168146	−	0.0809746i	−0.347918	−	0.937525i	$-0.613111\pi$
$839$	4.87042	−	2.34547i	0.168146	−	0.0809746i	0.516063	+	0.856550i	$0.327397\pi$
$840$		0			0
$841$	37.3398	+	17.9819i	1.28758	+	0.620066i
$842$	0.783135	+	5.19576i	0.0269886	+	0.179058i
$843$		0			0
$844$	25.1329	+	3.78818i	0.865110	+	0.130394i
$845$	2.89161	+	2.68302i	0.0994744	+	0.0922988i
$846$		0			0
$847$	4.63144	−	13.2936i	0.159138	−	0.456774i
$848$	−1.09896	+	0.876389i	−0.0377384	+	0.0300953i
$849$		0			0
$850$	1.58328	+	5.13286i	0.0543060	+	0.176056i
$851$	51.2533	−	29.5911i	1.75694	−	1.01437i
$852$		0			0
$853$	−44.4951	−	10.1557i	−1.52348	−	0.347725i	−0.622864	−	0.782330i	$-0.714031\pi$
$853$	−44.4951	−	10.1557i	−1.52348	−	0.347725i	−0.900621	+	0.434605i	$0.856888\pi$
$854$	−17.5868	−	7.64470i	−0.601808	−	0.261596i
$855$		0			0
$856$	12.9241	+	3.98657i	0.441738	+	0.136258i
$857$	−10.8202	+	27.5694i	−0.369611	+	0.941754i	0.618189	+	0.786029i	$0.287866\pi$
$857$	−10.8202	+	27.5694i	−0.369611	+	0.941754i	−0.987801	+	0.155725i	$0.950229\pi$
$858$		0			0
$859$	2.05143	−	6.65059i	0.0699940	−	0.226915i	−0.913816	−	0.406128i	$-0.866879\pi$
$859$	2.05143	−	6.65059i	0.0699940	−	0.226915i	0.983810	+	0.179213i	$0.0573550\pi$
$860$	10.0856	+	44.1878i	0.343915	+	1.50679i
$861$		0			0
$862$	−4.37711	+	19.1774i	−0.149085	+	0.653185i
$863$	−5.11882	−	2.95535i	−0.174247	−	0.100601i	0.410340	−	0.911933i	$-0.365410\pi$
$863$	−5.11882	−	2.95535i	−0.174247	−	0.100601i	−0.584587	+	0.811331i	$0.698743\pi$
$864$		0			0
$865$	10.9570	−	3.37978i	0.372549	−	0.114916i
$866$	−0.532881	+	7.11081i	−0.0181080	+	0.241635i
$867$		0			0
$868$	14.1191	+	4.91903i	0.479234	+	0.166963i
$869$	−19.6413	−	15.6634i	−0.666285	−	0.531344i
$870$		0			0
$871$	−1.84810	+	12.2614i	−0.0626206	+	0.415460i
$872$	14.1096	−	20.6950i	0.477812	−	0.700822i
$873$		0			0
$874$	13.8689	−	28.7991i	0.469123	−	0.974143i
$875$	15.8849	−	3.02788i	0.537008	−	0.102361i
$876$		0			0
$877$	15.8857	−	10.8307i	0.536422	−	0.365727i	−0.264603	−	0.964358i	$-0.585241\pi$
$877$	15.8857	−	10.8307i	0.536422	−	0.365727i	0.801025	+	0.598631i	$0.204288\pi$
$878$	−5.64614	+	5.23886i	−0.190548	+	0.176803i
$879$		0			0
$880$	11.7722	−	4.62025i	0.396841	−	0.155749i
$881$	−14.0219			−0.472411			−0.236205	−	0.971703i	$-0.575904\pi$
$881$	−14.0219			−0.472411			−0.236205	+	0.971703i	$0.575904\pi$
$882$		0			0
$883$	24.7279			0.832161			0.416080	−	0.909328i	$-0.363404\pi$
$883$	24.7279			0.832161			0.416080	+	0.909328i	$0.363404\pi$
$884$	17.9557	−	7.04708i	0.603914	−	0.237019i
$885$		0			0
$886$	6.44602	−	5.98103i	0.216558	−	0.200937i
$887$	−41.2910	+	28.1517i	−1.38641	+	0.945241i	−0.386680	+	0.922214i	$0.626378\pi$
$887$	−41.2910	+	28.1517i	−1.38641	+	0.945241i	−0.999735	+	0.0230274i	$0.992669\pi$
$888$		0			0
$889$	49.4985	+	13.1912i	1.66013	+	0.442420i
$890$	−8.88349	+	18.4468i	−0.297775	+	0.618337i
$891$		0			0
$892$	2.12956	−	3.12349i	0.0713029	−	0.104582i
$893$	−3.96639	+	26.3153i	−0.132730	+	0.880607i
$894$		0			0
$895$	22.5707	+	17.9996i	0.754456	+	0.601659i
$896$	−16.0367	+	25.5991i	−0.535748	+	0.855207i
$897$		0			0
$898$	−0.883349	+	11.7875i	−0.0294777	+	0.393353i
$899$	27.8656	−	8.59541i	0.929371	−	0.286673i
$900$		0			0
$901$	−2.00313	−	1.15651i	−0.0667338	−	0.0385288i
$902$	−0.897828	+	3.93364i	−0.0298944	+	0.130976i
$903$		0			0
$904$	0.205035	+	0.898317i	0.00681936	+	0.0298776i
$905$	13.8173	−	44.7945i	0.459302	−	1.48902i
$906$		0			0
$907$	3.10190	−	7.90350i	0.102997	−	0.262432i	−0.870081	−	0.492909i	$-0.835934\pi$
$907$	3.10190	−	7.90350i	0.102997	−	0.262432i	0.973078	+	0.230477i	$0.0740288\pi$
$908$	−19.1250	−	5.89929i	−0.634687	−	0.195775i
$909$		0			0
$910$	−4.46330	−	16.5675i	−0.147957	−	0.549206i
$911$	−39.7604	−	9.07505i	−1.31732	−	0.300670i	−0.494603	−	0.869119i	$-0.664686\pi$
$911$	−39.7604	−	9.07505i	−1.31732	−	0.300670i	−0.822718	+	0.568449i	$0.807544\pi$
$912$		0			0
$913$	−20.6173	+	11.9034i	−0.682334	+	0.393946i
$914$	6.16221	+	19.9774i	0.203828	+	0.660793i
$915$		0			0
$916$	7.34573	−	5.85802i	0.242710	−	0.193554i
$917$	−57.1381	−	6.35956i	−1.88687	−	0.210011i
$918$		0			0
$919$	−1.42923	−	1.32613i	−0.0471459	−	0.0437450i	0.656248	−	0.754545i	$-0.272143\pi$
$919$	−1.42923	−	1.32613i	−0.0471459	−	0.0437450i	−0.703394	+	0.710800i	$0.748333\pi$
$920$	−50.1794	−	7.56332i	−1.65437	−	0.249355i
$921$		0			0
$922$	0.875691	+	5.80983i	0.0288394	+	0.191337i
$923$	15.1592	+	7.30030i	0.498972	+	0.240292i
$924$		0			0
$925$	18.3143	−	8.81972i	0.602172	−	0.289991i
$926$	−6.40798	−	9.39879i	−0.210579	−	0.308863i
$927$		0			0
$928$	3.50798	+	46.8108i	0.115155	+	1.53664i
$929$	17.3665	+	44.2492i	0.569778	+	1.45177i	0.867656	+	0.497166i	$0.165626\pi$
$929$	17.3665	+	44.2492i	0.569778	+	1.45177i	−0.297878	+	0.954604i	$0.596279\pi$
$930$		0			0
$931$	36.9978	+	25.0781i	1.21255	+	0.821903i
$932$		−	10.7259i		−	0.351338i
$933$		0			0
$934$	6.99122	−	0.523920i	0.228760	−	0.0171432i
$935$	14.1545	+	15.2550i	0.462903	+	0.498891i
$936$		0			0
$937$	−20.5224	−	42.6153i	−0.670439	−	1.39218i	−0.907236	−	0.420622i	$-0.861812\pi$
$937$	−20.5224	−	42.6153i	−0.670439	−	1.39218i	0.236797	−	0.971559i	$-0.423902\pi$
$938$	3.43970	−	4.00798i	0.112310	−	0.130865i
$939$		0			0
$940$	18.7373	−	2.82420i	0.611144	−	0.0921151i
$941$	36.2680	+	24.7271i	1.18230	+	0.806080i	0.984710	−	0.174204i	$-0.0557353\pi$
$941$	36.2680	+	24.7271i	1.18230	+	0.806080i	0.197592	+	0.980284i	$0.436688\pi$
$942$		0			0
$943$	−15.4344	+	16.6343i	−0.502612	+	0.541687i
$944$	−3.98217	+	4.99348i	−0.129608	+	0.162524i
$945$		0			0
$946$	−9.05283	−	11.3519i	−0.294333	−	0.369082i
$947$	24.2406	+	1.81658i	0.787713	+	0.0590309i	0.462511	−	0.886614i	$-0.346949\pi$
$947$	24.2406	+	1.81658i	0.787713	+	0.0590309i	0.325202	+	0.945645i	$0.394568\pi$
$948$		0			0
$949$	17.1969	+	29.7859i	0.558235	+	0.966892i
$950$	5.48945	−	9.50801i	0.178101	−	0.308481i
$951$		0			0
$952$	−18.0040	−	3.38129i	−0.583513	−	0.109588i
$953$	16.7697	−	3.82758i	0.543225	−	0.123988i	0.0579016	−	0.998322i	$-0.481559\pi$
$953$	16.7697	−	3.82758i	0.543225	−	0.123988i	0.485323	+	0.874335i	$0.338702\pi$
$954$		0			0
$955$	−9.81190	−	3.85089i	−0.317506	−	0.124612i
$956$	5.21050	+	2.04497i	0.168519	+	0.0661390i
$957$		0			0
$958$	20.1678	−	4.60317i	0.651592	−	0.148722i
$959$	−5.46919	−	4.02502i	−0.176609	−	0.129975i
$960$		0			0
$961$	−9.46418	+	16.3924i	−0.305296	+	0.528789i
$962$	8.38141	+	14.5170i	0.270227	+	0.468048i
$963$		0			0
$964$	−22.4022	−	1.67881i	−0.721527	−	0.0540710i
$965$	−15.6696	−	19.6490i	−0.504422	−	0.632525i
$966$		0			0
$967$	−15.8386	+	19.8609i	−0.509334	+	0.638685i	−0.968306	−	0.249766i	$-0.919646\pi$
$967$	−15.8386	+	19.8609i	−0.509334	+	0.638685i	0.458972	+	0.888451i	$0.348218\pi$
$968$	8.02098	−	8.64456i	0.257804	−	0.277847i
$969$		0			0
$970$	−5.28088	−	3.60044i	−0.169559	−	0.115603i
$971$	14.8623	−	2.24014i	0.476955	−	0.0718894i	0.0938345	−	0.995588i	$-0.470088\pi$
$971$	14.8623	−	2.24014i	0.476955	−	0.0718894i	0.383120	+	0.923698i	$0.374849\pi$
$972$		0			0
$973$	13.6074	+	7.16813i	0.436232	+	0.229800i
$974$	−5.15634	−	10.7073i	−0.165220	−	0.343083i
$975$		0			0
$976$	15.3140	+	16.5045i	0.490188	+	0.528297i
$977$	−48.4182	+	3.62844i	−1.54903	+	0.116084i	−0.821589	−	0.570081i	$-0.806912\pi$
$977$	−48.4182	+	3.62844i	−1.54903	+	0.116084i	−0.727446	+	0.686165i	$0.759293\pi$
$978$		0			0
$979$			28.5618i			0.912838i
$980$	9.29821	−	30.4365i	0.297020	−	0.972259i
$981$		0			0
$982$	−2.92242	−	7.44619i	−0.0932580	−	0.237618i
$983$	0.954006	+	12.7303i	0.0304281	+	0.406034i	0.991533	+	0.129852i	$0.0414503\pi$
$983$	0.954006	+	12.7303i	0.0304281	+	0.406034i	−0.961105	+	0.276182i	$0.910931\pi$
$984$		0			0
$985$	39.0298	+	57.2463i	1.24359	+	1.82402i
$986$	−14.4375	+	6.95274i	−0.459784	+	0.221420i
$987$		0			0
$988$	−35.5209	−	17.1060i	−1.13007	−	0.544213i
$989$	−12.1706	−	80.7467i	−0.387003	−	2.56759i
$990$		0			0
$991$	−6.47142	−	0.975410i	−0.205571	−	0.0309849i	0.0454492	−	0.998967i	$-0.485528\pi$
$991$	−6.47142	−	0.975410i	−0.205571	−	0.0309849i	−0.251021	+	0.967982i	$0.580766\pi$
$992$	14.2448	+	13.2173i	0.452274	+	0.419649i
$993$		0			0
$994$	−3.82111	−	6.06302i	−0.121198	−	0.192307i
$995$	14.1075	−	11.2503i	0.447237	−	0.356659i
$996$		0			0
$997$	2.22927	+	7.22711i	0.0706016	+	0.228885i	0.983996	−	0.178191i	$-0.0570246\pi$
$997$	2.22927	+	7.22711i	0.0706016	+	0.228885i	−0.913394	+	0.407076i	$0.866548\pi$
$998$	5.51639	−	3.18489i	0.174618	−	0.100816i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.bg.a.278.8	✓	216
3.2	odd	2	inner	441.2.bg.a.278.11	yes	216
49.3	odd	42	inner	441.2.bg.a.395.11	yes	216
147.101	even	42	inner	441.2.bg.a.395.8	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.bg.a.278.8	✓	216	1.1	even	1	trivial
441.2.bg.a.278.11	yes	216	3.2	odd	2	inner
441.2.bg.a.395.8	yes	216	147.101	even	42	inner
441.2.bg.a.395.11	yes	216	49.3	odd	42	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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.bg (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.568908 + 0.223280i) q^{2} +(-1.19230 + 1.10629i) q^{4} +(2.30954 - 1.57462i) q^{5} +(0.0953467 - 2.64403i) q^{7} +(0.961636 - 1.99686i) q^{8} +O(q^{10})\)	\(q+(-0.568908 + 0.223280i) q^{2} +(-1.19230 + 1.10629i) q^{4} +(2.30954 - 1.57462i) q^{5} +(0.0953467 - 2.64403i) q^{7} +(0.961636 - 1.99686i) q^{8} +(-0.962336 + 1.41149i) q^{10} +(-0.355186 + 2.35651i) q^{11} +(-2.96799 - 2.36690i) q^{13} +(0.536116 + 1.52550i) q^{14} +(0.141871 - 1.89314i) q^{16} +(2.98520 - 0.920812i) q^{17} +(-5.52972 - 3.19259i) q^{19} +(-1.01168 + 4.43246i) q^{20} +(-0.324092 - 1.41994i) q^{22} +(2.41439 - 7.82724i) q^{23} +(1.02786 - 2.61894i) q^{25} +(2.21699 + 0.683852i) q^{26} +(2.81140 + 3.25797i) q^{28} +(8.18266 + 1.86764i) q^{29} +(3.00894 - 1.73721i) q^{31} +(1.64855 + 5.34446i) q^{32} +(-1.49270 + 1.19039i) q^{34} +(-3.94314 - 6.25665i) q^{35} +(5.29640 + 4.91434i) q^{37} +(3.85874 + 0.581612i) q^{38} +(-0.923353 - 6.12604i) q^{40} +(-2.49594 - 1.20198i) q^{41} +(8.98188 - 4.32545i) q^{43} +(-2.18350 - 3.20261i) q^{44} +(0.374103 + 4.99206i) q^{46} +(-1.52269 - 3.87975i) q^{47} +(-6.98182 - 0.504199i) q^{49} +1.71944i q^{50} +(6.15723 - 0.461421i) q^{52} +(-0.503602 - 0.542754i) q^{53} +(2.89028 + 6.00174i) q^{55} +(-5.18807 - 2.73299i) q^{56} +(-5.07218 + 0.764509i) q^{58} +(-2.77969 - 1.89516i) q^{59} +(-8.06655 + 8.69368i) q^{61} +(-1.32392 + 1.66015i) q^{62} +(0.236150 + 0.296123i) q^{64} +(-10.5817 - 0.792987i) q^{65} +(-1.63319 - 2.82877i) q^{67} +(-2.54057 + 4.40039i) q^{68} +(3.64026 + 2.67903i) q^{70} +(-4.32106 + 0.986253i) q^{71} +(-8.43376 - 3.31001i) q^{73} +(-4.11044 - 1.61323i) q^{74} +(10.1250 - 2.31097i) q^{76} +(6.19681 + 1.16381i) q^{77} +(-5.27084 + 9.12936i) q^{79} +(-2.65332 - 4.59569i) q^{80} +(1.68834 + 0.126523i) q^{82} +(6.22852 + 7.81031i) q^{83} +(5.44452 - 6.82721i) q^{85} +(-4.14407 + 4.46625i) q^{86} +(4.36405 + 2.97536i) q^{88} +(11.8511 - 1.78627i) q^{89} +(-6.54114 + 7.62180i) q^{91} +(5.78056 + 12.0035i) q^{92} +(1.73254 + 1.86723i) q^{94} +(-17.7983 + 1.33379i) q^{95} +3.74135i q^{97} +(4.08459 - 1.27206i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 16 q^{4} + 2 q^{7}+O(q^{10}) \) 216 * q - 16 * q^4 + 2 * q^7	\( 216 q - 16 q^{4} + 2 q^{7} + 12 q^{10} + 12 q^{16} - 6 q^{19} + 44 q^{22} + 26 q^{25} + 84 q^{28} - 6 q^{31} - 112 q^{34} + 60 q^{37} - 304 q^{40} + 20 q^{43} - 20 q^{46} - 86 q^{49} - 168 q^{52} - 84 q^{55} - 120 q^{58} - 2 q^{61} + 32 q^{64} + 22 q^{67} - 136 q^{70} - 6 q^{73} + 84 q^{76} + 2 q^{79} - 104 q^{82} + 96 q^{85} - 12 q^{88} + 58 q^{91} + 52 q^{94}+O(q^{100}) \) 216 * q - 16 * q^4 + 2 * q^7 + 12 * q^10 + 12 * q^16 - 6 * q^19 + 44 * q^22 + 26 * q^25 + 84 * q^28 - 6 * q^31 - 112 * q^34 + 60 * q^37 - 304 * q^40 + 20 * q^43 - 20 * q^46 - 86 * q^49 - 168 * q^52 - 84 * q^55 - 120 * q^58 - 2 * q^61 + 32 * q^64 + 22 * q^67 - 136 * q^70 - 6 * q^73 + 84 * q^76 + 2 * q^79 - 104 * q^82 + 96 * q^85 - 12 * q^88 + 58 * q^91 + 52 * q^94

Introduction

L-functions

Modular forms

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