LMFDB - Embedded newform 441.2.bg.a.395.11

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			395.11
Character	$\chi$	$=$	441.395
Dual form			441.2.bg.a.278.11

$q$-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 $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

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

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	$-0.311627\pi$
$2$	0.568908	+	0.223280i	0.402278	+	0.157883i	−0.155571	+	0.987825i	$0.549722\pi$
$3$		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	$-0.524440\pi$
$5$	−2.30954	−	1.57462i	−1.03286	−	0.704192i	−0.956155	+	0.292862i	$0.905392\pi$
$6$		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	0.976357	+	0.216165i	$0.0693550\pi$
$11$	0.355186	+	2.35651i	0.107093	+	0.710513i	−0.869264	+	0.494348i	$0.835407\pi$
$12$		0			0
$13$	−2.96799	+	2.36690i	−0.823173	+	0.656459i	−0.941686	−	0.336494i	$-0.890759\pi$
$13$	−2.96799	+	2.36690i	−0.823173	+	0.656459i	0.118512	+	0.992953i	$0.462187\pi$
$14$	−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	$-0.528439\pi$
$17$	−2.98520	−	0.920812i	−0.724017	−	0.223330i	−0.634793	+	0.772682i	$0.718915\pi$
$18$		0			0
$19$	−5.52972	+	3.19259i	−1.26861	+	0.732430i	−0.974724	−	0.223412i	$-0.928280\pi$
$19$	−5.52972	+	3.19259i	−1.26861	+	0.732430i	−0.293881	+	0.955842i	$0.594947\pi$
$20$	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	−0.748896	−	0.662687i	$-0.769416\pi$
$23$	−2.41439	−	7.82724i	−0.503434	−	1.63209i	0.245462	−	0.969406i	$-0.421060\pi$
$24$		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	$-0.855843\pi$
$29$	−8.18266	+	1.86764i	−1.51948	+	0.346812i	−0.620293	+	0.784371i	$0.712986\pi$
$30$		0			0
$31$	3.00894	+	1.73721i	0.540422	+	0.312013i	0.745250	−	0.666785i	$-0.232330\pi$
$31$	3.00894	+	1.73721i	0.540422	+	0.312013i	−0.204828	+	0.978798i	$0.565664\pi$
$32$	−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	−0.111862	−	0.993724i	$-0.535682\pi$
$37$	5.29640	−	4.91434i	0.870723	−	0.807913i	0.982586	+	0.185811i	$0.0594911\pi$
$38$	−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	$-0.573451\pi$
$41$	2.49594	−	1.20198i	0.389801	−	0.187718i	0.618510	+	0.785777i	$0.287736\pi$
$42$		0			0
$43$	8.98188	+	4.32545i	1.36972	+	0.659624i	0.966782	−	0.255601i	$-0.0822735\pi$
$43$	8.98188	+	4.32545i	1.36972	+	0.659624i	0.402942	+	0.915226i	$0.367988\pi$
$44$	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	$-0.782639\pi$
$47$	1.52269	−	3.87975i	0.222107	−	0.565920i	0.997879	+	0.0650934i	$0.0207345\pi$
$48$		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	$-0.745711\pi$
$53$	0.503602	−	0.542754i	0.0691751	−	0.0745530i	0.766691	+	0.642016i	$0.221902\pi$
$54$		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	$-0.620198\pi$
$59$	2.77969	−	1.89516i	0.361884	−	0.246729i	0.730588	+	0.682818i	$0.239246\pi$
$60$		0			0
$61$	−8.06655	−	8.69368i	−1.03282	−	1.11311i	−0.993494	−	0.113885i	$-0.963671\pi$
$61$	−8.06655	−	8.69368i	−1.03282	−	1.11311i	−0.0393222	−	0.999227i	$-0.512520\pi$
$62$	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	−0.948375	−	0.317152i	$-0.897274\pi$
$67$	−1.63319	+	2.82877i	−0.199526	+	0.345589i	0.748849	+	0.662741i	$0.230607\pi$
$68$	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	$-0.343859\pi$
$71$	4.32106	+	0.986253i	0.512815	+	0.117047i	0.0417204	+	0.999129i	$0.486716\pi$
$72$		0			0
$73$	−8.43376	+	3.31001i	−0.987097	+	0.387407i	−0.803311	−	0.595559i	$-0.796930\pi$
$73$	−8.43376	+	3.31001i	−0.987097	+	0.387407i	−0.183786	+	0.982966i	$0.558835\pi$
$74$	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	−0.993824	−	0.110971i	$-0.964604\pi$
$79$	−5.27084	−	9.12936i	−0.593016	−	1.02713i	0.400808	−	0.916162i	$-0.368730\pi$
$80$	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	$-0.970424\pi$
$83$	−6.22852	+	7.81031i	−0.683669	+	0.857293i	0.312018	+	0.950076i	$0.398995\pi$
$84$		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	$-0.671465\pi$
$89$	−11.8511	−	1.78627i	−1.25622	−	0.189345i	−0.743222	+	0.669045i	$0.766703\pi$
$90$		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	$-0.939171\pi$
$97$		−	3.74135i		−	0.379877i	0.981796	−	0.189938i	$-0.0608289\pi$
$98$	−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	0.695834	+	0.718202i	$0.255035\pi$
$101$	−0.997657	+	13.3128i	−0.0992706	+	1.32467i	−0.795105	+	0.606472i	$0.792584\pi$
$102$		0			0
$103$	−6.25546	+	9.17507i	−0.616369	+	0.904047i	−0.999809	−	0.0195185i	$-0.993787\pi$
$103$	−6.25546	+	9.17507i	−0.616369	+	0.904047i	0.383441	+	0.923565i	$0.374739\pi$
$104$	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	0.900871	+	0.434086i	$0.142929\pi$
$107$	−0.909514	+	6.03423i	−0.0879261	+	0.583351i	−0.988797	+	0.149265i	$0.952309\pi$
$108$		0			0
$109$	11.1749	−	1.68435i	1.07036	−	0.161331i	0.409856	−	0.912150i	$-0.365579\pi$
$109$	11.1749	−	1.68435i	1.07036	−	0.161331i	0.660508	+	0.750819i	$0.270341\pi$
$110$	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	$-0.279489\pi$
$113$	0.325037	+	0.259208i	0.0305769	+	0.0243843i	−0.608082	+	0.793874i	$0.708061\pi$
$114$		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	−0.690238	−	0.723583i	$-0.742494\pi$
$127$	−4.30837	−	18.8762i	−0.382306	−	1.67499i	0.307932	−	0.951408i	$-0.400363\pi$
$128$	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	−0.384555	−	0.923102i	$-0.625645\pi$
$131$	−1.62385	−	21.6688i	−0.141876	−	1.89321i	0.242678	−	0.970107i	$-0.421974\pi$
$132$		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	$-0.225446\pi$
$137$	−1.44583	−	2.12064i	−0.123526	−	0.181179i	−0.883020	+	0.469335i	$0.844494\pi$
$138$		0			0
$139$	−2.52220	−	5.23739i	−0.213930	−	0.444230i	0.766196	−	0.642607i	$-0.222147\pi$
$139$	−2.52220	−	5.23739i	−0.213930	−	0.444230i	−0.980126	+	0.198377i	$0.936433\pi$
$140$	−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	$-0.322667\pi$
$149$	4.13806	+	1.62407i	0.339003	+	0.133049i	−0.189732	+	0.981836i	$0.560762\pi$
$150$		0			0
$151$	−7.68138	−	7.12727i	−0.625101	−	0.580009i	0.302699	−	0.953086i	$-0.402112\pi$
$151$	−7.68138	−	7.12727i	−0.625101	−	0.580009i	−0.927800	+	0.373077i	$0.878303\pi$
$152$	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	0.992791	−	0.119855i	$-0.0382429\pi$
$157$	6.49697	+	9.52930i	0.518514	+	0.760521i	−0.474277	+	0.880376i	$0.657291\pi$
$158$	−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	0.984287	+	0.176574i	$0.0565013\pi$
$163$	0.476350	+	6.35645i	0.0373106	+	0.497875i	−0.946977	+	0.321302i	$0.895880\pi$
$164$	−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	0.924083	+	0.382192i	$0.124831\pi$
$167$	3.32556	+	14.5702i	0.257340	+	1.12748i	−0.666743	+	0.745288i	$0.732312\pi$
$168$		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	$-0.645078\pi$
$173$	−3.91986	+	1.20912i	−0.298021	+	0.0919274i	0.142139	+	0.989847i	$0.454602\pi$
$174$		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	0.767759	+	0.640739i	$0.221372\pi$
$179$	−3.04420	+	9.86906i	−0.227534	+	0.737648i	−0.995293	+	0.0969091i	$0.969104\pi$
$180$		0			0
$181$	13.1115	+	10.4561i	0.974573	+	0.777196i	0.974863	−	0.222804i	$-0.0715211\pi$
$181$	13.1115	+	10.4561i	0.974573	+	0.777196i	−0.000290678		1.00000i	$0.500093\pi$
$182$	−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	$-0.765962\pi$
$191$	2.12421	−	3.11564i	0.153702	−	0.225440i	0.895365	+	0.445333i	$0.146915\pi$
$192$		0			0
$193$	−0.671898	+	8.96585i	−0.0483643	+	0.645376i	0.919369	+	0.393397i	$0.128700\pi$
$193$	−0.671898	+	8.96585i	−0.0483643	+	0.645376i	−0.967733	+	0.251979i	$0.918919\pi$
$194$	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	0.300909	−	0.953653i	$-0.402710\pi$
$199$	6.43723	+	0.482404i	0.456323	+	0.0341967i	0.155414	+	0.987849i	$0.450329\pi$
$200$	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	−0.994465	−	0.105065i	$-0.966495\pi$
$211$	−9.74313	+	12.2175i	−0.670745	+	0.841087i	0.323721	+	0.946153i	$0.395066\pi$
$212$	−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	0.145976	−	0.989288i	$-0.453368\pi$
$223$	−2.26598	−	0.517194i	−0.151741	−	0.0346339i	−0.297717	+	0.954654i	$0.596225\pi$
$224$	−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	$-0.967233\pi$
$227$	−6.15258	+	10.6566i	−0.408361	+	0.707302i	0.586345	+	0.810061i	$0.300566\pi$
$228$		0			0
$229$	−5.76042	+	0.431684i	−0.380659	+	0.0285265i	−0.263686	−	0.964609i	$-0.584938\pi$
$229$	−5.76042	+	0.431684i	−0.380659	+	0.0285265i	−0.116973	+	0.993135i	$0.537319\pi$
$230$	−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	$-0.168791\pi$
$233$	4.48540	+	4.83411i	0.293848	+	0.316693i	−0.568821	+	0.822461i	$0.692600\pi$
$234$		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	$-0.821640\pi$
$239$	1.49317	−	3.10061i	0.0965853	−	0.200562i	0.943663	+	0.330907i	$0.107355\pi$
$240$		0			0
$241$	9.39452	−	10.1249i	0.605155	−	0.652201i	−0.353946	−	0.935266i	$-0.615160\pi$
$241$	9.39452	−	10.1249i	0.605155	−	0.652201i	0.959101	+	0.283064i	$0.0913510\pi$
$242$	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	$-0.389591\pi$
$251$	−2.90508	−	1.39901i	−0.183367	−	0.0883049i	−0.523315	+	0.852139i	$0.675305\pi$
$252$		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	$-0.938664\pi$
$257$	−13.8489	+	12.8499i	−0.863871	+	0.801555i	0.117621	+	0.993059i	$0.462473\pi$
$258$		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	−0.995844	−	0.0910776i	$-0.970969\pi$
$263$	−25.5040	−	14.7247i	−1.57264	−	0.907965i	−0.576797	−	0.816887i	$-0.695698\pi$
$264$		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	−0.846109	−	0.533010i	$-0.821061\pi$
$269$	−9.65058	−	24.5893i	−0.588406	−	1.49923i	0.257703	−	0.966224i	$-0.417035\pi$
$270$		0			0
$271$	−0.761616	−	2.46910i	−0.0462649	−	0.149987i	0.929493	−	0.368840i	$-0.120245\pi$
$271$	−0.761616	−	2.46910i	−0.0462649	−	0.149987i	−0.975758	+	0.218852i	$0.929769\pi$
$272$	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	0.560720	−	0.828005i	$-0.310524\pi$
$277$	9.27993	+	2.86248i	0.557577	+	0.171990i	−0.00314320	+	0.999995i	$0.501001\pi$
$278$	−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	$-0.925701\pi$
$281$	−16.1573	+	12.8850i	−0.963863	+	0.768655i	0.00901855	+	0.999959i	$0.497129\pi$
$282$		0			0
$283$	0.766715	+	5.08682i	0.0455765	+	0.302380i	0.999992	+	0.00390027i	$0.00124150\pi$
$283$	0.766715	+	5.08682i	0.0455765	+	0.302380i	−0.954416	+	0.298480i	$0.903520\pi$
$284$	−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	$-0.261876\pi$
$293$	23.2876			1.36048			0.680238	+	0.732991i	$0.261876\pi$
$294$		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	−0.826313	−	0.563211i	$-0.809566\pi$
$307$	−8.07903	+	6.44281i	−0.461094	+	0.367710i	0.365219	+	0.930922i	$0.380994\pi$
$308$	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	$-0.421849\pi$
$311$	−1.80833	−	0.557795i	−0.102541	−	0.0316297i	−0.345601	+	0.938382i	$0.612325\pi$
$312$		0			0
$313$	−21.9225	+	12.6570i	−1.23913	+	0.715413i	−0.968917	−	0.247387i	$-0.920428\pi$
$313$	−21.9225	+	12.6570i	−1.23913	+	0.715413i	−0.270215	+	0.962800i	$0.587095\pi$
$314$	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	$-0.0698197\pi$
$317$	0.837254	+	2.71431i	0.0470249	+	0.152451i	−0.929015	+	0.370041i	$0.879344\pi$
$318$		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	−0.458105	−	0.888898i	$-0.651472\pi$
$331$	7.16952	−	6.65235i	0.394073	−	0.365646i	0.852178	+	0.523252i	$0.175281\pi$
$332$	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	0.485497	−	0.874238i	$-0.338639\pi$
$337$	1.92190	+	0.925541i	0.104693	+	0.0504174i	−0.380804	+	0.924656i	$0.624353\pi$
$338$	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	−0.0192725	+	0.999814i	$0.506135\pi$
$347$	−18.9046	+	20.3743i	−1.01485	+	1.09375i	−0.995578	+	0.0939348i	$0.970055\pi$
$348$		0			0
$349$	12.8147	−	26.6100i	0.685955	−	1.42440i	−0.208853	−	0.977947i	$-0.566973\pi$
$349$	12.8147	−	26.6100i	0.685955	−	1.42440i	0.894807	−	0.446452i	$-0.147313\pi$
$350$	−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	$-0.804155\pi$
$353$	−10.8537	+	7.39996i	−0.577687	+	0.393860i	0.238933	+	0.971036i	$0.423202\pi$
$354$		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	$-0.373195\pi$
$359$	17.2207	−	1.29051i	0.908871	−	0.0681105i	0.520955	+	0.853584i	$0.325576\pi$
$360$		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	−0.422803	−	0.906222i	$-0.638954\pi$
$367$	−2.22898	+	0.874809i	−0.116352	+	0.0456647i	0.306451	+	0.951886i	$0.400858\pi$
$368$	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	0.969569	−	0.244818i	$-0.0787282\pi$
$373$	5.26798	+	9.12442i	0.272766	+	0.472444i	−0.696803	+	0.717262i	$0.745395\pi$
$374$	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	0.717399	−	0.696663i	$-0.245332\pi$
$379$	−2.36405	−	2.96442i	−0.121433	−	0.152272i	−0.838832	+	0.544390i	$0.816761\pi$
$380$	−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	$-0.669101\pi$
$383$	−24.3620	−	3.67198i	−1.24484	−	0.187629i	−0.738232	+	0.674547i	$0.764339\pi$
$384$		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	$-0.552004\pi$
$389$	−9.28049	−	0.695476i	−0.470539	−	0.0352621i	−0.307890	+	0.951422i	$0.599623\pi$
$390$		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	−0.391489	−	0.920183i	$-0.628040\pi$
$397$	12.1166	−	17.7717i	0.608112	−	0.891937i	0.999601	+	0.0282461i	$0.00899219\pi$
$398$	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	0.728779	+	0.684749i	$0.240088\pi$
$401$	−3.39335	+	22.5134i	−0.169456	+	1.12426i	−0.898235	+	0.439516i	$0.855150\pi$
$402$		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	−0.369845	−	0.929094i	$-0.620589\pi$
$409$	9.28497	−	30.1011i	0.459112	−	1.48841i	0.828957	−	0.559312i	$-0.188935\pi$
$410$	−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	−0.229963	−	0.973199i	$-0.573860\pi$
$419$	8.17719	−	35.8266i	0.399482	−	1.75024i	0.629445	−	0.777045i	$-0.283282\pi$
$420$		0			0
$421$	1.91314	+	8.38202i	0.0932408	+	0.408515i	0.999911	−	0.0133251i	$-0.00424165\pi$
$421$	1.91314	+	8.38202i	0.0932408	+	0.408515i	−0.906670	+	0.421840i	$0.861385\pi$
$422$	−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	−0.958647	−	0.284598i	$-0.908140\pi$
$431$	−18.1310	−	26.5933i	−0.873339	−	1.28095i	0.0853083	−	0.996355i	$-0.472812\pi$
$432$		0			0
$433$	5.06241	+	10.5122i	0.243284	+	0.505184i	0.986478	−	0.163891i	$-0.0524046\pi$
$433$	5.06241	+	10.5122i	0.243284	+	0.505184i	−0.743194	+	0.669076i	$0.766690\pi$
$434$	−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	0.628386	−	0.777901i	$-0.283716\pi$
$439$	11.7316	+	4.60431i	0.559919	+	0.219752i	−0.0684676	+	0.997653i	$0.521811\pi$
$440$	−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	$-0.269915\pi$
$443$	13.3936	+	5.25659i	0.636348	+	0.249748i	−0.0251633	+	0.999683i	$0.508011\pi$
$444$		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	−0.999684	−	0.0251283i	$-0.992001\pi$
$449$	−8.39188	−	17.4259i	−0.396037	−	0.822380i	0.603647	−	0.797252i	$-0.293714\pi$
$450$		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	0.658000	+	0.753018i	$0.271403\pi$
$457$	2.55635	+	34.1121i	0.119581	+	1.59569i	−0.538419	+	0.842677i	$0.680978\pi$
$458$	−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	−0.999999	−	0.00139152i	$-0.999557\pi$
$461$	−2.13925	−	9.37267i	−0.0996348	−	0.436529i	0.900364	−	0.435137i	$-0.143300\pi$
$462$		0			0
$463$	4.14177	−	18.1463i	0.192484	−	0.843330i	−0.782782	−	0.622296i	$-0.786200\pi$
$463$	4.14177	−	18.1463i	0.192484	−	0.843330i	0.975266	−	0.221033i	$-0.0709429\pi$
$464$	−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	$-0.509728\pi$
$467$	10.9618	−	3.38127i	0.507252	−	0.156466i	0.537809	+	0.843067i	$0.319252\pi$
$468$		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	$-0.266233\pi$
$479$	33.4701	−	5.04481i	1.52929	−	0.230503i	0.859147	+	0.511729i	$0.170995\pi$
$480$		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	−0.862280	−	0.506433i	$-0.830964\pi$
$487$	1.45316	−	19.3911i	0.0658489	−	0.878692i	0.928129	−	0.372260i	$-0.121417\pi$
$488$	−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	−0.0857528	−	0.996316i	$-0.527330\pi$
$499$	−10.3061	−	1.55340i	−0.461365	−	0.0695396i	−0.375612	+	0.926777i	$0.622568\pi$
$500$	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	$-0.249821\pi$
$503$	−3.11566	−	3.90692i	−0.138921	−	0.174201i	−0.846425	+	0.532508i	$0.821250\pi$
$504$		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	$-0.177571\pi$
$509$	−0.772687	−	1.33833i	−0.0342487	−	0.0593205i	−0.882642	+	0.470046i	$0.844237\pi$
$510$		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	−0.288319	−	0.957534i	$-0.593096\pi$
$521$	15.6375	−	27.0849i	0.685090	−	1.18661i	0.973409	−	0.229076i	$-0.0735704\pi$
$522$		0			0
$523$	3.05590	−	0.229008i	0.133625	−	0.0100138i	−0.00774962	−	0.999970i	$-0.502467\pi$
$523$	3.05590	−	0.229008i	0.133625	−	0.0100138i	0.141375	+	0.989956i	$0.454848\pi$
$524$	−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	0.283881	+	0.958859i	$0.408378\pi$
$541$	−13.4069	+	34.1603i	−0.576408	+	1.46866i	−0.860290	+	0.509805i	$0.829717\pi$
$542$	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	−0.976680	−	0.214699i	$-0.931123\pi$
$547$	−33.1589	+	15.9685i	−1.41777	+	0.682763i	−0.441092	+	0.897462i	$0.645409\pi$
$548$	−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	$-0.634352\pi$
$557$	−33.1476	−	19.1378i	−1.40451	−	0.810894i	−0.994851	+	0.101344i	$0.967686\pi$
$558$		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	$-0.0306504\pi$
$563$	4.75307	+	12.1106i	0.200318	+	0.510402i	−0.795050	+	0.606544i	$0.792555\pi$
$564$		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	$-0.849116\pi$
$569$	−22.4059	+	12.9361i	−0.939305	+	0.542308i	−0.0495625	+	0.998771i	$0.515783\pi$
$570$		0			0
$571$	37.0368	+	11.4243i	1.54994	+	0.478093i	0.947415	−	0.320006i	$-0.103685\pi$
$571$	37.0368	+	11.4243i	1.54994	+	0.478093i	0.602525	+	0.798100i	$0.294161\pi$
$572$	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	0.961861	−	0.273537i	$-0.0881937\pi$
$577$	−0.910238	−	6.03904i	−0.0378937	−	0.251408i	−0.999755	+	0.0221289i	$0.992956\pi$
$578$	−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	$-0.556240\pi$
$587$	−8.51684			−0.351528			−0.175764	+	0.984432i	$0.556240\pi$
$588$		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	$-0.0856700\pi$
$593$	26.0237	+	17.7427i	1.06867	+	0.728605i	0.104667	+	0.994507i	$0.466622\pi$
$594$		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	−0.855897	−	0.517146i	$-0.826994\pi$
$599$	−4.66133	−	30.9259i	−0.190457	−	1.26360i	0.665441	−	0.746451i	$-0.268244\pi$
$600$		0			0
$601$	−8.61014	+	6.86636i	−0.351215	+	0.280084i	−0.783166	−	0.621812i	$-0.786397\pi$
$601$	−8.61014	+	6.86636i	−0.351215	+	0.280084i	0.431951	+	0.901897i	$0.357825\pi$
$602$	−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	0.0631048	−	0.998007i	$-0.479900\pi$
$607$	23.6262	−	13.6406i	0.958956	−	0.553654i	0.895852	+	0.444353i	$0.146566\pi$
$608$	−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	0.958454	−	0.285247i	$-0.0920756\pi$
$613$	1.53110	+	3.90117i	0.0618404	+	0.157567i	−0.896614	+	0.442814i	$0.853980\pi$
$614$	−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	$-0.408064\pi$
$617$	23.7804	−	5.42771i	0.957361	−	0.218511i	0.672533	+	0.740067i	$0.265206\pi$
$618$		0			0
$619$	11.2869	+	6.51647i	0.453657	+	0.261919i	0.709374	−	0.704833i	$-0.248978\pi$
$619$	11.2869	+	6.51647i	0.453657	+	0.261919i	−0.255716	+	0.966752i	$0.582311\pi$
$620$	−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	−0.453810	−	0.891099i	$-0.649935\pi$
$631$	−36.0077	−	17.3404i	−1.43344	−	0.690310i	−0.979635	+	0.200788i	$0.935650\pi$
$632$	−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	$-0.840077\pi$
$641$	−8.37354	+	9.02453i	−0.330735	+	0.356447i	0.545689	+	0.837988i	$0.316268\pi$
$642$		0			0
$643$	8.45630	−	17.5597i	0.333484	−	0.692486i	−0.665040	−	0.746808i	$-0.731585\pi$
$643$	8.45630	−	17.5597i	0.333484	−	0.692486i	0.998523	+	0.0543217i	$0.0172997\pi$
$644$	−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	$-0.765054\pi$
$647$	−9.75819	+	6.65302i	−0.383634	+	0.261557i	0.356112	+	0.934443i	$0.384102\pi$
$648$		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	$-0.750184\pi$
$653$	−33.2661	+	2.49295i	−1.30180	+	0.0975566i	−0.594286	+	0.804253i	$0.702565\pi$
$654$		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	$-0.467075\pi$
$659$	−6.03998	−	1.37859i	−0.235284	−	0.0537021i	−0.338537	+	0.940953i	$0.609932\pi$
$660$		0			0
$661$	−2.24012	+	0.879184i	−0.0871307	+	0.0341963i	−0.408506	−	0.912756i	$-0.633950\pi$
$661$	−2.24012	+	0.879184i	−0.0871307	+	0.0341963i	0.321375	+	0.946952i	$0.395855\pi$
$662$	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	0.302228	−	0.953236i	$-0.402270\pi$
$673$	−18.0133	−	22.5879i	−0.694360	−	0.870700i	−0.996588	+	0.0825354i	$0.973698\pi$
$674$	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	$-0.765467\pi$
$677$	−42.8377	−	6.45674i	−1.64639	−	0.248153i	−0.905768	+	0.423773i	$0.860705\pi$
$678$		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	$-0.661443\pi$
$683$	−28.6509	−	2.14709i	−1.09630	−	0.0821560i	−0.610575	+	0.791958i	$0.709062\pi$
$684$		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	−0.838368	−	0.545105i	$-0.816490\pi$
$691$	−0.648065	+	0.950537i	−0.0246536	+	0.0361601i	0.813714	+	0.581265i	$0.197442\pi$
$692$	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	$-0.315248\pi$
$701$	−3.83572	−	3.05888i	−0.144873	−	0.115532i	−0.693245	+	0.720702i	$0.743819\pi$
$702$		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	−0.955341	−	0.295507i	$-0.904512\pi$
$709$	−42.0232	+	12.9624i	−1.57822	+	0.486815i	−0.622875	+	0.782322i	$0.714035\pi$
$710$	−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	0.900671	+	0.434501i	$0.143075\pi$
$719$	2.00621	+	26.7709i	0.0748188	+	0.998388i	−0.825852	+	0.563886i	$0.809306\pi$
$720$		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	0.990740	−	0.135775i	$-0.0433523\pi$
$727$	7.19562	+	14.9419i	0.266871	+	0.554163i	−0.723869	+	0.689937i	$0.757638\pi$
$728$	−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	−0.0787029	−	0.996898i	$-0.525078\pi$
$733$	−22.0506	−	8.65424i	−0.814459	−	0.319652i	−0.735756	+	0.677246i	$0.763173\pi$
$734$	−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	−0.000412314	−	1.00000i	$-0.500131\pi$
$739$	−27.1206	−	25.1642i	−0.997647	−	0.925681i	−0.997235	+	0.0743189i	$0.976322\pi$
$740$	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	0.988753	+	0.149557i	$0.0477847\pi$
$743$	13.3347	+	27.6899i	0.489204	+	1.01584i	−0.499549	+	0.866286i	$0.666501\pi$
$744$		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	−0.742760	−	0.669558i	$-0.766484\pi$
$751$	−2.96210	−	39.5264i	−0.108088	−	1.44234i	0.634671	−	0.772782i	$-0.281135\pi$
$752$	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	−0.0855975	−	0.996330i	$-0.527280\pi$
$757$	11.6607	−	51.0888i	0.423814	−	1.85685i	0.509412	−	0.860523i	$-0.329863\pi$
$758$	−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	$-0.447402\pi$
$761$	23.6151	−	7.28430i	0.856047	−	0.264055i	0.691556	+	0.722323i	$0.256926\pi$
$762$		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	0.497424	−	0.867507i	$-0.334279\pi$
$769$	−6.59012	−	5.25545i	−0.237646	−	0.189516i	−0.735070	+	0.677991i	$0.762851\pi$
$770$	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	$-0.222187\pi$
$773$	46.9211	−	7.07222i	1.68764	−	0.254370i	0.921520	+	0.388332i	$0.126949\pi$
$774$		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	0.807510	−	0.589854i	$-0.200815\pi$
$787$	42.5877	+	3.19151i	1.51809	+	0.113765i	0.710577	+	0.703619i	$0.248434\pi$
$788$	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	$-0.409501\pi$
$797$	−20.2618	−	25.4075i	−0.717711	−	0.899981i	−0.998206	+	0.0598743i	$0.980930\pi$
$798$		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	$-0.504683\pi$
$809$	18.6189	−	7.30737i	0.654605	−	0.256914i	0.669316	+	0.742978i	$0.266587\pi$
$810$		0			0
$811$	−26.4713	−	6.04190i	−0.929533	−	0.212160i	−0.269158	−	0.963096i	$-0.586745\pi$
$811$	−26.4713	−	6.04190i	−0.929533	−	0.212160i	−0.660375	+	0.750936i	$0.729603\pi$
$812$	−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	$-0.156719\pi$
$821$	9.85662	+	10.6229i	0.343998	+	0.370742i	−0.537228	+	0.843437i	$0.680528\pi$
$822$		0			0
$823$	−28.5534	+	19.4673i	−0.995307	+	0.678589i	−0.947330	−	0.320259i	$-0.896230\pi$
$823$	−28.5534	+	19.4673i	−0.995307	+	0.678589i	−0.0479774	+	0.998848i	$0.515278\pi$
$824$	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	−0.348480	−	0.937316i	$-0.613302\pi$
$827$	17.3011	−	35.9261i	0.601617	−	1.24927i	0.950097	−	0.311955i	$-0.100984\pi$
$828$		0			0
$829$	−3.86949	+	4.17032i	−0.134393	+	0.144841i	−0.796662	−	0.604425i	$-0.793403\pi$
$829$	−3.86949	+	4.17032i	−0.134393	+	0.144841i	0.662269	+	0.749266i	$0.269594\pi$
$830$	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	$-0.386889\pi$
$839$	−4.87042	−	2.34547i	−0.168146	−	0.0809746i	−0.516063	+	0.856550i	$0.672603\pi$
$840$		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	−0.900621	−	0.434605i	$-0.856888\pi$
$853$	−44.4951	+	10.1557i	−1.52348	+	0.347725i	−0.622864	+	0.782330i	$0.714031\pi$
$854$	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	0.987801	+	0.155725i	$0.0497712\pi$
$857$	10.8202	+	27.5694i	0.369611	+	0.941754i	−0.618189	+	0.786029i	$0.712134\pi$
$858$		0			0
$859$	2.05143	+	6.65059i	0.0699940	+	0.226915i	0.983810	−	0.179213i	$-0.0573550\pi$
$859$	2.05143	+	6.65059i	0.0699940	+	0.226915i	−0.913816	+	0.406128i	$0.866879\pi$
$860$	−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	$-0.634590\pi$
$863$	5.11882	−	2.95535i	0.174247	−	0.100601i	0.584587	+	0.811331i	$0.301257\pi$
$864$		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	0.801025	−	0.598631i	$-0.204288\pi$
$877$	15.8857	+	10.8307i	0.536422	+	0.365727i	−0.264603	+	0.964358i	$0.585241\pi$
$878$	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	$-0.424096\pi$
$881$	14.0219			0.472411			0.236205	+	0.971703i	$0.424096\pi$
$882$		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	0.999735	+	0.0230274i	$0.00733050\pi$
$887$	41.2910	+	28.1517i	1.38641	+	0.945241i	0.386680	+	0.922214i	$0.373622\pi$
$888$		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	0.973078	−	0.230477i	$-0.0740288\pi$
$907$	3.10190	+	7.90350i	0.102997	+	0.262432i	−0.870081	+	0.492909i	$0.835934\pi$
$908$	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	$-0.335314\pi$
$911$	39.7604	−	9.07505i	1.31732	−	0.300670i	0.822718	+	0.568449i	$0.192456\pi$
$912$		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	−0.703394	−	0.710800i	$-0.748333\pi$
$919$	−1.42923	+	1.32613i	−0.0471459	+	0.0437450i	0.656248	+	0.754545i	$0.272143\pi$
$920$	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	0.297878	+	0.954604i	$0.403721\pi$
$929$	−17.3665	+	44.2492i	−0.569778	+	1.45177i	−0.867656	+	0.497166i	$0.834374\pi$
$930$		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	0.236797	+	0.971559i	$0.423902\pi$
$937$	−20.5224	+	42.6153i	−0.670439	+	1.39218i	−0.907236	+	0.420622i	$0.861812\pi$
$938$	−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	$-0.944265\pi$
$941$	−36.2680	+	24.7271i	−1.18230	+	0.806080i	−0.197592	+	0.980284i	$0.563312\pi$
$942$		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	$-0.653051\pi$
$947$	−24.2406	+	1.81658i	−0.787713	+	0.0590309i	−0.325202	+	0.945645i	$0.605432\pi$
$948$		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	$-0.518441\pi$
$953$	−16.7697	−	3.82758i	−0.543225	−	0.123988i	−0.485323	+	0.874335i	$0.661298\pi$
$954$		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	0.458972	−	0.888451i	$-0.348218\pi$
$967$	−15.8386	−	19.8609i	−0.509334	−	0.638685i	−0.968306	+	0.249766i	$0.919646\pi$
$968$	−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	$-0.529912\pi$
$971$	−14.8623	−	2.24014i	−0.476955	−	0.0718894i	−0.383120	+	0.923698i	$0.625151\pi$
$972$		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	$-0.193088\pi$
$977$	48.4182	+	3.62844i	1.54903	+	0.116084i	0.727446	+	0.686165i	$0.240707\pi$
$978$		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	0.961105	+	0.276182i	$0.0890693\pi$
$983$	−0.954006	+	12.7303i	−0.0304281	+	0.406034i	−0.991533	+	0.129852i	$0.958550\pi$
$984$		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	−0.251021	−	0.967982i	$-0.580766\pi$
$991$	−6.47142	+	0.975410i	−0.205571	+	0.0309849i	0.0454492	+	0.998967i	$0.485528\pi$
$992$	−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	−0.913394	−	0.407076i	$-0.866548\pi$
$997$	2.22927	−	7.22711i	0.0706016	−	0.228885i	0.983996	+	0.178191i	$0.0570246\pi$
$998$	−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.395.11	yes	216
3.2	odd	2	inner	441.2.bg.a.395.8	yes	216
49.33	odd	42	inner	441.2.bg.a.278.8	✓	216
147.131	even	42	inner	441.2.bg.a.278.11	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.bg.a.278.8	✓	216	49.33	odd	42	inner
441.2.bg.a.278.11	yes	216	147.131	even	42	inner
441.2.bg.a.395.8	yes	216	3.2	odd	2	inner
441.2.bg.a.395.11	yes	216	1.1	even	1	trivial

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

Varieties

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Database

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