LMFDB - Embedded newform 819.2.dl.e.298.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(298,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 3]))

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

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

chi := DirichletCharacter("819.298");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.dl (of order $6$, degree $2$, 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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 11x^{14} + 85x^{12} - 334x^{10} + 952x^{8} - 1050x^{6} + 853x^{4} - 93x^{2} + 9 $ x^16 - 11x^14 + 85x^12 - 334x^10 + 952x^8 - 1050x^6 + 853x^4 - 93*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			298.3
Root			$0.929293 + 0.536527i$ of defining polynomial
Character	$\chi$	$=$	819.298
Dual form			819.2.dl.e.415.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.929293 + 0.536527i) q^{2} +(-0.424277 + 0.734868i) q^{4} +(0.541640 - 0.312716i) q^{5} +(-2.34996 + 1.21561i) q^{7} -3.05665i q^{8} +O(q^{10})$	\(q+(-0.929293 + 0.536527i) q^{2} +(-0.424277 + 0.734868i) q^{4} +(0.541640 - 0.312716i) q^{5} +(-2.34996 + 1.21561i) q^{7} -3.05665i q^{8} +(-0.335561 + 0.581209i) q^{10} +(-0.613597 - 0.354260i) q^{11} +(0.848553 - 3.50428i) q^{13} +(1.53159 - 2.39047i) q^{14} +(0.791426 + 1.37079i) q^{16} +(1.67157 - 2.89524i) q^{17} +(4.50573 - 2.60138i) q^{19} +0.530712i q^{20} +0.760282 q^{22} +(2.21570 + 3.83771i) q^{23} +(-2.30442 + 3.99137i) q^{25} +(1.09159 + 3.71177i) q^{26} +(0.103717 - 2.24266i) q^{28} +6.59711 q^{29} +(-3.80238 - 2.19530i) q^{31} +(3.82335 + 2.20741i) q^{32} +3.58737i q^{34} +(-0.892689 + 1.39329i) q^{35} +(0.366683 - 0.211704i) q^{37} +(-2.79143 + 4.83489i) q^{38} +(-0.955864 - 1.65561i) q^{40} -5.01604i q^{41} +11.2059 q^{43} +(0.520670 - 0.300609i) q^{44} +(-4.11807 - 2.37757i) q^{46} +(-6.99116 + 4.03635i) q^{47} +(4.04458 - 5.71326i) q^{49} -4.94553i q^{50} +(2.21516 + 2.11036i) q^{52} +(-0.348553 + 0.603712i) q^{53} -0.443132 q^{55} +(3.71570 + 7.18300i) q^{56} +(-6.13065 + 3.53953i) q^{58} +(8.54177 + 4.93159i) q^{59} +(-2.34855 - 4.06781i) q^{61} +4.71136 q^{62} -7.90305 q^{64} +(-0.636233 - 2.16341i) q^{65} +(9.02470 + 5.21041i) q^{67} +(1.41841 + 2.45676i) q^{68} +(0.0820297 - 1.77373i) q^{70} -14.0876i q^{71} +(4.40273 + 2.54191i) q^{73} +(-0.227170 + 0.393471i) q^{74} +4.41482i q^{76} +(1.87257 + 0.0866008i) q^{77} +(1.95586 + 3.38766i) q^{79} +(0.857336 + 0.494983i) q^{80} +(2.69124 + 4.66137i) q^{82} +10.2035i q^{83} -2.09090i q^{85} +(-10.4136 + 6.01230i) q^{86} +(-1.08285 + 1.87555i) q^{88} +(11.5866 - 6.68955i) q^{89} +(2.26578 + 9.26640i) q^{91} -3.76028 q^{92} +(4.33122 - 7.50190i) q^{94} +(1.62699 - 2.81802i) q^{95} +0.202023i q^{97} +(-0.693276 + 7.47932i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{4}+O(q^{10}) $ 16 * q + 6 * q^4	$ 16 q + 6 q^{4} - 6 q^{10} - 12 q^{13} + 26 q^{14} + 2 q^{16} - 8 q^{17} - 36 q^{22} + 12 q^{23} + 6 q^{26} + 16 q^{29} - 34 q^{38} - 4 q^{40} + 16 q^{43} + 40 q^{49} - 42 q^{52} + 20 q^{53} + 24 q^{55} + 36 q^{56} - 12 q^{61} - 44 q^{62} + 88 q^{64} + 30 q^{65} + 2 q^{68} - 42 q^{74} + 76 q^{77} + 20 q^{79} - 16 q^{82} + 4 q^{88} + 56 q^{91} - 12 q^{92} - 26 q^{94} + 16 q^{95}+O(q^{100}) $ 16 * q + 6 * q^4 - 6 * q^10 - 12 * q^13 + 26 * q^14 + 2 * q^16 - 8 * q^17 - 36 * q^22 + 12 * q^23 + 6 * q^26 + 16 * q^29 - 34 * q^38 - 4 * q^40 + 16 * q^43 + 40 * q^49 - 42 * q^52 + 20 * q^53 + 24 * q^55 + 36 * q^56 - 12 * q^61 - 44 * q^62 + 88 * q^64 + 30 * q^65 + 2 * q^68 - 42 * q^74 + 76 * q^77 + 20 * q^79 - 16 * q^82 + 4 * q^88 + 56 * q^91 - 12 * q^92 - 26 * q^94 + 16 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.929293	+	0.536527i	−0.657109	+	0.379382i	−0.791175	−	0.611590i	$-0.790530\pi$
$2$	−0.929293	+	0.536527i	−0.657109	+	0.379382i	0.134065	+	0.990972i	$0.457197\pi$
$3$		0			0
$3$		0			0
$4$	−0.424277	+	0.734868i	−0.212138	+	0.367434i
$5$	0.541640	−	0.312716i	0.242229	−	0.139851i	−0.373972	−	0.927440i	$-0.622004\pi$
$5$	0.541640	−	0.312716i	0.242229	−	0.139851i	0.616201	+	0.787589i	$0.288671\pi$
$6$		0			0
$7$	−2.34996	+	1.21561i	−0.888200	+	0.459458i
$7$	−2.34996	+	1.21561i	−0.888200	+	0.459458i
$8$		−	3.05665i		−	1.08069i
$9$		0			0
$10$	−0.335561	+	0.581209i	−0.106114	+	0.183795i
$11$	−0.613597	−	0.354260i	−0.185006	−	0.106814i	0.404636	−	0.914478i	$-0.367398\pi$
$11$	−0.613597	−	0.354260i	−0.185006	−	0.106814i	−0.589643	+	0.807664i	$0.700731\pi$
$12$		0			0
$13$	0.848553	−	3.50428i	0.235346	−	0.971912i
$13$	0.848553	−	3.50428i	0.235346	−	0.971912i
$14$	1.53159	−	2.39047i	0.409334	−	0.638881i
$15$		0			0
$16$	0.791426	+	1.37079i	0.197856	+	0.342697i
$17$	1.67157	−	2.89524i	0.405414	−	0.702199i	−0.588955	−	0.808166i	$-0.700461\pi$
$17$	1.67157	−	2.89524i	0.405414	−	0.702199i	0.994370	+	0.105967i	$0.0337939\pi$
$18$		0			0
$19$	4.50573	−	2.60138i	1.03368	−	0.596798i	0.115646	−	0.993290i	$-0.463106\pi$
$19$	4.50573	−	2.60138i	1.03368	−	0.596798i	0.918038	+	0.396492i	$0.129773\pi$
$20$			0.530712i			0.118671i
$21$		0			0
$22$	0.760282			0.162093
$23$	2.21570	+	3.83771i	0.462006	+	0.800218i	0.999061	−	0.0433296i	$-0.0137966\pi$
$23$	2.21570	+	3.83771i	0.462006	+	0.800218i	−0.537055	+	0.843547i	$0.680463\pi$
$24$		0			0
$25$	−2.30442	+	3.99137i	−0.460883	+	0.798274i
$26$	1.09159	+	3.71177i	0.214078	+	0.727938i
$27$		0			0
$28$	0.103717	−	2.24266i	0.0196006	−	0.423824i
$29$	6.59711			1.22505			0.612526	−	0.790450i	$-0.290153\pi$
$29$	6.59711			1.22505			0.612526	+	0.790450i	$0.290153\pi$
$30$		0			0
$31$	−3.80238	−	2.19530i	−0.682927	−	0.394288i	0.118030	−	0.993010i	$-0.462342\pi$
$31$	−3.80238	−	2.19530i	−0.682927	−	0.394288i	−0.800957	+	0.598722i	$0.795675\pi$
$32$	3.82335	+	2.20741i	0.675879	+	0.390219i
$33$		0			0
$34$			3.58737i			0.615228i
$35$	−0.892689	+	1.39329i	−0.150892	+	0.235509i
$36$		0			0
$37$	0.366683	−	0.211704i	0.0602823	−	0.0348040i	−0.469556	−	0.882903i	$-0.655586\pi$
$37$	0.366683	−	0.211704i	0.0602823	−	0.0348040i	0.529838	+	0.848099i	$0.322253\pi$
$38$	−2.79143	+	4.83489i	−0.452829	+	0.784323i
$39$		0			0
$40$	−0.955864	−	1.65561i	−0.151135	−	0.261774i
$41$		−	5.01604i		−	0.783374i	−0.920099	−	0.391687i	$-0.871892\pi$
$41$		−	5.01604i		−	0.783374i	0.920099	−	0.391687i	$-0.128108\pi$
$42$		0			0
$43$	11.2059			1.70889			0.854445	−	0.519542i	$-0.173897\pi$
$43$	11.2059			1.70889			0.854445	+	0.519542i	$0.173897\pi$
$44$	0.520670	−	0.300609i	0.0784939	−	0.0453185i
$45$		0			0
$46$	−4.11807	−	2.37757i	−0.607177	−	0.350554i
$47$	−6.99116	+	4.03635i	−1.01977	+	0.588762i	−0.914036	−	0.405633i	$-0.867051\pi$
$47$	−6.99116	+	4.03635i	−1.01977	+	0.588762i	−0.105729	+	0.994395i	$0.533718\pi$
$48$		0			0
$49$	4.04458	−	5.71326i	0.577797	−	0.816180i
$50$		−	4.94553i		−	0.699404i
$51$		0			0
$52$	2.21516	+	2.11036i	0.307188	+	0.292654i
$53$	−0.348553	+	0.603712i	−0.0478774	+	0.0829262i	−0.888971	−	0.457964i	$-0.848579\pi$
$53$	−0.348553	+	0.603712i	−0.0478774	+	0.0829262i	0.841094	+	0.540890i	$0.181912\pi$
$54$		0			0
$55$	−0.443132			−0.0597519
$56$	3.71570	+	7.18300i	0.496532	+	0.959869i
$57$		0			0
$58$	−6.13065	+	3.53953i	−0.804993	+	0.464763i
$59$	8.54177	+	4.93159i	1.11204	+	0.642039i	0.939358	−	0.342938i	$-0.111422\pi$
$59$	8.54177	+	4.93159i	1.11204	+	0.642039i	0.172686	+	0.984977i	$0.444756\pi$
$60$		0			0
$61$	−2.34855	−	4.06781i	−0.300701	−	0.520830i	0.675594	−	0.737274i	$-0.263887\pi$
$61$	−2.34855	−	4.06781i	−0.300701	−	0.520830i	−0.976295	+	0.216444i	$0.930554\pi$
$62$	4.71136			0.598344
$63$		0			0
$64$	−7.90305			−0.987881
$65$	−0.636233	−	2.16341i	−0.0789150	−	0.268338i
$66$		0			0
$67$	9.02470	+	5.21041i	1.10254	+	0.636553i	0.936888	−	0.349631i	$-0.113693\pi$
$67$	9.02470	+	5.21041i	1.10254	+	0.636553i	0.165655	+	0.986184i	$0.447026\pi$
$68$	1.41841	+	2.45676i	0.172008	+	0.297926i
$69$		0			0
$70$	0.0820297	−	1.77373i	0.00980443	−	0.212001i
$71$		−	14.0876i		−	1.67189i	−0.548812	−	0.835946i	$-0.684920\pi$
$71$		−	14.0876i		−	1.67189i	0.548812	−	0.835946i	$-0.315080\pi$
$72$		0			0
$73$	4.40273	+	2.54191i	0.515300	+	0.297509i	0.735010	−	0.678057i	$-0.237178\pi$
$73$	4.40273	+	2.54191i	0.515300	+	0.297509i	−0.219710	+	0.975565i	$0.570511\pi$
$74$	−0.227170	+	0.393471i	−0.0264080	+	0.0457400i
$75$		0			0
$76$			4.41482i			0.506415i
$77$	1.87257	+	0.0866008i	0.213399	+	0.00986908i
$78$		0			0
$79$	1.95586	+	3.38766i	0.220052	+	0.381141i	0.954823	−	0.297174i	$-0.0960440\pi$
$79$	1.95586	+	3.38766i	0.220052	+	0.381141i	−0.734772	+	0.678315i	$0.762711\pi$
$80$	0.857336	+	0.494983i	0.0958530	+	0.0553408i
$81$		0			0
$82$	2.69124	+	4.66137i	0.297198	+	0.514762i
$83$			10.2035i			1.11998i	0.828499	+	0.559990i	$0.189195\pi$
$83$			10.2035i			1.11998i	−0.828499	+	0.559990i	$0.810805\pi$
$84$		0			0
$85$		−	2.09090i		−	0.226790i
$86$	−10.4136	+	6.01230i	−1.12293	+	0.648323i
$87$		0			0
$88$	−1.08285	+	1.87555i	−0.115432	+	0.199935i
$89$	11.5866	−	6.68955i	1.22818	−	0.709090i	0.261532	−	0.965195i	$-0.415772\pi$
$89$	11.5866	−	6.68955i	1.22818	−	0.709090i	0.966649	+	0.256104i	$0.0824391\pi$
$90$		0			0
$91$	2.26578	+	9.26640i	0.237518	+	0.971383i
$92$	−3.76028			−0.392036
$93$		0			0
$94$	4.33122	−	7.50190i	0.446731	−	0.773761i
$95$	1.62699	−	2.81802i	0.166925	−	0.289123i
$96$		0			0
$97$			0.202023i			0.0205123i	0.999947	+	0.0102562i	$0.00326470\pi$
$97$			0.202023i			0.0205123i	−0.999947	+	0.0102562i	$0.996735\pi$
$98$	−0.693276	+	7.47932i	−0.0700315	+	0.755526i
$99$		0			0
$100$	−1.95542	−	3.38689i	−0.195542	−	0.338689i
$101$	8.66723	−	15.0121i	0.862421	−	1.49376i	−0.00716374	−	0.999974i	$-0.502280\pi$
$101$	8.66723	−	15.0121i	0.862421	−	1.49376i	0.869585	−	0.493783i	$-0.164386\pi$
$102$		0			0
$103$	−5.40739	−	9.36587i	−0.532806	−	0.922847i	−0.999266	−	0.0383047i	$-0.987804\pi$
$103$	−5.40739	−	9.36587i	−0.532806	−	0.922847i	0.466460	−	0.884542i	$-0.345529\pi$
$104$	−10.7114	−	2.59373i	−1.05034	−	0.254336i
$105$		0			0
$106$		−	0.748033i		−	0.0726554i
$107$	−3.05839	−	5.29729i	−0.295666	−	0.512108i	0.679474	−	0.733700i	$-0.262208\pi$
$107$	−3.05839	−	5.29729i	−0.295666	−	0.512108i	−0.975140	+	0.221592i	$0.928875\pi$
$108$		0			0
$109$	9.87196	+	5.69958i	0.945563	+	0.545921i	0.891700	−	0.452628i	$-0.149513\pi$
$109$	9.87196	+	5.69958i	0.945563	+	0.545921i	0.0538629	+	0.998548i	$0.482847\pi$
$110$	0.411799	−	0.237752i	0.0392635	−	0.0226688i
$111$		0			0
$112$	−3.52616	−	2.25923i	−0.333191	−	0.213477i
$113$	0.923456			0.0868714			0.0434357	−	0.999056i	$-0.486170\pi$
$113$	0.923456			0.0868714			0.0434357	+	0.999056i	$0.486170\pi$
$114$		0			0
$115$	2.40023	+	1.38577i	0.223822	+	0.129224i
$116$	−2.79900	+	4.84801i	−0.259880	+	0.450126i
$117$		0			0
$118$	−10.5837			−0.974312
$119$	−0.408623	+	8.83566i	−0.0374584	+	0.809963i
$120$		0			0
$121$	−5.24900	−	9.09153i	−0.477182	−	0.826503i
$122$	4.36499	+	2.52013i	0.395187	+	0.228162i
$123$		0			0
$124$	3.22652	−	1.86283i	0.289750	−	0.167287i
$125$			6.00967i			0.537521i
$126$		0			0
$127$	8.50972			0.755116			0.377558	−	0.925986i	$-0.376764\pi$
$127$	8.50972			0.755116			0.377558	+	0.925986i	$0.376764\pi$
$128$	−0.302447	+	0.174618i	−0.0267328	+	0.0154342i
$129$		0			0
$130$	1.75198	+	1.66909i	0.153659	+	0.146389i
$131$	−3.50152	−	6.06482i	−0.305930	−	0.529885i	0.671538	−	0.740970i	$-0.265634\pi$
$131$	−3.50152	−	6.06482i	−0.305930	−	0.529885i	−0.977468	+	0.211084i	$0.932301\pi$
$132$		0			0
$133$	−7.42599	+	11.5903i	−0.643915	+	1.00501i
$134$	−11.1821			−0.965988
$135$		0			0
$136$	−8.84974	−	5.10940i	−0.758859	−	0.438128i
$137$	−5.38403	−	3.10847i	−0.459989	−	0.265575i	0.252051	−	0.967714i	$-0.418895\pi$
$137$	−5.38403	−	3.10847i	−0.459989	−	0.265575i	−0.712040	+	0.702139i	$0.752228\pi$
$138$		0			0
$139$	6.53140			0.553986			0.276993	−	0.960872i	$-0.410662\pi$
$139$	6.53140			0.553986			0.276993	+	0.960872i	$0.410662\pi$
$140$	−0.645140	−	1.24715i	−0.0545242	−	0.105403i
$141$		0			0
$142$	7.55839	+	13.0915i	0.634286	+	1.09862i
$143$	−1.76210	+	1.84961i	−0.147354	+	0.154672i
$144$		0			0
$145$	3.57326	−	2.06302i	0.296743	−	0.171325i
$146$	−5.45523			−0.451478
$147$		0			0
$148$			0.359285i			0.0295330i
$149$	−3.20203	+	1.84869i	−0.262320	+	0.151451i	−0.625393	−	0.780310i	$-0.715061\pi$
$149$	−3.20203	+	1.84869i	−0.262320	+	0.151451i	0.363072	+	0.931761i	$0.381728\pi$
$150$		0			0
$151$	4.22425	+	2.43887i	0.343764	+	0.198473i	0.661935	−	0.749561i	$-0.269735\pi$
$151$	4.22425	+	2.43887i	0.343764	+	0.198473i	−0.318171	+	0.948033i	$0.603069\pi$
$152$	−7.95152	−	13.7724i	−0.644954	−	1.11709i
$153$		0			0
$154$	−1.78663	+	0.924207i	−0.143971	+	0.0744747i
$155$	−2.74603			−0.220566
$156$		0			0
$157$	4.75984	−	8.24428i	0.379876	−	0.657965i	−0.611168	−	0.791501i	$-0.709300\pi$
$157$	4.75984	−	8.24428i	0.379876	−	0.657965i	0.991044	+	0.133536i	$0.0426332\pi$
$158$	−3.63514	−	2.09875i	−0.289196	−	0.166968i
$159$		0			0
$160$	2.76117			0.218290
$161$	−9.87196	−	6.32501i	−0.778020	−	0.498481i
$162$		0			0
$163$	−20.5325	+	11.8544i	−1.60823	+	0.928511i	−0.618461	+	0.785815i	$0.712244\pi$
$163$	−20.5325	+	11.8544i	−1.60823	+	0.928511i	−0.989767	+	0.142696i	$0.954423\pi$
$164$	3.68613	+	2.12819i	0.287838	+	0.166184i
$165$		0			0
$166$	−5.47446	−	9.48204i	−0.424901	−	0.735949i
$167$		−	1.13193i		−	0.0875914i	−0.999041	−	0.0437957i	$-0.986055\pi$
$167$		−	1.13193i		−	0.0875914i	0.999041	−	0.0437957i	$-0.0139451\pi$
$168$		0			0
$169$	−11.5599	−	5.94713i	−0.889224	−	0.457472i
$170$	1.12183	+	1.94306i	0.0860402	+	0.149026i
$171$		0			0
$172$	−4.75442	+	8.23489i	−0.362521	+	0.627905i
$173$	−5.99458	−	10.3829i	−0.455760	−	0.789399i	0.542972	−	0.839751i	$-0.317299\pi$
$173$	−5.99458	−	10.3829i	−0.455760	−	0.789399i	−0.998732	+	0.0503522i	$0.983966\pi$
$174$		0			0
$175$	0.563327	−	12.1808i	0.0425835	−	0.920783i
$176$		−	1.12148i		−	0.0845350i
$177$		0			0
$178$	−7.17825	+	12.4331i	−0.538033	+	0.931900i
$179$	−4.73538	+	8.20192i	−0.353939	+	0.613040i	−0.986936	−	0.161114i	$-0.948491\pi$
$179$	−4.73538	+	8.20192i	−0.353939	+	0.613040i	0.632997	+	0.774154i	$0.281825\pi$
$180$		0			0
$181$	−11.4314			−0.849690			−0.424845	−	0.905266i	$-0.639671\pi$
$181$	−11.4314			−0.849690			−0.424845	+	0.905266i	$0.639671\pi$
$182$	−7.07725	−	7.39555i	−0.524601	−	0.548195i
$183$		0			0
$184$	11.7305	−	6.77264i	0.864788	−	0.499285i
$185$	0.132407	−	0.229335i	0.00973473	−	0.0168611i
$186$		0			0
$187$	−2.05134	+	1.18434i	−0.150009	+	0.0866075i
$188$		−	6.85011i		−	0.499595i
$189$		0			0
$190$			3.49169i			0.253314i
$191$	7.84377	+	13.5858i	0.567555	+	0.983034i	0.996807	+	0.0798496i	$0.0254440\pi$
$191$	7.84377	+	13.5858i	0.567555	+	0.983034i	−0.429252	+	0.903185i	$0.641223\pi$
$192$		0			0
$193$	−19.9248	−	11.5036i	−1.43422	−	0.828045i	−0.436776	−	0.899570i	$-0.643880\pi$
$193$	−19.9248	−	11.5036i	−1.43422	−	0.828045i	−0.997439	+	0.0715256i	$0.977213\pi$
$194$	−0.108391	−	0.187739i	−0.00778202	−	0.0134788i
$195$		0			0
$196$	2.48248	+	5.39624i	0.177320	+	0.385446i
$197$		−	10.2035i		−	0.726970i	−0.931600	−	0.363485i	$-0.881587\pi$
$197$		−	10.2035i		−	0.726970i	0.931600	−	0.363485i	$-0.118413\pi$
$198$		0			0
$199$	5.96173	−	10.3260i	0.422616	−	0.731992i	−0.573579	−	0.819150i	$-0.694445\pi$
$199$	5.96173	−	10.3260i	0.422616	−	0.731992i	0.996194	+	0.0871586i	$0.0277787\pi$
$200$	12.2002	+	7.04381i	0.862687	+	0.498072i
$201$		0			0
$202$			18.6008i			1.30875i
$203$	−15.5029	+	8.01952i	−1.08809	+	0.562860i
$204$		0			0
$205$	−1.56860	−	2.71689i	−0.109555	−	0.189756i
$206$	10.0501	+	5.80243i	0.700223	+	0.404274i
$207$		0			0
$208$	5.47519	−	1.61019i	0.379636	−	0.111646i
$209$	−3.68627			−0.254984
$210$		0			0
$211$	−15.5893			−1.07321			−0.536606	−	0.843833i	$-0.680294\pi$
$211$	−15.5893			−1.07321			−0.536606	+	0.843833i	$0.680294\pi$
$212$	−0.295766	−	0.512281i	−0.0203133	−	0.0351836i
$213$		0			0
$214$	5.68428	+	3.28182i	0.388570	+	0.224341i
$215$	6.06959	−	3.50428i	0.413942	−	0.238990i
$216$		0			0
$217$	11.6041	+	0.536653i	0.787734	+	0.0364304i
$218$	−12.2319			−0.828451
$219$		0			0
$220$	0.188010	−	0.325643i	0.0126757	−	0.0219549i
$221$	−8.72731	−	8.31440i	−0.587062	−	0.559287i
$222$		0			0
$223$		−	6.76662i		−	0.453126i	−0.973996	−	0.226563i	$-0.927251\pi$
$223$		−	6.76662i		−	0.453126i	0.973996	−	0.226563i	$-0.0727490\pi$
$224$	−11.6680	−	0.539613i	−0.779604	−	0.0360544i
$225$		0			0
$226$	−0.858161	+	0.495459i	−0.0570840	+	0.0329575i
$227$	14.5704	+	8.41225i	0.967074	+	0.558340i	0.898343	−	0.439295i	$-0.144772\pi$
$227$	14.5704	+	8.41225i	0.967074	+	0.558340i	0.0687311	+	0.997635i	$0.478105\pi$
$228$		0			0
$229$	−9.54855	+	5.51286i	−0.630986	+	0.364300i	−0.781134	−	0.624364i	$-0.785358\pi$
$229$	−9.54855	+	5.51286i	−0.630986	+	0.364300i	0.150148	+	0.988664i	$0.452025\pi$
$230$	−2.97402			−0.196101
$231$		0			0
$232$		−	20.1651i		−	1.32390i
$233$	−8.67743	−	15.0298i	−0.568477	−	0.984632i	−0.996717	−	0.0809664i	$-0.974199\pi$
$233$	−8.67743	−	15.0298i	−0.568477	−	0.984632i	0.428239	−	0.903665i	$-0.359134\pi$
$234$		0			0
$235$	−2.52446	+	4.37249i	−0.164678	+	0.285230i
$236$	−7.24814	+	4.18472i	−0.471814	+	0.272402i
$237$		0			0
$238$	−4.36084	−	8.43015i	−0.282671	−	0.546445i
$239$		−	19.7223i		−	1.27573i	−0.770148	−	0.637865i	$-0.779818\pi$
$239$		−	19.7223i		−	1.27573i	0.770148	−	0.637865i	$-0.220182\pi$
$240$		0			0
$241$	2.41112	+	1.39206i	0.155314	+	0.0896706i	0.575643	−	0.817701i	$-0.304752\pi$
$241$	2.41112	+	1.39206i	0.155314	+	0.0896706i	−0.420329	+	0.907372i	$0.638085\pi$
$242$	9.75571	+	5.63246i	0.627121	+	0.362069i
$243$		0			0
$244$	3.98574			0.255161
$245$	0.404077	−	4.35934i	0.0258155	−	0.278508i
$246$		0			0
$247$	−5.29262	−	17.9967i	−0.336761	−	1.14510i
$248$	−6.71028	+	11.6226i	−0.426103	+	0.738033i
$249$		0			0
$250$	−3.22435	−	5.58475i	−0.203926	−	0.353210i
$251$	23.5608			1.48714			0.743572	−	0.668655i	$-0.233130\pi$
$251$	23.5608			1.48714			0.743572	+	0.668655i	$0.233130\pi$
$252$		0			0
$253$		−	3.13974i		−	0.197394i
$254$	−7.90803	+	4.56570i	−0.496194	+	0.286478i
$255$		0			0
$256$	8.09042	−	14.0130i	0.505651	−	0.875814i
$257$	1.71615	+	2.97245i	0.107050	+	0.185417i	0.914574	−	0.404419i	$-0.132526\pi$
$257$	1.71615	+	2.97245i	0.107050	+	0.185417i	−0.807524	+	0.589835i	$0.799193\pi$
$258$		0			0
$259$	−0.604338	+	0.943239i	−0.0375517	+	0.0586100i
$260$	1.85976	+	0.450337i	0.115338	+	0.0279287i
$261$		0			0
$262$	6.50788	+	3.75733i	0.402058	+	0.232128i
$263$	−10.7245	+	18.5754i	−0.661303	+	1.14541i	0.318970	+	0.947765i	$0.396663\pi$
$263$	−10.7245	+	18.5754i	−0.661303	+	1.14541i	−0.980273	+	0.197646i	$0.936670\pi$
$264$		0			0
$265$			0.435992i			0.0267828i
$266$	0.682378	−	14.7551i	0.0418393	−	0.904691i
$267$		0			0
$268$	−7.65794	+	4.42131i	−0.467783	+	0.270075i
$269$	7.32843	−	12.6932i	0.446822	−	0.773919i	−0.551355	−	0.834271i	$-0.685889\pi$
$269$	7.32843	−	12.6932i	0.446822	−	0.773919i	0.998177	+	0.0603517i	$0.0192222\pi$
$270$		0			0
$271$	1.76986	−	1.02183i	0.107511	−	0.0620717i	−0.445280	−	0.895391i	$-0.646896\pi$
$271$	1.76986	−	1.02183i	0.107511	−	0.0620717i	0.552792	+	0.833320i	$0.313563\pi$
$272$	5.29168			0.320856
$273$		0			0
$274$	6.67112			0.403017
$275$	2.82797	−	1.63273i	0.170533	−	0.0984572i
$276$		0			0
$277$	−2.71678	+	4.70560i	−0.163236	+	0.282732i	−0.936027	−	0.351927i	$-0.885526\pi$
$277$	−2.71678	+	4.70560i	−0.163236	+	0.282732i	0.772792	+	0.634660i	$0.218860\pi$
$278$	−6.06959	+	3.50428i	−0.364030	+	0.210173i
$279$		0			0
$280$	4.25881	+	2.72864i	0.254513	+	0.163067i
$281$			20.2356i			1.20715i	0.797305	+	0.603577i	$0.206258\pi$
$281$			20.2356i			1.20715i	−0.797305	+	0.603577i	$0.793742\pi$
$282$		0			0
$283$	0.867593	−	1.50272i	0.0515731	−	0.0893272i	−0.839086	−	0.543998i	$-0.816910\pi$
$283$	0.867593	−	1.50272i	0.0515731	−	0.0893272i	0.890659	+	0.454671i	$0.150243\pi$
$284$	10.3525	+	5.97704i	0.614310	+	0.354672i
$285$		0			0
$286$	0.645140	−	2.66424i	0.0381479	−	0.157540i
$287$	6.09755	+	11.7875i	0.359927	+	0.695792i
$288$		0			0
$289$	2.91173	+	5.04326i	0.171278	+	0.296662i
$290$	−2.21373	+	3.83430i	−0.129995	+	0.225158i
$291$		0			0
$292$	−3.73595	+	2.15695i	−0.218630	+	0.126226i
$293$			27.2441i			1.59162i	0.605547	+	0.795810i	$0.292954\pi$
$293$			27.2441i			1.59162i	−0.605547	+	0.795810i	$0.707046\pi$
$294$		0			0
$295$	6.16875			0.359159
$296$	−0.647107	−	1.12082i	−0.0376123	−	0.0651465i
$297$		0			0
$298$	1.98375	−	3.43595i	0.114915	−	0.199039i
$299$	15.3285	−	4.50794i	0.886472	−	0.260701i
$300$		0			0
$301$	−26.3335	+	13.6221i	−1.51784	+	0.785163i
$302$	−5.23409			−0.301188
$303$		0			0
$304$	7.13190	+	4.11760i	0.409042	+	0.236161i
$305$	−2.54414	−	1.46886i	−0.145677	−	0.0841067i
$306$		0			0
$307$		−	12.7138i		−	0.725612i	−0.931865	−	0.362806i	$-0.881819\pi$
$307$		−	12.7138i		−	0.725612i	0.931865	−	0.362806i	$-0.118181\pi$
$308$	−0.858127	+	1.33935i	−0.0488963	+	0.0763165i
$309$		0			0
$310$	2.55186	−	1.47332i	0.144936	−	0.0836788i
$311$	−4.80939	+	8.33011i	−0.272716	+	0.472357i	−0.969556	−	0.244869i	$-0.921255\pi$
$311$	−4.80939	+	8.33011i	−0.272716	+	0.472357i	0.696841	+	0.717226i	$0.254588\pi$
$312$		0			0
$313$	4.51273	+	7.81628i	0.255075	+	0.441802i	0.964916	−	0.262559i	$-0.0845666\pi$
$313$	4.51273	+	7.81628i	0.255075	+	0.441802i	−0.709841	+	0.704362i	$0.751233\pi$
$314$			10.2151i			0.576473i
$315$		0			0
$316$	−3.31931			−0.186726
$317$	−21.3269	+	12.3131i	−1.19784	+	0.691572i	−0.960073	−	0.279750i	$-0.909748\pi$
$317$	−21.3269	+	12.3131i	−1.19784	+	0.691572i	−0.237766	+	0.971323i	$0.576415\pi$
$318$		0			0
$319$	−4.04797	−	2.33709i	−0.226643	−	0.130852i
$320$	−4.28061	+	2.47141i	−0.239293	+	0.138156i
$321$		0			0
$322$	12.5675	+	0.581209i	0.700359	+	0.0323895i
$323$		−	17.3935i		−	0.967802i
$324$		0			0
$325$	12.0314	+	11.4622i	0.667384	+	0.635809i
$326$	12.7205	−	22.0325i	0.704521	−	1.22027i
$327$		0			0
$328$	−15.3323			−0.846584
$329$	11.5223	−	17.9838i	0.635244	−	0.991477i
$330$		0			0
$331$	11.4071	−	6.58591i	0.626993	−	0.361994i	−0.152594	−	0.988289i	$-0.548763\pi$
$331$	11.4071	−	6.58591i	0.626993	−	0.361994i	0.779586	+	0.626295i	$0.215429\pi$
$332$	−7.49823	−	4.32911i	−0.411519	−	0.237591i
$333$		0			0
$334$	0.607311	+	1.05189i	0.0332306	+	0.0575571i
$335$	6.51752			0.356090
$336$		0			0
$337$	17.0307			0.927720			0.463860	−	0.885909i	$-0.346464\pi$
$337$	17.0307			0.927720			0.463860	+	0.885909i	$0.346464\pi$
$338$	13.9333	−	0.675587i	0.757874	−	0.0367471i
$339$		0			0
$340$	1.53654	+	0.887121i	0.0833305	+	0.0481109i
$341$	1.55542	+	2.69406i	0.0842306	+	0.145892i
$342$		0			0
$343$	−2.55948	+	18.3425i	−0.138199	+	0.990405i
$344$		−	34.2527i		−	1.84678i
$345$		0			0
$346$	11.1414	+	6.43251i	0.598968	+	0.345814i
$347$	0.229959	−	0.398300i	0.0123448	−	0.0213819i	−0.859787	−	0.510653i	$-0.829404\pi$
$347$	0.229959	−	0.398300i	0.0123448	−	0.0213819i	0.872132	+	0.489271i	$0.162737\pi$
$348$		0			0
$349$			6.87822i			0.368183i	0.982909	+	0.184091i	$0.0589342\pi$
$349$			6.87822i			0.368183i	−0.982909	+	0.184091i	$0.941066\pi$
$350$	6.01184	+	11.6218i	0.321347	+	0.621210i
$351$		0			0
$352$	−1.56400	−	2.70892i	−0.0833613	−	0.144386i
$353$	1.32784	+	0.766631i	0.0706740	+	0.0408036i	0.534921	−	0.844902i	$-0.320342\pi$
$353$	1.32784	+	0.766631i	0.0706740	+	0.0408036i	−0.464247	+	0.885706i	$0.653675\pi$
$354$		0			0
$355$	−4.40542	−	7.63041i	−0.233815	−	0.404980i
$356$			11.3529i			0.601701i
$357$		0			0
$358$		−	10.1626i		−	0.537112i
$359$	−23.5617	+	13.6034i	−1.24354	+	0.717959i	−0.969813	−	0.243848i	$-0.921590\pi$
$359$	−23.5617	+	13.6034i	−1.24354	+	0.717959i	−0.273728	+	0.961807i	$0.588257\pi$
$360$		0			0
$361$	4.03438	−	6.98774i	0.212336	−	0.367776i
$362$	10.6231	−	6.13326i	0.558339	−	0.322357i
$363$		0			0
$364$	−7.77090	−	2.26647i	−0.407306	−	0.118795i
$365$	3.17959			0.166427
$366$		0			0
$367$	−13.4907	+	23.3666i	−0.704208	+	1.21972i	0.262769	+	0.964859i	$0.415364\pi$
$367$	−13.4907	+	23.3666i	−0.704208	+	1.21972i	−0.966977	+	0.254865i	$0.917969\pi$
$368$	−3.50713	+	6.07452i	−0.182822	+	0.316656i
$369$		0			0
$370$			0.284159i			0.0147727i
$371$	0.0852056	−	1.84240i	0.00442365	−	0.0956526i
$372$		0			0
$373$	−1.98619	−	3.44018i	−0.102841	−	0.178126i	0.810013	−	0.586412i	$-0.199460\pi$
$373$	−1.98619	−	3.44018i	−0.102841	−	0.178126i	−0.912854	+	0.408286i	$0.866127\pi$
$374$	1.27086	−	2.20120i	0.0657147	−	0.113821i
$375$		0			0
$376$	12.3377	+	21.3695i	0.636269	+	1.10205i
$377$	5.59800	−	23.1181i	0.288311	−	1.19064i
$378$		0			0
$379$		−	11.4059i		−	0.585884i	−0.956130	−	0.292942i	$-0.905366\pi$
$379$		−	11.4059i		−	0.585884i	0.956130	−	0.292942i	$-0.0946343\pi$
$380$	1.38058	+	2.39124i	0.0708225	+	0.122668i
$381$		0			0
$382$	−14.5783	−	8.41680i	−0.745892	−	0.430641i
$383$	20.6044	−	11.8960i	1.05284	−	0.607856i	0.129395	−	0.991593i	$-0.458696\pi$
$383$	20.6044	−	11.8960i	1.05284	−	0.607856i	0.923442	+	0.383737i	$0.125363\pi$
$384$		0			0
$385$	1.04134	−	0.538676i	0.0530716	−	0.0274535i
$386$	24.6879			1.25658
$387$		0			0
$388$	−0.148460	−	0.0857137i	−0.00753694	−	0.00435145i
$389$	14.2055	−	24.6046i	0.720247	−	1.24751i	−0.240653	−	0.970611i	$-0.577362\pi$
$389$	14.2055	−	24.6046i	0.720247	−	1.24751i	0.960901	−	0.276894i	$-0.0893051\pi$
$390$		0			0
$391$	14.8148			0.749216
$392$	−17.4635	−	12.3629i	−0.882038	−	0.624420i
$393$		0			0
$394$	5.47446	+	9.48204i	0.275799	+	0.477698i
$395$	2.11875	+	1.22326i	0.106606	+	0.0615489i
$396$		0			0
$397$	8.53825	−	4.92956i	0.428522	−	0.247408i	−0.270195	−	0.962806i	$-0.587088\pi$
$397$	8.53825	−	4.92956i	0.428522	−	0.247408i	0.698717	+	0.715398i	$0.253755\pi$
$398$			12.7945i			0.641332i
$399$		0			0
$400$	−7.29510			−0.364755
$401$	10.9287	−	6.30971i	0.545756	−	0.315092i	−0.201653	−	0.979457i	$-0.564631\pi$
$401$	10.9287	−	6.30971i	0.545756	−	0.315092i	0.747408	+	0.664365i	$0.231298\pi$
$402$		0			0
$403$	−10.9195	+	11.4618i	−0.543938	+	0.570950i
$404$	7.35460	+	12.7385i	0.365905	+	0.633766i
$405$		0			0
$406$	10.1041	−	15.7702i	0.501456	−	0.782663i
$407$	−0.299994			−0.0148701
$408$		0			0
$409$	15.6381	+	9.02867i	0.773255	+	0.446439i	0.834035	−	0.551712i	$-0.186025\pi$
$409$	15.6381	+	9.02867i	0.773255	+	0.446439i	−0.0607793	+	0.998151i	$0.519359\pi$
$410$	2.91537	+	1.68319i	0.143980	+	0.0831268i
$411$		0			0
$412$	9.17691			0.452114
$413$	−26.0677	−	1.20555i	−1.28271	−	0.0593214i
$414$		0			0
$415$	3.19080	+	5.52663i	0.156630	+	0.271291i
$416$	10.9797	−	11.5250i	0.538324	−	0.565058i
$417$		0			0
$418$	3.42562	−	1.97778i	0.167553	−	0.0967366i
$419$	−14.2805			−0.697647			−0.348823	−	0.937188i	$-0.613419\pi$
$419$	−14.2805			−0.697647			−0.348823	+	0.937188i	$0.613419\pi$
$420$		0			0
$421$			4.27439i			0.208321i	0.994561	+	0.104160i	$0.0332155\pi$
$421$			4.27439i			0.208321i	−0.994561	+	0.104160i	$0.966784\pi$
$422$	14.4870	−	8.36410i	0.705218	−	0.407158i
$423$		0			0
$424$	1.84534	+	1.06541i	0.0896175	+	0.0517407i
$425$	7.70398	+	13.3437i	0.373698	+	0.647263i
$426$		0			0
$427$	10.4639	+	6.70425i	0.506382	+	0.324441i
$428$	5.19042			0.250888
$429$		0			0
$430$	−3.76028	+	6.51300i	−0.181337	+	0.314085i
$431$	12.6498	+	7.30335i	0.609318	+	0.351790i	0.772698	−	0.634773i	$-0.218906\pi$
$431$	12.6498	+	7.30335i	0.609318	+	0.351790i	−0.163381	+	0.986563i	$0.552240\pi$
$432$		0			0
$433$	28.0099			1.34607			0.673035	−	0.739611i	$-0.264991\pi$
$433$	28.0099			1.34607			0.673035	+	0.739611i	$0.264991\pi$
$434$	−11.0715	+	5.72718i	−0.531449	+	0.274914i
$435$		0			0
$436$	−8.37688	+	4.83640i	−0.401180	+	0.231621i
$437$	19.9667	+	11.5278i	0.955137	+	0.551448i
$438$		0			0
$439$	8.53872	+	14.7895i	0.407531	+	0.705864i	0.994612	−	0.103664i	$-0.0330566\pi$
$439$	8.53872	+	14.7895i	0.407531	+	0.705864i	−0.587082	+	0.809528i	$0.699723\pi$
$440$			1.35450i			0.0645733i
$441$		0			0
$442$	12.5711	+	3.04407i	0.597947	+	0.144792i
$443$	6.90783	+	11.9647i	0.328201	+	0.568461i	0.982155	−	0.188073i	$-0.0602243\pi$
$443$	6.90783	+	11.9647i	0.328201	+	0.568461i	−0.653954	+	0.756534i	$0.726891\pi$
$444$		0			0
$445$	4.18386	−	7.24665i	0.198334	−	0.343524i
$446$	3.63048	+	6.28817i	0.171908	+	0.297754i
$447$		0			0
$448$	18.5718	−	9.60703i	0.877436	−	0.453890i
$449$			32.6410i			1.54042i	0.637789	+	0.770211i	$0.279849\pi$
$449$			32.6410i			1.54042i	−0.637789	+	0.770211i	$0.720151\pi$
$450$		0			0
$451$	−1.77698	+	3.07783i	−0.0836749	+	0.144929i
$452$	−0.391801	+	0.678619i	−0.0184287	+	0.0319195i
$453$		0			0
$454$	−18.0536			−0.847298
$455$	4.12499	+	4.31051i	0.193382	+	0.202080i
$456$		0			0
$457$	−2.74559	+	1.58517i	−0.128433	+	0.0741511i	−0.562840	−	0.826566i	$-0.690291\pi$
$457$	−2.74559	+	1.58517i	−0.128433	+	0.0741511i	0.434407	+	0.900717i	$0.356958\pi$
$458$	5.91560	−	10.2461i	0.276418	−	0.478769i
$459$		0			0
$460$	−2.03672	+	1.17590i	−0.0949625	+	0.0548266i
$461$			0.202023i			0.00940915i	0.999989	+	0.00470458i	$0.00149752\pi$
$461$			0.202023i			0.00940915i	−0.999989	+	0.00470458i	$0.998502\pi$
$462$		0			0
$463$			17.2121i			0.799912i	0.916534	+	0.399956i	$0.130975\pi$
$463$			17.2121i			0.799912i	−0.916534	+	0.399956i	$0.869025\pi$
$464$	5.22112	+	9.04325i	0.242384	+	0.419822i
$465$		0			0
$466$	16.1277	+	9.31136i	0.747103	+	0.431340i
$467$	0.0955845	+	0.165557i	0.00442312	+	0.00766108i	0.868228	−	0.496165i	$-0.165259\pi$
$467$	0.0955845	+	0.165557i	0.00442312	+	0.00766108i	−0.863805	+	0.503826i	$0.831925\pi$
$468$		0			0
$469$	−27.5415	−	1.27371i	−1.27175	−	0.0588146i
$470$		−	5.41777i		−	0.249903i
$471$		0			0
$472$	15.0742	−	26.1092i	0.693845	−	1.20177i
$473$	−6.87593	−	3.96982i	−0.316156	−	0.182533i
$474$		0			0
$475$			23.9787i			1.10022i
$476$	−6.31968	−	4.04905i	−0.289662	−	0.185588i
$477$		0			0
$478$	10.5816	+	18.3278i	0.483989	+	0.838294i
$479$	−18.6009	−	10.7392i	−0.849897	−	0.490688i	0.0107189	−	0.999943i	$-0.496588\pi$
$479$	−18.6009	−	10.7392i	−0.849897	−	0.490688i	−0.860616	+	0.509254i	$0.829921\pi$
$480$		0			0
$481$	−0.430721	−	1.46460i	−0.0196392	−	0.0667800i
$482$	−2.98752			−0.136078
$483$		0			0
$484$	8.90811			0.404914
$485$	0.0631758	+	0.109424i	0.00286867	+	0.00496868i
$486$		0			0
$487$	−16.4964	−	9.52422i	−0.747525	−	0.431584i	0.0772740	−	0.997010i	$-0.475378\pi$
$487$	−16.4964	−	9.52422i	−0.747525	−	0.431584i	−0.824799	+	0.565426i	$0.808712\pi$
$488$	−12.4339	+	7.17871i	−0.562856	+	0.324965i
$489$		0			0
$490$	1.96340	+	4.26790i	0.0886973	+	0.192804i
$491$	35.7559			1.61364			0.806821	−	0.590796i	$-0.201186\pi$
$491$	35.7559			1.61364			0.806821	+	0.590796i	$0.201186\pi$
$492$		0			0
$493$	11.0275	−	19.1002i	0.496654	−	0.860230i
$494$	14.5741	+	13.8846i	0.655721	+	0.624697i
$495$		0			0
$496$		−	6.94968i		−	0.312050i
$497$	17.1251	+	33.1053i	0.768164	+	1.48497i
$498$		0			0
$499$	15.3192	−	8.84457i	0.685784	−	0.395937i	−0.116247	−	0.993220i	$-0.537086\pi$
$499$	15.3192	−	8.84457i	0.685784	−	0.395937i	0.802031	+	0.597283i	$0.203753\pi$
$500$	−4.41632	−	2.54976i	−0.197504	−	0.114029i
$501$		0			0
$502$	−21.8949	+	12.6410i	−0.977217	+	0.564196i
$503$	−11.3305			−0.505203			−0.252601	−	0.967570i	$-0.581286\pi$
$503$	−11.3305			−0.505203			−0.252601	+	0.967570i	$0.581286\pi$
$504$		0			0
$505$		−	10.8415i		−	0.482441i
$506$	1.68456	+	2.91774i	0.0748878	+	0.129709i
$507$		0			0
$508$	−3.61048	+	6.25353i	−0.160189	+	0.277455i
$509$	16.7588	−	9.67569i	0.742821	−	0.428868i	−0.0802734	−	0.996773i	$-0.525579\pi$
$509$	16.7588	−	9.67569i	0.742821	−	0.428868i	0.823094	+	0.567905i	$0.192246\pi$
$510$		0			0
$511$	−13.4362	−	0.621384i	−0.594382	−	0.0274884i
$512$			16.6645i			0.736472i
$513$		0			0
$514$	−3.18961	−	1.84152i	−0.140687	−	0.0812259i
$515$	−5.85772	−	3.38195i	−0.258122	−	0.149027i
$516$		0			0
$517$	5.71967			0.251551
$518$	0.0555330	−	1.20079i	0.00243998	−	0.0527597i
$519$		0			0
$520$	−6.61280	+	1.94474i	−0.289991	+	0.0852827i
$521$	−3.85550	+	6.67791i	−0.168912	+	0.292565i	−0.938038	−	0.346533i	$-0.887359\pi$
$521$	−3.85550	+	6.67791i	−0.168912	+	0.292565i	0.769125	+	0.639098i	$0.220692\pi$
$522$		0			0
$523$	17.5251	+	30.3543i	0.766317	+	1.32730i	0.939547	+	0.342419i	$0.111246\pi$
$523$	17.5251	+	30.3543i	0.766317	+	1.32730i	−0.173230	+	0.984881i	$0.555420\pi$
$524$	5.94246			0.259597
$525$		0			0
$526$		−	23.0160i		−	1.00355i
$527$	−12.7119	+	7.33919i	−0.553737	+	0.319700i
$528$		0			0
$529$	1.68133	−	2.91214i	0.0731011	−	0.126615i
$530$	−0.233922	−	0.405165i	−0.0101609	−	0.0175992i
$531$		0			0
$532$	−5.36671	−	10.3746i	−0.232676	−	0.449797i
$533$	−17.5776	−	4.25637i	−0.761370	−	0.184364i
$534$		0			0
$535$	−3.31309	−	1.91282i	−0.143238	−	0.0826982i
$536$	15.9264	−	27.5854i	0.687917	−	1.19151i
$537$		0			0
$538$			15.7276i			0.678066i
$539$	−4.50573	+	2.07281i	−0.194075	+	0.0892821i
$540$		0			0
$541$	−10.5079	+	6.06674i	−0.451770	+	0.260829i	−0.708577	−	0.705633i	$-0.750663\pi$
$541$	−10.5079	+	6.06674i	−0.451770	+	0.260829i	0.256807	+	0.966463i	$0.417329\pi$
$542$	−1.09648	+	1.89916i	−0.0470978	+	0.0815758i
$543$		0			0
$544$	12.7820	−	7.37967i	0.548022	−	0.316401i
$545$	7.12940			0.305390
$546$		0			0
$547$	−5.12546			−0.219149			−0.109575	−	0.993979i	$-0.534949\pi$
$547$	−5.12546			−0.219149			−0.109575	+	0.993979i	$0.534949\pi$
$548$	4.56864	−	2.63770i	0.195162	−	0.112677i
$549$		0			0
$550$	−1.75201	+	3.03457i	−0.0747058	+	0.129394i
$551$	29.7248	−	17.1616i	1.26632	−	0.731109i
$552$		0			0
$553$	−8.71427	−	5.58327i	−0.370568	−	0.237425i
$554$		−	5.83051i		−	0.247715i
$555$		0			0
$556$	−2.77112	+	4.79972i	−0.117522	+	0.203554i
$557$	−32.5267	−	18.7793i	−1.37820	−	0.795705i	−0.386258	−	0.922391i	$-0.626233\pi$
$557$	−32.5267	−	18.7793i	−1.37820	−	0.795705i	−0.991943	+	0.126686i	$0.959566\pi$
$558$		0			0
$559$	9.50884	−	39.2687i	0.402181	−	1.66089i
$560$	−2.61641	−	0.121001i	−0.110563	−	0.00511323i
$561$		0			0
$562$	−10.8569	−	18.8048i	−0.457973	−	0.793232i
$563$	−14.3504	+	24.8557i	−0.604799	+	1.04754i	0.387284	+	0.921960i	$0.373413\pi$
$563$	−14.3504	+	24.8557i	−0.604799	+	1.04754i	−0.992083	+	0.125583i	$0.959920\pi$
$564$		0			0
$565$	0.500180	−	0.288779i	0.0210428	−	0.0121490i
$566$			1.86195i			0.0782636i
$567$		0			0
$568$	−43.0610			−1.80680
$569$	−8.97417	−	15.5437i	−0.376217	−	0.651627i	0.614291	−	0.789079i	$-0.289442\pi$
$569$	−8.97417	−	15.5437i	−0.376217	−	0.651627i	−0.990508	+	0.137452i	$0.956109\pi$
$570$		0			0
$571$	8.91370	−	15.4390i	0.373027	−	0.646101i	−0.617003	−	0.786961i	$-0.711653\pi$
$571$	8.91370	−	15.4390i	0.373027	−	0.646101i	0.990030	+	0.140860i	$0.0449867\pi$
$572$	−0.611601	−	2.07965i	−0.0255723	−	0.0869547i
$573$		0			0
$574$	−11.9907	−	7.68250i	−0.500483	−	0.320662i
$575$	−20.4236			−0.851724
$576$		0			0
$577$	−28.6282	−	16.5285i	−1.19181	−	0.688091i	−0.233092	−	0.972455i	$-0.574884\pi$
$577$	−28.6282	−	16.5285i	−1.19181	−	0.688091i	−0.958717	+	0.284363i	$0.908218\pi$
$578$	−5.41170	−	3.12445i	−0.225097	−	0.129960i
$579$		0			0
$580$			3.50117i			0.145378i
$581$	−12.4035	−	23.9778i	−0.514584	−	0.994766i
$582$		0			0
$583$	0.427742	−	0.246957i	0.0177153	−	0.0102279i
$584$	7.76975	−	13.4576i	0.321515	−	0.556880i
$585$		0			0
$586$	−14.6172	−	25.3178i	−0.603832	−	1.04587i
$587$		−	14.7295i		−	0.607953i	−0.952680	−	0.303976i	$-0.901686\pi$
$587$		−	14.7295i		−	0.607953i	0.952680	−	0.303976i	$-0.0983144\pi$
$588$		0			0
$589$	−22.8433			−0.941241
$590$	−5.73258	+	3.30970i	−0.236006	+	0.136258i
$591$		0			0
$592$	0.580404	+	0.335097i	0.0238545	+	0.0137724i
$593$	−7.97598	+	4.60494i	−0.327534	+	0.189102i	−0.654746	−	0.755849i	$-0.727224\pi$
$593$	−7.97598	+	4.60494i	−0.327534	+	0.189102i	0.327212	+	0.944951i	$0.393891\pi$
$594$		0			0
$595$	2.54172	+	4.91353i	0.104201	+	0.201435i
$596$		−	3.13743i		−	0.128514i
$597$		0			0
$598$	−11.8261	+	12.4134i	−0.483604	+	0.507621i
$599$	−5.28727	+	9.15782i	−0.216032	+	0.374178i	−0.953591	−	0.301104i	$-0.902645\pi$
$599$	−5.28727	+	9.15782i	−0.216032	+	0.374178i	0.737559	+	0.675282i	$0.235978\pi$
$600$		0			0
$601$	4.08916			0.166800			0.0834001	−	0.996516i	$-0.473422\pi$
$601$	4.08916			0.166800			0.0834001	+	0.996516i	$0.473422\pi$
$602$	17.1629	−	26.7875i	0.699507	−	1.09178i
$603$		0			0
$604$	−3.58450	+	2.06951i	−0.145851	+	0.0842072i
$605$	−5.68613	−	3.28289i	−0.231174	−	0.133469i
$606$		0			0
$607$	−1.80353	−	3.12380i	−0.0732030	−	0.126791i	0.827100	−	0.562054i	$-0.189989\pi$
$607$	−1.80353	−	3.12380i	−0.0732030	−	0.126791i	−0.900303	+	0.435263i	$0.856655\pi$
$608$	22.9693			0.931527
$609$		0			0
$610$	3.15233			0.127634
$611$	8.21211	+	27.9240i	0.332226	+	1.12968i
$612$		0			0
$613$	33.3285	+	19.2422i	1.34613	+	0.777186i	0.987698	−	0.156371i	$-0.0499796\pi$
$613$	33.3285	+	19.2422i	1.34613	+	0.777186i	0.358428	+	0.933557i	$0.383313\pi$
$614$	6.82128	+	11.8148i	0.275284	+	0.476806i
$615$		0			0
$616$	0.264709	−	5.72379i	0.0106654	−	0.230618i
$617$			3.09503i			0.124601i	0.998057	+	0.0623007i	$0.0198438\pi$
$617$			3.09503i			0.124601i	−0.998057	+	0.0623007i	$0.980156\pi$
$618$		0			0
$619$	10.6255	+	6.13462i	0.427074	+	0.246571i	0.698099	−	0.716001i	$-0.254029\pi$
$619$	10.6255	+	6.13462i	0.427074	+	0.246571i	−0.271025	+	0.962572i	$0.587363\pi$
$620$	1.16507	−	2.01797i	0.0467905	−	0.0810435i
$621$		0			0
$622$		−	10.3215i		−	0.413854i
$623$	−19.0962	+	29.8050i	−0.765073	+	1.19411i
$624$		0			0
$625$	−9.64277	−	16.7018i	−0.385711	−	0.668071i
$626$	−8.38730	−	4.84241i	−0.335224	−	0.193542i
$627$		0			0
$628$	4.03897	+	6.99571i	0.161173	+	0.279159i
$629$		−	1.41551i		−	0.0564402i
$630$		0			0
$631$			5.31780i			0.211698i	0.994382	+	0.105849i	$0.0337561\pi$
$631$			5.31780i			0.211698i	−0.994382	+	0.105849i	$0.966244\pi$
$632$	10.3549	−	5.97840i	0.411896	−	0.237808i
$633$		0			0
$634$	13.2126	−	22.8849i	0.524740	−	0.908877i
$635$	4.60921	−	2.66113i	0.182911	−	0.105604i
$636$		0			0
$637$	−16.5888	−	19.0213i	−0.657273	−	0.753653i
$638$	5.01566			0.198572
$639$		0			0
$640$	−0.109212	+	0.189160i	−0.00431697	+	0.00747721i
$641$	−6.09521	+	10.5572i	−0.240746	+	0.416985i	−0.960927	−	0.276801i	$-0.910726\pi$
$641$	−6.09521	+	10.5572i	−0.240746	+	0.416985i	0.720181	+	0.693787i	$0.244059\pi$
$642$		0			0
$643$		−	18.9733i		−	0.748235i	−0.927381	−	0.374117i	$-0.877946\pi$
$643$		−	18.9733i		−	0.748235i	0.927381	−	0.374117i	$-0.122054\pi$
$644$	8.83649	−	4.57104i	0.348207	−	0.180124i
$645$		0			0
$646$	9.33211	+	16.1637i	0.367167	+	0.635952i
$647$	−9.85587	+	17.0709i	−0.387474	+	0.671125i	−0.992109	−	0.125378i	$-0.959986\pi$
$647$	−9.85587	+	17.0709i	−0.387474	+	0.671125i	0.604635	+	0.796503i	$0.293319\pi$
$648$		0			0
$649$	−3.49414	−	6.05202i	−0.137157	−	0.237563i
$650$	−17.3305	−	4.19655i	−0.679759	−	0.164602i
$651$		0			0
$652$		−	20.1182i		−	0.787891i
$653$	−10.1986	−	17.6645i	−0.399103	−	0.691267i	0.594512	−	0.804087i	$-0.297345\pi$
$653$	−10.1986	−	17.6645i	−0.399103	−	0.691267i	−0.993616	+	0.112819i	$0.964012\pi$
$654$		0			0
$655$	−3.79313	−	2.18996i	−0.148210	−	0.0855690i
$656$	6.87593	−	3.96982i	0.268460	−	0.154996i
$657$		0			0
$658$	−1.05879	+	22.8942i	−0.0412759	+	0.892509i
$659$	−32.6628			−1.27236			−0.636181	−	0.771540i	$-0.719487\pi$
$659$	−32.6628			−1.27236			−0.636181	+	0.771540i	$0.719487\pi$
$660$		0			0
$661$	−8.43242	−	4.86846i	−0.327983	−	0.189361i	0.326962	−	0.945037i	$-0.393975\pi$
$661$	−8.43242	−	4.86846i	−0.327983	−	0.189361i	−0.654945	+	0.755676i	$0.727308\pi$
$662$	−7.06704	+	12.2405i	−0.274668	+	0.475740i
$663$		0			0
$664$	31.1886			1.21035
$665$	−0.397725	+	8.60002i	−0.0154231	+	0.333494i
$666$		0			0
$667$	14.6172	+	25.3178i	0.565981	+	0.980308i
$668$	0.831819	+	0.480251i	0.0321841	+	0.0185815i
$669$		0			0
$670$	−6.05668	+	3.49683i	−0.233990	+	0.135094i
$671$			3.32800i			0.128476i
$672$		0			0
$673$	−39.4512			−1.52073			−0.760367	−	0.649494i	$-0.774981\pi$
$673$	−39.4512			−1.52073			−0.760367	+	0.649494i	$0.774981\pi$
$674$	−15.8265	+	9.13742i	−0.609613	+	0.351960i
$675$		0			0
$676$	9.27496	−	5.97179i	0.356729	−	0.229684i
$677$	−24.3169	−	42.1182i	−0.934576	−	1.61873i	−0.775389	−	0.631484i	$-0.782446\pi$
$677$	−24.3169	−	42.1182i	−0.934576	−	1.61873i	−0.159187	−	0.987248i	$-0.550887\pi$
$678$		0			0
$679$	−0.245582	−	0.474745i	−0.00942455	−	0.0182191i
$680$	−6.39117			−0.245090
$681$		0			0
$682$	−2.89088	−	1.66905i	−0.110697	−	0.0639112i
$683$	−4.94304	−	2.85387i	−0.189140	−	0.109200i	0.402440	−	0.915446i	$-0.368162\pi$
$683$	−4.94304	−	2.85387i	−0.189140	−	0.109200i	−0.591580	+	0.806246i	$0.701496\pi$
$684$		0			0
$685$	−3.88828			−0.148563
$686$	−7.46278	−	18.4188i	−0.284930	−	0.703234i
$687$		0			0
$688$	8.86867	+	15.3610i	0.338115	+	0.585632i
$689$	1.81981	+	1.73371i	0.0693291	+	0.0660490i
$690$		0			0
$691$	−36.1766	+	20.8866i	−1.37622	+	0.794563i	−0.991703	−	0.128553i	$-0.958967\pi$
$691$	−36.1766	+	20.8866i	−1.37622	+	0.794563i	−0.384521	+	0.923116i	$0.625633\pi$
$692$	10.1734			0.386736
$693$		0			0
$694$			0.493517i			0.0187336i
$695$	3.53767	−	2.04247i	0.134191	−	0.0774754i
$696$		0			0
$697$	−14.5226	−	8.38464i	−0.550084	−	0.317591i
$698$	−3.69035	−	6.39188i	−0.139682	−	0.241936i
$699$		0			0
$700$	8.71229	+	5.58200i	0.329294	+	0.210980i
$701$	−22.4361			−0.847399			−0.423700	−	0.905803i	$-0.639269\pi$
$701$	−22.4361			−0.847399			−0.423700	+	0.905803i	$0.639269\pi$
$702$		0			0
$703$	1.10145	−	1.90776i	0.0415419	−	0.0719527i
$704$	4.84929	+	2.79974i	0.182764	+	0.105519i
$705$		0			0
$706$	−1.64527			−0.0619207
$707$	−2.11875	+	45.8137i	−0.0796837	+	1.72300i
$708$		0			0
$709$	24.8955	−	14.3734i	0.934969	−	0.539804i	0.0465891	−	0.998914i	$-0.485165\pi$
$709$	24.8955	−	14.3734i	0.934969	−	0.539804i	0.888380	+	0.459110i	$0.151832\pi$
$710$	8.18785	+	4.72726i	0.307285	+	0.177411i
$711$		0			0
$712$	−20.4476	−	35.4163i	−0.766307	−	1.32728i
$713$		−	19.4566i		−	0.728654i
$714$		0			0
$715$	−0.376021	+	1.55286i	−0.0140624	+	0.0580735i
$716$	−4.01822	−	6.95976i	−0.150168	−	0.260098i
$717$		0			0
$718$	14.5972	−	25.2830i	0.544762	−	0.943555i
$719$	2.10450	+	3.64509i	0.0784844	+	0.135939i	0.902596	−	0.430488i	$-0.141659\pi$
$719$	2.10450	+	3.64509i	0.0784844	+	0.135939i	−0.824112	+	0.566427i	$0.808325\pi$
$720$		0			0
$721$	24.0924	+	15.4361i	0.897247	+	0.574870i
$722$			8.65821i			0.322225i
$723$		0			0
$724$	4.85008	−	8.40058i	0.180252	−	0.312205i
$725$	−15.2025	+	26.3315i	−0.564606	+	0.977927i
$726$		0			0
$727$	−43.4680			−1.61214			−0.806070	−	0.591820i	$-0.798409\pi$
$727$	−43.4680			−1.61214			−0.806070	+	0.591820i	$0.798409\pi$
$728$	28.3242	−	6.92569i	1.04976	−	0.256683i
$729$		0			0
$730$	−2.95477	+	1.70594i	−0.109361	+	0.0631396i
$731$	18.7315	−	32.4439i	0.692809	−	1.19998i
$732$		0			0
$733$	−7.87581	+	4.54710i	−0.290900	+	0.167951i	−0.638348	−	0.769748i	$-0.720382\pi$
$733$	−7.87581	+	4.54710i	−0.290900	+	0.167951i	0.347448	+	0.937699i	$0.387048\pi$
$734$		−	28.9525i		−	1.06866i
$735$		0			0
$736$			19.5639i			0.721133i
$737$	−3.69169	−	6.39419i	−0.135985	−	0.235533i
$738$		0			0
$739$	−8.32135	−	4.80433i	−0.306106	−	0.176730i	0.339077	−	0.940759i	$-0.389885\pi$
$739$	−8.32135	−	4.80433i	−0.306106	−	0.176730i	−0.645183	+	0.764028i	$0.723219\pi$
$740$	0.112354	+	0.194603i	0.00413022	+	0.00715375i
$741$		0			0
$742$	0.909317	+	1.75784i	0.0333821	+	0.0645325i
$743$			32.1771i			1.18046i	0.807234	+	0.590231i	$0.200964\pi$
$743$			32.1771i			1.18046i	−0.807234	+	0.590231i	$0.799036\pi$
$744$		0			0
$745$	−1.15623	+	2.00265i	−0.0423610	+	0.0733714i
$746$	3.69150	+	2.13129i	0.135155	+	0.0780320i
$747$		0			0
$748$		−	2.00995i		−	0.0734911i
$749$	13.6265	+	8.73058i	0.497903	+	0.319008i
$750$		0			0
$751$	3.89892	+	6.75313i	0.142274	+	0.246425i	0.928352	−	0.371701i	$-0.121225\pi$
$751$	3.89892	+	6.75313i	0.142274	+	0.246425i	−0.786079	+	0.618126i	$0.787892\pi$
$752$	−11.0660	−	6.38894i	−0.403534	−	0.232981i
$753$		0			0
$754$	7.20132	+	24.4870i	0.262256	+	0.891762i
$755$	3.05070			0.111026
$756$		0			0
$757$	17.9970			0.654110			0.327055	−	0.945005i	$-0.393944\pi$
$757$	17.9970			0.654110			0.327055	+	0.945005i	$0.393944\pi$
$758$	6.11960	+	10.5995i	0.222274	+	0.384990i
$759$		0			0
$760$	−8.61373	−	4.97314i	−0.312453	−	0.180395i
$761$	−35.2290	+	20.3395i	−1.27705	+	0.737306i	−0.976305	−	0.216398i	$-0.930569\pi$
$761$	−35.2290	+	20.3395i	−1.27705	+	0.737306i	−0.300746	+	0.953704i	$0.597236\pi$
$762$		0			0
$763$	−30.1271	−	1.39329i	−1.09068	−	0.0504406i
$764$	−13.3117			−0.481601
$765$		0			0
$766$	−12.7650	+	22.1097i	−0.461220	+	0.798856i
$767$	24.5298	−	25.7480i	0.885720	−	0.929707i
$768$		0			0
$769$			39.3098i			1.41755i	0.705435	+	0.708774i	$0.250752\pi$
$769$			39.3098i			1.41755i	−0.705435	+	0.708774i	$0.749248\pi$
$770$	−0.678695	+	1.05929i	−0.0244585	+	0.0381743i
$771$		0			0
$772$	16.9072	−	9.76138i	0.608504	−	0.351320i
$773$	11.6685	+	6.73679i	0.419685	+	0.242306i	0.694943	−	0.719065i	$-0.255430\pi$
$773$	11.6685	+	6.73679i	0.419685	+	0.242306i	−0.275257	+	0.961371i	$0.588763\pi$
$774$		0			0
$775$	17.5245	−	10.1178i	0.629500	−	0.363442i
$776$	0.617515			0.0221675
$777$		0			0
$778$			30.4866i			1.09300i
$779$	−13.0486	−	22.6009i	−0.467516	−	0.809761i
$780$		0			0
$781$	−4.99068	+	8.64412i	−0.178581	+	0.309311i
$782$	−13.7673	+	7.94854i	−0.492316	+	0.284239i
$783$		0			0
$784$	11.0327	+	1.02264i	0.394024	+	0.0365230i
$785$		−	5.95391i		−	0.212504i
$786$		0			0
$787$	34.4930	+	19.9145i	1.22954	+	0.709877i	0.966934	−	0.255026i	$-0.0820839\pi$
$787$	34.4930	+	19.9145i	1.22954	+	0.709877i	0.262608	+	0.964903i	$0.415417\pi$
$788$	7.49823	+	4.32911i	0.267114	+	0.154218i
$789$		0			0
$790$	−2.62525			−0.0934022
$791$	−2.17008	+	1.12256i	−0.0771592	+	0.0399137i
$792$		0			0
$793$	−16.2476	+	4.77823i	−0.576970	+	0.169680i
$794$	−5.28969	+	9.16201i	−0.187724	+	0.325148i
$795$		0			0
$796$	5.05884	+	8.76217i	0.179306	+	0.310567i
$797$	−21.2530			−0.752821			−0.376410	−	0.926453i	$-0.622842\pi$
$797$	−21.2530			−0.752821			−0.376410	+	0.926453i	$0.622842\pi$
$798$		0			0
$799$			26.9881i			0.954770i
$800$	−17.6212	+	10.1736i	−0.623003	+	0.359691i
$801$		0			0
$802$	−6.77067	+	11.7271i	−0.239081	+	0.414100i
$803$	−1.80100	−	3.11942i	−0.0635559	−	0.110082i
$804$		0			0
$805$	−7.32498	−	0.338759i	−0.258172	−	0.0119397i
$806$	3.99784	−	16.5099i	0.140818	−	0.581537i
$807$		0			0
$808$	−45.8867	−	26.4927i	−1.61429	−	0.932010i
$809$	10.7088	−	18.5481i	0.376500	−	0.652117i	−0.614050	−	0.789267i	$-0.710461\pi$
$809$	10.7088	−	18.5481i	0.376500	−	0.652117i	0.990550	+	0.137150i	$0.0437942\pi$
$810$		0			0
$811$		−	11.0116i		−	0.386669i	−0.981133	−	0.193335i	$-0.938070\pi$
$811$		−	11.0116i		−	0.386669i	0.981133	−	0.193335i	$-0.0619303\pi$
$812$	0.684230	−	14.7951i	0.0240118	−	0.519206i
$813$		0			0
$814$	0.278782	−	0.160955i	0.00977131	−	0.00564147i
$815$	−7.41414	+	12.8417i	−0.259706	+	0.449824i
$816$		0			0
$817$	50.4909	−	29.1509i	1.76645	−	1.01986i
$818$	−19.3765			−0.677484
$819$		0			0
$820$	2.66207			0.0929636
$821$	33.4879	−	19.3342i	1.16873	−	0.674769i	0.215353	−	0.976536i	$-0.430910\pi$
$821$	33.4879	−	19.3342i	1.16873	−	0.674769i	0.953382	+	0.301767i	$0.0975764\pi$
$822$		0			0
$823$	−10.2283	+	17.7160i	−0.356537	+	0.617540i	−0.987380	−	0.158371i	$-0.949376\pi$
$823$	−10.2283	+	17.7160i	−0.356537	+	0.617540i	0.630843	+	0.775911i	$0.282709\pi$
$824$	−28.6282	+	16.5285i	−0.997312	+	0.575798i
$825$		0			0
$826$	24.8713	−	12.8657i	0.865384	−	0.447655i
$827$			27.3451i			0.950881i	0.879748	+	0.475440i	$0.157711\pi$
$827$			27.3451i			0.950881i	−0.879748	+	0.475440i	$0.842289\pi$
$828$		0			0
$829$	−12.5043	+	21.6581i	−0.434292	+	0.752217i	−0.997238	−	0.0742776i	$-0.976335\pi$
$829$	−12.5043	+	21.6581i	−0.434292	+	0.752217i	0.562945	+	0.826494i	$0.309668\pi$
$830$	−5.93037	−	3.42390i	−0.205846	−	0.118845i
$831$		0			0
$832$	−6.70616	+	27.6945i	−0.232494	+	0.960133i
$833$	−9.78048	−	21.2601i	−0.338873	−	0.736620i
$834$		0			0
$835$	−0.353972	−	0.613098i	−0.0122497	−	0.0212171i
$836$	1.56400	−	2.70892i	0.0540920	−	0.0936900i
$837$		0			0
$838$	13.2707	−	7.66187i	0.458430	−	0.264675i
$839$			8.76981i			0.302768i	0.988475	+	0.151384i	$0.0483729\pi$
$839$			8.76981i			0.302768i	−0.988475	+	0.151384i	$0.951627\pi$
$840$		0			0
$841$	14.5218			0.500753
$842$	−2.29333	−	3.97216i	−0.0790332	−	0.136890i
$843$		0			0
$844$	6.61418	−	11.4561i	0.227669	−	0.394335i
$845$	−8.12107	+	0.393767i	−0.279373	+	0.0135460i
$846$		0			0
$847$	23.3867	+	14.9840i	0.803576	+	0.514855i
$848$	−1.10342			−0.0378914
$849$		0			0
$850$	−14.3185	−	8.26679i	−0.491120	−	0.283549i
$851$	1.62492	+	0.938148i	0.0557015	+	0.0321593i
$852$		0			0
$853$		−	19.8232i		−	0.678734i	−0.940654	−	0.339367i	$-0.889787\pi$
$853$		−	19.8232i		−	0.678734i	0.940654	−	0.339367i	$-0.110213\pi$
$854$	−13.3210	−	0.616058i	−0.455836	−	0.0210811i
$855$		0			0
$856$	−16.1920	+	9.34845i	−0.553431	+	0.319523i
$857$	1.33518	−	2.31261i	0.0456090	−	0.0789972i	−0.842320	−	0.538978i	$-0.818810\pi$
$857$	1.33518	−	2.31261i	0.0456090	−	0.0789972i	0.887929	+	0.459981i	$0.152144\pi$
$858$		0			0
$859$	19.4798	+	33.7401i	0.664644	+	1.15120i	0.979382	+	0.202018i	$0.0647500\pi$
$859$	19.4798	+	33.7401i	0.664644	+	1.15120i	−0.314738	+	0.949179i	$0.601917\pi$
$860$			5.94713i			0.202795i
$861$		0			0
$862$	−15.6738			−0.533851
$863$	21.4754	−	12.3988i	0.731030	−	0.422060i	−0.0877689	−	0.996141i	$-0.527974\pi$
$863$	21.4754	−	12.3988i	0.731030	−	0.422060i	0.818799	+	0.574081i	$0.194640\pi$
$864$		0			0
$865$	−6.49381	−	3.74920i	−0.220796	−	0.127477i
$866$	−26.0294	+	15.0281i	−0.884514	+	0.510675i
$867$		0			0
$868$	−5.31770	+	8.29976i	−0.180494	+	0.281712i
$869$		−	2.77154i		−	0.0940181i
$870$		0			0
$871$	25.9167	−	27.2037i	0.878153	−	0.921763i
$872$	17.4216	−	30.1752i	0.589971	−	1.02186i
$873$		0			0
$874$	−24.7399			−0.836839
$875$	−7.30542	−	14.1225i	−0.246968	−	0.477426i
$876$		0			0
$877$	1.71335	−	0.989201i	0.0578556	−	0.0334029i	−0.470793	−	0.882244i	$-0.656032\pi$
$877$	1.71335	−	0.989201i	0.0578556	−	0.0334029i	0.528649	+	0.848841i	$0.322699\pi$
$878$	−15.8699	−	9.16251i	−0.535584	−	0.309220i
$879$		0			0
$880$	−0.350706	−	0.607440i	−0.0118223	−	0.0204768i
$881$	17.1466			0.577683			0.288841	−	0.957377i	$-0.406730\pi$
$881$	17.1466			0.577683			0.288841	+	0.957377i	$0.406730\pi$
$882$		0			0
$883$	10.2168			0.343822			0.171911	−	0.985112i	$-0.445006\pi$
$883$	10.2168			0.343822			0.171911	+	0.985112i	$0.445006\pi$
$884$	9.81278	−	2.88582i	0.330039	−	0.0970606i
$885$		0			0
$886$	−12.8388	−	7.41248i	−0.431328	−	0.249027i
$887$	25.4965	+	44.1613i	0.856090	+	1.48279i	0.875630	+	0.482983i	$0.160447\pi$
$887$	25.4965	+	44.1613i	0.856090	+	1.48279i	−0.0195395	+	0.999809i	$0.506220\pi$
$888$		0			0
$889$	−19.9975	+	10.3445i	−0.670694	+	0.346944i
$890$			8.97901i			0.300977i
$891$		0			0
$892$	4.97258	+	2.87092i	0.166494	+	0.0961255i
$893$	−21.0002	+	36.3733i	−0.702743	+	1.21719i
$894$		0			0
$895$			5.92331i			0.197995i
$896$	0.498470	−	0.778003i	0.0166527	−	0.0259913i
$897$		0			0
$898$	−17.5128	−	30.3330i	−0.584409	−	1.01223i
$899$	−25.0847	−	14.4827i	−0.836621	−	0.483024i
$900$		0			0
$901$	1.16526	+	2.01829i	0.0388204	+	0.0672389i
$902$		−	3.81360i		−	0.126979i
$903$		0			0
$904$		−	2.82268i		−	0.0938811i
$905$	−6.19170	+	3.57478i	−0.205819	+	0.118830i
$906$		0			0
$907$	−2.89269	+	5.01028i	−0.0960501	+	0.166364i	−0.910046	−	0.414506i	$-0.863954\pi$
$907$	−2.89269	+	5.01028i	−0.0960501	+	0.166364i	0.813996	+	0.580870i	$0.197288\pi$
$908$	−12.3638	+	7.13824i	−0.410307	+	0.236891i
$909$		0			0
$910$	−6.14603	−	1.79256i	−0.203739	−	0.0594227i
$911$	1.70706			0.0565573			0.0282787	−	0.999600i	$-0.490997\pi$
$911$	1.70706			0.0565573			0.0282787	+	0.999600i	$0.490997\pi$
$912$		0			0
$913$	3.61470	−	6.26084i	0.119629	−	0.207204i
$914$	1.70097	−	2.94617i	0.0562632	−	0.0974507i
$915$		0			0
$916$		−	9.35590i		−	0.309128i
$917$	15.6009	+	9.99556i	0.515187	+	0.330082i
$918$		0			0
$919$	−18.6025	−	32.2205i	−0.613640	−	1.06286i	−0.990622	−	0.136634i	$-0.956371\pi$
$919$	−18.6025	−	32.2205i	−0.613640	−	1.06286i	0.376982	−	0.926221i	$-0.376962\pi$
$920$	4.23582	−	7.33666i	0.139651	−	0.241882i
$921$		0			0
$922$	−0.108391	−	0.187739i	−0.00356967	−	0.00618284i
$923$	−49.3669	−	11.9541i	−1.62493	−	0.393474i
$924$		0			0
$925$			1.95142i			0.0641623i
$926$	−9.23474	−	15.9950i	−0.303472	−	0.525630i
$927$		0			0
$928$	25.2230	+	14.5625i	0.827987	+	0.478038i
$929$	17.2379	−	9.95229i	0.565556	−	0.326524i	−0.189816	−	0.981820i	$-0.560789\pi$
$929$	17.2379	−	9.95229i	0.565556	−	0.326524i	0.755373	+	0.655296i	$0.227456\pi$
$930$		0			0
$931$	3.36139	−	36.2639i	0.110165	−	1.18850i
$932$	14.7265			0.482383
$933$		0			0
$934$	−0.177652	−	0.102567i	−0.00581295	−	0.00335611i
$935$	−0.740724	+	1.28297i	−0.0242243	+	0.0419577i
$936$		0			0
$937$	7.16949			0.234217			0.117109	−	0.993119i	$-0.462637\pi$
$937$	7.16949			0.234217			0.117109	+	0.993119i	$0.462637\pi$
$938$	26.2775	−	13.5931i	0.857990	−	0.443831i
$939$		0			0
$940$	−2.14214	−	3.71029i	−0.0698688	−	0.121016i
$941$	−2.65066	−	1.53036i	−0.0864091	−	0.0498883i	0.456173	−	0.889891i	$-0.349220\pi$
$941$	−2.65066	−	1.53036i	−0.0864091	−	0.0498883i	−0.542582	+	0.840003i	$0.682553\pi$
$942$		0			0
$943$	19.2501	−	11.1140i	0.626869	−	0.361923i
$944$			15.6120i			0.508126i
$945$		0			0
$946$	8.51968			0.276999
$947$	38.2832	−	22.1028i	1.24404	−	0.718244i	0.274122	−	0.961695i	$-0.411613\pi$
$947$	38.2832	−	22.1028i	1.24404	−	0.718244i	0.969913	+	0.243451i	$0.0782794\pi$
$948$		0			0
$949$	12.6435	−	13.2714i	0.410426	−	0.430809i
$950$	−12.8652	−	22.2832i	−0.417403	−	0.722963i
$951$		0			0
$952$	27.0075	+	1.24902i	0.875320	+	0.0404810i
$953$	−13.7002			−0.443791			−0.221896	−	0.975070i	$-0.571224\pi$
$953$	−13.7002			−0.443791			−0.221896	+	0.975070i	$0.571224\pi$
$954$		0			0
$955$	8.49700	+	4.90574i	0.274956	+	0.158746i
$956$	14.4933	+	8.36771i	0.468747	+	0.270631i
$957$		0			0
$958$	23.0476			0.744634
$959$	16.4309	+	0.759882i	0.530582	+	0.0245379i
$960$		0			0
$961$	−5.86129	−	10.1520i	−0.189074	−	0.327485i
$962$	1.18606	+	1.12995i	0.0382403	+	0.0364310i
$963$		0			0
$964$	−2.04597	+	1.18124i	−0.0658961	+	0.0380451i
$965$	−14.3894			−0.463211
$966$		0			0
$967$			43.9429i			1.41311i	0.707659	+	0.706554i	$0.249751\pi$
$967$			43.9429i			1.41311i	−0.707659	+	0.706554i	$0.750249\pi$
$968$	−27.7897	+	16.0444i	−0.893194	+	0.515686i
$969$		0			0
$970$	−0.117418	−	0.0677912i	−0.00377006	−	0.00217664i
$971$	−10.6585	−	18.4611i	−0.342049	−	0.592446i	0.642764	−	0.766064i	$-0.277788\pi$
$971$	−10.6585	−	18.4611i	−0.342049	−	0.592446i	−0.984813	+	0.173618i	$0.944454\pi$
$972$		0			0
$973$	−15.3485	+	7.93965i	−0.492050	+	0.254533i
$974$	20.4400			0.654941
$975$		0			0
$976$	3.71741	−	6.43874i	0.118991	−	0.206099i
$977$	14.2432	+	8.22330i	0.455679	+	0.263087i	0.710226	−	0.703974i	$-0.248593\pi$
$977$	14.2432	+	8.22330i	0.455679	+	0.263087i	−0.254547	+	0.967061i	$0.581926\pi$
$978$		0			0
$979$	−9.47937			−0.302962
$980$	3.03210	+	2.14651i	0.0968568	+	0.0685677i
$981$		0			0
$982$	−33.2277	+	19.1840i	−1.06034	+	0.612187i
$983$	10.1415	+	5.85521i	0.323464	+	0.186752i	0.652936	−	0.757413i	$-0.273537\pi$
$983$	10.1415	+	5.85521i	0.323464	+	0.186752i	−0.329471	+	0.944166i	$0.606871\pi$
$984$		0			0
$985$	−3.19080	−	5.52663i	−0.101667	−	0.176093i
$986$			23.6662i			0.753687i
$987$		0			0
$988$	15.4708	+	3.74621i	0.492190	+	0.119183i
$989$	24.8290	+	43.0051i	0.789517	+	1.36748i
$990$		0			0
$991$	15.6873	−	27.1713i	0.498325	−	0.863124i	−0.501673	−	0.865057i	$-0.667282\pi$
$991$	15.6873	−	27.1713i	0.498325	−	0.863124i	0.999998	+	0.00193305i	$0.000615311\pi$
$992$	−9.69187	−	16.7868i	−0.307717	−	0.532982i
$993$		0			0
$994$	−33.6761	−	21.5764i	−1.06814	−	0.684362i
$995$		−	7.45731i		−	0.236413i
$996$		0			0
$997$	2.34855	−	4.06781i	0.0743794	−	0.128829i	−0.826437	−	0.563029i	$-0.809636\pi$
$997$	2.34855	−	4.06781i	0.0743794	−	0.128829i	0.900816	+	0.434201i	$0.142969\pi$
$998$	−9.49071	+	16.4384i	−0.300423	+	0.520348i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.dl.e.298.3		16
3.2	odd	2		91.2.r.a.25.6	yes	16
7.2	even	3	inner	819.2.dl.e.415.6		16
13.12	even	2	inner	819.2.dl.e.298.6		16
21.2	odd	6		91.2.r.a.51.3	yes	16
21.5	even	6		637.2.r.f.324.3		16
21.11	odd	6		637.2.c.f.246.6		8
21.17	even	6		637.2.c.e.246.6		8
21.20	even	2		637.2.r.f.116.6		16
39.5	even	4		1183.2.e.i.508.3		16
39.8	even	4		1183.2.e.i.508.6		16
39.38	odd	2		91.2.r.a.25.3	✓	16
91.51	even	6	inner	819.2.dl.e.415.3		16
273.38	even	6		637.2.c.e.246.3		8
273.44	even	12		1183.2.e.i.170.3		16
273.86	even	12		1183.2.e.i.170.6		16
273.116	odd	6		637.2.c.f.246.3		8
273.122	odd	12		8281.2.a.cj.1.6		8
273.164	odd	12		8281.2.a.cj.1.3		8
273.194	even	6		637.2.r.f.324.6		16
273.200	even	12		8281.2.a.ck.1.6		8
273.233	odd	6		91.2.r.a.51.6	yes	16
273.242	even	12		8281.2.a.ck.1.3		8
273.272	even	2		637.2.r.f.116.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.r.a.25.3	✓	16	39.38	odd	2
91.2.r.a.25.6	yes	16	3.2	odd	2
91.2.r.a.51.3	yes	16	21.2	odd	6
91.2.r.a.51.6	yes	16	273.233	odd	6
637.2.c.e.246.3		8	273.38	even	6
637.2.c.e.246.6		8	21.17	even	6
637.2.c.f.246.3		8	273.116	odd	6
637.2.c.f.246.6		8	21.11	odd	6
637.2.r.f.116.3		16	273.272	even	2
637.2.r.f.116.6		16	21.20	even	2
637.2.r.f.324.3		16	21.5	even	6
637.2.r.f.324.6		16	273.194	even	6
819.2.dl.e.298.3		16	1.1	even	1	trivial
819.2.dl.e.298.6		16	13.12	even	2	inner
819.2.dl.e.415.3		16	91.51	even	6	inner
819.2.dl.e.415.6		16	7.2	even	3	inner
1183.2.e.i.170.3		16	273.44	even	12
1183.2.e.i.170.6		16	273.86	even	12
1183.2.e.i.508.3		16	39.5	even	4
1183.2.e.i.508.6		16	39.8	even	4
8281.2.a.cj.1.3		8	273.164	odd	12
8281.2.a.cj.1.6		8	273.122	odd	12
8281.2.a.ck.1.3		8	273.242	even	12
8281.2.a.ck.1.6		8	273.200	even	12

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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.dl (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.929293 + 0.536527i) q^{2} +(-0.424277 + 0.734868i) q^{4} +(0.541640 - 0.312716i) q^{5} +(-2.34996 + 1.21561i) q^{7} -3.05665i q^{8} +O(q^{10})\)	\(q+(-0.929293 + 0.536527i) q^{2} +(-0.424277 + 0.734868i) q^{4} +(0.541640 - 0.312716i) q^{5} +(-2.34996 + 1.21561i) q^{7} -3.05665i q^{8} +(-0.335561 + 0.581209i) q^{10} +(-0.613597 - 0.354260i) q^{11} +(0.848553 - 3.50428i) q^{13} +(1.53159 - 2.39047i) q^{14} +(0.791426 + 1.37079i) q^{16} +(1.67157 - 2.89524i) q^{17} +(4.50573 - 2.60138i) q^{19} +0.530712i q^{20} +0.760282 q^{22} +(2.21570 + 3.83771i) q^{23} +(-2.30442 + 3.99137i) q^{25} +(1.09159 + 3.71177i) q^{26} +(0.103717 - 2.24266i) q^{28} +6.59711 q^{29} +(-3.80238 - 2.19530i) q^{31} +(3.82335 + 2.20741i) q^{32} +3.58737i q^{34} +(-0.892689 + 1.39329i) q^{35} +(0.366683 - 0.211704i) q^{37} +(-2.79143 + 4.83489i) q^{38} +(-0.955864 - 1.65561i) q^{40} -5.01604i q^{41} +11.2059 q^{43} +(0.520670 - 0.300609i) q^{44} +(-4.11807 - 2.37757i) q^{46} +(-6.99116 + 4.03635i) q^{47} +(4.04458 - 5.71326i) q^{49} -4.94553i q^{50} +(2.21516 + 2.11036i) q^{52} +(-0.348553 + 0.603712i) q^{53} -0.443132 q^{55} +(3.71570 + 7.18300i) q^{56} +(-6.13065 + 3.53953i) q^{58} +(8.54177 + 4.93159i) q^{59} +(-2.34855 - 4.06781i) q^{61} +4.71136 q^{62} -7.90305 q^{64} +(-0.636233 - 2.16341i) q^{65} +(9.02470 + 5.21041i) q^{67} +(1.41841 + 2.45676i) q^{68} +(0.0820297 - 1.77373i) q^{70} -14.0876i q^{71} +(4.40273 + 2.54191i) q^{73} +(-0.227170 + 0.393471i) q^{74} +4.41482i q^{76} +(1.87257 + 0.0866008i) q^{77} +(1.95586 + 3.38766i) q^{79} +(0.857336 + 0.494983i) q^{80} +(2.69124 + 4.66137i) q^{82} +10.2035i q^{83} -2.09090i q^{85} +(-10.4136 + 6.01230i) q^{86} +(-1.08285 + 1.87555i) q^{88} +(11.5866 - 6.68955i) q^{89} +(2.26578 + 9.26640i) q^{91} -3.76028 q^{92} +(4.33122 - 7.50190i) q^{94} +(1.62699 - 2.81802i) q^{95} +0.202023i q^{97} +(-0.693276 + 7.47932i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{4}+O(q^{10}) \) 16 * q + 6 * q^4	\( 16 q + 6 q^{4} - 6 q^{10} - 12 q^{13} + 26 q^{14} + 2 q^{16} - 8 q^{17} - 36 q^{22} + 12 q^{23} + 6 q^{26} + 16 q^{29} - 34 q^{38} - 4 q^{40} + 16 q^{43} + 40 q^{49} - 42 q^{52} + 20 q^{53} + 24 q^{55} + 36 q^{56} - 12 q^{61} - 44 q^{62} + 88 q^{64} + 30 q^{65} + 2 q^{68} - 42 q^{74} + 76 q^{77} + 20 q^{79} - 16 q^{82} + 4 q^{88} + 56 q^{91} - 12 q^{92} - 26 q^{94} + 16 q^{95}+O(q^{100}) \) 16 * q + 6 * q^4 - 6 * q^10 - 12 * q^13 + 26 * q^14 + 2 * q^16 - 8 * q^17 - 36 * q^22 + 12 * q^23 + 6 * q^26 + 16 * q^29 - 34 * q^38 - 4 * q^40 + 16 * q^43 + 40 * q^49 - 42 * q^52 + 20 * q^53 + 24 * q^55 + 36 * q^56 - 12 * q^61 - 44 * q^62 + 88 * q^64 + 30 * q^65 + 2 * q^68 - 42 * q^74 + 76 * q^77 + 20 * q^79 - 16 * q^82 + 4 * q^88 + 56 * q^91 - 12 * q^92 - 26 * q^94 + 16 * q^95

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