LMFDB - Embedded newform 504.2.bk.b.19.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(19,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 0, 5]))

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

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

chi := DirichletCharacter("504.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.bk (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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.6
Character	$\chi$	$=$	504.19
Dual form			504.2.bk.b.451.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809233 + 1.15980i) q^{2} +(-0.690284 - 1.87710i) q^{4} +(-1.03180 + 1.78713i) q^{5} +(2.39181 - 1.13104i) q^{7} +(2.73567 + 0.718419i) q^{8} +O(q^{10})$	\(q+(-0.809233 + 1.15980i) q^{2} +(-0.690284 - 1.87710i) q^{4} +(-1.03180 + 1.78713i) q^{5} +(2.39181 - 1.13104i) q^{7} +(2.73567 + 0.718419i) q^{8} +(-1.23775 - 2.64289i) q^{10} +(-0.982155 - 1.70114i) q^{11} +4.20219 q^{13} +(-0.623755 + 3.68930i) q^{14} +(-3.04702 + 2.59146i) q^{16} +(3.09983 - 1.78969i) q^{17} +(-4.36777 - 2.52173i) q^{19} +(4.06686 + 0.703166i) q^{20} +(2.76778 + 0.237515i) q^{22} +(5.31120 + 3.06642i) q^{23} +(0.370777 + 0.642204i) q^{25} +(-3.40055 + 4.87371i) q^{26} +(-3.77410 - 3.70894i) q^{28} +6.34977i q^{29} +(3.42356 + 5.92978i) q^{31} +(-0.539841 - 5.63104i) q^{32} +(-0.432800 + 5.04346i) q^{34} +(-0.446563 + 5.44148i) q^{35} +(3.56564 + 2.05862i) q^{37} +(6.45925 - 3.02508i) q^{38} +(-4.10657 + 4.14773i) q^{40} +2.45849i q^{41} +4.33560 q^{43} +(-2.51525 + 3.01788i) q^{44} +(-7.85444 + 3.67849i) q^{46} +(4.88612 - 8.46301i) q^{47} +(4.44152 - 5.41045i) q^{49} +(-1.04487 - 0.0896650i) q^{50} +(-2.90070 - 7.88793i) q^{52} +(-11.2291 + 6.48313i) q^{53} +4.05355 q^{55} +(7.35576 - 1.37581i) q^{56} +(-7.36447 - 5.13844i) q^{58} +(6.17173 - 3.56325i) q^{59} +(-1.03175 + 1.78704i) q^{61} +(-9.64783 - 0.827920i) q^{62} +(6.96775 + 3.93071i) q^{64} +(-4.33582 + 7.50986i) q^{65} +(2.77372 + 4.80422i) q^{67} +(-5.49918 - 4.58330i) q^{68} +(-5.94967 - 4.92135i) q^{70} -9.44037i q^{71} +(-10.7122 + 6.18471i) q^{73} +(-5.27303 + 2.46953i) q^{74} +(-1.71855 + 9.93945i) q^{76} +(-4.27318 - 2.95796i) q^{77} +(0.778628 + 0.449541i) q^{79} +(-1.48737 - 8.11929i) q^{80} +(-2.85137 - 1.98949i) q^{82} -9.58499i q^{83} +7.38639i q^{85} +(-3.50851 + 5.02844i) q^{86} +(-1.46472 - 5.35936i) q^{88} +(-12.6502 - 7.30359i) q^{89} +(10.0508 - 4.75282i) q^{91} +(2.08975 - 12.0864i) q^{92} +(5.86141 + 12.5155i) q^{94} +(9.01332 - 5.20384i) q^{95} -0.550439i q^{97} +(2.68082 + 9.52959i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{4}+O(q^{10}) $ 32 * q + 2 * q^4	$ 32 q + 2 q^{4} + 18 q^{10} - 10 q^{16} - 12 q^{22} - 16 q^{25} - 6 q^{28} - 30 q^{40} + 16 q^{43} + 16 q^{46} + 8 q^{49} - 72 q^{52} - 38 q^{58} + 44 q^{64} + 16 q^{67} - 18 q^{70} - 24 q^{73} - 96 q^{82} - 30 q^{88} - 8 q^{91} - 72 q^{94}+O(q^{100}) $ 32 * q + 2 * q^4 + 18 * q^10 - 10 * q^16 - 12 * q^22 - 16 * q^25 - 6 * q^28 - 30 * q^40 + 16 * q^43 + 16 * q^46 + 8 * q^49 - 72 * q^52 - 38 * q^58 + 44 * q^64 + 16 * q^67 - 18 * q^70 - 24 * q^73 - 96 * q^82 - 30 * q^88 - 8 * q^91 - 72 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$	$1$

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 $

$2$	−0.809233	+	1.15980i	−0.572214	+	0.820104i
$2$	−0.809233	+	1.15980i	−0.572214	+	0.820104i
$3$		0			0
$3$		0			0
$4$	−0.690284	−	1.87710i	−0.345142	−	0.938551i
$5$	−1.03180	+	1.78713i	−0.461435	+	0.799229i	−0.999033	−	0.0439725i	$-0.985999\pi$
$5$	−1.03180	+	1.78713i	−0.461435	+	0.799229i	0.537598	+	0.843201i	$0.319332\pi$
$6$		0			0
$7$	2.39181	−	1.13104i	0.904020	−	0.427491i
$7$	2.39181	−	1.13104i	0.904020	−	0.427491i
$8$	2.73567	+	0.718419i	0.967204	+	0.254000i
$9$		0			0
$10$	−1.23775	−	2.64289i	−0.391411	−	0.835755i
$11$	−0.982155	−	1.70114i	−0.296131	−	0.512914i	0.679116	−	0.734031i	$-0.262363\pi$
$11$	−0.982155	−	1.70114i	−0.296131	−	0.512914i	−0.975247	+	0.221117i	$0.929030\pi$
$12$		0			0
$13$	4.20219			1.16548			0.582738	−	0.812660i	$-0.301981\pi$
$13$	4.20219			1.16548			0.582738	+	0.812660i	$0.301981\pi$
$14$	−0.623755	+	3.68930i	−0.166705	+	0.986007i
$15$		0			0
$16$	−3.04702	+	2.59146i	−0.761754	+	0.647866i
$17$	3.09983	−	1.78969i	0.751819	−	0.434063i	−0.0745321	−	0.997219i	$-0.523746\pi$
$17$	3.09983	−	1.78969i	0.751819	−	0.434063i	0.826351	+	0.563156i	$0.190413\pi$
$18$		0			0
$19$	−4.36777	−	2.52173i	−1.00203	−	0.578525i	−0.0931845	−	0.995649i	$-0.529705\pi$
$19$	−4.36777	−	2.52173i	−1.00203	−	0.578525i	−0.908849	+	0.417124i	$0.863038\pi$
$20$	4.06686	+	0.703166i	0.909377	+	0.157233i
$21$		0			0
$22$	2.76778	+	0.237515i	0.590093	+	0.0506383i
$23$	5.31120	+	3.06642i	1.10746	+	0.639393i	0.938171	−	0.346173i	$-0.112519\pi$
$23$	5.31120	+	3.06642i	1.10746	+	0.639393i	0.169291	+	0.985566i	$0.445852\pi$
$24$		0			0
$25$	0.370777	+	0.642204i	0.0741553	+	0.128441i
$26$	−3.40055	+	4.87371i	−0.666902	+	0.955813i
$27$		0			0
$28$	−3.77410	−	3.70894i	−0.713237	−	0.700923i
$29$			6.34977i			1.17912i	0.807724	+	0.589561i	$0.200699\pi$
$29$			6.34977i			1.17912i	−0.807724	+	0.589561i	$0.799301\pi$
$30$		0			0
$31$	3.42356	+	5.92978i	0.614889	+	1.06502i	0.990404	+	0.138203i	$0.0441327\pi$
$31$	3.42356	+	5.92978i	0.614889	+	1.06502i	−0.375514	+	0.926817i	$0.622534\pi$
$32$	−0.539841	−	5.63104i	−0.0954313	−	0.995436i
$33$		0			0
$34$	−0.432800	+	5.04346i	−0.0742246	+	0.864946i
$35$	−0.446563	+	5.44148i	−0.0754830	+	0.919778i
$36$		0			0
$37$	3.56564	+	2.05862i	0.586188	+	0.338436i	0.763589	−	0.645703i	$-0.223436\pi$
$37$	3.56564	+	2.05862i	0.586188	+	0.338436i	−0.177401	+	0.984139i	$0.556769\pi$
$38$	6.45925	−	3.02508i	1.04783	−	0.490732i
$39$		0			0
$40$	−4.10657	+	4.14773i	−0.649306	+	0.655813i
$41$			2.45849i			0.383952i	0.981400	+	0.191976i	$0.0614896\pi$
$41$			2.45849i			0.383952i	−0.981400	+	0.191976i	$0.938510\pi$
$42$		0			0
$43$	4.33560			0.661173			0.330586	−	0.943776i	$-0.392753\pi$
$43$	4.33560			0.661173			0.330586	+	0.943776i	$0.392753\pi$
$44$	−2.51525	+	3.01788i	−0.379188	+	0.454962i
$45$		0			0
$46$	−7.85444	+	3.67849i	−1.15807	+	0.542364i
$47$	4.88612	−	8.46301i	0.712714	−	1.23446i	−0.251121	−	0.967956i	$-0.580799\pi$
$47$	4.88612	−	8.46301i	0.712714	−	1.23446i	0.963835	−	0.266501i	$-0.0858676\pi$
$48$		0			0
$49$	4.44152	−	5.41045i	0.634503	−	0.772921i
$50$	−1.04487	−	0.0896650i	−0.147768	−	0.0126805i
$51$		0			0
$52$	−2.90070	−	7.88793i	−0.402255	−	1.09386i
$53$	−11.2291	+	6.48313i	−1.54244	+	0.890527i	−0.543754	+	0.839245i	$0.682998\pi$
$53$	−11.2291	+	6.48313i	−1.54244	+	0.890527i	−0.998684	+	0.0512824i	$0.983669\pi$
$54$		0			0
$55$	4.05355			0.546581
$56$	7.35576	−	1.37581i	0.982954	−	0.183851i
$57$		0			0
$58$	−7.36447	−	5.13844i	−0.967003	−	0.674710i
$59$	6.17173	−	3.56325i	0.803491	−	0.463896i	−0.0411994	−	0.999151i	$-0.513118\pi$
$59$	6.17173	−	3.56325i	0.803491	−	0.463896i	0.844690	+	0.535255i	$0.179785\pi$
$60$		0			0
$61$	−1.03175	+	1.78704i	−0.132102	+	0.228807i	−0.924487	−	0.381214i	$-0.875506\pi$
$61$	−1.03175	+	1.78704i	−0.132102	+	0.228807i	0.792385	+	0.610022i	$0.208839\pi$
$62$	−9.64783	−	0.827920i	−1.22528	−	0.105146i
$63$		0			0
$64$	6.96775	+	3.93071i	0.870968	+	0.491339i
$65$	−4.33582	+	7.50986i	−0.537792	+	0.931483i
$66$		0			0
$67$	2.77372	+	4.80422i	0.338864	+	0.586929i	0.984219	−	0.176953i	$-0.0566242\pi$
$67$	2.77372	+	4.80422i	0.338864	+	0.586929i	−0.645356	+	0.763882i	$0.723291\pi$
$68$	−5.49918	−	4.58330i	−0.666874	−	0.555806i
$69$		0			0
$70$	−5.94967	−	4.92135i	−0.711121	−	0.588214i
$71$		−	9.44037i		−	1.12037i	−0.828369	−	0.560183i	$-0.810731\pi$
$71$		−	9.44037i		−	1.12037i	0.828369	−	0.560183i	$-0.189269\pi$
$72$		0			0
$73$	−10.7122	+	6.18471i	−1.25377	+	0.723865i	−0.971856	−	0.235574i	$-0.924303\pi$
$73$	−10.7122	+	6.18471i	−1.25377	+	0.723865i	−0.281915	+	0.959439i	$0.590970\pi$
$74$	−5.27303	+	2.46953i	−0.612978	+	0.287077i
$75$		0			0
$76$	−1.71855	+	9.93945i	−0.197131	+	1.14013i
$77$	−4.27318	−	2.95796i	−0.486974	−	0.337091i
$78$		0			0
$79$	0.778628	+	0.449541i	0.0876025	+	0.0505773i	0.543161	−	0.839628i	$-0.317227\pi$
$79$	0.778628	+	0.449541i	0.0876025	+	0.0505773i	−0.455559	+	0.890206i	$0.650561\pi$
$80$	−1.48737	−	8.11929i	−0.166293	−	0.907764i
$81$		0			0
$82$	−2.85137	−	1.98949i	−0.314881	−	0.219703i
$83$		−	9.58499i		−	1.05209i	−0.850457	−	0.526045i	$-0.823674\pi$
$83$		−	9.58499i		−	1.05209i	0.850457	−	0.526045i	$-0.176326\pi$
$84$		0			0
$85$			7.38639i			0.801167i
$86$	−3.50851	+	5.02844i	−0.378332	+	0.542231i
$87$		0			0
$88$	−1.46472	−	5.35936i	−0.156139	−	0.571310i
$89$	−12.6502	−	7.30359i	−1.34092	−	0.774179i	−0.353975	−	0.935255i	$-0.615170\pi$
$89$	−12.6502	−	7.30359i	−1.34092	−	0.774179i	−0.986942	+	0.161076i	$0.948504\pi$
$90$		0			0
$91$	10.0508	−	4.75282i	1.05361	−	0.498231i
$92$	2.08975	−	12.0864i	0.217871	−	1.26009i
$93$		0			0
$94$	5.86141	+	12.5155i	0.604558	+	1.29087i
$95$	9.01332	−	5.20384i	0.924747	−	0.533903i
$96$		0			0
$97$		−	0.550439i		−	0.0558886i	−0.999609	−	0.0279443i	$-0.991104\pi$
$97$		−	0.550439i		−	0.0558886i	0.999609	−	0.0279443i	$-0.00889611\pi$
$98$	2.68082	+	9.52959i	0.270804	+	0.962634i
$99$		0			0
$100$	0.949541	−	1.13929i	0.0949541	−	0.113929i
$101$	−0.425077	−	0.736255i	−0.0422967	−	0.0732601i	0.844102	−	0.536183i	$-0.180134\pi$
$101$	−0.425077	−	0.736255i	−0.0422967	−	0.0732601i	−0.886399	+	0.462922i	$0.846801\pi$
$102$		0			0
$103$	0.216400	−	0.374816i	0.0213225	−	0.0369317i	−0.855167	−	0.518352i	$-0.826546\pi$
$103$	0.216400	−	0.374816i	0.0213225	−	0.0369317i	0.876490	+	0.481420i	$0.159879\pi$
$104$	11.4958	+	3.01893i	1.12725	+	0.296031i
$105$		0			0
$106$	1.56782	−	18.2699i	0.152280	−	1.77453i
$107$	−4.77094	+	8.26350i	−0.461224	+	0.798863i	−0.999022	−	0.0442104i	$-0.985923\pi$
$107$	−4.77094	+	8.26350i	−0.461224	+	0.798863i	0.537798	+	0.843073i	$0.319256\pi$
$108$		0			0
$109$	15.0609	−	8.69539i	1.44257	−	0.832867i	0.444547	−	0.895755i	$-0.353365\pi$
$109$	15.0609	−	8.69539i	1.44257	−	0.832867i	0.998021	+	0.0628884i	$0.0200312\pi$
$110$	−3.28027	+	4.70132i	−0.312761	+	0.448253i
$111$		0			0
$112$	−4.35685	+	9.64458i	−0.411684	+	0.911327i
$113$	17.4719			1.64362			0.821811	−	0.569761i	$-0.192964\pi$
$113$	17.4719			1.64362			0.821811	+	0.569761i	$0.192964\pi$
$114$		0			0
$115$	−10.9602	+	6.32787i	−1.02204	+	0.590077i
$116$	11.9192	−	4.38314i	1.10667	−	0.406964i
$117$		0			0
$118$	−0.861702	+	10.0415i	−0.0793261	+	0.924394i
$119$	5.39000	−	7.78660i	0.494101	−	0.713797i
$120$		0			0
$121$	3.57074	−	6.18471i	0.324613	−	0.562246i
$122$	−1.23769	−	2.64276i	−0.112055	−	0.239264i
$123$		0			0
$124$	8.76757	−	10.5196i	0.787351	−	0.944688i
$125$	−11.8483			−1.05974
$126$		0			0
$127$		−	13.6577i		−	1.21193i	−0.795493	−	0.605963i	$-0.792788\pi$
$127$		−	13.6577i		−	1.21193i	0.795493	−	0.605963i	$-0.207212\pi$
$128$	−10.1974	+	4.90035i	−0.901330	+	0.433134i
$129$		0			0
$130$	−5.20126	−	11.1059i	−0.456181	−	0.974053i
$131$	−7.01700	−	4.05127i	−0.613078	−	0.353961i	0.161091	−	0.986940i	$-0.448499\pi$
$131$	−7.01700	−	4.05127i	−0.613078	−	0.353961i	−0.774169	+	0.632979i	$0.781832\pi$
$132$		0			0
$133$	−13.2990	−	1.09141i	−1.15317	−	0.0946368i
$134$	−7.81653	−	0.670769i	−0.675245	−	0.0579456i
$135$		0			0
$136$	9.76584	−	2.66901i	0.837414	−	0.228866i
$137$	−3.50702	−	6.07434i	−0.299625	−	0.518966i	0.676425	−	0.736512i	$-0.263528\pi$
$137$	−3.50702	−	6.07434i	−0.299625	−	0.518966i	−0.976050	+	0.217545i	$0.930195\pi$
$138$		0			0
$139$		−	5.14626i		−	0.436500i	−0.975893	−	0.218250i	$-0.929965\pi$
$139$		−	5.14626i		−	0.436500i	0.975893	−	0.218250i	$-0.0700348\pi$
$140$	10.5225	−	2.91792i	0.889310	−	0.246609i
$141$		0			0
$142$	10.9490	+	7.63946i	0.918816	+	0.641089i
$143$	−4.12720	−	7.14852i	−0.345134	−	0.597789i
$144$		0			0
$145$	−11.3479	−	6.55169i	−0.942388	−	0.544088i
$146$	1.49565	−	17.4289i	0.123781	−	1.44243i
$147$		0			0
$148$	1.40294	−	8.11411i	0.115321	−	0.666975i
$149$	2.48868	+	1.43684i	0.203880	+	0.117710i	0.598464	−	0.801150i	$-0.295778\pi$
$149$	2.48868	+	1.43684i	0.203880	+	0.117710i	−0.394584	+	0.918860i	$0.629111\pi$
$150$		0			0
$151$	−11.2968	+	6.52218i	−0.919317	+	0.530768i	−0.883417	−	0.468588i	$-0.844763\pi$
$151$	−11.2968	+	6.52218i	−0.919317	+	0.530768i	−0.0358996	+	0.999355i	$0.511430\pi$
$152$	−10.1371	−	10.0365i	−0.822227	−	0.814068i
$153$		0			0
$154$	6.88865	−	2.56237i	0.555103	−	0.206482i
$155$	−14.1297			−1.13493
$156$		0			0
$157$	−5.06779	−	8.77767i	−0.404453	−	0.700534i	0.589804	−	0.807546i	$-0.299205\pi$
$157$	−5.06779	−	8.77767i	−0.404453	−	0.700534i	−0.994258	+	0.107012i	$0.965872\pi$
$158$	−1.15147	+	0.539271i	−0.0916060	+	0.0429021i
$159$		0			0
$160$	10.6204	+	4.84534i	0.839617	+	0.383058i
$161$	16.1716	+	1.32715i	1.27450	+	0.104594i
$162$		0			0
$163$	0.741553	−	1.28441i	0.0580829	−	0.100603i	−0.835522	−	0.549457i	$-0.814835\pi$
$163$	0.741553	−	1.28441i	0.0580829	−	0.100603i	0.893605	+	0.448855i	$0.148168\pi$
$164$	4.61484	−	1.69706i	0.360358	−	0.132518i
$165$		0			0
$166$	11.1167	+	7.75649i	0.862823	+	0.602021i
$167$	8.09679			0.626549			0.313274	−	0.949663i	$-0.398574\pi$
$167$	8.09679			0.626549			0.313274	+	0.949663i	$0.398574\pi$
$168$		0			0
$169$	4.65838			0.358337
$170$	−8.56676	−	5.97731i	−0.657040	−	0.458439i
$171$		0			0
$172$	−2.99279	−	8.13836i	−0.228198	−	0.620544i
$173$	−7.79366	+	13.4990i	−0.592541	+	1.02631i	0.401348	+	0.915926i	$0.368542\pi$
$173$	−7.79366	+	13.4990i	−0.592541	+	1.02631i	−0.993889	+	0.110385i	$0.964791\pi$
$174$		0			0
$175$	1.61318	+	1.11667i	0.121945	+	0.0844122i
$176$	7.40110	+	2.63819i	0.557879	+	0.198861i
$177$		0			0
$178$	18.7077	−	8.76141i	1.40220	−	0.656696i
$179$	5.91790	+	10.2501i	0.442324	+	0.766128i	0.997862	−	0.0653634i	$-0.0208207\pi$
$179$	5.91790	+	10.2501i	0.442324	+	0.766128i	−0.555537	+	0.831492i	$0.687487\pi$
$180$		0			0
$181$	−15.2646			−1.13461			−0.567304	−	0.823508i	$-0.692014\pi$
$181$	−15.2646			−1.13461			−0.567304	+	0.823508i	$0.692014\pi$
$182$	−2.62113	+	15.5031i	−0.194291	+	1.14917i
$183$		0			0
$184$	12.3267	+	12.2044i	0.908736	+	0.899718i
$185$	−7.35806	+	4.24818i	−0.540975	+	0.312332i
$186$		0			0
$187$	−6.08902	−	3.51550i	−0.445274	−	0.257079i
$188$	−19.2587	−	3.32986i	−1.40459	−	0.242855i
$189$		0			0
$190$	−1.25845	+	14.6648i	−0.0912973	+	1.06390i
$191$	−0.333843	−	0.192744i	−0.0241560	−	0.0139465i	0.487873	−	0.872914i	$-0.337773\pi$
$191$	−0.333843	−	0.192744i	−0.0241560	−	0.0139465i	−0.512029	+	0.858968i	$0.671106\pi$
$192$		0			0
$193$	12.9186	+	22.3757i	0.929901	+	1.61064i	0.783483	+	0.621414i	$0.213441\pi$
$193$	12.9186	+	22.3757i	0.929901	+	1.61064i	0.146419	+	0.989223i	$0.453225\pi$
$194$	0.638401	+	0.445434i	0.0458345	+	0.0319803i
$195$		0			0
$196$	−13.2219	−	4.60244i	−0.944419	−	0.328745i
$197$		−	7.58382i		−	0.540325i	−0.962815	−	0.270163i	$-0.912923\pi$
$197$		−	7.58382i		−	0.540325i	0.962815	−	0.270163i	$-0.0870774\pi$
$198$		0			0
$199$	1.32902	+	2.30193i	0.0942115	+	0.163179i	0.909279	−	0.416187i	$-0.136634\pi$
$199$	1.32902	+	2.30193i	0.0942115	+	0.163179i	−0.815068	+	0.579366i	$0.803300\pi$
$200$	0.552950	+	2.02323i	0.0390995	+	0.143064i
$201$		0			0
$202$	1.19790	+	0.102796i	0.0842837	+	0.00723273i
$203$	7.18181	+	15.1874i	0.504064	+	1.06595i
$204$		0			0
$205$	−4.39365	−	2.53667i	−0.306866	−	0.177169i
$206$	0.259594	+	0.554295i	0.0180868	+	0.0386195i
$207$		0			0
$208$	−12.8041	+	10.8898i	−0.887807	+	0.755073i
$209$			9.90692i			0.685276i
$210$		0			0
$211$	−13.8830			−0.955748			−0.477874	−	0.878428i	$-0.658592\pi$
$211$	−13.8830			−0.955748			−0.477874	+	0.878428i	$0.658592\pi$
$212$	19.9208	+	16.6030i	1.36816	+	1.14030i
$213$		0			0
$214$	−5.72323	−	12.2204i	−0.391232	−	0.835372i
$215$	−4.47347	+	7.74828i	−0.305088	+	0.528429i
$216$		0			0
$217$	14.8953	+	10.3107i	1.01116	+	0.699939i
$218$	−2.10281	+	24.5042i	−0.142420	+	1.65963i
$219$		0			0
$220$	−2.79810	−	7.60893i	−0.188648	−	0.512994i
$221$	13.0261	−	7.52060i	0.876227	−	0.505890i
$222$		0			0
$223$	−26.4494			−1.77119			−0.885593	−	0.464463i	$-0.846247\pi$
$223$	−26.4494			−1.77119			−0.885593	+	0.464463i	$0.846247\pi$
$224$	−7.66010	−	12.8578i	−0.511812	−	0.859098i
$225$		0			0
$226$	−14.1389	+	20.2640i	−0.940503	+	1.34794i
$227$	15.5967	−	9.00473i	1.03519	−	0.597665i	0.116720	−	0.993165i	$-0.462762\pi$
$227$	15.5967	−	9.00473i	1.03519	−	0.597665i	0.918466	+	0.395500i	$0.129429\pi$
$228$		0			0
$229$	−6.00160	+	10.3951i	−0.396597	+	0.686926i	−0.993304	−	0.115533i	$-0.963142\pi$
$229$	−6.00160	+	10.3951i	−0.396597	+	0.686926i	0.596707	+	0.802459i	$0.296476\pi$
$230$	1.53027	−	17.8324i	0.100903	−	1.17583i
$231$		0			0
$232$	−4.56179	+	17.3708i	−0.299496	+	1.14045i
$233$	−4.80735	+	8.32657i	−0.314940	+	0.545492i	−0.979425	−	0.201810i	$-0.935318\pi$
$233$	−4.80735	+	8.32657i	−0.314940	+	0.545492i	0.664485	+	0.747302i	$0.268651\pi$
$234$		0			0
$235$	10.0830	+	17.4643i	0.657742	+	1.13924i
$236$	−10.9488	−	9.12531i	−0.712708	−	0.594007i
$237$		0			0
$238$	4.66916	+	12.5525i	0.302656	+	0.813659i
$239$			21.7827i			1.40901i	0.709701	+	0.704503i	$0.248830\pi$
$239$			21.7827i			1.40901i	−0.709701	+	0.704503i	$0.751170\pi$
$240$		0			0
$241$	−6.56572	+	3.79072i	−0.422935	+	0.244182i	−0.696332	−	0.717720i	$-0.745186\pi$
$241$	−6.56572	+	3.79072i	−0.422935	+	0.244182i	0.273397	+	0.961901i	$0.411853\pi$
$242$	4.28348	+	9.14622i	0.275352	+	0.587941i
$243$		0			0
$244$	4.06666	+	0.703131i	0.260341	+	0.0450133i
$245$	5.08641	+	13.5201i	0.324959	+	0.863766i
$246$		0			0
$247$	−18.3542	−	10.5968i	−1.16785	−	0.674257i
$248$	5.10565	+	18.6815i	0.324209	+	1.18627i
$249$		0			0
$250$	9.58801	−	13.7417i	0.606399	−	0.869099i
$251$		−	31.3509i		−	1.97885i	−0.145038	−	0.989426i	$-0.546330\pi$
$251$		−	31.3509i		−	1.97885i	0.145038	−	0.989426i	$-0.453670\pi$
$252$		0			0
$253$		−	12.0468i		−	0.757376i
$254$	15.8403	+	11.0523i	0.993906	+	0.693482i
$255$		0			0
$256$	2.56862	−	15.7925i	0.160539	−	0.987030i
$257$	−23.4653	−	13.5477i	−1.46373	−	0.845084i	−0.464547	−	0.885549i	$-0.653783\pi$
$257$	−23.4653	−	13.5477i	−1.46373	−	0.845084i	−0.999181	+	0.0404650i	$0.987116\pi$
$258$		0			0
$259$	10.8567	+	0.890973i	0.674604	+	0.0553624i
$260$	17.0897	+	2.95484i	1.05986	+	0.183251i
$261$		0			0
$262$	10.3771	−	4.85992i	0.641097	−	0.300247i
$263$	−11.5439	+	6.66486i	−0.711826	+	0.410973i	−0.811737	−	0.584023i	$-0.801478\pi$
$263$	−11.5439	+	6.66486i	−0.711826	+	0.410973i	0.0999108	+	0.994996i	$0.468144\pi$
$264$		0			0
$265$		−	26.7572i		−	1.64368i
$266$	12.0278	−	14.5411i	0.737474	−	0.891569i
$267$		0			0
$268$	7.10335	−	8.52282i	0.433906	−	0.520614i
$269$	4.69826	+	8.13762i	0.286458	+	0.496160i	0.972962	−	0.230967i	$-0.0741888\pi$
$269$	4.69826	+	8.13762i	0.286458	+	0.496160i	−0.686504	+	0.727126i	$0.740855\pi$
$270$		0			0
$271$	0.995028	−	1.72344i	0.0604436	−	0.104691i	−0.834220	−	0.551432i	$-0.814082\pi$
$271$	0.995028	−	1.72344i	0.0604436	−	0.104691i	0.894664	+	0.446740i	$0.147415\pi$
$272$	−4.80732	+	13.4863i	−0.291486	+	0.817727i
$273$		0			0
$274$	9.88304	+	0.848104i	0.597056	+	0.0512358i
$275$	0.728321	−	1.26149i	0.0439194	−	0.0760706i
$276$		0			0
$277$	−22.2114	+	12.8238i	−1.33455	+	0.770505i	−0.985994	−	0.166782i	$-0.946663\pi$
$277$	−22.2114	+	12.8238i	−1.33455	+	0.770505i	−0.348560	+	0.937287i	$0.613329\pi$
$278$	5.96864	+	4.16452i	0.357975	+	0.249771i
$279$		0			0
$280$	−5.13091	+	14.5653i	−0.306631	+	0.870441i
$281$	16.3449			0.975055			0.487528	−	0.873108i	$-0.337899\pi$
$281$	16.3449			0.975055			0.487528	+	0.873108i	$0.337899\pi$
$282$		0			0
$283$	−19.1923	+	11.0807i	−1.14086	+	0.658679i	−0.946645	−	0.322279i	$-0.895551\pi$
$283$	−19.1923	+	11.0807i	−1.14086	+	0.658679i	−0.194220	+	0.980958i	$0.562218\pi$
$284$	−17.7205	+	6.51653i	−1.05152	+	0.386685i
$285$		0			0
$286$	11.6307	+	0.998082i	0.687740	+	0.0590178i
$287$	2.78064	+	5.88025i	0.164136	+	0.347100i
$288$		0			0
$289$	−2.09405	+	3.62700i	−0.123179	+	0.213353i
$290$	16.7817	−	7.85943i	0.985457	−	0.461522i
$291$		0			0
$292$	19.0038	+	15.8387i	1.11211	+	0.926891i
$293$	11.0720			0.646831			0.323416	−	0.946257i	$-0.395169\pi$
$293$	11.0720			0.646831			0.323416	+	0.946257i	$0.395169\pi$
$294$		0			0
$295$			14.7063i			0.856231i
$296$	8.27545	+	8.19334i	0.481001	+	0.476228i
$297$		0			0
$298$	−3.68037	+	1.72364i	−0.213198	+	0.0998476i
$299$	22.3186	+	12.8857i	1.29072	+	0.745198i
$300$		0			0
$301$	10.3699	−	4.90372i	0.597713	−	0.282646i
$302$	1.57726	−	18.3800i	0.0907612	−	1.05765i
$303$		0			0
$304$	19.8436	−	3.63516i	1.13811	−	0.208490i
$305$	−2.12912	−	3.68774i	−0.121913	−	0.211159i
$306$		0			0
$307$		−	29.0896i		−	1.66023i	−0.557592	−	0.830115i	$-0.688275\pi$
$307$		−	29.0896i		−	1.66023i	0.557592	−	0.830115i	$-0.311725\pi$
$308$	−2.60268	+	10.0630i	−0.148302	+	0.573394i
$309$		0			0
$310$	11.4342	−	16.3877i	0.649421	−	0.930758i
$311$	6.99160	+	12.1098i	0.396457	+	0.686684i	0.993286	−	0.115685i	$-0.0369062\pi$
$311$	6.99160	+	12.1098i	0.396457	+	0.686684i	−0.596829	+	0.802369i	$0.703573\pi$
$312$		0			0
$313$	−1.58902	−	0.917424i	−0.0898170	−	0.0518558i	0.454419	−	0.890788i	$-0.349847\pi$
$313$	−1.58902	−	0.917424i	−0.0898170	−	0.0518558i	−0.544236	+	0.838932i	$0.683180\pi$
$314$	14.2814	+	1.22554i	0.805945	+	0.0691615i
$315$		0			0
$316$	0.306360	−	1.77187i	0.0172341	−	0.0996757i
$317$	0.691742	+	0.399378i	0.0388521	+	0.0224313i	0.519300	−	0.854592i	$-0.326193\pi$
$317$	0.691742	+	0.399378i	0.0388521	+	0.0224313i	−0.480448	+	0.877023i	$0.659526\pi$
$318$		0			0
$319$	10.8019	−	6.23646i	0.604788	−	0.349175i
$320$	−14.2140	+	8.39656i	−0.794588	+	0.469382i
$321$		0			0
$322$	−14.6258	+	17.6819i	−0.815066	+	0.985374i
$323$	−18.0524			−1.00446
$324$		0			0
$325$	1.55807	+	2.69866i	0.0864263	+	0.149695i
$326$	0.889570	+	1.89944i	0.0492687	+	0.105200i
$327$		0			0
$328$	−1.76623	+	6.72562i	−0.0975236	+	0.371360i
$329$	2.11471	−	25.7683i	0.116588	−	1.42065i
$330$		0			0
$331$	6.56773	−	11.3756i	0.360995	−	0.625262i	−0.627130	−	0.778915i	$-0.715770\pi$
$331$	6.56773	−	11.3756i	0.360995	−	0.625262i	0.988125	+	0.153653i	$0.0491038\pi$
$332$	−17.9920	+	6.61637i	−0.987439	+	0.363120i
$333$		0			0
$334$	−6.55219	+	9.39068i	−0.358520	+	0.513835i
$335$	−11.4477			−0.625454
$336$		0			0
$337$	−28.3541			−1.54455			−0.772273	−	0.635291i	$-0.780880\pi$
$337$	−28.3541			−1.54455			−0.772273	+	0.635291i	$0.780880\pi$
$338$	−3.76971	+	5.40280i	−0.205045	+	0.293873i
$339$		0			0
$340$	13.8650	−	5.09871i	0.751936	−	0.276516i
$341$	6.72493	−	11.6479i	0.364176	−	0.630771i
$342$		0			0
$343$	4.50387	−	17.9643i	0.243186	−	0.969980i
$344$	11.8608	+	3.11478i	0.639489	+	0.167938i
$345$		0			0
$346$	−9.34931	−	19.9630i	−0.502622	−	1.07322i
$347$	−2.55279	−	4.42156i	−0.137041	−	0.237362i	0.789334	−	0.613964i	$-0.210426\pi$
$347$	−2.55279	−	4.42156i	−0.137041	−	0.237362i	−0.926375	+	0.376602i	$0.877093\pi$
$348$		0			0
$349$	15.3398			0.821120			0.410560	−	0.911834i	$-0.365333\pi$
$349$	15.3398			0.821120			0.410560	+	0.911834i	$0.365333\pi$
$350$	−2.60056	+	0.967328i	−0.139006	+	0.0517059i
$351$		0			0
$352$	−9.04899	+	6.44890i	−0.482313	+	0.343728i
$353$	6.55692	−	3.78564i	0.348990	−	0.201489i	−0.315251	−	0.949008i	$-0.602089\pi$
$353$	6.55692	−	3.78564i	0.348990	−	0.201489i	0.664240	+	0.747519i	$0.268755\pi$
$354$		0			0
$355$	16.8712	+	9.74057i	0.895429	+	0.516976i
$356$	−4.97735	+	28.7872i	−0.263799	+	1.52572i
$357$		0			0
$358$	−16.6770	−	1.43113i	−0.881409	−	0.0756374i
$359$	−25.7846	−	14.8868i	−1.36086	−	0.785694i	−0.371123	−	0.928584i	$-0.621027\pi$
$359$	−25.7846	−	14.8868i	−1.36086	−	0.785694i	−0.989739	+	0.142890i	$0.954360\pi$
$360$		0			0
$361$	3.21825	+	5.57417i	0.169381	+	0.293377i
$362$	12.3526	−	17.7039i	0.649239	−	0.930497i
$363$		0			0
$364$	−15.8595	−	15.5856i	−0.831261	−	0.816909i
$365$		−	25.5255i		−	1.33607i
$366$		0			0
$367$	2.10765	+	3.65055i	0.110018	+	0.190557i	0.915777	−	0.401686i	$-0.131576\pi$
$367$	2.10765	+	3.65055i	0.110018	+	0.190557i	−0.805759	+	0.592243i	$0.798242\pi$
$368$	−24.1298	+	4.42035i	−1.25785	+	0.230426i
$369$		0			0
$370$	1.02734	−	11.9717i	0.0534088	−	0.622377i
$371$	−19.5253	+	28.2070i	−1.01370	+	1.46443i
$372$		0			0
$373$	−10.1033	−	5.83313i	−0.523128	−	0.302028i	0.215085	−	0.976595i	$-0.430997\pi$
$373$	−10.1033	−	5.83313i	−0.523128	−	0.302028i	−0.738214	+	0.674567i	$0.764330\pi$
$374$	9.00473	−	4.21721i	0.465623	−	0.218067i
$375$		0			0
$376$	19.4468	−	19.6417i	1.00289	−	1.01294i
$377$			26.6829i			1.37424i
$378$		0			0
$379$	−5.40673			−0.277725			−0.138863	−	0.990312i	$-0.544345\pi$
$379$	−5.40673			−0.277725			−0.138863	+	0.990312i	$0.544345\pi$
$380$	−15.9899	−	13.3268i	−0.820264	−	0.683650i
$381$		0			0
$382$	0.493702	−	0.231217i	0.0252600	−	0.0118301i
$383$	−18.3729	+	31.8228i	−0.938812	+	1.62607i	−0.171121	+	0.985250i	$0.554739\pi$
$383$	−18.3729	+	31.8228i	−0.938812	+	1.62607i	−0.767691	+	0.640820i	$0.778594\pi$
$384$		0			0
$385$	9.69533	−	4.58471i	0.494120	−	0.233659i
$386$	−36.4055	−	3.12411i	−1.85299	−	0.159013i
$387$		0			0
$388$	−1.03323	+	0.379959i	−0.0524543	+	0.0192895i
$389$	17.1039	−	9.87494i	0.867202	−	0.500679i	0.000784673	−	1.00000i	$-0.499750\pi$
$389$	17.1039	−	9.87494i	0.867202	−	0.500679i	0.866417	+	0.499320i	$0.166417\pi$
$390$		0			0
$391$	21.9517			1.11015
$392$	16.0375	−	11.6103i	0.810015	−	0.586409i
$393$		0			0
$394$	8.79574	+	6.13708i	0.443123	+	0.309182i
$395$	−1.60678	+	0.927673i	−0.0808457	+	0.0466763i
$396$		0			0
$397$	16.3033	−	28.2382i	0.818240	−	1.41723i	−0.0887372	−	0.996055i	$-0.528283\pi$
$397$	16.3033	−	28.2382i	0.818240	−	1.41723i	0.906978	−	0.421179i	$-0.138384\pi$
$398$	−3.74526	−	0.321397i	−0.187733	−	0.0161102i
$399$		0			0
$400$	−2.79401	−	0.995952i	−0.139701	−	0.0497976i
$401$	−5.79246	+	10.0328i	−0.289262	+	0.501016i	−0.973634	−	0.228117i	$-0.926743\pi$
$401$	−5.79246	+	10.0328i	−0.289262	+	0.501016i	0.684372	+	0.729133i	$0.260076\pi$
$402$		0			0
$403$	14.3864	+	24.9180i	0.716639	+	1.24126i
$404$	−1.08860	+	1.30614i	−0.0541599	+	0.0649828i
$405$		0			0
$406$	−23.4262	−	3.96070i	−1.16262	−	0.196566i
$407$		−	8.08756i		−	0.400885i
$408$		0			0
$409$	−18.1957	+	10.5053i	−0.899720	+	0.519454i	−0.877109	−	0.480290i	$-0.840531\pi$
$409$	−18.1957	+	10.5053i	−0.899720	+	0.519454i	−0.0226110	+	0.999744i	$0.507198\pi$
$410$	6.49752	−	3.04300i	0.320890	−	0.150283i
$411$		0			0
$412$	−0.852945	−	0.147475i	−0.0420216	−	0.00726559i
$413$	10.7315	−	15.5031i	0.528060	−	0.762856i
$414$		0			0
$415$	17.1296	+	9.88980i	0.840861	+	0.485471i
$416$	−2.26851	−	23.6627i	−0.111223	−	1.16016i
$417$		0			0
$418$	−11.4901	−	8.01701i	−0.561998	−	0.392125i
$419$		−	13.0738i		−	0.638695i	−0.947638	−	0.319348i	$-0.896536\pi$
$419$		−	13.0738i		−	0.638695i	0.947638	−	0.319348i	$-0.103464\pi$
$420$		0			0
$421$			30.7209i			1.49724i	0.662998	+	0.748622i	$0.269284\pi$
$421$			30.7209i			1.49724i	−0.662998	+	0.748622i	$0.730716\pi$
$422$	11.2346	−	16.1016i	0.546892	−	0.783813i
$423$		0			0
$424$	−35.3767	+	9.66848i	−1.71805	+	0.469543i
$425$	2.29869	+	1.32715i	0.111503	+	0.0643761i
$426$		0			0
$427$	−0.446541	+	5.44121i	−0.0216096	+	0.263319i
$428$	18.8047	+	3.25137i	0.908961	+	0.157161i
$429$		0			0
$430$	−5.36640	−	11.4585i	−0.258791	−	0.552579i
$431$	−1.43904	+	0.830828i	−0.0693159	+	0.0400196i	−0.534257	−	0.845322i	$-0.679409\pi$
$431$	−1.43904	+	0.830828i	−0.0693159	+	0.0400196i	0.464941	+	0.885341i	$0.346075\pi$
$432$		0			0
$433$		−	27.3884i		−	1.31620i	−0.752930	−	0.658101i	$-0.771360\pi$
$433$		−	27.3884i		−	1.31620i	0.752930	−	0.658101i	$-0.228640\pi$
$434$	−24.0122	+	8.93181i	−1.15262	+	0.428741i
$435$		0			0
$436$	−26.7184	−	22.2685i	−1.27958	−	1.06647i
$437$	−15.4654	−	26.7868i	−0.739809	−	1.28139i
$438$		0			0
$439$	−4.22139	+	7.31167i	−0.201476	+	0.348967i	−0.949004	−	0.315263i	$-0.897907\pi$
$439$	−4.22139	+	7.31167i	−0.201476	+	0.348967i	0.747528	+	0.664230i	$0.231241\pi$
$440$	11.0892	+	2.91215i	0.528655	+	0.138831i
$441$		0			0
$442$	−1.81871	+	21.1936i	−0.0865071	+	1.00808i
$443$	2.07830	−	3.59973i	0.0987432	−	0.171028i	−0.812421	−	0.583071i	$-0.801851\pi$
$443$	2.07830	−	3.59973i	0.0987432	−	0.171028i	0.911165	+	0.412042i	$0.135184\pi$
$444$		0			0
$445$	26.1049	−	15.0717i	1.23749	−	0.714467i
$446$	21.4038	−	30.6761i	1.01350	−	1.45256i
$447$		0			0
$448$	21.1113	+	1.52075i	0.997416	+	0.0718487i
$449$	18.8169			0.888024			0.444012	−	0.896021i	$-0.353555\pi$
$449$	18.8169			0.888024			0.444012	+	0.896021i	$0.353555\pi$
$450$		0			0
$451$	4.18225	−	2.41462i	0.196934	−	0.113700i
$452$	−12.0606	−	32.7966i	−0.567283	−	1.54262i
$453$		0			0
$454$	−2.17762	+	25.3760i	−0.102201	+	1.19095i
$455$	−1.87654	+	22.8661i	−0.0879737	+	1.07198i
$456$		0			0
$457$	2.83560	−	4.91140i	0.132644	−	0.229746i	−0.792051	−	0.610455i	$-0.790987\pi$
$457$	2.83560	−	4.91140i	0.132644	−	0.229746i	0.924695	+	0.380709i	$0.124320\pi$
$458$	−7.19954	−	15.3727i	−0.336413	−	0.718320i
$459$		0			0
$460$	19.4437	+	16.2054i	0.906567	+	0.755579i
$461$	30.3245			1.41235			0.706176	−	0.708036i	$-0.250419\pi$
$461$	30.3245			1.41235			0.706176	+	0.708036i	$0.250419\pi$
$462$		0			0
$463$			8.41268i			0.390970i	0.980707	+	0.195485i	$0.0626282\pi$
$463$			8.41268i			0.390970i	−0.980707	+	0.195485i	$0.937372\pi$
$464$	−16.4552	−	19.3478i	−0.763913	−	0.898201i
$465$		0			0
$466$	−5.76691	−	12.3137i	−0.267147	−	0.570421i
$467$	28.1557	+	16.2557i	1.30289	+	0.752225i	0.980899	−	0.194517i	$-0.0623140\pi$
$467$	28.1557	+	16.2557i	1.30289	+	0.752225i	0.321993	+	0.946742i	$0.395647\pi$
$468$		0			0
$469$	12.0680	+	8.35361i	0.557246	+	0.385734i
$470$	−28.4146	−	2.43837i	−1.31067	−	0.112474i
$471$		0			0
$472$	19.4437	−	5.31398i	0.894969	−	0.244596i
$473$	−4.25823	−	7.37548i	−0.195794	−	0.339125i
$474$		0			0
$475$		−	3.74000i		−	0.171603i
$476$	−18.3369	−	4.74261i	−0.840469	−	0.217377i
$477$		0			0
$478$	−25.2636	−	17.6273i	−1.15553	−	0.806253i
$479$	−14.4033	−	24.9473i	−0.658105	−	1.13987i	−0.981106	−	0.193472i	$-0.938025\pi$
$479$	−14.4033	−	24.9473i	−0.658105	−	1.13987i	0.323001	−	0.946399i	$-0.395308\pi$
$480$		0			0
$481$	14.9835	+	8.65073i	0.683189	+	0.394439i
$482$	0.916710	−	10.6825i	0.0417550	−	0.486575i
$483$		0			0
$484$	−14.0741	−	2.43344i	−0.639734	−	0.110611i
$485$	0.983707	+	0.567943i	0.0446678	+	0.0257890i
$486$		0			0
$487$	21.8839	−	12.6347i	0.991654	−	0.572532i	0.0858860	−	0.996305i	$-0.472628\pi$
$487$	21.8839	−	12.6347i	0.991654	−	0.572532i	0.905768	+	0.423773i	$0.139295\pi$
$488$	−4.10637	+	4.14752i	−0.185886	+	0.187749i
$489$		0			0
$490$	−19.7967	−	5.04165i	−0.894324	−	0.227759i
$491$	−25.8080			−1.16470			−0.582350	−	0.812938i	$-0.697867\pi$
$491$	−25.8080			−1.16470			−0.582350	+	0.812938i	$0.697867\pi$
$492$		0			0
$493$	11.3641	+	19.6832i	0.511813	+	0.886486i
$494$	27.1430	−	12.7119i	1.22122	−	0.571937i
$495$		0			0
$496$	−25.7985	−	9.19610i	−1.15838	−	0.412917i
$497$	−10.6774	−	22.5796i	−0.478946	−	1.01283i
$498$		0			0
$499$	11.3093	−	19.5883i	0.506273	−	0.876891i	−0.493701	−	0.869632i	$-0.664356\pi$
$499$	11.3093	−	19.5883i	0.506273	−	0.876891i	0.999974	−	0.00725870i	$-0.00231054\pi$
$500$	8.17867	+	22.2404i	0.365761	+	0.994621i
$501$		0			0
$502$	36.3609	+	25.3702i	1.62287	+	1.13233i
$503$	−30.3245			−1.35210			−0.676051	−	0.736855i	$-0.736310\pi$
$503$	−30.3245			−1.35210			−0.676051	+	0.736855i	$0.736310\pi$
$504$		0			0
$505$	1.75438			0.0780688
$506$	13.9719	+	9.74868i	0.621128	+	0.433382i
$507$		0			0
$508$	−25.6369	+	9.42770i	−1.13745	+	0.418287i
$509$	16.5822	−	28.7212i	0.734993	−	1.27305i	−0.219734	−	0.975560i	$-0.570519\pi$
$509$	16.5822	−	28.7212i	0.734993	−	1.27305i	0.954726	−	0.297485i	$-0.0961479\pi$
$510$		0			0
$511$	−18.6265	+	26.9086i	−0.823988	+	1.19036i
$512$	16.2375	+	15.7589i	0.717605	+	0.696451i
$513$		0			0
$514$	34.7016	−	16.2519i	1.53062	−	0.716840i
$515$	0.446563	+	0.773470i	0.0196779	+	0.0340832i
$516$		0			0
$517$	−19.1957			−0.844227
$518$	−9.81897	+	11.8706i	−0.431421	+	0.521566i
$519$		0			0
$520$	−17.2566	+	17.4295i	−0.756751	+	0.764335i
$521$	−20.1778	+	11.6497i	−0.884006	+	0.510381i	−0.871977	−	0.489546i	$-0.837162\pi$
$521$	−20.1778	+	11.6497i	−0.884006	+	0.510381i	−0.0120290	+	0.999928i	$0.503829\pi$
$522$		0			0
$523$	−29.9745	−	17.3058i	−1.31069	−	0.756728i	−0.328481	−	0.944511i	$-0.606537\pi$
$523$	−29.9745	−	17.3058i	−1.31069	−	0.756728i	−0.982211	+	0.187782i	$0.939870\pi$
$524$	−2.76092	+	15.9682i	−0.120611	+	0.697572i
$525$		0			0
$526$	1.61176	−	18.7820i	0.0702763	−	0.818936i
$527$	21.2249	+	12.2542i	0.924571	+	0.533801i
$528$		0			0
$529$	7.30588	+	12.6542i	0.317647	+	0.550181i
$530$	31.0331	+	21.6528i	1.34799	+	0.940538i
$531$		0			0
$532$	7.13143	+	25.7170i	0.309187	+	1.11497i
$533$			10.3310i			0.447487i
$534$		0			0
$535$	−9.84531	−	17.0526i	−0.425650	−	0.737247i
$536$	4.13652	+	15.1354i	0.178671	+	0.653751i
$537$		0			0
$538$	−13.2400	−	1.13618i	−0.570818	−	0.0489842i
$539$	−13.5662	−	2.24176i	−0.584338	−	0.0965594i
$540$		0			0
$541$	27.1035	+	15.6482i	1.16527	+	0.672769i	0.952561	−	0.304347i	$-0.0984381\pi$
$541$	27.1035	+	15.6482i	1.16527	+	0.672769i	0.212709	+	0.977116i	$0.431771\pi$
$542$	1.19364	+	2.54870i	0.0512712	+	0.109476i
$543$		0			0
$544$	−11.7512	−	16.4891i	−0.503829	−	0.706964i
$545$			35.8876i			1.53726i
$546$		0			0
$547$	−6.11696			−0.261542			−0.130771	−	0.991413i	$-0.541745\pi$
$547$	−6.11696			−0.261542			−0.130771	+	0.991413i	$0.541745\pi$
$548$	−8.98131	+	10.7761i	−0.383663	+	0.460330i
$549$		0			0
$550$	0.873696	+	1.86555i	0.0372545	+	0.0795472i
$551$	16.0124	−	27.7343i	0.682151	−	1.18152i
$552$		0			0
$553$	2.37078	+	0.194561i	0.100816	+	0.00827359i
$554$	3.10117	−	36.1382i	0.131756	−	1.53537i
$555$		0			0
$556$	−9.66004	+	3.55238i	−0.409677	+	0.150654i
$557$	−5.79102	+	3.34345i	−0.245374	+	0.141666i	−0.617644	−	0.786458i	$-0.711913\pi$
$557$	−5.79102	+	3.34345i	−0.245374	+	0.141666i	0.372270	+	0.928124i	$0.378579\pi$
$558$		0			0
$559$	18.2190			0.770582
$560$	−12.7407	−	17.7375i	−0.538394	−	0.749548i
$561$		0			0
$562$	−13.2268	+	18.9569i	−0.557940	+	0.799647i
$563$	6.41527	−	3.70386i	0.270372	−	0.156099i	−0.358685	−	0.933459i	$-0.616775\pi$
$563$	6.41527	−	3.70386i	0.270372	−	0.156099i	0.629056	+	0.777360i	$0.283441\pi$
$564$		0			0
$565$	−18.0275	+	31.2246i	−0.758425	+	1.31363i
$566$	2.67965	−	31.2262i	0.112634	−	1.31253i
$567$		0			0
$568$	6.78214	−	25.8257i	0.284572	−	1.08362i
$569$	12.2574	−	21.2304i	0.513857	−	0.890026i	−0.486014	−	0.873951i	$-0.661550\pi$
$569$	12.2574	−	21.2304i	0.513857	−	0.890026i	0.999871	−	0.0160749i	$-0.00511701\pi$
$570$		0			0
$571$	−4.88466	−	8.46048i	−0.204417	−	0.354060i	0.745530	−	0.666472i	$-0.232196\pi$
$571$	−4.88466	−	8.46048i	−0.204417	−	0.354060i	−0.949947	+	0.312412i	$0.898863\pi$
$572$	−10.5696	+	12.6817i	−0.441935	+	0.530248i
$573$		0			0
$574$	−9.07011	−	1.53350i	−0.378579	−	0.0640069i
$575$			4.54783i			0.189658i
$576$		0			0
$577$	8.36436	−	4.82917i	0.348213	−	0.201041i	−0.315685	−	0.948864i	$-0.602234\pi$
$577$	8.36436	−	4.82917i	0.348213	−	0.201041i	0.663898	+	0.747823i	$0.268901\pi$
$578$	−2.51203	−	5.36377i	−0.104487	−	0.223103i
$579$		0			0
$580$	−4.46494	+	25.8236i	−0.185397	+	1.07227i
$581$	−10.8410	−	22.9255i	−0.449759	−	0.951110i
$582$		0			0
$583$	22.0575	+	12.7349i	0.913527	+	0.527425i
$584$	−33.7483	+	9.22343i	−1.39651	+	0.381668i
$585$		0			0
$586$	−8.95980	+	12.8413i	−0.370126	+	0.530469i
$587$		−	2.08560i		−	0.0860820i	−0.999073	−	0.0430410i	$-0.986295\pi$
$587$		−	2.08560i		−	0.0860820i	0.999073	−	0.0430410i	$-0.0137046\pi$
$588$		0			0
$589$		−	34.5332i		−	1.42291i
$590$	−17.0563	−	11.9008i	−0.702199	−	0.489948i
$591$		0			0
$592$	−16.1994	+	2.96757i	−0.665792	+	0.121967i
$593$	−27.3663	−	15.7999i	−1.12380	−	0.648826i	−0.181431	−	0.983404i	$-0.558073\pi$
$593$	−27.3663	−	15.7999i	−1.12380	−	0.648826i	−0.942368	+	0.334578i	$0.891406\pi$
$594$		0			0
$595$	8.35427	+	17.6669i	0.342492	+	0.724271i
$596$	0.979198	−	5.66333i	0.0401095	−	0.231979i
$597$		0			0
$598$	−33.0058	+	15.4577i	−1.34971	+	0.632113i
$599$	−26.7061	+	15.4188i	−1.09118	+	0.629995i	−0.933891	−	0.357558i	$-0.883610\pi$
$599$	−26.7061	+	15.4188i	−1.09118	+	0.629995i	−0.157292	+	0.987552i	$0.550276\pi$
$600$		0			0
$601$			16.8538i			0.687481i	0.939065	+	0.343741i	$0.111694\pi$
$601$			16.8538i			0.687481i	−0.939065	+	0.343741i	$0.888306\pi$
$602$	−2.70435	+	15.9953i	−0.110221	+	0.651921i
$603$		0			0
$604$	20.0408	+	16.7030i	0.815447	+	0.679635i
$605$	7.36858	+	12.7628i	0.299576	+	0.518880i
$606$		0			0
$607$	2.84212	−	4.92270i	0.115358	−	0.199806i	−0.802565	−	0.596565i	$-0.796532\pi$
$607$	2.84212	−	4.92270i	0.115358	−	0.199806i	0.917923	+	0.396759i	$0.129865\pi$
$608$	−11.8421	+	25.9564i	−0.480259	+	1.05267i
$609$		0			0
$610$	6.00000	+	0.514885i	0.242933	+	0.0208471i
$611$	20.5324	−	35.5631i	0.830652	−	1.43873i
$612$		0			0
$613$	−14.7968	+	8.54292i	−0.597636	+	0.345045i	−0.768111	−	0.640317i	$-0.778803\pi$
$613$	−14.7968	+	8.54292i	−0.597636	+	0.345045i	0.170475	+	0.985362i	$0.445470\pi$
$614$	33.7382	+	23.5403i	1.36156	+	0.950007i
$615$		0			0
$616$	−9.56495	−	11.1619i	−0.385383	−	0.449727i
$617$	34.1007			1.37284			0.686421	−	0.727205i	$-0.259181\pi$
$617$	34.1007			1.37284			0.686421	+	0.727205i	$0.259181\pi$
$618$		0			0
$619$	−14.3212	+	8.26832i	−0.575616	+	0.332332i	−0.759389	−	0.650637i	$-0.774502\pi$
$619$	−14.3212	+	8.26832i	−0.575616	+	0.332332i	0.183773	+	0.982969i	$0.441169\pi$
$620$	9.75351	+	26.5229i	0.391711	+	1.06519i
$621$		0			0
$622$	−19.7028	−	1.69078i	−0.790011	−	0.0677941i
$623$	−38.5175	−	3.16099i	−1.54317	−	0.126643i
$624$		0			0
$625$	10.3712	−	17.9634i	0.414847	−	0.718535i
$626$	2.34992	−	1.10054i	0.0939217	−	0.0439866i
$627$		0			0
$628$	−12.9784	+	15.5718i	−0.517893	+	0.621384i
$629$	14.7372			0.587609
$630$		0			0
$631$			26.8671i			1.06956i	0.844991	+	0.534781i	$0.179606\pi$
$631$			26.8671i			1.06956i	−0.844991	+	0.534781i	$0.820394\pi$
$632$	1.80711	+	1.78918i	0.0718829	+	0.0711696i
$633$		0			0
$634$	−1.02298	+	0.479095i	−0.0406277	+	0.0190273i
$635$	24.4081	+	14.0920i	0.968607	+	0.559226i
$636$		0			0
$637$	18.6641	−	22.7357i	0.739498	−	0.900821i
$638$	−1.50816	+	17.5748i	−0.0597088	+	0.695792i
$639$		0			0
$640$	1.76410	−	23.2802i	0.0697321	−	0.920232i
$641$	−14.0425	−	24.3223i	−0.554645	−	0.960674i	−0.997931	−	0.0642934i	$-0.979521\pi$
$641$	−14.0425	−	24.3223i	−0.554645	−	0.960674i	0.443286	−	0.896380i	$-0.353813\pi$
$642$		0			0
$643$		−	23.4648i		−	0.925363i	−0.886525	−	0.462682i	$-0.846887\pi$
$643$		−	23.4648i		−	0.925363i	0.886525	−	0.462682i	$-0.153113\pi$
$644$	−8.67181	−	31.2719i	−0.341717	−	1.23228i
$645$		0			0
$646$	14.6086	−	20.9372i	0.574768	−	0.823765i
$647$	23.4291	+	40.5803i	0.921092	+	1.59538i	0.797729	+	0.603017i	$0.206035\pi$
$647$	23.4291	+	40.5803i	0.921092	+	1.59538i	0.123363	+	0.992362i	$0.460632\pi$
$648$		0			0
$649$	−12.1232	−	6.99933i	−0.475877	−	0.274748i
$650$	−4.39076	−	0.376789i	−0.172220	−	0.0147789i
$651$		0			0
$652$	−2.92285	−	0.505365i	−0.114467	−	0.0197916i
$653$	−12.2356	−	7.06424i	−0.478817	−	0.276445i	0.241106	−	0.970499i	$-0.422490\pi$
$653$	−12.2356	−	7.06424i	−0.478817	−	0.276445i	−0.719923	+	0.694054i	$0.755823\pi$
$654$		0			0
$655$	14.4803	−	8.36020i	0.565792	−	0.326660i
$656$	−6.37110	−	7.49107i	−0.248750	−	0.292477i
$657$		0			0
$658$	28.1748	+	23.3052i	1.09837	+	0.908531i
$659$	−37.6955			−1.46841			−0.734205	−	0.678928i	$-0.762445\pi$
$659$	−37.6955			−1.46841			−0.734205	+	0.678928i	$0.762445\pi$
$660$		0			0
$661$	20.9383	+	36.2662i	0.814406	+	1.41059i	0.909754	+	0.415148i	$0.136270\pi$
$661$	20.9383	+	36.2662i	0.814406	+	1.41059i	−0.0953478	+	0.995444i	$0.530396\pi$
$662$	7.87867	+	16.8228i	0.306213	+	0.653837i
$663$		0			0
$664$	6.88605	−	26.2214i	0.267230	−	1.01759i
$665$	15.6724	−	22.6410i	0.607751	−	0.877980i
$666$		0			0
$667$	−19.4711	+	33.7249i	−0.753922	+	1.30583i
$668$	−5.58908	−	15.1985i	−0.216248	−	0.588048i
$669$		0			0
$670$	9.26385	−	13.2771i	0.357894	−	0.512938i
$671$	4.05335			0.156478
$672$		0			0
$673$	15.2830			0.589115			0.294558	−	0.955634i	$-0.404828\pi$
$673$	15.2830			0.589115			0.294558	+	0.955634i	$0.404828\pi$
$674$	22.9451	−	32.8852i	0.883811	−	1.26669i
$675$		0			0
$676$	−3.21560	−	8.74424i	−0.123677	−	0.336317i
$677$	−7.97531	+	13.8136i	−0.306516	+	0.530901i	−0.977598	−	0.210482i	$-0.932497\pi$
$677$	−7.97531	+	13.8136i	−0.306516	+	0.530901i	0.671082	+	0.741383i	$0.265830\pi$
$678$		0			0
$679$	−0.622566	−	1.31655i	−0.0238919	−	0.0505244i
$680$	−5.30653	+	20.2067i	−0.203496	+	0.774892i
$681$		0			0
$682$	8.06726	+	17.2255i	0.308911	+	0.659598i
$683$	20.4434	+	35.4089i	0.782244	+	1.35489i	0.930632	+	0.365957i	$0.119258\pi$
$683$	20.4434	+	35.4089i	0.782244	+	1.35489i	−0.148388	+	0.988929i	$0.547409\pi$
$684$		0			0
$685$	14.4742			0.553030
$686$	17.1903	+	19.7609i	0.656330	+	0.754474i
$687$		0			0
$688$	−13.2106	+	11.2356i	−0.503651	+	0.428352i
$689$	−47.1869	+	27.2433i	−1.79768	+	1.03789i
$690$		0			0
$691$	−3.32796	−	1.92140i	−0.126601	−	0.0730933i	0.435362	−	0.900256i	$-0.356620\pi$
$691$	−3.32796	−	1.92140i	−0.126601	−	0.0730933i	−0.561963	+	0.827162i	$0.689954\pi$
$692$	30.7189	+	5.31134i	1.16776	+	0.201907i
$693$		0			0
$694$	7.19394	+	0.617342i	0.273078	+	0.0234340i
$695$	9.19703	+	5.30991i	0.348863	+	0.201416i
$696$		0			0
$697$	4.39993	+	7.62090i	0.166659	+	0.288662i
$698$	−12.4135	+	17.7911i	−0.469857	+	0.673404i
$699$		0			0
$700$	0.982547	−	3.79893i	0.0371368	−	0.143586i
$701$			20.0865i			0.758657i	0.925262	+	0.379328i	$0.123845\pi$
$701$			20.0865i			0.758657i	−0.925262	+	0.379328i	$0.876155\pi$
$702$		0			0
$703$	−10.3826	−	17.9832i	−0.391587	−	0.678248i
$704$	−0.156708	−	15.7137i	−0.00590614	−	0.592233i
$705$		0			0
$706$	−0.915482	+	10.6682i	−0.0344546	+	0.401503i
$707$	−1.84943	−	1.28021i	−0.0695551	−	0.0481471i
$708$		0			0
$709$	−26.4625	−	15.2782i	−0.993821	−	0.573783i	−0.0874070	−	0.996173i	$-0.527858\pi$
$709$	−26.4625	−	15.2782i	−0.993821	−	0.573783i	−0.906414	+	0.422390i	$0.861191\pi$
$710$	−24.9498	+	11.6848i	−0.936351	+	0.438524i
$711$		0			0
$712$	−29.3597	−	29.0683i	−1.10030	−	1.08938i
$713$			41.9923i			1.57262i
$714$		0			0
$715$	17.0338			0.637027
$716$	15.1554	−	18.1840i	0.566385	−	0.679567i
$717$		0			0
$718$	38.1315	−	17.8582i	1.42305	−	0.666463i
$719$	8.17064	−	14.1520i	0.304714	−	0.527779i	−0.672484	−	0.740112i	$-0.734773\pi$
$719$	8.17064	−	14.1520i	0.304714	−	0.527779i	0.977198	+	0.212332i	$0.0681059\pi$
$720$		0			0
$721$	0.0936580	−	1.14124i	0.00348801	−	0.0425022i
$722$	−9.06925	−	0.778270i	−0.337522	−	0.0289642i
$723$		0			0
$724$	10.5369	+	28.6532i	0.391601	+	1.06489i
$725$	−4.07785	+	2.35435i	−0.151447	+	0.0874382i
$726$		0			0
$727$	−22.7202			−0.842646			−0.421323	−	0.906911i	$-0.638434\pi$
$727$	−22.7202			−0.842646			−0.421323	+	0.906911i	$0.638434\pi$
$728$	30.9103	−	5.78142i	1.14561	−	0.214274i
$729$		0			0
$730$	29.6046	+	20.6561i	1.09571	+	0.764516i
$731$	13.4396	−	7.75936i	0.497082	−	0.286990i
$732$		0			0
$733$	23.1635	−	40.1204i	0.855565	−	1.48188i	−0.0205547	−	0.999789i	$-0.506543\pi$
$733$	23.1635	−	40.1204i	0.855565	−	1.48188i	0.876120	−	0.482093i	$-0.160123\pi$
$734$	−5.93949	−	0.509692i	−0.219231	−	0.0188131i
$735$		0			0
$736$	14.3999	−	31.5629i	0.530788	−	1.16343i
$737$	5.44844	−	9.43698i	0.200696	−	0.347616i
$738$		0			0
$739$	−7.30928	−	12.6600i	−0.268876	−	0.465707i	0.699696	−	0.714441i	$-0.253319\pi$
$739$	−7.30928	−	12.6600i	−0.268876	−	0.465707i	−0.968572	+	0.248734i	$0.919986\pi$
$740$	13.0534	+	10.8794i	0.479853	+	0.399934i
$741$		0			0
$742$	−16.9140	−	45.4715i	−0.620933	−	1.66931i
$743$			21.9948i			0.806912i	0.914999	+	0.403456i	$0.132191\pi$
$743$			21.9948i			0.806912i	−0.914999	+	0.403456i	$0.867809\pi$
$744$		0			0
$745$	−5.13564	+	2.96506i	−0.188155	+	0.108631i
$746$	14.9412	−	6.99745i	0.547036	−	0.256195i
$747$		0			0
$748$	−2.39579	+	13.8564i	−0.0875989	+	0.506640i
$749$	−2.06486	+	25.1608i	−0.0754484	+	0.919357i
$750$		0			0
$751$	6.81783	+	3.93627i	0.248786	+	0.143637i	0.619208	−	0.785227i	$-0.287454\pi$
$751$	6.81783	+	3.93627i	0.248786	+	0.143637i	−0.370422	+	0.928863i	$0.620787\pi$
$752$	7.04350	+	38.4491i	0.256850	+	1.40210i
$753$		0			0
$754$	−30.9469	−	21.5927i	−1.12702	−	0.786359i
$755$		−	26.9184i		−	0.979659i
$756$		0			0
$757$		−	31.6014i		−	1.14857i	−0.818655	−	0.574285i	$-0.805280\pi$
$757$		−	31.6014i		−	1.14857i	0.818655	−	0.574285i	$-0.194720\pi$
$758$	4.37531	−	6.27074i	0.158918	−	0.227764i
$759$		0			0
$760$	28.3960	−	7.76064i	1.03003	−	0.281508i
$761$	21.1485	+	12.2101i	0.766634	+	0.442616i	0.831672	−	0.555267i	$-0.187384\pi$
$761$	21.1485	+	12.2101i	0.766634	+	0.442616i	−0.0650388	+	0.997883i	$0.520717\pi$
$762$		0			0
$763$	26.1879	−	37.8321i	0.948066	−	1.36961i
$764$	−0.131354	+	0.759705i	−0.00475223	+	0.0274852i
$765$		0			0
$766$	−22.0402	−	47.0610i	−0.796346	−	1.70038i
$767$	25.9348	−	14.9734i	0.936450	−	0.540660i
$768$		0			0
$769$			15.1803i			0.547415i	0.961813	+	0.273707i	$0.0882500\pi$
$769$			15.1803i			0.547415i	−0.961813	+	0.273707i	$0.911750\pi$
$770$	−2.52842	+	14.9548i	−0.0911180	+	0.538932i
$771$		0			0
$772$	33.0839	−	39.6951i	1.19072	−	1.42866i
$773$	24.1092	+	41.7583i	0.867147	+	1.50194i	0.864899	+	0.501946i	$0.167382\pi$
$773$	24.1092	+	41.7583i	0.867147	+	1.50194i	0.00224824	+	0.999997i	$0.499284\pi$
$774$		0			0
$775$	−2.53875	+	4.39725i	−0.0911947	+	0.157954i
$776$	0.395446	−	1.50582i	0.0141957	−	0.0540557i
$777$		0			0
$778$	−2.38806	+	27.8283i	−0.0856161	+	0.997692i
$779$	6.19965	−	10.7381i	0.222126	−	0.384733i
$780$		0			0
$781$	−16.0594	+	9.27191i	−0.574651	+	0.331775i
$782$	−17.7641	+	25.4597i	−0.635242	+	0.910436i
$783$		0			0
$784$	0.487599	+	27.9958i	0.0174142	+	0.999848i
$785$	20.9158			0.746516
$786$		0			0
$787$	17.0492	−	9.84337i	0.607739	−	0.350878i	−0.164341	−	0.986404i	$-0.552550\pi$
$787$	17.0492	−	9.84337i	0.607739	−	0.350878i	0.772080	+	0.635525i	$0.219216\pi$
$788$	−14.2356	+	5.23499i	−0.507122	+	0.186489i
$789$		0			0
$790$	0.224339	−	2.61425i	0.00798163	−	0.0930107i
$791$	41.7896	−	19.7614i	1.48587	−	0.702634i
$792$		0			0
$793$	−4.33560	+	7.50948i	−0.153962	+	0.266669i
$794$	19.5575	+	41.7599i	0.694071	+	1.48200i
$795$		0			0
$796$	3.40355	−	4.08368i	0.120636	−	0.144742i
$797$	−25.6614			−0.908975			−0.454487	−	0.890753i	$-0.650178\pi$
$797$	−25.6614			−0.908975			−0.454487	+	0.890753i	$0.650178\pi$
$798$		0			0
$799$		−	34.9785i		−	1.23745i
$800$	3.41611	−	2.43455i	0.120778	−	0.0860742i
$801$		0			0
$802$	−6.94866	−	14.8370i	−0.245366	−	0.523913i
$803$	21.0421	+	12.1487i	0.742561	+	0.428718i
$804$		0			0
$805$	−19.0577	+	27.5314i	−0.671694	+	0.970355i
$806$	−40.5420	−	3.47908i	−1.42803	−	0.122545i
$807$		0			0
$808$	−0.633929	−	2.31953i	−0.0223016	−	0.0816009i
$809$	16.1716	+	28.0101i	0.568564	+	0.984781i	0.996708	+	0.0810709i	$0.0258340\pi$
$809$	16.1716	+	28.0101i	0.568564	+	0.984781i	−0.428145	+	0.903710i	$0.640833\pi$
$810$		0			0
$811$			45.9933i			1.61504i	0.589838	+	0.807521i	$0.299191\pi$
$811$			45.9933i			1.61504i	−0.589838	+	0.807521i	$0.700809\pi$
$812$	23.5509	−	23.9646i	0.826474	−	0.840994i
$813$		0			0
$814$	9.37997	+	6.54472i	0.328768	+	0.229392i
$815$	1.53027	+	2.65051i	0.0536030	+	0.0928431i
$816$		0			0
$817$	−18.9369	−	10.9332i	−0.662518	−	0.382505i
$818$	2.54050	−	29.6047i	0.0888265	−	1.03510i
$819$		0			0
$820$	−1.72873	+	9.99834i	−0.0603698	+	0.349157i
$821$	12.8183	+	7.40064i	0.447361	+	0.258284i	0.706715	−	0.707498i	$-0.250176\pi$
$821$	12.8183	+	7.40064i	0.447361	+	0.258284i	−0.259354	+	0.965782i	$0.583510\pi$
$822$		0			0
$823$	−11.2556	+	6.49843i	−0.392346	+	0.226521i	−0.683176	−	0.730254i	$-0.739402\pi$
$823$	−11.2556	+	6.49843i	−0.392346	+	0.226521i	0.290830	+	0.956775i	$0.406069\pi$
$824$	0.861274	−	0.869906i	0.0300039	−	0.0303046i
$825$		0			0
$826$	9.29625	+	24.9920i	0.323458	+	0.869582i
$827$	−37.8013			−1.31448			−0.657240	−	0.753681i	$-0.728276\pi$
$827$	−37.8013			−1.31448			−0.657240	+	0.753681i	$0.728276\pi$
$828$		0			0
$829$	−8.63343	−	14.9535i	−0.299851	−	0.519358i	0.676250	−	0.736672i	$-0.263604\pi$
$829$	−8.63343	−	14.9535i	−0.299851	−	0.519358i	−0.976102	+	0.217314i	$0.930270\pi$
$830$	−25.3321	+	11.8638i	−0.879289	+	0.411800i
$831$		0			0
$832$	29.2798	+	16.5176i	1.01509	+	0.572644i
$833$	4.08494	−	24.7204i	0.141535	−	0.856510i
$834$		0			0
$835$	−8.35427	+	14.4700i	−0.289112	+	0.500756i
$836$	18.5963	−	6.83859i	0.643166	−	0.236518i
$837$		0			0
$838$	15.1630	+	10.5797i	0.523796	+	0.365470i
$839$	2.55046			0.0880517			0.0440259	−	0.999030i	$-0.485982\pi$
$839$	2.55046			0.0880517			0.0440259	+	0.999030i	$0.485982\pi$
$840$		0			0
$841$	−11.3195			−0.390329
$842$	−35.6301	−	24.8603i	−1.22790	−	0.856744i
$843$		0			0
$844$	9.58323	+	26.0599i	0.329869	+	0.897017i
$845$	−4.80651	+	8.32513i	−0.165349	+	0.286393i
$846$		0			0
$847$	1.54542	−	18.8313i	0.0531012	−	0.647050i
$848$	17.4145	−	48.8541i	0.598016	−	1.67766i
$849$		0			0
$850$	−3.39940	+	1.59205i	−0.116599	+	0.0546069i
$851$	12.6252	+	21.8675i	0.432787	+	0.749609i
$852$		0			0
$853$	−14.8204			−0.507442			−0.253721	−	0.967277i	$-0.581655\pi$
$853$	−14.8204			−0.507442			−0.253721	+	0.967277i	$0.581655\pi$
$854$	−5.94937	−	4.92110i	−0.203583	−	0.168397i
$855$		0			0
$856$	−18.9884	+	19.1787i	−0.649009	+	0.655513i
$857$	−7.96620	+	4.59929i	−0.272120	+	0.157109i	−0.629851	−	0.776716i	$-0.716884\pi$
$857$	−7.96620	+	4.59929i	−0.272120	+	0.157109i	0.357730	+	0.933825i	$0.383551\pi$
$858$		0			0
$859$	23.1202	+	13.3484i	0.788850	+	0.455443i	0.839558	−	0.543271i	$-0.182814\pi$
$859$	23.1202	+	13.3484i	0.788850	+	0.455443i	−0.0507075	+	0.998714i	$0.516148\pi$
$860$	17.6323	+	3.04865i	0.601256	+	0.103958i
$861$		0			0
$862$	0.200919	−	2.34133i	0.00684334	−	0.0797460i
$863$	−0.837724	−	0.483660i	−0.0285165	−	0.0164640i	0.485674	−	0.874140i	$-0.338574\pi$
$863$	−0.837724	−	0.483660i	−0.0285165	−	0.0164640i	−0.514190	+	0.857676i	$0.671908\pi$
$864$		0			0
$865$	−16.0830	−	27.8566i	−0.546838	−	0.947152i
$866$	31.7651	+	22.1636i	1.07942	+	0.753149i
$867$		0			0
$868$	9.07232	−	35.0773i	0.307935	−	1.19060i
$869$		−	1.76608i		−	0.0599100i
$870$		0			0
$871$	11.6557	+	20.1882i	0.394938	+	0.684052i
$872$	47.4484	−	12.9677i	1.60681	−	0.439141i
$873$		0			0
$874$	43.5825	+	3.74000i	1.47420	+	0.126507i
$875$	−28.3388	+	13.4008i	−0.958027	+	0.453030i
$876$		0			0
$877$	−3.70815	−	2.14090i	−0.125215	−	0.0722932i	0.436084	−	0.899906i	$-0.356365\pi$
$877$	−3.70815	−	2.14090i	−0.125215	−	0.0722932i	−0.561299	+	0.827613i	$0.689698\pi$
$878$	−5.06400	−	10.8128i	−0.170902	−	0.364915i
$879$		0			0
$880$	−12.3512	+	10.5046i	−0.416360	+	0.354111i
$881$		−	20.1386i		−	0.678487i	−0.940699	−	0.339244i	$-0.889829\pi$
$881$		−	20.1386i		−	0.678487i	0.940699	−	0.339244i	$-0.110171\pi$
$882$		0			0
$883$	3.01850			0.101580			0.0507902	−	0.998709i	$-0.483826\pi$
$883$	3.01850			0.101580			0.0507902	+	0.998709i	$0.483826\pi$
$884$	−23.1086	−	19.2599i	−0.777226	−	0.647780i
$885$		0			0
$886$	2.49314	+	5.32344i	0.0837587	+	0.178845i
$887$	6.56652	−	11.3736i	0.220482	−	0.381886i	−0.734472	−	0.678639i	$-0.762570\pi$
$887$	6.56652	−	11.3736i	0.220482	−	0.381886i	0.954955	+	0.296752i	$0.0959036\pi$
$888$		0			0
$889$	−15.4474	−	32.6667i	−0.518088	−	1.09561i
$890$	−3.64479	+	42.4731i	−0.122174	+	1.42370i
$891$		0			0
$892$	18.2576	+	49.6483i	0.611310	+	1.66235i
$893$	−42.6829	+	24.6430i	−1.42833	+	0.824645i
$894$		0			0
$895$	−24.4244			−0.816416
$896$	−18.8477	+	23.2543i	−0.629659	+	0.776872i
$897$		0			0
$898$	−15.2272	+	21.8239i	−0.508140	+	0.728272i
$899$	−37.6527	+	21.7388i	−1.25579	+	0.725030i
$900$		0			0
$901$	−23.2056	+	40.1932i	−0.773089	+	1.33903i
$902$	−0.583928	+	6.80457i	−0.0194427	+	0.226567i
$903$		0			0
$904$	47.7974	+	12.5522i	1.58972	+	0.417479i
$905$	15.7500	−	27.2798i	0.523548	−	0.906812i
$906$		0			0
$907$	−10.8627	−	18.8148i	−0.360691	−	0.624736i	0.627383	−	0.778711i	$-0.284126\pi$
$907$	−10.8627	−	18.8148i	−0.360691	−	0.624736i	−0.988075	+	0.153975i	$0.950793\pi$
$908$	−27.6689	−	23.0607i	−0.918225	−	0.765295i
$909$		0			0
$910$	−25.0016	−	20.6804i	−0.828796	−	0.685550i
$911$		−	8.27670i		−	0.274219i	−0.990556	−	0.137110i	$-0.956219\pi$
$911$		−	8.27670i		−	0.274219i	0.990556	−	0.137110i	$-0.0437813\pi$
$912$		0			0
$913$	−16.3054	+	9.41395i	−0.539632	+	0.311556i
$914$	3.40160	+	7.26321i	0.112515	+	0.240246i
$915$		0			0
$916$	23.6554	+	4.09006i	0.781597	+	0.135139i
$917$	−21.3655	−	1.75339i	−0.705550	−	0.0579020i
$918$		0			0
$919$	−48.2363	−	27.8492i	−1.59117	−	0.918661i	−0.993107	−	0.117211i	$-0.962605\pi$
$919$	−48.2363	−	27.8492i	−1.59117	−	0.918661i	−0.598061	−	0.801451i	$-0.704062\pi$
$920$	−34.5295	+	9.43693i	−1.13840	+	0.311126i
$921$		0			0
$922$	−24.5396	+	35.1704i	−0.808168	+	1.15828i
$923$		−	39.6702i		−	1.30576i
$924$		0			0
$925$			3.05316i			0.100387i
$926$	−9.75705	−	6.80782i	−0.320636	−	0.223719i
$927$		0			0
$928$	35.7558	−	3.42786i	1.17374	−	0.112525i
$929$	0.357266	+	0.206268i	0.0117215	+	0.00676743i	0.505849	−	0.862622i	$-0.331179\pi$
$929$	0.357266	+	0.206268i	0.0117215	+	0.00676743i	−0.494128	+	0.869389i	$0.664513\pi$
$930$		0			0
$931$	−33.0432	+	12.4312i	−1.08295	+	0.407418i
$932$	18.9482	+	3.27618i	0.620670	+	0.107315i
$933$		0			0
$934$	−41.6380	+	19.5004i	−1.36244	+	0.638073i
$935$	12.5653	−	7.25459i	0.410930	−	0.237250i
$936$		0			0
$937$			30.5249i			0.997204i	0.866831	+	0.498602i	$0.166153\pi$
$937$			30.5249i			0.997204i	−0.866831	+	0.498602i	$0.833847\pi$
$938$	−19.4543	+	7.23642i	−0.635206	+	0.236278i
$939$		0			0
$940$	25.8221	−	30.9821i	0.842223	−	1.01053i
$941$	−20.5887	−	35.6607i	−0.671173	−	1.16251i	−0.977572	−	0.210602i	$-0.932457\pi$
$941$	−20.5887	−	35.6607i	−0.671173	−	1.16251i	0.306399	−	0.951903i	$-0.400876\pi$
$942$		0			0
$943$	−7.53877	+	13.0575i	−0.245496	+	0.425212i
$944$	−9.57133	+	26.8511i	−0.311520	+	0.873929i
$945$		0			0
$946$	12.0000	+	1.02977i	0.390154	+	0.0334807i
$947$	−0.870237	+	1.50729i	−0.0282789	+	0.0489805i	−0.879819	−	0.475310i	$-0.842336\pi$
$947$	−0.870237	+	1.50729i	−0.0282789	+	0.0489805i	0.851540	+	0.524290i	$0.175669\pi$
$948$		0			0
$949$	−45.0148	+	25.9893i	−1.46124	+	0.843648i
$950$	4.33766	+	3.02653i	0.140732	+	0.0981935i
$951$		0			0
$952$	20.3393	−	17.4293i	0.659200	−	0.564886i
$953$	11.1171			0.360119			0.180059	−	0.983656i	$-0.442371\pi$
$953$	11.1171			0.360119			0.180059	+	0.983656i	$0.442371\pi$
$954$		0			0
$955$	0.688919	−	0.397747i	0.0222929	−	0.0128708i
$956$	40.8883	−	15.0362i	1.32242	−	0.486307i
$957$		0			0
$958$	40.5896	+	3.48316i	1.31139	+	0.112536i
$959$	−15.2584	−	10.5621i	−0.492720	−	0.341068i
$960$		0			0
$961$	−7.94152	+	13.7551i	−0.256178	+	0.443713i
$962$	−22.1583	+	10.3774i	−0.714411	+	0.334582i
$963$		0			0
$964$	11.6478	+	9.70785i	0.375149	+	0.312669i
$965$	−53.3177			−1.71636
$966$		0			0
$967$		−	6.95681i		−	0.223716i	−0.993724	−	0.111858i	$-0.964320\pi$
$967$		−	6.95681i		−	0.223716i	0.993724	−	0.111858i	$-0.0356801\pi$
$968$	14.2116	−	14.3540i	0.456777	−	0.461355i
$969$		0			0
$970$	−1.45475	+	0.681307i	−0.0467092	+	0.0218754i
$971$	21.5086	+	12.4180i	0.690245	+	0.398513i	0.803704	−	0.595030i	$-0.202860\pi$
$971$	21.5086	+	12.4180i	0.690245	+	0.398513i	−0.113459	+	0.993543i	$0.536193\pi$
$972$		0			0
$973$	−5.82060	−	12.3089i	−0.186600	−	0.394604i
$974$	−3.05545	+	35.6054i	−0.0979028	+	1.14087i
$975$		0			0
$976$	−1.48730	−	8.11888i	−0.0476073	−	0.259879i
$977$	5.38526	+	9.32755i	0.172290	+	0.298415i	0.939220	−	0.343316i	$-0.111550\pi$
$977$	5.38526	+	9.32755i	0.172290	+	0.298415i	−0.766930	+	0.641731i	$0.778217\pi$
$978$		0			0
$979$			28.6930i			0.917033i
$980$	21.8675	−	18.8804i	0.698531	−	0.603112i
$981$		0			0
$982$	20.8847	−	29.9322i	0.666458	−	0.955176i
$983$	−20.3158	−	35.1881i	−0.647974	−	1.12232i	−0.983606	−	0.180331i	$-0.942283\pi$
$983$	−20.3158	−	35.1881i	−0.647974	−	1.12232i	0.335631	−	0.941993i	$-0.391050\pi$
$984$		0			0
$985$	13.5533	+	7.82499i	0.431844	+	0.249325i
$986$	−32.0248	−	2.74818i	−1.01988	−	0.0875199i
$987$		0			0
$988$	−7.22165	+	41.7674i	−0.229751	+	1.32880i
$989$	23.0272	+	13.2948i	0.732223	+	0.422749i
$990$		0			0
$991$	−30.4544	+	17.5829i	−0.967417	+	0.558538i	−0.898448	−	0.439080i	$-0.855304\pi$
$991$	−30.4544	+	17.5829i	−0.967417	+	0.558538i	−0.0689690	+	0.997619i	$0.521971\pi$
$992$	31.5426	−	22.4793i	1.00148	−	0.713719i
$993$		0			0
$994$	34.8283	+	5.88847i	1.10469	+	0.186771i
$995$	−5.48512			−0.173890
$996$		0			0
$997$	−26.8018	−	46.4221i	−0.848822	−	1.47020i	−0.882260	−	0.470762i	$-0.843979\pi$
$997$	−26.8018	−	46.4221i	−0.848822	−	1.47020i	0.0334384	−	0.999441i	$-0.489354\pi$
$998$	13.5667	+	28.9680i	0.429445	+	0.916966i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.bk.b.19.6	✓	32
3.2	odd	2	inner	504.2.bk.b.19.11	yes	32
4.3	odd	2		2016.2.bs.b.271.6		32
7.3	odd	6	inner	504.2.bk.b.451.7	yes	32
8.3	odd	2	inner	504.2.bk.b.19.7	yes	32
8.5	even	2		2016.2.bs.b.271.12		32
12.11	even	2		2016.2.bs.b.271.11		32
21.17	even	6	inner	504.2.bk.b.451.10	yes	32
24.5	odd	2		2016.2.bs.b.271.5		32
24.11	even	2	inner	504.2.bk.b.19.10	yes	32
28.3	even	6		2016.2.bs.b.1711.12		32
56.3	even	6	inner	504.2.bk.b.451.6	yes	32
56.45	odd	6		2016.2.bs.b.1711.6		32
84.59	odd	6		2016.2.bs.b.1711.5		32
168.59	odd	6	inner	504.2.bk.b.451.11	yes	32
168.101	even	6		2016.2.bs.b.1711.11		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bk.b.19.6	✓	32	1.1	even	1	trivial
504.2.bk.b.19.7	yes	32	8.3	odd	2	inner
504.2.bk.b.19.10	yes	32	24.11	even	2	inner
504.2.bk.b.19.11	yes	32	3.2	odd	2	inner
504.2.bk.b.451.6	yes	32	56.3	even	6	inner
504.2.bk.b.451.7	yes	32	7.3	odd	6	inner
504.2.bk.b.451.10	yes	32	21.17	even	6	inner
504.2.bk.b.451.11	yes	32	168.59	odd	6	inner
2016.2.bs.b.271.5		32	24.5	odd	2
2016.2.bs.b.271.6		32	4.3	odd	2
2016.2.bs.b.271.11		32	12.11	even	2
2016.2.bs.b.271.12		32	8.5	even	2
2016.2.bs.b.1711.5		32	84.59	odd	6
2016.2.bs.b.1711.6		32	56.45	odd	6
2016.2.bs.b.1711.11		32	168.101	even	6
2016.2.bs.b.1711.12		32	28.3	even	6

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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809233 + 1.15980i) q^{2} +(-0.690284 - 1.87710i) q^{4} +(-1.03180 + 1.78713i) q^{5} +(2.39181 - 1.13104i) q^{7} +(2.73567 + 0.718419i) q^{8} +O(q^{10})\)	\(q+(-0.809233 + 1.15980i) q^{2} +(-0.690284 - 1.87710i) q^{4} +(-1.03180 + 1.78713i) q^{5} +(2.39181 - 1.13104i) q^{7} +(2.73567 + 0.718419i) q^{8} +(-1.23775 - 2.64289i) q^{10} +(-0.982155 - 1.70114i) q^{11} +4.20219 q^{13} +(-0.623755 + 3.68930i) q^{14} +(-3.04702 + 2.59146i) q^{16} +(3.09983 - 1.78969i) q^{17} +(-4.36777 - 2.52173i) q^{19} +(4.06686 + 0.703166i) q^{20} +(2.76778 + 0.237515i) q^{22} +(5.31120 + 3.06642i) q^{23} +(0.370777 + 0.642204i) q^{25} +(-3.40055 + 4.87371i) q^{26} +(-3.77410 - 3.70894i) q^{28} +6.34977i q^{29} +(3.42356 + 5.92978i) q^{31} +(-0.539841 - 5.63104i) q^{32} +(-0.432800 + 5.04346i) q^{34} +(-0.446563 + 5.44148i) q^{35} +(3.56564 + 2.05862i) q^{37} +(6.45925 - 3.02508i) q^{38} +(-4.10657 + 4.14773i) q^{40} +2.45849i q^{41} +4.33560 q^{43} +(-2.51525 + 3.01788i) q^{44} +(-7.85444 + 3.67849i) q^{46} +(4.88612 - 8.46301i) q^{47} +(4.44152 - 5.41045i) q^{49} +(-1.04487 - 0.0896650i) q^{50} +(-2.90070 - 7.88793i) q^{52} +(-11.2291 + 6.48313i) q^{53} +4.05355 q^{55} +(7.35576 - 1.37581i) q^{56} +(-7.36447 - 5.13844i) q^{58} +(6.17173 - 3.56325i) q^{59} +(-1.03175 + 1.78704i) q^{61} +(-9.64783 - 0.827920i) q^{62} +(6.96775 + 3.93071i) q^{64} +(-4.33582 + 7.50986i) q^{65} +(2.77372 + 4.80422i) q^{67} +(-5.49918 - 4.58330i) q^{68} +(-5.94967 - 4.92135i) q^{70} -9.44037i q^{71} +(-10.7122 + 6.18471i) q^{73} +(-5.27303 + 2.46953i) q^{74} +(-1.71855 + 9.93945i) q^{76} +(-4.27318 - 2.95796i) q^{77} +(0.778628 + 0.449541i) q^{79} +(-1.48737 - 8.11929i) q^{80} +(-2.85137 - 1.98949i) q^{82} -9.58499i q^{83} +7.38639i q^{85} +(-3.50851 + 5.02844i) q^{86} +(-1.46472 - 5.35936i) q^{88} +(-12.6502 - 7.30359i) q^{89} +(10.0508 - 4.75282i) q^{91} +(2.08975 - 12.0864i) q^{92} +(5.86141 + 12.5155i) q^{94} +(9.01332 - 5.20384i) q^{95} -0.550439i q^{97} +(2.68082 + 9.52959i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{4}+O(q^{10}) \) 32 * q + 2 * q^4	\( 32 q + 2 q^{4} + 18 q^{10} - 10 q^{16} - 12 q^{22} - 16 q^{25} - 6 q^{28} - 30 q^{40} + 16 q^{43} + 16 q^{46} + 8 q^{49} - 72 q^{52} - 38 q^{58} + 44 q^{64} + 16 q^{67} - 18 q^{70} - 24 q^{73} - 96 q^{82} - 30 q^{88} - 8 q^{91} - 72 q^{94}+O(q^{100}) \) 32 * q + 2 * q^4 + 18 * q^10 - 10 * q^16 - 12 * q^22 - 16 * q^25 - 6 * q^28 - 30 * q^40 + 16 * q^43 + 16 * q^46 + 8 * q^49 - 72 * q^52 - 38 * q^58 + 44 * q^64 + 16 * q^67 - 18 * q^70 - 24 * q^73 - 96 * q^82 - 30 * q^88 - 8 * q^91 - 72 * q^94

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