LMFDB - Embedded newform 882.2.v.a.251.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(125,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 1]))

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

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

chi := DirichletCharacter("882.125");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.v (of order $14$, degree $6$, 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:	$7.04280545828$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			251.13
Character	$\chi$	$=$	882.251
Dual form			882.2.v.a.629.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.781831 + 0.623490i) q^{2} +(0.222521 + 0.974928i) q^{4} +(-0.815549 - 0.392748i) q^{5} +(-2.62718 - 0.312901i) q^{7} +(-0.433884 + 0.900969i) q^{8} +O(q^{10})$	\(q+(0.781831 + 0.623490i) q^{2} +(0.222521 + 0.974928i) q^{4} +(-0.815549 - 0.392748i) q^{5} +(-2.62718 - 0.312901i) q^{7} +(-0.433884 + 0.900969i) q^{8} +(-0.392748 - 0.815549i) q^{10} +(-1.75469 - 1.39932i) q^{11} +(-2.08202 - 1.66035i) q^{13} +(-1.85892 - 1.88266i) q^{14} +(-0.900969 + 0.433884i) q^{16} +(-1.16736 + 5.11454i) q^{17} -0.423228i q^{19} +(0.201424 - 0.882496i) q^{20} +(-0.499412 - 2.18807i) q^{22} +(-5.71651 + 1.30476i) q^{23} +(-2.60658 - 3.26855i) q^{25} +(-0.592573 - 2.59623i) q^{26} +(-0.279548 - 2.63094i) q^{28} +(-6.67860 - 1.52435i) q^{29} +2.46422i q^{31} +(-0.974928 - 0.222521i) q^{32} +(-4.10154 + 3.27087i) q^{34} +(2.01971 + 1.28701i) q^{35} +(2.08037 - 9.11469i) q^{37} +(0.263879 - 0.330893i) q^{38} +(0.707707 - 0.564378i) q^{40} +(-0.0430939 - 0.0207529i) q^{41} +(2.98706 - 1.43849i) q^{43} +(0.973781 - 2.02208i) q^{44} +(-5.28285 - 2.54409i) q^{46} +(-4.38175 + 5.49454i) q^{47} +(6.80419 + 1.64409i) q^{49} -4.18063i q^{50} +(1.15543 - 2.39928i) q^{52} +(8.18250 - 1.86760i) q^{53} +(0.881458 + 1.83037i) q^{55} +(1.42181 - 2.23125i) q^{56} +(-4.27112 - 5.35582i) q^{58} +(-7.08850 + 3.41364i) q^{59} +(1.07627 + 0.245652i) q^{61} +(-1.53642 + 1.92660i) q^{62} +(-0.623490 - 0.781831i) q^{64} +(1.04589 + 2.17181i) q^{65} +9.87707 q^{67} -5.24607 q^{68} +(0.776635 + 2.26549i) q^{70} +(-8.69903 + 1.98550i) q^{71} +(-6.02295 + 4.80314i) q^{73} +(7.30941 - 5.82906i) q^{74} +(0.412617 - 0.0941772i) q^{76} +(4.17205 + 4.22532i) q^{77} -11.5004 q^{79} +0.905191 q^{80} +(-0.0207529 - 0.0430939i) q^{82} +(0.716068 + 0.897921i) q^{83} +(2.96076 - 3.71268i) q^{85} +(3.23226 + 0.737743i) q^{86} +(2.02208 - 0.973781i) q^{88} +(9.70608 + 12.1710i) q^{89} +(4.95032 + 5.01352i) q^{91} +(-2.54409 - 5.28285i) q^{92} +(-6.85158 + 1.56383i) q^{94} +(-0.166222 + 0.345164i) q^{95} -11.2502i q^{97} +(4.29465 + 5.52775i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 16 q^{4}+O(q^{10}) $ 96 * q + 16 * q^4	$ 96 q + 16 q^{4} - 16 q^{16} + 20 q^{22} - 8 q^{25} + 76 q^{37} + 28 q^{40} - 8 q^{43} + 112 q^{49} + 28 q^{52} + 28 q^{55} + 20 q^{58} + 84 q^{61} + 16 q^{64} - 8 q^{67} + 28 q^{70} + 112 q^{85} + 8 q^{88} - 56 q^{91} - 56 q^{94}+O(q^{100}) $ 96 * q + 16 * q^4 - 16 * q^16 + 20 * q^22 - 8 * q^25 + 76 * q^37 + 28 * q^40 - 8 * q^43 + 112 * q^49 + 28 * q^52 + 28 * q^55 + 20 * q^58 + 84 * q^61 + 16 * q^64 - 8 * q^67 + 28 * q^70 + 112 * q^85 + 8 * q^88 - 56 * q^91 - 56 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{9}{14}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.781831	+	0.623490i	0.552838	+	0.440874i
$2$	0.781831	+	0.623490i	0.552838	+	0.440874i
$3$		0			0
$3$		0			0
$4$	0.222521	+	0.974928i	0.111260	+	0.487464i
$5$	−0.815549	−	0.392748i	−0.364725	−	0.175642i	0.242541	−	0.970141i	$-0.422019\pi$
$5$	−0.815549	−	0.392748i	−0.364725	−	0.175642i	−0.607265	+	0.794499i	$0.707734\pi$
$6$		0			0
$7$	−2.62718	−	0.312901i	−0.992982	−	0.118265i
$7$	−2.62718	−	0.312901i	−0.992982	−	0.118265i
$8$	−0.433884	+	0.900969i	−0.153401	+	0.318541i
$9$		0			0
$10$	−0.392748	−	0.815549i	−0.124198	−	0.257899i
$11$	−1.75469	−	1.39932i	−0.529060	−	0.421911i	0.322187	−	0.946676i	$-0.395582\pi$
$11$	−1.75469	−	1.39932i	−0.529060	−	0.421911i	−0.851247	+	0.524765i	$0.824153\pi$
$12$		0			0
$13$	−2.08202	−	1.66035i	−0.577448	−	0.460499i	0.290694	−	0.956816i	$-0.406114\pi$
$13$	−2.08202	−	1.66035i	−0.577448	−	0.460499i	−0.868141	+	0.496317i	$0.834685\pi$
$14$	−1.85892	−	1.88266i	−0.496818	−	0.503161i
$15$		0			0
$16$	−0.900969	+	0.433884i	−0.225242	+	0.108471i
$17$	−1.16736	+	5.11454i	−0.283126	+	1.24046i	0.610634	+	0.791913i	$0.290915\pi$
$17$	−1.16736	+	5.11454i	−0.283126	+	1.24046i	−0.893760	+	0.448545i	$0.851942\pi$
$18$		0			0
$19$		−	0.423228i		−	0.0970952i	−0.998821	−	0.0485476i	$-0.984541\pi$
$19$		−	0.423228i		−	0.0970952i	0.998821	−	0.0485476i	$-0.0154593\pi$
$20$	0.201424	−	0.882496i	0.0450398	−	0.197332i
$21$		0			0
$22$	−0.499412	−	2.18807i	−0.106475	−	0.466497i
$23$	−5.71651	+	1.30476i	−1.19198	+	0.272061i	−0.772088	−	0.635515i	$-0.780788\pi$
$23$	−5.71651	+	1.30476i	−1.19198	+	0.272061i	−0.419888	+	0.907576i	$0.637930\pi$
$24$		0			0
$25$	−2.60658	−	3.26855i	−0.521316	−	0.653709i
$26$	−0.592573	−	2.59623i	−0.116213	−	0.509163i
$27$		0			0
$28$	−0.279548	−	2.63094i	−0.0528296	−	0.497201i
$29$	−6.67860	−	1.52435i	−1.24018	−	0.283064i	−0.448383	−	0.893842i	$-0.648000\pi$
$29$	−6.67860	−	1.52435i	−1.24018	−	0.283064i	−0.791802	+	0.610778i	$0.790857\pi$
$30$		0			0
$31$			2.46422i			0.442587i	0.975207	+	0.221294i	$0.0710279\pi$
$31$			2.46422i			0.442587i	−0.975207	+	0.221294i	$0.928972\pi$
$32$	−0.974928	−	0.222521i	−0.172345	−	0.0393365i
$33$		0			0
$34$	−4.10154	+	3.27087i	−0.703409	+	0.560950i
$35$	2.01971	+	1.28701i	0.341393	+	0.217544i
$36$		0			0
$37$	2.08037	−	9.11469i	0.342010	−	1.49845i	−0.452814	−	0.891605i	$-0.649580\pi$
$37$	2.08037	−	9.11469i	0.342010	−	1.49845i	0.794824	−	0.606840i	$-0.207563\pi$
$38$	0.263879	−	0.330893i	0.0428067	−	0.0536780i
$39$		0			0
$40$	0.707707	−	0.564378i	0.111898	−	0.0892359i
$41$	−0.0430939	−	0.0207529i	−0.00673014	−	0.00324106i	0.430516	−	0.902583i	$-0.358332\pi$
$41$	−0.0430939	−	0.0207529i	−0.00673014	−	0.00324106i	−0.437246	+	0.899342i	$0.644046\pi$
$42$		0			0
$43$	2.98706	−	1.43849i	0.455522	−	0.219368i	−0.192030	−	0.981389i	$-0.561507\pi$
$43$	2.98706	−	1.43849i	0.455522	−	0.219368i	0.647552	+	0.762021i	$0.275793\pi$
$44$	0.973781	−	2.02208i	0.146803	−	0.304840i
$45$		0			0
$46$	−5.28285	−	2.54409i	−0.778914	−	0.375105i
$47$	−4.38175	+	5.49454i	−0.639144	+	0.801461i	−0.990896	−	0.134632i	$-0.957015\pi$
$47$	−4.38175	+	5.49454i	−0.639144	+	0.801461i	0.351752	+	0.936093i	$0.385586\pi$
$48$		0			0
$49$	6.80419	+	1.64409i	0.972027	+	0.234871i
$50$		−	4.18063i		−	0.591230i
$51$		0			0
$52$	1.15543	−	2.39928i	0.160230	−	0.332720i
$53$	8.18250	−	1.86760i	1.12395	−	0.256535i	0.380144	−	0.924927i	$-0.375874\pi$
$53$	8.18250	−	1.86760i	1.12395	−	0.256535i	0.743809	+	0.668392i	$0.233017\pi$
$54$		0			0
$55$	0.881458	+	1.83037i	0.118856	+	0.246807i
$56$	1.42181	−	2.23125i	0.189997	−	0.298163i
$57$		0			0
$58$	−4.27112	−	5.35582i	−0.560826	−	0.703254i
$59$	−7.08850	+	3.41364i	−0.922845	+	0.444419i	−0.834086	−	0.551635i	$-0.814004\pi$
$59$	−7.08850	+	3.41364i	−0.922845	+	0.444419i	−0.0887588	+	0.996053i	$0.528290\pi$
$60$		0			0
$61$	1.07627	+	0.245652i	0.137802	+	0.0314525i	0.290866	−	0.956764i	$-0.406057\pi$
$61$	1.07627	+	0.245652i	0.137802	+	0.0314525i	−0.153063	+	0.988216i	$0.548914\pi$
$62$	−1.53642	+	1.92660i	−0.195125	+	0.244679i
$63$		0			0
$64$	−0.623490	−	0.781831i	−0.0779362	−	0.0977289i
$65$	1.04589	+	2.17181i	0.129726	+	0.269380i
$66$		0			0
$67$	9.87707			1.20668			0.603338	−	0.797485i	$-0.293837\pi$
$67$	9.87707			1.20668			0.603338	+	0.797485i	$0.293837\pi$
$68$	−5.24607			−0.636179
$69$		0			0
$70$	0.776635	+	2.26549i	0.0928256	+	0.270778i
$71$	−8.69903	+	1.98550i	−1.03239	+	0.235635i	−0.704964	−	0.709243i	$-0.749037\pi$
$71$	−8.69903	+	1.98550i	−1.03239	+	0.235635i	−0.327422	+	0.944878i	$0.606180\pi$
$72$		0			0
$73$	−6.02295	+	4.80314i	−0.704933	+	0.562165i	−0.909002	−	0.416791i	$-0.863155\pi$
$73$	−6.02295	+	4.80314i	−0.704933	+	0.562165i	0.204070	+	0.978956i	$0.434583\pi$
$74$	7.30941	−	5.82906i	0.849702	−	0.677615i
$75$		0			0
$76$	0.412617	−	0.0941772i	0.0473304	−	0.0108029i
$77$	4.17205	+	4.22532i	0.475450	+	0.481520i
$78$		0			0
$79$	−11.5004			−1.29389			−0.646947	−	0.762535i	$-0.723955\pi$
$79$	−11.5004			−1.29389			−0.646947	+	0.762535i	$0.723955\pi$
$80$	0.905191			0.101203
$81$		0			0
$82$	−0.0207529	−	0.0430939i	−0.00229178	−	0.00475893i
$83$	0.716068	+	0.897921i	0.0785987	+	0.0985596i	0.819576	−	0.572970i	$-0.194209\pi$
$83$	0.716068	+	0.897921i	0.0785987	+	0.0985596i	−0.740978	+	0.671530i	$0.765638\pi$
$84$		0			0
$85$	2.96076	−	3.71268i	0.321140	−	0.402697i
$86$	3.23226	+	0.737743i	0.348544	+	0.0795529i
$87$		0			0
$88$	2.02208	−	0.973781i	0.215554	−	0.103805i
$89$	9.70608	+	12.1710i	1.02884	+	1.29013i	0.956183	+	0.292770i	$0.0945771\pi$
$89$	9.70608	+	12.1710i	1.02884	+	1.29013i	0.0726592	+	0.997357i	$0.476851\pi$
$90$		0			0
$91$	4.95032	+	5.01352i	0.518934	+	0.525559i
$92$	−2.54409	−	5.28285i	−0.265240	−	0.550776i
$93$		0			0
$94$	−6.85158	+	1.56383i	−0.706686	+	0.161297i
$95$	−0.166222	+	0.345164i	−0.0170540	+	0.0354130i
$96$		0			0
$97$		−	11.2502i		−	1.14229i	−0.820850	−	0.571144i	$-0.806500\pi$
$97$		−	11.2502i		−	1.14229i	0.820850	−	0.571144i	$-0.193500\pi$
$98$	4.29465	+	5.52775i	0.433825	+	0.558387i
$99$		0			0
$100$	2.60658	−	3.26855i	0.260658	−	0.326855i
$101$	7.84676	+	3.77880i	0.780782	+	0.376005i	0.781428	−	0.623995i	$-0.214491\pi$
$101$	7.84676	+	3.77880i	0.780782	+	0.376005i	−0.000646313		1.00000i	$0.500206\pi$
$102$		0			0
$103$	7.22681	−	15.0066i	0.712078	−	1.47865i	−0.158884	−	0.987297i	$-0.550790\pi$
$103$	7.22681	−	15.0066i	0.712078	−	1.47865i	0.870963	−	0.491349i	$-0.163496\pi$
$104$	2.39928	−	1.15543i	0.235269	−	0.113299i
$105$		0			0
$106$	7.56177	+	3.64156i	0.734464	+	0.353699i
$107$	0.897776	−	0.715952i	0.0867913	−	0.0692137i	−0.579133	−	0.815233i	$-0.696609\pi$
$107$	0.897776	−	0.715952i	0.0867913	−	0.0692137i	0.665924	+	0.746019i	$0.268037\pi$
$108$		0			0
$109$	−6.01457	+	7.54204i	−0.576092	+	0.722396i	−0.981441	−	0.191766i	$-0.938579\pi$
$109$	−6.01457	+	7.54204i	−0.576092	+	0.722396i	0.405349	+	0.914162i	$0.367150\pi$
$110$	−0.452063	+	1.98062i	−0.0431026	+	0.188845i
$111$		0			0
$112$	2.50277	−	0.857978i	0.236490	−	0.0810713i
$113$	2.37599	−	1.89479i	0.223514	−	0.178246i	−0.505330	−	0.862926i	$-0.668629\pi$
$113$	2.37599	−	1.89479i	0.223514	−	0.178246i	0.728844	+	0.684680i	$0.240058\pi$
$114$		0			0
$115$	5.17454	+	1.18105i	0.482528	+	0.110134i
$116$		−	6.85035i		−	0.636039i
$117$		0			0
$118$	−7.67039	−	1.75072i	−0.706116	−	0.161166i
$119$	4.66721	−	13.0716i	0.427843	−	1.19827i
$120$		0			0
$121$	−1.32688	−	5.81345i	−0.120626	−	0.528495i
$122$	0.688301	+	0.863102i	0.0623159	+	0.0781416i
$123$		0			0
$124$	−2.40244	+	0.548341i	−0.215745	+	0.0492424i
$125$	1.84920	+	8.10187i	0.165397	+	0.724653i
$126$		0			0
$127$	−1.19687	+	5.24382i	−0.106205	+	0.465314i	0.893658	+	0.448749i	$0.148130\pi$
$127$	−1.19687	+	5.24382i	−0.106205	+	0.465314i	−0.999863	+	0.0165652i	$0.994727\pi$
$128$		−	1.00000i		−	0.0883883i
$129$		0			0
$130$	−0.536392	+	2.35009i	−0.0470447	+	0.206116i
$131$	−10.6984	+	5.15209i	−0.934726	+	0.450140i	−0.838306	−	0.545201i	$-0.816454\pi$
$131$	−10.6984	+	5.15209i	−0.934726	+	0.450140i	−0.0964201	+	0.995341i	$0.530739\pi$
$132$		0			0
$133$	−0.132428	+	1.11190i	−0.0114830	+	0.0964138i
$134$	7.72221	+	6.15825i	0.667097	+	0.531992i
$135$		0			0
$136$	−4.10154	−	3.27087i	−0.351704	−	0.280475i
$137$	0.0586204	+	0.121727i	0.00500828	+	0.0103998i	0.903458	−	0.428677i	$-0.141020\pi$
$137$	0.0586204	+	0.121727i	0.00500828	+	0.0103998i	−0.898450	+	0.439076i	$0.855306\pi$
$138$		0			0
$139$	−5.96144	+	12.3791i	−0.505643	+	1.04998i	0.479389	+	0.877603i	$0.340858\pi$
$139$	−5.96144	+	12.3791i	−0.505643	+	1.04998i	−0.985031	+	0.172375i	$0.944856\pi$
$140$	−0.805312	+	2.25545i	−0.0680613	+	0.190621i
$141$		0			0
$142$	−8.03912	−	3.87143i	−0.674628	−	0.324884i
$143$	1.32993	+	5.82682i	0.111215	+	0.487263i
$144$		0			0
$145$	4.84804	+	3.86619i	0.402608	+	0.321069i
$146$	−7.70364			−0.637558
$147$		0			0
$148$	9.34909			0.768490
$149$	−3.10180	−	2.47360i	−0.254109	−	0.202645i	0.488147	−	0.872761i	$-0.337673\pi$
$149$	−3.10180	−	2.47360i	−0.254109	−	0.202645i	−0.742256	+	0.670116i	$0.766244\pi$
$150$		0			0
$151$	1.74043	+	7.62533i	0.141634	+	0.620540i	0.995056	+	0.0993187i	$0.0316663\pi$
$151$	1.74043	+	7.62533i	0.141634	+	0.620540i	−0.853421	+	0.521222i	$0.825477\pi$
$152$	0.381316	+	0.183632i	0.0309288	+	0.0148945i
$153$		0			0
$154$	0.627399	+	5.90472i	0.0505573	+	0.475816i
$155$	0.967817	−	2.00969i	0.0777369	−	0.161422i
$156$		0			0
$157$	8.40155	+	17.4460i	0.670517	+	1.39234i	0.907177	+	0.420750i	$0.138233\pi$
$157$	8.40155	+	17.4460i	0.670517	+	1.39234i	−0.236660	+	0.971593i	$0.576053\pi$
$158$	−8.99136	−	7.17037i	−0.715314	−	0.570444i
$159$		0			0
$160$	0.707707	+	0.564378i	0.0559492	+	0.0446180i
$161$	15.4266	−	1.63914i	1.21579	−	0.129182i
$162$		0			0
$163$	−0.360509	+	0.173612i	−0.0282373	+	0.0135983i	−0.447949	−	0.894059i	$-0.647845\pi$
$163$	−0.360509	+	0.173612i	−0.0282373	+	0.0135983i	0.419712	+	0.907657i	$0.362131\pi$
$164$	0.0106433	−	0.0466314i	0.000831104	−	0.00364130i
$165$		0			0
$166$			1.14848i			0.0891396i
$167$	2.07539	−	9.09286i	0.160598	−	0.703627i	−0.828938	−	0.559341i	$-0.811054\pi$
$167$	2.07539	−	9.09286i	0.160598	−	0.703627i	0.989536	−	0.144286i	$-0.0460885\pi$
$168$		0			0
$169$	−1.31475	−	5.76029i	−0.101135	−	0.443099i
$170$	4.62964	−	1.05668i	0.355077	−	0.0810440i
$171$		0			0
$172$	2.06711	+	2.59207i	0.157616	+	0.197644i
$173$	−4.33727	−	19.0028i	−0.329757	−	1.44476i	−0.819594	−	0.572944i	$-0.805801\pi$
$173$	−4.33727	−	19.0028i	−0.329757	−	1.44476i	0.489838	−	0.871814i	$-0.337056\pi$
$174$		0			0
$175$	5.82523	+	9.40267i	0.440346	+	0.710775i
$176$	2.18807	+	0.499412i	0.164932	+	0.0376446i
$177$		0			0
$178$			15.5673i			1.16682i
$179$	1.54650	+	0.352979i	0.115591	+	0.0263829i	0.279925	−	0.960022i	$-0.409690\pi$
$179$	1.54650	+	0.352979i	0.115591	+	0.0263829i	−0.164334	+	0.986405i	$0.552548\pi$
$180$		0			0
$181$	−9.01685	+	7.19070i	−0.670217	+	0.534481i	−0.898422	−	0.439133i	$-0.855286\pi$
$181$	−9.01685	+	7.19070i	−0.670217	+	0.534481i	0.228205	+	0.973613i	$0.426714\pi$
$182$	0.744436	+	7.00620i	0.0551812	+	0.519334i
$183$		0			0
$184$	1.30476	−	5.71651i	0.0961880	−	0.421427i
$185$	−5.27642	+	6.61642i	−0.387930	+	0.486449i
$186$		0			0
$187$	9.20524	−	7.34094i	0.673154	−	0.536822i
$188$	−6.33181	−	3.04924i	−0.461795	−	0.222389i
$189$		0			0
$190$	−0.345164	+	0.166222i	−0.0250408	+	0.0120590i
$191$	−1.85311	+	3.84801i	−0.134086	+	0.278433i	−0.957191	−	0.289456i	$-0.906525\pi$
$191$	−1.85311	+	3.84801i	−0.134086	+	0.278433i	0.823105	+	0.567889i	$0.192240\pi$
$192$		0			0
$193$	19.4779	+	9.38005i	1.40205	+	0.675191i	0.973576	−	0.228364i	$-0.0733376\pi$
$193$	19.4779	+	9.38005i	1.40205	+	0.675191i	0.428472	+	0.903555i	$0.359052\pi$
$194$	7.01441	−	8.79579i	0.503605	−	0.631501i
$195$		0			0
$196$	−0.0888001	+	6.99944i	−0.00634286	+	0.499960i
$197$		−	20.6608i		−	1.47202i	−0.676969	−	0.736011i	$-0.736707\pi$
$197$		−	20.6608i		−	1.47202i	0.676969	−	0.736011i	$-0.263293\pi$
$198$		0			0
$199$	−7.81778	+	16.2338i	−0.554187	+	1.15078i	0.416210	+	0.909268i	$0.363358\pi$
$199$	−7.81778	+	16.2338i	−0.554187	+	1.15078i	−0.970397	+	0.241513i	$0.922356\pi$
$200$	4.07581	−	0.930277i	0.288203	−	0.0657805i
$201$		0			0
$202$	3.77880	+	7.84676i	0.265876	+	0.552096i
$203$	17.0689	+	6.09448i	1.19800	+	0.427748i
$204$		0			0
$205$	0.0269945	+	0.0338501i	0.00188538	+	0.00236419i
$206$	15.0066	−	7.22681i	1.04556	−	0.503515i
$207$		0			0
$208$	2.59623	+	0.592573i	0.180016	+	0.0410876i
$209$	−0.592232	+	0.742636i	−0.0409656	+	0.0513692i
$210$		0			0
$211$	6.11877	+	7.67269i	0.421233	+	0.528210i	0.946490	−	0.322734i	$-0.104602\pi$
$211$	6.11877	+	7.67269i	0.421233	+	0.528210i	−0.525256	+	0.850944i	$0.676031\pi$
$212$	3.64156	+	7.56177i	0.250103	+	0.519345i
$213$		0			0
$214$	1.14830			0.0784961
$215$	−3.00106			−0.204671
$216$		0			0
$217$	0.771056	−	6.47396i	0.0523427	−	0.439481i
$218$	−9.40477	+	2.14658i	−0.636971	+	0.145385i
$219$		0			0
$220$	−1.58833	+	1.26665i	−0.107085	+	0.0853978i
$221$	10.9224	−	8.71033i	0.734721	−	0.585920i
$222$		0			0
$223$	−26.0235	+	5.93969i	−1.74266	+	0.397751i	−0.971151	−	0.238464i	$-0.923356\pi$
$223$	−26.0235	+	5.93969i	−1.74266	+	0.397751i	−0.771511	+	0.636216i	$0.780499\pi$
$224$	2.49169	+	0.889659i	0.166483	+	0.0594428i
$225$		0			0
$226$	3.03900			0.202151
$227$	−17.1400			−1.13762			−0.568810	−	0.822469i	$-0.692596\pi$
$227$	−17.1400			−1.13762			−0.568810	+	0.822469i	$0.692596\pi$
$228$		0			0
$229$	−6.97444	−	14.4826i	−0.460884	−	0.957035i	−0.993833	−	0.110888i	$-0.964631\pi$
$229$	−6.97444	−	14.4826i	−0.460884	−	0.957035i	0.532949	−	0.846147i	$-0.321084\pi$
$230$	3.30924	+	4.14966i	0.218205	+	0.273620i
$231$		0			0
$232$	4.27112	−	5.35582i	0.280413	−	0.351627i
$233$	1.36387	+	0.311295i	0.0893502	+	0.0203936i	0.266962	−	0.963707i	$-0.413980\pi$
$233$	1.36387	+	0.311295i	0.0893502	+	0.0203936i	−0.177612	+	0.984101i	$0.556837\pi$
$234$		0			0
$235$	5.73150	−	2.76015i	0.373882	−	0.180052i
$236$	−4.90540	−	6.15117i	−0.319314	−	0.400407i
$237$		0			0
$238$	11.7990	−	7.30980i	0.764813	−	0.473824i
$239$	−8.33389	−	17.3055i	−0.539075	−	1.11940i	−0.975569	−	0.219693i	$-0.929494\pi$
$239$	−8.33389	−	17.3055i	−0.539075	−	1.11940i	0.436494	−	0.899707i	$-0.356220\pi$
$240$		0			0
$241$	4.70790	−	1.07455i	0.303263	−	0.0692177i	−0.0681817	−	0.997673i	$-0.521720\pi$
$241$	4.70790	−	1.07455i	0.303263	−	0.0692177i	0.371444	+	0.928455i	$0.378863\pi$
$242$	2.58723	−	5.37243i	0.166313	−	0.345353i
$243$		0			0
$244$			1.10395i			0.0706731i
$245$	−4.90343	−	4.01317i	−0.313269	−	0.256392i
$246$		0			0
$247$	−0.702709	+	0.881169i	−0.0447123	+	0.0560674i
$248$	−2.22019	−	1.06919i	−0.140982	−	0.0678933i
$249$		0			0
$250$	−3.60567	+	7.48725i	−0.228043	+	0.473536i
$251$	2.54251	−	1.22441i	0.160482	−	0.0772840i	−0.351919	−	0.936031i	$-0.614471\pi$
$251$	2.54251	−	1.22441i	0.160482	−	0.0772840i	0.512400	+	0.858747i	$0.328756\pi$
$252$		0			0
$253$	11.8565	+	5.70979i	0.745412	+	0.358971i
$254$	−4.20522	+	3.35355i	−0.263859	+	0.210421i
$255$		0			0
$256$	0.623490	−	0.781831i	0.0389681	−	0.0488645i
$257$	−3.94733	+	17.2944i	−0.246227	+	1.07879i	0.689004	+	0.724757i	$0.258048\pi$
$257$	−3.94733	+	17.2944i	−0.246227	+	1.07879i	−0.935232	+	0.354036i	$0.884809\pi$
$258$		0			0
$259$	−8.31750	+	23.2950i	−0.516824	+	1.44748i
$260$	−1.88462	+	1.50294i	−0.116879	+	0.0932082i
$261$		0			0
$262$	−11.5766	−	2.64229i	−0.715207	−	0.163241i
$263$		−	3.74709i		−	0.231055i	−0.993304	−	0.115528i	$-0.963144\pi$
$263$		−	3.74709i		−	0.231055i	0.993304	−	0.115528i	$-0.0368559\pi$
$264$		0			0
$265$	−7.40673	−	1.69054i	−0.454992	−	0.103849i
$266$	−0.796794	+	0.786749i	−0.0488546	+	0.0482387i
$267$		0			0
$268$	2.19786	+	9.62943i	0.134255	+	0.588211i
$269$	17.7487	+	22.2562i	1.08216	+	1.35698i	0.929550	+	0.368697i	$0.120196\pi$
$269$	17.7487	+	22.2562i	1.08216	+	1.35698i	0.152609	+	0.988287i	$0.451233\pi$
$270$		0			0
$271$	13.3731	−	3.05233i	0.812360	−	0.185416i	0.203891	−	0.978994i	$-0.434641\pi$
$271$	13.3731	−	3.05233i	0.812360	−	0.185416i	0.608469	+	0.793578i	$0.291784\pi$
$272$	−1.16736	−	5.11454i	−0.0707816	−	0.310115i
$273$		0			0
$274$	−0.0300640	+	0.131719i	−0.00181623	+	0.00795743i
$275$			9.38274i			0.565800i
$276$		0			0
$277$	2.77036	−	12.1377i	0.166455	−	0.729287i	−0.820940	−	0.571014i	$-0.806550\pi$
$277$	2.77036	−	12.1377i	0.166455	−	0.729287i	0.987395	−	0.158273i	$-0.0505926\pi$
$278$	−12.3791	+	5.96144i	−0.742447	+	0.357543i
$279$		0			0
$280$	−2.03587	+	1.26128i	−0.121667	+	0.0753760i
$281$	−17.1712	−	13.6935i	−1.02434	−	0.816888i	−0.0410959	−	0.999155i	$-0.513085\pi$
$281$	−17.1712	−	13.6935i	−1.02434	−	0.816888i	−0.983249	+	0.182267i	$0.941656\pi$
$282$		0			0
$283$	−4.19403	−	3.34462i	−0.249309	−	0.198817i	0.490859	−	0.871239i	$-0.336683\pi$
$283$	−4.19403	−	3.34462i	−0.249309	−	0.198817i	−0.740168	+	0.672421i	$0.765254\pi$
$284$	−3.87143	−	8.03912i	−0.229727	−	0.477034i
$285$		0			0
$286$	−2.59318	+	5.38479i	−0.153338	+	0.318409i
$287$	0.106722	+	0.0680059i	0.00629960	+	0.00401426i
$288$		0			0
$289$	−9.47932	−	4.56500i	−0.557607	−	0.268529i
$290$	1.37983	+	6.04541i	0.0810261	+	0.354999i
$291$		0			0
$292$	−6.02295	−	4.80314i	−0.352466	−	0.281082i
$293$	8.26663			0.482942			0.241471	−	0.970408i	$-0.422370\pi$
$293$	8.26663			0.482942			0.241471	+	0.970408i	$0.422370\pi$
$294$		0			0
$295$	7.12173			0.414643
$296$	7.30941	+	5.82906i	0.424851	+	0.338807i
$297$		0			0
$298$	−0.882818	−	3.86788i	−0.0511403	−	0.224060i
$299$	14.0682	+	6.77491i	0.813587	+	0.391803i
$300$		0			0
$301$	−8.29766	+	2.84453i	−0.478269	+	0.163956i
$302$	−3.39359	+	7.04686i	−0.195279	+	0.405501i
$303$		0			0
$304$	0.183632	+	0.381316i	0.0105320	+	0.0218699i
$305$	−0.781273	−	0.623044i	−0.0447356	−	0.0356754i
$306$		0			0
$307$	−19.6658	−	15.6829i	−1.12238	−	0.895072i	−0.127083	−	0.991892i	$-0.540561\pi$
$307$	−19.6658	−	15.6829i	−1.12238	−	0.895072i	−0.995302	+	0.0968205i	$0.969133\pi$
$308$	−3.19101	+	5.00767i	−0.181825	+	0.285339i
$309$		0			0
$310$	2.00969	−	0.967817i	0.114143	−	0.0549683i
$311$	5.50680	−	24.1269i	0.312262	−	1.36811i	−0.538529	−	0.842607i	$-0.681020\pi$
$311$	5.50680	−	24.1269i	0.312262	−	1.36811i	0.850792	−	0.525503i	$-0.176123\pi$
$312$		0			0
$313$		−	21.8951i		−	1.23759i	−0.785554	−	0.618793i	$-0.787622\pi$
$313$		−	21.8951i		−	1.23759i	0.785554	−	0.618793i	$-0.212378\pi$
$314$	−4.30881	+	18.8781i	−0.243160	+	1.06535i
$315$		0			0
$316$	−2.55908	−	11.2120i	−0.143959	−	0.630727i
$317$	−15.9863	+	3.64877i	−0.897881	+	0.204936i	−0.646465	−	0.762944i	$-0.723753\pi$
$317$	−15.9863	+	3.64877i	−0.897881	+	0.204936i	−0.251416	+	0.967879i	$0.580896\pi$
$318$		0			0
$319$	9.58584	+	12.0203i	0.536704	+	0.673006i
$320$	0.201424	+	0.882496i	0.0112599	+	0.0493330i
$321$		0			0
$322$	13.0830	+	8.33679i	0.729086	+	0.464591i
$323$	2.16462	+	0.494060i	0.120443	+	0.0274902i
$324$		0			0
$325$			11.1330i			0.617549i
$326$	−0.390103	−	0.0890384i	−0.0216058	−	0.00493138i
$327$		0			0
$328$	0.0373955	−	0.0298219i	0.00206482	−	0.00164664i
$329$	13.2309	−	13.0641i	0.729443	−	0.720248i
$330$		0			0
$331$	1.88939	−	8.27797i	0.103850	−	0.454999i	−0.896088	−	0.443877i	$-0.853603\pi$
$331$	1.88939	−	8.27797i	0.103850	−	0.454999i	0.999938	−	0.0111215i	$-0.00354017\pi$
$332$	−0.716068	+	0.897921i	−0.0392993	+	0.0492798i
$333$		0			0
$334$	7.29191	−	5.81510i	0.398995	−	0.318188i
$335$	−8.05524	−	3.87920i	−0.440105	−	0.211943i
$336$		0			0
$337$	−11.1510	+	5.37004i	−0.607434	+	0.292525i	−0.712205	−	0.701972i	$-0.752303\pi$
$337$	−11.1510	+	5.37004i	−0.607434	+	0.292525i	0.104771	+	0.994496i	$0.466589\pi$
$338$	2.56357	−	5.32331i	0.139440	−	0.289550i
$339$		0			0
$340$	4.27843	+	2.06038i	0.232030	+	0.111740i
$341$	3.44824	−	4.32395i	0.186732	−	0.234155i
$342$		0			0
$343$	−17.3614	−	6.44837i	−0.937428	−	0.348179i
$344$			3.31539i			0.178754i
$345$		0			0
$346$	8.45705	−	17.5612i	0.454654	−	0.944099i
$347$	0.409729	−	0.0935180i	0.0219954	−	0.00502031i	−0.211509	−	0.977376i	$-0.567838\pi$
$347$	0.409729	−	0.0935180i	0.0219954	−	0.00502031i	0.233504	+	0.972356i	$0.424981\pi$
$348$		0			0
$349$	4.01663	+	8.34062i	0.215005	+	0.446463i	0.980379	−	0.197123i	$-0.0631600\pi$
$349$	4.01663	+	8.34062i	0.215005	+	0.446463i	−0.765373	+	0.643586i	$0.777446\pi$
$350$	−1.30812	+	10.9833i	−0.0699220	+	0.587081i
$351$		0			0
$352$	1.39932	+	1.75469i	0.0745841	+	0.0935255i
$353$	18.2862	−	8.80616i	0.973275	−	0.468705i	0.121488	−	0.992593i	$-0.461233\pi$
$353$	18.2862	−	8.80616i	0.973275	−	0.468705i	0.851787	+	0.523888i	$0.175519\pi$
$354$		0			0
$355$	7.87429	+	1.79726i	0.417924	+	0.0953884i
$356$	−9.70608	+	12.1710i	−0.514421	+	0.645064i
$357$		0			0
$358$	0.989024	+	1.24020i	0.0522715	+	0.0655464i
$359$	−3.88395	−	8.06511i	−0.204987	−	0.425660i	0.772977	−	0.634434i	$-0.218767\pi$
$359$	−3.88395	−	8.06511i	−0.204987	−	0.425660i	−0.977964	+	0.208774i	$0.933053\pi$
$360$		0			0
$361$	18.8209			0.990573
$362$	−11.5330			−0.606160
$363$		0			0
$364$	−3.78627	+	5.94181i	−0.198454	+	0.311436i
$365$	6.79843	−	1.55170i	0.355846	−	0.0812196i
$366$		0			0
$367$	−21.0203	+	16.7631i	−1.09725	+	0.875029i	−0.992834	−	0.119504i	$-0.961869\pi$
$367$	−21.0203	+	16.7631i	−1.09725	+	0.875029i	−0.104418	+	0.994533i	$0.533298\pi$
$368$	4.58429	−	3.65585i	0.238973	−	0.190574i
$369$		0			0
$370$	−8.25054	+	1.88313i	−0.428925	+	0.0978993i
$371$	−22.0813	+	2.34623i	−1.14640	+	0.121810i
$372$		0			0
$373$	−25.6234			−1.32673			−0.663365	−	0.748296i	$-0.730872\pi$
$373$	−25.6234			−1.32673			−0.663365	+	0.748296i	$0.730872\pi$
$374$	11.7739			0.608816
$375$		0			0
$376$	−3.04924	−	6.33181i	−0.157253	−	0.326538i
$377$	11.3740	+	14.2626i	0.585791	+	0.734559i
$378$		0			0
$379$	−14.4950	+	18.1762i	−0.744559	+	0.933647i	−0.999445	−	0.0333240i	$-0.989391\pi$
$379$	−14.4950	+	18.1762i	−0.744559	+	0.933647i	0.254886	+	0.966971i	$0.417962\pi$
$380$	−0.373497	−	0.0852483i	−0.0191600	−	0.00437315i
$381$		0			0
$382$	−3.84801	+	1.85311i	−0.196882	+	0.0948131i
$383$	−15.9317	−	19.9777i	−0.814072	−	1.02081i	−0.999273	−	0.0381138i	$-0.987865\pi$
$383$	−15.9317	−	19.9777i	−0.814072	−	1.02081i	0.185201	−	0.982701i	$-0.440706\pi$
$384$		0			0
$385$	−1.74303	−	5.08452i	−0.0888330	−	0.259131i
$386$	9.38005	+	19.4779i	0.477432	+	0.991398i
$387$		0			0
$388$	10.9682	−	2.50341i	0.556825	−	0.127092i
$389$	2.33752	−	4.85390i	0.118517	−	0.246102i	−0.833268	−	0.552869i	$-0.813533\pi$
$389$	2.33752	−	4.85390i	0.118517	−	0.246102i	0.951785	+	0.306767i	$0.0992472\pi$
$390$		0			0
$391$		−	30.7605i		−	1.55562i
$392$	−4.43350	+	5.41701i	−0.223926	+	0.273601i
$393$		0			0
$394$	12.8818	−	16.1533i	0.648976	−	0.813791i
$395$	9.37913	+	4.51675i	0.471915	+	0.227262i
$396$		0			0
$397$	9.80951	−	20.3697i	0.492325	−	1.02232i	−0.495766	−	0.868456i	$-0.665113\pi$
$397$	9.80951	−	20.3697i	0.492325	−	1.02232i	0.988091	−	0.153868i	$-0.0491730\pi$
$398$	−16.2338	+	7.81778i	−0.813726	+	0.391870i
$399$		0			0
$400$	3.76662	+	1.81391i	0.188331	+	0.0906953i
$401$	−15.1898	+	12.1135i	−0.758542	+	0.604917i	−0.924485	−	0.381218i	$-0.875505\pi$
$401$	−15.1898	+	12.1135i	−0.758542	+	0.604917i	0.165943	+	0.986135i	$0.446933\pi$
$402$		0			0
$403$	4.09148	−	5.13055i	0.203811	−	0.255571i
$404$	−1.93799	+	8.49089i	−0.0964186	+	0.422438i
$405$		0			0
$406$	9.54519	+	15.4072i	0.473720	+	0.764645i
$407$	−16.4048	+	13.0824i	−0.813155	+	0.648469i
$408$		0			0
$409$	0.585022	+	0.133527i	0.0289275	+	0.00660251i	0.236960	−	0.971519i	$-0.423849\pi$
$409$	0.585022	+	0.133527i	0.0289275	+	0.00660251i	−0.208033	+	0.978122i	$0.566706\pi$
$410$			0.0432959i			0.00213823i
$411$		0			0
$412$	16.2385	+	3.70633i	0.800013	+	0.182598i
$413$	19.6909	−	6.75027i	0.968927	−	0.332159i
$414$		0			0
$415$	−0.231332	−	1.01353i	−0.0113557	−	0.0497524i
$416$	1.66035	+	2.08202i	0.0814055	+	0.102079i
$417$		0			0
$418$	−0.926052	+	0.211365i	−0.0452947	+	0.0103382i
$419$	5.37981	+	23.5705i	0.262821	+	1.15149i	0.918176	+	0.396172i	$0.129662\pi$
$419$	5.37981	+	23.5705i	0.262821	+	1.15149i	−0.655356	+	0.755321i	$0.727481\pi$
$420$		0			0
$421$	7.70186	−	33.7441i	0.375366	−	1.64458i	−0.336072	−	0.941836i	$-0.609099\pi$
$421$	7.70186	−	33.7441i	0.375366	−	1.64458i	0.711438	−	0.702749i	$-0.248044\pi$
$422$			9.81374i			0.477725i
$423$		0			0
$424$	−1.86760	+	8.18250i	−0.0906988	+	0.397378i
$425$	19.7599	−	9.51588i	0.958497	−	0.461588i
$426$		0			0
$427$	−2.75070	−	0.982138i	−0.133116	−	0.0475290i
$428$	0.897776	+	0.715952i	0.0433956	+	0.0346069i
$429$		0			0
$430$	−2.34632	−	1.87113i	−0.113150	−	0.0902339i
$431$	0.0607165	+	0.126079i	0.00292461	+	0.00607302i	0.902426	−	0.430845i	$-0.141784\pi$
$431$	0.0607165	+	0.126079i	0.00292461	+	0.00607302i	−0.899501	+	0.436918i	$0.856070\pi$
$432$		0			0
$433$	9.64933	−	20.0370i	0.463717	−	0.962918i	−0.529681	−	0.848197i	$-0.677688\pi$
$433$	9.64933	−	20.0370i	0.463717	−	0.962918i	0.993398	−	0.114721i	$-0.0365975\pi$
$434$	4.63928	−	4.58080i	0.222693	−	0.219885i
$435$		0			0
$436$	−8.69131	−	4.18552i	−0.416238	−	0.200450i
$437$	0.552210	+	2.41939i	0.0264158	+	0.115735i
$438$		0			0
$439$	−26.3633	−	21.0241i	−1.25825	−	1.00342i	−0.999295	−	0.0375355i	$-0.988049\pi$
$439$	−26.3633	−	21.0241i	−1.25825	−	1.00342i	−0.258959	−	0.965888i	$-0.583379\pi$
$440$	−2.03155			−0.0968506
$441$		0			0
$442$	13.9703			0.664499
$443$	−26.0066	−	20.7396i	−1.23561	−	0.985366i	−0.999908	−	0.0135402i	$-0.995690\pi$
$443$	−26.0066	−	20.7396i	−1.23561	−	0.985366i	−0.235701	−	0.971826i	$-0.575739\pi$
$444$		0			0
$445$	−3.13564	−	13.7381i	−0.148643	−	0.651249i
$446$	−24.0493	−	11.5815i	−1.13877	−	0.548402i
$447$		0			0
$448$	1.39339	+	2.24911i	0.0658313	+	0.106260i
$449$	15.3874	−	31.9523i	0.726177	−	1.50792i	−0.130154	−	0.991494i	$-0.541547\pi$
$449$	15.3874	−	31.9523i	0.726177	−	1.50792i	0.856331	−	0.516428i	$-0.172739\pi$
$450$		0			0
$451$	0.0465766	+	0.0967173i	0.00219321	+	0.00455424i
$452$	2.37599	+	1.89479i	0.111757	+	0.0891232i
$453$		0			0
$454$	−13.4006	−	10.6866i	−0.628920	−	0.501547i
$455$	−2.06818	−	6.03300i	−0.0969577	−	0.282831i
$456$		0			0
$457$	−5.43435	+	2.61705i	−0.254208	+	0.122420i	−0.556649	−	0.830748i	$-0.687913\pi$
$457$	−5.43435	+	2.61705i	−0.254208	+	0.122420i	0.302440	+	0.953168i	$0.402199\pi$
$458$	3.57690	−	15.6714i	0.167137	−	0.732277i
$459$		0			0
$460$			5.30761i			0.247469i
$461$	1.21741	−	5.33381i	0.0567003	−	0.248420i	−0.938633	−	0.344918i	$-0.887907\pi$
$461$	1.21741	−	5.33381i	0.0567003	−	0.248420i	0.995333	+	0.0964975i	$0.0307640\pi$
$462$		0			0
$463$	−5.69880	−	24.9681i	−0.264846	−	1.16036i	−0.915923	−	0.401354i	$-0.868540\pi$
$463$	−5.69880	−	24.9681i	−0.264846	−	1.16036i	0.651077	−	0.759011i	$-0.274317\pi$
$464$	6.67860	−	1.52435i	0.310046	−	0.0707660i
$465$		0			0
$466$	0.872229	+	1.09374i	0.0404052	+	0.0506665i
$467$	3.89898	+	17.0825i	0.180423	+	0.790486i	0.981428	+	0.191828i	$0.0614417\pi$
$467$	3.89898	+	17.0825i	0.180423	+	0.790486i	−0.801005	+	0.598657i	$0.795701\pi$
$468$		0			0
$469$	−25.9489	−	3.09054i	−1.19821	−	0.142708i
$470$	6.20199	+	1.41556i	0.286076	+	0.0652951i
$471$		0			0
$472$		−	7.86765i		−	0.362138i
$473$	−7.25429	−	1.65574i	−0.333552	−	0.0761312i
$474$		0			0
$475$	−1.38334	+	1.10318i	−0.0634721	+	0.0506173i
$476$	13.7824	+	1.64150i	0.631715	+	0.0752380i
$477$		0			0
$478$	4.27411	−	18.7261i	0.195493	−	0.856511i
$479$	−21.4408	+	26.8859i	−0.979654	+	1.22845i	−0.00610273	+	0.999981i	$0.501943\pi$
$479$	−21.4408	+	26.8859i	−0.979654	+	1.22845i	−0.973552	+	0.228467i	$0.926629\pi$
$480$		0			0
$481$	−19.4650	+	15.5228i	−0.887526	+	0.707778i
$482$	4.35076	+	2.09521i	0.198172	+	0.0954344i
$483$		0			0
$484$	5.37243	−	2.58723i	0.244202	−	0.117601i
$485$	−4.41851	+	9.17512i	−0.200634	+	0.416621i
$486$		0			0
$487$	18.4010	+	8.86146i	0.833830	+	0.401551i	0.801550	−	0.597928i	$-0.204009\pi$
$487$	18.4010	+	8.86146i	0.833830	+	0.401551i	0.0322797	+	0.999479i	$0.489723\pi$
$488$	−0.688301	+	0.863102i	−0.0311579	+	0.0390708i
$489$		0			0
$490$	−1.33149	−	6.19486i	−0.0601505	−	0.279855i
$491$		−	6.78508i		−	0.306207i	−0.988210	−	0.153103i	$-0.951073\pi$
$491$		−	6.78508i		−	0.306207i	0.988210	−	0.153103i	$-0.0489267\pi$
$492$		0			0
$493$	15.5927	−	32.3785i	0.702258	−	1.45825i
$494$	−1.09880	+	0.250794i	−0.0494373	+	0.0112837i
$495$		0			0
$496$	−1.06919	−	2.22019i	−0.0480078	−	0.0996893i
$497$	23.4752	−	2.49433i	1.05301	−	0.111886i
$498$		0			0
$499$	12.5306	+	15.7129i	0.560948	+	0.703406i	0.978733	−	0.205140i	$-0.0657649\pi$
$499$	12.5306	+	15.7129i	0.560948	+	0.703406i	−0.417785	+	0.908546i	$0.637194\pi$
$500$	−7.48725	+	3.60567i	−0.334840	+	0.161251i
$501$		0			0
$502$	2.75122	+	0.627948i	0.122793	+	0.0280267i
$503$	−4.63191	+	5.80823i	−0.206527	+	0.258976i	−0.874297	−	0.485391i	$-0.838677\pi$
$503$	−4.63191	+	5.80823i	−0.206527	+	0.258976i	0.667771	+	0.744367i	$0.267249\pi$
$504$		0			0
$505$	−4.91531	−	6.16360i	−0.218728	−	0.274276i
$506$	5.70979	+	11.8565i	0.253831	+	0.527086i
$507$		0			0
$508$	−5.37868			−0.238640
$509$	−22.5675			−1.00029			−0.500144	−	0.865942i	$-0.666720\pi$
$509$	−22.5675			−1.00029			−0.500144	+	0.865942i	$0.666720\pi$
$510$		0			0
$511$	17.3263	−	10.7341i	0.766470	−	0.474851i
$512$	0.974928	−	0.222521i	0.0430861	−	0.00983413i
$513$		0			0
$514$	−13.8690	+	11.0602i	−0.611736	+	0.487843i
$515$	−11.7876	+	9.40032i	−0.519425	+	0.414228i
$516$		0			0
$517$	15.3773	−	3.50976i	0.676291	−	0.154359i
$518$	−21.0271	+	13.0269i	−0.923877	+	0.572369i
$519$		0			0
$520$	−2.41052			−0.105709
$521$	−19.3368			−0.847162			−0.423581	−	0.905858i	$-0.639227\pi$
$521$	−19.3368			−0.847162			−0.423581	+	0.905858i	$0.639227\pi$
$522$		0			0
$523$	−5.55358	−	11.5321i	−0.242841	−	0.504265i	0.743550	−	0.668680i	$-0.233141\pi$
$523$	−5.55358	−	11.5321i	−0.242841	−	0.504265i	−0.986391	+	0.164415i	$0.947426\pi$
$524$	−7.40354	−	9.28375i	−0.323425	−	0.405562i
$525$		0			0
$526$	2.33627	−	2.92959i	0.101866	−	0.127736i
$527$	−12.6034	−	2.87663i	−0.549011	−	0.125308i
$528$		0			0
$529$	10.2539	−	4.93800i	0.445820	−	0.214696i
$530$	−4.73678	−	5.93974i	−0.205753	−	0.258006i
$531$		0			0
$532$	−1.11349	+	0.118313i	−0.0482759	+	0.00512950i
$533$	0.0552651	+	0.114759i	0.00239380	+	0.00497077i
$534$		0			0
$535$	−1.01337	+	0.231295i	−0.0438118	+	0.00999975i
$536$	−4.28550	+	8.89894i	−0.185105	+	0.384375i
$537$		0			0
$538$			28.4667i			1.22729i
$539$	−9.63864	−	12.4061i	−0.415166	−	0.534370i
$540$		0			0
$541$	−6.25049	+	7.83787i	−0.268730	+	0.336976i	−0.897825	−	0.440351i	$-0.854854\pi$
$541$	−6.25049	+	7.83787i	−0.268730	+	0.336976i	0.629096	+	0.777328i	$0.283425\pi$
$542$	12.3586	+	5.95160i	0.530849	+	0.255643i
$543$		0			0
$544$	2.27618	−	4.72655i	0.0975906	−	0.202649i
$545$	7.86730	−	3.78869i	0.336998	−	0.162290i
$546$		0			0
$547$	12.9256	+	6.22464i	0.552659	+	0.266147i	0.689302	−	0.724474i	$-0.257917\pi$
$547$	12.9256	+	6.22464i	0.552659	+	0.266147i	−0.136643	+	0.990620i	$0.543631\pi$
$548$	−0.105630	+	0.0842374i	−0.00451230	+	0.00359844i
$549$		0			0
$550$	−5.85004	+	7.33572i	−0.249447	+	0.312796i
$551$	−0.645147	+	2.82657i	−0.0274842	+	0.120416i
$552$		0			0
$553$	30.2136	+	3.59848i	1.28481	+	0.153023i
$554$	9.73372	−	7.76238i	0.413546	−	0.329792i
$555$		0			0
$556$	−13.3952	−	3.05738i	−0.568085	−	0.129662i
$557$			22.2295i			0.941895i	0.882161	+	0.470947i	$0.156088\pi$
$557$			22.2295i			0.941895i	−0.882161	+	0.470947i	$0.843912\pi$
$558$		0			0
$559$	−8.60752	−	1.96461i	−0.364059	−	0.0830941i
$560$	−2.37810	−	0.283235i	−0.100493	−	0.0119689i
$561$		0			0
$562$	−4.88717	−	21.4121i	−0.206153	−	0.903214i
$563$	−8.90240	−	11.1633i	−0.375191	−	0.470475i	0.558007	−	0.829836i	$-0.311566\pi$
$563$	−8.90240	−	11.1633i	−0.375191	−	0.470475i	−0.933199	+	0.359361i	$0.882995\pi$
$564$		0			0
$565$	−2.68191	+	0.612128i	−0.112829	+	0.0257524i
$566$	−1.19368	−	5.22987i	−0.0501742	−	0.219828i
$567$		0			0
$568$	1.98550	−	8.69903i	0.0833096	−	0.365003i
$569$			33.4433i			1.40202i	0.713153	+	0.701008i	$0.247266\pi$
$569$			33.4433i			1.40202i	−0.713153	+	0.701008i	$0.752734\pi$
$570$		0			0
$571$	−4.13540	+	18.1184i	−0.173061	+	0.758231i	0.811665	+	0.584123i	$0.198561\pi$
$571$	−4.13540	+	18.1184i	−0.173061	+	0.758231i	−0.984727	+	0.174108i	$0.944296\pi$
$572$	−5.38479	+	2.59318i	−0.225150	+	0.108426i
$573$		0			0
$574$	0.0410377	+	0.119709i	0.00171288	+	0.00499657i
$575$	19.1652	+	15.2837i	0.799244	+	0.637376i
$576$		0			0
$577$	−14.0695	−	11.2200i	−0.585721	−	0.467097i	0.285235	−	0.958458i	$-0.407928\pi$
$577$	−14.0695	−	11.2200i	−0.585721	−	0.467097i	−0.870956	+	0.491361i	$0.836500\pi$
$578$	−4.56500	−	9.47932i	−0.189879	−	0.394288i
$579$		0			0
$580$	−2.69046	+	5.58680i	−0.111715	+	0.231979i
$581$	−1.60028	−	2.58306i	−0.0663909	−	0.107163i
$582$		0			0
$583$	−16.9712	−	8.17288i	−0.702874	−	0.338486i
$584$	−1.71422	−	7.51049i	−0.0709350	−	0.310786i
$585$		0			0
$586$	6.46311	+	5.15416i	0.266989	+	0.212916i
$587$	9.62505			0.397268			0.198634	−	0.980074i	$-0.436349\pi$
$587$	9.62505			0.397268			0.198634	+	0.980074i	$0.436349\pi$
$588$		0			0
$589$	1.04293			0.0429731
$590$	5.56799	+	4.44032i	0.229230	+	0.182805i
$591$		0			0
$592$	2.08037	+	9.11469i	0.0855026	+	0.374611i
$593$	−4.49038	−	2.16246i	−0.184398	−	0.0888014i	0.339407	−	0.940640i	$-0.389774\pi$
$593$	−4.49038	−	2.16246i	−0.184398	−	0.0888014i	−0.523805	+	0.851838i	$0.675488\pi$
$594$		0			0
$595$	−8.94017	+	8.82747i	−0.366511	+	0.361891i
$596$	1.72137	−	3.57446i	0.0705099	−	0.146415i
$597$		0			0
$598$	6.77491	+	14.0682i	0.277047	+	0.575293i
$599$	−18.9751	−	15.1321i	−0.775301	−	0.618282i	0.153803	−	0.988102i	$-0.450848\pi$
$599$	−18.9751	−	15.1321i	−0.775301	−	0.618282i	−0.929103	+	0.369820i	$0.879419\pi$
$600$		0			0
$601$	−16.5270	−	13.1798i	−0.674149	−	0.537616i	0.225493	−	0.974245i	$-0.427601\pi$
$601$	−16.5270	−	13.1798i	−0.674149	−	0.537616i	−0.899642	+	0.436629i	$0.856172\pi$
$602$	−8.26091	−	2.94956i	−0.336689	−	0.120215i
$603$		0			0
$604$	−7.04686	+	3.39359i	−0.286733	+	0.138083i
$605$	−1.20108	+	5.26228i	−0.0488309	+	0.213942i
$606$		0			0
$607$			37.0718i			1.50470i	0.658764	+	0.752350i	$0.271080\pi$
$607$			37.0718i			1.50470i	−0.658764	+	0.752350i	$0.728920\pi$
$608$	−0.0941772	+	0.412617i	−0.00381939	+	0.0167338i
$609$		0			0
$610$	−0.222362	−	0.974231i	−0.00900317	−	0.0394455i
$611$	18.2458	−	4.16447i	0.738144	−	0.168477i
$612$		0			0
$613$	−19.9192	−	24.9778i	−0.804527	−	1.00884i	−0.999606	−	0.0280574i	$-0.991068\pi$
$613$	−19.9192	−	24.9778i	−0.804527	−	1.00884i	0.195079	−	0.980787i	$-0.437504\pi$
$614$	−5.59717	−	24.5228i	−0.225883	−	0.989660i
$615$		0			0
$616$	−5.61707	+	1.92559i	−0.226318	+	0.0775843i
$617$	10.0056	+	2.28372i	0.402811	+	0.0919389i	0.419126	−	0.907928i	$-0.362336\pi$
$617$	10.0056	+	2.28372i	0.402811	+	0.0919389i	−0.0163155	+	0.999867i	$0.505194\pi$
$618$		0			0
$619$			35.9492i			1.44492i	0.691413	+	0.722460i	$0.256989\pi$
$619$			35.9492i			1.44492i	−0.691413	+	0.722460i	$0.743011\pi$
$620$	2.17467	+	0.496353i	0.0873367	+	0.0199340i
$621$		0			0
$622$	19.3483	−	15.4297i	0.775794	−	0.618675i
$623$	−21.6913	−	35.0126i	−0.869044	−	1.40275i
$624$		0			0
$625$	−2.97751	+	13.0453i	−0.119100	+	0.521813i
$626$	13.6514	−	17.1183i	0.545620	−	0.684185i
$627$		0			0
$628$	−15.1391	+	12.0730i	−0.604115	+	0.481765i
$629$	44.1889	+	21.2802i	1.76193	+	0.848499i
$630$		0			0
$631$	17.9033	−	8.62179i	0.712720	−	0.343228i	−0.0421418	−	0.999112i	$-0.513418\pi$
$631$	17.9033	−	8.62179i	0.712720	−	0.343228i	0.754862	+	0.655884i	$0.227704\pi$
$632$	4.98983	−	10.3615i	0.198485	−	0.412158i
$633$		0			0
$634$	−14.7736	−	7.11458i	−0.586734	−	0.282556i
$635$	3.03561	−	3.80653i	0.120464	−	0.151057i
$636$		0			0
$637$	−11.4367	−	14.7204i	−0.453137	−	0.583243i
$638$			15.3745i			0.608682i
$639$		0			0
$640$	−0.392748	+	0.815549i	−0.0155247	+	0.0322374i
$641$	12.6332	−	2.88345i	0.498983	−	0.113890i	0.0343802	−	0.999409i	$-0.489054\pi$
$641$	12.6332	−	2.88345i	0.498983	−	0.113890i	0.464603	+	0.885519i	$0.346197\pi$
$642$		0			0
$643$	0.577387	+	1.19896i	0.0227699	+	0.0472822i	0.912044	−	0.410093i	$-0.134504\pi$
$643$	0.577387	+	1.19896i	0.0227699	+	0.0472822i	−0.889274	+	0.457375i	$0.848790\pi$
$644$	5.03078	+	14.6751i	0.198240	+	0.578279i
$645$		0			0
$646$	1.38433	+	1.73589i	0.0544655	+	0.0682976i
$647$	17.4434	−	8.40027i	0.685769	−	0.330249i	−0.0583499	−	0.998296i	$-0.518584\pi$
$647$	17.4434	−	8.40027i	0.685769	−	0.330249i	0.744119	+	0.668047i	$0.232870\pi$
$648$		0			0
$649$	17.2149	+	3.92920i	0.675745	+	0.154234i
$650$	−6.94132	+	8.70414i	−0.272261	+	0.341405i
$651$		0			0
$652$	−0.249480	−	0.312838i	−0.00977039	−	0.0122517i
$653$	−15.9944	−	33.2127i	−0.625909	−	1.29971i	−0.936999	−	0.349333i	$-0.886408\pi$
$653$	−15.9944	−	33.2127i	−0.625909	−	1.29971i	0.311089	−	0.950381i	$-0.399306\pi$
$654$		0			0
$655$	10.7486			0.419981
$656$	0.0478306			0.00186747
$657$		0			0
$658$	18.4897	−	1.96460i	0.720803	−	0.0765881i
$659$	−33.6212	+	7.67382i	−1.30970	+	0.298930i	−0.819699	−	0.572794i	$-0.805859\pi$
$659$	−33.6212	+	7.67382i	−1.30970	+	0.298930i	−0.489998	+	0.871724i	$0.663002\pi$
$660$		0			0
$661$	−23.4142	+	18.6722i	−0.910706	+	0.726264i	−0.962181	−	0.272411i	$-0.912179\pi$
$661$	−23.4142	+	18.6722i	−0.910706	+	0.726264i	0.0514752	+	0.998674i	$0.483608\pi$
$662$	6.63842	−	5.29396i	0.258010	−	0.205756i
$663$		0			0
$664$	−1.11969	+	0.255562i	−0.0434524	+	0.00991772i
$665$	0.544698	−	0.854797i	0.0211225	−	0.0331476i
$666$		0			0
$667$	40.1672			1.55528
$668$	9.32670			0.360861
$669$		0			0
$670$	−3.87920	−	8.05524i	−0.149867	−	0.311201i
$671$	−1.54478	−	1.93709i	−0.0596356	−	0.0747806i
$672$		0			0
$673$	−22.0493	+	27.6490i	−0.849939	+	1.06579i	0.147117	+	0.989119i	$0.453000\pi$
$673$	−22.0493	+	27.6490i	−0.849939	+	1.06579i	−0.997056	+	0.0766707i	$0.975571\pi$
$674$	−12.0664	−	2.75407i	−0.464779	−	0.106083i
$675$		0			0
$676$	5.32331	−	2.56357i	0.204743	−	0.0985989i
$677$	2.44943	+	3.07149i	0.0941393	+	0.118047i	0.826670	−	0.562687i	$-0.190232\pi$
$677$	2.44943	+	3.07149i	0.0941393	+	0.118047i	−0.732531	+	0.680734i	$0.761661\pi$
$678$		0			0
$679$	−3.52021	+	29.5564i	−0.135093	+	1.13427i
$680$	2.06038	+	4.27843i	0.0790121	+	0.164070i
$681$		0			0
$682$	5.39188	−	1.23066i	0.206466	−	0.0471244i
$683$	−18.3246	+	38.0515i	−0.701172	+	1.45600i	0.180227	+	0.983625i	$0.442317\pi$
$683$	−18.3246	+	38.0515i	−0.701172	+	1.45600i	−0.881399	+	0.472373i	$0.843397\pi$
$684$		0			0
$685$		−	0.122297i		−	0.00467273i
$686$	−9.55320	−	15.8662i	−0.364743	−	0.605774i
$687$		0			0
$688$	−2.06711	+	2.59207i	−0.0788078	+	0.0988219i
$689$	−20.1370	−	9.69747i	−0.767159	−	0.369444i
$690$		0			0
$691$	10.9227	−	22.6813i	0.415521	−	0.862838i	−0.583203	−	0.812327i	$-0.698201\pi$
$691$	10.9227	−	22.6813i	0.415521	−	0.862838i	0.998723	−	0.0505111i	$-0.0160850\pi$
$692$	17.5612	−	8.45705i	0.667578	−	0.321489i
$693$		0			0
$694$	0.378647	+	0.182347i	0.0143732	+	0.00692178i
$695$	9.72370	−	7.75439i	0.368841	−	0.294141i
$696$		0			0
$697$	0.156448	−	0.196179i	0.00592588	−	0.00743082i
$698$	−2.05996	+	9.02528i	−0.0779707	+	0.341612i
$699$		0			0
$700$	−7.87069	+	7.77147i	−0.297484	+	0.293734i
$701$	−8.39429	+	6.69422i	−0.317048	+	0.252837i	−0.769063	−	0.639173i	$-0.779277\pi$
$701$	−8.39429	+	6.69422i	−0.317048	+	0.252837i	0.452015	+	0.892010i	$0.350705\pi$
$702$		0			0
$703$	−3.85759	−	0.880470i	−0.145492	−	0.0332076i
$704$			2.24434i			0.0845866i
$705$		0			0
$706$	19.7873	+	4.51631i	0.744703	+	0.169974i
$707$	−19.4325	−	12.3829i	−0.730834	−	0.465705i
$708$		0			0
$709$	7.26354	+	31.8237i	0.272788	+	1.19516i	0.906706	+	0.421763i	$0.138588\pi$
$709$	7.26354	+	31.8237i	0.272788	+	1.19516i	−0.633918	+	0.773400i	$0.718554\pi$
$710$	5.03580	+	6.31469i	0.188990	+	0.236986i
$711$		0			0
$712$	−15.1770	+	3.46406i	−0.568783	+	0.129821i
$713$	−3.21521	−	14.0867i	−0.120411	−	0.527553i
$714$		0			0
$715$	1.20384	−	5.27439i	0.0450212	−	0.197251i
$716$			1.58627i			0.0592817i
$717$		0			0
$718$	1.99192	−	8.72716i	0.0743377	−	0.325695i
$719$	30.7934	−	14.8293i	1.14840	−	0.553041i	0.239848	−	0.970811i	$-0.422902\pi$
$719$	30.7934	−	14.8293i	1.14840	−	0.553041i	0.908553	+	0.417770i	$0.137188\pi$
$720$		0			0
$721$	−23.6817	+	37.1639i	−0.881954	+	1.38405i
$722$	14.7148	+	11.7346i	0.547626	+	0.436718i
$723$		0			0
$724$	−9.01685	−	7.19070i	−0.335109	−	0.267240i
$725$	12.4259	+	25.8026i	0.461486	+	0.958286i
$726$		0			0
$727$	−15.2890	+	31.7480i	−0.567038	+	1.17747i	0.398491	+	0.917172i	$0.369534\pi$
$727$	−15.2890	+	31.7480i	−0.567038	+	1.17747i	−0.965529	+	0.260294i	$0.916180\pi$
$728$	−6.66489	+	2.28480i	−0.247017	+	0.0846802i
$729$		0			0
$730$	6.28270	+	3.02559i	0.232533	+	0.111982i
$731$	3.87025	+	16.9567i	0.143146	+	0.627165i
$732$		0			0
$733$	17.2637	+	13.7673i	0.637648	+	0.508507i	0.888117	−	0.459618i	$-0.152013\pi$
$733$	17.2637	+	13.7673i	0.637648	+	0.508507i	−0.250469	+	0.968125i	$0.580585\pi$
$734$	−26.8860			−0.992380
$735$		0			0
$736$	5.86353			0.216132
$737$	−17.3312	−	13.8212i	−0.638404	−	0.509110i
$738$		0			0
$739$	4.65841	+	20.4098i	0.171362	+	0.750788i	0.985439	+	0.170030i	$0.0543865\pi$
$739$	4.65841	+	20.4098i	0.171362	+	0.750788i	−0.814076	+	0.580758i	$0.802756\pi$
$740$	−7.62464	−	3.67183i	−0.280287	−	0.134979i
$741$		0			0
$742$	−18.7267	−	11.9331i	−0.687479	−	0.438079i
$743$	16.3075	−	33.8629i	0.598265	−	1.24231i	−0.353487	−	0.935440i	$-0.615004\pi$
$743$	16.3075	−	33.8629i	0.598265	−	1.24231i	0.951751	−	0.306870i	$-0.0992817\pi$
$744$		0			0
$745$	1.55817	+	3.23557i	0.0570868	+	0.118542i
$746$	−20.0332	−	15.9759i	−0.733467	−	0.584920i
$747$		0			0
$748$	9.20524	+	7.34094i	0.336577	+	0.268411i
$749$	−2.58264	+	1.60002i	−0.0943678	+	0.0584636i
$750$		0			0
$751$	−26.6429	+	12.8305i	−0.972213	+	0.468193i	−0.851420	−	0.524485i	$-0.824258\pi$
$751$	−26.6429	+	12.8305i	−0.972213	+	0.468193i	−0.120793	+	0.992678i	$0.538544\pi$
$752$	1.56383	−	6.85158i	0.0570269	−	0.249851i
$753$		0			0
$754$			18.2425i			0.664352i
$755$	1.57542	−	6.90238i	0.0573355	−	0.251203i
$756$		0			0
$757$	0.210861	+	0.923844i	0.00766388	+	0.0335777i	0.978615	−	0.205699i	$-0.0659468\pi$
$757$	0.210861	+	0.923844i	0.00766388	+	0.0335777i	−0.970951	+	0.239277i	$0.923090\pi$
$758$	−22.6653	+	5.17321i	−0.823241	+	0.187899i
$759$		0			0
$760$	−0.238861	−	0.299522i	−0.00866438	−	0.0108648i
$761$	−2.16611	−	9.49034i	−0.0785213	−	0.344024i	0.920373	−	0.391042i	$-0.127885\pi$
$761$	−2.16611	−	9.49034i	−0.0785213	−	0.344024i	−0.998894	+	0.0470179i	$0.985028\pi$
$762$		0			0
$763$	18.1613	−	17.9324i	0.657483	−	0.649195i
$764$	−4.16389	−	0.950381i	−0.150644	−	0.0343836i
$765$		0			0
$766$		−	25.5525i		−	0.923249i
$767$	20.4262	+	4.66216i	0.737549	+	0.168341i
$768$		0			0
$769$	0.918088	−	0.732150i	0.0331071	−	0.0264020i	−0.606796	−	0.794857i	$-0.707546\pi$
$769$	0.918088	−	0.732150i	0.0331071	−	0.0264020i	0.639904	+	0.768455i	$0.278974\pi$
$770$	1.80739	−	5.06200i	0.0651338	−	0.182422i
$771$		0			0
$772$	−4.81064	+	21.0768i	−0.173139	+	0.758570i
$773$	−10.9510	+	13.7321i	−0.393878	+	0.493908i	−0.938744	−	0.344616i	$-0.888009\pi$
$773$	−10.9510	+	13.7321i	−0.393878	+	0.493908i	0.544866	+	0.838523i	$0.316581\pi$
$774$		0			0
$775$	8.05442	−	6.42319i	0.289323	−	0.230728i
$776$	10.1361	+	4.88130i	0.363865	+	0.175228i
$777$		0			0
$778$	4.85390	−	2.33752i	0.174021	−	0.0838040i
$779$	−0.00878323	+	0.0182386i	−0.000314692	+	0.000653464i
$780$		0			0
$781$	18.0425	+	8.68880i	0.645611	+	0.310910i
$782$	19.1788	−	24.0495i	0.685834	−	0.860008i
$783$		0			0
$784$	−6.84371	+	1.47095i	−0.244418	+	0.0525338i
$785$		−	17.5278i		−	0.625593i
$786$		0			0
$787$	18.5777	−	38.5770i	0.662223	−	1.37512i	−0.251131	−	0.967953i	$-0.580802\pi$
$787$	18.5777	−	38.5770i	0.662223	−	1.37512i	0.913354	−	0.407167i	$-0.133483\pi$
$788$	20.1428	−	4.59747i	0.717558	−	0.163778i
$789$		0			0
$790$	4.51675	+	9.37913i	0.160699	+	0.333694i
$791$	−6.83503	+	4.23450i	−0.243026	+	0.150562i
$792$		0			0
$793$	−1.83295	−	2.29844i	−0.0650898	−	0.0816201i
$794$	20.3697	−	9.80951i	0.722892	−	0.348127i
$795$		0			0
$796$	−17.5664	−	4.00941i	−0.622624	−	0.142110i
$797$	−20.7627	+	26.0356i	−0.735454	+	0.922230i	−0.999101	−	0.0423892i	$-0.986503\pi$
$797$	−20.7627	+	26.0356i	−0.735454	+	0.922230i	0.263647	+	0.964619i	$0.415074\pi$
$798$		0			0
$799$	−22.9870	−	28.8247i	−0.813220	−	1.01975i
$800$	1.81391	+	3.76662i	0.0641313	+	0.133170i
$801$		0			0
$802$	−19.4285			−0.686043
$803$	17.2896			0.610135
$804$		0			0
$805$	−13.2249	−	4.72196i	−0.466117	−	0.166427i
$806$	6.39769	−	1.46023i	0.225349	−	0.0514344i
$807$		0			0
$808$	−6.80917	+	5.43013i	−0.239546	+	0.191031i
$809$	24.5099	−	19.5460i	0.861724	−	0.687202i	−0.0894052	−	0.995995i	$-0.528497\pi$
$809$	24.5099	−	19.5460i	0.861724	−	0.687202i	0.951129	+	0.308793i	$0.0999252\pi$
$810$		0			0
$811$	45.6355	−	10.4160i	1.60248	−	0.365755i	0.674467	−	0.738305i	$-0.264374\pi$
$811$	45.6355	−	10.4160i	1.60248	−	0.365755i	0.928012	+	0.372550i	$0.121516\pi$
$812$	−2.14348	+	17.9971i	−0.0752214	+	0.631576i
$813$		0			0
$814$	−20.9825			−0.735436
$815$	0.362199			0.0126873
$816$		0			0
$817$	−0.608811	−	1.26421i	−0.0212996	−	0.0442290i
$818$	0.374136	+	0.469151i	0.0130813	+	0.0164035i
$819$		0			0
$820$	−0.0269945	+	0.0338501i	−0.000942690	+	0.00118210i
$821$	−19.5262	−	4.45673i	−0.681470	−	0.155541i	−0.132247	−	0.991217i	$-0.542219\pi$
$821$	−19.5262	−	4.45673i	−0.681470	−	0.155541i	−0.549223	+	0.835676i	$0.685076\pi$
$822$		0			0
$823$	7.60614	−	3.66292i	0.265133	−	0.127681i	−0.296595	−	0.955003i	$-0.595851\pi$
$823$	7.60614	−	3.66292i	0.265133	−	0.127681i	0.561728	+	0.827322i	$0.310137\pi$
$824$	10.3849	+	13.0223i	0.361775	+	0.453652i
$825$		0			0
$826$	19.6037	+	6.99952i	0.682101	+	0.243545i
$827$	16.6077	+	34.4862i	0.577505	+	1.19920i	0.961228	+	0.275753i	$0.0889273\pi$
$827$	16.6077	+	34.4862i	0.577505	+	1.19920i	−0.383723	+	0.923448i	$0.625358\pi$
$828$		0			0
$829$	30.7409	−	7.01641i	1.06768	−	0.243690i	0.347641	−	0.937628i	$-0.386983\pi$
$829$	30.7409	−	7.01641i	1.06768	−	0.243690i	0.720035	+	0.693938i	$0.244126\pi$
$830$	0.451065	−	0.936645i	0.0156567	−	0.0325114i
$831$		0			0
$832$			2.66300i			0.0923229i
$833$	−16.3517	+	32.8810i	−0.566554	+	1.13926i
$834$		0			0
$835$	−5.26378	+	6.60057i	−0.182161	+	0.228422i
$836$	−0.855800	−	0.412132i	−0.0295985	−	0.0142539i
$837$		0			0
$838$	−10.4898	+	21.7824i	−0.362366	+	0.752460i
$839$	50.5543	−	24.3457i	1.74533	−	0.840506i	0.764763	−	0.644312i	$-0.222856\pi$
$839$	50.5543	−	24.3457i	1.74533	−	0.840506i	0.980565	−	0.196193i	$-0.0628580\pi$
$840$		0			0
$841$	16.1520	+	7.77837i	0.556964	+	0.268220i
$842$	27.0606	−	21.5801i	0.932571	−	0.743701i
$843$		0			0
$844$	−6.11877	+	7.67269i	−0.210617	+	0.264105i
$845$	−1.19010	+	5.21417i	−0.0409407	+	0.179373i
$846$		0			0
$847$	1.66693	+	15.6882i	0.0572764	+	0.539052i
$848$	−6.56186	+	5.23291i	−0.225335	+	0.179699i
$849$		0			0
$850$	21.3820	+	4.88030i	0.733396	+	0.167393i
$851$			54.8186i			1.87916i
$852$		0			0
$853$	40.5179	+	9.24795i	1.38731	+	0.316644i	0.850017	−	0.526755i	$-0.176591\pi$
$853$	40.5179	+	9.24795i	1.38731	+	0.316644i	0.537289	+	0.843398i	$0.319448\pi$
$854$	−1.53823	−	2.48290i	−0.0526371	−	0.0849630i
$855$		0			0
$856$	0.255520	+	1.11951i	0.00873351	+	0.0382640i
$857$	22.4682	+	28.1743i	0.767500	+	0.962414i	0.999948	−	0.0101946i	$-0.00324509\pi$
$857$	22.4682	+	28.1743i	0.767500	+	0.962414i	−0.232448	+	0.972609i	$0.574674\pi$
$858$		0			0
$859$	−22.3925	+	5.11094i	−0.764022	+	0.174383i	−0.586738	−	0.809777i	$-0.699588\pi$
$859$	−22.3925	+	5.11094i	−0.764022	+	0.174383i	−0.177284	+	0.984160i	$0.556731\pi$
$860$	−0.667798	−	2.92582i	−0.0227717	−	0.0997695i
$861$		0			0
$862$	−0.0311390	+	0.136429i	−0.00106060	+	0.00464678i
$863$		−	5.74215i		−	0.195465i	−0.995213	−	0.0977325i	$-0.968841\pi$
$863$		−	5.74215i		−	0.195465i	0.995213	−	0.0977325i	$-0.0311590\pi$
$864$		0			0
$865$	−3.92606	+	17.2012i	−0.133490	+	0.584858i
$866$	20.0370	−	9.64933i	0.680886	−	0.327898i
$867$		0			0
$868$	6.48322	−	0.688867i	0.220055	−	0.0233817i
$869$	20.1796	+	16.0927i	0.684547	+	0.545908i
$870$		0			0
$871$	−20.5642	−	16.3994i	−0.696793	−	0.555674i
$872$	−4.18552	−	8.69131i	−0.141739	−	0.294325i
$873$		0			0
$874$	−1.07673	+	2.23585i	−0.0364209	+	0.0756289i
$875$	−2.32310	−	21.8637i	−0.0785353	−	0.739129i
$876$		0			0
$877$	50.9087	+	24.5164i	1.71907	+	0.827858i	0.989601	+	0.143840i	$0.0459450\pi$
$877$	50.9087	+	24.5164i	1.71907	+	0.827858i	0.729465	+	0.684018i	$0.239769\pi$
$878$	−7.50340	−	32.8746i	−0.253228	−	1.10946i
$879$		0			0
$880$	−1.58833	−	1.26665i	−0.0535427	−	0.0426989i
$881$	−34.1349			−1.15004			−0.575018	−	0.818141i	$-0.695005\pi$
$881$	−34.1349			−1.15004			−0.575018	+	0.818141i	$0.695005\pi$
$882$		0			0
$883$	53.5962			1.80366			0.901828	−	0.432095i	$-0.142225\pi$
$883$	53.5962			1.80366			0.901828	+	0.432095i	$0.142225\pi$
$884$	10.9224	+	8.71033i	0.367360	+	0.292960i
$885$		0			0
$886$	−7.40186	−	32.4297i	−0.248670	−	1.08950i
$887$	45.9732	+	22.1395i	1.54363	+	0.743373i	0.995655	−	0.0931216i	$-0.0296845\pi$
$887$	45.9732	+	22.1395i	1.54363	+	0.743373i	0.547975	+	0.836495i	$0.315399\pi$
$888$		0			0
$889$	4.78519	−	13.4020i	0.160490	−	0.449488i
$890$	6.11404	−	12.6959i	0.204943	−	0.425569i
$891$		0			0
$892$	−11.5815	−	24.0493i	−0.387779	−	0.805231i
$893$	2.32544	+	1.85448i	0.0778180	+	0.0620578i
$894$		0			0
$895$	−1.12262	−	0.895256i	−0.0375249	−	0.0299251i
$896$	−0.312901	+	2.62718i	−0.0104533	+	0.0877680i
$897$		0			0
$898$	31.9523	−	15.3874i	1.06626	−	0.513485i
$899$	3.75633	−	16.4575i	0.125280	−	0.548890i
$900$		0			0
$901$			44.0299i			1.46685i
$902$	−0.0238872	+	0.104657i	−0.000795357	+	0.00348468i
$903$		0			0
$904$	0.676241	+	2.96281i	0.0224914	+	0.0985415i
$905$	10.1778	−	2.32302i	0.338322	−	0.0772198i
$906$		0			0
$907$	0.647388	+	0.811798i	0.0214962	+	0.0269553i	0.792463	−	0.609919i	$-0.208798\pi$
$907$	0.647388	+	0.811798i	0.0214962	+	0.0269553i	−0.770967	+	0.636875i	$0.780227\pi$
$908$	−3.81400	−	16.7102i	−0.126572	−	0.554549i
$909$		0			0
$910$	2.14454	−	6.00627i	0.0710910	−	0.199106i
$911$	−27.8371	−	6.35363i	−0.922283	−	0.210505i	−0.265087	−	0.964225i	$-0.585401\pi$
$911$	−27.8371	−	6.35363i	−0.922283	−	0.210505i	−0.657196	+	0.753719i	$0.728258\pi$
$912$		0			0
$913$		−	2.57758i		−	0.0853056i
$914$	−5.88045	−	1.34217i	−0.194508	−	0.0443952i
$915$		0			0
$916$	12.5675	−	10.0222i	0.415242	−	0.331144i
$917$	29.7188	−	10.1879i	0.981402	−	0.336435i
$918$		0			0
$919$	−1.50711	+	6.60307i	−0.0497149	+	0.217815i	−0.993683	−	0.112221i	$-0.964204\pi$
$919$	−1.50711	+	6.60307i	−0.0497149	+	0.217815i	0.943968	+	0.330036i	$0.107061\pi$
$920$	−3.30924	+	4.14966i	−0.109102	+	0.136810i
$921$		0			0
$922$	4.27738	−	3.41110i	0.140868	−	0.112339i
$923$	21.4082	+	10.3096i	0.704658	+	0.339346i
$924$		0			0
$925$	−35.2144	+	16.9584i	−1.15784	+	0.557588i
$926$	11.1118	−	23.0740i	0.365158	−	0.758258i
$927$		0			0
$928$	6.17195	+	2.97226i	0.202604	+	0.0975691i
$929$	11.4622	−	14.3731i	0.376062	−	0.471567i	−0.557400	−	0.830244i	$-0.688201\pi$
$929$	11.4622	−	14.3731i	0.376062	−	0.471567i	0.933461	+	0.358678i	$0.116772\pi$
$930$		0			0
$931$	0.695827	−	2.87972i	0.0228048	−	0.0943791i
$932$			1.39895i			0.0458240i
$933$		0			0
$934$	−7.60245	+	15.7866i	−0.248760	+	0.516555i
$935$	−10.3905	+	2.37156i	−0.339805	+	0.0775582i
$936$		0			0
$937$	19.9150	+	41.3540i	0.650595	+	1.35098i	0.921503	+	0.388370i	$0.126962\pi$
$937$	19.9150	+	41.3540i	0.650595	+	1.35098i	−0.270908	+	0.962605i	$0.587324\pi$
$938$	−18.3607	−	18.5951i	−0.599499	−	0.607153i
$939$		0			0
$940$	3.96632	+	4.97361i	0.129367	+	0.162221i
$941$	5.99804	−	2.88850i	0.195530	−	0.0941625i	−0.333557	−	0.942730i	$-0.608249\pi$
$941$	5.99804	−	2.88850i	0.195530	−	0.0941625i	0.529087	+	0.848568i	$0.322535\pi$
$942$		0			0
$943$	0.273425	+	0.0624074i	0.00890393	+	0.00203226i
$944$	4.90540	−	6.15117i	0.159657	−	0.200204i
$945$		0			0
$946$	−4.63929	−	5.81749i	−0.150836	−	0.189143i
$947$	15.6745	+	32.5484i	0.509353	+	1.05768i	0.984109	+	0.177565i	$0.0568220\pi$
$947$	15.6745	+	32.5484i	0.509353	+	1.05768i	−0.474756	+	0.880117i	$0.657464\pi$
$948$		0			0
$949$	20.5148			0.665938
$950$	−1.76936			−0.0574056
$951$		0			0
$952$	9.75205	+	9.87655i	0.316066	+	0.320101i
$953$	−0.456608	+	0.104218i	−0.0147910	+	0.00337594i	−0.229910	−	0.973212i	$-0.573843\pi$
$953$	−0.456608	+	0.104218i	−0.0147910	+	0.00337594i	0.215119	+	0.976588i	$0.430986\pi$
$954$		0			0
$955$	3.02260	−	2.41044i	0.0978090	−	0.0780001i
$956$	15.0172	−	11.9758i	0.485690	−	0.387324i
$957$		0			0
$958$	−33.5262	+	7.65213i	−1.08318	+	0.247229i
$959$	−0.115918	−	0.338140i	−0.00374320	−	0.0109191i
$960$		0			0
$961$	24.9276			0.804117
$962$	−24.8966			−0.802699
$963$		0			0
$964$	2.09521	+	4.35076i	0.0674823	+	0.140128i
$965$	−12.2012	−	15.2998i	−0.392770	−	0.492518i
$966$		0			0
$967$	−30.5015	+	38.2477i	−0.980862	+	1.22996i	−0.00766925	+	0.999971i	$0.502441\pi$
$967$	−30.5015	+	38.2477i	−0.980862	+	1.22996i	−0.973193	+	0.229991i	$0.926130\pi$
$968$	5.81345	+	1.32688i	0.186851	+	0.0426476i
$969$		0			0
$970$	−9.17512	+	4.41851i	−0.294595	+	0.141870i
$971$	16.0335	+	20.1053i	0.514538	+	0.645210i	0.969439	−	0.245332i	$-0.0788968\pi$
$971$	16.0335	+	20.1053i	0.514538	+	0.645210i	−0.454901	+	0.890542i	$0.650325\pi$
$972$		0			0
$973$	19.5352	−	30.6567i	0.626270	−	0.982809i
$974$	8.86146	+	18.4010i	0.283940	+	0.589607i
$975$		0			0
$976$	−1.07627	+	0.245652i	−0.0344506	+	0.00786312i
$977$	−3.02659	+	6.28478i	−0.0968292	+	0.201068i	−0.943757	−	0.330640i	$-0.892735\pi$
$977$	−3.02659	+	6.28478i	−0.0968292	+	0.201068i	0.846928	+	0.531708i	$0.178450\pi$
$978$		0			0
$979$		−	34.9383i		−	1.11663i
$980$	2.82143	−	5.67351i	0.0901274	−	0.181234i
$981$		0			0
$982$	4.23043	−	5.30479i	0.134998	−	0.169283i
$983$	−24.4935	−	11.7954i	−0.781221	−	0.376216i	0.000376074	−	1.00000i	$-0.499880\pi$
$983$	−24.4935	−	11.7954i	−0.781221	−	0.376216i	−0.781597	+	0.623784i	$0.785595\pi$
$984$		0			0
$985$	−8.11449	+	16.8499i	−0.258549	+	0.536883i
$986$	32.3785	−	15.5927i	1.03114	−	0.496572i
$987$		0			0
$988$	−1.01544	−	0.489012i	−0.0323056	−	0.0155575i
$989$	−15.1987	+	12.1205i	−0.483290	+	0.385411i
$990$		0			0
$991$	−24.5197	+	30.7467i	−0.778893	+	0.976701i	0.221106	+	0.975250i	$0.429033\pi$
$991$	−24.5197	+	30.7467i	−0.778893	+	0.976701i	−0.999999	+	0.00145088i	$0.999538\pi$
$992$	0.548341	−	2.40244i	0.0174098	−	0.0762775i
$993$		0			0
$994$	19.9089	+	12.6864i	0.631471	+	0.402389i
$995$	12.7516	−	10.1690i	0.404252	−	0.322380i
$996$		0			0
$997$	36.4469	+	8.31877i	1.15429	+	0.263458i	0.756483	−	0.654013i	$-0.226916\pi$
$997$	36.4469	+	8.31877i	1.15429	+	0.263458i	0.397802	+	0.917471i	$0.369773\pi$
$998$			20.0976i			0.636177i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.v.a.251.13	yes	96
3.2	odd	2	inner	882.2.v.a.251.4	✓	96
49.41	odd	14	inner	882.2.v.a.629.4	yes	96
147.41	even	14	inner	882.2.v.a.629.13	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.v.a.251.4	✓	96	3.2	odd	2	inner
882.2.v.a.251.13	yes	96	1.1	even	1	trivial
882.2.v.a.629.4	yes	96	49.41	odd	14	inner
882.2.v.a.629.13	yes	96	147.41	even	14	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.v (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.781831 + 0.623490i) q^{2} +(0.222521 + 0.974928i) q^{4} +(-0.815549 - 0.392748i) q^{5} +(-2.62718 - 0.312901i) q^{7} +(-0.433884 + 0.900969i) q^{8} +O(q^{10})\)	\(q+(0.781831 + 0.623490i) q^{2} +(0.222521 + 0.974928i) q^{4} +(-0.815549 - 0.392748i) q^{5} +(-2.62718 - 0.312901i) q^{7} +(-0.433884 + 0.900969i) q^{8} +(-0.392748 - 0.815549i) q^{10} +(-1.75469 - 1.39932i) q^{11} +(-2.08202 - 1.66035i) q^{13} +(-1.85892 - 1.88266i) q^{14} +(-0.900969 + 0.433884i) q^{16} +(-1.16736 + 5.11454i) q^{17} -0.423228i q^{19} +(0.201424 - 0.882496i) q^{20} +(-0.499412 - 2.18807i) q^{22} +(-5.71651 + 1.30476i) q^{23} +(-2.60658 - 3.26855i) q^{25} +(-0.592573 - 2.59623i) q^{26} +(-0.279548 - 2.63094i) q^{28} +(-6.67860 - 1.52435i) q^{29} +2.46422i q^{31} +(-0.974928 - 0.222521i) q^{32} +(-4.10154 + 3.27087i) q^{34} +(2.01971 + 1.28701i) q^{35} +(2.08037 - 9.11469i) q^{37} +(0.263879 - 0.330893i) q^{38} +(0.707707 - 0.564378i) q^{40} +(-0.0430939 - 0.0207529i) q^{41} +(2.98706 - 1.43849i) q^{43} +(0.973781 - 2.02208i) q^{44} +(-5.28285 - 2.54409i) q^{46} +(-4.38175 + 5.49454i) q^{47} +(6.80419 + 1.64409i) q^{49} -4.18063i q^{50} +(1.15543 - 2.39928i) q^{52} +(8.18250 - 1.86760i) q^{53} +(0.881458 + 1.83037i) q^{55} +(1.42181 - 2.23125i) q^{56} +(-4.27112 - 5.35582i) q^{58} +(-7.08850 + 3.41364i) q^{59} +(1.07627 + 0.245652i) q^{61} +(-1.53642 + 1.92660i) q^{62} +(-0.623490 - 0.781831i) q^{64} +(1.04589 + 2.17181i) q^{65} +9.87707 q^{67} -5.24607 q^{68} +(0.776635 + 2.26549i) q^{70} +(-8.69903 + 1.98550i) q^{71} +(-6.02295 + 4.80314i) q^{73} +(7.30941 - 5.82906i) q^{74} +(0.412617 - 0.0941772i) q^{76} +(4.17205 + 4.22532i) q^{77} -11.5004 q^{79} +0.905191 q^{80} +(-0.0207529 - 0.0430939i) q^{82} +(0.716068 + 0.897921i) q^{83} +(2.96076 - 3.71268i) q^{85} +(3.23226 + 0.737743i) q^{86} +(2.02208 - 0.973781i) q^{88} +(9.70608 + 12.1710i) q^{89} +(4.95032 + 5.01352i) q^{91} +(-2.54409 - 5.28285i) q^{92} +(-6.85158 + 1.56383i) q^{94} +(-0.166222 + 0.345164i) q^{95} -11.2502i q^{97} +(4.29465 + 5.52775i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 16 q^{4}+O(q^{10}) \) 96 * q + 16 * q^4	\( 96 q + 16 q^{4} - 16 q^{16} + 20 q^{22} - 8 q^{25} + 76 q^{37} + 28 q^{40} - 8 q^{43} + 112 q^{49} + 28 q^{52} + 28 q^{55} + 20 q^{58} + 84 q^{61} + 16 q^{64} - 8 q^{67} + 28 q^{70} + 112 q^{85} + 8 q^{88} - 56 q^{91} - 56 q^{94}+O(q^{100}) \) 96 * q + 16 * q^4 - 16 * q^16 + 20 * q^22 - 8 * q^25 + 76 * q^37 + 28 * q^40 - 8 * q^43 + 112 * q^49 + 28 * q^52 + 28 * q^55 + 20 * q^58 + 84 * q^61 + 16 * q^64 - 8 * q^67 + 28 * q^70 + 112 * q^85 + 8 * q^88 - 56 * q^91 - 56 * q^94

Introduction

L-functions

Modular forms

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Database

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