LMFDB - Embedded newform 490.2.l.d.117.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [490,2,Mod(117,490)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(490, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([3, 10]))

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

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

chi := DirichletCharacter("490.117");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 490 = 2 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	490.l (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.91266969904$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			117.3
Character	$\chi$	$=$	490.117
Dual form			490.2.l.d.423.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.965926 + 0.258819i) q^{2} +(0.550608 - 2.05490i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.20905 + 1.88101i) q^{5} +2.12738i q^{6} +(-0.707107 + 0.707107i) q^{8} +(-1.32135 - 0.762882i) q^{9} +(-1.65469 - 1.50399i) q^{10} +(0.814115 + 1.41009i) q^{11} +(-0.550608 - 2.05490i) q^{12} +(4.65861 + 4.65861i) q^{13} +(4.53099 - 1.44877i) q^{15} +(0.500000 - 0.866025i) q^{16} +(2.59984 + 0.696624i) q^{17} +(1.47377 + 0.394897i) q^{18} +(-2.14608 + 3.71713i) q^{19} +(1.98757 + 1.02448i) q^{20} +(-1.15133 - 1.15133i) q^{22} +(-1.91659 - 7.15281i) q^{23} +(1.06369 + 1.84237i) q^{24} +(-2.07641 + 4.54846i) q^{25} +(-5.70561 - 3.29413i) q^{26} +(2.21768 - 2.21768i) q^{27} -3.26022i q^{29} +(-4.00163 + 2.57211i) q^{30} +(-7.13157 + 4.11741i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(3.34584 - 0.896515i) q^{33} -2.69155 q^{34} -1.52576 q^{36} +(10.8338 - 2.90291i) q^{37} +(1.11089 - 4.14592i) q^{38} +(12.1380 - 7.00789i) q^{39} +(-2.18500 - 0.475150i) q^{40} -3.04106i q^{41} +(1.67710 - 1.67710i) q^{43} +(1.41009 + 0.814115i) q^{44} +(-0.162586 - 3.40783i) q^{45} +(3.70257 + 6.41303i) q^{46} +(-1.82248 - 6.80159i) q^{47} +(-1.50429 - 1.50429i) q^{48} +(0.828427 - 4.93089i) q^{50} +(2.86298 - 4.95883i) q^{51} +(6.36378 + 1.70517i) q^{52} +(-5.67082 - 1.51949i) q^{53} +(-1.56813 + 2.71609i) q^{54} +(-1.66809 + 3.23622i) q^{55} +(6.45666 + 6.45666i) q^{57} +(0.843807 + 3.14913i) q^{58} +(3.01632 + 5.22442i) q^{59} +(3.19957 - 3.52017i) q^{60} +(6.78484 + 3.91723i) q^{61} +(5.82290 - 5.82290i) q^{62} -1.00000i q^{64} +(-3.13042 + 14.3954i) q^{65} +(-2.99980 + 1.73193i) q^{66} +(1.63125 - 6.08791i) q^{67} +(2.59984 - 0.696624i) q^{68} -15.7536 q^{69} -6.85705 q^{71} +(1.47377 - 0.394897i) q^{72} +(-0.656029 + 2.44833i) q^{73} +(-9.71332 + 5.60799i) q^{74} +(8.20333 + 6.77122i) q^{75} +4.29217i q^{76} +(-9.91065 + 9.91065i) q^{78} +(-8.52689 - 4.92300i) q^{79} +(2.23353 - 0.106560i) q^{80} +(-5.62467 - 9.74221i) q^{81} +(0.787084 + 2.93744i) q^{82} +(4.51286 + 4.51286i) q^{83} +(1.83297 + 5.73258i) q^{85} +(-1.18589 + 2.05401i) q^{86} +(-6.69941 - 1.79510i) q^{87} +(-1.57275 - 0.421417i) q^{88} +(1.42768 - 2.47281i) q^{89} +(1.03906 + 3.24963i) q^{90} +(-5.23622 - 5.23622i) q^{92} +(4.53416 + 16.9217i) q^{93} +(3.52076 + 6.09814i) q^{94} +(-9.58668 + 0.457374i) q^{95} +(1.84237 + 1.06369i) q^{96} +(2.26618 - 2.26618i) q^{97} -2.48429i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{11} - 48 q^{15} + 16 q^{16} + 16 q^{18} + 32 q^{22} - 16 q^{23} - 32 q^{25} - 40 q^{30} - 96 q^{36} + 48 q^{37} + 32 q^{43} + 16 q^{46} - 64 q^{50} + 80 q^{51} - 32 q^{53} + 96 q^{57} - 16 q^{58}+ \cdots - 40 q^{95}+O(q^{100}) $ 32 * q + 16 * q^11 - 48 * q^15 + 16 * q^16 + 16 * q^18 + 32 * q^22 - 16 * q^23 - 32 * q^25 - 40 * q^30 - 96 * q^36 + 48 * q^37 + 32 * q^43 + 16 * q^46 - 64 * q^50 + 80 * q^51 - 32 * q^53 + 96 * q^57 - 16 * q^58 - 40 * q^60 - 32 * q^65 - 16 * q^67 + 32 * q^71 + 16 * q^72 + 112 * q^81 + 48 * q^85 - 48 * q^86 + 16 * q^88 + 32 * q^92 - 64 * q^93 - 40 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/490\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$3$	0.550608	−	2.05490i	0.317893	−	1.18639i	−0.603372	−	0.797460i	$-0.706177\pi$
$3$	0.550608	−	2.05490i	0.317893	−	1.18639i	0.921265	−	0.388934i	$-0.127157\pi$
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	1.20905	+	1.88101i	0.540702	+	0.841214i
$5$	1.20905	+	1.88101i	0.540702	+	0.841214i
$6$			2.12738i			0.868501i
$7$		0			0
$7$		0			0
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−1.32135	−	0.762882i	−0.440450	−	0.254294i
$10$	−1.65469	−	1.50399i	−0.523259	−	0.475604i
$11$	0.814115	+	1.41009i	0.245465	+	0.425158i	0.962262	−	0.272124i	$-0.0877261\pi$
$11$	0.814115	+	1.41009i	0.245465	+	0.425158i	−0.716797	+	0.697282i	$0.754393\pi$
$12$	−0.550608	−	2.05490i	−0.158947	−	0.593197i
$13$	4.65861	+	4.65861i	1.29207	+	1.29207i	0.933507	+	0.358559i	$0.116732\pi$
$13$	4.65861	+	4.65861i	1.29207	+	1.29207i	0.358559	+	0.933507i	$0.383268\pi$
$14$		0			0
$15$	4.53099	−	1.44877i	1.16990	−	0.374070i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	2.59984	+	0.696624i	0.630553	+	0.168956i	0.559921	−	0.828546i	$-0.310832\pi$
$17$	2.59984	+	0.696624i	0.630553	+	0.168956i	0.0706325	+	0.997502i	$0.477498\pi$
$18$	1.47377	+	0.394897i	0.347372	+	0.0930780i
$19$	−2.14608	+	3.71713i	−0.492345	+	0.852767i	−0.999961	−	0.00881622i	$-0.997194\pi$
$19$	−2.14608	+	3.71713i	−0.492345	+	0.852767i	0.507616	+	0.861584i	$0.330527\pi$
$20$	1.98757	+	1.02448i	0.444435	+	0.229081i
$21$		0			0
$22$	−1.15133	−	1.15133i	−0.245465	−	0.245465i
$23$	−1.91659	−	7.15281i	−0.399636	−	1.49146i	−0.813738	−	0.581232i	$-0.802571\pi$
$23$	−1.91659	−	7.15281i	−0.399636	−	1.49146i	0.414101	−	0.910231i	$-0.364096\pi$
$24$	1.06369	+	1.84237i	0.217125	+	0.376072i
$25$	−2.07641	+	4.54846i	−0.415282	+	0.909693i
$26$	−5.70561	−	3.29413i	−1.11896	−	0.646033i
$27$	2.21768	−	2.21768i	0.426792	−	0.426792i
$28$		0			0
$29$		−	3.26022i		−	0.605408i	−0.953085	−	0.302704i	$-0.902111\pi$
$29$		−	3.26022i		−	0.605408i	0.953085	−	0.302704i	$-0.0978893\pi$
$30$	−4.00163	+	2.57211i	−0.730595	+	0.469601i
$31$	−7.13157	+	4.11741i	−1.28087	+	0.739509i	−0.977007	−	0.213207i	$-0.931609\pi$
$31$	−7.13157	+	4.11741i	−1.28087	+	0.739509i	−0.303861	+	0.952716i	$0.598276\pi$
$32$	−0.258819	+	0.965926i	−0.0457532	+	0.170753i
$33$	3.34584	−	0.896515i	0.582436	−	0.156063i
$34$	−2.69155			−0.461597
$35$		0			0
$36$	−1.52576			−0.254294
$37$	10.8338	−	2.90291i	1.78107	−	0.477235i	0.790289	−	0.612735i	$-0.209931\pi$
$37$	10.8338	−	2.90291i	1.78107	−	0.477235i	0.990777	+	0.135500i	$0.0432639\pi$
$38$	1.11089	−	4.14592i	0.180211	−	0.672556i
$39$	12.1380	−	7.00789i	1.94364	−	1.12216i
$40$	−2.18500	−	0.475150i	−0.345479	−	0.0751279i
$41$		−	3.04106i		−	0.474934i	−0.971396	−	0.237467i	$-0.923683\pi$
$41$		−	3.04106i		−	0.474934i	0.971396	−	0.237467i	$-0.0763171\pi$
$42$		0			0
$43$	1.67710	−	1.67710i	0.255755	−	0.255755i	−0.567570	−	0.823325i	$-0.692116\pi$
$43$	1.67710	−	1.67710i	0.255755	−	0.255755i	0.823325	+	0.567570i	$0.192116\pi$
$44$	1.41009	+	0.814115i	0.212579	+	0.122732i
$45$	−0.162586	−	3.40783i	−0.0242368	−	0.508010i
$46$	3.70257	+	6.41303i	0.545913	+	0.945550i
$47$	−1.82248	−	6.80159i	−0.265836	−	0.992114i	−0.961737	−	0.273976i	$-0.911661\pi$
$47$	−1.82248	−	6.80159i	−0.265836	−	0.992114i	0.695900	−	0.718138i	$-0.255006\pi$
$48$	−1.50429	−	1.50429i	−0.217125	−	0.217125i
$49$		0			0
$50$	0.828427	−	4.93089i	0.117157	−	0.697334i
$51$	2.86298	−	4.95883i	0.400897	−	0.694375i
$52$	6.36378	+	1.70517i	0.882497	+	0.236464i
$53$	−5.67082	−	1.51949i	−0.778948	−	0.208718i	−0.152627	−	0.988284i	$-0.548773\pi$
$53$	−5.67082	−	1.51949i	−0.778948	−	0.208718i	−0.626321	+	0.779565i	$0.715440\pi$
$54$	−1.56813	+	2.71609i	−0.213396	+	0.369613i
$55$	−1.66809	+	3.23622i	−0.224925	+	0.436372i
$56$		0			0
$57$	6.45666	+	6.45666i	0.855205	+	0.855205i
$58$	0.843807	+	3.14913i	0.110797	+	0.413501i
$59$	3.01632	+	5.22442i	0.392692	+	0.680162i	0.992804	−	0.119754i	$-0.0382107\pi$
$59$	3.01632	+	5.22442i	0.392692	+	0.680162i	−0.600112	+	0.799916i	$0.704877\pi$
$60$	3.19957	−	3.52017i	0.413063	−	0.454451i
$61$	6.78484	+	3.91723i	0.868710	+	0.501550i	0.866919	−	0.498448i	$-0.166097\pi$
$61$	6.78484	+	3.91723i	0.868710	+	0.501550i	0.00179074	+	0.999998i	$0.499430\pi$
$62$	5.82290	−	5.82290i	0.739509	−	0.739509i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	−3.13042	+	14.3954i	−0.388281	+	1.78553i
$66$	−2.99980	+	1.73193i	−0.369250	+	0.213186i
$67$	1.63125	−	6.08791i	0.199289	−	0.743756i	−0.791826	−	0.610747i	$-0.790869\pi$
$67$	1.63125	−	6.08791i	0.199289	−	0.743756i	0.991115	−	0.133009i	$-0.0424640\pi$
$68$	2.59984	−	0.696624i	0.315277	−	0.0844781i
$69$	−15.7536			−1.89651
$70$		0			0
$71$	−6.85705			−0.813782			−0.406891	−	0.913477i	$-0.633387\pi$
$71$	−6.85705			−0.813782			−0.406891	+	0.913477i	$0.633387\pi$
$72$	1.47377	−	0.394897i	0.173686	−	0.0465390i
$73$	−0.656029	+	2.44833i	−0.0767824	+	0.286556i	−0.993632	−	0.112678i	$-0.964057\pi$
$73$	−0.656029	+	2.44833i	−0.0767824	+	0.286556i	0.916849	+	0.399234i	$0.130724\pi$
$74$	−9.71332	+	5.60799i	−1.12915	+	0.651915i
$75$	8.20333	+	6.77122i	0.947239	+	0.781873i
$76$			4.29217i			0.492345i
$77$		0			0
$78$	−9.91065	+	9.91065i	−1.12216	+	1.12216i
$79$	−8.52689	−	4.92300i	−0.959350	−	0.553881i	−0.0633773	−	0.997990i	$-0.520187\pi$
$79$	−8.52689	−	4.92300i	−0.959350	−	0.553881i	−0.895973	+	0.444108i	$0.853520\pi$
$80$	2.23353	−	0.106560i	0.249716	−	0.0119138i
$81$	−5.62467	−	9.74221i	−0.624963	−	1.08247i
$82$	0.787084	+	2.93744i	0.0869189	+	0.324386i
$83$	4.51286	+	4.51286i	0.495351	+	0.495351i	0.909987	−	0.414636i	$-0.136091\pi$
$83$	4.51286	+	4.51286i	0.495351	+	0.495351i	−0.414636	+	0.909987i	$0.636091\pi$
$84$		0			0
$85$	1.83297	+	5.73258i	0.198813	+	0.621785i
$86$	−1.18589	+	2.05401i	−0.127877	+	0.221490i
$87$	−6.69941	−	1.79510i	−0.718252	−	0.192455i
$88$	−1.57275	−	0.421417i	−0.167656	−	0.0449232i
$89$	1.42768	−	2.47281i	0.151333	−	0.262117i	−0.780385	−	0.625300i	$-0.784977\pi$
$89$	1.42768	−	2.47281i	0.151333	−	0.262117i	0.931718	+	0.363183i	$0.118310\pi$
$90$	1.03906	+	3.24963i	0.109526	+	0.342542i
$91$		0			0
$92$	−5.23622	−	5.23622i	−0.545913	−	0.545913i
$93$	4.53416	+	16.9217i	0.470170	+	1.75470i
$94$	3.52076	+	6.09814i	0.363139	+	0.628975i
$95$	−9.58668	+	0.457374i	−0.983572	+	0.0469256i
$96$	1.84237	+	1.06369i	0.188036	+	0.108563i
$97$	2.26618	−	2.26618i	0.230096	−	0.230096i	−0.582637	−	0.812733i	$-0.697979\pi$
$97$	2.26618	−	2.26618i	0.230096	−	0.230096i	0.812733	+	0.582637i	$0.197979\pi$
$98$		0			0
$99$		−	2.48429i		−	0.249681i
$100$	0.476010	+	4.97729i	0.0476010	+	0.497729i
$101$	1.13976	−	0.658039i	0.113410	−	0.0654773i	−0.442222	−	0.896906i	$-0.645810\pi$
$101$	1.13976	−	0.658039i	0.113410	−	0.0654773i	0.555632	+	0.831428i	$0.312476\pi$
$102$	−1.48199	+	5.53085i	−0.146739	+	0.547636i
$103$	−6.58950	+	1.76565i	−0.649283	+	0.173975i	−0.568405	−	0.822749i	$-0.692439\pi$
$103$	−6.58950	+	1.76565i	−0.649283	+	0.173975i	−0.0808783	+	0.996724i	$0.525773\pi$
$104$	−6.58827			−0.646033
$105$		0			0
$106$	5.87087			0.570229
$107$	−5.66719	+	1.51852i	−0.547868	+	0.146801i	−0.522127	−	0.852868i	$-0.674861\pi$
$107$	−5.66719	+	1.51852i	−0.547868	+	0.146801i	−0.0257412	+	0.999669i	$0.508195\pi$
$108$	0.811726	−	3.02940i	0.0781084	−	0.291504i
$109$	−9.89866	+	5.71500i	−0.948120	+	0.547397i	−0.892496	−	0.451054i	$-0.851048\pi$
$109$	−9.89866	+	5.71500i	−0.948120	+	0.547397i	−0.0556236	+	0.998452i	$0.517715\pi$
$110$	0.773654	−	3.55768i	0.0737650	−	0.339212i
$111$		−	23.8607i		−	2.26476i
$112$		0			0
$113$	−3.06911	+	3.06911i	−0.288717	+	0.288717i	−0.836573	−	0.547856i	$-0.815444\pi$
$113$	−3.06911	+	3.06911i	−0.288717	+	0.288717i	0.547856	+	0.836573i	$0.315444\pi$
$114$	−7.90776	−	4.56555i	−0.740629	−	0.427603i
$115$	11.1373	−	12.2532i	1.03856	−	1.14262i
$116$	−1.63011	−	2.82343i	−0.151352	−	0.262149i
$117$	−2.60168	−	9.70962i	−0.240526	−	0.897655i
$118$	−4.26572	−	4.26572i	−0.392692	−	0.392692i
$119$		0			0
$120$	−2.17946	+	4.22833i	−0.198957	+	0.385992i
$121$	4.17443	−	7.23033i	0.379494	−	0.657303i
$122$	−7.56751	−	2.02771i	−0.685130	−	0.183580i
$123$	−6.24906	−	1.67443i	−0.563459	−	0.150978i
$124$	−4.11741	+	7.13157i	−0.369755	+	0.640434i
$125$	−11.0662	+	1.59356i	−0.989790	+	0.142533i
$126$		0			0
$127$	2.16891	+	2.16891i	0.192460	+	0.192460i	0.796758	−	0.604298i	$-0.206546\pi$
$127$	2.16891	+	2.16891i	0.192460	+	0.192460i	−0.604298	+	0.796758i	$0.706546\pi$
$128$	0.258819	+	0.965926i	0.0228766	+	0.0853766i
$129$	−2.52283	−	4.36968i	−0.222123	−	0.384729i
$130$	−0.702047	−	14.7151i	−0.0615736	−	1.29060i
$131$	−5.98618	−	3.45612i	−0.523015	−	0.301963i	0.215152	−	0.976581i	$-0.430975\pi$
$131$	−5.98618	−	3.45612i	−0.523015	−	0.301963i	−0.738167	+	0.674618i	$0.764309\pi$
$132$	2.44933	−	2.44933i	0.213186	−	0.213186i
$133$		0			0
$134$			6.30266i			0.544467i
$135$	6.85275	+	1.49020i	0.589791	+	0.128256i
$136$	−2.33095	+	1.34578i	−0.199877	+	0.115399i
$137$	−1.52047	+	5.67446i	−0.129902	+	0.484802i	−0.999967	−	0.00813584i	$-0.997410\pi$
$137$	−1.52047	+	5.67446i	−0.129902	+	0.484802i	0.870065	+	0.492938i	$0.164077\pi$
$138$	15.2168	−	4.07732i	1.29534	−	0.347085i
$139$	0.531682			0.0450966			0.0225483	−	0.999746i	$-0.492822\pi$
$139$	0.531682			0.0450966			0.0225483	+	0.999746i	$0.492822\pi$
$140$		0			0
$141$	−14.9800			−1.26155
$142$	6.62340	−	1.77474i	0.555824	−	0.148933i
$143$	−2.77641	+	10.3617i	−0.232175	+	0.866488i
$144$	−1.32135	+	0.762882i	−0.110112	+	0.0635735i
$145$	6.13251	−	3.94176i	0.509278	−	0.327346i
$146$		−	2.53470i		−	0.209773i
$147$		0			0
$148$	7.93089	−	7.93089i	0.651915	−	0.651915i
$149$	−17.9071	−	10.3387i	−1.46701	−	0.846978i	−0.467690	−	0.883892i	$-0.654914\pi$
$149$	−17.9071	−	10.3387i	−1.46701	−	0.846978i	−0.999318	+	0.0369143i	$0.988247\pi$
$150$	−9.67633	−	4.41732i	−0.790069	−	0.360672i
$151$	9.13109	+	15.8155i	0.743078	+	1.28705i	0.951088	+	0.308922i	$0.0999680\pi$
$151$	9.13109	+	15.8155i	0.743078	+	1.28705i	−0.208010	+	0.978127i	$0.566699\pi$
$152$	−1.11089	−	4.14592i	−0.0901055	−	0.336278i
$153$	−2.90385	−	2.90385i	−0.234763	−	0.234763i
$154$		0			0
$155$	−16.3673	−	8.43642i	−1.31465	−	0.677629i
$156$	7.00789	−	12.1380i	0.561080	−	0.971819i
$157$	−15.2120	−	4.07605i	−1.21405	−	0.325304i	−0.405701	−	0.914006i	$-0.632973\pi$
$157$	−15.2120	−	4.07605i	−1.21405	−	0.325304i	−0.808350	+	0.588702i	$0.799639\pi$
$158$	9.51051	+	2.54833i	0.756616	+	0.202735i
$159$	−6.24480	+	10.8163i	−0.495245	+	0.857789i
$160$	−2.12984	+	0.681009i	−0.168379	+	0.0538385i
$161$		0			0
$162$	7.95448	+	7.95448i	0.624963	+	0.624963i
$163$	1.20983	+	4.51516i	0.0947614	+	0.353654i	0.996983	−	0.0776180i	$-0.0247315\pi$
$163$	1.20983	+	4.51516i	0.0947614	+	0.353654i	−0.902222	+	0.431272i	$0.858065\pi$
$164$	−1.52053	−	2.63364i	−0.118733	−	0.205652i
$165$	5.73164	+	5.20964i	0.446207	+	0.405570i
$166$	−5.52711	−	3.19108i	−0.428987	−	0.247676i
$167$	4.25477	−	4.25477i	0.329244	−	0.329244i	−0.523055	−	0.852299i	$-0.675208\pi$
$167$	4.25477	−	4.25477i	0.329244	−	0.329244i	0.852299	+	0.523055i	$0.175208\pi$
$168$		0			0
$169$			30.4053i			2.33887i
$170$	−3.25421	−	5.06284i	−0.249587	−	0.388302i
$171$	5.67146	−	3.27442i	0.433707	−	0.250401i
$172$	0.613859	−	2.29095i	0.0468063	−	0.174684i
$173$	−1.49004	+	0.399255i	−0.113286	+	0.0303548i	−0.315016	−	0.949086i	$-0.602010\pi$
$173$	−1.49004	+	0.399255i	−0.113286	+	0.0303548i	0.201731	+	0.979441i	$0.435343\pi$
$174$	6.93574			0.525797
$175$		0			0
$176$	1.62823			0.122732
$177$	12.3964	−	3.32162i	0.931774	−	0.249668i
$178$	−0.739019	+	2.75806i	−0.0553918	+	0.206725i
$179$	9.56629	−	5.52310i	0.715018	−	0.412816i	−0.0978980	−	0.995196i	$-0.531212\pi$
$179$	9.56629	−	5.52310i	0.715018	−	0.412816i	0.812916	+	0.582380i	$0.197879\pi$
$180$	−1.84472	−	2.86998i	−0.137497	−	0.213916i
$181$		−	0.221608i		−	0.0164720i	−0.999966	−	0.00823601i	$-0.997378\pi$
$181$		−	0.221608i		−	0.0164720i	0.999966	−	0.00823601i	$-0.00262163\pi$
$182$		0			0
$183$	11.7853	−	11.7853i	0.871193	−	0.871193i
$184$	6.41303	+	3.70257i	0.472775	+	0.272957i
$185$	18.5590	+	16.8688i	1.36448	+	1.24022i
$186$	−8.75932	−	15.1716i	−0.642265	−	1.11243i
$187$	1.13426	+	4.23313i	0.0829456	+	0.309557i
$188$	−4.97911	−	4.97911i	−0.363139	−	0.363139i
$189$		0			0
$190$	9.14164	−	2.92300i	0.663204	−	0.212057i
$191$	−3.75143	+	6.49767i	−0.271444	+	0.470155i	−0.969232	−	0.246150i	$-0.920835\pi$
$191$	−3.75143	+	6.49767i	−0.271444	+	0.470155i	0.697788	+	0.716305i	$0.254168\pi$
$192$	−2.05490	−	0.550608i	−0.148299	−	0.0397367i
$193$	−7.58744	−	2.03305i	−0.546156	−	0.146342i	−0.0248172	−	0.999692i	$-0.507900\pi$
$193$	−7.58744	−	2.03305i	−0.546156	−	0.146342i	−0.521338	+	0.853350i	$0.674567\pi$
$194$	−1.60243	+	2.77549i	−0.115048	+	0.199269i
$195$	27.8574	+	14.3589i	1.99491	+	1.02826i
$196$		0			0
$197$	−14.8820	−	14.8820i	−1.06030	−	1.06030i	−0.998061	−	0.0622393i	$-0.980176\pi$
$197$	−14.8820	−	14.8820i	−1.06030	−	1.06030i	−0.0622393	−	0.998061i	$-0.519824\pi$
$198$	0.642982	+	2.39964i	0.0456948	+	0.170535i
$199$	−0.421896	−	0.730744i	−0.0299074	−	0.0518011i	0.850684	−	0.525677i	$-0.176188\pi$
$199$	−0.421896	−	0.730744i	−0.0299074	−	0.0518011i	−0.880592	+	0.473876i	$0.842855\pi$
$200$	−1.74801	−	4.68449i	−0.123603	−	0.331244i
$201$	−11.6118	−	6.70409i	−0.819035	−	0.472870i
$202$	−0.930607	+	0.930607i	−0.0654773	+	0.0654773i
$203$		0			0
$204$		−	5.72596i		−	0.400897i
$205$	5.72027	−	3.67679i	0.399521	−	0.256798i
$206$	5.90799	−	3.41098i	0.411629	−	0.237654i
$207$	−2.92426	+	10.9135i	−0.203250	+	0.758540i
$208$	6.36378	−	1.70517i	0.441249	−	0.118232i
$209$	−6.98863			−0.483414
$210$		0			0
$211$	7.11825			0.490040			0.245020	−	0.969518i	$-0.421205\pi$
$211$	7.11825			0.490040			0.245020	+	0.969518i	$0.421205\pi$
$212$	−5.67082	+	1.51949i	−0.389474	+	0.104359i
$213$	−3.77554	+	14.0905i	−0.258696	+	0.965467i
$214$	5.08106	−	2.93355i	0.347334	−	0.200534i
$215$	5.18232	+	1.12695i	0.353431	+	0.0768572i
$216$			3.13627i			0.213396i
$217$		0			0
$218$	8.08223	−	8.08223i	0.547397	−	0.547397i
$219$	4.66986	+	2.69614i	0.315560	+	0.182188i
$220$	0.173504	+	3.63669i	0.0116977	+	0.245186i
$221$	8.86633	+	15.3569i	0.596414	+	1.03302i
$222$	6.17560	+	23.0477i	0.414479	+	1.54686i
$223$	16.8996	+	16.8996i	1.13168	+	1.13168i	0.989897	+	0.141785i	$0.0452842\pi$
$223$	16.8996	+	16.8996i	1.13168	+	1.13168i	0.141785	+	0.989897i	$0.454716\pi$
$224$		0			0
$225$	6.21360	−	4.42606i	0.414240	−	0.295071i
$226$	2.17019	−	3.75887i	0.144359	−	0.250036i
$227$	−3.15645	−	0.845767i	−0.209501	−	0.0561355i	0.152542	−	0.988297i	$-0.451254\pi$
$227$	−3.15645	−	0.845767i	−0.209501	−	0.0561355i	−0.362043	+	0.932161i	$0.617921\pi$
$228$	8.81996	+	2.36330i	0.584116	+	0.156513i
$229$	−4.03653	+	6.99148i	−0.266742	+	0.462010i	−0.968018	−	0.250879i	$-0.919280\pi$
$229$	−4.03653	+	6.99148i	−0.266742	+	0.462010i	0.701277	+	0.712889i	$0.252614\pi$
$230$	−7.58641	+	14.7182i	−0.500233	+	0.970491i
$231$		0			0
$232$	2.30532	+	2.30532i	0.151352	+	0.151352i
$233$	2.59968	+	9.70215i	0.170311	+	0.635609i	0.997303	+	0.0733953i	$0.0233835\pi$
$233$	2.59968	+	9.70215i	0.170311	+	0.635609i	−0.826992	+	0.562214i	$0.809950\pi$
$234$	5.02607	+	8.70541i	0.328564	+	0.569090i
$235$	10.5904	−	11.6516i	0.690842	−	0.760064i
$236$	5.22442	+	3.01632i	0.340081	+	0.196346i
$237$	−14.8112	+	14.8112i	−0.962093	+	0.962093i
$238$		0			0
$239$		−	23.8618i		−	1.54349i	−0.635932	−	0.771745i	$-0.719384\pi$
$239$		−	23.8618i		−	1.54349i	0.635932	−	0.771745i	$-0.280616\pi$
$240$	1.01083	−	4.64834i	0.0652486	−	0.300049i
$241$	19.3604	−	11.1777i	1.24711	−	0.720022i	0.276581	−	0.960990i	$-0.410798\pi$
$241$	19.3604	−	11.1777i	1.24711	−	0.720022i	0.970533	+	0.240969i	$0.0774651\pi$
$242$	−2.16085	+	8.06439i	−0.138904	+	0.518399i
$243$	−14.0280	+	3.75879i	−0.899897	+	0.241127i
$244$	7.83446			0.501550
$245$		0			0
$246$	6.46950			0.412480
$247$	−27.3144	+	7.31887i	−1.73797	+	0.465689i
$248$	2.13133	−	7.95423i	0.135340	−	0.505094i
$249$	11.7583	−	6.78864i	0.745151	−	0.430213i
$250$	10.2767	−	4.40340i	0.649954	−	0.278496i
$251$			27.2733i			1.72147i	0.509051	+	0.860736i	$0.329996\pi$
$251$			27.2733i			1.72147i	−0.509051	+	0.860736i	$0.670004\pi$
$252$		0			0
$253$	8.52576	−	8.52576i	0.536010	−	0.536010i
$254$	−2.65636	−	1.53365i	−0.166675	−	0.0962299i
$255$	12.7891	−	0.610159i	0.800884	−	0.0382096i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−8.14501	−	30.3976i	−0.508072	−	1.89615i	−0.438876	−	0.898548i	$-0.644623\pi$
$257$	−8.14501	−	30.3976i	−0.508072	−	1.89615i	−0.0691962	−	0.997603i	$-0.522043\pi$
$258$	3.56783	+	3.56783i	0.222123	+	0.222123i
$259$		0			0
$260$	4.48667	+	14.0320i	0.278251	+	0.870226i
$261$	−2.48716	+	4.30789i	−0.153952	+	0.266652i
$262$	6.67672	+	1.78902i	0.412489	+	0.110526i
$263$	23.8613	+	6.39362i	1.47135	+	0.394248i	0.903395	−	0.428810i	$-0.141067\pi$
$263$	23.8613	+	6.39362i	1.47135	+	0.394248i	0.567958	+	0.823058i	$0.307734\pi$
$264$	−1.73193	+	2.99980i	−0.106593	+	0.184625i
$265$	−3.99811	−	12.5040i	−0.245602	−	0.768116i
$266$		0			0
$267$	−4.29527	−	4.29527i	−0.262866	−	0.262866i
$268$	−1.63125	−	6.08791i	−0.0996444	−	0.371878i
$269$	−8.65918	−	14.9981i	−0.527960	−	0.914453i	−0.999469	−	0.0325916i	$-0.989624\pi$
$269$	−8.65918	−	14.9981i	−0.527960	−	0.914453i	0.471509	−	0.881861i	$-0.343709\pi$
$270$	−7.00494	+	0.334201i	−0.426307	+	0.0203388i
$271$	−0.574354	−	0.331603i	−0.0348895	−	0.0201435i	0.482454	−	0.875921i	$-0.339746\pi$
$271$	−0.574354	−	0.331603i	−0.0348895	−	0.0201435i	−0.517343	+	0.855778i	$0.673079\pi$
$272$	1.90321	−	1.90321i	0.115399	−	0.115399i
$273$		0			0
$274$		−	5.87463i		−	0.354900i
$275$	−8.10417	+	0.775053i	−0.488700	+	0.0467375i
$276$	−13.6430	+	7.87678i	−0.821211	+	0.474126i
$277$	3.08968	−	11.5308i	0.185641	−	0.692820i	−0.808852	−	0.588012i	$-0.799911\pi$
$277$	3.08968	−	11.5308i	0.185641	−	0.692820i	0.994493	−	0.104808i	$-0.0334227\pi$
$278$	−0.513565	+	0.137609i	−0.0308016	+	0.00825326i
$279$	12.5644			0.752211
$280$		0			0
$281$	18.7374			1.11778			0.558890	−	0.829242i	$-0.311228\pi$
$281$	18.7374			1.11778			0.558890	+	0.829242i	$0.311228\pi$
$282$	14.4696	−	3.87712i	0.861652	−	0.230879i
$283$	5.78655	−	21.5957i	0.343975	−	1.28373i	−0.549830	−	0.835276i	$-0.685308\pi$
$283$	5.78655	−	21.5957i	0.343975	−	1.28373i	0.893805	−	0.448455i	$-0.148026\pi$
$284$	−5.93838	+	3.42853i	−0.352378	+	0.203446i
$285$	−4.33864	+	19.9514i	−0.256999	+	1.18182i
$286$		−	10.7272i		−	0.634313i
$287$		0			0
$288$	1.07888	−	1.07888i	0.0635735	−	0.0635735i
$289$	−8.44856	−	4.87778i	−0.496974	−	0.286928i
$290$	−4.90335	+	5.39466i	−0.287935	+	0.316785i
$291$	−3.40898	−	5.90453i	−0.199838	−	0.346130i
$292$	0.656029	+	2.44833i	0.0383912	+	0.143278i
$293$	−10.6128	−	10.6128i	−0.620008	−	0.620008i	0.325525	−	0.945533i	$-0.394459\pi$
$293$	−10.6128	−	10.6128i	−0.620008	−	0.620008i	−0.945533	+	0.325525i	$0.894459\pi$
$294$		0			0
$295$	−6.18032	+	11.9903i	−0.359832	+	0.698103i
$296$	−5.60799	+	9.71332i	−0.325958	+	0.564575i
$297$	4.93256	+	1.32168i	0.286216	+	0.0766914i
$298$	19.9728	+	5.35170i	1.15699	+	0.310015i
$299$	24.3935	−	42.2508i	1.41071	−	2.44343i
$300$	10.4899	+	1.76238i	0.605635	+	0.101751i
$301$		0			0
$302$	−12.9133	−	12.9133i	−0.743078	−	0.743078i
$303$	−0.724642	−	2.70440i	−0.0416296	−	0.155364i
$304$	2.14608	+	3.71713i	0.123086	+	0.213192i
$305$	0.834841	+	17.4985i	0.0478029	+	1.00196i
$306$	3.55648	+	2.05333i	0.203310	+	0.117381i
$307$	−3.24317	+	3.24317i	−0.185098	+	0.185098i	−0.793573	−	0.608475i	$-0.791782\pi$
$307$	−3.24317	+	3.24317i	−0.185098	+	0.185098i	0.608475	+	0.793573i	$0.291782\pi$
$308$		0			0
$309$			14.5129i			0.825611i
$310$	17.9931	+	3.91278i	1.02194	+	0.222231i
$311$	−11.7581	+	6.78856i	−0.666742	+	0.384944i	−0.794841	−	0.606818i	$-0.792446\pi$
$311$	−11.7581	+	6.78856i	−0.666742	+	0.384944i	0.128099	+	0.991761i	$0.459112\pi$
$312$	−3.62755	+	13.5382i	−0.205370	+	0.766450i
$313$	−13.3879	+	3.58727i	−0.756728	+	0.202765i	−0.616500	−	0.787355i	$-0.711450\pi$
$313$	−13.3879	+	3.58727i	−0.756728	+	0.202765i	−0.140227	+	0.990119i	$0.544783\pi$
$314$	15.7486			0.888747
$315$		0			0
$316$	−9.84601			−0.553881
$317$	17.2619	−	4.62532i	0.969527	−	0.259784i	0.260899	−	0.965366i	$-0.415981\pi$
$317$	17.2619	−	4.62532i	0.969527	−	0.259784i	0.708628	+	0.705582i	$0.249314\pi$
$318$	3.23255	−	12.0640i	0.181272	−	0.676517i
$319$	4.59720	−	2.65419i	0.257394	−	0.148606i
$320$	1.88101	−	1.20905i	0.105152	−	0.0675878i
$321$			12.4816i			0.696654i
$322$		0			0
$323$	−8.16891	+	8.16891i	−0.454530	+	0.454530i
$324$	−9.74221	−	5.62467i	−0.541234	−	0.312482i
$325$	−30.8627	+	11.5163i	−1.71195	+	0.638812i
$326$	−2.33722	−	4.04818i	−0.129446	−	0.224208i
$327$	6.29344	+	23.4874i	0.348028	+	1.29886i
$328$	2.15035	+	2.15035i	0.118733	+	0.118733i
$329$		0			0
$330$	−6.88469	−	3.54866i	−0.378990	−	0.195348i
$331$	10.3530	−	17.9319i	0.569052	−	0.985627i	−0.427608	−	0.903964i	$-0.640644\pi$
$331$	10.3530	−	17.9319i	0.569052	−	0.985627i	0.996660	−	0.0816629i	$-0.0260231\pi$
$332$	6.16469	+	1.65182i	0.338331	+	0.0906555i
$333$	−16.5298	−	4.42915i	−0.905828	−	0.242716i
$334$	−3.00858	+	5.21101i	−0.164622	+	0.285134i
$335$	13.4237	−	4.29217i	0.733414	−	0.234506i
$336$		0			0
$337$	−3.68449	−	3.68449i	−0.200707	−	0.200707i	0.599596	−	0.800303i	$-0.295328\pi$
$337$	−3.68449	−	3.68449i	−0.200707	−	0.200707i	−0.800303	+	0.599596i	$0.795328\pi$
$338$	−7.86947	−	29.3693i	−0.428043	−	1.59748i
$339$	4.61682	+	7.99657i	0.250751	+	0.434314i
$340$	4.45369	+	4.04807i	0.241535	+	0.219538i
$341$	−11.6118	−	6.70409i	−0.628816	−	0.363047i
$342$	−4.63072	+	4.63072i	−0.250401	+	0.250401i
$343$		0			0
$344$			2.37177i			0.127877i
$345$	−19.0468	−	29.6326i	−1.02545	−	1.59537i
$346$	1.33593	−	0.771301i	0.0718202	−	0.0414654i
$347$	6.11175	−	22.8094i	0.328096	−	1.22447i	−0.583067	−	0.812424i	$-0.698147\pi$
$347$	6.11175	−	22.8094i	0.328096	−	1.22447i	0.911163	−	0.412046i	$-0.135186\pi$
$348$	−6.69941	+	1.79510i	−0.359126	+	0.0962276i
$349$	−6.19099			−0.331396			−0.165698	−	0.986177i	$-0.552988\pi$
$349$	−6.19099			−0.331396			−0.165698	+	0.986177i	$0.552988\pi$
$350$		0			0
$351$	20.6626			1.10289
$352$	−1.57275	+	0.421417i	−0.0838278	+	0.0224616i
$353$	0.208182	−	0.776947i	0.0110804	−	0.0413527i	−0.960164	−	0.279436i	$-0.909852\pi$
$353$	0.208182	−	0.776947i	0.0110804	−	0.0413527i	0.971245	+	0.238083i	$0.0765192\pi$
$354$	−11.1144	+	6.41687i	−0.590721	+	0.341053i
$355$	−8.29050	−	12.8982i	−0.440014	−	0.684565i
$356$		−	2.85535i		−	0.151333i
$357$		0			0
$358$	−7.81085	+	7.81085i	−0.412816	+	0.412816i
$359$	30.6450	+	17.6929i	1.61738	+	0.933794i	0.987595	+	0.157024i	$0.0501900\pi$
$359$	30.6450	+	17.6929i	1.61738	+	0.933794i	0.629784	+	0.776770i	$0.283143\pi$
$360$	2.52467	+	2.29474i	0.133062	+	0.120943i
$361$	0.288645	+	0.499947i	0.0151918	+	0.0263130i
$362$	0.0573565	+	0.214057i	0.00301459	+	0.0112506i
$363$	−12.5591	−	12.5591i	−0.659182	−	0.659182i
$364$		0			0
$365$	−5.39851	+	1.72615i	−0.282571	+	0.0903510i
$366$	−8.33345	+	14.4340i	−0.435597	+	0.754476i
$367$	−31.8892	−	8.54468i	−1.66460	−	0.446029i	−0.700954	−	0.713206i	$-0.747242\pi$
$367$	−31.8892	−	8.54468i	−1.66460	−	0.446029i	−0.963647	+	0.267177i	$0.913909\pi$
$368$	−7.15281	−	1.91659i	−0.372866	−	0.0999091i
$369$	−2.31997	+	4.01830i	−0.120773	+	0.209185i
$370$	−22.2926	−	11.4905i	−1.15893	−	0.597365i
$371$		0			0
$372$	12.3875	+	12.3875i	0.642265	+	0.642265i
$373$	−2.67567	−	9.98573i	−0.138541	−	0.517041i	−0.999958	−	0.00914361i	$-0.997089\pi$
$373$	−2.67567	−	9.98573i	−0.138541	−	0.517041i	0.861417	−	0.507898i	$-0.169577\pi$
$374$	−2.19123	−	3.79532i	−0.113306	−	0.196251i
$375$	−2.81852	+	23.6173i	−0.145548	+	1.21959i
$376$	6.09814	+	3.52076i	0.314488	+	0.181570i
$377$	15.1881	−	15.1881i	0.782227	−	0.782227i
$378$		0			0
$379$		−	1.05446i		−	0.0541639i	−0.999633	−	0.0270820i	$-0.991378\pi$
$379$		−	1.05446i		−	0.0541639i	0.999633	−	0.0270820i	$-0.00862151\pi$
$380$	−8.07362	+	5.18944i	−0.414168	+	0.266212i
$381$	5.65111	−	3.26267i	0.289515	−	0.167152i
$382$	1.94188	−	7.24721i	0.0993554	−	0.370799i
$383$	−4.34521	+	1.16430i	−0.222030	+	0.0594927i	−0.368119	−	0.929779i	$-0.619998\pi$
$383$	−4.34521	+	1.16430i	−0.222030	+	0.0594927i	0.146089	+	0.989271i	$0.453331\pi$
$384$	2.12738			0.108563
$385$		0			0
$386$	7.85509			0.399814
$387$	−3.49545	+	0.936604i	−0.177684	+	0.0476103i
$388$	0.829479	−	3.09566i	0.0421104	−	0.157158i
$389$	−17.4551	+	10.0777i	−0.885007	+	0.510959i	−0.872306	−	0.488961i	$-0.837376\pi$
$389$	−17.4551	+	10.0777i	−0.885007	+	0.510959i	−0.0127007	+	0.999919i	$0.504043\pi$
$390$	−30.6245	−	6.65960i	−1.55073	−	0.337222i
$391$		−	19.9313i		−	1.00797i
$392$		0			0
$393$	−10.3980	+	10.3980i	−0.524510	+	0.524510i
$394$	18.2267	+	10.5232i	0.918247	+	0.530150i
$395$	−1.04919	−	21.9913i	−0.0527906	−	1.10650i
$396$	−1.24215	−	2.15146i	−0.0624202	−	0.108115i
$397$	6.00663	+	22.4170i	0.301464	+	1.12508i	0.935947	+	0.352142i	$0.114546\pi$
$397$	6.00663	+	22.4170i	0.301464	+	1.12508i	−0.634483	+	0.772937i	$0.718787\pi$
$398$	0.596650	+	0.596650i	0.0299074	+	0.0299074i
$399$		0			0
$400$	2.90088	+	4.07245i	0.145044	+	0.203623i
$401$	−5.86752	+	10.1628i	−0.293010	+	0.507508i	−0.974520	−	0.224301i	$-0.927990\pi$
$401$	−5.86752	+	10.1628i	−0.293010	+	0.507508i	0.681510	+	0.731809i	$0.261324\pi$
$402$	12.9513	+	3.47029i	0.645953	+	0.173083i
$403$	−52.4046	−	14.0418i	−2.61046	−	0.699471i
$404$	0.658039	−	1.13976i	0.0327386	−	0.0567050i
$405$	11.5247	−	22.3589i	0.572668	−	1.11102i
$406$		0			0
$407$	12.9133	+	12.9133i	0.640089	+	0.640089i
$408$	1.48199	+	5.53085i	0.0733693	+	0.273818i
$409$	5.51502	+	9.55229i	0.272700	+	0.472331i	0.969552	−	0.244884i	$-0.0787500\pi$
$409$	5.51502	+	9.55229i	0.272700	+	0.472331i	−0.696852	+	0.717215i	$0.745417\pi$
$410$	−4.57373	+	5.03202i	−0.225881	+	0.248514i
$411$	10.8232	+	6.24880i	0.533871	+	0.308231i
$412$	−4.82385	+	4.82385i	−0.237654	+	0.237654i
$413$		0			0
$414$		−	11.2985i		−	0.555290i
$415$	−3.03248	+	13.9450i	−0.148859	+	0.684534i
$416$	−5.70561	+	3.29413i	−0.279740	+	0.161508i
$417$	0.292748	−	1.09255i	0.0143359	−	0.0535024i
$418$	6.75050	−	1.80879i	0.330178	−	0.0884709i
$419$	−11.5026			−0.561940			−0.280970	−	0.959717i	$-0.590656\pi$
$419$	−11.5026			−0.561940			−0.280970	+	0.959717i	$0.590656\pi$
$420$		0			0
$421$	−16.0720			−0.783303			−0.391652	−	0.920114i	$-0.628096\pi$
$421$	−16.0720			−0.783303			−0.391652	+	0.920114i	$0.628096\pi$
$422$	−6.87570	+	1.84234i	−0.334704	+	0.0896836i
$423$	−2.78067	+	10.3776i	−0.135201	+	0.504577i
$424$	5.08432	−	2.93543i	0.246917	−	0.142557i
$425$	−8.56690	+	10.3788i	−0.415555	+	0.503445i
$426$		−	14.5876i		−	0.706771i
$427$		0			0
$428$	−4.14867	+	4.14867i	−0.200534	+	0.200534i
$429$	19.7635	+	11.4105i	0.954190	+	0.550902i
$430$	−5.29741	+	0.252736i	−0.255464	+	0.0121880i
$431$	−4.21778	−	7.30541i	−0.203163	−	0.351889i	0.746383	−	0.665517i	$-0.231789\pi$
$431$	−4.21778	−	7.30541i	−0.203163	−	0.351889i	−0.949546	+	0.313628i	$0.898456\pi$
$432$	−0.811726	−	3.02940i	−0.0390542	−	0.145752i
$433$	0.268074	+	0.268074i	0.0128828	+	0.0128828i	0.713519	−	0.700636i	$-0.247100\pi$
$433$	0.268074	+	0.268074i	0.0128828	+	0.0128828i	−0.700636	+	0.713519i	$0.747100\pi$
$434$		0			0
$435$	−4.72330	−	14.7720i	−0.226465	−	0.708265i
$436$	−5.71500	+	9.89866i	−0.273699	+	0.474060i
$437$	30.7011	+	8.22632i	1.46863	+	0.393518i
$438$	−5.20855	−	1.39563i	−0.248874	−	0.0666856i
$439$	12.8017	−	22.1732i	0.610992	−	1.05827i	−0.380082	−	0.924953i	$-0.624104\pi$
$439$	12.8017	−	22.1732i	0.610992	−	1.05827i	0.991074	−	0.133316i	$-0.0425626\pi$
$440$	−1.10884	−	3.46787i	−0.0528618	−	0.165324i
$441$		0			0
$442$	−12.5389	−	12.5389i	−0.596414	−	0.596414i
$443$	−7.75547	−	28.9438i	−0.368474	−	1.37516i	−0.862650	−	0.505801i	$-0.831197\pi$
$443$	−7.75547	−	28.9438i	−0.368474	−	1.37516i	0.494177	−	0.869361i	$-0.335470\pi$
$444$	−11.9303	−	20.6640i	−0.566189	−	0.980668i
$445$	6.37750	−	0.304267i	0.302323	−	0.0144236i
$446$	−20.6977	−	11.9498i	−0.980066	−	0.565841i
$447$	−31.1047	+	31.1047i	−1.47120	+	1.47120i
$448$		0			0
$449$		−	1.51864i		−	0.0716691i	−0.999358	−	0.0358345i	$-0.988591\pi$
$449$		−	1.51864i		−	0.0716691i	0.999358	−	0.0358345i	$-0.0114089\pi$
$450$	−4.85633	+	5.88344i	−0.228930	+	0.277348i
$451$	4.28816	−	2.47577i	0.201922	−	0.116580i
$452$	−1.12337	+	4.19248i	−0.0528389	+	0.197198i
$453$	37.5269	−	10.0553i	1.76317	−	0.472439i
$454$	3.26779			0.153365
$455$		0			0
$456$	−9.13109			−0.427603
$457$	−3.90527	+	1.04641i	−0.182681	+	0.0489491i	−0.349000	−	0.937123i	$-0.613479\pi$
$457$	−3.90527	+	1.04641i	−0.182681	+	0.0489491i	0.166319	+	0.986072i	$0.446812\pi$
$458$	2.08946	−	7.79798i	0.0976342	−	0.364376i
$459$	7.31049	−	4.22071i	0.341224	−	0.197006i
$460$	3.51855	−	16.1802i	0.164053	−	0.754407i
$461$			17.2603i			0.803894i	0.915663	+	0.401947i	$0.131666\pi$
$461$			17.2603i			0.803894i	−0.915663	+	0.401947i	$0.868334\pi$
$462$		0			0
$463$	−20.3757	+	20.3757i	−0.946939	+	0.946939i	−0.998661	−	0.0517227i	$-0.983529\pi$
$463$	−20.3757	+	20.3757i	−0.946939	+	0.946939i	0.0517227	+	0.998661i	$0.483529\pi$
$464$	−2.82343	−	1.63011i	−0.131075	−	0.0756760i
$465$	−26.3479	+	28.9880i	−1.22186	+	1.34428i
$466$	−5.02220	−	8.69871i	−0.232649	−	0.402960i
$467$	7.89410	+	29.4612i	0.365296	+	1.36330i	0.867020	+	0.498274i	$0.166033\pi$
$467$	7.89410	+	29.4612i	0.365296	+	1.36330i	−0.501724	+	0.865028i	$0.667301\pi$
$468$	−7.10794	−	7.10794i	−0.328564	−	0.328564i
$469$		0			0
$470$	−7.21390	+	13.9955i	−0.332753	+	0.645566i
$471$	−16.7517	+	29.0148i	−0.771878	+	1.33693i
$472$	−5.82709	−	1.56136i	−0.268213	−	0.0718675i
$473$	3.73020	+	0.999504i	0.171515	+	0.0459572i
$474$	10.4731	−	18.1400i	0.481046	−	0.833197i
$475$	−12.4511	−	17.4797i	−0.571294	−	0.802022i
$476$		0			0
$477$	6.33395	+	6.33395i	0.290012	+	0.290012i
$478$	6.17588	+	23.0487i	0.282478	+	1.05422i
$479$	−0.724343	−	1.25460i	−0.0330961	−	0.0573241i	0.849003	−	0.528388i	$-0.177203\pi$
$479$	−0.724343	−	1.25460i	−0.0330961	−	0.0573241i	−0.882099	+	0.471064i	$0.843870\pi$
$480$	0.226694	+	4.75157i	0.0103471	+	0.216879i
$481$	63.9940	+	36.9469i	2.91787	+	1.68464i
$482$	−15.8077	+	15.8077i	−0.720022	+	0.720022i
$483$		0			0
$484$		−	8.34887i		−	0.379494i
$485$	7.00263	+	1.52279i	0.317973	+	0.0691463i
$486$	12.5772	−	7.26143i	0.570512	−	0.329385i
$487$	4.49568	−	16.7781i	0.203719	−	0.760288i	−0.786118	−	0.618077i	$-0.787912\pi$
$487$	4.49568	−	16.7781i	0.203719	−	0.760288i	0.989836	−	0.142211i	$-0.0454213\pi$
$488$	−7.56751	+	2.02771i	−0.342565	+	0.0917900i
$489$	9.94432			0.449698
$490$		0			0
$491$	0.267503			0.0120722			0.00603612	−	0.999982i	$-0.498079\pi$
$491$	0.267503			0.0120722			0.00603612	+	0.999982i	$0.498079\pi$
$492$	−6.24906	+	1.67443i	−0.281729	+	0.0754892i
$493$	2.27115	−	8.47605i	0.102287	−	0.381742i
$494$	24.4894	−	14.1390i	1.10183	−	0.636143i
$495$	4.67298	−	3.00363i	0.210035	−	0.135003i
$496$			8.23483i			0.369755i
$497$		0			0
$498$	−9.60059	+	9.60059i	−0.430213	+	0.430213i
$499$	17.2504	+	9.95952i	0.772234	+	0.445849i	0.833671	−	0.552262i	$-0.186235\pi$
$499$	17.2504	+	9.95952i	0.772234	+	0.445849i	−0.0614372	+	0.998111i	$0.519568\pi$
$500$	−8.78682	+	6.91316i	−0.392959	+	0.309166i
$501$	−6.40040	−	11.0858i	−0.285949	−	0.495277i
$502$	−7.05884	−	26.3439i	−0.315051	−	1.17579i
$503$	−20.2026	−	20.2026i	−0.900788	−	0.900788i	0.0947161	−	0.995504i	$-0.469806\pi$
$503$	−20.2026	−	20.2026i	−0.900788	−	0.900788i	−0.995504	+	0.0947161i	$0.969806\pi$
$504$		0			0
$505$	2.61580	+	1.34829i	0.116401	+	0.0599983i
$506$	−6.02862	+	10.4419i	−0.268005	+	0.464198i
$507$	62.4797	+	16.7414i	2.77482	+	0.743511i
$508$	2.96279	+	0.793877i	0.131453	+	0.0352226i
$509$	3.67009	−	6.35678i	0.162674	−	0.281759i	−0.773153	−	0.634220i	$-0.781321\pi$
$509$	3.67009	−	6.35678i	0.162674	−	0.281759i	0.935827	+	0.352460i	$0.114655\pi$
$510$	−12.1954	+	3.89943i	−0.540021	+	0.172670i
$511$		0			0
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	3.48406	+	13.0027i	0.153825	+	0.574083i
$514$	15.7350	+	27.2538i	0.694039	+	1.20211i
$515$	−11.2882	−	10.2602i	−0.497419	−	0.452117i
$516$	−4.36968	−	2.52283i	−0.192364	−	0.111062i
$517$	8.10713	−	8.10713i	0.356551	−	0.356551i
$518$		0			0
$519$			3.28171i			0.144051i
$520$	−7.96553	−	12.3926i	−0.349312	−	0.543452i
$521$	−0.819218	+	0.472976i	−0.0358906	+	0.0207214i	−0.517838	−	0.855479i	$-0.673263\pi$
$521$	−0.819218	+	0.472976i	−0.0358906	+	0.0207214i	0.481947	+	0.876200i	$0.339930\pi$
$522$	1.28745	−	4.80483i	0.0563502	−	0.210302i
$523$	−24.9770	+	6.69258i	−1.09217	+	0.292646i	−0.759572	−	0.650423i	$-0.774592\pi$
$523$	−24.9770	+	6.69258i	−1.09217	+	0.292646i	−0.332598	+	0.943069i	$0.607925\pi$
$524$	−6.91225			−0.301963
$525$		0			0
$526$	−24.7031			−1.07710
$527$	−21.4092	+	5.73658i	−0.932600	+	0.249889i
$528$	0.896515	−	3.34584i	0.0390158	−	0.145609i
$529$	−27.5707	+	15.9180i	−1.19873	+	0.692086i
$530$	7.09816	+	11.0432i	0.308324	+	0.479685i
$531$		−	9.20438i		−	0.399436i
$532$		0			0
$533$	14.1671	−	14.1671i	0.613646	−	0.613646i
$534$	5.26061	+	3.03721i	0.227649	+	0.131433i
$535$	−9.70825	−	8.82409i	−0.419724	−	0.381499i
$536$	3.15133	+	5.45827i	0.136117	+	0.235761i
$537$	−6.08212	−	22.6988i	−0.262463	−	0.979525i
$538$	12.2459	+	12.2459i	0.527960	+	0.527960i
$539$		0			0
$540$	6.67976	−	2.13583i	0.287451	−	0.0919113i
$541$	−6.96871	+	12.0702i	−0.299608	+	0.518937i	−0.976046	−	0.217563i	$-0.930189\pi$
$541$	−6.96871	+	12.0702i	−0.299608	+	0.518937i	0.676438	+	0.736500i	$0.263523\pi$
$542$	0.640608	+	0.171650i	0.0275165	+	0.00737302i
$543$	−0.455382	−	0.122019i	−0.0195423	−	0.00523635i
$544$	−1.34578	+	2.33095i	−0.0576996	+	0.0999387i
$545$	−22.7179	−	11.7098i	−0.973129	−	0.501593i
$546$		0			0
$547$	−4.48736	−	4.48736i	−0.191865	−	0.191865i	0.604636	−	0.796502i	$-0.293318\pi$
$547$	−4.48736	−	4.48736i	−0.191865	−	0.191865i	−0.796502	+	0.604636i	$0.793318\pi$
$548$	1.52047	+	5.67446i	0.0649511	+	0.242401i
$549$	−5.97677	−	10.3521i	−0.255082	−	0.441815i
$550$	7.62743	−	2.84616i	0.325235	−	0.121361i
$551$	12.1187	+	6.99671i	0.516272	+	0.298070i
$552$	11.1394	−	11.1394i	0.474126	−	0.474126i
$553$		0			0
$554$			11.9376i			0.507180i
$555$	44.8822	−	28.8487i	1.90514	−	1.22456i
$556$	0.460450	−	0.265841i	0.0195274	−	0.0112742i
$557$	2.26636	−	8.45817i	0.0960288	−	0.358384i	−0.901145	−	0.433519i	$-0.857272\pi$
$557$	2.26636	−	8.45817i	0.0960288	−	0.358384i	0.997173	+	0.0751342i	$0.0239385\pi$
$558$	−12.1363	+	3.25191i	−0.513769	+	0.137664i
$559$	15.6259			0.660904
$560$		0			0
$561$	9.32318			0.393625
$562$	−18.0989	+	4.84959i	−0.763457	+	0.204568i
$563$	−6.39800	+	23.8777i	−0.269644	+	1.00632i	0.689703	+	0.724092i	$0.257741\pi$
$563$	−6.39800	+	23.8777i	−0.269644	+	1.00632i	−0.959346	+	0.282231i	$0.908926\pi$
$564$	−12.9731	+	7.49002i	−0.546266	+	0.315387i
$565$	−9.48372	−	2.06233i	−0.398983	−	0.0867628i
$566$			22.3575i			0.939757i
$567$		0			0
$568$	4.84867	−	4.84867i	0.203446	−	0.203446i
$569$	28.2859	+	16.3309i	1.18581	+	0.684626i	0.957351	−	0.288928i	$-0.0932989\pi$
$569$	28.2859	+	16.3309i	1.18581	+	0.684626i	0.228456	+	0.973554i	$0.426632\pi$
$570$	−0.973010	−	20.3945i	−0.0407549	−	0.854233i
$571$	19.1252	+	33.1258i	0.800363	+	1.38627i	0.919377	+	0.393377i	$0.128693\pi$
$571$	19.1252	+	33.1258i	0.800363	+	1.38627i	−0.119014	+	0.992893i	$0.537973\pi$
$572$	2.77641	+	10.3617i	0.116087	+	0.433244i
$573$	11.2865	+	11.2865i	0.471499	+	0.471499i
$574$		0			0
$575$	36.5139	+	6.13461i	1.52274	+	0.255831i
$576$	−0.762882	+	1.32135i	−0.0317867	+	0.0550562i
$577$	−7.23144	−	1.93766i	−0.301049	−	0.0806658i	0.105133	−	0.994458i	$-0.466473\pi$
$577$	−7.23144	−	1.93766i	−0.301049	−	0.0806658i	−0.406182	+	0.913792i	$0.633140\pi$
$578$	9.42315	+	2.52492i	0.391951	+	0.105023i
$579$	−8.35540	+	14.4720i	−0.347238	+	0.601435i
$580$	3.34003	−	6.47992i	0.138687	−	0.269064i
$581$		0			0
$582$	4.82103	+	4.82103i	0.199838	+	0.199838i
$583$	−2.47408	−	9.23340i	−0.102466	−	0.382408i
$584$	−1.26735	−	2.19512i	−0.0524434	−	0.0908346i
$585$	15.1183	−	16.6332i	0.625067	−	0.687698i
$586$	12.9980	+	7.50440i	0.536943	+	0.310004i
$587$	4.29105	−	4.29105i	0.177110	−	0.177110i	−0.612985	−	0.790095i	$-0.710031\pi$
$587$	4.29105	−	4.29105i	0.177110	−	0.177110i	0.790095	+	0.612985i	$0.210031\pi$
$588$		0			0
$589$		−	35.3453i		−	1.45638i
$590$	2.86641	−	13.1813i	0.118008	−	0.542667i
$591$	−38.7752	+	22.3869i	−1.59500	+	0.920872i
$592$	2.90291	−	10.8338i	0.119309	−	0.445267i
$593$	−19.9126	+	5.33556i	−0.817711	+	0.219105i	−0.643346	−	0.765576i	$-0.722454\pi$
$593$	−19.9126	+	5.33556i	−0.817711	+	0.219105i	−0.174366	+	0.984681i	$0.555788\pi$
$594$	−5.10656			−0.209525
$595$		0			0
$596$	−20.6774			−0.846978
$597$	−1.73390	+	0.464598i	−0.0709639	+	0.0190147i
$598$	−12.6270	+	47.1246i	−0.516357	+	1.92707i
$599$	−16.5036	+	9.52833i	−0.674317	+	0.389317i	−0.797710	−	0.603041i	$-0.793956\pi$
$599$	−16.5036	+	9.52833i	−0.674317	+	0.389317i	0.123393	+	0.992358i	$0.460622\pi$
$600$	−10.5886	+	1.01266i	−0.432278	+	0.0413415i
$601$			6.47395i			0.264078i	0.991245	+	0.132039i	$0.0421524\pi$
$601$			6.47395i			0.264078i	−0.991245	+	0.132039i	$0.957848\pi$
$602$		0			0
$603$	−6.79980	+	6.79980i	−0.276909	+	0.276909i
$604$	15.8155	+	9.13109i	0.643524	+	0.371539i
$605$	18.6474	−	0.889657i	0.758126	−	0.0361697i
$606$	1.39990	+	2.42470i	0.0568671	+	0.0984967i
$607$	−1.25777	−	4.69407i	−0.0510514	−	0.190527i	0.935691	−	0.352821i	$-0.114777\pi$
$607$	−1.25777	−	4.69407i	−0.0510514	−	0.190527i	−0.986742	+	0.162294i	$0.948111\pi$
$608$	−3.03502	−	3.03502i	−0.123086	−	0.123086i
$609$		0			0
$610$	−5.33534	−	16.6862i	−0.216021	−	0.675603i
$611$	23.1957	−	40.1762i	0.938399	−	1.62535i
$612$	−3.96674	−	1.06288i	−0.160346	−	0.0429645i
$613$	5.47325	+	1.46655i	0.221062	+	0.0592335i	0.367650	−	0.929964i	$-0.380162\pi$
$613$	5.47325	+	1.46655i	0.221062	+	0.0592335i	−0.146588	+	0.989198i	$0.546829\pi$
$614$	2.29327	−	3.97206i	0.0925489	−	0.160299i
$615$	−4.40579	−	13.7790i	−0.177658	−	0.555624i
$616$		0			0
$617$	4.72792	+	4.72792i	0.190339	+	0.190339i	0.795843	−	0.605504i	$-0.207028\pi$
$617$	4.72792	+	4.72792i	0.190339	+	0.190339i	−0.605504	+	0.795843i	$0.707028\pi$
$618$	−3.75622	−	14.0184i	−0.151097	−	0.563903i
$619$	−10.6005	−	18.3606i	−0.426069	−	0.737974i	0.570450	−	0.821332i	$-0.306769\pi$
$619$	−10.6005	−	18.3606i	−0.426069	−	0.737974i	−0.996520	+	0.0833583i	$0.973435\pi$
$620$	−18.3927	+	0.877504i	−0.738669	+	0.0352414i
$621$	−20.1130	−	11.6122i	−0.807106	−	0.465983i
$622$	9.60047	−	9.60047i	0.384944	−	0.384944i
$623$		0			0
$624$		−	14.0158i		−	0.561080i
$625$	−16.3771	−	18.8889i	−0.655082	−	0.755558i
$626$	12.0032	−	6.93008i	0.479746	−	0.276982i
$627$	−3.84799	+	14.3609i	−0.153674	+	0.573520i
$628$	−15.2120	+	4.07605i	−0.607026	+	0.162652i
$629$	30.1884			1.20369
$630$		0			0
$631$	8.27796			0.329540			0.164770	−	0.986332i	$-0.447312\pi$
$631$	8.27796			0.329540			0.164770	+	0.986332i	$0.447312\pi$
$632$	9.51051	−	2.54833i	0.378308	−	0.101367i
$633$	3.91936	−	14.6272i	0.155781	−	0.581381i
$634$	−15.4766	+	8.93543i	−0.614655	+	0.354871i
$635$	−1.45743	+	6.70207i	−0.0578364	+	0.265963i
$636$			12.4896i			0.495245i
$637$		0			0
$638$	−3.75360	+	3.75360i	−0.148606	+	0.148606i
$639$	9.06056	+	5.23112i	0.358430	+	0.206940i
$640$	−1.50399	+	1.65469i	−0.0594505	+	0.0654074i
$641$	−17.9082	−	31.0178i	−0.707330	−	1.22513i	−0.965844	−	0.259124i	$-0.916566\pi$
$641$	−17.9082	−	31.0178i	−0.707330	−	1.22513i	0.258514	−	0.966007i	$-0.416767\pi$
$642$	−3.23047	−	12.0563i	−0.127497	−	0.475824i
$643$	−14.3653	−	14.3653i	−0.566512	−	0.566512i	0.364637	−	0.931150i	$-0.381193\pi$
$643$	−14.3653	−	14.3653i	−0.566512	−	0.566512i	−0.931150	+	0.364637i	$0.881193\pi$
$644$		0			0
$645$	5.16919	−	10.0286i	0.203536	−	0.394877i
$646$	5.77629	−	10.0048i	0.227265	−	0.393635i
$647$	−5.62996	−	1.50854i	−0.221337	−	0.0593069i	0.146446	−	0.989219i	$-0.453216\pi$
$647$	−5.62996	−	1.50854i	−0.221337	−	0.0593069i	−0.367783	+	0.929912i	$0.619883\pi$
$648$	10.8660	+	2.91154i	0.426858	+	0.114376i
$649$	−4.91126	+	8.50656i	−0.192784	+	0.333912i
$650$	26.8304	−	19.1118i	1.05238	−	0.749626i
$651$		0			0
$652$	3.30532	+	3.30532i	0.129446	+	0.129446i
$653$	−5.50158	−	20.5322i	−0.215293	−	0.803486i	−0.986063	−	0.166372i	$-0.946795\pi$
$653$	−5.50158	−	20.5322i	−0.215293	−	0.803486i	0.770770	−	0.637114i	$-0.219872\pi$
$654$	−12.1580	−	21.0583i	−0.475415	−	0.823443i
$655$	−0.736570	−	15.4387i	−0.0287802	−	0.603240i
$656$	−2.63364	−	1.52053i	−0.102826	−	0.0593667i
$657$	2.73463	−	2.73463i	0.106688	−	0.106688i
$658$		0			0
$659$			16.4385i			0.640353i	0.947358	+	0.320176i	$0.103742\pi$
$659$			16.4385i			0.640353i	−0.947358	+	0.320176i	$0.896258\pi$
$660$	7.56856	+	1.64586i	0.294606	+	0.0640649i
$661$	32.6573	−	18.8547i	1.27022	−	0.733363i	0.295193	−	0.955438i	$-0.404616\pi$
$661$	32.6573	−	18.8547i	1.27022	−	0.733363i	0.975030	+	0.222074i	$0.0712828\pi$
$662$	−5.35911	+	20.0005i	−0.208288	+	0.777340i
$663$	36.4388	−	9.76373i	1.41516	−	0.379192i
$664$	−6.38215			−0.247676
$665$		0			0
$666$	17.1129			0.663112
$667$	−23.3197	+	6.24850i	−0.902944	+	0.241943i
$668$	1.55735	−	5.81212i	0.0602558	−	0.224878i
$669$	44.0320	−	25.4219i	1.70238	−	0.982867i
$670$	−11.8554	+	7.62022i	−0.458013	+	0.294395i
$671$			12.7563i			0.492452i
$672$		0			0
$673$	17.9856	−	17.9856i	0.693294	−	0.693294i	−0.269661	−	0.962955i	$-0.586912\pi$
$673$	17.9856	−	17.9856i	0.693294	−	0.693294i	0.962955	+	0.269661i	$0.0869118\pi$
$674$	4.51256	+	2.60533i	0.173817	+	0.100353i
$675$	5.48222	+	14.6918i	0.211011	+	0.565489i
$676$	15.2026	+	26.3318i	0.584717	+	1.01276i
$677$	1.45193	+	5.41868i	0.0558023	+	0.208257i	0.988198	−	0.153182i	$-0.0489522\pi$
$677$	1.45193	+	5.41868i	0.0558023	+	0.208257i	−0.932396	+	0.361439i	$0.882286\pi$
$678$	−6.52917	−	6.52917i	−0.250751	−	0.250751i
$679$		0			0
$680$	−5.34965	−	2.75744i	−0.205150	−	0.105743i
$681$	−3.47593	+	6.02048i	−0.133198	+	0.230705i
$682$	12.9513	+	3.47029i	0.495931	+	0.132884i
$683$	38.4949	+	10.3147i	1.47297	+	0.394680i	0.903947	−	0.427644i	$-0.140656\pi$
$683$	38.4949	+	10.3147i	1.47297	+	0.394680i	0.569019	+	0.822324i	$0.307323\pi$
$684$	3.27442	−	5.67146i	0.125200	−	0.216854i
$685$	−12.5120	+	4.00068i	−0.478060	+	0.152858i
$686$		0			0
$687$	12.1442	+	12.1442i	0.463330	+	0.463330i
$688$	−0.613859	−	2.29095i	−0.0234032	−	0.0873418i
$689$	−19.3394	−	33.4969i	−0.736774	−	1.27613i
$690$	26.0673	+	23.6932i	0.992364	+	0.901986i
$691$	−40.5796	−	23.4286i	−1.54372	−	0.891267i	−0.998599	−	0.0529098i	$-0.983150\pi$
$691$	−40.5796	−	23.4286i	−1.54372	−	0.891267i	−0.545121	−	0.838357i	$-0.683516\pi$
$692$	−1.09078	+	1.09078i	−0.0414654	+	0.0414654i
$693$		0			0
$694$			23.6140i			0.896375i
$695$	0.642828	+	1.00010i	0.0243839	+	0.0379359i
$696$	6.00653	−	3.46787i	0.227677	−	0.131449i
$697$	2.11848	−	7.90626i	0.0802430	−	0.299471i
$698$	5.98004	−	1.60235i	0.226348	−	0.0606497i
$699$	21.3683			0.808224
$700$		0			0
$701$	−10.7255			−0.405098			−0.202549	−	0.979272i	$-0.564923\pi$
$701$	−10.7255			−0.405098			−0.202549	+	0.979272i	$0.564923\pi$
$702$	−19.9585	+	5.34787i	−0.753286	+	0.201842i
$703$	−12.4598	+	46.5005i	−0.469929	+	1.75380i
$704$	1.41009	−	0.814115i	0.0531447	−	0.0306831i
$705$	−18.1116	−	28.1776i	−0.682121	−	1.06123i
$706$			0.804355i			0.0302723i
$707$		0			0
$708$	9.07483	−	9.07483i	0.341053	−	0.341053i
$709$	−45.6808	−	26.3738i	−1.71558	−	0.990489i	−0.926584	−	0.376088i	$-0.877269\pi$
$709$	−45.6808	−	26.3738i	−1.71558	−	0.990489i	−0.788994	−	0.614401i	$-0.789398\pi$
$710$	11.3463	+	10.3130i	0.425819	+	0.387038i
$711$	7.51134	+	13.0100i	0.281697	+	0.487914i
$712$	0.739019	+	2.75806i	0.0276959	+	0.103363i
$713$	43.1193	+	43.1193i	1.61483	+	1.61483i
$714$		0			0
$715$	−22.8473	+	7.30532i	−0.854439	+	0.273204i
$716$	5.52310	−	9.56629i	0.206408	−	0.357509i
$717$	−49.0335	−	13.1385i	−1.83119	−	0.490665i
$718$	−34.1800	−	9.15851i	−1.27559	−	0.341792i
$719$	−15.3355	+	26.5619i	−0.571917	+	0.990590i	0.424452	+	0.905451i	$0.360467\pi$
$719$	−15.3355	+	26.5619i	−0.571917	+	0.990590i	−0.996369	+	0.0851394i	$0.972866\pi$
$720$	−3.03256	−	1.56311i	−0.113017	−	0.0582538i
$721$		0			0
$722$	−0.408205	−	0.408205i	−0.0151918	−	0.0151918i
$723$	−12.3091	−	45.9382i	−0.457780	−	1.70846i
$724$	−0.110804	−	0.191919i	−0.00411801	−	0.00713260i
$725$	14.8290	+	6.76955i	0.550735	+	0.251415i
$726$	15.3817	+	8.88063i	0.570868	+	0.329591i
$727$	−22.5178	+	22.5178i	−0.835139	+	0.835139i	−0.988214	−	0.153076i	$-0.951082\pi$
$727$	−22.5178	+	22.5178i	−0.835139	+	0.835139i	0.153076	+	0.988214i	$0.451082\pi$
$728$		0			0
$729$		−	2.85232i		−	0.105641i
$730$	4.76780	−	3.06457i	0.176464	−	0.113425i
$731$	5.52848	−	3.19187i	0.204478	−	0.118056i
$732$	4.31371	−	16.0990i	0.159439	−	0.595036i
$733$	10.8555	−	2.90873i	0.400959	−	0.107437i	−0.0527037	−	0.998610i	$-0.516784\pi$
$733$	10.8555	−	2.90873i	0.400959	−	0.107437i	0.453662	+	0.891174i	$0.350117\pi$
$734$	33.0141			1.21857
$735$		0			0
$736$	7.40513			0.272957
$737$	9.91251	−	2.65605i	0.365132	−	0.0978368i
$738$	1.20090	−	4.48184i	0.0442059	−	0.164979i
$739$	−37.7723	+	21.8079i	−1.38948	+	0.802215i	−0.993256	−	0.115941i	$-0.963012\pi$
$739$	−37.7723	+	21.8079i	−1.38948	+	0.802215i	−0.396221	+	0.918155i	$0.629678\pi$
$740$	24.5069	+	5.32927i	0.900893	+	0.195908i
$741$			60.1581i			2.20996i
$742$		0			0
$743$	5.11739	−	5.11739i	0.187739	−	0.187739i	−0.606979	−	0.794718i	$-0.707619\pi$
$743$	5.11739	−	5.11739i	0.187739	−	0.187739i	0.794718	+	0.606979i	$0.207619\pi$
$744$	−15.1716	−	8.75932i	−0.556217	−	0.321132i
$745$	−2.20338	−	46.1835i	−0.0807257	−	1.69203i
$746$	5.16899	+	8.95296i	0.189250	+	0.327791i
$747$	−2.52029	−	9.40585i	−0.0922126	−	0.344142i
$748$	3.09887	+	3.09887i	0.113306	+	0.113306i
$749$		0			0
$750$	−3.39012	−	23.5420i	−0.123790	−	0.859634i
$751$	−8.20286	+	14.2078i	−0.299327	+	0.518449i	−0.975982	−	0.217851i	$-0.930095\pi$
$751$	−8.20286	+	14.2078i	−0.299327	+	0.518449i	0.676655	+	0.736300i	$0.263429\pi$
$752$	−6.80159	−	1.82248i	−0.248029	−	0.0664591i
$753$	56.0437	+	15.0169i	2.04235	+	0.547245i
$754$	−10.7396	+	18.6015i	−0.391113	+	0.677428i
$755$	−18.7092	+	36.2974i	−0.680899	+	1.32100i
$756$		0			0
$757$	30.8170	+	30.8170i	1.12006	+	1.12006i	0.991732	+	0.128330i	$0.0409616\pi$
$757$	30.8170	+	30.8170i	1.12006	+	1.12006i	0.128330	+	0.991732i	$0.459038\pi$
$758$	0.272914	+	1.01853i	0.00991269	+	0.0369947i
$759$	−12.8252	−	22.2139i	−0.465525	−	0.806313i
$760$	6.45539	−	7.10222i	0.234162	−	0.257624i
$761$	42.3500	+	24.4508i	1.53518	+	0.886339i	0.999111	+	0.0421686i	$0.0134267\pi$
$761$	42.3500	+	24.4508i	1.53518	+	0.886339i	0.536074	+	0.844171i	$0.319907\pi$
$762$	−4.61411	+	4.61411i	−0.167152	+	0.167152i
$763$		0			0
$764$			7.50286i			0.271444i
$765$	1.95128	−	8.97308i	0.0705488	−	0.324422i
$766$	3.89581	−	2.24925i	0.140761	−	0.0812686i
$767$	−10.2867	+	38.3904i	−0.371430	+	1.38620i
$768$	−2.05490	+	0.550608i	−0.0741496	+	0.0198683i
$769$	40.2063			1.44988			0.724938	−	0.688814i	$-0.241869\pi$
$769$	40.2063			1.44988			0.724938	+	0.688814i	$0.241869\pi$
$770$		0			0
$771$	−66.9486			−2.41110
$772$	−7.58744	+	2.03305i	−0.273078	+	0.0731710i
$773$	−0.104368	+	0.389505i	−0.00375384	+	0.0140095i	−0.967777	−	0.251807i	$-0.918975\pi$
$773$	−0.104368	+	0.389505i	−0.00375384	+	0.0140095i	0.964024	+	0.265817i	$0.0856417\pi$
$774$	3.13394	−	1.80938i	0.112647	−	0.0650368i
$775$	−3.91986	−	40.9871i	−0.140806	−	1.47230i
$776$			3.20486i			0.115048i
$777$		0			0
$778$	14.2520	−	14.2520i	0.510959	−	0.510959i
$779$	11.3040	+	6.52637i	0.405008	+	0.233831i
$780$	31.3046	−	1.49352i	1.12089	−	0.0534767i
$781$	−5.58243	−	9.66905i	−0.199755	−	0.345986i
$782$	5.15859	+	19.2521i	0.184471	+	0.688455i
$783$	−7.23012	−	7.23012i	−0.258383	−	0.258383i
$784$		0			0
$785$	−10.7250	−	33.5421i	−0.382790	−	1.19717i
$786$	7.35250	−	12.7349i	0.262255	−	0.454239i
$787$	36.4779	+	9.77424i	1.30030	+	0.348414i	0.841563	−	0.540159i	$-0.181636\pi$
$787$	36.4779	+	9.77424i	1.30030	+	0.348414i	0.458735	+	0.888573i	$0.348303\pi$
$788$	−20.3292	−	5.44720i	−0.724199	−	0.194048i
$789$	26.2764	−	45.5121i	0.935466	−	1.62028i
$790$	6.70522	+	20.9704i	0.238561	+	0.746095i
$791$		0			0
$792$	1.75666	+	1.75666i	0.0624202	+	0.0624202i
$793$	13.3591	+	49.8568i	0.474395	+	1.77047i
$794$	−11.6039	−	20.0986i	−0.411807	−	0.713271i
$795$	−27.8959	+	1.33089i	−0.989364	+	0.0472019i
$796$	−0.730744	−	0.421896i	−0.0259006	−	0.0149537i
$797$	31.9162	−	31.9162i	1.13053	−	1.13053i	0.140439	−	0.990089i	$-0.455149\pi$
$797$	31.9162	−	31.9162i	1.13053	−	1.13053i	0.990089	−	0.140439i	$-0.0448515\pi$
$798$		0			0
$799$		−	18.9526i		−	0.670496i
$800$	−3.85607	−	3.18289i	−0.136332	−	0.112532i
$801$	−3.77292	+	2.17829i	−0.133309	+	0.0769662i
$802$	3.03725	−	11.3352i	0.107249	−	0.400259i
$803$	−3.98645	+	1.06817i	−0.140679	+	0.0376948i
$804$	−13.4082			−0.472870
$805$		0			0
$806$	54.2533			1.91099
$807$	−35.5874	+	9.53562i	−1.25274	+	0.335670i
$808$	−0.340626	+	1.27123i	−0.0119832	+	0.0447218i
$809$	27.4449	−	15.8453i	0.964911	−	0.557091i	0.0672297	−	0.997738i	$-0.478584\pi$
$809$	27.4449	−	15.8453i	0.964911	−	0.557091i	0.897681	+	0.440646i	$0.145251\pi$
$810$	−5.34513	+	24.5798i	−0.187809	+	0.863647i
$811$		−	23.8233i		−	0.836549i	−0.908321	−	0.418274i	$-0.862635\pi$
$811$		−	23.8233i		−	0.836549i	0.908321	−	0.418274i	$-0.137365\pi$
$812$		0			0
$813$	−0.997653	+	0.997653i	−0.0349892	+	0.0349892i
$814$	−15.8155	−	9.13109i	−0.554333	−	0.320045i
$815$	−7.03032	+	7.73475i	−0.246261	+	0.270936i
$816$	−2.86298	−	4.95883i	−0.100224	−	0.173594i
$817$	2.63479	+	9.83316i	0.0921796	+	0.344019i
$818$	−7.79942	−	7.79942i	−0.272700	−	0.272700i
$819$		0			0
$820$	3.11550	−	6.04432i	0.108798	−	0.211077i
$821$	−21.8626	+	37.8672i	−0.763012	+	1.32157i	0.178280	+	0.983980i	$0.442947\pi$
$821$	−21.8626	+	37.8672i	−0.763012	+	1.32157i	−0.941291	+	0.337595i	$0.890387\pi$
$822$	−12.0718	−	3.23462i	−0.421051	−	0.112820i
$823$	32.3374	+	8.66479i	1.12721	+	0.302035i	0.773798	−	0.633432i	$-0.218354\pi$
$823$	32.3374	+	8.66479i	1.12721	+	0.302035i	0.353413	+	0.935467i	$0.385021\pi$
$824$	3.41098	−	5.90799i	0.118827	−	0.205814i
$825$	−2.86956	+	17.0800i	−0.0999054	+	0.594648i
$826$		0			0
$827$	28.3471	+	28.3471i	0.985724	+	0.985724i	0.999900	−	0.0141754i	$-0.00451232\pi$
$827$	28.3471	+	28.3471i	0.985724	+	0.985724i	−0.0141754	+	0.999900i	$0.504512\pi$
$828$	2.92426	+	10.9135i	0.101625	+	0.379270i
$829$	23.0889	+	39.9911i	0.801909	+	1.38895i	0.918358	+	0.395751i	$0.129516\pi$
$829$	23.0889	+	39.9911i	0.801909	+	1.38895i	−0.116448	+	0.993197i	$0.537151\pi$
$830$	−0.680083	−	14.2547i	−0.0236060	−	0.494788i
$831$	−21.9934	−	12.6979i	−0.762944	−	0.440486i
$832$	4.65861	−	4.65861i	0.161508	−	0.161508i
$833$		0			0
$834$			1.13109i			0.0391665i
$835$	13.1475	+	2.85905i	0.454987	+	0.0989415i
$836$	−6.05234	+	3.49432i	−0.209324	+	0.120853i
$837$	−6.68442	+	24.9466i	−0.231047	+	0.862281i
$838$	11.1107	−	2.97710i	0.383812	−	0.102842i
$839$	−40.2865			−1.39085			−0.695423	−	0.718601i	$-0.744783\pi$
$839$	−40.2865			−1.39085			−0.695423	+	0.718601i	$0.744783\pi$
$840$		0			0
$841$	18.3710			0.633481
$842$	15.5244	−	4.15975i	0.535006	−	0.143354i
$843$	10.3169	−	38.5034i	0.355335	−	1.32613i
$844$	6.16458	−	3.55912i	0.212194	−	0.122510i
$845$	−57.1927	+	36.7614i	−1.96749	+	1.26463i
$846$		−	10.7437i		−	0.369376i
$847$		0			0
$848$	−4.15133	+	4.15133i	−0.142557	+	0.142557i
$849$	−41.1908	−	23.7815i	−1.41366	−	0.816180i
$850$	5.58876	−	12.2424i	0.191693	−	0.419912i
$851$	−41.5279	−	71.9284i	−1.42356	−	2.46567i
$852$	3.77554	+	14.0905i	0.129348	+	0.482733i
$853$	19.9948	+	19.9948i	0.684609	+	0.684609i	0.961035	−	0.276426i	$-0.0891501\pi$
$853$	19.9948	+	19.9948i	0.684609	+	0.684609i	−0.276426	+	0.961035i	$0.589150\pi$
$854$		0			0
$855$	13.0163	+	6.70915i	0.445147	+	0.229448i
$856$	2.93355	−	5.08106i	0.100267	−	0.173667i
$857$	−4.10936	−	1.10110i	−0.140373	−	0.0376128i	0.187948	−	0.982179i	$-0.439816\pi$
$857$	−4.10936	−	1.10110i	−0.140373	−	0.0376128i	−0.328321	+	0.944566i	$0.606483\pi$
$858$	−22.0433	−	5.90648i	−0.752546	−	0.201644i
$859$	−13.9351	+	24.1363i	−0.475459	+	0.823518i	−0.999605	−	0.0281099i	$-0.991051\pi$
$859$	−13.9351	+	24.1363i	−0.475459	+	0.823518i	0.524146	+	0.851628i	$0.324385\pi$
$860$	5.05150	−	1.61520i	0.172255	−	0.0550777i
$861$		0			0
$862$	5.96484	+	5.96484i	0.203163	+	0.203163i
$863$	9.23929	+	34.4815i	0.314509	+	1.17376i	0.924446	+	0.381314i	$0.124528\pi$
$863$	9.23929	+	34.4815i	0.314509	+	1.17376i	−0.609937	+	0.792450i	$0.708805\pi$
$864$	1.56813	+	2.71609i	0.0533490	+	0.0924032i
$865$	−2.55253	−	2.32006i	−0.0867886	−	0.0788845i
$866$	−0.328323	−	0.189557i	−0.0111569	−	0.00644142i
$867$	−14.6752	+	14.6752i	−0.498395	+	0.498395i
$868$		0			0
$869$		−	16.0316i		−	0.543833i
$870$	8.38564	+	13.0462i	0.284300	+	0.442308i
$871$	35.9605	−	20.7618i	1.21848	−	0.703488i
$872$	2.95830	−	11.0405i	0.100181	−	0.373879i
$873$	−4.72324	+	1.26559i	−0.159857	+	0.0428337i
$874$	−31.7841			−1.07511
$875$		0			0
$876$	5.39228			0.182188
$877$	20.9529	−	5.61431i	0.707528	−	0.189582i	0.112928	−	0.993603i	$-0.463977\pi$
$877$	20.9529	−	5.61431i	0.707528	−	0.189582i	0.594600	+	0.804021i	$0.297310\pi$
$878$	−6.62665	+	24.7310i	−0.223639	+	0.834631i
$879$	−27.6518	+	15.9647i	−0.932670	+	0.538478i
$880$	1.96861	+	3.06272i	0.0663617	+	0.103244i
$881$		−	4.60383i		−	0.155107i	−0.996988	−	0.0775535i	$-0.975289\pi$
$881$		−	4.60383i		−	0.155107i	0.996988	−	0.0775535i	$-0.0247108\pi$
$882$		0			0
$883$	18.3524	−	18.3524i	0.617607	−	0.617607i	−0.327310	−	0.944917i	$-0.606142\pi$
$883$	18.3524	−	18.3524i	0.617607	−	0.617607i	0.944917	+	0.327310i	$0.106142\pi$
$884$	15.3569	+	8.86633i	0.516509	+	0.298207i
$885$	21.2359	+	19.3019i	0.713837	+	0.648825i
$886$	14.9824	+	25.9503i	0.503344	+	0.871818i
$887$	8.50803	+	31.7524i	0.285672	+	1.06614i	0.948347	+	0.317235i	$0.102754\pi$
$887$	8.50803	+	31.7524i	0.285672	+	1.06614i	−0.662675	+	0.748907i	$0.730579\pi$
$888$	16.8721	+	16.8721i	0.566189	+	0.566189i
$889$		0			0
$890$	−6.08145	+	1.94452i	−0.203851	+	0.0651804i
$891$	9.15825	−	15.8626i	0.306813	−	0.531416i
$892$	23.0853	+	6.18569i	0.772954	+	0.207112i
$893$	29.1936	+	7.82240i	0.976926	+	0.261767i
$894$	21.9944	−	38.0953i	0.735601	−	1.27410i
$895$	21.9551	+	11.3166i	0.733879	+	0.378273i
$896$		0			0
$897$	−73.3897	−	73.3897i	−2.45041	−	2.45041i
$898$	0.393053	+	1.46689i	0.0131164	+	0.0489509i
$899$	13.4237	+	23.2505i	0.447705	+	0.775447i
$900$	3.16811	−	6.93988i	0.105604	−	0.231329i
$901$	−13.6847	−	7.90087i	−0.455904	−	0.263216i
$902$	−3.50127	+	3.50127i	−0.116580	+	0.116580i
$903$		0			0
$904$		−	4.34037i		−	0.144359i
$905$	0.416848	−	0.267935i	0.0138565	−	0.00890647i
$906$	−33.6457	+	19.4253i	−1.11780	+	0.645364i
$907$	−3.86557	+	14.4265i	−0.128354	+	0.479024i	−0.999937	−	0.0112243i	$-0.996427\pi$
$907$	−3.86557	+	14.4265i	−0.128354	+	0.479024i	0.871583	+	0.490248i	$0.163094\pi$
$908$	−3.15645	+	0.845767i	−0.104750	+	0.0280678i
$909$	−2.00802			−0.0666019
$910$		0			0
$911$	14.3027			0.473868			0.236934	−	0.971526i	$-0.423857\pi$
$911$	14.3027			0.473868			0.236934	+	0.971526i	$0.423857\pi$
$912$	8.81996	−	2.36330i	0.292058	−	0.0782567i
$913$	−2.68955	+	10.0375i	−0.0890110	+	0.332193i
$914$	3.50137	−	2.02151i	0.115815	−	0.0668658i
$915$	36.4172	+	7.91929i	1.20392	+	0.261804i
$916$			8.07306i			0.266742i
$917$		0			0
$918$	−5.96899	+	5.96899i	−0.197006	+	0.197006i
$919$	3.95343	+	2.28252i	0.130412	+	0.0752932i	0.563787	−	0.825921i	$-0.309344\pi$
$919$	3.95343	+	2.28252i	0.130412	+	0.0752932i	−0.433375	+	0.901214i	$0.642677\pi$
$920$	0.789092	+	16.5396i	0.0260156	+	0.545293i
$921$	4.87867	+	8.45010i	0.160758	+	0.278440i
$922$	−4.46731	−	16.6722i	−0.147123	−	0.549070i
$923$	−31.9443	−	31.9443i	−1.05146	−	1.05146i
$924$		0			0
$925$	−9.29162	+	55.3048i	−0.305507	+	1.81841i
$926$	14.4078	−	24.9550i	0.473469	−	0.820073i
$927$	10.0540	+	2.69397i	0.330217	+	0.0884815i
$928$	3.14913	+	0.843807i	0.103375	+	0.0276993i
$929$	−14.7804	+	25.6004i	−0.484929	+	0.839922i	−0.999850	−	0.0173154i	$-0.994488\pi$
$929$	−14.7804	+	25.6004i	−0.484929	+	0.839922i	0.514921	+	0.857238i	$0.327821\pi$
$930$	17.9475	−	34.8196i	0.588522	−	1.14178i
$931$		0			0
$932$	7.10247	+	7.10247i	0.232649	+	0.232649i
$933$	7.47566	+	27.8995i	0.244742	+	0.913390i
$934$	−15.2502	−	26.4142i	−0.499003	−	0.864299i
$935$	−6.59119	+	7.25162i	−0.215555	+	0.237153i
$936$	8.70541	+	5.02607i	0.284545	+	0.164282i
$937$	1.72596	−	1.72596i	0.0563846	−	0.0563846i	−0.678352	−	0.734737i	$-0.737306\pi$
$937$	1.72596	−	1.72596i	0.0563846	−	0.0563846i	0.734737	+	0.678352i	$0.237306\pi$
$938$		0			0
$939$			29.4859i			0.962235i
$940$	3.34578	−	15.3857i	0.109127	−	0.501828i
$941$	−30.8031	+	17.7842i	−1.00415	+	0.579748i	−0.909474	−	0.415760i	$-0.863516\pi$
$941$	−30.8031	+	17.7842i	−1.00415	+	0.579748i	−0.0946785	+	0.995508i	$0.530182\pi$
$942$	8.67132	−	32.3618i	0.282527	−	1.05440i
$943$	−21.7521	+	5.82846i	−0.708346	+	0.189801i
$944$	6.03264			0.196346
$945$		0			0
$946$	−3.86179			−0.125558
$947$	35.2538	−	9.44624i	1.14560	−	0.306961i	0.364397	−	0.931244i	$-0.381275\pi$
$947$	35.2538	−	9.44624i	1.14560	−	0.306961i	0.781199	+	0.624282i	$0.214608\pi$
$948$	−5.42129	+	20.2325i	−0.176075	+	0.657122i
$949$	−14.4620	+	8.34965i	−0.469457	+	0.271041i
$950$	16.5509	+	13.6615i	0.536982	+	0.443237i
$951$		−	38.0182i		−	1.23282i
$952$		0			0
$953$	−32.0649	+	32.0649i	−1.03868	+	1.03868i	−0.0394635	+	0.999221i	$0.512565\pi$
$953$	−32.0649	+	32.0649i	−1.03868	+	1.03868i	−0.999221	+	0.0394635i	$0.987435\pi$
$954$	−7.75747	−	4.47878i	−0.251157	−	0.145006i
$955$	−16.7578	+	0.799506i	−0.542271	+	0.0258714i
$956$	−11.9309	−	20.6649i	−0.385873	−	0.668351i
$957$	−2.92284	−	10.9082i	−0.0944819	−	0.352611i
$958$	1.02438	+	1.02438i	0.0330961	+	0.0330961i
$959$		0			0
$960$	−1.44877	−	4.53099i	−0.0467588	−	0.146237i
$961$	18.4062	−	31.8805i	0.593748	−	1.02840i
$962$	−71.3760	−	19.1251i	−2.30125	−	0.616619i
$963$	8.64679	+	2.31690i	0.278639	+	0.0746611i
$964$	11.1777	−	19.3604i	0.360011	−	0.623557i
$965$	−5.34938	−	16.7301i	−0.172203	−	0.538561i
$966$		0			0
$967$	−29.7096	−	29.7096i	−0.955398	−	0.955398i	0.0436492	−	0.999047i	$-0.486102\pi$
$967$	−29.7096	−	29.7096i	−0.955398	−	0.955398i	−0.999047	+	0.0436492i	$0.986102\pi$
$968$	2.16085	+	8.06439i	0.0694522	+	0.259199i
$969$	12.2884	+	21.2841i	0.394760	+	0.683745i
$970$	−7.15814	+	0.341510i	−0.229834	+	0.0109652i
$971$	−7.13489	−	4.11933i	−0.228969	−	0.132196i	0.381127	−	0.924523i	$-0.375536\pi$
$971$	−7.13489	−	4.11933i	−0.228969	−	0.132196i	−0.610097	+	0.792327i	$0.708869\pi$
$972$	−10.2692	+	10.2692i	−0.329385	+	0.329385i
$973$		0			0
$974$			17.3700i			0.556570i
$975$	6.67165	+	69.7606i	0.213664	+	2.23413i
$976$	6.78484	−	3.91723i	0.217178	−	0.125388i
$977$	−3.65498	+	13.6406i	−0.116933	+	0.436401i	−0.999424	−	0.0339285i	$-0.989198\pi$
$977$	−3.65498	+	13.6406i	−0.116933	+	0.436401i	0.882491	+	0.470329i	$0.155865\pi$
$978$	−9.60547	+	2.57378i	−0.307149	+	0.0823004i
$979$	4.64917			0.148588
$980$		0			0
$981$	17.4395			0.556799
$982$	−0.258388	+	0.0692349i	−0.00824550	+	0.00220937i
$983$	0.902186	−	3.36700i	0.0287753	−	0.107391i	−0.950045	−	0.312114i	$-0.898963\pi$
$983$	0.902186	−	3.36700i	0.0287753	−	0.107391i	0.978820	+	0.204723i	$0.0656295\pi$
$984$	5.60275	−	3.23475i	0.178609	−	0.103120i
$985$	10.0002	−	45.9863i	0.318632	−	1.46525i
$986$			8.77505i			0.279454i
$987$		0			0
$988$	−19.9955	+	19.9955i	−0.636143	+	0.636143i
$989$	−15.2102	−	8.78164i	−0.483657	−	0.279240i
$990$	−3.73636	+	4.11074i	−0.118749	+	0.130648i
$991$	22.2165	+	38.4801i	0.705729	+	1.22236i	0.966428	+	0.256939i	$0.0827139\pi$
$991$	22.2165	+	38.4801i	0.705729	+	1.22236i	−0.260698	+	0.965420i	$0.583953\pi$
$992$	−2.13133	−	7.95423i	−0.0676698	−	0.252547i
$993$	−31.1478	−	31.1478i	−0.988445	−	0.988445i
$994$		0			0
$995$	0.864447	−	1.67710i	0.0274048	−	0.0531675i
$996$	6.78864	−	11.7583i	0.215106	−	0.372575i
$997$	5.76517	+	1.54477i	0.182585	+	0.0489234i	0.348953	−	0.937140i	$-0.386537\pi$
$997$	5.76517	+	1.54477i	0.182585	+	0.0489234i	−0.166368	+	0.986064i	$0.553204\pi$
$998$	−19.2403	−	5.15543i	−0.609041	−	0.163192i
$999$	17.5882	−	30.4636i	0.556465	−	0.963825i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.2.l.d.117.3		32
5.3	odd	4	inner	490.2.l.d.313.7		32
7.2	even	3		490.2.g.b.97.7	yes	16
7.3	odd	6	inner	490.2.l.d.227.7		32
7.4	even	3	inner	490.2.l.d.227.6		32
7.5	odd	6		490.2.g.b.97.6	✓	16
7.6	odd	2	inner	490.2.l.d.117.2		32
35.3	even	12	inner	490.2.l.d.423.3		32
35.13	even	4	inner	490.2.l.d.313.6		32
35.18	odd	12	inner	490.2.l.d.423.2		32
35.23	odd	12		490.2.g.b.293.6	yes	16
35.33	even	12		490.2.g.b.293.7	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
490.2.g.b.97.6	✓	16	7.5	odd	6
490.2.g.b.97.7	yes	16	7.2	even	3
490.2.g.b.293.6	yes	16	35.23	odd	12
490.2.g.b.293.7	yes	16	35.33	even	12
490.2.l.d.117.2		32	7.6	odd	2	inner
490.2.l.d.117.3		32	1.1	even	1	trivial
490.2.l.d.227.6		32	7.4	even	3	inner
490.2.l.d.227.7		32	7.3	odd	6	inner
490.2.l.d.313.6		32	35.13	even	4	inner
490.2.l.d.313.7		32	5.3	odd	4	inner
490.2.l.d.423.2		32	35.18	odd	12	inner
490.2.l.d.423.3		32	35.3	even	12	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:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	490.l (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{2} +(0.550608 - 2.05490i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.20905 + 1.88101i) q^{5} +2.12738i q^{6} +(-0.707107 + 0.707107i) q^{8} +(-1.32135 - 0.762882i) q^{9} +(-1.65469 - 1.50399i) q^{10} +(0.814115 + 1.41009i) q^{11} +(-0.550608 - 2.05490i) q^{12} +(4.65861 + 4.65861i) q^{13} +(4.53099 - 1.44877i) q^{15} +(0.500000 - 0.866025i) q^{16} +(2.59984 + 0.696624i) q^{17} +(1.47377 + 0.394897i) q^{18} +(-2.14608 + 3.71713i) q^{19} +(1.98757 + 1.02448i) q^{20} +(-1.15133 - 1.15133i) q^{22} +(-1.91659 - 7.15281i) q^{23} +(1.06369 + 1.84237i) q^{24} +(-2.07641 + 4.54846i) q^{25} +(-5.70561 - 3.29413i) q^{26} +(2.21768 - 2.21768i) q^{27} -3.26022i q^{29} +(-4.00163 + 2.57211i) q^{30} +(-7.13157 + 4.11741i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(3.34584 - 0.896515i) q^{33} -2.69155 q^{34} -1.52576 q^{36} +(10.8338 - 2.90291i) q^{37} +(1.11089 - 4.14592i) q^{38} +(12.1380 - 7.00789i) q^{39} +(-2.18500 - 0.475150i) q^{40} -3.04106i q^{41} +(1.67710 - 1.67710i) q^{43} +(1.41009 + 0.814115i) q^{44} +(-0.162586 - 3.40783i) q^{45} +(3.70257 + 6.41303i) q^{46} +(-1.82248 - 6.80159i) q^{47} +(-1.50429 - 1.50429i) q^{48} +(0.828427 - 4.93089i) q^{50} +(2.86298 - 4.95883i) q^{51} +(6.36378 + 1.70517i) q^{52} +(-5.67082 - 1.51949i) q^{53} +(-1.56813 + 2.71609i) q^{54} +(-1.66809 + 3.23622i) q^{55} +(6.45666 + 6.45666i) q^{57} +(0.843807 + 3.14913i) q^{58} +(3.01632 + 5.22442i) q^{59} +(3.19957 - 3.52017i) q^{60} +(6.78484 + 3.91723i) q^{61} +(5.82290 - 5.82290i) q^{62} -1.00000i q^{64} +(-3.13042 + 14.3954i) q^{65} +(-2.99980 + 1.73193i) q^{66} +(1.63125 - 6.08791i) q^{67} +(2.59984 - 0.696624i) q^{68} -15.7536 q^{69} -6.85705 q^{71} +(1.47377 - 0.394897i) q^{72} +(-0.656029 + 2.44833i) q^{73} +(-9.71332 + 5.60799i) q^{74} +(8.20333 + 6.77122i) q^{75} +4.29217i q^{76} +(-9.91065 + 9.91065i) q^{78} +(-8.52689 - 4.92300i) q^{79} +(2.23353 - 0.106560i) q^{80} +(-5.62467 - 9.74221i) q^{81} +(0.787084 + 2.93744i) q^{82} +(4.51286 + 4.51286i) q^{83} +(1.83297 + 5.73258i) q^{85} +(-1.18589 + 2.05401i) q^{86} +(-6.69941 - 1.79510i) q^{87} +(-1.57275 - 0.421417i) q^{88} +(1.42768 - 2.47281i) q^{89} +(1.03906 + 3.24963i) q^{90} +(-5.23622 - 5.23622i) q^{92} +(4.53416 + 16.9217i) q^{93} +(3.52076 + 6.09814i) q^{94} +(-9.58668 + 0.457374i) q^{95} +(1.84237 + 1.06369i) q^{96} +(2.26618 - 2.26618i) q^{97} -2.48429i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{11} - 48 q^{15} + 16 q^{16} + 16 q^{18} + 32 q^{22} - 16 q^{23} - 32 q^{25} - 40 q^{30} - 96 q^{36} + 48 q^{37} + 32 q^{43} + 16 q^{46} - 64 q^{50} + 80 q^{51} - 32 q^{53} + 96 q^{57} - 16 q^{58}+ \cdots - 40 q^{95}+O(q^{100}) \) 32 * q + 16 * q^11 - 48 * q^15 + 16 * q^16 + 16 * q^18 + 32 * q^22 - 16 * q^23 - 32 * q^25 - 40 * q^30 - 96 * q^36 + 48 * q^37 + 32 * q^43 + 16 * q^46 - 64 * q^50 + 80 * q^51 - 32 * q^53 + 96 * q^57 - 16 * q^58 - 40 * q^60 - 32 * q^65 - 16 * q^67 + 32 * q^71 + 16 * q^72 + 112 * q^81 + 48 * q^85 - 48 * q^86 + 16 * q^88 + 32 * q^92 - 64 * q^93 - 40 * q^95

Introduction

L-functions

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