LMFDB - Embedded newform 644.2.bc.a.145.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [644,2,Mod(5,644)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(644, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 55, 3]))

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

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

chi := DirichletCharacter("644.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 644 = 2^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	644.bc (of order $66$, degree $20$, 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:	$5.14236589017$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$16$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			145.1
Character	$\chi$	$=$	644.145
Dual form			644.2.bc.a.493.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.39754 + 2.71086i) q^{3} +(-1.84559 - 0.176232i) q^{5} +(-1.47931 - 2.19354i) q^{7} +(-3.65545 - 5.13336i) q^{9} +(3.83965 + 1.32892i) q^{11} +(0.754092 - 2.56820i) q^{13} +(3.05703 - 4.75684i) q^{15} +(-2.87318 + 1.15025i) q^{17} +(-0.834503 - 0.334085i) q^{19} +(8.01379 - 0.944630i) q^{21} +(1.71607 - 4.47829i) q^{23} +(-1.53450 - 0.295750i) q^{25} +(9.96788 - 1.43316i) q^{27} +(0.0489273 - 0.340297i) q^{29} +(6.41276 + 0.305478i) q^{31} +(-8.96858 + 8.55152i) q^{33} +(2.34363 + 4.30909i) q^{35} +(8.89620 - 6.33496i) q^{37} +(5.90815 + 5.63341i) q^{39} +(0.0451801 - 0.0206330i) q^{41} +(0.464852 + 0.723324i) q^{43} +(5.84179 + 10.1183i) q^{45} +(0.203874 + 0.117706i) q^{47} +(-2.62327 + 6.48987i) q^{49} +(0.897238 - 9.39630i) q^{51} +(-3.25266 + 3.41129i) q^{53} +(-6.85222 - 3.12930i) q^{55} +(2.07191 - 1.79532i) q^{57} +(5.56031 - 1.34892i) q^{59} +(-6.26017 + 3.22734i) q^{61} +(-5.85270 + 15.6122i) q^{63} +(-1.84435 + 4.60695i) q^{65} +(3.00837 - 15.6089i) q^{67} +(9.74173 + 10.9106i) q^{69} +(8.53411 - 9.84889i) q^{71} +(-5.86046 - 7.45218i) q^{73} +(2.94627 - 3.74648i) q^{75} +(-2.76501 - 10.3883i) q^{77} +(-5.67299 - 5.94966i) q^{79} +(-3.86202 + 11.1586i) q^{81} +(2.99479 - 6.55767i) q^{83} +(5.50542 - 1.61654i) q^{85} +(0.854117 + 0.608214i) q^{87} +(0.494689 + 10.3848i) q^{89} +(-6.74900 + 2.14504i) q^{91} +(-9.79023 + 16.9572i) q^{93} +(1.48127 + 0.763650i) q^{95} +(-6.46235 - 14.1506i) q^{97} +(-7.21383 - 24.5681i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q - 20 q^{9} + 66 q^{21} + 21 q^{23} - 8 q^{25} - 12 q^{29} - 6 q^{31} - 38 q^{35} + 44 q^{37} - 20 q^{39} - 88 q^{43} - 42 q^{47} - 74 q^{49} + 44 q^{51} - 88 q^{57} + 55 q^{63} + 77 q^{65} - 32 q^{71}+ \cdots + 242 q^{99}+O(q^{100}) $ 320 * q - 20 * q^9 + 66 * q^21 + 21 * q^23 - 8 * q^25 - 12 * q^29 - 6 * q^31 - 38 * q^35 + 44 * q^37 - 20 * q^39 - 88 * q^43 - 42 * q^47 - 74 * q^49 + 44 * q^51 - 88 * q^57 + 55 * q^63 + 77 * q^65 - 32 * q^71 - 36 * q^73 + 24 * q^75 + 105 * q^77 + 44 * q^79 - 36 * q^81 + 60 * q^85 - 96 * q^87 - 20 * q^93 - 31 * q^95 + 242 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/644\mathbb{Z}\right)^\times$.

$n$	$185$	$281$	$323$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{19}{22}\right)$	$1$

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			0
$2$		0			0
$3$	−1.39754	+	2.71086i	−0.806872	+	1.56511i	0.0180291	+	0.999837i	$0.494261\pi$
$3$	−1.39754	+	2.71086i	−0.806872	+	1.56511i	−0.824901	+	0.565277i	$0.808769\pi$
$4$		0			0
$5$	−1.84559	−	0.176232i	−0.825373	−	0.0788136i	−0.326184	−	0.945306i	$-0.605763\pi$
$5$	−1.84559	−	0.176232i	−0.825373	−	0.0788136i	−0.499189	+	0.866493i	$0.666369\pi$
$6$		0			0
$7$	−1.47931	−	2.19354i	−0.559127	−	0.829082i
$7$	−1.47931	−	2.19354i	−0.559127	−	0.829082i
$8$		0			0
$9$	−3.65545	−	5.13336i	−1.21848	−	1.71112i
$10$		0			0
$11$	3.83965	+	1.32892i	1.15770	+	0.400683i	0.837377	−	0.546626i	$-0.184088\pi$
$11$	3.83965	+	1.32892i	1.15770	+	0.400683i	0.320321	+	0.947309i	$0.396209\pi$
$12$		0			0
$13$	0.754092	−	2.56820i	0.209148	−	0.712291i	−0.786374	−	0.617751i	$-0.788044\pi$
$13$	0.754092	−	2.56820i	0.209148	−	0.712291i	0.995521	−	0.0945399i	$-0.0301380\pi$
$14$		0			0
$15$	3.05703	−	4.75684i	0.789323	−	1.22821i
$16$		0			0
$17$	−2.87318	+	1.15025i	−0.696848	+	0.278976i	−0.692918	−	0.721016i	$-0.743675\pi$
$17$	−2.87318	+	1.15025i	−0.696848	+	0.278976i	−0.00393019	+	0.999992i	$0.501251\pi$
$18$		0			0
$19$	−0.834503	−	0.334085i	−0.191448	−	0.0766442i	0.273957	−	0.961742i	$-0.411667\pi$
$19$	−0.834503	−	0.334085i	−0.191448	−	0.0766442i	−0.465406	+	0.885098i	$0.654091\pi$
$20$		0			0
$21$	8.01379	−	0.944630i	1.74875	−	0.206135i
$22$		0			0
$23$	1.71607	−	4.47829i	0.357825	−	0.933789i
$23$	1.71607	−	4.47829i	0.357825	−	0.933789i
$24$		0			0
$25$	−1.53450	−	0.295750i	−0.306900	−	0.0591501i
$26$		0			0
$27$	9.96788	−	1.43316i	1.91832	−	0.275813i
$28$		0			0
$29$	0.0489273	−	0.340297i	0.00908556	−	0.0631915i	−0.984774	−	0.173838i	$-0.944383\pi$
$29$	0.0489273	−	0.340297i	0.00908556	−	0.0631915i	0.993860	+	0.110647i	$0.0352922\pi$
$30$		0			0
$31$	6.41276	+	0.305478i	1.15177	+	0.0548654i	0.614761	−	0.788713i	$-0.289252\pi$
$31$	6.41276	+	0.305478i	1.15177	+	0.0548654i	0.537005	+	0.843579i	$0.319555\pi$
$32$		0			0
$33$	−8.96858	+	8.55152i	−1.56123	+	1.48863i
$34$		0			0
$35$	2.34363	+	4.30909i	0.396146	+	0.728368i
$36$		0			0
$37$	8.89620	−	6.33496i	1.46253	−	1.04146i	0.475712	−	0.879601i	$-0.342190\pi$
$37$	8.89620	−	6.33496i	1.46253	−	1.04146i	0.986814	−	0.161859i	$-0.0517491\pi$
$38$		0			0
$39$	5.90815	+	5.63341i	0.946062	+	0.902068i
$40$		0			0
$41$	0.0451801	−	0.0206330i	0.00705594	−	0.00322234i	−0.411884	−	0.911236i	$-0.635129\pi$
$41$	0.0451801	−	0.0206330i	0.00705594	−	0.00322234i	0.418940	+	0.908014i	$0.362402\pi$
$42$		0			0
$43$	0.464852	+	0.723324i	0.0708893	+	0.110306i	0.874888	−	0.484325i	$-0.160935\pi$
$43$	0.464852	+	0.723324i	0.0708893	+	0.110306i	−0.803999	+	0.594631i	$0.797298\pi$
$44$		0			0
$45$	5.84179	+	10.1183i	0.870843	+	1.50834i
$46$		0			0
$47$	0.203874	+	0.117706i	0.0297380	+	0.0171693i	0.514795	−	0.857313i	$-0.327868\pi$
$47$	0.203874	+	0.117706i	0.0297380	+	0.0171693i	−0.485057	+	0.874482i	$0.661201\pi$
$48$		0			0
$49$	−2.62327	+	6.48987i	−0.374753	+	0.927125i
$50$		0			0
$51$	0.897238	−	9.39630i	0.125638	−	1.31575i
$52$		0			0
$53$	−3.25266	+	3.41129i	−0.446787	+	0.468577i	−0.908156	−	0.418631i	$-0.862510\pi$
$53$	−3.25266	+	3.41129i	−0.446787	+	0.468577i	0.461369	+	0.887208i	$0.347358\pi$
$54$		0			0
$55$	−6.85222	−	3.12930i	−0.923953	−	0.421955i
$56$		0			0
$57$	2.07191	−	1.79532i	0.274431	−	0.237796i
$58$		0			0
$59$	5.56031	−	1.34892i	0.723890	−	0.175614i	0.143148	−	0.989701i	$-0.454278\pi$
$59$	5.56031	−	1.34892i	0.723890	−	0.175614i	0.580742	+	0.814087i	$0.302762\pi$
$60$		0			0
$61$	−6.26017	+	3.22734i	−0.801532	+	0.413219i	−0.809770	−	0.586747i	$-0.800408\pi$
$61$	−6.26017	+	3.22734i	−0.801532	+	0.413219i	0.00823769	+	0.999966i	$0.497378\pi$
$62$		0			0
$63$	−5.85270	+	15.6122i	−0.737370	+	1.96695i
$64$		0			0
$65$	−1.84435	+	4.60695i	−0.228763	+	0.571422i
$66$		0			0
$67$	3.00837	−	15.6089i	0.367531	−	1.90693i	−0.0509390	−	0.998702i	$-0.516221\pi$
$67$	3.00837	−	15.6089i	0.367531	−	1.90693i	0.418470	−	0.908231i	$-0.362566\pi$
$68$		0			0
$69$	9.74173	+	10.9106i	1.17277	+	1.31348i
$70$		0			0
$71$	8.53411	−	9.84889i	1.01281	−	1.16885i	0.0272342	−	0.999629i	$-0.491330\pi$
$71$	8.53411	−	9.84889i	1.01281	−	1.16885i	0.985578	−	0.169219i	$-0.0541245\pi$
$72$		0			0
$73$	−5.86046	−	7.45218i	−0.685915	−	0.872212i	0.311023	−	0.950402i	$-0.399328\pi$
$73$	−5.86046	−	7.45218i	−0.685915	−	0.872212i	−0.996938	+	0.0781903i	$0.975086\pi$
$74$		0			0
$75$	2.94627	−	3.74648i	0.340206	−	0.432607i
$76$		0			0
$77$	−2.76501	−	10.3883i	−0.315102	−	1.18386i
$78$		0			0
$79$	−5.67299	−	5.94966i	−0.638261	−	0.669389i	0.322563	−	0.946548i	$-0.395456\pi$
$79$	−5.67299	−	5.94966i	−0.638261	−	0.669389i	−0.960824	+	0.277159i	$0.910607\pi$
$80$		0			0
$81$	−3.86202	+	11.1586i	−0.429113	+	1.23984i
$82$		0			0
$83$	2.99479	−	6.55767i	0.328721	−	0.719798i	−0.671046	−	0.741416i	$-0.734155\pi$
$83$	2.99479	−	6.55767i	0.328721	−	0.719798i	0.999766	+	0.0216181i	$0.00688179\pi$
$84$		0			0
$85$	5.50542	−	1.61654i	0.597147	−	0.175338i
$86$		0			0
$87$	0.854117	+	0.608214i	0.0915710	+	0.0652074i
$88$		0			0
$89$	0.494689	+	10.3848i	0.0524369	+	1.10079i	0.859767	+	0.510686i	$0.170609\pi$
$89$	0.494689	+	10.3848i	0.0524369	+	1.10079i	−0.807330	+	0.590100i	$0.799088\pi$
$90$		0			0
$91$	−6.74900	+	2.14504i	−0.707488	+	0.224861i
$92$		0			0
$93$	−9.79023	+	16.9572i	−1.01520	+	1.75838i
$94$		0			0
$95$	1.48127	+	0.763650i	0.151975	+	0.0783488i
$96$		0			0
$97$	−6.46235	−	14.1506i	−0.656152	−	1.43677i	−0.886065	−	0.463562i	$-0.846571\pi$
$97$	−6.46235	−	14.1506i	−0.656152	−	1.43677i	0.229912	−	0.973211i	$-0.426156\pi$
$98$		0			0
$99$	−7.21383	−	24.5681i	−0.725018	−	2.46918i
$100$		0			0
$101$	−1.77973	−	18.6382i	−0.177090	−	1.85457i	−0.450635	−	0.892708i	$-0.648802\pi$
$101$	−1.77973	−	18.6382i	−0.177090	−	1.85457i	0.273545	−	0.961859i	$-0.411804\pi$
$102$		0			0
$103$	−17.8024	+	3.43112i	−1.75412	+	0.338079i	−0.962158	−	0.272493i	$-0.912152\pi$
$103$	−17.8024	+	3.43112i	−1.75412	+	0.338079i	−0.791961	+	0.610572i	$0.790940\pi$
$104$		0			0
$105$	−14.9566	+	0.331110i	−1.45962	+	0.0323130i
$106$		0			0
$107$	2.42311	+	4.70018i	0.234251	+	0.454383i	0.976435	−	0.215813i	$-0.0692402\pi$
$107$	2.42311	+	4.70018i	0.234251	+	0.454383i	−0.742184	+	0.670196i	$0.766210\pi$
$108$		0			0
$109$	−4.33911	−	10.8386i	−0.415611	−	1.03815i	−0.977500	−	0.210934i	$-0.932349\pi$
$109$	−4.33911	−	10.8386i	−0.415611	−	1.03815i	0.561889	−	0.827213i	$-0.310075\pi$
$110$		0			0
$111$	4.74033	+	32.9697i	0.449932	+	3.12935i
$112$		0			0
$113$	−2.84922	−	2.46886i	−0.268032	−	0.232251i	0.510466	−	0.859898i	$-0.329473\pi$
$113$	−2.84922	−	2.46886i	−0.268032	−	0.232251i	−0.778498	+	0.627647i	$0.784018\pi$
$114$		0			0
$115$	−3.95638	+	7.96267i	−0.368934	+	0.742523i
$116$		0			0
$117$	−15.9400	+	5.51690i	−1.47366	+	0.510038i
$118$		0			0
$119$	6.77345	+	4.60087i	0.620921	+	0.421761i
$120$		0			0
$121$	4.33030	+	3.40539i	0.393664	+	0.309581i
$122$		0			0
$123$	−0.00720789	+	0.151312i	−0.000649914	+	0.0136434i
$124$		0			0
$125$	11.6744	+	3.42790i	1.04419	+	0.306601i
$126$		0			0
$127$	−4.65401	−	5.37101i	−0.412977	−	0.476600i	0.510708	−	0.859754i	$-0.329383\pi$
$127$	−4.65401	−	5.37101i	−0.412977	−	0.476600i	−0.923685	+	0.383154i	$0.874838\pi$
$128$		0			0
$129$	−2.61048	+	0.249271i	−0.229840	+	0.0219471i
$130$		0			0
$131$	1.31639	+	0.319352i	0.115013	+	0.0279019i	0.292852	−	0.956158i	$-0.405396\pi$
$131$	1.31639	+	0.319352i	0.115013	+	0.0279019i	−0.177839	+	0.984060i	$0.556911\pi$
$132$		0			0
$133$	0.501661	+	2.32473i	0.0434995	+	0.201580i
$134$		0			0
$135$	−18.6492	+	0.888370i	−1.60507	+	0.0764587i
$136$		0			0
$137$	−1.50791	+	0.870592i	−0.128829	+	0.0743797i	−0.563030	−	0.826437i	$-0.690364\pi$
$137$	−1.50791	+	0.870592i	−0.128829	+	0.0743797i	0.434200	+	0.900816i	$0.357031\pi$
$138$		0			0
$139$			11.4078i			0.967594i	0.875180	+	0.483797i	$0.160743\pi$
$139$			11.4078i			0.967594i	−0.875180	+	0.483797i	$0.839257\pi$
$140$		0			0
$141$	−0.604008	+	0.388172i	−0.0508666	+	0.0326900i
$142$		0			0
$143$	6.30837	−	8.85887i	0.527533	−	0.740816i
$144$		0			0
$145$	−0.150271	+	0.619425i	−0.0124793	+	0.0514405i
$146$		0			0
$147$	−13.9270	−	16.1812i	−1.14868	−	1.33460i
$148$		0			0
$149$	−1.41179	−	7.32506i	−0.115658	−	0.600092i	−0.992792	−	0.119847i	$-0.961760\pi$
$149$	−1.41179	−	7.32506i	−0.115658	−	0.600092i	0.877134	−	0.480246i	$-0.159452\pi$
$150$		0			0
$151$	3.33628	+	13.7523i	0.271503	+	1.11915i	0.930291	+	0.366821i	$0.119554\pi$
$151$	3.33628	+	13.7523i	0.271503	+	1.11915i	−0.658789	+	0.752328i	$0.728931\pi$
$152$		0			0
$153$	16.4074	+	10.5444i	1.32646	+	0.852463i
$154$		0			0
$155$	−11.7815	−	1.69392i	−0.946313	−	0.136059i
$156$		0			0
$157$	1.55291	−	1.22122i	0.123936	−	0.0974640i	−0.554267	−	0.832339i	$-0.687001\pi$
$157$	1.55291	−	1.22122i	0.123936	−	0.0974640i	0.678203	+	0.734875i	$0.262759\pi$
$158$		0			0
$159$	−4.70179	−	13.5849i	−0.372876	−	1.07735i
$160$		0			0
$161$	−12.3619	+	2.86053i	−0.974257	+	0.225441i
$162$		0			0
$163$	−5.33732	−	15.4212i	−0.418051	−	1.20788i	−0.935857	−	0.352381i	$-0.885372\pi$
$163$	−5.33732	−	15.4212i	−0.418051	−	1.20788i	0.517806	−	0.855498i	$-0.326749\pi$
$164$		0			0
$165$	18.0594	−	14.2020i	1.40592	−	1.10563i
$166$		0			0
$167$	23.9241	+	3.43976i	1.85130	+	0.266177i	0.976058	−	0.217511i	$-0.0697937\pi$
$167$	23.9241	+	3.43976i	1.85130	+	0.266177i	0.875241	+	0.483687i	$0.160703\pi$
$168$		0			0
$169$	4.90929	+	3.15501i	0.377638	+	0.242693i
$170$		0			0
$171$	1.33551	+	5.50503i	0.102129	+	0.420980i
$172$		0			0
$173$	2.63094	+	13.6506i	0.200027	+	1.03784i	0.933624	+	0.358254i	$0.116628\pi$
$173$	2.63094	+	13.6506i	0.200027	+	1.03784i	−0.733597	+	0.679584i	$0.762160\pi$
$174$		0			0
$175$	1.62126	+	3.80350i	0.122556	+	0.287517i
$176$		0			0
$177$	−4.11405	+	16.9584i	−0.309231	+	1.27467i
$178$		0			0
$179$	−1.33003	+	1.86777i	−0.0994115	+	0.139604i	−0.861285	−	0.508121i	$-0.830340\pi$
$179$	−1.33003	+	1.86777i	−0.0994115	+	0.139604i	0.761874	+	0.647725i	$0.224280\pi$
$180$		0			0
$181$	−7.06707	+	4.54173i	−0.525291	+	0.337584i	−0.776262	−	0.630411i	$-0.782887\pi$
$181$	−7.06707	+	4.54173i	−0.525291	+	0.337584i	0.250971	+	0.967995i	$0.419250\pi$
$182$		0			0
$183$		−	21.4808i		−	1.58790i
$184$		0			0
$185$	−17.5352	+	10.1239i	−1.28921	+	0.744326i
$186$		0			0
$187$	−12.5606	+	0.598334i	−0.918521	+	0.0437545i
$188$		0			0
$189$	−17.8893	−	19.7449i	−1.30126	−	1.43623i
$190$		0			0
$191$	21.1263	+	5.12518i	1.52864	+	0.370845i	0.909926	−	0.414770i	$-0.136138\pi$
$191$	21.1263	+	5.12518i	1.52864	+	0.370845i	0.618716	+	0.785614i	$0.287653\pi$
$192$		0			0
$193$	−12.1588	+	1.16102i	−0.875207	+	0.0835721i	−0.522983	−	0.852343i	$-0.675181\pi$
$193$	−12.1588	+	1.16102i	−0.875207	+	0.0835721i	−0.352225	+	0.935916i	$0.614575\pi$
$194$		0			0
$195$	−9.91124	−	11.4382i	−0.709758	−	0.819105i
$196$		0			0
$197$	15.6291	+	4.58913i	1.11353	+	0.326962i	0.786215	−	0.617953i	$-0.212038\pi$
$197$	15.6291	+	4.58913i	1.11353	+	0.326962i	0.327316	+	0.944915i	$0.393856\pi$
$198$		0			0
$199$	−0.390537	+	8.19838i	−0.0276844	+	0.581168i	0.941824	+	0.336108i	$0.109111\pi$
$199$	−0.390537	+	8.19838i	−0.0276844	+	0.581168i	−0.969508	+	0.245060i	$0.921192\pi$
$200$		0			0
$201$	38.1092	+	29.9694i	2.68802	+	2.11388i
$202$		0			0
$203$	−0.818834	+	0.396081i	−0.0574709	+	0.0277994i
$204$		0			0
$205$	−0.0870201	+	0.0301179i	−0.00607775	+	0.00210353i
$206$		0			0
$207$	−29.2617	+	7.56098i	−2.03383	+	0.525524i
$208$		0			0
$209$	−2.76023	−	2.39175i	−0.190929	−	0.165441i
$210$		0			0
$211$	2.95873	+	20.5784i	0.203688	+	1.41668i	0.793221	+	0.608934i	$0.208403\pi$
$211$	2.95873	+	20.5784i	0.203688	+	1.41668i	−0.589533	+	0.807744i	$0.700688\pi$
$212$		0			0
$213$	14.7721	+	36.8990i	1.01217	+	2.52828i
$214$		0			0
$215$	−0.730454	−	1.41688i	−0.0498165	−	0.0966306i
$216$		0			0
$217$	−8.81640	−	14.5186i	−0.598496	−	0.985585i
$218$		0			0
$219$	28.3921	−	5.47212i	1.91856	−	0.369772i
$220$		0			0
$221$	0.787426	+	8.24630i	0.0529680	+	0.554706i
$222$		0			0
$223$	−2.49454	−	8.49562i	−0.167047	−	0.568909i	−0.999882	−	0.0153872i	$-0.995102\pi$
$223$	−2.49454	−	8.49562i	−0.167047	−	0.568909i	0.832835	−	0.553521i	$-0.186716\pi$
$224$		0			0
$225$	4.09109	+	8.95823i	0.272739	+	0.597215i
$226$		0			0
$227$	−17.0758	−	8.80318i	−1.13336	−	0.584288i	−0.213660	−	0.976908i	$-0.568538\pi$
$227$	−17.0758	−	8.80318i	−1.13336	−	0.584288i	−0.919701	+	0.392620i	$0.871569\pi$
$228$		0			0
$229$	3.06866	−	5.31508i	0.202783	−	0.351230i	−0.746641	−	0.665227i	$-0.768335\pi$
$229$	3.06866	−	5.31508i	0.202783	−	0.351230i	0.949424	+	0.313997i	$0.101668\pi$
$230$		0			0
$231$	32.0255	+	7.02260i	2.10712	+	0.462053i
$232$		0			0
$233$	0.829938	+	17.4226i	0.0543711	+	1.14139i	0.846968	+	0.531644i	$0.178425\pi$
$233$	0.829938	+	17.4226i	0.0543711	+	1.14139i	−0.792597	+	0.609746i	$0.791272\pi$
$234$		0			0
$235$	−0.355523	−	0.253167i	−0.0231918	−	0.0165148i
$236$		0			0
$237$	24.0569	−	7.06376i	1.56267	−	0.458840i
$238$		0			0
$239$	−12.5066	+	27.3857i	−0.808988	+	1.77144i	−0.197288	+	0.980346i	$0.563213\pi$
$239$	−12.5066	+	27.3857i	−0.808988	+	1.77144i	−0.611700	+	0.791090i	$0.709514\pi$
$240$		0			0
$241$	10.0945	−	29.1662i	0.650246	−	1.87876i	0.222220	−	0.974997i	$-0.428670\pi$
$241$	10.0945	−	29.1662i	0.650246	−	1.87876i	0.428027	−	0.903766i	$-0.359209\pi$
$242$		0			0
$243$	−4.00388	−	4.19915i	−0.256849	−	0.269376i
$244$		0			0
$245$	5.98521	−	11.5153i	0.382381	−	0.735688i
$246$		0			0
$247$	−1.48729	+	1.89124i	−0.0946339	+	0.120337i
$248$		0			0
$249$	13.5916	+	17.2831i	0.861330	+	1.09527i
$250$		0			0
$251$	10.3345	−	11.9267i	0.652311	−	0.752807i	−0.329190	−	0.944264i	$-0.606776\pi$
$251$	10.3345	−	11.9267i	0.652311	−	0.752807i	0.981501	+	0.191457i	$0.0613212\pi$
$252$		0			0
$253$	12.5404	−	14.9146i	0.788406	−	0.937671i
$254$		0			0
$255$	−3.31187	+	17.1836i	−0.207397	+	1.07608i
$256$		0			0
$257$	7.63840	−	19.0798i	0.476470	−	1.19017i	−0.474326	−	0.880349i	$-0.657308\pi$
$257$	7.63840	−	19.0798i	0.476470	−	1.19017i	0.950797	−	0.309816i	$-0.100267\pi$
$258$		0			0
$259$	−27.0563	−	10.1428i	−1.68119	−	0.630245i
$260$		0			0
$261$	−1.92571	+	0.992775i	−0.119199	+	0.0614512i
$262$		0			0
$263$	−8.66004	+	2.10090i	−0.534001	+	0.129547i	−0.493687	−	0.869640i	$-0.664351\pi$
$263$	−8.66004	+	2.10090i	−0.534001	+	0.129547i	−0.0403143	+	0.999187i	$0.512836\pi$
$264$		0			0
$265$	6.60426	−	5.72262i	0.405696	−	0.351538i
$266$		0			0
$267$	−28.8430	−	13.1722i	−1.76517	−	0.806124i
$268$		0			0
$269$	−11.9818	+	12.5662i	−0.730545	+	0.766173i	−0.979305	−	0.202392i	$-0.935129\pi$
$269$	−11.9818	+	12.5662i	−0.730545	+	0.766173i	0.248760	+	0.968565i	$0.419977\pi$
$270$		0			0
$271$	0.512718	−	5.36942i	0.0311454	−	0.326169i	−0.966450	−	0.256856i	$-0.917313\pi$
$271$	0.512718	−	5.36942i	0.0311454	−	0.326169i	0.997595	−	0.0693129i	$-0.0220807\pi$
$272$		0			0
$273$	3.61713	−	21.2934i	0.218919	−	1.28873i
$274$		0			0
$275$	−5.49891	−	3.17480i	−0.331597	−	0.191447i
$276$		0			0
$277$	0.645784	+	1.11853i	0.0388014	+	0.0672060i	0.884774	−	0.466020i	$-0.154313\pi$
$277$	0.645784	+	1.11853i	0.0388014	+	0.0672060i	−0.845973	+	0.533226i	$0.820979\pi$
$278$		0			0
$279$	−21.8734	−	34.0357i	−1.30953	−	2.03766i
$280$		0			0
$281$	−14.0197	+	6.40257i	−0.836344	+	0.381945i	−0.787088	−	0.616841i	$-0.788412\pi$
$281$	−14.0197	+	6.40257i	−0.836344	+	0.381945i	−0.0492558	+	0.998786i	$0.515685\pi$
$282$		0			0
$283$	−2.82774	−	2.69625i	−0.168092	−	0.160275i	0.601364	−	0.798975i	$-0.294624\pi$
$283$	−2.82774	−	2.69625i	−0.168092	−	0.160275i	−0.769456	+	0.638700i	$0.779473\pi$
$284$		0			0
$285$	−4.14029	+	2.94829i	−0.245250	+	0.174641i
$286$		0			0
$287$	−0.112095	−	0.0685817i	−0.00661675	−	0.00404825i
$288$		0			0
$289$	−5.37139	+	5.12161i	−0.315964	+	0.301271i
$290$		0			0
$291$	47.3916	+	2.25754i	2.77814	+	0.132339i
$292$		0			0
$293$	3.86152	−	26.8574i	0.225592	−	1.56903i	−0.490763	−	0.871293i	$-0.663282\pi$
$293$	3.86152	−	26.8574i	0.225592	−	1.56903i	0.716356	−	0.697735i	$-0.245809\pi$
$294$		0			0
$295$	−10.4998	+	1.50964i	−0.611320	+	0.0878946i
$296$		0			0
$297$	40.1777	+	7.74362i	2.33135	+	0.449330i
$298$		0			0
$299$	−10.2071	−	7.78425i	−0.590291	−	0.450175i
$300$		0			0
$301$	0.898982	−	2.08970i	0.0518165	−	0.120448i
$302$		0			0
$303$	53.0127	+	21.2231i	3.04550	+	1.21923i
$304$		0			0
$305$	12.1225	−	4.85310i	0.694130	−	0.277888i
$306$		0			0
$307$	−3.75513	+	5.84310i	−0.214317	+	0.333484i	−0.931722	−	0.363173i	$-0.881693\pi$
$307$	−3.75513	+	5.84310i	−0.214317	+	0.333484i	0.717405	+	0.696656i	$0.245330\pi$
$308$		0			0
$309$	15.5783	−	53.0548i	0.886218	−	3.01818i
$310$		0			0
$311$	−9.01569	−	3.12036i	−0.511233	−	0.176939i	0.0592591	−	0.998243i	$-0.481126\pi$
$311$	−9.01569	−	3.12036i	−0.511233	−	0.176939i	−0.570492	+	0.821303i	$0.693247\pi$
$312$		0			0
$313$	−2.09060	−	2.93584i	−0.118168	−	0.165943i	0.751255	−	0.660012i	$-0.229449\pi$
$313$	−2.09060	−	2.93584i	−0.118168	−	0.165943i	−0.869423	+	0.494068i	$0.835509\pi$
$314$		0			0
$315$	13.5531	−	27.7823i	0.763628	−	1.56536i
$316$		0			0
$317$	−22.9687	−	2.19325i	−1.29005	−	0.123185i	−0.572624	−	0.819818i	$-0.694074\pi$
$317$	−22.9687	−	2.19325i	−1.29005	−	0.123185i	−0.717427	+	0.696633i	$0.754680\pi$
$318$		0			0
$319$	0.640089	−	1.24160i	0.0358381	−	0.0695162i
$320$		0			0
$321$	−16.1279			−0.900172
$322$		0			0
$323$	2.78196			0.154792
$324$		0			0
$325$	−1.91670	+	3.71788i	−0.106319	+	0.206231i
$326$		0			0
$327$	35.4459	+	3.38468i	1.96016	+	0.187173i
$328$		0			0
$329$	−0.0433984	−	0.621330i	−0.00239263	−	0.0342550i
$330$		0			0
$331$	15.6366	+	21.9586i	0.859467	+	1.20695i	0.976863	+	0.213867i	$0.0686059\pi$
$331$	15.6366	+	21.9586i	0.859467	+	1.20695i	−0.117396	+	0.993085i	$0.537455\pi$
$332$		0			0
$333$	−65.0392	−	22.5103i	−3.56412	−	1.23356i
$334$		0			0
$335$	−8.30302	+	28.2775i	−0.453642	+	1.54496i
$336$		0			0
$337$	−17.9490	+	27.9291i	−0.977742	+	1.52140i	−0.129642	+	0.991561i	$0.541383\pi$
$337$	−17.9490	+	27.9291i	−0.977742	+	1.52140i	−0.848100	+	0.529836i	$0.822254\pi$
$338$		0			0
$339$	10.6746	−	4.27348i	0.579767	−	0.232104i
$340$		0			0
$341$	24.2168	+	9.69495i	1.31141	+	0.525011i
$342$		0			0
$343$	18.1165	−	3.84629i	0.978197	−	0.207680i
$344$		0			0
$345$	−16.0564	−	21.8534i	−0.864450	−	1.17654i
$346$		0			0
$347$	−10.6271	−	2.04820i	−0.570491	−	0.109953i	−0.104155	−	0.994561i	$-0.533214\pi$
$347$	−10.6271	−	2.04820i	−0.570491	−	0.109953i	−0.466335	+	0.884608i	$0.654426\pi$
$348$		0			0
$349$	15.1377	−	2.17647i	0.810303	−	0.116504i	0.275305	−	0.961357i	$-0.411221\pi$
$349$	15.1377	−	2.17647i	0.810303	−	0.116504i	0.534998	+	0.844853i	$0.320312\pi$
$350$		0			0
$351$	3.83604	−	26.6803i	0.204753	−	1.42409i
$352$		0			0
$353$	−22.8419	−	1.08810i	−1.21575	−	0.0579135i	−0.570120	−	0.821561i	$-0.693103\pi$
$353$	−22.8419	−	1.08810i	−1.21575	−	0.0579135i	−0.645633	+	0.763648i	$0.723407\pi$
$354$		0			0
$355$	−17.4862	+	16.6730i	−0.928069	+	0.884912i
$356$		0			0
$357$	−21.9385	+	11.9319i	−1.16111	+	0.631505i
$358$		0			0
$359$	10.5899	−	7.54103i	0.558913	−	0.398000i	−0.265396	−	0.964139i	$-0.585503\pi$
$359$	10.5899	−	7.54103i	0.558913	−	0.398000i	0.824310	+	0.566139i	$0.191563\pi$
$360$		0			0
$361$	−13.1662	−	12.5539i	−0.692956	−	0.660732i
$362$		0			0
$363$	−15.2833	+	6.97965i	−0.802166	+	0.366337i
$364$		0			0
$365$	9.50269	+	14.7865i	0.497394	+	0.773960i
$366$		0			0
$367$	−4.45159	−	7.71038i	−0.232371	−	0.402479i	0.726134	−	0.687553i	$-0.241315\pi$
$367$	−4.45159	−	7.71038i	−0.232371	−	0.402479i	−0.958505	+	0.285074i	$0.907982\pi$
$368$		0			0
$369$	−0.271070	−	0.156502i	−0.0141113	−	0.00814719i
$370$		0			0
$371$	12.2945	+	2.08849i	0.638300	+	0.108429i
$372$		0			0
$373$	−1.03843	+	10.8749i	−0.0537677	+	0.563081i	0.927946	+	0.372716i	$0.121573\pi$
$373$	−1.03843	+	10.8749i	−0.0537677	+	0.563081i	−0.981713	+	0.190365i	$0.939033\pi$
$374$		0			0
$375$	−25.6080	+	26.8569i	−1.32239	+	1.38688i
$376$		0			0
$377$	−0.837055	−	0.382270i	−0.0431105	−	0.0196879i
$378$		0			0
$379$	−3.49220	+	3.02601i	−0.179382	+	0.155436i	−0.739924	−	0.672691i	$-0.765139\pi$
$379$	−3.49220	+	3.02601i	−0.179382	+	0.155436i	0.560541	+	0.828126i	$0.310593\pi$
$380$		0			0
$381$	21.0642	−	5.11013i	1.07915	−	0.261800i
$382$		0			0
$383$	−2.11061	+	1.08809i	−0.107847	+	0.0555990i	−0.511306	−	0.859399i	$-0.670838\pi$
$383$	−2.11061	+	1.08809i	−0.107847	+	0.0555990i	0.403459	+	0.914998i	$0.367808\pi$
$384$		0			0
$385$	3.27231	+	19.6599i	0.166772	+	1.00196i
$386$		0			0
$387$	2.01384	−	5.03033i	0.102369	−	0.255706i
$388$		0			0
$389$	4.63925	−	24.0707i	0.235219	−	1.22043i	−0.651688	−	0.758487i	$-0.725939\pi$
$389$	4.63925	−	24.0707i	0.235219	−	1.22043i	0.886908	−	0.461947i	$-0.152849\pi$
$390$		0			0
$391$	0.220577	+	14.8408i	0.0111551	+	0.750534i
$392$		0			0
$393$	−2.70543	+	3.12223i	−0.136471	+	0.157496i
$394$		0			0
$395$	9.42149	+	11.9804i	0.474047	+	0.602800i
$396$		0			0
$397$	6.84032	−	8.69817i	0.343306	−	0.436549i	−0.583487	−	0.812123i	$-0.698312\pi$
$397$	6.84032	−	8.69817i	0.343306	−	0.436549i	0.926792	+	0.375574i	$0.122554\pi$
$398$		0			0
$399$	−7.00311	−	1.88899i	−0.350594	−	0.0945676i
$400$		0			0
$401$	−4.26915	−	4.47735i	−0.213191	−	0.223588i	0.608452	−	0.793591i	$-0.291791\pi$
$401$	−4.26915	−	4.47735i	−0.213191	−	0.223588i	−0.821643	+	0.570002i	$0.806942\pi$
$402$		0			0
$403$	5.62034	−	16.2389i	0.279969	−	0.808918i
$404$		0			0
$405$	9.09421	−	19.9135i	0.451895	−	0.989512i
$406$		0			0
$407$	42.5769	−	12.5017i	2.11046	−	0.619687i
$408$		0			0
$409$	22.7684	+	16.2133i	1.12583	+	0.801697i	0.982182	−	0.187932i	$-0.0601784\pi$
$409$	22.7684	+	16.2133i	1.12583	+	0.801697i	0.143644	+	0.989629i	$0.454118\pi$
$410$		0			0
$411$	−0.252681	−	5.30442i	−0.0124638	−	0.261648i
$412$		0			0
$413$	−11.1843	−	10.2013i	−0.550345	−	0.501974i
$414$		0			0
$415$	−6.68283	+	11.5750i	−0.328047	+	0.568194i
$416$		0			0
$417$	−30.9248	−	15.9428i	−1.51439	−	0.780724i
$418$		0			0
$419$	8.79756	+	19.2640i	0.429789	+	0.941106i	0.993361	+	0.115039i	$0.0366994\pi$
$419$	8.79756	+	19.2640i	0.429789	+	0.941106i	−0.563572	+	0.826067i	$0.690573\pi$
$420$		0			0
$421$	−5.62080	−	19.1427i	−0.273941	−	0.932958i	−0.975436	−	0.220283i	$-0.929302\pi$
$421$	−5.62080	−	19.1427i	−0.273941	−	0.932958i	0.701495	−	0.712675i	$-0.252516\pi$
$422$		0			0
$423$	−0.141020	−	1.47683i	−0.00685661	−	0.0718057i
$424$		0			0
$425$	4.74908	−	0.915309i	0.230364	−	0.0443990i
$426$		0			0
$427$	16.3401	+	8.95771i	0.790751	+	0.433494i
$428$		0			0
$429$	15.1989	+	29.4818i	0.733810	+	1.42339i
$430$		0			0
$431$	−1.60903	−	4.01916i	−0.0775042	−	0.193596i	0.884556	−	0.466435i	$-0.154462\pi$
$431$	−1.60903	−	4.01916i	−0.0775042	−	0.193596i	−0.962060	+	0.272839i	$0.912038\pi$
$432$		0			0
$433$	−2.50284	−	17.4076i	−0.120279	−	0.836558i	−0.957240	−	0.289295i	$-0.906579\pi$
$433$	−2.50284	−	17.4076i	−0.120279	−	0.836558i	0.836961	−	0.547262i	$-0.184330\pi$
$434$		0			0
$435$	−1.46916	−	1.27304i	−0.0704410	−	0.0610375i
$436$		0			0
$437$	−2.92819	+	3.16384i	−0.140074	+	0.151347i
$438$		0			0
$439$	33.5118	−	11.5985i	1.59943	−	0.553568i	0.625462	−	0.780255i	$-0.284911\pi$
$439$	33.5118	−	11.5985i	1.59943	−	0.553568i	0.973968	+	0.226687i	$0.0727894\pi$
$440$		0			0
$441$	42.9041	−	10.2572i	2.04305	−	0.488438i
$442$		0			0
$443$	14.5548	+	11.4461i	0.691522	+	0.543819i	0.900906	−	0.434015i	$-0.142903\pi$
$443$	14.5548	+	11.4461i	0.691522	+	0.543819i	−0.209384	+	0.977833i	$0.567146\pi$
$444$		0			0
$445$	0.917146	−	19.2533i	0.0434769	−	0.912692i
$446$		0			0
$447$	21.8302	+	6.40994i	1.03253	+	0.303180i
$448$		0			0
$449$	9.36865	+	10.8120i	0.442134	+	0.510250i	0.932452	−	0.361294i	$-0.117665\pi$
$449$	9.36865	+	10.8120i	0.442134	+	0.510250i	−0.490318	+	0.871543i	$0.663119\pi$
$450$		0			0
$451$	0.200895	−	0.0191832i	0.00945978	−	0.000903300i
$452$		0			0
$453$	−41.9432	−	10.1753i	−1.97066	−	0.478078i
$454$		0			0
$455$	12.8339	−	2.76947i	0.601663	−	0.129835i
$456$		0			0
$457$	5.93822	−	0.282872i	0.277778	−	0.0132322i	0.0917693	−	0.995780i	$-0.470748\pi$
$457$	5.93822	−	0.282872i	0.277778	−	0.0132322i	0.186009	+	0.982548i	$0.440445\pi$
$458$		0			0
$459$	−26.9910	+	15.5833i	−1.25983	+	0.727365i
$460$		0			0
$461$			13.0169i			0.606259i	0.952949	+	0.303129i	$0.0980314\pi$
$461$			13.0169i			0.606259i	−0.952949	+	0.303129i	$0.901969\pi$
$462$		0			0
$463$	2.83339	−	1.82091i	0.131679	−	0.0846248i	−0.473143	−	0.880986i	$-0.656881\pi$
$463$	2.83339	−	1.82091i	0.131679	−	0.0846248i	0.604822	+	0.796361i	$0.293244\pi$
$464$		0			0
$465$	21.0571	−	29.5706i	0.976502	−	1.37130i
$466$		0			0
$467$	−7.89413	+	32.5400i	−0.365297	+	1.50577i	0.431827	+	0.901957i	$0.357869\pi$
$467$	−7.89413	+	32.5400i	−0.365297	+	1.50577i	−0.797123	+	0.603816i	$0.793646\pi$
$468$		0			0
$469$	−38.6892	+	16.4915i	−1.78650	+	0.761505i
$470$		0			0
$471$	1.14030	+	5.91642i	0.0525421	+	0.272614i
$472$		0			0
$473$	0.823633	+	3.39506i	0.0378707	+	0.156105i
$474$		0			0
$475$	1.18174	+	0.759457i	0.0542219	+	0.0348463i
$476$		0			0
$477$	29.4013	+	4.22727i	1.34619	+	0.193553i
$478$		0			0
$479$	−17.7241	+	13.9384i	−0.809835	+	0.636861i	−0.934750	−	0.355306i	$-0.884377\pi$
$479$	−17.7241	+	13.9384i	−0.809835	+	0.636861i	0.124915	+	0.992167i	$0.460134\pi$
$480$		0			0
$481$	−9.56089	−	27.6244i	−0.435939	−	1.25956i
$482$		0			0
$483$	9.52187	−	37.5091i	0.433260	−	1.70673i
$484$		0			0
$485$	9.43306	+	27.2550i	0.428333	+	1.23759i
$486$		0			0
$487$	−3.47348	+	2.73158i	−0.157398	+	0.123779i	−0.693752	−	0.720214i	$-0.744044\pi$
$487$	−3.47348	+	2.73158i	−0.157398	+	0.123779i	0.536354	+	0.843993i	$0.319801\pi$
$488$		0			0
$489$	49.2637	+	7.08305i	2.22778	+	0.320307i
$490$		0			0
$491$	35.3730	+	22.7329i	1.59636	+	1.02592i	0.968958	+	0.247227i	$0.0795192\pi$
$491$	35.3730	+	22.7329i	1.59636	+	1.02592i	0.627405	+	0.778693i	$0.284117\pi$
$492$		0			0
$493$	0.250848	+	1.03401i	0.0112976	+	0.0465695i
$494$		0			0
$495$	8.98409	+	46.6139i	0.403805	+	2.09514i
$496$		0			0
$497$	−34.2286	−	4.15037i	−1.53536	−	0.186169i
$498$		0			0
$499$	5.06055	−	20.8599i	0.226541	−	0.933816i	−0.739029	−	0.673674i	$-0.764715\pi$
$499$	5.06055	−	20.8599i	0.226541	−	0.933816i	0.965570	−	0.260142i	$-0.0837695\pi$
$500$		0			0
$501$	−42.7596	+	60.0475i	−1.91036	+	2.68272i
$502$		0			0
$503$	−19.8386	+	12.7495i	−0.884558	+	0.568471i	−0.902173	−	0.431374i	$-0.858029\pi$
$503$	−19.8386	+	12.7495i	−0.884558	+	0.568471i	0.0176155	+	0.999845i	$0.494393\pi$
$504$		0			0
$505$			34.7121i			1.54467i
$506$		0			0
$507$	−15.4137	+	8.89912i	−0.684547	+	0.395224i
$508$		0			0
$509$	31.7811	−	1.51392i	1.40867	−	0.0671034i	0.670597	−	0.741821i	$-0.266038\pi$
$509$	31.7811	−	1.51392i	1.40867	−	0.0671034i	0.738076	+	0.674718i	$0.235735\pi$
$510$		0			0
$511$	−7.67724	+	23.8793i	−0.339621	+	1.05636i
$512$		0			0
$513$	−8.79702	−	2.13413i	−0.388398	−	0.0942243i
$514$		0			0
$515$	33.4605	−	3.19509i	1.47445	−	0.140793i
$516$		0			0
$517$	0.626381	+	0.722882i	0.0275482	+	0.0317923i
$518$		0			0
$519$	−40.6818	−	11.9452i	−1.78573	−	0.524338i
$520$		0			0
$521$	1.90205	−	39.9290i	0.0833305	−	1.74932i	−0.440728	−	0.897641i	$-0.645280\pi$
$521$	1.90205	−	39.9290i	0.0833305	−	1.74932i	0.524058	−	0.851682i	$-0.324417\pi$
$522$		0			0
$523$	−6.09934	−	4.79657i	−0.266705	−	0.209739i	0.475846	−	0.879529i	$-0.342142\pi$
$523$	−6.09934	−	4.79657i	−0.266705	−	0.209739i	−0.742551	+	0.669789i	$0.766384\pi$
$524$		0			0
$525$	−12.5765	−	0.920548i	−0.548884	−	0.0401760i
$526$		0			0
$527$	−18.7764	+	6.49857i	−0.817913	+	0.283082i
$528$		0			0
$529$	−17.1102	−	15.3701i	−0.743923	−	0.668265i
$530$		0			0
$531$	−27.2499	−	23.6121i	−1.18254	−	1.02468i
$532$		0			0
$533$	−0.0189199	−	0.131591i	−0.000819512	−	0.00569983i
$534$		0			0
$535$	−3.64374	−	9.10163i	−0.157533	−	0.393498i
$536$		0			0
$537$	−3.20448	−	6.21583i	−0.138284	−	0.268233i
$538$		0			0
$539$	−18.6969	+	21.4327i	−0.805334	+	0.923173i
$540$		0			0
$541$	−33.1894	+	6.39674i	−1.42692	+	0.275017i	−0.843491	−	0.537144i	$-0.819503\pi$
$541$	−33.1894	+	6.39674i	−1.42692	+	0.275017i	−0.583434	+	0.812161i	$0.698291\pi$
$542$		0			0
$543$	−2.43544	−	25.5051i	−0.104515	−	1.09453i
$544$		0			0
$545$	6.09811	+	20.7683i	0.261214	+	0.889614i
$546$		0			0
$547$	0.105008	+	0.229936i	0.00448984	+	0.00983137i	0.911864	−	0.410493i	$-0.134643\pi$
$547$	0.105008	+	0.229936i	0.00448984	+	0.00983137i	−0.907374	+	0.420325i	$0.861916\pi$
$548$		0			0
$549$	39.4508	+	20.3383i	1.68372	+	0.868017i
$550$		0			0
$551$	−0.154518	+	0.267633i	−0.00658268	+	0.0114015i
$552$		0			0
$553$	−4.65872	+	21.2454i	−0.198109	+	0.903445i
$554$		0			0
$555$	−2.93837	−	61.6840i	−0.124727	−	2.61834i
$556$		0			0
$557$	28.9581	+	20.6210i	1.22699	+	0.873739i	0.995088	−	0.0989990i	$-0.0315641\pi$
$557$	28.9581	+	20.6210i	1.22699	+	0.873739i	0.231907	+	0.972738i	$0.425503\pi$
$558$		0			0
$559$	2.20818	−	0.648382i	0.0933963	−	0.0274236i
$560$		0			0
$561$	15.9320	−	34.8861i	0.672648	−	1.47289i
$562$		0			0
$563$	0.373061	−	1.07789i	0.0157226	−	0.0454276i	−0.936866	−	0.349687i	$-0.886288\pi$
$563$	0.373061	−	1.07789i	0.0157226	−	0.0454276i	0.952589	+	0.304260i	$0.0984091\pi$
$564$		0			0
$565$	4.82340	+	5.05864i	0.202922	+	0.212818i
$566$		0			0
$567$	30.1900	−	8.03550i	1.26786	−	0.337459i
$568$		0			0
$569$	0.962005	−	1.22329i	0.0403294	−	0.0512830i	−0.765470	−	0.643471i	$-0.777494\pi$
$569$	0.962005	−	1.22329i	0.0403294	−	0.0512830i	0.805799	+	0.592189i	$0.201736\pi$
$570$		0			0
$571$	6.98267	+	8.87919i	0.292216	+	0.371582i	0.909889	−	0.414853i	$-0.136167\pi$
$571$	6.98267	+	8.87919i	0.292216	+	0.371582i	−0.617673	+	0.786435i	$0.711924\pi$
$572$		0			0
$573$	−43.4185	+	50.1076i	−1.81383	+	2.09328i
$574$		0			0
$575$	−3.95776	+	6.36441i	−0.165050	+	0.265414i
$576$		0			0
$577$	−2.17962	+	11.3090i	−0.0907389	+	0.470798i	0.907926	+	0.419132i	$0.137665\pi$
$577$	−2.17962	+	11.3090i	−0.0907389	+	0.470798i	−0.998664	+	0.0516665i	$0.983547\pi$
$578$		0			0
$579$	13.8450	−	34.5833i	0.575380	−	1.43723i
$580$		0			0
$581$	−18.8148	+	3.13164i	−0.780568	+	0.129922i
$582$		0			0
$583$	−17.0224	+	8.77565i	−0.704995	+	0.363450i
$584$		0			0
$585$	30.3910	−	7.37279i	1.25651	−	0.304827i
$586$		0			0
$587$	28.5271	−	24.7189i	1.17744	−	1.02026i	0.178098	−	0.984013i	$-0.443005\pi$
$587$	28.5271	−	24.7189i	1.17744	−	1.02026i	0.999343	−	0.0362460i	$-0.0115400\pi$
$588$		0			0
$589$	−5.24941	−	2.39733i	−0.216298	−	0.0987801i
$590$		0			0
$591$	−34.2829	+	35.9549i	−1.41021	+	1.47899i
$592$		0			0
$593$	0.782478	−	8.19448i	0.0321325	−	0.336507i	−0.965084	−	0.261942i	$-0.915637\pi$
$593$	0.782478	−	8.19448i	0.0321325	−	0.336507i	0.997216	−	0.0745650i	$-0.0237568\pi$
$594$		0			0
$595$	−11.6902	−	9.68502i	−0.479251	−	0.397047i
$596$		0			0
$597$	−21.6788	−	12.5163i	−0.887256	−	0.512257i
$598$		0			0
$599$	−12.7957	−	22.1629i	−0.522820	−	0.905551i	−0.999647	−	0.0265539i	$-0.991547\pi$
$599$	−12.7957	−	22.1629i	−0.522820	−	0.905551i	0.476827	−	0.878997i	$-0.341787\pi$
$600$		0			0
$601$	−23.9256	−	37.2289i	−0.975944	−	1.51860i	−0.850149	−	0.526542i	$-0.823488\pi$
$601$	−23.9256	−	37.2289i	−0.975944	−	1.51860i	−0.125795	−	0.992056i	$-0.540148\pi$
$602$		0			0
$603$	−91.1231	+	41.6145i	−3.71082	+	1.69467i
$604$		0			0
$605$	−7.39182	−	7.04809i	−0.300520	−	0.286546i
$606$		0			0
$607$	−17.8402	+	12.7040i	−0.724113	+	0.515638i	−0.881667	−	0.471872i	$-0.843578\pi$
$607$	−17.8402	+	12.7040i	−0.724113	+	0.515638i	0.157554	+	0.987510i	$0.449639\pi$
$608$		0			0
$609$	0.0706384	−	2.77328i	0.00286241	−	0.112379i
$610$		0			0
$611$	0.456034	−	0.434827i	0.0184491	−	0.0175912i
$612$		0			0
$613$	39.9370	+	1.90244i	1.61304	+	0.0768386i	0.834592	−	0.550869i	$-0.185703\pi$
$613$	39.9370	+	1.90244i	1.61304	+	0.0768386i	0.778449	+	0.627707i	$0.216007\pi$
$614$		0			0
$615$	0.0399689	−	0.277990i	0.00161170	−	0.0112096i
$616$		0			0
$617$	−42.5996	+	6.12490i	−1.71500	+	0.246579i	−0.928584	−	0.371123i	$-0.878973\pi$
$617$	−42.5996	+	6.12490i	−1.71500	+	0.246579i	−0.786412	+	0.617702i	$0.788064\pi$
$618$		0			0
$619$	2.98618	+	0.575538i	0.120025	+	0.0231328i	0.248910	−	0.968527i	$-0.419928\pi$
$619$	2.98618	+	0.575538i	0.120025	+	0.0231328i	−0.128885	+	0.991660i	$0.541140\pi$
$620$		0			0
$621$	10.6874	−	47.0985i	0.428871	−	1.89000i
$622$		0			0
$623$	22.0477	−	16.4475i	0.883323	−	0.658954i
$624$		0			0
$625$	−13.6880	−	5.47985i	−0.547520	−	0.219194i
$626$		0			0
$627$	10.3412	−	4.14001i	0.412989	−	0.165336i
$628$		0			0
$629$	−18.2736	+	28.4343i	−0.728617	+	1.13375i
$630$		0			0
$631$	9.31767	−	31.7331i	0.370930	−	1.26327i	−0.536796	−	0.843712i	$-0.680366\pi$
$631$	9.31767	−	31.7331i	0.370930	−	1.26327i	0.907727	−	0.419561i	$-0.137816\pi$
$632$		0			0
$633$	−59.9202	−	20.7386i	−2.38161	−	0.824285i
$634$		0			0
$635$	7.64285	+	10.7329i	0.303297	+	0.425921i
$636$		0			0
$637$	14.6891	+	11.6311i	0.582004	+	0.460839i
$638$		0			0
$639$	−81.7538	−	7.80655i	−3.23413	−	0.308822i
$640$		0			0
$641$	10.9825	−	21.3032i	0.433784	−	0.841424i	−0.566070	−	0.824357i	$-0.691537\pi$
$641$	10.9825	−	21.3032i	0.433784	−	0.841424i	0.999854	−	0.0170671i	$-0.00543288\pi$
$642$		0			0
$643$	−3.03496			−0.119687			−0.0598435	−	0.998208i	$-0.519060\pi$
$643$	−3.03496			−0.119687			−0.0598435	+	0.998208i	$0.519060\pi$
$644$		0			0
$645$	4.86181			0.191433
$646$		0			0
$647$	−0.271767	+	0.527155i	−0.0106843	+	0.0207246i	−0.894117	−	0.447833i	$-0.852196\pi$
$647$	−0.271767	+	0.527155i	−0.0106843	+	0.0207246i	0.883433	+	0.468558i	$0.155226\pi$
$648$		0			0
$649$	23.1422	+	2.20981i	0.908411	+	0.0867428i
$650$		0			0
$651$	51.6791	−	3.60966i	2.02546	−	0.141474i
$652$		0			0
$653$	−13.5582	−	19.0398i	−0.530572	−	0.745084i	0.459108	−	0.888381i	$-0.348169\pi$
$653$	−13.5582	−	19.0398i	−0.530572	−	0.745084i	−0.989680	+	0.143296i	$0.954230\pi$
$654$		0			0
$655$	−2.37323	−	0.821384i	−0.0927298	−	0.0320941i
$656$		0			0
$657$	−16.8321	+	57.3249i	−0.656683	+	2.23646i
$658$		0			0
$659$	12.1075	−	18.8396i	0.471641	−	0.733887i	−0.521187	−	0.853443i	$-0.674511\pi$
$659$	12.1075	−	18.8396i	0.471641	−	0.733887i	0.992828	+	0.119555i	$0.0381469\pi$
$660$		0			0
$661$	−20.0749	+	8.03676i	−0.780822	+	0.312594i	−0.727612	−	0.685989i	$-0.759370\pi$
$661$	−20.0749	+	8.03676i	−0.780822	+	0.312594i	−0.0532103	+	0.998583i	$0.516945\pi$
$662$		0			0
$663$	−23.4550	−	9.38996i	−0.910917	−	0.364676i
$664$		0			0
$665$	−0.516167	−	4.37891i	−0.0200161	−	0.169807i
$666$		0			0
$667$	−1.43999	−	0.803082i	−0.0557565	−	0.0310955i
$668$		0			0
$669$	26.5166	+	5.11066i	1.02519	+	0.197590i
$670$		0			0
$671$	−28.3257	+	4.07262i	−1.09350	+	0.157222i
$672$		0			0
$673$	4.41024	−	30.6739i	0.170002	−	1.18239i	−0.708872	−	0.705337i	$-0.750796\pi$
$673$	4.41024	−	30.6739i	0.170002	−	1.18239i	0.878874	−	0.477054i	$-0.158295\pi$
$674$		0			0
$675$	−15.7196	−	0.748815i	−0.605046	−	0.0288219i
$676$		0			0
$677$	−8.25623	+	7.87230i	−0.317313	+	0.302557i	−0.831950	−	0.554851i	$-0.812775\pi$
$677$	−8.25623	+	7.87230i	−0.317313	+	0.302557i	0.514637	+	0.857408i	$0.327927\pi$
$678$		0			0
$679$	−21.4801	+	35.1086i	−0.824329	+	1.34734i
$680$		0			0
$681$	47.7283	−	33.9872i	1.82895	−	1.30239i
$682$		0			0
$683$	33.6491	+	32.0844i	1.28755	+	1.22768i	0.959072	+	0.283163i	$0.0913838\pi$
$683$	33.6491	+	32.0844i	1.28755	+	1.22768i	0.328477	+	0.944512i	$0.393465\pi$
$684$		0			0
$685$	2.93641	−	1.34101i	0.112194	−	0.0512375i
$686$		0			0
$687$	10.1198	+	15.7468i	0.386095	+	0.600776i
$688$		0			0
$689$	6.30808	+	10.9259i	0.240319	+	0.416244i
$690$		0			0
$691$	−20.9079	−	12.0712i	−0.795374	−	0.459209i	0.0464770	−	0.998919i	$-0.485201\pi$
$691$	−20.9079	−	12.0712i	−0.795374	−	0.459209i	−0.841851	+	0.539710i	$0.818534\pi$
$692$		0			0
$693$	−43.2196	+	52.1677i	−1.64178	+	1.98169i
$694$		0			0
$695$	2.01042	−	21.0540i	0.0762595	−	0.798625i
$696$		0			0
$697$	−0.106077	+	0.111251i	−0.00401796	+	0.00421392i
$698$		0			0
$699$	−48.3899	−	22.0989i	−1.83028	−	0.835859i
$700$		0			0
$701$	−6.54003	+	5.66697i	−0.247014	+	0.214038i	−0.769564	−	0.638570i	$-0.779526\pi$
$701$	−6.54003	+	5.66697i	−0.247014	+	0.214038i	0.522550	+	0.852609i	$0.324981\pi$
$702$		0			0
$703$	−9.54031	+	2.31446i	−0.359820	+	0.0872913i
$704$		0			0
$705$	1.18316	−	0.609961i	0.0445604	−	0.0229725i
$706$		0			0
$707$	−38.2509	+	31.4756i	−1.43857	+	1.18376i
$708$		0			0
$709$	3.08674	−	7.71030i	0.115925	−	0.289566i	−0.859046	−	0.511898i	$-0.828943\pi$
$709$	3.08674	−	7.71030i	0.115925	−	0.289566i	0.974971	+	0.222332i	$0.0713668\pi$
$710$		0			0
$711$	−9.80442	+	50.8702i	−0.367694	+	1.90778i
$712$		0			0
$713$	12.3728	−	28.1940i	0.463363	−	1.05587i
$714$		0			0
$715$	−13.2039	+	15.2381i	−0.493798	+	0.569873i
$716$		0			0
$717$	−56.7602	−	72.1765i	−2.11975	−	2.69548i
$718$		0			0
$719$	−22.1494	+	28.1653i	−0.826035	+	1.05039i	0.171833	+	0.985126i	$0.445031\pi$
$719$	−22.1494	+	28.1653i	−0.826035	+	1.05039i	−0.997868	+	0.0652629i	$0.979211\pi$
$720$		0			0
$721$	33.8616	+	33.9746i	1.26107	+	1.26528i
$722$		0			0
$723$	64.9580	+	68.1259i	2.41581	+	2.53363i
$724$		0			0
$725$	−0.175722	+	0.507714i	−0.00652614	+	0.0188560i
$726$		0			0
$727$	11.6687	−	25.5510i	0.432769	−	0.947633i	−0.560100	−	0.828425i	$-0.689237\pi$
$727$	11.6687	−	25.5510i	0.432769	−	0.947633i	0.992869	−	0.119208i	$-0.0380354\pi$
$728$		0			0
$729$	−17.0102	+	4.99465i	−0.630007	+	0.184987i
$730$		0			0
$731$	−2.16761	−	1.54355i	−0.0801718	−	0.0570901i
$732$		0			0
$733$	0.411419	+	8.63675i	0.0151961	+	0.319005i	0.993648	+	0.112531i	$0.0358959\pi$
$733$	0.411419	+	8.63675i	0.0151961	+	0.319005i	−0.978452	+	0.206474i	$0.933801\pi$
$734$		0			0
$735$	22.8518	+	32.3182i	0.842903	+	1.19208i
$736$		0			0
$737$	32.2940	−	55.9349i	1.18957	−	2.06039i
$738$		0			0
$739$	12.4357	+	6.41105i	0.457455	+	0.235834i	0.671522	−	0.740985i	$-0.265641\pi$
$739$	12.4357	+	6.41105i	0.457455	+	0.235834i	−0.214067	+	0.976819i	$0.568671\pi$
$740$		0			0
$741$	−3.04833	−	6.67492i	−0.111983	−	0.245209i
$742$		0			0
$743$	−3.67874	−	12.5286i	−0.134960	−	0.459631i	0.864084	−	0.503347i	$-0.167898\pi$
$743$	−3.67874	−	12.5286i	−0.134960	−	0.459631i	−0.999044	+	0.0437166i	$0.986080\pi$
$744$		0			0
$745$	1.31467	+	13.7679i	0.0481658	+	0.504416i
$746$		0			0
$747$	−44.6102	+	8.59790i	−1.63220	+	0.314581i
$748$		0			0
$749$	6.72551	−	12.2682i	0.245745	−	0.448271i
$750$		0			0
$751$	−1.63556	−	3.17254i	−0.0596824	−	0.115768i	0.857107	−	0.515138i	$-0.172259\pi$
$751$	−1.63556	−	3.17254i	−0.0596824	−	0.115768i	−0.916790	+	0.399370i	$0.869229\pi$
$752$		0			0
$753$	17.8886	+	44.6836i	0.651897	+	1.62836i
$754$		0			0
$755$	−3.73380	−	25.9691i	−0.135887	−	0.945114i
$756$		0			0
$757$	26.2936	+	22.7836i	0.955658	+	0.828082i	0.985187	−	0.171482i	$-0.0548554\pi$
$757$	26.2936	+	22.7836i	0.955658	+	0.828082i	−0.0295295	+	0.999564i	$0.509401\pi$
$758$		0			0
$759$	22.9055	+	54.8389i	0.831418	+	1.99053i
$760$		0			0
$761$	−8.49374	+	2.93971i	−0.307898	+	0.106565i	−0.476648	−	0.879094i	$-0.658148\pi$
$761$	−8.49374	+	2.93971i	−0.307898	+	0.106565i	0.168750	+	0.985659i	$0.446027\pi$
$762$		0			0
$763$	−17.3560	+	25.5517i	−0.628329	+	0.925032i
$764$		0			0
$765$	−28.4230	−	22.3521i	−1.02764	−	0.808143i
$766$		0			0
$767$	0.728695	−	15.2972i	0.0263117	−	0.552350i
$768$		0			0
$769$	3.42687	+	1.00622i	0.123576	+	0.0362853i	0.342936	−	0.939359i	$-0.388579\pi$
$769$	3.42687	+	1.00622i	0.123576	+	0.0362853i	−0.219360	+	0.975644i	$0.570397\pi$
$770$		0			0
$771$	41.0476	+	47.3715i	1.47829	+	1.70604i
$772$		0			0
$773$	9.25746	−	0.883981i	0.332968	−	0.0317946i	0.0727666	−	0.997349i	$-0.476817\pi$
$773$	9.25746	−	0.883981i	0.332968	−	0.0317946i	0.260201	+	0.965554i	$0.416211\pi$
$774$		0			0
$775$	−9.75003	−	2.36533i	−0.350232	−	0.0849653i
$776$		0			0
$777$	65.3081	−	59.1706i	2.34291	−	2.12273i
$778$		0			0
$779$	−0.0445961	+	0.00212437i	−0.00159782	+	7.61135e-5i
$780$		0			0
$781$	45.8563	−	26.4752i	1.64087	−	0.947356i
$782$		0			0
$783$		−	3.46216i		−	0.123727i
$784$		0			0
$785$	−3.08125	+	1.98020i	−0.109975	+	0.0706764i
$786$		0			0
$787$	21.2129	−	29.7894i	0.756159	−	1.06188i	−0.239690	−	0.970850i	$-0.577046\pi$
$787$	21.2129	−	29.7894i	0.756159	−	1.06188i	0.995848	−	0.0910269i	$-0.0290149\pi$
$788$		0			0
$789$	6.40754	−	26.4122i	0.228115	−	0.940301i
$790$		0			0
$791$	−1.20067	+	9.90211i	−0.0426911	+	0.352079i
$792$		0			0
$793$	3.56772	+	18.5111i	0.126693	+	0.657348i
$794$		0			0
$795$	6.28347	+	25.9008i	0.222852	+	0.918607i
$796$		0			0
$797$	21.2193	+	13.6368i	0.751627	+	0.483041i	0.859508	−	0.511123i	$-0.170770\pi$
$797$	21.2193	+	13.6368i	0.751627	+	0.483041i	−0.107881	+	0.994164i	$0.534407\pi$
$798$		0			0
$799$	−0.721157	−	0.103687i	−0.0255127	−	0.00366817i
$800$		0			0
$801$	51.5005	−	40.5005i	1.81968	−	1.43101i
$802$		0			0
$803$	−12.5988	−	36.4018i	−0.444602	−	1.28459i
$804$		0			0
$805$	23.3192	−	3.10078i	0.821893	−	0.109288i
$806$		0			0
$807$	−17.3200	−	50.0428i	−0.609692	−	1.76159i
$808$		0			0
$809$	−6.72433	+	5.28807i	−0.236415	+	0.185919i	−0.729337	−	0.684155i	$-0.760171\pi$
$809$	−6.72433	+	5.28807i	−0.236415	+	0.185919i	0.492922	+	0.870074i	$0.335929\pi$
$810$		0			0
$811$	34.6922	+	4.98799i	1.21821	+	0.175152i	0.721282	−	0.692641i	$-0.243553\pi$
$811$	34.6922	+	4.98799i	1.21821	+	0.175152i	0.496926	+	0.867793i	$0.334462\pi$
$812$		0			0
$813$	13.8392	+	8.89391i	0.485362	+	0.311923i
$814$		0			0
$815$	7.13279	+	29.4018i	0.249851	+	1.02990i
$816$		0			0
$817$	−0.146269	−	0.758916i	−0.00511731	−	0.0265511i
$818$		0			0
$819$	35.6819	+	26.8040i	1.24683	+	0.936606i
$820$		0			0
$821$	−2.30797	+	9.51358i	−0.0805487	+	0.332026i	−0.997801	−	0.0662804i	$-0.978887\pi$
$821$	−2.30797	+	9.51358i	−0.0805487	+	0.332026i	0.917252	+	0.398307i	$0.130402\pi$
$822$		0			0
$823$	−0.600931	+	0.843890i	−0.0209471	+	0.0294162i	−0.824917	−	0.565254i	$-0.808778\pi$
$823$	−0.600931	+	0.843890i	−0.0209471	+	0.0294162i	0.803970	+	0.594670i	$0.202717\pi$
$824$		0			0
$825$	16.2914	−	10.4698i	0.567193	−	0.364513i
$826$		0			0
$827$			42.5045i			1.47802i	0.673692	+	0.739012i	$0.264708\pi$
$827$			42.5045i			1.47802i	−0.673692	+	0.739012i	$0.735292\pi$
$828$		0			0
$829$	13.3676	−	7.71777i	0.464275	−	0.268049i	−0.249565	−	0.968358i	$-0.580288\pi$
$829$	13.3676	−	7.71777i	0.464275	−	0.268049i	0.713840	+	0.700309i	$0.246954\pi$
$830$		0			0
$831$	−3.93469	+	0.187432i	−0.136493	+	0.00650196i
$832$		0			0
$833$	0.0721667	−	21.6640i	0.00250043	−	0.750612i
$834$		0			0
$835$	−43.5478	−	10.5646i	−1.50703	−	0.365602i
$836$		0			0
$837$	64.3595	−	6.14558i	2.22459	−	0.212422i
$838$		0			0
$839$	−23.3595	−	26.9583i	−0.806459	−	0.930704i	0.192258	−	0.981344i	$-0.438419\pi$
$839$	−23.3595	−	26.9583i	−0.806459	−	0.930704i	−0.998717	+	0.0506409i	$0.983874\pi$
$840$		0			0
$841$	27.7119	+	8.13694i	0.955582	+	0.280584i
$842$		0			0
$843$	2.23666	−	46.9532i	0.0770346	−	1.61715i
$844$		0			0
$845$	−8.50452	−	6.68803i	−0.292564	−	0.230075i
$846$		0			0
$847$	1.06400	−	14.5363i	0.0365594	−	0.499475i
$848$		0			0
$849$	11.2610	−	3.89748i	0.386478	−	0.133761i
$850$		0			0
$851$	−13.1033	−	50.7110i	−0.449176	−	1.73835i
$852$		0			0
$853$	5.85326	+	5.07188i	0.200412	+	0.173658i	0.749285	−	0.662248i	$-0.230397\pi$
$853$	5.85326	+	5.07188i	0.200412	+	0.173658i	−0.548873	+	0.835906i	$0.684943\pi$
$854$		0			0
$855$	−1.49463	−	10.3954i	−0.0511153	−	0.355515i
$856$		0			0
$857$	−0.739235	−	1.84652i	−0.0252518	−	0.0630759i	0.915206	−	0.402986i	$-0.132028\pi$
$857$	−0.739235	−	1.84652i	−0.0252518	−	0.0630759i	−0.940458	+	0.339910i	$0.889603\pi$
$858$		0			0
$859$	−8.33309	−	16.1639i	−0.284321	−	0.551506i	0.702818	−	0.711370i	$-0.251925\pi$
$859$	−8.33309	−	16.1639i	−0.284321	−	0.551506i	−0.987139	+	0.159863i	$0.948895\pi$
$860$		0			0
$861$	0.342573	−	0.208027i	0.0116749	−	0.00708955i
$862$		0			0
$863$	18.7078	−	3.60563i	0.636821	−	0.122737i	0.139386	−	0.990238i	$-0.455487\pi$
$863$	18.7078	−	3.60563i	0.636821	−	0.122737i	0.497435	+	0.867501i	$0.334275\pi$
$864$		0			0
$865$	−2.44996	−	25.6571i	−0.0833011	−	0.872368i
$866$		0			0
$867$	−6.37720	−	21.7187i	−0.216581	−	0.737607i
$868$		0			0
$869$	−13.8757	−	30.3835i	−0.470701	−	1.03069i
$870$		0			0
$871$	−37.8183	−	19.4967i	−1.28142	−	0.660619i
$872$		0			0
$873$	−49.0172	+	84.9002i	−1.65898	+	2.87344i
$874$		0			0
$875$	−9.75077	−	30.6792i	−0.329636	−	1.03715i
$876$		0			0
$877$	0.579244	+	12.1598i	0.0195597	+	0.410608i	0.987321	+	0.158738i	$0.0507426\pi$
$877$	0.579244	+	12.1598i	0.0195597	+	0.410608i	−0.967761	+	0.251870i	$0.918954\pi$
$878$		0			0
$879$	67.4100	+	48.0025i	2.27368	+	1.61908i
$880$		0			0
$881$	4.15953	−	1.22135i	0.140138	−	0.0411483i	−0.210911	−	0.977505i	$-0.567643\pi$
$881$	4.15953	−	1.22135i	0.140138	−	0.0411483i	0.351049	+	0.936357i	$0.385825\pi$
$882$		0			0
$883$	−6.83203	+	14.9600i	−0.229916	+	0.503446i	−0.989067	−	0.147469i	$-0.952887\pi$
$883$	−6.83203	+	14.9600i	−0.229916	+	0.503446i	0.759151	+	0.650915i	$0.225615\pi$
$884$		0			0
$885$	10.5815	−	30.5732i	0.355692	−	1.02771i
$886$		0			0
$887$	23.0545	+	24.1789i	0.774095	+	0.811848i	0.986228	−	0.165393i	$-0.0528893\pi$
$887$	23.0545	+	24.1789i	0.774095	+	0.811848i	−0.212132	+	0.977241i	$0.568041\pi$
$888$		0			0
$889$	−4.89682	+	18.1542i	−0.164234	+	0.608872i
$890$		0			0
$891$	−29.6576	+	37.7127i	−0.993567	+	1.26342i
$892$		0			0
$893$	−0.130809	−	0.166337i	−0.00437736	−	0.00556627i
$894$		0			0
$895$	2.78386	−	3.21275i	0.0930542	−	0.107390i
$896$		0			0
$897$	35.3669	−	16.7911i	1.18087	−	0.560639i
$898$		0			0
$899$	0.417712	−	2.16730i	0.0139315	−	0.0722833i
$900$		0			0
$901$	5.42165	−	13.5426i	0.180621	−	0.451170i
$902$		0			0
$903$	4.40850	+	5.35745i	0.146706	+	0.178285i
$904$		0			0
$905$	13.8433	−	7.13672i	0.460167	−	0.237233i
$906$		0			0
$907$	30.1051	−	7.30341i	0.999622	−	0.242506i	0.297623	−	0.954683i	$-0.403806\pi$
$907$	30.1051	−	7.30341i	0.999622	−	0.242506i	0.701999	+	0.712178i	$0.252291\pi$
$908$		0			0
$909$	−89.1707	+	77.2668i	−2.95760	+	2.56278i
$910$		0			0
$911$	27.0362	+	12.3470i	0.895749	+	0.409075i	0.809446	−	0.587194i	$-0.199768\pi$
$911$	27.0362	+	12.3470i	0.895749	+	0.409075i	0.0863027	+	0.996269i	$0.472495\pi$
$912$		0			0
$913$	20.2135	−	21.1993i	0.668970	−	0.701596i
$914$		0			0
$915$	−3.78561	+	39.6447i	−0.125148	+	1.31061i
$916$		0			0
$917$	−1.24684	−	3.35998i	−0.0411741	−	0.110956i
$918$		0			0
$919$	23.6640	+	13.6624i	0.780604	+	0.450682i	0.836644	−	0.547747i	$-0.184514\pi$
$919$	23.6640	+	13.6624i	0.780604	+	0.450682i	−0.0560404	+	0.998428i	$0.517848\pi$
$920$		0			0
$921$	−10.5919	−	18.3456i	−0.349013	−	0.604509i
$922$		0			0
$923$	−18.8584	−	29.3443i	−0.620733	−	0.965879i
$924$		0			0
$925$	−15.5248	+	7.08993i	−0.510451	+	0.233115i
$926$		0			0
$927$	82.6887	+	78.8436i	2.71585	+	2.58956i
$928$		0			0
$929$	−16.2027	+	11.5379i	−0.531594	+	0.378547i	−0.814105	−	0.580717i	$-0.802772\pi$
$929$	−16.2027	+	11.5379i	−0.531594	+	0.378547i	0.282511	+	0.959264i	$0.408833\pi$
$930$		0			0
$931$	4.35729	−	4.53942i	0.142804	−	0.148774i
$932$		0			0
$933$	21.0587	−	20.0794i	0.689430	−	0.657370i
$934$		0			0
$935$	23.2871	+	1.10930i	0.761571	+	0.0362781i
$936$		0			0
$937$	−1.96445	+	13.6631i	−0.0641759	+	0.446353i	0.932245	+	0.361827i	$0.117847\pi$
$937$	−1.96445	+	13.6631i	−0.0641759	+	0.446353i	−0.996421	+	0.0845266i	$0.973062\pi$
$938$		0			0
$939$	10.8803	−	1.56436i	0.355067	−	0.0510509i
$940$		0			0
$941$	−7.05586	−	1.35991i	−0.230014	−	0.0443316i	0.0729415	−	0.997336i	$-0.476761\pi$
$941$	−7.05586	−	1.35991i	−0.230014	−	0.0443316i	−0.302956	+	0.953005i	$0.597973\pi$
$942$		0			0
$943$	−0.0148688	−	0.237737i	−0.000484195	−	0.00774179i
$944$		0			0
$945$	29.5367	+	39.5936i	0.960827	+	1.28798i
$946$		0			0
$947$	−15.3111	−	6.12964i	−0.497544	−	0.199187i	0.109298	−	0.994009i	$-0.465140\pi$
$947$	−15.3111	−	6.12964i	−0.497544	−	0.199187i	−0.606842	+	0.794822i	$0.707564\pi$
$948$		0			0
$949$	−23.5580	+	9.43122i	−0.764726	+	0.306150i
$950$		0			0
$951$	38.0454	−	59.1997i	1.23371	−	1.91968i
$952$		0			0
$953$	−9.61171	+	32.7345i	−0.311354	+	1.06037i	0.644028	+	0.765002i	$0.277262\pi$
$953$	−9.61171	+	32.7345i	−0.311354	+	1.06037i	−0.955382	+	0.295372i	$0.904556\pi$
$954$		0			0
$955$	−38.0872	−	13.1821i	−1.23247	−	0.426563i
$956$		0			0
$957$	2.47125	+	3.47038i	0.0798840	+	0.112181i
$958$		0			0
$959$	4.14035	+	2.01979i	0.133699	+	0.0652224i
$960$		0			0
$961$	10.1706	+	0.971175i	0.328084	+	0.0313282i
$962$		0			0
$963$	15.2701	−	29.6199i	0.492073	−	0.954489i
$964$		0			0
$965$	22.6447			0.728959
$966$		0			0
$967$	49.3752			1.58780			0.793900	−	0.608048i	$-0.208047\pi$
$967$	49.3752			1.58780			0.793900	+	0.608048i	$0.208047\pi$
$968$		0			0
$969$	−3.88791	+	7.54148i	−0.124898	+	0.242267i
$970$		0			0
$971$	−37.2297	−	3.55501i	−1.19476	−	0.114086i	−0.521342	−	0.853348i	$-0.674568\pi$
$971$	−37.2297	−	3.55501i	−1.19476	−	0.114086i	−0.673418	+	0.739262i	$0.735174\pi$
$972$		0			0
$973$	25.0234	−	16.8756i	0.802214	−	0.541008i
$974$		0			0
$975$	−7.39997	−	10.3918i	−0.236989	−	0.332804i
$976$		0			0
$977$	−12.2626	−	4.24413i	−0.392316	−	0.135782i	0.123786	−	0.992309i	$-0.460496\pi$
$977$	−12.2626	−	4.24413i	−0.392316	−	0.135782i	−0.516102	+	0.856527i	$0.672617\pi$
$978$		0			0
$979$	−11.9011	+	40.5314i	−0.380360	+	1.29539i
$980$		0			0
$981$	−39.7769	+	61.8940i	−1.26998	+	1.97612i
$982$		0			0
$983$	−18.2333	+	7.29953i	−0.581553	+	0.232819i	−0.643738	−	0.765246i	$-0.722617\pi$
$983$	−18.2333	+	7.29953i	−0.581553	+	0.232819i	0.0621850	+	0.998065i	$0.480193\pi$
$984$		0			0
$985$	−28.0362	−	11.2240i	−0.893309	−	0.357627i
$986$		0			0
$987$	1.74499	+	0.750690i	0.0555436	+	0.0238947i
$988$		0			0
$989$	4.03698	−	0.840472i	0.128368	−	0.0267255i
$990$		0			0
$991$	−42.9255	−	8.27321i	−1.36357	−	0.262807i	−0.545591	−	0.838051i	$-0.683695\pi$
$991$	−42.9255	−	8.27321i	−1.36357	−	0.262807i	−0.817982	+	0.575244i	$0.804907\pi$
$992$		0			0
$993$	−81.3794	+	11.7006i	−2.58250	+	0.371307i
$994$		0			0
$995$	2.16559	−	15.0620i	0.0686539	−	0.477498i
$996$		0			0
$997$	52.9956	+	2.52449i	1.67839	+	0.0799515i	0.865000	−	0.501771i	$-0.167318\pi$
$997$	52.9956	+	2.52449i	1.67839	+	0.0799515i	0.813387	+	0.581723i	$0.197621\pi$
$998$		0			0
$999$	79.5972	−	75.8958i	2.51834	−	2.40124i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	644.2.bc.a.145.1	yes	320
7.3	odd	6	inner	644.2.bc.a.605.1	yes	320
23.10	odd	22	inner	644.2.bc.a.33.1	✓	320
161.10	even	66	inner	644.2.bc.a.493.1	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
644.2.bc.a.33.1	✓	320	23.10	odd	22	inner
644.2.bc.a.145.1	yes	320	1.1	even	1	trivial
644.2.bc.a.493.1	yes	320	161.10	even	66	inner
644.2.bc.a.605.1	yes	320	7.3	odd	6	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:	\( N \)	\(=\)	\( 644 = 2^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	644.bc (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39754 + 2.71086i) q^{3} +(-1.84559 - 0.176232i) q^{5} +(-1.47931 - 2.19354i) q^{7} +(-3.65545 - 5.13336i) q^{9} +(3.83965 + 1.32892i) q^{11} +(0.754092 - 2.56820i) q^{13} +(3.05703 - 4.75684i) q^{15} +(-2.87318 + 1.15025i) q^{17} +(-0.834503 - 0.334085i) q^{19} +(8.01379 - 0.944630i) q^{21} +(1.71607 - 4.47829i) q^{23} +(-1.53450 - 0.295750i) q^{25} +(9.96788 - 1.43316i) q^{27} +(0.0489273 - 0.340297i) q^{29} +(6.41276 + 0.305478i) q^{31} +(-8.96858 + 8.55152i) q^{33} +(2.34363 + 4.30909i) q^{35} +(8.89620 - 6.33496i) q^{37} +(5.90815 + 5.63341i) q^{39} +(0.0451801 - 0.0206330i) q^{41} +(0.464852 + 0.723324i) q^{43} +(5.84179 + 10.1183i) q^{45} +(0.203874 + 0.117706i) q^{47} +(-2.62327 + 6.48987i) q^{49} +(0.897238 - 9.39630i) q^{51} +(-3.25266 + 3.41129i) q^{53} +(-6.85222 - 3.12930i) q^{55} +(2.07191 - 1.79532i) q^{57} +(5.56031 - 1.34892i) q^{59} +(-6.26017 + 3.22734i) q^{61} +(-5.85270 + 15.6122i) q^{63} +(-1.84435 + 4.60695i) q^{65} +(3.00837 - 15.6089i) q^{67} +(9.74173 + 10.9106i) q^{69} +(8.53411 - 9.84889i) q^{71} +(-5.86046 - 7.45218i) q^{73} +(2.94627 - 3.74648i) q^{75} +(-2.76501 - 10.3883i) q^{77} +(-5.67299 - 5.94966i) q^{79} +(-3.86202 + 11.1586i) q^{81} +(2.99479 - 6.55767i) q^{83} +(5.50542 - 1.61654i) q^{85} +(0.854117 + 0.608214i) q^{87} +(0.494689 + 10.3848i) q^{89} +(-6.74900 + 2.14504i) q^{91} +(-9.79023 + 16.9572i) q^{93} +(1.48127 + 0.763650i) q^{95} +(-6.46235 - 14.1506i) q^{97} +(-7.21383 - 24.5681i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q - 20 q^{9} + 66 q^{21} + 21 q^{23} - 8 q^{25} - 12 q^{29} - 6 q^{31} - 38 q^{35} + 44 q^{37} - 20 q^{39} - 88 q^{43} - 42 q^{47} - 74 q^{49} + 44 q^{51} - 88 q^{57} + 55 q^{63} + 77 q^{65} - 32 q^{71}+ \cdots + 242 q^{99}+O(q^{100}) \) 320 * q - 20 * q^9 + 66 * q^21 + 21 * q^23 - 8 * q^25 - 12 * q^29 - 6 * q^31 - 38 * q^35 + 44 * q^37 - 20 * q^39 - 88 * q^43 - 42 * q^47 - 74 * q^49 + 44 * q^51 - 88 * q^57 + 55 * q^63 + 77 * q^65 - 32 * q^71 - 36 * q^73 + 24 * q^75 + 105 * q^77 + 44 * q^79 - 36 * q^81 + 60 * q^85 - 96 * q^87 - 20 * q^93 - 31 * q^95 + 242 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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