LMFDB - Embedded newform 2028.2.i.n.529.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2028,2,Mod(529,2028)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2028, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("2028.529");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2028 = 2^{2} \cdot 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2028.i (of order $3$, degree $2$, 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:	$16.1936615299$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.70892257536.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 21x^{6} + 320x^{4} + 2541x^{2} + 14641 $ x^8 + 21x^6 + 320x^4 + 2541*x^2 + 14641
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 156)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			529.4
Root			$-1.20635 - 3.08945i$ of defining polynomial
Character	$\chi$	$=$	2028.529
Dual form			2028.2.i.n.2005.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{3} +4.14474 q^{5} +(-1.20635 - 2.08945i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(1.73205 - 3.00000i) q^{11} +(-2.07237 + 3.58945i) q^{15} +(2.58945 + 4.48507i) q^{17} +(-1.73205 - 3.00000i) q^{19} +2.41269 q^{21} +(-1.00000 + 1.73205i) q^{23} +12.1789 q^{25} +1.00000 q^{27} +(-1.58945 + 2.75302i) q^{29} +1.05141 q^{31} +(1.73205 + 3.00000i) q^{33} +(-5.00000 - 8.66025i) q^{35} +(3.80442 - 6.58945i) q^{37} +(0.340322 - 0.589454i) q^{41} +(-6.08945 - 10.5472i) q^{43} +(-2.07237 - 3.58945i) q^{45} +10.3923 q^{47} +(0.589454 - 1.02096i) q^{49} -5.17891 q^{51} +1.17891 q^{53} +(7.17891 - 12.4342i) q^{55} +3.46410 q^{57} +(5.87680 + 10.1789i) q^{59} +(-2.50000 - 4.33013i) q^{61} +(-1.20635 + 2.08945i) q^{63} +(1.20635 - 2.08945i) q^{67} +(-1.00000 - 1.73205i) q^{69} +(-1.73205 - 3.00000i) q^{71} -14.8469 q^{73} +(-6.08945 + 10.5472i) q^{75} -8.35782 q^{77} +1.82109 q^{79} +(-0.500000 + 0.866025i) q^{81} -1.36129 q^{83} +(10.7326 + 18.5895i) q^{85} +(-1.58945 - 2.75302i) q^{87} +(3.46410 - 6.00000i) q^{89} +(-0.525704 + 0.910546i) q^{93} +(-7.17891 - 12.4342i) q^{95} +(8.81519 + 15.2684i) q^{97} -3.46410 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} - 4 q^{9} - 2 q^{17} - 8 q^{23} + 52 q^{25} + 8 q^{27} + 10 q^{29} - 40 q^{35} - 26 q^{43} - 18 q^{49} + 4 q^{51} - 36 q^{53} + 12 q^{55} - 20 q^{61} - 8 q^{69} - 26 q^{75} + 24 q^{77} + 60 q^{79}+ \cdots - 12 q^{95}+O(q^{100}) $ 8 * q - 4 * q^3 - 4 * q^9 - 2 * q^17 - 8 * q^23 + 52 * q^25 + 8 * q^27 + 10 * q^29 - 40 * q^35 - 26 * q^43 - 18 * q^49 + 4 * q^51 - 36 * q^53 + 12 * q^55 - 20 * q^61 - 8 * q^69 - 26 * q^75 + 24 * q^77 + 60 * q^79 - 4 * q^81 + 10 * q^87 - 12 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2028\mathbb{Z}\right)^\times$.

$n$	$677$	$1015$	$1861$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$		0			0
$5$	4.14474			1.85359			0.926793	−	0.375572i	$-0.122554\pi$
$5$	4.14474			1.85359			0.926793	+	0.375572i	$0.122554\pi$
$6$		0			0
$7$	−1.20635	−	2.08945i	−0.455956	−	0.789739i	0.542786	−	0.839871i	$-0.317369\pi$
$7$	−1.20635	−	2.08945i	−0.455956	−	0.789739i	−0.998743	+	0.0501314i	$0.984036\pi$
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	1.73205	−	3.00000i	0.522233	−	0.904534i	−0.477432	−	0.878668i	$-0.658432\pi$
$11$	1.73205	−	3.00000i	0.522233	−	0.904534i	0.999665	−	0.0258656i	$-0.00823419\pi$
$12$		0			0
$13$		0			0
$13$		0			0
$14$		0			0
$15$	−2.07237	+	3.58945i	−0.535084	+	0.926793i
$16$		0			0
$17$	2.58945	+	4.48507i	0.628035	+	1.08779i	0.987946	+	0.154802i	$0.0494738\pi$
$17$	2.58945	+	4.48507i	0.628035	+	1.08779i	−0.359911	+	0.932987i	$0.617193\pi$
$18$		0			0
$19$	−1.73205	−	3.00000i	−0.397360	−	0.688247i	0.596040	−	0.802955i	$-0.296740\pi$
$19$	−1.73205	−	3.00000i	−0.397360	−	0.688247i	−0.993399	+	0.114708i	$0.963407\pi$
$20$		0			0
$21$	2.41269			0.526493
$22$		0			0
$23$	−1.00000	+	1.73205i	−0.208514	+	0.361158i	−0.951247	−	0.308431i	$-0.900196\pi$
$23$	−1.00000	+	1.73205i	−0.208514	+	0.361158i	0.742732	+	0.669588i	$0.233529\pi$
$24$		0			0
$25$	12.1789			2.43578
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	−1.58945	+	2.75302i	−0.295154	+	0.511222i	−0.975021	−	0.222114i	$-0.928704\pi$
$29$	−1.58945	+	2.75302i	−0.295154	+	0.511222i	0.679867	+	0.733336i	$0.262038\pi$
$30$		0			0
$31$	1.05141			0.188838			0.0944192	−	0.995533i	$-0.469901\pi$
$31$	1.05141			0.188838			0.0944192	+	0.995533i	$0.469901\pi$
$32$		0			0
$33$	1.73205	+	3.00000i	0.301511	+	0.522233i
$34$		0			0
$35$	−5.00000	−	8.66025i	−0.845154	−	1.46385i
$36$		0			0
$37$	3.80442	−	6.58945i	0.625443	−	1.08330i	−0.363012	−	0.931785i	$-0.618251\pi$
$37$	3.80442	−	6.58945i	0.625443	−	1.08330i	0.988455	−	0.151515i	$-0.0484152\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	0.340322	−	0.589454i	0.0531493	−	0.0920573i	−0.838227	−	0.545322i	$-0.816407\pi$
$41$	0.340322	−	0.589454i	0.0531493	−	0.0920573i	0.891376	+	0.453265i	$0.149741\pi$
$42$		0			0
$43$	−6.08945	−	10.5472i	−0.928633	−	1.60844i	−0.785612	−	0.618720i	$-0.787652\pi$
$43$	−6.08945	−	10.5472i	−0.928633	−	1.60844i	−0.143022	−	0.989720i	$-0.545682\pi$
$44$		0			0
$45$	−2.07237	−	3.58945i	−0.308931	−	0.535084i
$46$		0			0
$47$	10.3923			1.51587			0.757937	−	0.652328i	$-0.226208\pi$
$47$	10.3923			1.51587			0.757937	+	0.652328i	$0.226208\pi$
$48$		0			0
$49$	0.589454	−	1.02096i	0.0842077	−	0.145852i
$50$		0			0
$51$	−5.17891			−0.725192
$52$		0			0
$53$	1.17891			0.161936			0.0809678	−	0.996717i	$-0.474199\pi$
$53$	1.17891			0.161936			0.0809678	+	0.996717i	$0.474199\pi$
$54$		0			0
$55$	7.17891	−	12.4342i	0.968004	−	1.67663i
$56$		0			0
$57$	3.46410			0.458831
$58$		0			0
$59$	5.87680	+	10.1789i	0.765094	+	1.32518i	0.940197	+	0.340631i	$0.110641\pi$
$59$	5.87680	+	10.1789i	0.765094	+	1.32518i	−0.175103	+	0.984550i	$0.556026\pi$
$60$		0			0
$61$	−2.50000	−	4.33013i	−0.320092	−	0.554416i	0.660415	−	0.750901i	$-0.270381\pi$
$61$	−2.50000	−	4.33013i	−0.320092	−	0.554416i	−0.980507	+	0.196485i	$0.937047\pi$
$62$		0			0
$63$	−1.20635	+	2.08945i	−0.151985	+	0.263246i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	1.20635	−	2.08945i	0.147379	−	0.255267i	−0.782879	−	0.622174i	$-0.786250\pi$
$67$	1.20635	−	2.08945i	0.147379	−	0.255267i	0.930258	+	0.366906i	$0.119583\pi$
$68$		0			0
$69$	−1.00000	−	1.73205i	−0.120386	−	0.208514i
$70$		0			0
$71$	−1.73205	−	3.00000i	−0.205557	−	0.356034i	0.744753	−	0.667340i	$-0.232567\pi$
$71$	−1.73205	−	3.00000i	−0.205557	−	0.356034i	−0.950310	+	0.311305i	$0.899234\pi$
$72$		0			0
$73$	−14.8469			−1.73770			−0.868851	−	0.495074i	$-0.835141\pi$
$73$	−14.8469			−1.73770			−0.868851	+	0.495074i	$0.835141\pi$
$74$		0			0
$75$	−6.08945	+	10.5472i	−0.703150	+	1.21789i
$76$		0			0
$77$	−8.35782			−0.952462
$78$		0			0
$79$	1.82109			0.204889			0.102444	−	0.994739i	$-0.467334\pi$
$79$	1.82109			0.204889			0.102444	+	0.994739i	$0.467334\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	−1.36129			−0.149421			−0.0747103	−	0.997205i	$-0.523803\pi$
$83$	−1.36129			−0.149421			−0.0747103	+	0.997205i	$0.523803\pi$
$84$		0			0
$85$	10.7326	+	18.5895i	1.16412	+	2.01631i
$86$		0			0
$87$	−1.58945	−	2.75302i	−0.170407	−	0.295154i
$88$		0			0
$89$	3.46410	−	6.00000i	0.367194	−	0.635999i	−0.621932	−	0.783072i	$-0.713652\pi$
$89$	3.46410	−	6.00000i	0.367194	−	0.635999i	0.989126	+	0.147073i	$0.0469852\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−0.525704	+	0.910546i	−0.0545130	+	0.0944192i
$94$		0			0
$95$	−7.17891	−	12.4342i	−0.736540	−	1.27573i
$96$		0			0
$97$	8.81519	+	15.2684i	0.895047	+	1.55027i	0.833746	+	0.552148i	$0.186192\pi$
$97$	8.81519	+	15.2684i	0.895047	+	1.55027i	0.0613012	+	0.998119i	$0.480475\pi$
$98$		0			0
$99$	−3.46410			−0.348155
$100$		0			0
$101$	0.410546	−	0.711086i	0.0408508	−	0.0707557i	−0.844877	−	0.534960i	$-0.820326\pi$
$101$	0.410546	−	0.711086i	0.0408508	−	0.0707557i	0.885728	+	0.464205i	$0.153660\pi$
$102$		0			0
$103$	8.17891			0.805892			0.402946	−	0.915224i	$-0.367986\pi$
$103$	8.17891			0.805892			0.402946	+	0.915224i	$0.367986\pi$
$104$		0			0
$105$	10.0000			0.975900
$106$		0			0
$107$	5.00000	−	8.66025i	0.483368	−	0.837218i	−0.516449	−	0.856318i	$-0.672747\pi$
$107$	5.00000	−	8.66025i	0.483368	−	0.837218i	0.999818	+	0.0190994i	$0.00607989\pi$
$108$		0			0
$109$	1.05141			0.100707			0.0503533	−	0.998731i	$-0.483965\pi$
$109$	1.05141			0.100707			0.0503533	+	0.998731i	$0.483965\pi$
$110$		0			0
$111$	3.80442	+	6.58945i	0.361100	+	0.625443i
$112$		0			0
$113$	−0.410546	−	0.711086i	−0.0386209	−	0.0668934i	0.846069	−	0.533074i	$-0.178963\pi$
$113$	−0.410546	−	0.711086i	−0.0386209	−	0.0668934i	−0.884690	+	0.466180i	$0.845630\pi$
$114$		0			0
$115$	−4.14474	+	7.17891i	−0.386499	+	0.669437i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	6.24756	−	10.8211i	0.572713	−	0.991968i
$120$		0			0
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$		0			0
$123$	0.340322	+	0.589454i	0.0306858	+	0.0531493i
$124$		0			0
$125$	29.7547			2.66135
$126$		0			0
$127$	−7.08945	+	12.2793i	−0.629087	+	1.08961i	0.358648	+	0.933473i	$0.383238\pi$
$127$	−7.08945	+	12.2793i	−0.629087	+	1.08961i	−0.987735	+	0.156138i	$0.950095\pi$
$128$		0			0
$129$	12.1789			1.07229
$130$		0			0
$131$	−16.3578			−1.42919			−0.714595	−	0.699539i	$-0.753389\pi$
$131$	−16.3578			−1.42919			−0.714595	+	0.699539i	$0.753389\pi$
$132$		0			0
$133$	−4.17891	+	7.23808i	−0.362357	+	0.627621i
$134$		0			0
$135$	4.14474			0.356723
$136$		0			0
$137$	3.12378	+	5.41055i	0.266883	+	0.462254i	0.968055	−	0.250737i	$-0.0806731\pi$
$137$	3.12378	+	5.41055i	0.266883	+	0.462254i	−0.701173	+	0.712992i	$0.747340\pi$
$138$		0			0
$139$	−2.91055	−	5.04121i	−0.246869	−	0.427590i	0.715786	−	0.698319i	$-0.246068\pi$
$139$	−2.91055	−	5.04121i	−0.246869	−	0.427590i	−0.962656	+	0.270729i	$0.912735\pi$
$140$		0			0
$141$	−5.19615	+	9.00000i	−0.437595	+	0.757937i
$142$		0			0
$143$		0			0
$144$		0			0
$145$	−6.58788	+	11.4105i	−0.547094	+	0.947594i
$146$		0			0
$147$	0.589454	+	1.02096i	0.0486174	+	0.0842077i
$148$		0			0
$149$	−0.340322	−	0.589454i	−0.0278802	−	0.0482900i	0.851749	−	0.523951i	$-0.175542\pi$
$149$	−0.340322	−	0.589454i	−0.0278802	−	0.0482900i	−0.879629	+	0.475661i	$0.842209\pi$
$150$		0			0
$151$	6.18667			0.503464			0.251732	−	0.967797i	$-0.419000\pi$
$151$	6.18667			0.503464			0.251732	+	0.967797i	$0.419000\pi$
$152$		0			0
$153$	2.58945	−	4.48507i	0.209345	−	0.362596i
$154$		0			0
$155$	4.35782			0.350028
$156$		0			0
$157$	7.00000			0.558661			0.279330	−	0.960195i	$-0.409888\pi$
$157$	7.00000			0.558661			0.279330	+	0.960195i	$0.409888\pi$
$158$		0			0
$159$	−0.589454	+	1.02096i	−0.0467468	+	0.0809678i
$160$		0			0
$161$	4.82539			0.380294
$162$		0			0
$163$	0.525704	+	0.910546i	0.0411763	+	0.0713195i	0.885879	−	0.463916i	$-0.153556\pi$
$163$	0.525704	+	0.910546i	0.0411763	+	0.0713195i	−0.844703	+	0.535236i	$0.820223\pi$
$164$		0			0
$165$	7.17891	+	12.4342i	0.558877	+	0.968004i
$166$		0			0
$167$	3.46410	−	6.00000i	0.268060	−	0.464294i	−0.700301	−	0.713848i	$-0.746951\pi$
$167$	3.46410	−	6.00000i	0.268060	−	0.464294i	0.968361	+	0.249554i	$0.0802840\pi$
$168$		0			0
$169$		0			0
$170$		0			0
$171$	−1.73205	+	3.00000i	−0.132453	+	0.229416i
$172$		0			0
$173$	9.00000	+	15.5885i	0.684257	+	1.18517i	0.973670	+	0.227964i	$0.0732068\pi$
$173$	9.00000	+	15.5885i	0.684257	+	1.18517i	−0.289412	+	0.957205i	$0.593460\pi$
$174$		0			0
$175$	−14.6920	−	25.4473i	−1.11061	−	1.92363i
$176$		0			0
$177$	−11.7536			−0.883454
$178$		0			0
$179$	7.17891	−	12.4342i	0.536577	−	0.929378i	−0.462508	−	0.886615i	$-0.653051\pi$
$179$	7.17891	−	12.4342i	0.536577	−	0.929378i	0.999085	−	0.0427634i	$-0.0136162\pi$
$180$		0			0
$181$	−13.5367			−1.00618			−0.503088	−	0.864235i	$-0.667803\pi$
$181$	−13.5367			−1.00618			−0.503088	+	0.864235i	$0.667803\pi$
$182$		0			0
$183$	5.00000			0.369611
$184$		0			0
$185$	15.7684	−	27.3116i	1.15931	−	2.00799i
$186$		0			0
$187$	17.9403			1.31192
$188$		0			0
$189$	−1.20635	−	2.08945i	−0.0877488	−	0.151985i
$190$		0			0
$191$	−10.1789	−	17.6304i	−0.736520	−	1.27569i	−0.954053	−	0.299637i	$-0.903134\pi$
$191$	−10.1789	−	17.6304i	−0.736520	−	1.27569i	0.217533	−	0.976053i	$-0.430199\pi$
$192$		0			0
$193$	−0.185382	+	0.321092i	−0.0133441	+	0.0231127i	−0.872620	−	0.488399i	$-0.837581\pi$
$193$	−0.185382	+	0.321092i	−0.0133441	+	0.0231127i	0.859276	+	0.511512i	$0.170914\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−8.28949	+	14.3578i	−0.590602	+	1.02295i	0.403550	+	0.914958i	$0.367776\pi$
$197$	−8.28949	+	14.3578i	−0.590602	+	1.02295i	−0.994152	+	0.107994i	$0.965557\pi$
$198$		0			0
$199$	6.26836	+	10.8571i	0.444352	+	0.769641i	0.998007	−	0.0631055i	$-0.0201005\pi$
$199$	6.26836	+	10.8571i	0.444352	+	0.769641i	−0.553654	+	0.832747i	$0.686767\pi$
$200$		0			0
$201$	1.20635	+	2.08945i	0.0850892	+	0.147379i
$202$		0			0
$203$	7.66973			0.538310
$204$		0			0
$205$	1.41055	−	2.44314i	0.0985168	−	0.170636i
$206$		0			0
$207$	2.00000			0.139010
$208$		0			0
$209$	−12.0000			−0.830057
$210$		0			0
$211$	−9.26836	+	16.0533i	−0.638060	+	1.10515i	0.347798	+	0.937570i	$0.386930\pi$
$211$	−9.26836	+	16.0533i	−0.638060	+	1.10515i	−0.985858	+	0.167583i	$0.946404\pi$
$212$		0			0
$213$	3.46410			0.237356
$214$		0			0
$215$	−25.2392	−	43.7156i	−1.72130	−	2.98138i
$216$		0			0
$217$	−1.26836	−	2.19687i	−0.0861021	−	0.149133i
$218$		0			0
$219$	7.42346	−	12.8578i	0.501631	−	0.868851i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	1.05141	−	1.82109i	0.0704075	−	0.121949i	−0.828672	−	0.559734i	$-0.810903\pi$
$223$	1.05141	−	1.82109i	0.0704075	−	0.121949i	0.899080	+	0.437784i	$0.144237\pi$
$224$		0			0
$225$	−6.08945	−	10.5472i	−0.405964	−	0.703150i
$226$		0			0
$227$	11.0729	+	19.1789i	0.734937	+	1.27295i	0.954751	+	0.297407i	$0.0961218\pi$
$227$	11.0729	+	19.1789i	0.734937	+	1.27295i	−0.219813	+	0.975542i	$0.570545\pi$
$228$		0			0
$229$	16.5790			1.09557			0.547785	−	0.836619i	$-0.315471\pi$
$229$	16.5790			1.09557			0.547785	+	0.836619i	$0.315471\pi$
$230$		0			0
$231$	4.17891	−	7.23808i	0.274952	−	0.476231i
$232$		0			0
$233$	22.7156			1.48815			0.744075	−	0.668096i	$-0.232890\pi$
$233$	22.7156			1.48815			0.744075	+	0.668096i	$0.232890\pi$
$234$		0			0
$235$	43.0735			2.80980
$236$		0			0
$237$	−0.910546	+	1.57711i	−0.0591463	+	0.102444i
$238$		0			0
$239$	−15.2177			−0.984351			−0.492175	−	0.870496i	$-0.663798\pi$
$239$	−15.2177			−0.984351			−0.492175	+	0.870496i	$0.663798\pi$
$240$		0			0
$241$	0.340322	+	0.589454i	0.0219220	+	0.0379701i	0.876778	−	0.480895i	$-0.159688\pi$
$241$	0.340322	+	0.589454i	0.0219220	+	0.0379701i	−0.854856	+	0.518865i	$0.826355\pi$
$242$		0			0
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$		0			0
$245$	2.44314	−	4.23164i	0.156086	−	0.270349i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	0.680643	−	1.17891i	0.0431340	−	0.0747103i
$250$		0			0
$251$	12.3578	+	21.4044i	0.780018	+	1.35103i	0.931930	+	0.362638i	$0.118124\pi$
$251$	12.3578	+	21.4044i	0.780018	+	1.35103i	−0.151912	+	0.988394i	$0.548543\pi$
$252$		0			0
$253$	3.46410	+	6.00000i	0.217786	+	0.377217i
$254$		0			0
$255$	−21.4653			−1.34421
$256$		0			0
$257$	5.41055	−	9.37134i	0.337501	−	0.584568i	−0.646461	−	0.762947i	$-0.723752\pi$
$257$	5.41055	−	9.37134i	0.337501	−	0.584568i	0.983962	+	0.178379i	$0.0570852\pi$
$258$		0			0
$259$	−18.3578			−1.14070
$260$		0			0
$261$	3.17891			0.196769
$262$		0			0
$263$	−4.82109	+	8.35038i	−0.297281	+	0.514906i	−0.975513	−	0.219942i	$-0.929413\pi$
$263$	−4.82109	+	8.35038i	−0.297281	+	0.514906i	0.678232	+	0.734848i	$0.262747\pi$
$264$		0			0
$265$	4.88627			0.300161
$266$		0			0
$267$	3.46410	+	6.00000i	0.212000	+	0.367194i
$268$		0			0
$269$	−5.17891	−	8.97013i	−0.315764	−	0.546919i	0.663836	−	0.747878i	$-0.268927\pi$
$269$	−5.17891	−	8.97013i	−0.315764	−	0.546919i	−0.979600	+	0.200960i	$0.935594\pi$
$270$		0			0
$271$	−3.98981	+	6.91055i	−0.242363	+	0.419786i	−0.961387	−	0.275200i	$-0.911256\pi$
$271$	−3.98981	+	6.91055i	−0.242363	+	0.419786i	0.719024	+	0.694986i	$0.244589\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	21.0945	−	36.5367i	1.27205	−	2.20325i
$276$		0			0
$277$	5.58945	+	9.68122i	0.335838	+	0.581688i	0.983645	−	0.180116i	$-0.0576473\pi$
$277$	5.58945	+	9.68122i	0.335838	+	0.581688i	−0.647808	+	0.761804i	$0.724314\pi$
$278$		0			0
$279$	−0.525704	−	0.910546i	−0.0314731	−	0.0545130i
$280$		0			0
$281$	−18.0012			−1.07386			−0.536929	−	0.843627i	$-0.680416\pi$
$281$	−18.0012			−1.07386			−0.536929	+	0.843627i	$0.680416\pi$
$282$		0			0
$283$	−7.91055	+	13.7015i	−0.470233	+	0.814468i	−0.999421	−	0.0340373i	$-0.989164\pi$
$283$	−7.91055	+	13.7015i	−0.470233	+	0.814468i	0.529187	+	0.848505i	$0.322497\pi$
$284$		0			0
$285$	14.3578			0.850484
$286$		0			0
$287$	−1.64218			−0.0969350
$288$		0			0
$289$	−4.91055	+	8.50531i	−0.288856	+	0.500313i
$290$		0			0
$291$	−17.6304			−1.03351
$292$		0			0
$293$	−0.0304432	−	0.0527291i	−0.00177851	−	0.00308047i	0.865135	−	0.501539i	$-0.167233\pi$
$293$	−0.0304432	−	0.0527291i	−0.00177851	−	0.00308047i	−0.866913	+	0.498459i	$0.833899\pi$
$294$		0			0
$295$	24.3578	+	42.1890i	1.41817	+	2.45634i
$296$		0			0
$297$	1.73205	−	3.00000i	0.100504	−	0.174078i
$298$		0			0
$299$		0			0
$300$		0			0
$301$	−14.6920	+	25.4473i	−0.846832	+	1.46676i
$302$		0			0
$303$	0.410546	+	0.711086i	0.0235852	+	0.0408508i
$304$		0			0
$305$	−10.3619	−	17.9473i	−0.593318	−	1.02766i
$306$		0			0
$307$	−4.51551			−0.257714			−0.128857	−	0.991663i	$-0.541131\pi$
$307$	−4.51551			−0.257714			−0.128857	+	0.991663i	$0.541131\pi$
$308$		0			0
$309$	−4.08945	+	7.08314i	−0.232641	+	0.402946i
$310$		0			0
$311$	−34.3578			−1.94825			−0.974127	−	0.226003i	$-0.927434\pi$
$311$	−34.3578			−1.94825			−0.974127	+	0.226003i	$0.927434\pi$
$312$		0			0
$313$	−28.8945			−1.63322			−0.816608	−	0.577193i	$-0.804148\pi$
$313$	−28.8945			−1.63322			−0.816608	+	0.577193i	$0.804148\pi$
$314$		0			0
$315$	−5.00000	+	8.66025i	−0.281718	+	0.487950i
$316$		0			0
$317$	−15.8983			−0.892939			−0.446470	−	0.894799i	$-0.647319\pi$
$317$	−15.8983			−0.892939			−0.446470	+	0.894799i	$0.647319\pi$
$318$		0			0
$319$	5.50603	+	9.53673i	0.308279	+	0.533954i
$320$		0			0
$321$	5.00000	+	8.66025i	0.279073	+	0.483368i
$322$		0			0
$323$	8.97013	−	15.5367i	0.499112	−	0.864487i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−0.525704	+	0.910546i	−0.0290715	+	0.0503533i
$328$		0			0
$329$	−12.5367	−	21.7142i	−0.691172	−	1.19715i
$330$		0			0
$331$	−13.3307	−	23.0895i	−0.732722	−	1.26911i	−0.955716	−	0.294291i	$-0.904916\pi$
$331$	−13.3307	−	23.0895i	−0.732722	−	1.26911i	0.222994	−	0.974820i	$-0.428417\pi$
$332$		0			0
$333$	−7.60885			−0.416962
$334$		0			0
$335$	5.00000	−	8.66025i	0.273179	−	0.473160i
$336$		0			0
$337$	2.64218			0.143929			0.0719644	−	0.997407i	$-0.477073\pi$
$337$	2.64218			0.143929			0.0719644	+	0.997407i	$0.477073\pi$
$338$		0			0
$339$	0.821092			0.0445956
$340$		0			0
$341$	1.82109	−	3.15422i	0.0986176	−	0.170811i
$342$		0			0
$343$	−19.7332			−1.06549
$344$		0			0
$345$	−4.14474	−	7.17891i	−0.223146	−	0.386499i
$346$		0			0
$347$	1.17891	+	2.04193i	0.0632871	+	0.109617i	0.895933	−	0.444189i	$-0.146508\pi$
$347$	1.17891	+	2.04193i	0.0632871	+	0.109617i	−0.832646	+	0.553806i	$0.813175\pi$
$348$		0			0
$349$	−11.2279	+	19.4473i	−0.601015	+	1.04099i	0.391653	+	0.920113i	$0.371903\pi$
$349$	−11.2279	+	19.4473i	−0.601015	+	1.04099i	−0.992668	+	0.120875i	$0.961430\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	6.89776	−	11.9473i	0.367131	−	0.635889i	−0.621985	−	0.783029i	$-0.713673\pi$
$353$	6.89776	−	11.9473i	0.367131	−	0.635889i	0.989116	+	0.147140i	$0.0470068\pi$
$354$		0			0
$355$	−7.17891	−	12.4342i	−0.381017	−	0.659941i
$356$		0			0
$357$	6.24756	+	10.8211i	0.330656	+	0.572713i
$358$		0			0
$359$	5.56692			0.293811			0.146905	−	0.989151i	$-0.453069\pi$
$359$	5.56692			0.293811			0.146905	+	0.989151i	$0.453069\pi$
$360$		0			0
$361$	3.50000	−	6.06218i	0.184211	−	0.319062i
$362$		0			0
$363$	1.00000			0.0524864
$364$		0			0
$365$	−61.5367			−3.22098
$366$		0			0
$367$	−12.0895	+	20.9395i	−0.631064	+	1.09304i	0.356270	+	0.934383i	$0.384048\pi$
$367$	−12.0895	+	20.9395i	−0.631064	+	1.09304i	−0.987334	+	0.158653i	$0.949285\pi$
$368$		0			0
$369$	−0.680643			−0.0354329
$370$		0			0
$371$	−1.42217	−	2.46327i	−0.0738355	−	0.127887i
$372$		0			0
$373$	−5.67891	−	9.83616i	−0.294043	−	0.509297i	0.680719	−	0.732545i	$-0.261667\pi$
$373$	−5.67891	−	9.83616i	−0.294043	−	0.509297i	−0.974762	+	0.223248i	$0.928334\pi$
$374$		0			0
$375$	−14.8774	+	25.7684i	−0.768264	+	1.33067i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	6.40250	−	11.0895i	0.328874	−	0.569627i	−0.653414	−	0.757000i	$-0.726664\pi$
$379$	6.40250	−	11.0895i	0.328874	−	0.569627i	0.982289	+	0.187373i	$0.0599974\pi$
$380$		0			0
$381$	−7.08945	−	12.2793i	−0.363204	−	0.629087i
$382$		0			0
$383$	16.5790	+	28.7156i	0.847146	+	1.46730i	0.883744	+	0.467970i	$0.155015\pi$
$383$	16.5790	+	28.7156i	0.847146	+	1.46730i	−0.0365980	+	0.999330i	$0.511652\pi$
$384$		0			0
$385$	−34.6410			−1.76547
$386$		0			0
$387$	−6.08945	+	10.5472i	−0.309544	+	0.536147i
$388$		0			0
$389$	−27.5367			−1.39617			−0.698084	−	0.716016i	$-0.745964\pi$
$389$	−27.5367			−1.39617			−0.698084	+	0.716016i	$0.745964\pi$
$390$		0			0
$391$	−10.3578			−0.523817
$392$		0			0
$393$	8.17891	−	14.1663i	0.412571	−	0.714595i
$394$		0			0
$395$	7.54796			0.379779
$396$		0			0
$397$	−7.45391	−	12.9105i	−0.374101	−	0.647962i	0.616091	−	0.787675i	$-0.288715\pi$
$397$	−7.45391	−	12.9105i	−0.374101	−	0.647962i	−0.990192	+	0.139713i	$0.955382\pi$
$398$		0			0
$399$	−4.17891	−	7.23808i	−0.209207	−	0.362357i
$400$		0			0
$401$	−4.48507	+	7.76836i	−0.223974	+	0.387934i	−0.956011	−	0.293331i	$-0.905236\pi$
$401$	−4.48507	+	7.76836i	−0.223974	+	0.387934i	0.732037	+	0.681264i	$0.238570\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−2.07237	+	3.58945i	−0.102977	+	0.178361i
$406$		0			0
$407$	−13.1789	−	22.8265i	−0.653254	−	1.13147i
$408$		0			0
$409$	12.6196	+	21.8578i	0.624000	+	1.08080i	0.988733	+	0.149688i	$0.0478268\pi$
$409$	12.6196	+	21.8578i	0.624000	+	1.08080i	−0.364733	+	0.931112i	$0.618840\pi$
$410$		0			0
$411$	−6.24756			−0.308169
$412$		0			0
$413$	14.1789	−	24.5586i	0.697698	−	1.20845i
$414$		0			0
$415$	−5.64218			−0.276964
$416$		0			0
$417$	5.82109			0.285060
$418$		0			0
$419$	−16.3578	+	28.3326i	−0.799132	+	1.38414i	0.121051	+	0.992646i	$0.461374\pi$
$419$	−16.3578	+	28.3326i	−0.799132	+	1.38414i	−0.920182	+	0.391490i	$0.871960\pi$
$420$		0			0
$421$	−5.93768			−0.289385			−0.144692	−	0.989477i	$-0.546219\pi$
$421$	−5.93768			−0.289385			−0.144692	+	0.989477i	$0.546219\pi$
$422$		0			0
$423$	−5.19615	−	9.00000i	−0.252646	−	0.437595i
$424$		0			0
$425$	31.5367	+	54.6232i	1.52976	+	2.64961i
$426$		0			0
$427$	−6.03173	+	10.4473i	−0.291896	+	0.505579i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	2.78346	−	4.82109i	0.134074	−	0.232224i	−0.791169	−	0.611598i	$-0.790527\pi$
$431$	2.78346	−	4.82109i	0.134074	−	0.232224i	0.925244	+	0.379374i	$0.123861\pi$
$432$		0			0
$433$	−12.6789	−	21.9605i	−0.609309	−	1.05535i	−0.991354	−	0.131211i	$-0.958113\pi$
$433$	−12.6789	−	21.9605i	−0.609309	−	1.05535i	0.382045	−	0.924144i	$-0.375220\pi$
$434$		0			0
$435$	−6.58788	−	11.4105i	−0.315865	−	0.547094i
$436$		0			0
$437$	6.92820			0.331421
$438$		0			0
$439$	−16.4473	+	28.4875i	−0.784985	+	1.35963i	0.144022	+	0.989574i	$0.453996\pi$
$439$	−16.4473	+	28.4875i	−0.784985	+	1.35963i	−0.929008	+	0.370060i	$0.879337\pi$
$440$		0			0
$441$	−1.17891			−0.0561385
$442$		0			0
$443$	8.00000			0.380091			0.190046	−	0.981775i	$-0.439136\pi$
$443$	8.00000			0.380091			0.190046	+	0.981775i	$0.439136\pi$
$444$		0			0
$445$	14.3578	−	24.8685i	0.680626	−	1.17888i
$446$		0			0
$447$	0.680643			0.0321933
$448$		0			0
$449$	−14.1663	−	24.5367i	−0.668548	−	1.15796i	−0.978310	−	0.207145i	$-0.933583\pi$
$449$	−14.1663	−	24.5367i	−0.668548	−	1.15796i	0.309762	−	0.950814i	$-0.399751\pi$
$450$		0			0
$451$	−1.17891	−	2.04193i	−0.0555126	−	0.0961507i
$452$		0			0
$453$	−3.09334	+	5.35782i	−0.145338	+	0.251732i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−10.2069	+	17.6789i	−0.477460	+	0.826984i	−0.999666	−	0.0258346i	$-0.991776\pi$
$457$	−10.2069	+	17.6789i	−0.477460	+	0.826984i	0.522207	+	0.852819i	$0.325109\pi$
$458$		0			0
$459$	2.58945	+	4.48507i	0.120865	+	0.209345i
$460$		0			0
$461$	−2.44314	−	4.23164i	−0.113788	−	0.197087i	0.803506	−	0.595296i	$-0.202965\pi$
$461$	−2.44314	−	4.23164i	−0.113788	−	0.197087i	−0.917295	+	0.398209i	$0.869632\pi$
$462$		0			0
$463$	−21.0945			−0.980344			−0.490172	−	0.871626i	$-0.663066\pi$
$463$	−21.0945			−0.980344			−0.490172	+	0.871626i	$0.663066\pi$
$464$		0			0
$465$	−2.17891	+	3.77398i	−0.101044	+	0.175014i
$466$		0			0
$467$	6.00000			0.277647			0.138823	−	0.990317i	$-0.455668\pi$
$467$	6.00000			0.277647			0.138823	+	0.990317i	$0.455668\pi$
$468$		0			0
$469$	−5.82109			−0.268793
$470$		0			0
$471$	−3.50000	+	6.06218i	−0.161271	+	0.279330i
$472$		0			0
$473$	−42.1890			−1.93985
$474$		0			0
$475$	−21.0945	−	36.5367i	−0.967881	−	1.67642i
$476$		0			0
$477$	−0.589454	−	1.02096i	−0.0269893	−	0.0467468i
$478$		0			0
$479$	−3.46410	+	6.00000i	−0.158279	+	0.274147i	−0.934248	−	0.356624i	$-0.883928\pi$
$479$	−3.46410	+	6.00000i	−0.158279	+	0.274147i	0.775969	+	0.630771i	$0.217261\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$	−2.41269	+	4.17891i	−0.109781	+	0.190147i
$484$		0			0
$485$	36.5367	+	63.2835i	1.65905	+	2.87355i
$486$		0			0
$487$	12.1244	+	21.0000i	0.549407	+	0.951601i	0.998315	+	0.0580230i	$0.0184797\pi$
$487$	12.1244	+	21.0000i	0.549407	+	0.951601i	−0.448908	+	0.893578i	$0.648187\pi$
$488$		0			0
$489$	−1.05141			−0.0475463
$490$		0			0
$491$	−13.3578	+	23.1364i	−0.602830	+	1.04413i	0.389561	+	0.921001i	$0.372627\pi$
$491$	−13.3578	+	23.1364i	−0.602830	+	1.04413i	−0.992390	+	0.123131i	$0.960706\pi$
$492$		0			0
$493$	−16.4633			−0.741469
$494$		0			0
$495$	−14.3578			−0.645336
$496$		0			0
$497$	−4.17891	+	7.23808i	−0.187450	+	0.324672i
$498$		0			0
$499$	−11.7536			−0.526163			−0.263081	−	0.964774i	$-0.584739\pi$
$499$	−11.7536			−0.526163			−0.263081	+	0.964774i	$0.584739\pi$
$500$		0			0
$501$	3.46410	+	6.00000i	0.154765	+	0.268060i
$502$		0			0
$503$	−3.00000	−	5.19615i	−0.133763	−	0.231685i	0.791361	−	0.611349i	$-0.209373\pi$
$503$	−3.00000	−	5.19615i	−0.133763	−	0.231685i	−0.925124	+	0.379664i	$0.876040\pi$
$504$		0			0
$505$	1.70161	−	2.94727i	0.0757205	−	0.131152i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−2.75302	+	4.76836i	−0.122025	+	0.211354i	−0.920566	−	0.390587i	$-0.872272\pi$
$509$	−2.75302	+	4.76836i	−0.122025	+	0.211354i	0.798541	+	0.601940i	$0.205606\pi$
$510$		0			0
$511$	17.9105	+	31.0220i	0.792316	+	1.37233i
$512$		0			0
$513$	−1.73205	−	3.00000i	−0.0764719	−	0.132453i
$514$		0			0
$515$	33.8995			1.49379
$516$		0			0
$517$	18.0000	−	31.1769i	0.791639	−	1.37116i
$518$		0			0
$519$	−18.0000			−0.790112
$520$		0			0
$521$	17.8945			0.783974			0.391987	−	0.919971i	$-0.371788\pi$
$521$	17.8945			0.783974			0.391987	+	0.919971i	$0.371788\pi$
$522$		0			0
$523$	−0.821092	+	1.42217i	−0.0359038	+	0.0621873i	−0.883419	−	0.468584i	$-0.844764\pi$
$523$	−0.821092	+	1.42217i	−0.0359038	+	0.0621873i	0.847515	+	0.530771i	$0.178098\pi$
$524$		0			0
$525$	29.3840			1.28242
$526$		0			0
$527$	2.72257	+	4.71563i	0.118597	+	0.205416i
$528$		0			0
$529$	9.50000	+	16.4545i	0.413043	+	0.715412i
$530$		0			0
$531$	5.87680	−	10.1789i	0.255031	−	0.441727i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	20.7237	−	35.8945i	0.895965	−	1.55186i
$536$		0			0
$537$	7.17891	+	12.4342i	0.309793	+	0.536577i
$538$		0			0
$539$	−2.04193	−	3.53673i	−0.0879521	−	0.152338i
$540$		0			0
$541$	−10.0215			−0.430860			−0.215430	−	0.976519i	$-0.569115\pi$
$541$	−10.0215			−0.430860			−0.215430	+	0.976519i	$0.569115\pi$
$542$		0			0
$543$	6.76836	−	11.7231i	0.290458	−	0.503088i
$544$		0			0
$545$	4.35782			0.186668
$546$		0			0
$547$	−20.5367			−0.878087			−0.439043	−	0.898466i	$-0.644683\pi$
$547$	−20.5367			−0.878087			−0.439043	+	0.898466i	$0.644683\pi$
$548$		0			0
$549$	−2.50000	+	4.33013i	−0.106697	+	0.184805i
$550$		0			0
$551$	11.0121			0.469130
$552$		0			0
$553$	−2.19687	−	3.80509i	−0.0934203	−	0.161809i
$554$		0			0
$555$	15.7684	+	27.3116i	0.669330	+	1.15931i
$556$		0			0
$557$	13.4552	−	23.3051i	0.570115	−	0.987468i	−0.426439	−	0.904517i	$-0.640232\pi$
$557$	13.4552	−	23.3051i	0.570115	−	0.987468i	0.996554	−	0.0829517i	$-0.0264347\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−8.97013	+	15.5367i	−0.378719	+	0.655961i
$562$		0			0
$563$	2.17891	+	3.77398i	0.0918300	+	0.159054i	0.908281	−	0.418360i	$-0.137395\pi$
$563$	2.17891	+	3.77398i	0.0918300	+	0.159054i	−0.816451	+	0.577414i	$0.804062\pi$
$564$		0			0
$565$	−1.70161	−	2.94727i	−0.0715872	−	0.123993i
$566$		0			0
$567$	2.41269			0.101324
$568$		0			0
$569$	7.35782	−	12.7441i	0.308456	−	0.534261i	−0.669569	−	0.742750i	$-0.733521\pi$
$569$	7.35782	−	12.7441i	0.308456	−	0.534261i	0.978025	+	0.208489i	$0.0668545\pi$
$570$		0			0
$571$	30.3578			1.27044			0.635218	−	0.772333i	$-0.280910\pi$
$571$	30.3578			1.27044			0.635218	+	0.772333i	$0.280910\pi$
$572$		0			0
$573$	20.3578			0.850460
$574$		0			0
$575$	−12.1789	+	21.0945i	−0.507896	+	0.879701i
$576$		0			0
$577$	10.4532			0.435172			0.217586	−	0.976041i	$-0.430182\pi$
$577$	10.4532			0.435172			0.217586	+	0.976041i	$0.430182\pi$
$578$		0			0
$579$	−0.185382	−	0.321092i	−0.00770423	−	0.0133441i
$580$		0			0
$581$	1.64218	+	2.84434i	0.0681292	+	0.118003i
$582$		0			0
$583$	2.04193	−	3.53673i	0.0845681	−	0.146476i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	4.51551	−	7.82109i	0.186375	−	0.322811i	−0.757664	−	0.652645i	$-0.773659\pi$
$587$	4.51551	−	7.82109i	0.186375	−	0.322811i	0.944039	+	0.329834i	$0.106993\pi$
$588$		0			0
$589$	−1.82109	−	3.15422i	−0.0750368	−	0.129968i
$590$		0			0
$591$	−8.28949	−	14.3578i	−0.340984	−	0.590602i
$592$		0			0
$593$	−0.0608864			−0.00250030			−0.00125015	−	0.999999i	$-0.500398\pi$
$593$	−0.0608864			−0.00250030			−0.00125015	+	0.999999i	$0.500398\pi$
$594$		0			0
$595$	25.8945	−	44.8507i	1.06157	−	1.83870i
$596$		0			0
$597$	−12.5367			−0.513094
$598$		0			0
$599$	32.3578			1.32210			0.661052	−	0.750340i	$-0.270110\pi$
$599$	32.3578			1.32210			0.661052	+	0.750340i	$0.270110\pi$
$600$		0			0
$601$	−5.58945	+	9.68122i	−0.227999	+	0.394905i	−0.957215	−	0.289378i	$-0.906551\pi$
$601$	−5.58945	+	9.68122i	−0.227999	+	0.394905i	0.729216	+	0.684283i	$0.239885\pi$
$602$		0			0
$603$	−2.41269			−0.0982525
$604$		0			0
$605$	−2.07237	−	3.58945i	−0.0842539	−	0.145932i
$606$		0			0
$607$	−8.00000	−	13.8564i	−0.324710	−	0.562414i	0.656744	−	0.754114i	$-0.271933\pi$
$607$	−8.00000	−	13.8564i	−0.324710	−	0.562414i	−0.981454	+	0.191700i	$0.938600\pi$
$608$		0			0
$609$	−3.83487	+	6.64218i	−0.155397	+	0.269155i
$610$		0			0
$611$		0			0
$612$		0			0
$613$	14.3517	−	24.8578i	0.579658	−	1.00400i	−0.415860	−	0.909429i	$-0.636519\pi$
$613$	14.3517	−	24.8578i	0.579658	−	1.00400i	0.995518	−	0.0945691i	$-0.0301473\pi$
$614$		0			0
$615$	1.41055	+	2.44314i	0.0568787	+	0.0985168i
$616$		0			0
$617$	−2.07237	−	3.58945i	−0.0834306	−	0.144506i	0.821291	−	0.570510i	$-0.193254\pi$
$617$	−2.07237	−	3.58945i	−0.0834306	−	0.144506i	−0.904721	+	0.426004i	$0.859921\pi$
$618$		0			0
$619$	−22.4558			−0.902574			−0.451287	−	0.892379i	$-0.649035\pi$
$619$	−22.4558			−0.902574			−0.451287	+	0.892379i	$0.649035\pi$
$620$		0			0
$621$	−1.00000	+	1.73205i	−0.0401286	+	0.0695048i
$622$		0			0
$623$	−16.7156			−0.669698
$624$		0			0
$625$	62.4313			2.49725
$626$		0			0
$627$	6.00000	−	10.3923i	0.239617	−	0.415029i
$628$		0			0
$629$	39.4055			1.57120
$630$		0			0
$631$	−6.40250	−	11.0895i	−0.254879	−	0.441464i	0.709983	−	0.704219i	$-0.248702\pi$
$631$	−6.40250	−	11.0895i	−0.254879	−	0.441464i	−0.964863	+	0.262754i	$0.915369\pi$
$632$		0			0
$633$	−9.26836	−	16.0533i	−0.368384	−	0.638060i
$634$		0			0
$635$	−29.3840	+	50.8945i	−1.16607	+	2.01969i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−1.73205	+	3.00000i	−0.0685189	+	0.118678i
$640$		0			0
$641$	16.7684	+	29.0437i	0.662310	+	1.14716i	0.980007	+	0.198963i	$0.0637574\pi$
$641$	16.7684	+	29.0437i	0.662310	+	1.14716i	−0.317697	+	0.948192i	$0.602909\pi$
$642$		0			0
$643$	1.88699	+	3.26836i	0.0744156	+	0.128892i	0.900832	−	0.434168i	$-0.142958\pi$
$643$	1.88699	+	3.26836i	0.0744156	+	0.128892i	−0.826416	+	0.563059i	$0.809624\pi$
$644$		0			0
$645$	50.4785			1.98759
$646$		0			0
$647$	18.1789	−	31.4868i	0.714687	−	1.23787i	−0.248394	−	0.968659i	$-0.579903\pi$
$647$	18.1789	−	31.4868i	0.714687	−	1.23787i	0.963080	−	0.269214i	$-0.0867640\pi$
$648$		0			0
$649$	40.7156			1.59823
$650$		0			0
$651$	2.53673			0.0994221
$652$		0			0
$653$	11.1789	−	19.3624i	0.437464	−	0.757711i	−0.560029	−	0.828473i	$-0.689210\pi$
$653$	11.1789	−	19.3624i	0.437464	−	0.757711i	0.997493	+	0.0707625i	$0.0225432\pi$
$654$		0			0
$655$	−67.7990			−2.64913
$656$		0			0
$657$	7.42346	+	12.8578i	0.289617	+	0.501631i
$658$		0			0
$659$	−18.3578	−	31.7967i	−0.715119	−	1.23862i	−0.962914	−	0.269810i	$-0.913039\pi$
$659$	−18.3578	−	31.7967i	−0.715119	−	1.23862i	0.247795	−	0.968813i	$-0.420294\pi$
$660$		0			0
$661$	19.5478	−	33.8578i	0.760322	−	1.31692i	−0.182363	−	0.983231i	$-0.558374\pi$
$661$	19.5478	−	33.8578i	0.760322	−	1.31692i	0.942685	−	0.333685i	$-0.108292\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−17.3205	+	30.0000i	−0.671660	+	1.16335i
$666$		0			0
$667$	−3.17891	−	5.50603i	−0.123088	−	0.213194i
$668$		0			0
$669$	1.05141	+	1.82109i	0.0406498	+	0.0704075i
$670$		0			0
$671$	−17.3205			−0.668651
$672$		0			0
$673$	8.67891	−	15.0323i	0.334547	−	0.579453i	−0.648850	−	0.760916i	$-0.724750\pi$
$673$	8.67891	−	15.0323i	0.334547	−	0.579453i	0.983398	+	0.181463i	$0.0580833\pi$
$674$		0			0
$675$	12.1789			0.468766
$676$		0			0
$677$	−26.3578			−1.01301			−0.506507	−	0.862236i	$-0.669063\pi$
$677$	−26.3578			−1.01301			−0.506507	+	0.862236i	$0.669063\pi$
$678$		0			0
$679$	21.2684	−	36.8379i	0.816205	−	1.41371i
$680$		0			0
$681$	−22.1459			−0.848633
$682$		0			0
$683$	−10.7022	−	18.5367i	−0.409508	−	0.709288i	0.585327	−	0.810797i	$-0.300966\pi$
$683$	−10.7022	−	18.5367i	−0.409508	−	0.709288i	−0.994835	+	0.101509i	$0.967633\pi$
$684$		0			0
$685$	12.9473	+	22.4253i	0.494690	+	0.856828i
$686$		0			0
$687$	−8.28949	+	14.3578i	−0.316264	+	0.547785i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−18.8367	+	32.6262i	−0.716583	+	1.24116i	0.245763	+	0.969330i	$0.420962\pi$
$691$	−18.8367	+	32.6262i	−0.716583	+	1.24116i	−0.962346	+	0.271828i	$0.912372\pi$
$692$		0			0
$693$	4.17891	+	7.23808i	0.158744	+	0.274952i
$694$		0			0
$695$	−12.0635	−	20.8945i	−0.457593	−	0.792575i
$696$		0			0
$697$	3.52499			0.133518
$698$		0			0
$699$	−11.3578	+	19.6723i	−0.429592	+	0.744075i
$700$		0			0
$701$	−25.6422			−0.968492			−0.484246	−	0.874932i	$-0.660906\pi$
$701$	−25.6422			−0.968492			−0.484246	+	0.874932i	$0.660906\pi$
$702$		0			0
$703$	−26.3578			−0.994104
$704$		0			0
$705$	−21.5367	+	37.3027i	−0.811120	+	1.40490i
$706$		0			0
$707$	−1.98104			−0.0745048
$708$		0			0
$709$	−14.7224	−	25.5000i	−0.552913	−	0.957673i	−0.998063	−	0.0622167i	$-0.980183\pi$
$709$	−14.7224	−	25.5000i	−0.552913	−	0.957673i	0.445150	−	0.895456i	$-0.353150\pi$
$710$		0			0
$711$	−0.910546	−	1.57711i	−0.0341481	−	0.0591463i
$712$		0			0
$713$	−1.05141	+	1.82109i	−0.0393755	+	0.0682004i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	7.60885	−	13.1789i	0.284158	−	0.492175i
$718$		0			0
$719$	−3.82109	−	6.61832i	−0.142503	−	0.246822i	0.785936	−	0.618308i	$-0.212182\pi$
$719$	−3.82109	−	6.61832i	−0.142503	−	0.246822i	−0.928438	+	0.371486i	$0.878848\pi$
$720$		0			0
$721$	−9.86660	−	17.0895i	−0.367451	−	0.636445i
$722$		0			0
$723$	−0.680643			−0.0253134
$724$		0			0
$725$	−19.3578	+	33.5287i	−0.718931	+	1.24523i
$726$		0			0
$727$	16.5367			0.613313			0.306657	−	0.951820i	$-0.400790\pi$
$727$	16.5367			0.613313			0.306657	+	0.951820i	$0.400790\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	31.5367	−	54.6232i	1.16643	−	2.02031i
$732$		0			0
$733$	41.8182			1.54459			0.772295	−	0.635264i	$-0.219109\pi$
$733$	41.8182			1.54459			0.772295	+	0.635264i	$0.219109\pi$
$734$		0			0
$735$	2.44314	+	4.23164i	0.0901165	+	0.156086i
$736$		0			0
$737$	−4.17891	−	7.23808i	−0.153932	−	0.266618i
$738$		0			0
$739$	−1.05141	+	1.82109i	−0.0386767	+	0.0669899i	−0.884716	−	0.466131i	$-0.845648\pi$
$739$	−1.05141	+	1.82109i	−0.0386767	+	0.0669899i	0.846039	+	0.533121i	$0.178981\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−5.87680	+	10.1789i	−0.215599	+	0.373428i	−0.953458	−	0.301527i	$-0.902504\pi$
$743$	−5.87680	+	10.1789i	−0.215599	+	0.373428i	0.737859	+	0.674955i	$0.235837\pi$
$744$		0			0
$745$	−1.41055	−	2.44314i	−0.0516784	−	0.0895096i
$746$		0			0
$747$	0.680643	+	1.17891i	0.0249034	+	0.0431340i
$748$		0			0
$749$	−24.1269			−0.881579
$750$		0			0
$751$	−21.1789	+	36.6829i	−0.772829	+	1.33858i	0.163177	+	0.986597i	$0.447826\pi$
$751$	−21.1789	+	36.6829i	−0.772829	+	1.33858i	−0.936006	+	0.351983i	$0.885508\pi$
$752$		0			0
$753$	−24.7156			−0.900688
$754$		0			0
$755$	25.6422			0.933215
$756$		0			0
$757$	−3.35782	+	5.81591i	−0.122042	+	0.211383i	−0.920573	−	0.390571i	$-0.872278\pi$
$757$	−3.35782	+	5.81591i	−0.122042	+	0.211383i	0.798531	+	0.601954i	$0.205611\pi$
$758$		0			0
$759$	−6.92820			−0.251478
$760$		0			0
$761$	24.2487	+	42.0000i	0.879015	+	1.52250i	0.852423	+	0.522852i	$0.175132\pi$
$761$	24.2487	+	42.0000i	0.879015	+	1.52250i	0.0265919	+	0.999646i	$0.491535\pi$
$762$		0			0
$763$	−1.26836	−	2.19687i	−0.0459178	−	0.0795320i
$764$		0			0
$765$	10.7326	−	18.5895i	0.388039	−	0.672103i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	3.46410	−	6.00000i	0.124919	−	0.216366i	−0.796782	−	0.604266i	$-0.793466\pi$
$769$	3.46410	−	6.00000i	0.124919	−	0.216366i	0.921701	+	0.387901i	$0.126800\pi$
$770$		0			0
$771$	5.41055	+	9.37134i	0.194856	+	0.337501i
$772$		0			0
$773$	3.77398	+	6.53673i	0.135741	+	0.235110i	0.925880	−	0.377817i	$-0.123325\pi$
$773$	3.77398	+	6.53673i	0.135741	+	0.235110i	−0.790140	+	0.612927i	$0.789992\pi$
$774$		0			0
$775$	12.8050			0.459969
$776$		0			0
$777$	9.17891	−	15.8983i	0.329292	−	0.570350i
$778$		0			0
$779$	−2.35782			−0.0844775
$780$		0			0
$781$	−12.0000			−0.429394
$782$		0			0
$783$	−1.58945	+	2.75302i	−0.0568025	+	0.0983847i
$784$		0			0
$785$	29.0132			1.03553
$786$		0			0
$787$	20.2589	+	35.0895i	0.722152	+	1.25080i	0.960136	+	0.279535i	$0.0901802\pi$
$787$	20.2589	+	35.0895i	0.722152	+	1.25080i	−0.237984	+	0.971269i	$0.576486\pi$
$788$		0			0
$789$	−4.82109	−	8.35038i	−0.171635	−	0.297281i
$790$		0			0
$791$	−0.990521	+	1.71563i	−0.0352189	+	0.0610009i
$792$		0			0
$793$		0			0
$794$		0			0
$795$	−2.44314	+	4.23164i	−0.0866491	+	0.150081i
$796$		0			0
$797$	−25.5367	−	44.2309i	−0.904557	−	1.56674i	−0.821510	−	0.570193i	$-0.806868\pi$
$797$	−25.5367	−	44.2309i	−0.904557	−	1.56674i	−0.0830467	−	0.996546i	$-0.526465\pi$
$798$		0			0
$799$	26.9104	+	46.6102i	0.952021	+	1.64895i
$800$		0			0
$801$	−6.92820			−0.244796
$802$		0			0
$803$	−25.7156	+	44.5408i	−0.907485	+	1.57181i
$804$		0			0
$805$	20.0000			0.704907
$806$		0			0
$807$	10.3578			0.364612
$808$		0			0
$809$	−6.23164	+	10.7935i	−0.219093	+	0.379480i	−0.954531	−	0.298112i	$-0.903643\pi$
$809$	−6.23164	+	10.7935i	−0.219093	+	0.379480i	0.735438	+	0.677592i	$0.236976\pi$
$810$		0			0
$811$	−5.87680			−0.206362			−0.103181	−	0.994663i	$-0.532902\pi$
$811$	−5.87680			−0.206362			−0.103181	+	0.994663i	$0.532902\pi$
$812$		0			0
$813$	−3.98981	−	6.91055i	−0.139929	−	0.242363i
$814$		0			0
$815$	2.17891	+	3.77398i	0.0763238	+	0.132197i
$816$		0			0
$817$	−21.0945	+	36.5367i	−0.738003	+	1.27826i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	3.77398	−	6.53673i	0.131713	−	0.228133i	−0.792624	−	0.609711i	$-0.791286\pi$
$821$	3.77398	−	6.53673i	0.131713	−	0.228133i	0.924337	+	0.381577i	$0.124619\pi$
$822$		0			0
$823$	−12.0000	−	20.7846i	−0.418294	−	0.724506i	0.577474	−	0.816409i	$-0.304038\pi$
$823$	−12.0000	−	20.7846i	−0.418294	−	0.724506i	−0.995768	+	0.0919029i	$0.970705\pi$
$824$		0			0
$825$	21.0945	+	36.5367i	0.734416	+	1.27205i
$826$		0			0
$827$	42.8087			1.48861			0.744303	−	0.667842i	$-0.232782\pi$
$827$	42.8087			1.48861			0.744303	+	0.667842i	$0.232782\pi$
$828$		0			0
$829$	0.321092	−	0.556147i	0.0111520	−	0.0193158i	−0.860396	−	0.509627i	$-0.829783\pi$
$829$	0.321092	−	0.556147i	0.0111520	−	0.0193158i	0.871548	+	0.490311i	$0.163117\pi$
$830$		0			0
$831$	−11.1789			−0.387792
$832$		0			0
$833$	6.10546			0.211542
$834$		0			0
$835$	14.3578	−	24.8685i	0.496873	−	0.860609i
$836$		0			0
$837$	1.05141			0.0363420
$838$		0			0
$839$	1.05141	+	1.82109i	0.0362986	+	0.0628711i	0.883604	−	0.468235i	$-0.155110\pi$
$839$	1.05141	+	1.82109i	0.0362986	+	0.0628711i	−0.847305	+	0.531106i	$0.821777\pi$
$840$		0			0
$841$	9.44727	+	16.3632i	0.325768	+	0.564247i
$842$		0			0
$843$	9.00058	−	15.5895i	0.309996	−	0.536929i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−1.20635	+	2.08945i	−0.0414506	+	0.0717945i
$848$		0			0
$849$	−7.91055	−	13.7015i	−0.271489	−	0.470233i
$850$		0			0
$851$	7.60885	+	13.1789i	0.260828	+	0.451767i
$852$		0			0
$853$	37.7344			1.29200			0.646000	−	0.763338i	$-0.276441\pi$
$853$	37.7344			1.29200			0.646000	+	0.763338i	$0.276441\pi$
$854$		0			0
$855$	−7.17891	+	12.4342i	−0.245513	+	0.425242i
$856$		0			0
$857$	8.82109			0.301323			0.150661	−	0.988585i	$-0.451860\pi$
$857$	8.82109			0.301323			0.150661	+	0.988585i	$0.451860\pi$
$858$		0			0
$859$	−25.2524			−0.861599			−0.430800	−	0.902448i	$-0.641768\pi$
$859$	−25.2524			−0.861599			−0.430800	+	0.902448i	$0.641768\pi$
$860$		0			0
$861$	0.821092	−	1.42217i	0.0279827	−	0.0484675i
$862$		0			0
$863$	−6.18667			−0.210597			−0.105298	−	0.994441i	$-0.533580\pi$
$863$	−6.18667			−0.210597			−0.105298	+	0.994441i	$0.533580\pi$
$864$		0			0
$865$	37.3027	+	64.6102i	1.26833	+	2.19681i
$866$		0			0
$867$	−4.91055	−	8.50531i	−0.166771	−	0.288856i
$868$		0			0
$869$	3.15422	−	5.46327i	0.107000	−	0.185329i
$870$		0			0
$871$		0			0
$872$		0			0
$873$	8.81519	−	15.2684i	0.298349	−	0.516756i
$874$		0			0
$875$	−35.8945	−	62.1712i	−1.21346	−	2.10177i
$876$		0			0
$877$	3.12378	+	5.41055i	0.105483	+	0.182701i	0.913935	−	0.405860i	$-0.133028\pi$
$877$	3.12378	+	5.41055i	0.105483	+	0.182701i	−0.808453	+	0.588561i	$0.799695\pi$
$878$		0			0
$879$	0.0608864			0.00205365
$880$		0			0
$881$	−24.5895	+	42.5902i	−0.828440	+	1.43490i	0.0708220	+	0.997489i	$0.477438\pi$
$881$	−24.5895	+	42.5902i	−0.828440	+	1.43490i	−0.899262	+	0.437411i	$0.855896\pi$
$882$		0			0
$883$	−38.8945			−1.30891			−0.654453	−	0.756103i	$-0.727101\pi$
$883$	−38.8945			−1.30891			−0.654453	+	0.756103i	$0.727101\pi$
$884$		0			0
$885$	−48.7156			−1.63756
$886$		0			0
$887$	−22.1789	+	38.4150i	−0.744695	+	1.28985i	0.205642	+	0.978627i	$0.434072\pi$
$887$	−22.1789	+	38.4150i	−0.744695	+	1.28985i	−0.950337	+	0.311222i	$0.899262\pi$
$888$		0			0
$889$	34.2094			1.14735
$890$		0			0
$891$	1.73205	+	3.00000i	0.0580259	+	0.100504i
$892$		0			0
$893$	−18.0000	−	31.1769i	−0.602347	−	1.04330i
$894$		0			0
$895$	29.7547	−	51.5367i	0.994591	−	1.72268i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−1.67116	+	2.89454i	−0.0557365	+	0.0965384i
$900$		0			0
$901$	3.05273	+	5.28748i	0.101701	+	0.176152i
$902$		0			0
$903$	−14.6920	−	25.4473i	−0.488919	−	0.846832i
$904$		0			0
$905$	−56.1063			−1.86504
$906$		0			0
$907$	14.0000	−	24.2487i	0.464862	−	0.805165i	−0.534333	−	0.845274i	$-0.679437\pi$
$907$	14.0000	−	24.2487i	0.464862	−	0.805165i	0.999195	+	0.0401089i	$0.0127705\pi$
$908$		0			0
$909$	−0.821092			−0.0272339
$910$		0			0
$911$	−40.7156			−1.34897			−0.674485	−	0.738289i	$-0.735634\pi$
$911$	−40.7156			−1.34897			−0.674485	+	0.738289i	$0.735634\pi$
$912$		0			0
$913$	−2.35782	+	4.08386i	−0.0780323	+	0.135156i
$914$		0			0
$915$	20.7237			0.685105
$916$		0			0
$917$	19.7332	+	34.1789i	0.651648	+	1.12869i
$918$		0			0
$919$	−12.0000	−	20.7846i	−0.395843	−	0.685621i	0.597365	−	0.801970i	$-0.296214\pi$
$919$	−12.0000	−	20.7846i	−0.395843	−	0.685621i	−0.993208	+	0.116348i	$0.962881\pi$
$920$		0			0
$921$	2.25775	−	3.91055i	0.0743955	−	0.128857i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	46.3337	−	80.2524i	1.52344	−	2.63868i
$926$		0			0
$927$	−4.08945	−	7.08314i	−0.134315	−	0.232641i
$928$		0			0
$929$	−5.90724	−	10.2316i	−0.193810	−	0.335689i	0.752700	−	0.658364i	$-0.228751\pi$
$929$	−5.90724	−	10.2316i	−0.193810	−	0.335689i	−0.946510	+	0.322675i	$0.895418\pi$
$930$		0			0
$931$	−4.08386			−0.133843
$932$		0			0
$933$	17.1789	−	29.7547i	0.562412	−	0.974127i
$934$		0			0
$935$	74.3578			2.43176
$936$		0			0
$937$	−7.89454			−0.257903			−0.128952	−	0.991651i	$-0.541161\pi$
$937$	−7.89454			−0.257903			−0.128952	+	0.991651i	$0.541161\pi$
$938$		0			0
$939$	14.4473	−	25.0234i	0.471469	−	0.816608i
$940$		0			0
$941$	−54.5623			−1.77868			−0.889340	−	0.457246i	$-0.848836\pi$
$941$	−54.5623			−1.77868			−0.889340	+	0.457246i	$0.848836\pi$
$942$		0			0
$943$	0.680643	+	1.17891i	0.0221648	+	0.0383905i
$944$		0			0
$945$	−5.00000	−	8.66025i	−0.162650	−	0.281718i
$946$		0			0
$947$	−2.10282	+	3.64218i	−0.0683323	+	0.118355i	−0.898167	−	0.439654i	$-0.855101\pi$
$947$	−2.10282	+	3.64218i	−0.0683323	+	0.118355i	0.829835	+	0.558009i	$0.188434\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	7.94917	−	13.7684i	0.257769	−	0.446470i
$952$		0			0
$953$	3.00000	+	5.19615i	0.0971795	+	0.168320i	0.910516	−	0.413473i	$-0.135685\pi$
$953$	3.00000	+	5.19615i	0.0971795	+	0.168320i	−0.813337	+	0.581793i	$0.802351\pi$
$954$		0			0
$955$	−42.1890	−	73.0735i	−1.36520	−	2.36460i
$956$		0			0
$957$	−11.0121			−0.355969
$958$		0			0
$959$	7.53673	−	13.0540i	0.243374	−	0.421535i
$960$		0			0
$961$	−29.8945			−0.964340
$962$		0			0
$963$	−10.0000			−0.322245
$964$		0			0
$965$	−0.768363	+	1.33084i	−0.0247345	+	0.0428413i
$966$		0			0
$967$	61.6123			1.98132			0.990659	−	0.136363i	$-0.0435412\pi$
$967$	61.6123			1.98132			0.990659	+	0.136363i	$0.0435412\pi$
$968$		0			0
$969$	8.97013	+	15.5367i	0.288162	+	0.499112i
$970$		0			0
$971$	20.3578	+	35.2608i	0.653313	+	1.13157i	0.982314	+	0.187242i	$0.0599549\pi$
$971$	20.3578	+	35.2608i	0.653313	+	1.13157i	−0.329000	+	0.944330i	$0.606712\pi$
$972$		0			0
$973$	−7.02226	+	12.1629i	−0.225123	+	0.389925i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−18.3415	+	31.7684i	−0.586796	+	1.01636i	0.407853	+	0.913047i	$0.366277\pi$
$977$	−18.3415	+	31.7684i	−0.586796	+	1.01636i	−0.994649	+	0.103312i	$0.967056\pi$
$978$		0			0
$979$	−12.0000	−	20.7846i	−0.383522	−	0.664279i
$980$		0			0
$981$	−0.525704	−	0.910546i	−0.0167844	−	0.0290715i
$982$		0			0
$983$	14.4762			0.461718			0.230859	−	0.972987i	$-0.425846\pi$
$983$	14.4762			0.461718			0.230859	+	0.972987i	$0.425846\pi$
$984$		0			0
$985$	−34.3578	+	59.5095i	−1.09473	+	1.89613i
$986$		0			0
$987$	25.0735			0.798097
$988$		0			0
$989$	24.3578			0.774534
$990$		0			0
$991$	−11.5367	+	19.9822i	−0.366476	+	0.634755i	−0.989012	−	0.147836i	$-0.952769\pi$
$991$	−11.5367	+	19.9822i	−0.366476	+	0.634755i	0.622536	+	0.782591i	$0.286103\pi$
$992$		0			0
$993$	26.6614			0.846074
$994$		0			0
$995$	25.9808	+	45.0000i	0.823646	+	1.42660i
$996$		0			0
$997$	−6.32109	−	10.9485i	−0.200191	−	0.346741i	0.748399	−	0.663249i	$-0.230823\pi$
$997$	−6.32109	−	10.9485i	−0.200191	−	0.346741i	−0.948590	+	0.316508i	$0.897490\pi$
$998$		0			0
$999$	3.80442	−	6.58945i	0.120367	−	0.208481i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2028.2.i.n.529.4		8
13.2	odd	12		2028.2.q.f.361.1		4
13.3	even	3	inner	2028.2.i.n.2005.4		8
13.4	even	6		2028.2.a.m.1.1		4
13.5	odd	4		156.2.q.b.121.1	yes	4
13.6	odd	12		2028.2.b.e.337.1		4
13.7	odd	12		2028.2.b.e.337.4		4
13.8	odd	4		2028.2.q.f.1837.2		4
13.9	even	3		2028.2.a.m.1.4		4
13.10	even	6	inner	2028.2.i.n.2005.1		8
13.11	odd	12		156.2.q.b.49.2	✓	4
13.12	even	2	inner	2028.2.i.n.529.1		8
39.5	even	4		468.2.t.d.433.2		4
39.11	even	12		468.2.t.d.361.1		4
39.17	odd	6		6084.2.a.bd.1.4		4
39.20	even	12		6084.2.b.o.4393.1		4
39.32	even	12		6084.2.b.o.4393.4		4
39.35	odd	6		6084.2.a.bd.1.1		4
52.11	even	12		624.2.bv.f.49.2		4
52.31	even	4		624.2.bv.f.433.1		4
52.35	odd	6		8112.2.a.cr.1.4		4
52.43	odd	6		8112.2.a.cr.1.1		4
65.18	even	4		3900.2.bw.j.2149.1		8
65.24	odd	12		3900.2.cd.i.2701.1		4
65.37	even	12		3900.2.bw.j.49.1		8
65.44	odd	4		3900.2.cd.i.901.1		4
65.57	even	4		3900.2.bw.j.2149.4		8
65.63	even	12		3900.2.bw.j.49.4		8
156.11	odd	12		1872.2.by.j.1297.1		4
156.83	odd	4		1872.2.by.j.433.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
156.2.q.b.49.2	✓	4	13.11	odd	12
156.2.q.b.121.1	yes	4	13.5	odd	4
468.2.t.d.361.1		4	39.11	even	12
468.2.t.d.433.2		4	39.5	even	4
624.2.bv.f.49.2		4	52.11	even	12
624.2.bv.f.433.1		4	52.31	even	4
1872.2.by.j.433.2		4	156.83	odd	4
1872.2.by.j.1297.1		4	156.11	odd	12
2028.2.a.m.1.1		4	13.4	even	6
2028.2.a.m.1.4		4	13.9	even	3
2028.2.b.e.337.1		4	13.6	odd	12
2028.2.b.e.337.4		4	13.7	odd	12
2028.2.i.n.529.1		8	13.12	even	2	inner
2028.2.i.n.529.4		8	1.1	even	1	trivial
2028.2.i.n.2005.1		8	13.10	even	6	inner
2028.2.i.n.2005.4		8	13.3	even	3	inner
2028.2.q.f.361.1		4	13.2	odd	12
2028.2.q.f.1837.2		4	13.8	odd	4
3900.2.bw.j.49.1		8	65.37	even	12
3900.2.bw.j.49.4		8	65.63	even	12
3900.2.bw.j.2149.1		8	65.18	even	4
3900.2.bw.j.2149.4		8	65.57	even	4
3900.2.cd.i.901.1		4	65.44	odd	4
3900.2.cd.i.2701.1		4	65.24	odd	12
6084.2.a.bd.1.1		4	39.35	odd	6
6084.2.a.bd.1.4		4	39.17	odd	6
6084.2.b.o.4393.1		4	39.20	even	12
6084.2.b.o.4393.4		4	39.32	even	12
8112.2.a.cr.1.1		4	52.43	odd	6
8112.2.a.cr.1.4		4	52.35	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2028 = 2^{2} \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2028.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{3} +4.14474 q^{5} +(-1.20635 - 2.08945i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(1.73205 - 3.00000i) q^{11} +(-2.07237 + 3.58945i) q^{15} +(2.58945 + 4.48507i) q^{17} +(-1.73205 - 3.00000i) q^{19} +2.41269 q^{21} +(-1.00000 + 1.73205i) q^{23} +12.1789 q^{25} +1.00000 q^{27} +(-1.58945 + 2.75302i) q^{29} +1.05141 q^{31} +(1.73205 + 3.00000i) q^{33} +(-5.00000 - 8.66025i) q^{35} +(3.80442 - 6.58945i) q^{37} +(0.340322 - 0.589454i) q^{41} +(-6.08945 - 10.5472i) q^{43} +(-2.07237 - 3.58945i) q^{45} +10.3923 q^{47} +(0.589454 - 1.02096i) q^{49} -5.17891 q^{51} +1.17891 q^{53} +(7.17891 - 12.4342i) q^{55} +3.46410 q^{57} +(5.87680 + 10.1789i) q^{59} +(-2.50000 - 4.33013i) q^{61} +(-1.20635 + 2.08945i) q^{63} +(1.20635 - 2.08945i) q^{67} +(-1.00000 - 1.73205i) q^{69} +(-1.73205 - 3.00000i) q^{71} -14.8469 q^{73} +(-6.08945 + 10.5472i) q^{75} -8.35782 q^{77} +1.82109 q^{79} +(-0.500000 + 0.866025i) q^{81} -1.36129 q^{83} +(10.7326 + 18.5895i) q^{85} +(-1.58945 - 2.75302i) q^{87} +(3.46410 - 6.00000i) q^{89} +(-0.525704 + 0.910546i) q^{93} +(-7.17891 - 12.4342i) q^{95} +(8.81519 + 15.2684i) q^{97} -3.46410 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} - 4 q^{9} - 2 q^{17} - 8 q^{23} + 52 q^{25} + 8 q^{27} + 10 q^{29} - 40 q^{35} - 26 q^{43} - 18 q^{49} + 4 q^{51} - 36 q^{53} + 12 q^{55} - 20 q^{61} - 8 q^{69} - 26 q^{75} + 24 q^{77} + 60 q^{79}+ \cdots - 12 q^{95}+O(q^{100}) \) 8 * q - 4 * q^3 - 4 * q^9 - 2 * q^17 - 8 * q^23 + 52 * q^25 + 8 * q^27 + 10 * q^29 - 40 * q^35 - 26 * q^43 - 18 * q^49 + 4 * q^51 - 36 * q^53 + 12 * q^55 - 20 * q^61 - 8 * q^69 - 26 * q^75 + 24 * q^77 + 60 * q^79 - 4 * q^81 + 10 * q^87 - 12 * q^95

Introduction

L-functions

Modular forms

Varieties

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Database

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