LMFDB - Embedded newform 2028.2.i.n.2005.3

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			2005.3
Root			$-2.07237 + 2.58945i$ of defining polynomial
Character	$\chi$	$=$	2028.2005
Dual form			2028.2.i.n.529.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{3} +2.41269 q^{5} +(-2.07237 + 3.58945i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(-1.73205 - 3.00000i) q^{11} +(-1.20635 - 2.08945i) q^{15} +(-3.08945 + 5.35109i) q^{17} +(1.73205 - 3.00000i) q^{19} +4.14474 q^{21} +(-1.00000 - 1.73205i) q^{23} +0.821092 q^{25} +1.00000 q^{27} +(4.08945 + 7.08314i) q^{29} -7.60885 q^{31} +(-1.73205 + 3.00000i) q^{33} +(-5.00000 + 8.66025i) q^{35} +(-0.525704 - 0.910546i) q^{37} +(2.93840 + 5.08945i) q^{41} +(-0.410546 + 0.711086i) q^{43} +(-1.20635 + 2.08945i) q^{45} -10.3923 q^{47} +(-5.08945 - 8.81519i) q^{49} +6.17891 q^{51} -10.1789 q^{53} +(-4.17891 - 7.23808i) q^{55} -3.46410 q^{57} +(0.680643 - 1.17891i) q^{59} +(-2.50000 + 4.33013i) q^{61} +(-2.07237 - 3.58945i) q^{63} +(2.07237 + 3.58945i) q^{67} +(-1.00000 + 1.73205i) q^{69} +(1.73205 - 3.00000i) q^{71} -11.3828 q^{73} +(-0.410546 - 0.711086i) q^{75} +14.3578 q^{77} +13.1789 q^{79} +(-0.500000 - 0.866025i) q^{81} -11.7536 q^{83} +(-7.45391 + 12.9105i) q^{85} +(4.08945 - 7.08314i) q^{87} +(-3.46410 - 6.00000i) q^{89} +(3.80442 + 6.58945i) q^{93} +(4.17891 - 7.23808i) q^{95} +(1.02096 - 1.76836i) q^{97} +3.46410 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2028\mathbb{Z}\right)^\times$.

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

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
$5$	2.41269			1.07899			0.539495	−	0.841989i	$-0.318615\pi$
$5$	2.41269			1.07899			0.539495	+	0.841989i	$0.318615\pi$
$6$		0			0
$7$	−2.07237	+	3.58945i	−0.783283	+	1.35669i	0.146736	+	0.989176i	$0.453123\pi$
$7$	−2.07237	+	3.58945i	−0.783283	+	1.35669i	−0.930019	+	0.367511i	$0.880210\pi$
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	−1.73205	−	3.00000i	−0.522233	−	0.904534i	−0.999665	−	0.0258656i	$-0.991766\pi$
$11$	−1.73205	−	3.00000i	−0.522233	−	0.904534i	0.477432	−	0.878668i	$-0.341568\pi$
$12$		0			0
$13$		0			0
$13$		0			0
$14$		0			0
$15$	−1.20635	−	2.08945i	−0.311477	−	0.539495i
$16$		0			0
$17$	−3.08945	+	5.35109i	−0.749303	+	1.29783i	0.198855	+	0.980029i	$0.436278\pi$
$17$	−3.08945	+	5.35109i	−0.749303	+	1.29783i	−0.948157	+	0.317801i	$0.897055\pi$
$18$		0			0
$19$	1.73205	−	3.00000i	0.397360	−	0.688247i	−0.596040	−	0.802955i	$-0.703260\pi$
$19$	1.73205	−	3.00000i	0.397360	−	0.688247i	0.993399	+	0.114708i	$0.0365932\pi$
$20$		0			0
$21$	4.14474			0.904457
$22$		0			0
$23$	−1.00000	−	1.73205i	−0.208514	−	0.361158i	0.742732	−	0.669588i	$-0.233529\pi$
$23$	−1.00000	−	1.73205i	−0.208514	−	0.361158i	−0.951247	+	0.308431i	$0.900196\pi$
$24$		0			0
$25$	0.821092			0.164218
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	4.08945	+	7.08314i	0.759393	+	1.31531i	0.943161	+	0.332337i	$0.107837\pi$
$29$	4.08945	+	7.08314i	0.759393	+	1.31531i	−0.183768	+	0.982970i	$0.558830\pi$
$30$		0			0
$31$	−7.60885			−1.36659			−0.683295	−	0.730143i	$-0.739454\pi$
$31$	−7.60885			−1.36659			−0.683295	+	0.730143i	$0.739454\pi$
$32$		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
$37$	−0.525704	−	0.910546i	−0.0864252	−	0.149693i	0.819572	−	0.572976i	$-0.194211\pi$
$37$	−0.525704	−	0.910546i	−0.0864252	−	0.149693i	−0.905998	+	0.423283i	$0.860878\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	2.93840	+	5.08945i	0.458901	+	0.794839i	0.998903	−	0.0468242i	$-0.0149101\pi$
$41$	2.93840	+	5.08945i	0.458901	+	0.794839i	−0.540003	+	0.841663i	$0.681577\pi$
$42$		0			0
$43$	−0.410546	+	0.711086i	−0.0626077	+	0.108440i	−0.895630	−	0.444799i	$-0.853275\pi$
$43$	−0.410546	+	0.711086i	−0.0626077	+	0.108440i	0.833023	+	0.553239i	$0.186608\pi$
$44$		0			0
$45$	−1.20635	+	2.08945i	−0.179832	+	0.311477i
$46$		0			0
$47$	−10.3923			−1.51587			−0.757937	−	0.652328i	$-0.773792\pi$
$47$	−10.3923			−1.51587			−0.757937	+	0.652328i	$0.773792\pi$
$48$		0			0
$49$	−5.08945	−	8.81519i	−0.727065	−	1.25931i
$50$		0			0
$51$	6.17891			0.865220
$52$		0			0
$53$	−10.1789			−1.39818			−0.699090	−	0.715033i	$-0.746411\pi$
$53$	−10.1789			−1.39818			−0.699090	+	0.715033i	$0.746411\pi$
$54$		0			0
$55$	−4.17891	−	7.23808i	−0.563484	−	0.975983i
$56$		0			0
$57$	−3.46410			−0.458831
$58$		0			0
$59$	0.680643	−	1.17891i	0.0886122	−	0.153481i	−0.818313	−	0.574773i	$-0.805090\pi$
$59$	0.680643	−	1.17891i	0.0886122	−	0.153481i	0.906925	+	0.421293i	$0.138423\pi$
$60$		0			0
$61$	−2.50000	+	4.33013i	−0.320092	+	0.554416i	−0.980507	−	0.196485i	$-0.937047\pi$
$61$	−2.50000	+	4.33013i	−0.320092	+	0.554416i	0.660415	+	0.750901i	$0.270381\pi$
$62$		0			0
$63$	−2.07237	−	3.58945i	−0.261094	−	0.452229i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	2.07237	+	3.58945i	0.253181	+	0.438522i	0.964400	−	0.264449i	$-0.0851900\pi$
$67$	2.07237	+	3.58945i	0.253181	+	0.438522i	−0.711219	+	0.702970i	$0.751857\pi$
$68$		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	$-0.767433\pi$
$71$	1.73205	−	3.00000i	0.205557	−	0.356034i	0.950310	+	0.311305i	$0.100766\pi$
$72$		0			0
$73$	−11.3828			−1.33226			−0.666130	−	0.745836i	$-0.732050\pi$
$73$	−11.3828			−1.33226			−0.666130	+	0.745836i	$0.732050\pi$
$74$		0			0
$75$	−0.410546	−	0.711086i	−0.0474057	−	0.0821092i
$76$		0			0
$77$	14.3578			1.63623
$78$		0			0
$79$	13.1789			1.48274			0.741372	−	0.671095i	$-0.234176\pi$
$79$	13.1789			1.48274			0.741372	+	0.671095i	$0.234176\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	−11.7536			−1.29012			−0.645062	−	0.764130i	$-0.723169\pi$
$83$	−11.7536			−1.29012			−0.645062	+	0.764130i	$0.723169\pi$
$84$		0			0
$85$	−7.45391	+	12.9105i	−0.808490	+	1.40035i
$86$		0			0
$87$	4.08945	−	7.08314i	0.438436	−	0.759393i
$88$		0			0
$89$	−3.46410	−	6.00000i	−0.367194	−	0.635999i	0.621932	−	0.783072i	$-0.286348\pi$
$89$	−3.46410	−	6.00000i	−0.367194	−	0.635999i	−0.989126	+	0.147073i	$0.953015\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	3.80442	+	6.58945i	0.394500	+	0.683295i
$94$		0			0
$95$	4.17891	−	7.23808i	0.428747	−	0.742612i
$96$		0			0
$97$	1.02096	−	1.76836i	0.103663	−	0.179550i	−0.809528	−	0.587081i	$-0.800277\pi$
$97$	1.02096	−	1.76836i	0.103663	−	0.179550i	0.913191	+	0.407531i	$0.133610\pi$
$98$		0			0
$99$	3.46410			0.348155
$100$		0			0
$101$	6.08945	+	10.5472i	0.605923	+	1.04949i	0.991905	+	0.126983i	$0.0405295\pi$
$101$	6.08945	+	10.5472i	0.605923	+	1.04949i	−0.385981	+	0.922507i	$0.626137\pi$
$102$		0			0
$103$	−3.17891			−0.313227			−0.156614	−	0.987660i	$-0.550058\pi$
$103$	−3.17891			−0.313227			−0.156614	+	0.987660i	$0.550058\pi$
$104$		0			0
$105$	10.0000			0.975900
$106$		0			0
$107$	5.00000	+	8.66025i	0.483368	+	0.837218i	0.999818	−	0.0190994i	$-0.00607989\pi$
$107$	5.00000	+	8.66025i	0.483368	+	0.837218i	−0.516449	+	0.856318i	$0.672747\pi$
$108$		0			0
$109$	−7.60885			−0.728795			−0.364398	−	0.931243i	$-0.618725\pi$
$109$	−7.60885			−0.728795			−0.364398	+	0.931243i	$0.618725\pi$
$110$		0			0
$111$	−0.525704	+	0.910546i	−0.0498976	+	0.0864252i
$112$		0			0
$113$	−6.08945	+	10.5472i	−0.572848	+	0.992201i	0.423424	+	0.905932i	$0.360828\pi$
$113$	−6.08945	+	10.5472i	−0.572848	+	0.992201i	−0.996272	+	0.0862697i	$0.972505\pi$
$114$		0			0
$115$	−2.41269	−	4.17891i	−0.224985	−	0.389685i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−12.8050	−	22.1789i	−1.17383	−	2.03314i
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$		0			0
$123$	2.93840	−	5.08945i	0.264946	−	0.458901i
$124$		0			0
$125$	−10.0824			−0.901800
$126$		0			0
$127$	−1.41055	−	2.44314i	−0.125166	−	0.216793i	0.796632	−	0.604465i	$-0.206613\pi$
$127$	−1.41055	−	2.44314i	−0.125166	−	0.216793i	−0.921798	+	0.387671i	$0.873280\pi$
$128$		0			0
$129$	0.821092			0.0722931
$130$		0			0
$131$	6.35782			0.555485			0.277743	−	0.960656i	$-0.410414\pi$
$131$	6.35782			0.555485			0.277743	+	0.960656i	$0.410414\pi$
$132$		0			0
$133$	7.17891	+	12.4342i	0.622490	+	1.07818i
$134$		0			0
$135$	2.41269			0.207652
$136$		0			0
$137$	−6.40250	+	11.0895i	−0.547002	+	0.947436i	0.451476	+	0.892284i	$0.350898\pi$
$137$	−6.40250	+	11.0895i	−0.547002	+	0.947436i	−0.998478	+	0.0551525i	$0.982436\pi$
$138$		0			0
$139$	−8.58945	+	14.8774i	−0.728548	+	1.26188i	0.228949	+	0.973438i	$0.426471\pi$
$139$	−8.58945	+	14.8774i	−0.728548	+	1.26188i	−0.957497	+	0.288444i	$0.906862\pi$
$140$		0			0
$141$	5.19615	+	9.00000i	0.437595	+	0.757937i
$142$		0			0
$143$		0			0
$144$		0			0
$145$	9.86660	+	17.0895i	0.819377	+	1.41920i
$146$		0			0
$147$	−5.08945	+	8.81519i	−0.419771	+	0.727065i
$148$		0			0
$149$	−2.93840	+	5.08945i	−0.240723	+	0.416944i	−0.960920	−	0.276825i	$-0.910718\pi$
$149$	−2.93840	+	5.08945i	−0.240723	+	0.416944i	0.720197	+	0.693769i	$0.244051\pi$
$150$		0			0
$151$	20.0431			1.63108			0.815541	−	0.578699i	$-0.196439\pi$
$151$	20.0431			1.63108			0.815541	+	0.578699i	$0.196439\pi$
$152$		0			0
$153$	−3.08945	−	5.35109i	−0.249768	−	0.432610i
$154$		0			0
$155$	−18.3578			−1.47454
$156$		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
$159$	5.08945	+	8.81519i	0.403620	+	0.699090i
$160$		0			0
$161$	8.28949			0.653303
$162$		0			0
$163$	−3.80442	+	6.58945i	−0.297985	+	0.516126i	−0.975675	−	0.219222i	$-0.929648\pi$
$163$	−3.80442	+	6.58945i	−0.297985	+	0.516126i	0.677690	+	0.735348i	$0.262981\pi$
$164$		0			0
$165$	−4.17891	+	7.23808i	−0.325328	+	0.563484i
$166$		0			0
$167$	−3.46410	−	6.00000i	−0.268060	−	0.464294i	0.700301	−	0.713848i	$-0.253049\pi$
$167$	−3.46410	−	6.00000i	−0.268060	−	0.464294i	−0.968361	+	0.249554i	$0.919716\pi$
$168$		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	−0.289412	−	0.957205i	$-0.593460\pi$
$173$	9.00000	−	15.5885i	0.684257	−	1.18517i	0.973670	−	0.227964i	$-0.0732068\pi$
$174$		0			0
$175$	−1.70161	+	2.94727i	−0.128629	+	0.222793i
$176$		0			0
$177$	−1.36129			−0.102321
$178$		0			0
$179$	−4.17891	−	7.23808i	−0.312346	−	0.541000i	0.666524	−	0.745484i	$-0.267782\pi$
$179$	−4.17891	−	7.23808i	−0.312346	−	0.541000i	−0.978870	+	0.204484i	$0.934448\pi$
$180$		0			0
$181$	20.5367			1.52648			0.763241	−	0.646113i	$-0.223607\pi$
$181$	20.5367			1.52648			0.763241	+	0.646113i	$0.223607\pi$
$182$		0			0
$183$	5.00000			0.369611
$184$		0			0
$185$	−1.26836	−	2.19687i	−0.0932519	−	0.161517i
$186$		0			0
$187$	21.4044			1.56524
$188$		0			0
$189$	−2.07237	+	3.58945i	−0.150743	+	0.261094i
$190$		0			0
$191$	1.17891	−	2.04193i	0.0853028	−	0.147749i	−0.820217	−	0.572052i	$-0.806148\pi$
$191$	1.17891	−	2.04193i	0.0853028	−	0.147749i	0.905520	+	0.424303i	$0.139481\pi$
$192$		0			0
$193$	6.74282	+	11.6789i	0.485359	+	0.840666i	0.999858	−	0.0168244i	$-0.00535563\pi$
$193$	6.74282	+	11.6789i	0.485359	+	0.840666i	−0.514500	+	0.857491i	$0.672022\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−4.82539	−	8.35782i	−0.343795	−	0.595470i	0.641339	−	0.767257i	$-0.278379\pi$
$197$	−4.82539	−	8.35782i	−0.343795	−	0.595470i	−0.985134	+	0.171788i	$0.945046\pi$
$198$		0			0
$199$	−10.7684	+	18.6514i	−0.763349	+	1.32216i	0.177766	+	0.984073i	$0.443113\pi$
$199$	−10.7684	+	18.6514i	−0.763349	+	1.32216i	−0.941115	+	0.338086i	$0.890220\pi$
$200$		0			0
$201$	2.07237	−	3.58945i	0.146174	−	0.253181i
$202$		0			0
$203$	−33.8995			−2.37928
$204$		0			0
$205$	7.08945	+	12.2793i	0.495149	+	0.857623i
$206$		0			0
$207$	2.00000			0.139010
$208$		0			0
$209$	−12.0000			−0.830057
$210$		0			0
$211$	7.76836	+	13.4552i	0.534796	+	0.926294i	0.999173	+	0.0406565i	$0.0129449\pi$
$211$	7.76836	+	13.4552i	0.534796	+	0.926294i	−0.464377	+	0.885638i	$0.653722\pi$
$212$		0			0
$213$	−3.46410			−0.237356
$214$		0			0
$215$	−0.990521	+	1.71563i	−0.0675530	+	0.117005i
$216$		0			0
$217$	15.7684	−	27.3116i	1.07043	−	1.85403i
$218$		0			0
$219$	5.69141	+	9.85782i	0.384590	+	0.666130i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−7.60885	−	13.1789i	−0.509526	−	0.882525i	−0.999939	−	0.0110349i	$-0.996487\pi$
$223$	−7.60885	−	13.1789i	−0.509526	−	0.882525i	0.490413	−	0.871490i	$-0.336846\pi$
$224$		0			0
$225$	−0.410546	+	0.711086i	−0.0273697	+	0.0474057i
$226$		0			0
$227$	−4.51551	+	7.82109i	−0.299705	+	0.519104i	−0.976068	−	0.217464i	$-0.930222\pi$
$227$	−4.51551	+	7.82109i	−0.299705	+	0.519104i	0.676363	+	0.736568i	$0.263555\pi$
$228$		0			0
$229$	9.65078			0.637741			0.318871	−	0.947798i	$-0.396696\pi$
$229$	9.65078			0.637741			0.318871	+	0.947798i	$0.396696\pi$
$230$		0			0
$231$	−7.17891	−	12.4342i	−0.472337	−	0.818113i
$232$		0			0
$233$	−22.7156			−1.48815			−0.744075	−	0.668096i	$-0.767110\pi$
$233$	−22.7156			−1.48815			−0.744075	+	0.668096i	$0.767110\pi$
$234$		0			0
$235$	−25.0735			−1.63561
$236$		0			0
$237$	−6.58945	−	11.4133i	−0.428031	−	0.741372i
$238$		0			0
$239$	2.10282			0.136020			0.0680099	−	0.997685i	$-0.478335\pi$
$239$	2.10282			0.136020			0.0680099	+	0.997685i	$0.478335\pi$
$240$		0			0
$241$	2.93840	−	5.08945i	0.189279	−	0.327841i	−0.755731	−	0.654882i	$-0.772718\pi$
$241$	2.93840	−	5.08945i	0.189279	−	0.327841i	0.945010	+	0.327041i	$0.106052\pi$
$242$		0			0
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$		0			0
$245$	−12.2793	−	21.2684i	−0.784495	−	1.35879i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	5.87680	+	10.1789i	0.372427	+	0.645062i
$250$		0			0
$251$	−10.3578	+	17.9403i	−0.653780	+	1.13238i	0.328419	+	0.944532i	$0.393484\pi$
$251$	−10.3578	+	17.9403i	−0.653780	+	1.13238i	−0.982198	+	0.187847i	$0.939849\pi$
$252$		0			0
$253$	−3.46410	+	6.00000i	−0.217786	+	0.377217i
$254$		0			0
$255$	14.9078			0.933564
$256$		0			0
$257$	11.0895	+	19.2075i	0.691741	+	1.19813i	0.971267	+	0.237993i	$0.0764894\pi$
$257$	11.0895	+	19.2075i	0.691741	+	1.19813i	−0.279526	+	0.960138i	$0.590177\pi$
$258$		0			0
$259$	4.35782			0.270782
$260$		0			0
$261$	−8.17891			−0.506262
$262$		0			0
$263$	−16.1789	−	28.0227i	−0.997634	−	1.72795i	−0.558352	−	0.829604i	$-0.688566\pi$
$263$	−16.1789	−	28.0227i	−0.997634	−	1.72795i	−0.439282	−	0.898349i	$-0.644767\pi$
$264$		0			0
$265$	−24.5586			−1.50862
$266$		0			0
$267$	−3.46410	+	6.00000i	−0.212000	+	0.367194i
$268$		0			0
$269$	6.17891	−	10.7022i	0.376735	−	0.652524i	−0.613850	−	0.789422i	$-0.710380\pi$
$269$	6.17891	−	10.7022i	0.376735	−	0.652524i	0.990585	+	0.136899i	$0.0437135\pi$
$270$		0			0
$271$	7.26852	+	12.5895i	0.441531	+	0.764755i	0.997803	−	0.0662455i	$-0.0211020\pi$
$271$	7.26852	+	12.5895i	0.441531	+	0.764755i	−0.556272	+	0.831000i	$0.687769\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−1.42217	−	2.46327i	−0.0857602	−	0.148541i
$276$		0			0
$277$	−0.0894542	+	0.154939i	−0.00537478	+	0.00930939i	−0.868700	−	0.495338i	$-0.835044\pi$
$277$	−0.0894542	+	0.154939i	−0.00537478	+	0.00930939i	0.863326	+	0.504647i	$0.168378\pi$
$278$		0			0
$279$	3.80442	−	6.58945i	0.227765	−	0.394500i
$280$		0			0
$281$	11.4437			0.682675			0.341337	−	0.939941i	$-0.389120\pi$
$281$	11.4437			0.682675			0.341337	+	0.939941i	$0.389120\pi$
$282$		0			0
$283$	−13.5895	−	23.5376i	−0.807809	−	1.39917i	−0.914378	−	0.404861i	$-0.867320\pi$
$283$	−13.5895	−	23.5376i	−0.807809	−	1.39917i	0.106569	−	0.994305i	$-0.466014\pi$
$284$		0			0
$285$	−8.35782			−0.495074
$286$		0			0
$287$	−24.3578			−1.43780
$288$		0			0
$289$	−10.5895	−	18.3415i	−0.622909	−	1.07891i
$290$		0			0
$291$	−2.04193			−0.119700
$292$		0			0
$293$	16.4240	−	28.4473i	0.959503	−	1.66191i	0.235792	−	0.971803i	$-0.424232\pi$
$293$	16.4240	−	28.4473i	0.959503	−	1.66191i	0.723710	−	0.690104i	$-0.242435\pi$
$294$		0			0
$295$	1.64218	−	2.84434i	0.0956116	−	0.165604i
$296$		0			0
$297$	−1.73205	−	3.00000i	−0.100504	−	0.174078i
$298$		0			0
$299$		0			0
$300$		0			0
$301$	−1.70161	−	2.94727i	−0.0980790	−	0.169878i
$302$		0			0
$303$	6.08945	−	10.5472i	0.349830	−	0.605923i
$304$		0			0
$305$	−6.03173	+	10.4473i	−0.345376	+	0.598209i
$306$		0			0
$307$	11.0729			0.631967			0.315983	−	0.948765i	$-0.397666\pi$
$307$	11.0729			0.631967			0.315983	+	0.948765i	$0.397666\pi$
$308$		0			0
$309$	1.58945	+	2.75302i	0.0904209	+	0.156614i
$310$		0			0
$311$	−11.6422			−0.660168			−0.330084	−	0.943952i	$-0.607077\pi$
$311$	−11.6422			−0.660168			−0.330084	+	0.943952i	$0.607077\pi$
$312$		0			0
$313$	27.8945			1.57669			0.788346	−	0.615232i	$-0.210938\pi$
$313$	27.8945			1.57669			0.788346	+	0.615232i	$0.210938\pi$
$314$		0			0
$315$	−5.00000	−	8.66025i	−0.281718	−	0.487950i
$316$		0			0
$317$	−3.77398			−0.211968			−0.105984	−	0.994368i	$-0.533799\pi$
$317$	−3.77398			−0.211968			−0.105984	+	0.994368i	$0.533799\pi$
$318$		0			0
$319$	14.1663	−	24.5367i	0.793160	−	1.37379i
$320$		0			0
$321$	5.00000	−	8.66025i	0.279073	−	0.483368i
$322$		0			0
$323$	10.7022	+	18.5367i	0.595485	+	1.03141i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	3.80442	+	6.58945i	0.210385	+	0.364398i
$328$		0			0
$329$	21.5367	−	37.3027i	1.18736	−	2.05656i
$330$		0			0
$331$	10.0520	−	17.4105i	0.552507	−	0.956970i	−0.445586	−	0.895239i	$-0.647005\pi$
$331$	10.0520	−	17.4105i	0.552507	−	0.956970i	0.998093	−	0.0617309i	$-0.0196621\pi$
$332$		0			0
$333$	1.05141			0.0576168
$334$		0			0
$335$	5.00000	+	8.66025i	0.273179	+	0.473160i
$336$		0			0
$337$	25.3578			1.38133			0.690664	−	0.723176i	$-0.257318\pi$
$337$	25.3578			1.38133			0.690664	+	0.723176i	$0.257318\pi$
$338$		0			0
$339$	12.1789			0.661468
$340$		0			0
$341$	13.1789	+	22.8265i	0.713678	+	1.23613i
$342$		0			0
$343$	13.1758			0.711424
$344$		0			0
$345$	−2.41269	+	4.17891i	−0.129895	+	0.224985i
$346$		0			0
$347$	−10.1789	+	17.6304i	−0.546432	+	0.946449i	0.452083	+	0.891976i	$0.350681\pi$
$347$	−10.1789	+	17.6304i	−0.546432	+	0.946449i	−0.998515	+	0.0544728i	$0.982652\pi$
$348$		0			0
$349$	−5.16571	−	8.94727i	−0.276514	−	0.478936i	0.694002	−	0.719973i	$-0.255846\pi$
$349$	−5.16571	−	8.94727i	−0.276514	−	0.478936i	−0.970516	+	0.241037i	$0.922513\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	9.49584	+	16.4473i	0.505412	+	0.875400i	0.999980	+	0.00626098i	$0.00199294\pi$
$353$	9.49584	+	16.4473i	0.505412	+	0.875400i	−0.494568	+	0.869139i	$0.664674\pi$
$354$		0			0
$355$	4.17891	−	7.23808i	0.221793	−	0.384157i
$356$		0			0
$357$	−12.8050	+	22.1789i	−0.677712	+	1.17383i
$358$		0			0
$359$	−18.6818			−0.985987			−0.492994	−	0.870033i	$-0.664097\pi$
$359$	−18.6818			−0.985987			−0.492994	+	0.870033i	$0.664097\pi$
$360$		0			0
$361$	3.50000	+	6.06218i	0.184211	+	0.319062i
$362$		0			0
$363$	1.00000			0.0524864
$364$		0			0
$365$	−27.4633			−1.43749
$366$		0			0
$367$	−6.41055	−	11.1034i	−0.334628	−	0.579592i	0.648785	−	0.760971i	$-0.275277\pi$
$367$	−6.41055	−	11.1034i	−0.334628	−	0.579592i	−0.983413	+	0.181379i	$0.941944\pi$
$368$		0			0
$369$	−5.87680			−0.305934
$370$		0			0
$371$	21.0945	−	36.5367i	1.09517	−	1.89689i
$372$		0			0
$373$	5.67891	−	9.83616i	0.294043	−	0.509297i	−0.680719	−	0.732545i	$-0.738333\pi$
$373$	5.67891	−	9.83616i	0.294043	−	0.509297i	0.974762	+	0.223248i	$0.0716659\pi$
$374$		0			0
$375$	5.04121	+	8.73164i	0.260327	+	0.450900i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−3.12378	−	5.41055i	−0.160458	−	0.277921i	0.774575	−	0.632482i	$-0.217964\pi$
$379$	−3.12378	−	5.41055i	−0.160458	−	0.277921i	−0.935033	+	0.354561i	$0.884630\pi$
$380$		0			0
$381$	−1.41055	+	2.44314i	−0.0722645	+	0.125166i
$382$		0			0
$383$	9.65078	−	16.7156i	0.493132	−	0.854129i	−0.506837	−	0.862042i	$-0.669185\pi$
$383$	9.65078	−	16.7156i	0.493132	−	0.854129i	0.999969	+	0.00791288i	$0.00251878\pi$
$384$		0			0
$385$	34.6410			1.76547
$386$		0			0
$387$	−0.410546	−	0.711086i	−0.0208692	−	0.0361465i
$388$		0			0
$389$	6.53673			0.331425			0.165713	−	0.986174i	$-0.447008\pi$
$389$	6.53673			0.331425			0.165713	+	0.986174i	$0.447008\pi$
$390$		0			0
$391$	12.3578			0.624962
$392$		0			0
$393$	−3.17891	−	5.50603i	−0.160355	−	0.277743i
$394$		0			0
$395$	31.7967			1.59986
$396$		0			0
$397$	10.7326	−	18.5895i	0.538655	−	0.932978i	−0.460322	−	0.887752i	$-0.652266\pi$
$397$	10.7326	−	18.5895i	0.538655	−	0.932978i	0.998977	−	0.0452258i	$-0.0144007\pi$
$398$		0			0
$399$	7.17891	−	12.4342i	0.359395	−	0.622490i
$400$		0			0
$401$	−5.35109	−	9.26836i	−0.267221	−	0.462840i	0.700922	−	0.713238i	$-0.252772\pi$
$401$	−5.35109	−	9.26836i	−0.267221	−	0.462840i	−0.968143	+	0.250398i	$0.919439\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−1.20635	−	2.08945i	−0.0599439	−	0.103826i
$406$		0			0
$407$	−1.82109	+	3.15422i	−0.0902682	+	0.156349i
$408$		0			0
$409$	0.495261	−	0.857817i	0.0244891	−	0.0424163i	−0.853521	−	0.521058i	$-0.825537\pi$
$409$	0.495261	−	0.857817i	0.0244891	−	0.0424163i	0.878010	+	0.478642i	$0.158871\pi$
$410$		0			0
$411$	12.8050			0.631624
$412$		0			0
$413$	2.82109	+	4.88627i	0.138817	+	0.240438i
$414$		0			0
$415$	−28.3578			−1.39203
$416$		0			0
$417$	17.1789			0.841255
$418$		0			0
$419$	6.35782	+	11.0121i	0.310600	+	0.537974i	0.978492	−	0.206283i	$-0.0661368\pi$
$419$	6.35782	+	11.0121i	0.310600	+	0.537974i	−0.667893	+	0.744258i	$0.732803\pi$
$420$		0			0
$421$	32.1674			1.56774			0.783872	−	0.620922i	$-0.213242\pi$
$421$	32.1674			1.56774			0.783872	+	0.620922i	$0.213242\pi$
$422$		0			0
$423$	5.19615	−	9.00000i	0.252646	−	0.437595i
$424$		0			0
$425$	−2.53673	+	4.39374i	−0.123049	+	0.213128i
$426$		0			0
$427$	−10.3619	−	17.9473i	−0.501446	−	0.868529i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−9.34090	−	16.1789i	−0.449935	−	0.779311i	0.548446	−	0.836186i	$-0.315220\pi$
$431$	−9.34090	−	16.1789i	−0.449935	−	0.779311i	−0.998381	+	0.0568753i	$0.981886\pi$
$432$		0			0
$433$	−1.32109	+	2.28820i	−0.0634876	+	0.109964i	−0.896022	−	0.444009i	$-0.853556\pi$
$433$	−1.32109	+	2.28820i	−0.0634876	+	0.109964i	0.832535	+	0.553973i	$0.186889\pi$
$434$		0			0
$435$	9.86660	−	17.0895i	0.473067	−	0.819377i
$436$		0			0
$437$	−6.92820			−0.331421
$438$		0			0
$439$	11.9473	+	20.6933i	0.570212	+	0.987636i	0.996544	+	0.0830694i	$0.0264723\pi$
$439$	11.9473	+	20.6933i	0.570212	+	0.987636i	−0.426332	+	0.904567i	$0.640194\pi$
$440$		0			0
$441$	10.1789			0.484710
$442$		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
$445$	−8.35782	−	14.4762i	−0.396199	−	0.686236i
$446$		0			0
$447$	5.87680			0.277963
$448$		0			0
$449$	−5.50603	+	9.53673i	−0.259846	+	0.450066i	−0.966200	−	0.257792i	$-0.917005\pi$
$449$	−5.50603	+	9.53673i	−0.259846	+	0.450066i	0.706355	+	0.707858i	$0.250338\pi$
$450$		0			0
$451$	10.1789	−	17.6304i	0.479306	−	0.830182i
$452$		0			0
$453$	−10.0215	−	17.3578i	−0.470853	−	0.815541i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	3.64948	+	6.32109i	0.170716	+	0.295688i	0.938670	−	0.344816i	$-0.112059\pi$
$457$	3.64948	+	6.32109i	0.170716	+	0.295688i	−0.767955	+	0.640504i	$0.778725\pi$
$458$		0			0
$459$	−3.08945	+	5.35109i	−0.144203	+	0.249768i
$460$		0			0
$461$	12.2793	−	21.2684i	0.571904	−	0.990566i	−0.424467	−	0.905444i	$-0.639538\pi$
$461$	12.2793	−	21.2684i	0.571904	−	0.990566i	0.996370	−	0.0851228i	$-0.0271283\pi$
$462$		0			0
$463$	1.42217			0.0660940			0.0330470	−	0.999454i	$-0.489479\pi$
$463$	1.42217			0.0660940			0.0330470	+	0.999454i	$0.489479\pi$
$464$		0			0
$465$	9.17891	+	15.8983i	0.425662	+	0.737268i
$466$		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
$469$	−17.1789			−0.793248
$470$		0			0
$471$	−3.50000	−	6.06218i	−0.161271	−	0.279330i
$472$		0			0
$473$	2.84434			0.130783
$474$		0			0
$475$	1.42217	−	2.46327i	0.0652537	−	0.113023i
$476$		0			0
$477$	5.08945	−	8.81519i	0.233030	−	0.403620i
$478$		0			0
$479$	3.46410	+	6.00000i	0.158279	+	0.274147i	0.934248	−	0.356624i	$-0.116072\pi$
$479$	3.46410	+	6.00000i	0.158279	+	0.274147i	−0.775969	+	0.630771i	$0.782739\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$	−4.14474	−	7.17891i	−0.188592	−	0.326652i
$484$		0			0
$485$	2.46327	−	4.26652i	0.111852	−	0.193733i
$486$		0			0
$487$	−12.1244	+	21.0000i	−0.549407	+	0.951601i	0.448908	+	0.893578i	$0.351813\pi$
$487$	−12.1244	+	21.0000i	−0.549407	+	0.951601i	−0.998315	+	0.0580230i	$0.981520\pi$
$488$		0			0
$489$	7.60885			0.344084
$490$		0			0
$491$	9.35782	+	16.2082i	0.422312	+	0.731466i	0.996165	−	0.0874920i	$-0.0278852\pi$
$491$	9.35782	+	16.2082i	0.422312	+	0.731466i	−0.573853	+	0.818958i	$0.694552\pi$
$492$		0			0
$493$	−50.5367			−2.27606
$494$		0			0
$495$	8.35782			0.375656
$496$		0			0
$497$	7.17891	+	12.4342i	0.322018	+	0.557752i
$498$		0			0
$499$	−1.36129			−0.0609395			−0.0304698	−	0.999536i	$-0.509700\pi$
$499$	−1.36129			−0.0609395			−0.0304698	+	0.999536i	$0.509700\pi$
$500$		0			0
$501$	−3.46410	+	6.00000i	−0.154765	+	0.268060i
$502$		0			0
$503$	−3.00000	+	5.19615i	−0.133763	+	0.231685i	−0.925124	−	0.379664i	$-0.876040\pi$
$503$	−3.00000	+	5.19615i	−0.133763	+	0.231685i	0.791361	+	0.611349i	$0.209373\pi$
$504$		0			0
$505$	14.6920	+	25.4473i	0.653785	+	1.13239i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−7.08314	−	12.2684i	−0.313955	−	0.543786i	0.665260	−	0.746612i	$-0.268321\pi$
$509$	−7.08314	−	12.2684i	−0.313955	−	0.543786i	−0.979215	+	0.202826i	$0.934987\pi$
$510$		0			0
$511$	23.5895	−	40.8581i	1.04354	−	1.80746i
$512$		0			0
$513$	1.73205	−	3.00000i	0.0764719	−	0.132453i
$514$		0			0
$515$	−7.66973			−0.337969
$516$		0			0
$517$	18.0000	+	31.1769i	0.791639	+	1.37116i
$518$		0			0
$519$	−18.0000			−0.790112
$520$		0			0
$521$	−38.8945			−1.70400			−0.852000	−	0.523541i	$-0.824611\pi$
$521$	−38.8945			−1.70400			−0.852000	+	0.523541i	$0.824611\pi$
$522$		0			0
$523$	−12.1789	−	21.0945i	−0.532546	−	0.922398i	−0.999278	−	0.0379984i	$-0.987902\pi$
$523$	−12.1789	−	21.0945i	−0.532546	−	0.922398i	0.466731	−	0.884399i	$-0.345432\pi$
$524$		0			0
$525$	3.40322			0.148528
$526$		0			0
$527$	23.5072	−	40.7156i	1.02399	−	1.77360i
$528$		0			0
$529$	9.50000	−	16.4545i	0.413043	−	0.715412i
$530$		0			0
$531$	0.680643	+	1.17891i	0.0295374	+	0.0511603i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	12.0635	+	20.8945i	0.521549	+	0.903350i
$536$		0			0
$537$	−4.17891	+	7.23808i	−0.180333	+	0.312346i
$538$		0			0
$539$	−17.6304	+	30.5367i	−0.759395	+	1.31531i
$540$		0			0
$541$	−3.09334			−0.132993			−0.0664965	−	0.997787i	$-0.521182\pi$
$541$	−3.09334			−0.132993			−0.0664965	+	0.997787i	$0.521182\pi$
$542$		0			0
$543$	−10.2684	−	17.7853i	−0.440658	−	0.763241i
$544$		0			0
$545$	−18.3578			−0.786362
$546$		0			0
$547$	13.5367			0.578789			0.289394	−	0.957210i	$-0.406546\pi$
$547$	13.5367			0.578789			0.289394	+	0.957210i	$0.406546\pi$
$548$		0			0
$549$	−2.50000	−	4.33013i	−0.106697	−	0.184805i
$550$		0			0
$551$	28.3326			1.20701
$552$		0			0
$553$	−27.3116	+	47.3051i	−1.16141	+	2.01162i
$554$		0			0
$555$	−1.26836	+	2.19687i	−0.0538390	+	0.0932519i
$556$		0			0
$557$	16.0533	+	27.8051i	0.680199	+	1.17814i	0.974920	+	0.222556i	$0.0714400\pi$
$557$	16.0533	+	27.8051i	0.680199	+	1.17814i	−0.294721	+	0.955583i	$0.595227\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−10.7022	−	18.5367i	−0.451847	−	0.782621i
$562$		0			0
$563$	−9.17891	+	15.8983i	−0.386845	+	0.670035i	−0.992023	−	0.126055i	$-0.959768\pi$
$563$	−9.17891	+	15.8983i	−0.386845	+	0.670035i	0.605178	+	0.796090i	$0.293102\pi$
$564$		0			0
$565$	−14.6920	+	25.4473i	−0.618097	+	1.07057i
$566$		0			0
$567$	4.14474			0.174063
$568$		0			0
$569$	−15.3578	−	26.6005i	−0.643833	−	1.11515i	−0.984570	−	0.174993i	$-0.944010\pi$
$569$	−15.3578	−	26.6005i	−0.643833	−	1.11515i	0.340737	−	0.940159i	$-0.389324\pi$
$570$		0			0
$571$	7.64218			0.319815			0.159908	−	0.987132i	$-0.448880\pi$
$571$	7.64218			0.319815			0.159908	+	0.987132i	$0.448880\pi$
$572$		0			0
$573$	−2.35782			−0.0984992
$574$		0			0
$575$	−0.821092	−	1.42217i	−0.0342419	−	0.0593087i
$576$		0			0
$577$	−43.2404			−1.80012			−0.900060	−	0.435765i	$-0.856478\pi$
$577$	−43.2404			−1.80012			−0.900060	+	0.435765i	$0.856478\pi$
$578$		0			0
$579$	6.74282	−	11.6789i	0.280222	−	0.485359i
$580$		0			0
$581$	24.3578	−	42.1890i	1.01053	−	1.75029i
$582$		0			0
$583$	17.6304	+	30.5367i	0.730176	+	1.26470i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−11.0729	−	19.1789i	−0.457029	−	0.791598i	0.541773	−	0.840525i	$-0.317753\pi$
$587$	−11.0729	−	19.1789i	−0.457029	−	0.791598i	−0.998802	+	0.0489266i	$0.984420\pi$
$588$		0			0
$589$	−13.1789	+	22.8265i	−0.543027	+	0.940551i
$590$		0			0
$591$	−4.82539	+	8.35782i	−0.198490	+	0.343795i
$592$		0			0
$593$	32.8481			1.34891			0.674454	−	0.738316i	$-0.264379\pi$
$593$	32.8481			1.34891			0.674454	+	0.738316i	$0.264379\pi$
$594$		0			0
$595$	−30.8945	−	53.5109i	−1.26655	−	2.19373i
$596$		0			0
$597$	21.5367			0.881439
$598$		0			0
$599$	9.64218			0.393969			0.196984	−	0.980407i	$-0.436885\pi$
$599$	9.64218			0.393969			0.196984	+	0.980407i	$0.436885\pi$
$600$		0			0
$601$	0.0894542	+	0.154939i	0.00364891	+	0.00632010i	0.867844	−	0.496837i	$-0.165505\pi$
$601$	0.0894542	+	0.154939i	0.00364891	+	0.00632010i	−0.864195	+	0.503157i	$0.832172\pi$
$602$		0			0
$603$	−4.14474			−0.168787
$604$		0			0
$605$	−1.20635	+	2.08945i	−0.0490450	+	0.0849484i
$606$		0			0
$607$	−8.00000	+	13.8564i	−0.324710	+	0.562414i	−0.981454	−	0.191700i	$-0.938600\pi$
$607$	−8.00000	+	13.8564i	−0.324710	+	0.562414i	0.656744	+	0.754114i	$0.271933\pi$
$608$		0			0
$609$	16.9497	+	29.3578i	0.686838	+	1.18964i
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−1.23679	−	2.14218i	−0.0499535	−	0.0865220i	0.839967	−	0.542637i	$-0.182574\pi$
$613$	−1.23679	−	2.14218i	−0.0499535	−	0.0865220i	−0.889921	+	0.456115i	$0.849241\pi$
$614$		0			0
$615$	7.08945	−	12.2793i	0.285874	−	0.495149i
$616$		0			0
$617$	−1.20635	+	2.08945i	−0.0485657	+	0.0841183i	−0.889286	−	0.457351i	$-0.848798\pi$
$617$	−1.20635	+	2.08945i	−0.0485657	+	0.0841183i	0.840721	+	0.541469i	$0.182132\pi$
$618$		0			0
$619$	−10.3314			−0.415255			−0.207627	−	0.978208i	$-0.566574\pi$
$619$	−10.3314			−0.415255			−0.207627	+	0.978208i	$0.566574\pi$
$620$		0			0
$621$	−1.00000	−	1.73205i	−0.0401286	−	0.0695048i
$622$		0			0
$623$	28.7156			1.15047
$624$		0			0
$625$	−28.4313			−1.13725
$626$		0			0
$627$	6.00000	+	10.3923i	0.239617	+	0.415029i
$628$		0			0
$629$	6.49655			0.259034
$630$		0			0
$631$	3.12378	−	5.41055i	0.124356	−	0.215390i	−0.797125	−	0.603814i	$-0.793647\pi$
$631$	3.12378	−	5.41055i	0.124356	−	0.215390i	0.921481	+	0.388424i	$0.126980\pi$
$632$		0			0
$633$	7.76836	−	13.4552i	0.308765	−	0.534796i
$634$		0			0
$635$	−3.40322	−	5.89454i	−0.135052	−	0.233918i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	1.73205	+	3.00000i	0.0685189	+	0.118678i
$640$		0			0
$641$	−0.268363	+	0.464818i	−0.0105997	+	0.0183592i	−0.871277	−	0.490792i	$-0.836707\pi$
$641$	−0.268363	+	0.464818i	−0.0105997	+	0.0183592i	0.860677	+	0.509152i	$0.170041\pi$
$642$		0			0
$643$	7.94917	−	13.7684i	0.313485	−	0.542971i	−0.665630	−	0.746282i	$-0.731837\pi$
$643$	7.94917	−	13.7684i	0.313485	−	0.542971i	0.979114	+	0.203311i	$0.0651703\pi$
$644$		0			0
$645$	1.98104			0.0780035
$646$		0			0
$647$	6.82109	+	11.8145i	0.268165	+	0.464475i	0.968388	−	0.249449i	$-0.0802495\pi$
$647$	6.82109	+	11.8145i	0.268165	+	0.464475i	−0.700223	+	0.713924i	$0.746916\pi$
$648$		0			0
$649$	−4.71563			−0.185105
$650$		0			0
$651$	−31.5367			−1.23602
$652$		0			0
$653$	−0.178908	−	0.309878i	−0.00700122	−	0.0121265i	0.862504	−	0.506051i	$-0.168895\pi$
$653$	−0.178908	−	0.309878i	−0.00700122	−	0.0121265i	−0.869505	+	0.493925i	$0.835562\pi$
$654$		0			0
$655$	15.3395			0.599363
$656$		0			0
$657$	5.69141	−	9.85782i	0.222043	−	0.384590i
$658$		0			0
$659$	4.35782	−	7.54796i	0.169756	−	0.294027i	−0.768578	−	0.639756i	$-0.779035\pi$
$659$	4.35782	−	7.54796i	0.169756	−	0.294027i	0.938334	+	0.345730i	$0.112369\pi$
$660$		0			0
$661$	−6.43294	−	11.1422i	−0.250212	−	0.433381i	0.713372	−	0.700786i	$-0.247167\pi$
$661$	−6.43294	−	11.1422i	−0.250212	−	0.433381i	−0.963584	+	0.267405i	$0.913834\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	17.3205	+	30.0000i	0.671660	+	1.16335i
$666$		0			0
$667$	8.17891	−	14.1663i	0.316689	−	0.548521i
$668$		0			0
$669$	−7.60885	+	13.1789i	−0.294175	+	0.509526i
$670$		0			0
$671$	17.3205			0.668651
$672$		0			0
$673$	−2.67891	−	4.64001i	−0.103264	−	0.178859i	0.809763	−	0.586757i	$-0.199595\pi$
$673$	−2.67891	−	4.64001i	−0.103264	−	0.178859i	−0.913028	+	0.407897i	$0.866262\pi$
$674$		0			0
$675$	0.821092			0.0316038
$676$		0			0
$677$	−3.64218			−0.139980			−0.0699902	−	0.997548i	$-0.522297\pi$
$677$	−3.64218			−0.139980			−0.0699902	+	0.997548i	$0.522297\pi$
$678$		0			0
$679$	4.23164	+	7.32941i	0.162395	+	0.281277i
$680$		0			0
$681$	9.03102			0.346069
$682$		0			0
$683$	−8.97013	+	15.5367i	−0.343233	+	0.594496i	−0.985031	−	0.172377i	$-0.944855\pi$
$683$	−8.97013	+	15.5367i	−0.343233	+	0.594496i	0.641798	+	0.766873i	$0.278189\pi$
$684$		0			0
$685$	−15.4473	+	26.7555i	−0.590210	+	1.02227i
$686$		0			0
$687$	−4.82539	−	8.35782i	−0.184100	−	0.318871i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−4.11430	−	7.12618i	−0.156515	−	0.271093i	0.777094	−	0.629384i	$-0.216693\pi$
$691$	−4.11430	−	7.12618i	−0.156515	−	0.271093i	−0.933610	+	0.358291i	$0.883359\pi$
$692$		0			0
$693$	−7.17891	+	12.4342i	−0.272704	+	0.472337i
$694$		0			0
$695$	−20.7237	+	35.8945i	−0.786096	+	1.36156i
$696$		0			0
$697$	−36.3122			−1.37542
$698$		0			0
$699$	11.3578	+	19.6723i	0.429592	+	0.744075i
$700$		0			0
$701$	−48.3578			−1.82645			−0.913225	−	0.407456i	$-0.866416\pi$
$701$	−48.3578			−1.82645			−0.913225	+	0.407456i	$0.866416\pi$
$702$		0			0
$703$	−3.64218			−0.137368
$704$		0			0
$705$	12.5367	+	21.7142i	0.472160	+	0.817806i
$706$		0			0
$707$	−50.4785			−1.89844
$708$		0			0
$709$	14.7224	−	25.5000i	0.552913	−	0.957673i	−0.445150	−	0.895456i	$-0.646850\pi$
$709$	14.7224	−	25.5000i	0.552913	−	0.957673i	0.998063	−	0.0622167i	$-0.0198170\pi$
$710$		0			0
$711$	−6.58945	+	11.4133i	−0.247124	+	0.428031i
$712$		0			0
$713$	7.60885	+	13.1789i	0.284954	+	0.493554i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−1.05141	−	1.82109i	−0.0392655	−	0.0680099i
$718$		0			0
$719$	−15.1789	+	26.2906i	−0.566078	+	0.980475i	0.430871	+	0.902414i	$0.358206\pi$
$719$	−15.1789	+	26.2906i	−0.566078	+	0.980475i	−0.996949	+	0.0780618i	$0.975127\pi$
$720$		0			0
$721$	6.58788	−	11.4105i	0.245346	−	0.424951i
$722$		0			0
$723$	−5.87680			−0.218560
$724$		0			0
$725$	3.35782	+	5.81591i	0.124706	+	0.215997i
$726$		0			0
$727$	−17.5367			−0.650401			−0.325201	−	0.945645i	$-0.605432\pi$
$727$	−17.5367			−0.650401			−0.325201	+	0.945645i	$0.605432\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−2.53673	−	4.39374i	−0.0938242	−	0.162508i
$732$		0			0
$733$	10.6413			0.393045			0.196523	−	0.980499i	$-0.437035\pi$
$733$	10.6413			0.393045			0.196523	+	0.980499i	$0.437035\pi$
$734$		0			0
$735$	−12.2793	+	21.2684i	−0.452929	+	0.784495i
$736$		0			0
$737$	7.17891	−	12.4342i	0.264438	−	0.458021i
$738$		0			0
$739$	7.60885	+	13.1789i	0.279896	+	0.484794i	0.971359	−	0.237618i	$-0.0763667\pi$
$739$	7.60885	+	13.1789i	0.279896	+	0.484794i	−0.691463	+	0.722412i	$0.743033\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−0.680643	−	1.17891i	−0.0249704	−	0.0432500i	0.853270	−	0.521469i	$-0.174616\pi$
$743$	−0.680643	−	1.17891i	−0.0249704	−	0.0432500i	−0.878241	+	0.478219i	$0.841282\pi$
$744$		0			0
$745$	−7.08945	+	12.2793i	−0.259738	+	0.449879i
$746$		0			0
$747$	5.87680	−	10.1789i	0.215021	−	0.372427i
$748$		0			0
$749$	−41.4474			−1.51446
$750$		0			0
$751$	−9.82109	−	17.0106i	−0.358377	−	0.620727i	0.629313	−	0.777152i	$-0.283336\pi$
$751$	−9.82109	−	17.0106i	−0.358377	−	0.620727i	−0.987690	+	0.156425i	$0.950003\pi$
$752$		0			0
$753$	20.7156			0.754920
$754$		0			0
$755$	48.3578			1.75992
$756$		0			0
$757$	19.3578	+	33.5287i	0.703572	+	1.21862i	0.967204	+	0.253999i	$0.0817460\pi$
$757$	19.3578	+	33.5287i	0.703572	+	1.21862i	−0.263633	+	0.964623i	$0.584921\pi$
$758$		0			0
$759$	6.92820			0.251478
$760$		0			0
$761$	−24.2487	+	42.0000i	−0.879015	+	1.52250i	−0.0265919	+	0.999646i	$0.508465\pi$
$761$	−24.2487	+	42.0000i	−0.879015	+	1.52250i	−0.852423	+	0.522852i	$0.824868\pi$
$762$		0			0
$763$	15.7684	−	27.3116i	0.570853	−	0.988746i
$764$		0			0
$765$	−7.45391	−	12.9105i	−0.269497	−	0.466782i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	−3.46410	−	6.00000i	−0.124919	−	0.216366i	0.796782	−	0.604266i	$-0.206534\pi$
$769$	−3.46410	−	6.00000i	−0.124919	−	0.216366i	−0.921701	+	0.387901i	$0.873200\pi$
$770$		0			0
$771$	11.0895	−	19.2075i	0.399377	−	0.691741i
$772$		0			0
$773$	15.8983	−	27.5367i	0.571823	−	0.990427i	−0.424555	−	0.905402i	$-0.639570\pi$
$773$	15.8983	−	27.5367i	0.571823	−	0.990427i	0.996379	−	0.0850252i	$-0.0270971\pi$
$774$		0			0
$775$	−6.24756			−0.224419
$776$		0			0
$777$	−2.17891	−	3.77398i	−0.0781679	−	0.135391i
$778$		0			0
$779$	20.3578			0.729394
$780$		0			0
$781$	−12.0000			−0.429394
$782$		0			0
$783$	4.08945	+	7.08314i	0.146145	+	0.253131i
$784$		0			0
$785$	16.8889			0.602789
$786$		0			0
$787$	−16.9802	+	29.4105i	−0.605278	+	1.04837i	0.386729	+	0.922193i	$0.373605\pi$
$787$	−16.9802	+	29.4105i	−0.605278	+	1.04837i	−0.992007	+	0.126179i	$0.959729\pi$
$788$		0			0
$789$	−16.1789	+	28.0227i	−0.575984	+	0.997634i
$790$		0			0
$791$	−25.2392	−	43.7156i	−0.897404	−	1.55435i
$792$		0			0
$793$		0			0
$794$		0			0
$795$	12.2793	+	21.2684i	0.435502	+	0.754311i
$796$		0			0
$797$	8.53673	−	14.7860i	0.302386	−	0.523748i	−0.674290	−	0.738467i	$-0.735550\pi$
$797$	8.53673	−	14.7860i	0.302386	−	0.523748i	0.976676	+	0.214718i	$0.0688834\pi$
$798$		0			0
$799$	32.1065	−	55.6102i	1.13585	−	1.96735i
$800$		0			0
$801$	6.92820			0.244796
$802$		0			0
$803$	19.7156	+	34.1485i	0.695750	+	1.20507i
$804$		0			0
$805$	20.0000			0.704907
$806$		0			0
$807$	−12.3578			−0.435016
$808$		0			0
$809$	−23.2684	−	40.3020i	−0.818072	−	1.41694i	−0.907101	−	0.420913i	$-0.861710\pi$
$809$	−23.2684	−	40.3020i	−0.818072	−	1.41694i	0.0890288	−	0.996029i	$-0.471624\pi$
$810$		0			0
$811$	−0.680643			−0.0239006			−0.0119503	−	0.999929i	$-0.503804\pi$
$811$	−0.680643			−0.0239006			−0.0119503	+	0.999929i	$0.503804\pi$
$812$		0			0
$813$	7.26852	−	12.5895i	0.254918	−	0.441531i
$814$		0			0
$815$	−9.17891	+	15.8983i	−0.321523	+	0.556894i
$816$		0			0
$817$	1.42217	+	2.46327i	0.0497555	+	0.0861791i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	15.8983	+	27.5367i	0.554856	+	0.961038i	0.997915	+	0.0645459i	$0.0205599\pi$
$821$	15.8983	+	27.5367i	0.554856	+	0.961038i	−0.443059	+	0.896492i	$0.646107\pi$
$822$		0			0
$823$	−12.0000	+	20.7846i	−0.418294	+	0.724506i	−0.995768	−	0.0919029i	$-0.970705\pi$
$823$	−12.0000	+	20.7846i	−0.418294	+	0.724506i	0.577474	+	0.816409i	$0.304038\pi$
$824$		0			0
$825$	−1.42217	+	2.46327i	−0.0495137	+	0.0857602i
$826$		0			0
$827$	35.8805			1.24769			0.623844	−	0.781549i	$-0.285570\pi$
$827$	35.8805			1.24769			0.623844	+	0.781549i	$0.285570\pi$
$828$		0			0
$829$	11.6789	+	20.2285i	0.405625	+	0.702564i	0.994394	−	0.105738i	$-0.0337205\pi$
$829$	11.6789	+	20.2285i	0.405625	+	0.702564i	−0.588769	+	0.808302i	$0.700387\pi$
$830$		0			0
$831$	0.178908			0.00620626
$832$		0			0
$833$	62.8945			2.17917
$834$		0			0
$835$	−8.35782	−	14.4762i	−0.289234	−	0.500968i
$836$		0			0
$837$	−7.60885			−0.263000
$838$		0			0
$839$	−7.60885	+	13.1789i	−0.262687	+	0.454986i	−0.966955	−	0.254947i	$-0.917942\pi$
$839$	−7.60885	+	13.1789i	−0.262687	+	0.454986i	0.704268	+	0.709934i	$0.251275\pi$
$840$		0			0
$841$	−18.9473	+	32.8176i	−0.653354	+	1.13164i
$842$		0			0
$843$	−5.72186	−	9.91055i	−0.197071	−	0.341337i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−2.07237	−	3.58945i	−0.0712076	−	0.123335i
$848$		0			0
$849$	−13.5895	+	23.5376i	−0.466389	+	0.807809i
$850$		0			0
$851$	−1.05141	+	1.82109i	−0.0360418	+	0.0624262i
$852$		0			0
$853$	−24.6195			−0.842955			−0.421477	−	0.906839i	$-0.638488\pi$
$853$	−24.6195			−0.842955			−0.421477	+	0.906839i	$0.638488\pi$
$854$		0			0
$855$	4.17891	+	7.23808i	0.142916	+	0.247537i
$856$		0			0
$857$	20.1789			0.689298			0.344649	−	0.938732i	$-0.387998\pi$
$857$	20.1789			0.689298			0.344649	+	0.938732i	$0.387998\pi$
$858$		0			0
$859$	54.2524			1.85107			0.925533	−	0.378666i	$-0.123617\pi$
$859$	54.2524			1.85107			0.925533	+	0.378666i	$0.123617\pi$
$860$		0			0
$861$	12.1789	+	21.0945i	0.415056	+	0.718898i
$862$		0			0
$863$	−20.0431			−0.682274			−0.341137	−	0.940014i	$-0.610812\pi$
$863$	−20.0431			−0.682274			−0.341137	+	0.940014i	$0.610812\pi$
$864$		0			0
$865$	21.7142	−	37.6102i	0.738306	−	1.27878i
$866$		0			0
$867$	−10.5895	+	18.3415i	−0.359637	+	0.622909i
$868$		0			0
$869$	−22.8265	−	39.5367i	−0.774337	−	1.34119i
$870$		0			0
$871$		0			0
$872$		0			0
$873$	1.02096	+	1.76836i	0.0345544	+	0.0598500i
$874$		0			0
$875$	20.8945	−	36.1904i	0.706364	−	1.22346i
$876$		0			0
$877$	−6.40250	+	11.0895i	−0.216197	+	0.374464i	−0.953642	−	0.300943i	$-0.902699\pi$
$877$	−6.40250	+	11.0895i	−0.216197	+	0.374464i	0.737445	+	0.675407i	$0.236032\pi$
$878$		0			0
$879$	−32.8481			−1.10794
$880$		0			0
$881$	−18.9105	−	32.7540i	−0.637112	−	1.10351i	−0.986063	−	0.166370i	$-0.946795\pi$
$881$	−18.9105	−	32.7540i	−0.637112	−	1.10351i	0.348951	−	0.937141i	$-0.386538\pi$
$882$		0			0
$883$	17.8945			0.602199			0.301100	−	0.953593i	$-0.402646\pi$
$883$	17.8945			0.602199			0.301100	+	0.953593i	$0.402646\pi$
$884$		0			0
$885$	−3.28437			−0.110403
$886$		0			0
$887$	−10.8211	−	18.7427i	−0.363337	−	0.629318i	0.625171	−	0.780488i	$-0.285029\pi$
$887$	−10.8211	−	18.7427i	−0.363337	−	0.629318i	−0.988508	+	0.151170i	$0.951696\pi$
$888$		0			0
$889$	11.6927			0.392161
$890$		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
$895$	−10.0824	−	17.4633i	−0.337018	−	0.583733i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−31.1160	−	53.8945i	−1.03778	−	1.79748i
$900$		0			0
$901$	31.4473	−	54.4683i	1.04766	−	1.81460i
$902$		0			0
$903$	−1.70161	+	2.94727i	−0.0566260	+	0.0980790i
$904$		0			0
$905$	49.5488			1.64706
$906$		0			0
$907$	14.0000	+	24.2487i	0.464862	+	0.805165i	0.999195	−	0.0401089i	$-0.0127705\pi$
$907$	14.0000	+	24.2487i	0.464862	+	0.805165i	−0.534333	+	0.845274i	$0.679437\pi$
$908$		0			0
$909$	−12.1789			−0.403949
$910$		0			0
$911$	4.71563			0.156236			0.0781180	−	0.996944i	$-0.475109\pi$
$911$	4.71563			0.156236			0.0781180	+	0.996944i	$0.475109\pi$
$912$		0			0
$913$	20.3578	+	35.2608i	0.673745	+	1.16696i
$914$		0			0
$915$	12.0635			0.398806
$916$		0			0
$917$	−13.1758	+	22.8211i	−0.435102	+	0.753619i
$918$		0			0
$919$	−12.0000	+	20.7846i	−0.395843	+	0.685621i	−0.993208	−	0.116348i	$-0.962881\pi$
$919$	−12.0000	+	20.7846i	−0.395843	+	0.685621i	0.597365	+	0.801970i	$0.296214\pi$
$920$		0			0
$921$	−5.53647	−	9.58945i	−0.182433	−	0.315983i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−0.431651	−	0.747642i	−0.0141926	−	0.0245823i
$926$		0			0
$927$	1.58945	−	2.75302i	0.0522045	−	0.0904209i
$928$		0			0
$929$	15.7434	−	27.2684i	0.516524	−	0.894646i	−0.483292	−	0.875459i	$-0.660559\pi$
$929$	15.7434	−	27.2684i	0.516524	−	0.894646i	0.999816	−	0.0191866i	$-0.00610767\pi$
$930$		0			0
$931$	−35.2608			−1.15563
$932$		0			0
$933$	5.82109	+	10.0824i	0.190574	+	0.330084i
$934$		0			0
$935$	51.6422			1.68888
$936$		0			0
$937$	48.8945			1.59732			0.798658	−	0.601786i	$-0.205544\pi$
$937$	48.8945			1.59732			0.798658	+	0.601786i	$0.205544\pi$
$938$		0			0
$939$	−13.9473	−	24.1574i	−0.455152	−	0.788346i
$940$		0			0
$941$	−37.2418			−1.21405			−0.607024	−	0.794683i	$-0.707637\pi$
$941$	−37.2418			−1.21405			−0.607024	+	0.794683i	$0.707637\pi$
$942$		0			0
$943$	5.87680	−	10.1789i	0.191375	−	0.331471i
$944$		0			0
$945$	−5.00000	+	8.66025i	−0.162650	+	0.281718i
$946$		0			0
$947$	15.2177	+	26.3578i	0.494509	+	0.856514i	0.999980	−	0.00632940i	$-0.00201472\pi$
$947$	15.2177	+	26.3578i	0.494509	+	0.856514i	−0.505471	+	0.862843i	$0.668681\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	1.88699	+	3.26836i	0.0611898	+	0.105984i
$952$		0			0
$953$	3.00000	−	5.19615i	0.0971795	−	0.168320i	−0.813337	−	0.581793i	$-0.802351\pi$
$953$	3.00000	−	5.19615i	0.0971795	−	0.168320i	0.910516	+	0.413473i	$0.135685\pi$
$954$		0			0
$955$	2.84434	−	4.92655i	0.0920408	−	0.159419i
$956$		0			0
$957$	−28.3326			−0.915862
$958$		0			0
$959$	−26.5367	−	45.9630i	−0.856916	−	1.48422i
$960$		0			0
$961$	26.8945			0.867566
$962$		0			0
$963$	−10.0000			−0.322245
$964$		0			0
$965$	16.2684	+	28.1776i	0.523697	+	0.907070i
$966$		0			0
$967$	−35.3825			−1.13783			−0.568913	−	0.822398i	$-0.692636\pi$
$967$	−35.3825			−1.13783			−0.568913	+	0.822398i	$0.692636\pi$
$968$		0			0
$969$	10.7022	−	18.5367i	0.343804	−	0.595485i
$970$		0			0
$971$	−2.35782	+	4.08386i	−0.0756659	+	0.131057i	−0.901376	−	0.433038i	$-0.857442\pi$
$971$	−2.35782	+	4.08386i	−0.0756659	+	0.131057i	0.825710	+	0.564095i	$0.190775\pi$
$972$		0			0
$973$	−35.6011	−	61.6629i	−1.14132	−	1.97682i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	8.50531	+	14.7316i	0.272109	+	0.471307i	0.969402	−	0.245480i	$-0.0789455\pi$
$977$	8.50531	+	14.7316i	0.272109	+	0.471307i	−0.697293	+	0.716787i	$0.745612\pi$
$978$		0			0
$979$	−12.0000	+	20.7846i	−0.383522	+	0.664279i
$980$		0			0
$981$	3.80442	−	6.58945i	0.121466	−	0.210385i
$982$		0			0
$983$	24.8685			0.793181			0.396590	−	0.917996i	$-0.370193\pi$
$983$	24.8685			0.793181			0.396590	+	0.917996i	$0.370193\pi$
$984$		0			0
$985$	−11.6422	−	20.1649i	−0.370951	−	0.642506i
$986$		0			0
$987$	−43.0735			−1.37104
$988$		0			0
$989$	1.64218			0.0522184
$990$		0			0
$991$	22.5367	+	39.0348i	0.715903	+	1.23998i	0.962610	+	0.270890i	$0.0873179\pi$
$991$	22.5367	+	39.0348i	0.715903	+	1.23998i	−0.246708	+	0.969090i	$0.579349\pi$
$992$		0			0
$993$	−20.1040			−0.637980
$994$		0			0
$995$	−25.9808	+	45.0000i	−0.823646	+	1.42660i
$996$		0			0
$997$	−17.6789	+	30.6208i	−0.559897	+	0.969769i	0.437608	+	0.899166i	$0.355826\pi$
$997$	−17.6789	+	30.6208i	−0.559897	+	0.969769i	−0.997504	+	0.0706035i	$0.977507\pi$
$998$		0			0
$999$	−0.525704	−	0.910546i	−0.0166325	−	0.0288084i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2028.2.i.n.2005.3		8
13.2	odd	12		2028.2.b.e.337.2		4
13.3	even	3		2028.2.a.m.1.3		4
13.4	even	6	inner	2028.2.i.n.529.2		8
13.5	odd	4		156.2.q.b.49.1	✓	4
13.6	odd	12		2028.2.q.f.1837.1		4
13.7	odd	12		156.2.q.b.121.2	yes	4
13.8	odd	4		2028.2.q.f.361.2		4
13.9	even	3	inner	2028.2.i.n.529.3		8
13.10	even	6		2028.2.a.m.1.2		4
13.11	odd	12		2028.2.b.e.337.3		4
13.12	even	2	inner	2028.2.i.n.2005.2		8
39.2	even	12		6084.2.b.o.4393.3		4
39.5	even	4		468.2.t.d.361.2		4
39.11	even	12		6084.2.b.o.4393.2		4
39.20	even	12		468.2.t.d.433.1		4
39.23	odd	6		6084.2.a.bd.1.3		4
39.29	odd	6		6084.2.a.bd.1.2		4
52.3	odd	6		8112.2.a.cr.1.3		4
52.7	even	12		624.2.bv.f.433.2		4
52.23	odd	6		8112.2.a.cr.1.2		4
52.31	even	4		624.2.bv.f.49.1		4
65.7	even	12		3900.2.bw.j.2149.3		8
65.18	even	4		3900.2.bw.j.49.3		8
65.33	even	12		3900.2.bw.j.2149.2		8
65.44	odd	4		3900.2.cd.i.2701.2		4
65.57	even	4		3900.2.bw.j.49.2		8
65.59	odd	12		3900.2.cd.i.901.2		4
156.59	odd	12		1872.2.by.j.433.1		4
156.83	odd	4		1872.2.by.j.1297.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
156.2.q.b.49.1	✓	4	13.5	odd	4
156.2.q.b.121.2	yes	4	13.7	odd	12
468.2.t.d.361.2		4	39.5	even	4
468.2.t.d.433.1		4	39.20	even	12
624.2.bv.f.49.1		4	52.31	even	4
624.2.bv.f.433.2		4	52.7	even	12
1872.2.by.j.433.1		4	156.59	odd	12
1872.2.by.j.1297.2		4	156.83	odd	4
2028.2.a.m.1.2		4	13.10	even	6
2028.2.a.m.1.3		4	13.3	even	3
2028.2.b.e.337.2		4	13.2	odd	12
2028.2.b.e.337.3		4	13.11	odd	12
2028.2.i.n.529.2		8	13.4	even	6	inner
2028.2.i.n.529.3		8	13.9	even	3	inner
2028.2.i.n.2005.2		8	13.12	even	2	inner
2028.2.i.n.2005.3		8	1.1	even	1	trivial
2028.2.q.f.361.2		4	13.8	odd	4
2028.2.q.f.1837.1		4	13.6	odd	12
3900.2.bw.j.49.2		8	65.57	even	4
3900.2.bw.j.49.3		8	65.18	even	4
3900.2.bw.j.2149.2		8	65.33	even	12
3900.2.bw.j.2149.3		8	65.7	even	12
3900.2.cd.i.901.2		4	65.59	odd	12
3900.2.cd.i.2701.2		4	65.44	odd	4
6084.2.a.bd.1.2		4	39.29	odd	6
6084.2.a.bd.1.3		4	39.23	odd	6
6084.2.b.o.4393.2		4	39.11	even	12
6084.2.b.o.4393.3		4	39.2	even	12
8112.2.a.cr.1.2		4	52.23	odd	6
8112.2.a.cr.1.3		4	52.3	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)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{3} +2.41269 q^{5} +(-2.07237 + 3.58945i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(-1.73205 - 3.00000i) q^{11} +(-1.20635 - 2.08945i) q^{15} +(-3.08945 + 5.35109i) q^{17} +(1.73205 - 3.00000i) q^{19} +4.14474 q^{21} +(-1.00000 - 1.73205i) q^{23} +0.821092 q^{25} +1.00000 q^{27} +(4.08945 + 7.08314i) q^{29} -7.60885 q^{31} +(-1.73205 + 3.00000i) q^{33} +(-5.00000 + 8.66025i) q^{35} +(-0.525704 - 0.910546i) q^{37} +(2.93840 + 5.08945i) q^{41} +(-0.410546 + 0.711086i) q^{43} +(-1.20635 + 2.08945i) q^{45} -10.3923 q^{47} +(-5.08945 - 8.81519i) q^{49} +6.17891 q^{51} -10.1789 q^{53} +(-4.17891 - 7.23808i) q^{55} -3.46410 q^{57} +(0.680643 - 1.17891i) q^{59} +(-2.50000 + 4.33013i) q^{61} +(-2.07237 - 3.58945i) q^{63} +(2.07237 + 3.58945i) q^{67} +(-1.00000 + 1.73205i) q^{69} +(1.73205 - 3.00000i) q^{71} -11.3828 q^{73} +(-0.410546 - 0.711086i) q^{75} +14.3578 q^{77} +13.1789 q^{79} +(-0.500000 - 0.866025i) q^{81} -11.7536 q^{83} +(-7.45391 + 12.9105i) q^{85} +(4.08945 - 7.08314i) q^{87} +(-3.46410 - 6.00000i) q^{89} +(3.80442 + 6.58945i) q^{93} +(4.17891 - 7.23808i) q^{95} +(1.02096 - 1.76836i) q^{97} +3.46410 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} - 4 q^{9} - 2 q^{17} - 8 q^{23} + 52 q^{25} + 8 q^{27} + 10 q^{29} - 40 q^{35} - 26 q^{43} - 18 q^{49} + 4 q^{51} - 36 q^{53} + 12 q^{55} - 20 q^{61} - 8 q^{69} - 26 q^{75} + 24 q^{77} + 60 q^{79}+ \cdots - 12 q^{95}+O(q^{100}) \) 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

Fields

Representations

Groups

Database

Properties

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