LMFDB - Embedded newform 2028.2.q.i.1837.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2028,2,Mod(361,2028)]

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, 5]))

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

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

chi := DirichletCharacter("2028.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2028 = 2^{2} \cdot 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2028.q (of order $6$, 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:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.17213603549184.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5x^{10} + 19x^{8} - 28x^{6} + 31x^{4} - 6x^{2} + 1 $ x^12 - 5x^10 + 19x^8 - 28x^6 + 31x^4 - 6*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1837.1
Root			$-0.385418 - 0.222521i$ of defining polynomial
Character	$\chi$	$=$	2028.1837
Dual form			2028.2.q.i.361.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{3} -3.04892i q^{5} +(-4.37249 + 2.52446i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(3.29257 + 1.90097i) q^{11} +(2.64044 + 1.52446i) q^{15} +(-0.178448 - 0.309081i) q^{17} +(5.31485 - 3.06853i) q^{19} -5.04892i q^{21} +(-3.96950 + 6.87538i) q^{23} -4.29590 q^{25} +1.00000 q^{27} +(-0.708947 + 1.22793i) q^{29} -5.78986i q^{31} +(-3.29257 + 1.90097i) q^{33} +(7.69687 + 13.3314i) q^{35} +(-0.0235101 - 0.0135735i) q^{37} +(-7.95529 - 4.59299i) q^{41} +(-0.609916 - 1.05641i) q^{43} +(-2.64044 + 1.52446i) q^{45} -9.56465i q^{47} +(9.24578 - 16.0142i) q^{49} +0.356896 q^{51} -4.73556 q^{53} +(5.79590 - 10.0388i) q^{55} +6.13706i q^{57} +(11.7134 - 6.76271i) q^{59} +(-0.288364 - 0.499461i) q^{61} +(4.37249 + 2.52446i) q^{63} +(-6.88584 - 3.97554i) q^{67} +(-3.96950 - 6.87538i) q^{69} +(2.66395 - 1.53803i) q^{71} -14.0368i q^{73} +(2.14795 - 3.72036i) q^{75} -19.1957 q^{77} -0.841166 q^{79} +(-0.500000 + 0.866025i) q^{81} +0.192685i q^{83} +(-0.942362 + 0.544073i) q^{85} +(-0.708947 - 1.22793i) q^{87} +(-7.97880 - 4.60656i) q^{89} +(5.01416 + 2.89493i) q^{93} +(-9.35570 - 16.2045i) q^{95} +(0.590918 - 0.341166i) q^{97} -3.80194i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{3} - 6 q^{9} + 6 q^{17} - 28 q^{23} + 4 q^{25} + 12 q^{27} - 20 q^{29} + 28 q^{35} - 10 q^{43} + 10 q^{49} - 12 q^{51} - 12 q^{53} + 14 q^{55} + 2 q^{61} - 28 q^{69} - 2 q^{75} - 84 q^{77} - 44 q^{79}+ \cdots - 14 q^{95}+O(q^{100}) $ 12 * q - 6 * q^3 - 6 * q^9 + 6 * q^17 - 28 * q^23 + 4 * q^25 + 12 * q^27 - 20 * q^29 + 28 * q^35 - 10 * q^43 + 10 * q^49 - 12 * q^51 - 12 * q^53 + 14 * q^55 + 2 * q^61 - 28 * q^69 - 2 * q^75 - 84 * q^77 - 44 * q^79 - 6 * q^81 - 20 * q^87 - 14 * q^95

Character values

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

$n$	$677$	$1015$	$1861$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{6}\right)$

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
$5$		−	3.04892i		−	1.36352i	−0.731577	−	0.681759i	$-0.761215\pi$
$5$		−	3.04892i		−	1.36352i	0.731577	−	0.681759i	$-0.238785\pi$
$6$		0			0
$7$	−4.37249	+	2.52446i	−1.65265	+	0.954156i	−0.676668	+	0.736289i	$0.736577\pi$
$7$	−4.37249	+	2.52446i	−1.65265	+	0.954156i	−0.975978	+	0.217867i	$0.930090\pi$
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	3.29257	+	1.90097i	0.992749	+	0.573164i	0.906095	−	0.423075i	$-0.139049\pi$
$11$	3.29257	+	1.90097i	0.992749	+	0.573164i	0.0866539	+	0.996238i	$0.472383\pi$
$12$		0			0
$13$		0			0
$13$		0			0
$14$		0			0
$15$	2.64044	+	1.52446i	0.681759	+	0.393614i
$16$		0			0
$17$	−0.178448	−	0.309081i	−0.0432800	−	0.0749631i	0.843574	−	0.537013i	$-0.180447\pi$
$17$	−0.178448	−	0.309081i	−0.0432800	−	0.0749631i	−0.886854	+	0.462050i	$0.847114\pi$
$18$		0			0
$19$	5.31485	−	3.06853i	1.21931	−	0.703969i	0.254540	−	0.967062i	$-0.418076\pi$
$19$	5.31485	−	3.06853i	1.21931	−	0.703969i	0.964771	+	0.263093i	$0.0847425\pi$
$20$		0			0
$21$		−	5.04892i		−	1.10176i
$22$		0			0
$23$	−3.96950	+	6.87538i	−0.827698	+	1.43362i	0.0721416	+	0.997394i	$0.477017\pi$
$23$	−3.96950	+	6.87538i	−0.827698	+	1.43362i	−0.899840	+	0.436221i	$0.856317\pi$
$24$		0			0
$25$	−4.29590			−0.859179
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	−0.708947	+	1.22793i	−0.131648	+	0.228021i	−0.924312	−	0.381638i	$-0.875360\pi$
$29$	−0.708947	+	1.22793i	−0.131648	+	0.228021i	0.792664	+	0.609659i	$0.208694\pi$
$30$		0			0
$31$		−	5.78986i		−	1.03989i	−0.854200	−	0.519944i	$-0.825953\pi$
$31$		−	5.78986i		−	1.03989i	0.854200	−	0.519944i	$-0.174047\pi$
$32$		0			0
$33$	−3.29257	+	1.90097i	−0.573164	+	0.330916i
$34$		0			0
$35$	7.69687	+	13.3314i	1.30101	+	2.25341i
$36$		0			0
$37$	−0.0235101	−	0.0135735i	−0.00386503	−	0.00223148i	0.498066	−	0.867139i	$-0.334044\pi$
$37$	−0.0235101	−	0.0135735i	−0.00386503	−	0.00223148i	−0.501931	+	0.864908i	$0.667377\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−7.95529	−	4.59299i	−1.24241	−	0.717305i	−0.272824	−	0.962064i	$-0.587958\pi$
$41$	−7.95529	−	4.59299i	−1.24241	−	0.717305i	−0.969584	+	0.244759i	$0.921291\pi$
$42$		0			0
$43$	−0.609916	−	1.05641i	−0.0930114	−	0.161100i	0.815766	−	0.578383i	$-0.196316\pi$
$43$	−0.609916	−	1.05641i	−0.0930114	−	0.161100i	−0.908777	+	0.417282i	$0.862983\pi$
$44$		0			0
$45$	−2.64044	+	1.52446i	−0.393614	+	0.227253i
$46$		0			0
$47$		−	9.56465i		−	1.39515i	−0.716513	−	0.697574i	$-0.754263\pi$
$47$		−	9.56465i		−	1.39515i	0.716513	−	0.697574i	$-0.245737\pi$
$48$		0			0
$49$	9.24578	−	16.0142i	1.32083	−	2.28774i
$50$		0			0
$51$	0.356896			0.0499754
$52$		0			0
$53$	−4.73556			−0.650479			−0.325240	−	0.945632i	$-0.605445\pi$
$53$	−4.73556			−0.650479			−0.325240	+	0.945632i	$0.605445\pi$
$54$		0			0
$55$	5.79590	−	10.0388i	0.781519	−	1.35363i
$56$		0			0
$57$			6.13706i			0.812874i
$58$		0			0
$59$	11.7134	−	6.76271i	1.52495	−	0.880430i	0.525386	−	0.850864i	$-0.323921\pi$
$59$	11.7134	−	6.76271i	1.52495	−	0.880430i	0.999563	−	0.0295658i	$-0.00941247\pi$
$60$		0			0
$61$	−0.288364	−	0.499461i	−0.0369213	−	0.0639495i	0.846974	−	0.531634i	$-0.178422\pi$
$61$	−0.288364	−	0.499461i	−0.0369213	−	0.0639495i	−0.883896	+	0.467684i	$0.845088\pi$
$62$		0			0
$63$	4.37249	+	2.52446i	0.550882	+	0.318052i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−6.88584	−	3.97554i	−0.841239	−	0.485690i	0.0164461	−	0.999865i	$-0.494765\pi$
$67$	−6.88584	−	3.97554i	−0.841239	−	0.485690i	−0.857685	+	0.514175i	$0.828098\pi$
$68$		0			0
$69$	−3.96950	−	6.87538i	−0.477872	−	0.827698i
$70$		0			0
$71$	2.66395	−	1.53803i	0.316153	−	0.182531i	−0.333524	−	0.942742i	$-0.608238\pi$
$71$	2.66395	−	1.53803i	0.316153	−	0.182531i	0.649676	+	0.760211i	$0.274904\pi$
$72$		0			0
$73$		−	14.0368i		−	1.64289i	−0.570290	−	0.821444i	$-0.693169\pi$
$73$		−	14.0368i		−	1.64289i	0.570290	−	0.821444i	$-0.306831\pi$
$74$		0			0
$75$	2.14795	−	3.72036i	0.248024	−	0.429590i
$76$		0			0
$77$	−19.1957			−2.18755
$78$		0			0
$79$	−0.841166			−0.0946386			−0.0473193	−	0.998880i	$-0.515068\pi$
$79$	−0.841166			−0.0946386			−0.0473193	+	0.998880i	$0.515068\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$			0.192685i			0.0211500i	0.999944	+	0.0105750i	$0.00336619\pi$
$83$			0.192685i			0.0211500i	−0.999944	+	0.0105750i	$0.996634\pi$
$84$		0			0
$85$	−0.942362	+	0.544073i	−0.102214	+	0.0590130i
$86$		0			0
$87$	−0.708947	−	1.22793i	−0.0760071	−	0.131648i
$88$		0			0
$89$	−7.97880	−	4.60656i	−0.845751	−	0.488295i	0.0134637	−	0.999909i	$-0.495714\pi$
$89$	−7.97880	−	4.60656i	−0.845751	−	0.488295i	−0.859215	+	0.511615i	$0.829048\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	5.01416	+	2.89493i	0.519944	+	0.300190i
$94$		0			0
$95$	−9.35570	−	16.2045i	−0.959875	−	1.66255i
$96$		0			0
$97$	0.590918	−	0.341166i	0.0599986	−	0.0346402i	−0.469701	−	0.882826i	$-0.655638\pi$
$97$	0.590918	−	0.341166i	0.0599986	−	0.0346402i	0.529699	+	0.848186i	$0.322305\pi$
$98$		0			0
$99$		−	3.80194i		−	0.382109i
$100$		0			0
$101$	3.37531	−	5.84621i	0.335856	−	0.581720i	−0.647793	−	0.761817i	$-0.724308\pi$
$101$	3.37531	−	5.84621i	0.335856	−	0.581720i	0.983649	+	0.180097i	$0.0576410\pi$
$102$		0			0
$103$	−7.78017			−0.766603			−0.383301	−	0.923623i	$-0.625213\pi$
$103$	−7.78017			−0.766603			−0.383301	+	0.923623i	$0.625213\pi$
$104$		0			0
$105$	−15.3937			−1.50227
$106$		0			0
$107$	−4.25786	+	7.37484i	−0.411623	+	0.712953i	−0.995067	−	0.0992008i	$-0.968371\pi$
$107$	−4.25786	+	7.37484i	−0.411623	+	0.712953i	0.583444	+	0.812153i	$0.301705\pi$
$108$		0			0
$109$			1.08815i			0.104225i	0.998641	+	0.0521127i	$0.0165955\pi$
$109$			1.08815i			0.104225i	−0.998641	+	0.0521127i	$0.983404\pi$
$110$		0			0
$111$	0.0235101	−	0.0135735i	0.00223148	−	0.00128834i
$112$		0			0
$113$	−1.83728	−	3.18226i	−0.172837	−	0.299362i	0.766574	−	0.642156i	$-0.221960\pi$
$113$	−1.83728	−	3.18226i	−0.172837	−	0.299362i	−0.939411	+	0.342794i	$0.888627\pi$
$114$		0			0
$115$	20.9625	+	12.1027i	1.95476	+	1.12858i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	1.56052	+	0.900969i	0.143053	+	0.0825917i
$120$		0			0
$121$	1.72737	+	2.99188i	0.157033	+	0.271989i
$122$		0			0
$123$	7.95529	−	4.59299i	0.717305	−	0.414136i
$124$		0			0
$125$		−	2.14675i		−	0.192011i
$126$		0			0
$127$	5.90581	−	10.2292i	0.524056	−	0.907692i	−0.475552	−	0.879688i	$-0.657752\pi$
$127$	5.90581	−	10.2292i	0.524056	−	0.907692i	0.999608	−	0.0280041i	$-0.00891515\pi$
$128$		0			0
$129$	1.21983			0.107400
$130$		0			0
$131$	12.5579			1.09719			0.548596	−	0.836087i	$-0.315162\pi$
$131$	12.5579			1.09719			0.548596	+	0.836087i	$0.315162\pi$
$132$		0			0
$133$	−15.4928	+	26.8343i	−1.34339	+	2.32682i
$134$		0			0
$135$		−	3.04892i		−	0.262409i
$136$		0			0
$137$	−5.76614	+	3.32908i	−0.492635	+	0.284423i	−0.725667	−	0.688046i	$-0.758469\pi$
$137$	−5.76614	+	3.32908i	−0.492635	+	0.284423i	0.233032	+	0.972469i	$0.425135\pi$
$138$		0			0
$139$	3.08695	+	5.34675i	0.261832	+	0.453506i	0.966729	−	0.255804i	$-0.0823401\pi$
$139$	3.08695	+	5.34675i	0.261832	+	0.453506i	−0.704897	+	0.709310i	$0.749007\pi$
$140$		0			0
$141$	8.28323	+	4.78232i	0.697574	+	0.402744i
$142$		0			0
$143$		0			0
$144$		0			0
$145$	3.74387	+	2.16152i	0.310911	+	0.179505i
$146$		0			0
$147$	9.24578	+	16.0142i	0.762579	+	1.32083i
$148$		0			0
$149$	0.127091	−	0.0733760i	0.0104117	−	0.00601120i	−0.494785	−	0.869015i	$-0.664753\pi$
$149$	0.127091	−	0.0733760i	0.0104117	−	0.00601120i	0.505197	+	0.863004i	$0.331420\pi$
$150$		0			0
$151$			9.36658i			0.762242i	0.924525	+	0.381121i	$0.124462\pi$
$151$			9.36658i			0.762242i	−0.924525	+	0.381121i	$0.875538\pi$
$152$		0			0
$153$	−0.178448	+	0.309081i	−0.0144267	+	0.0249877i
$154$		0			0
$155$	−17.6528			−1.41791
$156$		0			0
$157$	−4.03146			−0.321745			−0.160873	−	0.986975i	$-0.551431\pi$
$157$	−4.03146			−0.321745			−0.160873	+	0.986975i	$0.551431\pi$
$158$		0			0
$159$	2.36778	−	4.10112i	0.187777	−	0.325240i
$160$		0			0
$161$		−	40.0834i		−	3.15901i
$162$		0			0
$163$	9.02475	−	5.21044i	0.706873	−	0.408113i	−0.103029	−	0.994678i	$-0.532854\pi$
$163$	9.02475	−	5.21044i	0.706873	−	0.408113i	0.809902	+	0.586565i	$0.199520\pi$
$164$		0			0
$165$	5.79590	+	10.0388i	0.451210	+	0.781519i
$166$		0			0
$167$	−8.92490	−	5.15279i	−0.690629	−	0.398735i	0.113218	−	0.993570i	$-0.463884\pi$
$167$	−8.92490	−	5.15279i	−0.690629	−	0.398735i	−0.803848	+	0.594835i	$0.797217\pi$
$168$		0			0
$169$		0			0
$170$		0			0
$171$	−5.31485	−	3.06853i	−0.406437	−	0.234656i
$172$		0			0
$173$	−11.1516	−	19.3151i	−0.847840	−	1.46850i	−0.883132	−	0.469125i	$-0.844569\pi$
$173$	−11.1516	−	19.3151i	−0.847840	−	1.46850i	0.0352915	−	0.999377i	$-0.488764\pi$
$174$		0			0
$175$	18.7838	−	10.8448i	1.41992	−	0.819791i
$176$		0			0
$177$			13.5254i			1.01663i
$178$		0			0
$179$	−8.68867	+	15.0492i	−0.649422	+	1.12483i	0.333840	+	0.942630i	$0.391656\pi$
$179$	−8.68867	+	15.0492i	−0.649422	+	1.12483i	−0.983261	+	0.182201i	$0.941678\pi$
$180$		0			0
$181$	24.4644			1.81843			0.909213	−	0.416331i	$-0.136684\pi$
$181$	24.4644			1.81843			0.909213	+	0.416331i	$0.136684\pi$
$182$		0			0
$183$	0.576728			0.0426330
$184$		0			0
$185$	−0.0413846	+	0.0716802i	−0.00304266	+	0.00527003i
$186$		0			0
$187$		−	1.35690i		−	0.0992261i
$188$		0			0
$189$	−4.37249	+	2.52446i	−0.318052	+	0.183627i
$190$		0			0
$191$	−10.7044	−	18.5406i	−0.774543	−	1.34155i	−0.935051	−	0.354513i	$-0.884647\pi$
$191$	−10.7044	−	18.5406i	−0.774543	−	1.34155i	0.160508	−	0.987035i	$-0.448687\pi$
$192$		0			0
$193$	12.4947	+	7.21379i	0.899385	+	0.519260i	0.877001	−	0.480489i	$-0.159541\pi$
$193$	12.4947	+	7.21379i	0.899385	+	0.519260i	0.0223843	+	0.999749i	$0.492874\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−1.77234	−	1.02326i	−0.126274	−	0.0729044i	0.435532	−	0.900173i	$-0.356560\pi$
$197$	−1.77234	−	1.02326i	−0.126274	−	0.0729044i	−0.561807	+	0.827269i	$0.689893\pi$
$198$		0			0
$199$	−2.77748	−	4.81073i	−0.196890	−	0.341024i	0.750628	−	0.660725i	$-0.229751\pi$
$199$	−2.77748	−	4.81073i	−0.196890	−	0.341024i	−0.947519	+	0.319701i	$0.896418\pi$
$200$		0			0
$201$	6.88584	−	3.97554i	0.485690	−	0.280413i
$202$		0			0
$203$		−	7.15883i		−	0.502452i
$204$		0			0
$205$	−14.0036	+	24.2550i	−0.978057	+	1.69404i
$206$		0			0
$207$	7.93900			0.551799
$208$		0			0
$209$	23.3327			1.61396
$210$		0			0
$211$	10.9046	−	18.8874i	0.750705	−	1.30026i	−0.196777	−	0.980448i	$-0.563047\pi$
$211$	10.9046	−	18.8874i	0.750705	−	1.30026i	0.947482	−	0.319810i	$-0.103619\pi$
$212$		0			0
$213$			3.07606i			0.210768i
$214$		0			0
$215$	−3.22089	+	1.85958i	−0.219663	+	0.126823i
$216$		0			0
$217$	14.6163	+	25.3161i	0.992216	+	1.71857i
$218$		0			0
$219$	12.1563	+	7.01842i	0.821444	+	0.474261i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	22.1715	+	12.8007i	1.48472	+	0.857201i	0.999849	−	0.0173869i	$-0.00553470\pi$
$223$	22.1715	+	12.8007i	1.48472	+	0.857201i	0.484867	+	0.874588i	$0.338868\pi$
$224$		0			0
$225$	2.14795	+	3.72036i	0.143197	+	0.248024i
$226$		0			0
$227$	−2.36068	+	1.36294i	−0.156684	+	0.0904613i	−0.576292	−	0.817244i	$-0.695501\pi$
$227$	−2.36068	+	1.36294i	−0.156684	+	0.0904613i	0.419608	+	0.907705i	$0.362167\pi$
$228$		0			0
$229$		−	18.1075i		−	1.19658i	−0.801280	−	0.598289i	$-0.795847\pi$
$229$		−	18.1075i		−	1.19658i	0.801280	−	0.598289i	$-0.204153\pi$
$230$		0			0
$231$	9.59783	−	16.6239i	0.631491	−	1.09377i
$232$		0			0
$233$	18.9051			1.23852			0.619259	−	0.785187i	$-0.287433\pi$
$233$	18.9051			1.23852			0.619259	+	0.785187i	$0.287433\pi$
$234$		0			0
$235$	−29.1618			−1.90231
$236$		0			0
$237$	0.420583	−	0.728471i	0.0273198	−	0.0473193i
$238$		0			0
$239$			20.3099i			1.31374i	0.754005	+	0.656869i	$0.228120\pi$
$239$			20.3099i			1.31374i	−0.754005	+	0.656869i	$0.771880\pi$
$240$		0			0
$241$	−13.6782	+	7.89708i	−0.881087	+	0.508696i	−0.871017	−	0.491253i	$-0.836539\pi$
$241$	−13.6782	+	7.89708i	−0.881087	+	0.508696i	−0.0100704	+	0.999949i	$0.503206\pi$
$242$		0			0
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$		0			0
$245$	−48.8259	−	28.1896i	−3.11937	−	1.80097i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	−0.166870	−	0.0963427i	−0.0105750	−	0.00610547i
$250$		0			0
$251$	−3.94116	−	6.82628i	−0.248764	−	0.430871i	0.714419	−	0.699718i	$-0.246691\pi$
$251$	−3.94116	−	6.82628i	−0.248764	−	0.430871i	−0.963183	+	0.268846i	$0.913358\pi$
$252$		0			0
$253$	−26.1398	+	15.0918i	−1.64339	+	0.948813i
$254$		0			0
$255$		−	1.08815i		−	0.0681423i
$256$		0			0
$257$	9.29859	−	16.1056i	0.580030	−	1.00464i	−0.415445	−	0.909618i	$-0.636374\pi$
$257$	9.29859	−	16.1056i	0.580030	−	1.00464i	0.995475	−	0.0950229i	$-0.0302924\pi$
$258$		0			0
$259$	0.137063			0.00851670
$260$		0			0
$261$	1.41789			0.0877655
$262$		0			0
$263$	−0.628334	+	1.08831i	−0.0387447	+	0.0671079i	−0.884748	−	0.466071i	$-0.845669\pi$
$263$	−0.628334	+	1.08831i	−0.0387447	+	0.0671079i	0.846003	+	0.533179i	$0.179003\pi$
$264$		0			0
$265$			14.4383i			0.886940i
$266$		0			0
$267$	7.97880	−	4.60656i	0.488295	−	0.281917i
$268$		0			0
$269$	9.44720	+	16.3630i	0.576006	+	0.997671i	0.995932	+	0.0901129i	$0.0287228\pi$
$269$	9.44720	+	16.3630i	0.576006	+	0.997671i	−0.419926	+	0.907558i	$0.637944\pi$
$270$		0			0
$271$	−17.8472	−	10.3041i	−1.08414	−	0.625929i	−0.152131	−	0.988360i	$-0.548613\pi$
$271$	−17.8472	−	10.3041i	−1.08414	−	0.625929i	−0.932010	+	0.362431i	$0.881947\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−14.1446	−	8.16637i	−0.852949	−	0.492450i
$276$		0			0
$277$	5.94451	+	10.2962i	0.357171	+	0.618638i	0.987487	−	0.157700i	$-0.0504080\pi$
$277$	5.94451	+	10.2962i	0.357171	+	0.618638i	−0.630316	+	0.776339i	$0.717075\pi$
$278$		0			0
$279$	−5.01416	+	2.89493i	−0.300190	+	0.173315i
$280$		0			0
$281$			7.74333i			0.461928i	0.972962	+	0.230964i	$0.0741880\pi$
$281$			7.74333i			0.461928i	−0.972962	+	0.230964i	$0.925812\pi$
$282$		0			0
$283$	−6.11745	+	10.5957i	−0.363645	+	0.629851i	−0.988558	−	0.150843i	$-0.951801\pi$
$283$	−6.11745	+	10.5957i	−0.363645	+	0.629851i	0.624913	+	0.780694i	$0.285134\pi$
$284$		0			0
$285$	18.7114			1.10837
$286$		0			0
$287$	46.3793			2.73768
$288$		0			0
$289$	8.43631	−	14.6121i	0.496254	−	0.859537i
$290$		0			0
$291$			0.682333i			0.0399991i
$292$		0			0
$293$	16.1068	−	9.29925i	0.940968	−	0.543268i	0.0507042	−	0.998714i	$-0.483853\pi$
$293$	16.1068	−	9.29925i	0.940968	−	0.543268i	0.890264	+	0.455446i	$0.150520\pi$
$294$		0			0
$295$	−20.6189	−	35.7131i	−1.20048	−	2.07929i
$296$		0			0
$297$	3.29257	+	1.90097i	0.191055	+	0.110305i
$298$		0			0
$299$		0			0
$300$		0			0
$301$	5.33371	+	3.07942i	0.307430	+	0.177495i
$302$		0			0
$303$	3.37531	+	5.84621i	0.193907	+	0.335856i
$304$		0			0
$305$	−1.52282	+	0.879199i	−0.0871962	+	0.0503428i
$306$		0			0
$307$		−	3.32006i		−	0.189486i	−0.995502	−	0.0947429i	$-0.969797\pi$
$307$		−	3.32006i		−	0.189486i	0.995502	−	0.0947429i	$-0.0302029\pi$
$308$		0			0
$309$	3.89008	−	6.73782i	0.221299	−	0.383301i
$310$		0			0
$311$	−20.2881			−1.15043			−0.575217	−	0.818001i	$-0.695082\pi$
$311$	−20.2881			−1.15043			−0.575217	+	0.818001i	$0.695082\pi$
$312$		0			0
$313$	−14.3870			−0.813203			−0.406601	−	0.913606i	$-0.633286\pi$
$313$	−14.3870			−0.813203			−0.406601	+	0.913606i	$0.633286\pi$
$314$		0			0
$315$	7.69687	−	13.3314i	0.433669	−	0.751137i
$316$		0			0
$317$		−	12.4450i		−	0.698983i	−0.936939	−	0.349492i	$-0.886354\pi$
$317$		−	12.4450i		−	0.698983i	0.936939	−	0.349492i	$-0.113646\pi$
$318$		0			0
$319$	−4.66852	+	2.69537i	−0.261387	+	0.150912i
$320$		0			0
$321$	−4.25786	−	7.37484i	−0.237651	−	0.411623i
$322$		0			0
$323$	−1.89685	−	1.09515i	−0.105544	−	0.0609356i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−0.942362	−	0.544073i	−0.0521127	−	0.0300873i
$328$		0			0
$329$	24.1456	+	41.8213i	1.33119	+	2.30568i
$330$		0			0
$331$	−2.87411	+	1.65937i	−0.157975	+	0.0912070i	−0.576904	−	0.816812i	$-0.695739\pi$
$331$	−2.87411	+	1.65937i	−0.157975	+	0.0912070i	0.418928	+	0.908019i	$0.362406\pi$
$332$		0			0
$333$			0.0271471i			0.00148765i
$334$		0			0
$335$	−12.1211	+	20.9944i	−0.662246	+	1.14704i
$336$		0			0
$337$	12.3515			0.672830			0.336415	−	0.941714i	$-0.390786\pi$
$337$	12.3515			0.672830			0.336415	+	0.941714i	$0.390786\pi$
$338$		0			0
$339$	3.67456			0.199575
$340$		0			0
$341$	11.0063	−	19.0635i	0.596027	−	1.03235i
$342$		0			0
$343$			58.0200i			3.13278i
$344$		0			0
$345$	−20.9625	+	12.1027i	−1.12858	+	0.651586i
$346$		0			0
$347$	−5.24847	−	9.09062i	−0.281753	−	0.488010i	0.690064	−	0.723749i	$-0.257582\pi$
$347$	−5.24847	−	9.09062i	−0.281753	−	0.488010i	−0.971817	+	0.235739i	$0.924249\pi$
$348$		0			0
$349$	12.2184	+	7.05429i	0.654036	+	0.377608i	0.790001	−	0.613106i	$-0.210080\pi$
$349$	12.2184	+	7.05429i	0.654036	+	0.377608i	−0.135965	+	0.990714i	$0.543413\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−12.5736	−	7.25936i	−0.669224	−	0.386377i	0.126559	−	0.991959i	$-0.459607\pi$
$353$	−12.5736	−	7.25936i	−0.669224	−	0.386377i	−0.795782	+	0.605583i	$0.792940\pi$
$354$		0			0
$355$	−4.68933	−	8.12216i	−0.248884	−	0.431080i
$356$		0			0
$357$	−1.56052	+	0.900969i	−0.0825917	+	0.0476843i
$358$		0			0
$359$			24.7144i			1.30438i	0.758058	+	0.652188i	$0.226149\pi$
$359$			24.7144i			1.30438i	−0.758058	+	0.652188i	$0.773851\pi$
$360$		0			0
$361$	9.33177	−	16.1631i	0.491146	−	0.850690i
$362$		0			0
$363$	−3.45473			−0.181326
$364$		0			0
$365$	−42.7972			−2.24011
$366$		0			0
$367$	−9.75332	+	16.8932i	−0.509119	+	0.881820i	0.490825	+	0.871258i	$0.336695\pi$
$367$	−9.75332	+	16.8932i	−0.509119	+	0.881820i	−0.999944	+	0.0105619i	$0.996638\pi$
$368$		0			0
$369$			9.18598i			0.478203i
$370$		0			0
$371$	20.7062	−	11.9547i	1.07501	−	0.620659i
$372$		0			0
$373$	1.90097	+	3.29257i	0.0984284	+	0.170483i	0.911034	−	0.412331i	$-0.135285\pi$
$373$	1.90097	+	3.29257i	0.0984284	+	0.170483i	−0.812606	+	0.582814i	$0.801952\pi$
$374$		0			0
$375$	1.85914	+	1.07338i	0.0960057	+	0.0554289i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−1.90823	−	1.10172i	−0.0980194	−	0.0565915i	0.450189	−	0.892933i	$-0.351357\pi$
$379$	−1.90823	−	1.10172i	−0.0980194	−	0.0565915i	−0.548208	+	0.836342i	$0.684690\pi$
$380$		0			0
$381$	5.90581	+	10.2292i	0.302564	+	0.524056i
$382$		0			0
$383$	−26.8201	+	15.4846i	−1.37044	+	0.791224i	−0.990983	−	0.133985i	$-0.957223\pi$
$383$	−26.8201	+	15.4846i	−1.37044	+	0.791224i	−0.379457	+	0.925209i	$0.623889\pi$
$384$		0			0
$385$			58.5260i			2.98276i
$386$		0			0
$387$	−0.609916	+	1.05641i	−0.0310038	+	0.0537001i
$388$		0			0
$389$	−24.4470			−1.23951			−0.619755	−	0.784795i	$-0.712768\pi$
$389$	−24.4470			−1.23951			−0.619755	+	0.784795i	$0.712768\pi$
$390$		0			0
$391$	2.83340			0.143291
$392$		0			0
$393$	−6.27897	+	10.8755i	−0.316732	+	0.548596i
$394$		0			0
$395$			2.56465i			0.129041i
$396$		0			0
$397$	−0.631209	+	0.364429i	−0.0316795	+	0.0182901i	−0.515756	−	0.856735i	$-0.672489\pi$
$397$	−0.631209	+	0.364429i	−0.0316795	+	0.0182901i	0.484077	+	0.875026i	$0.339156\pi$
$398$		0			0
$399$	−15.4928	−	26.8343i	−0.775608	−	1.34339i
$400$		0			0
$401$	8.88512	+	5.12983i	0.443702	+	0.256171i	0.705167	−	0.709042i	$-0.250872\pi$
$401$	8.88512	+	5.12983i	0.443702	+	0.256171i	−0.261465	+	0.965213i	$0.584206\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	2.64044	+	1.52446i	0.131205	+	0.0757510i
$406$		0			0
$407$	−0.0516057	−	0.0893838i	−0.00255800	−	0.00443059i
$408$		0			0
$409$	−19.7194	+	11.3850i	−0.975062	+	0.562952i	−0.900776	−	0.434285i	$-0.857001\pi$
$409$	−19.7194	+	11.3850i	−0.975062	+	0.562952i	−0.0742861	+	0.997237i	$0.523668\pi$
$410$		0			0
$411$		−	6.65817i		−	0.328423i
$412$		0			0
$413$	−34.1444	+	59.1398i	−1.68013	+	2.91008i
$414$		0			0
$415$	0.587482			0.0288384
$416$		0			0
$417$	−6.17390			−0.302337
$418$		0			0
$419$	−9.54652	+	16.5351i	−0.466378	+	0.807791i	−0.999263	−	0.0383973i	$-0.987775\pi$
$419$	−9.54652	+	16.5351i	−0.466378	+	0.807791i	0.532884	+	0.846188i	$0.321108\pi$
$420$		0			0
$421$		−	15.8629i		−	0.773112i	−0.922266	−	0.386556i	$-0.873665\pi$
$421$		−	15.8629i		−	0.773112i	0.922266	−	0.386556i	$-0.126335\pi$
$422$		0			0
$423$	−8.28323	+	4.78232i	−0.402744	+	0.232525i
$424$		0			0
$425$	0.766594	+	1.32778i	0.0371853	+	0.0644068i
$426$		0			0
$427$	2.52174	+	1.45593i	0.122036	+	0.0704572i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−21.4033	−	12.3572i	−1.03096	−	0.595225i	−0.113700	−	0.993515i	$-0.536270\pi$
$431$	−21.4033	−	12.3572i	−1.03096	−	0.595225i	−0.917259	+	0.398290i	$0.869604\pi$
$432$		0			0
$433$	8.09999	+	14.0296i	0.389261	+	0.674219i	0.992350	−	0.123454i	$-0.0393972\pi$
$433$	8.09999	+	14.0296i	0.389261	+	0.674219i	−0.603090	+	0.797673i	$0.706064\pi$
$434$		0			0
$435$	−3.74387	+	2.16152i	−0.179505	+	0.103637i
$436$		0			0
$437$			48.7222i			2.33070i
$438$		0			0
$439$	−11.0025	+	19.0568i	−0.525118	+	0.909532i	0.474454	+	0.880280i	$0.342646\pi$
$439$	−11.0025	+	19.0568i	−0.525118	+	0.909532i	−0.999572	+	0.0292512i	$0.990688\pi$
$440$		0			0
$441$	−18.4916			−0.880551
$442$		0			0
$443$	4.33273			0.205854			0.102927	−	0.994689i	$-0.467179\pi$
$443$	4.33273			0.205854			0.102927	+	0.994689i	$0.467179\pi$
$444$		0			0
$445$	−14.0450	+	24.3267i	−0.665798	+	1.15320i
$446$		0			0
$447$			0.146752i			0.00694113i
$448$		0			0
$449$	13.9374	−	8.04676i	0.657747	−	0.379750i	−0.133671	−	0.991026i	$-0.542677\pi$
$449$	13.9374	−	8.04676i	0.657747	−	0.379750i	0.791418	+	0.611276i	$0.209343\pi$
$450$		0			0
$451$	−17.4623	−	30.2455i	−0.822266	−	1.42421i
$452$		0			0
$453$	−8.11170	−	4.68329i	−0.381121	−	0.220040i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	0.938628	+	0.541917i	0.0439072	+	0.0253498i	0.521793	−	0.853072i	$-0.325263\pi$
$457$	0.938628	+	0.541917i	0.0439072	+	0.0253498i	−0.477886	+	0.878422i	$0.658597\pi$
$458$		0			0
$459$	−0.178448	−	0.309081i	−0.00832924	−	0.0144267i
$460$		0			0
$461$	−29.5871	+	17.0821i	−1.37801	+	0.795593i	−0.991919	−	0.126869i	$-0.959507\pi$
$461$	−29.5871	+	17.0821i	−1.37801	+	0.795593i	−0.386088	+	0.922462i	$0.626174\pi$
$462$		0			0
$463$		−	23.7560i		−	1.10404i	−0.833832	−	0.552018i	$-0.813858\pi$
$463$		−	23.7560i		−	1.10404i	0.833832	−	0.552018i	$-0.186142\pi$
$464$		0			0
$465$	8.82640	−	15.2878i	0.409314	−	0.708953i
$466$		0			0
$467$	42.8189			1.98142			0.990712	−	0.135979i	$-0.0434180\pi$
$467$	42.8189			1.98142			0.990712	+	0.135979i	$0.0434180\pi$
$468$		0			0
$469$	40.1444			1.85369
$470$		0			0
$471$	2.01573	−	3.49135i	0.0928799	−	0.160873i
$472$		0			0
$473$		−	4.63773i		−	0.213243i
$474$		0			0
$475$	−22.8321	+	13.1821i	−1.04761	+	0.604836i
$476$		0			0
$477$	2.36778	+	4.10112i	0.108413	+	0.187777i
$478$		0			0
$479$	4.90685	+	2.83297i	0.224200	+	0.129442i	0.607893	−	0.794019i	$-0.292015\pi$
$479$	4.90685	+	2.83297i	0.224200	+	0.129442i	−0.383694	+	0.923460i	$0.625348\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$	34.7132	+	20.0417i	1.57951	+	0.911928i
$484$		0			0
$485$	−1.04019	−	1.80166i	−0.0472325	−	0.0818091i
$486$		0			0
$487$	10.6099	−	6.12565i	0.480782	−	0.277580i	−0.239960	−	0.970783i	$-0.577134\pi$
$487$	10.6099	−	6.12565i	0.480782	−	0.277580i	0.720742	+	0.693203i	$0.243801\pi$
$488$		0			0
$489$			10.4209i			0.471248i
$490$		0			0
$491$	−2.48307	+	4.30081i	−0.112060	+	0.194093i	−0.916601	−	0.399804i	$-0.869078\pi$
$491$	−2.48307	+	4.30081i	−0.112060	+	0.194093i	0.804541	+	0.593897i	$0.202411\pi$
$492$		0			0
$493$	0.506041			0.0227909
$494$		0			0
$495$	−11.5918			−0.521012
$496$		0			0
$497$	−7.76540	+	13.4501i	−0.348326	+	0.603318i
$498$		0			0
$499$		−	16.2500i		−	0.727448i	−0.931507	−	0.363724i	$-0.881505\pi$
$499$		−	16.2500i		−	0.727448i	0.931507	−	0.363724i	$-0.118495\pi$
$500$		0			0
$501$	8.92490	−	5.15279i	0.398735	−	0.230210i
$502$		0			0
$503$	6.12296	+	10.6053i	0.273009	+	0.472866i	0.969631	−	0.244573i	$-0.0786477\pi$
$503$	6.12296	+	10.6053i	0.273009	+	0.472866i	−0.696622	+	0.717439i	$0.745314\pi$
$504$		0			0
$505$	−17.8246	−	10.2911i	−0.793185	−	0.457946i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	3.33235	+	1.92394i	0.147704	+	0.0852769i	0.572031	−	0.820232i	$-0.306156\pi$
$509$	3.33235	+	1.92394i	0.147704	+	0.0852769i	−0.424327	+	0.905509i	$0.639489\pi$
$510$		0			0
$511$	35.4354	+	61.3759i	1.56757	+	2.71511i
$512$		0			0
$513$	5.31485	−	3.06853i	0.234656	−	0.135479i
$514$		0			0
$515$			23.7211i			1.04528i
$516$		0			0
$517$	18.1821	−	31.4923i	0.799648	−	1.38503i
$518$		0			0
$519$	22.3032			0.979002
$520$		0			0
$521$	−9.42626			−0.412972			−0.206486	−	0.978450i	$-0.566203\pi$
$521$	−9.42626			−0.412972			−0.206486	+	0.978450i	$0.566203\pi$
$522$		0			0
$523$	20.2969	−	35.1552i	0.887520	−	1.53723i	0.0447212	−	0.999000i	$-0.485760\pi$
$523$	20.2969	−	35.1552i	0.887520	−	1.53723i	0.842798	−	0.538229i	$-0.180907\pi$
$524$		0			0
$525$			21.6896i			0.946613i
$526$		0			0
$527$	−1.78953	+	1.03319i	−0.0779533	+	0.0450064i
$528$		0			0
$529$	−20.0139	−	34.6650i	−0.870168	−	1.50718i
$530$		0			0
$531$	−11.7134	−	6.76271i	−0.508316	−	0.293477i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	22.4853	+	12.9819i	0.972123	+	0.561256i
$536$		0			0
$537$	−8.68867	−	15.0492i	−0.374944	−	0.649422i
$538$		0			0
$539$	60.8849	−	35.1519i	2.62250	−	1.51410i
$540$		0			0
$541$			4.32006i			0.185734i	0.995679	+	0.0928669i	$0.0296031\pi$
$541$			4.32006i			0.185734i	−0.995679	+	0.0928669i	$0.970397\pi$
$542$		0			0
$543$	−12.2322	+	21.1868i	−0.524934	+	0.909213i
$544$		0			0
$545$	3.31767			0.142113
$546$		0			0
$547$	35.8702			1.53370			0.766850	−	0.641826i	$-0.221823\pi$
$547$	35.8702			1.53370			0.766850	+	0.641826i	$0.221823\pi$
$548$		0			0
$549$	−0.288364	+	0.499461i	−0.0123071	+	0.0213165i
$550$		0			0
$551$			8.70171i			0.370705i
$552$		0			0
$553$	3.67799	−	2.12349i	0.156404	−	0.0903000i
$554$		0			0
$555$	−0.0413846	−	0.0716802i	−0.00175668	−	0.00304266i
$556$		0			0
$557$	−26.3960	−	15.2397i	−1.11843	−	0.645729i	−0.177434	−	0.984133i	$-0.556780\pi$
$557$	−26.3960	−	15.2397i	−1.11843	−	0.645729i	−0.941001	+	0.338404i	$0.890113\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	1.17511	+	0.678448i	0.0496130	+	0.0286441i
$562$		0			0
$563$	−16.3855	−	28.3806i	−0.690568	−	1.19610i	−0.971652	−	0.236416i	$-0.924027\pi$
$563$	−16.3855	−	28.3806i	−0.690568	−	1.19610i	0.281084	−	0.959683i	$-0.409306\pi$
$564$		0			0
$565$	−9.70246	+	5.60172i	−0.408186	+	0.235666i
$566$		0			0
$567$		−	5.04892i		−	0.212035i
$568$		0			0
$569$	−1.45593	+	2.52174i	−0.0610356	+	0.105717i	−0.894929	−	0.446209i	$-0.852774\pi$
$569$	−1.45593	+	2.52174i	−0.0610356	+	0.105717i	0.833893	+	0.551926i	$0.186107\pi$
$570$		0			0
$571$	22.8592			0.956628			0.478314	−	0.878189i	$-0.341248\pi$
$571$	22.8592			0.956628			0.478314	+	0.878189i	$0.341248\pi$
$572$		0			0
$573$	21.4088			0.894365
$574$		0			0
$575$	17.0526	−	29.5359i	0.711141	−	1.23173i
$576$		0			0
$577$			7.78315i			0.324017i	0.986789	+	0.162008i	$0.0517972\pi$
$577$			7.78315i			0.324017i	−0.986789	+	0.162008i	$0.948203\pi$
$578$		0			0
$579$	−12.4947	+	7.21379i	−0.519260	+	0.299795i
$580$		0			0
$581$	−0.486426	−	0.842515i	−0.0201804	−	0.0349534i
$582$		0			0
$583$	−15.5922	−	9.00216i	−0.645763	−	0.372831i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−2.34090	−	1.35152i	−0.0966193	−	0.0557832i	0.450912	−	0.892569i	$-0.351099\pi$
$587$	−2.34090	−	1.35152i	−0.0966193	−	0.0557832i	−0.547531	+	0.836785i	$0.684432\pi$
$588$		0			0
$589$	−17.7664	−	30.7722i	−0.732050	−	1.26795i
$590$		0			0
$591$	1.77234	−	1.02326i	0.0729044	−	0.0420914i
$592$		0			0
$593$		−	38.8961i		−	1.59727i	−0.601816	−	0.798635i	$-0.705556\pi$
$593$		−	38.8961i		−	1.59727i	0.601816	−	0.798635i	$-0.294444\pi$
$594$		0			0
$595$	2.74698	−	4.75791i	0.112615	−	0.195055i
$596$		0			0
$597$	5.55496			0.227349
$598$		0			0
$599$	13.5308			0.552853			0.276427	−	0.961035i	$-0.410850\pi$
$599$	13.5308			0.552853			0.276427	+	0.961035i	$0.410850\pi$
$600$		0			0
$601$	13.1256	−	22.7343i	0.535406	−	0.927351i	−0.463737	−	0.885973i	$-0.653492\pi$
$601$	13.1256	−	22.7343i	0.535406	−	0.927351i	0.999144	−	0.0413781i	$-0.0131748\pi$
$602$		0			0
$603$			7.95108i			0.323793i
$604$		0			0
$605$	9.12201	−	5.26659i	0.370862	−	0.214117i
$606$		0			0
$607$	19.0591	+	33.0114i	0.773587	+	1.33989i	0.935585	+	0.353100i	$0.114873\pi$
$607$	19.0591	+	33.0114i	0.773587	+	1.33989i	−0.161999	+	0.986791i	$0.551794\pi$
$608$		0			0
$609$	6.19973	+	3.57942i	0.251226	+	0.145045i
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−17.1402	−	9.89589i	−0.692285	−	0.399691i	0.112182	−	0.993688i	$-0.464216\pi$
$613$	−17.1402	−	9.89589i	−0.692285	−	0.399691i	−0.804468	+	0.593997i	$0.797549\pi$
$614$		0			0
$615$	−14.0036	−	24.2550i	−0.564682	−	0.978057i
$616$		0			0
$617$	−42.2680	+	24.4034i	−1.70164	+	0.982445i	−0.757545	+	0.652783i	$0.773601\pi$
$617$	−42.2680	+	24.4034i	−1.70164	+	0.982445i	−0.944099	+	0.329662i	$0.893065\pi$
$618$		0			0
$619$			24.8702i			0.999619i	0.866135	+	0.499810i	$0.166597\pi$
$619$			24.8702i			0.999619i	−0.866135	+	0.499810i	$0.833403\pi$
$620$		0			0
$621$	−3.96950	+	6.87538i	−0.159291	+	0.275899i
$622$		0			0
$623$	46.5163			1.86364
$624$		0			0
$625$	−28.0248			−1.12099
$626$		0			0
$627$	−11.6664	+	20.2067i	−0.465910	+	0.806979i
$628$		0			0
$629$			0.00968868i			0.000386313i
$630$		0			0
$631$	40.5897	−	23.4345i	1.61585	−	0.932911i	0.627871	−	0.778318i	$-0.283927\pi$
$631$	40.5897	−	23.4345i	1.61585	−	0.932911i	0.987978	−	0.154593i	$-0.0494067\pi$
$632$		0			0
$633$	10.9046	+	18.8874i	0.433420	+	0.750705i
$634$		0			0
$635$	−31.1879	−	18.0063i	−1.23765	−	0.714560i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−2.66395	−	1.53803i	−0.105384	−	0.0608436i
$640$		0			0
$641$	9.05525	+	15.6842i	0.357661	+	0.619487i	0.987570	−	0.157182i	$-0.0502410\pi$
$641$	9.05525	+	15.6842i	0.357661	+	0.619487i	−0.629909	+	0.776669i	$0.716908\pi$
$642$		0			0
$643$	20.3792	−	11.7659i	0.803677	−	0.464003i	−0.0410784	−	0.999156i	$-0.513079\pi$
$643$	20.3792	−	11.7659i	0.803677	−	0.464003i	0.844755	+	0.535153i	$0.179746\pi$
$644$		0			0
$645$		−	3.71917i		−	0.146442i
$646$		0			0
$647$	2.02297	−	3.50388i	0.0795310	−	0.137752i	−0.823517	−	0.567292i	$-0.807991\pi$
$647$	2.02297	−	3.50388i	0.0795310	−	0.137752i	0.903048	+	0.429540i	$0.141324\pi$
$648$		0			0
$649$	51.4228			2.01852
$650$		0			0
$651$	−29.2325			−1.14571
$652$		0			0
$653$	−5.11260	+	8.85529i	−0.200072	+	0.346534i	−0.948551	−	0.316623i	$-0.897451\pi$
$653$	−5.11260	+	8.85529i	−0.200072	+	0.346534i	0.748480	+	0.663158i	$0.230784\pi$
$654$		0			0
$655$		−	38.2881i		−	1.49604i
$656$		0			0
$657$	−12.1563	+	7.01842i	−0.474261	+	0.273815i
$658$		0			0
$659$	12.9378	+	22.4089i	0.503985	+	0.872928i	0.999989	+	0.00460797i	$0.00146677\pi$
$659$	12.9378	+	22.4089i	0.503985	+	0.872928i	−0.496004	+	0.868320i	$0.665200\pi$
$660$		0			0
$661$	−6.36172	−	3.67294i	−0.247442	−	0.142861i	0.371150	−	0.928573i	$-0.378963\pi$
$661$	−6.36172	−	3.67294i	−0.247442	−	0.142861i	−0.618592	+	0.785712i	$0.712297\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	81.8154	+	47.2362i	3.17267	+	1.83174i
$666$		0			0
$667$	−5.62833	−	9.74856i	−0.217930	−	0.377466i
$668$		0			0
$669$	−22.1715	+	12.8007i	−0.857201	+	0.494905i
$670$		0			0
$671$		−	2.19269i		−	0.0846477i
$672$		0			0
$673$	17.4167	−	30.1666i	0.671364	−	1.16284i	−0.306153	−	0.951982i	$-0.599042\pi$
$673$	17.4167	−	30.1666i	0.671364	−	1.16284i	0.977517	−	0.210855i	$-0.0676248\pi$
$674$		0			0
$675$	−4.29590			−0.165349
$676$		0			0
$677$	−17.2000			−0.661049			−0.330524	−	0.943797i	$-0.607226\pi$
$677$	−17.2000			−0.661049			−0.330524	+	0.943797i	$0.607226\pi$
$678$		0			0
$679$	−1.72252	+	2.98349i	−0.0661043	+	0.114496i
$680$		0			0
$681$		−	2.72587i		−	0.104456i
$682$		0			0
$683$	−29.3073	+	16.9206i	−1.12141	+	0.647448i	−0.941761	−	0.336282i	$-0.890830\pi$
$683$	−29.3073	+	16.9206i	−1.12141	+	0.647448i	−0.179652	+	0.983730i	$0.557497\pi$
$684$		0			0
$685$	10.1501	+	17.5805i	0.387816	+	0.671716i
$686$		0			0
$687$	15.6816	+	9.05376i	0.598289	+	0.345423i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−15.3374	−	8.85504i	−0.583461	−	0.336861i	0.179047	−	0.983841i	$-0.442699\pi$
$691$	−15.3374	−	8.85504i	−0.583461	−	0.336861i	−0.762508	+	0.646979i	$0.776032\pi$
$692$		0			0
$693$	9.59783	+	16.6239i	0.364592	+	0.631491i
$694$		0			0
$695$	16.3018	−	9.41185i	0.618363	−	0.357012i
$696$		0			0
$697$			3.27844i			0.124180i
$698$		0			0
$699$	−9.45257	+	16.3723i	−0.357529	+	0.619259i
$700$		0			0
$701$	−9.22952			−0.348594			−0.174297	−	0.984693i	$-0.555765\pi$
$701$	−9.22952			−0.348594			−0.174297	+	0.984693i	$0.555765\pi$
$702$		0			0
$703$	−0.166603			−0.00628356
$704$		0			0
$705$	14.5809	−	25.2549i	0.549149	−	0.951154i
$706$		0			0
$707$			34.0834i			1.28184i
$708$		0			0
$709$	−0.551138	+	0.318200i	−0.0206984	+	0.0119502i	−0.510314	−	0.859988i	$-0.670471\pi$
$709$	−0.551138	+	0.318200i	−0.0206984	+	0.0119502i	0.489615	+	0.871939i	$0.337137\pi$
$710$		0			0
$711$	0.420583	+	0.728471i	0.0157731	+	0.0273198i
$712$		0			0
$713$	39.8074	+	22.9828i	1.49080	+	0.860714i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−17.5889	−	10.1549i	−0.656869	−	0.379244i
$718$		0			0
$719$	4.21983	+	7.30896i	0.157373	+	0.272578i	0.933921	−	0.357480i	$-0.116364\pi$
$719$	4.21983	+	7.30896i	0.157373	+	0.272578i	−0.776547	+	0.630059i	$0.783031\pi$
$720$		0			0
$721$	34.0187	−	19.6407i	1.26692	−	0.731458i
$722$		0			0
$723$		−	15.7942i		−	0.587391i
$724$		0			0
$725$	3.04556	−	5.27507i	0.113109	−	0.195911i
$726$		0			0
$727$	19.9922			0.741471			0.370735	−	0.928739i	$-0.379106\pi$
$727$	19.9922			0.741471			0.370735	+	0.928739i	$0.379106\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−0.217677	+	0.377027i	−0.00805106	+	0.0139448i
$732$		0			0
$733$		−	3.93767i		−	0.145441i	−0.997352	−	0.0727206i	$-0.976832\pi$
$733$		−	3.93767i		−	0.145441i	0.997352	−	0.0727206i	$-0.0231681\pi$
$734$		0			0
$735$	48.8259	−	28.1896i	1.80097	−	1.03979i
$736$		0			0
$737$	−15.1148	−	26.1795i	−0.556759	−	0.964336i
$738$		0			0
$739$	20.5707	+	11.8765i	0.756706	+	0.436884i	0.828112	−	0.560563i	$-0.189415\pi$
$739$	20.5707	+	11.8765i	0.756706	+	0.436884i	−0.0714057	+	0.997447i	$0.522749\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−32.1042	−	18.5353i	−1.17779	−	0.679996i	−0.222286	−	0.974982i	$-0.571352\pi$
$743$	−32.1042	−	18.5353i	−1.17779	−	0.679996i	−0.955502	+	0.294986i	$0.904685\pi$
$744$		0			0
$745$	−0.223717	−	0.387490i	−0.00819637	−	0.0141965i
$746$		0			0
$747$	0.166870	−	0.0963427i	0.00610547	−	0.00352500i
$748$		0			0
$749$		−	42.9952i		−	1.57101i
$750$		0			0
$751$	−5.27987	+	9.14501i	−0.192665	+	0.333706i	−0.946133	−	0.323779i	$-0.895046\pi$
$751$	−5.27987	+	9.14501i	−0.192665	+	0.333706i	0.753467	+	0.657485i	$0.228380\pi$
$752$		0			0
$753$	7.88231			0.287247
$754$		0			0
$755$	28.5579			1.03933
$756$		0			0
$757$	1.45162	−	2.51427i	0.0527598	−	0.0913827i	−0.838439	−	0.544995i	$-0.816532\pi$
$757$	1.45162	−	2.51427i	0.0527598	−	0.0913827i	0.891199	+	0.453612i	$0.149865\pi$
$758$		0			0
$759$		−	30.1836i		−	1.09559i
$760$		0			0
$761$	20.1125	−	11.6119i	0.729077	−	0.420933i	−0.0890077	−	0.996031i	$-0.528370\pi$
$761$	20.1125	−	11.6119i	0.729077	−	0.420933i	0.818084	+	0.575098i	$0.195036\pi$
$762$		0			0
$763$	−2.74698	−	4.75791i	−0.0994473	−	0.172248i
$764$		0			0
$765$	0.942362	+	0.544073i	0.0340712	+	0.0196710i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	−34.4036	−	19.8629i	−1.24063	−	0.716276i	−0.271404	−	0.962465i	$-0.587488\pi$
$769$	−34.4036	−	19.8629i	−1.24063	−	0.716276i	−0.969222	+	0.246190i	$0.920821\pi$
$770$		0			0
$771$	9.29859	+	16.1056i	0.334880	+	0.580030i
$772$		0			0
$773$	−2.74609	+	1.58546i	−0.0987701	+	0.0570249i	−0.548571	−	0.836104i	$-0.684828\pi$
$773$	−2.74609	+	1.58546i	−0.0987701	+	0.0570249i	0.449801	+	0.893129i	$0.351495\pi$
$774$		0			0
$775$			24.8726i			0.893451i
$776$		0			0
$777$	−0.0685317	+	0.118700i	−0.00245856	+	0.00425835i
$778$		0			0
$779$	−56.3749			−2.01984
$780$		0			0
$781$	11.6950			0.418480
$782$		0			0
$783$	−0.708947	+	1.22793i	−0.0253357	+	0.0438827i
$784$		0			0
$785$			12.2916i			0.438705i
$786$		0			0
$787$	−6.49088	+	3.74751i	−0.231375	+	0.133584i	−0.611206	−	0.791471i	$-0.709315\pi$
$787$	−6.49088	+	3.74751i	−0.231375	+	0.133584i	0.379831	+	0.925056i	$0.375982\pi$
$788$		0			0
$789$	−0.628334	−	1.08831i	−0.0223693	−	0.0387447i
$790$		0			0
$791$	16.0670	+	9.27628i	0.571276	+	0.329827i
$792$		0			0
$793$		0			0
$794$		0			0
$795$	−12.5040	−	7.21917i	−0.443470	−	0.256038i
$796$		0			0
$797$	−19.8388	−	34.3618i	−0.702725	−	1.21716i	−0.967506	−	0.252847i	$-0.918633\pi$
$797$	−19.8388	−	34.3618i	−0.702725	−	1.21716i	0.264781	−	0.964309i	$-0.414700\pi$
$798$		0			0
$799$	−2.95625	+	1.70679i	−0.104585	+	0.0603819i
$800$		0			0
$801$			9.21313i			0.325530i
$802$		0			0
$803$	26.6836	−	46.2173i	0.941643	−	1.63097i
$804$		0			0
$805$	−122.211			−4.30737
$806$		0			0
$807$	−18.8944			−0.665114
$808$		0			0
$809$	−25.0090	+	43.3169i	−0.879270	+	1.52294i	−0.0271276	+	0.999632i	$0.508636\pi$
$809$	−25.0090	+	43.3169i	−0.879270	+	1.52294i	−0.852143	+	0.523309i	$0.824697\pi$
$810$		0			0
$811$		−	28.7590i		−	1.00986i	−0.863159	−	0.504932i	$-0.831517\pi$
$811$		−	28.7590i		−	1.00986i	0.863159	−	0.504932i	$-0.168483\pi$
$812$		0			0
$813$	17.8472	−	10.3041i	0.625929	−	0.361380i
$814$		0			0
$815$	−15.8862	−	27.5157i	−0.556469	−	0.963833i
$816$		0			0
$817$	−6.48323	−	3.74309i	−0.226820	−	0.130954i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	33.5325	+	19.3600i	1.17029	+	0.675669i	0.953749	−	0.300604i	$-0.0971882\pi$
$821$	33.5325	+	19.3600i	1.17029	+	0.675669i	0.216544	+	0.976273i	$0.430522\pi$
$822$		0			0
$823$	−1.54623	−	2.67815i	−0.0538982	−	0.0933543i	0.837818	−	0.545950i	$-0.183831\pi$
$823$	−1.54623	−	2.67815i	−0.0538982	−	0.0933543i	−0.891716	+	0.452596i	$0.850498\pi$
$824$		0			0
$825$	14.1446	−	8.16637i	0.492450	−	0.284316i
$826$		0			0
$827$			4.80194i			0.166980i	0.996509	+	0.0834899i	$0.0266066\pi$
$827$			4.80194i			0.166980i	−0.996509	+	0.0834899i	$0.973393\pi$
$828$		0			0
$829$	−10.4906	+	18.1703i	−0.364354	+	0.631079i	−0.988672	−	0.150091i	$-0.952043\pi$
$829$	−10.4906	+	18.1703i	−0.364354	+	0.631079i	0.624318	+	0.781170i	$0.285377\pi$
$830$		0			0
$831$	−11.8890			−0.412425
$832$		0			0
$833$	−6.59956			−0.228661
$834$		0			0
$835$	−15.7104	+	27.2113i	−0.543682	+	0.941685i
$836$		0			0
$837$		−	5.78986i		−	0.200127i
$838$		0			0
$839$	−28.9480	+	16.7131i	−0.999395	+	0.577001i	−0.908069	−	0.418820i	$-0.862444\pi$
$839$	−28.9480	+	16.7131i	−0.999395	+	0.577001i	−0.0913261	+	0.995821i	$0.529111\pi$
$840$		0			0
$841$	13.4948	+	23.3737i	0.465337	+	0.805988i
$842$		0			0
$843$	−6.70592	−	3.87167i	−0.230964	−	0.133347i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−15.1058	−	8.72132i	−0.519041	−	0.299668i
$848$		0			0
$849$	−6.11745	−	10.5957i	−0.209950	−	0.363645i
$850$		0			0
$851$	0.186646	−	0.107760i	0.00639816	−	0.00369398i
$852$		0			0
$853$			51.1527i			1.75144i	0.482823	+	0.875718i	$0.339611\pi$
$853$			51.1527i			1.75144i	−0.482823	+	0.875718i	$0.660389\pi$
$854$		0			0
$855$	−9.35570	+	16.2045i	−0.319958	+	0.554184i
$856$		0			0
$857$	−12.7004			−0.433837			−0.216918	−	0.976190i	$-0.569601\pi$
$857$	−12.7004			−0.433837			−0.216918	+	0.976190i	$0.569601\pi$
$858$		0			0
$859$	−34.0455			−1.16162			−0.580808	−	0.814041i	$-0.697263\pi$
$859$	−34.0455			−1.16162			−0.580808	+	0.814041i	$0.697263\pi$
$860$		0			0
$861$	−23.1896	+	40.1656i	−0.790300	+	1.36884i
$862$		0			0
$863$		−	23.8775i		−	0.812801i	−0.913695	−	0.406400i	$-0.866784\pi$
$863$		−	23.8775i		−	0.812801i	0.913695	−	0.406400i	$-0.133216\pi$
$864$		0			0
$865$	−58.8902	+	34.0003i	−2.00233	+	1.15604i
$866$		0			0
$867$	8.43631	+	14.6121i	0.286512	+	0.496254i
$868$		0			0
$869$	−2.76960	−	1.59903i	−0.0939524	−	0.0542434i
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−0.590918	−	0.341166i	−0.0199995	−	0.0115467i
$874$		0			0
$875$	5.41939	+	9.38665i	0.183209	+	0.317327i
$876$		0			0
$877$	13.4275	−	7.75236i	0.453414	−	0.261778i	−0.255857	−	0.966715i	$-0.582358\pi$
$877$	13.4275	−	7.75236i	0.453414	−	0.261778i	0.709271	+	0.704936i	$0.249024\pi$
$878$		0			0
$879$			18.5985i			0.627312i
$880$		0			0
$881$	20.9659	−	36.3140i	0.706359	−	1.22345i	−0.259839	−	0.965652i	$-0.583670\pi$
$881$	20.9659	−	36.3140i	0.706359	−	1.22345i	0.966199	−	0.257799i	$-0.0829971\pi$
$882$		0			0
$883$	−58.8219			−1.97951			−0.989757	−	0.142760i	$-0.954402\pi$
$883$	−58.8219			−1.97951			−0.989757	+	0.142760i	$0.954402\pi$
$884$		0			0
$885$	41.2379			1.38620
$886$		0			0
$887$	−5.14622	+	8.91351i	−0.172793	+	0.299287i	−0.939395	−	0.342836i	$-0.888613\pi$
$887$	−5.14622	+	8.91351i	−0.172793	+	0.299287i	0.766602	+	0.642122i	$0.221946\pi$
$888$		0			0
$889$			59.6359i			2.00012i
$890$		0			0
$891$	−3.29257	+	1.90097i	−0.110305	+	0.0636849i
$892$		0			0
$893$	−29.3494	−	50.8347i	−0.982141	−	1.70112i
$894$		0			0
$895$	45.8838	+	26.4910i	1.53373	+	0.885498i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	7.10955	+	4.10470i	0.237117	+	0.136900i
$900$		0			0
$901$	0.845051	+	1.46367i	0.0281527	+	0.0487620i
$902$		0			0
$903$	−5.33371	+	3.07942i	−0.177495	+	0.102477i
$904$		0			0
$905$		−	74.5900i		−	2.47946i
$906$		0			0
$907$	−11.3503	+	19.6593i	−0.376881	+	0.652778i	−0.990607	−	0.136742i	$-0.956337\pi$
$907$	−11.3503	+	19.6593i	−0.376881	+	0.652778i	0.613725	+	0.789520i	$0.289670\pi$
$908$		0			0
$909$	−6.75063			−0.223904
$910$		0			0
$911$	−37.3019			−1.23587			−0.617933	−	0.786231i	$-0.712030\pi$
$911$	−37.3019			−1.23587			−0.617933	+	0.786231i	$0.712030\pi$
$912$		0			0
$913$	−0.366289	+	0.634431i	−0.0121224	+	0.0209966i
$914$		0			0
$915$		−	1.75840i		−	0.0581308i
$916$		0			0
$917$	−54.9095	+	31.7020i	−1.81327	+	1.04689i
$918$		0			0
$919$	4.74214	+	8.21362i	0.156429	+	0.270942i	0.933578	−	0.358373i	$-0.116669\pi$
$919$	4.74214	+	8.21362i	0.156429	+	0.270942i	−0.777150	+	0.629316i	$0.783335\pi$
$920$		0			0
$921$	2.87526	+	1.66003i	0.0947429	+	0.0546999i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	0.100997	+	0.0583105i	0.00332075	+	0.00191724i
$926$		0			0
$927$	3.89008	+	6.73782i	0.127767	+	0.221299i
$928$		0			0
$929$	4.60938	−	2.66123i	0.151229	−	0.0873120i	−0.422476	−	0.906374i	$-0.638839\pi$
$929$	4.60938	−	2.66123i	0.151229	−	0.0873120i	0.573705	+	0.819062i	$0.305506\pi$
$930$		0			0
$931$		−	113.484i		−	3.71929i
$932$		0			0
$933$	10.1441	−	17.5700i	0.332102	−	0.575217i
$934$		0			0
$935$	−4.13706			−0.135296
$936$		0			0
$937$	−20.2097			−0.660221			−0.330111	−	0.943942i	$-0.607086\pi$
$937$	−20.2097			−0.660221			−0.330111	+	0.943942i	$0.607086\pi$
$938$		0			0
$939$	7.19351	−	12.4595i	0.234751	−	0.406601i
$940$		0			0
$941$		−	43.1135i		−	1.40546i	−0.711457	−	0.702730i	$-0.751964\pi$
$941$		−	43.1135i		−	1.40546i	0.711457	−	0.702730i	$-0.248036\pi$
$942$		0			0
$943$	63.1571	−	36.4638i	2.05668	−	1.18742i
$944$		0			0
$945$	7.69687	+	13.3314i	0.250379	+	0.433669i
$946$		0			0
$947$	48.4651	+	27.9813i	1.57490	+	0.909272i	0.995554	+	0.0941931i	$0.0300271\pi$
$947$	48.4651	+	27.9813i	1.57490	+	0.909272i	0.579351	+	0.815078i	$0.303306\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	10.7777	+	6.22252i	0.349492	+	0.201779i
$952$		0			0
$953$	−7.59150	−	13.1489i	−0.245913	−	0.425933i	0.716475	−	0.697613i	$-0.245754\pi$
$953$	−7.59150	−	13.1489i	−0.245913	−	0.425933i	−0.962388	+	0.271679i	$0.912421\pi$
$954$		0			0
$955$	−56.5286	+	32.6368i	−1.82922	+	1.05610i
$956$		0			0
$957$		−	5.39075i		−	0.174258i
$958$		0			0
$959$	16.8083	−	29.1128i	0.542767	−	0.940101i
$960$		0			0
$961$	−2.52243			−0.0813688
$962$		0			0
$963$	8.51573			0.274416
$964$		0			0
$965$	21.9943	−	38.0952i	0.708020	−	1.22633i
$966$		0			0
$967$		−	15.4064i		−	0.495437i	−0.968832	−	0.247718i	$-0.920319\pi$
$967$		−	15.4064i		−	0.495437i	0.968832	−	0.247718i	$-0.0796807\pi$
$968$		0			0
$969$	1.89685	−	1.09515i	0.0609356	−	0.0351812i
$970$		0			0
$971$	−3.00066	−	5.19730i	−0.0962959	−	0.166789i	0.813853	−	0.581071i	$-0.197366\pi$
$971$	−3.00066	−	5.19730i	−0.0962959	−	0.166789i	−0.910149	+	0.414282i	$0.864033\pi$
$972$		0			0
$973$	−26.9953	−	15.5858i	−0.865430	−	0.499656i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−17.6610	−	10.1966i	−0.565025	−	0.326217i	0.190135	−	0.981758i	$-0.439107\pi$
$977$	−17.6610	−	10.1966i	−0.565025	−	0.326217i	−0.755160	+	0.655541i	$0.772441\pi$
$978$		0			0
$979$	−17.5139	−	30.3349i	−0.559746	−	0.969508i
$980$		0			0
$981$	0.942362	−	0.544073i	0.0300873	−	0.0173709i
$982$		0			0
$983$			29.9764i			0.956100i	0.878333	+	0.478050i	$0.158656\pi$
$983$			29.9764i			0.956100i	−0.878333	+	0.478050i	$0.841344\pi$
$984$		0			0
$985$	−3.11984	+	5.40372i	−0.0994064	+	0.172177i
$986$		0			0
$987$	−48.2911			−1.53712
$988$		0			0
$989$	9.68425			0.307941
$990$		0			0
$991$	−18.2361	+	31.5858i	−0.579289	+	1.00336i	0.416272	+	0.909240i	$0.363336\pi$
$991$	−18.2361	+	31.5858i	−0.579289	+	1.00336i	−0.995561	+	0.0941174i	$0.969997\pi$
$992$		0			0
$993$		−	3.31873i		−	0.105317i
$994$		0			0
$995$	−14.6675	+	8.46830i	−0.464992	+	0.268463i
$996$		0			0
$997$	10.9799	+	19.0177i	0.347735	+	0.602295i	0.985847	−	0.167649i	$-0.0536174\pi$
$997$	10.9799	+	19.0177i	0.347735	+	0.602295i	−0.638111	+	0.769944i	$0.720284\pi$
$998$		0			0
$999$	−0.0235101	−	0.0135735i	−0.000743825	−	0.000429448i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2028.2.q.i.1837.1		12
13.2	odd	12		2028.2.i.j.2005.1		6
13.3	even	3	inner	2028.2.q.i.361.1		12
13.4	even	6		2028.2.b.g.337.6		6
13.5	odd	4		2028.2.i.j.529.1		6
13.6	odd	12		2028.2.a.l.1.1	yes	3
13.7	odd	12		2028.2.a.k.1.3	✓	3
13.8	odd	4		2028.2.i.k.529.3		6
13.9	even	3		2028.2.b.g.337.1		6
13.10	even	6	inner	2028.2.q.i.361.6		12
13.11	odd	12		2028.2.i.k.2005.3		6
13.12	even	2	inner	2028.2.q.i.1837.6		12
39.17	odd	6		6084.2.b.q.4393.1		6
39.20	even	12		6084.2.a.z.1.1		3
39.32	even	12		6084.2.a.ba.1.3		3
39.35	odd	6		6084.2.b.q.4393.6		6
52.7	even	12		8112.2.a.cd.1.3		3
52.19	even	12		8112.2.a.ca.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2028.2.a.k.1.3	✓	3	13.7	odd	12
2028.2.a.l.1.1	yes	3	13.6	odd	12
2028.2.b.g.337.1		6	13.9	even	3
2028.2.b.g.337.6		6	13.4	even	6
2028.2.i.j.529.1		6	13.5	odd	4
2028.2.i.j.2005.1		6	13.2	odd	12
2028.2.i.k.529.3		6	13.8	odd	4
2028.2.i.k.2005.3		6	13.11	odd	12
2028.2.q.i.361.1		12	13.3	even	3	inner
2028.2.q.i.361.6		12	13.10	even	6	inner
2028.2.q.i.1837.1		12	1.1	even	1	trivial
2028.2.q.i.1837.6		12	13.12	even	2	inner
6084.2.a.z.1.1		3	39.20	even	12
6084.2.a.ba.1.3		3	39.32	even	12
6084.2.b.q.4393.1		6	39.17	odd	6
6084.2.b.q.4393.6		6	39.35	odd	6
8112.2.a.ca.1.1		3	52.19	even	12
8112.2.a.cd.1.3		3	52.7	even	12

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.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{3} -3.04892i q^{5} +(-4.37249 + 2.52446i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(3.29257 + 1.90097i) q^{11} +(2.64044 + 1.52446i) q^{15} +(-0.178448 - 0.309081i) q^{17} +(5.31485 - 3.06853i) q^{19} -5.04892i q^{21} +(-3.96950 + 6.87538i) q^{23} -4.29590 q^{25} +1.00000 q^{27} +(-0.708947 + 1.22793i) q^{29} -5.78986i q^{31} +(-3.29257 + 1.90097i) q^{33} +(7.69687 + 13.3314i) q^{35} +(-0.0235101 - 0.0135735i) q^{37} +(-7.95529 - 4.59299i) q^{41} +(-0.609916 - 1.05641i) q^{43} +(-2.64044 + 1.52446i) q^{45} -9.56465i q^{47} +(9.24578 - 16.0142i) q^{49} +0.356896 q^{51} -4.73556 q^{53} +(5.79590 - 10.0388i) q^{55} +6.13706i q^{57} +(11.7134 - 6.76271i) q^{59} +(-0.288364 - 0.499461i) q^{61} +(4.37249 + 2.52446i) q^{63} +(-6.88584 - 3.97554i) q^{67} +(-3.96950 - 6.87538i) q^{69} +(2.66395 - 1.53803i) q^{71} -14.0368i q^{73} +(2.14795 - 3.72036i) q^{75} -19.1957 q^{77} -0.841166 q^{79} +(-0.500000 + 0.866025i) q^{81} +0.192685i q^{83} +(-0.942362 + 0.544073i) q^{85} +(-0.708947 - 1.22793i) q^{87} +(-7.97880 - 4.60656i) q^{89} +(5.01416 + 2.89493i) q^{93} +(-9.35570 - 16.2045i) q^{95} +(0.590918 - 0.341166i) q^{97} -3.80194i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{3} - 6 q^{9} + 6 q^{17} - 28 q^{23} + 4 q^{25} + 12 q^{27} - 20 q^{29} + 28 q^{35} - 10 q^{43} + 10 q^{49} - 12 q^{51} - 12 q^{53} + 14 q^{55} + 2 q^{61} - 28 q^{69} - 2 q^{75} - 84 q^{77} - 44 q^{79}+ \cdots - 14 q^{95}+O(q^{100}) \) 12 * q - 6 * q^3 - 6 * q^9 + 6 * q^17 - 28 * q^23 + 4 * q^25 + 12 * q^27 - 20 * q^29 + 28 * q^35 - 10 * q^43 + 10 * q^49 - 12 * q^51 - 12 * q^53 + 14 * q^55 + 2 * q^61 - 28 * q^69 - 2 * q^75 - 84 * q^77 - 44 * q^79 - 6 * q^81 - 20 * q^87 - 14 * q^95

Introduction

L-functions

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