LMFDB - Embedded newform 3564.2.i.t.2377.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3564,2,Mod(1189,3564)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3564, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("3564.1189");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3564 = 2^{2} \cdot 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3564.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:	$28.4586832804$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 18x^{9} + 152x^{8} - 204x^{7} + 162x^{6} - 408x^{5} + 2800x^{4} - 4422x^{3} + 3528x^{2} - 252x + 9 $ x^12 - 18x^9 + 152x^8 - 204x^7 + 162x^6 - 408x^5 + 2800x^4 - 4422x^3 + 3528x^2 - 252*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			2377.1
Root			$-1.52436 + 1.52436i$ of defining polynomial
Character	$\chi$	$=$	3564.2377
Dual form			3564.2.i.t.1189.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.08231 + 3.60667i) q^{5} +(1.24765 + 2.16099i) q^{7} +O(q^{10})$	$q+(-2.08231 + 3.60667i) q^{5} +(1.24765 + 2.16099i) q^{7} +(0.500000 + 0.866025i) q^{11} +(3.44834 - 5.97270i) q^{13} -1.55342 q^{17} -6.43789 q^{19} +(-3.13803 + 5.43523i) q^{23} +(-6.17205 - 10.6903i) q^{25} +(-2.41564 - 4.18401i) q^{29} +(-0.212652 + 0.368324i) q^{31} -10.3920 q^{35} -10.5615 q^{37} +(0.651973 - 1.12925i) q^{41} +(2.18493 + 3.78440i) q^{43} +(4.46296 + 7.73007i) q^{47} +(0.386749 - 0.669869i) q^{49} +3.84349 q^{53} -4.16462 q^{55} +(3.46870 - 6.00797i) q^{59} +(-2.63077 - 4.55663i) q^{61} +(14.3610 + 24.8740i) q^{65} +(2.79000 - 4.83243i) q^{67} -11.7180 q^{71} -0.320752 q^{73} +(-1.24765 + 2.16099i) q^{77} +(6.78326 + 11.7489i) q^{79} +(-8.48660 - 14.6992i) q^{83} +(3.23471 - 5.60268i) q^{85} -14.5661 q^{89} +17.2092 q^{91} +(13.4057 - 23.2193i) q^{95} +(-4.08471 - 7.07493i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{7}+O(q^{10}) $ 12 * q + 2 * q^7	$ 12 q + 2 q^{7} + 6 q^{11} + 6 q^{13} - 8 q^{17} + 4 q^{23} - 10 q^{25} - 4 q^{29} - 6 q^{31} - 28 q^{35} - 12 q^{37} + 22 q^{41} + 10 q^{43} + 20 q^{47} - 6 q^{49} - 8 q^{53} + 24 q^{59} + 10 q^{61} + 40 q^{65} + 6 q^{67} - 80 q^{71} - 16 q^{73} - 2 q^{77} + 14 q^{79} + 12 q^{83} - 6 q^{85} - 48 q^{89} + 20 q^{91} + 44 q^{95} - 20 q^{97}+O(q^{100}) $ 12 * q + 2 * q^7 + 6 * q^11 + 6 * q^13 - 8 * q^17 + 4 * q^23 - 10 * q^25 - 4 * q^29 - 6 * q^31 - 28 * q^35 - 12 * q^37 + 22 * q^41 + 10 * q^43 + 20 * q^47 - 6 * q^49 - 8 * q^53 + 24 * q^59 + 10 * q^61 + 40 * q^65 + 6 * q^67 - 80 * q^71 - 16 * q^73 - 2 * q^77 + 14 * q^79 + 12 * q^83 - 6 * q^85 - 48 * q^89 + 20 * q^91 + 44 * q^95 - 20 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3564\mathbb{Z}\right)^\times$.

$n$	$1541$	$1783$	$2917$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−2.08231	+	3.60667i	−0.931238	+	1.61295i	−0.150030	+	0.988681i	$0.547937\pi$
$5$	−2.08231	+	3.60667i	−0.931238	+	1.61295i	−0.781208	+	0.624271i	$0.785396\pi$
$6$		0			0
$7$	1.24765	+	2.16099i	0.471567	+	0.816777i	0.999471	−	0.0325265i	$-0.0103553\pi$
$7$	1.24765	+	2.16099i	0.471567	+	0.816777i	−0.527904	+	0.849304i	$0.677022\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$		0			0
$13$	3.44834	−	5.97270i	0.956397	−	1.65653i	0.225258	−	0.974299i	$-0.427677\pi$
$13$	3.44834	−	5.97270i	0.956397	−	1.65653i	0.731139	−	0.682229i	$-0.238989\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.55342			−0.376760			−0.188380	−	0.982096i	$-0.560324\pi$
$17$	−1.55342			−0.376760			−0.188380	+	0.982096i	$0.560324\pi$
$18$		0			0
$19$	−6.43789			−1.47695			−0.738476	−	0.674279i	$-0.764454\pi$
$19$	−6.43789			−1.47695			−0.738476	+	0.674279i	$0.764454\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.13803	+	5.43523i	−0.654325	+	1.13332i	0.327738	+	0.944769i	$0.393714\pi$
$23$	−3.13803	+	5.43523i	−0.654325	+	1.13332i	−0.982063	+	0.188555i	$0.939620\pi$
$24$		0			0
$25$	−6.17205	−	10.6903i	−1.23441	−	2.13806i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−2.41564	−	4.18401i	−0.448573	−	0.776951i	0.549720	−	0.835349i	$-0.314734\pi$
$29$	−2.41564	−	4.18401i	−0.448573	−	0.776951i	−0.998293	+	0.0583973i	$0.981401\pi$
$30$		0			0
$31$	−0.212652	+	0.368324i	−0.0381934	+	0.0661529i	−0.884490	−	0.466559i	$-0.845494\pi$
$31$	−0.212652	+	0.368324i	−0.0381934	+	0.0661529i	0.846297	+	0.532712i	$0.178827\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−10.3920			−1.75656
$36$		0			0
$37$	−10.5615			−1.73631			−0.868153	−	0.496297i	$-0.834693\pi$
$37$	−10.5615			−1.73631			−0.868153	+	0.496297i	$0.834693\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	0.651973	−	1.12925i	0.101821	−	0.176359i	−0.810614	−	0.585581i	$-0.800866\pi$
$41$	0.651973	−	1.12925i	0.101821	−	0.176359i	0.912435	+	0.409222i	$0.134200\pi$
$42$		0			0
$43$	2.18493	+	3.78440i	0.333198	+	0.577116i	0.983137	−	0.182870i	$-0.0585389\pi$
$43$	2.18493	+	3.78440i	0.333198	+	0.577116i	−0.649939	+	0.759986i	$0.725206\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	4.46296	+	7.73007i	0.650989	+	1.12755i	0.982883	+	0.184230i	$0.0589790\pi$
$47$	4.46296	+	7.73007i	0.650989	+	1.12755i	−0.331894	+	0.943317i	$0.607688\pi$
$48$		0			0
$49$	0.386749	−	0.669869i	0.0552498	−	0.0956955i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	3.84349			0.527944			0.263972	−	0.964530i	$-0.414967\pi$
$53$	3.84349			0.527944			0.263972	+	0.964530i	$0.414967\pi$
$54$		0			0
$55$	−4.16462			−0.561558
$56$		0			0
$57$		0			0
$58$		0			0
$59$	3.46870	−	6.00797i	0.451587	−	0.782171i	−0.546898	−	0.837199i	$-0.684192\pi$
$59$	3.46870	−	6.00797i	0.451587	−	0.782171i	0.998485	+	0.0550281i	$0.0175248\pi$
$60$		0			0
$61$	−2.63077	−	4.55663i	−0.336836	−	0.583417i	0.647000	−	0.762490i	$-0.276023\pi$
$61$	−2.63077	−	4.55663i	−0.336836	−	0.583417i	−0.983836	+	0.179073i	$0.942690\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	14.3610	+	24.8740i	1.78127	+	3.08524i
$66$		0			0
$67$	2.79000	−	4.83243i	0.340853	−	0.590375i	−0.643738	−	0.765246i	$-0.722617\pi$
$67$	2.79000	−	4.83243i	0.340853	−	0.590375i	0.984591	+	0.174871i	$0.0559507\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−11.7180			−1.39068			−0.695338	−	0.718683i	$-0.744745\pi$
$71$	−11.7180			−1.39068			−0.695338	+	0.718683i	$0.744745\pi$
$72$		0			0
$73$	−0.320752			−0.0375412			−0.0187706	−	0.999824i	$-0.505975\pi$
$73$	−0.320752			−0.0375412			−0.0187706	+	0.999824i	$0.505975\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.24765	+	2.16099i	−0.142183	+	0.246268i
$78$		0			0
$79$	6.78326	+	11.7489i	0.763176	+	1.32186i	0.941205	+	0.337835i	$0.109694\pi$
$79$	6.78326	+	11.7489i	0.763176	+	1.32186i	−0.178029	+	0.984025i	$0.556972\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−8.48660	−	14.6992i	−0.931526	−	1.61345i	−0.780715	−	0.624887i	$-0.785145\pi$
$83$	−8.48660	−	14.6992i	−0.931526	−	1.61345i	−0.150811	−	0.988563i	$-0.548188\pi$
$84$		0			0
$85$	3.23471	−	5.60268i	0.350853	−	0.607696i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−14.5661			−1.54401			−0.772003	−	0.635618i	$-0.780745\pi$
$89$	−14.5661			−1.54401			−0.772003	+	0.635618i	$0.780745\pi$
$90$		0			0
$91$	17.2092			1.80402
$92$		0			0
$93$		0			0
$94$		0			0
$95$	13.4057	−	23.2193i	1.37540	−	2.38225i
$96$		0			0
$97$	−4.08471	−	7.07493i	−0.414740	−	0.718350i	0.580661	−	0.814145i	$-0.302794\pi$
$97$	−4.08471	−	7.07493i	−0.414740	−	0.718350i	−0.995401	+	0.0957948i	$0.969461\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	2.00363	+	3.47040i	0.199369	+	0.345317i	0.948324	−	0.317303i	$-0.102777\pi$
$101$	2.00363	+	3.47040i	0.199369	+	0.345317i	−0.748955	+	0.662621i	$0.769444\pi$
$102$		0			0
$103$	1.14478	−	1.98282i	0.112798	−	0.195373i	−0.804099	−	0.594495i	$-0.797352\pi$
$103$	1.14478	−	1.98282i	0.112798	−	0.195373i	0.916898	+	0.399123i	$0.130685\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	2.80276			0.270953			0.135476	−	0.990781i	$-0.456743\pi$
$107$	2.80276			0.270953			0.135476	+	0.990781i	$0.456743\pi$
$108$		0			0
$109$	2.66984			0.255724			0.127862	−	0.991792i	$-0.459188\pi$
$109$	2.66984			0.255724			0.127862	+	0.991792i	$0.459188\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−2.04997	+	3.55066i	−0.192845	+	0.334018i	−0.946192	−	0.323606i	$-0.895105\pi$
$113$	−2.04997	+	3.55066i	−0.192845	+	0.334018i	0.753347	+	0.657623i	$0.228438\pi$
$114$		0			0
$115$	−13.0687	−	22.6357i	−1.21866	−	2.11079i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−1.93812	−	3.35693i	−0.177667	−	0.307729i
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	30.5854			2.73564
$126$		0			0
$127$	−12.9794			−1.15173			−0.575867	−	0.817543i	$-0.695335\pi$
$127$	−12.9794			−1.15173			−0.575867	+	0.817543i	$0.695335\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	5.28894	−	9.16071i	0.462097	−	0.800375i	−0.536968	−	0.843602i	$-0.680431\pi$
$131$	5.28894	−	9.16071i	0.462097	−	0.800375i	0.999065	+	0.0432271i	$0.0137639\pi$
$132$		0			0
$133$	−8.03222	−	13.9122i	−0.696482	−	1.20634i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−3.84670	−	6.66268i	−0.328646	−	0.569232i	0.653597	−	0.756842i	$-0.273259\pi$
$137$	−3.84670	−	6.66268i	−0.328646	−	0.569232i	−0.982243	+	0.187611i	$0.939926\pi$
$138$		0			0
$139$	5.94653	−	10.2997i	0.504378	−	0.873608i	−0.495609	−	0.868545i	$-0.665055\pi$
$139$	5.94653	−	10.2997i	0.504378	−	0.873608i	0.999987	−	0.00506236i	$-0.00161140\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	6.89668			0.576729
$144$		0			0
$145$	20.1205			1.67091
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−1.49868	+	2.59578i	−0.122776	+	0.212655i	−0.920862	−	0.389890i	$-0.872513\pi$
$149$	−1.49868	+	2.59578i	−0.122776	+	0.212655i	0.798085	+	0.602545i	$0.205846\pi$
$150$		0			0
$151$	−4.74045	−	8.21071i	−0.385773	−	0.668178i	0.606103	−	0.795386i	$-0.292732\pi$
$151$	−4.74045	−	8.21071i	−0.385773	−	0.668178i	−0.991876	+	0.127208i	$0.959398\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−0.885616	−	1.53393i	−0.0711344	−	0.123208i
$156$		0			0
$157$	−10.9258	+	18.9241i	−0.871976	+	1.51031i	−0.0120256	+	0.999928i	$0.503828\pi$
$157$	−10.9258	+	18.9241i	−0.871976	+	1.51031i	−0.859950	+	0.510378i	$0.829505\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−15.6606			−1.23423
$162$		0			0
$163$	15.0108			1.17574			0.587868	−	0.808957i	$-0.299968\pi$
$163$	15.0108			1.17574			0.587868	+	0.808957i	$0.299968\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	6.97742	−	12.0852i	0.539929	−	0.935185i	−0.458978	−	0.888448i	$-0.651784\pi$
$167$	6.97742	−	12.0852i	0.539929	−	0.935185i	0.998907	−	0.0467370i	$-0.0148823\pi$
$168$		0			0
$169$	−17.2821	−	29.9334i	−1.32939	−	2.30257i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	7.86194	+	13.6173i	0.597732	+	1.03530i	0.993155	+	0.116803i	$0.0372646\pi$
$173$	7.86194	+	13.6173i	0.597732	+	1.03530i	−0.395423	+	0.918499i	$0.629402\pi$
$174$		0			0
$175$	15.4011	−	26.6755i	1.16421	−	2.01648i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−2.69470			−0.201411			−0.100706	−	0.994916i	$-0.532110\pi$
$179$	−2.69470			−0.201411			−0.100706	+	0.994916i	$0.532110\pi$
$180$		0			0
$181$	3.41058			0.253507			0.126753	−	0.991934i	$-0.459544\pi$
$181$	3.41058			0.253507			0.126753	+	0.991934i	$0.459544\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	21.9924	−	38.0920i	1.61691	−	2.80058i
$186$		0			0
$187$	−0.776710	−	1.34530i	−0.0567987	−	0.0983782i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	0.445772	+	0.772099i	0.0322549	+	0.0558671i	0.881702	−	0.471806i	$-0.156398\pi$
$191$	0.445772	+	0.772099i	0.0322549	+	0.0558671i	−0.849447	+	0.527673i	$0.823064\pi$
$192$		0			0
$193$	−0.206986	+	0.358510i	−0.0148992	+	0.0258061i	−0.873379	−	0.487041i	$-0.838076\pi$
$193$	−0.206986	+	0.358510i	−0.0148992	+	0.0258061i	0.858480	+	0.512848i	$0.171409\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	11.4019			0.812351			0.406176	−	0.913795i	$-0.366862\pi$
$197$	11.4019			0.812351			0.406176	+	0.913795i	$0.366862\pi$
$198$		0			0
$199$	−22.2002			−1.57373			−0.786865	−	0.617126i	$-0.788297\pi$
$199$	−22.2002			−1.57373			−0.786865	+	0.617126i	$0.788297\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	6.02774	−	10.4403i	0.423064	−	0.732769i
$204$		0			0
$205$	2.71522	+	4.70290i	0.189639	+	0.328465i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−3.21894	−	5.57537i	−0.222659	−	0.385657i
$210$		0			0
$211$	6.95940	−	12.0540i	0.479105	−	0.829834i	−0.520608	−	0.853796i	$-0.674295\pi$
$211$	6.95940	−	12.0540i	0.479105	−	0.829834i	0.999713	+	0.0239620i	$0.00762809\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−18.1988			−1.24115
$216$		0			0
$217$	−1.06126			−0.0720430
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−5.35672	+	9.27811i	−0.360332	+	0.624113i
$222$		0			0
$223$	−1.62788	−	2.81957i	−0.109011	−	0.188813i	0.806359	−	0.591427i	$-0.201435\pi$
$223$	−1.62788	−	2.81957i	−0.109011	−	0.188813i	−0.915370	+	0.402614i	$0.868102\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	11.3746	+	19.7014i	0.754960	+	1.30763i	0.945394	+	0.325929i	$0.105677\pi$
$227$	11.3746	+	19.7014i	0.754960	+	1.30763i	−0.190435	+	0.981700i	$0.560990\pi$
$228$		0			0
$229$	9.06136	−	15.6947i	0.598792	−	1.03714i	−0.394208	−	0.919021i	$-0.628981\pi$
$229$	9.06136	−	15.6947i	0.598792	−	1.03714i	0.993000	−	0.118117i	$-0.0376857\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−17.6688			−1.15752			−0.578759	−	0.815498i	$-0.696463\pi$
$233$	−17.6688			−1.15752			−0.578759	+	0.815498i	$0.696463\pi$
$234$		0			0
$235$	−37.1731			−2.42490
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−2.38900	+	4.13788i	−0.154532	+	0.267657i	−0.932888	−	0.360165i	$-0.882720\pi$
$239$	−2.38900	+	4.13788i	−0.154532	+	0.267657i	0.778357	+	0.627822i	$0.216054\pi$
$240$		0			0
$241$	11.5079	+	19.9324i	0.741292	+	1.28396i	0.951907	+	0.306386i	$0.0991200\pi$
$241$	11.5079	+	19.9324i	0.741292	+	1.28396i	−0.210615	+	0.977569i	$0.567547\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	1.61066	+	2.78975i	0.102902	+	0.178231i
$246$		0			0
$247$	−22.2000	+	38.4515i	−1.41255	+	2.44661i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−19.0356			−1.20152			−0.600758	−	0.799431i	$-0.705135\pi$
$251$	−19.0356			−1.20152			−0.600758	+	0.799431i	$0.705135\pi$
$252$		0			0
$253$	−6.27606			−0.394573
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−15.4813	+	26.8143i	−0.965694	+	1.67263i	−0.257955	+	0.966157i	$0.583049\pi$
$257$	−15.4813	+	26.8143i	−0.965694	+	1.67263i	−0.707739	+	0.706474i	$0.750285\pi$
$258$		0			0
$259$	−13.1771	−	22.8234i	−0.818784	−	1.41818i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−10.4067	−	18.0249i	−0.641702	−	1.11146i	−0.985053	−	0.172253i	$-0.944895\pi$
$263$	−10.4067	−	18.0249i	−0.641702	−	1.11146i	0.343351	−	0.939207i	$-0.388438\pi$
$264$		0			0
$265$	−8.00335	+	13.8622i	−0.491642	+	0.851548i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	9.61723			0.586373			0.293187	−	0.956055i	$-0.405284\pi$
$269$	9.61723			0.586373			0.293187	+	0.956055i	$0.405284\pi$
$270$		0			0
$271$	24.6423			1.49691			0.748457	−	0.663183i	$-0.230795\pi$
$271$	24.6423			1.49691			0.748457	+	0.663183i	$0.230795\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	6.17205	−	10.6903i	0.372189	−	0.644650i
$276$		0			0
$277$	−8.77979	−	15.2070i	−0.527526	−	0.913702i	−0.999485	−	0.0320817i	$-0.989786\pi$
$277$	−8.77979	−	15.2070i	−0.527526	−	0.913702i	0.471959	−	0.881620i	$-0.343547\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−8.18755	−	14.1813i	−0.488428	−	0.845983i	0.511483	−	0.859293i	$-0.329096\pi$
$281$	−8.18755	−	14.1813i	−0.488428	−	0.845983i	−0.999911	+	0.0133107i	$0.995763\pi$
$282$		0			0
$283$	−1.20255	+	2.08289i	−0.0714844	+	0.123815i	−0.899552	−	0.436814i	$-0.856107\pi$
$283$	−1.20255	+	2.08289i	−0.0714844	+	0.123815i	0.828068	+	0.560628i	$0.189440\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	3.25373			0.192062
$288$		0			0
$289$	−14.5869			−0.858052
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−12.3521	+	21.3944i	−0.721616	+	1.24988i	0.238735	+	0.971085i	$0.423267\pi$
$293$	−12.3521	+	21.3944i	−0.721616	+	1.24988i	−0.960352	+	0.278792i	$0.910066\pi$
$294$		0			0
$295$	14.4458	+	25.0209i	0.841070	+	1.45678i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	21.6420	+	37.4850i	1.25159	+	2.16781i
$300$		0			0
$301$	−5.45204	+	9.44321i	−0.314250	+	0.544297i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	21.9124			1.25470
$306$		0			0
$307$	0.848964			0.0484529			0.0242265	−	0.999706i	$-0.492288\pi$
$307$	0.848964			0.0484529			0.0242265	+	0.999706i	$0.492288\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	1.97175	−	3.41517i	0.111808	−	0.193657i	−0.804691	−	0.593693i	$-0.797669\pi$
$311$	1.97175	−	3.41517i	0.111808	−	0.193657i	0.916499	+	0.400037i	$0.131003\pi$
$312$		0			0
$313$	4.53916	+	7.86206i	0.256569	+	0.444390i	0.965320	−	0.261068i	$-0.0840747\pi$
$313$	4.53916	+	7.86206i	0.256569	+	0.444390i	−0.708752	+	0.705458i	$0.750741\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−3.73331	−	6.46628i	−0.209683	−	0.363182i	0.741931	−	0.670476i	$-0.233910\pi$
$317$	−3.73331	−	6.46628i	−0.209683	−	0.363182i	−0.951615	+	0.307294i	$0.900577\pi$
$318$		0			0
$319$	2.41564	−	4.18401i	0.135250	−	0.234260i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	10.0007			0.556457
$324$		0			0
$325$	−85.1332			−4.72234
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−11.1364	+	19.2888i	−0.613970	+	1.06343i
$330$		0			0
$331$	3.02887	+	5.24616i	0.166482	+	0.288355i	0.937181	−	0.348845i	$-0.113426\pi$
$331$	3.02887	+	5.24616i	0.166482	+	0.288355i	−0.770699	+	0.637200i	$0.780093\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	11.6193	+	20.1253i	0.634831	+	1.09956i
$336$		0			0
$337$	5.63037	−	9.75209i	0.306706	−	0.531230i	−0.670934	−	0.741517i	$-0.734107\pi$
$337$	5.63037	−	9.75209i	0.306706	−	0.531230i	0.977640	+	0.210287i	$0.0674399\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−0.425304			−0.0230315
$342$		0			0
$343$	19.3972			1.04735
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−12.1085	+	20.9725i	−0.650019	+	1.12587i	0.333099	+	0.942892i	$0.391906\pi$
$347$	−12.1085	+	20.9725i	−0.650019	+	1.12587i	−0.983118	+	0.182974i	$0.941428\pi$
$348$		0			0
$349$	−7.00531	−	12.1336i	−0.374986	−	0.649495i	0.615339	−	0.788263i	$-0.289019\pi$
$349$	−7.00531	−	12.1336i	−0.374986	−	0.649495i	−0.990325	+	0.138768i	$0.955686\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−11.9500	−	20.6980i	−0.636034	−	1.10164i	−0.986295	−	0.164991i	$-0.947240\pi$
$353$	−11.9500	−	20.6980i	−0.636034	−	1.10164i	0.350261	−	0.936652i	$-0.386093\pi$
$354$		0			0
$355$	24.4006	−	42.2631i	1.29505	−	2.24309i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	4.52896			0.239029			0.119515	−	0.992832i	$-0.461866\pi$
$359$	4.52896			0.239029			0.119515	+	0.992832i	$0.461866\pi$
$360$		0			0
$361$	22.4464			1.18139
$362$		0			0
$363$		0			0
$364$		0			0
$365$	0.667906	−	1.15685i	0.0349598	−	0.0605521i
$366$		0			0
$367$	−2.20537	−	3.81982i	−0.115119	−	0.199393i	0.802708	−	0.596372i	$-0.203392\pi$
$367$	−2.20537	−	3.81982i	−0.115119	−	0.199393i	−0.917827	+	0.396979i	$0.870058\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	4.79532	+	8.30574i	0.248961	+	0.431213i
$372$		0			0
$373$	5.26445	−	9.11830i	0.272583	−	0.472128i	−0.696939	−	0.717130i	$-0.745455\pi$
$373$	5.26445	−	9.11830i	0.272583	−	0.472128i	0.969523	+	0.245002i	$0.0787887\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−33.3198			−1.71606
$378$		0			0
$379$	21.9479			1.12739			0.563694	−	0.825984i	$-0.309380\pi$
$379$	21.9479			1.12739			0.563694	+	0.825984i	$0.309380\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	10.1703	−	17.6154i	0.519677	−	0.900106i	−0.480062	−	0.877235i	$-0.659386\pi$
$383$	10.1703	−	17.6154i	0.519677	−	0.900106i	0.999738	−	0.0228716i	$-0.00728089\pi$
$384$		0			0
$385$	−5.19599	−	8.99971i	−0.264812	−	0.458668i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−1.71260	−	2.96631i	−0.0868322	−	0.150398i	0.819338	−	0.573310i	$-0.194341\pi$
$389$	−1.71260	−	2.96631i	−0.0868322	−	0.150398i	−0.906171	+	0.422913i	$0.861008\pi$
$390$		0			0
$391$	4.87468	−	8.44320i	0.246523	−	0.426991i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−56.4994			−2.84280
$396$		0			0
$397$	−29.4465			−1.47788			−0.738940	−	0.673772i	$-0.764673\pi$
$397$	−29.4465			−1.47788			−0.738940	+	0.673772i	$0.764673\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−8.08384	+	14.0016i	−0.403688	+	0.699208i	−0.994168	−	0.107845i	$-0.965605\pi$
$401$	−8.08384	+	14.0016i	−0.403688	+	0.699208i	0.590480	+	0.807052i	$0.298938\pi$
$402$		0			0
$403$	1.46659	+	2.54021i	0.0730561	+	0.126537i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−5.28077	−	9.14656i	−0.261758	−	0.453378i
$408$		0			0
$409$	4.48963	−	7.77627i	0.221998	−	0.384512i	−0.733416	−	0.679780i	$-0.762075\pi$
$409$	4.48963	−	7.77627i	0.221998	−	0.384512i	0.955415	+	0.295268i	$0.0954088\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	17.3109			0.851813
$414$		0			0
$415$	70.6870			3.46989
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−7.67284	+	13.2898i	−0.374843	+	0.649247i	−0.990304	−	0.138921i	$-0.955637\pi$
$419$	−7.67284	+	13.2898i	−0.374843	+	0.649247i	0.615461	+	0.788168i	$0.288970\pi$
$420$		0			0
$421$	14.4991	+	25.1132i	0.706644	+	1.22394i	0.966095	+	0.258187i	$0.0831251\pi$
$421$	14.4991	+	25.1132i	0.706644	+	1.22394i	−0.259451	+	0.965756i	$0.583542\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	9.58779	+	16.6065i	0.465076	+	0.805536i
$426$		0			0
$427$	6.56456	−	11.3701i	0.317681	−	0.550240i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−20.2540			−0.975599			−0.487799	−	0.872956i	$-0.662200\pi$
$431$	−20.2540			−0.975599			−0.487799	+	0.872956i	$0.662200\pi$
$432$		0			0
$433$	−13.0017			−0.624823			−0.312411	−	0.949947i	$-0.601137\pi$
$433$	−13.0017			−0.624823			−0.312411	+	0.949947i	$0.601137\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	20.2023	−	34.9914i	0.966407	−	1.67387i
$438$		0			0
$439$	1.35760	+	2.35144i	0.0647948	+	0.112228i	0.896603	−	0.442835i	$-0.146027\pi$
$439$	1.35760	+	2.35144i	0.0647948	+	0.112228i	−0.831808	+	0.555063i	$0.812694\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−2.07940	−	3.60162i	−0.0987951	−	0.171118i	0.812391	−	0.583113i	$-0.198165\pi$
$443$	−2.07940	−	3.60162i	−0.0987951	−	0.171118i	−0.911186	+	0.411995i	$0.864832\pi$
$444$		0			0
$445$	30.3312	−	52.5352i	1.43784	−	2.49041i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−4.31965			−0.203857			−0.101928	−	0.994792i	$-0.532501\pi$
$449$	−4.31965			−0.203857			−0.101928	+	0.994792i	$0.532501\pi$
$450$		0			0
$451$	1.30395			0.0614004
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−35.8350	+	62.0681i	−1.67997	+	2.90980i
$456$		0			0
$457$	4.41236	+	7.64244i	0.206402	+	0.357498i	0.950578	−	0.310485i	$-0.100491\pi$
$457$	4.41236	+	7.64244i	0.206402	+	0.357498i	−0.744177	+	0.667983i	$0.767158\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	10.2444	+	17.7438i	0.477130	+	0.826413i	0.999656	−	0.0262100i	$-0.00834385\pi$
$461$	10.2444	+	17.7438i	0.477130	+	0.826413i	−0.522527	+	0.852623i	$0.675011\pi$
$462$		0			0
$463$	6.23229	−	10.7946i	0.289639	−	0.501669i	−0.684085	−	0.729403i	$-0.739798\pi$
$463$	6.23229	−	10.7946i	0.289639	−	0.501669i	0.973724	+	0.227733i	$0.0731315\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	17.3320			0.802030			0.401015	−	0.916072i	$-0.368658\pi$
$467$	17.3320			0.802030			0.401015	+	0.916072i	$0.368658\pi$
$468$		0			0
$469$	13.9238			0.642940
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−2.18493	+	3.78440i	−0.100463	+	0.174007i
$474$		0			0
$475$	39.7350	+	68.8230i	1.82317	+	3.15781i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−7.77123	−	13.4602i	−0.355077	−	0.615011i	0.632054	−	0.774924i	$-0.282212\pi$
$479$	−7.77123	−	13.4602i	−0.355077	−	0.615011i	−0.987131	+	0.159913i	$0.948879\pi$
$480$		0			0
$481$	−36.4197	+	63.0808i	−1.66060	+	2.87624i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	34.0226			1.54489
$486$		0			0
$487$	2.87612			0.130329			0.0651646	−	0.997875i	$-0.479243\pi$
$487$	2.87612			0.130329			0.0651646	+	0.997875i	$0.479243\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	4.05682	−	7.02662i	0.183082	−	0.317107i	−0.759847	−	0.650102i	$-0.774726\pi$
$491$	4.05682	−	7.02662i	0.183082	−	0.317107i	0.942928	+	0.332995i	$0.108059\pi$
$492$		0			0
$493$	3.75251	+	6.49953i	0.169004	+	0.292724i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−14.6200	−	25.3226i	−0.655796	−	1.13587i
$498$		0			0
$499$	−19.0641	+	33.0200i	−0.853426	+	1.47818i	0.0246708	+	0.999696i	$0.492146\pi$
$499$	−19.0641	+	33.0200i	−0.853426	+	1.47818i	−0.878097	+	0.478482i	$0.841187\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	12.6053			0.562043			0.281021	−	0.959702i	$-0.409327\pi$
$503$	12.6053			0.562043			0.281021	+	0.959702i	$0.409327\pi$
$504$		0			0
$505$	−16.6888			−0.742641
$506$		0			0
$507$		0			0
$508$		0			0
$509$	4.94045	−	8.55712i	0.218982	−	0.379288i	−0.735515	−	0.677508i	$-0.763060\pi$
$509$	4.94045	−	8.55712i	0.218982	−	0.379288i	0.954497	+	0.298221i	$0.0963931\pi$
$510$		0			0
$511$	−0.400186	−	0.693142i	−0.0177032	−	0.0306628i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	4.76757	+	8.25768i	0.210084	+	0.363877i
$516$		0			0
$517$	−4.46296	+	7.73007i	−0.196281	+	0.339968i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−19.9572			−0.874339			−0.437169	−	0.899379i	$-0.644019\pi$
$521$	−19.9572			−0.874339			−0.437169	+	0.899379i	$0.644019\pi$
$522$		0			0
$523$	21.8432			0.955138			0.477569	−	0.878594i	$-0.341518\pi$
$523$	21.8432			0.955138			0.477569	+	0.878594i	$0.341518\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	0.330338	−	0.572162i	0.0143898	−	0.0249238i
$528$		0			0
$529$	−8.19449	−	14.1933i	−0.356282	−	0.617099i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−4.49645	−	7.78807i	−0.194763	−	0.337339i
$534$		0			0
$535$	−5.83622	+	10.1086i	−0.252322	+	0.437034i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	0.773498			0.0333169
$540$		0			0
$541$	11.8553			0.509699			0.254850	−	0.966981i	$-0.417974\pi$
$541$	11.8553			0.509699			0.254850	+	0.966981i	$0.417974\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−5.55944	+	9.62923i	−0.238140	+	0.412471i
$546$		0			0
$547$	−8.58597	−	14.8713i	−0.367110	−	0.635853i	0.622003	−	0.783015i	$-0.286319\pi$
$547$	−8.58597	−	14.8713i	−0.367110	−	0.635853i	−0.989112	+	0.147163i	$0.952986\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	15.5516	+	26.9362i	0.662521	+	1.14752i
$552$		0			0
$553$	−16.9262	+	29.3171i	−0.719777	+	1.24669i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−30.8360			−1.30656			−0.653281	−	0.757116i	$-0.726608\pi$
$557$	−30.8360			−1.30656			−0.653281	+	0.757116i	$0.726608\pi$
$558$		0			0
$559$	30.1375			1.27468
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−11.5978	+	20.0880i	−0.488790	+	0.846609i	−0.999917	−	0.0128965i	$-0.995895\pi$
$563$	−11.5978	+	20.0880i	−0.488790	+	0.846609i	0.511127	+	0.859505i	$0.329228\pi$
$564$		0			0
$565$	−8.53737	−	14.7872i	−0.359170	−	0.622100i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−22.4367	−	38.8615i	−0.940595	−	1.62916i	−0.764340	−	0.644813i	$-0.776935\pi$
$569$	−22.4367	−	38.8615i	−0.940595	−	1.62916i	−0.176254	−	0.984345i	$-0.556398\pi$
$570$		0			0
$571$	−15.4176	+	26.7041i	−0.645207	+	1.11753i	0.339047	+	0.940769i	$0.389895\pi$
$571$	−15.4176	+	26.7041i	−0.645207	+	1.11753i	−0.984254	+	0.176762i	$0.943438\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	77.4724			3.23082
$576$		0			0
$577$	−36.6270			−1.52480			−0.762402	−	0.647104i	$-0.775980\pi$
$577$	−36.6270			−1.52480			−0.762402	+	0.647104i	$0.775980\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	21.1766	−	36.6789i	0.878553	−	1.52170i
$582$		0			0
$583$	1.92174	+	3.32856i	0.0795905	+	0.137855i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−6.19961	−	10.7380i	−0.255885	−	0.443206i	0.709250	−	0.704957i	$-0.249034\pi$
$587$	−6.19961	−	10.7380i	−0.255885	−	0.443206i	−0.965136	+	0.261750i	$0.915700\pi$
$588$		0			0
$589$	1.36903	−	2.37123i	0.0564099	−	0.0977048i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−40.2691			−1.65365			−0.826827	−	0.562456i	$-0.809856\pi$
$593$	−40.2691			−1.65365			−0.826827	+	0.562456i	$0.809856\pi$
$594$		0			0
$595$	16.1431			0.661803
$596$		0			0
$597$		0			0
$598$		0			0
$599$	10.7732	−	18.6598i	0.440182	−	0.762417i	−0.557521	−	0.830163i	$-0.688247\pi$
$599$	10.7732	−	18.6598i	0.440182	−	0.762417i	0.997703	+	0.0677456i	$0.0215806\pi$
$600$		0			0
$601$	21.5445	+	37.3162i	0.878819	+	1.52216i	0.852639	+	0.522501i	$0.175001\pi$
$601$	21.5445	+	37.3162i	0.878819	+	1.52216i	0.0261799	+	0.999657i	$0.491666\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−2.08231	−	3.60667i	−0.0846580	−	0.146632i
$606$		0			0
$607$	−9.02897	+	15.6386i	−0.366475	+	0.634753i	−0.989012	−	0.147838i	$-0.952769\pi$
$607$	−9.02897	+	15.6386i	−0.366475	+	0.634753i	0.622537	+	0.782590i	$0.286102\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	61.5591			2.49042
$612$		0			0
$613$	−17.3265			−0.699811			−0.349906	−	0.936785i	$-0.613786\pi$
$613$	−17.3265			−0.699811			−0.349906	+	0.936785i	$0.613786\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	8.57058	−	14.8447i	0.345038	−	0.597624i	−0.640322	−	0.768106i	$-0.721199\pi$
$617$	8.57058	−	14.8447i	0.345038	−	0.597624i	0.985361	+	0.170482i	$0.0545325\pi$
$618$		0			0
$619$	−1.77582	−	3.07581i	−0.0713763	−	0.123627i	0.828128	−	0.560538i	$-0.189406\pi$
$619$	−1.77582	−	3.07581i	−0.0713763	−	0.123627i	−0.899505	+	0.436911i	$0.856072\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−18.1734	−	31.4773i	−0.728102	−	1.26111i
$624$		0			0
$625$	−32.8281	+	56.8600i	−1.31313	+	2.27440i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	16.4065			0.654170
$630$		0			0
$631$	−46.4677			−1.84985			−0.924925	−	0.380149i	$-0.875873\pi$
$631$	−46.4677			−1.84985			−0.924925	+	0.380149i	$0.875873\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	27.0271	−	46.8124i	1.07254	−	1.85769i
$636$		0			0
$637$	−2.66728	−	4.61987i	−0.105682	−	0.183046i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	0.853433	+	1.47819i	0.0337086	+	0.0583850i	0.882388	−	0.470523i	$-0.155935\pi$
$641$	0.853433	+	1.47819i	0.0337086	+	0.0583850i	−0.848679	+	0.528908i	$0.822602\pi$
$642$		0			0
$643$	−10.4044	+	18.0209i	−0.410309	+	0.710676i	−0.994923	−	0.100635i	$-0.967913\pi$
$643$	−10.4044	+	18.0209i	−0.410309	+	0.710676i	0.584614	+	0.811311i	$0.301246\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	7.00045			0.275216			0.137608	−	0.990487i	$-0.456059\pi$
$647$	7.00045			0.275216			0.137608	+	0.990487i	$0.456059\pi$
$648$		0			0
$649$	6.93741			0.272317
$650$		0			0
$651$		0			0
$652$		0			0
$653$	7.84471	−	13.5874i	0.306987	−	0.531718i	−0.670714	−	0.741716i	$-0.734012\pi$
$653$	7.84471	−	13.5874i	0.306987	−	0.531718i	0.977702	+	0.209998i	$0.0673457\pi$
$654$		0			0
$655$	22.0265	+	38.1509i	0.860645	+	1.49068i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−3.47586	−	6.02037i	−0.135400	−	0.234520i	0.790350	−	0.612656i	$-0.209899\pi$
$659$	−3.47586	−	6.02037i	−0.135400	−	0.234520i	−0.925750	+	0.378135i	$0.876565\pi$
$660$		0			0
$661$	9.24907	−	16.0199i	0.359747	−	0.623100i	−0.628171	−	0.778075i	$-0.716196\pi$
$661$	9.24907	−	16.0199i	0.359747	−	0.623100i	0.987918	+	0.154975i	$0.0495296\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	66.9023			2.59436
$666$		0			0
$667$	30.3214			1.17405
$668$		0			0
$669$		0			0
$670$		0			0
$671$	2.63077	−	4.55663i	0.101560	−	0.175907i
$672$		0			0
$673$	8.16223	+	14.1374i	0.314631	+	0.544956i	0.979359	−	0.202129i	$-0.0647860\pi$
$673$	8.16223	+	14.1374i	0.314631	+	0.544956i	−0.664728	+	0.747085i	$0.731453\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−2.34451	−	4.06081i	−0.0901068	−	0.156070i	0.817449	−	0.576001i	$-0.195388\pi$
$677$	−2.34451	−	4.06081i	−0.0901068	−	0.156070i	−0.907556	+	0.419931i	$0.862054\pi$
$678$		0			0
$679$	10.1926	−	17.6540i	0.391155	−	0.677500i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	2.53422			0.0969692			0.0484846	−	0.998824i	$-0.484561\pi$
$683$	2.53422			0.0969692			0.0484846	+	0.998824i	$0.484561\pi$
$684$		0			0
$685$	32.0401			1.22419
$686$		0			0
$687$		0			0
$688$		0			0
$689$	13.2537	−	22.9560i	0.504924	−	0.874554i
$690$		0			0
$691$	−13.5948	−	23.5468i	−0.517169	−	0.895763i	−0.999801	−	0.0199396i	$-0.993653\pi$
$691$	−13.5948	−	23.5468i	−0.517169	−	0.895763i	0.482632	−	0.875823i	$-0.339681\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	24.7650	+	42.8943i	0.939392	+	1.62707i
$696$		0			0
$697$	−1.01279	+	1.75420i	−0.0383621	+	0.0664451i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	9.01483			0.340486			0.170243	−	0.985402i	$-0.445545\pi$
$701$	9.01483			0.340486			0.170243	+	0.985402i	$0.445545\pi$
$702$		0			0
$703$	67.9940			2.56444
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−4.99966	+	8.65967i	−0.188032	+	0.325680i
$708$		0			0
$709$	−1.23736	−	2.14316i	−0.0464699	−	0.0804882i	0.841855	−	0.539704i	$-0.181464\pi$
$709$	−1.23736	−	2.14316i	−0.0464699	−	0.0804882i	−0.888325	+	0.459216i	$0.848130\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−1.33462	−	2.31163i	−0.0499818	−	0.0865710i
$714$		0			0
$715$	−14.3610	+	24.8740i	−0.537072	+	0.930236i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−53.4035			−1.99161			−0.995807	−	0.0914814i	$-0.970840\pi$
$719$	−53.4035			−1.99161			−0.995807	+	0.0914814i	$0.970840\pi$
$720$		0			0
$721$	5.71312			0.212768
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−29.8189	+	51.6479i	−1.10745	+	1.91815i
$726$		0			0
$727$	10.4641	+	18.1244i	0.388093	+	0.672197i	0.992193	−	0.124711i	$-0.0398005\pi$
$727$	10.4641	+	18.1244i	0.388093	+	0.672197i	−0.604100	+	0.796909i	$0.706467\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−3.39411	−	5.87877i	−0.125536	−	0.217434i
$732$		0			0
$733$	2.37060	−	4.10600i	0.0875602	−	0.151659i	−0.818919	−	0.573909i	$-0.805426\pi$
$733$	2.37060	−	4.10600i	0.0875602	−	0.151659i	0.906479	+	0.422250i	$0.138760\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	5.58001			0.205542
$738$		0			0
$739$	−22.6235			−0.832217			−0.416109	−	0.909315i	$-0.636606\pi$
$739$	−22.6235			−0.832217			−0.416109	+	0.909315i	$0.636606\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−15.3219	+	26.5382i	−0.562104	+	0.973593i	0.435208	+	0.900330i	$0.356675\pi$
$743$	−15.3219	+	26.5382i	−0.562104	+	0.973593i	−0.997313	+	0.0732634i	$0.976659\pi$
$744$		0			0
$745$	−6.24142	−	10.8105i	−0.228668	−	0.396065i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	3.49686	+	6.05673i	0.127772	+	0.221308i
$750$		0			0
$751$	−3.96933	+	6.87509i	−0.144843	+	0.250876i	−0.929314	−	0.369290i	$-0.879601\pi$
$751$	−3.96933	+	6.87509i	−0.144843	+	0.250876i	0.784471	+	0.620165i	$0.212934\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	39.4844			1.43699
$756$		0			0
$757$	26.7247			0.971325			0.485663	−	0.874146i	$-0.338578\pi$
$757$	26.7247			0.971325			0.485663	+	0.874146i	$0.338578\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−5.59264	+	9.68674i	−0.202733	+	0.351144i	−0.949408	−	0.314045i	$-0.898316\pi$
$761$	−5.59264	+	9.68674i	−0.202733	+	0.351144i	0.746675	+	0.665189i	$0.231649\pi$
$762$		0			0
$763$	3.33102	+	5.76950i	0.120591	+	0.208870i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−23.9225	−	41.4350i	−0.863792	−	1.49613i
$768$		0			0
$769$	−6.36084	+	11.0173i	−0.229378	+	0.397294i	−0.957624	−	0.288022i	$-0.907002\pi$
$769$	−6.36084	+	11.0173i	−0.229378	+	0.397294i	0.728246	+	0.685316i	$0.240336\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	13.3740			0.481031			0.240515	−	0.970645i	$-0.422684\pi$
$773$	13.3740			0.481031			0.240515	+	0.970645i	$0.422684\pi$
$774$		0			0
$775$	5.24999			0.188585
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−4.19733	+	7.26998i	−0.150385	+	0.260474i
$780$		0			0
$781$	−5.85902	−	10.1481i	−0.209652	−	0.363128i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−45.5020	−	78.8117i	−1.62403	−	2.81291i
$786$		0			0
$787$	1.81606	−	3.14550i	0.0647354	−	0.112125i	−0.831841	−	0.555014i	$-0.812713\pi$
$787$	1.81606	−	3.14550i	0.0647354	−	0.112125i	0.896577	+	0.442889i	$0.146046\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−10.2306			−0.363758
$792$		0			0
$793$	−36.2872			−1.28860
$794$		0			0
$795$		0			0
$796$		0			0
$797$	2.04384	−	3.54004i	0.0723967	−	0.125395i	−0.827555	−	0.561385i	$-0.810269\pi$
$797$	2.04384	−	3.54004i	0.0723967	−	0.125395i	0.899951	+	0.435991i	$0.143602\pi$
$798$		0			0
$799$	−6.93285	−	12.0080i	−0.245267	−	0.424814i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−0.160376	−	0.277779i	−0.00565955	−	0.00980262i
$804$		0			0
$805$	32.6103	−	56.4828i	1.14936	−	1.99076i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−27.8454			−0.978994			−0.489497	−	0.872005i	$-0.662820\pi$
$809$	−27.8454			−0.978994			−0.489497	+	0.872005i	$0.662820\pi$
$810$		0			0
$811$	−4.24075			−0.148913			−0.0744565	−	0.997224i	$-0.523722\pi$
$811$	−4.24075			−0.148913			−0.0744565	+	0.997224i	$0.523722\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−31.2571	+	54.1390i	−1.09489	+	1.89641i
$816$		0			0
$817$	−14.0663	−	24.3636i	−0.492118	−	0.852373i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−19.3650	−	33.5411i	−0.675842	−	1.17059i	−0.976222	−	0.216773i	$-0.930447\pi$
$821$	−19.3650	−	33.5411i	−0.675842	−	1.17059i	0.300380	−	0.953820i	$-0.402886\pi$
$822$		0			0
$823$	−17.3297	+	30.0160i	−0.604077	+	1.04629i	0.388120	+	0.921609i	$0.373125\pi$
$823$	−17.3297	+	30.0160i	−0.604077	+	1.04629i	−0.992197	+	0.124683i	$0.960209\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−38.3962			−1.33517			−0.667584	−	0.744534i	$-0.732672\pi$
$827$	−38.3962			−1.33517			−0.667584	+	0.744534i	$0.732672\pi$
$828$		0			0
$829$	31.4431			1.09206			0.546032	−	0.837764i	$-0.316138\pi$
$829$	31.4431			1.09206			0.546032	+	0.837764i	$0.316138\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−0.600784	+	1.04059i	−0.0208159	+	0.0360542i
$834$		0			0
$835$	29.0583	+	50.3305i	1.00561	+	1.74176i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	24.4439	+	42.3380i	0.843896	+	1.46167i	0.886576	+	0.462582i	$0.153077\pi$
$839$	24.4439	+	42.3380i	0.843896	+	1.46167i	−0.0426804	+	0.999089i	$0.513590\pi$
$840$		0			0
$841$	2.82936	−	4.90060i	0.0975643	−	0.168986i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	143.947			4.95192
$846$		0			0
$847$	−2.49530			−0.0857394
$848$		0			0
$849$		0			0
$850$		0			0
$851$	33.1424	−	57.4044i	1.13611	−	1.96780i
$852$		0			0
$853$	−0.900962	−	1.56051i	−0.0308483	−	0.0534309i	0.850189	−	0.526477i	$-0.176488\pi$
$853$	−0.900962	−	1.56051i	−0.0308483	−	0.0534309i	−0.881037	+	0.473047i	$0.843154\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−4.45381	−	7.71422i	−0.152139	−	0.263513i	0.779874	−	0.625936i	$-0.215283\pi$
$857$	−4.45381	−	7.71422i	−0.152139	−	0.263513i	−0.932014	+	0.362423i	$0.881950\pi$
$858$		0			0
$859$	−10.2815	+	17.8081i	−0.350800	+	0.607604i	−0.986390	−	0.164423i	$-0.947424\pi$
$859$	−10.2815	+	17.8081i	−0.350800	+	0.607604i	0.635589	+	0.772027i	$0.280757\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	14.1832			0.482802			0.241401	−	0.970425i	$-0.422393\pi$
$863$	14.1832			0.482802			0.241401	+	0.970425i	$0.422393\pi$
$864$		0			0
$865$	−65.4840			−2.22652
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−6.78326	+	11.7489i	−0.230106	+	0.398556i
$870$		0			0
$871$	−19.2418	−	33.3277i	−0.651982	−	1.12927i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	38.1598	+	66.0948i	1.29004	+	2.23441i
$876$		0			0
$877$	−10.5912	+	18.3444i	−0.357638	+	0.619447i	−0.987566	−	0.157207i	$-0.949751\pi$
$877$	−10.5912	+	18.3444i	−0.357638	+	0.619447i	0.629928	+	0.776654i	$0.283084\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	0.814697			0.0274478			0.0137239	−	0.999906i	$-0.495631\pi$
$881$	0.814697			0.0274478			0.0137239	+	0.999906i	$0.495631\pi$
$882$		0			0
$883$	−1.86432			−0.0627394			−0.0313697	−	0.999508i	$-0.509987\pi$
$883$	−1.86432			−0.0627394			−0.0313697	+	0.999508i	$0.509987\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−8.03345	+	13.9143i	−0.269737	+	0.467198i	−0.968794	−	0.247868i	$-0.920270\pi$
$887$	−8.03345	+	13.9143i	−0.269737	+	0.467198i	0.699057	+	0.715066i	$0.253603\pi$
$888$		0			0
$889$	−16.1937	−	28.0483i	−0.543120	−	0.940711i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−28.7320	−	49.7653i	−0.961480	−	1.66533i
$894$		0			0
$895$	5.61120	−	9.71889i	0.187562	−	0.324867i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	2.05476			0.0685302
$900$		0			0
$901$	−5.97056			−0.198908
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−7.10190	+	12.3008i	−0.236075	+	0.408894i
$906$		0			0
$907$	25.0634	+	43.4110i	0.832215	+	1.44144i	0.896278	+	0.443493i	$0.146261\pi$
$907$	25.0634	+	43.4110i	0.832215	+	1.44144i	−0.0640623	+	0.997946i	$0.520406\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−29.0060	−	50.2399i	−0.961013	−	1.66452i	−0.719966	−	0.694010i	$-0.755842\pi$
$911$	−29.0060	−	50.2399i	−0.961013	−	1.66452i	−0.241047	−	0.970513i	$-0.577491\pi$
$912$		0			0
$913$	8.48660	−	14.6992i	0.280866	−	0.486474i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	26.3949			0.871638
$918$		0			0
$919$	−25.9456			−0.855867			−0.427933	−	0.903810i	$-0.640758\pi$
$919$	−25.9456			−0.855867			−0.427933	+	0.903810i	$0.640758\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−40.4078	+	69.9883i	−1.33004	+	2.30369i
$924$		0			0
$925$	65.1863	+	112.906i	2.14331	+	3.71233i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−14.2592	−	24.6977i	−0.467830	−	0.810305i	0.531495	−	0.847062i	$-0.321631\pi$
$929$	−14.2592	−	24.6977i	−0.467830	−	0.810305i	−0.999324	+	0.0367569i	$0.988297\pi$
$930$		0			0
$931$	−2.48985	+	4.31254i	−0.0816014	+	0.141338i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	6.46942			0.211572
$936$		0			0
$937$	18.7492			0.612510			0.306255	−	0.951950i	$-0.400924\pi$
$937$	18.7492			0.612510			0.306255	+	0.951950i	$0.400924\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−17.5280	+	30.3593i	−0.571395	+	0.989686i	0.425028	+	0.905180i	$0.360264\pi$
$941$	−17.5280	+	30.3593i	−0.571395	+	0.989686i	−0.996423	+	0.0845053i	$0.973069\pi$
$942$		0			0
$943$	4.09182	+	7.08725i	0.133248	+	0.230792i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−7.15922	−	12.4001i	−0.232643	−	0.402950i	0.725942	−	0.687756i	$-0.241404\pi$
$947$	−7.15922	−	12.4001i	−0.232643	−	0.402950i	−0.958585	+	0.284806i	$0.908071\pi$
$948$		0			0
$949$	−1.10606	+	1.91575i	−0.0359043	+	0.0621880i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−27.2625			−0.883118			−0.441559	−	0.897232i	$-0.645574\pi$
$953$	−27.2625			−0.883118			−0.441559	+	0.897232i	$0.645574\pi$
$954$		0			0
$955$	−3.71294			−0.120148
$956$		0			0
$957$		0			0
$958$		0			0
$959$	9.59866	−	16.6254i	0.309957	−	0.536861i
$960$		0			0
$961$	15.4096	+	26.6901i	0.497083	+	0.860972i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−0.862018	−	1.49306i	−0.0277493	−	0.0480633i
$966$		0			0
$967$	9.95906	−	17.2496i	0.320262	−	0.554710i	−0.660280	−	0.751019i	$-0.729562\pi$
$967$	9.95906	−	17.2496i	0.320262	−	0.554710i	0.980542	+	0.196310i	$0.0628957\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−39.3160			−1.26171			−0.630855	−	0.775901i	$-0.717296\pi$
$971$	−39.3160			−1.26171			−0.630855	+	0.775901i	$0.717296\pi$
$972$		0			0
$973$	29.6767			0.951391
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−11.9664	+	20.7264i	−0.382840	+	0.663098i	−0.991467	−	0.130359i	$-0.958387\pi$
$977$	−11.9664	+	20.7264i	−0.382840	+	0.663098i	0.608627	+	0.793456i	$0.291720\pi$
$978$		0			0
$979$	−7.28307	−	12.6146i	−0.232768	−	0.403166i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	22.8633	+	39.6005i	0.729227	+	1.26306i	0.957210	+	0.289394i	$0.0934536\pi$
$983$	22.8633	+	39.6005i	0.729227	+	1.26306i	−0.227983	+	0.973665i	$0.573213\pi$
$984$		0			0
$985$	−23.7423	+	41.1229i	−0.756493	+	1.31028i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−27.4255			−0.872079
$990$		0			0
$991$	17.1171			0.543742			0.271871	−	0.962334i	$-0.412358\pi$
$991$	17.1171			0.543742			0.271871	+	0.962334i	$0.412358\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	46.2277	−	80.0687i	1.46552	−	2.53835i
$996$		0			0
$997$	0.263700	+	0.456743i	0.00835148	+	0.0144652i	0.870171	−	0.492750i	$-0.164008\pi$
$997$	0.263700	+	0.456743i	0.00835148	+	0.0144652i	−0.861819	+	0.507215i	$0.830675\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3564.2.i.t.2377.1		12
3.2	odd	2		3564.2.i.s.2377.6		12
9.2	odd	6		3564.2.i.s.1189.6		12
9.4	even	3		3564.2.a.o.1.6	✓	6
9.5	odd	6		3564.2.a.p.1.1	yes	6
9.7	even	3	inner	3564.2.i.t.1189.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3564.2.a.o.1.6	✓	6	9.4	even	3
3564.2.a.p.1.1	yes	6	9.5	odd	6
3564.2.i.s.1189.6		12	9.2	odd	6
3564.2.i.s.2377.6		12	3.2	odd	2
3564.2.i.t.1189.1		12	9.7	even	3	inner
3564.2.i.t.2377.1		12	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 3564 = 2^{2} \cdot 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3564.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.08231 + 3.60667i) q^{5} +(1.24765 + 2.16099i) q^{7} +O(q^{10})\)	\(q+(-2.08231 + 3.60667i) q^{5} +(1.24765 + 2.16099i) q^{7} +(0.500000 + 0.866025i) q^{11} +(3.44834 - 5.97270i) q^{13} -1.55342 q^{17} -6.43789 q^{19} +(-3.13803 + 5.43523i) q^{23} +(-6.17205 - 10.6903i) q^{25} +(-2.41564 - 4.18401i) q^{29} +(-0.212652 + 0.368324i) q^{31} -10.3920 q^{35} -10.5615 q^{37} +(0.651973 - 1.12925i) q^{41} +(2.18493 + 3.78440i) q^{43} +(4.46296 + 7.73007i) q^{47} +(0.386749 - 0.669869i) q^{49} +3.84349 q^{53} -4.16462 q^{55} +(3.46870 - 6.00797i) q^{59} +(-2.63077 - 4.55663i) q^{61} +(14.3610 + 24.8740i) q^{65} +(2.79000 - 4.83243i) q^{67} -11.7180 q^{71} -0.320752 q^{73} +(-1.24765 + 2.16099i) q^{77} +(6.78326 + 11.7489i) q^{79} +(-8.48660 - 14.6992i) q^{83} +(3.23471 - 5.60268i) q^{85} -14.5661 q^{89} +17.2092 q^{91} +(13.4057 - 23.2193i) q^{95} +(-4.08471 - 7.07493i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{7}+O(q^{10}) \) 12 * q + 2 * q^7	\( 12 q + 2 q^{7} + 6 q^{11} + 6 q^{13} - 8 q^{17} + 4 q^{23} - 10 q^{25} - 4 q^{29} - 6 q^{31} - 28 q^{35} - 12 q^{37} + 22 q^{41} + 10 q^{43} + 20 q^{47} - 6 q^{49} - 8 q^{53} + 24 q^{59} + 10 q^{61} + 40 q^{65} + 6 q^{67} - 80 q^{71} - 16 q^{73} - 2 q^{77} + 14 q^{79} + 12 q^{83} - 6 q^{85} - 48 q^{89} + 20 q^{91} + 44 q^{95} - 20 q^{97}+O(q^{100}) \) 12 * q + 2 * q^7 + 6 * q^11 + 6 * q^13 - 8 * q^17 + 4 * q^23 - 10 * q^25 - 4 * q^29 - 6 * q^31 - 28 * q^35 - 12 * q^37 + 22 * q^41 + 10 * q^43 + 20 * q^47 - 6 * q^49 - 8 * q^53 + 24 * q^59 + 10 * q^61 + 40 * q^65 + 6 * q^67 - 80 * q^71 - 16 * q^73 - 2 * q^77 + 14 * q^79 + 12 * q^83 - 6 * q^85 - 48 * q^89 + 20 * q^91 + 44 * q^95 - 20 * q^97

Introduction

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