LMFDB - Embedded newform 3564.2.i.t.2377.5

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			2377.5
Root			$-2.71284 - 2.71284i$ of defining polynomial
Character	$\chi$	$=$	3564.2377
Dual form			3564.2.i.t.1189.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.992970 - 1.71987i) q^{5} +(0.287680 + 0.498276i) q^{7} +O(q^{10})$	$q+(0.992970 - 1.71987i) q^{5} +(0.287680 + 0.498276i) q^{7} +(0.500000 + 0.866025i) q^{11} +(-1.35899 + 2.35385i) q^{13} -5.85033 q^{17} +7.40818 q^{19} +(-1.63450 + 2.83103i) q^{23} +(0.528023 + 0.914563i) q^{25} +(2.00882 + 3.47937i) q^{29} +(-2.36072 + 4.08888i) q^{31} +1.14263 q^{35} -8.38727 q^{37} +(-5.57236 + 9.65161i) q^{41} +(0.458432 + 0.794027i) q^{43} +(0.0712536 + 0.123415i) q^{47} +(3.33448 - 5.77549i) q^{49} +3.52288 q^{53} +1.98594 q^{55} +(6.19580 - 10.7314i) q^{59} +(2.94826 + 5.10653i) q^{61} +(2.69888 + 4.67460i) q^{65} +(-4.93786 + 8.55263i) q^{67} -9.86439 q^{71} +9.04993 q^{73} +(-0.287680 + 0.498276i) q^{77} +(4.74133 + 8.21222i) q^{79} +(2.98249 + 5.16583i) q^{83} +(-5.80920 + 10.0618i) q^{85} -6.94155 q^{89} -1.56382 q^{91} +(7.35610 - 12.7411i) q^{95} +(9.45109 + 16.3698i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	0.992970	−	1.71987i	0.444069	−	0.769151i	−0.553917	−	0.832572i	$-0.686868\pi$
$5$	0.992970	−	1.71987i	0.444069	−	0.769151i	0.997987	+	0.0634207i	$0.0202010\pi$
$6$		0			0
$7$	0.287680	+	0.498276i	0.108733	+	0.188331i	0.915257	−	0.402870i	$-0.131987\pi$
$7$	0.287680	+	0.498276i	0.108733	+	0.188331i	−0.806524	+	0.591201i	$0.798654\pi$
$8$		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
$13$	−1.35899	+	2.35385i	−0.376917	+	0.652840i	−0.990612	−	0.136703i	$-0.956349\pi$
$13$	−1.35899	+	2.35385i	−0.376917	+	0.652840i	0.613695	+	0.789543i	$0.289683\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−5.85033			−1.41891			−0.709456	−	0.704749i	$-0.751059\pi$
$17$	−5.85033			−1.41891			−0.709456	+	0.704749i	$0.751059\pi$
$18$		0			0
$19$	7.40818			1.69955			0.849776	−	0.527143i	$-0.176737\pi$
$19$	7.40818			1.69955			0.849776	+	0.527143i	$0.176737\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.63450	+	2.83103i	−0.340816	+	0.590311i	−0.984585	−	0.174909i	$-0.944037\pi$
$23$	−1.63450	+	2.83103i	−0.340816	+	0.590311i	0.643768	+	0.765221i	$0.277370\pi$
$24$		0			0
$25$	0.528023	+	0.914563i	0.105605	+	0.182913i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	2.00882	+	3.47937i	0.373028	+	0.646103i	0.990030	−	0.140859i	$-0.0449863\pi$
$29$	2.00882	+	3.47937i	0.373028	+	0.646103i	−0.617002	+	0.786962i	$0.711653\pi$
$30$		0			0
$31$	−2.36072	+	4.08888i	−0.423998	+	0.734385i	−0.996326	−	0.0856390i	$-0.972707\pi$
$31$	−2.36072	+	4.08888i	−0.423998	+	0.734385i	0.572329	+	0.820024i	$0.306040\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	1.14263			0.193140
$36$		0			0
$37$	−8.38727			−1.37886			−0.689429	−	0.724353i	$-0.742139\pi$
$37$	−8.38727			−1.37886			−0.689429	+	0.724353i	$0.742139\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−5.57236	+	9.65161i	−0.870257	+	1.50733i	−0.00852538	+	0.999964i	$0.502714\pi$
$41$	−5.57236	+	9.65161i	−0.870257	+	1.50733i	−0.861731	+	0.507365i	$0.830620\pi$
$42$		0			0
$43$	0.458432	+	0.794027i	0.0699102	+	0.121088i	0.898862	−	0.438233i	$-0.144395\pi$
$43$	0.458432	+	0.794027i	0.0699102	+	0.121088i	−0.828951	+	0.559321i	$0.811062\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	0.0712536	+	0.123415i	0.0103934	+	0.0180019i	0.871175	−	0.490972i	$-0.163358\pi$
$47$	0.0712536	+	0.123415i	0.0103934	+	0.0180019i	−0.860782	+	0.508974i	$0.830025\pi$
$48$		0			0
$49$	3.33448	−	5.77549i	0.476354	−	0.825070i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	3.52288			0.483905			0.241953	−	0.970288i	$-0.422212\pi$
$53$	3.52288			0.483905			0.241953	+	0.970288i	$0.422212\pi$
$54$		0			0
$55$	1.98594			0.267784
$56$		0			0
$57$		0			0
$58$		0			0
$59$	6.19580	−	10.7314i	0.806624	−	1.39711i	−0.108565	−	0.994089i	$-0.534626\pi$
$59$	6.19580	−	10.7314i	0.806624	−	1.39711i	0.915189	−	0.403024i	$-0.132041\pi$
$60$		0			0
$61$	2.94826	+	5.10653i	0.377485	+	0.653824i	0.990696	−	0.136096i	$-0.0434555\pi$
$61$	2.94826	+	5.10653i	0.377485	+	0.653824i	−0.613210	+	0.789920i	$0.710122\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	2.69888	+	4.67460i	0.334755	+	0.579813i
$66$		0			0
$67$	−4.93786	+	8.55263i	−0.603256	+	1.04487i	0.389068	+	0.921209i	$0.372797\pi$
$67$	−4.93786	+	8.55263i	−0.603256	+	1.04487i	−0.992324	+	0.123661i	$0.960536\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−9.86439			−1.17069			−0.585344	−	0.810785i	$-0.699040\pi$
$71$	−9.86439			−1.17069			−0.585344	+	0.810785i	$0.699040\pi$
$72$		0			0
$73$	9.04993			1.05921			0.529607	−	0.848243i	$-0.322339\pi$
$73$	9.04993			1.05921			0.529607	+	0.848243i	$0.322339\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.287680	+	0.498276i	−0.0327842	+	0.0567839i
$78$		0			0
$79$	4.74133	+	8.21222i	0.533441	+	0.923947i	0.999237	+	0.0390549i	$0.0124347\pi$
$79$	4.74133	+	8.21222i	0.533441	+	0.923947i	−0.465796	+	0.884892i	$0.654232\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	2.98249	+	5.16583i	0.327371	+	0.567023i	0.981989	−	0.188936i	$-0.0605040\pi$
$83$	2.98249	+	5.16583i	0.327371	+	0.567023i	−0.654618	+	0.755960i	$0.727171\pi$
$84$		0			0
$85$	−5.80920	+	10.0618i	−0.630096	+	1.09136i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−6.94155			−0.735803			−0.367902	−	0.929865i	$-0.619924\pi$
$89$	−6.94155			−0.735803			−0.367902	+	0.929865i	$0.619924\pi$
$90$		0			0
$91$	−1.56382			−0.163933
$92$		0			0
$93$		0			0
$94$		0			0
$95$	7.35610	−	12.7411i	0.754719	−	1.30721i
$96$		0			0
$97$	9.45109	+	16.3698i	0.959612	+	1.66210i	0.723441	+	0.690386i	$0.242559\pi$
$97$	9.45109	+	16.3698i	0.959612	+	1.66210i	0.236171	+	0.971711i	$0.424107\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−1.48766	−	2.57671i	−0.148028	−	0.256392i	0.782471	−	0.622688i	$-0.213959\pi$
$101$	−1.48766	−	2.57671i	−0.148028	−	0.256392i	−0.930499	+	0.366296i	$0.880626\pi$
$102$		0			0
$103$	−6.04469	+	10.4697i	−0.595601	+	1.03161i	0.397860	+	0.917446i	$0.369753\pi$
$103$	−6.04469	+	10.4697i	−0.595601	+	1.03161i	−0.993462	+	0.114166i	$0.963580\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−12.5867			−1.21680			−0.608401	−	0.793630i	$-0.708189\pi$
$107$	−12.5867			−1.21680			−0.608401	+	0.793630i	$0.708189\pi$
$108$		0			0
$109$	8.20065			0.785479			0.392740	−	0.919650i	$-0.371527\pi$
$109$	8.20065			0.785479			0.392740	+	0.919650i	$0.371527\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	3.49708	−	6.05711i	0.328977	−	0.569805i	−0.653332	−	0.757072i	$-0.726629\pi$
$113$	3.49708	−	6.05711i	0.328977	−	0.569805i	0.982309	+	0.187266i	$0.0599627\pi$
$114$		0			0
$115$	3.24601	+	5.62226i	0.302692	+	0.524278i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−1.68302	−	2.91508i	−0.154282	−	0.267225i
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	12.0269			1.07572
$126$		0			0
$127$	−15.4384			−1.36994			−0.684968	−	0.728573i	$-0.740184\pi$
$127$	−15.4384			−1.36994			−0.684968	+	0.728573i	$0.740184\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	7.25545	−	12.5668i	0.633912	−	1.09797i	−0.352833	−	0.935686i	$-0.614782\pi$
$131$	7.25545	−	12.5668i	0.633912	−	1.09797i	0.986745	−	0.162281i	$-0.0518851\pi$
$132$		0			0
$133$	2.13118	+	3.69132i	0.184797	+	0.320078i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	0.220914	+	0.382634i	0.0188740	+	0.0326906i	0.875308	−	0.483566i	$-0.160659\pi$
$137$	0.220914	+	0.382634i	0.0188740	+	0.0326906i	−0.856434	+	0.516256i	$0.827325\pi$
$138$		0			0
$139$	7.23042	−	12.5235i	0.613276	−	1.06223i	−0.377408	−	0.926047i	$-0.623185\pi$
$139$	7.23042	−	12.5235i	0.613276	−	1.06223i	0.990684	−	0.136179i	$-0.0434821\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−2.71799			−0.227290
$144$		0			0
$145$	7.97877			0.662601
$146$		0			0
$147$		0			0
$148$		0			0
$149$	8.79328	−	15.2304i	0.720373	−	1.24772i	−0.240477	−	0.970655i	$-0.577304\pi$
$149$	8.79328	−	15.2304i	0.720373	−	1.24772i	0.960850	−	0.277068i	$-0.0893628\pi$
$150$		0			0
$151$	−2.81535	−	4.87632i	−0.229110	−	0.396830i	0.728435	−	0.685115i	$-0.240248\pi$
$151$	−2.81535	−	4.87632i	−0.229110	−	0.396830i	−0.957545	+	0.288285i	$0.906915\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	4.68824	+	8.12028i	0.376569	+	0.652236i
$156$		0			0
$157$	1.18031	−	2.04436i	0.0941992	−	0.163158i	−0.815075	−	0.579356i	$-0.803304\pi$
$157$	1.18031	−	2.04436i	0.0941992	−	0.163158i	0.909274	+	0.416198i	$0.136638\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−1.88085			−0.148232
$162$		0			0
$163$	7.00734			0.548857			0.274429	−	0.961608i	$-0.411511\pi$
$163$	7.00734			0.548857			0.274429	+	0.961608i	$0.411511\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−3.43174	+	5.94395i	−0.265556	+	0.459956i	−0.967709	−	0.252070i	$-0.918889\pi$
$167$	−3.43174	+	5.94395i	−0.265556	+	0.459956i	0.702153	+	0.712026i	$0.252222\pi$
$168$		0			0
$169$	2.80627	+	4.86059i	0.215867	+	0.373892i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	6.23602	+	10.8011i	0.474116	+	0.821193i	0.999561	−	0.0296348i	$-0.00943443\pi$
$173$	6.23602	+	10.8011i	0.474116	+	0.821193i	−0.525445	+	0.850828i	$0.676101\pi$
$174$		0			0
$175$	−0.303803	+	0.526203i	−0.0229654	+	0.0397772i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−4.87051			−0.364039			−0.182019	−	0.983295i	$-0.558263\pi$
$179$	−4.87051			−0.364039			−0.182019	+	0.983295i	$0.558263\pi$
$180$		0			0
$181$	15.0264			1.11691			0.558454	−	0.829536i	$-0.311395\pi$
$181$	15.0264			1.11691			0.558454	+	0.829536i	$0.311395\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−8.32830	+	14.4250i	−0.612309	+	1.06055i
$186$		0			0
$187$	−2.92516	−	5.06653i	−0.213909	−	0.370501i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	4.54097	+	7.86519i	0.328573	+	0.569105i	0.982229	−	0.187687i	$-0.0600989\pi$
$191$	4.54097	+	7.86519i	0.328573	+	0.569105i	−0.653656	+	0.756792i	$0.726766\pi$
$192$		0			0
$193$	−2.39413	+	4.14676i	−0.172334	+	0.298490i	−0.939235	−	0.343274i	$-0.888464\pi$
$193$	−2.39413	+	4.14676i	−0.172334	+	0.298490i	0.766902	+	0.641765i	$0.221797\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	13.4686			0.959598			0.479799	−	0.877379i	$-0.340710\pi$
$197$	13.4686			0.959598			0.479799	+	0.877379i	$0.340710\pi$
$198$		0			0
$199$	−20.5485			−1.45664			−0.728321	−	0.685236i	$-0.759699\pi$
$199$	−20.5485			−1.45664			−0.728321	+	0.685236i	$0.759699\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−1.15579	+	2.00189i	−0.0811207	+	0.140505i
$204$		0			0
$205$	11.0664	+	19.1675i	0.772909	+	1.33872i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	3.70409	+	6.41567i	0.256217	+	0.443781i
$210$		0			0
$211$	−1.88874	+	3.27140i	−0.130026	+	0.225212i	−0.923686	−	0.383149i	$-0.874840\pi$
$211$	−1.88874	+	3.27140i	−0.130026	+	0.225212i	0.793660	+	0.608361i	$0.208173\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	1.82084			0.124180
$216$		0			0
$217$	−2.71653			−0.184410
$218$		0			0
$219$		0			0
$220$		0			0
$221$	7.95056	−	13.7708i	0.534813	−	0.926323i
$222$		0			0
$223$	11.9623	+	20.7193i	0.801056	+	1.38747i	0.918922	+	0.394439i	$0.129061\pi$
$223$	11.9623	+	20.7193i	0.801056	+	1.38747i	−0.117866	+	0.993029i	$0.537605\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−2.15369	−	3.73030i	−0.142946	−	0.247589i	0.785659	−	0.618660i	$-0.212324\pi$
$227$	−2.15369	−	3.73030i	−0.142946	−	0.247589i	−0.928605	+	0.371071i	$0.878991\pi$
$228$		0			0
$229$	−3.59351	+	6.22414i	−0.237466	+	0.411303i	−0.959986	−	0.280047i	$-0.909650\pi$
$229$	−3.59351	+	6.22414i	−0.237466	+	0.411303i	0.722521	+	0.691349i	$0.242983\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	2.58221			0.169166			0.0845830	−	0.996416i	$-0.473044\pi$
$233$	2.58221			0.169166			0.0845830	+	0.996416i	$0.473044\pi$
$234$		0			0
$235$	0.283011			0.0184616
$236$		0			0
$237$		0			0
$238$		0			0
$239$	9.20903	−	15.9505i	0.595682	−	1.03175i	−0.397768	−	0.917486i	$-0.630215\pi$
$239$	9.20903	−	15.9505i	0.595682	−	1.03175i	0.993450	−	0.114266i	$-0.0364516\pi$
$240$		0			0
$241$	9.66178	+	16.7347i	0.622370	+	1.07798i	0.989043	+	0.147627i	$0.0471634\pi$
$241$	9.66178	+	16.7347i	0.622370	+	1.07798i	−0.366673	+	0.930350i	$0.619503\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−6.62207	−	11.4698i	−0.423069	−	0.732777i
$246$		0			0
$247$	−10.0677	+	17.4377i	−0.640591	+	1.10954i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−6.11394			−0.385908			−0.192954	−	0.981208i	$-0.561807\pi$
$251$	−6.11394			−0.385908			−0.192954	+	0.981208i	$0.561807\pi$
$252$		0			0
$253$	−3.26900			−0.205520
$254$		0			0
$255$		0			0
$256$		0			0
$257$	3.06330	−	5.30579i	0.191083	−	0.330966i	−0.754526	−	0.656270i	$-0.772133\pi$
$257$	3.06330	−	5.30579i	0.191083	−	0.330966i	0.945610	+	0.325304i	$0.105467\pi$
$258$		0			0
$259$	−2.41285	−	4.17918i	−0.149927	−	0.259682i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−2.39804	−	4.15353i	−0.147869	−	0.256117i	0.782570	−	0.622562i	$-0.213908\pi$
$263$	−2.39804	−	4.15353i	−0.147869	−	0.256117i	−0.930440	+	0.366445i	$0.880575\pi$
$264$		0			0
$265$	3.49812	−	6.05891i	0.214888	−	0.372196i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−17.6991			−1.07913			−0.539567	−	0.841942i	$-0.681412\pi$
$269$	−17.6991			−1.07913			−0.539567	+	0.841942i	$0.681412\pi$
$270$		0			0
$271$	8.24853			0.501063			0.250531	−	0.968108i	$-0.419395\pi$
$271$	8.24853			0.501063			0.250531	+	0.968108i	$0.419395\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−0.528023	+	0.914563i	−0.0318410	+	0.0551502i
$276$		0			0
$277$	9.50146	+	16.4570i	0.570888	+	0.988806i	0.996475	+	0.0838891i	$0.0267341\pi$
$277$	9.50146	+	16.4570i	0.570888	+	0.988806i	−0.425588	+	0.904917i	$0.639933\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	2.24819	+	3.89399i	0.134116	+	0.232296i	0.925259	−	0.379335i	$-0.123847\pi$
$281$	2.24819	+	3.89399i	0.134116	+	0.232296i	−0.791143	+	0.611631i	$0.790514\pi$
$282$		0			0
$283$	−5.43241	+	9.40921i	−0.322923	+	0.559319i	−0.981090	−	0.193553i	$-0.937999\pi$
$283$	−5.43241	+	9.40921i	−0.322923	+	0.559319i	0.658167	+	0.752872i	$0.271332\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−6.41223			−0.378502
$288$		0			0
$289$	17.2263			1.01331
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−15.3408	+	26.5711i	−0.896221	+	1.55230i	−0.0639350	+	0.997954i	$0.520365\pi$
$293$	−15.3408	+	26.5711i	−0.896221	+	1.55230i	−0.832286	+	0.554346i	$0.812968\pi$
$294$		0			0
$295$	−12.3045	−	21.3120i	−0.716394	−	1.24083i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−4.44255	−	7.69472i	−0.256919	−	0.444997i
$300$		0			0
$301$	−0.263763	+	0.456851i	−0.0152031	+	0.0263325i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	11.7101			0.670519
$306$		0			0
$307$	3.68451			0.210286			0.105143	−	0.994457i	$-0.466470\pi$
$307$	3.68451			0.210286			0.105143	+	0.994457i	$0.466470\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−0.606153	+	1.04989i	−0.0343718	+	0.0595337i	−0.882700	−	0.469938i	$-0.844276\pi$
$311$	−0.606153	+	1.04989i	−0.0343718	+	0.0595337i	0.848328	+	0.529471i	$0.177610\pi$
$312$		0			0
$313$	−7.19197	−	12.4569i	−0.406514	−	0.704104i	0.587982	−	0.808874i	$-0.299923\pi$
$313$	−7.19197	−	12.4569i	−0.406514	−	0.704104i	−0.994496	+	0.104770i	$0.966589\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	7.65481	+	13.2585i	0.429937	+	0.744673i	0.996867	−	0.0790929i	$-0.0252024\pi$
$317$	7.65481	+	13.2585i	0.429937	+	0.744673i	−0.566930	+	0.823766i	$0.691869\pi$
$318$		0			0
$319$	−2.00882	+	3.47937i	−0.112472	+	0.194807i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−43.3403			−2.41152
$324$		0			0
$325$	−2.87032			−0.159217
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−0.0409965	+	0.0710080i	−0.00226021	+	0.00391480i
$330$		0			0
$331$	4.36693	+	7.56375i	0.240028	+	0.415741i	0.960722	−	0.277512i	$-0.0895100\pi$
$331$	4.36693	+	7.56375i	0.240028	+	0.415741i	−0.720694	+	0.693254i	$0.756177\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	9.80630	+	16.9850i	0.535775	+	0.927990i
$336$		0			0
$337$	−8.91462	+	15.4406i	−0.485610	+	0.841102i	−0.999863	−	0.0165370i	$-0.994736\pi$
$337$	−8.91462	+	15.4406i	−0.485610	+	0.841102i	0.514253	+	0.857638i	$0.328069\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−4.72144			−0.255680
$342$		0			0
$343$	7.86457			0.424647
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−1.76355	+	3.05455i	−0.0946722	+	0.163977i	−0.909472	−	0.415766i	$-0.863514\pi$
$347$	−1.76355	+	3.05455i	−0.0946722	+	0.163977i	0.814800	+	0.579743i	$0.196847\pi$
$348$		0			0
$349$	4.15429	+	7.19544i	0.222374	+	0.385163i	0.955528	−	0.294899i	$-0.0952861\pi$
$349$	4.15429	+	7.19544i	0.222374	+	0.385163i	−0.733154	+	0.680062i	$0.761953\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−14.3676	−	24.8854i	−0.764710	−	1.32452i	−0.940400	−	0.340071i	$-0.889549\pi$
$353$	−14.3676	−	24.8854i	−0.764710	−	1.32452i	0.175690	−	0.984446i	$-0.443784\pi$
$354$		0			0
$355$	−9.79504	+	16.9655i	−0.519867	+	0.900435i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	9.18975			0.485017			0.242508	−	0.970149i	$-0.422030\pi$
$359$	9.18975			0.485017			0.242508	+	0.970149i	$0.422030\pi$
$360$		0			0
$361$	35.8811			1.88848
$362$		0			0
$363$		0			0
$364$		0			0
$365$	8.98630	−	15.5647i	0.470364	−	0.814695i
$366$		0			0
$367$	−15.1712	−	26.2773i	−0.791929	−	1.37166i	−0.924771	−	0.380524i	$-0.875743\pi$
$367$	−15.1712	−	26.2773i	−0.791929	−	1.37166i	0.132842	−	0.991137i	$-0.457590\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	1.01346	+	1.75537i	0.0526164	+	0.0911343i
$372$		0			0
$373$	7.38248	−	12.7868i	0.382250	−	0.662077i	−0.609133	−	0.793068i	$-0.708483\pi$
$373$	7.38248	−	12.7868i	0.382250	−	0.662077i	0.991384	+	0.130991i	$0.0418159\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−10.9199			−0.562402
$378$		0			0
$379$	−31.3491			−1.61029			−0.805147	−	0.593076i	$-0.797913\pi$
$379$	−31.3491			−1.61029			−0.805147	+	0.593076i	$0.797913\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−16.3899	+	28.3881i	−0.837485	+	1.45057i	0.0545061	+	0.998513i	$0.482642\pi$
$383$	−16.3899	+	28.3881i	−0.837485	+	1.45057i	−0.891991	+	0.452053i	$0.850692\pi$
$384$		0			0
$385$	0.571315	+	0.989546i	0.0291169	+	0.0504320i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	10.3078	+	17.8536i	0.522625	+	0.905213i	0.999653	+	0.0263255i	$0.00838063\pi$
$389$	10.3078	+	17.8536i	0.522625	+	0.905213i	−0.477028	+	0.878888i	$0.658286\pi$
$390$		0			0
$391$	9.56235	−	16.5625i	0.483589	−	0.837600i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	18.8320			0.947540
$396$		0			0
$397$	3.22545			0.161880			0.0809402	−	0.996719i	$-0.474208\pi$
$397$	3.22545			0.161880			0.0809402	+	0.996719i	$0.474208\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−6.01278	+	10.4144i	−0.300264	+	0.520072i	−0.976196	−	0.216892i	$-0.930408\pi$
$401$	−6.01278	+	10.4144i	−0.300264	+	0.520072i	0.675932	+	0.736964i	$0.263741\pi$
$402$		0			0
$403$	−6.41641	−	11.1135i	−0.319624	−	0.553605i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−4.19364	−	7.26359i	−0.207871	−	0.360043i
$408$		0			0
$409$	17.7144	−	30.6822i	0.875920	−	1.51714i	0.0201412	−	0.999797i	$-0.493588\pi$
$409$	17.7144	−	30.6822i	0.875920	−	1.51714i	0.855779	−	0.517341i	$-0.173078\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	7.12963			0.350826
$414$		0			0
$415$	11.8461			0.581502
$416$		0			0
$417$		0			0
$418$		0			0
$419$	12.6843	−	21.9698i	0.619666	−	1.07329i	−0.369880	−	0.929079i	$-0.620601\pi$
$419$	12.6843	−	21.9698i	0.619666	−	1.07329i	0.989547	−	0.144214i	$-0.0460654\pi$
$420$		0			0
$421$	−18.2225	−	31.5623i	−0.888112	−	1.53825i	−0.842105	−	0.539313i	$-0.818684\pi$
$421$	−18.2225	−	31.5623i	−0.888112	−	1.53825i	−0.0460065	−	0.998941i	$-0.514650\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−3.08911	−	5.35049i	−0.149844	−	0.259537i
$426$		0			0
$427$	−1.69631	+	2.93809i	−0.0820901	+	0.142184i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	26.9989			1.30049			0.650246	−	0.759724i	$-0.274666\pi$
$431$	26.9989			1.30049			0.650246	+	0.759724i	$0.274666\pi$
$432$		0			0
$433$	−22.1196			−1.06300			−0.531500	−	0.847058i	$-0.678372\pi$
$433$	−22.1196			−1.06300			−0.531500	+	0.847058i	$0.678372\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−12.1087	+	20.9728i	−0.579235	+	1.00326i
$438$		0			0
$439$	6.79680	+	11.7724i	0.324394	+	0.561866i	0.981389	−	0.192028i	$-0.0615064\pi$
$439$	6.79680	+	11.7724i	0.324394	+	0.561866i	−0.656996	+	0.753894i	$0.728173\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	15.4024	+	26.6778i	0.731791	+	1.26750i	0.956117	+	0.292985i	$0.0946485\pi$
$443$	15.4024	+	26.6778i	0.731791	+	1.26750i	−0.224326	+	0.974514i	$0.572018\pi$
$444$		0			0
$445$	−6.89275	+	11.9386i	−0.326748	+	0.565944i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−33.8606			−1.59798			−0.798990	−	0.601344i	$-0.794632\pi$
$449$	−33.8606			−1.59798			−0.798990	+	0.601344i	$0.794632\pi$
$450$		0			0
$451$	−11.1447			−0.524784
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−1.55283	+	2.68958i	−0.0727977	+	0.126089i
$456$		0			0
$457$	0.624561	+	1.08177i	0.0292157	+	0.0506032i	0.880264	−	0.474485i	$-0.157366\pi$
$457$	0.624561	+	1.08177i	0.0292157	+	0.0506032i	−0.851048	+	0.525088i	$0.824032\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−16.2617	−	28.1661i	−0.757383	−	1.31183i	−0.944181	−	0.329427i	$-0.893144\pi$
$461$	−16.2617	−	28.1661i	−0.757383	−	1.31183i	0.186798	−	0.982398i	$-0.440189\pi$
$462$		0			0
$463$	16.3591	−	28.3349i	0.760274	−	1.31683i	−0.182435	−	0.983218i	$-0.558398\pi$
$463$	16.3591	−	28.3349i	0.760274	−	1.31683i	0.942709	−	0.333616i	$-0.108269\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	27.1398			1.25588			0.627940	−	0.778261i	$-0.283898\pi$
$467$	27.1398			1.25588			0.627940	+	0.778261i	$0.283898\pi$
$468$		0			0
$469$	−5.68210			−0.262375
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−0.458432	+	0.794027i	−0.0210787	+	0.0365094i
$474$		0			0
$475$	3.91169	+	6.77524i	0.179481	+	0.310870i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	3.37649	+	5.84825i	0.154276	+	0.267213i	0.932795	−	0.360407i	$-0.117362\pi$
$479$	3.37649	+	5.84825i	0.154276	+	0.267213i	−0.778519	+	0.627621i	$0.784029\pi$
$480$		0			0
$481$	11.3983	−	19.7424i	0.519716	−	0.900174i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	37.5386			1.70454
$486$		0			0
$487$	−3.85480			−0.174678			−0.0873388	−	0.996179i	$-0.527836\pi$
$487$	−3.85480			−0.174678			−0.0873388	+	0.996179i	$0.527836\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−8.72854	+	15.1183i	−0.393913	+	0.682278i	−0.992962	−	0.118435i	$-0.962212\pi$
$491$	−8.72854	+	15.1183i	−0.393913	+	0.682278i	0.599048	+	0.800713i	$0.295546\pi$
$492$		0			0
$493$	−11.7522	−	20.3555i	−0.529294	−	0.916763i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−2.83779	−	4.91519i	−0.127292	−	0.220476i
$498$		0			0
$499$	−7.98731	+	13.8344i	−0.357561	+	0.619314i	−0.987553	−	0.157288i	$-0.949725\pi$
$499$	−7.98731	+	13.8344i	−0.357561	+	0.619314i	0.629992	+	0.776602i	$0.283058\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−32.9141			−1.46757			−0.733784	−	0.679383i	$-0.762248\pi$
$503$	−32.9141			−1.46757			−0.733784	+	0.679383i	$0.762248\pi$
$504$		0			0
$505$	−5.90881			−0.262939
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−17.8081	+	30.8446i	−0.789332	+	1.36716i	0.137045	+	0.990565i	$0.456240\pi$
$509$	−17.8081	+	30.8446i	−0.789332	+	1.36716i	−0.926377	+	0.376598i	$0.877094\pi$
$510$		0			0
$511$	2.60348	+	4.50936i	0.115171	+	0.199483i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	12.0044	+	20.7922i	0.528977	+	0.916215i
$516$		0			0
$517$	−0.0712536	+	0.123415i	−0.00313373	+	0.00542778i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−11.4481			−0.501552			−0.250776	−	0.968045i	$-0.580686\pi$
$521$	−11.4481			−0.501552			−0.250776	+	0.968045i	$0.580686\pi$
$522$		0			0
$523$	−33.9589			−1.48492			−0.742460	−	0.669890i	$-0.766341\pi$
$523$	−33.9589			−1.48492			−0.742460	+	0.669890i	$0.766341\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	13.8110	−	23.9213i	0.601615	−	1.04203i
$528$		0			0
$529$	6.15683	+	10.6639i	0.267688	+	0.463650i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−15.1456	−	26.2330i	−0.656030	−	1.13628i
$534$		0			0
$535$	−12.4982	+	21.6475i	−0.540345	+	0.935904i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	6.66896			0.287252
$540$		0			0
$541$	23.0541			0.991174			0.495587	−	0.868558i	$-0.334953\pi$
$541$	23.0541			0.991174			0.495587	+	0.868558i	$0.334953\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	8.14299	−	14.1041i	0.348807	−	0.604152i
$546$		0			0
$547$	−8.41476	−	14.5748i	−0.359789	−	0.623173i	0.628136	−	0.778103i	$-0.283818\pi$
$547$	−8.41476	−	14.5748i	−0.359789	−	0.623173i	−0.987925	+	0.154930i	$0.950485\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	14.8817	+	25.7758i	0.633980	+	1.09809i
$552$		0			0
$553$	−2.72797	+	4.72498i	−0.116005	+	0.200927i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	5.61763			0.238026			0.119013	−	0.992893i	$-0.462027\pi$
$557$	5.61763			0.238026			0.119013	+	0.992893i	$0.462027\pi$
$558$		0			0
$559$	−2.49203			−0.105401
$560$		0			0
$561$		0			0
$562$		0			0
$563$	13.5847	−	23.5293i	0.572525	−	0.991643i	−0.423780	−	0.905765i	$-0.639297\pi$
$563$	13.5847	−	23.5293i	0.572525	−	0.991643i	0.996306	−	0.0858780i	$-0.0273695\pi$
$564$		0			0
$565$	−6.94498	−	12.0291i	−0.292177	−	0.506066i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−14.3601	−	24.8724i	−0.602006	−	1.04270i	−0.992517	−	0.122106i	$-0.961035\pi$
$569$	−14.3601	−	24.8724i	−0.602006	−	1.04270i	0.390512	−	0.920598i	$-0.372298\pi$
$570$		0			0
$571$	5.21946	−	9.04037i	0.218428	−	0.378328i	−0.735900	−	0.677090i	$-0.763241\pi$
$571$	5.21946	−	9.04037i	0.218428	−	0.378328i	0.954327	+	0.298763i	$0.0965739\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−3.45221			−0.143967
$576$		0			0
$577$	26.3489			1.09692			0.548459	−	0.836177i	$-0.315215\pi$
$577$	26.3489			1.09692			0.548459	+	0.836177i	$0.315215\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−1.71601	+	2.97221i	−0.0711919	+	0.123308i
$582$		0			0
$583$	1.76144	+	3.05091i	0.0729515	+	0.126356i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−7.99910	−	13.8548i	−0.330158	−	0.571851i	0.652384	−	0.757888i	$-0.273769\pi$
$587$	−7.99910	−	13.8548i	−0.330158	−	0.571851i	−0.982543	+	0.186037i	$0.940435\pi$
$588$		0			0
$589$	−17.4886	+	30.2912i	−0.720606	+	1.24813i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	15.4966			0.636370			0.318185	−	0.948029i	$-0.396927\pi$
$593$	15.4966			0.636370			0.318185	+	0.948029i	$0.396927\pi$
$594$		0			0
$595$	−6.68476			−0.274048
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−2.39957	+	4.15618i	−0.0980438	+	0.169817i	−0.910875	−	0.412683i	$-0.864592\pi$
$599$	−2.39957	+	4.15618i	−0.0980438	+	0.169817i	0.812831	+	0.582499i	$0.197925\pi$
$600$		0			0
$601$	−3.71317	−	6.43141i	−0.151464	−	0.262343i	0.780302	−	0.625403i	$-0.215065\pi$
$601$	−3.71317	−	6.43141i	−0.151464	−	0.262343i	−0.931766	+	0.363060i	$0.881732\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	0.992970	+	1.71987i	0.0403700	+	0.0699228i
$606$		0			0
$607$	20.2661	−	35.1019i	0.822576	−	1.42474i	−0.0811815	−	0.996699i	$-0.525869\pi$
$607$	20.2661	−	35.1019i	0.822576	−	1.42474i	0.903758	−	0.428044i	$-0.140797\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−0.387333			−0.0156698
$612$		0			0
$613$	−0.298767			−0.0120671			−0.00603355	−	0.999982i	$-0.501921\pi$
$613$	−0.298767			−0.0120671			−0.00603355	+	0.999982i	$0.501921\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	16.3567	−	28.3307i	0.658498	−	1.14055i	−0.322507	−	0.946567i	$-0.604526\pi$
$617$	16.3567	−	28.3307i	0.658498	−	1.14055i	0.981005	−	0.193984i	$-0.0621411\pi$
$618$		0			0
$619$	−11.3415	−	19.6440i	−0.455853	−	0.789561i	0.542884	−	0.839808i	$-0.317332\pi$
$619$	−11.3415	−	19.6440i	−0.455853	−	0.789561i	−0.998737	+	0.0502473i	$0.983999\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−1.99695	−	3.45881i	−0.0800059	−	0.138574i
$624$		0			0
$625$	9.30227	−	16.1120i	0.372091	−	0.644480i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	49.0683			1.95648
$630$		0			0
$631$	−21.0600			−0.838385			−0.419192	−	0.907897i	$-0.637687\pi$
$631$	−21.0600			−0.838385			−0.419192	+	0.907897i	$0.637687\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−15.3299	+	26.5521i	−0.608347	+	1.05369i
$636$		0			0
$637$	9.06308	+	15.6977i	0.359092	+	0.621966i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−12.9476	−	22.4260i	−0.511401	−	0.885773i	−0.999913	−	0.0132153i	$-0.995793\pi$
$641$	−12.9476	−	22.4260i	−0.511401	−	0.885773i	0.488512	−	0.872557i	$-0.337540\pi$
$642$		0			0
$643$	−0.458209	+	0.793641i	−0.0180700	+	0.0312982i	−0.874919	−	0.484269i	$-0.839086\pi$
$643$	−0.458209	+	0.793641i	−0.0180700	+	0.0312982i	0.856849	+	0.515567i	$0.172419\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−26.2401			−1.03160			−0.515802	−	0.856708i	$-0.672506\pi$
$647$	−26.2401			−1.03160			−0.515802	+	0.856708i	$0.672506\pi$
$648$		0			0
$649$	12.3916			0.486413
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−3.52936	+	6.11303i	−0.138115	+	0.239221i	−0.926783	−	0.375597i	$-0.877438\pi$
$653$	−3.52936	+	6.11303i	−0.138115	+	0.239221i	0.788668	+	0.614819i	$0.210771\pi$
$654$		0			0
$655$	−14.4089	−	24.9569i	−0.563002	−	0.975147i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−16.7964	−	29.0922i	−0.654295	−	1.13327i	−0.982070	−	0.188517i	$-0.939632\pi$
$659$	−16.7964	−	29.0922i	−0.654295	−	1.13327i	0.327775	−	0.944756i	$-0.393701\pi$
$660$		0			0
$661$	1.92307	−	3.33085i	0.0747987	−	0.129555i	−0.826200	−	0.563377i	$-0.809502\pi$
$661$	1.92307	−	3.33085i	0.0747987	−	0.129555i	0.900999	+	0.433822i	$0.142835\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	8.46481			0.328251
$666$		0			0
$667$	−13.1336			−0.508536
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−2.94826	+	5.10653i	−0.113816	+	0.197135i
$672$		0			0
$673$	6.28919	+	10.8932i	0.242430	+	0.419902i	0.961406	−	0.275134i	$-0.0887221\pi$
$673$	6.28919	+	10.8932i	0.242430	+	0.419902i	−0.718976	+	0.695035i	$0.755389\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−9.58970	−	16.6098i	−0.368562	−	0.638368i	0.620779	−	0.783986i	$-0.286816\pi$
$677$	−9.58970	−	16.6098i	−0.368562	−	0.638368i	−0.989341	+	0.145617i	$0.953483\pi$
$678$		0			0
$679$	−5.43778	+	9.41851i	−0.208683	+	0.361449i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	38.6508			1.47893			0.739466	−	0.673194i	$-0.235078\pi$
$683$	38.6508			1.47893			0.739466	+	0.673194i	$0.235078\pi$
$684$		0			0
$685$	0.877443			0.0335254
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−4.78758	+	8.29233i	−0.182392	+	0.315913i
$690$		0			0
$691$	−3.39764	−	5.88489i	−0.129252	−	0.223872i	0.794135	−	0.607742i	$-0.207924\pi$
$691$	−3.39764	−	5.88489i	−0.129252	−	0.223872i	−0.923387	+	0.383870i	$0.874591\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−14.3592	−	24.8708i	−0.544674	−	0.943404i
$696$		0			0
$697$	32.6001	−	56.4651i	1.23482	−	2.13877i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	3.22013			0.121623			0.0608113	−	0.998149i	$-0.480631\pi$
$701$	3.22013			0.121623			0.0608113	+	0.998149i	$0.480631\pi$
$702$		0			0
$703$	−62.1344			−2.34344
$704$		0			0
$705$		0			0
$706$		0			0
$707$	0.855942	−	1.48253i	0.0321910	−	0.0557564i
$708$		0			0
$709$	−12.7774	−	22.1310i	−0.479864	−	0.831148i	0.519870	−	0.854246i	$-0.325981\pi$
$709$	−12.7774	−	22.1310i	−0.479864	−	0.831148i	−0.999733	+	0.0230975i	$0.992647\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−7.71718	−	13.3665i	−0.289011	−	0.500581i
$714$		0			0
$715$	−2.69888	+	4.67460i	−0.100932	+	0.174820i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	27.5706			1.02821			0.514105	−	0.857727i	$-0.328124\pi$
$719$	27.5706			1.02821			0.514105	+	0.857727i	$0.328124\pi$
$720$		0			0
$721$	−6.95575			−0.259046
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−2.12140	+	3.67438i	−0.0787869	+	0.136463i
$726$		0			0
$727$	−22.4154	−	38.8246i	−0.831341	−	1.43992i	−0.896975	−	0.442081i	$-0.854240\pi$
$727$	−22.4154	−	38.8246i	−0.831341	−	1.43992i	0.0656340	−	0.997844i	$-0.479093\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−2.68198	−	4.64532i	−0.0991964	−	0.171813i
$732$		0			0
$733$	3.89848	−	6.75237i	0.143994	−	0.249405i	−0.785003	−	0.619492i	$-0.787339\pi$
$733$	3.89848	−	6.75237i	0.143994	−	0.249405i	0.928997	+	0.370087i	$0.120672\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−9.87573			−0.363777
$738$		0			0
$739$	−42.7823			−1.57377			−0.786886	−	0.617098i	$-0.788308\pi$
$739$	−42.7823			−1.57377			−0.786886	+	0.617098i	$0.788308\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	17.7375	−	30.7222i	0.650724	−	1.12709i	−0.332223	−	0.943201i	$-0.607799\pi$
$743$	17.7375	−	30.7222i	0.650724	−	1.12709i	0.982947	−	0.183887i	$-0.0588680\pi$
$744$		0			0
$745$	−17.4629	−	30.2466i	−0.639791	−	1.10815i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−3.62094	−	6.27165i	−0.132306	−	0.229161i
$750$		0			0
$751$	21.2764	−	36.8517i	0.776385	−	1.34474i	−0.157628	−	0.987499i	$-0.550385\pi$
$751$	21.2764	−	36.8517i	0.776385	−	1.34474i	0.934013	−	0.357240i	$-0.116282\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−11.1822			−0.406963
$756$		0			0
$757$	47.2389			1.71693			0.858464	−	0.512874i	$-0.171419\pi$
$757$	47.2389			1.71693			0.858464	+	0.512874i	$0.171419\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	1.07908	−	1.86902i	0.0391165	−	0.0677518i	−0.845804	−	0.533493i	$-0.820879\pi$
$761$	1.07908	−	1.86902i	0.0391165	−	0.0677518i	0.884921	+	0.465741i	$0.154212\pi$
$762$		0			0
$763$	2.35916	+	4.08619i	0.0854074	+	0.147930i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	16.8401	+	29.1679i	0.608061	+	1.05319i
$768$		0			0
$769$	22.1773	−	38.4122i	0.799733	−	1.38518i	−0.120056	−	0.992767i	$-0.538307\pi$
$769$	22.1773	−	38.4122i	0.799733	−	1.38518i	0.919790	−	0.392412i	$-0.128359\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	48.5617			1.74664			0.873322	−	0.487143i	$-0.161961\pi$
$773$	48.5617			1.74664			0.873322	+	0.487143i	$0.161961\pi$
$774$		0			0
$775$	−4.98606			−0.179104
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−41.2810	+	71.5009i	−1.47905	+	2.56178i
$780$		0			0
$781$	−4.93219	−	8.54281i	−0.176488	−	0.305686i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−2.34403	−	4.05998i	−0.0836620	−	0.144907i
$786$		0			0
$787$	20.7367	−	35.9170i	0.739182	−	1.28030i	−0.213682	−	0.976903i	$-0.568545\pi$
$787$	20.7367	−	35.9170i	0.739182	−	1.28030i	0.952864	−	0.303398i	$-0.0981212\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	4.02416			0.143082
$792$		0			0
$793$	−16.0267			−0.569123
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−14.1627	+	24.5306i	−0.501669	+	0.868917i	0.498329	+	0.866988i	$0.333947\pi$
$797$	−14.1627	+	24.5306i	−0.501669	+	0.868917i	−0.999998	+	0.00192869i	$0.999386\pi$
$798$		0			0
$799$	−0.416857	−	0.722017i	−0.0147473	−	0.0255431i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	4.52496	+	7.83747i	0.159682	+	0.276578i
$804$		0			0
$805$	−1.86763	+	3.23482i	−0.0658252	+	0.114013i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	26.4597			0.930274			0.465137	−	0.885239i	$-0.346005\pi$
$809$	26.4597			0.930274			0.465137	+	0.885239i	$0.346005\pi$
$810$		0			0
$811$	−3.34212			−0.117358			−0.0586789	−	0.998277i	$-0.518689\pi$
$811$	−3.34212			−0.117358			−0.0586789	+	0.998277i	$0.518689\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	6.95807	−	12.0517i	0.243731	−	0.422154i
$816$		0			0
$817$	3.39614	+	5.88229i	0.118816	+	0.205795i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−5.80722	−	10.0584i	−0.202673	−	0.351041i	0.746716	−	0.665144i	$-0.231630\pi$
$821$	−5.80722	−	10.0584i	−0.202673	−	0.351041i	−0.949389	+	0.314103i	$0.898296\pi$
$822$		0			0
$823$	−10.7425	+	18.6066i	−0.374461	+	0.648586i	−0.990246	−	0.139329i	$-0.955506\pi$
$823$	−10.7425	+	18.6066i	−0.374461	+	0.648586i	0.615785	+	0.787914i	$0.288839\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−43.3480			−1.50736			−0.753678	−	0.657244i	$-0.771722\pi$
$827$	−43.3480			−1.50736			−0.753678	+	0.657244i	$0.771722\pi$
$828$		0			0
$829$	25.6941			0.892393			0.446196	−	0.894935i	$-0.352778\pi$
$829$	25.6941			0.892393			0.446196	+	0.894935i	$0.352778\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−19.5078	+	33.7885i	−0.675905	+	1.17070i
$834$		0			0
$835$	6.81522	+	11.8043i	0.235851	+	0.408505i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	8.40978	+	14.5662i	0.290338	+	0.502880i	0.973890	−	0.227022i	$-0.0728990\pi$
$839$	8.40978	+	14.5662i	0.290338	+	0.502880i	−0.683552	+	0.729902i	$0.739566\pi$
$840$		0			0
$841$	6.42932	−	11.1359i	0.221701	−	0.383997i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	11.1461			0.383439
$846$		0			0
$847$	−0.575360			−0.0197696
$848$		0			0
$849$		0			0
$850$		0			0
$851$	13.7090	−	23.7446i	0.469938	−	0.813956i
$852$		0			0
$853$	19.8073	+	34.3072i	0.678187	+	1.17465i	0.975526	+	0.219883i	$0.0705675\pi$
$853$	19.8073	+	34.3072i	0.678187	+	1.17465i	−0.297339	+	0.954772i	$0.596099\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	3.54068	+	6.13264i	0.120947	+	0.209487i	0.920142	−	0.391586i	$-0.128073\pi$
$857$	3.54068	+	6.13264i	0.120947	+	0.209487i	−0.799194	+	0.601073i	$0.794740\pi$
$858$		0			0
$859$	−2.33555	+	4.04529i	−0.0796879	+	0.138023i	−0.903115	−	0.429398i	$-0.858726\pi$
$859$	−2.33555	+	4.04529i	−0.0796879	+	0.138023i	0.823427	+	0.567422i	$0.192059\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−3.72380			−0.126760			−0.0633798	−	0.997989i	$-0.520188\pi$
$863$	−3.72380			−0.126760			−0.0633798	+	0.997989i	$0.520188\pi$
$864$		0			0
$865$	24.7687			0.842162
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−4.74133	+	8.21222i	−0.160839	+	0.278581i
$870$		0			0
$871$	−13.4211	−	23.2460i	−0.454755	−	0.787659i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	3.45991	+	5.99274i	0.116966	+	0.202592i
$876$		0			0
$877$	−13.3581	+	23.1369i	−0.451071	+	0.781278i	−0.998453	−	0.0556050i	$-0.982291\pi$
$877$	−13.3581	+	23.1369i	−0.451071	+	0.781278i	0.547382	+	0.836883i	$0.315625\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−21.8872			−0.737400			−0.368700	−	0.929548i	$-0.620197\pi$
$881$	−21.8872			−0.737400			−0.368700	+	0.929548i	$0.620197\pi$
$882$		0			0
$883$	−0.675656			−0.0227376			−0.0113688	−	0.999935i	$-0.503619\pi$
$883$	−0.675656			−0.0227376			−0.0113688	+	0.999935i	$0.503619\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	17.8271	−	30.8774i	0.598574	−	1.03676i	−0.394458	−	0.918914i	$-0.629068\pi$
$887$	17.8271	−	30.8774i	0.598574	−	1.03676i	0.993032	−	0.117847i	$-0.0375991\pi$
$888$		0			0
$889$	−4.44132	−	7.69259i	−0.148957	−	0.258001i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	0.527859	+	0.914279i	0.0176641	+	0.0305952i
$894$		0			0
$895$	−4.83627	+	8.37666i	−0.161659	+	0.280001i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−18.9690			−0.632651
$900$		0			0
$901$	−20.6100			−0.686619
$902$		0			0
$903$		0			0
$904$		0			0
$905$	14.9208	−	25.8436i	0.495984	−	0.859070i
$906$		0			0
$907$	−16.3495	−	28.3182i	−0.542877	−	0.940290i	−0.998737	−	0.0502390i	$-0.984002\pi$
$907$	−16.3495	−	28.3182i	−0.542877	−	0.940290i	0.455860	−	0.890051i	$-0.349332\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	1.50025	+	2.59851i	0.0497055	+	0.0860925i	0.889808	−	0.456336i	$-0.150838\pi$
$911$	1.50025	+	2.59851i	0.0497055	+	0.0860925i	−0.840102	+	0.542428i	$0.817505\pi$
$912$		0			0
$913$	−2.98249	+	5.16583i	−0.0987061	+	0.170964i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	8.34899			0.275708
$918$		0			0
$919$	22.2784			0.734895			0.367447	−	0.930044i	$-0.380232\pi$
$919$	22.2784			0.734895			0.367447	+	0.930044i	$0.380232\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	13.4057	−	23.2193i	0.441252	−	0.764272i
$924$		0			0
$925$	−4.42867	−	7.67069i	−0.145614	−	0.252211i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	25.1665	+	43.5897i	0.825687	+	1.43013i	0.901393	+	0.433001i	$0.142545\pi$
$929$	25.1665	+	43.5897i	0.825687	+	1.43013i	−0.0757069	+	0.997130i	$0.524121\pi$
$930$		0			0
$931$	24.7024	−	42.7859i	0.809589	−	1.40225i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−11.6184			−0.379962
$936$		0			0
$937$	−31.9868			−1.04496			−0.522482	−	0.852651i	$-0.674994\pi$
$937$	−31.9868			−1.04496			−0.522482	+	0.852651i	$0.674994\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−5.91271	+	10.2411i	−0.192749	+	0.333851i	−0.946160	−	0.323699i	$-0.895074\pi$
$941$	−5.91271	+	10.2411i	−0.192749	+	0.333851i	0.753411	+	0.657549i	$0.228407\pi$
$942$		0			0
$943$	−18.2160	−	31.5511i	−0.593195	−	1.02744i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−14.8511	−	25.7228i	−0.482595	−	0.835879i	0.517205	−	0.855861i	$-0.326972\pi$
$947$	−14.8511	−	25.7228i	−0.482595	−	0.835879i	−0.999800	+	0.0199821i	$0.993639\pi$
$948$		0			0
$949$	−12.2988	+	21.3022i	−0.399236	+	0.691497i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	50.8712			1.64788			0.823939	−	0.566678i	$-0.191772\pi$
$953$	50.8712			1.64788			0.823939	+	0.566678i	$0.191772\pi$
$954$		0			0
$955$	18.0362			0.583637
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−0.127105	+	0.220152i	−0.00410444	+	0.00710909i
$960$		0			0
$961$	4.35402	+	7.54138i	0.140452	+	0.243270i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	4.75460	+	8.23522i	0.153056	+	0.265101i
$966$		0			0
$967$	10.3609	−	17.9457i	0.333185	−	0.577094i	−0.649949	−	0.759978i	$-0.725210\pi$
$967$	10.3609	−	17.9457i	0.333185	−	0.577094i	0.983135	+	0.182884i	$0.0585432\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−0.799831			−0.0256678			−0.0128339	−	0.999918i	$-0.504085\pi$
$971$	−0.799831			−0.0256678			−0.0128339	+	0.999918i	$0.504085\pi$
$972$		0			0
$973$	8.32019			0.266733
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−11.9743	+	20.7402i	−0.383093	+	0.663536i	−0.991503	−	0.130087i	$-0.958474\pi$
$977$	−11.9743	+	20.7402i	−0.383093	+	0.663536i	0.608410	+	0.793623i	$0.291808\pi$
$978$		0			0
$979$	−3.47078	−	6.01156i	−0.110926	−	0.192130i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−17.6877	−	30.6359i	−0.564149	−	0.977135i	−0.997128	−	0.0757311i	$-0.975871\pi$
$983$	−17.6877	−	30.6359i	−0.564149	−	0.977135i	0.432979	−	0.901404i	$-0.357462\pi$
$984$		0			0
$985$	13.3739	−	23.1643i	0.426128	−	0.738075i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−2.99722			−0.0953061
$990$		0			0
$991$	−17.9943			−0.571607			−0.285804	−	0.958288i	$-0.592261\pi$
$991$	−17.9943			−0.571607			−0.285804	+	0.958288i	$0.592261\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−20.4040	+	35.3407i	−0.646850	+	1.12038i
$996$		0			0
$997$	5.19303	+	8.99459i	0.164465	+	0.284861i	0.936465	−	0.350761i	$-0.114077\pi$
$997$	5.19303	+	8.99459i	0.164465	+	0.284861i	−0.772000	+	0.635622i	$0.780744\pi$
$998$		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.2377.5		12
3.2	odd	2		3564.2.i.s.2377.2		12
9.2	odd	6		3564.2.i.s.1189.2		12
9.4	even	3		3564.2.a.o.1.2	✓	6
9.5	odd	6		3564.2.a.p.1.5	yes	6
9.7	even	3	inner	3564.2.i.t.1189.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3564.2.a.o.1.2	✓	6	9.4	even	3
3564.2.a.p.1.5	yes	6	9.5	odd	6
3564.2.i.s.1189.2		12	9.2	odd	6
3564.2.i.s.2377.2		12	3.2	odd	2
3564.2.i.t.1189.5		12	9.7	even	3	inner
3564.2.i.t.2377.5		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)

\(f(q)\)	\(=\)	\(q+(0.992970 - 1.71987i) q^{5} +(0.287680 + 0.498276i) q^{7} +O(q^{10})\)	\(q+(0.992970 - 1.71987i) q^{5} +(0.287680 + 0.498276i) q^{7} +(0.500000 + 0.866025i) q^{11} +(-1.35899 + 2.35385i) q^{13} -5.85033 q^{17} +7.40818 q^{19} +(-1.63450 + 2.83103i) q^{23} +(0.528023 + 0.914563i) q^{25} +(2.00882 + 3.47937i) q^{29} +(-2.36072 + 4.08888i) q^{31} +1.14263 q^{35} -8.38727 q^{37} +(-5.57236 + 9.65161i) q^{41} +(0.458432 + 0.794027i) q^{43} +(0.0712536 + 0.123415i) q^{47} +(3.33448 - 5.77549i) q^{49} +3.52288 q^{53} +1.98594 q^{55} +(6.19580 - 10.7314i) q^{59} +(2.94826 + 5.10653i) q^{61} +(2.69888 + 4.67460i) q^{65} +(-4.93786 + 8.55263i) q^{67} -9.86439 q^{71} +9.04993 q^{73} +(-0.287680 + 0.498276i) q^{77} +(4.74133 + 8.21222i) q^{79} +(2.98249 + 5.16583i) q^{83} +(-5.80920 + 10.0618i) q^{85} -6.94155 q^{89} -1.56382 q^{91} +(7.35610 - 12.7411i) q^{95} +(9.45109 + 16.3698i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{7}+O(q^{10}) \) 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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