LMFDB - Embedded newform 3564.2.i.t.1189.4

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			1189.4
Root			$0.0374740 + 0.0374740i$ of defining polynomial
Character	$\chi$	$=$	3564.1189
Dual form			3564.2.i.t.2377.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0511904 + 0.0886644i) q^{5} +(-1.64629 + 2.85145i) q^{7} +O(q^{10})$	$q+(0.0511904 + 0.0886644i) q^{5} +(-1.64629 + 2.85145i) q^{7} +(0.500000 - 0.866025i) q^{11} +(1.31483 + 2.27736i) q^{13} -4.21763 q^{17} +4.73034 q^{19} +(1.31774 + 2.28238i) q^{23} +(2.49476 - 4.32105i) q^{25} +(4.68934 - 8.12217i) q^{29} +(2.66629 + 4.61814i) q^{31} -0.337096 q^{35} -4.31421 q^{37} +(4.53607 + 7.85670i) q^{41} +(0.811855 - 1.40617i) q^{43} +(-4.76053 + 8.24547i) q^{47} +(-1.92052 - 3.32644i) q^{49} -0.801039 q^{53} +0.102381 q^{55} +(-2.50793 - 4.34386i) q^{59} +(-7.60225 + 13.1675i) q^{61} +(-0.134614 + 0.233158i) q^{65} +(2.21833 + 3.84227i) q^{67} -10.1152 q^{71} -7.68143 q^{73} +(1.64629 + 2.85145i) q^{77} +(-4.81845 + 8.34581i) q^{79} +(5.80529 - 10.0550i) q^{83} +(-0.215902 - 0.373953i) q^{85} +1.65414 q^{89} -8.65838 q^{91} +(0.242148 + 0.419413i) q^{95} +(-8.72924 + 15.1195i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/3564\mathbb{Z}\right)^\times$.

$n$	$1541$	$1783$	$2917$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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
$5$	0.0511904	+	0.0886644i	0.0228931	+	0.0396519i	0.877245	−	0.480043i	$-0.159379\pi$
$5$	0.0511904	+	0.0886644i	0.0228931	+	0.0396519i	−0.854352	+	0.519695i	$0.826046\pi$
$6$		0			0
$7$	−1.64629	+	2.85145i	−0.622238	+	1.07775i	0.366830	+	0.930288i	$0.380443\pi$
$7$	−1.64629	+	2.85145i	−0.622238	+	1.07775i	−0.989068	+	0.147460i	$0.952890\pi$
$8$		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
$13$	1.31483	+	2.27736i	0.364670	+	0.631626i	0.988723	−	0.149755i	$-0.0478486\pi$
$13$	1.31483	+	2.27736i	0.364670	+	0.631626i	−0.624053	+	0.781382i	$0.714515\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−4.21763			−1.02292			−0.511462	−	0.859306i	$-0.670896\pi$
$17$	−4.21763			−1.02292			−0.511462	+	0.859306i	$0.670896\pi$
$18$		0			0
$19$	4.73034			1.08521			0.542607	−	0.839987i	$-0.317437\pi$
$19$	4.73034			1.08521			0.542607	+	0.839987i	$0.317437\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.31774	+	2.28238i	0.274767	+	0.475910i	0.970076	−	0.242800i	$-0.0780660\pi$
$23$	1.31774	+	2.28238i	0.274767	+	0.475910i	−0.695309	+	0.718710i	$0.744733\pi$
$24$		0			0
$25$	2.49476	−	4.32105i	0.498952	−	0.864210i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	4.68934	−	8.12217i	0.870788	−	1.50825i	0.00960471	−	0.999954i	$-0.496943\pi$
$29$	4.68934	−	8.12217i	0.870788	−	1.50825i	0.861183	−	0.508295i	$-0.169724\pi$
$30$		0			0
$31$	2.66629	+	4.61814i	0.478879	+	0.829443i	0.999707	−	0.0242187i	$-0.00770981\pi$
$31$	2.66629	+	4.61814i	0.478879	+	0.829443i	−0.520827	+	0.853662i	$0.674376\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.337096			−0.0569797
$36$		0			0
$37$	−4.31421			−0.709251			−0.354626	−	0.935008i	$-0.615392\pi$
$37$	−4.31421			−0.709251			−0.354626	+	0.935008i	$0.615392\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	4.53607	+	7.85670i	0.708415	+	1.22701i	0.965445	+	0.260607i	$0.0839228\pi$
$41$	4.53607	+	7.85670i	0.708415	+	1.22701i	−0.257030	+	0.966403i	$0.582744\pi$
$42$		0			0
$43$	0.811855	−	1.40617i	0.123807	−	0.214440i	−0.797459	−	0.603373i	$-0.793823\pi$
$43$	0.811855	−	1.40617i	0.123807	−	0.214440i	0.921266	+	0.388933i	$0.127156\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−4.76053	+	8.24547i	−0.694394	+	1.20273i	0.275990	+	0.961160i	$0.410994\pi$
$47$	−4.76053	+	8.24547i	−0.694394	+	1.20273i	−0.970384	+	0.241566i	$0.922339\pi$
$48$		0			0
$49$	−1.92052	−	3.32644i	−0.274360	−	0.475205i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−0.801039			−0.110031			−0.0550156	−	0.998485i	$-0.517521\pi$
$53$	−0.801039			−0.110031			−0.0550156	+	0.998485i	$0.517521\pi$
$54$		0			0
$55$	0.102381			0.0138050
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−2.50793	−	4.34386i	−0.326504	−	0.565522i	0.655311	−	0.755359i	$-0.272537\pi$
$59$	−2.50793	−	4.34386i	−0.326504	−	0.565522i	−0.981816	+	0.189837i	$0.939204\pi$
$60$		0			0
$61$	−7.60225	+	13.1675i	−0.973368	+	1.68592i	−0.288149	+	0.957586i	$0.593040\pi$
$61$	−7.60225	+	13.1675i	−0.973368	+	1.68592i	−0.685219	+	0.728337i	$0.740293\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−0.134614	+	0.233158i	−0.0166968	+	0.0289197i
$66$		0			0
$67$	2.21833	+	3.84227i	0.271013	+	0.469408i	0.969121	−	0.246584i	$-0.0793081\pi$
$67$	2.21833	+	3.84227i	0.271013	+	0.469408i	−0.698109	+	0.715992i	$0.745975\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−10.1152			−1.20046			−0.600229	−	0.799828i	$-0.704924\pi$
$71$	−10.1152			−1.20046			−0.600229	+	0.799828i	$0.704924\pi$
$72$		0			0
$73$	−7.68143			−0.899044			−0.449522	−	0.893269i	$-0.648406\pi$
$73$	−7.68143			−0.899044			−0.449522	+	0.893269i	$0.648406\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.64629	+	2.85145i	0.187612	+	0.324953i
$78$		0			0
$79$	−4.81845	+	8.34581i	−0.542118	+	0.938977i	0.456664	+	0.889639i	$0.349044\pi$
$79$	−4.81845	+	8.34581i	−0.542118	+	0.938977i	−0.998782	+	0.0493373i	$0.984289\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	5.80529	−	10.0550i	0.637213	−	1.10369i	−0.348829	−	0.937186i	$-0.613421\pi$
$83$	5.80529	−	10.0550i	0.637213	−	1.10369i	0.986042	−	0.166499i	$-0.0532461\pi$
$84$		0			0
$85$	−0.215902	−	0.373953i	−0.0234179	−	0.0405609i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	1.65414			0.175338			0.0876690	−	0.996150i	$-0.472058\pi$
$89$	1.65414			0.175338			0.0876690	+	0.996150i	$0.472058\pi$
$90$		0			0
$91$	−8.65838			−0.907645
$92$		0			0
$93$		0			0
$94$		0			0
$95$	0.242148	+	0.419413i	0.0248439	+	0.0430308i
$96$		0			0
$97$	−8.72924	+	15.1195i	−0.886320	+	1.53515i	−0.0421273	+	0.999112i	$0.513414\pi$
$97$	−8.72924	+	15.1195i	−0.886320	+	1.53515i	−0.844193	+	0.536039i	$0.819920\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	2.74907	−	4.76153i	0.273543	−	0.473790i	−0.696224	−	0.717825i	$-0.745138\pi$
$101$	2.74907	−	4.76153i	0.273543	−	0.473790i	0.969766	+	0.244035i	$0.0784711\pi$
$102$		0			0
$103$	7.71905	+	13.3698i	0.760581	+	1.31736i	0.942552	+	0.334061i	$0.108419\pi$
$103$	7.71905	+	13.3698i	0.760581	+	1.31736i	−0.181971	+	0.983304i	$0.558248\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	5.84449			0.565008			0.282504	−	0.959266i	$-0.408835\pi$
$107$	5.84449			0.565008			0.282504	+	0.959266i	$0.408835\pi$
$108$		0			0
$109$	−16.2666			−1.55806			−0.779028	−	0.626989i	$-0.784287\pi$
$109$	−16.2666			−1.55806			−0.779028	+	0.626989i	$0.784287\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	3.51914	+	6.09534i	0.331053	+	0.573401i	0.982719	−	0.185106i	$-0.0592627\pi$
$113$	3.51914	+	6.09534i	0.331053	+	0.573401i	−0.651665	+	0.758507i	$0.725929\pi$
$114$		0			0
$115$	−0.134911	+	0.233672i	−0.0125805	+	0.0217901i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	6.94342	−	12.0264i	0.636502	−	1.10245i
$120$		0			0
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	1.02274			0.0914762
$126$		0			0
$127$	2.20947			0.196059			0.0980293	−	0.995184i	$-0.468746\pi$
$127$	2.20947			0.196059			0.0980293	+	0.995184i	$0.468746\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	3.67114	+	6.35861i	0.320749	+	0.555554i	0.980643	−	0.195805i	$-0.0627320\pi$
$131$	3.67114	+	6.35861i	0.320749	+	0.555554i	−0.659894	+	0.751359i	$0.729399\pi$
$132$		0			0
$133$	−7.78749	+	13.4883i	−0.675261	+	1.16959i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−5.14881	+	8.91801i	−0.439893	+	0.761917i	−0.997681	−	0.0680668i	$-0.978317\pi$
$137$	−5.14881	+	8.91801i	−0.439893	+	0.761917i	0.557788	+	0.829984i	$0.311650\pi$
$138$		0			0
$139$	−3.13877	−	5.43652i	−0.266227	−	0.461119i	0.701657	−	0.712515i	$-0.252444\pi$
$139$	−3.13877	−	5.43652i	−0.266227	−	0.461119i	−0.967884	+	0.251395i	$0.919111\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	2.62967			0.219904
$144$		0			0
$145$	0.960196			0.0797400
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−6.68488	−	11.5786i	−0.547647	−	0.948552i	−0.998435	−	0.0559215i	$-0.982190\pi$
$149$	−6.68488	−	11.5786i	−0.547647	−	0.948552i	0.450788	−	0.892631i	$-0.351143\pi$
$150$		0			0
$151$	−4.53670	+	7.85779i	−0.369191	+	0.639458i	−0.989439	−	0.144948i	$-0.953699\pi$
$151$	−4.53670	+	7.85779i	−0.369191	+	0.639458i	0.620248	+	0.784406i	$0.287032\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−0.272977	+	0.472810i	−0.0219260	+	0.0379770i
$156$		0			0
$157$	8.36753	+	14.4930i	0.667802	+	1.15667i	0.978518	+	0.206164i	$0.0660979\pi$
$157$	8.36753	+	14.4930i	0.667802	+	1.15667i	−0.310716	+	0.950503i	$0.600569\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−8.67748			−0.683881
$162$		0			0
$163$	17.5631			1.37565			0.687823	−	0.725879i	$-0.258567\pi$
$163$	17.5631			1.37565			0.687823	+	0.725879i	$0.258567\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−3.44537	−	5.96755i	−0.266611	−	0.461783i	0.701374	−	0.712794i	$-0.252570\pi$
$167$	−3.44537	−	5.96755i	−0.266611	−	0.461783i	−0.967984	+	0.251011i	$0.919237\pi$
$168$		0			0
$169$	3.04242	−	5.26962i	0.234032	−	0.405356i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−6.61872	+	11.4640i	−0.503212	+	0.871588i	0.496781	+	0.867876i	$0.334515\pi$
$173$	−6.61872	+	11.4640i	−0.503212	+	0.871588i	−0.999993	+	0.00371249i	$0.998818\pi$
$174$		0			0
$175$	8.21418	+	14.2274i	0.620933	+	1.07549i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−25.7862			−1.92735			−0.963675	−	0.267077i	$-0.913942\pi$
$179$	−25.7862			−1.92735			−0.963675	+	0.267077i	$0.913942\pi$
$180$		0			0
$181$	−7.02182			−0.521927			−0.260964	−	0.965349i	$-0.584040\pi$
$181$	−7.02182			−0.521927			−0.260964	+	0.965349i	$0.584040\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−0.220846	−	0.382517i	−0.0162369	−	0.0281232i
$186$		0			0
$187$	−2.10881	+	3.65257i	−0.154212	+	0.267102i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	2.60927	−	4.51938i	0.188800	−	0.327011i	−0.756051	−	0.654513i	$-0.772874\pi$
$191$	2.60927	−	4.51938i	0.188800	−	0.327011i	0.944850	+	0.327502i	$0.106207\pi$
$192$		0			0
$193$	−2.25855	−	3.91193i	−0.162574	−	0.281587i	0.773217	−	0.634141i	$-0.218646\pi$
$193$	−2.25855	−	3.91193i	−0.162574	−	0.281587i	−0.935791	+	0.352555i	$0.885313\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−7.53453			−0.536813			−0.268406	−	0.963306i	$-0.586497\pi$
$197$	−7.53453			−0.536813			−0.268406	+	0.963306i	$0.586497\pi$
$198$		0			0
$199$	−2.80430			−0.198792			−0.0993959	−	0.995048i	$-0.531691\pi$
$199$	−2.80430			−0.198792			−0.0993959	+	0.995048i	$0.531691\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	15.4400	+	26.7428i	1.08367	+	1.87698i
$204$		0			0
$205$	−0.464407	+	0.804376i	−0.0324356	+	0.0561801i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	2.36517	−	4.09659i	0.163602	−	0.283367i
$210$		0			0
$211$	1.17153	+	2.02915i	0.0806513	+	0.139692i	0.903530	−	0.428525i	$-0.140967\pi$
$211$	1.17153	+	2.02915i	0.0806513	+	0.139692i	−0.822879	+	0.568217i	$0.807633\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	0.166237			0.0113373
$216$		0			0
$217$	−17.5579			−1.19191
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−5.54548	−	9.60506i	−0.373029	−	0.646106i
$222$		0			0
$223$	−7.76328	+	13.4464i	−0.519868	+	0.900438i	0.479865	+	0.877342i	$0.340686\pi$
$223$	−7.76328	+	13.4464i	−0.519868	+	0.900438i	−0.999733	+	0.0230955i	$0.992648\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	3.68297	−	6.37910i	0.244448	−	0.423396i	−0.717529	−	0.696529i	$-0.754727\pi$
$227$	3.68297	−	6.37910i	0.244448	−	0.423396i	0.961976	+	0.273133i	$0.0880601\pi$
$228$		0			0
$229$	−6.20971	−	10.7555i	−0.410349	−	0.710746i	0.584579	−	0.811337i	$-0.301260\pi$
$229$	−6.20971	−	10.7555i	−0.410349	−	0.710746i	−0.994928	+	0.100591i	$0.967927\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−1.77406			−0.116223			−0.0581113	−	0.998310i	$-0.518508\pi$
$233$	−1.77406			−0.116223			−0.0581113	+	0.998310i	$0.518508\pi$
$234$		0			0
$235$	−0.974774			−0.0635872
$236$		0			0
$237$		0			0
$238$		0			0
$239$	10.6830	+	18.5035i	0.691025	+	1.19689i	0.971502	+	0.237030i	$0.0761741\pi$
$239$	10.6830	+	18.5035i	0.691025	+	1.19689i	−0.280477	+	0.959861i	$0.590493\pi$
$240$		0			0
$241$	−2.43102	+	4.21066i	−0.156596	+	0.271232i	−0.933639	−	0.358215i	$-0.883385\pi$
$241$	−2.43102	+	4.21066i	−0.156596	+	0.271232i	0.777043	+	0.629448i	$0.216719\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	0.196624	−	0.340564i	0.0125619	−	0.0217578i
$246$		0			0
$247$	6.21961	+	10.7727i	0.395745	+	0.685450i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	21.1239			1.33333			0.666665	−	0.745357i	$-0.267721\pi$
$251$	21.1239			1.33333			0.666665	+	0.745357i	$0.267721\pi$
$252$		0			0
$253$	2.63547			0.165691
$254$		0			0
$255$		0			0
$256$		0			0
$257$	14.8421	+	25.7073i	0.925827	+	1.60358i	0.790225	+	0.612817i	$0.209964\pi$
$257$	14.8421	+	25.7073i	0.925827	+	1.60358i	0.135602	+	0.990763i	$0.456703\pi$
$258$		0			0
$259$	7.10242	−	12.3018i	0.441323	−	0.764394i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	13.4753	−	23.3398i	0.830920	−	1.43920i	−0.0663888	−	0.997794i	$-0.521148\pi$
$263$	13.4753	−	23.3398i	0.830920	−	1.43920i	0.897309	−	0.441402i	$-0.145519\pi$
$264$		0			0
$265$	−0.0410055	−	0.0710237i	−0.00251895	−	0.00436295i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−1.14348			−0.0697190			−0.0348595	−	0.999392i	$-0.511098\pi$
$269$	−1.14348			−0.0697190			−0.0348595	+	0.999392i	$0.511098\pi$
$270$		0			0
$271$	20.9173			1.27063			0.635317	−	0.772252i	$-0.280870\pi$
$271$	20.9173			1.27063			0.635317	+	0.772252i	$0.280870\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−2.49476	−	4.32105i	−0.150440	−	0.260569i
$276$		0			0
$277$	2.53623	−	4.39288i	0.152387	−	0.263943i	−0.779717	−	0.626132i	$-0.784637\pi$
$277$	2.53623	−	4.39288i	0.152387	−	0.263943i	0.932105	+	0.362189i	$0.117971\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	15.5725	−	26.9724i	0.928980	−	1.60904i	0.143949	−	0.989585i	$-0.454020\pi$
$281$	15.5725	−	26.9724i	0.928980	−	1.60904i	0.785031	−	0.619456i	$-0.212647\pi$
$282$		0			0
$283$	8.74039	+	15.1388i	0.519562	+	0.899908i	0.999741	+	0.0227380i	$0.00723835\pi$
$283$	8.74039	+	15.1388i	0.519562	+	0.899908i	−0.480179	+	0.877170i	$0.659428\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−29.8707			−1.76321
$288$		0			0
$289$	0.788365			0.0463744
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−4.01222	−	6.94937i	−0.234396	−	0.405987i	0.724701	−	0.689064i	$-0.241978\pi$
$293$	−4.01222	−	6.94937i	−0.234396	−	0.405987i	−0.959097	+	0.283077i	$0.908645\pi$
$294$		0			0
$295$	0.256764	−	0.444728i	0.0149494	−	0.0258931i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−3.46521	+	6.00192i	−0.200398	+	0.347100i
$300$		0			0
$301$	2.67309	+	4.62993i	0.154074	+	0.266865i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−1.55665			−0.0891335
$306$		0			0
$307$	5.65793			0.322915			0.161458	−	0.986880i	$-0.448381\pi$
$307$	5.65793			0.322915			0.161458	+	0.986880i	$0.448381\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	13.0168	+	22.5457i	0.738114	+	1.27845i	0.953343	+	0.301888i	$0.0976168\pi$
$311$	13.0168	+	22.5457i	0.738114	+	1.27845i	−0.215229	+	0.976564i	$0.569050\pi$
$312$		0			0
$313$	−11.6005	+	20.0927i	−0.655701	+	1.13571i	0.326017	+	0.945364i	$0.394293\pi$
$313$	−11.6005	+	20.0927i	−0.655701	+	1.13571i	−0.981718	+	0.190343i	$0.939040\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−1.28786	+	2.23063i	−0.0723331	+	0.125285i	−0.899923	−	0.436048i	$-0.856378\pi$
$317$	−1.28786	+	2.23063i	−0.0723331	+	0.125285i	0.827590	+	0.561333i	$0.189711\pi$
$318$		0			0
$319$	−4.68934	−	8.12217i	−0.262552	−	0.454754i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−19.9508			−1.11009
$324$		0			0
$325$	13.1208			0.727810
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−15.6744	−	27.1488i	−0.864157	−	1.49676i
$330$		0			0
$331$	10.7465	−	18.6135i	0.590680	−	1.02309i	−0.403461	−	0.914997i	$-0.632193\pi$
$331$	10.7465	−	18.6135i	0.590680	−	1.02309i	0.994141	−	0.108091i	$-0.0344739\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−0.227115	+	0.393375i	−0.0124086	+	0.0214924i
$336$		0			0
$337$	3.28773	+	5.69451i	0.179094	+	0.310200i	0.941570	−	0.336816i	$-0.109350\pi$
$337$	3.28773	+	5.69451i	0.179094	+	0.310200i	−0.762477	+	0.647016i	$0.776017\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	5.33257			0.288775
$342$		0			0
$343$	−10.4011			−0.561607
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−13.1249	−	22.7330i	−0.704583	−	1.22037i	−0.966842	−	0.255376i	$-0.917801\pi$
$347$	−13.1249	−	22.7330i	−0.704583	−	1.22037i	0.262259	−	0.964997i	$-0.415532\pi$
$348$		0			0
$349$	−0.104094	+	0.180297i	−0.00557204	+	0.00965105i	−0.868798	−	0.495167i	$-0.835107\pi$
$349$	−0.104094	+	0.180297i	−0.00557204	+	0.00965105i	0.863226	+	0.504818i	$0.168440\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	1.41731	−	2.45485i	0.0754357	−	0.130658i	−0.825840	−	0.563905i	$-0.809299\pi$
$353$	1.41731	−	2.45485i	0.0754357	−	0.130658i	0.901276	+	0.433246i	$0.142632\pi$
$354$		0			0
$355$	−0.517804	−	0.896862i	−0.0274822	−	0.0476005i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	13.0930			0.691020			0.345510	−	0.938415i	$-0.387706\pi$
$359$	13.0930			0.691020			0.345510	+	0.938415i	$0.387706\pi$
$360$		0			0
$361$	3.37609			0.177689
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−0.393216	−	0.681070i	−0.0205819	−	0.0356488i
$366$		0			0
$367$	−5.16653	+	8.94869i	−0.269691	+	0.467118i	−0.968782	−	0.247915i	$-0.920255\pi$
$367$	−5.16653	+	8.94869i	−0.269691	+	0.467118i	0.699091	+	0.715032i	$0.253588\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	1.31874	−	2.28412i	0.0684656	−	0.118586i
$372$		0			0
$373$	1.96301	+	3.40003i	0.101641	+	0.176047i	0.912361	−	0.409387i	$-0.134258\pi$
$373$	1.96301	+	3.40003i	0.101641	+	0.176047i	−0.810720	+	0.585434i	$0.800924\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	24.6628			1.27020
$378$		0			0
$379$	1.67371			0.0859726			0.0429863	−	0.999076i	$-0.486313\pi$
$379$	1.67371			0.0859726			0.0429863	+	0.999076i	$0.486313\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	9.05692	+	15.6870i	0.462787	+	0.801571i	0.999099	−	0.0424494i	$-0.0135161\pi$
$383$	9.05692	+	15.6870i	0.462787	+	0.801571i	−0.536312	+	0.844020i	$0.680183\pi$
$384$		0			0
$385$	−0.168548	+	0.291934i	−0.00859001	+	0.0148783i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−16.4888	+	28.5595i	−0.836017	+	1.44802i	0.0571823	+	0.998364i	$0.481788\pi$
$389$	−16.4888	+	28.5595i	−0.836017	+	1.44802i	−0.893200	+	0.449661i	$0.851545\pi$
$390$		0			0
$391$	−5.55771	−	9.62624i	−0.281066	−	0.486820i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−0.986635			−0.0496430
$396$		0			0
$397$	−10.7457			−0.539312			−0.269656	−	0.962957i	$-0.586910\pi$
$397$	−10.7457			−0.539312			−0.269656	+	0.962957i	$0.586910\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−8.19066	−	14.1866i	−0.409022	−	0.708447i	0.585758	−	0.810486i	$-0.300797\pi$
$401$	−8.19066	−	14.1866i	−0.409022	−	0.708447i	−0.994780	+	0.102039i	$0.967464\pi$
$402$		0			0
$403$	−7.01146	+	12.1442i	−0.349265	+	0.604946i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−2.15710	+	3.73621i	−0.106924	+	0.185197i
$408$		0			0
$409$	7.62858	+	13.2131i	0.377209	+	0.653345i	0.990655	−	0.136392i	$-0.0435506\pi$
$409$	7.62858	+	13.2131i	0.377209	+	0.653345i	−0.613446	+	0.789737i	$0.710217\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	16.5151			0.812654
$414$		0			0
$415$	1.18870			0.0583510
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−6.25880	−	10.8406i	−0.305763	−	0.529596i	0.671668	−	0.740852i	$-0.265578\pi$
$419$	−6.25880	−	10.8406i	−0.305763	−	0.529596i	−0.977431	+	0.211256i	$0.932245\pi$
$420$		0			0
$421$	1.53395	−	2.65688i	0.0747602	−	0.129488i	−0.826222	−	0.563345i	$-0.809514\pi$
$421$	1.53395	−	2.65688i	0.0747602	−	0.129488i	0.900982	+	0.433857i	$0.142848\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−10.5220	+	18.2246i	−0.510390	+	0.884021i
$426$		0			0
$427$	−25.0310	−	43.3549i	−1.21133	−	2.09809i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−32.4948			−1.56522			−0.782609	−	0.622514i	$-0.786112\pi$
$431$	−32.4948			−1.56522			−0.782609	+	0.622514i	$0.786112\pi$
$432$		0			0
$433$	−22.0257			−1.05849			−0.529245	−	0.848469i	$-0.677525\pi$
$433$	−22.0257			−1.05849			−0.529245	+	0.848469i	$0.677525\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	6.23333	+	10.7964i	0.298181	+	0.516464i
$438$		0			0
$439$	14.0767	−	24.3815i	0.671843	−	1.16367i	−0.305538	−	0.952180i	$-0.598836\pi$
$439$	14.0767	−	24.3815i	0.671843	−	1.16367i	0.977381	−	0.211487i	$-0.0678305\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−9.62884	+	16.6776i	−0.457480	+	0.792378i	−0.998827	−	0.0484208i	$-0.984581\pi$
$443$	−9.62884	+	16.6776i	−0.457480	+	0.792378i	0.541347	+	0.840799i	$0.317914\pi$
$444$		0			0
$445$	0.0846759	+	0.146663i	0.00401402	+	0.00695249i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	31.3265			1.47839			0.739194	−	0.673492i	$-0.235207\pi$
$449$	31.3265			1.47839			0.739194	+	0.673492i	$0.235207\pi$
$450$		0			0
$451$	9.07214			0.427190
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−0.443226	−	0.767690i	−0.0207788	−	0.0359899i
$456$		0			0
$457$	−1.90219	+	3.29469i	−0.0889807	+	0.154119i	−0.907081	−	0.420957i	$-0.861694\pi$
$457$	−1.90219	+	3.29469i	−0.0889807	+	0.154119i	0.818100	+	0.575076i	$0.195028\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−10.6108	+	18.3784i	−0.494193	+	0.855968i	−0.999978	−	0.00669225i	$-0.997870\pi$
$461$	−10.6108	+	18.3784i	−0.494193	+	0.855968i	0.505784	+	0.862660i	$0.331203\pi$
$462$		0			0
$463$	8.51897	+	14.7553i	0.395910	+	0.685736i	0.993217	−	0.116277i	$-0.0370959\pi$
$463$	8.51897	+	14.7553i	0.395910	+	0.685736i	−0.597307	+	0.802013i	$0.703763\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	31.8183			1.47238			0.736188	−	0.676777i	$-0.236624\pi$
$467$	31.8183			1.47238			0.736188	+	0.676777i	$0.236624\pi$
$468$		0			0
$469$	−14.6081			−0.674537
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−0.811855	−	1.40617i	−0.0373291	−	0.0646560i
$474$		0			0
$475$	11.8011	−	20.4400i	0.541469	−	0.937853i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−6.54595	+	11.3379i	−0.299092	+	0.518043i	−0.975929	−	0.218091i	$-0.930017\pi$
$479$	−6.54595	+	11.3379i	−0.299092	+	0.518043i	0.676836	+	0.736134i	$0.263350\pi$
$480$		0			0
$481$	−5.67247	−	9.82500i	−0.258642	−	0.447982i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−1.78741			−0.0811623
$486$		0			0
$487$	−1.41284			−0.0640221			−0.0320110	−	0.999488i	$-0.510191\pi$
$487$	−1.41284			−0.0640221			−0.0320110	+	0.999488i	$0.510191\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	5.17978	+	8.97164i	0.233760	+	0.404885i	0.958912	−	0.283705i	$-0.0915636\pi$
$491$	5.17978	+	8.97164i	0.233760	+	0.404885i	−0.725151	+	0.688589i	$0.758230\pi$
$492$		0			0
$493$	−19.7779	+	34.2563i	−0.890750	+	1.54282i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	16.6526	−	28.8431i	0.746971	−	1.29379i
$498$		0			0
$499$	−8.51977	−	14.7567i	−0.381398	−	0.660600i	0.609865	−	0.792505i	$-0.291224\pi$
$499$	−8.51977	−	14.7567i	−0.381398	−	0.660600i	−0.991262	+	0.131906i	$0.957890\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−12.8329			−0.572189			−0.286094	−	0.958201i	$-0.592357\pi$
$503$	−12.8329			−0.572189			−0.286094	+	0.958201i	$0.592357\pi$
$504$		0			0
$505$	0.562905			0.0250489
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−10.5248	−	18.2294i	−0.466502	−	0.808005i	0.532766	−	0.846263i	$-0.321153\pi$
$509$	−10.5248	−	18.2294i	−0.466502	−	0.808005i	−0.999268	+	0.0382573i	$0.987819\pi$
$510$		0			0
$511$	12.6458	−	21.9032i	0.559419	−	0.968942i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−0.790283	+	1.36881i	−0.0348240	+	0.0603170i
$516$		0			0
$517$	4.76053	+	8.24547i	0.209368	+	0.362636i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	8.75777			0.383685			0.191843	−	0.981426i	$-0.438554\pi$
$521$	8.75777			0.383685			0.191843	+	0.981426i	$0.438554\pi$
$522$		0			0
$523$	1.84542			0.0806944			0.0403472	−	0.999186i	$-0.487154\pi$
$523$	1.84542			0.0806944			0.0403472	+	0.999186i	$0.487154\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−11.2454	−	19.4776i	−0.489857	−	0.848458i
$528$		0			0
$529$	8.02715	−	13.9034i	0.349006	−	0.604497i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−11.9284	+	20.6605i	−0.516675	+	0.894907i
$534$		0			0
$535$	0.299182	+	0.518198i	0.0129348	+	0.0224037i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−3.84104			−0.165445
$540$		0			0
$541$	−31.1515			−1.33931			−0.669654	−	0.742673i	$-0.733558\pi$
$541$	−31.1515			−1.33931			−0.669654	+	0.742673i	$0.733558\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−0.832693	−	1.44227i	−0.0356687	−	0.0617799i
$546$		0			0
$547$	1.32111	−	2.28823i	0.0564866	−	0.0978376i	−0.836399	−	0.548120i	$-0.815344\pi$
$547$	1.32111	−	2.28823i	0.0564866	−	0.0978376i	0.892886	+	0.450283i	$0.148677\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	22.1821	−	38.4206i	0.944991	−	1.63677i
$552$		0			0
$553$	−15.8651	−	27.4792i	−0.674653	−	1.16853i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	22.8577			0.968510			0.484255	−	0.874927i	$-0.339091\pi$
$557$	22.8577			0.968510			0.484255	+	0.874927i	$0.339091\pi$
$558$		0			0
$559$	4.26982			0.180594
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−17.8302	−	30.8827i	−0.751451	−	1.30155i	−0.947119	−	0.320882i	$-0.896021\pi$
$563$	−17.8302	−	30.8827i	−0.751451	−	1.30155i	0.195668	−	0.980670i	$-0.437312\pi$
$564$		0			0
$565$	−0.360293	+	0.624046i	−0.0151576	+	0.0262538i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−19.0573	+	33.0082i	−0.798924	+	1.38378i	0.121393	+	0.992604i	$0.461264\pi$
$569$	−19.0573	+	33.0082i	−0.798924	+	1.38378i	−0.920317	+	0.391173i	$0.872070\pi$
$570$		0			0
$571$	0.884596	+	1.53217i	0.0370192	+	0.0641191i	0.883941	−	0.467598i	$-0.154880\pi$
$571$	0.884596	+	1.53217i	0.0370192	+	0.0641191i	−0.846922	+	0.531717i	$0.821547\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	13.1497			0.548382
$576$		0			0
$577$	11.8426			0.493016			0.246508	−	0.969141i	$-0.420717\pi$
$577$	11.8426			0.493016			0.246508	+	0.969141i	$0.420717\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	19.1143	+	33.1070i	0.792996	+	1.37351i
$582$		0			0
$583$	−0.400519	+	0.693720i	−0.0165878	+	0.0287310i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	9.00051	−	15.5893i	0.371491	−	0.643441i	−0.618304	−	0.785939i	$-0.712180\pi$
$587$	9.00051	−	15.5893i	0.371491	−	0.643441i	0.989795	+	0.142498i	$0.0455135\pi$
$588$		0			0
$589$	12.6124	+	21.8454i	0.519686	+	0.900123i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−45.7212			−1.87754			−0.938772	−	0.344539i	$-0.888035\pi$
$593$	−45.7212			−1.87754			−0.938772	+	0.344539i	$0.888035\pi$
$594$		0			0
$595$	1.42175			0.0582859
$596$		0			0
$597$		0			0
$598$		0			0
$599$	8.36902	+	14.4956i	0.341949	+	0.592273i	0.984795	−	0.173723i	$-0.0555797\pi$
$599$	8.36902	+	14.4956i	0.341949	+	0.592273i	−0.642846	+	0.765996i	$0.722246\pi$
$600$		0			0
$601$	−3.73646	+	6.47174i	−0.152413	+	0.263988i	−0.932114	−	0.362164i	$-0.882038\pi$
$601$	−3.73646	+	6.47174i	−0.152413	+	0.263988i	0.779701	+	0.626152i	$0.215371\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	0.0511904	−	0.0886644i	0.00208119	−	0.00360472i
$606$		0			0
$607$	−7.97746	−	13.8174i	−0.323795	−	0.560830i	0.657473	−	0.753478i	$-0.271626\pi$
$607$	−7.97746	−	13.8174i	−0.323795	−	0.560830i	−0.981268	+	0.192649i	$0.938292\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−25.0372			−1.01290
$612$		0			0
$613$	40.5441			1.63756			0.818781	−	0.574105i	$-0.194650\pi$
$613$	40.5441			1.63756			0.818781	+	0.574105i	$0.194650\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−15.0923	−	26.1406i	−0.607593	−	1.05238i	−0.991636	−	0.129067i	$-0.958802\pi$
$617$	−15.0923	−	26.1406i	−0.607593	−	1.05238i	0.384042	−	0.923315i	$-0.374532\pi$
$618$		0			0
$619$	16.3442	−	28.3090i	0.656929	−	1.13783i	−0.324478	−	0.945893i	$-0.605188\pi$
$619$	16.3442	−	28.3090i	0.656929	−	1.13783i	0.981406	−	0.191941i	$-0.0614782\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−2.72318	+	4.71669i	−0.109102	+	0.188970i
$624$		0			0
$625$	−12.4214	−	21.5146i	−0.496858	−	0.860583i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	18.1957			0.725510
$630$		0			0
$631$	28.8485			1.14844			0.574220	−	0.818701i	$-0.305305\pi$
$631$	28.8485			1.14844			0.574220	+	0.818701i	$0.305305\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	0.113104	+	0.195901i	0.00448838	+	0.00777410i
$636$		0			0
$637$	5.05033	−	8.74743i	0.200102	−	0.346586i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−1.72883	+	2.99443i	−0.0682848	+	0.118273i	−0.898146	−	0.439697i	$-0.855086\pi$
$641$	−1.72883	+	2.99443i	−0.0682848	+	0.118273i	0.829862	+	0.557969i	$0.188419\pi$
$642$		0			0
$643$	6.09196	+	10.5516i	0.240243	+	0.416114i	0.960784	−	0.277299i	$-0.0894394\pi$
$643$	6.09196	+	10.5516i	0.240243	+	0.416114i	−0.720540	+	0.693413i	$0.756106\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−4.41141			−0.173430			−0.0867152	−	0.996233i	$-0.527637\pi$
$647$	−4.41141			−0.173430			−0.0867152	+	0.996233i	$0.527637\pi$
$648$		0			0
$649$	−5.01586			−0.196890
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−18.1817	−	31.4916i	−0.711504	−	1.23236i	−0.964292	−	0.264840i	$-0.914681\pi$
$653$	−18.1817	−	31.4916i	−0.711504	−	1.23236i	0.252788	−	0.967522i	$-0.418652\pi$
$654$		0			0
$655$	−0.375855	+	0.651000i	−0.0146859	+	0.0254367i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−3.30238	+	5.71988i	−0.128642	+	0.222815i	−0.923151	−	0.384438i	$-0.874395\pi$
$659$	−3.30238	+	5.71988i	−0.128642	+	0.222815i	0.794509	+	0.607253i	$0.207729\pi$
$660$		0			0
$661$	−7.16535	−	12.4107i	−0.278700	−	0.482722i	0.692362	−	0.721550i	$-0.256570\pi$
$661$	−7.16535	−	12.4107i	−0.278700	−	0.482722i	−0.971062	+	0.238828i	$0.923237\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−1.59458			−0.0618352
$666$		0			0
$667$	24.7172			0.957054
$668$		0			0
$669$		0			0
$670$		0			0
$671$	7.60225	+	13.1675i	0.293481	+	0.508325i
$672$		0			0
$673$	13.2197	−	22.8971i	0.509580	−	0.882619i	−0.490358	−	0.871521i	$-0.663134\pi$
$673$	13.2197	−	22.8971i	0.509580	−	0.882619i	0.999938	−	0.0110978i	$-0.00353262\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	2.60099	−	4.50505i	0.0999642	−	0.173143i	−0.811705	−	0.584067i	$-0.801461\pi$
$677$	2.60099	−	4.50505i	0.0999642	−	0.173143i	0.911670	+	0.410924i	$0.134794\pi$
$678$		0			0
$679$	−28.7417	−	49.7820i	−1.10300	−	1.91046i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	31.3316			1.19887			0.599436	−	0.800423i	$-0.295392\pi$
$683$	31.3316			1.19887			0.599436	+	0.800423i	$0.295392\pi$
$684$		0			0
$685$	−1.05428			−0.0402820
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−1.05323	−	1.82425i	−0.0401250	−	0.0694986i
$690$		0			0
$691$	7.49555	−	12.9827i	0.285144	−	0.493884i	−0.687500	−	0.726184i	$-0.741292\pi$
$691$	7.49555	−	12.9827i	0.285144	−	0.493884i	0.972644	+	0.232300i	$0.0746252\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	0.321350	−	0.556595i	0.0121895	−	0.0211129i
$696$		0			0
$697$	−19.1314	−	33.1366i	−0.724655	−	1.25514i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	47.0821			1.77827			0.889133	−	0.457649i	$-0.151308\pi$
$701$	47.0821			1.77827			0.889133	+	0.457649i	$0.151308\pi$
$702$		0			0
$703$	−20.4076			−0.769689
$704$		0			0
$705$		0			0
$706$		0			0
$707$	9.05152	+	15.6777i	0.340417	+	0.589620i
$708$		0			0
$709$	12.5857	−	21.7990i	0.472665	−	0.818679i	−0.526846	−	0.849961i	$-0.676626\pi$
$709$	12.5857	−	21.7990i	0.472665	−	0.818679i	0.999511	+	0.0312815i	$0.00995884\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−7.02692	+	12.1710i	−0.263160	+	0.455807i
$714$		0			0
$715$	0.134614	+	0.233158i	0.00503428	+	0.00871962i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	13.8795			0.517618			0.258809	−	0.965928i	$-0.416670\pi$
$719$	13.8795			0.517618			0.258809	+	0.965928i	$0.416670\pi$
$720$		0			0
$721$	−50.8311			−1.89305
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−23.3975	−	40.5257i	−0.868962	−	1.50509i
$726$		0			0
$727$	24.9694	−	43.2483i	0.926063	−	1.60399i	0.136222	−	0.990678i	$-0.456504\pi$
$727$	24.9694	−	43.2483i	0.926063	−	1.60399i	0.789842	−	0.613311i	$-0.210163\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−3.42410	+	5.93072i	−0.126645	+	0.219355i
$732$		0			0
$733$	4.91299	+	8.50954i	0.181465	+	0.314307i	0.942380	−	0.334545i	$-0.108583\pi$
$733$	4.91299	+	8.50954i	0.181465	+	0.314307i	−0.760914	+	0.648852i	$0.775249\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	4.43667			0.163427
$738$		0			0
$739$	47.9255			1.76297			0.881484	−	0.472213i	$-0.156545\pi$
$739$	47.9255			1.76297			0.881484	+	0.472213i	$0.156545\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	2.37968	+	4.12172i	0.0873019	+	0.151211i	0.906370	−	0.422485i	$-0.138842\pi$
$743$	2.37968	+	4.12172i	0.0873019	+	0.151211i	−0.819068	+	0.573697i	$0.805509\pi$
$744$		0			0
$745$	0.684404	−	1.18542i	0.0250746	−	0.0434305i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−9.62170	+	16.6653i	−0.351569	+	0.608936i
$750$		0			0
$751$	11.1092	+	19.2418i	0.405382	+	0.702142i	0.994366	−	0.106003i	$-0.0338052\pi$
$751$	11.1092	+	19.2418i	0.405382	+	0.702142i	−0.588984	+	0.808145i	$0.700472\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−0.928942			−0.0338077
$756$		0			0
$757$	35.0976			1.27564			0.637821	−	0.770184i	$-0.279836\pi$
$757$	35.0976			1.27564			0.637821	+	0.770184i	$0.279836\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−8.81352	−	15.2655i	−0.319490	−	0.553373i	0.660892	−	0.750481i	$-0.270178\pi$
$761$	−8.81352	−	15.2655i	−0.319490	−	0.553373i	−0.980382	+	0.197109i	$0.936845\pi$
$762$		0			0
$763$	26.7795	−	46.3834i	0.969481	−	1.67919i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	6.59502	−	11.4229i	0.238132	−	0.412458i
$768$		0			0
$769$	8.63954	+	14.9641i	0.311550	+	0.539620i	0.978698	−	0.205305i	$-0.0658186\pi$
$769$	8.63954	+	14.9641i	0.311550	+	0.539620i	−0.667148	+	0.744925i	$0.732485\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	40.6614			1.46249			0.731244	−	0.682116i	$-0.238940\pi$
$773$	40.6614			1.46249			0.731244	+	0.682116i	$0.238940\pi$
$774$		0			0
$775$	26.6070			0.955751
$776$		0			0
$777$		0			0
$778$		0			0
$779$	21.4571	+	37.1649i	0.768782	+	1.33157i
$780$		0			0
$781$	−5.05762	+	8.76006i	−0.180976	+	0.313460i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−0.856675	+	1.48380i	−0.0305760	+	0.0529593i
$786$		0			0
$787$	11.3815	+	19.7133i	0.405706	+	0.702703i	0.994403	−	0.105650i	$-0.0336924\pi$
$787$	11.3815	+	19.7133i	0.405706	+	0.702703i	−0.588697	+	0.808353i	$0.700359\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−23.1741			−0.823975
$792$		0			0
$793$	−39.9828			−1.41983
$794$		0			0
$795$		0			0
$796$		0			0
$797$	0.211031	+	0.365516i	0.00747509	+	0.0129472i	0.869739	−	0.493512i	$-0.164287\pi$
$797$	0.211031	+	0.365516i	0.00747509	+	0.0129472i	−0.862264	+	0.506460i	$0.830954\pi$
$798$		0			0
$799$	20.0781	−	34.7763i	0.710313	−	1.23030i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−3.84072	+	6.65231i	−0.135536	+	0.234755i
$804$		0			0
$805$	−0.444204	−	0.769384i	−0.0156561	−	0.0271172i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−22.7307			−0.799168			−0.399584	−	0.916696i	$-0.630845\pi$
$809$	−22.7307			−0.799168			−0.399584	+	0.916696i	$0.630845\pi$
$810$		0			0
$811$	39.1961			1.37636			0.688181	−	0.725539i	$-0.258410\pi$
$811$	39.1961			1.37636			0.688181	+	0.725539i	$0.258410\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	0.899061	+	1.55722i	0.0314927	+	0.0545470i
$816$		0			0
$817$	3.84035	−	6.65168i	0.134357	−	0.232713i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	2.83194	−	4.90506i	0.0988352	−	0.171188i	−0.812368	−	0.583146i	$-0.801822\pi$
$821$	2.83194	−	4.90506i	0.0988352	−	0.171188i	0.911203	+	0.411958i	$0.135155\pi$
$822$		0			0
$823$	26.5760	+	46.0309i	0.926380	+	1.60454i	0.789327	+	0.613974i	$0.210430\pi$
$823$	26.5760	+	46.0309i	0.926380	+	1.60454i	0.137054	+	0.990564i	$0.456237\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−28.8641			−1.00370			−0.501852	−	0.864954i	$-0.667348\pi$
$827$	−28.8641			−1.00370			−0.501852	+	0.864954i	$0.667348\pi$
$828$		0			0
$829$	30.3603			1.05446			0.527229	−	0.849723i	$-0.323231\pi$
$829$	30.3603			1.05446			0.527229	+	0.849723i	$0.323231\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	8.10003	+	14.0297i	0.280650	+	0.486099i
$834$		0			0
$835$	0.352740	−	0.610963i	0.0122071	−	0.0211432i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−1.72445	+	2.98684i	−0.0595346	+	0.103117i	−0.894257	−	0.447555i	$-0.852295\pi$
$839$	−1.72445	+	2.98684i	−0.0595346	+	0.103117i	0.834722	+	0.550672i	$0.185628\pi$
$840$		0			0
$841$	−29.4797	−	51.0604i	−1.01654	−	1.76070i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	0.622971			0.0214308
$846$		0			0
$847$	3.29257			0.113134
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−5.68498	−	9.84668i	−0.194879	−	0.337540i
$852$		0			0
$853$	19.8067	−	34.3062i	0.678169	−	1.17462i	−0.297363	−	0.954765i	$-0.596107\pi$
$853$	19.8067	−	34.3062i	0.678169	−	1.17462i	0.975532	−	0.219859i	$-0.0705596\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−1.49853	+	2.59552i	−0.0511886	+	0.0886613i	−0.890484	−	0.455014i	$-0.849634\pi$
$857$	−1.49853	+	2.59552i	−0.0511886	+	0.0886613i	0.839296	+	0.543675i	$0.182968\pi$
$858$		0			0
$859$	19.0054	+	32.9183i	0.648455	+	1.12316i	0.983492	+	0.180952i	$0.0579179\pi$
$859$	19.0054	+	32.9183i	0.648455	+	1.12316i	−0.335037	+	0.942205i	$0.608749\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	48.4129			1.64800			0.823998	−	0.566593i	$-0.191739\pi$
$863$	48.4129			1.64800			0.823998	+	0.566593i	$0.191739\pi$
$864$		0			0
$865$	−1.35526			−0.0460802
$866$		0			0
$867$		0			0
$868$		0			0
$869$	4.81845	+	8.34581i	0.163455	+	0.283112i
$870$		0			0
$871$	−5.83349	+	10.1039i	−0.197660	+	0.342357i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−1.68372	+	2.91628i	−0.0569200	+	0.0985883i
$876$		0			0
$877$	−17.9671	−	31.1199i	−0.606706	−	1.05085i	−0.991779	−	0.127960i	$-0.959157\pi$
$877$	−17.9671	−	31.1199i	−0.606706	−	1.05085i	0.385073	−	0.922886i	$-0.374176\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−36.3256			−1.22384			−0.611920	−	0.790919i	$-0.709603\pi$
$881$	−36.3256			−1.22384			−0.611920	+	0.790919i	$0.709603\pi$
$882$		0			0
$883$	43.1342			1.45158			0.725790	−	0.687916i	$-0.241474\pi$
$883$	43.1342			1.45158			0.725790	+	0.687916i	$0.241474\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−14.4794	−	25.0791i	−0.486172	−	0.842074i	0.513702	−	0.857969i	$-0.328274\pi$
$887$	−14.4794	−	25.0791i	−0.486172	−	0.842074i	−0.999874	+	0.0158947i	$0.994940\pi$
$888$		0			0
$889$	−3.63742	+	6.30019i	−0.121995	+	0.211302i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−22.5189	+	39.0039i	−0.753566	+	1.30521i
$894$		0			0
$895$	−1.32001	−	2.28632i	−0.0441229	−	0.0764232i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	50.0125			1.66801
$900$		0			0
$901$	3.37848			0.112554
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−0.359450	−	0.622585i	−0.0119485	−	0.0206954i
$906$		0			0
$907$	−19.2512	+	33.3441i	−0.639227	+	1.10717i	0.346376	+	0.938096i	$0.387412\pi$
$907$	−19.2512	+	33.3441i	−0.639227	+	1.10717i	−0.985603	+	0.169077i	$0.945921\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−26.2712	+	45.5030i	−0.870402	+	1.50758i	−0.00882097	+	0.999961i	$0.502808\pi$
$911$	−26.2712	+	45.5030i	−0.870402	+	1.50758i	−0.861581	+	0.507620i	$0.830525\pi$
$912$		0			0
$913$	−5.80529	−	10.0550i	−0.192127	−	0.332774i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−24.1750			−0.798329
$918$		0			0
$919$	12.7755			0.421426			0.210713	−	0.977548i	$-0.432421\pi$
$919$	12.7755			0.421426			0.210713	+	0.977548i	$0.432421\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−13.2999	−	23.0361i	−0.437771	−	0.758241i
$924$		0			0
$925$	−10.7629	+	18.6419i	−0.353882	+	0.612942i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	21.1738	−	36.6742i	0.694691	−	1.20324i	−0.275594	−	0.961274i	$-0.588874\pi$
$929$	21.1738	−	36.6742i	0.694691	−	1.20324i	0.970285	−	0.241966i	$-0.0777922\pi$
$930$		0			0
$931$	−9.08471	−	15.7352i	−0.297739	−	0.515700i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−0.431804			−0.0141215
$936$		0			0
$937$	−59.5376			−1.94501			−0.972504	−	0.232888i	$-0.925183\pi$
$937$	−59.5376			−1.94501			−0.972504	+	0.232888i	$0.925183\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−13.8776	−	24.0367i	−0.452397	−	0.783575i	0.546137	−	0.837696i	$-0.316098\pi$
$941$	−13.8776	−	24.0367i	−0.452397	−	0.783575i	−0.998534	+	0.0541207i	$0.982764\pi$
$942$		0			0
$943$	−11.9547	+	20.7061i	−0.389298	+	0.674284i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−17.6929	+	30.6449i	−0.574940	+	0.995826i	0.421108	+	0.907011i	$0.361641\pi$
$947$	−17.6929	+	30.6449i	−0.574940	+	0.995826i	−0.996048	+	0.0888154i	$0.971692\pi$
$948$		0			0
$949$	−10.0998	−	17.4934i	−0.327854	−	0.567860i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−22.7389			−0.736585			−0.368292	−	0.929710i	$-0.620057\pi$
$953$	−22.7389			−0.736585			−0.368292	+	0.929710i	$0.620057\pi$
$954$		0			0
$955$	0.534278			0.0172888
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−16.9528	−	29.3632i	−0.547436	−	0.948187i
$960$		0			0
$961$	1.28182	−	2.22019i	0.0413492	−	0.0716189i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	0.231232	−	0.400506i	0.00744364	−	0.0128928i
$966$		0			0
$967$	−5.88368	−	10.1908i	−0.189206	−	0.327715i	0.755779	−	0.654826i	$-0.227258\pi$
$967$	−5.88368	−	10.1908i	−0.189206	−	0.327715i	−0.944986	+	0.327111i	$0.893925\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−54.0871			−1.73574			−0.867869	−	0.496793i	$-0.834511\pi$
$971$	−54.0871			−1.73574			−0.867869	+	0.496793i	$0.834511\pi$
$972$		0			0
$973$	20.6693			0.662627
$974$		0			0
$975$		0			0
$976$		0			0
$977$	28.9945	+	50.2200i	0.927616	+	1.60668i	0.787298	+	0.616572i	$0.211479\pi$
$977$	28.9945	+	50.2200i	0.927616	+	1.60668i	0.140318	+	0.990107i	$0.455188\pi$
$978$		0			0
$979$	0.827068	−	1.43252i	0.0264332	−	0.0457836i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	10.3030	−	17.8454i	0.328616	−	0.569179i	−0.653622	−	0.756821i	$-0.726751\pi$
$983$	10.3030	−	17.8454i	0.328616	−	0.569179i	0.982237	+	0.187642i	$0.0600846\pi$
$984$		0			0
$985$	−0.385696	−	0.668045i	−0.0122893	−	0.0212857i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	4.27924			0.136072
$990$		0			0
$991$	−24.5713			−0.780534			−0.390267	−	0.920702i	$-0.627617\pi$
$991$	−24.5713			−0.780534			−0.390267	+	0.920702i	$0.627617\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−0.143553	−	0.248642i	−0.00455095	−	0.00788248i
$996$		0			0
$997$	8.21105	−	14.2219i	0.260046	−	0.450414i	−0.706208	−	0.708005i	$-0.749595\pi$
$997$	8.21105	−	14.2219i	0.260046	−	0.450414i	0.966254	+	0.257591i	$0.0829288\pi$
$998$		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.1189.4		12
3.2	odd	2		3564.2.i.s.1189.3		12
9.2	odd	6		3564.2.a.p.1.4	yes	6
9.4	even	3	inner	3564.2.i.t.2377.4		12
9.5	odd	6		3564.2.i.s.2377.3		12
9.7	even	3		3564.2.a.o.1.3	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3564.2.a.o.1.3	✓	6	9.7	even	3
3564.2.a.p.1.4	yes	6	9.2	odd	6
3564.2.i.s.1189.3		12	3.2	odd	2
3564.2.i.s.2377.3		12	9.5	odd	6
3564.2.i.t.1189.4		12	1.1	even	1	trivial
3564.2.i.t.2377.4		12	9.4	even	3	inner

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)

\(f(q)\)	\(=\)	\(q+(0.0511904 + 0.0886644i) q^{5} +(-1.64629 + 2.85145i) q^{7} +O(q^{10})\)	\(q+(0.0511904 + 0.0886644i) q^{5} +(-1.64629 + 2.85145i) q^{7} +(0.500000 - 0.866025i) q^{11} +(1.31483 + 2.27736i) q^{13} -4.21763 q^{17} +4.73034 q^{19} +(1.31774 + 2.28238i) q^{23} +(2.49476 - 4.32105i) q^{25} +(4.68934 - 8.12217i) q^{29} +(2.66629 + 4.61814i) q^{31} -0.337096 q^{35} -4.31421 q^{37} +(4.53607 + 7.85670i) q^{41} +(0.811855 - 1.40617i) q^{43} +(-4.76053 + 8.24547i) q^{47} +(-1.92052 - 3.32644i) q^{49} -0.801039 q^{53} +0.102381 q^{55} +(-2.50793 - 4.34386i) q^{59} +(-7.60225 + 13.1675i) q^{61} +(-0.134614 + 0.233158i) q^{65} +(2.21833 + 3.84227i) q^{67} -10.1152 q^{71} -7.68143 q^{73} +(1.64629 + 2.85145i) q^{77} +(-4.81845 + 8.34581i) q^{79} +(5.80529 - 10.0550i) q^{83} +(-0.215902 - 0.373953i) q^{85} +1.65414 q^{89} -8.65838 q^{91} +(0.242148 + 0.419413i) q^{95} +(-8.72924 + 15.1195i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{7}+O(q^{10}) \) 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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