LMFDB - Embedded newform 2520.2.bi.r.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2520,2,Mod(361,2520)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2520, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("2520.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2520 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2520.bi (of order $3$, degree $2$, 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:	$20.1223013094$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 29x^{8} + 247x^{6} + 855x^{4} + 1212x^{2} + 588 $ x^10 + 29x^8 + 247x^6 + 855x^4 + 1212x^2 + 588
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.1
Root			$1.05780i$ of defining polynomial
Character	$\chi$	$=$	2520.361
Dual form			2520.2.bi.r.1801.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{5} +(-2.62478 - 0.332488i) q^{7} +O(q^{10})$	$q+(-0.500000 - 0.866025i) q^{5} +(-2.62478 - 0.332488i) q^{7} +(-1.41608 + 2.45273i) q^{11} -1.08882 q^{13} +(-2.23314 + 3.86791i) q^{17} +(2.06886 + 3.58337i) q^{19} +(-3.69363 - 6.39756i) q^{23} +(-0.500000 + 0.866025i) q^{25} +9.17054 q^{29} +(5.37788 - 9.31476i) q^{31} +(1.02445 + 2.43937i) q^{35} +(0.0244456 + 0.0423411i) q^{37} +9.66694 q^{41} +6.20962 q^{43} +(-0.371671 - 0.643754i) q^{47} +(6.77890 + 1.74541i) q^{49} +(-3.46049 + 5.99375i) q^{53} +2.83217 q^{55} +(-1.75311 + 3.03647i) q^{59} +(-3.68070 - 6.37515i) q^{61} +(0.544411 + 0.942948i) q^{65} +(6.87433 - 11.9067i) q^{67} -7.50621 q^{71} +(4.97691 - 8.62026i) q^{73} +(4.53240 - 5.96703i) q^{77} +(-8.73001 - 15.1208i) q^{79} -12.5319 q^{83} +4.46628 q^{85} +(-1.33572 - 2.31353i) q^{89} +(2.85792 + 0.362020i) q^{91} +(2.06886 - 3.58337i) q^{95} +13.9725 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 5 q^{5} - q^{7}+O(q^{10}) $ 10 * q - 5 * q^5 - q^7	$ 10 q - 5 q^{5} - q^{7} - 2 q^{11} + 6 q^{13} + 2 q^{17} + q^{19} + 8 q^{23} - 5 q^{25} + 7 q^{31} - q^{35} - 11 q^{37} + 20 q^{41} + 6 q^{43} - 23 q^{49} - 14 q^{53} + 4 q^{55} + 4 q^{59} - 6 q^{61} - 3 q^{65} - 7 q^{67} - 32 q^{71} + 3 q^{73} + 8 q^{77} - 19 q^{79} + 28 q^{83} - 4 q^{85} - 18 q^{89} - 21 q^{91} + q^{95} + 48 q^{97}+O(q^{100}) $ 10 * q - 5 * q^5 - q^7 - 2 * q^11 + 6 * q^13 + 2 * q^17 + q^19 + 8 * q^23 - 5 * q^25 + 7 * q^31 - q^35 - 11 * q^37 + 20 * q^41 + 6 * q^43 - 23 * q^49 - 14 * q^53 + 4 * q^55 + 4 * q^59 - 6 * q^61 - 3 * q^65 - 7 * q^67 - 32 * q^71 + 3 * q^73 + 8 * q^77 - 19 * q^79 + 28 * q^83 - 4 * q^85 - 18 * q^89 - 21 * q^91 + q^95 + 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2520\mathbb{Z}\right)^\times$.

$n$	$281$	$631$	$1081$	$1261$	$2017$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$		0			0
$7$	−2.62478	−	0.332488i	−0.992072	−	0.125668i
$7$	−2.62478	−	0.332488i	−0.992072	−	0.125668i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1.41608	+	2.45273i	−0.426965	+	0.739525i	−0.996602	−	0.0823715i	$-0.973751\pi$
$11$	−1.41608	+	2.45273i	−0.426965	+	0.739525i	0.569637	+	0.821897i	$0.307084\pi$
$12$		0			0
$13$	−1.08882			−0.301985			−0.150993	−	0.988535i	$-0.548247\pi$
$13$	−1.08882			−0.301985			−0.150993	+	0.988535i	$0.548247\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.23314	+	3.86791i	−0.541616	+	0.938106i	0.457196	+	0.889366i	$0.348854\pi$
$17$	−2.23314	+	3.86791i	−0.541616	+	0.938106i	−0.998811	+	0.0487401i	$0.984479\pi$
$18$		0			0
$19$	2.06886	+	3.58337i	0.474628	+	0.822080i	0.999578	−	0.0290530i	$-0.00924915\pi$
$19$	2.06886	+	3.58337i	0.474628	+	0.822080i	−0.524950	+	0.851133i	$0.675916\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.69363	−	6.39756i	−0.770176	−	1.33398i	−0.937466	−	0.348076i	$-0.886835\pi$
$23$	−3.69363	−	6.39756i	−0.770176	−	1.33398i	0.167290	−	0.985908i	$-0.446498\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	9.17054			1.70293			0.851463	−	0.524414i	$-0.175716\pi$
$29$	9.17054			1.70293			0.851463	+	0.524414i	$0.175716\pi$
$30$		0			0
$31$	5.37788	−	9.31476i	0.965896	−	1.67298i	0.258708	−	0.965956i	$-0.416703\pi$
$31$	5.37788	−	9.31476i	0.965896	−	1.67298i	0.707188	−	0.707026i	$-0.249963\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	1.02445	+	2.43937i	0.173163	+	0.412328i
$36$		0			0
$37$	0.0244456	+	0.0423411i	0.00401884	+	0.00696083i	0.868028	−	0.496516i	$-0.165387\pi$
$37$	0.0244456	+	0.0423411i	0.00401884	+	0.00696083i	−0.864009	+	0.503476i	$0.832054\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	9.66694			1.50972			0.754861	−	0.655884i	$-0.227704\pi$
$41$	9.66694			1.50972			0.754861	+	0.655884i	$0.227704\pi$
$42$		0			0
$43$	6.20962			0.946958			0.473479	−	0.880805i	$-0.342998\pi$
$43$	6.20962			0.946958			0.473479	+	0.880805i	$0.342998\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−0.371671	−	0.643754i	−0.0542138	−	0.0939011i	0.837645	−	0.546215i	$-0.183932\pi$
$47$	−0.371671	−	0.643754i	−0.0542138	−	0.0939011i	−0.891859	+	0.452314i	$0.850599\pi$
$48$		0			0
$49$	6.77890	+	1.74541i	0.968415	+	0.249344i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−3.46049	+	5.99375i	−0.475335	+	0.823305i	−0.999601	−	0.0282498i	$-0.991007\pi$
$53$	−3.46049	+	5.99375i	−0.475335	+	0.823305i	0.524265	+	0.851555i	$0.324340\pi$
$54$		0			0
$55$	2.83217			0.381889
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−1.75311	+	3.03647i	−0.228235	+	0.395314i	−0.957285	−	0.289146i	$-0.906629\pi$
$59$	−1.75311	+	3.03647i	−0.228235	+	0.395314i	0.729050	+	0.684460i	$0.239962\pi$
$60$		0			0
$61$	−3.68070	−	6.37515i	−0.471265	−	0.816255i	0.528195	−	0.849123i	$-0.322869\pi$
$61$	−3.68070	−	6.37515i	−0.471265	−	0.816255i	−0.999460	+	0.0328685i	$0.989536\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	0.544411	+	0.942948i	0.0675259	+	0.116958i
$66$		0			0
$67$	6.87433	−	11.9067i	0.839833	−	1.45463i	−0.0502009	−	0.998739i	$-0.515986\pi$
$67$	6.87433	−	11.9067i	0.839833	−	1.45463i	0.890034	−	0.455894i	$-0.150681\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−7.50621			−0.890823			−0.445412	−	0.895326i	$-0.646943\pi$
$71$	−7.50621			−0.890823			−0.445412	+	0.895326i	$0.646943\pi$
$72$		0			0
$73$	4.97691	−	8.62026i	0.582503	−	1.00892i	−0.412679	−	0.910877i	$-0.635407\pi$
$73$	4.97691	−	8.62026i	0.582503	−	1.00892i	0.995182	−	0.0980481i	$-0.0312599\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	4.53240	−	5.96703i	0.516515	−	0.680006i
$78$		0			0
$79$	−8.73001	−	15.1208i	−0.982203	−	1.70123i	−0.653760	−	0.756702i	$-0.726809\pi$
$79$	−8.73001	−	15.1208i	−0.982203	−	1.70123i	−0.328443	−	0.944524i	$-0.606524\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−12.5319			−1.37556			−0.687779	−	0.725920i	$-0.741414\pi$
$83$	−12.5319			−1.37556			−0.687779	+	0.725920i	$0.741414\pi$
$84$		0			0
$85$	4.46628			0.484436
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−1.33572	−	2.31353i	−0.141586	−	0.245234i	0.786508	−	0.617580i	$-0.211887\pi$
$89$	−1.33572	−	2.31353i	−0.141586	−	0.245234i	−0.928094	+	0.372346i	$0.878553\pi$
$90$		0			0
$91$	2.85792	+	0.362020i	0.299591	+	0.0379500i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	2.06886	−	3.58337i	0.212260	−	0.367646i
$96$		0			0
$97$	13.9725			1.41869			0.709346	−	0.704861i	$-0.248991\pi$
$97$	13.9725			1.41869			0.709346	+	0.704861i	$0.248991\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	4.95377	−	8.58018i	0.492918	−	0.853759i	−0.507048	−	0.861918i	$-0.669263\pi$
$101$	4.95377	−	8.58018i	0.492918	−	0.853759i	0.999967	+	0.00815809i	$0.00259683\pi$
$102$		0			0
$103$	7.24252	+	12.5444i	0.713627	+	1.23604i	0.963487	+	0.267756i	$0.0862822\pi$
$103$	7.24252	+	12.5444i	0.713627	+	1.23604i	−0.249859	+	0.968282i	$0.580384\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.23314	−	2.13586i	−0.119212	−	0.206481i	0.800244	−	0.599675i	$-0.204704\pi$
$107$	−1.23314	−	2.13586i	−0.119212	−	0.206481i	−0.919456	+	0.393194i	$0.871370\pi$
$108$		0			0
$109$	5.64119	−	9.77083i	0.540328	−	0.935876i	−0.458557	−	0.888665i	$-0.651633\pi$
$109$	5.64119	−	9.77083i	0.540328	−	0.935876i	0.998885	−	0.0472106i	$-0.0150332\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−8.49911			−0.799529			−0.399764	−	0.916618i	$-0.630908\pi$
$113$	−8.49911			−0.799529			−0.399764	+	0.916618i	$0.630908\pi$
$114$		0			0
$115$	−3.69363	+	6.39756i	−0.344433	+	0.596576i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	7.14752	−	9.40991i	0.655212	−	0.862605i
$120$		0			0
$121$	1.48942	+	2.57975i	0.135402	+	0.234523i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	8.85094			0.785394			0.392697	−	0.919668i	$-0.371542\pi$
$127$	8.85094			0.785394			0.392697	+	0.919668i	$0.371542\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−3.16919	−	5.48919i	−0.276893	−	0.479593i	0.693718	−	0.720247i	$-0.255972\pi$
$131$	−3.16919	−	5.48919i	−0.276893	−	0.479593i	−0.970611	+	0.240654i	$0.922638\pi$
$132$		0			0
$133$	−4.23886	−	10.0934i	−0.367556	−	0.875209i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−1.72693	+	2.99113i	−0.147542	+	0.255549i	−0.930318	−	0.366753i	$-0.880469\pi$
$137$	−1.72693	+	2.99113i	−0.147542	+	0.255549i	0.782777	+	0.622303i	$0.213803\pi$
$138$		0			0
$139$	15.7158			1.33300			0.666500	−	0.745505i	$-0.267792\pi$
$139$	15.7158			1.33300			0.666500	+	0.745505i	$0.267792\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	1.54186	−	2.67058i	0.128937	−	0.223326i
$144$		0			0
$145$	−4.58527	−	7.94192i	−0.380786	−	0.659541i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	11.4362	+	19.8080i	0.936887	+	1.62274i	0.771235	+	0.636551i	$0.219639\pi$
$149$	11.4362	+	19.8080i	0.936887	+	1.62274i	0.165652	+	0.986184i	$0.447027\pi$
$150$		0			0
$151$	−8.40102	+	14.5510i	−0.683666	+	1.18414i	0.290189	+	0.956969i	$0.406282\pi$
$151$	−8.40102	+	14.5510i	−0.683666	+	1.18414i	−0.973854	+	0.227174i	$0.927051\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−10.7558			−0.863924
$156$		0			0
$157$	2.03147	−	3.51862i	0.162129	−	0.280816i	−0.773503	−	0.633793i	$-0.781497\pi$
$157$	2.03147	−	3.51862i	0.162129	−	0.280816i	0.935632	+	0.352977i	$0.114831\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	7.56785	+	18.0203i	0.596430	+	1.42020i
$162$		0			0
$163$	−5.32857	−	9.22935i	−0.417365	−	0.722898i	0.578308	−	0.815818i	$-0.303713\pi$
$163$	−5.32857	−	9.22935i	−0.417365	−	0.722898i	−0.995674	+	0.0929203i	$0.970380\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	9.38727			0.726409			0.363204	−	0.931710i	$-0.381683\pi$
$167$	9.38727			0.726409			0.363204	+	0.931710i	$0.381683\pi$
$168$		0			0
$169$	−11.8145			−0.908805
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−8.71005	−	15.0862i	−0.662213	−	1.14699i	−0.980033	−	0.198835i	$-0.936284\pi$
$173$	−8.71005	−	15.0862i	−0.662213	−	1.14699i	0.317820	−	0.948151i	$-0.397049\pi$
$174$		0			0
$175$	1.60033	−	2.10688i	0.120974	−	0.159265i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−1.12030	+	1.94041i	−0.0837349	+	0.145033i	−0.904851	−	0.425727i	$-0.860018\pi$
$179$	−1.12030	+	1.94041i	−0.0837349	+	0.145033i	0.821117	+	0.570761i	$0.193352\pi$
$180$		0			0
$181$	22.6432			1.68305			0.841527	−	0.540215i	$-0.181657\pi$
$181$	22.6432			1.68305			0.841527	+	0.540215i	$0.181657\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	0.0244456	−	0.0423411i	0.00179728	−	0.00311298i
$186$		0			0
$187$	−6.32462	−	10.9546i	−0.462502	−	0.801077i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	8.71583	+	15.0963i	0.630655	+	1.09233i	0.987418	+	0.158132i	$0.0505472\pi$
$191$	8.71583	+	15.0963i	0.630655	+	1.09233i	−0.356762	+	0.934195i	$0.616119\pi$
$192$		0			0
$193$	−3.99297	+	6.91603i	−0.287420	+	0.497827i	−0.973193	−	0.229989i	$-0.926131\pi$
$193$	−3.99297	+	6.91603i	−0.287420	+	0.497827i	0.685773	+	0.727816i	$0.259464\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	22.4457			1.59919			0.799596	−	0.600539i	$-0.205047\pi$
$197$	22.4457			1.59919			0.799596	+	0.600539i	$0.205047\pi$
$198$		0			0
$199$	4.89742	−	8.48258i	0.347169	−	0.601314i	−0.638576	−	0.769558i	$-0.720476\pi$
$199$	4.89742	−	8.48258i	0.347169	−	0.601314i	0.985745	+	0.168244i	$0.0538097\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−24.0706	−	3.04909i	−1.68943	−	0.214004i
$204$		0			0
$205$	−4.83347	−	8.37182i	−0.337584	−	0.584713i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−11.7187			−0.810599
$210$		0			0
$211$	−2.31451			−0.159337			−0.0796687	−	0.996821i	$-0.525386\pi$
$211$	−2.31451			−0.159337			−0.0796687	+	0.996821i	$0.525386\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−3.10481	−	5.37769i	−0.211746	−	0.366755i
$216$		0			0
$217$	−17.2128	+	22.6611i	−1.16848	+	1.53834i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	2.43149	−	4.21147i	0.163560	−	0.283294i
$222$		0			0
$223$	3.67854			0.246333			0.123167	−	0.992386i	$-0.460695\pi$
$223$	3.67854			0.246333			0.123167	+	0.992386i	$0.460695\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	0.312151	−	0.540662i	0.0207182	−	0.0358850i	−0.855480	−	0.517835i	$-0.826738\pi$
$227$	0.312151	−	0.540662i	0.0207182	−	0.0358850i	0.876199	+	0.481950i	$0.160071\pi$
$228$		0			0
$229$	8.17012	+	14.1511i	0.539896	+	0.935128i	0.998909	+	0.0466983i	$0.0148699\pi$
$229$	8.17012	+	14.1511i	0.539896	+	0.935128i	−0.459013	+	0.888430i	$0.651797\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−5.18661	−	8.98346i	−0.339786	−	0.588526i	0.644606	−	0.764515i	$-0.277021\pi$
$233$	−5.18661	−	8.98346i	−0.339786	−	0.588526i	−0.984392	+	0.175988i	$0.943688\pi$
$234$		0			0
$235$	−0.371671	+	0.643754i	−0.0242452	+	0.0419939i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−13.3287			−0.862159			−0.431080	−	0.902314i	$-0.641867\pi$
$239$	−13.3287			−0.862159			−0.431080	+	0.902314i	$0.641867\pi$
$240$		0			0
$241$	6.31798	−	10.9431i	0.406977	−	0.704905i	−0.587572	−	0.809172i	$-0.699916\pi$
$241$	6.31798	−	10.9431i	0.406977	−	0.704905i	0.994549	+	0.104267i	$0.0332495\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−1.87788	−	6.74341i	−0.119973	−	0.430821i
$246$		0			0
$247$	−2.25262	−	3.90165i	−0.143331	−	0.248256i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	18.5764			1.17253			0.586265	−	0.810120i	$-0.300598\pi$
$251$	18.5764			1.17253			0.586265	+	0.810120i	$0.300598\pi$
$252$		0			0
$253$	20.9220			1.31535
$254$		0			0
$255$		0			0
$256$		0			0
$257$	13.3247	+	23.0790i	0.831170	+	1.43963i	0.897111	+	0.441805i	$0.145662\pi$
$257$	13.3247	+	23.0790i	0.831170	+	1.43963i	−0.0659410	+	0.997824i	$0.521005\pi$
$258$		0			0
$259$	−0.0500864	−	0.119264i	−0.00311222	−	0.00741069i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−2.65798	+	4.60376i	−0.163898	+	0.283880i	−0.936263	−	0.351299i	$-0.885740\pi$
$263$	−2.65798	+	4.60376i	−0.163898	+	0.283880i	0.772365	+	0.635179i	$0.219074\pi$
$264$		0			0
$265$	6.92099			0.425153
$266$		0			0
$267$		0			0
$268$		0			0
$269$	7.70687	−	13.3487i	0.469896	−	0.813884i	−0.529511	−	0.848303i	$-0.677625\pi$
$269$	7.70687	−	13.3487i	0.469896	−	0.813884i	0.999408	+	0.0344187i	$0.0109580\pi$
$270$		0			0
$271$	0.710817	+	1.23117i	0.0431791	+	0.0747883i	0.886807	−	0.462140i	$-0.152918\pi$
$271$	0.710817	+	1.23117i	0.0431791	+	0.0747883i	−0.843628	+	0.536928i	$0.819585\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−1.41608	−	2.45273i	−0.0853930	−	0.147905i
$276$		0			0
$277$	−5.64114	+	9.77074i	−0.338943	+	0.587067i	−0.984234	−	0.176870i	$-0.943403\pi$
$277$	−5.64114	+	9.77074i	−0.338943	+	0.587067i	0.645291	+	0.763937i	$0.276736\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	21.2388			1.26700			0.633500	−	0.773742i	$-0.281617\pi$
$281$	21.2388			1.26700			0.633500	+	0.773742i	$0.281617\pi$
$282$		0			0
$283$	2.67846	−	4.63923i	0.159218	−	0.275774i	−0.775369	−	0.631509i	$-0.782436\pi$
$283$	2.67846	−	4.63923i	0.159218	−	0.275774i	0.934587	+	0.355735i	$0.115769\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−25.3736	−	3.21414i	−1.49775	−	0.189725i
$288$		0			0
$289$	−1.47382	−	2.55274i	−0.0866955	−	0.150161i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	18.9585			1.10757			0.553785	−	0.832660i	$-0.313183\pi$
$293$	18.9585			1.10757			0.553785	+	0.832660i	$0.313183\pi$
$294$		0			0
$295$	3.50621			0.204139
$296$		0			0
$297$		0			0
$298$		0			0
$299$	4.02171	+	6.96581i	0.232582	+	0.402843i
$300$		0			0
$301$	−16.2989	−	2.06462i	−0.939451	−	0.119003i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−3.68070	+	6.37515i	−0.210756	+	0.365040i
$306$		0			0
$307$	−23.1572			−1.32165			−0.660825	−	0.750540i	$-0.729794\pi$
$307$	−23.1572			−1.32165			−0.660825	+	0.750540i	$0.729794\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−4.46362	+	7.73122i	−0.253109	+	0.438397i	−0.964380	−	0.264520i	$-0.914786\pi$
$311$	−4.46362	+	7.73122i	−0.253109	+	0.438397i	0.711271	+	0.702917i	$0.248120\pi$
$312$		0			0
$313$	−1.77625	−	3.07655i	−0.100399	−	0.173897i	0.811450	−	0.584422i	$-0.198679\pi$
$313$	−1.77625	−	3.07655i	−0.100399	−	0.173897i	−0.911849	+	0.410525i	$0.865345\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	5.49876	+	9.52413i	0.308841	+	0.534928i	0.978109	−	0.208093i	$-0.0667256\pi$
$317$	5.49876	+	9.52413i	0.308841	+	0.534928i	−0.669268	+	0.743021i	$0.733392\pi$
$318$		0			0
$319$	−12.9862	+	22.4928i	−0.727090	+	1.25936i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−18.4802			−1.02826
$324$		0			0
$325$	0.544411	−	0.942948i	0.0301985	−	0.0523053i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	0.761514	+	1.81329i	0.0419836	+	0.0999697i
$330$		0			0
$331$	0.950215	+	1.64582i	0.0522285	+	0.0904625i	0.890958	−	0.454086i	$-0.150034\pi$
$331$	0.950215	+	1.64582i	0.0522285	+	0.0904625i	−0.838729	+	0.544549i	$0.816701\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−13.7487			−0.751170
$336$		0			0
$337$	21.3951			1.16546			0.582732	−	0.812664i	$-0.301984\pi$
$337$	21.3951			1.16546			0.582732	+	0.812664i	$0.301984\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	15.2311	+	26.3810i	0.824808	+	1.42861i
$342$		0			0
$343$	−17.2128	−	6.83522i	−0.929403	−	0.369067i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	2.54353	−	4.40553i	0.136544	−	0.236501i	−0.789642	−	0.613568i	$-0.789734\pi$
$347$	2.54353	−	4.40553i	0.136544	−	0.236501i	0.926186	+	0.377066i	$0.123067\pi$
$348$		0			0
$349$	−4.41924			−0.236557			−0.118278	−	0.992980i	$-0.537738\pi$
$349$	−4.41924			−0.236557			−0.118278	+	0.992980i	$0.537738\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−6.46663	+	11.2005i	−0.344184	+	0.596144i	−0.985205	−	0.171379i	$-0.945178\pi$
$353$	−6.46663	+	11.2005i	−0.344184	+	0.596144i	0.641021	+	0.767523i	$0.278511\pi$
$354$		0			0
$355$	3.75311	+	6.50057i	0.199194	+	0.345014i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−13.5507	−	23.4704i	−0.715176	−	1.23872i	−0.962892	−	0.269889i	$-0.913013\pi$
$359$	−13.5507	−	23.4704i	−0.715176	−	1.23872i	0.247715	−	0.968833i	$-0.420320\pi$
$360$		0			0
$361$	0.939662	−	1.62754i	0.0494559	−	0.0856601i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−9.95382			−0.521007
$366$		0			0
$367$	8.55337	−	14.8149i	0.446482	−	0.773330i	−0.551672	−	0.834061i	$-0.686010\pi$
$367$	8.55337	−	14.8149i	0.446482	−	0.773330i	0.998154	+	0.0607312i	$0.0193432\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	11.0759	−	14.5817i	0.575031	−	0.757043i
$372$		0			0
$373$	−14.0680	−	24.3666i	−0.728415	−	1.26165i	−0.957553	−	0.288258i	$-0.906924\pi$
$373$	−14.0680	−	24.3666i	−0.728415	−	1.26165i	0.229137	−	0.973394i	$-0.426410\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−9.98509			−0.514258
$378$		0			0
$379$	−1.47949			−0.0759960			−0.0379980	−	0.999278i	$-0.512098\pi$
$379$	−1.47949			−0.0759960			−0.0379980	+	0.999278i	$0.512098\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−2.05468	−	3.55880i	−0.104989	−	0.181846i	0.808745	−	0.588160i	$-0.200147\pi$
$383$	−2.05468	−	3.55880i	−0.104989	−	0.181846i	−0.913734	+	0.406314i	$0.866814\pi$
$384$		0			0
$385$	−7.43380	−	0.941660i	−0.378862	−	0.0479914i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−0.391713	+	0.678466i	−0.0198606	+	0.0343996i	−0.875785	−	0.482702i	$-0.839656\pi$
$389$	−0.391713	+	0.678466i	−0.0198606	+	0.0343996i	0.855924	+	0.517101i	$0.172989\pi$
$390$		0			0
$391$	32.9936			1.66856
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−8.73001	+	15.1208i	−0.439255	+	0.760811i
$396$		0			0
$397$	12.0097	+	20.8015i	0.602751	+	1.04400i	0.992403	+	0.123033i	$0.0392622\pi$
$397$	12.0097	+	20.8015i	0.602751	+	1.04400i	−0.389651	+	0.920963i	$0.627404\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−7.64257	−	13.2373i	−0.381652	−	0.661040i	0.609647	−	0.792673i	$-0.291311\pi$
$401$	−7.64257	−	13.2373i	−0.381652	−	0.661040i	−0.991299	+	0.131633i	$0.957978\pi$
$402$		0			0
$403$	−5.85556	+	10.1421i	−0.291686	+	0.505215i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−0.138468			−0.00686361
$408$		0			0
$409$	0.799763	−	1.38523i	0.0395458	−	0.0684953i	−0.845575	−	0.533857i	$-0.820742\pi$
$409$	0.799763	−	1.38523i	0.0395458	−	0.0684953i	0.885121	+	0.465361i	$0.154076\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	5.61110	−	7.38716i	0.276104	−	0.363498i
$414$		0			0
$415$	6.26597	+	10.8530i	0.307584	+	0.532751i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	0.416537			0.0203492			0.0101746	−	0.999948i	$-0.496761\pi$
$419$	0.416537			0.0203492			0.0101746	+	0.999948i	$0.496761\pi$
$420$		0			0
$421$	−35.1154			−1.71142			−0.855709	−	0.517457i	$-0.826879\pi$
$421$	−35.1154			−1.71142			−0.855709	+	0.517457i	$0.826879\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−2.23314	−	3.86791i	−0.108323	−	0.187621i
$426$		0			0
$427$	7.54135	+	17.9571i	0.364951	+	0.869007i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	15.5292	−	26.8974i	0.748017	−	1.29560i	−0.200756	−	0.979641i	$-0.564340\pi$
$431$	15.5292	−	26.8974i	0.748017	−	1.29560i	0.948772	−	0.315961i	$-0.102327\pi$
$432$		0			0
$433$	−3.62276			−0.174099			−0.0870494	−	0.996204i	$-0.527744\pi$
$433$	−3.62276			−0.174099			−0.0870494	+	0.996204i	$0.527744\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	15.2832	−	26.4713i	0.731095	−	1.26629i
$438$		0			0
$439$	−1.94631	−	3.37111i	−0.0928925	−	0.160894i	0.815835	−	0.578285i	$-0.196278\pi$
$439$	−1.94631	−	3.37111i	−0.0928925	−	0.160894i	−0.908727	+	0.417391i	$0.862945\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−11.2585	−	19.5003i	−0.534908	−	0.926488i	−0.999168	−	0.0407889i	$-0.987013\pi$
$443$	−11.2585	−	19.5003i	−0.534908	−	0.926488i	0.464260	−	0.885699i	$-0.346320\pi$
$444$		0			0
$445$	−1.33572	+	2.31353i	−0.0633191	+	0.109672i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	7.40582			0.349502			0.174751	−	0.984613i	$-0.444088\pi$
$449$	7.40582			0.349502			0.174751	+	0.984613i	$0.444088\pi$
$450$		0			0
$451$	−13.6892	+	23.7104i	−0.644599	+	1.11648i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−1.11544	−	2.65604i	−0.0522926	−	0.124517i
$456$		0			0
$457$	−12.6107	−	21.8424i	−0.589905	−	1.02174i	−0.994244	−	0.107136i	$-0.965832\pi$
$457$	−12.6107	−	21.8424i	−0.589905	−	1.02174i	0.404340	−	0.914609i	$-0.367501\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	31.2593			1.45589			0.727946	−	0.685634i	$-0.240475\pi$
$461$	31.2593			1.45589			0.727946	+	0.685634i	$0.240475\pi$
$462$		0			0
$463$	−17.2062			−0.799641			−0.399821	−	0.916593i	$-0.630928\pi$
$463$	−17.2062			−0.799641			−0.399821	+	0.916593i	$0.630928\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	1.38456	+	2.39813i	0.0640698	+	0.110972i	0.896281	−	0.443487i	$-0.146259\pi$
$467$	1.38456	+	2.39813i	0.0640698	+	0.110972i	−0.832211	+	0.554459i	$0.812925\pi$
$468$		0			0
$469$	−22.0024	+	28.9668i	−1.01598	+	1.33756i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−8.79334	+	15.2305i	−0.404318	+	0.700300i
$474$		0			0
$475$	−4.13771			−0.189851
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−13.5969	+	23.5505i	−0.621258	+	1.07605i	0.367994	+	0.929828i	$0.380045\pi$
$479$	−13.5969	+	23.5505i	−0.621258	+	1.07605i	−0.989252	+	0.146222i	$0.953289\pi$
$480$		0			0
$481$	−0.0266169	−	0.0461019i	−0.00121363	−	0.00210207i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−6.98624	−	12.1005i	−0.317229	−	0.549457i
$486$		0			0
$487$	−1.07229	+	1.85725i	−0.0485899	+	0.0841601i	−0.889297	−	0.457329i	$-0.848806\pi$
$487$	−1.07229	+	1.85725i	−0.0485899	+	0.0841601i	0.840708	+	0.541489i	$0.182139\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	22.9253			1.03460			0.517302	−	0.855803i	$-0.326937\pi$
$491$	22.9253			1.03460			0.517302	+	0.855803i	$0.326937\pi$
$492$		0			0
$493$	−20.4791	+	35.4708i	−0.922332	+	1.59753i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	19.7021	+	2.49572i	0.883761	+	0.111948i
$498$		0			0
$499$	−8.34505	−	14.4541i	−0.373576	−	0.647053i	0.616537	−	0.787326i	$-0.288535\pi$
$499$	−8.34505	−	14.4541i	−0.373576	−	0.647053i	−0.990113	+	0.140274i	$0.955202\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−42.1562			−1.87965			−0.939825	−	0.341656i	$-0.889012\pi$
$503$	−42.1562			−1.87965			−0.939825	+	0.341656i	$0.889012\pi$
$504$		0			0
$505$	−9.90753			−0.440879
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−14.3712	−	24.8917i	−0.636992	−	1.10330i	−0.986089	−	0.166217i	$-0.946845\pi$
$509$	−14.3712	−	24.8917i	−0.636992	−	1.10330i	0.349097	−	0.937087i	$-0.386488\pi$
$510$		0			0
$511$	−15.9294	+	20.9715i	−0.704675	+	0.927724i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	7.24252	−	12.5444i	0.319144	−	0.552773i
$516$		0			0
$517$	2.10527			0.0925897
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−20.6053	+	35.6895i	−0.902737	+	1.56359i	−0.0788096	+	0.996890i	$0.525112\pi$
$521$	−20.6053	+	35.6895i	−0.902737	+	1.56359i	−0.823927	+	0.566696i	$0.808221\pi$
$522$		0			0
$523$	7.57589	+	13.1218i	0.331270	+	0.573777i	0.982761	−	0.184879i	$-0.0591895\pi$
$523$	7.57589	+	13.1218i	0.331270	+	0.573777i	−0.651491	+	0.758656i	$0.725856\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	24.0191	+	41.6023i	1.04629	+	1.81223i
$528$		0			0
$529$	−15.7859	+	27.3419i	−0.686342	+	1.18878i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−10.5256			−0.455914
$534$		0			0
$535$	−1.23314	+	2.13586i	−0.0533133	+	0.0923413i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−13.8805	+	14.1552i	−0.597876	+	0.609706i
$540$		0			0
$541$	−19.4197	−	33.6359i	−0.834917	−	1.44612i	−0.894098	−	0.447871i	$-0.852182\pi$
$541$	−19.4197	−	33.6359i	−0.834917	−	1.44612i	0.0591814	−	0.998247i	$-0.481151\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−11.2824			−0.483284
$546$		0			0
$547$	−25.2415			−1.07925			−0.539625	−	0.841906i	$-0.681434\pi$
$547$	−25.2415			−1.07925			−0.539625	+	0.841906i	$0.681434\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	18.9725	+	32.8614i	0.808257	+	1.39994i
$552$		0			0
$553$	17.8868	+	42.5914i	0.760626	+	1.81117i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	4.58475	−	7.94103i	0.194262	−	0.336472i	−0.752396	−	0.658711i	$-0.771102\pi$
$557$	4.58475	−	7.94103i	0.194262	−	0.336472i	0.946658	+	0.322239i	$0.104435\pi$
$558$		0			0
$559$	−6.76118			−0.285967
$560$		0			0
$561$		0			0
$562$		0			0
$563$	7.69021	−	13.3198i	0.324104	−	0.561364i	−0.657227	−	0.753693i	$-0.728271\pi$
$563$	7.69021	−	13.3198i	0.324104	−	0.561364i	0.981331	+	0.192329i	$0.0616041\pi$
$564$		0			0
$565$	4.24955	+	7.36044i	0.178780	+	0.309656i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	8.03413	+	13.9155i	0.336808	+	0.583369i	0.983831	−	0.179102i	$-0.0573192\pi$
$569$	8.03413	+	13.9155i	0.336808	+	0.583369i	−0.647022	+	0.762471i	$0.723986\pi$
$570$		0			0
$571$	−19.6200	+	33.9829i	−0.821073	+	1.42214i	0.0838115	+	0.996482i	$0.473291\pi$
$571$	−19.6200	+	33.9829i	−0.821073	+	1.42214i	−0.904884	+	0.425658i	$0.860043\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	7.38727			0.308070
$576$		0			0
$577$	−11.0351	+	19.1133i	−0.459396	+	0.795696i	−0.998929	−	0.0462677i	$-0.985267\pi$
$577$	−11.0351	+	19.1133i	−0.459396	+	0.795696i	0.539534	+	0.841964i	$0.318601\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	32.8935	+	4.16671i	1.36465	+	0.172864i
$582$		0			0
$583$	−9.80069	−	16.9753i	−0.405903	−	0.703045i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	23.6421			0.975815			0.487908	−	0.872895i	$-0.337760\pi$
$587$	23.6421			0.975815			0.487908	+	0.872895i	$0.337760\pi$
$588$		0			0
$589$	44.5043			1.83377
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−15.2120	−	26.3479i	−0.624681	−	1.08198i	−0.988602	−	0.150550i	$-0.951896\pi$
$593$	−15.2120	−	26.3479i	−0.624681	−	1.08198i	0.363921	−	0.931430i	$-0.381438\pi$
$594$		0			0
$595$	−11.7230	−	1.48498i	−0.480596	−	0.0608783i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	11.3685	−	19.6908i	0.464504	−	0.804545i	−0.534675	−	0.845058i	$-0.679566\pi$
$599$	11.3685	−	19.6908i	0.464504	−	0.804545i	0.999179	+	0.0405131i	$0.0128992\pi$
$600$		0			0
$601$	−10.5185			−0.429058			−0.214529	−	0.976718i	$-0.568822\pi$
$601$	−10.5185			−0.429058			−0.214529	+	0.976718i	$0.568822\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	1.48942	−	2.57975i	0.0605535	−	0.104882i
$606$		0			0
$607$	8.60311	+	14.9010i	0.349190	+	0.604814i	0.986106	−	0.166119i	$-0.0531236\pi$
$607$	8.60311	+	14.9010i	0.349190	+	0.604814i	−0.636916	+	0.770933i	$0.719790\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	0.404684	+	0.700934i	0.0163718	+	0.0283567i
$612$		0			0
$613$	−14.4449	+	25.0193i	−0.583425	+	1.01052i	0.411645	+	0.911344i	$0.364954\pi$
$613$	−14.4449	+	25.0193i	−0.583425	+	1.01052i	−0.995070	+	0.0991770i	$0.968379\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−31.7125			−1.27670			−0.638349	−	0.769747i	$-0.720382\pi$
$617$	−31.7125			−1.27670			−0.638349	+	0.769747i	$0.720382\pi$
$618$		0			0
$619$	8.70701	−	15.0810i	0.349964	−	0.606156i	−0.636278	−	0.771460i	$-0.719527\pi$
$619$	8.70701	−	15.0810i	0.349964	−	0.606156i	0.986243	+	0.165303i	$0.0528604\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	2.73674	+	6.51661i	0.109645	+	0.261082i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−0.218362			−0.00870666
$630$		0			0
$631$	−7.02512			−0.279666			−0.139833	−	0.990175i	$-0.544657\pi$
$631$	−7.02512			−0.279666			−0.139833	+	0.990175i	$0.544657\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−4.42547	−	7.66514i	−0.175619	−	0.304182i
$636$		0			0
$637$	−7.38102	−	1.90044i	−0.292447	−	0.0752983i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−12.7864	+	22.1468i	−0.505034	+	0.874744i	0.494949	+	0.868922i	$0.335187\pi$
$641$	−12.7864	+	22.1468i	−0.505034	+	0.874744i	−0.999983	+	0.00582234i	$0.998147\pi$
$642$		0			0
$643$	40.5232			1.59808			0.799039	−	0.601279i	$-0.205342\pi$
$643$	40.5232			1.59808			0.799039	+	0.601279i	$0.205342\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	15.4893	−	26.8283i	0.608948	−	1.05473i	−0.382466	−	0.923970i	$-0.624925\pi$
$647$	15.4893	−	26.8283i	0.608948	−	1.05473i	0.991414	−	0.130760i	$-0.0417417\pi$
$648$		0			0
$649$	−4.96508	−	8.59978i	−0.194897	−	0.337571i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−14.4724	−	25.0670i	−0.566349	−	0.980946i	−0.996923	−	0.0783902i	$-0.975022\pi$
$653$	−14.4724	−	25.0670i	−0.566349	−	0.980946i	0.430573	−	0.902556i	$-0.358311\pi$
$654$		0			0
$655$	−3.16919	+	5.48919i	−0.123830	+	0.214481i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−9.18836			−0.357928			−0.178964	−	0.983856i	$-0.557275\pi$
$659$	−9.18836			−0.357928			−0.178964	+	0.983856i	$0.557275\pi$
$660$		0			0
$661$	8.11457	−	14.0549i	0.315620	−	0.546670i	−0.663949	−	0.747778i	$-0.731121\pi$
$661$	8.11457	−	14.0549i	0.315620	−	0.546670i	0.979569	+	0.201108i	$0.0644541\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−6.62171	+	8.71766i	−0.256779	+	0.338057i
$666$		0			0
$667$	−33.8726	−	58.6691i	−1.31155	−	2.27168i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	20.8487			0.804854
$672$		0			0
$673$	−3.68822			−0.142171			−0.0710853	−	0.997470i	$-0.522646\pi$
$673$	−3.68822			−0.142171			−0.0710853	+	0.997470i	$0.522646\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−12.9857	−	22.4919i	−0.499082	−	0.864436i	0.500917	−	0.865495i	$-0.332996\pi$
$677$	−12.9857	−	22.4919i	−0.499082	−	0.864436i	−0.999999	+	0.00105961i	$0.999663\pi$
$678$		0			0
$679$	−36.6747	−	4.64568i	−1.40744	−	0.178285i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	16.0050	−	27.7214i	0.612413	−	1.06073i	−0.378419	−	0.925634i	$-0.623532\pi$
$683$	16.0050	−	27.7214i	0.612413	−	1.06073i	0.990832	−	0.135096i	$-0.0431344\pi$
$684$		0			0
$685$	3.45386			0.131965
$686$		0			0
$687$		0			0
$688$		0			0
$689$	3.76786	−	6.52613i	0.143544	−	0.248626i
$690$		0			0
$691$	13.8191	+	23.9354i	0.525705	+	0.910547i	0.999552	+	0.0299401i	$0.00953166\pi$
$691$	13.8191	+	23.9354i	0.525705	+	0.910547i	−0.473847	+	0.880607i	$0.657135\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−7.85792	−	13.6103i	−0.298068	−	0.516268i
$696$		0			0
$697$	−21.5876	+	37.3909i	−0.817690	+	1.41628i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	33.7157			1.27342			0.636712	−	0.771102i	$-0.280294\pi$
$701$	33.7157			1.27342			0.636712	+	0.771102i	$0.280294\pi$
$702$		0			0
$703$	−0.101149	+	0.175195i	−0.00381491	+	0.00660761i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−15.8553	+	20.8740i	−0.596301	+	0.785047i
$708$		0			0
$709$	2.26863	+	3.92937i	0.0852000	+	0.147571i	0.905476	−	0.424397i	$-0.139514\pi$
$709$	2.26863	+	3.92937i	0.0852000	+	0.147571i	−0.820276	+	0.571967i	$0.806180\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−79.4557			−2.97564
$714$		0			0
$715$	−3.08373			−0.115325
$716$		0			0
$717$		0			0
$718$		0			0
$719$	9.18661	+	15.9117i	0.342603	+	0.593405i	0.984915	−	0.173038i	$-0.0553582\pi$
$719$	9.18661	+	15.9117i	0.342603	+	0.593405i	−0.642313	+	0.766443i	$0.722025\pi$
$720$		0			0
$721$	−14.8391	−	35.3344i	−0.552639	−	1.31592i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−4.58527	+	7.94192i	−0.170293	+	0.294956i
$726$		0			0
$727$	17.7650			0.658866			0.329433	−	0.944179i	$-0.393142\pi$
$727$	17.7650			0.658866			0.329433	+	0.944179i	$0.393142\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−13.8670	+	24.0183i	−0.512888	+	0.888348i
$732$		0			0
$733$	6.11096	+	10.5845i	0.225713	+	0.390947i	0.956533	−	0.291623i	$-0.0941954\pi$
$733$	6.11096	+	10.5845i	0.225713	+	0.390947i	−0.730820	+	0.682570i	$0.760862\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	19.4692	+	33.7217i	0.717159	+	1.24216i
$738$		0			0
$739$	6.02182	−	10.4301i	0.221516	−	0.383677i	−0.733752	−	0.679417i	$-0.762233\pi$
$739$	6.02182	−	10.4301i	0.221516	−	0.383677i	0.955269	+	0.295740i	$0.0955661\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−46.7408			−1.71475			−0.857376	−	0.514690i	$-0.827907\pi$
$743$	−46.7408			−1.71475			−0.857376	+	0.514690i	$0.827907\pi$
$744$		0			0
$745$	11.4362	−	19.8080i	0.418988	−	0.725709i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	2.52657	+	6.01616i	0.0923188	+	0.219826i
$750$		0			0
$751$	10.4924	+	18.1734i	0.382874	+	0.663157i	0.991472	−	0.130322i	$-0.0416010\pi$
$751$	10.4924	+	18.1734i	0.382874	+	0.663157i	−0.608598	+	0.793479i	$0.708268\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	16.8020			0.611489
$756$		0			0
$757$	−37.3254			−1.35661			−0.678307	−	0.734778i	$-0.737286\pi$
$757$	−37.3254			−1.35661			−0.678307	+	0.734778i	$0.737286\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−21.1880	−	36.6987i	−0.768065	−	1.33033i	−0.938611	−	0.344977i	$-0.887887\pi$
$761$	−21.1880	−	36.6987i	−0.768065	−	1.33033i	0.170546	−	0.985350i	$-0.445447\pi$
$762$		0			0
$763$	−18.0555	+	23.7706i	−0.653655	+	0.860554i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	1.90882	−	3.30617i	0.0689235	−	0.119379i
$768$		0			0
$769$	−7.14491			−0.257652			−0.128826	−	0.991667i	$-0.541121\pi$
$769$	−7.14491			−0.257652			−0.128826	+	0.991667i	$0.541121\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−4.60566	+	7.97724i	−0.165654	+	0.286921i	−0.936887	−	0.349631i	$-0.886307\pi$
$773$	−4.60566	+	7.97724i	−0.165654	+	0.286921i	0.771233	+	0.636553i	$0.219640\pi$
$774$		0			0
$775$	5.37788	+	9.31476i	0.193179	+	0.334596i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	19.9995	+	34.6402i	0.716557	+	1.24111i
$780$		0			0
$781$	10.6294	−	18.4107i	0.380350	−	0.658786i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−4.06295			−0.145013
$786$		0			0
$787$	19.5089	−	33.7904i	0.695418	−	1.20450i	−0.274622	−	0.961552i	$-0.588553\pi$
$787$	19.5089	−	33.7904i	0.695418	−	1.20450i	0.970040	−	0.242947i	$-0.0781140\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	22.3083	+	2.82585i	0.793190	+	0.100476i
$792$		0			0
$793$	4.00763	+	6.94141i	0.142315	+	0.246497i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−15.4359			−0.546769			−0.273384	−	0.961905i	$-0.588143\pi$
$797$	−15.4359			−0.546769			−0.273384	+	0.961905i	$0.588143\pi$
$798$		0			0
$799$	3.31998			0.117452
$800$		0			0
$801$		0			0
$802$		0			0
$803$	14.0954	+	24.4140i	0.497417	+	0.861551i
$804$		0			0
$805$	11.8221	−	15.5641i	0.416673	−	0.548562i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−20.6194	+	35.7139i	−0.724940	+	1.25563i	0.234059	+	0.972222i	$0.424799\pi$
$809$	−20.6194	+	35.7139i	−0.724940	+	1.25563i	−0.958999	+	0.283410i	$0.908534\pi$
$810$		0			0
$811$	30.1064			1.05718			0.528590	−	0.848877i	$-0.322721\pi$
$811$	30.1064			1.05718			0.528590	+	0.848877i	$0.322721\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−5.32857	+	9.22935i	−0.186651	+	0.323290i
$816$		0			0
$817$	12.8468	+	22.2513i	0.449453	+	0.778476i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−19.8978	−	34.4640i	−0.694437	−	1.20280i	−0.970370	−	0.241623i	$-0.922320\pi$
$821$	−19.8978	−	34.4640i	−0.694437	−	1.20280i	0.275933	−	0.961177i	$-0.411013\pi$
$822$		0			0
$823$	3.61410	−	6.25981i	0.125980	−	0.218203i	−0.796136	−	0.605118i	$-0.793126\pi$
$823$	3.61410	−	6.25981i	0.125980	−	0.218203i	0.922116	+	0.386915i	$0.126459\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	35.0639			1.21929			0.609645	−	0.792675i	$-0.291312\pi$
$827$	35.0639			1.21929			0.609645	+	0.792675i	$0.291312\pi$
$828$		0			0
$829$	6.88889	−	11.9319i	0.239261	−	0.414412i	−0.721241	−	0.692684i	$-0.756428\pi$
$829$	6.88889	−	11.9319i	0.239261	−	0.414412i	0.960502	+	0.278272i	$0.0897615\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−21.8893	+	22.3225i	−0.758420	+	0.773427i
$834$		0			0
$835$	−4.69363	−	8.12961i	−0.162430	−	0.281337i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	30.7017			1.05994			0.529970	−	0.848016i	$-0.322203\pi$
$839$	30.7017			1.05994			0.529970	+	0.848016i	$0.322203\pi$
$840$		0			0
$841$	55.0988			1.89996
$842$		0			0
$843$		0			0
$844$		0			0
$845$	5.90723	+	10.2316i	0.203215	+	0.351979i
$846$		0			0
$847$	−3.05166	−	7.26648i	−0.104856	−	0.249679i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	0.180586	−	0.312785i	0.00619042	−	0.0107221i
$852$		0			0
$853$	13.4895			0.461873			0.230937	−	0.972969i	$-0.425821\pi$
$853$	13.4895			0.461873			0.230937	+	0.972969i	$0.425821\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	23.5086	−	40.7180i	0.803037	−	1.39090i	−0.114571	−	0.993415i	$-0.536549\pi$
$857$	23.5086	−	40.7180i	0.803037	−	1.39090i	0.917608	−	0.397486i	$-0.130117\pi$
$858$		0			0
$859$	1.94631	+	3.37111i	0.0664074	+	0.115021i	0.897317	−	0.441386i	$-0.145513\pi$
$859$	1.94631	+	3.37111i	0.0664074	+	0.115021i	−0.830910	+	0.556407i	$0.812180\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	14.3113	+	24.7880i	0.487163	+	0.843792i	0.999891	−	0.0147595i	$-0.00469826\pi$
$863$	14.3113	+	24.7880i	0.487163	+	0.843792i	−0.512728	+	0.858551i	$0.671365\pi$
$864$		0			0
$865$	−8.71005	+	15.0862i	−0.296150	+	0.512948i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	49.4497			1.67747
$870$		0			0
$871$	−7.48493	+	12.9643i	−0.253617	+	0.439278i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−2.62478	−	0.332488i	−0.0887336	−	0.0112401i
$876$		0			0
$877$	26.9392	+	46.6601i	0.909673	+	1.57560i	0.814519	+	0.580137i	$0.197001\pi$
$877$	26.9392	+	46.6601i	0.909673	+	1.57560i	0.0951545	+	0.995463i	$0.469665\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	4.97237			0.167523			0.0837616	−	0.996486i	$-0.473307\pi$
$881$	4.97237			0.167523			0.0837616	+	0.996486i	$0.473307\pi$
$882$		0			0
$883$	−18.8864			−0.635577			−0.317789	−	0.948162i	$-0.602940\pi$
$883$	−18.8864			−0.635577			−0.317789	+	0.948162i	$0.602940\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	16.3735	+	28.3597i	0.549767	+	0.952225i	0.998290	+	0.0584533i	$0.0186169\pi$
$887$	16.3735	+	28.3597i	0.549767	+	0.952225i	−0.448523	+	0.893771i	$0.648050\pi$
$888$		0			0
$889$	−23.2317	−	2.94283i	−0.779167	−	0.0986992i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	1.53787	−	2.66367i	0.0514629	−	0.0891363i
$894$		0			0
$895$	2.24059			0.0748948
$896$		0			0
$897$		0			0
$898$		0			0
$899$	49.3181	−	85.4214i	1.64485	−	2.84896i
$900$		0			0
$901$	−15.4555	−	26.7698i	−0.514898	−	0.891830i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−11.3216	−	19.6096i	−0.376342	−	0.651844i
$906$		0			0
$907$	−14.5818	+	25.2563i	−0.484179	+	0.838623i	−0.999835	−	0.0181731i	$-0.994215\pi$
$907$	−14.5818	+	25.2563i	−0.484179	+	0.838623i	0.515656	+	0.856796i	$0.327548\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−13.1370			−0.435249			−0.217624	−	0.976033i	$-0.569831\pi$
$911$	−13.1370			−0.435249			−0.217624	+	0.976033i	$0.569831\pi$
$912$		0			0
$913$	17.7463	−	30.7374i	0.587315	−	1.01726i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	6.49332	+	15.4616i	0.214428	+	0.510588i
$918$		0			0
$919$	4.00939	+	6.94446i	0.132257	+	0.229077i	0.924546	−	0.381069i	$-0.124444\pi$
$919$	4.00939	+	6.94446i	0.132257	+	0.229077i	−0.792289	+	0.610146i	$0.791111\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	8.17293			0.269015
$924$		0			0
$925$	−0.0488912			−0.00160753
$926$		0			0
$927$		0			0
$928$		0			0
$929$	10.9186	+	18.9117i	0.358229	+	0.620471i	0.987665	−	0.156581i	$-0.0500473\pi$
$929$	10.9186	+	18.9117i	0.358229	+	0.620471i	−0.629436	+	0.777052i	$0.716714\pi$
$930$		0			0
$931$	7.77014	+	27.9023i	0.254656	+	0.914461i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−6.32462	+	10.9546i	−0.206837	+	0.358253i
$936$		0			0
$937$	40.2895			1.31620			0.658100	−	0.752930i	$-0.271360\pi$
$937$	40.2895			1.31620			0.658100	+	0.752930i	$0.271360\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	8.29400	−	14.3656i	0.270377	−	0.468306i	−0.698582	−	0.715530i	$-0.746185\pi$
$941$	8.29400	−	14.3656i	0.270377	−	0.468306i	0.968958	+	0.247224i	$0.0795184\pi$
$942$		0			0
$943$	−35.7061	−	61.8448i	−1.16275	−	2.01395i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−16.8050	−	29.1071i	−0.546089	−	0.945854i	−0.998537	−	0.0540637i	$-0.982783\pi$
$947$	−16.8050	−	29.1071i	−0.546089	−	0.945854i	0.452448	−	0.891791i	$-0.350551\pi$
$948$		0			0
$949$	−5.41897	+	9.38593i	−0.175907	+	0.304680i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	0.344657			0.0111645			0.00558227	−	0.999984i	$-0.498223\pi$
$953$	0.344657			0.0111645			0.00558227	+	0.999984i	$0.498223\pi$
$954$		0			0
$955$	8.71583	−	15.0963i	0.282038	−	0.488504i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	5.52732	−	7.27686i	0.178486	−	0.234982i
$960$		0			0
$961$	−42.3432	−	73.3406i	−1.36591	−	2.36583i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	7.98594			0.257077
$966$		0			0
$967$	22.1298			0.711645			0.355823	−	0.934554i	$-0.384201\pi$
$967$	22.1298			0.711645			0.355823	+	0.934554i	$0.384201\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	11.9215	+	20.6486i	0.382579	+	0.662646i	0.991430	−	0.130638i	$-0.0417027\pi$
$971$	11.9215	+	20.6486i	0.382579	+	0.662646i	−0.608851	+	0.793284i	$0.708369\pi$
$972$		0			0
$973$	−41.2505	−	5.22532i	−1.32243	−	0.167516i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−28.3485	+	49.1011i	−0.906950	+	1.57088i	−0.0886720	+	0.996061i	$0.528262\pi$
$977$	−28.3485	+	49.1011i	−0.906950	+	1.57088i	−0.818278	+	0.574823i	$0.805071\pi$
$978$		0			0
$979$	7.56595			0.241809
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−5.81978	+	10.0802i	−0.185622	+	0.321507i	−0.943786	−	0.330557i	$-0.892763\pi$
$983$	−5.81978	+	10.0802i	−0.185622	+	0.321507i	0.758164	+	0.652064i	$0.226097\pi$
$984$		0			0
$985$	−11.2229	−	19.4386i	−0.357590	−	0.619364i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−22.9361	−	39.7264i	−0.729324	−	1.26323i
$990$		0			0
$991$	−27.3065	+	47.2962i	−0.867419	+	1.50241i	−0.00279476	+	0.999996i	$0.500890\pi$
$991$	−27.3065	+	47.2962i	−0.867419	+	1.50241i	−0.864625	+	0.502418i	$0.832444\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−9.79484			−0.310517
$996$		0			0
$997$	−0.727355	+	1.25981i	−0.0230355	+	0.0398987i	−0.877313	−	0.479918i	$-0.840666\pi$
$997$	−0.727355	+	1.25981i	−0.0230355	+	0.0398987i	0.854278	+	0.519817i	$0.174000\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2520.2.bi.r.361.1	✓	10
3.2	odd	2		2520.2.bi.s.361.1	yes	10
7.2	even	3	inner	2520.2.bi.r.1801.1	yes	10
21.2	odd	6		2520.2.bi.s.1801.1	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2520.2.bi.r.361.1	✓	10	1.1	even	1	trivial
2520.2.bi.r.1801.1	yes	10	7.2	even	3	inner
2520.2.bi.s.361.1	yes	10	3.2	odd	2
2520.2.bi.s.1801.1	yes	10	21.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2520 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2520.bi (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{5} +(-2.62478 - 0.332488i) q^{7} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{5} +(-2.62478 - 0.332488i) q^{7} +(-1.41608 + 2.45273i) q^{11} -1.08882 q^{13} +(-2.23314 + 3.86791i) q^{17} +(2.06886 + 3.58337i) q^{19} +(-3.69363 - 6.39756i) q^{23} +(-0.500000 + 0.866025i) q^{25} +9.17054 q^{29} +(5.37788 - 9.31476i) q^{31} +(1.02445 + 2.43937i) q^{35} +(0.0244456 + 0.0423411i) q^{37} +9.66694 q^{41} +6.20962 q^{43} +(-0.371671 - 0.643754i) q^{47} +(6.77890 + 1.74541i) q^{49} +(-3.46049 + 5.99375i) q^{53} +2.83217 q^{55} +(-1.75311 + 3.03647i) q^{59} +(-3.68070 - 6.37515i) q^{61} +(0.544411 + 0.942948i) q^{65} +(6.87433 - 11.9067i) q^{67} -7.50621 q^{71} +(4.97691 - 8.62026i) q^{73} +(4.53240 - 5.96703i) q^{77} +(-8.73001 - 15.1208i) q^{79} -12.5319 q^{83} +4.46628 q^{85} +(-1.33572 - 2.31353i) q^{89} +(2.85792 + 0.362020i) q^{91} +(2.06886 - 3.58337i) q^{95} +13.9725 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 5 q^{5} - q^{7}+O(q^{10}) \) 10 * q - 5 * q^5 - q^7	\( 10 q - 5 q^{5} - q^{7} - 2 q^{11} + 6 q^{13} + 2 q^{17} + q^{19} + 8 q^{23} - 5 q^{25} + 7 q^{31} - q^{35} - 11 q^{37} + 20 q^{41} + 6 q^{43} - 23 q^{49} - 14 q^{53} + 4 q^{55} + 4 q^{59} - 6 q^{61} - 3 q^{65} - 7 q^{67} - 32 q^{71} + 3 q^{73} + 8 q^{77} - 19 q^{79} + 28 q^{83} - 4 q^{85} - 18 q^{89} - 21 q^{91} + q^{95} + 48 q^{97}+O(q^{100}) \) 10 * q - 5 * q^5 - q^7 - 2 * q^11 + 6 * q^13 + 2 * q^17 + q^19 + 8 * q^23 - 5 * q^25 + 7 * q^31 - q^35 - 11 * q^37 + 20 * q^41 + 6 * q^43 - 23 * q^49 - 14 * q^53 + 4 * q^55 + 4 * q^59 - 6 * q^61 - 3 * q^65 - 7 * q^67 - 32 * q^71 + 3 * q^73 + 8 * q^77 - 19 * q^79 + 28 * q^83 - 4 * q^85 - 18 * q^89 - 21 * q^91 + q^95 + 48 * q^97

Introduction

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