LMFDB - Embedded newform 1260.2.s.a.541.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1260,2,Mod(361,1260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1260, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("1260.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1260.s (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:	$10.0611506547$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 420)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			541.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1260.541
Dual form			1260.2.s.a.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{5} +(-2.50000 + 0.866025i) q^{7} +O(q^{10})$	$q+(-0.500000 + 0.866025i) q^{5} +(-2.50000 + 0.866025i) q^{7} +(-2.00000 - 3.46410i) q^{11} +7.00000 q^{13} +(-3.00000 - 5.19615i) q^{17} +(-1.50000 + 2.59808i) q^{19} +(-1.00000 + 1.73205i) q^{23} +(-0.500000 - 0.866025i) q^{25} +2.00000 q^{29} +(-3.50000 - 6.06218i) q^{31} +(0.500000 - 2.59808i) q^{35} +(3.50000 - 6.06218i) q^{37} +8.00000 q^{41} +5.00000 q^{43} +(5.00000 - 8.66025i) q^{47} +(5.50000 - 4.33013i) q^{49} +(-4.00000 - 6.92820i) q^{53} +4.00000 q^{55} +(5.00000 + 8.66025i) q^{59} +(3.00000 - 5.19615i) q^{61} +(-3.50000 + 6.06218i) q^{65} +(-1.50000 - 2.59808i) q^{67} +(-7.50000 - 12.9904i) q^{73} +(8.00000 + 6.92820i) q^{77} +(-0.500000 + 0.866025i) q^{79} -8.00000 q^{83} +6.00000 q^{85} +(1.00000 - 1.73205i) q^{89} +(-17.5000 + 6.06218i) q^{91} +(-1.50000 - 2.59808i) q^{95} -10.0000 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{5} - 5 q^{7}+O(q^{10}) $ 2 * q - q^5 - 5 * q^7	$ 2 q - q^{5} - 5 q^{7} - 4 q^{11} + 14 q^{13} - 6 q^{17} - 3 q^{19} - 2 q^{23} - q^{25} + 4 q^{29} - 7 q^{31} + q^{35} + 7 q^{37} + 16 q^{41} + 10 q^{43} + 10 q^{47} + 11 q^{49} - 8 q^{53} + 8 q^{55} + 10 q^{59} + 6 q^{61} - 7 q^{65} - 3 q^{67} - 15 q^{73} + 16 q^{77} - q^{79} - 16 q^{83} + 12 q^{85} + 2 q^{89} - 35 q^{91} - 3 q^{95} - 20 q^{97}+O(q^{100}) $ 2 * q - q^5 - 5 * q^7 - 4 * q^11 + 14 * q^13 - 6 * q^17 - 3 * q^19 - 2 * q^23 - q^25 + 4 * q^29 - 7 * q^31 + q^35 + 7 * q^37 + 16 * q^41 + 10 * q^43 + 10 * q^47 + 11 * q^49 - 8 * q^53 + 8 * q^55 + 10 * q^59 + 6 * q^61 - 7 * q^65 - 3 * q^67 - 15 * q^73 + 16 * q^77 - q^79 - 16 * q^83 + 12 * q^85 + 2 * q^89 - 35 * q^91 - 3 * q^95 - 20 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1260\mathbb{Z}\right)^\times$.

$n$	$281$	$631$	$757$	$1081$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			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
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−2.00000	−	3.46410i	−0.603023	−	1.04447i	−0.992361	−	0.123371i	$-0.960630\pi$
$11$	−2.00000	−	3.46410i	−0.603023	−	1.04447i	0.389338	−	0.921095i	$-0.372704\pi$
$12$		0			0
$13$	7.00000			1.94145			0.970725	−	0.240192i	$-0.0772105\pi$
$13$	7.00000			1.94145			0.970725	+	0.240192i	$0.0772105\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.00000	−	5.19615i	−0.727607	−	1.26025i	−0.957892	−	0.287129i	$-0.907299\pi$
$17$	−3.00000	−	5.19615i	−0.727607	−	1.26025i	0.230285	−	0.973123i	$-0.426034\pi$
$18$		0			0
$19$	−1.50000	+	2.59808i	−0.344124	+	0.596040i	−0.985194	−	0.171442i	$-0.945157\pi$
$19$	−1.50000	+	2.59808i	−0.344124	+	0.596040i	0.641071	+	0.767482i	$0.278491\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.00000	+	1.73205i	−0.208514	+	0.361158i	−0.951247	−	0.308431i	$-0.900196\pi$
$23$	−1.00000	+	1.73205i	−0.208514	+	0.361158i	0.742732	+	0.669588i	$0.233529\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	2.00000			0.371391			0.185695	−	0.982607i	$-0.440546\pi$
$29$	2.00000			0.371391			0.185695	+	0.982607i	$0.440546\pi$
$30$		0			0
$31$	−3.50000	−	6.06218i	−0.628619	−	1.08880i	−0.987829	−	0.155543i	$-0.950287\pi$
$31$	−3.50000	−	6.06218i	−0.628619	−	1.08880i	0.359211	−	0.933257i	$-0.383046\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	0.500000	−	2.59808i	0.0845154	−	0.439155i
$36$		0			0
$37$	3.50000	−	6.06218i	0.575396	−	0.996616i	−0.420602	−	0.907245i	$-0.638181\pi$
$37$	3.50000	−	6.06218i	0.575396	−	0.996616i	0.995998	−	0.0893706i	$-0.0284856\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	8.00000			1.24939			0.624695	−	0.780869i	$-0.285223\pi$
$41$	8.00000			1.24939			0.624695	+	0.780869i	$0.285223\pi$
$42$		0			0
$43$	5.00000			0.762493			0.381246	−	0.924473i	$-0.375495\pi$
$43$	5.00000			0.762493			0.381246	+	0.924473i	$0.375495\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	5.00000	−	8.66025i	0.729325	−	1.26323i	−0.227844	−	0.973698i	$-0.573168\pi$
$47$	5.00000	−	8.66025i	0.729325	−	1.26323i	0.957169	−	0.289530i	$-0.0934991\pi$
$48$		0			0
$49$	5.50000	−	4.33013i	0.785714	−	0.618590i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−4.00000	−	6.92820i	−0.549442	−	0.951662i	−0.998313	−	0.0580651i	$-0.981507\pi$
$53$	−4.00000	−	6.92820i	−0.549442	−	0.951662i	0.448871	−	0.893597i	$-0.351826\pi$
$54$		0			0
$55$	4.00000			0.539360
$56$		0			0
$57$		0			0
$58$		0			0
$59$	5.00000	+	8.66025i	0.650945	+	1.12747i	0.982894	+	0.184172i	$0.0589603\pi$
$59$	5.00000	+	8.66025i	0.650945	+	1.12747i	−0.331949	+	0.943297i	$0.607706\pi$
$60$		0			0
$61$	3.00000	−	5.19615i	0.384111	−	0.665299i	−0.607535	−	0.794293i	$-0.707841\pi$
$61$	3.00000	−	5.19615i	0.384111	−	0.665299i	0.991645	+	0.128994i	$0.0411748\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−3.50000	+	6.06218i	−0.434122	+	0.751921i
$66$		0			0
$67$	−1.50000	−	2.59808i	−0.183254	−	0.317406i	0.759733	−	0.650236i	$-0.225330\pi$
$67$	−1.50000	−	2.59808i	−0.183254	−	0.317406i	−0.942987	+	0.332830i	$0.891996\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	−7.50000	−	12.9904i	−0.877809	−	1.52041i	−0.853740	−	0.520699i	$-0.825671\pi$
$73$	−7.50000	−	12.9904i	−0.877809	−	1.52041i	−0.0240681	−	0.999710i	$-0.507662\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	8.00000	+	6.92820i	0.911685	+	0.789542i
$78$		0			0
$79$	−0.500000	+	0.866025i	−0.0562544	+	0.0974355i	−0.892781	−	0.450490i	$-0.851249\pi$
$79$	−0.500000	+	0.866025i	−0.0562544	+	0.0974355i	0.836527	+	0.547926i	$0.184582\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−8.00000			−0.878114			−0.439057	−	0.898459i	$-0.644687\pi$
$83$	−8.00000			−0.878114			−0.439057	+	0.898459i	$0.644687\pi$
$84$		0			0
$85$	6.00000			0.650791
$86$		0			0
$87$		0			0
$88$		0			0
$89$	1.00000	−	1.73205i	0.106000	−	0.183597i	−0.808146	−	0.588982i	$-0.799529\pi$
$89$	1.00000	−	1.73205i	0.106000	−	0.183597i	0.914146	+	0.405385i	$0.132862\pi$
$90$		0			0
$91$	−17.5000	+	6.06218i	−1.83450	+	0.635489i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−1.50000	−	2.59808i	−0.153897	−	0.266557i
$96$		0			0
$97$	−10.0000			−1.01535			−0.507673	−	0.861550i	$-0.669494\pi$
$97$	−10.0000			−1.01535			−0.507673	+	0.861550i	$0.669494\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	6.00000	+	10.3923i	0.597022	+	1.03407i	0.993258	+	0.115924i	$0.0369830\pi$
$101$	6.00000	+	10.3923i	0.597022	+	1.03407i	−0.396236	+	0.918149i	$0.629684\pi$
$102$		0			0
$103$	3.50000	−	6.06218i	0.344865	−	0.597324i	−0.640464	−	0.767988i	$-0.721258\pi$
$103$	3.50000	−	6.06218i	0.344865	−	0.597324i	0.985329	+	0.170664i	$0.0545913\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.00000	−	1.73205i	0.0966736	−	0.167444i	−0.813632	−	0.581380i	$-0.802513\pi$
$107$	1.00000	−	1.73205i	0.0966736	−	0.167444i	0.910306	+	0.413936i	$0.135846\pi$
$108$		0			0
$109$	1.50000	+	2.59808i	0.143674	+	0.248851i	0.928877	−	0.370387i	$-0.120775\pi$
$109$	1.50000	+	2.59808i	0.143674	+	0.248851i	−0.785203	+	0.619238i	$0.787442\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−18.0000			−1.69330			−0.846649	−	0.532152i	$-0.821383\pi$
$113$	−18.0000			−1.69330			−0.846649	+	0.532152i	$0.821383\pi$
$114$		0			0
$115$	−1.00000	−	1.73205i	−0.0932505	−	0.161515i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	12.0000	+	10.3923i	1.10004	+	0.952661i
$120$		0			0
$121$	−2.50000	+	4.33013i	−0.227273	+	0.393648i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	13.0000			1.15356			0.576782	−	0.816898i	$-0.304308\pi$
$127$	13.0000			1.15356			0.576782	+	0.816898i	$0.304308\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	11.0000	−	19.0526i	0.961074	−	1.66463i	0.241264	−	0.970460i	$-0.422438\pi$
$131$	11.0000	−	19.0526i	0.961074	−	1.66463i	0.719811	−	0.694170i	$-0.244228\pi$
$132$		0			0
$133$	1.50000	−	7.79423i	0.130066	−	0.675845i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	9.00000	+	15.5885i	0.768922	+	1.33181i	0.938148	+	0.346235i	$0.112540\pi$
$137$	9.00000	+	15.5885i	0.768922	+	1.33181i	−0.169226	+	0.985577i	$0.554127\pi$
$138$		0			0
$139$	−13.0000			−1.10265			−0.551323	−	0.834292i	$-0.685877\pi$
$139$	−13.0000			−1.10265			−0.551323	+	0.834292i	$0.685877\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−14.0000	−	24.2487i	−1.17074	−	2.02778i
$144$		0			0
$145$	−1.00000	+	1.73205i	−0.0830455	+	0.143839i
$146$		0			0
$147$		0			0
$148$		0			0
$149$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$149$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$150$		0			0
$151$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$151$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	7.00000			0.562254
$156$		0			0
$157$	−7.00000	−	12.1244i	−0.558661	−	0.967629i	−0.997609	−	0.0691164i	$-0.977982\pi$
$157$	−7.00000	−	12.1244i	−0.558661	−	0.967629i	0.438948	−	0.898513i	$-0.355351\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	1.00000	−	5.19615i	0.0788110	−	0.409514i
$162$		0			0
$163$	−2.00000	+	3.46410i	−0.156652	+	0.271329i	−0.933659	−	0.358162i	$-0.883403\pi$
$163$	−2.00000	+	3.46410i	−0.156652	+	0.271329i	0.777007	+	0.629492i	$0.216737\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−24.0000			−1.85718			−0.928588	−	0.371113i	$-0.878976\pi$
$167$	−24.0000			−1.85718			−0.928588	+	0.371113i	$0.878976\pi$
$168$		0			0
$169$	36.0000			2.76923
$170$		0			0
$171$		0			0
$172$		0			0
$173$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$173$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$174$		0			0
$175$	2.00000	+	1.73205i	0.151186	+	0.130931i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	7.00000	+	12.1244i	0.523205	+	0.906217i	0.999635	+	0.0270049i	$0.00859697\pi$
$179$	7.00000	+	12.1244i	0.523205	+	0.906217i	−0.476431	+	0.879212i	$0.658070\pi$
$180$		0			0
$181$	−3.00000			−0.222988			−0.111494	−	0.993765i	$-0.535564\pi$
$181$	−3.00000			−0.222988			−0.111494	+	0.993765i	$0.535564\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	3.50000	+	6.06218i	0.257325	+	0.445700i
$186$		0			0
$187$	−12.0000	+	20.7846i	−0.877527	+	1.51992i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−9.00000	+	15.5885i	−0.651217	+	1.12794i	0.331611	+	0.943416i	$0.392408\pi$
$191$	−9.00000	+	15.5885i	−0.651217	+	1.12794i	−0.982828	+	0.184525i	$0.940925\pi$
$192$		0			0
$193$	11.5000	+	19.9186i	0.827788	+	1.43377i	0.899770	+	0.436365i	$0.143734\pi$
$193$	11.5000	+	19.9186i	0.827788	+	1.43377i	−0.0719816	+	0.997406i	$0.522932\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−2.00000			−0.142494			−0.0712470	−	0.997459i	$-0.522698\pi$
$197$	−2.00000			−0.142494			−0.0712470	+	0.997459i	$0.522698\pi$
$198$		0			0
$199$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$199$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−5.00000	+	1.73205i	−0.350931	+	0.121566i
$204$		0			0
$205$	−4.00000	+	6.92820i	−0.279372	+	0.483887i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	12.0000			0.830057
$210$		0			0
$211$	−4.00000			−0.275371			−0.137686	−	0.990476i	$-0.543966\pi$
$211$	−4.00000			−0.275371			−0.137686	+	0.990476i	$0.543966\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−2.50000	+	4.33013i	−0.170499	+	0.295312i
$216$		0			0
$217$	14.0000	+	12.1244i	0.950382	+	0.823055i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−21.0000	−	36.3731i	−1.41261	−	2.44672i
$222$		0			0
$223$	−12.0000			−0.803579			−0.401790	−	0.915732i	$-0.631612\pi$
$223$	−12.0000			−0.803579			−0.401790	+	0.915732i	$0.631612\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	4.00000	+	6.92820i	0.265489	+	0.459841i	0.967692	−	0.252136i	$-0.0811332\pi$
$227$	4.00000	+	6.92820i	0.265489	+	0.459841i	−0.702202	+	0.711977i	$0.747800\pi$
$228$		0			0
$229$	−8.50000	+	14.7224i	−0.561696	+	0.972886i	0.435653	+	0.900115i	$0.356518\pi$
$229$	−8.50000	+	14.7224i	−0.561696	+	0.972886i	−0.997349	+	0.0727709i	$0.976816\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	3.00000	−	5.19615i	0.196537	−	0.340411i	−0.750867	−	0.660454i	$-0.770364\pi$
$233$	3.00000	−	5.19615i	0.196537	−	0.340411i	0.947403	+	0.320043i	$0.103697\pi$
$234$		0			0
$235$	5.00000	+	8.66025i	0.326164	+	0.564933i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−6.00000			−0.388108			−0.194054	−	0.980991i	$-0.562164\pi$
$239$	−6.00000			−0.388108			−0.194054	+	0.980991i	$0.562164\pi$
$240$		0			0
$241$	7.00000	+	12.1244i	0.450910	+	0.780998i	0.998443	−	0.0557856i	$-0.0177663\pi$
$241$	7.00000	+	12.1244i	0.450910	+	0.780998i	−0.547533	+	0.836784i	$0.684433\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	1.00000	+	6.92820i	0.0638877	+	0.442627i
$246$		0			0
$247$	−10.5000	+	18.1865i	−0.668099	+	1.15718i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−22.0000			−1.38863			−0.694314	−	0.719672i	$-0.744292\pi$
$251$	−22.0000			−1.38863			−0.694314	+	0.719672i	$0.744292\pi$
$252$		0			0
$253$	8.00000			0.502956
$254$		0			0
$255$		0			0
$256$		0			0
$257$	8.00000	−	13.8564i	0.499026	−	0.864339i	−0.500973	−	0.865463i	$-0.667024\pi$
$257$	8.00000	−	13.8564i	0.499026	−	0.864339i	0.999999	+	0.00112398i	$0.000357774\pi$
$258$		0			0
$259$	−3.50000	+	18.1865i	−0.217479	+	1.13006i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	6.00000	+	10.3923i	0.369976	+	0.640817i	0.989561	−	0.144112i	$-0.0460326\pi$
$263$	6.00000	+	10.3923i	0.369976	+	0.640817i	−0.619586	+	0.784929i	$0.712699\pi$
$264$		0			0
$265$	8.00000			0.491436
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−5.00000	−	8.66025i	−0.304855	−	0.528025i	0.672374	−	0.740212i	$-0.265275\pi$
$269$	−5.00000	−	8.66025i	−0.304855	−	0.528025i	−0.977229	+	0.212187i	$0.931941\pi$
$270$		0			0
$271$	8.00000	−	13.8564i	0.485965	−	0.841717i	−0.513905	−	0.857847i	$-0.671801\pi$
$271$	8.00000	−	13.8564i	0.485965	−	0.841717i	0.999870	+	0.0161307i	$0.00513477\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−2.00000	+	3.46410i	−0.120605	+	0.208893i
$276$		0			0
$277$	−11.5000	−	19.9186i	−0.690968	−	1.19679i	−0.971521	−	0.236953i	$-0.923851\pi$
$277$	−11.5000	−	19.9186i	−0.690968	−	1.19679i	0.280553	−	0.959839i	$-0.409482\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	16.0000			0.954480			0.477240	−	0.878773i	$-0.341637\pi$
$281$	16.0000			0.954480			0.477240	+	0.878773i	$0.341637\pi$
$282$		0			0
$283$	−12.5000	−	21.6506i	−0.743048	−	1.28700i	−0.951101	−	0.308879i	$-0.900046\pi$
$283$	−12.5000	−	21.6506i	−0.743048	−	1.28700i	0.208053	−	0.978117i	$-0.433287\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−20.0000	+	6.92820i	−1.18056	+	0.408959i
$288$		0			0
$289$	−9.50000	+	16.4545i	−0.558824	+	0.967911i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	12.0000			0.701047			0.350524	−	0.936554i	$-0.386004\pi$
$293$	12.0000			0.701047			0.350524	+	0.936554i	$0.386004\pi$
$294$		0			0
$295$	−10.0000			−0.582223
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−7.00000	+	12.1244i	−0.404820	+	0.701170i
$300$		0			0
$301$	−12.5000	+	4.33013i	−0.720488	+	0.249584i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	3.00000	+	5.19615i	0.171780	+	0.297531i
$306$		0			0
$307$	11.0000			0.627803			0.313902	−	0.949456i	$-0.398364\pi$
$307$	11.0000			0.627803			0.313902	+	0.949456i	$0.398364\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$311$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$312$		0			0
$313$	−10.5000	+	18.1865i	−0.593495	+	1.02796i	0.400262	+	0.916401i	$0.368919\pi$
$313$	−10.5000	+	18.1865i	−0.593495	+	1.02796i	−0.993757	+	0.111563i	$0.964414\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	9.00000	−	15.5885i	0.505490	−	0.875535i	−0.494489	−	0.869184i	$-0.664645\pi$
$317$	9.00000	−	15.5885i	0.505490	−	0.875535i	0.999980	−	0.00635137i	$-0.00202172\pi$
$318$		0			0
$319$	−4.00000	−	6.92820i	−0.223957	−	0.387905i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	18.0000			1.00155
$324$		0			0
$325$	−3.50000	−	6.06218i	−0.194145	−	0.336269i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−5.00000	+	25.9808i	−0.275659	+	1.43237i
$330$		0			0
$331$	3.50000	−	6.06218i	0.192377	−	0.333207i	−0.753660	−	0.657264i	$-0.771714\pi$
$331$	3.50000	−	6.06218i	0.192377	−	0.333207i	0.946038	+	0.324057i	$0.105047\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	3.00000			0.163908
$336$		0			0
$337$	15.0000			0.817102			0.408551	−	0.912735i	$-0.366034\pi$
$337$	15.0000			0.817102			0.408551	+	0.912735i	$0.366034\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−14.0000	+	24.2487i	−0.758143	+	1.31314i
$342$		0			0
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	4.00000	+	6.92820i	0.214731	+	0.371925i	0.953189	−	0.302374i	$-0.0977791\pi$
$347$	4.00000	+	6.92820i	0.214731	+	0.371925i	−0.738458	+	0.674299i	$0.764446\pi$
$348$		0			0
$349$	−6.00000			−0.321173			−0.160586	−	0.987022i	$-0.551338\pi$
$349$	−6.00000			−0.321173			−0.160586	+	0.987022i	$0.551338\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−6.00000	−	10.3923i	−0.319348	−	0.553127i	0.661004	−	0.750382i	$-0.270130\pi$
$353$	−6.00000	−	10.3923i	−0.319348	−	0.553127i	−0.980352	+	0.197256i	$0.936797\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−7.00000	+	12.1244i	−0.369446	+	0.639899i	−0.989479	−	0.144677i	$-0.953786\pi$
$359$	−7.00000	+	12.1244i	−0.369446	+	0.639899i	0.620033	+	0.784576i	$0.287119\pi$
$360$		0			0
$361$	5.00000	+	8.66025i	0.263158	+	0.455803i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	15.0000			0.785136
$366$		0			0
$367$	2.50000	+	4.33013i	0.130499	+	0.226031i	0.923869	−	0.382709i	$-0.125009\pi$
$367$	2.50000	+	4.33013i	0.130499	+	0.226031i	−0.793370	+	0.608740i	$0.791675\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	16.0000	+	13.8564i	0.830679	+	0.719389i
$372$		0			0
$373$	−4.50000	+	7.79423i	−0.233001	+	0.403570i	−0.958690	−	0.284453i	$-0.908188\pi$
$373$	−4.50000	+	7.79423i	−0.233001	+	0.403570i	0.725689	+	0.688023i	$0.241521\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	14.0000			0.721037
$378$		0			0
$379$	−7.00000			−0.359566			−0.179783	−	0.983706i	$-0.557540\pi$
$379$	−7.00000			−0.359566			−0.179783	+	0.983706i	$0.557540\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	4.00000	−	6.92820i	0.204390	−	0.354015i	−0.745548	−	0.666452i	$-0.767812\pi$
$383$	4.00000	−	6.92820i	0.204390	−	0.354015i	0.949938	+	0.312437i	$0.101145\pi$
$384$		0			0
$385$	−10.0000	+	3.46410i	−0.509647	+	0.176547i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	8.00000	+	13.8564i	0.405616	+	0.702548i	0.994393	−	0.105748i	$-0.0337237\pi$
$389$	8.00000	+	13.8564i	0.405616	+	0.702548i	−0.588777	+	0.808296i	$0.700390\pi$
$390$		0			0
$391$	12.0000			0.606866
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−0.500000	−	0.866025i	−0.0251577	−	0.0435745i
$396$		0			0
$397$	9.50000	−	16.4545i	0.476791	−	0.825827i	−0.522855	−	0.852422i	$-0.675133\pi$
$397$	9.50000	−	16.4545i	0.476791	−	0.825827i	0.999646	+	0.0265948i	$0.00846640\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−16.0000	+	27.7128i	−0.799002	+	1.38391i	0.121265	+	0.992620i	$0.461305\pi$
$401$	−16.0000	+	27.7128i	−0.799002	+	1.38391i	−0.920267	+	0.391292i	$0.872028\pi$
$402$		0			0
$403$	−24.5000	−	42.4352i	−1.22043	−	2.11385i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−28.0000			−1.38791
$408$		0			0
$409$	9.50000	+	16.4545i	0.469745	+	0.813622i	0.999402	−	0.0345902i	$-0.0110126\pi$
$409$	9.50000	+	16.4545i	0.469745	+	0.813622i	−0.529657	+	0.848212i	$0.677679\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−20.0000	−	17.3205i	−0.984136	−	0.852286i
$414$		0			0
$415$	4.00000	−	6.92820i	0.196352	−	0.340092i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	26.0000			1.27018			0.635092	−	0.772437i	$-0.280962\pi$
$419$	26.0000			1.27018			0.635092	+	0.772437i	$0.280962\pi$
$420$		0			0
$421$	13.0000			0.633581			0.316791	−	0.948495i	$-0.397395\pi$
$421$	13.0000			0.633581			0.316791	+	0.948495i	$0.397395\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−3.00000	+	5.19615i	−0.145521	+	0.252050i
$426$		0			0
$427$	−3.00000	+	15.5885i	−0.145180	+	0.754378i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−15.0000	−	25.9808i	−0.722525	−	1.25145i	−0.959985	−	0.280052i	$-0.909648\pi$
$431$	−15.0000	−	25.9808i	−0.722525	−	1.25145i	0.237460	−	0.971397i	$-0.423685\pi$
$432$		0			0
$433$	−23.0000			−1.10531			−0.552655	−	0.833410i	$-0.686385\pi$
$433$	−23.0000			−1.10531			−0.552655	+	0.833410i	$0.686385\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−3.00000	−	5.19615i	−0.143509	−	0.248566i
$438$		0			0
$439$	14.0000	−	24.2487i	0.668184	−	1.15733i	−0.310228	−	0.950662i	$-0.600405\pi$
$439$	14.0000	−	24.2487i	0.668184	−	1.15733i	0.978412	−	0.206666i	$-0.0662612\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	2.00000	−	3.46410i	0.0950229	−	0.164584i	−0.814595	−	0.580030i	$-0.803041\pi$
$443$	2.00000	−	3.46410i	0.0950229	−	0.164584i	0.909618	+	0.415445i	$0.136374\pi$
$444$		0			0
$445$	1.00000	+	1.73205i	0.0474045	+	0.0821071i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	34.0000			1.60456			0.802280	−	0.596948i	$-0.203620\pi$
$449$	34.0000			1.60456			0.802280	+	0.596948i	$0.203620\pi$
$450$		0			0
$451$	−16.0000	−	27.7128i	−0.753411	−	1.30495i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	3.50000	−	18.1865i	0.164083	−	0.852598i
$456$		0			0
$457$	4.50000	−	7.79423i	0.210501	−	0.364599i	−0.741370	−	0.671096i	$-0.765824\pi$
$457$	4.50000	−	7.79423i	0.210501	−	0.364599i	0.951871	+	0.306497i	$0.0991571\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−30.0000			−1.39724			−0.698620	−	0.715493i	$-0.746202\pi$
$461$	−30.0000			−1.39724			−0.698620	+	0.715493i	$0.746202\pi$
$462$		0			0
$463$	−1.00000			−0.0464739			−0.0232370	−	0.999730i	$-0.507397\pi$
$463$	−1.00000			−0.0464739			−0.0232370	+	0.999730i	$0.507397\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	9.00000	−	15.5885i	0.416470	−	0.721348i	−0.579111	−	0.815249i	$-0.696600\pi$
$467$	9.00000	−	15.5885i	0.416470	−	0.721348i	0.995582	+	0.0939008i	$0.0299336\pi$
$468$		0			0
$469$	6.00000	+	5.19615i	0.277054	+	0.239936i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−10.0000	−	17.3205i	−0.459800	−	0.796398i
$474$		0			0
$475$	3.00000			0.137649
$476$		0			0
$477$		0			0
$478$		0			0
$479$	20.0000	+	34.6410i	0.913823	+	1.58279i	0.808615	+	0.588338i	$0.200218\pi$
$479$	20.0000	+	34.6410i	0.913823	+	1.58279i	0.105208	+	0.994450i	$0.466449\pi$
$480$		0			0
$481$	24.5000	−	42.4352i	1.11710	−	1.93488i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	5.00000	−	8.66025i	0.227038	−	0.393242i
$486$		0			0
$487$	−11.5000	−	19.9186i	−0.521115	−	0.902597i	−0.999698	−	0.0245553i	$-0.992183\pi$
$487$	−11.5000	−	19.9186i	−0.521115	−	0.902597i	0.478584	−	0.878042i	$-0.341150\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	4.00000			0.180517			0.0902587	−	0.995918i	$-0.471231\pi$
$491$	4.00000			0.180517			0.0902587	+	0.995918i	$0.471231\pi$
$492$		0			0
$493$	−6.00000	−	10.3923i	−0.270226	−	0.468046i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−3.50000	+	6.06218i	−0.156682	+	0.271380i	−0.933670	−	0.358134i	$-0.883413\pi$
$499$	−3.50000	+	6.06218i	−0.156682	+	0.271380i	0.776989	+	0.629515i	$0.216746\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−6.00000			−0.267527			−0.133763	−	0.991013i	$-0.542706\pi$
$503$	−6.00000			−0.267527			−0.133763	+	0.991013i	$0.542706\pi$
$504$		0			0
$505$	−12.0000			−0.533993
$506$		0			0
$507$		0			0
$508$		0			0
$509$	7.00000	−	12.1244i	0.310270	−	0.537403i	−0.668151	−	0.744026i	$-0.732914\pi$
$509$	7.00000	−	12.1244i	0.310270	−	0.537403i	0.978421	+	0.206623i	$0.0662474\pi$
$510$		0			0
$511$	30.0000	+	25.9808i	1.32712	+	1.14932i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	3.50000	+	6.06218i	0.154228	+	0.267131i
$516$		0			0
$517$	−40.0000			−1.75920
$518$		0			0
$519$		0			0
$520$		0			0
$521$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$521$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$522$		0			0
$523$	0.500000	−	0.866025i	0.0218635	−	0.0378686i	−0.854887	−	0.518815i	$-0.826373\pi$
$523$	0.500000	−	0.866025i	0.0218635	−	0.0378686i	0.876750	+	0.480946i	$0.159707\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−21.0000	+	36.3731i	−0.914774	+	1.58444i
$528$		0			0
$529$	9.50000	+	16.4545i	0.413043	+	0.715412i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	56.0000			2.42563
$534$		0			0
$535$	1.00000	+	1.73205i	0.0432338	+	0.0748831i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−26.0000	−	10.3923i	−1.11990	−	0.447628i
$540$		0			0
$541$	−8.50000	+	14.7224i	−0.365444	+	0.632967i	−0.988847	−	0.148933i	$-0.952416\pi$
$541$	−8.50000	+	14.7224i	−0.365444	+	0.632967i	0.623404	+	0.781900i	$0.285749\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−3.00000			−0.128506
$546$		0			0
$547$	16.0000			0.684111			0.342055	−	0.939680i	$-0.388877\pi$
$547$	16.0000			0.684111			0.342055	+	0.939680i	$0.388877\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−3.00000	+	5.19615i	−0.127804	+	0.221364i
$552$		0			0
$553$	0.500000	−	2.59808i	0.0212622	−	0.110481i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−15.0000	−	25.9808i	−0.635570	−	1.10084i	−0.986394	−	0.164399i	$-0.947432\pi$
$557$	−15.0000	−	25.9808i	−0.635570	−	1.10084i	0.350824	−	0.936442i	$-0.385902\pi$
$558$		0			0
$559$	35.0000			1.48034
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−7.00000	−	12.1244i	−0.295015	−	0.510981i	0.679974	−	0.733237i	$-0.261991\pi$
$563$	−7.00000	−	12.1244i	−0.295015	−	0.510981i	−0.974988	+	0.222256i	$0.928658\pi$
$564$		0			0
$565$	9.00000	−	15.5885i	0.378633	−	0.655811i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	6.00000	−	10.3923i	0.251533	−	0.435668i	−0.712415	−	0.701758i	$-0.752399\pi$
$569$	6.00000	−	10.3923i	0.251533	−	0.435668i	0.963948	+	0.266090i	$0.0857319\pi$
$570$		0			0
$571$	20.5000	+	35.5070i	0.857898	+	1.48592i	0.873930	+	0.486052i	$0.161563\pi$
$571$	20.5000	+	35.5070i	0.857898	+	1.48592i	−0.0160316	+	0.999871i	$0.505103\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	2.00000			0.0834058
$576$		0			0
$577$	17.5000	+	30.3109i	0.728535	+	1.26186i	0.957503	+	0.288425i	$0.0931316\pi$
$577$	17.5000	+	30.3109i	0.728535	+	1.26186i	−0.228968	+	0.973434i	$0.573535\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	20.0000	−	6.92820i	0.829740	−	0.287430i
$582$		0			0
$583$	−16.0000	+	27.7128i	−0.662652	+	1.14775i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	18.0000			0.742940			0.371470	−	0.928445i	$-0.378854\pi$
$587$	18.0000			0.742940			0.371470	+	0.928445i	$0.378854\pi$
$588$		0			0
$589$	21.0000			0.865290
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−16.0000	+	27.7128i	−0.657041	+	1.13803i	0.324337	+	0.945942i	$0.394859\pi$
$593$	−16.0000	+	27.7128i	−0.657041	+	1.13803i	−0.981378	+	0.192087i	$0.938474\pi$
$594$		0			0
$595$	−15.0000	+	5.19615i	−0.614940	+	0.213021i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	10.0000	+	17.3205i	0.408589	+	0.707697i	0.994732	−	0.102511i	$-0.0326876\pi$
$599$	10.0000	+	17.3205i	0.408589	+	0.707697i	−0.586143	+	0.810208i	$0.699354\pi$
$600$		0			0
$601$	−17.0000			−0.693444			−0.346722	−	0.937968i	$-0.612705\pi$
$601$	−17.0000			−0.693444			−0.346722	+	0.937968i	$0.612705\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−2.50000	−	4.33013i	−0.101639	−	0.176045i
$606$		0			0
$607$	6.50000	−	11.2583i	0.263827	−	0.456962i	−0.703429	−	0.710766i	$-0.748349\pi$
$607$	6.50000	−	11.2583i	0.263827	−	0.456962i	0.967256	+	0.253804i	$0.0816819\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	35.0000	−	60.6218i	1.41595	−	2.45249i
$612$		0			0
$613$	−11.0000	−	19.0526i	−0.444286	−	0.769526i	0.553716	−	0.832705i	$-0.313209\pi$
$613$	−11.0000	−	19.0526i	−0.444286	−	0.769526i	−0.998002	+	0.0631797i	$0.979876\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	2.00000			0.0805170			0.0402585	−	0.999189i	$-0.487182\pi$
$617$	2.00000			0.0805170			0.0402585	+	0.999189i	$0.487182\pi$
$618$		0			0
$619$	−14.5000	−	25.1147i	−0.582804	−	1.00945i	−0.995145	−	0.0984169i	$-0.968622\pi$
$619$	−14.5000	−	25.1147i	−0.582804	−	1.00945i	0.412341	−	0.911030i	$-0.364711\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−1.00000	+	5.19615i	−0.0400642	+	0.208179i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−42.0000			−1.67465
$630$		0			0
$631$	−32.0000			−1.27390			−0.636950	−	0.770905i	$-0.719804\pi$
$631$	−32.0000			−1.27390			−0.636950	+	0.770905i	$0.719804\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−6.50000	+	11.2583i	−0.257945	+	0.446773i
$636$		0			0
$637$	38.5000	−	30.3109i	1.52543	−	1.20096i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	3.00000	+	5.19615i	0.118493	+	0.205236i	0.919171	−	0.393860i	$-0.128860\pi$
$641$	3.00000	+	5.19615i	0.118493	+	0.205236i	−0.800678	+	0.599095i	$0.795527\pi$
$642$		0			0
$643$	5.00000			0.197181			0.0985904	−	0.995128i	$-0.468567\pi$
$643$	5.00000			0.197181			0.0985904	+	0.995128i	$0.468567\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−22.0000	−	38.1051i	−0.864909	−	1.49807i	−0.867137	−	0.498069i	$-0.834043\pi$
$647$	−22.0000	−	38.1051i	−0.864909	−	1.49807i	0.00222801	−	0.999998i	$-0.499291\pi$
$648$		0			0
$649$	20.0000	−	34.6410i	0.785069	−	1.35978i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	14.0000	−	24.2487i	0.547862	−	0.948925i	−0.450558	−	0.892747i	$-0.648775\pi$
$653$	14.0000	−	24.2487i	0.547862	−	0.948925i	0.998421	−	0.0561784i	$-0.0178916\pi$
$654$		0			0
$655$	11.0000	+	19.0526i	0.429806	+	0.744445i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−12.0000			−0.467454			−0.233727	−	0.972302i	$-0.575092\pi$
$659$	−12.0000			−0.467454			−0.233727	+	0.972302i	$0.575092\pi$
$660$		0			0
$661$	−7.50000	−	12.9904i	−0.291716	−	0.505267i	0.682499	−	0.730886i	$-0.260893\pi$
$661$	−7.50000	−	12.9904i	−0.291716	−	0.505267i	−0.974216	+	0.225619i	$0.927560\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	6.00000	+	5.19615i	0.232670	+	0.201498i
$666$		0			0
$667$	−2.00000	+	3.46410i	−0.0774403	+	0.134131i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−24.0000			−0.926510
$672$		0			0
$673$	37.0000			1.42625			0.713123	−	0.701039i	$-0.247280\pi$
$673$	37.0000			1.42625			0.713123	+	0.701039i	$0.247280\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	1.00000	−	1.73205i	0.0384331	−	0.0665681i	−0.846169	−	0.532915i	$-0.821097\pi$
$677$	1.00000	−	1.73205i	0.0384331	−	0.0665681i	0.884602	+	0.466347i	$0.154430\pi$
$678$		0			0
$679$	25.0000	−	8.66025i	0.959412	−	0.332350i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	5.00000	+	8.66025i	0.191320	+	0.331375i	0.945688	−	0.325076i	$-0.105390\pi$
$683$	5.00000	+	8.66025i	0.191320	+	0.331375i	−0.754368	+	0.656452i	$0.772057\pi$
$684$		0			0
$685$	−18.0000			−0.687745
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−28.0000	−	48.4974i	−1.06672	−	1.84760i
$690$		0			0
$691$	25.5000	−	44.1673i	0.970066	−	1.68020i	0.274725	−	0.961523i	$-0.411413\pi$
$691$	25.5000	−	44.1673i	0.970066	−	1.68020i	0.695341	−	0.718680i	$-0.255253\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	6.50000	−	11.2583i	0.246559	−	0.427053i
$696$		0			0
$697$	−24.0000	−	41.5692i	−0.909065	−	1.57455i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−42.0000			−1.58632			−0.793159	−	0.609015i	$-0.791565\pi$
$701$	−42.0000			−1.58632			−0.793159	+	0.609015i	$0.791565\pi$
$702$		0			0
$703$	10.5000	+	18.1865i	0.396015	+	0.685918i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−24.0000	−	20.7846i	−0.902613	−	0.781686i
$708$		0			0
$709$	−7.00000	+	12.1244i	−0.262891	+	0.455340i	−0.967009	−	0.254743i	$-0.918009\pi$
$709$	−7.00000	+	12.1244i	−0.262891	+	0.455340i	0.704118	+	0.710083i	$0.251342\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	14.0000			0.524304
$714$		0			0
$715$	28.0000			1.04714
$716$		0			0
$717$		0			0
$718$		0			0
$719$	25.0000	−	43.3013i	0.932343	−	1.61486i	0.153037	−	0.988220i	$-0.451094\pi$
$719$	25.0000	−	43.3013i	0.932343	−	1.61486i	0.779305	−	0.626644i	$-0.215572\pi$
$720$		0			0
$721$	−3.50000	+	18.1865i	−0.130347	+	0.677302i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−1.00000	−	1.73205i	−0.0371391	−	0.0643268i
$726$		0			0
$727$	23.0000			0.853023			0.426511	−	0.904482i	$-0.359742\pi$
$727$	23.0000			0.853023			0.426511	+	0.904482i	$0.359742\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−15.0000	−	25.9808i	−0.554795	−	0.960933i
$732$		0			0
$733$	6.50000	−	11.2583i	0.240083	−	0.415836i	−0.720655	−	0.693294i	$-0.756159\pi$
$733$	6.50000	−	11.2583i	0.240083	−	0.415836i	0.960738	+	0.277458i	$0.0894920\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−6.00000	+	10.3923i	−0.221013	+	0.382805i
$738$		0			0
$739$	0.500000	+	0.866025i	0.0183928	+	0.0318573i	0.875075	−	0.483987i	$-0.160812\pi$
$739$	0.500000	+	0.866025i	0.0183928	+	0.0318573i	−0.856683	+	0.515844i	$0.827478\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	44.0000			1.61420			0.807102	−	0.590412i	$-0.201035\pi$
$743$	44.0000			1.61420			0.807102	+	0.590412i	$0.201035\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−1.00000	+	5.19615i	−0.0365392	+	0.189863i
$750$		0			0
$751$	12.5000	−	21.6506i	0.456131	−	0.790043i	−0.542621	−	0.839978i	$-0.682568\pi$
$751$	12.5000	−	21.6506i	0.456131	−	0.790043i	0.998752	+	0.0499348i	$0.0159013\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	2.00000			0.0726912			0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000			0.0726912			0.0363456	+	0.999339i	$0.488428\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−15.0000	+	25.9808i	−0.543750	+	0.941802i	0.454935	+	0.890525i	$0.349663\pi$
$761$	−15.0000	+	25.9808i	−0.543750	+	0.941802i	−0.998684	+	0.0512772i	$0.983671\pi$
$762$		0			0
$763$	−6.00000	−	5.19615i	−0.217215	−	0.188113i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	35.0000	+	60.6218i	1.26378	+	2.18893i
$768$		0			0
$769$	−29.0000			−1.04577			−0.522883	−	0.852404i	$-0.675144\pi$
$769$	−29.0000			−1.04577			−0.522883	+	0.852404i	$0.675144\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−6.00000	−	10.3923i	−0.215805	−	0.373785i	0.737716	−	0.675111i	$-0.235904\pi$
$773$	−6.00000	−	10.3923i	−0.215805	−	0.373785i	−0.953521	+	0.301326i	$0.902571\pi$
$774$		0			0
$775$	−3.50000	+	6.06218i	−0.125724	+	0.217760i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−12.0000	+	20.7846i	−0.429945	+	0.744686i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$		0			0
$785$	14.0000			0.499681
$786$		0			0
$787$	−2.00000	−	3.46410i	−0.0712923	−	0.123482i	0.828176	−	0.560469i	$-0.189379\pi$
$787$	−2.00000	−	3.46410i	−0.0712923	−	0.123482i	−0.899468	+	0.436987i	$0.856046\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	45.0000	−	15.5885i	1.60002	−	0.554262i
$792$		0			0
$793$	21.0000	−	36.3731i	0.745732	−	1.29165i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	42.0000			1.48772			0.743858	−	0.668338i	$-0.232994\pi$
$797$	42.0000			1.48772			0.743858	+	0.668338i	$0.232994\pi$
$798$		0			0
$799$	−60.0000			−2.12265
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−30.0000	+	51.9615i	−1.05868	+	1.83368i
$804$		0			0
$805$	4.00000	+	3.46410i	0.140981	+	0.122094i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−3.00000	−	5.19615i	−0.105474	−	0.182687i	0.808458	−	0.588555i	$-0.200303\pi$
$809$	−3.00000	−	5.19615i	−0.105474	−	0.182687i	−0.913932	+	0.405868i	$0.866969\pi$
$810$		0			0
$811$	12.0000			0.421377			0.210688	−	0.977553i	$-0.432429\pi$
$811$	12.0000			0.421377			0.210688	+	0.977553i	$0.432429\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−2.00000	−	3.46410i	−0.0700569	−	0.121342i
$816$		0			0
$817$	−7.50000	+	12.9904i	−0.262392	+	0.454476i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−6.00000	+	10.3923i	−0.209401	+	0.362694i	−0.951526	−	0.307568i	$-0.900485\pi$
$821$	−6.00000	+	10.3923i	−0.209401	+	0.362694i	0.742125	+	0.670262i	$0.233818\pi$
$822$		0			0
$823$	12.0000	+	20.7846i	0.418294	+	0.724506i	0.995768	−	0.0919029i	$-0.0292950\pi$
$823$	12.0000	+	20.7846i	0.418294	+	0.724506i	−0.577474	+	0.816409i	$0.695962\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	10.0000			0.347734			0.173867	−	0.984769i	$-0.444374\pi$
$827$	10.0000			0.347734			0.173867	+	0.984769i	$0.444374\pi$
$828$		0			0
$829$	−12.5000	−	21.6506i	−0.434143	−	0.751958i	0.563082	−	0.826401i	$-0.309615\pi$
$829$	−12.5000	−	21.6506i	−0.434143	−	0.751958i	−0.997225	+	0.0744432i	$0.976282\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−39.0000	−	15.5885i	−1.35127	−	0.540108i
$834$		0			0
$835$	12.0000	−	20.7846i	0.415277	−	0.719281i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	22.0000			0.759524			0.379762	−	0.925084i	$-0.376006\pi$
$839$	22.0000			0.759524			0.379762	+	0.925084i	$0.376006\pi$
$840$		0			0
$841$	−25.0000			−0.862069
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−18.0000	+	31.1769i	−0.619219	+	1.07252i
$846$		0			0
$847$	2.50000	−	12.9904i	0.0859010	−	0.446355i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	7.00000	+	12.1244i	0.239957	+	0.415618i
$852$		0			0
$853$	−23.0000			−0.787505			−0.393753	−	0.919216i	$-0.628823\pi$
$853$	−23.0000			−0.787505			−0.393753	+	0.919216i	$0.628823\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	11.0000	+	19.0526i	0.375753	+	0.650823i	0.990439	−	0.137948i	$-0.0440508\pi$
$857$	11.0000	+	19.0526i	0.375753	+	0.650823i	−0.614687	+	0.788771i	$0.710717\pi$
$858$		0			0
$859$	−18.0000	+	31.1769i	−0.614152	+	1.06374i	0.376381	+	0.926465i	$0.377169\pi$
$859$	−18.0000	+	31.1769i	−0.614152	+	1.06374i	−0.990533	+	0.137277i	$0.956165\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−1.00000	+	1.73205i	−0.0340404	+	0.0589597i	−0.882544	−	0.470230i	$-0.844171\pi$
$863$	−1.00000	+	1.73205i	−0.0340404	+	0.0589597i	0.848503	+	0.529190i	$0.177504\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		0			0
$868$		0			0
$869$	4.00000			0.135691
$870$		0			0
$871$	−10.5000	−	18.1865i	−0.355779	−	0.616227i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−2.50000	+	0.866025i	−0.0845154	+	0.0292770i
$876$		0			0
$877$	−25.0000	+	43.3013i	−0.844190	+	1.46218i	0.0421327	+	0.999112i	$0.486585\pi$
$877$	−25.0000	+	43.3013i	−0.844190	+	1.46218i	−0.886323	+	0.463068i	$0.846749\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−4.00000			−0.134763			−0.0673817	−	0.997727i	$-0.521465\pi$
$881$	−4.00000			−0.134763			−0.0673817	+	0.997727i	$0.521465\pi$
$882$		0			0
$883$	27.0000			0.908622			0.454311	−	0.890843i	$-0.349885\pi$
$883$	27.0000			0.908622			0.454311	+	0.890843i	$0.349885\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	16.0000	−	27.7128i	0.537227	−	0.930505i	−0.461825	−	0.886971i	$-0.652805\pi$
$887$	16.0000	−	27.7128i	0.537227	−	0.930505i	0.999052	−	0.0435339i	$-0.0138616\pi$
$888$		0			0
$889$	−32.5000	+	11.2583i	−1.09002	+	0.377592i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	15.0000	+	25.9808i	0.501956	+	0.869413i
$894$		0			0
$895$	−14.0000			−0.467968
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−7.00000	−	12.1244i	−0.233463	−	0.404370i
$900$		0			0
$901$	−24.0000	+	41.5692i	−0.799556	+	1.38487i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	1.50000	−	2.59808i	0.0498617	−	0.0863630i
$906$		0			0
$907$	18.5000	+	32.0429i	0.614282	+	1.06397i	0.990510	+	0.137441i	$0.0438878\pi$
$907$	18.5000	+	32.0429i	0.614282	+	1.06397i	−0.376228	+	0.926527i	$0.622779\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	50.0000			1.65657			0.828287	−	0.560304i	$-0.189316\pi$
$911$	50.0000			1.65657			0.828287	+	0.560304i	$0.189316\pi$
$912$		0			0
$913$	16.0000	+	27.7128i	0.529523	+	0.917160i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−11.0000	+	57.1577i	−0.363252	+	1.88751i
$918$		0			0
$919$	13.5000	−	23.3827i	0.445324	−	0.771324i	−0.552751	−	0.833347i	$-0.686422\pi$
$919$	13.5000	−	23.3827i	0.445324	−	0.771324i	0.998075	+	0.0620230i	$0.0197552\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−7.00000			−0.230159
$926$		0			0
$927$		0			0
$928$		0			0
$929$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$929$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$930$		0			0
$931$	3.00000	+	20.7846i	0.0983210	+	0.681188i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−12.0000	−	20.7846i	−0.392442	−	0.679729i
$936$		0			0
$937$	9.00000			0.294017			0.147009	−	0.989135i	$-0.453036\pi$
$937$	9.00000			0.294017			0.147009	+	0.989135i	$0.453036\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	27.0000	+	46.7654i	0.880175	+	1.52451i	0.851146	+	0.524929i	$0.175908\pi$
$941$	27.0000	+	46.7654i	0.880175	+	1.52451i	0.0290288	+	0.999579i	$0.490759\pi$
$942$		0			0
$943$	−8.00000	+	13.8564i	−0.260516	+	0.451227i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	2.00000	−	3.46410i	0.0649913	−	0.112568i	−0.831699	−	0.555227i	$-0.812631\pi$
$947$	2.00000	−	3.46410i	0.0649913	−	0.112568i	0.896690	+	0.442659i	$0.145965\pi$
$948$		0			0
$949$	−52.5000	−	90.9327i	−1.70422	−	2.95180i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−16.0000			−0.518291			−0.259145	−	0.965838i	$-0.583441\pi$
$953$	−16.0000			−0.518291			−0.259145	+	0.965838i	$0.583441\pi$
$954$		0			0
$955$	−9.00000	−	15.5885i	−0.291233	−	0.504431i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−36.0000	−	31.1769i	−1.16250	−	1.00676i
$960$		0			0
$961$	−9.00000	+	15.5885i	−0.290323	+	0.502853i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−23.0000			−0.740396
$966$		0			0
$967$	−17.0000			−0.546683			−0.273342	−	0.961917i	$-0.588129\pi$
$967$	−17.0000			−0.546683			−0.273342	+	0.961917i	$0.588129\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	24.0000	−	41.5692i	0.770197	−	1.33402i	−0.167258	−	0.985913i	$-0.553491\pi$
$971$	24.0000	−	41.5692i	0.770197	−	1.33402i	0.937455	−	0.348107i	$-0.113175\pi$
$972$		0			0
$973$	32.5000	−	11.2583i	1.04190	−	0.360925i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−12.0000	−	20.7846i	−0.383914	−	0.664959i	0.607704	−	0.794164i	$-0.292091\pi$
$977$	−12.0000	−	20.7846i	−0.383914	−	0.664959i	−0.991618	+	0.129205i	$0.958757\pi$
$978$		0			0
$979$	−8.00000			−0.255681
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−7.00000	−	12.1244i	−0.223265	−	0.386707i	0.732532	−	0.680732i	$-0.238338\pi$
$983$	−7.00000	−	12.1244i	−0.223265	−	0.386707i	−0.955798	+	0.294025i	$0.905005\pi$
$984$		0			0
$985$	1.00000	−	1.73205i	0.0318626	−	0.0551877i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−5.00000	+	8.66025i	−0.158991	+	0.275380i
$990$		0			0
$991$	−15.5000	−	26.8468i	−0.492374	−	0.852816i	0.507588	−	0.861600i	$-0.330537\pi$
$991$	−15.5000	−	26.8468i	−0.492374	−	0.852816i	−0.999961	+	0.00878379i	$0.997204\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−8.50000	−	14.7224i	−0.269198	−	0.466264i	0.699457	−	0.714675i	$-0.253425\pi$
$997$	−8.50000	−	14.7224i	−0.269198	−	0.466264i	−0.968655	+	0.248410i	$0.920092\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1260.2.s.a.541.1		2
3.2	odd	2		420.2.q.b.121.1	✓	2
7.2	even	3		8820.2.a.bb.1.1		1
7.4	even	3	inner	1260.2.s.a.361.1		2
7.5	odd	6		8820.2.a.l.1.1		1
12.11	even	2		1680.2.bg.j.961.1		2
15.2	even	4		2100.2.bc.d.1549.2		4
15.8	even	4		2100.2.bc.d.1549.1		4
15.14	odd	2		2100.2.q.d.1801.1		2
21.2	odd	6		2940.2.a.b.1.1		1
21.5	even	6		2940.2.a.k.1.1		1
21.11	odd	6		420.2.q.b.361.1	yes	2
21.17	even	6		2940.2.q.c.361.1		2
21.20	even	2		2940.2.q.c.961.1		2
84.11	even	6		1680.2.bg.j.1201.1		2
105.32	even	12		2100.2.bc.d.949.1		4
105.53	even	12		2100.2.bc.d.949.2		4
105.74	odd	6		2100.2.q.d.1201.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.q.b.121.1	✓	2	3.2	odd	2
420.2.q.b.361.1	yes	2	21.11	odd	6
1260.2.s.a.361.1		2	7.4	even	3	inner
1260.2.s.a.541.1		2	1.1	even	1	trivial
1680.2.bg.j.961.1		2	12.11	even	2
1680.2.bg.j.1201.1		2	84.11	even	6
2100.2.q.d.1201.1		2	105.74	odd	6
2100.2.q.d.1801.1		2	15.14	odd	2
2100.2.bc.d.949.1		4	105.32	even	12
2100.2.bc.d.949.2		4	105.53	even	12
2100.2.bc.d.1549.1		4	15.8	even	4
2100.2.bc.d.1549.2		4	15.2	even	4
2940.2.a.b.1.1		1	21.2	odd	6
2940.2.a.k.1.1		1	21.5	even	6
2940.2.q.c.361.1		2	21.17	even	6
2940.2.q.c.961.1		2	21.20	even	2
8820.2.a.l.1.1		1	7.5	odd	6
8820.2.a.bb.1.1		1	7.2	even	3

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:	\( N \)	\(=\)	\( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1260.s (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{5} +(-2.50000 + 0.866025i) q^{7} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{5} +(-2.50000 + 0.866025i) q^{7} +(-2.00000 - 3.46410i) q^{11} +7.00000 q^{13} +(-3.00000 - 5.19615i) q^{17} +(-1.50000 + 2.59808i) q^{19} +(-1.00000 + 1.73205i) q^{23} +(-0.500000 - 0.866025i) q^{25} +2.00000 q^{29} +(-3.50000 - 6.06218i) q^{31} +(0.500000 - 2.59808i) q^{35} +(3.50000 - 6.06218i) q^{37} +8.00000 q^{41} +5.00000 q^{43} +(5.00000 - 8.66025i) q^{47} +(5.50000 - 4.33013i) q^{49} +(-4.00000 - 6.92820i) q^{53} +4.00000 q^{55} +(5.00000 + 8.66025i) q^{59} +(3.00000 - 5.19615i) q^{61} +(-3.50000 + 6.06218i) q^{65} +(-1.50000 - 2.59808i) q^{67} +(-7.50000 - 12.9904i) q^{73} +(8.00000 + 6.92820i) q^{77} +(-0.500000 + 0.866025i) q^{79} -8.00000 q^{83} +6.00000 q^{85} +(1.00000 - 1.73205i) q^{89} +(-17.5000 + 6.06218i) q^{91} +(-1.50000 - 2.59808i) q^{95} -10.0000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{5} - 5 q^{7}+O(q^{10}) \) 2 * q - q^5 - 5 * q^7	\( 2 q - q^{5} - 5 q^{7} - 4 q^{11} + 14 q^{13} - 6 q^{17} - 3 q^{19} - 2 q^{23} - q^{25} + 4 q^{29} - 7 q^{31} + q^{35} + 7 q^{37} + 16 q^{41} + 10 q^{43} + 10 q^{47} + 11 q^{49} - 8 q^{53} + 8 q^{55} + 10 q^{59} + 6 q^{61} - 7 q^{65} - 3 q^{67} - 15 q^{73} + 16 q^{77} - q^{79} - 16 q^{83} + 12 q^{85} + 2 q^{89} - 35 q^{91} - 3 q^{95} - 20 q^{97}+O(q^{100}) \) 2 * q - q^5 - 5 * q^7 - 4 * q^11 + 14 * q^13 - 6 * q^17 - 3 * q^19 - 2 * q^23 - q^25 + 4 * q^29 - 7 * q^31 + q^35 + 7 * q^37 + 16 * q^41 + 10 * q^43 + 10 * q^47 + 11 * q^49 - 8 * q^53 + 8 * q^55 + 10 * q^59 + 6 * q^61 - 7 * q^65 - 3 * q^67 - 15 * q^73 + 16 * q^77 - q^79 - 16 * q^83 + 12 * q^85 + 2 * q^89 - 35 * q^91 - 3 * q^95 - 20 * q^97

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