LMFDB - Embedded newform 2340.2.q.f.1621.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2340,2,Mod(1621,2340)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2340, 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("2340.1621");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2340 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2340.q (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:	$18.6849940730$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 260)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1621.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	2340.1621
Dual form			2340.2.q.f.2161.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{5} +(0.500000 + 0.866025i) q^{7} +O(q^{10})$	$q+1.00000 q^{5} +(0.500000 + 0.866025i) q^{7} +(1.50000 - 2.59808i) q^{11} +(1.00000 + 3.46410i) q^{13} +(-1.50000 - 2.59808i) q^{17} +(-2.50000 - 4.33013i) q^{19} +(4.50000 - 7.79423i) q^{23} +1.00000 q^{25} +(-4.50000 + 7.79423i) q^{29} +8.00000 q^{31} +(0.500000 + 0.866025i) q^{35} +(3.50000 - 6.06218i) q^{37} +(1.50000 - 2.59808i) q^{41} +(0.500000 + 0.866025i) q^{43} +(3.00000 - 5.19615i) q^{49} -6.00000 q^{53} +(1.50000 - 2.59808i) q^{55} +(4.50000 + 7.79423i) q^{59} +(0.500000 + 0.866025i) q^{61} +(1.00000 + 3.46410i) q^{65} +(-2.50000 + 4.33013i) q^{67} +(4.50000 + 7.79423i) q^{71} +2.00000 q^{73} +3.00000 q^{77} +8.00000 q^{79} +(-1.50000 - 2.59808i) q^{85} +(1.50000 - 2.59808i) q^{89} +(-2.50000 + 2.59808i) q^{91} +(-2.50000 - 4.33013i) q^{95} +(-8.50000 - 14.7224i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{5} + q^{7}+O(q^{10}) $ 2 * q + 2 * q^5 + q^7	$ 2 q + 2 q^{5} + q^{7} + 3 q^{11} + 2 q^{13} - 3 q^{17} - 5 q^{19} + 9 q^{23} + 2 q^{25} - 9 q^{29} + 16 q^{31} + q^{35} + 7 q^{37} + 3 q^{41} + q^{43} + 6 q^{49} - 12 q^{53} + 3 q^{55} + 9 q^{59} + q^{61} + 2 q^{65} - 5 q^{67} + 9 q^{71} + 4 q^{73} + 6 q^{77} + 16 q^{79} - 3 q^{85} + 3 q^{89} - 5 q^{91} - 5 q^{95} - 17 q^{97}+O(q^{100}) $ 2 * q + 2 * q^5 + q^7 + 3 * q^11 + 2 * q^13 - 3 * q^17 - 5 * q^19 + 9 * q^23 + 2 * q^25 - 9 * q^29 + 16 * q^31 + q^35 + 7 * q^37 + 3 * q^41 + q^43 + 6 * q^49 - 12 * q^53 + 3 * q^55 + 9 * q^59 + q^61 + 2 * q^65 - 5 * q^67 + 9 * q^71 + 4 * q^73 + 6 * q^77 + 16 * q^79 - 3 * q^85 + 3 * q^89 - 5 * q^91 - 5 * q^95 - 17 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2340\mathbb{Z}\right)^\times$.

$n$	$937$	$1081$	$1171$	$2081$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$		0			0
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i	0.944911	−	0.327327i	$-0.106148\pi$
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i	−0.755929	+	0.654654i	$0.772814\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	−0.546259	−	0.837616i	$-0.683949\pi$
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	0.998526	+	0.0542666i	$0.0172821\pi$
$12$		0			0
$13$	1.00000	+	3.46410i	0.277350	+	0.960769i
$13$	1.00000	+	3.46410i	0.277350	+	0.960769i
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.50000	−	2.59808i	−0.363803	−	0.630126i	0.624780	−	0.780801i	$-0.285189\pi$
$17$	−1.50000	−	2.59808i	−0.363803	−	0.630126i	−0.988583	+	0.150675i	$0.951855\pi$
$18$		0			0
$19$	−2.50000	−	4.33013i	−0.573539	−	0.993399i	−0.996199	−	0.0871106i	$-0.972237\pi$
$19$	−2.50000	−	4.33013i	−0.573539	−	0.993399i	0.422659	−	0.906289i	$-0.361097\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	4.50000	−	7.79423i	0.938315	−	1.62521i	0.169701	−	0.985496i	$-0.445720\pi$
$23$	4.50000	−	7.79423i	0.938315	−	1.62521i	0.768613	−	0.639713i	$-0.220947\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−4.50000	+	7.79423i	−0.835629	+	1.44735i	0.0578882	+	0.998323i	$0.481563\pi$
$29$	−4.50000	+	7.79423i	−0.835629	+	1.44735i	−0.893517	+	0.449029i	$0.851770\pi$
$30$		0			0
$31$	8.00000			1.43684			0.718421	−	0.695608i	$-0.244865\pi$
$31$	8.00000			1.43684			0.718421	+	0.695608i	$0.244865\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	0.500000	+	0.866025i	0.0845154	+	0.146385i
$36$		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
$41$	1.50000	−	2.59808i	0.234261	−	0.405751i	−0.724797	−	0.688963i	$-0.758066\pi$
$41$	1.50000	−	2.59808i	0.234261	−	0.405751i	0.959058	+	0.283211i	$0.0913998\pi$
$42$		0			0
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i	0.901629	−	0.432511i	$-0.142372\pi$
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i	−0.825380	+	0.564578i	$0.809039\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		0			0			−	1.00000i	$-0.5\pi$
$47$		0			0				1.00000i	$0.5\pi$
$48$		0			0
$49$	3.00000	−	5.19615i	0.428571	−	0.742307i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−6.00000			−0.824163			−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000			−0.824163			−0.412082	+	0.911147i	$0.635198\pi$
$54$		0			0
$55$	1.50000	−	2.59808i	0.202260	−	0.350325i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	4.50000	+	7.79423i	0.585850	+	1.01472i	0.994769	+	0.102151i	$0.0325726\pi$
$59$	4.50000	+	7.79423i	0.585850	+	1.01472i	−0.408919	+	0.912571i	$0.634094\pi$
$60$		0			0
$61$	0.500000	+	0.866025i	0.0640184	+	0.110883i	0.896258	−	0.443533i	$-0.146275\pi$
$61$	0.500000	+	0.866025i	0.0640184	+	0.110883i	−0.832240	+	0.554416i	$0.812942\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	1.00000	+	3.46410i	0.124035	+	0.429669i
$66$		0			0
$67$	−2.50000	+	4.33013i	−0.305424	+	0.529009i	−0.977356	−	0.211604i	$-0.932131\pi$
$67$	−2.50000	+	4.33013i	−0.305424	+	0.529009i	0.671932	+	0.740613i	$0.265465\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	4.50000	+	7.79423i	0.534052	+	0.925005i	0.999209	+	0.0397765i	$0.0126646\pi$
$71$	4.50000	+	7.79423i	0.534052	+	0.925005i	−0.465157	+	0.885228i	$0.654002\pi$
$72$		0			0
$73$	2.00000			0.234082			0.117041	−	0.993127i	$-0.462659\pi$
$73$	2.00000			0.234082			0.117041	+	0.993127i	$0.462659\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	3.00000			0.341882
$78$		0			0
$79$	8.00000			0.900070			0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000			0.900070			0.450035	+	0.893011i	$0.351411\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$		0			0
$85$	−1.50000	−	2.59808i	−0.162698	−	0.281801i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	1.50000	−	2.59808i	0.159000	−	0.275396i	−0.775509	−	0.631337i	$-0.782506\pi$
$89$	1.50000	−	2.59808i	0.159000	−	0.275396i	0.934508	+	0.355942i	$0.115840\pi$
$90$		0			0
$91$	−2.50000	+	2.59808i	−0.262071	+	0.272352i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−2.50000	−	4.33013i	−0.256495	−	0.444262i
$96$		0			0
$97$	−8.50000	−	14.7224i	−0.863044	−	1.49484i	−0.868976	−	0.494854i	$-0.835222\pi$
$97$	−8.50000	−	14.7224i	−0.863044	−	1.49484i	0.00593185	−	0.999982i	$-0.498112\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	7.50000	−	12.9904i	0.746278	−	1.29259i	−0.203317	−	0.979113i	$-0.565172\pi$
$101$	7.50000	−	12.9904i	0.746278	−	1.29259i	0.949595	−	0.313478i	$-0.101494\pi$
$102$		0			0
$103$	8.00000			0.788263			0.394132	−	0.919054i	$-0.371045\pi$
$103$	8.00000			0.788263			0.394132	+	0.919054i	$0.371045\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.50000	+	2.59808i	−0.145010	+	0.251166i	−0.929377	−	0.369132i	$-0.879655\pi$
$107$	−1.50000	+	2.59808i	−0.145010	+	0.251166i	0.784366	+	0.620298i	$0.212988\pi$
$108$		0			0
$109$	14.0000			1.34096			0.670478	−	0.741929i	$-0.266089\pi$
$109$	14.0000			1.34096			0.670478	+	0.741929i	$0.266089\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−7.50000	−	12.9904i	−0.705541	−	1.22203i	−0.966496	−	0.256681i	$-0.917371\pi$
$113$	−7.50000	−	12.9904i	−0.705541	−	1.22203i	0.260955	−	0.965351i	$-0.415962\pi$
$114$		0			0
$115$	4.50000	−	7.79423i	0.419627	−	0.726816i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	1.50000	−	2.59808i	0.137505	−	0.238165i
$120$		0			0
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	−8.50000	+	14.7224i	−0.754253	+	1.30640i	0.191492	+	0.981494i	$0.438667\pi$
$127$	−8.50000	+	14.7224i	−0.754253	+	1.30640i	−0.945745	+	0.324910i	$0.894666\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$		0			0			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$		0			0
$133$	2.50000	−	4.33013i	0.216777	−	0.375470i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−1.50000	−	2.59808i	−0.128154	−	0.221969i	0.794808	−	0.606861i	$-0.207572\pi$
$137$	−1.50000	−	2.59808i	−0.128154	−	0.221969i	−0.922961	+	0.384893i	$0.874238\pi$
$138$		0			0
$139$	−2.50000	−	4.33013i	−0.212047	−	0.367277i	0.740308	−	0.672268i	$-0.234680\pi$
$139$	−2.50000	−	4.33013i	−0.212047	−	0.367277i	−0.952355	+	0.304991i	$0.901346\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	10.5000	+	2.59808i	0.878054	+	0.217262i
$144$		0			0
$145$	−4.50000	+	7.79423i	−0.373705	+	0.647275i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−4.50000	−	7.79423i	−0.368654	−	0.638528i	0.620701	−	0.784047i	$-0.286848\pi$
$149$	−4.50000	−	7.79423i	−0.368654	−	0.638528i	−0.989355	+	0.145519i	$0.953515\pi$
$150$		0			0
$151$	20.0000			1.62758			0.813788	−	0.581161i	$-0.197401\pi$
$151$	20.0000			1.62758			0.813788	+	0.581161i	$0.197401\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	8.00000			0.642575
$156$		0			0
$157$	14.0000			1.11732			0.558661	−	0.829396i	$-0.311315\pi$
$157$	14.0000			1.11732			0.558661	+	0.829396i	$0.311315\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	9.00000			0.709299
$162$		0			0
$163$	0.500000	+	0.866025i	0.0391630	+	0.0678323i	0.884943	−	0.465700i	$-0.154198\pi$
$163$	0.500000	+	0.866025i	0.0391630	+	0.0678323i	−0.845780	+	0.533533i	$0.820864\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−7.50000	+	12.9904i	−0.580367	+	1.00523i	0.415068	+	0.909790i	$0.363758\pi$
$167$	−7.50000	+	12.9904i	−0.580367	+	1.00523i	−0.995436	+	0.0954356i	$0.969576\pi$
$168$		0			0
$169$	−11.0000	+	6.92820i	−0.846154	+	0.532939i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	10.5000	+	18.1865i	0.798300	+	1.38270i	0.920722	+	0.390218i	$0.127601\pi$
$173$	10.5000	+	18.1865i	0.798300	+	1.38270i	−0.122422	+	0.992478i	$0.539066\pi$
$174$		0			0
$175$	0.500000	+	0.866025i	0.0377964	+	0.0654654i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	7.50000	−	12.9904i	0.560576	−	0.970947i	−0.436870	−	0.899525i	$-0.643913\pi$
$179$	7.50000	−	12.9904i	0.560576	−	0.970947i	0.997446	−	0.0714220i	$-0.0227537\pi$
$180$		0			0
$181$	−10.0000			−0.743294			−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000			−0.743294			−0.371647	+	0.928374i	$0.621207\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	3.50000	−	6.06218i	0.257325	−	0.445700i
$186$		0			0
$187$	−9.00000			−0.658145
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−1.50000	−	2.59808i	−0.108536	−	0.187990i	0.806641	−	0.591041i	$-0.201283\pi$
$191$	−1.50000	−	2.59808i	−0.108536	−	0.187990i	−0.915177	+	0.403051i	$0.867950\pi$
$192$		0			0
$193$	−2.50000	+	4.33013i	−0.179954	+	0.311689i	−0.941865	−	0.335993i	$-0.890928\pi$
$193$	−2.50000	+	4.33013i	−0.179954	+	0.311689i	0.761911	+	0.647682i	$0.224262\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−1.50000	+	2.59808i	−0.106871	+	0.185105i	−0.914501	−	0.404584i	$-0.867416\pi$
$197$	−1.50000	+	2.59808i	−0.106871	+	0.185105i	0.807630	+	0.589689i	$0.200750\pi$
$198$		0			0
$199$	3.50000	+	6.06218i	0.248108	+	0.429736i	0.963001	−	0.269498i	$-0.0868577\pi$
$199$	3.50000	+	6.06218i	0.248108	+	0.429736i	−0.714893	+	0.699234i	$0.753524\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−9.00000			−0.631676
$204$		0			0
$205$	1.50000	−	2.59808i	0.104765	−	0.181458i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−15.0000			−1.03757
$210$		0			0
$211$	12.5000	−	21.6506i	0.860535	−	1.49049i	−0.0108774	−	0.999941i	$-0.503462\pi$
$211$	12.5000	−	21.6506i	0.860535	−	1.49049i	0.871413	−	0.490550i	$-0.163204\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	0.500000	+	0.866025i	0.0340997	+	0.0590624i
$216$		0			0
$217$	4.00000	+	6.92820i	0.271538	+	0.470317i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	7.50000	−	7.79423i	0.504505	−	0.524297i
$222$		0			0
$223$	9.50000	−	16.4545i	0.636167	−	1.10187i	−0.350100	−	0.936713i	$-0.613852\pi$
$223$	9.50000	−	16.4545i	0.636167	−	1.10187i	0.986267	−	0.165161i	$-0.0528144\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	7.50000	+	12.9904i	0.497792	+	0.862202i	0.999997	−	0.00254715i	$-0.000810783\pi$
$227$	7.50000	+	12.9904i	0.497792	+	0.862202i	−0.502204	+	0.864749i	$0.667477\pi$
$228$		0			0
$229$	−22.0000			−1.45380			−0.726900	−	0.686743i	$-0.759040\pi$
$229$	−22.0000			−1.45380			−0.726900	+	0.686743i	$0.759040\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	6.00000			0.393073			0.196537	−	0.980497i	$-0.437031\pi$
$233$	6.00000			0.393073			0.196537	+	0.980497i	$0.437031\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−24.0000			−1.55243			−0.776215	−	0.630468i	$-0.782863\pi$
$239$	−24.0000			−1.55243			−0.776215	+	0.630468i	$0.782863\pi$
$240$		0			0
$241$	−11.5000	−	19.9186i	−0.740780	−	1.28307i	−0.952141	−	0.305661i	$-0.901123\pi$
$241$	−11.5000	−	19.9186i	−0.740780	−	1.28307i	0.211360	−	0.977408i	$-0.432211\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	3.00000	−	5.19615i	0.191663	−	0.331970i
$246$		0			0
$247$	12.5000	−	12.9904i	0.795356	−	0.826558i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	4.50000	+	7.79423i	0.284037	+	0.491967i	0.972375	−	0.233423i	$-0.0749927\pi$
$251$	4.50000	+	7.79423i	0.284037	+	0.491967i	−0.688338	+	0.725390i	$0.741659\pi$
$252$		0			0
$253$	−13.5000	−	23.3827i	−0.848738	−	1.47006i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−13.5000	+	23.3827i	−0.842107	+	1.45857i	0.0460033	+	0.998941i	$0.485352\pi$
$257$	−13.5000	+	23.3827i	−0.842107	+	1.45857i	−0.888110	+	0.459631i	$0.847982\pi$
$258$		0			0
$259$	7.00000			0.434959
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−1.50000	+	2.59808i	−0.0924940	+	0.160204i	−0.908560	−	0.417755i	$-0.862817\pi$
$263$	−1.50000	+	2.59808i	−0.0924940	+	0.160204i	0.816066	+	0.577959i	$0.196151\pi$
$264$		0			0
$265$	−6.00000			−0.368577
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−10.5000	−	18.1865i	−0.640196	−	1.10885i	−0.985389	−	0.170321i	$-0.945520\pi$
$269$	−10.5000	−	18.1865i	−0.640196	−	1.10885i	0.345192	−	0.938532i	$-0.387814\pi$
$270$		0			0
$271$	6.50000	−	11.2583i	0.394847	−	0.683895i	−0.598235	−	0.801321i	$-0.704131\pi$
$271$	6.50000	−	11.2583i	0.394847	−	0.683895i	0.993082	+	0.117426i	$0.0374643\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	1.50000	−	2.59808i	0.0904534	−	0.156670i
$276$		0			0
$277$	9.50000	+	16.4545i	0.570800	+	0.988654i	0.996484	+	0.0837823i	$0.0267000\pi$
$277$	9.50000	+	16.4545i	0.570800	+	0.988654i	−0.425684	+	0.904872i	$0.639967\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	18.0000			1.07379			0.536895	−	0.843649i	$-0.319597\pi$
$281$	18.0000			1.07379			0.536895	+	0.843649i	$0.319597\pi$
$282$		0			0
$283$	−8.50000	+	14.7224i	−0.505273	+	0.875158i	0.494709	+	0.869059i	$0.335275\pi$
$283$	−8.50000	+	14.7224i	−0.505273	+	0.875158i	−0.999981	+	0.00609896i	$0.998059\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	3.00000			0.177084
$288$		0			0
$289$	4.00000	−	6.92820i	0.235294	−	0.407541i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−1.50000	−	2.59808i	−0.0876309	−	0.151781i	0.818878	−	0.573967i	$-0.194596\pi$
$293$	−1.50000	−	2.59808i	−0.0876309	−	0.151781i	−0.906509	+	0.422186i	$0.861263\pi$
$294$		0			0
$295$	4.50000	+	7.79423i	0.262000	+	0.453798i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	31.5000	+	7.79423i	1.82169	+	0.450752i
$300$		0			0
$301$	−0.500000	+	0.866025i	−0.0288195	+	0.0499169i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	0.500000	+	0.866025i	0.0286299	+	0.0495885i
$306$		0			0
$307$	−4.00000			−0.228292			−0.114146	−	0.993464i	$-0.536413\pi$
$307$	−4.00000			−0.228292			−0.114146	+	0.993464i	$0.536413\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−12.0000			−0.680458			−0.340229	−	0.940343i	$-0.610505\pi$
$311$	−12.0000			−0.680458			−0.340229	+	0.940343i	$0.610505\pi$
$312$		0			0
$313$	−10.0000			−0.565233			−0.282617	−	0.959233i	$-0.591202\pi$
$313$	−10.0000			−0.565233			−0.282617	+	0.959233i	$0.591202\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	18.0000			1.01098			0.505490	−	0.862832i	$-0.331312\pi$
$317$	18.0000			1.01098			0.505490	+	0.862832i	$0.331312\pi$
$318$		0			0
$319$	13.5000	+	23.3827i	0.755855	+	1.30918i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−7.50000	+	12.9904i	−0.417311	+	0.722804i
$324$		0			0
$325$	1.00000	+	3.46410i	0.0554700	+	0.192154i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	9.50000	+	16.4545i	0.522167	+	0.904420i	0.999667	+	0.0257885i	$0.00820965\pi$
$331$	9.50000	+	16.4545i	0.522167	+	0.904420i	−0.477500	+	0.878632i	$0.658457\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−2.50000	+	4.33013i	−0.136590	+	0.236580i
$336$		0			0
$337$	−22.0000			−1.19842			−0.599208	−	0.800593i	$-0.704518\pi$
$337$	−22.0000			−1.19842			−0.599208	+	0.800593i	$0.704518\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	12.0000	−	20.7846i	0.649836	−	1.12555i
$342$		0			0
$343$	13.0000			0.701934
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−4.50000	−	7.79423i	−0.241573	−	0.418416i	0.719590	−	0.694399i	$-0.244330\pi$
$347$	−4.50000	−	7.79423i	−0.241573	−	0.418416i	−0.961162	+	0.275983i	$0.910997\pi$
$348$		0			0
$349$	−17.5000	+	30.3109i	−0.936754	+	1.62250i	−0.165277	+	0.986247i	$0.552852\pi$
$349$	−17.5000	+	30.3109i	−0.936754	+	1.62250i	−0.771477	+	0.636257i	$0.780482\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−13.5000	+	23.3827i	−0.718532	+	1.24453i	0.243049	+	0.970014i	$0.421853\pi$
$353$	−13.5000	+	23.3827i	−0.718532	+	1.24453i	−0.961581	+	0.274521i	$0.911481\pi$
$354$		0			0
$355$	4.50000	+	7.79423i	0.238835	+	0.413675i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		0			0			−	1.00000i	$-0.5\pi$
$359$		0			0				1.00000i	$0.5\pi$
$360$		0			0
$361$	−3.00000	+	5.19615i	−0.157895	+	0.273482i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	2.00000			0.104685
$366$		0			0
$367$	−8.50000	+	14.7224i	−0.443696	+	0.768505i	−0.997960	−	0.0638362i	$-0.979666\pi$
$367$	−8.50000	+	14.7224i	−0.443696	+	0.768505i	0.554264	+	0.832341i	$0.313000\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−3.00000	−	5.19615i	−0.155752	−	0.269771i
$372$		0			0
$373$	−2.50000	−	4.33013i	−0.129445	−	0.224205i	0.794017	−	0.607896i	$-0.207986\pi$
$373$	−2.50000	−	4.33013i	−0.129445	−	0.224205i	−0.923462	+	0.383691i	$0.874653\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−31.5000	−	7.79423i	−1.62233	−	0.401423i
$378$		0			0
$379$	−5.50000	+	9.52628i	−0.282516	+	0.489332i	−0.972004	−	0.234965i	$-0.924502\pi$
$379$	−5.50000	+	9.52628i	−0.282516	+	0.489332i	0.689488	+	0.724297i	$0.257836\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−10.5000	−	18.1865i	−0.536525	−	0.929288i	−0.999088	−	0.0427020i	$-0.986403\pi$
$383$	−10.5000	−	18.1865i	−0.536525	−	0.929288i	0.462563	−	0.886586i	$-0.346930\pi$
$384$		0			0
$385$	3.00000			0.152894
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−18.0000			−0.912636			−0.456318	−	0.889817i	$-0.650832\pi$
$389$	−18.0000			−0.912636			−0.456318	+	0.889817i	$0.650832\pi$
$390$		0			0
$391$	−27.0000			−1.36545
$392$		0			0
$393$		0			0
$394$		0			0
$395$	8.00000			0.402524
$396$		0			0
$397$	−14.5000	−	25.1147i	−0.727734	−	1.26047i	−0.957839	−	0.287307i	$-0.907240\pi$
$397$	−14.5000	−	25.1147i	−0.727734	−	1.26047i	0.230105	−	0.973166i	$-0.426093\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	7.50000	−	12.9904i	0.374532	−	0.648709i	−0.615725	−	0.787961i	$-0.711137\pi$
$401$	7.50000	−	12.9904i	0.374532	−	0.648709i	0.990257	+	0.139253i	$0.0444700\pi$
$402$		0			0
$403$	8.00000	+	27.7128i	0.398508	+	1.38047i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−10.5000	−	18.1865i	−0.520466	−	0.901473i
$408$		0			0
$409$	12.5000	+	21.6506i	0.618085	+	1.07056i	0.989835	+	0.142222i	$0.0454247\pi$
$409$	12.5000	+	21.6506i	0.618085	+	1.07056i	−0.371750	+	0.928333i	$0.621242\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−4.50000	+	7.79423i	−0.221431	+	0.383529i
$414$		0			0
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−10.5000	+	18.1865i	−0.512959	+	0.888470i	0.486928	+	0.873442i	$0.338117\pi$
$419$	−10.5000	+	18.1865i	−0.512959	+	0.888470i	−0.999887	+	0.0150285i	$0.995216\pi$
$420$		0			0
$421$	2.00000			0.0974740			0.0487370	−	0.998812i	$-0.484480\pi$
$421$	2.00000			0.0974740			0.0487370	+	0.998812i	$0.484480\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−1.50000	−	2.59808i	−0.0727607	−	0.126025i
$426$		0			0
$427$	−0.500000	+	0.866025i	−0.0241967	+	0.0419099i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	1.50000	−	2.59808i	0.0722525	−	0.125145i	−0.827636	−	0.561266i	$-0.810315\pi$
$431$	1.50000	−	2.59808i	0.0722525	−	0.125145i	0.899888	+	0.436121i	$0.143648\pi$
$432$		0			0
$433$	−2.50000	−	4.33013i	−0.120142	−	0.208093i	0.799681	−	0.600425i	$-0.205002\pi$
$433$	−2.50000	−	4.33013i	−0.120142	−	0.208093i	−0.919824	+	0.392332i	$0.871668\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−45.0000			−2.15264
$438$		0			0
$439$	0.500000	−	0.866025i	0.0238637	−	0.0413331i	−0.853847	−	0.520524i	$-0.825737\pi$
$439$	0.500000	−	0.866025i	0.0238637	−	0.0413331i	0.877711	+	0.479191i	$0.159070\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−12.0000			−0.570137			−0.285069	−	0.958507i	$-0.592016\pi$
$443$	−12.0000			−0.570137			−0.285069	+	0.958507i	$0.592016\pi$
$444$		0			0
$445$	1.50000	−	2.59808i	0.0711068	−	0.123161i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	7.50000	+	12.9904i	0.353947	+	0.613054i	0.986937	−	0.161106i	$-0.0515060\pi$
$449$	7.50000	+	12.9904i	0.353947	+	0.613054i	−0.632990	+	0.774160i	$0.718173\pi$
$450$		0			0
$451$	−4.50000	−	7.79423i	−0.211897	−	0.367016i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−2.50000	+	2.59808i	−0.117202	+	0.121800i
$456$		0			0
$457$	−20.5000	+	35.5070i	−0.958950	+	1.66095i	−0.233890	+	0.972263i	$0.575146\pi$
$457$	−20.5000	+	35.5070i	−0.958950	+	1.66095i	−0.725059	+	0.688686i	$0.758188\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	7.50000	+	12.9904i	0.349310	+	0.605022i	0.986127	−	0.165992i	$-0.0530827\pi$
$461$	7.50000	+	12.9904i	0.349310	+	0.605022i	−0.636817	+	0.771015i	$0.719749\pi$
$462$		0			0
$463$	−40.0000			−1.85896			−0.929479	−	0.368875i	$-0.879743\pi$
$463$	−40.0000			−1.85896			−0.929479	+	0.368875i	$0.879743\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	12.0000			0.555294			0.277647	−	0.960683i	$-0.410445\pi$
$467$	12.0000			0.555294			0.277647	+	0.960683i	$0.410445\pi$
$468$		0			0
$469$	−5.00000			−0.230879
$470$		0			0
$471$		0			0
$472$		0			0
$473$	3.00000			0.137940
$474$		0			0
$475$	−2.50000	−	4.33013i	−0.114708	−	0.198680i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	7.50000	−	12.9904i	0.342684	−	0.593546i	−0.642246	−	0.766498i	$-0.721997\pi$
$479$	7.50000	−	12.9904i	0.342684	−	0.593546i	0.984930	+	0.172953i	$0.0553307\pi$
$480$		0			0
$481$	24.5000	+	6.06218i	1.11710	+	0.276412i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−8.50000	−	14.7224i	−0.385965	−	0.668511i
$486$		0			0
$487$	−17.5000	−	30.3109i	−0.793001	−	1.37352i	−0.924101	−	0.382148i	$-0.875184\pi$
$487$	−17.5000	−	30.3109i	−0.793001	−	1.37352i	0.131100	−	0.991369i	$-0.458149\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	7.50000	−	12.9904i	0.338470	−	0.586248i	−0.645675	−	0.763612i	$-0.723424\pi$
$491$	7.50000	−	12.9904i	0.338470	−	0.586248i	0.984145	+	0.177365i	$0.0567572\pi$
$492$		0			0
$493$	27.0000			1.21602
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−4.50000	+	7.79423i	−0.201853	+	0.349619i
$498$		0			0
$499$	−4.00000			−0.179065			−0.0895323	−	0.995984i	$-0.528537\pi$
$499$	−4.00000			−0.179065			−0.0895323	+	0.995984i	$0.528537\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	19.5000	+	33.7750i	0.869462	+	1.50595i	0.862547	+	0.505976i	$0.168868\pi$
$503$	19.5000	+	33.7750i	0.869462	+	1.50595i	0.00691465	+	0.999976i	$0.497799\pi$
$504$		0			0
$505$	7.50000	−	12.9904i	0.333746	−	0.578064i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−16.5000	+	28.5788i	−0.731350	+	1.26673i	0.224957	+	0.974369i	$0.427776\pi$
$509$	−16.5000	+	28.5788i	−0.731350	+	1.26673i	−0.956306	+	0.292366i	$0.905557\pi$
$510$		0			0
$511$	1.00000	+	1.73205i	0.0442374	+	0.0766214i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	8.00000			0.352522
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−6.00000			−0.262865			−0.131432	−	0.991325i	$-0.541958\pi$
$521$	−6.00000			−0.262865			−0.131432	+	0.991325i	$0.541958\pi$
$522$		0			0
$523$	−2.50000	+	4.33013i	−0.109317	+	0.189343i	−0.915494	−	0.402332i	$-0.868200\pi$
$523$	−2.50000	+	4.33013i	−0.109317	+	0.189343i	0.806177	+	0.591675i	$0.201533\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−12.0000	−	20.7846i	−0.522728	−	0.905392i
$528$		0			0
$529$	−29.0000	−	50.2295i	−1.26087	−	2.18389i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	10.5000	+	2.59808i	0.454805	+	0.112535i
$534$		0			0
$535$	−1.50000	+	2.59808i	−0.0648507	+	0.112325i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−9.00000	−	15.5885i	−0.387657	−	0.671442i
$540$		0			0
$541$	2.00000			0.0859867			0.0429934	−	0.999075i	$-0.486311\pi$
$541$	2.00000			0.0859867			0.0429934	+	0.999075i	$0.486311\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	14.0000			0.599694
$546$		0			0
$547$	−28.0000			−1.19719			−0.598597	−	0.801050i	$-0.704275\pi$
$547$	−28.0000			−1.19719			−0.598597	+	0.801050i	$0.704275\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	45.0000			1.91706
$552$		0			0
$553$	4.00000	+	6.92820i	0.170097	+	0.294617i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−19.5000	+	33.7750i	−0.826242	+	1.43109i	0.0747252	+	0.997204i	$0.476192\pi$
$557$	−19.5000	+	33.7750i	−0.826242	+	1.43109i	−0.900967	+	0.433888i	$0.857141\pi$
$558$		0			0
$559$	−2.50000	+	2.59808i	−0.105739	+	0.109887i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−16.5000	−	28.5788i	−0.695392	−	1.20445i	−0.970048	−	0.242912i	$-0.921897\pi$
$563$	−16.5000	−	28.5788i	−0.695392	−	1.20445i	0.274656	−	0.961542i	$-0.411436\pi$
$564$		0			0
$565$	−7.50000	−	12.9904i	−0.315527	−	0.546509i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−16.5000	+	28.5788i	−0.691716	+	1.19809i	0.279559	+	0.960128i	$0.409812\pi$
$569$	−16.5000	+	28.5788i	−0.691716	+	1.19809i	−0.971275	+	0.237959i	$0.923522\pi$
$570$		0			0
$571$	44.0000			1.84134			0.920671	−	0.390339i	$-0.127642\pi$
$571$	44.0000			1.84134			0.920671	+	0.390339i	$0.127642\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	4.50000	−	7.79423i	0.187663	−	0.325042i
$576$		0			0
$577$	−22.0000			−0.915872			−0.457936	−	0.888985i	$-0.651411\pi$
$577$	−22.0000			−0.915872			−0.457936	+	0.888985i	$0.651411\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−9.00000	+	15.5885i	−0.372742	+	0.645608i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−13.5000	+	23.3827i	−0.557205	+	0.965107i	0.440524	+	0.897741i	$0.354793\pi$
$587$	−13.5000	+	23.3827i	−0.557205	+	0.965107i	−0.997728	+	0.0673658i	$0.978541\pi$
$588$		0			0
$589$	−20.0000	−	34.6410i	−0.824086	−	1.42736i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	6.00000			0.246390			0.123195	−	0.992382i	$-0.460686\pi$
$593$	6.00000			0.246390			0.123195	+	0.992382i	$0.460686\pi$
$594$		0			0
$595$	1.50000	−	2.59808i	0.0614940	−	0.106511i
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0			−	1.00000i	$-0.5\pi$
$599$		0			0				1.00000i	$0.5\pi$
$600$		0			0
$601$	0.500000	−	0.866025i	0.0203954	−	0.0353259i	−0.855648	−	0.517559i	$-0.826841\pi$
$601$	0.500000	−	0.866025i	0.0203954	−	0.0353259i	0.876043	+	0.482233i	$0.160174\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	1.00000	+	1.73205i	0.0406558	+	0.0704179i
$606$		0			0
$607$	−11.5000	−	19.9186i	−0.466771	−	0.808470i	0.532509	−	0.846424i	$-0.321249\pi$
$607$	−11.5000	−	19.9186i	−0.466771	−	0.808470i	−0.999279	+	0.0379540i	$0.987916\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−14.5000	+	25.1147i	−0.585649	+	1.01437i	0.409145	+	0.912470i	$0.365827\pi$
$613$	−14.5000	+	25.1147i	−0.585649	+	1.01437i	−0.994794	+	0.101905i	$0.967506\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−13.5000	−	23.3827i	−0.543490	−	0.941351i	−0.998700	−	0.0509678i	$-0.983769\pi$
$617$	−13.5000	−	23.3827i	−0.543490	−	0.941351i	0.455211	−	0.890384i	$-0.349564\pi$
$618$		0			0
$619$	−28.0000			−1.12542			−0.562708	−	0.826656i	$-0.690240\pi$
$619$	−28.0000			−1.12542			−0.562708	+	0.826656i	$0.690240\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	3.00000			0.120192
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−21.0000			−0.837325
$630$		0			0
$631$	3.50000	+	6.06218i	0.139333	+	0.241331i	0.927244	−	0.374457i	$-0.122171\pi$
$631$	3.50000	+	6.06218i	0.139333	+	0.241331i	−0.787911	+	0.615789i	$0.788838\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−8.50000	+	14.7224i	−0.337312	+	0.584242i
$636$		0			0
$637$	21.0000	+	5.19615i	0.832050	+	0.205879i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	1.50000	+	2.59808i	0.0592464	+	0.102618i	0.894127	−	0.447813i	$-0.147797\pi$
$641$	1.50000	+	2.59808i	0.0592464	+	0.102618i	−0.834881	+	0.550431i	$0.814464\pi$
$642$		0			0
$643$	12.5000	+	21.6506i	0.492952	+	0.853818i	0.999967	−	0.00811944i	$-0.00258453\pi$
$643$	12.5000	+	21.6506i	0.492952	+	0.853818i	−0.507015	+	0.861937i	$0.669251\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−13.5000	+	23.3827i	−0.530740	+	0.919268i	0.468617	+	0.883402i	$0.344753\pi$
$647$	−13.5000	+	23.3827i	−0.530740	+	0.919268i	−0.999357	+	0.0358667i	$0.988581\pi$
$648$		0			0
$649$	27.0000			1.05984
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−13.5000	+	23.3827i	−0.528296	+	0.915035i	0.471160	+	0.882048i	$0.343835\pi$
$653$	−13.5000	+	23.3827i	−0.528296	+	0.915035i	−0.999456	+	0.0329874i	$0.989498\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$	22.5000	+	38.9711i	0.876476	+	1.51810i	0.855183	+	0.518327i	$0.173445\pi$
$659$	22.5000	+	38.9711i	0.876476	+	1.51810i	0.0212930	+	0.999773i	$0.493222\pi$
$660$		0			0
$661$	−17.5000	+	30.3109i	−0.680671	+	1.17896i	0.294105	+	0.955773i	$0.404978\pi$
$661$	−17.5000	+	30.3109i	−0.680671	+	1.17896i	−0.974776	+	0.223184i	$0.928355\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	2.50000	−	4.33013i	0.0969458	−	0.167915i
$666$		0			0
$667$	40.5000	+	70.1481i	1.56817	+	2.71614i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	3.00000			0.115814
$672$		0			0
$673$	9.50000	−	16.4545i	0.366198	−	0.634274i	−0.622770	−	0.782405i	$-0.713993\pi$
$673$	9.50000	−	16.4545i	0.366198	−	0.634274i	0.988968	+	0.148132i	$0.0473259\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	18.0000			0.691796			0.345898	−	0.938272i	$-0.387574\pi$
$677$	18.0000			0.691796			0.345898	+	0.938272i	$0.387574\pi$
$678$		0			0
$679$	8.50000	−	14.7224i	0.326200	−	0.564995i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−10.5000	−	18.1865i	−0.401771	−	0.695888i	0.592168	−	0.805814i	$-0.298272\pi$
$683$	−10.5000	−	18.1865i	−0.401771	−	0.695888i	−0.993940	+	0.109926i	$0.964939\pi$
$684$		0			0
$685$	−1.50000	−	2.59808i	−0.0573121	−	0.0992674i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−6.00000	−	20.7846i	−0.228582	−	0.791831i
$690$		0			0
$691$	−11.5000	+	19.9186i	−0.437481	+	0.757739i	−0.997494	−	0.0707446i	$-0.977462\pi$
$691$	−11.5000	+	19.9186i	−0.437481	+	0.757739i	0.560014	+	0.828483i	$0.310796\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−2.50000	−	4.33013i	−0.0948304	−	0.164251i
$696$		0			0
$697$	−9.00000			−0.340899
$698$		0			0
$699$		0			0
$700$		0			0
$701$	30.0000			1.13308			0.566542	−	0.824033i	$-0.308281\pi$
$701$	30.0000			1.13308			0.566542	+	0.824033i	$0.308281\pi$
$702$		0			0
$703$	−35.0000			−1.32005
$704$		0			0
$705$		0			0
$706$		0			0
$707$	15.0000			0.564133
$708$		0			0
$709$	−17.5000	−	30.3109i	−0.657226	−	1.13835i	−0.981331	−	0.192328i	$-0.938396\pi$
$709$	−17.5000	−	30.3109i	−0.657226	−	1.13835i	0.324104	−	0.946021i	$-0.394937\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	36.0000	−	62.3538i	1.34821	−	2.33517i
$714$		0			0
$715$	10.5000	+	2.59808i	0.392678	+	0.0971625i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	22.5000	+	38.9711i	0.839108	+	1.45338i	0.890641	+	0.454707i	$0.150256\pi$
$719$	22.5000	+	38.9711i	0.839108	+	1.45338i	−0.0515326	+	0.998671i	$0.516411\pi$
$720$		0			0
$721$	4.00000	+	6.92820i	0.148968	+	0.258020i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−4.50000	+	7.79423i	−0.167126	+	0.289470i
$726$		0			0
$727$	8.00000			0.296704			0.148352	−	0.988935i	$-0.452603\pi$
$727$	8.00000			0.296704			0.148352	+	0.988935i	$0.452603\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	1.50000	−	2.59808i	0.0554795	−	0.0960933i
$732$		0			0
$733$	−34.0000			−1.25582			−0.627909	−	0.778287i	$-0.716089\pi$
$733$	−34.0000			−1.25582			−0.627909	+	0.778287i	$0.716089\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	7.50000	+	12.9904i	0.276266	+	0.478507i
$738$		0			0
$739$	−5.50000	+	9.52628i	−0.202321	+	0.350430i	−0.949276	−	0.314445i	$-0.898182\pi$
$739$	−5.50000	+	9.52628i	−0.202321	+	0.350430i	0.746955	+	0.664875i	$0.231515\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	16.5000	−	28.5788i	0.605326	−	1.04846i	−0.386674	−	0.922217i	$-0.626376\pi$
$743$	16.5000	−	28.5788i	0.605326	−	1.04846i	0.992000	−	0.126239i	$-0.0402907\pi$
$744$		0			0
$745$	−4.50000	−	7.79423i	−0.164867	−	0.285558i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−3.00000			−0.109618
$750$		0			0
$751$	6.50000	−	11.2583i	0.237188	−	0.410822i	−0.722718	−	0.691143i	$-0.757107\pi$
$751$	6.50000	−	11.2583i	0.237188	−	0.410822i	0.959906	+	0.280321i	$0.0904408\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	20.0000			0.727875
$756$		0			0
$757$	−2.50000	+	4.33013i	−0.0908640	+	0.157381i	−0.907875	−	0.419241i	$-0.862296\pi$
$757$	−2.50000	+	4.33013i	−0.0908640	+	0.157381i	0.817011	+	0.576622i	$0.195630\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−4.50000	−	7.79423i	−0.163125	−	0.282541i	0.772863	−	0.634573i	$-0.218824\pi$
$761$	−4.50000	−	7.79423i	−0.163125	−	0.282541i	−0.935988	+	0.352032i	$0.885491\pi$
$762$		0			0
$763$	7.00000	+	12.1244i	0.253417	+	0.438931i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−22.5000	+	23.3827i	−0.812428	+	0.844300i
$768$		0			0
$769$	−5.50000	+	9.52628i	−0.198335	+	0.343526i	−0.947989	−	0.318304i	$-0.896887\pi$
$769$	−5.50000	+	9.52628i	−0.198335	+	0.343526i	0.749654	+	0.661830i	$0.230220\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−7.50000	−	12.9904i	−0.269756	−	0.467232i	0.699043	−	0.715080i	$-0.253610\pi$
$773$	−7.50000	−	12.9904i	−0.269756	−	0.467232i	−0.968799	+	0.247849i	$0.920276\pi$
$774$		0			0
$775$	8.00000			0.287368
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−15.0000			−0.537431
$780$		0			0
$781$	27.0000			0.966136
$782$		0			0
$783$		0			0
$784$		0			0
$785$	14.0000			0.499681
$786$		0			0
$787$	24.5000	+	42.4352i	0.873331	+	1.51265i	0.858530	+	0.512763i	$0.171378\pi$
$787$	24.5000	+	42.4352i	0.873331	+	1.51265i	0.0148003	+	0.999890i	$0.495289\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	7.50000	−	12.9904i	0.266669	−	0.461885i
$792$		0			0
$793$	−2.50000	+	2.59808i	−0.0887776	+	0.0922604i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−13.5000	−	23.3827i	−0.478195	−	0.828257i	0.521493	−	0.853256i	$-0.325375\pi$
$797$	−13.5000	−	23.3827i	−0.478195	−	0.828257i	−0.999687	+	0.0249984i	$0.992042\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$		0			0
$802$		0			0
$803$	3.00000	−	5.19615i	0.105868	−	0.183368i
$804$		0			0
$805$	9.00000			0.317208
$806$		0			0
$807$		0			0
$808$		0			0
$809$	19.5000	−	33.7750i	0.685583	−	1.18747i	−0.287670	−	0.957730i	$-0.592880\pi$
$809$	19.5000	−	33.7750i	0.685583	−	1.18747i	0.973253	−	0.229736i	$-0.0737862\pi$
$810$		0			0
$811$	−16.0000			−0.561836			−0.280918	−	0.959732i	$-0.590639\pi$
$811$	−16.0000			−0.561836			−0.280918	+	0.959732i	$0.590639\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	0.500000	+	0.866025i	0.0175142	+	0.0303355i
$816$		0			0
$817$	2.50000	−	4.33013i	0.0874639	−	0.151492i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−10.5000	+	18.1865i	−0.366453	+	0.634714i	−0.989008	−	0.147861i	$-0.952761\pi$
$821$	−10.5000	+	18.1865i	−0.366453	+	0.634714i	0.622556	+	0.782576i	$0.286094\pi$
$822$		0			0
$823$	−23.5000	−	40.7032i	−0.819159	−	1.41882i	−0.906303	−	0.422628i	$-0.861108\pi$
$823$	−23.5000	−	40.7032i	−0.819159	−	1.41882i	0.0871445	−	0.996196i	$-0.472226\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−12.0000			−0.417281			−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000			−0.417281			−0.208640	+	0.977992i	$0.566904\pi$
$828$		0			0
$829$	−5.50000	+	9.52628i	−0.191023	+	0.330861i	−0.945589	−	0.325362i	$-0.894514\pi$
$829$	−5.50000	+	9.52628i	−0.191023	+	0.330861i	0.754567	+	0.656223i	$0.227847\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−18.0000			−0.623663
$834$		0			0
$835$	−7.50000	+	12.9904i	−0.259548	+	0.449551i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−7.50000	−	12.9904i	−0.258929	−	0.448478i	0.707026	−	0.707187i	$-0.250036\pi$
$839$	−7.50000	−	12.9904i	−0.258929	−	0.448478i	−0.965955	+	0.258709i	$0.916703\pi$
$840$		0			0
$841$	−26.0000	−	45.0333i	−0.896552	−	1.55287i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−11.0000	+	6.92820i	−0.378412	+	0.238337i
$846$		0			0
$847$	−1.00000	+	1.73205i	−0.0343604	+	0.0595140i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−31.5000	−	54.5596i	−1.07981	−	1.87028i
$852$		0			0
$853$	14.0000			0.479351			0.239675	−	0.970853i	$-0.422959\pi$
$853$	14.0000			0.479351			0.239675	+	0.970853i	$0.422959\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	42.0000			1.43469			0.717346	−	0.696717i	$-0.245357\pi$
$857$	42.0000			1.43469			0.717346	+	0.696717i	$0.245357\pi$
$858$		0			0
$859$	8.00000			0.272956			0.136478	−	0.990643i	$-0.456422\pi$
$859$	8.00000			0.272956			0.136478	+	0.990643i	$0.456422\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−48.0000			−1.63394			−0.816970	−	0.576681i	$-0.804348\pi$
$863$	−48.0000			−1.63394			−0.816970	+	0.576681i	$0.804348\pi$
$864$		0			0
$865$	10.5000	+	18.1865i	0.357011	+	0.618361i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	12.0000	−	20.7846i	0.407072	−	0.705070i
$870$		0			0
$871$	−17.5000	−	4.33013i	−0.592965	−	0.146721i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	0.500000	+	0.866025i	0.0169031	+	0.0292770i
$876$		0			0
$877$	−8.50000	−	14.7224i	−0.287025	−	0.497141i	0.686074	−	0.727532i	$-0.259333\pi$
$877$	−8.50000	−	14.7224i	−0.287025	−	0.497141i	−0.973098	+	0.230391i	$0.925999\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	1.50000	−	2.59808i	0.0505363	−	0.0875314i	−0.839651	−	0.543127i	$-0.817240\pi$
$881$	1.50000	−	2.59808i	0.0505363	−	0.0875314i	0.890187	+	0.455595i	$0.150574\pi$
$882$		0			0
$883$	56.0000			1.88455			0.942275	−	0.334840i	$-0.108682\pi$
$883$	56.0000			1.88455			0.942275	+	0.334840i	$0.108682\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	16.5000	−	28.5788i	0.554016	−	0.959583i	−0.443964	−	0.896045i	$-0.646428\pi$
$887$	16.5000	−	28.5788i	0.554016	−	0.959583i	0.997979	−	0.0635387i	$-0.0202386\pi$
$888$		0			0
$889$	−17.0000			−0.570162
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$	7.50000	−	12.9904i	0.250697	−	0.434221i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−36.0000	+	62.3538i	−1.20067	+	2.07962i
$900$		0			0
$901$	9.00000	+	15.5885i	0.299833	+	0.519327i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−10.0000			−0.332411
$906$		0			0
$907$	27.5000	−	47.6314i	0.913123	−	1.58157i	0.103495	−	0.994630i	$-0.466997\pi$
$907$	27.5000	−	47.6314i	0.913123	−	1.58157i	0.809627	−	0.586945i	$-0.199669\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	48.0000			1.59031			0.795155	−	0.606406i	$-0.207389\pi$
$911$	48.0000			1.59031			0.795155	+	0.606406i	$0.207389\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	3.50000	+	6.06218i	0.115454	+	0.199973i	0.917961	−	0.396670i	$-0.129834\pi$
$919$	3.50000	+	6.06218i	0.115454	+	0.199973i	−0.802507	+	0.596643i	$0.796501\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−22.5000	+	23.3827i	−0.740597	+	0.769650i
$924$		0			0
$925$	3.50000	−	6.06218i	0.115079	−	0.199323i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	1.50000	+	2.59808i	0.0492134	+	0.0852401i	0.889583	−	0.456774i	$-0.150995\pi$
$929$	1.50000	+	2.59808i	0.0492134	+	0.0852401i	−0.840369	+	0.542014i	$0.817662\pi$
$930$		0			0
$931$	−30.0000			−0.983210
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−9.00000			−0.294331
$936$		0			0
$937$	−22.0000			−0.718709			−0.359354	−	0.933201i	$-0.617003\pi$
$937$	−22.0000			−0.718709			−0.359354	+	0.933201i	$0.617003\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−18.0000			−0.586783			−0.293392	−	0.955992i	$-0.594784\pi$
$941$	−18.0000			−0.586783			−0.293392	+	0.955992i	$0.594784\pi$
$942$		0			0
$943$	−13.5000	−	23.3827i	−0.439620	−	0.761445i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−25.5000	+	44.1673i	−0.828639	+	1.43524i	0.0704677	+	0.997514i	$0.477551\pi$
$947$	−25.5000	+	44.1673i	−0.828639	+	1.43524i	−0.899106	+	0.437730i	$0.855783\pi$
$948$		0			0
$949$	2.00000	+	6.92820i	0.0649227	+	0.224899i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	10.5000	+	18.1865i	0.340128	+	0.589120i	0.984456	−	0.175630i	$-0.0561961\pi$
$953$	10.5000	+	18.1865i	0.340128	+	0.589120i	−0.644328	+	0.764749i	$0.722863\pi$
$954$		0			0
$955$	−1.50000	−	2.59808i	−0.0485389	−	0.0840718i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	1.50000	−	2.59808i	0.0484375	−	0.0838963i
$960$		0			0
$961$	33.0000			1.06452
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−2.50000	+	4.33013i	−0.0804778	+	0.139392i
$966$		0			0
$967$	−4.00000			−0.128631			−0.0643157	−	0.997930i	$-0.520486\pi$
$967$	−4.00000			−0.128631			−0.0643157	+	0.997930i	$0.520486\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−7.50000	−	12.9904i	−0.240686	−	0.416881i	0.720224	−	0.693742i	$-0.244039\pi$
$971$	−7.50000	−	12.9904i	−0.240686	−	0.416881i	−0.960910	+	0.276861i	$0.910706\pi$
$972$		0			0
$973$	2.50000	−	4.33013i	0.0801463	−	0.138817i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−1.50000	+	2.59808i	−0.0479893	+	0.0831198i	−0.889022	−	0.457864i	$-0.848615\pi$
$977$	−1.50000	+	2.59808i	−0.0479893	+	0.0831198i	0.841033	+	0.540984i	$0.181948\pi$
$978$		0			0
$979$	−4.50000	−	7.79423i	−0.143821	−	0.249105i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	48.0000			1.53096			0.765481	−	0.643458i	$-0.222501\pi$
$983$	48.0000			1.53096			0.765481	+	0.643458i	$0.222501\pi$
$984$		0			0
$985$	−1.50000	+	2.59808i	−0.0477940	+	0.0827816i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	9.00000			0.286183
$990$		0			0
$991$	24.5000	−	42.4352i	0.778268	−	1.34800i	−0.154671	−	0.987966i	$-0.549432\pi$
$991$	24.5000	−	42.4352i	0.778268	−	1.34800i	0.932939	−	0.360034i	$-0.117235\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	3.50000	+	6.06218i	0.110957	+	0.192184i
$996$		0			0
$997$	−2.50000	−	4.33013i	−0.0791758	−	0.137136i	0.823719	−	0.566999i	$-0.191896\pi$
$997$	−2.50000	−	4.33013i	−0.0791758	−	0.137136i	−0.902895	+	0.429862i	$0.858562\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2340.2.q.f.1621.1		2
3.2	odd	2		260.2.i.a.61.1	✓	2
12.11	even	2		1040.2.q.i.321.1		2
13.3	even	3	inner	2340.2.q.f.2161.1		2
15.2	even	4		1300.2.bb.b.1049.2		4
15.8	even	4		1300.2.bb.b.1049.1		4
15.14	odd	2		1300.2.i.d.1101.1		2
39.17	odd	6		3380.2.a.i.1.1		1
39.20	even	12		3380.2.f.d.3041.1		2
39.29	odd	6		260.2.i.a.81.1	yes	2
39.32	even	12		3380.2.f.d.3041.2		2
39.35	odd	6		3380.2.a.f.1.1		1
156.107	even	6		1040.2.q.i.81.1		2
195.29	odd	6		1300.2.i.d.601.1		2
195.68	even	12		1300.2.bb.b.549.2		4
195.107	even	12		1300.2.bb.b.549.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.i.a.61.1	✓	2	3.2	odd	2
260.2.i.a.81.1	yes	2	39.29	odd	6
1040.2.q.i.81.1		2	156.107	even	6
1040.2.q.i.321.1		2	12.11	even	2
1300.2.i.d.601.1		2	195.29	odd	6
1300.2.i.d.1101.1		2	15.14	odd	2
1300.2.bb.b.549.1		4	195.107	even	12
1300.2.bb.b.549.2		4	195.68	even	12
1300.2.bb.b.1049.1		4	15.8	even	4
1300.2.bb.b.1049.2		4	15.2	even	4
2340.2.q.f.1621.1		2	1.1	even	1	trivial
2340.2.q.f.2161.1		2	13.3	even	3	inner
3380.2.a.f.1.1		1	39.35	odd	6
3380.2.a.i.1.1		1	39.17	odd	6
3380.2.f.d.3041.1		2	39.20	even	12
3380.2.f.d.3041.2		2	39.32	even	12

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:	\( N \)	\(=\)	\( 2340 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2340.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{5} +(0.500000 + 0.866025i) q^{7} +O(q^{10})\)	\(q+1.00000 q^{5} +(0.500000 + 0.866025i) q^{7} +(1.50000 - 2.59808i) q^{11} +(1.00000 + 3.46410i) q^{13} +(-1.50000 - 2.59808i) q^{17} +(-2.50000 - 4.33013i) q^{19} +(4.50000 - 7.79423i) q^{23} +1.00000 q^{25} +(-4.50000 + 7.79423i) q^{29} +8.00000 q^{31} +(0.500000 + 0.866025i) q^{35} +(3.50000 - 6.06218i) q^{37} +(1.50000 - 2.59808i) q^{41} +(0.500000 + 0.866025i) q^{43} +(3.00000 - 5.19615i) q^{49} -6.00000 q^{53} +(1.50000 - 2.59808i) q^{55} +(4.50000 + 7.79423i) q^{59} +(0.500000 + 0.866025i) q^{61} +(1.00000 + 3.46410i) q^{65} +(-2.50000 + 4.33013i) q^{67} +(4.50000 + 7.79423i) q^{71} +2.00000 q^{73} +3.00000 q^{77} +8.00000 q^{79} +(-1.50000 - 2.59808i) q^{85} +(1.50000 - 2.59808i) q^{89} +(-2.50000 + 2.59808i) q^{91} +(-2.50000 - 4.33013i) q^{95} +(-8.50000 - 14.7224i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{5} + q^{7}+O(q^{10}) \) 2 * q + 2 * q^5 + q^7	\( 2 q + 2 q^{5} + q^{7} + 3 q^{11} + 2 q^{13} - 3 q^{17} - 5 q^{19} + 9 q^{23} + 2 q^{25} - 9 q^{29} + 16 q^{31} + q^{35} + 7 q^{37} + 3 q^{41} + q^{43} + 6 q^{49} - 12 q^{53} + 3 q^{55} + 9 q^{59} + q^{61} + 2 q^{65} - 5 q^{67} + 9 q^{71} + 4 q^{73} + 6 q^{77} + 16 q^{79} - 3 q^{85} + 3 q^{89} - 5 q^{91} - 5 q^{95} - 17 q^{97}+O(q^{100}) \) 2 * q + 2 * q^5 + q^7 + 3 * q^11 + 2 * q^13 - 3 * q^17 - 5 * q^19 + 9 * q^23 + 2 * q^25 - 9 * q^29 + 16 * q^31 + q^35 + 7 * q^37 + 3 * q^41 + q^43 + 6 * q^49 - 12 * q^53 + 3 * q^55 + 9 * q^59 + q^61 + 2 * q^65 - 5 * q^67 + 9 * q^71 + 4 * q^73 + 6 * q^77 + 16 * q^79 - 3 * q^85 + 3 * q^89 - 5 * q^91 - 5 * q^95 - 17 * q^97

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