LMFDB - Embedded newform 1064.2.q.d.305.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1064,2,Mod(305,1064)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1064, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1064.305");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1064 = 2^{3} \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1064.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:	$8.49608277506$
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:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			305.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1064.305
Dual form			1064.2.q.d.457.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 - 2.59808i) q^{5} +(-0.500000 + 2.59808i) q^{7} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	$q+(-1.50000 - 2.59808i) q^{5} +(-0.500000 + 2.59808i) q^{7} +(1.50000 + 2.59808i) q^{9} +(0.500000 - 0.866025i) q^{11} +(3.00000 - 5.19615i) q^{17} +(0.500000 + 0.866025i) q^{19} +(1.50000 + 2.59808i) q^{23} +(-2.00000 + 3.46410i) q^{25} +6.00000 q^{29} +(-1.00000 + 1.73205i) q^{31} +(7.50000 - 2.59808i) q^{35} +6.00000 q^{41} +9.00000 q^{43} +(4.50000 - 7.79423i) q^{45} +(1.50000 + 2.59808i) q^{47} +(-6.50000 - 2.59808i) q^{49} +(1.00000 - 1.73205i) q^{53} -3.00000 q^{55} +(6.00000 - 10.3923i) q^{59} +(-5.50000 - 9.52628i) q^{61} +(-7.50000 + 2.59808i) q^{63} +(4.00000 - 6.92820i) q^{67} +6.00000 q^{71} +(7.50000 - 12.9904i) q^{73} +(2.00000 + 1.73205i) q^{77} +(6.00000 + 10.3923i) q^{79} +(-4.50000 + 7.79423i) q^{81} +7.00000 q^{83} -18.0000 q^{85} +(4.00000 + 6.92820i) q^{89} +(1.50000 - 2.59808i) q^{95} -6.00000 q^{97} +3.00000 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{5} - q^{7} + 3 q^{9}+O(q^{10}) $ 2 * q - 3 * q^5 - q^7 + 3 * q^9	$ 2 q - 3 q^{5} - q^{7} + 3 q^{9} + q^{11} + 6 q^{17} + q^{19} + 3 q^{23} - 4 q^{25} + 12 q^{29} - 2 q^{31} + 15 q^{35} + 12 q^{41} + 18 q^{43} + 9 q^{45} + 3 q^{47} - 13 q^{49} + 2 q^{53} - 6 q^{55} + 12 q^{59} - 11 q^{61} - 15 q^{63} + 8 q^{67} + 12 q^{71} + 15 q^{73} + 4 q^{77} + 12 q^{79} - 9 q^{81} + 14 q^{83} - 36 q^{85} + 8 q^{89} + 3 q^{95} - 12 q^{97} + 6 q^{99}+O(q^{100}) $ 2 * q - 3 * q^5 - q^7 + 3 * q^9 + q^11 + 6 * q^17 + q^19 + 3 * q^23 - 4 * q^25 + 12 * q^29 - 2 * q^31 + 15 * q^35 + 12 * q^41 + 18 * q^43 + 9 * q^45 + 3 * q^47 - 13 * q^49 + 2 * q^53 - 6 * q^55 + 12 * q^59 - 11 * q^61 - 15 * q^63 + 8 * q^67 + 12 * q^71 + 15 * q^73 + 4 * q^77 + 12 * q^79 - 9 * q^81 + 14 * q^83 - 36 * q^85 + 8 * q^89 + 3 * q^95 - 12 * q^97 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1064\mathbb{Z}\right)^\times$.

$n$	$533$	$799$	$913$	$1009$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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		−0.866025	−	0.500000i	$-0.833333\pi$
$3$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$4$		0			0
$5$	−1.50000	−	2.59808i	−0.670820	−	1.16190i	−0.977672	−	0.210138i	$-0.932609\pi$
$5$	−1.50000	−	2.59808i	−0.670820	−	1.16190i	0.306851	−	0.951757i	$-0.400725\pi$
$6$		0			0
$7$	−0.500000	+	2.59808i	−0.188982	+	0.981981i
$7$	−0.500000	+	2.59808i	−0.188982	+	0.981981i
$8$		0			0
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$		0			0
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i	−0.780750	−	0.624844i	$-0.785163\pi$
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i	0.931505	+	0.363727i	$0.118496\pi$
$12$		0			0
$13$		0			0			−	1.00000i	$-0.5\pi$
$13$		0			0				1.00000i	$0.5\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.00000	−	5.19615i	0.727607	−	1.26025i	−0.230285	−	0.973123i	$-0.573966\pi$
$17$	3.00000	−	5.19615i	0.727607	−	1.26025i	0.957892	−	0.287129i	$-0.0927008\pi$
$18$		0			0
$19$	0.500000	+	0.866025i	0.114708	+	0.198680i
$19$	0.500000	+	0.866025i	0.114708	+	0.198680i
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.50000	+	2.59808i	0.312772	+	0.541736i	0.978961	−	0.204046i	$-0.0654092\pi$
$23$	1.50000	+	2.59808i	0.312772	+	0.541736i	−0.666190	+	0.745782i	$0.732076\pi$
$24$		0			0
$25$	−2.00000	+	3.46410i	−0.400000	+	0.692820i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	6.00000			1.11417			0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000			1.11417			0.557086	+	0.830455i	$0.311919\pi$
$30$		0			0
$31$	−1.00000	+	1.73205i	−0.179605	+	0.311086i	−0.941745	−	0.336327i	$-0.890815\pi$
$31$	−1.00000	+	1.73205i	−0.179605	+	0.311086i	0.762140	+	0.647412i	$0.224149\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	7.50000	−	2.59808i	1.26773	−	0.439155i
$36$		0			0
$37$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$37$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	6.00000			0.937043			0.468521	−	0.883452i	$-0.344787\pi$
$41$	6.00000			0.937043			0.468521	+	0.883452i	$0.344787\pi$
$42$		0			0
$43$	9.00000			1.37249			0.686244	−	0.727372i	$-0.259258\pi$
$43$	9.00000			1.37249			0.686244	+	0.727372i	$0.259258\pi$
$44$		0			0
$45$	4.50000	−	7.79423i	0.670820	−	1.16190i
$46$		0			0
$47$	1.50000	+	2.59808i	0.218797	+	0.378968i	0.954441	−	0.298401i	$-0.0964533\pi$
$47$	1.50000	+	2.59808i	0.218797	+	0.378968i	−0.735643	+	0.677369i	$0.763120\pi$
$48$		0			0
$49$	−6.50000	−	2.59808i	−0.928571	−	0.371154i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	1.00000	−	1.73205i	0.137361	−	0.237915i	−0.789136	−	0.614218i	$-0.789471\pi$
$53$	1.00000	−	1.73205i	0.137361	−	0.237915i	0.926497	+	0.376303i	$0.122805\pi$
$54$		0			0
$55$	−3.00000			−0.404520
$56$		0			0
$57$		0			0
$58$		0			0
$59$	6.00000	−	10.3923i	0.781133	−	1.35296i	−0.150148	−	0.988663i	$-0.547975\pi$
$59$	6.00000	−	10.3923i	0.781133	−	1.35296i	0.931282	−	0.364299i	$-0.118692\pi$
$60$		0			0
$61$	−5.50000	−	9.52628i	−0.704203	−	1.21972i	−0.966978	−	0.254858i	$-0.917971\pi$
$61$	−5.50000	−	9.52628i	−0.704203	−	1.21972i	0.262776	−	0.964857i	$-0.415362\pi$
$62$		0			0
$63$	−7.50000	+	2.59808i	−0.944911	+	0.327327i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	4.00000	−	6.92820i	0.488678	−	0.846415i	−0.511237	−	0.859440i	$-0.670813\pi$
$67$	4.00000	−	6.92820i	0.488678	−	0.846415i	0.999915	+	0.0130248i	$0.00414604\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	6.00000			0.712069			0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000			0.712069			0.356034	+	0.934473i	$0.384129\pi$
$72$		0			0
$73$	7.50000	−	12.9904i	0.877809	−	1.52041i	0.0240681	−	0.999710i	$-0.492338\pi$
$73$	7.50000	−	12.9904i	0.877809	−	1.52041i	0.853740	−	0.520699i	$-0.174329\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	2.00000	+	1.73205i	0.227921	+	0.197386i
$78$		0			0
$79$	6.00000	+	10.3923i	0.675053	+	1.16923i	0.976453	+	0.215728i	$0.0692125\pi$
$79$	6.00000	+	10.3923i	0.675053	+	1.16923i	−0.301401	+	0.953498i	$0.597454\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$		0			0
$83$	7.00000			0.768350			0.384175	−	0.923260i	$-0.374486\pi$
$83$	7.00000			0.768350			0.384175	+	0.923260i	$0.374486\pi$
$84$		0			0
$85$	−18.0000			−1.95237
$86$		0			0
$87$		0			0
$88$		0			0
$89$	4.00000	+	6.92820i	0.423999	+	0.734388i	0.996326	−	0.0856373i	$-0.0272926\pi$
$89$	4.00000	+	6.92820i	0.423999	+	0.734388i	−0.572327	+	0.820025i	$0.693959\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$	1.50000	−	2.59808i	0.153897	−	0.266557i
$96$		0			0
$97$	−6.00000			−0.609208			−0.304604	−	0.952479i	$-0.598524\pi$
$97$	−6.00000			−0.609208			−0.304604	+	0.952479i	$0.598524\pi$
$98$		0			0
$99$	3.00000			0.301511
$100$		0			0
$101$	−4.50000	+	7.79423i	−0.447767	+	0.775555i	−0.998240	−	0.0592978i	$-0.981114\pi$
$101$	−4.50000	+	7.79423i	−0.447767	+	0.775555i	0.550474	+	0.834853i	$0.314447\pi$
$102$		0			0
$103$	7.00000	+	12.1244i	0.689730	+	1.19465i	0.971925	+	0.235291i	$0.0756043\pi$
$103$	7.00000	+	12.1244i	0.689730	+	1.19465i	−0.282194	+	0.959357i	$0.591062\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	2.00000	+	3.46410i	0.193347	+	0.334887i	0.946357	−	0.323122i	$-0.104732\pi$
$107$	2.00000	+	3.46410i	0.193347	+	0.334887i	−0.753010	+	0.658009i	$0.771399\pi$
$108$		0			0
$109$	−2.00000	+	3.46410i	−0.191565	+	0.331801i	−0.945769	−	0.324840i	$-0.894690\pi$
$109$	−2.00000	+	3.46410i	−0.191565	+	0.331801i	0.754204	+	0.656640i	$0.228023\pi$
$110$		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
$115$	4.50000	−	7.79423i	0.419627	−	0.726816i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	12.0000	+	10.3923i	1.10004	+	0.952661i
$120$		0			0
$121$	5.00000	+	8.66025i	0.454545	+	0.787296i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−3.00000			−0.268328
$126$		0			0
$127$	−16.0000			−1.41977			−0.709885	−	0.704317i	$-0.751253\pi$
$127$	−16.0000			−1.41977			−0.709885	+	0.704317i	$0.751253\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	4.00000	+	6.92820i	0.349482	+	0.605320i	0.986157	−	0.165812i	$-0.0530244\pi$
$131$	4.00000	+	6.92820i	0.349482	+	0.605320i	−0.636676	+	0.771132i	$0.719691\pi$
$132$		0			0
$133$	−2.50000	+	0.866025i	−0.216777	+	0.0750939i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	1.50000	−	2.59808i	0.128154	−	0.221969i	−0.794808	−	0.606861i	$-0.792428\pi$
$137$	1.50000	−	2.59808i	0.128154	−	0.221969i	0.922961	+	0.384893i	$0.125762\pi$
$138$		0			0
$139$	−17.0000			−1.44192			−0.720961	−	0.692976i	$-0.756299\pi$
$139$	−17.0000			−1.44192			−0.720961	+	0.692976i	$0.756299\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$		0			0
$145$	−9.00000	−	15.5885i	−0.747409	−	1.29455i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	1.50000	+	2.59808i	0.122885	+	0.212843i	0.920904	−	0.389789i	$-0.127452\pi$
$149$	1.50000	+	2.59808i	0.122885	+	0.212843i	−0.798019	+	0.602632i	$0.794119\pi$
$150$		0			0
$151$	−3.00000	+	5.19615i	−0.244137	+	0.422857i	−0.961888	−	0.273442i	$-0.911838\pi$
$151$	−3.00000	+	5.19615i	−0.244137	+	0.422857i	0.717752	+	0.696299i	$0.245171\pi$
$152$		0			0
$153$	18.0000			1.45521
$154$		0			0
$155$	6.00000			0.481932
$156$		0			0
$157$	3.50000	−	6.06218i	0.279330	−	0.483814i	−0.691888	−	0.722005i	$-0.743221\pi$
$157$	3.50000	−	6.06218i	0.279330	−	0.483814i	0.971219	+	0.238190i	$0.0765542\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−7.50000	+	2.59808i	−0.591083	+	0.204757i
$162$		0			0
$163$	9.50000	+	16.4545i	0.744097	+	1.28881i	0.950615	+	0.310372i	$0.100454\pi$
$163$	9.50000	+	16.4545i	0.744097	+	1.28881i	−0.206518	+	0.978443i	$0.566213\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−14.0000			−1.08335			−0.541676	−	0.840587i	$-0.682210\pi$
$167$	−14.0000			−1.08335			−0.541676	+	0.840587i	$0.682210\pi$
$168$		0			0
$169$	−13.0000			−1.00000
$170$		0			0
$171$	−1.50000	+	2.59808i	−0.114708	+	0.198680i
$172$		0			0
$173$	−4.00000	−	6.92820i	−0.304114	−	0.526742i	0.672949	−	0.739689i	$-0.265027\pi$
$173$	−4.00000	−	6.92820i	−0.304114	−	0.526742i	−0.977064	+	0.212947i	$0.931694\pi$
$174$		0			0
$175$	−8.00000	−	6.92820i	−0.604743	−	0.523723i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	5.00000	−	8.66025i	0.373718	−	0.647298i	−0.616417	−	0.787420i	$-0.711416\pi$
$179$	5.00000	−	8.66025i	0.373718	−	0.647298i	0.990134	+	0.140122i	$0.0447496\pi$
$180$		0			0
$181$	22.0000			1.63525			0.817624	−	0.575753i	$-0.195291\pi$
$181$	22.0000			1.63525			0.817624	+	0.575753i	$0.195291\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−3.00000	−	5.19615i	−0.219382	−	0.379980i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−2.50000	−	4.33013i	−0.180894	−	0.313317i	0.761291	−	0.648410i	$-0.224566\pi$
$191$	−2.50000	−	4.33013i	−0.180894	−	0.313317i	−0.942185	+	0.335093i	$0.891232\pi$
$192$		0			0
$193$	10.0000	−	17.3205i	0.719816	−	1.24676i	−0.241257	−	0.970461i	$-0.577560\pi$
$193$	10.0000	−	17.3205i	0.719816	−	1.24676i	0.961073	−	0.276296i	$-0.0891071\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	3.00000			0.213741			0.106871	−	0.994273i	$-0.465917\pi$
$197$	3.00000			0.213741			0.106871	+	0.994273i	$0.465917\pi$
$198$		0			0
$199$	−2.50000	+	4.33013i	−0.177220	+	0.306955i	−0.940927	−	0.338608i	$-0.890044\pi$
$199$	−2.50000	+	4.33013i	−0.177220	+	0.306955i	0.763707	+	0.645563i	$0.223377\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−3.00000	+	15.5885i	−0.210559	+	1.09410i
$204$		0			0
$205$	−9.00000	−	15.5885i	−0.628587	−	1.08875i
$206$		0			0
$207$	−4.50000	+	7.79423i	−0.312772	+	0.541736i
$208$		0			0
$209$	1.00000			0.0691714
$210$		0			0
$211$	−20.0000			−1.37686			−0.688428	−	0.725304i	$-0.741699\pi$
$211$	−20.0000			−1.37686			−0.688428	+	0.725304i	$0.741699\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−13.5000	−	23.3827i	−0.920692	−	1.59469i
$216$		0			0
$217$	−4.00000	−	3.46410i	−0.271538	−	0.235159i
$218$		0			0
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−2.00000			−0.133930			−0.0669650	−	0.997755i	$-0.521332\pi$
$223$	−2.00000			−0.133930			−0.0669650	+	0.997755i	$0.521332\pi$
$224$		0			0
$225$	−12.0000			−0.800000
$226$		0			0
$227$	−6.00000	+	10.3923i	−0.398234	+	0.689761i	−0.993508	−	0.113761i	$-0.963710\pi$
$227$	−6.00000	+	10.3923i	−0.398234	+	0.689761i	0.595274	+	0.803523i	$0.297043\pi$
$228$		0			0
$229$	−7.00000	−	12.1244i	−0.462573	−	0.801200i	0.536515	−	0.843891i	$-0.319740\pi$
$229$	−7.00000	−	12.1244i	−0.462573	−	0.801200i	−0.999088	+	0.0426906i	$0.986407\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−7.00000	−	12.1244i	−0.458585	−	0.794293i	0.540301	−	0.841472i	$-0.318310\pi$
$233$	−7.00000	−	12.1244i	−0.458585	−	0.794293i	−0.998886	+	0.0471787i	$0.984977\pi$
$234$		0			0
$235$	4.50000	−	7.79423i	0.293548	−	0.508439i
$236$		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
$241$	−2.00000	+	3.46410i	−0.128831	+	0.223142i	−0.923224	−	0.384262i	$-0.874456\pi$
$241$	−2.00000	+	3.46410i	−0.128831	+	0.223142i	0.794393	+	0.607404i	$0.207789\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	3.00000	+	20.7846i	0.191663	+	1.32788i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$		0			0
$251$	3.00000			0.189358			0.0946792	−	0.995508i	$-0.469817\pi$
$251$	3.00000			0.189358			0.0946792	+	0.995508i	$0.469817\pi$
$252$		0			0
$253$	3.00000			0.188608
$254$		0			0
$255$		0			0
$256$		0			0
$257$	11.0000	+	19.0526i	0.686161	+	1.18847i	0.973070	+	0.230508i	$0.0740389\pi$
$257$	11.0000	+	19.0526i	0.686161	+	1.18847i	−0.286909	+	0.957958i	$0.592628\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	9.00000	+	15.5885i	0.557086	+	0.964901i
$262$		0			0
$263$	12.0000	−	20.7846i	0.739952	−	1.28163i	−0.212565	−	0.977147i	$-0.568182\pi$
$263$	12.0000	−	20.7846i	0.739952	−	1.28163i	0.952517	−	0.304487i	$-0.0984850\pi$
$264$		0			0
$265$	−6.00000			−0.368577
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−12.0000	+	20.7846i	−0.731653	+	1.26726i	0.224523	+	0.974469i	$0.427917\pi$
$269$	−12.0000	+	20.7846i	−0.731653	+	1.26726i	−0.956176	+	0.292791i	$0.905416\pi$
$270$		0			0
$271$	−7.50000	−	12.9904i	−0.455593	−	0.789109i	0.543130	−	0.839649i	$-0.317239\pi$
$271$	−7.50000	−	12.9904i	−0.455593	−	0.789109i	−0.998722	+	0.0505395i	$0.983906\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	2.00000	+	3.46410i	0.120605	+	0.208893i
$276$		0			0
$277$	−8.50000	+	14.7224i	−0.510716	+	0.884585i	0.489207	+	0.872167i	$0.337286\pi$
$277$	−8.50000	+	14.7224i	−0.510716	+	0.884585i	−0.999923	+	0.0124177i	$0.996047\pi$
$278$		0			0
$279$	−6.00000			−0.359211
$280$		0			0
$281$	6.00000			0.357930			0.178965	−	0.983855i	$-0.442725\pi$
$281$	6.00000			0.357930			0.178965	+	0.983855i	$0.442725\pi$
$282$		0			0
$283$	−0.500000	+	0.866025i	−0.0297219	+	0.0514799i	−0.880504	−	0.474039i	$-0.842796\pi$
$283$	−0.500000	+	0.866025i	−0.0297219	+	0.0514799i	0.850782	+	0.525519i	$0.176129\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−3.00000	+	15.5885i	−0.177084	+	0.920158i
$288$		0			0
$289$	−9.50000	−	16.4545i	−0.558824	−	0.967911i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	14.0000			0.817889			0.408944	−	0.912559i	$-0.365897\pi$
$293$	14.0000			0.817889			0.408944	+	0.912559i	$0.365897\pi$
$294$		0			0
$295$	−36.0000			−2.09600
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$		0			0
$301$	−4.50000	+	23.3827i	−0.259376	+	1.34776i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−16.5000	+	28.5788i	−0.944787	+	1.63642i
$306$		0			0
$307$	22.0000			1.25561			0.627803	−	0.778372i	$-0.283954\pi$
$307$	22.0000			1.25561			0.627803	+	0.778372i	$0.283954\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$311$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$312$		0			0
$313$	6.50000	+	11.2583i	0.367402	+	0.636358i	0.989158	−	0.146852i	$-0.0469141\pi$
$313$	6.50000	+	11.2583i	0.367402	+	0.636358i	−0.621757	+	0.783210i	$0.713581\pi$
$314$		0			0
$315$	18.0000	+	15.5885i	1.01419	+	0.878310i
$316$		0			0
$317$	1.00000	+	1.73205i	0.0561656	+	0.0972817i	0.892741	−	0.450570i	$-0.148779\pi$
$317$	1.00000	+	1.73205i	0.0561656	+	0.0972817i	−0.836576	+	0.547852i	$0.815446\pi$
$318$		0			0
$319$	3.00000	−	5.19615i	0.167968	−	0.290929i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	6.00000			0.333849
$324$		0			0
$325$		0			0
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−7.50000	+	2.59808i	−0.413488	+	0.143237i
$330$		0			0
$331$	11.0000	+	19.0526i	0.604615	+	1.04722i	0.992112	+	0.125353i	$0.0400062\pi$
$331$	11.0000	+	19.0526i	0.604615	+	1.04722i	−0.387498	+	0.921871i	$0.626660\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−24.0000			−1.31126
$336$		0			0
$337$	6.00000			0.326841			0.163420	−	0.986557i	$-0.447747\pi$
$337$	6.00000			0.326841			0.163420	+	0.986557i	$0.447747\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	1.00000	+	1.73205i	0.0541530	+	0.0937958i
$342$		0			0
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	2.50000	−	4.33013i	0.134207	−	0.232453i	−0.791087	−	0.611703i	$-0.790485\pi$
$347$	2.50000	−	4.33013i	0.134207	−	0.232453i	0.925294	+	0.379250i	$0.123818\pi$
$348$		0			0
$349$	22.0000			1.17763			0.588817	−	0.808267i	$-0.299594\pi$
$349$	22.0000			1.17763			0.588817	+	0.808267i	$0.299594\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	15.0000	−	25.9808i	0.798369	−	1.38282i	−0.122308	−	0.992492i	$-0.539030\pi$
$353$	15.0000	−	25.9808i	0.798369	−	1.38282i	0.920677	−	0.390324i	$-0.127637\pi$
$354$		0			0
$355$	−9.00000	−	15.5885i	−0.477670	−	0.827349i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	2.50000	+	4.33013i	0.131945	+	0.228535i	0.924426	−	0.381361i	$-0.124544\pi$
$359$	2.50000	+	4.33013i	0.131945	+	0.228535i	−0.792481	+	0.609896i	$0.791211\pi$
$360$		0			0
$361$	−0.500000	+	0.866025i	−0.0263158	+	0.0455803i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−45.0000			−2.35541
$366$		0			0
$367$	4.00000	−	6.92820i	0.208798	−	0.361649i	−0.742538	−	0.669804i	$-0.766378\pi$
$367$	4.00000	−	6.92820i	0.208798	−	0.361649i	0.951336	+	0.308155i	$0.0997115\pi$
$368$		0			0
$369$	9.00000	+	15.5885i	0.468521	+	0.811503i
$370$		0			0
$371$	4.00000	+	3.46410i	0.207670	+	0.179847i
$372$		0			0
$373$	−16.0000	−	27.7128i	−0.828449	−	1.43492i	−0.899255	−	0.437425i	$-0.855891\pi$
$373$	−16.0000	−	27.7128i	−0.828449	−	1.43492i	0.0708063	−	0.997490i	$-0.477443\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−28.0000			−1.43826			−0.719132	−	0.694874i	$-0.755460\pi$
$379$	−28.0000			−1.43826			−0.719132	+	0.694874i	$0.755460\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	4.00000	+	6.92820i	0.204390	+	0.354015i	0.949938	−	0.312437i	$-0.101145\pi$
$383$	4.00000	+	6.92820i	0.204390	+	0.354015i	−0.745548	+	0.666452i	$0.767812\pi$
$384$		0			0
$385$	1.50000	−	7.79423i	0.0764471	−	0.397231i
$386$		0			0
$387$	13.5000	+	23.3827i	0.686244	+	1.18861i
$388$		0			0
$389$	−9.00000	+	15.5885i	−0.456318	+	0.790366i	−0.998763	−	0.0497253i	$-0.984165\pi$
$389$	−9.00000	+	15.5885i	−0.456318	+	0.790366i	0.542445	+	0.840091i	$0.317499\pi$
$390$		0			0
$391$	18.0000			0.910299
$392$		0			0
$393$		0			0
$394$		0			0
$395$	18.0000	−	31.1769i	0.905678	−	1.56868i
$396$		0			0
$397$	−17.0000	−	29.4449i	−0.853206	−	1.47780i	−0.878300	−	0.478110i	$-0.841322\pi$
$397$	−17.0000	−	29.4449i	−0.853206	−	1.47780i	0.0250943	−	0.999685i	$-0.492011\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$401$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	27.0000			1.34164
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−1.00000	+	1.73205i	−0.0494468	+	0.0856444i	−0.889689	−	0.456566i	$-0.849079\pi$
$409$	−1.00000	+	1.73205i	−0.0494468	+	0.0856444i	0.840243	+	0.542211i	$0.182412\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	24.0000	+	20.7846i	1.18096	+	1.02274i
$414$		0			0
$415$	−10.5000	−	18.1865i	−0.515425	−	0.892742i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−5.00000			−0.244266			−0.122133	−	0.992514i	$-0.538973\pi$
$419$	−5.00000			−0.244266			−0.122133	+	0.992514i	$0.538973\pi$
$420$		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
$423$	−4.50000	+	7.79423i	−0.218797	+	0.378968i
$424$		0			0
$425$	12.0000	+	20.7846i	0.582086	+	1.00820i
$426$		0			0
$427$	27.5000	−	9.52628i	1.33082	−	0.461009i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	3.00000	−	5.19615i	0.144505	−	0.250290i	−0.784683	−	0.619897i	$-0.787174\pi$
$431$	3.00000	−	5.19615i	0.144505	−	0.250290i	0.929188	+	0.369607i	$0.120508\pi$
$432$		0			0
$433$	−24.0000			−1.15337			−0.576683	−	0.816968i	$-0.695653\pi$
$433$	−24.0000			−1.15337			−0.576683	+	0.816968i	$0.695653\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−1.50000	+	2.59808i	−0.0717547	+	0.124283i
$438$		0			0
$439$	−10.0000	−	17.3205i	−0.477274	−	0.826663i	0.522387	−	0.852709i	$-0.325042\pi$
$439$	−10.0000	−	17.3205i	−0.477274	−	0.826663i	−0.999661	+	0.0260459i	$0.991708\pi$
$440$		0			0
$441$	−3.00000	−	20.7846i	−0.142857	−	0.989743i
$442$		0			0
$443$	−14.0000	−	24.2487i	−0.665160	−	1.15209i	−0.979242	−	0.202695i	$-0.935030\pi$
$443$	−14.0000	−	24.2487i	−0.665160	−	1.15209i	0.314082	−	0.949396i	$-0.398303\pi$
$444$		0			0
$445$	12.0000	−	20.7846i	0.568855	−	0.985285i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	36.0000			1.69895			0.849473	−	0.527633i	$-0.176920\pi$
$449$	36.0000			1.69895			0.849473	+	0.527633i	$0.176920\pi$
$450$		0			0
$451$	3.00000	−	5.19615i	0.141264	−	0.244677i
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	12.5000	+	21.6506i	0.584725	+	1.01277i	0.994910	+	0.100771i	$0.0321310\pi$
$457$	12.5000	+	21.6506i	0.584725	+	1.01277i	−0.410184	+	0.912003i	$0.634536\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	1.00000			0.0465746			0.0232873	−	0.999729i	$-0.492587\pi$
$461$	1.00000			0.0465746			0.0232873	+	0.999729i	$0.492587\pi$
$462$		0			0
$463$	13.0000			0.604161			0.302081	−	0.953282i	$-0.402319\pi$
$463$	13.0000			0.604161			0.302081	+	0.953282i	$0.402319\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−16.5000	−	28.5788i	−0.763529	−	1.32247i	−0.941021	−	0.338349i	$-0.890132\pi$
$467$	−16.5000	−	28.5788i	−0.763529	−	1.32247i	0.177492	−	0.984122i	$-0.443202\pi$
$468$		0			0
$469$	16.0000	+	13.8564i	0.738811	+	0.639829i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	4.50000	−	7.79423i	0.206910	−	0.358379i
$474$		0			0
$475$	−4.00000			−0.183533
$476$		0			0
$477$	6.00000			0.274721
$478$		0			0
$479$	−1.50000	+	2.59808i	−0.0685367	+	0.118709i	−0.898257	−	0.439470i	$-0.855166\pi$
$479$	−1.50000	+	2.59808i	−0.0685367	+	0.118709i	0.829721	+	0.558179i	$0.188500\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$		0			0
$485$	9.00000	+	15.5885i	0.408669	+	0.707835i
$486$		0			0
$487$	−13.0000	+	22.5167i	−0.589086	+	1.02033i	0.405266	+	0.914199i	$0.367179\pi$
$487$	−13.0000	+	22.5167i	−0.589086	+	1.02033i	−0.994352	+	0.106129i	$0.966154\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−33.0000			−1.48927			−0.744635	−	0.667472i	$-0.767376\pi$
$491$	−33.0000			−1.48927			−0.744635	+	0.667472i	$0.767376\pi$
$492$		0			0
$493$	18.0000	−	31.1769i	0.810679	−	1.40414i
$494$		0			0
$495$	−4.50000	−	7.79423i	−0.202260	−	0.350325i
$496$		0			0
$497$	−3.00000	+	15.5885i	−0.134568	+	0.699238i
$498$		0			0
$499$	6.50000	+	11.2583i	0.290980	+	0.503992i	0.974042	−	0.226369i	$-0.0726854\pi$
$499$	6.50000	+	11.2583i	0.290980	+	0.503992i	−0.683062	+	0.730361i	$0.739352\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	1.00000			0.0445878			0.0222939	−	0.999751i	$-0.492903\pi$
$503$	1.00000			0.0445878			0.0222939	+	0.999751i	$0.492903\pi$
$504$		0			0
$505$	27.0000			1.20148
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−3.00000	−	5.19615i	−0.132973	−	0.230315i	0.791849	−	0.610718i	$-0.209119\pi$
$509$	−3.00000	−	5.19615i	−0.132973	−	0.230315i	−0.924821	+	0.380402i	$0.875786\pi$
$510$		0			0
$511$	30.0000	+	25.9808i	1.32712	+	1.14932i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	21.0000	−	36.3731i	0.925371	−	1.60279i
$516$		0			0
$517$	3.00000			0.131940
$518$		0			0
$519$		0			0
$520$		0			0
$521$	6.00000	−	10.3923i	0.262865	−	0.455295i	−0.704137	−	0.710064i	$-0.748666\pi$
$521$	6.00000	−	10.3923i	0.262865	−	0.455295i	0.967002	+	0.254769i	$0.0819994\pi$
$522$		0			0
$523$	−9.00000	−	15.5885i	−0.393543	−	0.681636i	0.599371	−	0.800471i	$-0.295417\pi$
$523$	−9.00000	−	15.5885i	−0.393543	−	0.681636i	−0.992914	+	0.118835i	$0.962084\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	6.00000	+	10.3923i	0.261364	+	0.452696i
$528$		0			0
$529$	7.00000	−	12.1244i	0.304348	−	0.527146i
$530$		0			0
$531$	36.0000			1.56227
$532$		0			0
$533$		0			0
$534$		0			0
$535$	6.00000	−	10.3923i	0.259403	−	0.449299i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−5.50000	+	4.33013i	−0.236902	+	0.186512i
$540$		0			0
$541$	−5.50000	−	9.52628i	−0.236463	−	0.409567i	0.723234	−	0.690604i	$-0.242655\pi$
$541$	−5.50000	−	9.52628i	−0.236463	−	0.409567i	−0.959697	+	0.281037i	$0.909322\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	12.0000			0.514024
$546$		0			0
$547$	−2.00000			−0.0855138			−0.0427569	−	0.999086i	$-0.513614\pi$
$547$	−2.00000			−0.0855138			−0.0427569	+	0.999086i	$0.513614\pi$
$548$		0			0
$549$	16.5000	−	28.5788i	0.704203	−	1.21972i
$550$		0			0
$551$	3.00000	+	5.19615i	0.127804	+	0.221364i
$552$		0			0
$553$	−30.0000	+	10.3923i	−1.27573	+	0.441926i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	7.50000	−	12.9904i	0.317785	−	0.550420i	−0.662240	−	0.749291i	$-0.730394\pi$
$557$	7.50000	−	12.9904i	0.317785	−	0.550420i	0.980026	+	0.198871i	$0.0637276\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−12.0000	+	20.7846i	−0.505740	+	0.875967i	0.494238	+	0.869326i	$0.335447\pi$
$563$	−12.0000	+	20.7846i	−0.505740	+	0.875967i	−0.999978	+	0.00664037i	$0.997886\pi$
$564$		0			0
$565$	27.0000	+	46.7654i	1.13590	+	1.96743i
$566$		0			0
$567$	−18.0000	−	15.5885i	−0.755929	−	0.654654i
$568$		0			0
$569$	9.00000	+	15.5885i	0.377300	+	0.653502i	0.990668	−	0.136295i	$-0.0435194\pi$
$569$	9.00000	+	15.5885i	0.377300	+	0.653502i	−0.613369	+	0.789797i	$0.710186\pi$
$570$		0			0
$571$	−11.5000	+	19.9186i	−0.481260	+	0.833567i	−0.999769	−	0.0215055i	$-0.993154\pi$
$571$	−11.5000	+	19.9186i	−0.481260	+	0.833567i	0.518509	+	0.855072i	$0.326487\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−12.0000			−0.500435
$576$		0			0
$577$	−3.50000	+	6.06218i	−0.145707	+	0.252372i	−0.929636	−	0.368478i	$-0.879879\pi$
$577$	−3.50000	+	6.06218i	−0.145707	+	0.252372i	0.783930	+	0.620850i	$0.213212\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−3.50000	+	18.1865i	−0.145204	+	0.754505i
$582$		0			0
$583$	−1.00000	−	1.73205i	−0.0414158	−	0.0717342i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	12.0000			0.495293			0.247647	−	0.968850i	$-0.420343\pi$
$587$	12.0000			0.495293			0.247647	+	0.968850i	$0.420343\pi$
$588$		0			0
$589$	−2.00000			−0.0824086
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−1.50000	−	2.59808i	−0.0615976	−	0.106690i	0.833582	−	0.552396i	$-0.186286\pi$
$593$	−1.50000	−	2.59808i	−0.0615976	−	0.106690i	−0.895180	+	0.445705i	$0.852953\pi$
$594$		0			0
$595$	9.00000	−	46.7654i	0.368964	−	1.91719i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−7.00000	+	12.1244i	−0.286012	+	0.495388i	−0.972854	−	0.231419i	$-0.925663\pi$
$599$	−7.00000	+	12.1244i	−0.286012	+	0.495388i	0.686842	+	0.726807i	$0.258996\pi$
$600$		0			0
$601$	−16.0000			−0.652654			−0.326327	−	0.945257i	$-0.605811\pi$
$601$	−16.0000			−0.652654			−0.326327	+	0.945257i	$0.605811\pi$
$602$		0			0
$603$	24.0000			0.977356
$604$		0			0
$605$	15.0000	−	25.9808i	0.609837	−	1.05627i
$606$		0			0
$607$	−16.0000	−	27.7128i	−0.649420	−	1.12483i	−0.983262	−	0.182199i	$-0.941678\pi$
$607$	−16.0000	−	27.7128i	−0.649420	−	1.12483i	0.333842	−	0.942629i	$-0.391655\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	3.00000	−	5.19615i	0.121169	−	0.209871i	−0.799060	−	0.601251i	$-0.794669\pi$
$613$	3.00000	−	5.19615i	0.121169	−	0.209871i	0.920229	+	0.391381i	$0.128002\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	45.0000			1.81163			0.905816	−	0.423672i	$-0.139259\pi$
$617$	45.0000			1.81163			0.905816	+	0.423672i	$0.139259\pi$
$618$		0			0
$619$	0.500000	−	0.866025i	0.0200967	−	0.0348085i	−0.855802	−	0.517303i	$-0.826936\pi$
$619$	0.500000	−	0.866025i	0.0200967	−	0.0348085i	0.875899	+	0.482495i	$0.160269\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−20.0000	+	6.92820i	−0.801283	+	0.277573i
$624$		0			0
$625$	14.5000	+	25.1147i	0.580000	+	1.00459i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	−23.0000			−0.915616			−0.457808	−	0.889051i	$-0.651365\pi$
$631$	−23.0000			−0.915616			−0.457808	+	0.889051i	$0.651365\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	24.0000	+	41.5692i	0.952411	+	1.64962i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	9.00000	+	15.5885i	0.356034	+	0.616670i
$640$		0			0
$641$	−22.0000	+	38.1051i	−0.868948	+	1.50506i	−0.00587459	+	0.999983i	$0.501870\pi$
$641$	−22.0000	+	38.1051i	−0.868948	+	1.50506i	−0.863073	+	0.505079i	$0.831463\pi$
$642$		0			0
$643$	−32.0000			−1.26196			−0.630978	−	0.775800i	$-0.717346\pi$
$643$	−32.0000			−1.26196			−0.630978	+	0.775800i	$0.717346\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−12.5000	+	21.6506i	−0.491426	+	0.851174i	−0.999951	−	0.00987260i	$-0.996857\pi$
$647$	−12.5000	+	21.6506i	−0.491426	+	0.851174i	0.508526	+	0.861047i	$0.330191\pi$
$648$		0			0
$649$	−6.00000	−	10.3923i	−0.235521	−	0.407934i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−7.00000	−	12.1244i	−0.273931	−	0.474463i	0.695934	−	0.718106i	$-0.254991\pi$
$653$	−7.00000	−	12.1244i	−0.273931	−	0.474463i	−0.969865	+	0.243643i	$0.921657\pi$
$654$		0			0
$655$	12.0000	−	20.7846i	0.468879	−	0.812122i
$656$		0			0
$657$	45.0000			1.75562
$658$		0			0
$659$	50.0000			1.94772			0.973862	−	0.227142i	$-0.0729380\pi$
$659$	50.0000			1.94772			0.973862	+	0.227142i	$0.0729380\pi$
$660$		0			0
$661$	−16.0000	+	27.7128i	−0.622328	+	1.07790i	0.366723	+	0.930330i	$0.380480\pi$
$661$	−16.0000	+	27.7128i	−0.622328	+	1.07790i	−0.989051	+	0.147573i	$0.952854\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	6.00000	+	5.19615i	0.232670	+	0.201498i
$666$		0			0
$667$	9.00000	+	15.5885i	0.348481	+	0.603587i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−11.0000			−0.424650
$672$		0			0
$673$	28.0000			1.07932			0.539660	−	0.841883i	$-0.318553\pi$
$673$	28.0000			1.07932			0.539660	+	0.841883i	$0.318553\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	24.0000	+	41.5692i	0.922395	+	1.59763i	0.795698	+	0.605693i	$0.207104\pi$
$677$	24.0000	+	41.5692i	0.922395	+	1.59763i	0.126697	+	0.991941i	$0.459562\pi$
$678$		0			0
$679$	3.00000	−	15.5885i	0.115129	−	0.598230i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	21.0000	−	36.3731i	0.803543	−	1.39178i	−0.113728	−	0.993512i	$-0.536279\pi$
$683$	21.0000	−	36.3731i	0.803543	−	1.39178i	0.917270	−	0.398265i	$-0.130387\pi$
$684$		0			0
$685$	−9.00000			−0.343872
$686$		0			0
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$	2.00000	+	3.46410i	0.0760836	+	0.131781i	0.901557	−	0.432660i	$-0.142425\pi$
$691$	2.00000	+	3.46410i	0.0760836	+	0.131781i	−0.825473	+	0.564441i	$0.809092\pi$
$692$		0			0
$693$	−1.50000	+	7.79423i	−0.0569803	+	0.296078i
$694$		0			0
$695$	25.5000	+	44.1673i	0.967270	+	1.67536i
$696$		0			0
$697$	18.0000	−	31.1769i	0.681799	−	1.18091i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−19.0000			−0.717620			−0.358810	−	0.933411i	$-0.616817\pi$
$701$	−19.0000			−0.717620			−0.358810	+	0.933411i	$0.616817\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−18.0000	−	15.5885i	−0.676960	−	0.586264i
$708$		0			0
$709$	−6.50000	−	11.2583i	−0.244113	−	0.422815i	0.717769	−	0.696281i	$-0.245163\pi$
$709$	−6.50000	−	11.2583i	−0.244113	−	0.422815i	−0.961882	+	0.273466i	$0.911830\pi$
$710$		0			0
$711$	−18.0000	+	31.1769i	−0.675053	+	1.16923i
$712$		0			0
$713$	−6.00000			−0.224702
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−16.0000	−	27.7128i	−0.596699	−	1.03351i	−0.993305	−	0.115524i	$-0.963145\pi$
$719$	−16.0000	−	27.7128i	−0.596699	−	1.03351i	0.396605	−	0.917989i	$-0.370188\pi$
$720$		0			0
$721$	−35.0000	+	12.1244i	−1.30347	+	0.451535i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−12.0000	+	20.7846i	−0.445669	+	0.771921i
$726$		0			0
$727$	−33.0000			−1.22390			−0.611951	−	0.790896i	$-0.709615\pi$
$727$	−33.0000			−1.22390			−0.611951	+	0.790896i	$0.709615\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$	27.0000	−	46.7654i	0.998631	−	1.72968i
$732$		0			0
$733$	−13.0000	−	22.5167i	−0.480166	−	0.831672i	0.519575	−	0.854425i	$-0.326090\pi$
$733$	−13.0000	−	22.5167i	−0.480166	−	0.831672i	−0.999741	+	0.0227529i	$0.992757\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−4.00000	−	6.92820i	−0.147342	−	0.255204i
$738$		0			0
$739$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$739$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−32.0000			−1.17397			−0.586983	−	0.809599i	$-0.699684\pi$
$743$	−32.0000			−1.17397			−0.586983	+	0.809599i	$0.699684\pi$
$744$		0			0
$745$	4.50000	−	7.79423i	0.164867	−	0.285558i
$746$		0			0
$747$	10.5000	+	18.1865i	0.384175	+	0.665410i
$748$		0			0
$749$	−10.0000	+	3.46410i	−0.365392	+	0.126576i
$750$		0			0
$751$	20.0000	+	34.6410i	0.729810	+	1.26407i	0.956963	+	0.290209i	$0.0937250\pi$
$751$	20.0000	+	34.6410i	0.729810	+	1.26407i	−0.227153	+	0.973859i	$0.572942\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	18.0000			0.655087
$756$		0			0
$757$	−53.0000			−1.92632			−0.963159	−	0.268933i	$-0.913329\pi$
$757$	−53.0000			−1.92632			−0.963159	+	0.268933i	$0.913329\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−12.5000	−	21.6506i	−0.453125	−	0.784835i	0.545454	−	0.838141i	$-0.316357\pi$
$761$	−12.5000	−	21.6506i	−0.453125	−	0.784835i	−0.998578	+	0.0533061i	$0.983024\pi$
$762$		0			0
$763$	−8.00000	−	6.92820i	−0.289619	−	0.250818i
$764$		0			0
$765$	−27.0000	−	46.7654i	−0.976187	−	1.69081i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	19.0000			0.685158			0.342579	−	0.939489i	$-0.388700\pi$
$769$	19.0000			0.685158			0.342579	+	0.939489i	$0.388700\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	18.0000	−	31.1769i	0.647415	−	1.12136i	−0.336323	−	0.941747i	$-0.609183\pi$
$773$	18.0000	−	31.1769i	0.647415	−	1.12136i	0.983738	−	0.179609i	$-0.0574833\pi$
$774$		0			0
$775$	−4.00000	−	6.92820i	−0.143684	−	0.248868i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	3.00000	+	5.19615i	0.107486	+	0.186171i
$780$		0			0
$781$	3.00000	−	5.19615i	0.107348	−	0.185933i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−21.0000			−0.749522
$786$		0			0
$787$	−26.0000	+	45.0333i	−0.926800	+	1.60526i	−0.138159	+	0.990410i	$0.544119\pi$
$787$	−26.0000	+	45.0333i	−0.926800	+	1.60526i	−0.788641	+	0.614855i	$0.789215\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	9.00000	−	46.7654i	0.320003	−	1.66279i
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$	44.0000			1.55856			0.779280	−	0.626676i	$-0.215585\pi$
$797$	44.0000			1.55856			0.779280	+	0.626676i	$0.215585\pi$
$798$		0			0
$799$	18.0000			0.636794
$800$		0			0
$801$	−12.0000	+	20.7846i	−0.423999	+	0.734388i
$802$		0			0
$803$	−7.50000	−	12.9904i	−0.264669	−	0.458421i
$804$		0			0
$805$	18.0000	+	15.5885i	0.634417	+	0.549421i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	14.5000	−	25.1147i	0.509793	−	0.882987i	−0.490143	−	0.871642i	$-0.663055\pi$
$809$	14.5000	−	25.1147i	0.509793	−	0.882987i	0.999936	−	0.0113450i	$-0.00361129\pi$
$810$		0			0
$811$	−30.0000			−1.05344			−0.526721	−	0.850038i	$-0.676579\pi$
$811$	−30.0000			−1.05344			−0.526721	+	0.850038i	$0.676579\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	28.5000	−	49.3634i	0.998311	−	1.72913i
$816$		0			0
$817$	4.50000	+	7.79423i	0.157435	+	0.272686i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−12.5000	−	21.6506i	−0.436253	−	0.755612i	0.561144	−	0.827718i	$-0.310361\pi$
$821$	−12.5000	−	21.6506i	−0.436253	−	0.755612i	−0.997397	+	0.0721058i	$0.977028\pi$
$822$		0			0
$823$	22.5000	−	38.9711i	0.784301	−	1.35845i	−0.145115	−	0.989415i	$-0.546355\pi$
$823$	22.5000	−	38.9711i	0.784301	−	1.35845i	0.929416	−	0.369034i	$-0.120311\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	16.0000			0.556375			0.278187	−	0.960527i	$-0.410266\pi$
$827$	16.0000			0.556375			0.278187	+	0.960527i	$0.410266\pi$
$828$		0			0
$829$	12.0000	−	20.7846i	0.416777	−	0.721879i	−0.578836	−	0.815444i	$-0.696493\pi$
$829$	12.0000	−	20.7846i	0.416777	−	0.721879i	0.995613	+	0.0935647i	$0.0298262\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−33.0000	+	25.9808i	−1.14338	+	0.900180i
$834$		0			0
$835$	21.0000	+	36.3731i	0.726735	+	1.25874i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	4.00000			0.138095			0.0690477	−	0.997613i	$-0.478004\pi$
$839$	4.00000			0.138095			0.0690477	+	0.997613i	$0.478004\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$		0			0
$843$		0			0
$844$		0			0
$845$	19.5000	+	33.7750i	0.670820	+	1.16190i
$846$		0			0
$847$	−25.0000	+	8.66025i	−0.859010	+	0.297570i
$848$		0			0
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$	−9.00000			−0.308154			−0.154077	−	0.988059i	$-0.549240\pi$
$853$	−9.00000			−0.308154			−0.154077	+	0.988059i	$0.549240\pi$
$854$		0			0
$855$	9.00000			0.307794
$856$		0			0
$857$	12.0000	−	20.7846i	0.409912	−	0.709989i	−0.584967	−	0.811057i	$-0.698893\pi$
$857$	12.0000	−	20.7846i	0.409912	−	0.709989i	0.994880	+	0.101068i	$0.0322260\pi$
$858$		0			0
$859$	−6.50000	−	11.2583i	−0.221777	−	0.384129i	0.733571	−	0.679613i	$-0.237852\pi$
$859$	−6.50000	−	11.2583i	−0.221777	−	0.384129i	−0.955348	+	0.295484i	$0.904519\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−9.00000	−	15.5885i	−0.306364	−	0.530637i	0.671200	−	0.741276i	$-0.265779\pi$
$863$	−9.00000	−	15.5885i	−0.306364	−	0.530637i	−0.977564	+	0.210639i	$0.932446\pi$
$864$		0			0
$865$	−12.0000	+	20.7846i	−0.408012	+	0.706698i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	12.0000			0.407072
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−9.00000	−	15.5885i	−0.304604	−	0.527589i
$874$		0			0
$875$	1.50000	−	7.79423i	0.0507093	−	0.263493i
$876$		0			0
$877$	16.0000	+	27.7128i	0.540282	+	0.935795i	0.998888	+	0.0471555i	$0.0150156\pi$
$877$	16.0000	+	27.7128i	0.540282	+	0.935795i	−0.458606	+	0.888640i	$0.651651\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−54.0000			−1.81931			−0.909653	−	0.415369i	$-0.863653\pi$
$881$	−54.0000			−1.81931			−0.909653	+	0.415369i	$0.863653\pi$
$882$		0			0
$883$	−44.0000			−1.48072			−0.740359	−	0.672212i	$-0.765344\pi$
$883$	−44.0000			−1.48072			−0.740359	+	0.672212i	$0.765344\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	29.0000	+	50.2295i	0.973725	+	1.68654i	0.684081	+	0.729406i	$0.260204\pi$
$887$	29.0000	+	50.2295i	0.973725	+	1.68654i	0.289644	+	0.957135i	$0.406463\pi$
$888$		0			0
$889$	8.00000	−	41.5692i	0.268311	−	1.39419i
$890$		0			0
$891$	4.50000	+	7.79423i	0.150756	+	0.261116i
$892$		0			0
$893$	−1.50000	+	2.59808i	−0.0501956	+	0.0869413i
$894$		0			0
$895$	−30.0000			−1.00279
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−6.00000	+	10.3923i	−0.200111	+	0.346603i
$900$		0			0
$901$	−6.00000	−	10.3923i	−0.199889	−	0.346218i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−33.0000	−	57.1577i	−1.09696	−	1.89999i
$906$		0			0
$907$	−13.0000	+	22.5167i	−0.431658	+	0.747653i	−0.997016	−	0.0771920i	$-0.975405\pi$
$907$	−13.0000	+	22.5167i	−0.431658	+	0.747653i	0.565358	+	0.824845i	$0.308738\pi$
$908$		0			0
$909$	−27.0000			−0.895533
$910$		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
$913$	3.50000	−	6.06218i	0.115833	−	0.200629i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−20.0000	+	6.92820i	−0.660458	+	0.228789i
$918$		0			0
$919$	18.5000	+	32.0429i	0.610259	+	1.05700i	0.991197	+	0.132398i	$0.0422678\pi$
$919$	18.5000	+	32.0429i	0.610259	+	1.05700i	−0.380938	+	0.924601i	$0.624399\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−21.0000	+	36.3731i	−0.689730	+	1.19465i
$928$		0			0
$929$	12.5000	+	21.6506i	0.410112	+	0.710334i	0.994902	−	0.100851i	$-0.0321564\pi$
$929$	12.5000	+	21.6506i	0.410112	+	0.710334i	−0.584790	+	0.811185i	$0.698823\pi$
$930$		0			0
$931$	−1.00000	−	6.92820i	−0.0327737	−	0.227063i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−9.00000	+	15.5885i	−0.294331	+	0.509797i
$936$		0			0
$937$	−43.0000			−1.40475			−0.702374	−	0.711808i	$-0.747877\pi$
$937$	−43.0000			−1.40475			−0.702374	+	0.711808i	$0.747877\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	5.00000	−	8.66025i	0.162995	−	0.282316i	−0.772946	−	0.634472i	$-0.781218\pi$
$941$	5.00000	−	8.66025i	0.162995	−	0.282316i	0.935942	+	0.352155i	$0.114551\pi$
$942$		0			0
$943$	9.00000	+	15.5885i	0.293080	+	0.507630i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−6.00000	−	10.3923i	−0.194974	−	0.337705i	0.751918	−	0.659256i	$-0.229129\pi$
$947$	−6.00000	−	10.3923i	−0.194974	−	0.337705i	−0.946892	+	0.321552i	$0.895796\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	56.0000			1.81402			0.907009	−	0.421111i	$-0.138360\pi$
$953$	56.0000			1.81402			0.907009	+	0.421111i	$0.138360\pi$
$954$		0			0
$955$	−7.50000	+	12.9904i	−0.242694	+	0.420359i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	6.00000	+	5.19615i	0.193750	+	0.167793i
$960$		0			0
$961$	13.5000	+	23.3827i	0.435484	+	0.754280i
$962$		0			0
$963$	−6.00000	+	10.3923i	−0.193347	+	0.334887i
$964$		0			0
$965$	−60.0000			−1.93147
$966$		0			0
$967$	−40.0000			−1.28631			−0.643157	−	0.765735i	$-0.722376\pi$
$967$	−40.0000			−1.28631			−0.643157	+	0.765735i	$0.722376\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	4.00000	+	6.92820i	0.128366	+	0.222337i	0.923044	−	0.384695i	$-0.125693\pi$
$971$	4.00000	+	6.92820i	0.128366	+	0.222337i	−0.794678	+	0.607032i	$0.792360\pi$
$972$		0			0
$973$	8.50000	−	44.1673i	0.272497	−	1.41594i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−6.00000	+	10.3923i	−0.191957	+	0.332479i	−0.945899	−	0.324462i	$-0.894817\pi$
$977$	−6.00000	+	10.3923i	−0.191957	+	0.332479i	0.753942	+	0.656941i	$0.228150\pi$
$978$		0			0
$979$	8.00000			0.255681
$980$		0			0
$981$	−12.0000			−0.383131
$982$		0			0
$983$	−3.00000	+	5.19615i	−0.0956851	+	0.165732i	−0.909894	−	0.414840i	$-0.863838\pi$
$983$	−3.00000	+	5.19615i	−0.0956851	+	0.165732i	0.814209	+	0.580572i	$0.197171\pi$
$984$		0			0
$985$	−4.50000	−	7.79423i	−0.143382	−	0.248345i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	13.5000	+	23.3827i	0.429275	+	0.743526i
$990$		0			0
$991$	−26.0000	+	45.0333i	−0.825917	+	1.43053i	0.0752991	+	0.997161i	$0.476009\pi$
$991$	−26.0000	+	45.0333i	−0.825917	+	1.43053i	−0.901216	+	0.433370i	$0.857324\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	15.0000			0.475532
$996$		0			0
$997$	−21.0000	+	36.3731i	−0.665077	+	1.15195i	0.314188	+	0.949361i	$0.398268\pi$
$997$	−21.0000	+	36.3731i	−0.665077	+	1.15195i	−0.979265	+	0.202586i	$0.935066\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1064.2.q.d.305.1	✓	2
7.2	even	3	inner	1064.2.q.d.457.1	yes	2
7.3	odd	6		7448.2.a.h.1.1		1
7.4	even	3		7448.2.a.n.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1064.2.q.d.305.1	✓	2	1.1	even	1	trivial
1064.2.q.d.457.1	yes	2	7.2	even	3	inner
7448.2.a.h.1.1		1	7.3	odd	6
7448.2.a.n.1.1		1	7.4	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:	\( N \)	\(=\)	\( 1064 = 2^{3} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1064.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 - 2.59808i) q^{5} +(-0.500000 + 2.59808i) q^{7} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.50000 - 2.59808i) q^{5} +(-0.500000 + 2.59808i) q^{7} +(1.50000 + 2.59808i) q^{9} +(0.500000 - 0.866025i) q^{11} +(3.00000 - 5.19615i) q^{17} +(0.500000 + 0.866025i) q^{19} +(1.50000 + 2.59808i) q^{23} +(-2.00000 + 3.46410i) q^{25} +6.00000 q^{29} +(-1.00000 + 1.73205i) q^{31} +(7.50000 - 2.59808i) q^{35} +6.00000 q^{41} +9.00000 q^{43} +(4.50000 - 7.79423i) q^{45} +(1.50000 + 2.59808i) q^{47} +(-6.50000 - 2.59808i) q^{49} +(1.00000 - 1.73205i) q^{53} -3.00000 q^{55} +(6.00000 - 10.3923i) q^{59} +(-5.50000 - 9.52628i) q^{61} +(-7.50000 + 2.59808i) q^{63} +(4.00000 - 6.92820i) q^{67} +6.00000 q^{71} +(7.50000 - 12.9904i) q^{73} +(2.00000 + 1.73205i) q^{77} +(6.00000 + 10.3923i) q^{79} +(-4.50000 + 7.79423i) q^{81} +7.00000 q^{83} -18.0000 q^{85} +(4.00000 + 6.92820i) q^{89} +(1.50000 - 2.59808i) q^{95} -6.00000 q^{97} +3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{5} - q^{7} + 3 q^{9}+O(q^{10}) \) 2 * q - 3 * q^5 - q^7 + 3 * q^9	\( 2 q - 3 q^{5} - q^{7} + 3 q^{9} + q^{11} + 6 q^{17} + q^{19} + 3 q^{23} - 4 q^{25} + 12 q^{29} - 2 q^{31} + 15 q^{35} + 12 q^{41} + 18 q^{43} + 9 q^{45} + 3 q^{47} - 13 q^{49} + 2 q^{53} - 6 q^{55} + 12 q^{59} - 11 q^{61} - 15 q^{63} + 8 q^{67} + 12 q^{71} + 15 q^{73} + 4 q^{77} + 12 q^{79} - 9 q^{81} + 14 q^{83} - 36 q^{85} + 8 q^{89} + 3 q^{95} - 12 q^{97} + 6 q^{99}+O(q^{100}) \) 2 * q - 3 * q^5 - q^7 + 3 * q^9 + q^11 + 6 * q^17 + q^19 + 3 * q^23 - 4 * q^25 + 12 * q^29 - 2 * q^31 + 15 * q^35 + 12 * q^41 + 18 * q^43 + 9 * q^45 + 3 * q^47 - 13 * q^49 + 2 * q^53 - 6 * q^55 + 12 * q^59 - 11 * q^61 - 15 * q^63 + 8 * q^67 + 12 * q^71 + 15 * q^73 + 4 * q^77 + 12 * q^79 - 9 * q^81 + 14 * q^83 - 36 * q^85 + 8 * q^89 + 3 * q^95 - 12 * q^97 + 6 * q^99

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