LMFDB - Embedded newform 1512.2.s.l.865.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,2,Mod(865,1512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1512, 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("1512.865");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.s (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$12.0733807856$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			865.3
Root			$0.500000 - 2.05195i$ of defining polynomial
Character	$\chi$	$=$	1512.865
Dual form			1512.2.s.l.1297.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.23025 + 2.13086i) q^{5} +(-0.0665372 + 2.64491i) q^{7} +O(q^{10})$	$q+(1.23025 + 2.13086i) q^{5} +(-0.0665372 + 2.64491i) q^{7} +(0.433463 - 0.750780i) q^{11} -1.46050 q^{13} +(-0.933463 + 1.61680i) q^{17} +(1.29679 + 2.24611i) q^{19} +(0.796790 + 1.38008i) q^{23} +(-0.527042 + 0.912864i) q^{25} +5.78794 q^{29} +(-4.78434 + 8.28671i) q^{31} +(-5.71780 + 3.11213i) q^{35} +(1.66012 + 2.87541i) q^{37} +2.78074 q^{41} -10.7089 q^{43} +(-6.74484 - 11.6824i) q^{47} +(-6.99115 - 0.351971i) q^{49} +(3.32383 - 5.75705i) q^{53} +2.13307 q^{55} +(-3.21780 + 5.57339i) q^{59} +(3.09358 + 5.35824i) q^{61} +(-1.79679 - 3.11213i) q^{65} +(-0.850874 + 1.47376i) q^{67} +1.14027 q^{71} +(-5.08113 + 8.80077i) q^{73} +(1.95691 + 1.19643i) q^{77} +(3.39037 + 5.87229i) q^{79} -9.75583 q^{83} -4.59358 q^{85} +(-4.96050 - 8.59185i) q^{89} +(0.0971780 - 3.86291i) q^{91} +(-3.19076 + 5.52655i) q^{95} +2.81284 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{5} - 4 q^{7}+O(q^{10}) $ 6 * q + q^5 - 4 * q^7	$ 6 q + q^{5} - 4 q^{7} - q^{11} + 4 q^{13} - 2 q^{17} + 5 q^{19} + 2 q^{23} + 6 q^{25} + 2 q^{29} - 4 q^{31} - 6 q^{35} + 8 q^{37} - 6 q^{43} - 3 q^{47} - 12 q^{49} + 8 q^{53} + 20 q^{55} + 9 q^{59} + 13 q^{61} - 8 q^{65} + 16 q^{67} - 2 q^{71} - 3 q^{73} + 7 q^{77} + 12 q^{79} + 2 q^{83} - 22 q^{85} - 17 q^{89} - 13 q^{91} + 28 q^{97}+O(q^{100}) $ 6 * q + q^5 - 4 * q^7 - q^11 + 4 * q^13 - 2 * q^17 + 5 * q^19 + 2 * q^23 + 6 * q^25 + 2 * q^29 - 4 * q^31 - 6 * q^35 + 8 * q^37 - 6 * q^43 - 3 * q^47 - 12 * q^49 + 8 * q^53 + 20 * q^55 + 9 * q^59 + 13 * q^61 - 8 * q^65 + 16 * q^67 - 2 * q^71 - 3 * q^73 + 7 * q^77 + 12 * q^79 + 2 * q^83 - 22 * q^85 - 17 * q^89 - 13 * q^91 + 28 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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
$3$		0			0
$4$		0			0
$5$	1.23025	+	2.13086i	0.550186	+	0.952949i	0.998261	+	0.0589535i	$0.0187764\pi$
$5$	1.23025	+	2.13086i	0.550186	+	0.952949i	−0.448075	+	0.893996i	$0.647890\pi$
$6$		0			0
$7$	−0.0665372	+	2.64491i	−0.0251487	+	0.999684i
$7$	−0.0665372	+	2.64491i	−0.0251487	+	0.999684i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.433463	−	0.750780i	0.130694	−	0.226369i	−0.793250	−	0.608896i	$-0.791613\pi$
$11$	0.433463	−	0.750780i	0.130694	−	0.226369i	0.923944	+	0.382527i	$0.124946\pi$
$12$		0			0
$13$	−1.46050			−0.405071			−0.202536	−	0.979275i	$-0.564918\pi$
$13$	−1.46050			−0.405071			−0.202536	+	0.979275i	$0.564918\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.933463	+	1.61680i	−0.226398	+	0.392133i	−0.956738	−	0.290951i	$-0.906028\pi$
$17$	−0.933463	+	1.61680i	−0.226398	+	0.392133i	0.730340	+	0.683084i	$0.239362\pi$
$18$		0			0
$19$	1.29679	+	2.24611i	0.297504	+	0.515292i	0.975564	−	0.219714i	$-0.0705125\pi$
$19$	1.29679	+	2.24611i	0.297504	+	0.515292i	−0.678060	+	0.735006i	$0.737179\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.796790	+	1.38008i	0.166142	+	0.287767i	0.937060	−	0.349168i	$-0.113536\pi$
$23$	0.796790	+	1.38008i	0.166142	+	0.287767i	−0.770918	+	0.636934i	$0.780202\pi$
$24$		0			0
$25$	−0.527042	+	0.912864i	−0.105408	+	0.182573i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	5.78794			1.07479			0.537396	−	0.843330i	$-0.319408\pi$
$29$	5.78794			1.07479			0.537396	+	0.843330i	$0.319408\pi$
$30$		0			0
$31$	−4.78434	+	8.28671i	−0.859292	+	1.48834i	0.0133129	+	0.999911i	$0.495762\pi$
$31$	−4.78434	+	8.28671i	−0.859292	+	1.48834i	−0.872605	+	0.488426i	$0.837571\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−5.71780	+	3.11213i	−0.966485	+	0.526046i
$36$		0			0
$37$	1.66012	+	2.87541i	0.272921	+	0.472714i	0.969609	−	0.244661i	$-0.0786767\pi$
$37$	1.66012	+	2.87541i	0.272921	+	0.472714i	−0.696687	+	0.717375i	$0.745343\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	2.78074			0.434278			0.217139	−	0.976141i	$-0.430327\pi$
$41$	2.78074			0.434278			0.217139	+	0.976141i	$0.430327\pi$
$42$		0			0
$43$	−10.7089			−1.63310			−0.816549	−	0.577276i	$-0.804116\pi$
$43$	−10.7089			−1.63310			−0.816549	+	0.577276i	$0.804116\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−6.74484	−	11.6824i	−0.983836	−	1.70405i	−0.646998	−	0.762492i	$-0.723976\pi$
$47$	−6.74484	−	11.6824i	−0.983836	−	1.70405i	−0.336839	−	0.941562i	$-0.609358\pi$
$48$		0			0
$49$	−6.99115	−	0.351971i	−0.998735	−	0.0502815i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	3.32383	−	5.75705i	0.456563	−	0.790791i	−0.542213	−	0.840241i	$-0.682413\pi$
$53$	3.32383	−	5.75705i	0.456563	−	0.790791i	0.998777	+	0.0494499i	$0.0157468\pi$
$54$		0			0
$55$	2.13307			0.287624
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−3.21780	+	5.57339i	−0.418922	+	0.725594i	−0.995831	−	0.0912142i	$-0.970925\pi$
$59$	−3.21780	+	5.57339i	−0.418922	+	0.725594i	0.576909	+	0.816808i	$0.304259\pi$
$60$		0			0
$61$	3.09358	+	5.35824i	0.396092	+	0.686052i	0.993240	−	0.116079i	$-0.0370327\pi$
$61$	3.09358	+	5.35824i	0.396092	+	0.686052i	−0.597148	+	0.802131i	$0.703699\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.79679	−	3.11213i	−0.222864	−	0.386012i
$66$		0			0
$67$	−0.850874	+	1.47376i	−0.103951	+	0.180048i	−0.913309	−	0.407267i	$-0.866482\pi$
$67$	−0.850874	+	1.47376i	−0.103951	+	0.180048i	0.809358	+	0.587315i	$0.199815\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	1.14027			0.135325			0.0676627	−	0.997708i	$-0.478446\pi$
$71$	1.14027			0.135325			0.0676627	+	0.997708i	$0.478446\pi$
$72$		0			0
$73$	−5.08113	+	8.80077i	−0.594701	+	1.03005i	0.398888	+	0.917000i	$0.369396\pi$
$73$	−5.08113	+	8.80077i	−0.594701	+	1.03005i	−0.993589	+	0.113053i	$0.963937\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.95691	+	1.19643i	0.223010	+	0.136345i
$78$		0			0
$79$	3.39037	+	5.87229i	0.381446	+	0.660684i	0.991269	−	0.131853i	$-0.0420928\pi$
$79$	3.39037	+	5.87229i	0.381446	+	0.660684i	−0.609823	+	0.792538i	$0.708759\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−9.75583			−1.07084			−0.535421	−	0.844585i	$-0.679847\pi$
$83$	−9.75583			−1.07084			−0.535421	+	0.844585i	$0.679847\pi$
$84$		0			0
$85$	−4.59358			−0.498244
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−4.96050	−	8.59185i	−0.525812	−	0.910734i	−0.999548	−	0.0300667i	$-0.990428\pi$
$89$	−4.96050	−	8.59185i	−0.525812	−	0.910734i	0.473735	−	0.880667i	$-0.342905\pi$
$90$		0			0
$91$	0.0971780	−	3.86291i	0.0101870	−	0.404943i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−3.19076	+	5.52655i	−0.327365	+	0.567012i
$96$		0			0
$97$	2.81284			0.285601			0.142800	−	0.989752i	$-0.454389\pi$
$97$	2.81284			0.285601			0.142800	+	0.989752i	$0.454389\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−0.176168	+	0.305132i	−0.0175294	+	0.0303618i	−0.874657	−	0.484742i	$-0.838913\pi$
$101$	−0.176168	+	0.305132i	−0.0175294	+	0.0303618i	0.857128	+	0.515104i	$0.172247\pi$
$102$		0			0
$103$	5.09358	+	8.82234i	0.501885	+	0.869291i	0.999998	+	0.00217831i	$0.000693378\pi$
$103$	5.09358	+	8.82234i	0.501885	+	0.869291i	−0.498112	+	0.867113i	$0.665973\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.83628	+	3.18054i	0.177520	+	0.307474i	0.941031	−	0.338321i	$-0.109859\pi$
$107$	1.83628	+	3.18054i	0.177520	+	0.307474i	−0.763510	+	0.645796i	$0.776526\pi$
$108$		0			0
$109$	−3.97509	+	6.88506i	−0.380745	+	0.659470i	−0.991169	−	0.132605i	$-0.957666\pi$
$109$	−3.97509	+	6.88506i	−0.380745	+	0.659470i	0.610424	+	0.792075i	$0.290999\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	18.4035			1.73126			0.865628	−	0.500688i	$-0.166920\pi$
$113$	18.4035			1.73126			0.865628	+	0.500688i	$0.166920\pi$
$114$		0			0
$115$	−1.96050	+	3.39569i	−0.182818	+	0.316650i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−4.21420	−	2.57651i	−0.386315	−	0.236188i
$120$		0			0
$121$	5.12422	+	8.87541i	0.465838	+	0.806855i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	9.70895			0.868394
$126$		0			0
$127$	1.24844			0.110781			0.0553906	−	0.998465i	$-0.482360\pi$
$127$	1.24844			0.110781			0.0553906	+	0.998465i	$0.482360\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	4.84728	+	8.39573i	0.423508	+	0.733538i	0.996280	−	0.0861770i	$-0.0274651\pi$
$131$	4.84728	+	8.39573i	0.423508	+	0.733538i	−0.572771	+	0.819715i	$0.694132\pi$
$132$		0			0
$133$	−6.02704	+	3.28045i	−0.522611	+	0.284451i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	2.51459	−	4.35540i	0.214836	−	0.372107i	−0.738386	−	0.674378i	$-0.764412\pi$
$137$	2.51459	−	4.35540i	0.214836	−	0.372107i	0.953222	+	0.302272i	$0.0977450\pi$
$138$		0			0
$139$	2.80564			0.237972			0.118986	−	0.992896i	$-0.462036\pi$
$139$	2.80564			0.237972			0.118986	+	0.992896i	$0.462036\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−0.633074	+	1.09652i	−0.0529403	+	0.0916954i
$144$		0			0
$145$	7.12062	+	12.3333i	0.591335	+	1.02422i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	9.19289	+	15.9226i	0.753111	+	1.30443i	0.946308	+	0.323267i	$0.104781\pi$
$149$	9.19289	+	15.9226i	0.753111	+	1.30443i	−0.193197	+	0.981160i	$0.561886\pi$
$150$		0			0
$151$	7.39397	−	12.8067i	0.601713	−	1.04220i	−0.390849	−	0.920455i	$-0.627819\pi$
$151$	7.39397	−	12.8067i	0.601713	−	1.04220i	0.992562	−	0.121742i	$-0.0388480\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−23.5438			−1.89108
$156$		0			0
$157$	8.07227	−	13.9816i	0.644237	−	1.11585i	−0.340240	−	0.940339i	$-0.610508\pi$
$157$	8.07227	−	13.9816i	0.644237	−	1.11585i	0.984477	−	0.175513i	$-0.0561585\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−3.70321	+	2.01561i	−0.291854	+	0.158853i
$162$		0			0
$163$	−9.40496	−	16.2899i	−0.736653	−	1.27592i	−0.953994	−	0.299825i	$-0.903072\pi$
$163$	−9.40496	−	16.2899i	−0.736653	−	1.27592i	0.217341	−	0.976096i	$-0.430262\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	13.3025			1.02938			0.514690	−	0.857376i	$-0.327907\pi$
$167$	13.3025			1.02938			0.514690	+	0.857376i	$0.327907\pi$
$168$		0			0
$169$	−10.8669			−0.835917
$170$		0			0
$171$		0			0
$172$		0			0
$173$	0.379379	+	0.657103i	0.0288436	+	0.0499586i	0.880087	−	0.474813i	$-0.157484\pi$
$173$	0.379379	+	0.657103i	0.0288436	+	0.0499586i	−0.851243	+	0.524771i	$0.824151\pi$
$174$		0			0
$175$	−2.37938	−	1.45472i	−0.179864	−	0.109967i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−0.550486	+	0.953469i	−0.0411452	+	0.0712656i	−0.885865	−	0.463944i	$-0.846434\pi$
$179$	−0.550486	+	0.953469i	−0.0411452	+	0.0712656i	0.844719	+	0.535209i	$0.179767\pi$
$180$		0			0
$181$	−14.2235			−1.05723			−0.528613	−	0.848863i	$-0.677288\pi$
$181$	−14.2235			−1.05723			−0.528613	+	0.848863i	$0.677288\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−4.08472	+	7.07495i	−0.300315	+	0.520161i
$186$		0			0
$187$	0.809243	+	1.40165i	0.0591777	+	0.102499i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−1.80778	−	3.13117i	−0.130806	−	0.226563i	0.793181	−	0.608986i	$-0.208423\pi$
$191$	−1.80778	−	3.13117i	−0.130806	−	0.226563i	−0.923988	+	0.382422i	$0.875090\pi$
$192$		0			0
$193$	11.9050	−	20.6200i	0.856938	−	1.48426i	−0.0178981	−	0.999840i	$-0.505697\pi$
$193$	11.9050	−	20.6200i	0.856938	−	1.48426i	0.874836	−	0.484420i	$-0.160969\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	18.8348			1.34193			0.670963	−	0.741491i	$-0.265881\pi$
$197$	18.8348			1.34193			0.670963	+	0.741491i	$0.265881\pi$
$198$		0			0
$199$	−6.64027	+	11.5013i	−0.470716	+	0.815305i	−0.999439	−	0.0334899i	$-0.989338\pi$
$199$	−6.64027	+	11.5013i	−0.470716	+	0.815305i	0.528723	+	0.848795i	$0.322671\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−0.385113	+	15.3086i	−0.0270296	+	1.07445i
$204$		0			0
$205$	3.42101	+	5.92536i	0.238934	+	0.413845i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	2.24844			0.155528
$210$		0			0
$211$	−7.86693			−0.541581			−0.270791	−	0.962638i	$-0.587285\pi$
$211$	−7.86693			−0.541581			−0.270791	+	0.962638i	$0.587285\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−13.1747	−	22.8193i	−0.898507	−	1.55626i
$216$		0			0
$217$	−21.5993	−	13.2055i	−1.46626	−	0.896450i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	1.36333	−	2.36135i	0.0917073	−	0.158842i
$222$		0			0
$223$	15.0364			1.00691			0.503455	−	0.864021i	$-0.332062\pi$
$223$	15.0364			1.00691			0.503455	+	0.864021i	$0.332062\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	1.38298	−	2.39539i	0.0917914	−	0.158987i	−0.816474	−	0.577383i	$-0.804074\pi$
$227$	1.38298	−	2.39539i	0.0917914	−	0.158987i	0.908265	+	0.418395i	$0.137407\pi$
$228$		0			0
$229$	7.30399	+	12.6509i	0.482661	+	0.835993i	0.999802	−	0.0199069i	$-0.00633698\pi$
$229$	7.30399	+	12.6509i	0.482661	+	0.835993i	−0.517141	+	0.855900i	$0.673004\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−3.68716	−	6.38635i	−0.241554	−	0.418383i	0.719603	−	0.694385i	$-0.244324\pi$
$233$	−3.68716	−	6.38635i	−0.241554	−	0.418383i	−0.961157	+	0.276002i	$0.910990\pi$
$234$		0			0
$235$	16.5957	−	28.7446i	1.08259	−	1.87509i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−12.9531			−0.837867			−0.418934	−	0.908017i	$-0.637596\pi$
$239$	−12.9531			−0.837867			−0.418934	+	0.908017i	$0.637596\pi$
$240$		0			0
$241$	7.98968	−	13.8385i	0.514661	−	0.891419i	−0.485195	−	0.874406i	$-0.661251\pi$
$241$	7.98968	−	13.8385i	0.514661	−	0.891419i	0.999855	−	0.0170123i	$-0.00541545\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−7.85087	−	15.3302i	−0.501574	−	0.979408i
$246$		0			0
$247$	−1.89397	−	3.28045i	−0.120510	−	0.208730i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−11.5510			−0.729090			−0.364545	−	0.931186i	$-0.618776\pi$
$251$	−11.5510			−0.729090			−0.364545	+	0.931186i	$0.618776\pi$
$252$		0			0
$253$	1.38151			0.0868551
$254$		0			0
$255$		0			0
$256$		0			0
$257$	13.0687	+	22.6356i	0.815201	+	1.41197i	0.909183	+	0.416396i	$0.136707\pi$
$257$	13.0687	+	22.6356i	0.815201	+	1.41197i	−0.0939817	+	0.995574i	$0.529960\pi$
$258$		0			0
$259$	−7.71566	+	4.19954i	−0.479428	+	0.260947i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	10.5993	−	18.3586i	0.653582	−	1.13204i	−0.328666	−	0.944446i	$-0.606599\pi$
$263$	10.5993	−	18.3586i	0.653582	−	1.13204i	0.982247	−	0.187590i	$-0.0600677\pi$
$264$		0			0
$265$	16.3566			1.00478
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−2.05195	+	3.55408i	−0.125109	+	0.216696i	−0.921776	−	0.387723i	$-0.873262\pi$
$269$	−2.05195	+	3.55408i	−0.125109	+	0.216696i	0.796666	+	0.604419i	$0.206595\pi$
$270$		0			0
$271$	−0.710602	−	1.23080i	−0.0431660	−	0.0747657i	0.843635	−	0.536917i	$-0.180411\pi$
$271$	−0.710602	−	1.23080i	−0.0431660	−	0.0747657i	−0.886801	+	0.462151i	$0.847078\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	0.456906	+	0.791385i	0.0275525	+	0.0477223i
$276$		0			0
$277$	13.0811	−	22.6572i	0.785969	−	1.36134i	−0.142450	−	0.989802i	$-0.545498\pi$
$277$	13.0811	−	22.6572i	0.785969	−	1.36134i	0.928419	−	0.371536i	$-0.121169\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	0.111094			0.00662728			0.00331364	−	0.999995i	$-0.498945\pi$
$281$	0.111094			0.00662728			0.00331364	+	0.999995i	$0.498945\pi$
$282$		0			0
$283$	−5.66012	+	9.80361i	−0.336459	+	0.582764i	−0.983764	−	0.179467i	$-0.942563\pi$
$283$	−5.66012	+	9.80361i	−0.336459	+	0.582764i	0.647305	+	0.762231i	$0.275896\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−0.185023	+	7.35481i	−0.0109215	+	0.434141i
$288$		0			0
$289$	6.75729	+	11.7040i	0.397488	+	0.688469i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−13.5290			−0.790372			−0.395186	−	0.918601i	$-0.629320\pi$
$293$	−13.5290			−0.790372			−0.395186	+	0.918601i	$0.629320\pi$
$294$		0			0
$295$	−15.8348			−0.921939
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−1.16372	−	2.01561i	−0.0672994	−	0.116566i
$300$		0			0
$301$	0.712544	−	28.3242i	0.0410703	−	1.63258i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−7.61177	+	13.1840i	−0.435849	+	0.754912i
$306$		0			0
$307$	26.0187			1.48496			0.742482	−	0.669866i	$-0.233649\pi$
$307$	26.0187			1.48496			0.742482	+	0.669866i	$0.233649\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	17.5687	−	30.4298i	0.996228	−	1.72552i	0.422966	−	0.906146i	$-0.360989\pi$
$311$	17.5687	−	30.4298i	0.996228	−	1.72552i	0.573262	−	0.819372i	$-0.305678\pi$
$312$		0			0
$313$	−12.1768	−	21.0909i	−0.688276	−	1.19213i	−0.972395	−	0.233340i	$-0.925035\pi$
$313$	−12.1768	−	21.0909i	−0.688276	−	1.19213i	0.284119	−	0.958789i	$-0.408299\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−17.6264	−	30.5297i	−0.989995	−	1.71472i	−0.617197	−	0.786809i	$-0.711732\pi$
$317$	−17.6264	−	30.5297i	−0.989995	−	1.71472i	−0.372798	−	0.927913i	$-0.621602\pi$
$318$		0			0
$319$	2.50885	−	4.34546i	0.140469	−	0.243299i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−4.84202			−0.269417
$324$		0			0
$325$	0.769748	−	1.33324i	0.0426979	−	0.0739550i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	31.3478	−	17.0622i	1.72826	−	0.940670i
$330$		0			0
$331$	8.96410	+	15.5263i	0.492712	+	0.853402i	0.999965	−	0.00839547i	$-0.00267239\pi$
$331$	8.96410	+	15.5263i	0.492712	+	0.853402i	−0.507253	+	0.861797i	$0.669339\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−4.18716			−0.228769
$336$		0			0
$337$	18.5801			1.01212			0.506062	−	0.862497i	$-0.331101\pi$
$337$	18.5801			1.01212			0.506062	+	0.862497i	$0.331101\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	4.14766	+	7.18396i	0.224609	+	0.389033i
$342$		0			0
$343$	1.39610	−	18.4676i	0.0753825	−	0.997155i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−16.8171	+	29.1281i	−0.902790	+	1.56368i	−0.0789333	+	0.996880i	$0.525151\pi$
$347$	−16.8171	+	29.1281i	−0.902790	+	1.56368i	−0.823857	+	0.566798i	$0.808182\pi$
$348$		0			0
$349$	26.1301			1.39871			0.699357	−	0.714772i	$-0.253470\pi$
$349$	26.1301			1.39871			0.699357	+	0.714772i	$0.253470\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	6.61177	−	11.4519i	0.351909	−	0.609524i	−0.634675	−	0.772779i	$-0.718866\pi$
$353$	6.61177	−	11.4519i	0.351909	−	0.609524i	0.986584	+	0.163255i	$0.0521994\pi$
$354$		0			0
$355$	1.40282	+	2.42976i	0.0744541	+	0.128958i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	1.97296	+	3.41726i	0.104129	+	0.180356i	0.913382	−	0.407104i	$-0.133461\pi$
$359$	1.97296	+	3.41726i	0.104129	+	0.180356i	−0.809253	+	0.587460i	$0.800128\pi$
$360$		0			0
$361$	6.13667	−	10.6290i	0.322983	−	0.559423i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−25.0043			−1.30878
$366$		0			0
$367$	9.97509	−	17.2774i	0.520696	−	0.901871i	−0.479015	−	0.877807i	$-0.659006\pi$
$367$	9.97509	−	17.2774i	0.520696	−	0.901871i	0.999710	−	0.0240645i	$-0.00766071\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	15.0057	+	9.17431i	0.779059	+	0.476306i
$372$		0			0
$373$	−16.4035	−	28.4117i	−0.849341	−	1.47110i	−0.881797	−	0.471628i	$-0.843666\pi$
$373$	−16.4035	−	28.4117i	−0.849341	−	1.47110i	0.0324567	−	0.999473i	$-0.489667\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−8.45331			−0.435367
$378$		0			0
$379$	6.51886			0.334851			0.167426	−	0.985885i	$-0.446455\pi$
$379$	6.51886			0.334851			0.167426	+	0.985885i	$0.446455\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	14.1460	+	24.5016i	0.722827	+	1.25197i	0.959862	+	0.280472i	$0.0904911\pi$
$383$	14.1460	+	24.5016i	0.722827	+	1.25197i	−0.237035	+	0.971501i	$0.576176\pi$
$384$		0			0
$385$	−0.141929	+	5.64180i	−0.00723337	+	0.287533i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−7.86546	+	13.6234i	−0.398795	+	0.690733i	−0.993578	−	0.113154i	$-0.963905\pi$
$389$	−7.86546	+	13.6234i	−0.398795	+	0.690733i	0.594783	+	0.803887i	$0.297238\pi$
$390$		0			0
$391$	−2.97509			−0.150457
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−8.34202	+	14.4488i	−0.419733	+	0.726998i
$396$		0			0
$397$	15.7448	+	27.2709i	0.790211	+	1.36869i	0.925836	+	0.377925i	$0.123362\pi$
$397$	15.7448	+	27.2709i	0.790211	+	1.36869i	−0.135625	+	0.990760i	$0.543304\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	1.17111	+	2.02842i	0.0584823	+	0.101294i	0.893784	−	0.448497i	$-0.148041\pi$
$401$	1.17111	+	2.02842i	0.0584823	+	0.101294i	−0.835302	+	0.549791i	$0.814707\pi$
$402$		0			0
$403$	6.98755	−	12.1028i	0.348075	−	0.602883i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	2.87839			0.142677
$408$		0			0
$409$	−6.13142	+	10.6199i	−0.303179	+	0.525122i	−0.976854	−	0.213906i	$-0.931381\pi$
$409$	−6.13142	+	10.6199i	−0.303179	+	0.525122i	0.673675	+	0.739028i	$0.264715\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−14.5270	−	8.88164i	−0.714829	−	0.437037i
$414$		0			0
$415$	−12.0021	−	20.7883i	−0.589162	−	1.02046i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	13.3743			0.653378			0.326689	−	0.945132i	$-0.394067\pi$
$419$	13.3743			0.653378			0.326689	+	0.945132i	$0.394067\pi$
$420$		0			0
$421$	−34.0905			−1.66147			−0.830734	−	0.556670i	$-0.812079\pi$
$421$	−34.0905			−1.66147			−0.830734	+	0.556670i	$0.812079\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−0.983948	−	1.70425i	−0.0477285	−	0.0826682i
$426$		0			0
$427$	−14.3779	+	7.82573i	−0.695796	+	0.378714i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	20.3370	−	35.2246i	0.979597	−	1.69671i	0.315751	−	0.948842i	$-0.397744\pi$
$431$	20.3370	−	35.2246i	0.979597	−	1.69671i	0.663846	−	0.747869i	$-0.268923\pi$
$432$		0			0
$433$	−2.43560			−0.117047			−0.0585237	−	0.998286i	$-0.518639\pi$
$433$	−2.43560			−0.117047			−0.0585237	+	0.998286i	$0.518639\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−2.06654	+	3.57935i	−0.0988559	+	0.171223i
$438$		0			0
$439$	9.55408	+	16.5482i	0.455992	+	0.789801i	0.998745	−	0.0500918i	$-0.0159514\pi$
$439$	9.55408	+	16.5482i	0.455992	+	0.789801i	−0.542753	+	0.839892i	$0.682618\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	17.3224	+	30.0032i	0.823011	+	1.42550i	0.903430	+	0.428735i	$0.141041\pi$
$443$	17.3224	+	30.0032i	0.823011	+	1.42550i	−0.0804197	+	0.996761i	$0.525626\pi$
$444$		0			0
$445$	12.2053	−	21.1403i	0.578589	−	1.00215i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	18.9167			0.892736			0.446368	−	0.894849i	$-0.352717\pi$
$449$	18.9167			0.892736			0.446368	+	0.894849i	$0.352717\pi$
$450$		0			0
$451$	1.20535	−	2.08772i	0.0567575	−	0.0983070i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	8.35087	−	4.54528i	0.391495	−	0.213086i
$456$		0			0
$457$	−4.11702	−	7.13089i	−0.192586	−	0.333569i	0.753520	−	0.657425i	$-0.228354\pi$
$457$	−4.11702	−	7.13089i	−0.192586	−	0.333569i	−0.946107	+	0.323855i	$0.895021\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−4.78074			−0.222661			−0.111331	−	0.993783i	$-0.535511\pi$
$461$	−4.78074			−0.222661			−0.111331	+	0.993783i	$0.535511\pi$
$462$		0			0
$463$	−24.2163			−1.12543			−0.562714	−	0.826651i	$-0.690243\pi$
$463$	−24.2163			−1.12543			−0.562714	+	0.826651i	$0.690243\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	2.05622	+	3.56148i	0.0951505	+	0.164806i	0.909671	−	0.415329i	$-0.136333\pi$
$467$	2.05622	+	3.56148i	0.0951505	+	0.164806i	−0.814521	+	0.580134i	$0.803000\pi$
$468$		0			0
$469$	−3.84135	−	2.34855i	−0.177377	−	0.108446i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−4.64193	+	8.04006i	−0.213436	+	0.369682i
$474$		0			0
$475$	−2.73385			−0.125438
$476$		0			0
$477$		0			0
$478$		0			0
$479$	11.2917	−	19.5578i	0.515932	−	0.893621i	−0.483897	−	0.875125i	$-0.660779\pi$
$479$	11.2917	−	19.5578i	0.515932	−	0.893621i	0.999829	−	0.0184957i	$-0.00588771\pi$
$480$		0			0
$481$	−2.42461	−	4.19954i	−0.110553	−	0.191483i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	3.46050	+	5.99377i	0.157133	+	0.272163i
$486$		0			0
$487$	21.0957	−	36.5389i	0.955938	−	1.65573i	0.223731	−	0.974651i	$-0.428176\pi$
$487$	21.0957	−	36.5389i	0.955938	−	1.65573i	0.732207	−	0.681083i	$-0.238491\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−17.2911			−0.780334			−0.390167	−	0.920744i	$-0.627583\pi$
$491$	−17.2911			−0.780334			−0.390167	+	0.920744i	$0.627583\pi$
$492$		0			0
$493$	−5.40282	+	9.35796i	−0.243331	+	0.421461i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−0.0758705	+	3.01592i	−0.00340326	+	0.135283i
$498$		0			0
$499$	9.49494	+	16.4457i	0.425052	+	0.736211i	0.996425	−	0.0844788i	$-0.0269225\pi$
$499$	9.49494	+	16.4457i	0.425052	+	0.736211i	−0.571373	+	0.820690i	$0.693589\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	17.8961			0.797948			0.398974	−	0.916962i	$-0.369366\pi$
$503$	17.8961			0.797948			0.398974	+	0.916962i	$0.369366\pi$
$504$		0			0
$505$	−0.866926			−0.0385777
$506$		0			0
$507$		0			0
$508$		0			0
$509$	12.5125	+	21.6722i	0.554605	+	0.960604i	0.997934	+	0.0642448i	$0.0204639\pi$
$509$	12.5125	+	21.6722i	0.554605	+	0.960604i	−0.443329	+	0.896359i	$0.646203\pi$
$510$		0			0
$511$	−22.9392	−	14.0247i	−1.01477	−	0.620417i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−12.5328	+	21.7074i	−0.552260	+	0.956543i
$516$		0			0
$517$	−11.6946			−0.514326
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−17.8078	+	30.8440i	−0.780173	+	1.35130i	0.151668	+	0.988432i	$0.451536\pi$
$521$	−17.8078	+	30.8440i	−0.780173	+	1.35130i	−0.931841	+	0.362868i	$0.881798\pi$
$522$		0			0
$523$	9.47656	+	16.4139i	0.414381	+	0.717729i	0.995363	−	0.0961874i	$-0.0306648\pi$
$523$	9.47656	+	16.4139i	0.414381	+	0.717729i	−0.580982	+	0.813916i	$0.697331\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−8.93200	−	15.4707i	−0.389084	−	0.673913i
$528$		0			0
$529$	10.2303	−	17.7193i	0.444794	−	0.770405i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−4.06128			−0.175914
$534$		0			0
$535$	−4.51819	+	7.82573i	−0.195338	+	0.338336i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−3.29465	+	5.09624i	−0.141911	+	0.219511i
$540$		0			0
$541$	8.66012	+	14.9998i	0.372327	+	0.644890i	0.989923	−	0.141606i	$-0.0452265\pi$
$541$	8.66012	+	14.9998i	0.372327	+	0.644890i	−0.617596	+	0.786496i	$0.711893\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−19.5615			−0.837922
$546$		0			0
$547$	−6.06128			−0.259162			−0.129581	−	0.991569i	$-0.541363\pi$
$547$	−6.06128			−0.259162			−0.129581	+	0.991569i	$0.541363\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	7.50573	+	13.0003i	0.319755	+	0.553832i
$552$		0			0
$553$	−15.7573	+	8.57651i	−0.670068	+	0.364710i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	8.16372	−	14.1400i	0.345908	−	0.599130i	−0.639611	−	0.768699i	$-0.720904\pi$
$557$	8.16372	−	14.1400i	0.345908	−	0.599130i	0.985518	+	0.169569i	$0.0542377\pi$
$558$		0			0
$559$	15.6405			0.661521
$560$		0			0
$561$		0			0
$562$		0			0
$563$	12.5826	−	21.7937i	0.530293	−	0.918494i	−0.469082	−	0.883154i	$-0.655415\pi$
$563$	12.5826	−	21.7937i	0.530293	−	0.918494i	0.999375	−	0.0353399i	$-0.0112514\pi$
$564$		0			0
$565$	22.6409	+	39.2153i	0.952512	+	1.64980i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−17.1929	−	29.7790i	−0.720764	−	1.24840i	−0.960694	−	0.277609i	$-0.910458\pi$
$569$	−17.1929	−	29.7790i	−0.720764	−	1.24840i	0.239931	−	0.970790i	$-0.422875\pi$
$570$		0			0
$571$	4.28580	−	7.42322i	0.179355	−	0.310652i	−0.762305	−	0.647218i	$-0.775932\pi$
$571$	4.28580	−	7.42322i	0.179355	−	0.310652i	0.941660	+	0.336566i	$0.109266\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−1.67977			−0.0700511
$576$		0			0
$577$	−13.7199	+	23.7636i	−0.571168	+	0.989293i	0.425278	+	0.905063i	$0.360176\pi$
$577$	−13.7199	+	23.7636i	−0.571168	+	0.989293i	−0.996446	+	0.0842299i	$0.973157\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	0.649126	−	25.8033i	0.0269303	−	1.07050i
$582$		0			0
$583$	−2.88151	−	4.99093i	−0.119340	−	0.206703i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	11.8276			0.488178			0.244089	−	0.969753i	$-0.421511\pi$
$587$	11.8276			0.488178			0.244089	+	0.969753i	$0.421511\pi$
$588$		0			0
$589$	−24.8171			−1.02257
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−10.9964	−	19.0463i	−0.451568	−	0.782139i	0.546916	−	0.837188i	$-0.315802\pi$
$593$	−10.9964	−	19.0463i	−0.451568	−	0.782139i	−0.998484	+	0.0550489i	$0.982469\pi$
$594$		0			0
$595$	0.305644	−	12.1496i	0.0125302	−	0.498086i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	13.3640	−	23.1471i	0.546038	−	0.945766i	−0.452503	−	0.891763i	$-0.649469\pi$
$599$	13.3640	−	23.1471i	0.546038	−	0.945766i	0.998541	−	0.0540029i	$-0.0171980\pi$
$600$		0			0
$601$	−2.20914			−0.0901127			−0.0450563	−	0.998984i	$-0.514347\pi$
$601$	−2.20914			−0.0901127			−0.0450563	+	0.998984i	$0.514347\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−12.6082	+	21.8380i	−0.512595	+	0.887840i
$606$		0			0
$607$	8.66012	+	14.9998i	0.351503	+	0.608822i	0.986513	−	0.163683i	$-0.0523373\pi$
$607$	8.66012	+	14.9998i	0.351503	+	0.608822i	−0.635010	+	0.772504i	$0.719004\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	9.85087	+	17.0622i	0.398524	+	0.690263i
$612$		0			0
$613$	−8.18570	+	14.1780i	−0.330617	+	0.572646i	−0.982633	−	0.185560i	$-0.940590\pi$
$613$	−8.18570	+	14.1780i	−0.330617	+	0.572646i	0.652016	+	0.758205i	$0.273924\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−17.6198			−0.709348			−0.354674	−	0.934990i	$-0.615408\pi$
$617$	−17.6198			−0.709348			−0.354674	+	0.934990i	$0.615408\pi$
$618$		0			0
$619$	2.26236	−	3.91852i	0.0909318	−	0.157498i	−0.816972	−	0.576678i	$-0.804349\pi$
$619$	2.26236	−	3.91852i	0.0909318	−	0.157498i	0.907903	+	0.419179i	$0.137682\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	23.0548	−	12.5484i	0.923669	−	0.502742i
$624$		0			0
$625$	14.5797	+	25.2527i	0.583187	+	1.01011i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−6.19863			−0.247155
$630$		0			0
$631$	−4.99280			−0.198760			−0.0993802	−	0.995050i	$-0.531686\pi$
$631$	−4.99280			−0.198760			−0.0993802	+	0.995050i	$0.531686\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	1.53590	+	2.66025i	0.0609502	+	0.105569i
$636$		0			0
$637$	10.2106	+	0.514055i	0.404559	+	0.0203676i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−21.3602	+	36.9970i	−0.843677	+	1.46129i	0.0430873	+	0.999071i	$0.486281\pi$
$641$	−21.3602	+	36.9970i	−0.843677	+	1.46129i	−0.886765	+	0.462221i	$0.847053\pi$
$642$		0			0
$643$	16.8200			0.663318			0.331659	−	0.943399i	$-0.392392\pi$
$643$	16.8200			0.663318			0.331659	+	0.943399i	$0.392392\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	23.5548	−	40.7980i	0.926033	−	1.60394i	0.136142	−	0.990689i	$-0.456530\pi$
$647$	23.5548	−	40.7980i	0.926033	−	1.60394i	0.789891	−	0.613247i	$-0.210137\pi$
$648$		0			0
$649$	2.78959	+	4.83172i	0.109501	+	0.189661i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−21.6967	−	37.5798i	−0.849057	−	1.47061i	−0.882051	−	0.471154i	$-0.843838\pi$
$653$	−21.6967	−	37.5798i	−0.849057	−	1.47061i	0.0329939	−	0.999456i	$-0.489496\pi$
$654$		0			0
$655$	−11.9267	+	20.6577i	−0.466016	+	0.807164i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−31.1049			−1.21167			−0.605837	−	0.795589i	$-0.707161\pi$
$659$	−31.1049			−1.21167			−0.605837	+	0.795589i	$0.707161\pi$
$660$		0			0
$661$	1.74484	−	3.02215i	0.0678665	−	0.117548i	−0.830095	−	0.557621i	$-0.811714\pi$
$661$	1.74484	−	3.02215i	0.0678665	−	0.117548i	0.897962	+	0.440073i	$0.145047\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−14.4050	−	8.80700i	−0.558600	−	0.341521i
$666$		0			0
$667$	4.61177	+	7.98781i	0.178568	+	0.309289i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	5.36381			0.207067
$672$		0			0
$673$	−2.25175			−0.0867988			−0.0433994	−	0.999058i	$-0.513819\pi$
$673$	−2.25175			−0.0867988			−0.0433994	+	0.999058i	$0.513819\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	19.6623	+	34.0560i	0.755682	+	1.30888i	0.945035	+	0.326970i	$0.106028\pi$
$677$	19.6623	+	34.0560i	0.755682	+	1.30888i	−0.189353	+	0.981909i	$0.560639\pi$
$678$		0			0
$679$	−0.187159	+	7.43972i	−0.00718249	+	0.285510i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−3.24338	+	5.61770i	−0.124104	+	0.214955i	−0.921383	−	0.388657i	$-0.872939\pi$
$683$	−3.24338	+	5.61770i	−0.124104	+	0.214955i	0.797278	+	0.603612i	$0.206272\pi$
$684$		0			0
$685$	12.3743			0.472798
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−4.85447	+	8.40819i	−0.184941	+	0.320327i
$690$		0			0
$691$	10.7843	+	18.6790i	0.410256	+	0.710583i	0.994917	−	0.100694i	$-0.0321062\pi$
$691$	10.7843	+	18.6790i	0.410256	+	0.710583i	−0.584662	+	0.811277i	$0.698773\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	3.45165	+	5.97843i	0.130929	+	0.226775i
$696$		0			0
$697$	−2.59572	+	4.49591i	−0.0983197	+	0.170295i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	21.6329			0.817063			0.408531	−	0.912744i	$-0.366041\pi$
$701$	21.6329			0.817063			0.408531	+	0.912744i	$0.366041\pi$
$702$		0			0
$703$	−4.30564	+	7.45759i	−0.162390	+	0.281268i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−0.795327	−	0.486253i	−0.0299114	−	0.0182874i
$708$		0			0
$709$	10.8370	+	18.7702i	0.406991	+	0.704928i	0.994551	−	0.104252i	$-0.0332449\pi$
$709$	10.8370	+	18.7702i	0.406991	+	0.704928i	−0.587560	+	0.809180i	$0.699912\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−15.2484			−0.571059
$714$		0			0
$715$	−3.11537			−0.116508
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−18.8669	−	32.6785i	−0.703618	−	1.21870i	−0.967188	−	0.254061i	$-0.918234\pi$
$719$	−18.8669	−	32.6785i	−0.703618	−	1.21870i	0.263571	−	0.964640i	$-0.415100\pi$
$720$		0			0
$721$	−23.6732	+	12.8851i	−0.881638	+	0.479865i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−3.05049	+	5.28360i	−0.113292	+	0.196228i
$726$		0			0
$727$	−36.6414			−1.35896			−0.679478	−	0.733696i	$-0.737794\pi$
$727$	−36.6414			−1.35896			−0.679478	+	0.733696i	$0.737794\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	9.99640	−	17.3143i	0.369730	−	0.640392i
$732$		0			0
$733$	−5.69289	−	9.86038i	−0.210272	−	0.364201i	0.741528	−	0.670922i	$-0.234102\pi$
$733$	−5.69289	−	9.86038i	−0.210272	−	0.364201i	−0.951800	+	0.306721i	$0.900768\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	0.737644	+	1.27764i	0.0271715	+	0.0470624i
$738$		0			0
$739$	−16.0349	+	27.7733i	−0.589854	+	1.02166i	0.404397	+	0.914583i	$0.367481\pi$
$739$	−16.0349	+	27.7733i	−0.589854	+	1.02166i	−0.994251	+	0.107073i	$0.965852\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−25.7516			−0.944733			−0.472367	−	0.881402i	$-0.656600\pi$
$743$	−25.7516			−0.944733			−0.472367	+	0.881402i	$0.656600\pi$
$744$		0			0
$745$	−22.6192	+	39.1775i	−0.828702	+	1.43535i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−8.53443	+	4.64519i	−0.311841	+	0.169732i
$750$		0			0
$751$	7.64766	+	13.2461i	0.279067	+	0.483359i	0.971153	−	0.238456i	$-0.0766414\pi$
$751$	7.64766	+	13.2461i	0.279067	+	0.483359i	−0.692086	+	0.721815i	$0.743308\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	36.3858			1.32421
$756$		0			0
$757$	−37.2891			−1.35529			−0.677647	−	0.735387i	$-0.737000\pi$
$757$	−37.2891			−1.35529			−0.677647	+	0.735387i	$0.737000\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−18.1431	−	31.4247i	−0.657686	−	1.13915i	−0.981213	−	0.192927i	$-0.938202\pi$
$761$	−18.1431	−	31.4247i	−0.657686	−	1.13915i	0.323527	−	0.946219i	$-0.395131\pi$
$762$		0			0
$763$	−17.9459	−	10.9719i	−0.649686	−	0.397209i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	4.69961	−	8.13997i	0.169693	−	0.293917i
$768$		0			0
$769$	32.0908			1.15723			0.578613	−	0.815602i	$-0.303594\pi$
$769$	32.0908			1.15723			0.578613	+	0.815602i	$0.303594\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−18.7178	+	32.4202i	−0.673232	+	1.16607i	0.303750	+	0.952752i	$0.401761\pi$
$773$	−18.7178	+	32.4202i	−0.673232	+	1.16607i	−0.976982	+	0.213321i	$0.931572\pi$
$774$		0			0
$775$	−5.04309	−	8.73489i	−0.181153	−	0.313767i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	3.60603	+	6.24583i	0.129200	+	0.223780i
$780$		0			0
$781$	0.494265	−	0.856093i	0.0176862	−	0.0306334i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	39.7237			1.41780
$786$		0			0
$787$	−14.4751	+	25.0716i	−0.515981	+	0.893706i	0.483847	+	0.875153i	$0.339239\pi$
$787$	−14.4751	+	25.0716i	−0.515981	+	0.893706i	−0.999828	+	0.0185531i	$0.994094\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−1.22452	+	48.6757i	−0.0435388	+	1.73071i
$792$		0			0
$793$	−4.51819	−	7.82573i	−0.160446	−	0.277900i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−37.9941			−1.34582			−0.672911	−	0.739724i	$-0.734956\pi$
$797$	−37.9941			−1.34582			−0.672911	+	0.739724i	$0.734956\pi$
$798$		0			0
$799$	25.1842			0.890954
$800$		0			0
$801$		0			0
$802$		0			0
$803$	4.40496	+	7.62961i	0.155448	+	0.269243i
$804$		0			0
$805$	−8.85087	−	5.41131i	−0.311952	−	0.190724i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	1.47869	−	2.56117i	0.0519881	−	0.0900460i	−0.838860	−	0.544347i	$-0.816778\pi$
$809$	1.47869	−	2.56117i	0.0519881	−	0.0900460i	0.890848	+	0.454301i	$0.150111\pi$
$810$		0			0
$811$	−32.7204			−1.14897			−0.574485	−	0.818515i	$-0.694797\pi$
$811$	−32.7204			−1.14897			−0.574485	+	0.818515i	$0.694797\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	23.1409	−	40.0813i	0.810592	−	1.40399i
$816$		0			0
$817$	−13.8872	−	24.0534i	−0.485853	−	0.841523i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	16.1572	+	27.9851i	0.563890	+	0.976686i	0.997152	+	0.0754180i	$0.0240291\pi$
$821$	16.1572	+	27.9851i	0.563890	+	0.976686i	−0.433262	+	0.901268i	$0.642638\pi$
$822$		0			0
$823$	−2.41021	+	4.17461i	−0.0840148	+	0.145518i	−0.904971	−	0.425473i	$-0.860108\pi$
$823$	−2.41021	+	4.17461i	−0.0840148	+	0.145518i	0.820956	+	0.570991i	$0.193441\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	28.2383			0.981943			0.490971	−	0.871176i	$-0.336642\pi$
$827$	28.2383			0.981943			0.490971	+	0.871176i	$0.336642\pi$
$828$		0			0
$829$	−1.85301	+	3.20951i	−0.0643577	+	0.111471i	−0.896409	−	0.443228i	$-0.853833\pi$
$829$	−1.85301	+	3.20951i	−0.0643577	+	0.111471i	0.832051	+	0.554699i	$0.187167\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	7.09504	−	10.9748i	0.245829	−	0.380253i
$834$		0			0
$835$	16.3655	+	28.3458i	0.566350	+	0.980947i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	10.9430			0.377794			0.188897	−	0.981997i	$-0.439509\pi$
$839$	10.9430			0.377794			0.188897	+	0.981997i	$0.439509\pi$
$840$		0			0
$841$	4.50019			0.155179
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−13.3691	−	23.1559i	−0.459910	−	0.796587i
$846$		0			0
$847$	−23.8157	+	12.9626i	−0.818315	+	0.445399i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−2.64553	+	4.58219i	−0.0906875	+	0.157075i
$852$		0			0
$853$	24.4064			0.835660			0.417830	−	0.908525i	$-0.362791\pi$
$853$	24.4064			0.835660			0.417830	+	0.908525i	$0.362791\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−4.15292	+	7.19307i	−0.141861	+	0.245710i	−0.928197	−	0.372088i	$-0.878642\pi$
$857$	−4.15292	+	7.19307i	−0.141861	+	0.245710i	0.786336	+	0.617799i	$0.211975\pi$
$858$		0			0
$859$	18.3946	+	31.8605i	0.627617	+	1.08706i	0.988029	+	0.154271i	$0.0493030\pi$
$859$	18.3946	+	31.8605i	0.627617	+	1.08706i	−0.360411	+	0.932793i	$0.617364\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	24.1190	+	41.7753i	0.821019	+	1.42205i	0.904924	+	0.425573i	$0.139927\pi$
$863$	24.1190	+	41.7753i	0.821019	+	1.42205i	−0.0839050	+	0.996474i	$0.526739\pi$
$864$		0			0
$865$	−0.933463	+	1.61680i	−0.0317387	+	0.0549730i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	5.87839			0.199411
$870$		0			0
$871$	1.24271	−	2.15243i	0.0421075	−	0.0729323i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−0.646006	+	25.6793i	−0.0218390	+	0.868120i
$876$		0			0
$877$	−12.6840	−	21.9694i	−0.428310	−	0.741854i	0.568414	−	0.822743i	$-0.307557\pi$
$877$	−12.6840	−	21.9694i	−0.428310	−	0.741854i	−0.996723	+	0.0808891i	$0.974224\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−19.8636			−0.669222			−0.334611	−	0.942356i	$-0.608605\pi$
$881$	−19.8636			−0.669222			−0.334611	+	0.942356i	$0.608605\pi$
$882$		0			0
$883$	−43.6519			−1.46900			−0.734502	−	0.678606i	$-0.762584\pi$
$883$	−43.6519			−1.46900			−0.734502	+	0.678606i	$0.762584\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−5.13735	−	8.89815i	−0.172495	−	0.298770i	0.766796	−	0.641890i	$-0.221850\pi$
$887$	−5.13735	−	8.89815i	−0.172495	−	0.298770i	−0.939292	+	0.343120i	$0.888516\pi$
$888$		0			0
$889$	−0.0830678	+	3.30202i	−0.00278600	+	0.110746i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	17.4933	−	30.2993i	0.585390	−	1.01393i
$894$		0			0
$895$	−2.70895			−0.0905500
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−27.6914	+	47.9630i	−0.923561	+	1.59965i
$900$		0			0
$901$	6.20535	+	10.7480i	0.206730	+	0.358067i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−17.4985	−	30.3084i	−0.581671	−	1.00748i
$906$		0			0
$907$	−2.78074	+	4.81638i	−0.0923329	+	0.159925i	−0.908492	−	0.417901i	$-0.862766\pi$
$907$	−2.78074	+	4.81638i	−0.0923329	+	0.159925i	0.816159	+	0.577827i	$0.196099\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	28.9908			0.960509			0.480255	−	0.877129i	$-0.340544\pi$
$911$	28.9908			0.960509			0.480255	+	0.877129i	$0.340544\pi$
$912$		0			0
$913$	−4.22879	+	7.32448i	−0.139953	+	0.242405i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−22.5285	+	12.2620i	−0.743957	+	0.404927i
$918$		0			0
$919$	24.2132	+	41.9385i	0.798720	+	1.38342i	0.920450	+	0.390861i	$0.127823\pi$
$919$	24.2132	+	41.9385i	0.798720	+	1.38342i	−0.121729	+	0.992563i	$0.538844\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−1.66537			−0.0548164
$924$		0			0
$925$	−3.49981			−0.115073
$926$		0			0
$927$		0			0
$928$		0			0
$929$	18.3838	+	31.8418i	0.603154	+	1.04469i	0.992340	+	0.123535i	$0.0394231\pi$
$929$	18.3838	+	31.8418i	0.603154	+	1.04469i	−0.389186	+	0.921159i	$0.627244\pi$
$930$		0			0
$931$	−8.27548	−	16.1593i	−0.271218	−	0.529599i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−1.99115	+	3.44877i	−0.0651174	+	0.112787i
$936$		0			0
$937$	−17.6477			−0.576524			−0.288262	−	0.957552i	$-0.593077\pi$
$937$	−17.6477			−0.576524			−0.288262	+	0.957552i	$0.593077\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−0.879573	+	1.52347i	−0.0286733	+	0.0496636i	−0.880006	−	0.474963i	$-0.842462\pi$
$941$	−0.879573	+	1.52347i	−0.0286733	+	0.0496636i	0.851333	+	0.524626i	$0.175795\pi$
$942$		0			0
$943$	2.21566	+	3.83764i	0.0721519	+	0.124971i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	19.6139	+	33.9723i	0.637366	+	1.10395i	0.986009	+	0.166695i	$0.0533095\pi$
$947$	19.6139	+	33.9723i	0.637366	+	1.10395i	−0.348642	+	0.937256i	$0.613357\pi$
$948$		0			0
$949$	7.42101	−	12.8536i	0.240896	−	0.417244i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	37.4313			1.21252			0.606260	−	0.795267i	$-0.292669\pi$
$953$	37.4313			1.21252			0.606260	+	0.795267i	$0.292669\pi$
$954$		0			0
$955$	4.44805	−	7.70425i	0.143936	−	0.249304i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	11.3523	+	6.94067i	0.366586	+	0.224126i
$960$		0			0
$961$	−30.2798	−	52.4461i	−0.976766	−	1.69181i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	58.5844			1.88590
$966$		0			0
$967$	7.31731			0.235309			0.117654	−	0.993055i	$-0.462463\pi$
$967$	7.31731			0.235309			0.117654	+	0.993055i	$0.462463\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−22.0775	−	38.2394i	−0.708502	−	1.22716i	−0.965413	−	0.260726i	$-0.916038\pi$
$971$	−22.0775	−	38.2394i	−0.708502	−	1.22716i	0.256911	−	0.966435i	$-0.417295\pi$
$972$		0			0
$973$	−0.186680	+	7.42069i	−0.00598468	+	0.237896i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−1.57685	+	2.73119i	−0.0504480	+	0.0873786i	−0.890147	−	0.455674i	$-0.849398\pi$
$977$	−1.57685	+	2.73119i	−0.0504480	+	0.0873786i	0.839699	+	0.543053i	$0.182732\pi$
$978$		0			0
$979$	−8.60078			−0.274882
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−20.3338	+	35.2192i	−0.648549	+	1.12332i	0.334921	+	0.942246i	$0.391290\pi$
$983$	−20.3338	+	35.2192i	−0.648549	+	1.12332i	−0.983470	+	0.181073i	$0.942043\pi$
$984$		0			0
$985$	23.1716	+	40.1344i	0.738308	+	1.27879i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−8.53278	−	14.7792i	−0.271327	−	0.469951i
$990$		0			0
$991$	5.50360	−	9.53251i	0.174828	−	0.302810i	−0.765274	−	0.643705i	$-0.777397\pi$
$991$	5.50360	−	9.53251i	0.174828	−	0.302810i	0.940102	+	0.340894i	$0.110730\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−32.6768			−1.03593
$996$		0			0
$997$	−22.8368	+	39.5544i	−0.723248	+	1.25270i	0.236444	+	0.971645i	$0.424018\pi$
$997$	−22.8368	+	39.5544i	−0.723248	+	1.25270i	−0.959691	+	0.281056i	$0.909315\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.s.l.865.3	yes	6
3.2	odd	2		1512.2.s.k.865.1	✓	6
7.2	even	3	inner	1512.2.s.l.1297.3	yes	6
21.2	odd	6		1512.2.s.k.1297.1	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1512.2.s.k.865.1	✓	6	3.2	odd	2
1512.2.s.k.1297.1	yes	6	21.2	odd	6
1512.2.s.l.865.3	yes	6	1.1	even	1	trivial
1512.2.s.l.1297.3	yes	6	7.2	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.s (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.23025 + 2.13086i) q^{5} +(-0.0665372 + 2.64491i) q^{7} +O(q^{10})\)	\(q+(1.23025 + 2.13086i) q^{5} +(-0.0665372 + 2.64491i) q^{7} +(0.433463 - 0.750780i) q^{11} -1.46050 q^{13} +(-0.933463 + 1.61680i) q^{17} +(1.29679 + 2.24611i) q^{19} +(0.796790 + 1.38008i) q^{23} +(-0.527042 + 0.912864i) q^{25} +5.78794 q^{29} +(-4.78434 + 8.28671i) q^{31} +(-5.71780 + 3.11213i) q^{35} +(1.66012 + 2.87541i) q^{37} +2.78074 q^{41} -10.7089 q^{43} +(-6.74484 - 11.6824i) q^{47} +(-6.99115 - 0.351971i) q^{49} +(3.32383 - 5.75705i) q^{53} +2.13307 q^{55} +(-3.21780 + 5.57339i) q^{59} +(3.09358 + 5.35824i) q^{61} +(-1.79679 - 3.11213i) q^{65} +(-0.850874 + 1.47376i) q^{67} +1.14027 q^{71} +(-5.08113 + 8.80077i) q^{73} +(1.95691 + 1.19643i) q^{77} +(3.39037 + 5.87229i) q^{79} -9.75583 q^{83} -4.59358 q^{85} +(-4.96050 - 8.59185i) q^{89} +(0.0971780 - 3.86291i) q^{91} +(-3.19076 + 5.52655i) q^{95} +2.81284 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{5} - 4 q^{7}+O(q^{10}) \) 6 * q + q^5 - 4 * q^7	\( 6 q + q^{5} - 4 q^{7} - q^{11} + 4 q^{13} - 2 q^{17} + 5 q^{19} + 2 q^{23} + 6 q^{25} + 2 q^{29} - 4 q^{31} - 6 q^{35} + 8 q^{37} - 6 q^{43} - 3 q^{47} - 12 q^{49} + 8 q^{53} + 20 q^{55} + 9 q^{59} + 13 q^{61} - 8 q^{65} + 16 q^{67} - 2 q^{71} - 3 q^{73} + 7 q^{77} + 12 q^{79} + 2 q^{83} - 22 q^{85} - 17 q^{89} - 13 q^{91} + 28 q^{97}+O(q^{100}) \) 6 * q + q^5 - 4 * q^7 - q^11 + 4 * q^13 - 2 * q^17 + 5 * q^19 + 2 * q^23 + 6 * q^25 + 2 * q^29 - 4 * q^31 - 6 * q^35 + 8 * q^37 - 6 * q^43 - 3 * q^47 - 12 * q^49 + 8 * q^53 + 20 * q^55 + 9 * q^59 + 13 * q^61 - 8 * q^65 + 16 * q^67 - 2 * q^71 - 3 * q^73 + 7 * q^77 + 12 * q^79 + 2 * q^83 - 22 * q^85 - 17 * q^89 - 13 * q^91 + 28 * q^97

Introduction

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