LMFDB - Embedded newform 2412.2.l.e.1369.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2412,2,Mod(37,2412)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2412, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("2412.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2412 = 2^{2} \cdot 3^{2} \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2412.l (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:	$19.2599169675$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 11x^{6} + 4x^{5} + 91x^{4} - 6x^{3} + 129x^{2} + 36x + 144 $ x^8 - x^7 + 11x^6 + 4x^5 + 91x^4 - 6x^3 + 129x^2 + 36x + 144
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 804)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1369.4
Root			$-1.30177 - 2.25473i$ of defining polynomial
Character	$\chi$	$=$	2412.1369
Dual form			2412.2.l.e.37.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.60354 q^{5} +(-1.30177 - 2.25473i) q^{7} +O(q^{10})$	$q+2.60354 q^{5} +(-1.30177 - 2.25473i) q^{7} +(-1.00000 - 1.73205i) q^{11} +(2.19098 - 3.79488i) q^{13} +(1.69098 - 2.92886i) q^{17} +(-1.38921 + 2.40618i) q^{19} +(0.798983 - 1.38388i) q^{23} +1.77841 q^{25} +(-2.10075 - 3.63861i) q^{29} +(4.90252 + 8.49142i) q^{31} +(-3.38921 - 5.87028i) q^{35} +(-1.89199 + 3.27703i) q^{37} +(-4.48996 - 7.77684i) q^{41} -11.1870 q^{43} +(-4.48996 - 7.77684i) q^{47} +(0.110793 - 0.191900i) q^{49} -0.618048 q^{53} +(-2.60354 - 4.50946i) q^{55} -3.18045 q^{59} +(7.38474 - 12.7907i) q^{61} +(5.70429 - 9.88012i) q^{65} +(-4.38642 + 6.91081i) q^{67} +(3.40809 + 5.90299i) q^{71} +(-0.613580 + 1.06275i) q^{73} +(-2.60354 + 4.50946i) q^{77} +(5.01610 + 8.68814i) q^{79} +(2.69098 - 4.66091i) q^{83} +(4.40252 - 7.62539i) q^{85} +3.00557 q^{89} -11.4086 q^{91} +(-3.61685 + 6.26457i) q^{95} +(1.99721 - 3.45928i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{5} + q^{7}+O(q^{10}) $ 8 * q - 2 * q^5 + q^7	$ 8 q - 2 q^{5} + q^{7} - 8 q^{11} - 4 q^{17} - 5 q^{19} - q^{23} + 2 q^{25} + 2 q^{29} + 9 q^{31} - 21 q^{35} - 5 q^{37} - 11 q^{41} + 6 q^{43} - 11 q^{47} + 7 q^{49} - 40 q^{53} + 2 q^{55} - 28 q^{59} + 20 q^{61} + 4 q^{65} - 33 q^{67} - 11 q^{71} - 7 q^{73} + 2 q^{77} + 12 q^{79} + 4 q^{83} + 5 q^{85} + 16 q^{89} - 8 q^{91} + 18 q^{95} + 20 q^{97}+O(q^{100}) $ 8 * q - 2 * q^5 + q^7 - 8 * q^11 - 4 * q^17 - 5 * q^19 - q^23 + 2 * q^25 + 2 * q^29 + 9 * q^31 - 21 * q^35 - 5 * q^37 - 11 * q^41 + 6 * q^43 - 11 * q^47 + 7 * q^49 - 40 * q^53 + 2 * q^55 - 28 * q^59 + 20 * q^61 + 4 * q^65 - 33 * q^67 - 11 * q^71 - 7 * q^73 + 2 * q^77 + 12 * q^79 + 4 * q^83 + 5 * q^85 + 16 * q^89 - 8 * q^91 + 18 * q^95 + 20 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2412\mathbb{Z}\right)^\times$.

$n$	$1073$	$1207$	$1945$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	2.60354			1.16434			0.582169	−	0.813068i	$-0.302204\pi$
$5$	2.60354			1.16434			0.582169	+	0.813068i	$0.302204\pi$
$6$		0			0
$7$	−1.30177	−	2.25473i	−0.492023	−	0.852208i	0.507935	−	0.861395i	$-0.330409\pi$
$7$	−1.30177	−	2.25473i	−0.492023	−	0.852208i	−0.999958	+	0.00918719i	$0.997076\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	0.674967	−	0.737848i	$-0.264158\pi$
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	−0.976478	+	0.215615i	$0.930824\pi$
$12$		0			0
$13$	2.19098	−	3.79488i	0.607667	−	1.05251i	−0.383956	−	0.923351i	$-0.625439\pi$
$13$	2.19098	−	3.79488i	0.607667	−	1.05251i	0.991624	−	0.129160i	$-0.0412280\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.69098	−	2.92886i	0.410122	−	0.710352i	−0.584781	−	0.811191i	$-0.698819\pi$
$17$	1.69098	−	2.92886i	0.410122	−	0.710352i	0.994903	+	0.100839i	$0.0321528\pi$
$18$		0			0
$19$	−1.38921	+	2.40618i	−0.318706	+	0.552015i	−0.980218	−	0.197919i	$-0.936582\pi$
$19$	−1.38921	+	2.40618i	−0.318706	+	0.552015i	0.661512	+	0.749934i	$0.269915\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.798983	−	1.38388i	0.166599	−	0.288559i	−0.770623	−	0.637292i	$-0.780055\pi$
$23$	0.798983	−	1.38388i	0.166599	−	0.288559i	0.937222	+	0.348733i	$0.113388\pi$
$24$		0			0
$25$	1.77841			0.355683
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−2.10075	−	3.63861i	−0.390100	−	0.675673i	0.602362	−	0.798223i	$-0.294226\pi$
$29$	−2.10075	−	3.63861i	−0.390100	−	0.675673i	−0.992462	+	0.122550i	$0.960893\pi$
$30$		0			0
$31$	4.90252	+	8.49142i	0.880519	+	1.52510i	0.850765	+	0.525546i	$0.176139\pi$
$31$	4.90252	+	8.49142i	0.880519	+	1.52510i	0.0297538	+	0.999557i	$0.490528\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−3.38921	−	5.87028i	−0.572880	−	0.992258i
$36$		0			0
$37$	−1.89199	+	3.27703i	−0.311042	+	0.538740i	−0.978588	−	0.205828i	$-0.934011\pi$
$37$	−1.89199	+	3.27703i	−0.311042	+	0.538740i	0.667546	+	0.744568i	$0.267345\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−4.48996	−	7.77684i	−0.701214	−	1.21454i	−0.968041	−	0.250793i	$-0.919309\pi$
$41$	−4.48996	−	7.77684i	−0.701214	−	1.21454i	0.266827	−	0.963744i	$-0.414025\pi$
$42$		0			0
$43$	−11.1870			−1.70600			−0.853000	−	0.521910i	$-0.825220\pi$
$43$	−11.1870			−1.70600			−0.853000	+	0.521910i	$0.825220\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−4.48996	−	7.77684i	−0.654928	−	1.13437i	−0.981912	−	0.189338i	$-0.939366\pi$
$47$	−4.48996	−	7.77684i	−0.654928	−	1.13437i	0.326984	−	0.945030i	$-0.393968\pi$
$48$		0			0
$49$	0.110793	−	0.191900i	0.0158276	−	0.0274142i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−0.618048			−0.0848954			−0.0424477	−	0.999099i	$-0.513516\pi$
$53$	−0.618048			−0.0848954			−0.0424477	+	0.999099i	$0.513516\pi$
$54$		0			0
$55$	−2.60354	−	4.50946i	−0.351061	−	0.608056i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−3.18045			−0.414059			−0.207030	−	0.978335i	$-0.566380\pi$
$59$	−3.18045			−0.414059			−0.207030	+	0.978335i	$0.566380\pi$
$60$		0			0
$61$	7.38474	−	12.7907i	0.945519	−	1.63769i	0.190810	−	0.981627i	$-0.438889\pi$
$61$	7.38474	−	12.7907i	0.945519	−	1.63769i	0.754709	−	0.656060i	$-0.227778\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	5.70429	−	9.88012i	0.707530	−	1.22548i
$66$		0			0
$67$	−4.38642	+	6.91081i	−0.535887	+	0.844290i
$67$	−4.38642	+	6.91081i	−0.535887	+	0.844290i
$68$		0			0
$69$		0			0
$70$		0			0
$71$	3.40809	+	5.90299i	0.404466	+	0.700556i	0.994259	−	0.106998i	$-0.0341239\pi$
$71$	3.40809	+	5.90299i	0.404466	+	0.700556i	−0.589793	+	0.807555i	$0.700791\pi$
$72$		0			0
$73$	−0.613580	+	1.06275i	−0.0718141	+	0.124386i	−0.899696	−	0.436516i	$-0.856212\pi$
$73$	−0.613580	+	1.06275i	−0.0718141	+	0.124386i	0.827882	+	0.560902i	$0.189545\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−2.60354	+	4.50946i	−0.296701	+	0.513901i
$78$		0			0
$79$	5.01610	+	8.68814i	0.564355	+	0.977492i	0.997109	+	0.0759802i	$0.0242086\pi$
$79$	5.01610	+	8.68814i	0.564355	+	0.977492i	−0.432754	+	0.901512i	$0.642458\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	2.69098	−	4.66091i	0.295373	−	0.511601i	−0.679699	−	0.733492i	$-0.737889\pi$
$83$	2.69098	−	4.66091i	0.295373	−	0.511601i	0.975072	+	0.221890i	$0.0712227\pi$
$84$		0			0
$85$	4.40252	−	7.62539i	0.477521	−	0.827090i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	3.00557			0.318590			0.159295	−	0.987231i	$-0.449078\pi$
$89$	3.00557			0.318590			0.159295	+	0.987231i	$0.449078\pi$
$90$		0			0
$91$	−11.4086			−1.19594
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−3.61685	+	6.26457i	−0.371081	+	0.642732i
$96$		0			0
$97$	1.99721	−	3.45928i	0.202786	−	0.351236i	−0.746639	−	0.665230i	$-0.768334\pi$
$97$	1.99721	−	3.45928i	0.202786	−	0.351236i	0.949425	+	0.313993i	$0.101667\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−7.07293	−	12.2507i	−0.703783	−	1.21899i	−0.967129	−	0.254286i	$-0.918160\pi$
$101$	−7.07293	−	12.2507i	−0.703783	−	1.21899i	0.263346	−	0.964701i	$-0.415174\pi$
$102$		0			0
$103$	1.99275	+	3.45154i	0.196351	+	0.340090i	0.947343	−	0.320222i	$-0.103757\pi$
$103$	1.99275	+	3.45154i	0.196351	+	0.340090i	−0.750992	+	0.660312i	$0.770424\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	9.81062			0.948428			0.474214	−	0.880410i	$-0.342732\pi$
$107$	9.81062			0.948428			0.474214	+	0.880410i	$0.342732\pi$
$108$		0			0
$109$	5.79053			0.554633			0.277316	−	0.960779i	$-0.410555\pi$
$109$	5.79053			0.554633			0.277316	+	0.960779i	$0.410555\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−1.52336	−	2.63853i	−0.143305	−	0.248212i	0.785434	−	0.618945i	$-0.212440\pi$
$113$	−1.52336	−	2.63853i	−0.143305	−	0.248212i	−0.928739	+	0.370733i	$0.879106\pi$
$114$		0			0
$115$	2.08018	−	3.60298i	0.193978	−	0.335980i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−8.80504			−0.807157
$120$		0			0
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−8.38753			−0.750203
$126$		0			0
$127$	−3.08465	−	5.34277i	−0.273719	−	0.474094i	0.696093	−	0.717952i	$-0.254920\pi$
$127$	−3.08465	−	5.34277i	−0.273719	−	0.474094i	−0.969811	+	0.243858i	$0.921587\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	18.1313			1.58414			0.792072	−	0.610428i	$-0.209003\pi$
$131$	18.1313			1.58414			0.792072	+	0.610428i	$0.209003\pi$
$132$		0			0
$133$	7.23371			0.627242
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−10.9911			−0.939030			−0.469515	−	0.882925i	$-0.655571\pi$
$137$	−10.9911			−0.939030			−0.469515	+	0.882925i	$0.655571\pi$
$138$		0			0
$139$	3.21265			0.272493			0.136247	−	0.990675i	$-0.456496\pi$
$139$	3.21265			0.272493			0.136247	+	0.990675i	$0.456496\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−8.76390			−0.732874
$144$		0			0
$145$	−5.46939	−	9.47326i	−0.454208	−	0.786711i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	19.0588			1.56136			0.780680	−	0.624931i	$-0.214873\pi$
$149$	19.0588			1.56136			0.780680	+	0.624931i	$0.214873\pi$
$150$		0			0
$151$	−6.87470	+	11.9073i	−0.559455	+	0.969004i	0.438087	+	0.898933i	$0.355656\pi$
$151$	−6.87470	+	11.9073i	−0.559455	+	0.969004i	−0.997542	+	0.0700718i	$0.977677\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	12.7639	+	22.1077i	1.02522	+	1.77574i
$156$		0			0
$157$	−4.00557	+	6.93786i	−0.319680	+	0.553701i	−0.980421	−	0.196912i	$-0.936909\pi$
$157$	−4.00557	+	6.93786i	−0.319680	+	0.553701i	0.660742	+	0.750613i	$0.270242\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−4.16037			−0.327883
$162$		0			0
$163$	−9.17815	−	15.8970i	−0.718888	−	1.24515i	−0.961441	−	0.275012i	$-0.911318\pi$
$163$	−9.17815	−	15.8970i	−0.718888	−	1.24515i	0.242553	−	0.970138i	$-0.422015\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−6.11964	−	10.5995i	−0.473552	−	0.820216i	0.525990	−	0.850491i	$-0.323695\pi$
$167$	−6.11964	−	10.5995i	−0.473552	−	0.820216i	−0.999542	+	0.0302749i	$0.990362\pi$
$168$		0			0
$169$	−3.10075	−	5.37066i	−0.238519	−	0.413128i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−5.30177	+	9.18293i	−0.403086	+	0.698166i	−0.994097	−	0.108498i	$-0.965396\pi$
$173$	−5.30177	+	9.18293i	−0.403086	+	0.698166i	0.591011	+	0.806664i	$0.298729\pi$
$174$		0			0
$175$	−2.31508	−	4.00984i	−0.175004	−	0.303116i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	13.4086			1.00220			0.501102	−	0.865388i	$-0.332928\pi$
$179$	13.4086			1.00220			0.501102	+	0.865388i	$0.332928\pi$
$180$		0			0
$181$	3.68651	+	6.38522i	0.274016	+	0.474610i	0.969886	−	0.243558i	$-0.0783145\pi$
$181$	3.68651	+	6.38522i	0.274016	+	0.474610i	−0.695870	+	0.718167i	$0.744981\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−4.92588	+	8.53187i	−0.362158	+	0.627276i
$186$		0			0
$187$	−6.76390			−0.494626
$188$		0			0
$189$		0			0
$190$		0			0
$191$	12.5818	−	21.7923i	0.910385	−	1.57683i	0.0968646	−	0.995298i	$-0.469119\pi$
$191$	12.5818	−	21.7923i	0.910385	−	1.57683i	0.813521	−	0.581536i	$-0.197548\pi$
$192$		0			0
$193$	11.5634			0.832350			0.416175	−	0.909285i	$-0.363370\pi$
$193$	11.5634			0.832350			0.416175	+	0.909285i	$0.363370\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	12.7566	+	22.0952i	0.908874	+	1.57422i	0.815631	+	0.578572i	$0.196390\pi$
$197$	12.7566	+	22.0952i	0.908874	+	1.57422i	0.0932423	+	0.995643i	$0.470277\pi$
$198$		0			0
$199$	6.18372	−	10.7105i	0.438352	−	0.759249i	−0.559210	−	0.829026i	$-0.688896\pi$
$199$	6.18372	−	10.7105i	0.438352	−	0.759249i	0.997563	+	0.0697773i	$0.0222289\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−5.46939	+	9.47326i	−0.383876	+	0.664893i
$204$		0			0
$205$	−11.6898	−	20.2473i	−0.816450	−	1.41413i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	5.55683			0.384374
$210$		0			0
$211$	−3.69544	+	6.40070i	−0.254405	+	0.440642i	−0.964734	−	0.263228i	$-0.915213\pi$
$211$	−3.69544	+	6.40070i	−0.254405	+	0.440642i	0.710329	+	0.703870i	$0.248546\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−29.1258			−1.98636
$216$		0			0
$217$	12.7639	−	22.1077i	0.866470	−	1.50077i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−7.40978	−	12.8341i	−0.498435	−	0.863316i
$222$		0			0
$223$	−2.83963			−0.190156			−0.0950780	−	0.995470i	$-0.530310\pi$
$223$	−2.83963			−0.190156			−0.0950780	+	0.995470i	$0.530310\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−12.0923	−	20.9445i	−0.802594	−	1.39013i	−0.917903	−	0.396804i	$-0.870119\pi$
$227$	−12.0923	−	20.9445i	−0.802594	−	1.39013i	0.115309	−	0.993330i	$-0.463214\pi$
$228$		0			0
$229$	0.593010	−	1.02712i	0.0391872	−	0.0678743i	−0.845767	−	0.533553i	$-0.820856\pi$
$229$	0.593010	−	1.02712i	0.0391872	−	0.0678743i	0.884954	+	0.465679i	$0.154190\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	7.49602	+	12.9835i	0.491081	+	0.850576i	0.999947	−	0.0102689i	$-0.00326874\pi$
$233$	7.49602	+	12.9835i	0.491081	+	0.850576i	−0.508867	+	0.860845i	$0.669935\pi$
$234$		0			0
$235$	−11.6898	−	20.2473i	−0.762557	−	1.32079i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	0.00725462	+	0.0125654i	0.000469262	+	0.000812786i	0.866260	−	0.499594i	$-0.166517\pi$
$239$	0.00725462	+	0.0125654i	0.000469262	+	0.000812786i	−0.865791	+	0.500406i	$0.833184\pi$
$240$		0			0
$241$	1.36426			0.0878796			0.0439398	−	0.999034i	$-0.486009\pi$
$241$	1.36426			0.0878796			0.0439398	+	0.999034i	$0.486009\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	0.288455	−	0.499618i	0.0184287	−	0.0319194i
$246$		0			0
$247$	6.08744	+	10.5438i	0.387334	+	0.670883i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−0.817871	+	1.41659i	−0.0516235	+	0.0894146i	−0.890682	−	0.454626i	$-0.849773\pi$
$251$	−0.817871	+	1.41659i	−0.0516235	+	0.0894146i	0.839059	+	0.544041i	$0.183106\pi$
$252$		0			0
$253$	−3.19593			−0.200926
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−0.946034	−	1.63858i	−0.0590120	−	0.102212i	0.835010	−	0.550234i	$-0.185462\pi$
$257$	−0.946034	−	1.63858i	−0.0590120	−	0.102212i	−0.894022	+	0.448023i	$0.852128\pi$
$258$		0			0
$259$	9.85175			0.612158
$260$		0			0
$261$		0			0
$262$		0			0
$263$	3.42309			0.211077			0.105538	−	0.994415i	$-0.466343\pi$
$263$	3.42309			0.211077			0.105538	+	0.994415i	$0.466343\pi$
$264$		0			0
$265$	−1.60911			−0.0988469
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−2.48431			−0.151471			−0.0757356	−	0.997128i	$-0.524130\pi$
$269$	−2.48431			−0.151471			−0.0757356	+	0.997128i	$0.524130\pi$
$270$		0			0
$271$	17.0533			1.03591			0.517956	−	0.855407i	$-0.326693\pi$
$271$	17.0533			1.03591			0.517956	+	0.855407i	$0.326693\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−1.77841	−	3.08030i	−0.107242	−	0.185749i
$276$		0			0
$277$	−7.17487			−0.431096			−0.215548	−	0.976493i	$-0.569154\pi$
$277$	−7.17487			−0.431096			−0.215548	+	0.976493i	$0.569154\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	16.1664	−	28.0011i	0.964408	−	1.67040i	0.253211	−	0.967411i	$-0.418513\pi$
$281$	16.1664	−	28.0011i	0.964408	−	1.67040i	0.711197	−	0.702993i	$-0.248153\pi$
$282$		0			0
$283$	−0.737275			−0.0438264			−0.0219132	−	0.999760i	$-0.506976\pi$
$283$	−0.737275			−0.0438264			−0.0219132	+	0.999760i	$0.506976\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−11.6898	+	20.2473i	−0.690026	+	1.19516i
$288$		0			0
$289$	2.78120	+	4.81718i	0.163600	+	0.283364i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	27.9444			1.63253			0.816263	−	0.577680i	$-0.196042\pi$
$293$	27.9444			1.63253			0.816263	+	0.577680i	$0.196042\pi$
$294$		0			0
$295$	−8.28042			−0.482105
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−3.50110	−	6.06409i	−0.202474	−	0.350695i
$300$		0			0
$301$	14.5629	+	25.2237i	0.839391	+	1.45387i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	19.2265	−	33.3012i	1.10090	−	1.90682i
$306$		0			0
$307$	3.69376	−	6.39778i	0.210814	−	0.365141i	−0.741155	−	0.671333i	$-0.765722\pi$
$307$	3.69376	−	6.39778i	0.210814	−	0.365141i	0.951970	+	0.306193i	$0.0990552\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−6.94214			−0.393653			−0.196826	−	0.980438i	$-0.563064\pi$
$311$	−6.94214			−0.393653			−0.196826	+	0.980438i	$0.563064\pi$
$312$		0			0
$313$	−23.2303			−1.31306			−0.656528	−	0.754301i	$-0.727976\pi$
$313$	−23.2303			−1.31306			−0.656528	+	0.754301i	$0.727976\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−0.972176	+	1.68386i	−0.0546028	+	0.0945749i	−0.892035	−	0.451967i	$-0.850723\pi$
$317$	−0.972176	+	1.68386i	−0.0546028	+	0.0945749i	0.837432	+	0.546542i	$0.184056\pi$
$318$		0			0
$319$	−4.20150	+	7.27722i	−0.235239	+	0.407446i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	4.69823	+	8.13757i	0.261417	+	0.452787i
$324$		0			0
$325$	3.89646	−	6.74887i	0.216137	−	0.374360i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−11.6898	+	20.2473i	−0.644479	+	1.11627i
$330$		0			0
$331$	−2.93592	−	5.08516i	−0.161373	−	0.279506i	0.773989	−	0.633200i	$-0.218259\pi$
$331$	−2.93592	−	5.08516i	−0.161373	−	0.279506i	−0.935361	+	0.353694i	$0.884925\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−11.4202	+	17.9926i	−0.623953	+	0.983039i
$336$		0			0
$337$	−8.67974	+	15.0338i	−0.472816	+	0.818941i	−0.999516	−	0.0311104i	$-0.990096\pi$
$337$	−8.67974	+	15.0338i	−0.472816	+	0.818941i	0.526700	+	0.850051i	$0.323429\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	9.80504	−	16.9828i	0.530973	−	0.919672i
$342$		0			0
$343$	−18.8017			−1.01520
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−10.0116	−	17.3407i	−0.537453	−	0.930895i	−0.999040	−	0.0438007i	$-0.986053\pi$
$347$	−10.0116	−	17.3407i	−0.537453	−	0.930895i	0.461588	−	0.887095i	$-0.347280\pi$
$348$		0			0
$349$	−3.36187			−0.179957			−0.0899784	−	0.995944i	$-0.528680\pi$
$349$	−3.36187			−0.179957			−0.0899784	+	0.995944i	$0.528680\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−12.4008	+	21.4789i	−0.660030	+	1.14321i	0.320577	+	0.947222i	$0.396123\pi$
$353$	−12.4008	+	21.4789i	−0.660030	+	1.14321i	−0.980607	+	0.195983i	$0.937210\pi$
$354$		0			0
$355$	8.87311	+	15.3687i	0.470936	+	0.815684i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−23.6769			−1.24962			−0.624809	−	0.780778i	$-0.714823\pi$
$359$	−23.6769			−1.24962			−0.624809	+	0.780778i	$0.714823\pi$
$360$		0			0
$361$	5.64021	+	9.76913i	0.296853	+	0.514165i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−1.59748	+	2.76691i	−0.0836158	+	0.144827i
$366$		0			0
$367$	12.0734	+	20.9118i	0.630227	+	1.09159i	0.987505	+	0.157587i	$0.0503716\pi$
$367$	12.0734	+	20.9118i	0.630227	+	1.09159i	−0.357278	+	0.933998i	$0.616295\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	0.804556	+	1.39353i	0.0417705	+	0.0723485i
$372$		0			0
$373$	7.11517	+	12.3238i	0.368410	+	0.638104i	0.989317	−	0.145780i	$-0.0465691\pi$
$373$	7.11517	+	12.3238i	0.368410	+	0.638104i	−0.620907	+	0.783884i	$0.713236\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−18.4108			−0.948204
$378$		0			0
$379$	−0.607520	+	1.05225i	−0.0312062	+	0.0540507i	−0.881207	−	0.472731i	$-0.843268\pi$
$379$	−0.607520	+	1.05225i	−0.0312062	+	0.0540507i	0.850001	+	0.526782i	$0.176602\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	0.320657	−	0.555394i	0.0163848	−	0.0283793i	−0.857717	−	0.514123i	$-0.828118\pi$
$383$	0.320657	−	0.555394i	0.0163848	−	0.0283793i	0.874102	+	0.485743i	$0.161451\pi$
$384$		0			0
$385$	−6.77841	+	11.7406i	−0.345460	+	0.598354i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	3.98549	−	6.90307i	0.202072	−	0.350000i	−0.747124	−	0.664685i	$-0.768566\pi$
$389$	3.98549	−	6.90307i	0.202072	−	0.350000i	0.949196	+	0.314685i	$0.101899\pi$
$390$		0			0
$391$	−2.70212	−	4.68021i	−0.136652	−	0.236689i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	13.0596	+	22.6199i	0.657100	+	1.13813i
$396$		0			0
$397$	9.99106			0.501437			0.250719	−	0.968060i	$-0.419333\pi$
$397$	9.99106			0.501437			0.250719	+	0.968060i	$0.419333\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−15.4197			−0.770024			−0.385012	−	0.922911i	$-0.625803\pi$
$401$	−15.4197			−0.770024			−0.385012	+	0.922911i	$0.625803\pi$
$402$		0			0
$403$	42.9652			2.14025
$404$		0			0
$405$		0			0
$406$		0			0
$407$	7.56797			0.375130
$408$		0			0
$409$	−4.11190	−	7.12202i	−0.203320	−	0.352161i	0.746276	−	0.665637i	$-0.231840\pi$
$409$	−4.11190	−	7.12202i	−0.203320	−	0.352161i	−0.949596	+	0.313476i	$0.898507\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	4.14021	+	7.17105i	0.203726	+	0.352864i
$414$		0			0
$415$	7.00606	−	12.1349i	0.343914	−	0.595676i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	4.32791	−	7.49616i	0.211432	−	0.366212i	−0.740731	−	0.671802i	$-0.765521\pi$
$419$	4.32791	−	7.49616i	0.211432	−	0.366212i	0.952163	+	0.305591i	$0.0988539\pi$
$420$		0			0
$421$	−18.9682	+	32.8539i	−0.924453	+	1.60120i	−0.132015	+	0.991248i	$0.542145\pi$
$421$	−18.9682	+	32.8539i	−0.924453	+	1.60120i	−0.792438	+	0.609952i	$0.791189\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	3.00725	−	5.20872i	0.145873	−	0.252660i
$426$		0			0
$427$	−38.4529			−1.86087
$428$		0			0
$429$		0			0
$430$		0			0
$431$	7.75100	+	13.4251i	0.373353	+	0.646666i	0.990079	−	0.140512i	$-0.0448748\pi$
$431$	7.75100	+	13.4251i	0.373353	+	0.646666i	−0.616726	+	0.787178i	$0.711541\pi$
$432$		0			0
$433$	14.8222	+	25.6729i	0.712312	+	1.23376i	0.963987	+	0.265949i	$0.0856851\pi$
$433$	14.8222	+	25.6729i	0.712312	+	1.23376i	−0.251675	+	0.967812i	$0.580982\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	2.21990	+	3.84499i	0.106192	+	0.183931i
$438$		0			0
$439$	−14.9013	+	25.8099i	−0.711202	+	1.23184i	0.253205	+	0.967413i	$0.418515\pi$
$439$	−14.9013	+	25.8099i	−0.711202	+	1.23184i	−0.964406	+	0.264425i	$0.914818\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	3.07461	+	5.32538i	0.146079	+	0.253016i	0.929775	−	0.368128i	$-0.120001\pi$
$443$	3.07461	+	5.32538i	0.146079	+	0.253016i	−0.783696	+	0.621145i	$0.786668\pi$
$444$		0			0
$445$	7.82513			0.370947
$446$		0			0
$447$		0			0
$448$		0			0
$449$	14.3941	+	24.9313i	0.679298	+	1.17658i	0.975193	+	0.221358i	$0.0710491\pi$
$449$	14.3941	+	24.9313i	0.679298	+	1.17658i	−0.295894	+	0.955221i	$0.595618\pi$
$450$		0			0
$451$	−8.97992	+	15.5537i	−0.422848	+	0.732394i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−29.7027			−1.39248
$456$		0			0
$457$	8.52057	+	14.7581i	0.398575	+	0.690353i	0.993550	−	0.113391i	$-0.0361714\pi$
$457$	8.52057	+	14.7581i	0.398575	+	0.690353i	−0.594975	+	0.803744i	$0.702838\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	23.1781			1.07951			0.539755	−	0.841822i	$-0.318517\pi$
$461$	23.1781			1.07951			0.539755	+	0.841822i	$0.318517\pi$
$462$		0			0
$463$	8.26104	−	14.3085i	0.383923	−	0.664975i	−0.607696	−	0.794170i	$-0.707906\pi$
$463$	8.26104	−	14.3085i	0.383923	−	0.664975i	0.991619	+	0.129195i	$0.0412394\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−4.60403	+	7.97441i	−0.213049	+	0.369012i	−0.952667	−	0.304015i	$-0.901673\pi$
$467$	−4.60403	+	7.97441i	−0.213049	+	0.369012i	0.739618	+	0.673027i	$0.235006\pi$
$468$		0			0
$469$	21.2921	+	0.893914i	0.983179	+	0.0412771i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	11.1870	+	19.3764i	0.514379	+	0.890930i
$474$		0			0
$475$	−2.47058	+	4.27918i	−0.113358	+	0.196342i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−11.9260	+	20.6564i	−0.544911	+	0.943813i	0.453702	+	0.891154i	$0.350103\pi$
$479$	−11.9260	+	20.6564i	−0.544911	+	0.943813i	−0.998613	+	0.0526594i	$0.983230\pi$
$480$		0			0
$481$	8.29062	+	14.3598i	0.378020	+	0.654750i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	5.19982	−	9.00636i	0.236112	−	0.408958i
$486$		0			0
$487$	16.9081	−	29.2857i	0.766179	−	1.32706i	−0.173442	−	0.984844i	$-0.555489\pi$
$487$	16.9081	−	29.2857i	0.766179	−	1.32706i	0.939621	−	0.342217i	$-0.111178\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	9.41195			0.424755			0.212378	−	0.977188i	$-0.431879\pi$
$491$	9.41195			0.424755			0.212378	+	0.977188i	$0.431879\pi$
$492$		0			0
$493$	−14.2093			−0.639954
$494$		0			0
$495$		0			0
$496$		0			0
$497$	8.87311	−	15.3687i	0.398013	−	0.689379i
$498$		0			0
$499$	−6.40301	+	11.0903i	−0.286638	+	0.496472i	−0.973005	−	0.230784i	$-0.925871\pi$
$499$	−6.40301	+	11.0903i	−0.286638	+	0.496472i	0.686367	+	0.727255i	$0.259204\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	0.0741226	+	0.128384i	0.00330496	+	0.00572437i	0.867673	−	0.497135i	$-0.165615\pi$
$503$	0.0741226	+	0.128384i	0.00330496	+	0.00572437i	−0.864368	+	0.502859i	$0.832281\pi$
$504$		0			0
$505$	−18.4146	−	31.8951i	−0.819441	−	1.41931i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	2.84282			0.126006			0.0630029	−	0.998013i	$-0.479932\pi$
$509$	2.84282			0.126006			0.0630029	+	0.998013i	$0.479932\pi$
$510$		0			0
$511$	3.19496			0.141337
$512$		0			0
$513$		0			0
$514$		0			0
$515$	5.18819	+	8.98621i	0.228619	+	0.395980i
$516$		0			0
$517$	−8.97992	+	15.5537i	−0.394936	+	0.684050i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	7.78399			0.341023			0.170511	−	0.985356i	$-0.445458\pi$
$521$	7.78399			0.341023			0.170511	+	0.985356i	$0.445458\pi$
$522$		0			0
$523$	9.38244	−	16.2509i	0.410265	−	0.710601i	−0.584653	−	0.811283i	$-0.698769\pi$
$523$	9.38244	−	16.2509i	0.410265	−	0.710601i	0.994919	+	0.100683i	$0.0321027\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	33.1602			1.44448
$528$		0			0
$529$	10.2233	+	17.7072i	0.444489	+	0.769878i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−39.3496			−1.70442
$534$		0			0
$535$	25.5423			1.10429
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−0.443173			−0.0190888
$540$		0			0
$541$	−6.80186			−0.292435			−0.146217	−	0.989252i	$-0.546710\pi$
$541$	−6.80186			−0.292435			−0.146217	+	0.989252i	$0.546710\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	15.0759			0.645780
$546$		0			0
$547$	19.8863	+	34.4441i	0.850278	+	1.47272i	0.880957	+	0.473196i	$0.156900\pi$
$547$	19.8863	+	34.4441i	0.850278	+	1.47272i	−0.0306793	+	0.999529i	$0.509767\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	11.6735			0.497309
$552$		0			0
$553$	13.0596	−	22.6199i	0.555351	−	0.961897i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−7.24055	−	12.5410i	−0.306792	−	0.531379i	0.670867	−	0.741578i	$-0.265922\pi$
$557$	−7.24055	−	12.5410i	−0.306792	−	0.531379i	−0.977659	+	0.210199i	$0.932589\pi$
$558$		0			0
$559$	−24.5104	+	42.4533i	−1.03668	+	1.79558i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	4.13374			0.174216			0.0871081	−	0.996199i	$-0.472237\pi$
$563$	4.13374			0.174216			0.0871081	+	0.996199i	$0.472237\pi$
$564$		0			0
$565$	−3.96612	−	6.86951i	−0.166856	−	0.289003i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	18.0456	+	31.2559i	0.756511	+	1.31031i	0.944620	+	0.328167i	$0.106431\pi$
$569$	18.0456	+	31.2559i	0.756511	+	1.31031i	−0.188109	+	0.982148i	$0.560236\pi$
$570$		0			0
$571$	22.9275	+	39.7115i	0.959485	+	1.66188i	0.723754	+	0.690058i	$0.242415\pi$
$571$	22.9275	+	39.7115i	0.959485	+	1.66188i	0.235731	+	0.971818i	$0.424252\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	1.42092	−	2.46111i	0.0592565	−	0.102635i
$576$		0			0
$577$	−14.1079	−	24.4356i	−0.587320	−	1.01727i	−0.994582	−	0.103957i	$-0.966850\pi$
$577$	−14.1079	−	24.4356i	−0.587320	−	1.01727i	0.407262	−	0.913312i	$-0.366484\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−14.0121			−0.581321
$582$		0			0
$583$	0.618048	+	1.07049i	0.0255969	+	0.0443352i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−14.3006	+	24.7693i	−0.590248	+	1.02234i	0.403951	+	0.914781i	$0.367637\pi$
$587$	−14.3006	+	24.7693i	−0.590248	+	1.02234i	−0.994199	+	0.107559i	$0.965697\pi$
$588$		0			0
$589$	−27.2425			−1.12251
$590$		0			0
$591$		0			0
$592$		0			0
$593$	13.0177	−	22.5473i	0.534573	−	0.925907i	−0.464611	−	0.885515i	$-0.653806\pi$
$593$	13.0177	−	22.5473i	0.534573	−	0.925907i	0.999184	−	0.0403922i	$-0.0128607\pi$
$594$		0			0
$595$	−22.9243			−0.939803
$596$		0			0
$597$		0			0
$598$		0			0
$599$	21.1063	+	36.5572i	0.862381	+	1.49369i	0.869624	+	0.493714i	$0.164361\pi$
$599$	21.1063	+	36.5572i	0.862381	+	1.49369i	−0.00724324	+	0.999974i	$0.502306\pi$
$600$		0			0
$601$	−8.35860	+	14.4775i	−0.340954	+	0.590550i	−0.984610	−	0.174765i	$-0.944083\pi$
$601$	−8.35860	+	14.4775i	−0.340954	+	0.590550i	0.643656	+	0.765315i	$0.277417\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	9.11239	−	15.7831i	0.370471	−	0.641675i
$606$		0			0
$607$	5.15758	+	8.93319i	0.209340	+	0.362587i	0.951507	−	0.307628i	$-0.0995352\pi$
$607$	5.15758	+	8.93319i	0.209340	+	0.362587i	−0.742167	+	0.670215i	$0.766202\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−39.3496			−1.59191
$612$		0			0
$613$	17.6129	−	30.5064i	0.711377	−	1.23214i	−0.252963	−	0.967476i	$-0.581405\pi$
$613$	17.6129	−	30.5064i	0.711377	−	1.23214i	0.964340	−	0.264666i	$-0.0852616\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−16.8685			−0.679099			−0.339550	−	0.940588i	$-0.610275\pi$
$617$	−16.8685			−0.679099			−0.339550	+	0.940588i	$0.610275\pi$
$618$		0			0
$619$	8.02336	−	13.8969i	0.322486	−	0.558562i	−0.658514	−	0.752568i	$-0.728815\pi$
$619$	8.02336	−	13.8969i	0.322486	−	0.558562i	0.981000	+	0.194006i	$0.0621482\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−3.91256	−	6.77676i	−0.156754	−	0.271505i
$624$		0			0
$625$	−30.7293			−1.22917
$626$		0			0
$627$		0			0
$628$		0			0
$629$	6.39863	+	11.0828i	0.255130	+	0.441898i
$630$		0			0
$631$	0.737762	−	1.27784i	0.0293698	−	0.0508701i	−0.850967	−	0.525219i	$-0.823983\pi$
$631$	0.737762	−	1.27784i	0.0293698	−	0.0508701i	0.880337	+	0.474349i	$0.157317\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−8.03101	−	13.9101i	−0.318701	−	0.552006i
$636$		0			0
$637$	−0.485491	−	0.840895i	−0.0192358	−	0.0333175i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	16.0640	+	27.8237i	0.634490	+	1.09897i	0.986623	+	0.163018i	$0.0521230\pi$
$641$	16.0640	+	27.8237i	0.634490	+	1.09897i	−0.352134	+	0.935950i	$0.614544\pi$
$642$		0			0
$643$	−18.1202			−0.714591			−0.357295	−	0.933991i	$-0.616301\pi$
$643$	−18.1202			−0.714591			−0.357295	+	0.933991i	$0.616301\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	21.7966	−	37.7528i	0.856913	−	1.48422i	−0.0179468	−	0.999839i	$-0.505713\pi$
$647$	21.7966	−	37.7528i	0.856913	−	1.48422i	0.874859	−	0.484377i	$-0.160954\pi$
$648$		0			0
$649$	3.18045	+	5.50870i	0.124843	+	0.216235i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−9.58783	+	16.6066i	−0.375201	+	0.649867i	−0.990357	−	0.138538i	$-0.955760\pi$
$653$	−9.58783	+	16.6066i	−0.375201	+	0.649867i	0.615156	+	0.788405i	$0.289093\pi$
$654$		0			0
$655$	47.2057			1.84448
$656$		0			0
$657$		0			0
$658$		0			0
$659$	22.9932	+	39.8254i	0.895689	+	1.55138i	0.832949	+	0.553349i	$0.186651\pi$
$659$	22.9932	+	39.8254i	0.895689	+	1.55138i	0.0627398	+	0.998030i	$0.480016\pi$
$660$		0			0
$661$	48.1113			1.87131			0.935656	−	0.352914i	$-0.114809\pi$
$661$	48.1113			1.87131			0.935656	+	0.352914i	$0.114809\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	18.8332			0.730322
$666$		0			0
$667$	−6.71386			−0.259962
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−29.5390			−1.14034
$672$		0			0
$673$	19.6380			0.756987			0.378494	−	0.925604i	$-0.376442\pi$
$673$	19.6380			0.756987			0.378494	+	0.925604i	$0.376442\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−16.5757	−	28.7100i	−0.637056	−	1.10341i	−0.986075	−	0.166299i	$-0.946818\pi$
$677$	−16.5757	−	28.7100i	−0.637056	−	1.10341i	0.349019	−	0.937116i	$-0.386515\pi$
$678$		0			0
$679$	−10.3996			−0.399102
$680$		0			0
$681$		0			0
$682$		0			0
$683$	0.407607	−	0.705996i	0.0155967	−	0.0270142i	−0.858122	−	0.513446i	$-0.828369\pi$
$683$	0.407607	−	0.705996i	0.0155967	−	0.0270142i	0.873718	+	0.486432i	$0.161702\pi$
$684$		0			0
$685$	−28.6157			−1.09335
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−1.35413	+	2.34542i	−0.0515882	+	0.0893533i
$690$		0			0
$691$	−16.2928	−	28.2200i	−0.619809	−	1.07354i	−0.989520	−	0.144393i	$-0.953877\pi$
$691$	−16.2928	−	28.2200i	−0.619809	−	1.07354i	0.369712	−	0.929146i	$-0.379456\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	8.36426			0.317274
$696$		0			0
$697$	−30.3697			−1.15033
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−23.1730	−	40.1368i	−0.875231	−	1.51594i	−0.856516	−	0.516120i	$-0.827376\pi$
$701$	−23.1730	−	40.1368i	−0.875231	−	1.51594i	−0.0187148	−	0.999825i	$-0.505957\pi$
$702$		0			0
$703$	−5.25674	−	9.10494i	−0.198262	−	0.343399i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−18.4146	+	31.8951i	−0.692554	+	1.19954i
$708$		0			0
$709$	9.57452	−	16.5836i	0.359579	−	0.622808i	−0.628312	−	0.777962i	$-0.716254\pi$
$709$	9.57452	−	16.5836i	0.359579	−	0.622808i	0.987890	+	0.155153i	$0.0495871\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	15.6681			0.586776
$714$		0			0
$715$	−22.8172			−0.853314
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−18.4292	+	31.9204i	−0.687294	+	1.19043i	0.285416	+	0.958404i	$0.407868\pi$
$719$	−18.4292	+	31.9204i	−0.687294	+	1.19043i	−0.972710	+	0.232025i	$0.925465\pi$
$720$		0			0
$721$	5.18819	−	8.98621i	0.193218	−	0.334664i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−3.73601	−	6.47095i	−0.138752	−	0.240325i
$726$		0			0
$727$	25.6592	−	44.4430i	0.951646	−	1.64830i	0.209783	−	0.977748i	$-0.432724\pi$
$727$	25.6592	−	44.4430i	0.951646	−	1.64830i	0.741863	−	0.670551i	$-0.233942\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−18.9169	+	32.7651i	−0.699668	+	1.21186i
$732$		0			0
$733$	5.44157	+	9.42507i	0.200989	+	0.348123i	0.948847	−	0.315735i	$-0.102251\pi$
$733$	5.44157	+	9.42507i	0.200989	+	0.348123i	−0.747858	+	0.663858i	$0.768918\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	16.3563	+	0.686691i	0.602492	+	0.0252946i
$738$		0			0
$739$	22.1101	−	38.2958i	0.813333	−	1.40873i	−0.0971863	−	0.995266i	$-0.530984\pi$
$739$	22.1101	−	38.2958i	0.813333	−	1.40873i	0.910519	−	0.413467i	$-0.135682\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	5.29403	−	9.16952i	0.194219	−	0.336397i	−0.752425	−	0.658678i	$-0.771116\pi$
$743$	5.29403	−	9.16952i	0.194219	−	0.336397i	0.946644	+	0.322280i	$0.104449\pi$
$744$		0			0
$745$	49.6204			1.81795
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−12.7712	−	22.1203i	−0.466648	−	0.808258i
$750$		0			0
$751$	−32.7848			−1.19633			−0.598167	−	0.801372i	$-0.704104\pi$
$751$	−32.7848			−1.19633			−0.598167	+	0.801372i	$0.704104\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−17.8985	+	31.0012i	−0.651395	+	1.12825i
$756$		0			0
$757$	−7.02949	−	12.1754i	−0.255491	−	0.442524i	0.709538	−	0.704668i	$-0.248904\pi$
$757$	−7.02949	−	12.1754i	−0.255491	−	0.442524i	−0.965029	+	0.262144i	$0.915571\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−9.07237			−0.328873			−0.164437	−	0.986388i	$-0.552581\pi$
$761$	−9.07237			−0.328873			−0.164437	+	0.986388i	$0.552581\pi$
$762$		0			0
$763$	−7.53794	−	13.0561i	−0.272892	−	0.472662i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−6.96828	+	12.0694i	−0.251610	+	0.435802i
$768$		0			0
$769$	2.91654	+	5.05160i	0.105173	+	0.182165i	0.913809	−	0.406144i	$-0.133127\pi$
$769$	2.91654	+	5.05160i	0.105173	+	0.182165i	−0.808636	+	0.588310i	$0.799794\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	11.2594	+	19.5019i	0.404974	+	0.701435i	0.994318	−	0.106447i	$-0.0339473\pi$
$773$	11.2594	+	19.5019i	0.404974	+	0.701435i	−0.589345	+	0.807882i	$0.700614\pi$
$774$		0			0
$775$	8.71871	+	15.1012i	0.313185	+	0.542453i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	24.9499			0.893924
$780$		0			0
$781$	6.81619	−	11.8060i	0.243902	−	0.422451i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−10.4287	+	18.0630i	−0.372215	+	0.644695i
$786$		0			0
$787$	−17.4815	+	30.2789i	−0.623149	+	1.07932i	0.365747	+	0.930714i	$0.380813\pi$
$787$	−17.4815	+	30.2789i	−0.623149	+	1.07932i	−0.988896	+	0.148611i	$0.952520\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−3.96612	+	6.86951i	−0.141019	+	0.244252i
$792$		0			0
$793$	−32.3596	−	56.0484i	−1.14912	−	1.99034i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	15.1129	+	26.1763i	0.535325	+	0.927211i	0.999148	+	0.0412825i	$0.0131443\pi$
$797$	15.1129	+	26.1763i	0.535325	+	0.927211i	−0.463822	+	0.885928i	$0.653522\pi$
$798$		0			0
$799$	−30.3697			−1.07440
$800$		0			0
$801$		0			0
$802$		0			0
$803$	2.45432			0.0866110
$804$		0			0
$805$	−10.8317			−0.381766
$806$		0			0
$807$		0			0
$808$		0			0
$809$	16.3652			0.575371			0.287685	−	0.957725i	$-0.407114\pi$
$809$	16.3652			0.575371			0.287685	+	0.957725i	$0.407114\pi$
$810$		0			0
$811$	−18.7209	−	32.4255i	−0.657379	−	1.13861i	−0.981292	−	0.192527i	$-0.938332\pi$
$811$	−18.7209	−	32.4255i	−0.657379	−	1.13861i	0.323913	−	0.946087i	$-0.395002\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−23.8957	−	41.3885i	−0.837029	−	1.44978i
$816$		0			0
$817$	15.5410	−	26.9179i	0.543712	−	0.941738i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−20.2933	+	35.1491i	−0.708242	+	1.22671i	0.257267	+	0.966340i	$0.417178\pi$
$821$	−20.2933	+	35.1491i	−0.708242	+	1.22671i	−0.965509	+	0.260370i	$0.916155\pi$
$822$		0			0
$823$	17.1813	−	29.7589i	0.598904	−	1.03733i	−0.394080	−	0.919076i	$-0.628937\pi$
$823$	17.1813	−	29.7589i	0.598904	−	1.03733i	0.992983	−	0.118255i	$-0.0377301\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−9.77771	+	16.9355i	−0.340004	+	0.588904i	−0.984433	−	0.175760i	$-0.943762\pi$
$827$	−9.77771	+	16.9355i	−0.340004	+	0.588904i	0.644429	+	0.764664i	$0.277095\pi$
$828$		0			0
$829$	−44.4833			−1.54497			−0.772485	−	0.635034i	$-0.780986\pi$
$829$	−44.4833			−1.54497			−0.772485	+	0.635034i	$0.780986\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−0.374698	−	0.648995i	−0.0129825	−	0.0224863i
$834$		0			0
$835$	−15.9327	−	27.5963i	−0.551374	−	0.955009i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	1.32840	+	2.30085i	0.0458614	+	0.0794343i	0.888045	−	0.459757i	$-0.152063\pi$
$839$	1.32840	+	2.30085i	0.0458614	+	0.0794343i	−0.842183	+	0.539191i	$0.818730\pi$
$840$		0			0
$841$	5.67368	−	9.82710i	0.195644	−	0.338866i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−8.07293	−	13.9827i	−0.277717	−	0.481020i
$846$		0			0
$847$	−18.2248			−0.626211
$848$		0			0
$849$		0			0
$850$		0			0
$851$	3.02334	+	5.23658i	0.103639	+	0.179508i
$852$		0			0
$853$	25.2615	−	43.7542i	0.864938	−	1.49812i	−0.00217110	−	0.999998i	$-0.500691\pi$
$853$	25.2615	−	43.7542i	0.864938	−	1.49812i	0.867109	−	0.498119i	$-0.165976\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	33.8460			1.15616			0.578079	−	0.815981i	$-0.303803\pi$
$857$	33.8460			1.15616			0.578079	+	0.815981i	$0.303803\pi$
$858$		0			0
$859$	0.754570	+	1.30695i	0.0257456	+	0.0445927i	0.878611	−	0.477538i	$-0.158471\pi$
$859$	0.754570	+	1.30695i	0.0257456	+	0.0445927i	−0.852866	+	0.522131i	$0.825137\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−6.85830			−0.233459			−0.116730	−	0.993164i	$-0.537241\pi$
$863$	−6.85830			−0.233459			−0.116730	+	0.993164i	$0.537241\pi$
$864$		0			0
$865$	−13.8034	+	23.9081i	−0.469328	+	0.812901i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	10.0322	−	17.3763i	0.340319	−	0.589450i
$870$		0			0
$871$	16.6152	+	31.7874i	0.562984	+	1.07707i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	10.9186	+	18.9116i	0.369117	+	0.639329i
$876$		0			0
$877$	−26.4114	+	45.7458i	−0.891849	+	1.54473i	−0.0541914	+	0.998531i	$0.517258\pi$
$877$	−26.4114	+	45.7458i	−0.891849	+	1.54473i	−0.837657	+	0.546196i	$0.816075\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	26.1657	−	45.3204i	0.881545	−	1.52688i	0.0319229	−	0.999490i	$-0.489837\pi$
$881$	26.1657	−	45.3204i	0.881545	−	1.52688i	0.849623	−	0.527391i	$-0.176830\pi$
$882$		0			0
$883$	−0.0617824	−	0.107010i	−0.00207914	−	0.00360118i	0.864984	−	0.501800i	$-0.167328\pi$
$883$	−0.0617824	−	0.107010i	−0.00207914	−	0.00360118i	−0.867063	+	0.498198i	$0.833995\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−8.51730	+	14.7524i	−0.285983	+	0.495337i	−0.972847	−	0.231449i	$-0.925653\pi$
$887$	−8.51730	+	14.7524i	−0.285983	+	0.495337i	0.686864	+	0.726786i	$0.258987\pi$
$888$		0			0
$889$	−8.03101	+	13.9101i	−0.269351	+	0.466530i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	24.9499			0.834917
$894$		0			0
$895$	34.9098			1.16690
$896$		0			0
$897$		0			0
$898$		0			0
$899$	20.5980	−	35.6767i	0.686981	−	1.18989i
$900$		0			0
$901$	−1.04510	+	1.81017i	−0.0348175	+	0.0603056i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	9.59797	+	16.6242i	0.319047	+	0.552606i
$906$		0			0
$907$	15.7498	+	27.2795i	0.522964	+	0.905800i	0.999643	+	0.0267225i	$0.00850704\pi$
$907$	15.7498	+	27.2795i	0.522964	+	0.905800i	−0.476679	+	0.879077i	$0.658160\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−35.3408			−1.17089			−0.585447	−	0.810711i	$-0.699081\pi$
$911$	−35.3408			−1.17089			−0.585447	+	0.810711i	$0.699081\pi$
$912$		0			0
$913$	−10.7639			−0.356233
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−23.6028	−	40.8813i	−0.779434	−	1.35002i
$918$		0			0
$919$	2.35622	−	4.08110i	0.0777246	−	0.134623i	−0.824543	−	0.565799i	$-0.808568\pi$
$919$	2.35622	−	4.08110i	0.0777246	−	0.134623i	0.902268	+	0.431176i	$0.141901\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	29.8682			0.983124
$924$		0			0
$925$	−3.36475	+	5.82791i	−0.110632	+	0.191621i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	10.5344			0.345621			0.172811	−	0.984955i	$-0.444715\pi$
$929$	10.5344			0.345621			0.172811	+	0.984955i	$0.444715\pi$
$930$		0			0
$931$	0.307829	+	0.533176i	0.0100887	+	0.0174741i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−17.6101			−0.575911
$936$		0			0
$937$	13.6936			0.447350			0.223675	−	0.974664i	$-0.428195\pi$
$937$	13.6936			0.447350			0.223675	+	0.974664i	$0.428195\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−39.5055			−1.28784			−0.643922	−	0.765092i	$-0.722694\pi$
$941$	−39.5055			−1.28784			−0.643922	+	0.765092i	$0.722694\pi$
$942$		0			0
$943$	−14.3496			−0.467287
$944$		0			0
$945$		0			0
$946$		0			0
$947$	15.2860			0.496728			0.248364	−	0.968667i	$-0.420107\pi$
$947$	15.2860			0.496728			0.248364	+	0.968667i	$0.420107\pi$
$948$		0			0
$949$	2.68868	+	4.65692i	0.0872781	+	0.151170i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	32.3875			1.04913			0.524567	−	0.851369i	$-0.324227\pi$
$953$	32.3875			1.04913			0.524567	+	0.851369i	$0.324227\pi$
$954$		0			0
$955$	32.7571	−	56.7370i	1.06000	−	1.83597i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	14.3078	+	24.7819i	0.462024	+	0.800249i
$960$		0			0
$961$	−32.5694	+	56.4119i	−1.05063	+	1.81974i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	30.1057			0.969137
$966$		0			0
$967$	2.41305	+	4.17952i	0.0775985	+	0.134404i	0.902213	−	0.431290i	$-0.141941\pi$
$967$	2.41305	+	4.17952i	0.0775985	+	0.134404i	−0.824615	+	0.565695i	$0.808608\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−6.12181	−	10.6033i	−0.196458	−	0.340276i	0.750919	−	0.660394i	$-0.229611\pi$
$971$	−6.12181	−	10.6033i	−0.196458	−	0.340276i	−0.947378	+	0.320118i	$0.896277\pi$
$972$		0			0
$973$	−4.18213	−	7.24366i	−0.134073	−	0.232221i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	20.3490	−	35.2456i	0.651024	−	1.12761i	−0.331851	−	0.943332i	$-0.607673\pi$
$977$	20.3490	−	35.2456i	0.651024	−	1.12761i	0.982875	−	0.184274i	$-0.0589934\pi$
$978$		0			0
$979$	−3.00557	−	5.20580i	−0.0960585	−	0.166378i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−38.0387			−1.21325			−0.606624	−	0.794989i	$-0.707477\pi$
$983$	−38.0387			−1.21325			−0.606624	+	0.794989i	$0.707477\pi$
$984$		0			0
$985$	33.2124	+	57.5256i	1.05824	+	1.83292i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−8.93822	+	15.4814i	−0.284219	+	0.492281i
$990$		0			0
$991$	44.9074			1.42653			0.713265	−	0.700895i	$-0.247216\pi$
$991$	44.9074			1.42653			0.713265	+	0.700895i	$0.247216\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	16.0996	−	27.8853i	0.510390	−	0.884022i
$996$		0			0
$997$	4.11825			0.130426			0.0652132	−	0.997871i	$-0.479227\pi$
$997$	4.11825			0.130426			0.0652132	+	0.997871i	$0.479227\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2412.2.l.e.1369.4		8
3.2	odd	2		804.2.i.d.565.1	yes	8
67.37	even	3	inner	2412.2.l.e.37.4		8
201.104	odd	6		804.2.i.d.37.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.i.d.37.1	✓	8	201.104	odd	6
804.2.i.d.565.1	yes	8	3.2	odd	2
2412.2.l.e.37.4		8	67.37	even	3	inner
2412.2.l.e.1369.4		8	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 2412 = 2^{2} \cdot 3^{2} \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2412.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.60354 q^{5} +(-1.30177 - 2.25473i) q^{7} +O(q^{10})\)	\(q+2.60354 q^{5} +(-1.30177 - 2.25473i) q^{7} +(-1.00000 - 1.73205i) q^{11} +(2.19098 - 3.79488i) q^{13} +(1.69098 - 2.92886i) q^{17} +(-1.38921 + 2.40618i) q^{19} +(0.798983 - 1.38388i) q^{23} +1.77841 q^{25} +(-2.10075 - 3.63861i) q^{29} +(4.90252 + 8.49142i) q^{31} +(-3.38921 - 5.87028i) q^{35} +(-1.89199 + 3.27703i) q^{37} +(-4.48996 - 7.77684i) q^{41} -11.1870 q^{43} +(-4.48996 - 7.77684i) q^{47} +(0.110793 - 0.191900i) q^{49} -0.618048 q^{53} +(-2.60354 - 4.50946i) q^{55} -3.18045 q^{59} +(7.38474 - 12.7907i) q^{61} +(5.70429 - 9.88012i) q^{65} +(-4.38642 + 6.91081i) q^{67} +(3.40809 + 5.90299i) q^{71} +(-0.613580 + 1.06275i) q^{73} +(-2.60354 + 4.50946i) q^{77} +(5.01610 + 8.68814i) q^{79} +(2.69098 - 4.66091i) q^{83} +(4.40252 - 7.62539i) q^{85} +3.00557 q^{89} -11.4086 q^{91} +(-3.61685 + 6.26457i) q^{95} +(1.99721 - 3.45928i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{5} + q^{7}+O(q^{10}) \) 8 * q - 2 * q^5 + q^7	\( 8 q - 2 q^{5} + q^{7} - 8 q^{11} - 4 q^{17} - 5 q^{19} - q^{23} + 2 q^{25} + 2 q^{29} + 9 q^{31} - 21 q^{35} - 5 q^{37} - 11 q^{41} + 6 q^{43} - 11 q^{47} + 7 q^{49} - 40 q^{53} + 2 q^{55} - 28 q^{59} + 20 q^{61} + 4 q^{65} - 33 q^{67} - 11 q^{71} - 7 q^{73} + 2 q^{77} + 12 q^{79} + 4 q^{83} + 5 q^{85} + 16 q^{89} - 8 q^{91} + 18 q^{95} + 20 q^{97}+O(q^{100}) \) 8 * q - 2 * q^5 + q^7 - 8 * q^11 - 4 * q^17 - 5 * q^19 - q^23 + 2 * q^25 + 2 * q^29 + 9 * q^31 - 21 * q^35 - 5 * q^37 - 11 * q^41 + 6 * q^43 - 11 * q^47 + 7 * q^49 - 40 * q^53 + 2 * q^55 - 28 * q^59 + 20 * q^61 + 4 * q^65 - 33 * q^67 - 11 * q^71 - 7 * q^73 + 2 * q^77 + 12 * q^79 + 4 * q^83 + 5 * q^85 + 16 * q^89 - 8 * q^91 + 18 * q^95 + 20 * q^97

Introduction

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