LMFDB - Embedded newform 108.4.e.a.73.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,4,Mod(37,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("108.37");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	108.e (of order $3$, degree $2$, not 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:	$6.37220628062$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.6831243.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 13x^{4} + 49x^{2} + 48 $ x^6 + 13x^4 + 49x^2 + 48
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{5} $
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			73.1
Root			$-1.23396i$ of defining polynomial
Character	$\chi$	$=$	108.73
Dual form			108.4.e.a.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-6.92194 - 11.9892i) q^{5} +(-15.3540 + 26.5939i) q^{7} +O(q^{10})$	$q+(-6.92194 - 11.9892i) q^{5} +(-15.3540 + 26.5939i) q^{7} +(-21.9523 + 38.0225i) q^{11} +(6.11853 + 10.5976i) q^{13} -76.0286 q^{17} -44.1789 q^{19} +(-39.3135 - 68.0930i) q^{23} +(-33.3265 + 57.7232i) q^{25} +(-46.3903 + 80.3504i) q^{29} +(71.5329 + 123.899i) q^{31} +425.118 q^{35} -32.4741 q^{37} +(-167.778 - 290.599i) q^{41} +(249.166 - 431.567i) q^{43} +(-140.882 + 244.016i) q^{47} +(-299.990 - 519.599i) q^{49} +628.565 q^{53} +607.810 q^{55} +(252.327 + 437.043i) q^{59} +(-185.951 + 322.076i) q^{61} +(84.7041 - 146.712i) q^{65} +(81.3304 + 140.868i) q^{67} -433.512 q^{71} -629.645 q^{73} +(-674.111 - 1167.59i) q^{77} +(-86.3649 + 149.588i) q^{79} +(-87.4288 + 151.431i) q^{83} +(526.265 + 911.518i) q^{85} -336.716 q^{89} -375.775 q^{91} +(305.804 + 529.668i) q^{95} +(-42.1594 + 73.0222i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{5} - 6 q^{7}+O(q^{10}) $ 6 * q - 6 * q^5 - 6 * q^7	$ 6 q - 6 q^{5} - 6 q^{7} - 51 q^{11} + 12 q^{13} + 222 q^{17} + 30 q^{19} - 210 q^{23} - 3 q^{25} - 456 q^{29} + 48 q^{31} + 1104 q^{35} - 96 q^{37} - 897 q^{41} + 129 q^{43} - 522 q^{47} - 225 q^{49} + 2208 q^{53} - 216 q^{55} - 453 q^{59} - 402 q^{61} - 1110 q^{65} - 213 q^{67} - 120 q^{71} + 750 q^{73} - 1128 q^{77} + 552 q^{79} + 612 q^{83} + 1188 q^{85} + 924 q^{89} - 264 q^{91} + 2184 q^{95} + 93 q^{97}+O(q^{100}) $ 6 * q - 6 * q^5 - 6 * q^7 - 51 * q^11 + 12 * q^13 + 222 * q^17 + 30 * q^19 - 210 * q^23 - 3 * q^25 - 456 * q^29 + 48 * q^31 + 1104 * q^35 - 96 * q^37 - 897 * q^41 + 129 * q^43 - 522 * q^47 - 225 * q^49 + 2208 * q^53 - 216 * q^55 - 453 * q^59 - 402 * q^61 - 1110 * q^65 - 213 * q^67 - 120 * q^71 + 750 * q^73 - 1128 * q^77 + 552 * q^79 + 612 * q^83 + 1188 * q^85 + 924 * q^89 - 264 * q^91 + 2184 * q^95 + 93 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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
$5$	−6.92194	−	11.9892i	−0.619117	−	1.07234i	−0.989647	−	0.143522i	$-0.954157\pi$
$5$	−6.92194	−	11.9892i	−0.619117	−	1.07234i	0.370530	−	0.928821i	$-0.379176\pi$
$6$		0			0
$7$	−15.3540	+	26.5939i	−0.829038	+	1.43594i	0.0697558	+	0.997564i	$0.477778\pi$
$7$	−15.3540	+	26.5939i	−0.829038	+	1.43594i	−0.898794	+	0.438372i	$0.855555\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−21.9523	+	38.0225i	−0.601715	+	1.04220i	0.390846	+	0.920456i	$0.372182\pi$
$11$	−21.9523	+	38.0225i	−0.601715	+	1.04220i	−0.992561	+	0.121745i	$0.961151\pi$
$12$		0			0
$13$	6.11853	+	10.5976i	0.130536	+	0.226096i	0.923883	−	0.382674i	$-0.124997\pi$
$13$	6.11853	+	10.5976i	0.130536	+	0.226096i	−0.793347	+	0.608770i	$0.791663\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−76.0286			−1.08468			−0.542342	−	0.840158i	$-0.682462\pi$
$17$	−76.0286			−1.08468			−0.542342	+	0.840158i	$0.682462\pi$
$18$		0			0
$19$	−44.1789			−0.533439			−0.266720	−	0.963774i	$-0.585940\pi$
$19$	−44.1789			−0.533439			−0.266720	+	0.963774i	$0.585940\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−39.3135	−	68.0930i	−0.356410	−	0.617321i	0.630948	−	0.775825i	$-0.282666\pi$
$23$	−39.3135	−	68.0930i	−0.356410	−	0.617321i	−0.987358	+	0.158504i	$0.949333\pi$
$24$		0			0
$25$	−33.3265	+	57.7232i	−0.266612	+	0.461786i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−46.3903	+	80.3504i	−0.297050	+	0.514506i	−0.975460	−	0.220178i	$-0.929336\pi$
$29$	−46.3903	+	80.3504i	−0.297050	+	0.514506i	0.678409	+	0.734684i	$0.262670\pi$
$30$		0			0
$31$	71.5329	+	123.899i	0.414442	+	0.717834i	0.995370	−	0.0961208i	$-0.0306435\pi$
$31$	71.5329	+	123.899i	0.414442	+	0.717834i	−0.580928	+	0.813955i	$0.697310\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	425.118			2.05309
$36$		0			0
$37$	−32.4741			−0.144289			−0.0721447	−	0.997394i	$-0.522984\pi$
$37$	−32.4741			−0.144289			−0.0721447	+	0.997394i	$0.522984\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−167.778	−	290.599i	−0.639084	−	1.10693i	−0.985634	−	0.168895i	$-0.945980\pi$
$41$	−167.778	−	290.599i	−0.639084	−	1.10693i	0.346550	−	0.938031i	$-0.387353\pi$
$42$		0			0
$43$	249.166	−	431.567i	0.883660	−	1.53054i	0.0364186	−	0.999337i	$-0.488405\pi$
$43$	249.166	−	431.567i	0.883660	−	1.53054i	0.847242	−	0.531208i	$-0.178262\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−140.882	+	244.016i	−0.437230	+	0.757305i	−0.997475	−	0.0710223i	$-0.977374\pi$
$47$	−140.882	+	244.016i	−0.437230	+	0.757305i	0.560244	+	0.828327i	$0.310707\pi$
$48$		0			0
$49$	−299.990	−	519.599i	−0.874608	−	1.51487i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	628.565			1.62906			0.814529	−	0.580123i	$-0.196995\pi$
$53$	628.565			1.62906			0.814529	+	0.580123i	$0.196995\pi$
$54$		0			0
$55$	607.810			1.49013
$56$		0			0
$57$		0			0
$58$		0			0
$59$	252.327	+	437.043i	0.556782	+	0.964375i	0.997762	+	0.0668584i	$0.0212976\pi$
$59$	252.327	+	437.043i	0.556782	+	0.964375i	−0.440980	+	0.897517i	$0.645369\pi$
$60$		0			0
$61$	−185.951	+	322.076i	−0.390304	+	0.676026i	−0.992489	−	0.122330i	$-0.960963\pi$
$61$	−185.951	+	322.076i	−0.390304	+	0.676026i	0.602186	+	0.798356i	$0.294297\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	84.7041	−	146.712i	0.161635	−	0.279960i
$66$		0			0
$67$	81.3304	+	140.868i	0.148300	+	0.256863i	0.930599	−	0.366040i	$-0.119287\pi$
$67$	81.3304	+	140.868i	0.148300	+	0.256863i	−0.782299	+	0.622903i	$0.785953\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−433.512			−0.724626			−0.362313	−	0.932056i	$-0.618013\pi$
$71$	−433.512			−0.724626			−0.362313	+	0.932056i	$0.618013\pi$
$72$		0			0
$73$	−629.645			−1.00951			−0.504756	−	0.863262i	$-0.668418\pi$
$73$	−629.645			−1.00951			−0.504756	+	0.863262i	$0.668418\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−674.111	−	1167.59i	−0.997689	−	1.72805i
$78$		0			0
$79$	−86.3649	+	149.588i	−0.122998	+	0.213038i	−0.920948	−	0.389684i	$-0.872584\pi$
$79$	−86.3649	+	149.588i	−0.122998	+	0.213038i	0.797951	+	0.602723i	$0.205917\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−87.4288	+	151.431i	−0.115621	+	0.200262i	−0.918028	−	0.396516i	$-0.870219\pi$
$83$	−87.4288	+	151.431i	−0.115621	+	0.200262i	0.802407	+	0.596778i	$0.203553\pi$
$84$		0			0
$85$	526.265	+	911.518i	0.671547	+	1.16315i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−336.716			−0.401032			−0.200516	−	0.979690i	$-0.564262\pi$
$89$	−336.716			−0.401032			−0.200516	+	0.979690i	$0.564262\pi$
$90$		0			0
$91$	−375.775			−0.432879
$92$		0			0
$93$		0			0
$94$		0			0
$95$	305.804	+	529.668i	0.330261	+	0.572029i
$96$		0			0
$97$	−42.1594	+	73.0222i	−0.0441303	+	0.0764358i	−0.887247	−	0.461295i	$-0.847385\pi$
$97$	−42.1594	+	73.0222i	−0.0441303	+	0.0764358i	0.843117	+	0.537731i	$0.180718\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−874.902	+	1515.38i	−0.861941	+	1.49293i	0.00811161	+	0.999967i	$0.497418\pi$
$101$	−874.902	+	1515.38i	−0.861941	+	1.49293i	−0.870053	+	0.492959i	$0.835915\pi$
$102$		0			0
$103$	−55.6978	−	96.4714i	−0.0532822	−	0.0922875i	0.838154	−	0.545433i	$-0.183635\pi$
$103$	−55.6978	−	96.4714i	−0.0532822	−	0.0922875i	−0.891436	+	0.453146i	$0.850302\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−895.520			−0.809095			−0.404548	−	0.914517i	$-0.632571\pi$
$107$	−895.520			−0.809095			−0.404548	+	0.914517i	$0.632571\pi$
$108$		0			0
$109$	−716.957			−0.630019			−0.315009	−	0.949089i	$-0.602008\pi$
$109$	−716.957			−0.630019			−0.315009	+	0.949089i	$0.602008\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	115.526	+	200.096i	0.0961746	+	0.166579i	0.910098	−	0.414393i	$-0.136006\pi$
$113$	115.526	+	200.096i	0.0961746	+	0.166579i	−0.813924	+	0.580972i	$0.802673\pi$
$114$		0			0
$115$	−544.252	+	942.672i	−0.441320	+	0.764388i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	1167.34	−	2021.90i	0.899245	−	1.55754i
$120$		0			0
$121$	−298.306	−	516.681i	−0.224122	−	0.388190i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−807.748			−0.577978
$126$		0			0
$127$	1715.22			1.19843			0.599217	−	0.800586i	$-0.295478\pi$
$127$	1715.22			1.19843			0.599217	+	0.800586i	$0.295478\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	666.435	+	1154.30i	0.444479	+	0.769859i	0.998016	−	0.0629650i	$-0.0200557\pi$
$131$	666.435	+	1154.30i	0.444479	+	0.769859i	−0.553537	+	0.832824i	$0.686722\pi$
$132$		0			0
$133$	678.323	−	1174.89i	0.442241	−	0.765984i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	1259.49	−	2181.50i	0.785443	−	1.36043i	−0.143292	−	0.989680i	$-0.545769\pi$
$137$	1259.49	−	2181.50i	0.785443	−	1.36043i	0.928734	−	0.370746i	$-0.120898\pi$
$138$		0			0
$139$	−311.442	−	539.433i	−0.190044	−	0.329166i	0.755220	−	0.655471i	$-0.227530\pi$
$139$	−311.442	−	539.433i	−0.190044	−	0.329166i	−0.945265	+	0.326305i	$0.894196\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−537.263			−0.314183
$144$		0			0
$145$	1284.44			0.735636
$146$		0			0
$147$		0			0
$148$		0			0
$149$	1204.47	+	2086.21i	0.662243	+	1.14704i	0.980025	+	0.198875i	$0.0637289\pi$
$149$	1204.47	+	2086.21i	0.662243	+	1.14704i	−0.317781	+	0.948164i	$0.602938\pi$
$150$		0			0
$151$	−33.8218	+	58.5810i	−0.0182277	+	0.0315712i	−0.874995	−	0.484131i	$-0.839136\pi$
$151$	−33.8218	+	58.5810i	−0.0182277	+	0.0315712i	0.856768	+	0.515703i	$0.172469\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	990.293	−	1715.24i	0.513176	−	0.888847i
$156$		0			0
$157$	2.19676	+	3.80490i	0.00111669	+	0.00193417i	0.866583	−	0.499033i	$-0.166311\pi$
$157$	2.19676	+	3.80490i	0.00111669	+	0.00193417i	−0.865467	+	0.500967i	$0.832978\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	2414.48			1.18191
$162$		0			0
$163$	−2863.88			−1.37617			−0.688087	−	0.725628i	$-0.741549\pi$
$163$	−2863.88			−1.37617			−0.688087	+	0.725628i	$0.741549\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	214.757	+	371.970i	0.0995114	+	0.172359i	0.911483	−	0.411339i	$-0.134939\pi$
$167$	214.757	+	371.970i	0.0995114	+	0.172359i	−0.811971	+	0.583698i	$0.801605\pi$
$168$		0			0
$169$	1023.63	−	1772.97i	0.465920	−	0.806998i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−1287.14	+	2229.40i	−0.565663	+	0.979756i	0.431325	+	0.902197i	$0.358046\pi$
$173$	−1287.14	+	2229.40i	−0.565663	+	0.979756i	−0.996988	+	0.0775599i	$0.975287\pi$
$174$		0			0
$175$	−1023.39	−	1772.56i	−0.442063	−	0.765676i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−807.448			−0.337159			−0.168580	−	0.985688i	$-0.553918\pi$
$179$	−807.448			−0.337159			−0.168580	+	0.985688i	$0.553918\pi$
$180$		0			0
$181$	4296.57			1.76443			0.882215	−	0.470847i	$-0.156052\pi$
$181$	4296.57			1.76443			0.882215	+	0.470847i	$0.156052\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	224.784	+	389.337i	0.0893321	+	0.154728i
$186$		0			0
$187$	1669.00	−	2890.79i	0.652671	−	1.13046i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−153.147	+	265.259i	−0.0580176	+	0.100489i	−0.893575	−	0.448913i	$-0.851811\pi$
$191$	−153.147	+	265.259i	−0.0580176	+	0.100489i	0.835558	+	0.549402i	$0.185145\pi$
$192$		0			0
$193$	856.177	+	1482.94i	0.319321	+	0.553080i	0.980347	−	0.197283i	$-0.0632119\pi$
$193$	856.177	+	1482.94i	0.319321	+	0.553080i	−0.661026	+	0.750363i	$0.729879\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	263.636			0.0953466			0.0476733	−	0.998863i	$-0.484819\pi$
$197$	263.636			0.0953466			0.0476733	+	0.998863i	$0.484819\pi$
$198$		0			0
$199$	−3835.87			−1.36642			−0.683211	−	0.730221i	$-0.739417\pi$
$199$	−3835.87			−1.36642			−0.683211	+	0.730221i	$0.739417\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−1424.55	−	2467.40i	−0.492532	−	0.853091i
$204$		0			0
$205$	−2322.69	+	4023.02i	−0.791336	+	1.37063i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	969.829	−	1679.79i	0.320978	−	0.555951i
$210$		0			0
$211$	2034.66	+	3524.14i	0.663848	+	1.14982i	0.979596	+	0.200976i	$0.0644112\pi$
$211$	2034.66	+	3524.14i	0.663848	+	1.14982i	−0.315748	+	0.948843i	$0.602255\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−6898.84			−2.18836
$216$		0			0
$217$	−4393.27			−1.37435
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−465.183	−	805.720i	−0.141591	−	0.245243i
$222$		0			0
$223$	−3078.07	+	5331.38i	−0.924318	+	1.60097i	−0.131664	+	0.991294i	$0.542032\pi$
$223$	−3078.07	+	5331.38i	−0.924318	+	1.60097i	−0.792654	+	0.609672i	$0.791301\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	12.1307	−	21.0110i	0.00354689	−	0.00614339i	−0.864247	−	0.503069i	$-0.832204\pi$
$227$	12.1307	−	21.0110i	0.00354689	−	0.00614339i	0.867793	+	0.496925i	$0.165538\pi$
$228$		0			0
$229$	316.209	+	547.691i	0.0912476	+	0.158045i	0.908036	−	0.418891i	$-0.137581\pi$
$229$	316.209	+	547.691i	0.0912476	+	0.158045i	−0.816789	+	0.576937i	$0.804248\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	3163.59			0.889502			0.444751	−	0.895654i	$-0.353292\pi$
$233$	3163.59			0.889502			0.444751	+	0.895654i	$0.353292\pi$
$234$		0			0
$235$	3900.72			1.08279
$236$		0			0
$237$		0			0
$238$		0			0
$239$	1110.57	+	1923.57i	0.300573	+	0.520608i	0.976266	−	0.216575i	$-0.0694887\pi$
$239$	1110.57	+	1923.57i	0.300573	+	0.520608i	−0.675693	+	0.737183i	$0.736155\pi$
$240$		0			0
$241$	300.730	−	520.879i	0.0803805	−	0.139223i	−0.823033	−	0.567994i	$-0.807720\pi$
$241$	300.730	−	520.879i	0.0803805	−	0.139223i	0.903413	+	0.428771i	$0.141053\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−4153.03	+	7193.26i	−1.08297	+	1.87576i
$246$		0			0
$247$	−270.310	−	468.191i	−0.0696332	−	0.120608i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−1350.71			−0.339665			−0.169833	−	0.985473i	$-0.554323\pi$
$251$	−1350.71			−0.339665			−0.169833	+	0.985473i	$0.554323\pi$
$252$		0			0
$253$	3452.09			0.857830
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−3521.95	−	6100.20i	−0.854838	−	1.48062i	−0.876795	−	0.480865i	$-0.840323\pi$
$257$	−3521.95	−	6100.20i	−0.854838	−	1.48062i	0.0219564	−	0.999759i	$-0.493010\pi$
$258$		0			0
$259$	498.607	−	863.613i	0.119621	−	0.207190i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	1162.13	−	2012.87i	0.272472	−	0.471935i	−0.697022	−	0.717050i	$-0.745492\pi$
$263$	1162.13	−	2012.87i	0.272472	−	0.471935i	0.969494	+	0.245114i	$0.0788255\pi$
$264$		0			0
$265$	−4350.89	−	7535.97i	−1.00858	−	1.74691i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	3675.87			0.833167			0.416584	−	0.909097i	$-0.363227\pi$
$269$	3675.87			0.833167			0.416584	+	0.909097i	$0.363227\pi$
$270$		0			0
$271$	−1881.48			−0.421741			−0.210871	−	0.977514i	$-0.567630\pi$
$271$	−1881.48			−0.421741			−0.210871	+	0.977514i	$0.567630\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−1463.19	−	2534.31i	−0.320849	−	0.555727i
$276$		0			0
$277$	−732.008	+	1267.87i	−0.158780	+	0.275015i	−0.934429	−	0.356149i	$-0.884089\pi$
$277$	−732.008	+	1267.87i	−0.158780	+	0.275015i	0.775649	+	0.631165i	$0.217423\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−4116.28	+	7129.61i	−0.873867	+	1.51358i	−0.0159023	+	0.999874i	$0.505062\pi$
$281$	−4116.28	+	7129.61i	−0.873867	+	1.51358i	−0.857965	+	0.513709i	$0.828271\pi$
$282$		0			0
$283$	−844.364	−	1462.48i	−0.177358	−	0.307192i	0.763617	−	0.645669i	$-0.223422\pi$
$283$	−844.364	−	1462.48i	−0.177358	−	0.307192i	−0.940975	+	0.338477i	$0.890088\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	10304.2			2.11930
$288$		0			0
$289$	867.343			0.176540
$290$		0			0
$291$		0			0
$292$		0			0
$293$	255.866	+	443.173i	0.0510166	+	0.0883633i	0.890406	−	0.455167i	$-0.150421\pi$
$293$	255.866	+	443.173i	0.0510166	+	0.0883633i	−0.839389	+	0.543531i	$0.817087\pi$
$294$		0			0
$295$	3493.18	−	6050.37i	0.689427	−	1.19412i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	481.082	−	833.258i	0.0930491	−	0.161166i
$300$		0			0
$301$	7651.37	+	13252.6i	1.46518	+	2.53776i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	5148.55			0.966575
$306$		0			0
$307$	−3171.98			−0.589690			−0.294845	−	0.955545i	$-0.595268\pi$
$307$	−3171.98			−0.589690			−0.294845	+	0.955545i	$0.595268\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	2530.39	+	4382.76i	0.461367	+	0.799112i	0.999029	−	0.0440487i	$-0.0140257\pi$
$311$	2530.39	+	4382.76i	0.461367	+	0.799112i	−0.537662	+	0.843160i	$0.680692\pi$
$312$		0			0
$313$	4732.92	−	8197.66i	0.854698	−	1.48038i	−0.0222263	−	0.999753i	$-0.507075\pi$
$313$	4732.92	−	8197.66i	0.854698	−	1.48038i	0.876925	−	0.480628i	$-0.159591\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	3208.57	−	5557.40i	0.568489	−	0.984652i	−0.428226	−	0.903671i	$-0.640861\pi$
$317$	3208.57	−	5557.40i	0.568489	−	0.984652i	0.996716	−	0.0809808i	$-0.0258052\pi$
$318$		0			0
$319$	−2036.75	−	3527.75i	−0.357479	−	0.619172i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	3358.86			0.578613
$324$		0			0
$325$	−815.637			−0.139210
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−4326.22	−	7493.23i	−0.724961	−	1.25567i
$330$		0			0
$331$	−3332.37	+	5771.83i	−0.553364	+	0.958455i	0.444665	+	0.895697i	$0.353323\pi$
$331$	−3332.37	+	5771.83i	−0.553364	+	0.958455i	−0.998029	+	0.0627575i	$0.980011\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	1125.93	−	1950.17i	0.183630	−	0.318056i
$336$		0			0
$337$	−5244.05	−	9082.95i	−0.847660	−	1.46819i	−0.883291	−	0.468825i	$-0.844678\pi$
$337$	−5244.05	−	9082.95i	−0.847660	−	1.46819i	0.0356314	−	0.999365i	$-0.488656\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−6281.25			−0.997503
$342$		0			0
$343$	7891.37			1.24226
$344$		0			0
$345$		0			0
$346$		0			0
$347$	1074.48	+	1861.05i	0.166228	+	0.287915i	0.937091	−	0.349086i	$-0.113508\pi$
$347$	1074.48	+	1861.05i	0.166228	+	0.287915i	−0.770863	+	0.637001i	$0.780175\pi$
$348$		0			0
$349$	1388.53	−	2405.00i	0.212969	−	0.368874i	−0.739673	−	0.672966i	$-0.765020\pi$
$349$	1388.53	−	2405.00i	0.212969	−	0.368874i	0.952642	+	0.304093i	$0.0983532\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	3898.72	−	6752.78i	0.587841	−	1.01817i	−0.406673	−	0.913574i	$-0.633311\pi$
$353$	3898.72	−	6752.78i	0.587841	−	1.01817i	0.994515	−	0.104597i	$-0.0333554\pi$
$354$		0			0
$355$	3000.75	+	5197.45i	0.448629	+	0.777047i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−2309.31			−0.339500			−0.169750	−	0.985487i	$-0.554296\pi$
$359$	−2309.31			−0.339500			−0.169750	+	0.985487i	$0.554296\pi$
$360$		0			0
$361$	−4907.22			−0.715443
$362$		0			0
$363$		0			0
$364$		0			0
$365$	4358.36	+	7548.91i	0.625006	+	1.08254i
$366$		0			0
$367$	3105.66	−	5379.16i	0.441728	−	0.765095i	−0.556090	−	0.831122i	$-0.687699\pi$
$367$	3105.66	−	5379.16i	0.441728	−	0.765095i	0.997818	+	0.0660271i	$0.0210324\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−9650.99	+	16716.0i	−1.35055	+	2.33922i
$372$		0			0
$373$	−4349.61	−	7533.75i	−0.603792	−	1.04580i	−0.992241	−	0.124328i	$-0.960323\pi$
$373$	−4349.61	−	7533.75i	−0.603792	−	1.04580i	0.388450	−	0.921470i	$-0.373011\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−1135.36			−0.155104
$378$		0			0
$379$	5954.77			0.807061			0.403531	−	0.914966i	$-0.367783\pi$
$379$	5954.77			0.807061			0.403531	+	0.914966i	$0.367783\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	2128.35	+	3686.41i	0.283952	+	0.491819i	0.972354	−	0.233510i	$-0.0750211\pi$
$383$	2128.35	+	3686.41i	0.283952	+	0.491819i	−0.688403	+	0.725329i	$0.741688\pi$
$384$		0			0
$385$	−9332.31	+	16164.0i	−1.23537	+	2.13973i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	801.019	−	1387.41i	0.104404	−	0.180834i	−0.809090	−	0.587684i	$-0.800040\pi$
$389$	801.019	−	1387.41i	0.104404	−	0.180834i	0.913495	+	0.406851i	$0.133373\pi$
$390$		0			0
$391$	2988.95	+	5177.02i	0.386593	+	0.669598i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	2391.25			0.304600
$396$		0			0
$397$	−7987.87			−1.00982			−0.504912	−	0.863171i	$-0.668475\pi$
$397$	−7987.87			−1.00982			−0.504912	+	0.863171i	$0.668475\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−3534.75	−	6122.36i	−0.440191	−	0.762434i	0.557512	−	0.830169i	$-0.311756\pi$
$401$	−3534.75	−	6122.36i	−0.440191	−	0.762434i	−0.997703	+	0.0677350i	$0.978423\pi$
$402$		0			0
$403$	−875.352	+	1516.15i	−0.108200	+	0.187407i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	712.881	−	1234.75i	0.0868211	−	0.150379i
$408$		0			0
$409$	5932.38	+	10275.2i	0.717207	+	1.24224i	0.962102	+	0.272689i	$0.0879129\pi$
$409$	5932.38	+	10275.2i	0.717207	+	1.24224i	−0.244896	+	0.969549i	$0.578754\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−15496.9			−1.84637
$414$		0			0
$415$	2420.71			0.286332
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−6171.30	−	10689.0i	−0.719541	−	1.24628i	−0.961182	−	0.275916i	$-0.911019\pi$
$419$	−6171.30	−	10689.0i	−0.719541	−	1.24628i	0.241641	−	0.970366i	$-0.422314\pi$
$420$		0			0
$421$	−2732.93	+	4733.58i	−0.316377	+	0.547982i	−0.979729	−	0.200326i	$-0.935800\pi$
$421$	−2732.93	+	4733.58i	−0.316377	+	0.547982i	0.663352	+	0.748308i	$0.269133\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	2533.77	−	4388.61i	0.289190	−	0.500892i
$426$		0			0
$427$	−5710.17	−	9890.30i	−0.647153	−	1.12090i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−8997.67			−1.00557			−0.502787	−	0.864410i	$-0.667692\pi$
$431$	−8997.67			−1.00557			−0.502787	+	0.864410i	$0.667692\pi$
$432$		0			0
$433$	−10967.4			−1.21723			−0.608615	−	0.793466i	$-0.708275\pi$
$433$	−10967.4			−1.21723			−0.608615	+	0.793466i	$0.708275\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	1736.83	+	3008.28i	0.190123	+	0.329303i
$438$		0			0
$439$	−3563.51	+	6172.18i	−0.387419	+	0.671029i	−0.992102	−	0.125437i	$-0.959967\pi$
$439$	−3563.51	+	6172.18i	−0.387419	+	0.671029i	0.604683	+	0.796467i	$0.293300\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	4434.28	−	7680.39i	0.475573	−	0.823716i	−0.524036	−	0.851696i	$-0.675574\pi$
$443$	4434.28	−	7680.39i	0.475573	−	0.823716i	0.999608	+	0.0279799i	$0.00890744\pi$
$444$		0			0
$445$	2330.73	+	4036.94i	0.248286	+	0.430043i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−9835.05			−1.03373			−0.516865	−	0.856067i	$-0.672901\pi$
$449$	−9835.05			−1.03373			−0.516865	+	0.856067i	$0.672901\pi$
$450$		0			0
$451$	14732.4			1.53819
$452$		0			0
$453$		0			0
$454$		0			0
$455$	2601.09	+	4505.23i	0.268003	+	0.464194i
$456$		0			0
$457$	4443.25	−	7695.93i	0.454806	−	0.787747i	−0.543871	−	0.839169i	$-0.683042\pi$
$457$	4443.25	−	7695.93i	0.454806	−	0.787747i	0.998677	+	0.0514218i	$0.0163753\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	932.894	−	1615.82i	0.0942499	−	0.163246i	−0.815045	−	0.579397i	$-0.803288\pi$
$461$	932.894	−	1615.82i	0.0942499	−	0.163246i	0.909295	+	0.416151i	$0.136621\pi$
$462$		0			0
$463$	6811.70	+	11798.2i	0.683729	+	1.18425i	0.973834	+	0.227259i	$0.0729763\pi$
$463$	6811.70	+	11798.2i	0.683729	+	1.18425i	−0.290105	+	0.956995i	$0.593690\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	9328.97			0.924397			0.462199	−	0.886776i	$-0.347061\pi$
$467$	9328.97			0.924397			0.462199	+	0.886776i	$0.347061\pi$
$468$		0			0
$469$	−4994.99			−0.491785
$470$		0			0
$471$		0			0
$472$		0			0
$473$	10939.5	+	18947.8i	1.06342	+	1.84190i
$474$		0			0
$475$	1472.33	−	2550.15i	0.142221	−	0.246335i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	1330.15	−	2303.89i	0.126881	−	0.219765i	−0.795586	−	0.605841i	$-0.792837\pi$
$479$	1330.15	−	2303.89i	0.126881	−	0.219765i	0.922467	+	0.386077i	$0.126170\pi$
$480$		0			0
$481$	−198.694	−	344.147i	−0.0188350	−	0.0326232i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	1167.30			0.109287
$486$		0			0
$487$	−20450.7			−1.90289			−0.951447	−	0.307813i	$-0.900403\pi$
$487$	−20450.7			−1.90289			−0.951447	+	0.307813i	$0.900403\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	10327.4	+	17887.7i	0.949228	+	1.64411i	0.747055	+	0.664762i	$0.231467\pi$
$491$	10327.4	+	17887.7i	0.949228	+	1.64411i	0.202173	+	0.979350i	$0.435200\pi$
$492$		0			0
$493$	3526.99	−	6108.92i	0.322206	−	0.558077i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	6656.15	−	11528.8i	0.600743	−	1.04052i
$498$		0			0
$499$	−8733.31	−	15126.5i	−0.783480	−	1.35703i	−0.929903	−	0.367805i	$-0.880109\pi$
$499$	−8733.31	−	15126.5i	−0.783480	−	1.35703i	0.146423	−	0.989222i	$-0.453224\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−19951.2			−1.76855			−0.884275	−	0.466966i	$-0.845347\pi$
$503$	−19951.2			−1.76855			−0.884275	+	0.466966i	$0.845347\pi$
$504$		0			0
$505$	24224.1			2.13457
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−3638.88	−	6302.73i	−0.316878	−	0.548848i	0.662957	−	0.748657i	$-0.269301\pi$
$509$	−3638.88	−	6302.73i	−0.316878	−	0.548848i	−0.979835	+	0.199809i	$0.935968\pi$
$510$		0			0
$511$	9667.57	−	16744.7i	0.836924	−	1.44959i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−771.074	+	1335.54i	−0.0659759	+	0.114274i
$516$		0			0
$517$	−6185.39	−	10713.4i	−0.526176	−	0.911364i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	11664.5			0.980866			0.490433	−	0.871479i	$-0.336839\pi$
$521$	11664.5			0.980866			0.490433	+	0.871479i	$0.336839\pi$
$522$		0			0
$523$	−8925.51			−0.746243			−0.373122	−	0.927782i	$-0.621713\pi$
$523$	−8925.51			−0.746243			−0.373122	+	0.927782i	$0.621713\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−5438.55	−	9419.84i	−0.449539	−	0.778624i
$528$		0			0
$529$	2992.39	−	5182.98i	0.245943	−	0.425986i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	2053.10	−	3556.08i	0.166848	−	0.288988i
$534$		0			0
$535$	6198.74	+	10736.5i	0.500925	+	0.867627i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	26341.9			2.10506
$540$		0			0
$541$	12334.1			0.980193			0.490097	−	0.871668i	$-0.336962\pi$
$541$	12334.1			0.980193			0.490097	+	0.871668i	$0.336962\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	4962.74	+	8595.71i	0.390056	+	0.675596i
$546$		0			0
$547$	−2284.81	+	3957.41i	−0.178595	+	0.309336i	−0.941400	−	0.337293i	$-0.890489\pi$
$547$	−2284.81	+	3957.41i	−0.178595	+	0.309336i	0.762804	+	0.646629i	$0.223822\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	2049.47	−	3549.79i	0.158458	−	0.274458i
$552$		0			0
$553$	−2652.09	−	4593.56i	−0.203939	−	0.353233i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	8154.40			0.620310			0.310155	−	0.950686i	$-0.399619\pi$
$557$	8154.40			0.620310			0.310155	+	0.950686i	$0.399619\pi$
$558$		0			0
$559$	6098.10			0.461399
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−8086.82	−	14006.8i	−0.605362	−	1.04852i	−0.991994	−	0.126284i	$-0.959695\pi$
$563$	−8086.82	−	14006.8i	−0.605362	−	1.04852i	0.386632	−	0.922234i	$-0.373638\pi$
$564$		0			0
$565$	1599.32	−	2770.11i	0.119087	−	0.206264i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−4548.76	+	7878.69i	−0.335139	+	0.580478i	−0.983512	−	0.180845i	$-0.942117\pi$
$569$	−4548.76	+	7878.69i	−0.335139	+	0.580478i	0.648372	+	0.761323i	$0.275450\pi$
$570$		0			0
$571$	1647.54	+	2853.63i	0.120749	+	0.209143i	0.920063	−	0.391770i	$-0.128137\pi$
$571$	1647.54	+	2853.63i	0.120749	+	0.209143i	−0.799314	+	0.600913i	$0.794804\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	5240.73			0.380093
$576$		0			0
$577$	15544.7			1.12155			0.560775	−	0.827968i	$-0.310503\pi$
$577$	15544.7			1.12155			0.560775	+	0.827968i	$0.310503\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−2684.76	−	4650.14i	−0.191709	−	0.332049i
$582$		0			0
$583$	−13798.4	+	23899.6i	−0.980229	+	1.69781i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−2344.33	+	4060.50i	−0.164840	+	0.285511i	−0.936598	−	0.350405i	$-0.886044\pi$
$587$	−2344.33	+	4060.50i	−0.164840	+	0.285511i	0.771759	+	0.635916i	$0.219377\pi$
$588$		0			0
$589$	−3160.25	−	5473.71i	−0.221079	−	0.382921i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−16637.6			−1.15215			−0.576075	−	0.817397i	$-0.695416\pi$
$593$	−16637.6			−1.15215			−0.576075	+	0.817397i	$0.695416\pi$
$594$		0			0
$595$	−32321.1			−2.22695
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−2933.73	−	5081.37i	−0.200115	−	0.346610i	0.748450	−	0.663191i	$-0.230798\pi$
$599$	−2933.73	−	5081.37i	−0.200115	−	0.346610i	−0.948565	+	0.316581i	$0.897465\pi$
$600$		0			0
$601$	−10337.9	+	17905.8i	−0.701649	+	1.21529i	0.266238	+	0.963907i	$0.414219\pi$
$601$	−10337.9	+	17905.8i	−0.701649	+	1.21529i	−0.967887	+	0.251385i	$0.919114\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−4129.71	+	7152.87i	−0.277515	+	0.480671i
$606$		0			0
$607$	−6303.86	−	10918.6i	−0.421525	−	0.730103i	0.574564	−	0.818460i	$-0.305172\pi$
$607$	−6303.86	−	10918.6i	−0.421525	−	0.730103i	−0.996089	+	0.0883567i	$0.971838\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−3447.97			−0.228298
$612$		0			0
$613$	12469.7			0.821608			0.410804	−	0.911724i	$-0.365248\pi$
$613$	12469.7			0.821608			0.410804	+	0.911724i	$0.365248\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	9293.48	+	16096.8i	0.606388	+	1.05030i	0.991830	+	0.127563i	$0.0407156\pi$
$617$	9293.48	+	16096.8i	0.606388	+	1.05030i	−0.385442	+	0.922732i	$0.625951\pi$
$618$		0			0
$619$	5972.96	−	10345.5i	0.387841	−	0.671761i	−0.604318	−	0.796743i	$-0.706554\pi$
$619$	5972.96	−	10345.5i	0.387841	−	0.671761i	0.992159	+	0.124983i	$0.0398876\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	5169.94	−	8954.60i	0.332471	−	0.575856i
$624$		0			0
$625$	9757.00	+	16899.6i	0.624448	+	1.08158i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	2468.96			0.156509
$630$		0			0
$631$	4285.35			0.270360			0.135180	−	0.990821i	$-0.456839\pi$
$631$	4285.35			0.270360			0.135180	+	0.990821i	$0.456839\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−11872.7	−	20564.0i	−0.741972	−	1.28513i
$636$		0			0
$637$	3671.00	−	6358.36i	0.228336	−	0.395490i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−10879.1	+	18843.2i	−0.670357	+	1.16109i	0.307446	+	0.951566i	$0.400526\pi$
$641$	−10879.1	+	18843.2i	−0.670357	+	1.16109i	−0.977803	+	0.209527i	$0.932808\pi$
$642$		0			0
$643$	3671.54	+	6359.30i	0.225181	+	0.390025i	0.956374	−	0.292146i	$-0.0943692\pi$
$643$	3671.54	+	6359.30i	0.225181	+	0.390025i	−0.731193	+	0.682171i	$0.761036\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−9483.24			−0.576236			−0.288118	−	0.957595i	$-0.593030\pi$
$647$	−9483.24			−0.576236			−0.288118	+	0.957595i	$0.593030\pi$
$648$		0			0
$649$	−22156.6			−1.34010
$650$		0			0
$651$		0			0
$652$		0			0
$653$	2392.09	+	4143.23i	0.143353	+	0.248295i	0.928757	−	0.370688i	$-0.120878\pi$
$653$	2392.09	+	4143.23i	0.143353	+	0.248295i	−0.785404	+	0.618984i	$0.787545\pi$
$654$		0			0
$655$	9226.05	−	15980.0i	0.550369	−	0.953266i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−16034.0	+	27771.6i	−0.947791	+	1.64162i	−0.197727	+	0.980257i	$0.563356\pi$
$659$	−16034.0	+	27771.6i	−0.947791	+	1.64162i	−0.750064	+	0.661365i	$0.769977\pi$
$660$		0			0
$661$	3762.64	+	6517.09i	0.221407	+	0.383488i	0.955235	−	0.295847i	$-0.0956019\pi$
$661$	3762.64	+	6517.09i	0.221407	+	0.383488i	−0.733829	+	0.679335i	$0.762269\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−18781.3			−1.09520
$666$		0			0
$667$	7295.07			0.423487
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−8164.08	−	14140.6i	−0.469703	−	0.813550i
$672$		0			0
$673$	3670.98	−	6358.32i	0.210261	−	0.364183i	−0.741535	−	0.670914i	$-0.765902\pi$
$673$	3670.98	−	6358.32i	0.210261	−	0.364183i	0.951796	+	0.306731i	$0.0992352\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	4760.52	−	8245.45i	0.270253	−	0.468092i	−0.698673	−	0.715441i	$-0.746226\pi$
$677$	4760.52	−	8245.45i	0.270253	−	0.468092i	0.968927	+	0.247348i	$0.0795592\pi$
$678$		0			0
$679$	−1294.63	−	2242.36i	−0.0731713	−	0.126736i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	1475.06			0.0826377			0.0413188	−	0.999146i	$-0.486844\pi$
$683$	1475.06			0.0826377			0.0413188	+	0.999146i	$0.486844\pi$
$684$		0			0
$685$	−34872.5			−1.94512
$686$		0			0
$687$		0			0
$688$		0			0
$689$	3845.89	+	6661.28i	0.212651	+	0.368323i
$690$		0			0
$691$	−17080.4	+	29584.0i	−0.940329	+	1.62870i	−0.175484	+	0.984482i	$0.556149\pi$
$691$	−17080.4	+	29584.0i	−0.940329	+	1.62870i	−0.764844	+	0.644215i	$0.777184\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−4311.56	+	7467.84i	−0.235319	+	0.407585i
$696$		0			0
$697$	12755.9	+	22093.8i	0.693205	+	1.20067i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	29427.2			1.58552			0.792759	−	0.609535i	$-0.208644\pi$
$701$	29427.2			1.58552			0.792759	+	0.609535i	$0.208644\pi$
$702$		0			0
$703$	1434.67			0.0769696
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−26866.5	−	46534.1i	−1.42916	−	2.47538i
$708$		0			0
$709$	−9846.43	+	17054.5i	−0.521566	+	0.903379i	0.478119	+	0.878295i	$0.341319\pi$
$709$	−9846.43	+	17054.5i	−0.521566	+	0.903379i	−0.999685	+	0.0250840i	$0.992015\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	5624.42	−	9741.79i	0.295423	−	0.511687i
$714$		0			0
$715$	3718.90	+	6441.32i	0.194516	+	0.336912i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	33746.9			1.75041			0.875206	−	0.483751i	$-0.160726\pi$
$719$	33746.9			1.75041			0.875206	+	0.483751i	$0.160726\pi$
$720$		0			0
$721$	3420.74			0.176692
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−3092.05	−	5355.60i	−0.158395	−	0.274347i
$726$		0			0
$727$	−10380.4	+	17979.4i	−0.529558	+	0.917221i	0.469848	+	0.882748i	$0.344309\pi$
$727$	−10380.4	+	17979.4i	−0.529558	+	0.917221i	−0.999406	+	0.0344737i	$0.989025\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−18943.7	+	32811.4i	−0.958492	+	1.66016i
$732$		0			0
$733$	−7122.02	−	12335.7i	−0.358878	−	0.621596i	0.628895	−	0.777490i	$-0.283507\pi$
$733$	−7122.02	−	12335.7i	−0.358878	−	0.621596i	−0.987774	+	0.155894i	$0.950174\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−7141.55			−0.356937
$738$		0			0
$739$	27490.2			1.36839			0.684196	−	0.729298i	$-0.260153\pi$
$739$	27490.2			1.36839			0.684196	+	0.729298i	$0.260153\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	18234.0	+	31582.3i	0.900326	+	1.55941i	0.827072	+	0.562096i	$0.190005\pi$
$743$	18234.0	+	31582.3i	0.900326	+	1.55941i	0.0732537	+	0.997313i	$0.476662\pi$
$744$		0			0
$745$	16674.6	−	28881.2i	0.820013	−	1.42030i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	13749.8	−	23815.4i	0.670771	−	1.16181i
$750$		0			0
$751$	−19341.5	−	33500.5i	−0.939791	−	1.62777i	−0.765860	−	0.643007i	$-0.777686\pi$
$751$	−19341.5	−	33500.5i	−0.939791	−	1.62777i	−0.173931	−	0.984758i	$-0.555647\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	936.449			0.0451402
$756$		0			0
$757$	37768.4			1.81337			0.906683	−	0.421813i	$-0.138606\pi$
$757$	37768.4			1.81337			0.906683	+	0.421813i	$0.138606\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−10406.6	−	18024.7i	−0.495714	−	0.858603i	0.504273	−	0.863544i	$-0.331760\pi$
$761$	−10406.6	−	18024.7i	−0.495714	−	0.858603i	−0.999988	+	0.00494154i	$0.998427\pi$
$762$		0			0
$763$	11008.2	−	19066.7i	0.522310	−	0.904667i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−3087.74	+	5348.12i	−0.145361	+	0.251772i
$768$		0			0
$769$	−3060.85	−	5301.55i	−0.143533	−	0.248607i	0.785291	−	0.619126i	$-0.212513\pi$
$769$	−3060.85	−	5301.55i	−0.143533	−	0.248607i	−0.928825	+	0.370519i	$0.879180\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	34251.2			1.59370			0.796850	−	0.604177i	$-0.206498\pi$
$773$	34251.2			1.59370			0.796850	+	0.604177i	$0.206498\pi$
$774$		0			0
$775$	−9535.78			−0.441981
$776$		0			0
$777$		0			0
$778$		0			0
$779$	7412.23	+	12838.4i	0.340912	+	0.590478i
$780$		0			0
$781$	9516.59	−	16483.2i	0.436018	−	0.755206i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	30.4117	−	52.6746i	0.00138273	−	0.00239495i
$786$		0			0
$787$	4561.34	+	7900.47i	0.206600	+	0.357842i	0.950641	−	0.310292i	$-0.100427\pi$
$787$	4561.34	+	7900.47i	0.206600	+	0.357842i	−0.744041	+	0.668134i	$0.767093\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−7095.12			−0.318930
$792$		0			0
$793$	−4550.97			−0.203795
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−5006.12	−	8670.85i	−0.222492	−	0.385367i	0.733072	−	0.680151i	$-0.238086\pi$
$797$	−5006.12	−	8670.85i	−0.222492	−	0.385367i	−0.955564	+	0.294784i	$0.904752\pi$
$798$		0			0
$799$	10711.1	−	18552.2i	0.474257	−	0.821437i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	13822.1	−	23940.7i	0.607438	−	1.05211i
$804$		0			0
$805$	−16712.9	−	28947.6i	−0.731741	−	1.26741i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−22375.5			−0.972413			−0.486207	−	0.873844i	$-0.661620\pi$
$809$	−22375.5			−0.972413			−0.486207	+	0.873844i	$0.661620\pi$
$810$		0			0
$811$	970.867			0.0420367			0.0210183	−	0.999779i	$-0.493309\pi$
$811$	970.867			0.0420367			0.0210183	+	0.999779i	$0.493309\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	19823.6	+	34335.5i	0.852013	+	1.47573i
$816$		0			0
$817$	−11007.9	+	19066.2i	−0.471379	+	0.816452i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	1667.20	−	2887.67i	0.0708717	−	0.122753i	−0.828412	−	0.560119i	$-0.810755\pi$
$821$	1667.20	−	2887.67i	0.0708717	−	0.122753i	0.899284	+	0.437366i	$0.144089\pi$
$822$		0			0
$823$	−1857.14	−	3216.67i	−0.0786585	−	0.136241i	0.824013	−	0.566571i	$-0.191730\pi$
$823$	−1857.14	−	3216.67i	−0.0786585	−	0.136241i	−0.902671	+	0.430331i	$0.858397\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	30744.8			1.29275			0.646374	−	0.763020i	$-0.276284\pi$
$827$	30744.8			1.29275			0.646374	+	0.763020i	$0.276284\pi$
$828$		0			0
$829$	−29789.6			−1.24805			−0.624026	−	0.781404i	$-0.714504\pi$
$829$	−29789.6			−1.24805			−0.624026	+	0.781404i	$0.714504\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	22807.8	+	39504.3i	0.948674	+	1.64315i
$834$		0			0
$835$	2973.07	−	5149.51i	0.123218	−	0.213421i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	16152.0	−	27976.1i	0.664635	−	1.15118i	−0.314749	−	0.949175i	$-0.601920\pi$
$839$	16152.0	−	27976.1i	0.664635	−	1.15118i	0.979384	−	0.202007i	$-0.0647464\pi$
$840$		0			0
$841$	7890.38	+	13666.5i	0.323522	+	0.560357i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−28341.9			−1.15384
$846$		0			0
$847$	18320.8			0.743222
$848$		0			0
$849$		0			0
$850$		0			0
$851$	1276.67	+	2211.26i	0.0514263	+	0.0890729i
$852$		0			0
$853$	8710.28	−	15086.7i	0.349630	−	0.605577i	−0.636554	−	0.771232i	$-0.719641\pi$
$853$	8710.28	−	15086.7i	0.349630	−	0.605577i	0.986184	+	0.165655i	$0.0529740\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−17241.9	+	29863.8i	−0.687248	+	1.19035i	0.285476	+	0.958386i	$0.407848\pi$
$857$	−17241.9	+	29863.8i	−0.687248	+	1.19035i	−0.972725	+	0.231963i	$0.925485\pi$
$858$		0			0
$859$	7587.22	+	13141.5i	0.301365	+	0.521980i	0.976445	−	0.215764i	$-0.0692243\pi$
$859$	7587.22	+	13141.5i	0.301365	+	0.521980i	−0.675080	+	0.737744i	$0.735891\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−19314.7			−0.761852			−0.380926	−	0.924605i	$-0.624395\pi$
$863$	−19314.7			−0.761852			−0.380926	+	0.924605i	$0.624395\pi$
$864$		0			0
$865$	35638.1			1.40085
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−3791.82	−	6567.62i	−0.148019	−	0.256376i
$870$		0			0
$871$	−995.244	+	1723.81i	−0.0387171	+	0.0670599i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	12402.2	−	21481.2i	0.479165	−	0.829939i
$876$		0			0
$877$	6872.38	+	11903.3i	0.264611	+	0.458320i	0.967462	−	0.253018i	$-0.0814231\pi$
$877$	6872.38	+	11903.3i	0.264611	+	0.458320i	−0.702851	+	0.711337i	$0.748090\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	13269.0			0.507429			0.253714	−	0.967279i	$-0.418348\pi$
$881$	13269.0			0.507429			0.253714	+	0.967279i	$0.418348\pi$
$882$		0			0
$883$	−5785.26			−0.220487			−0.110243	−	0.993905i	$-0.535163\pi$
$883$	−5785.26			−0.220487			−0.110243	+	0.993905i	$0.535163\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	669.412	+	1159.46i	0.0253401	+	0.0438903i	0.878417	−	0.477894i	$-0.158600\pi$
$887$	669.412	+	1159.46i	0.0253401	+	0.0438903i	−0.853077	+	0.521785i	$0.825266\pi$
$888$		0			0
$889$	−26335.5	+	45614.4i	−0.993548	+	1.72088i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	6224.04	−	10780.4i	0.233236	−	0.403976i
$894$		0			0
$895$	5589.11	+	9680.62i	0.208741	+	0.361550i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−13273.7			−0.492440
$900$		0			0
$901$	−47788.9			−1.76701
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−29740.6	−	51512.3i	−1.09239	−	1.89207i
$906$		0			0
$907$	6823.74	−	11819.1i	0.249811	−	0.432685i	−0.713662	−	0.700490i	$-0.752965\pi$
$907$	6823.74	−	11819.1i	0.249811	−	0.432685i	0.963473	+	0.267805i	$0.0862982\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	19600.7	−	33949.3i	0.712842	−	1.23468i	−0.250944	−	0.968002i	$-0.580741\pi$
$911$	19600.7	−	33949.3i	0.712842	−	1.23468i	0.963786	−	0.266677i	$-0.0859255\pi$
$912$		0			0
$913$	−3838.52	−	6648.52i	−0.139142	−	0.241001i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−40929.8			−1.47396
$918$		0			0
$919$	−4733.10			−0.169892			−0.0849459	−	0.996386i	$-0.527072\pi$
$919$	−4733.10			−0.169892			−0.0849459	+	0.996386i	$0.527072\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−2652.46	−	4594.19i	−0.0945901	−	0.163835i
$924$		0			0
$925$	1082.25	−	1874.51i	0.0384693	−	0.0666308i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−14666.4	+	25402.9i	−0.517964	+	0.897140i	0.481818	+	0.876271i	$0.339977\pi$
$929$	−14666.4	+	25402.9i	−0.517964	+	0.897140i	−0.999782	+	0.0208688i	$0.993357\pi$
$930$		0			0
$931$	13253.3	+	22955.3i	0.466550	+	0.808088i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−46210.9			−1.61632
$936$		0			0
$937$	−39028.8			−1.36074			−0.680371	−	0.732867i	$-0.738182\pi$
$937$	−39028.8			−1.36074			−0.680371	+	0.732867i	$0.738182\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−13316.2	−	23064.4i	−0.461314	−	0.799020i	0.537712	−	0.843128i	$-0.319289\pi$
$941$	−13316.2	−	23064.4i	−0.461314	−	0.799020i	−0.999027	+	0.0441083i	$0.985955\pi$
$942$		0			0
$943$	−13191.9	+	22849.0i	−0.455552	+	0.789040i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−25606.1	+	44351.1i	−0.878657	+	1.52188i	−0.0258406	+	0.999666i	$0.508226\pi$
$947$	−25606.1	+	44351.1i	−0.878657	+	1.52188i	−0.852816	+	0.522212i	$0.825107\pi$
$948$		0			0
$949$	−3852.50	−	6672.72i	−0.131778	−	0.228246i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	6350.46			0.215857			0.107928	−	0.994159i	$-0.465578\pi$
$953$	6350.46			0.215857			0.107928	+	0.994159i	$0.465578\pi$
$954$		0			0
$955$	4240.31			0.143679
$956$		0			0
$957$		0			0
$958$		0			0
$959$	38676.5	+	66989.6i	1.30232	+	2.25569i
$960$		0			0
$961$	4661.58	−	8074.09i	0.156476	−	0.271024i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	11852.8	−	20529.7i	0.395394	−	0.684843i
$966$		0			0
$967$	19773.1	+	34247.9i	0.657558	+	1.13892i	0.981246	+	0.192760i	$0.0617438\pi$
$967$	19773.1	+	34247.9i	0.657558	+	1.13892i	−0.323688	+	0.946164i	$0.604923\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	21043.4			0.695483			0.347742	−	0.937590i	$-0.386949\pi$
$971$	21043.4			0.695483			0.347742	+	0.937590i	$0.386949\pi$
$972$		0			0
$973$	19127.5			0.630215
$974$		0			0
$975$		0			0
$976$		0			0
$977$	14409.0	+	24957.2i	0.471838	+	0.817248i	0.999481	−	0.0322185i	$-0.0102572\pi$
$977$	14409.0	+	24957.2i	0.471838	+	0.817248i	−0.527642	+	0.849467i	$0.676924\pi$
$978$		0			0
$979$	7391.69	−	12802.8i	0.241307	−	0.417956i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−14611.8	+	25308.4i	−0.474105	+	0.821174i	−0.999560	−	0.0296474i	$-0.990562\pi$
$983$	−14611.8	+	25308.4i	−0.474105	+	0.821174i	0.525456	+	0.850821i	$0.323895\pi$
$984$		0			0
$985$	−1824.87	−	3160.77i	−0.0590307	−	0.102244i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−39182.3			−1.25978
$990$		0			0
$991$	1667.46			0.0534496			0.0267248	−	0.999643i	$-0.491492\pi$
$991$	1667.46			0.0534496			0.0267248	+	0.999643i	$0.491492\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	26551.7	+	45988.9i	0.845975	+	1.46527i
$996$		0			0
$997$	−16986.0	+	29420.6i	−0.539571	+	0.934564i	0.459356	+	0.888252i	$0.348080\pi$
$997$	−16986.0	+	29420.6i	−0.539571	+	0.934564i	−0.998927	+	0.0463119i	$0.985253\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.4.e.a.73.1		6
3.2	odd	2		36.4.e.a.25.1	yes	6
4.3	odd	2		432.4.i.d.289.1		6
9.2	odd	6		324.4.a.c.1.1		3
9.4	even	3	inner	108.4.e.a.37.1		6
9.5	odd	6		36.4.e.a.13.1	✓	6
9.7	even	3		324.4.a.d.1.3		3
12.11	even	2		144.4.i.d.97.3		6
36.7	odd	6		1296.4.a.w.1.3		3
36.11	even	6		1296.4.a.v.1.1		3
36.23	even	6		144.4.i.d.49.3		6
36.31	odd	6		432.4.i.d.145.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.4.e.a.13.1	✓	6	9.5	odd	6
36.4.e.a.25.1	yes	6	3.2	odd	2
108.4.e.a.37.1		6	9.4	even	3	inner
108.4.e.a.73.1		6	1.1	even	1	trivial
144.4.i.d.49.3		6	36.23	even	6
144.4.i.d.97.3		6	12.11	even	2
324.4.a.c.1.1		3	9.2	odd	6
324.4.a.d.1.3		3	9.7	even	3
432.4.i.d.145.1		6	36.31	odd	6
432.4.i.d.289.1		6	4.3	odd	2
1296.4.a.v.1.1		3	36.11	even	6
1296.4.a.w.1.3		3	36.7	odd	6

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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	108.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-6.92194 - 11.9892i) q^{5} +(-15.3540 + 26.5939i) q^{7} +O(q^{10})\)	\(q+(-6.92194 - 11.9892i) q^{5} +(-15.3540 + 26.5939i) q^{7} +(-21.9523 + 38.0225i) q^{11} +(6.11853 + 10.5976i) q^{13} -76.0286 q^{17} -44.1789 q^{19} +(-39.3135 - 68.0930i) q^{23} +(-33.3265 + 57.7232i) q^{25} +(-46.3903 + 80.3504i) q^{29} +(71.5329 + 123.899i) q^{31} +425.118 q^{35} -32.4741 q^{37} +(-167.778 - 290.599i) q^{41} +(249.166 - 431.567i) q^{43} +(-140.882 + 244.016i) q^{47} +(-299.990 - 519.599i) q^{49} +628.565 q^{53} +607.810 q^{55} +(252.327 + 437.043i) q^{59} +(-185.951 + 322.076i) q^{61} +(84.7041 - 146.712i) q^{65} +(81.3304 + 140.868i) q^{67} -433.512 q^{71} -629.645 q^{73} +(-674.111 - 1167.59i) q^{77} +(-86.3649 + 149.588i) q^{79} +(-87.4288 + 151.431i) q^{83} +(526.265 + 911.518i) q^{85} -336.716 q^{89} -375.775 q^{91} +(305.804 + 529.668i) q^{95} +(-42.1594 + 73.0222i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{5} - 6 q^{7}+O(q^{10}) \) 6 * q - 6 * q^5 - 6 * q^7	\( 6 q - 6 q^{5} - 6 q^{7} - 51 q^{11} + 12 q^{13} + 222 q^{17} + 30 q^{19} - 210 q^{23} - 3 q^{25} - 456 q^{29} + 48 q^{31} + 1104 q^{35} - 96 q^{37} - 897 q^{41} + 129 q^{43} - 522 q^{47} - 225 q^{49} + 2208 q^{53} - 216 q^{55} - 453 q^{59} - 402 q^{61} - 1110 q^{65} - 213 q^{67} - 120 q^{71} + 750 q^{73} - 1128 q^{77} + 552 q^{79} + 612 q^{83} + 1188 q^{85} + 924 q^{89} - 264 q^{91} + 2184 q^{95} + 93 q^{97}+O(q^{100}) \) 6 * q - 6 * q^5 - 6 * q^7 - 51 * q^11 + 12 * q^13 + 222 * q^17 + 30 * q^19 - 210 * q^23 - 3 * q^25 - 456 * q^29 + 48 * q^31 + 1104 * q^35 - 96 * q^37 - 897 * q^41 + 129 * q^43 - 522 * q^47 - 225 * q^49 + 2208 * q^53 - 216 * q^55 - 453 * q^59 - 402 * q^61 - 1110 * q^65 - 213 * q^67 - 120 * q^71 + 750 * q^73 - 1128 * q^77 + 552 * q^79 + 612 * q^83 + 1188 * q^85 + 924 * q^89 - 264 * q^91 + 2184 * q^95 + 93 * q^97

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