LMFDB - Embedded newform 108.5.g.a.89.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,5,Mod(17,108)]

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, 5]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("108.17");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	108.g (of order $6$, 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:	$11.1639560131$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
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} - 3x^{7} + 6x^{6} + 121x^{5} + 1104x^{4} - 1647x^{3} + 6529x^{2} + 85254x + 440076 $ x^8 - 3x^7 + 6x^6 + 121x^5 + 1104x^4 - 1647x^3 + 6529x^2 + 85254*x + 440076
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{10} $
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			89.4
Root			$-3.41053 - 2.74723i$ of defining polynomial
Character	$\chi$	$=$	108.89
Dual form			108.5.g.a.17.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(34.8718 - 20.1332i) q^{5} +(-7.38688 + 12.7945i) q^{7} +O(q^{10})$	$q+(34.8718 - 20.1332i) q^{5} +(-7.38688 + 12.7945i) q^{7} +(70.7125 + 40.8259i) q^{11} +(-139.053 - 240.848i) q^{13} -10.8854i q^{17} +532.815 q^{19} +(702.045 - 405.326i) q^{23} +(498.193 - 862.895i) q^{25} +(257.640 + 148.749i) q^{29} +(-97.5447 - 168.952i) q^{31} +594.887i q^{35} -2097.18 q^{37} +(1359.41 - 784.854i) q^{41} +(46.0863 - 79.8239i) q^{43} +(-1849.15 - 1067.61i) q^{47} +(1091.37 + 1890.30i) q^{49} +2579.42i q^{53} +3287.82 q^{55} +(-1349.04 + 778.868i) q^{59} +(-2685.97 + 4652.24i) q^{61} +(-9698.07 - 5599.19i) q^{65} +(-457.641 - 792.658i) q^{67} +8215.93i q^{71} -3438.63 q^{73} +(-1044.69 + 603.152i) q^{77} +(-2316.17 + 4011.73i) q^{79} +(5195.52 + 2999.63i) q^{83} +(-219.158 - 379.593i) q^{85} -8434.43i q^{89} +4108.69 q^{91} +(18580.2 - 10727.3i) q^{95} +(3015.58 - 5223.13i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 9 q^{5} + 13 q^{7}+O(q^{10}) $ 8 * q + 9 * q^5 + 13 * q^7	$ 8 q + 9 q^{5} + 13 q^{7} + 18 q^{11} - 5 q^{13} + 562 q^{19} + 1719 q^{23} + 353 q^{25} - 2115 q^{29} + 187 q^{31} + 16 q^{37} + 7920 q^{41} - 68 q^{43} - 13689 q^{47} - 327 q^{49} - 1818 q^{55} + 20052 q^{59} - 1937 q^{61} - 25965 q^{65} + 154 q^{67} - 7802 q^{73} + 25641 q^{77} - 2195 q^{79} - 37017 q^{83} - 3042 q^{85} + 15830 q^{91} + 37116 q^{95} + 7282 q^{97}+O(q^{100}) $ 8 * q + 9 * q^5 + 13 * q^7 + 18 * q^11 - 5 * q^13 + 562 * q^19 + 1719 * q^23 + 353 * q^25 - 2115 * q^29 + 187 * q^31 + 16 * q^37 + 7920 * q^41 - 68 * q^43 - 13689 * q^47 - 327 * q^49 - 1818 * q^55 + 20052 * q^59 - 1937 * q^61 - 25965 * q^65 + 154 * q^67 - 7802 * q^73 + 25641 * q^77 - 2195 * q^79 - 37017 * q^83 - 3042 * q^85 + 15830 * q^91 + 37116 * q^95 + 7282 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

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
$5$	34.8718	−	20.1332i	1.39487	−	0.805329i	0.401021	−	0.916069i	$-0.368655\pi$
$5$	34.8718	−	20.1332i	1.39487	−	0.805329i	0.993849	+	0.110740i	$0.0353221\pi$
$6$		0			0
$7$	−7.38688	+	12.7945i	−0.150753	+	0.261111i	−0.931504	−	0.363730i	$-0.881503\pi$
$7$	−7.38688	+	12.7945i	−0.150753	+	0.261111i	0.780752	+	0.624841i	$0.214836\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	70.7125	+	40.8259i	0.584400	+	0.337404i	0.762880	−	0.646540i	$-0.223785\pi$
$11$	70.7125	+	40.8259i	0.584400	+	0.337404i	−0.178480	+	0.983944i	$0.557118\pi$
$12$		0			0
$13$	−139.053	−	240.848i	−0.822801	−	1.42513i	−0.903588	−	0.428402i	$-0.859077\pi$
$13$	−139.053	−	240.848i	−0.822801	−	1.42513i	0.0807868	−	0.996731i	$-0.474257\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	10.8854i		−	0.0376658i	−0.999823	−	0.0188329i	$-0.994005\pi$
$17$		−	10.8854i		−	0.0376658i	0.999823	−	0.0188329i	$-0.00599505\pi$
$18$		0			0
$19$	532.815			1.47594			0.737971	−	0.674833i	$-0.235784\pi$
$19$	532.815			1.47594			0.737971	+	0.674833i	$0.235784\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	702.045	−	405.326i	1.32712	−	0.766211i	0.342264	−	0.939604i	$-0.388806\pi$
$23$	702.045	−	405.326i	1.32712	−	0.766211i	0.984853	+	0.173393i	$0.0554730\pi$
$24$		0			0
$25$	498.193	−	862.895i	0.797109	−	1.38063i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	257.640	+	148.749i	0.306350	+	0.176871i	0.645292	−	0.763936i	$-0.276736\pi$
$29$	257.640	+	148.749i	0.306350	+	0.176871i	−0.338942	+	0.940807i	$0.610069\pi$
$30$		0			0
$31$	−97.5447	−	168.952i	−0.101503	−	0.175809i	0.810801	−	0.585322i	$-0.199032\pi$
$31$	−97.5447	−	168.952i	−0.101503	−	0.175809i	−0.912304	+	0.409513i	$0.865699\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$			594.887i			0.485622i
$36$		0			0
$37$	−2097.18			−1.53191			−0.765954	−	0.642896i	$-0.777733\pi$
$37$	−2097.18			−1.53191			−0.765954	+	0.642896i	$0.777733\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	1359.41	−	784.854i	0.808689	−	0.466897i	−0.0378113	−	0.999285i	$-0.512039\pi$
$41$	1359.41	−	784.854i	0.808689	−	0.466897i	0.846500	+	0.532388i	$0.178705\pi$
$42$		0			0
$43$	46.0863	−	79.8239i	0.0249250	−	0.0431714i	−0.853294	−	0.521430i	$-0.825399\pi$
$43$	46.0863	−	79.8239i	0.0249250	−	0.0431714i	0.878219	+	0.478259i	$0.158732\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1849.15	−	1067.61i	−0.837098	−	0.483299i	0.0191789	−	0.999816i	$-0.493895\pi$
$47$	−1849.15	−	1067.61i	−0.837098	−	0.483299i	−0.856277	+	0.516517i	$0.827228\pi$
$48$		0			0
$49$	1091.37	+	1890.30i	0.454547	+	0.787299i
$50$		0			0
$51$		0			0
$52$		0			0
$53$			2579.42i			0.918271i	0.888366	+	0.459135i	$0.151841\pi$
$53$			2579.42i			0.918271i	−0.888366	+	0.459135i	$0.848159\pi$
$54$		0			0
$55$	3287.82			1.08688
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−1349.04	+	778.868i	−0.387544	+	0.223748i	−0.681095	−	0.732195i	$-0.738496\pi$
$59$	−1349.04	+	778.868i	−0.387544	+	0.223748i	0.293552	+	0.955943i	$0.405163\pi$
$60$		0			0
$61$	−2685.97	+	4652.24i	−0.721842	+	1.25027i	0.238419	+	0.971162i	$0.423371\pi$
$61$	−2685.97	+	4652.24i	−0.721842	+	1.25027i	−0.960261	+	0.279105i	$0.909962\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−9698.07	−	5599.19i	−2.29540	−	1.32525i
$66$		0			0
$67$	−457.641	−	792.658i	−0.101947	−	0.176578i	0.810540	−	0.585684i	$-0.199174\pi$
$67$	−457.641	−	792.658i	−0.101947	−	0.176578i	−0.912487	+	0.409106i	$0.865841\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			8215.93i			1.62982i	0.579587	+	0.814910i	$0.303214\pi$
$71$			8215.93i			1.62982i	−0.579587	+	0.814910i	$0.696786\pi$
$72$		0			0
$73$	−3438.63			−0.645267			−0.322634	−	0.946524i	$-0.604568\pi$
$73$	−3438.63			−0.645267			−0.322634	+	0.946524i	$0.604568\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1044.69	+	603.152i	−0.176200	+	0.101729i
$78$		0			0
$79$	−2316.17	+	4011.73i	−0.371122	+	0.642802i	−0.989738	−	0.142891i	$-0.954360\pi$
$79$	−2316.17	+	4011.73i	−0.371122	+	0.642802i	0.618617	+	0.785693i	$0.287693\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	5195.52	+	2999.63i	0.754176	+	0.435424i	0.827201	−	0.561907i	$-0.189932\pi$
$83$	5195.52	+	2999.63i	0.754176	+	0.435424i	−0.0730250	+	0.997330i	$0.523265\pi$
$84$		0			0
$85$	−219.158	−	379.593i	−0.0303333	−	0.0525389i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		−	8434.43i		−	1.06482i	−0.846487	−	0.532409i	$-0.821287\pi$
$89$		−	8434.43i		−	1.06482i	0.846487	−	0.532409i	$-0.178713\pi$
$90$		0			0
$91$	4108.69			0.496158
$92$		0			0
$93$		0			0
$94$		0			0
$95$	18580.2	−	10727.3i	2.05875	−	1.18862i
$96$		0			0
$97$	3015.58	−	5223.13i	0.320499	−	0.555121i	−0.660092	−	0.751185i	$-0.729483\pi$
$97$	3015.58	−	5223.13i	0.320499	−	0.555121i	0.980591	+	0.196064i	$0.0628160\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−5181.24	−	2991.39i	−0.507915	−	0.293245i	0.224061	−	0.974575i	$-0.428069\pi$
$101$	−5181.24	−	2991.39i	−0.507915	−	0.293245i	−0.731976	+	0.681330i	$0.761402\pi$
$102$		0			0
$103$	765.718	+	1326.26i	0.0721763	+	0.125013i	0.899855	−	0.436189i	$-0.143672\pi$
$103$	765.718	+	1326.26i	0.0721763	+	0.125013i	−0.827679	+	0.561202i	$0.810339\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			20499.8i			1.79053i	0.445536	+	0.895264i	$0.353013\pi$
$107$			20499.8i			1.79053i	−0.445536	+	0.895264i	$0.646987\pi$
$108$		0			0
$109$	−9404.21			−0.791534			−0.395767	−	0.918351i	$-0.629521\pi$
$109$	−9404.21			−0.791534			−0.395767	+	0.918351i	$0.629521\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−2598.59	+	1500.29i	−0.203507	+	0.117495i	−0.598290	−	0.801279i	$-0.704153\pi$
$113$	−2598.59	+	1500.29i	−0.203507	+	0.117495i	0.394783	+	0.918774i	$0.370820\pi$
$114$		0			0
$115$	16321.0	−	28268.8i	1.23410	−	2.13753i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	139.273	+	80.4092i	0.00983496	+	0.00567822i
$120$		0			0
$121$	−3987.00	−	6905.69i	−0.272317	−	0.471668i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		−	14954.4i		−	0.957081i
$126$		0			0
$127$	9817.40			0.608680			0.304340	−	0.952563i	$-0.401564\pi$
$127$	9817.40			0.608680			0.304340	+	0.952563i	$0.401564\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	553.194	−	319.387i	0.0322356	−	0.0186112i	−0.483796	−	0.875181i	$-0.660742\pi$
$131$	553.194	−	319.387i	0.0322356	−	0.0186112i	0.516031	+	0.856570i	$0.327409\pi$
$132$		0			0
$133$	−3935.84	+	6817.07i	−0.222502	+	0.385385i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	27716.3	+	16002.0i	1.47670	+	0.852575i	0.999654	−	0.0263010i	$-0.00837284\pi$
$137$	27716.3	+	16002.0i	1.47670	+	0.852575i	0.477050	+	0.878876i	$0.341706\pi$
$138$		0			0
$139$	2792.13	+	4836.11i	0.144513	+	0.250303i	0.929191	−	0.369600i	$-0.120505\pi$
$139$	2792.13	+	4836.11i	0.144513	+	0.250303i	−0.784678	+	0.619903i	$0.787172\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		−	22707.9i		−	1.11047i
$144$		0			0
$145$	11979.2			0.569758
$146$		0			0
$147$		0			0
$148$		0			0
$149$	7118.75	−	4110.01i	0.320650	−	0.185127i	−0.331032	−	0.943619i	$-0.607397\pi$
$149$	7118.75	−	4110.01i	0.320650	−	0.185127i	0.651682	+	0.758492i	$0.274064\pi$
$150$		0			0
$151$	−10236.0	+	17729.2i	−0.448927	+	0.777564i	−0.998316	−	0.0580020i	$-0.981527\pi$
$151$	−10236.0	+	17729.2i	−0.448927	+	0.777564i	0.549389	+	0.835566i	$0.314860\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−6803.11	−	3927.78i	−0.283168	−	0.163487i
$156$		0			0
$157$	−12896.9	−	22338.2i	−0.523224	−	0.906250i	−0.999635	−	0.0270273i	$-0.991396\pi$
$157$	−12896.9	−	22338.2i	−0.523224	−	0.906250i	0.476411	−	0.879223i	$-0.341937\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$			11976.4i			0.462034i
$162$		0			0
$163$	−16488.3			−0.620584			−0.310292	−	0.950641i	$-0.600427\pi$
$163$	−16488.3			−0.620584			−0.310292	+	0.950641i	$0.600427\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−34263.0	+	19781.8i	−1.22855	+	0.709304i	−0.966727	−	0.255812i	$-0.917657\pi$
$167$	−34263.0	+	19781.8i	−1.22855	+	0.709304i	−0.261824	+	0.965116i	$0.584324\pi$
$168$		0			0
$169$	−24391.2	+	42246.8i	−0.854004	+	1.47918i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−4204.22	−	2427.31i	−0.140473	−	0.0811022i	0.428116	−	0.903724i	$-0.359177\pi$
$173$	−4204.22	−	2427.31i	−0.140473	−	0.0811022i	−0.568589	+	0.822621i	$0.692511\pi$
$174$		0			0
$175$	7360.19	+	12748.2i	0.240333	+	0.416268i
$176$		0			0
$177$		0			0
$178$		0			0
$179$		−	4764.02i		−	0.148685i	−0.997233	−	0.0743425i	$-0.976314\pi$
$179$		−	4764.02i		−	0.148685i	0.997233	−	0.0743425i	$-0.0236858\pi$
$180$		0			0
$181$	3741.40			0.114203			0.0571014	−	0.998368i	$-0.481814\pi$
$181$	3741.40			0.114203			0.0571014	+	0.998368i	$0.481814\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−73132.4	+	42223.0i	−2.13681	+	1.23369i
$186$		0			0
$187$	444.406	−	769.734i	0.0127086	−	0.0220119i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−9003.63	−	5198.25i	−0.246803	−	0.142492i	0.371496	−	0.928434i	$-0.378845\pi$
$191$	−9003.63	−	5198.25i	−0.246803	−	0.142492i	−0.618300	+	0.785943i	$0.712178\pi$
$192$		0			0
$193$	21606.1	+	37422.9i	0.580045	+	1.00467i	0.995473	+	0.0950419i	$0.0302985\pi$
$193$	21606.1	+	37422.9i	0.580045	+	1.00467i	−0.415428	+	0.909626i	$0.636368\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	49899.7i		−	1.28578i	−0.765960	−	0.642889i	$-0.777736\pi$
$197$		−	49899.7i		−	1.28578i	0.765960	−	0.642889i	$-0.222264\pi$
$198$		0			0
$199$	−7613.76			−0.192262			−0.0961310	−	0.995369i	$-0.530647\pi$
$199$	−7613.76			−0.192262			−0.0961310	+	0.995369i	$0.530647\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−3806.32	+	2197.58i	−0.0923662	+	0.0533276i
$204$		0			0
$205$	31603.3	−	54738.5i	0.752011	−	1.30252i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	37676.6	+	21752.6i	0.862541	+	0.497988i
$210$		0			0
$211$	28097.7	+	48666.7i	0.631112	+	1.09312i	0.987325	+	0.158713i	$0.0507344\pi$
$211$	28097.7	+	48666.7i	0.631112	+	1.09312i	−0.356213	+	0.934405i	$0.615932\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		−	3711.47i		−	0.0802913i
$216$		0			0
$217$	2882.21			0.0612076
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−2621.72	+	1513.65i	−0.0536788	+	0.0309915i
$222$		0			0
$223$	−18961.1	+	32841.6i	−0.381289	+	0.660412i	−0.991247	−	0.132022i	$-0.957853\pi$
$223$	−18961.1	+	32841.6i	−0.381289	+	0.660412i	0.609958	+	0.792434i	$0.291186\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−8461.24	−	4885.10i	−0.164203	−	0.0948029i	0.415646	−	0.909526i	$-0.363555\pi$
$227$	−8461.24	−	4885.10i	−0.164203	−	0.0948029i	−0.579850	+	0.814723i	$0.696889\pi$
$228$		0			0
$229$	−18965.0	−	32848.4i	−0.361645	−	0.626387i	0.626587	−	0.779352i	$-0.284451\pi$
$229$	−18965.0	−	32848.4i	−0.361645	−	0.626387i	−0.988232	+	0.152964i	$0.951118\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	3372.35i		−	0.0621185i	−0.999518	−	0.0310592i	$-0.990112\pi$
$233$		−	3372.35i		−	0.0621185i	0.999518	−	0.0310592i	$-0.00988805\pi$
$234$		0			0
$235$	−85977.4			−1.55686
$236$		0			0
$237$		0			0
$238$		0			0
$239$	64618.9	−	37307.7i	1.13126	−	0.653135i	0.187011	−	0.982358i	$-0.440120\pi$
$239$	64618.9	−	37307.7i	1.13126	−	0.653135i	0.944252	+	0.329223i	$0.106787\pi$
$240$		0			0
$241$	12127.1	−	21004.7i	0.208796	−	0.361645i	−0.742540	−	0.669802i	$-0.766379\pi$
$241$	12127.1	−	21004.7i	0.208796	−	0.361645i	0.951336	+	0.308157i	$0.0997122\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	76115.8	+	43945.5i	1.26807	+	0.732120i
$246$		0			0
$247$	−74089.7	−	128327.i	−1.21441	−	2.10341i
$248$		0			0
$249$		0			0
$250$		0			0
$251$			25543.7i			0.405449i	0.979236	+	0.202724i	$0.0649795\pi$
$251$			25543.7i			0.405449i	−0.979236	+	0.202724i	$0.935020\pi$
$252$		0			0
$253$	66191.1			1.03409
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−18961.7	+	10947.6i	−0.287086	+	0.165749i	−0.636627	−	0.771172i	$-0.719671\pi$
$257$	−18961.7	+	10947.6i	−0.287086	+	0.165749i	0.349541	+	0.936921i	$0.386338\pi$
$258$		0			0
$259$	15491.6	−	26832.3i	0.230939	−	0.399998i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−6539.22	−	3775.42i	−0.0945397	−	0.0545825i	0.451985	−	0.892026i	$-0.350716\pi$
$263$	−6539.22	−	3775.42i	−0.0945397	−	0.0545825i	−0.546524	+	0.837443i	$0.684049\pi$
$264$		0			0
$265$	51932.1	+	89949.0i	0.739510	+	1.28087i
$266$		0			0
$267$		0			0
$268$		0			0
$269$		−	106275.i		−	1.46868i	−0.678780	−	0.734342i	$-0.737491\pi$
$269$		−	106275.i		−	1.46868i	0.678780	−	0.734342i	$-0.262509\pi$
$270$		0			0
$271$	82971.5			1.12977			0.564885	−	0.825170i	$-0.308920\pi$
$271$	82971.5			1.12977			0.564885	+	0.825170i	$0.308920\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	70456.9	−	40678.3i	0.931661	−	0.537895i
$276$		0			0
$277$	32616.8	−	56494.0i	0.425091	−	0.736280i	−0.571338	−	0.820715i	$-0.693575\pi$
$277$	32616.8	−	56494.0i	0.425091	−	0.736280i	0.996429	+	0.0844353i	$0.0269086\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	82142.7	+	47425.1i	1.04029	+	0.600614i	0.919917	−	0.392114i	$-0.128256\pi$
$281$	82142.7	+	47425.1i	1.04029	+	0.600614i	0.120378	+	0.992728i	$0.461590\pi$
$282$		0			0
$283$	−52834.0	−	91511.3i	−0.659692	−	1.14262i	−0.980695	−	0.195542i	$-0.937354\pi$
$283$	−52834.0	−	91511.3i	−0.659692	−	1.14262i	0.321004	−	0.947078i	$-0.395980\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			23190.5i			0.281544i
$288$		0			0
$289$	83402.5			0.998581
$290$		0			0
$291$		0			0
$292$		0			0
$293$	61404.7	−	35452.0i	0.715264	−	0.412958i	−0.0977432	−	0.995212i	$-0.531162\pi$
$293$	61404.7	−	35452.0i	0.715264	−	0.412958i	0.813007	+	0.582254i	$0.197829\pi$
$294$		0			0
$295$	−31362.3	+	54321.0i	−0.360382	+	0.624200i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−195243.	−	112724.i	−2.18391	−	1.26088i
$300$		0			0
$301$	680.869	+	1179.30i	0.00751503	+	0.0130164i
$302$		0			0
$303$		0			0
$304$		0			0
$305$			216309.i			2.32528i
$306$		0			0
$307$	27339.7			0.290079			0.145040	−	0.989426i	$-0.453669\pi$
$307$	27339.7			0.290079			0.145040	+	0.989426i	$0.453669\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−88117.5	+	50874.6i	−0.911048	+	0.525994i	−0.880768	−	0.473548i	$-0.842973\pi$
$311$	−88117.5	+	50874.6i	−0.911048	+	0.525994i	−0.0302797	+	0.999541i	$0.509640\pi$
$312$		0			0
$313$	22810.8	−	39509.5i	0.232837	−	0.403286i	−0.725805	−	0.687901i	$-0.758532\pi$
$313$	22810.8	−	39509.5i	0.232837	−	0.403286i	0.958642	+	0.284615i	$0.0918658\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−20556.7	−	11868.4i	−0.204567	−	0.118107i	0.394217	−	0.919017i	$-0.371016\pi$
$317$	−20556.7	−	11868.4i	−0.204567	−	0.118107i	−0.598784	+	0.800911i	$0.704349\pi$
$318$		0			0
$319$	12145.6	+	21036.8i	0.119354	+	0.206727i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	5799.91i		−	0.0555925i
$324$		0			0
$325$	−277102.			−2.62345
$326$		0			0
$327$		0			0
$328$		0			0
$329$	27318.9	−	15772.6i	0.252389	−	0.145717i
$330$		0			0
$331$	−63701.2	+	110334.i	−0.581422	+	1.00705i	0.413889	+	0.910327i	$0.364170\pi$
$331$	−63701.2	+	110334.i	−0.581422	+	1.00705i	−0.995311	+	0.0967256i	$0.969163\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−31917.5	−	18427.6i	−0.284406	−	0.164202i
$336$		0			0
$337$	8353.80	+	14469.2i	0.0735571	+	0.127405i	0.900458	−	0.434943i	$-0.143232\pi$
$337$	8353.80	+	14469.2i	0.0735571	+	0.127405i	−0.826901	+	0.562348i	$0.809898\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		−	15929.4i		−	0.136990i
$342$		0			0
$343$	−67719.0			−0.575602
$344$		0			0
$345$		0			0
$346$		0			0
$347$	153069.	−	88374.3i	1.27124	−	0.733951i	0.296019	−	0.955182i	$-0.404341\pi$
$347$	153069.	−	88374.3i	1.27124	−	0.733951i	0.975221	+	0.221231i	$0.0710074\pi$
$348$		0			0
$349$	−49219.9	+	85251.3i	−0.404101	+	0.699923i	−0.994216	−	0.107396i	$-0.965749\pi$
$349$	−49219.9	+	85251.3i	−0.404101	+	0.699923i	0.590116	+	0.807319i	$0.299082\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−108285.	−	62518.3i	−0.868997	−	0.501716i	−0.00198242	−	0.999998i	$-0.500631\pi$
$353$	−108285.	−	62518.3i	−0.868997	−	0.501716i	−0.867015	+	0.498282i	$0.833964\pi$
$354$		0			0
$355$	165413.	+	286504.i	1.31254	+	2.27339i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			130777.i			1.01471i	0.861737	+	0.507356i	$0.169377\pi$
$359$			130777.i			1.01471i	−0.861737	+	0.507356i	$0.830623\pi$
$360$		0			0
$361$	153571.			1.17840
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−119911.	+	69230.7i	−0.900064	+	0.519652i
$366$		0			0
$367$	64119.3	−	111058.i	0.476054	−	0.824550i	−0.523569	−	0.851983i	$-0.675400\pi$
$367$	64119.3	−	111058.i	0.476054	−	0.824550i	0.999624	+	0.0274329i	$0.00873325\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−33002.3	−	19053.9i	−0.239771	−	0.138432i
$372$		0			0
$373$	−31604.2	−	54740.0i	−0.227157	−	0.393448i	0.729807	−	0.683653i	$-0.239610\pi$
$373$	−31604.2	−	54740.0i	−0.227157	−	0.393448i	−0.956964	+	0.290205i	$0.906276\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	82736.1i		−	0.582120i
$378$		0			0
$379$	−101202.			−0.704547			−0.352273	−	0.935897i	$-0.614591\pi$
$379$	−101202.			−0.704547			−0.352273	+	0.935897i	$0.614591\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	16878.5	−	9744.83i	0.115063	−	0.0664319i	−0.441364	−	0.897328i	$-0.645505\pi$
$383$	16878.5	−	9744.83i	0.115063	−	0.0664319i	0.556427	+	0.830896i	$0.312172\pi$
$384$		0			0
$385$	−24286.8	+	42065.9i	−0.163851	+	0.283798i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−49519.1	−	28589.9i	−0.327245	−	0.188935i	0.327372	−	0.944895i	$-0.393837\pi$
$389$	−49519.1	−	28589.9i	−0.327245	−	0.188935i	−0.654617	+	0.755960i	$0.727170\pi$
$390$		0			0
$391$	−4412.14	−	7642.04i	−0.0288599	−	0.0499869i
$392$		0			0
$393$		0			0
$394$		0			0
$395$			186528.i			1.19550i
$396$		0			0
$397$	−75878.7			−0.481436			−0.240718	−	0.970595i	$-0.577383\pi$
$397$	−75878.7			−0.481436			−0.240718	+	0.970595i	$0.577383\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−210130.	+	121319.i	−1.30677	+	0.754464i	−0.981556	−	0.191176i	$-0.938770\pi$
$401$	−210130.	+	121319.i	−1.30677	+	0.754464i	−0.325215	+	0.945640i	$0.605437\pi$
$402$		0			0
$403$	−27127.9	+	46986.8i	−0.167034	+	0.289312i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−148297.	−	85619.2i	−0.895248	−	0.516871i
$408$		0			0
$409$	−60915.8	−	105509.i	−0.364153	−	0.630731i	0.624487	−	0.781035i	$-0.285308\pi$
$409$	−60915.8	−	105509.i	−0.364153	−	0.630731i	−0.988640	+	0.150304i	$0.951975\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		−	23013.6i		−	0.134923i
$414$		0			0
$415$	241569.			1.40264
$416$		0			0
$417$		0			0
$418$		0			0
$419$	107882.	−	62285.6i	0.614498	−	0.354780i	−0.160226	−	0.987080i	$-0.551222\pi$
$419$	107882.	−	62285.6i	0.614498	−	0.354780i	0.774724	+	0.632300i	$0.217889\pi$
$420$		0			0
$421$	−12647.9	+	21906.8i	−0.0713600	+	0.123599i	−0.899498	−	0.436926i	$-0.856067\pi$
$421$	−12647.9	+	21906.8i	−0.0713600	+	0.123599i	0.828138	+	0.560525i	$0.189401\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−9392.97	−	5423.03i	−0.0520026	−	0.0300237i
$426$		0			0
$427$	−39682.0	−	68731.2i	−0.217639	−	0.376962i
$428$		0			0
$429$		0			0
$430$		0			0
$431$			153800.i			0.827944i	0.910290	+	0.413972i	$0.135859\pi$
$431$			153800.i			0.827944i	−0.910290	+	0.413972i	$0.864141\pi$
$432$		0			0
$433$	112975.			0.602569			0.301285	−	0.953534i	$-0.402585\pi$
$433$	112975.			0.602569			0.301285	+	0.953534i	$0.402585\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	374060.	−	215963.i	1.95875	−	1.13088i
$438$		0			0
$439$	89083.3	−	154297.i	0.462239	−	0.800622i	−0.536833	−	0.843689i	$-0.680379\pi$
$439$	89083.3	−	154297.i	0.462239	−	0.800622i	0.999072	+	0.0430665i	$0.0137127\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	258569.	+	149285.i	1.31756	+	0.760691i	0.983335	−	0.181804i	$-0.0581935\pi$
$443$	258569.	+	149285.i	1.31756	+	0.760691i	0.334221	+	0.942495i	$0.391527\pi$
$444$		0			0
$445$	−169812.	−	294123.i	−0.857529	−	1.48528i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	201956.i		−	1.00176i	−0.865516	−	0.500881i	$-0.833009\pi$
$449$		−	201956.i		−	1.00176i	0.865516	−	0.500881i	$-0.166991\pi$
$450$		0			0
$451$	128169.			0.630131
$452$		0			0
$453$		0			0
$454$		0			0
$455$	143277.	−	82721.1i	0.692076	−	0.399570i
$456$		0			0
$457$	−147659.	+	255752.i	−0.707011	+	1.22458i	0.258949	+	0.965891i	$0.416624\pi$
$457$	−147659.	+	255752.i	−0.707011	+	1.22458i	−0.965961	+	0.258689i	$0.916710\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	171120.	+	98796.4i	0.805193	+	0.464878i	0.845284	−	0.534318i	$-0.179431\pi$
$461$	171120.	+	98796.4i	0.805193	+	0.464878i	−0.0400909	+	0.999196i	$0.512765\pi$
$462$		0			0
$463$	−43231.3	−	74878.8i	−0.201668	−	0.349299i	0.747398	−	0.664376i	$-0.231303\pi$
$463$	−43231.3	−	74878.8i	−0.201668	−	0.349299i	−0.949066	+	0.315078i	$0.897969\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	249159.i		−	1.14247i	−0.820788	−	0.571233i	$-0.806465\pi$
$467$		−	249159.i		−	1.14247i	0.820788	−	0.571233i	$-0.193535\pi$
$468$		0			0
$469$	13522.2			0.0614753
$470$		0			0
$471$		0			0
$472$		0			0
$473$	6517.76	−	3763.03i	0.0291324	−	0.0168196i
$474$		0			0
$475$	265445.	−	459763.i	1.17649	−	2.03773i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	363916.	+	210107.i	1.58610	+	0.915734i	0.993941	+	0.109911i	$0.0350566\pi$
$479$	363916.	+	210107.i	1.58610	+	0.915734i	0.592157	+	0.805823i	$0.298277\pi$
$480$		0			0
$481$	291620.	+	505101.i	1.26046	+	2.18317i
$482$		0			0
$483$		0			0
$484$		0			0
$485$		−	242853.i		−	1.03243i
$486$		0			0
$487$	−394498.			−1.66336			−0.831680	−	0.555255i	$-0.812621\pi$
$487$	−394498.			−1.66336			−0.831680	+	0.555255i	$0.812621\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−291929.	+	168545.i	−1.21092	+	0.699123i	−0.962959	−	0.269647i	$-0.913093\pi$
$491$	−291929.	+	168545.i	−1.21092	+	0.699123i	−0.247958	+	0.968771i	$0.579760\pi$
$492$		0			0
$493$	1619.19	−	2804.52i	0.00666199	−	0.0115389i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−105118.	−	60690.1i	−0.425565	−	0.245700i
$498$		0			0
$499$	−227950.	−	394821.i	−0.915458	−	1.58562i	−0.806230	−	0.591602i	$-0.798496\pi$
$499$	−227950.	−	394821.i	−0.915458	−	1.58562i	−0.109227	−	0.994017i	$-0.534838\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$			33893.3i			0.133961i	0.997754	+	0.0669804i	$0.0213365\pi$
$503$			33893.3i			0.133961i	−0.997754	+	0.0669804i	$0.978663\pi$
$504$		0			0
$505$	−240905.			−0.944635
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−186058.	+	107421.i	−0.718147	+	0.414622i	−0.814070	−	0.580766i	$-0.802753\pi$
$509$	−186058.	+	107421.i	−0.718147	+	0.414622i	0.0959233	+	0.995389i	$0.469420\pi$
$510$		0			0
$511$	25400.7	−	43995.4i	0.0972758	−	0.168487i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	53403.9	+	30832.7i	0.201353	+	0.116251i
$516$		0			0
$517$	−87171.9	−	150986.i	−0.326134	−	0.564880i
$518$		0			0
$519$		0			0
$520$		0			0
$521$			256109.i			0.943516i	0.881728	+	0.471758i	$0.156380\pi$
$521$			256109.i			0.943516i	−0.881728	+	0.471758i	$0.843620\pi$
$522$		0			0
$523$	372105.			1.36038			0.680192	−	0.733034i	$-0.261896\pi$
$523$	372105.			1.36038			0.680192	+	0.733034i	$0.261896\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1839.12	+	1061.81i	−0.00662198	+	0.00382320i
$528$		0			0
$529$	188657.	−	326764.i	0.674159	−	1.16768i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−378060.	−	218273.i	−1.33078	−	0.768327i
$534$		0			0
$535$	412726.	+	714863.i	1.44196	+	2.49755i
$536$		0			0
$537$		0			0
$538$		0			0
$539$			178224.i			0.613464i
$540$		0			0
$541$	38292.3			0.130833			0.0654164	−	0.997858i	$-0.479162\pi$
$541$	38292.3			0.130833			0.0654164	+	0.997858i	$0.479162\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−327941.	+	189337.i	−1.10409	+	0.637445i
$546$		0			0
$547$	−251103.	+	434923.i	−0.839223	+	1.45358i	0.0513228	+	0.998682i	$0.483656\pi$
$547$	−251103.	+	434923.i	−0.839223	+	1.45358i	−0.890545	+	0.454894i	$0.849677\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	137275.	+	79255.5i	0.452155	+	0.261052i
$552$		0			0
$553$	−34218.6	−	59268.3i	−0.111895	−	0.193808i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	601940.i		−	1.94018i	−0.242737	−	0.970092i	$-0.578045\pi$
$557$		−	601940.i		−	1.94018i	0.242737	−	0.970092i	$-0.421955\pi$
$558$		0			0
$559$	−25633.9			−0.0820333
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−135970.	+	78502.5i	−0.428970	+	0.247666i	−0.698908	−	0.715212i	$-0.746330\pi$
$563$	−135970.	+	78502.5i	−0.428970	+	0.247666i	0.269938	+	0.962878i	$0.412997\pi$
$564$		0			0
$565$	−60411.5	+	104636.i	−0.189244	+	0.327781i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	422713.	+	244054.i	1.30563	+	0.753808i	0.981364	−	0.192156i	$-0.0615481\pi$
$569$	422713.	+	244054.i	1.30563	+	0.753808i	0.324270	+	0.945965i	$0.394881\pi$
$570$		0			0
$571$	85604.0	+	148270.i	0.262556	+	0.454760i	0.966920	−	0.255078i	$-0.0821013\pi$
$571$	85604.0	+	148270.i	0.262556	+	0.454760i	−0.704365	+	0.709838i	$0.748768\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	807721.i		−	2.44301i
$576$		0			0
$577$	−120517.			−0.361990			−0.180995	−	0.983484i	$-0.557932\pi$
$577$	−120517.			−0.361990			−0.180995	+	0.983484i	$0.557932\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−76757.3	+	44315.9i	−0.227388	+	0.131283i
$582$		0			0
$583$	−105307.	+	182397.i	−0.309828	+	0.536638i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−40161.9	−	23187.5i	−0.116557	−	0.0672942i	0.440588	−	0.897709i	$-0.354770\pi$
$587$	−40161.9	−	23187.5i	−0.116557	−	0.0672942i	−0.557145	+	0.830415i	$0.688103\pi$
$588$		0			0
$589$	−51973.3	−	90020.3i	−0.149813	−	0.259484i
$590$		0			0
$591$		0			0
$592$		0			0
$593$			511267.i			1.45391i	0.686683	+	0.726957i	$0.259066\pi$
$593$			511267.i			1.45391i	−0.686683	+	0.726957i	$0.740934\pi$
$594$		0			0
$595$	6475.59			0.0182913
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−558562.	+	322486.i	−1.55675	+	0.898787i	−0.559180	+	0.829046i	$0.688884\pi$
$599$	−558562.	+	322486.i	−1.55675	+	0.898787i	−0.997565	+	0.0697410i	$0.977783\pi$
$600$		0			0
$601$	−296605.	+	513735.i	−0.821163	+	1.42230i	0.0836541	+	0.996495i	$0.473341\pi$
$601$	−296605.	+	513735.i	−0.821163	+	1.42230i	−0.904817	+	0.425801i	$0.859992\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−278067.	−	160542.i	−0.759695	−	0.438610i
$606$		0			0
$607$	−220510.	−	381935.i	−0.598482	−	1.03660i	−0.993045	−	0.117733i	$-0.962437\pi$
$607$	−220510.	−	381935.i	−0.598482	−	1.03660i	0.394563	−	0.918869i	$-0.370896\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$			593817.i			1.59063i
$612$		0			0
$613$	−397447.			−1.05769			−0.528845	−	0.848718i	$-0.677375\pi$
$613$	−397447.			−1.05769			−0.528845	+	0.848718i	$0.677375\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1401.15	−	808.953i	0.00368056	−	0.00212497i	−0.498159	−	0.867086i	$-0.665990\pi$
$617$	1401.15	−	808.953i	0.00368056	−	0.00212497i	0.501839	+	0.864961i	$0.332657\pi$
$618$		0			0
$619$	−274485.	+	475422.i	−0.716370	+	1.24079i	0.246059	+	0.969255i	$0.420864\pi$
$619$	−274485.	+	475422.i	−0.716370	+	1.24079i	−0.962429	+	0.271535i	$0.912469\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	107914.	+	62304.1i	0.278036	+	0.160524i
$624$		0			0
$625$	10290.7	+	17824.0i	0.0263442	+	0.0456294i
$626$		0			0
$627$		0			0
$628$		0			0
$629$			22828.7i			0.0577005i
$630$		0			0
$631$	378413.			0.950403			0.475202	−	0.879877i	$-0.342375\pi$
$631$	378413.			0.950403			0.475202	+	0.879877i	$0.342375\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	342350.	−	197656.i	0.849030	−	0.490188i
$636$		0			0
$637$	303517.	−	525707.i	0.748004	−	1.29558i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	62090.7	+	35848.1i	0.151116	+	0.0872469i	0.573651	−	0.819100i	$-0.305526\pi$
$641$	62090.7	+	35848.1i	0.151116	+	0.0872469i	−0.422535	+	0.906346i	$0.638860\pi$
$642$		0			0
$643$	−83582.4	−	144769.i	−0.202159	−	0.350149i	0.747065	−	0.664751i	$-0.231462\pi$
$643$	−83582.4	−	144769.i	−0.202159	−	0.350149i	−0.949224	+	0.314602i	$0.898129\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	678022.i		−	1.61970i	−0.586635	−	0.809852i	$-0.699548\pi$
$647$		−	678022.i		−	1.61970i	0.586635	−	0.809852i	$-0.300452\pi$
$648$		0			0
$649$	−127192.			−0.301974
$650$		0			0
$651$		0			0
$652$		0			0
$653$	256473.	−	148075.i	0.601472	−	0.347260i	−0.168149	−	0.985762i	$-0.553779\pi$
$653$	256473.	−	148075.i	0.601472	−	0.347260i	0.769620	+	0.638502i	$0.220446\pi$
$654$		0			0
$655$	12860.6	−	22275.2i	0.0299763	−	0.0519204i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−684065.	−	394945.i	−1.57517	−	0.909423i	−0.995520	−	0.0945561i	$-0.969857\pi$
$659$	−684065.	−	394945.i	−1.57517	−	0.909423i	−0.579648	−	0.814867i	$-0.696810\pi$
$660$		0			0
$661$	212744.	+	368484.i	0.486917	+	0.843365i	0.999887	−	0.0150418i	$-0.00478812\pi$
$661$	212744.	+	368484.i	0.486917	+	0.843365i	−0.512970	+	0.858407i	$0.671455\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$			316964.i			0.716749i
$666$		0			0
$667$	241167.			0.542083
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−379864.	+	219314.i	−0.843690	+	0.487104i
$672$		0			0
$673$	181403.	−	314199.i	0.400511	−	0.693705i	−0.593277	−	0.804998i	$-0.702166\pi$
$673$	181403.	−	314199.i	0.400511	−	0.693705i	0.993788	+	0.111294i	$0.0354994\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	747854.	+	431774.i	1.63170	+	0.942061i	0.983570	+	0.180528i	$0.0577808\pi$
$677$	747854.	+	431774.i	1.63170	+	0.942061i	0.648127	+	0.761532i	$0.275553\pi$
$678$		0			0
$679$	44551.4	+	77165.3i	0.0966322	+	0.167372i
$680$		0			0
$681$		0			0
$682$		0			0
$683$		−	323967.i		−	0.694479i	−0.937776	−	0.347239i	$-0.887119\pi$
$683$		−	323967.i		−	0.694479i	0.937776	−	0.347239i	$-0.112881\pi$
$684$		0			0
$685$	1.28869e6			2.74641
$686$		0			0
$687$		0			0
$688$		0			0
$689$	621248.	−	358678.i	1.30866	−	0.755554i
$690$		0			0
$691$	328629.	−	569202.i	0.688255	−	1.19209i	−0.284147	−	0.958781i	$-0.591710\pi$
$691$	328629.	−	569202.i	0.688255	−	1.19209i	0.972402	−	0.233312i	$-0.0749563\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	194733.	+	112429.i	0.403153	+	0.232760i
$696$		0			0
$697$	−8543.45	−	14797.7i	−0.0175860	−	0.0304599i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			695995.i			1.41635i	0.706038	+	0.708174i	$0.250481\pi$
$701$			695995.i			1.41635i	−0.706038	+	0.708174i	$0.749519\pi$
$702$		0			0
$703$	−1.11741e6			−2.26101
$704$		0			0
$705$		0			0
$706$		0			0
$707$	76546.5	−	44194.1i	0.153139	−	0.0884150i
$708$		0			0
$709$	215242.	−	372810.i	0.428188	−	0.741643i	−0.568525	−	0.822666i	$-0.692486\pi$
$709$	215242.	−	372810.i	0.428188	−	0.741643i	0.996712	+	0.0810236i	$0.0258189\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−136961.	−	79074.7i	−0.269413	−	0.155546i
$714$		0			0
$715$	−457183.	−	791864.i	−0.894289	−	1.54895i
$716$		0			0
$717$		0			0
$718$		0			0
$719$		−	435311.i		−	0.842059i	−0.907047	−	0.421029i	$-0.861669\pi$
$719$		−	435311.i		−	0.842059i	0.907047	−	0.421029i	$-0.138331\pi$
$720$		0			0
$721$	−22625.1			−0.0435231
$722$		0			0
$723$		0			0
$724$		0			0
$725$	256709.	−	148211.i	0.488388	−	0.281971i
$726$		0			0
$727$	3053.98	−	5289.64i	0.00577826	−	0.0100082i	−0.863122	−	0.504996i	$-0.831494\pi$
$727$	3053.98	−	5289.64i	0.00577826	−	0.0100082i	0.868900	+	0.494988i	$0.164827\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−868.916	−	501.669i	−0.00162608	−	0.000938820i
$732$		0			0
$733$	184878.	+	320218.i	0.344094	+	0.595989i	0.985189	−	0.171473i	$-0.0548526\pi$
$733$	184878.	+	320218.i	0.344094	+	0.595989i	−0.641094	+	0.767462i	$0.721519\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	74734.4i		−	0.137590i
$738$		0			0
$739$	−381087.			−0.697807			−0.348904	−	0.937159i	$-0.613446\pi$
$739$	−381087.			−0.697807			−0.348904	+	0.937159i	$0.613446\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	370613.	−	213974.i	0.671341	−	0.387599i	−0.125243	−	0.992126i	$-0.539971\pi$
$743$	370613.	−	213974.i	0.671341	−	0.387599i	0.796585	+	0.604527i	$0.206638\pi$
$744$		0			0
$745$	165496.	−	286647.i	0.298177	−	0.516457i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−262283.	−	151429.i	−0.467527	−	0.269927i
$750$		0			0
$751$	211790.	+	366831.i	0.375514	+	0.650408i	0.990404	−	0.138204i	$-0.0441330\pi$
$751$	211790.	+	366831.i	0.375514	+	0.650408i	−0.614890	+	0.788613i	$0.710800\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$			824333.i			1.44614i
$756$		0			0
$757$	−910525.			−1.58891			−0.794457	−	0.607321i	$-0.792244\pi$
$757$	−910525.			−1.58891			−0.794457	+	0.607321i	$0.792244\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	612058.	−	353372.i	1.05687	−	0.610187i	0.132309	−	0.991209i	$-0.457761\pi$
$761$	612058.	−	353372.i	1.05687	−	0.610187i	0.924566	+	0.381022i	$0.124428\pi$
$762$		0			0
$763$	69467.8	−	120322.i	0.119326	−	0.206678i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	375177.	+	216609.i	0.637743	+	0.368201i
$768$		0			0
$769$	−247932.	−	429430.i	−0.419256	−	0.726173i	0.576609	−	0.817021i	$-0.304376\pi$
$769$	−247932.	−	429430.i	−0.419256	−	0.726173i	−0.995865	+	0.0908474i	$0.971042\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$			834415.i			1.39644i	0.715882	+	0.698221i	$0.246025\pi$
$773$			834415.i			1.39644i	−0.715882	+	0.698221i	$0.753975\pi$
$774$		0			0
$775$	−194384.			−0.323637
$776$		0			0
$777$		0			0
$778$		0			0
$779$	724312.	−	418182.i	1.19358	−	0.689112i
$780$		0			0
$781$	−335422.	+	580968.i	−0.549908	+	0.952468i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−899478.	−	519314.i	−1.45966	−	0.842734i
$786$		0			0
$787$	−64818.1	−	112268.i	−0.104652	−	0.181262i	0.808944	−	0.587886i	$-0.200039\pi$
$787$	−64818.1	−	112268.i	−0.104652	−	0.181262i	−0.913596	+	0.406623i	$0.866706\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		−	44330.0i		−	0.0708508i
$792$		0			0
$793$	1.49398e6			2.37573
$794$		0			0
$795$		0			0
$796$		0			0
$797$	146748.	−	84725.1i	0.231024	−	0.133382i	−0.380021	−	0.924978i	$-0.624083\pi$
$797$	146748.	−	84725.1i	0.231024	−	0.133382i	0.611044	+	0.791597i	$0.290750\pi$
$798$		0			0
$799$	−11621.3	+	20128.7i	−0.0182038	+	0.0315299i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−243154.	−	140385.i	−0.377094	−	0.217716i
$804$		0			0
$805$	241123.	+	417637.i	0.372089	+	0.644477i
$806$		0			0
$807$		0			0
$808$		0			0
$809$		−	622158.i		−	0.950613i	−0.879820	−	0.475307i	$-0.842337\pi$
$809$		−	622158.i		−	0.950613i	0.879820	−	0.475307i	$-0.157663\pi$
$810$		0			0
$811$	543177.			0.825846			0.412923	−	0.910766i	$-0.364508\pi$
$811$	543177.			0.825846			0.412923	+	0.910766i	$0.364508\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−574976.	+	331962.i	−0.865634	+	0.499774i
$816$		0			0
$817$	24555.5	−	42531.3i	0.0367878	−	0.0637184i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−213399.	−	123206.i	−0.316597	−	0.182787i	0.333278	−	0.942829i	$-0.391845\pi$
$821$	−213399.	−	123206.i	−0.316597	−	0.182787i	−0.649875	+	0.760041i	$0.725179\pi$
$822$		0			0
$823$	−8586.13	−	14871.6i	−0.0126765	−	0.0219563i	0.859618	−	0.510938i	$-0.170702\pi$
$823$	−8586.13	−	14871.6i	−0.0126765	−	0.0219563i	−0.872294	+	0.488982i	$0.837368\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	471086.i		−	0.688794i	−0.938824	−	0.344397i	$-0.888083\pi$
$827$		−	471086.i		−	0.688794i	0.938824	−	0.344397i	$-0.111917\pi$
$828$		0			0
$829$	197808.			0.287829			0.143915	−	0.989590i	$-0.454031\pi$
$829$	197808.			0.287829			0.143915	+	0.989590i	$0.454031\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	20576.7	−	11880.0i	0.0296542	−	0.0171209i
$834$		0			0
$835$	−796542.	+	1.37965e6i	−1.14245	+	1.97877i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−216362.	−	124917.i	−0.307367	−	0.177458i	0.338381	−	0.941009i	$-0.390121\pi$
$839$	−216362.	−	124917.i	−0.307367	−	0.177458i	−0.645748	+	0.763551i	$0.723454\pi$
$840$		0			0
$841$	−309388.	−	535876.i	−0.437433	−	0.757656i
$842$		0			0
$843$		0			0
$844$		0			0
$845$			1.96429e6i			2.75102i
$846$		0			0
$847$	117806.			0.164210
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−1.47232e6	+	850042.i	−2.03302	+	1.17376i
$852$		0			0
$853$	−96671.0	+	167439.i	−0.132861	+	0.230122i	−0.924778	−	0.380506i	$-0.875750\pi$
$853$	−96671.0	+	167439.i	−0.132861	+	0.230122i	0.791917	+	0.610629i	$0.209083\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−860714.	−	496934.i	−1.17192	−	0.676607i	−0.217787	−	0.975996i	$-0.569884\pi$
$857$	−860714.	−	496934.i	−1.17192	−	0.676607i	−0.954131	+	0.299389i	$0.903217\pi$
$858$		0			0
$859$	508451.	+	880664.i	0.689070	+	1.19350i	0.972139	+	0.234404i	$0.0753139\pi$
$859$	508451.	+	880664.i	0.689070	+	1.19350i	−0.283070	+	0.959099i	$0.591353\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$			17982.7i			0.0241453i	0.999927	+	0.0120727i	$0.00384294\pi$
$863$			17982.7i			0.0241453i	−0.999927	+	0.0120727i	$0.996157\pi$
$864$		0			0
$865$	−195478.			−0.261256
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−327564.	+	189119.i	−0.433768	+	0.250436i
$870$		0			0
$871$	−127273.	+	220444.i	−0.167765	+	0.290577i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	191333.	+	110466.i	0.249905	+	0.144282i
$876$		0			0
$877$	−267680.	−	463636.i	−0.348030	−	0.602806i	0.637869	−	0.770145i	$-0.279816\pi$
$877$	−267680.	−	463636.i	−0.348030	−	0.602806i	−0.985899	+	0.167339i	$0.946483\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	348052.i		−	0.448427i	−0.974540	−	0.224214i	$-0.928019\pi$
$881$		−	348052.i		−	0.448427i	0.974540	−	0.224214i	$-0.0719813\pi$
$882$		0			0
$883$	−1.28216e6			−1.64445			−0.822227	−	0.569160i	$-0.807268\pi$
$883$	−1.28216e6			−1.64445			−0.822227	+	0.569160i	$0.807268\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−538578.	+	310948.i	−0.684544	+	0.395222i	−0.801565	−	0.597908i	$-0.795999\pi$
$887$	−538578.	+	310948.i	−0.684544	+	0.395222i	0.117021	+	0.993129i	$0.462666\pi$
$888$		0			0
$889$	−72520.0	+	125608.i	−0.0917602	+	0.158933i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−985254.	−	568837.i	−1.23551	−	0.713320i
$894$		0			0
$895$	−95915.0	−	166130.i	−0.119740	−	0.207396i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		−	58038.6i		−	0.0718121i
$900$		0			0
$901$	28078.1			0.0345874
$902$		0			0
$903$		0			0
$904$		0			0
$905$	130469.	−	75326.4i	0.159298	−	0.0919709i
$906$		0			0
$907$	626846.	−	1.08573e6i	0.761985	−	1.31980i	−0.179841	−	0.983696i	$-0.557558\pi$
$907$	626846.	−	1.08573e6i	0.761985	−	1.31980i	0.941826	−	0.336101i	$-0.109108\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	455921.	+	263226.i	0.549355	+	0.317170i	0.748862	−	0.662726i	$-0.230601\pi$
$911$	455921.	+	263226.i	0.549355	+	0.317170i	−0.199507	+	0.979896i	$0.563934\pi$
$912$		0			0
$913$	244925.	+	424223.i	0.293827	+	0.508923i
$914$		0			0
$915$		0			0
$916$		0			0
$917$			9437.09i			0.0112228i
$918$		0			0
$919$	317984.			0.376508			0.188254	−	0.982120i	$-0.439717\pi$
$919$	317984.			0.376508			0.188254	+	0.982120i	$0.439717\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	1.97879e6	−	1.14245e6i	2.32271	−	1.34102i
$924$		0			0
$925$	−1.04480e6	+	1.80965e6i	−1.22110	+	2.11500i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	1.27158e6	+	734148.i	1.47337	+	0.850652i	0.999551	−	0.0299688i	$-0.00954081\pi$
$929$	1.27158e6	+	734148.i	1.47337	+	0.850652i	0.473822	+	0.880621i	$0.342874\pi$
$930$		0			0
$931$	581497.	+	1.00718e6i	0.670885	+	1.16201i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		−	35789.3i		−	0.0409383i
$936$		0			0
$937$	−672991.			−0.766532			−0.383266	−	0.923638i	$-0.625201\pi$
$937$	−672991.			−0.766532			−0.383266	+	0.923638i	$0.625201\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	75861.4	−	43798.6i	0.0856725	−	0.0494631i	−0.456552	−	0.889697i	$-0.650916\pi$
$941$	75861.4	−	43798.6i	0.0856725	−	0.0494631i	0.542224	+	0.840234i	$0.317582\pi$
$942$		0			0
$943$	636243.	−	1.10200e6i	0.715483	−	1.23925i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−786357.	−	454003.i	−0.876839	−	0.506243i	−0.00722389	−	0.999974i	$-0.502299\pi$
$947$	−786357.	−	454003.i	−0.876839	−	0.506243i	−0.869615	+	0.493731i	$0.835633\pi$
$948$		0			0
$949$	478153.	+	828185.i	0.530927	+	0.919592i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	747370.i		−	0.822905i	−0.911431	−	0.411452i	$-0.865022\pi$
$953$		−	747370.i		−	0.822905i	0.911431	−	0.411452i	$-0.134978\pi$
$954$		0			0
$955$	−418630.			−0.459011
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−409473.	+	236410.i	−0.445234	+	0.257056i
$960$		0			0
$961$	442731.	−	766832.i	0.479394	−	0.830335i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	1.50689e6	+	870001.i	1.61818	+	0.934254i
$966$		0			0
$967$	−162017.	−	280622.i	−0.173264	−	0.300102i	0.766295	−	0.642489i	$-0.222098\pi$
$967$	−162017.	−	280622.i	−0.173264	−	0.300102i	−0.939559	+	0.342387i	$0.888765\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$		−	873822.i		−	0.926797i	−0.886150	−	0.463398i	$-0.846630\pi$
$971$		−	873822.i		−	0.926797i	0.886150	−	0.463398i	$-0.153370\pi$
$972$		0			0
$973$	−82500.5			−0.0871427
$974$		0			0
$975$		0			0
$976$		0			0
$977$	246498.	−	142316.i	0.258240	−	0.149095i	−0.365291	−	0.930893i	$-0.619031\pi$
$977$	246498.	−	142316.i	0.258240	−	0.149095i	0.623532	+	0.781798i	$0.285697\pi$
$978$		0			0
$979$	344343.	−	596419.i	0.359274	−	0.622280i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	306.104	+	176.729i	0.000316783	+	0.000182895i	0.500158	−	0.865934i	$-0.333275\pi$
$983$	306.104	+	176.729i	0.000316783	+	0.000182895i	−0.499842	+	0.866117i	$0.666608\pi$
$984$		0			0
$985$	−1.00464e6	−	1.74009e6i	−1.03547	−	1.79349i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		−	74719.9i		−	0.0763913i
$990$		0			0
$991$	1.22572e6			1.24808			0.624041	−	0.781392i	$-0.285490\pi$
$991$	1.22572e6			1.24808			0.624041	+	0.781392i	$0.285490\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−265505.	+	153290.i	−0.268180	+	0.154834i
$996$		0			0
$997$	663483.	−	1.14919e6i	0.667482	−	1.15611i	−0.311124	−	0.950369i	$-0.600705\pi$
$997$	663483.	−	1.14919e6i	0.667482	−	1.15611i	0.978606	−	0.205744i	$-0.0659613\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.5.g.a.89.4		8
3.2	odd	2		36.5.g.a.29.2	yes	8
4.3	odd	2		432.5.q.c.305.4		8
9.2	odd	6		324.5.c.a.161.1		8
9.4	even	3		36.5.g.a.5.2	✓	8
9.5	odd	6	inner	108.5.g.a.17.4		8
9.7	even	3		324.5.c.a.161.8		8
12.11	even	2		144.5.q.c.65.3		8
36.7	odd	6		1296.5.e.g.161.8		8
36.11	even	6		1296.5.e.g.161.1		8
36.23	even	6		432.5.q.c.17.4		8
36.31	odd	6		144.5.q.c.113.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.5.g.a.5.2	✓	8	9.4	even	3
36.5.g.a.29.2	yes	8	3.2	odd	2
108.5.g.a.17.4		8	9.5	odd	6	inner
108.5.g.a.89.4		8	1.1	even	1	trivial
144.5.q.c.65.3		8	12.11	even	2
144.5.q.c.113.3		8	36.31	odd	6
324.5.c.a.161.1		8	9.2	odd	6
324.5.c.a.161.8		8	9.7	even	3
432.5.q.c.17.4		8	36.23	even	6
432.5.q.c.305.4		8	4.3	odd	2
1296.5.e.g.161.1		8	36.11	even	6
1296.5.e.g.161.8		8	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:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	108.g (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(34.8718 - 20.1332i) q^{5} +(-7.38688 + 12.7945i) q^{7} +O(q^{10})\)	\(q+(34.8718 - 20.1332i) q^{5} +(-7.38688 + 12.7945i) q^{7} +(70.7125 + 40.8259i) q^{11} +(-139.053 - 240.848i) q^{13} -10.8854i q^{17} +532.815 q^{19} +(702.045 - 405.326i) q^{23} +(498.193 - 862.895i) q^{25} +(257.640 + 148.749i) q^{29} +(-97.5447 - 168.952i) q^{31} +594.887i q^{35} -2097.18 q^{37} +(1359.41 - 784.854i) q^{41} +(46.0863 - 79.8239i) q^{43} +(-1849.15 - 1067.61i) q^{47} +(1091.37 + 1890.30i) q^{49} +2579.42i q^{53} +3287.82 q^{55} +(-1349.04 + 778.868i) q^{59} +(-2685.97 + 4652.24i) q^{61} +(-9698.07 - 5599.19i) q^{65} +(-457.641 - 792.658i) q^{67} +8215.93i q^{71} -3438.63 q^{73} +(-1044.69 + 603.152i) q^{77} +(-2316.17 + 4011.73i) q^{79} +(5195.52 + 2999.63i) q^{83} +(-219.158 - 379.593i) q^{85} -8434.43i q^{89} +4108.69 q^{91} +(18580.2 - 10727.3i) q^{95} +(3015.58 - 5223.13i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 9 q^{5} + 13 q^{7}+O(q^{10}) \) 8 * q + 9 * q^5 + 13 * q^7	\( 8 q + 9 q^{5} + 13 q^{7} + 18 q^{11} - 5 q^{13} + 562 q^{19} + 1719 q^{23} + 353 q^{25} - 2115 q^{29} + 187 q^{31} + 16 q^{37} + 7920 q^{41} - 68 q^{43} - 13689 q^{47} - 327 q^{49} - 1818 q^{55} + 20052 q^{59} - 1937 q^{61} - 25965 q^{65} + 154 q^{67} - 7802 q^{73} + 25641 q^{77} - 2195 q^{79} - 37017 q^{83} - 3042 q^{85} + 15830 q^{91} + 37116 q^{95} + 7282 q^{97}+O(q^{100}) \) 8 * q + 9 * q^5 + 13 * q^7 + 18 * q^11 - 5 * q^13 + 562 * q^19 + 1719 * q^23 + 353 * q^25 - 2115 * q^29 + 187 * q^31 + 16 * q^37 + 7920 * q^41 - 68 * q^43 - 13689 * q^47 - 327 * q^49 - 1818 * q^55 + 20052 * q^59 - 1937 * q^61 - 25965 * q^65 + 154 * q^67 - 7802 * q^73 + 25641 * q^77 - 2195 * q^79 - 37017 * q^83 - 3042 * q^85 + 15830 * q^91 + 37116 * q^95 + 7282 * q^97

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