LMFDB - Embedded newform 108.5.g.a.89.2

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			89.2
Root			$4.23522 - 4.06612i$ of defining polynomial
Character	$\chi$	$=$	108.89
Dual form			108.5.g.a.17.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-10.6364 + 6.14094i) q^{5} +(7.14202 - 12.3703i) q^{7} +O(q^{10})$	$q+(-10.6364 + 6.14094i) q^{5} +(7.14202 - 12.3703i) q^{7} +(-90.2145 - 52.0854i) q^{11} +(-37.6173 - 65.1551i) q^{13} -341.998i q^{17} -706.329 q^{19} +(516.421 - 298.156i) q^{23} +(-237.078 + 410.630i) q^{25} +(-1127.90 - 651.194i) q^{29} +(-514.510 - 891.158i) q^{31} +175.435i q^{35} +563.132 q^{37} +(-85.8619 + 49.5724i) q^{41} +(448.257 - 776.404i) q^{43} +(-372.885 - 215.285i) q^{47} +(1098.48 + 1902.63i) q^{49} +5271.47i q^{53} +1279.41 q^{55} +(4883.74 - 2819.63i) q^{59} +(-565.626 + 979.693i) q^{61} +(800.227 + 462.012i) q^{65} +(676.412 + 1171.58i) q^{67} +5681.42i q^{71} +4236.54 q^{73} +(-1288.63 + 743.990i) q^{77} +(3067.71 - 5313.43i) q^{79} +(-6503.75 - 3754.94i) q^{83} +(2100.19 + 3637.64i) q^{85} +8721.70i q^{89} -1074.65 q^{91} +(7512.81 - 4337.53i) q^{95} +(-2720.65 + 4712.31i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−10.6364	+	6.14094i	−0.425457	+	0.245638i	−0.697409	−	0.716673i	$-0.745664\pi$
$5$	−10.6364	+	6.14094i	−0.425457	+	0.245638i	0.271952	+	0.962311i	$0.412331\pi$
$6$		0			0
$7$	7.14202	−	12.3703i	0.145756	−	0.252456i	−0.783899	−	0.620888i	$-0.786772\pi$
$7$	7.14202	−	12.3703i	0.145756	−	0.252456i	0.929655	+	0.368432i	$0.120105\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−90.2145	−	52.0854i	−0.745575	−	0.430458i	0.0785180	−	0.996913i	$-0.474981\pi$
$11$	−90.2145	−	52.0854i	−0.745575	−	0.430458i	−0.824093	+	0.566455i	$0.808315\pi$
$12$		0			0
$13$	−37.6173	−	65.1551i	−0.222588	−	0.385533i	0.733005	−	0.680223i	$-0.238117\pi$
$13$	−37.6173	−	65.1551i	−0.222588	−	0.385533i	−0.955593	+	0.294690i	$0.904784\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	341.998i		−	1.18338i	−0.806164	−	0.591692i	$-0.798460\pi$
$17$		−	341.998i		−	1.18338i	0.806164	−	0.591692i	$-0.201540\pi$
$18$		0			0
$19$	−706.329			−1.95659			−0.978295	−	0.207218i	$-0.933559\pi$
$19$	−706.329			−1.95659			−0.978295	+	0.207218i	$0.933559\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	516.421	−	298.156i	0.976222	−	0.563622i	0.0750946	−	0.997176i	$-0.476074\pi$
$23$	516.421	−	298.156i	0.976222	−	0.563622i	0.901127	+	0.433554i	$0.142741\pi$
$24$		0			0
$25$	−237.078	+	410.630i	−0.379324	+	0.657009i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−1127.90	−	651.194i	−1.34114	−	0.774309i	−0.354168	−	0.935182i	$-0.615236\pi$
$29$	−1127.90	−	651.194i	−1.34114	−	0.774309i	−0.986975	+	0.160873i	$0.948569\pi$
$30$		0			0
$31$	−514.510	−	891.158i	−0.535391	−	0.927324i	−0.999144	−	0.0413597i	$-0.986831\pi$
$31$	−514.510	−	891.158i	−0.535391	−	0.927324i	0.463754	−	0.885964i	$-0.346502\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$			175.435i			0.143212i
$36$		0			0
$37$	563.132			0.411346			0.205673	−	0.978621i	$-0.434062\pi$
$37$	563.132			0.411346			0.205673	+	0.978621i	$0.434062\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−85.8619	+	49.5724i	−0.0510779	+	0.0294898i	−0.525321	−	0.850904i	$-0.676055\pi$
$41$	−85.8619	+	49.5724i	−0.0510779	+	0.0294898i	0.474244	+	0.880394i	$0.342722\pi$
$42$		0			0
$43$	448.257	−	776.404i	0.242432	−	0.419905i	−0.718974	−	0.695037i	$-0.755388\pi$
$43$	448.257	−	776.404i	0.242432	−	0.419905i	0.961407	+	0.275132i	$0.0887215\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−372.885	−	215.285i	−0.168802	−	0.0974581i	0.413219	−	0.910632i	$-0.364405\pi$
$47$	−372.885	−	215.285i	−0.168802	−	0.0974581i	−0.582021	+	0.813174i	$0.697738\pi$
$48$		0			0
$49$	1098.48	+	1902.63i	0.457511	+	0.792432i
$50$		0			0
$51$		0			0
$52$		0			0
$53$			5271.47i			1.87664i	0.345773	+	0.938318i	$0.387617\pi$
$53$			5271.47i			1.87664i	−0.345773	+	0.938318i	$0.612383\pi$
$54$		0			0
$55$	1279.41			0.422947
$56$		0			0
$57$		0			0
$58$		0			0
$59$	4883.74	−	2819.63i	1.40297	−	0.810005i	0.408274	−	0.912859i	$-0.366131\pi$
$59$	4883.74	−	2819.63i	1.40297	−	0.810005i	0.994696	+	0.102854i	$0.0327975\pi$
$60$		0			0
$61$	−565.626	+	979.693i	−0.152009	+	0.263287i	−0.931966	−	0.362546i	$-0.881908\pi$
$61$	−565.626	+	979.693i	−0.152009	+	0.263287i	0.779957	+	0.625833i	$0.215241\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	800.227	+	462.012i	0.189403	+	0.109352i
$66$		0			0
$67$	676.412	+	1171.58i	0.150682	+	0.260989i	0.931478	−	0.363797i	$-0.118520\pi$
$67$	676.412	+	1171.58i	0.150682	+	0.260989i	−0.780796	+	0.624786i	$0.785186\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			5681.42i			1.12704i	0.826101	+	0.563522i	$0.190554\pi$
$71$			5681.42i			1.12704i	−0.826101	+	0.563522i	$0.809446\pi$
$72$		0			0
$73$	4236.54			0.794996			0.397498	−	0.917603i	$-0.369878\pi$
$73$	4236.54			0.794996			0.397498	+	0.917603i	$0.369878\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1288.63	+	743.990i	−0.217343	+	0.125483i
$78$		0			0
$79$	3067.71	−	5313.43i	0.491542	−	0.851375i	−0.508411	−	0.861115i	$-0.669767\pi$
$79$	3067.71	−	5313.43i	0.491542	−	0.851375i	0.999953	+	0.00973957i	$0.00310025\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−6503.75	−	3754.94i	−0.944077	−	0.545063i	−0.0528411	−	0.998603i	$-0.516828\pi$
$83$	−6503.75	−	3754.94i	−0.944077	−	0.545063i	−0.891236	+	0.453540i	$0.850161\pi$
$84$		0			0
$85$	2100.19	+	3637.64i	0.290684	+	0.503479i
$86$		0			0
$87$		0			0
$88$		0			0
$89$			8721.70i			1.10109i	0.834807	+	0.550543i	$0.185579\pi$
$89$			8721.70i			1.10109i	−0.834807	+	0.550543i	$0.814421\pi$
$90$		0			0
$91$	−1074.65			−0.129774
$92$		0			0
$93$		0			0
$94$		0			0
$95$	7512.81	−	4337.53i	0.832445	−	0.480612i
$96$		0			0
$97$	−2720.65	+	4712.31i	−0.289154	+	0.500830i	−0.973608	−	0.228226i	$-0.926707\pi$
$97$	−2720.65	+	4712.31i	−0.289154	+	0.500830i	0.684454	+	0.729056i	$0.260041\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−6480.14	−	3741.31i	−0.635246	−	0.366759i	0.147535	−	0.989057i	$-0.452866\pi$
$101$	−6480.14	−	3741.31i	−0.635246	−	0.366759i	−0.782781	+	0.622297i	$0.786199\pi$
$102$		0			0
$103$	−6788.27	−	11757.6i	−0.639860	−	1.10827i	−0.985463	−	0.169889i	$-0.945659\pi$
$103$	−6788.27	−	11757.6i	−0.639860	−	1.10827i	0.345604	−	0.938381i	$-0.387674\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	16741.7i		−	1.46229i	−0.682224	−	0.731143i	$-0.738987\pi$
$107$		−	16741.7i		−	1.46229i	0.682224	−	0.731143i	$-0.261013\pi$
$108$		0			0
$109$	−12068.7			−1.01579			−0.507897	−	0.861418i	$-0.669577\pi$
$109$	−12068.7			−1.01579			−0.507897	+	0.861418i	$0.669577\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−610.202	+	352.300i	−0.0477878	+	0.0275903i	−0.523704	−	0.851901i	$-0.675450\pi$
$113$	−610.202	+	352.300i	−0.0477878	+	0.0275903i	0.475916	+	0.879491i	$0.342117\pi$
$114$		0			0
$115$	−3661.92	+	6342.63i	−0.276894	+	0.479594i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−4230.63	−	2442.56i	−0.298752	−	0.172485i
$120$		0			0
$121$	−1894.72	−	3281.76i	−0.129412	−	0.224148i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		−	13499.7i		−	0.863981i
$126$		0			0
$127$	−16050.0			−0.995105			−0.497552	−	0.867434i	$-0.665768\pi$
$127$	−16050.0			−0.995105			−0.497552	+	0.867434i	$0.665768\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	13427.1	−	7752.17i	0.782422	−	0.451732i	−0.0548658	−	0.998494i	$-0.517473\pi$
$131$	13427.1	−	7752.17i	0.782422	−	0.451732i	0.837288	+	0.546762i	$0.184140\pi$
$132$		0			0
$133$	−5044.62	+	8737.53i	−0.285184	+	0.493953i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	771.295	+	445.307i	0.0410941	+	0.0237257i	0.520406	−	0.853919i	$-0.325781\pi$
$137$	771.295	+	445.307i	0.0410941	+	0.0237257i	−0.479312	+	0.877644i	$0.659114\pi$
$138$		0			0
$139$	−4679.09	−	8104.42i	−0.242176	−	0.419462i	0.719158	−	0.694847i	$-0.244528\pi$
$139$	−4679.09	−	8104.42i	−0.242176	−	0.419462i	−0.961334	+	0.275385i	$0.911195\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$			7837.25i			0.383258i
$144$		0			0
$145$	15995.8			0.760798
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−35220.7	+	20334.7i	−1.58645	+	0.915937i	−0.592563	+	0.805524i	$0.701884\pi$
$149$	−35220.7	+	20334.7i	−1.58645	+	0.915937i	−0.993886	+	0.110412i	$0.964783\pi$
$150$		0			0
$151$	12487.2	−	21628.5i	0.547661	−	0.948577i	−0.450773	−	0.892639i	$-0.648852\pi$
$151$	12487.2	−	21628.5i	0.547661	−	0.948577i	0.998434	−	0.0559386i	$-0.0178151\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	10945.1	+	6319.16i	0.455572	+	0.263024i
$156$		0			0
$157$	16459.2	+	28508.2i	0.667743	+	1.15656i	0.978534	+	0.206086i	$0.0660727\pi$
$157$	16459.2	+	28508.2i	0.667743	+	1.15656i	−0.310791	+	0.950478i	$0.600594\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		−	8517.75i		−	0.328604i
$162$		0			0
$163$	13796.3			0.519262			0.259631	−	0.965708i	$-0.416399\pi$
$163$	13796.3			0.519262			0.259631	+	0.965708i	$0.416399\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−9814.14	+	5666.20i	−0.351900	+	0.203170i	−0.665522	−	0.746378i	$-0.731791\pi$
$167$	−9814.14	+	5666.20i	−0.351900	+	0.203170i	0.313622	+	0.949548i	$0.398458\pi$
$168$		0			0
$169$	11450.4	−	19832.6i	0.400910	−	0.694396i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	33922.6	+	19585.2i	1.13344	+	0.654389i	0.944797	−	0.327657i	$-0.106259\pi$
$173$	33922.6	+	19585.2i	1.13344	+	0.654389i	0.188639	+	0.982047i	$0.439592\pi$
$174$		0			0
$175$	3386.43	+	5865.47i	0.110577	+	0.191525i
$176$		0			0
$177$		0			0
$178$		0			0
$179$			24097.3i			0.752078i	0.926604	+	0.376039i	$0.122714\pi$
$179$			24097.3i			0.752078i	−0.926604	+	0.376039i	$0.877286\pi$
$180$		0			0
$181$	10277.1			0.313699			0.156850	−	0.987623i	$-0.449866\pi$
$181$	10277.1			0.313699			0.156850	+	0.987623i	$0.449866\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−5989.72	+	3458.16i	−0.175010	+	0.101042i
$186$		0			0
$187$	−17813.1	+	30853.2i	−0.509397	+	0.882301i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	30337.2	+	17515.2i	0.831590	+	0.480119i	0.854397	−	0.519621i	$-0.173927\pi$
$191$	30337.2	+	17515.2i	0.831590	+	0.480119i	−0.0228068	+	0.999740i	$0.507260\pi$
$192$		0			0
$193$	−2620.27	−	4538.45i	−0.0703448	−	0.121841i	0.828708	−	0.559682i	$-0.189077\pi$
$193$	−2620.27	−	4538.45i	−0.0703448	−	0.121841i	−0.899052	+	0.437841i	$0.855743\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	42421.5i		−	1.09308i	−0.837431	−	0.546542i	$-0.815944\pi$
$197$		−	42421.5i		−	1.09308i	0.837431	−	0.546542i	$-0.184056\pi$
$198$		0			0
$199$	31270.0			0.789627			0.394814	−	0.918761i	$-0.370809\pi$
$199$	31270.0			0.789627			0.394814	+	0.918761i	$0.370809\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−16111.0	+	9301.69i	−0.390958	+	0.225720i
$204$		0			0
$205$	608.843	−	1054.55i	0.0144876	−	0.0250933i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	63721.1	+	36789.4i	1.45878	+	0.842229i
$210$		0			0
$211$	15562.2	+	26954.6i	0.349548	+	0.605435i	0.986169	−	0.165742i	$-0.0530019\pi$
$211$	15562.2	+	26954.6i	0.349548	+	0.605435i	−0.636621	+	0.771177i	$0.719669\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$			11010.9i			0.238202i
$216$		0			0
$217$	−14698.6			−0.312145
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−22282.9	+	12865.0i	−0.456234	+	0.263407i
$222$		0			0
$223$	−8013.95	+	13880.6i	−0.161153	+	0.279124i	−0.935282	−	0.353903i	$-0.884854\pi$
$223$	−8013.95	+	13880.6i	−0.161153	+	0.279124i	0.774130	+	0.633027i	$0.218188\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−58481.7	−	33764.5i	−1.13493	−	0.655251i	−0.189759	−	0.981831i	$-0.560771\pi$
$227$	−58481.7	−	33764.5i	−1.13493	−	0.655251i	−0.945170	+	0.326579i	$0.894104\pi$
$228$		0			0
$229$	−39032.9	−	67607.0i	−0.744321	−	1.28920i	−0.950512	−	0.310689i	$-0.899440\pi$
$229$	−39032.9	−	67607.0i	−0.744321	−	1.28920i	0.206191	−	0.978512i	$-0.433893\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	61204.9i		−	1.12739i	−0.825983	−	0.563696i	$-0.809379\pi$
$233$		−	61204.9i		−	1.12739i	0.825983	−	0.563696i	$-0.190621\pi$
$234$		0			0
$235$	5288.21			0.0957576
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−37373.3	+	21577.5i	−0.654282	+	0.377750i	−0.790095	−	0.612984i	$-0.789969\pi$
$239$	−37373.3	+	21577.5i	−0.654282	+	0.377750i	0.135813	+	0.990735i	$0.456635\pi$
$240$		0			0
$241$	28103.8	−	48677.2i	0.483873	−	0.838092i	−0.515956	−	0.856615i	$-0.672563\pi$
$241$	28103.8	−	48677.2i	0.483873	−	0.838092i	0.999828	+	0.0185233i	$0.00589649\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−23367.9	−	13491.4i	−0.389302	−	0.224764i
$246$		0			0
$247$	26570.2	+	46020.9i	0.435513	+	0.754330i
$248$		0			0
$249$		0			0
$250$		0			0
$251$			15739.4i			0.249828i	0.992168	+	0.124914i	$0.0398655\pi$
$251$			15739.4i			0.249828i	−0.992168	+	0.124914i	$0.960135\pi$
$252$		0			0
$253$	−62118.3			−0.970462
$254$		0			0
$255$		0			0
$256$		0			0
$257$	50887.7	−	29380.0i	0.770454	−	0.444822i	−0.0625827	−	0.998040i	$-0.519934\pi$
$257$	50887.7	−	29380.0i	0.770454	−	0.444822i	0.833036	+	0.553218i	$0.186600\pi$
$258$		0			0
$259$	4021.91	−	6966.14i	0.0599560	−	0.103847i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−81699.8	−	47169.4i	−1.18116	−	0.681944i	−0.224879	−	0.974387i	$-0.572199\pi$
$263$	−81699.8	−	47169.4i	−1.18116	−	0.681944i	−0.956283	+	0.292443i	$0.905532\pi$
$264$		0			0
$265$	−32371.8	−	56069.6i	−0.460973	−	0.798428i
$266$		0			0
$267$		0			0
$268$		0			0
$269$		−	79782.6i		−	1.10256i	−0.834319	−	0.551282i	$-0.814139\pi$
$269$		−	79782.6i		−	1.10256i	0.834319	−	0.551282i	$-0.185861\pi$
$270$		0			0
$271$	−76677.1			−1.04406			−0.522032	−	0.852926i	$-0.674826\pi$
$271$	−76677.1			−1.04406			−0.522032	+	0.852926i	$0.674826\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	42775.7	−	24696.6i	0.565629	−	0.326566i
$276$		0			0
$277$	−56577.9	+	97995.9i	−0.737374	+	1.27717i	0.216300	+	0.976327i	$0.430601\pi$
$277$	−56577.9	+	97995.9i	−0.737374	+	1.27717i	−0.953674	+	0.300842i	$0.902732\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	83614.5	+	48274.8i	1.05893	+	0.611376i	0.925137	−	0.379633i	$-0.123950\pi$
$281$	83614.5	+	48274.8i	1.05893	+	0.611376i	0.133797	+	0.991009i	$0.457283\pi$
$282$		0			0
$283$	−15268.5	−	26445.9i	−0.190645	−	0.330206i	0.754819	−	0.655933i	$-0.227725\pi$
$283$	−15268.5	−	26445.9i	−0.190645	−	0.330206i	−0.945464	+	0.325726i	$0.894391\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			1416.19i			0.0171932i
$288$		0			0
$289$	−33441.6			−0.400397
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−3511.45	+	2027.34i	−0.0409026	+	0.0236151i	−0.520312	−	0.853976i	$-0.674184\pi$
$293$	−3511.45	+	2027.34i	−0.0409026	+	0.0236151i	0.479409	+	0.877591i	$0.340851\pi$
$294$		0			0
$295$	−34630.4	+	59981.5i	−0.397936	+	0.689245i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−38852.8	−	22431.7i	−0.434590	−	0.250911i
$300$		0			0
$301$	−6402.92	−	11090.2i	−0.0706717	−	0.122407i
$302$		0			0
$303$		0			0
$304$		0			0
$305$		−	13893.9i		−	0.149357i
$306$		0			0
$307$	44297.5			0.470005			0.235002	−	0.971995i	$-0.424490\pi$
$307$	44297.5			0.470005			0.235002	+	0.971995i	$0.424490\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	82350.1	−	47544.8i	0.851419	−	0.491567i	−0.00971065	−	0.999953i	$-0.503091\pi$
$311$	82350.1	−	47544.8i	0.851419	−	0.491567i	0.861129	+	0.508386i	$0.169758\pi$
$312$		0			0
$313$	85286.0	−	147720.i	0.870541	−	1.50782i	0.00910220	−	0.999959i	$-0.497103\pi$
$313$	85286.0	−	147720.i	0.870541	−	1.50782i	0.861438	−	0.507862i	$-0.169564\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−105654.	−	60999.2i	−1.05140	−	0.607024i	−0.128356	−	0.991728i	$-0.540970\pi$
$317$	−105654.	−	60999.2i	−1.05140	−	0.607024i	−0.923040	+	0.384704i	$0.874303\pi$
$318$		0			0
$319$	67835.4	+	117494.i	0.666615	+	1.15461i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			241563.i			2.31540i
$324$		0			0
$325$	35672.9			0.337731
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−5326.30	+	3075.14i	−0.0492078	+	0.0284101i
$330$		0			0
$331$	47607.1	−	82457.9i	0.434526	−	0.752621i	−0.562731	−	0.826640i	$-0.690249\pi$
$331$	47607.1	−	82457.9i	0.434526	−	0.752621i	0.997257	+	0.0740192i	$0.0235826\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−14389.2	−	8307.62i	−0.128218	−	0.0740265i
$336$		0			0
$337$	−4204.88	−	7283.07i	−0.0370249	−	0.0641291i	0.846919	−	0.531722i	$-0.178455\pi$
$337$	−4204.88	−	7283.07i	−0.0370249	−	0.0641291i	−0.883944	+	0.467593i	$0.845121\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$			107194.i			0.921852i
$342$		0			0
$343$	65677.6			0.558250
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−5224.52	+	3016.38i	−0.0433897	+	0.0250511i	−0.521538	−	0.853228i	$-0.674642\pi$
$347$	−5224.52	+	3016.38i	−0.0433897	+	0.0250511i	0.478148	+	0.878279i	$0.341308\pi$
$348$		0			0
$349$	−69799.9	+	120897.i	−0.573065	+	0.992577i	0.423184	+	0.906044i	$0.360912\pi$
$349$	−69799.9	+	120897.i	−0.573065	+	0.992577i	−0.996249	+	0.0865335i	$0.972421\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	73954.5	+	42697.7i	0.593493	+	0.342653i	0.766477	−	0.642271i	$-0.222008\pi$
$353$	73954.5	+	42697.7i	0.593493	+	0.342653i	−0.172985	+	0.984925i	$0.555341\pi$
$354$		0			0
$355$	−34889.3	−	60430.1i	−0.276844	−	0.479508i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			90712.4i			0.703846i	0.936029	+	0.351923i	$0.114472\pi$
$359$			90712.4i			0.703846i	−0.936029	+	0.351923i	$0.885528\pi$
$360$		0			0
$361$	368579.			2.82824
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−45061.6	+	26016.3i	−0.338237	+	0.195281i
$366$		0			0
$367$	12770.7	−	22119.5i	0.0948160	−	0.164226i	−0.814716	−	0.579860i	$-0.803107\pi$
$367$	12770.7	−	22119.5i	0.0948160	−	0.164226i	0.909532	+	0.415634i	$0.136440\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	65209.9	+	37649.0i	0.473768	+	0.273530i
$372$		0			0
$373$	117264.	+	203107.i	0.842844	+	1.45985i	0.887480	+	0.460846i	$0.152454\pi$
$373$	117264.	+	203107.i	0.842844	+	1.45985i	−0.0446361	+	0.999003i	$0.514213\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			97984.7i			0.689407i
$378$		0			0
$379$	−107483.			−0.748278			−0.374139	−	0.927373i	$-0.622062\pi$
$379$	−107483.			−0.748278			−0.374139	+	0.927373i	$0.622062\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	142398.	−	82213.7i	0.970750	−	0.560463i	0.0712849	−	0.997456i	$-0.477290\pi$
$383$	142398.	−	82213.7i	0.970750	−	0.560463i	0.899465	+	0.436993i	$0.143957\pi$
$384$		0			0
$385$	9137.60	−	15826.8i	0.0616468	−	0.106775i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−158396.	−	91449.9i	−1.04675	−	0.604343i	−0.125015	−	0.992155i	$-0.539898\pi$
$389$	−158396.	−	91449.9i	−1.04675	−	0.604343i	−0.921739	+	0.387811i	$0.873231\pi$
$390$		0			0
$391$	−101969.	−	176615.i	−0.666981	−	1.15525i
$392$		0			0
$393$		0			0
$394$		0			0
$395$			75354.6i			0.482965i
$396$		0			0
$397$	−277717.			−1.76206			−0.881031	−	0.473059i	$-0.843150\pi$
$397$	−277717.			−1.76206			−0.881031	+	0.473059i	$0.843150\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	145546.	−	84030.8i	0.905128	−	0.522576i	0.0262679	−	0.999655i	$-0.491638\pi$
$401$	145546.	−	84030.8i	0.905128	−	0.522576i	0.878861	+	0.477079i	$0.158304\pi$
$402$		0			0
$403$	−38709.0	+	67046.0i	−0.238343	+	0.412822i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−50802.7	−	29331.0i	−0.306689	−	0.177067i
$408$		0			0
$409$	44190.6	+	76540.3i	0.264170	+	0.457555i	0.967346	−	0.253461i	$-0.0815688\pi$
$409$	44190.6	+	76540.3i	0.264170	+	0.457555i	−0.703176	+	0.711016i	$0.748235\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		−	80551.4i		−	0.472251i
$414$		0			0
$415$	92235.5			0.535552
$416$		0			0
$417$		0			0
$418$		0			0
$419$	131141.	−	75714.4i	0.746983	−	0.431271i	−0.0776195	−	0.996983i	$-0.524732\pi$
$419$	131141.	−	75714.4i	0.746983	−	0.431271i	0.824603	+	0.565712i	$0.191399\pi$
$420$		0			0
$421$	66110.2	−	114506.i	0.372996	−	0.646048i	−0.617029	−	0.786940i	$-0.711664\pi$
$421$	66110.2	−	114506.i	0.372996	−	0.646048i	0.990025	+	0.140893i	$0.0449972\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	140435.	+	81080.0i	0.777494	+	0.448886i
$426$		0			0
$427$	8079.43	+	13994.0i	0.0443124	+	0.0767512i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		−	231482.i		−	1.24613i	−0.782170	−	0.623065i	$-0.785887\pi$
$431$		−	231482.i		−	1.24613i	0.782170	−	0.623065i	$-0.214113\pi$
$432$		0			0
$433$	−218090.			−1.16321			−0.581607	−	0.813470i	$-0.697576\pi$
$433$	−218090.			−1.16321			−0.581607	+	0.813470i	$0.697576\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−364763.	+	210596.i	−1.91007	+	1.10278i
$438$		0			0
$439$	−44778.5	+	77558.6i	−0.232349	+	0.402440i	−0.958499	−	0.285096i	$-0.907974\pi$
$439$	−44778.5	+	77558.6i	−0.232349	+	0.402440i	0.726150	+	0.687536i	$0.241308\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−228878.	−	132143.i	−1.16626	−	0.673343i	−0.213467	−	0.976950i	$-0.568476\pi$
$443$	−228878.	−	132143.i	−1.16626	−	0.673343i	−0.952797	+	0.303607i	$0.901809\pi$
$444$		0			0
$445$	−53559.5	−	92767.7i	−0.270468	−	0.468465i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	33967.2i		−	0.168487i	−0.996445	−	0.0842435i	$-0.973153\pi$
$449$		−	33967.2i		−	0.168487i	0.996445	−	0.0842435i	$-0.0268474\pi$
$450$		0			0
$451$	10328.0			0.0507765
$452$		0			0
$453$		0			0
$454$		0			0
$455$	11430.5	−	6599.40i	0.0552131	−	0.0318773i
$456$		0			0
$457$	−41636.9	+	72117.2i	−0.199363	+	0.345308i	−0.948322	−	0.317309i	$-0.897221\pi$
$457$	−41636.9	+	72117.2i	−0.199363	+	0.345308i	0.748959	+	0.662617i	$0.230554\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	49805.5	+	28755.2i	0.234355	+	0.135305i	0.612580	−	0.790409i	$-0.290132\pi$
$461$	49805.5	+	28755.2i	0.234355	+	0.135305i	−0.378224	+	0.925714i	$0.623465\pi$
$462$		0			0
$463$	−40897.0	−	70835.6i	−0.190778	−	0.330438i	0.754730	−	0.656035i	$-0.227768\pi$
$463$	−40897.0	−	70835.6i	−0.190778	−	0.330438i	−0.945508	+	0.325598i	$0.894434\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	161762.i		−	0.741726i	−0.928688	−	0.370863i	$-0.879062\pi$
$467$		−	161762.i		−	0.741726i	0.928688	−	0.370863i	$-0.120938\pi$
$468$		0			0
$469$	19323.8			0.0878511
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−80878.6	+	46695.3i	−0.361503	+	0.208714i
$474$		0			0
$475$	167455.	−	290040.i	0.742182	−	1.28550i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−111249.	−	64229.4i	−0.484868	−	0.279939i	0.237575	−	0.971369i	$-0.423648\pi$
$479$	−111249.	−	64229.4i	−0.484868	−	0.279939i	−0.722443	+	0.691430i	$0.756981\pi$
$480$		0			0
$481$	−21183.5	−	36690.9i	−0.0915605	−	0.158587i
$482$		0			0
$483$		0			0
$484$		0			0
$485$		−	66829.5i		−	0.284109i
$486$		0			0
$487$	−255021.			−1.07527			−0.537636	−	0.843177i	$-0.680682\pi$
$487$	−255021.			−1.07527			−0.537636	+	0.843177i	$0.680682\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	151163.	−	87274.1i	0.627023	−	0.362012i	−0.152575	−	0.988292i	$-0.548757\pi$
$491$	151163.	−	87274.1i	0.627023	−	0.362012i	0.779598	+	0.626280i	$0.215423\pi$
$492$		0			0
$493$	−222707.	+	385740.i	−0.916305	+	1.58709i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	70281.2	+	40576.9i	0.284529	+	0.164273i
$498$		0			0
$499$	−104865.	−	181631.i	−0.421141	−	0.729438i	0.574910	−	0.818216i	$-0.305037\pi$
$499$	−104865.	−	181631.i	−0.421141	−	0.729438i	−0.996051	+	0.0887787i	$0.971704\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		−	288148.i		−	1.13888i	−0.822031	−	0.569442i	$-0.807159\pi$
$503$		−	288148.i		−	1.13888i	0.822031	−	0.569442i	$-0.192841\pi$
$504$		0			0
$505$	91900.8			0.360360
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−73335.8	+	42340.5i	−0.283061	+	0.163426i	−0.634809	−	0.772669i	$-0.718921\pi$
$509$	−73335.8	+	42340.5i	−0.283061	+	0.163426i	0.351747	+	0.936095i	$0.385588\pi$
$510$		0			0
$511$	30257.4	−	52407.4i	0.115875	−	0.200702i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	144406.	+	83372.8i	0.544466	+	0.314347i
$516$		0			0
$517$	22426.4	+	38843.7i	0.0839032	+	0.145325i
$518$		0			0
$519$		0			0
$520$		0			0
$521$			80148.3i			0.295270i	0.989042	+	0.147635i	$0.0471660\pi$
$521$			80148.3i			0.295270i	−0.989042	+	0.147635i	$0.952834\pi$
$522$		0			0
$523$	127783.			0.467163			0.233581	−	0.972337i	$-0.424955\pi$
$523$	127783.			0.467163			0.233581	+	0.972337i	$0.424955\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−304774.	+	175962.i	−1.09738	+	0.633573i
$528$		0			0
$529$	37873.6	−	65598.9i	0.135340	−	0.234415i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	6459.79	+	3729.56i	0.0227386	+	0.0131281i
$534$		0			0
$535$	102810.	+	178072.i	0.359193	+	0.622140i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		−	228860.i		−	0.787756i
$540$		0			0
$541$	1167.97			0.00399060			0.00199530	−	0.999998i	$-0.499365\pi$
$541$	1167.97			0.00399060			0.00199530	+	0.999998i	$0.499365\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	128367.	−	74112.9i	0.432177	−	0.249518i
$546$		0			0
$547$	−138903.	+	240586.i	−0.464232	+	0.804074i	−0.999167	−	0.0408196i	$-0.987003\pi$
$547$	−138903.	+	240586.i	−0.464232	+	0.804074i	0.534934	+	0.844894i	$0.320336\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	796669.	+	459957.i	2.62407	+	1.51501i
$552$		0			0
$553$	−43819.3	−	75897.3i	−0.143290	−	0.248185i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			127126.i			0.409755i	0.978788	+	0.204877i	$0.0656795\pi$
$557$			127126.i			0.409755i	−0.978788	+	0.204877i	$0.934320\pi$
$558$		0			0
$559$	−67448.9			−0.215850
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−107207.	+	61896.1i	−0.338226	+	0.195275i	−0.659487	−	0.751716i	$-0.729227\pi$
$563$	−107207.	+	61896.1i	−0.338226	+	0.195275i	0.321261	+	0.946991i	$0.395893\pi$
$564$		0			0
$565$	4326.91	−	7494.43i	0.0135544	−	0.0234770i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−53531.2	−	30906.3i	−0.165342	−	0.0954601i	0.415046	−	0.909801i	$-0.363766\pi$
$569$	−53531.2	−	30906.3i	−0.165342	−	0.0954601i	−0.580388	+	0.814340i	$0.697099\pi$
$570$		0			0
$571$	102067.	+	176786.i	0.313050	+	0.542219i	0.979021	−	0.203759i	$-0.0653158\pi$
$571$	102067.	+	176786.i	0.313050	+	0.542219i	−0.665971	+	0.745978i	$0.731982\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			282745.i			0.855182i
$576$		0			0
$577$	555504.			1.66854			0.834269	−	0.551358i	$-0.185890\pi$
$577$	555504.			1.66854			0.834269	+	0.551358i	$0.185890\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−92899.9	+	53635.8i	−0.275209	+	0.158892i
$582$		0			0
$583$	274567.	−	475563.i	0.807813	−	1.39917i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−6076.70	−	3508.38i	−0.0176357	−	0.0101820i	0.491156	−	0.871071i	$-0.336574\pi$
$587$	−6076.70	−	3508.38i	−0.0176357	−	0.0101820i	−0.508792	+	0.860890i	$0.669908\pi$
$588$		0			0
$589$	363414.	+	629451.i	1.04754	+	1.81439i
$590$		0			0
$591$		0			0
$592$		0			0
$593$			77064.9i			0.219153i	0.993978	+	0.109576i	$0.0349494\pi$
$593$			77064.9i			0.219153i	−0.993978	+	0.109576i	$0.965051\pi$
$594$		0			0
$595$	59998.4			0.169475
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−473683.	+	273481.i	−1.32018	+	0.762208i	−0.983757	−	0.179503i	$-0.942551\pi$
$599$	−473683.	+	273481.i	−1.32018	+	0.762208i	−0.336425	+	0.941710i	$0.609218\pi$
$600$		0			0
$601$	269988.	−	467633.i	0.747473	−	1.29466i	−0.201558	−	0.979477i	$-0.564600\pi$
$601$	269988.	−	467633.i	0.747473	−	1.29466i	0.949030	−	0.315184i	$-0.102066\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	40306.2	+	23270.8i	0.110119	+	0.0635770i
$606$		0			0
$607$	−249663.	−	432429.i	−0.677606	−	1.17365i	−0.975700	−	0.219111i	$-0.929684\pi$
$607$	−249663.	−	432429.i	−0.677606	−	1.17365i	0.298094	−	0.954536i	$-0.403649\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$			32393.8i			0.0867719i
$612$		0			0
$613$	80551.4			0.214364			0.107182	−	0.994239i	$-0.465817\pi$
$613$	80551.4			0.214364			0.107182	+	0.994239i	$0.465817\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−385247.	+	222423.i	−1.01197	+	0.584263i	−0.911769	−	0.410703i	$-0.865283\pi$
$617$	−385247.	+	222423.i	−1.01197	+	0.584263i	−0.100205	+	0.994967i	$0.531950\pi$
$618$		0			0
$619$	−280471.	+	485789.i	−0.731992	+	1.26785i	0.224039	+	0.974580i	$0.428076\pi$
$619$	−280471.	+	485789.i	−0.731992	+	1.26785i	−0.956031	+	0.293267i	$0.905258\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	107890.	+	62290.6i	0.277976	+	0.160489i
$624$		0			0
$625$	−65272.6	−	113055.i	−0.167098	−	0.289422i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		−	192590.i		−	0.486780i
$630$		0			0
$631$	621772.			1.56161			0.780805	−	0.624775i	$-0.214809\pi$
$631$	621772.			1.56161			0.780805	+	0.624775i	$0.214809\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	170715.	−	98562.4i	0.423374	−	0.244435i
$636$		0			0
$637$	82643.9	−	143144.i	0.203672	−	0.352771i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	279418.	+	161322.i	0.680045	+	0.392624i	0.799872	−	0.600171i	$-0.204901\pi$
$641$	279418.	+	161322.i	0.680045	+	0.392624i	−0.119827	+	0.992795i	$0.538234\pi$
$642$		0			0
$643$	244906.	+	424190.i	0.592350	+	1.02598i	0.993915	+	0.110149i	$0.0351329\pi$
$643$	244906.	+	424190.i	0.592350	+	1.02598i	−0.401565	+	0.915830i	$0.631534\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	26885.7i		−	0.0642263i	−0.999484	−	0.0321132i	$-0.989776\pi$
$647$		−	26885.7i		−	0.0642263i	0.999484	−	0.0321132i	$-0.0102237\pi$
$648$		0			0
$649$	−587446.			−1.39469
$650$		0			0
$651$		0			0
$652$		0			0
$653$	618540.	−	357114.i	1.45058	−	0.837492i	0.452065	−	0.891985i	$-0.350687\pi$
$653$	618540.	−	357114.i	1.45058	−	0.837492i	0.998514	+	0.0544925i	$0.0173541\pi$
$654$		0			0
$655$	−95211.2	+	164911.i	−0.221925	+	0.384385i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−203254.	−	117349.i	−0.468024	−	0.270214i	0.247388	−	0.968916i	$-0.420428\pi$
$659$	−203254.	−	117349.i	−0.468024	−	0.270214i	−0.715412	+	0.698703i	$0.753761\pi$
$660$		0			0
$661$	−313281.	−	542619.i	−0.717020	−	1.24191i	−0.962175	−	0.272431i	$-0.912172\pi$
$661$	−313281.	−	542619.i	−0.717020	−	1.24191i	0.245155	−	0.969484i	$-0.421161\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		−	123915.i		−	0.280208i
$666$		0			0
$667$	−776630.			−1.74567
$668$		0			0
$669$		0			0
$670$		0			0
$671$	102055.	−	58921.7i	0.226668	−	0.130867i
$672$		0			0
$673$	−320999.	+	555987.i	−0.708718	+	1.22754i	0.256614	+	0.966514i	$0.417393\pi$
$673$	−320999.	+	555987.i	−0.708718	+	1.22754i	−0.965333	+	0.261022i	$0.915940\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−568932.	−	328473.i	−1.24132	−	0.716675i	−0.271955	−	0.962310i	$-0.587670\pi$
$677$	−568932.	−	328473.i	−1.24132	−	0.716675i	−0.969362	+	0.245635i	$0.921004\pi$
$678$		0			0
$679$	38861.9	+	67310.9i	0.0842917	+	0.145998i
$680$		0			0
$681$		0			0
$682$		0			0
$683$			76710.6i			0.164442i	0.996614	+	0.0822212i	$0.0262014\pi$
$683$			76710.6i			0.164442i	−0.996614	+	0.0822212i	$0.973799\pi$
$684$		0			0
$685$	−10938.4			−0.0233117
$686$		0			0
$687$		0			0
$688$		0			0
$689$	343463.	−	198299.i	0.723505	−	0.417716i
$690$		0			0
$691$	285435.	−	494387.i	0.597793	−	1.03541i	−0.395354	−	0.918529i	$-0.629378\pi$
$691$	285435.	−	494387.i	0.597793	−	1.03541i	0.993146	−	0.116878i	$-0.0372887\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	99537.6	+	57468.1i	0.206071	+	0.118975i
$696$		0			0
$697$	16953.7	+	29364.6i	0.0348978	+	0.0604447i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			4271.71i			0.00869292i	0.999991	+	0.00434646i	$0.00138353\pi$
$701$			4271.71i			0.00869292i	−0.999991	+	0.00434646i	$0.998616\pi$
$702$		0			0
$703$	−397757.			−0.804835
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−92562.7	+	53441.1i	−0.185181	+	0.106914i
$708$		0			0
$709$	−74221.7	+	128556.i	−0.147652	+	0.255740i	−0.930359	−	0.366650i	$-0.880505\pi$
$709$	−74221.7	+	128556.i	−0.147652	+	0.255740i	0.782707	+	0.622390i	$0.213838\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−531408.	−	306809.i	−1.04532	−	0.603516i
$714$		0			0
$715$	−48128.1	−	83360.3i	−0.0941427	−	0.163060i
$716$		0			0
$717$		0			0
$718$		0			0
$719$		−	549881.i		−	1.06368i	−0.846845	−	0.531840i	$-0.821501\pi$
$719$		−	549881.i		−	1.06368i	0.846845	−	0.531840i	$-0.178499\pi$
$720$		0			0
$721$	−193928.			−0.373052
$722$		0			0
$723$		0			0
$724$		0			0
$725$	534800.	−	308767.i	1.01746	−	0.587429i
$726$		0			0
$727$	−322003.	+	557726.i	−0.609244	+	1.05524i	0.382121	+	0.924112i	$0.375194\pi$
$727$	−322003.	+	557726.i	−0.609244	+	1.05524i	−0.991365	+	0.131130i	$0.958139\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−265528.	−	153303.i	−0.496908	−	0.286890i
$732$		0			0
$733$	−416415.	−	721253.i	−0.775031	−	1.34239i	−0.934777	−	0.355234i	$-0.884401\pi$
$733$	−416415.	−	721253.i	−0.775031	−	1.34239i	0.159747	−	0.987158i	$-0.448932\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	140925.i		−	0.259449i
$738$		0			0
$739$	472487.			0.865170			0.432585	−	0.901593i	$-0.357602\pi$
$739$	472487.			0.865170			0.432585	+	0.901593i	$0.357602\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−847338.	+	489211.i	−1.53490	+	0.886173i	−0.535771	+	0.844363i	$0.679979\pi$
$743$	−847338.	+	489211.i	−1.53490	+	0.886173i	−0.999126	+	0.0418100i	$0.986688\pi$
$744$		0			0
$745$	249749.	−	432577.i	0.449977	−	0.779383i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−207101.	−	119570.i	−0.369163	−	0.213136i
$750$		0			0
$751$	83140.6	+	144004.i	0.147412	+	0.255325i	0.930270	−	0.366875i	$-0.119572\pi$
$751$	83140.6	+	144004.i	0.147412	+	0.255325i	−0.782858	+	0.622200i	$0.786239\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$			306733.i			0.538105i
$756$		0			0
$757$	−238453.			−0.416114			−0.208057	−	0.978117i	$-0.566714\pi$
$757$	−238453.			−0.416114			−0.208057	+	0.978117i	$0.566714\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	518174.	−	299168.i	0.894759	−	0.516589i	0.0192628	−	0.999814i	$-0.493868\pi$
$761$	518174.	−	299168.i	0.894759	−	0.516589i	0.875496	+	0.483225i	$0.160535\pi$
$762$		0			0
$763$	−86194.6	+	149294.i	−0.148058	+	0.256444i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−367426.	−	212134.i	−0.624568	−	0.360594i
$768$		0			0
$769$	−333662.	−	577919.i	−0.564227	−	0.977270i	−0.997121	−	0.0758248i	$-0.975841\pi$
$769$	−333662.	−	577919.i	−0.564227	−	0.977270i	0.432894	−	0.901445i	$-0.357492\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$			848153.i			1.41943i	0.704487	+	0.709717i	$0.251177\pi$
$773$			848153.i			1.41943i	−0.704487	+	0.709717i	$0.748823\pi$
$774$		0			0
$775$	487916.			0.812347
$776$		0			0
$777$		0			0
$778$		0			0
$779$	60646.7	−	35014.4i	0.0999384	−	0.0576995i
$780$		0			0
$781$	295919.	−	512547.i	0.485145	−	0.840295i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−350134.	−	202150.i	−0.568192	−	0.328046i
$786$		0			0
$787$	483866.	+	838081.i	0.781225	+	1.35312i	0.931229	+	0.364436i	$0.118738\pi$
$787$	483866.	+	838081.i	0.781225	+	1.35312i	−0.150004	+	0.988685i	$0.547929\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$			10064.6i			0.0160858i
$792$		0			0
$793$	85109.3			0.135341
$794$		0			0
$795$		0			0
$796$		0			0
$797$	583828.	−	337073.i	0.919111	−	0.530649i	0.0357599	−	0.999360i	$-0.488615\pi$
$797$	583828.	−	337073.i	0.919111	−	0.530649i	0.883351	+	0.468711i	$0.155282\pi$
$798$		0			0
$799$	−73627.0	+	127526.i	−0.115330	+	0.199758i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−382197.	−	220662.i	−0.592729	−	0.342212i
$804$		0			0
$805$	52307.0	+	90598.4i	0.0807176	+	0.139807i
$806$		0			0
$807$		0			0
$808$		0			0
$809$			570317.i			0.871403i	0.900091	+	0.435702i	$0.143500\pi$
$809$			570317.i			0.871403i	−0.900091	+	0.435702i	$0.856500\pi$
$810$		0			0
$811$	−111731.			−0.169876			−0.0849379	−	0.996386i	$-0.527069\pi$
$811$	−111731.			−0.169876			−0.0849379	+	0.996386i	$0.527069\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−146743.	+	84722.1i	−0.220923	+	0.127550i
$816$		0			0
$817$	−316617.	+	548396.i	−0.474340	+	0.821581i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	902069.	+	520810.i	1.33830	+	0.772668i	0.986555	−	0.163429i	$-0.0522553\pi$
$821$	902069.	+	520810.i	1.33830	+	0.772668i	0.351744	+	0.936096i	$0.385589\pi$
$822$		0			0
$823$	54486.5	+	94373.5i	0.0804432	+	0.139332i	0.903440	−	0.428714i	$-0.141033\pi$
$823$	54486.5	+	94373.5i	0.0804432	+	0.139332i	−0.822997	+	0.568045i	$0.807700\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			550908.i			0.805505i	0.915309	+	0.402753i	$0.131947\pi$
$827$			550908.i			0.805505i	−0.915309	+	0.402753i	$0.868053\pi$
$828$		0			0
$829$	−57256.0			−0.0833128			−0.0416564	−	0.999132i	$-0.513263\pi$
$829$	−57256.0			−0.0833128			−0.0416564	+	0.999132i	$0.513263\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	650695.	−	375679.i	0.937751	−	0.541411i
$834$		0			0
$835$	69591.6	−	120536.i	0.0998122	−	0.172880i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	824201.	+	475853.i	1.17087	+	0.676003i	0.953885	−	0.300172i	$-0.0970439\pi$
$839$	824201.	+	475853.i	1.17087	+	0.676003i	0.216986	+	0.976175i	$0.430377\pi$
$840$		0			0
$841$	494467.	+	856442.i	0.699110	+	1.21089i
$842$		0			0
$843$		0			0
$844$		0			0
$845$			281264.i			0.393914i
$846$		0			0
$847$	−54128.7			−0.0754502
$848$		0			0
$849$		0			0
$850$		0			0
$851$	290814.	−	167901.i	0.401565	−	0.231844i
$852$		0			0
$853$	511433.	−	885829.i	0.702896	−	1.21745i	−0.264550	−	0.964372i	$-0.585223\pi$
$853$	511433.	−	885829.i	0.702896	−	1.21745i	0.967446	−	0.253079i	$-0.0814434\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−572818.	−	330717.i	−0.779929	−	0.450292i	0.0564763	−	0.998404i	$-0.482013\pi$
$857$	−572818.	−	330717.i	−0.779929	−	0.450292i	−0.836405	+	0.548112i	$0.815347\pi$
$858$		0			0
$859$	−51374.6	−	88983.5i	−0.0696246	−	0.120593i	0.829112	−	0.559083i	$-0.188847\pi$
$859$	−51374.6	−	88983.5i	−0.0696246	−	0.120593i	−0.898736	+	0.438490i	$0.855513\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	168806.i		−	0.226655i	−0.993558	−	0.113328i	$-0.963849\pi$
$863$		−	168806.i		−	0.226655i	0.993558	−	0.113328i	$-0.0361509\pi$
$864$		0			0
$865$	−481087.			−0.642971
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−553504.	+	319566.i	−0.732962	+	0.423176i
$870$		0			0
$871$	50889.6	−	88143.4i	0.0670800	−	0.116186i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−166996.	−	96415.2i	−0.218117	−	0.125930i
$876$		0			0
$877$	95077.8	+	164680.i	0.123618	+	0.214112i	0.921192	−	0.389109i	$-0.127217\pi$
$877$	95077.8	+	164680.i	0.123618	+	0.214112i	−0.797574	+	0.603221i	$0.793884\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			171490.i			0.220946i	0.993879	+	0.110473i	$0.0352366\pi$
$881$			171490.i			0.220946i	−0.993879	+	0.110473i	$0.964763\pi$
$882$		0			0
$883$	869284.			1.11491			0.557456	−	0.830207i	$-0.311778\pi$
$883$	869284.			1.11491			0.557456	+	0.830207i	$0.311778\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−125013.	+	72176.4i	−0.158894	+	0.0917378i	−0.577339	−	0.816505i	$-0.695909\pi$
$887$	−125013.	+	72176.4i	−0.158894	+	0.0917378i	0.418444	+	0.908242i	$0.362575\pi$
$888$		0			0
$889$	−114630.	+	198545.i	−0.145042	+	0.251220i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	263379.	+	152062.i	0.330277	+	0.190686i
$894$		0			0
$895$	−147980.	−	256309.i	−0.184739	−	0.319977i
$896$		0			0
$897$		0			0
$898$		0			0
$899$			1.34018e6i			1.65823i
$900$		0			0
$901$	1.80283e6			2.22078
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−109312.	+	63111.1i	−0.133466	+	0.0770563i
$906$		0			0
$907$	−53848.5	+	93268.3i	−0.0654574	+	0.113376i	−0.896897	−	0.442240i	$-0.854184\pi$
$907$	−53848.5	+	93268.3i	−0.0654574	+	0.113376i	0.831439	+	0.555615i	$0.187517\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	617457.	+	356489.i	0.743994	+	0.429545i	0.823520	−	0.567287i	$-0.192007\pi$
$911$	617457.	+	356489.i	0.743994	+	0.429545i	−0.0795255	+	0.996833i	$0.525341\pi$
$912$		0			0
$913$	391155.	+	677501.i	0.469253	+	0.812771i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		−	221465.i		−	0.263370i
$918$		0			0
$919$	239512.			0.283594			0.141797	−	0.989896i	$-0.454712\pi$
$919$	239512.			0.283594			0.141797	+	0.989896i	$0.454712\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	370174.	−	213720.i	0.434512	−	0.250866i
$924$		0			0
$925$	−133506.	+	231239.i	−0.156033	+	0.270258i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−1.11204e6	−	642036.i	−1.28851	−	0.743923i	−0.310123	−	0.950696i	$-0.600370\pi$
$929$	−1.11204e6	−	642036.i	−1.28851	−	0.743923i	−0.978389	+	0.206774i	$0.933704\pi$
$930$		0			0
$931$	−775890.	−	1.34388e6i	−0.895160	−	1.55046i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		−	437557.i		−	0.500508i
$936$		0			0
$937$	−471000.			−0.536466			−0.268233	−	0.963354i	$-0.586440\pi$
$937$	−471000.			−0.536466			−0.268233	+	0.963354i	$0.586440\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−624803.	+	360730.i	−0.705608	+	0.407383i	−0.809433	−	0.587212i	$-0.800225\pi$
$941$	−624803.	+	360730.i	−0.705608	+	0.407383i	0.103825	+	0.994596i	$0.466892\pi$
$942$		0			0
$943$	−29560.6	+	51200.5i	−0.0332422	+	0.0575772i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	524423.	+	302776.i	0.584766	+	0.337615i	0.763025	−	0.646369i	$-0.223713\pi$
$947$	524423.	+	302776.i	0.584766	+	0.337615i	−0.178259	+	0.983984i	$0.557047\pi$
$948$		0			0
$949$	−159367.	−	276032.i	−0.176956	−	0.306497i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			527043.i			0.580310i	0.956980	+	0.290155i	$0.0937069\pi$
$953$			527043.i			0.580310i	−0.956980	+	0.290155i	$0.906293\pi$
$954$		0			0
$955$	−430240.			−0.471741
$956$		0			0
$957$		0			0
$958$		0			0
$959$	11017.2	−	6360.79i	0.0119794	−	0.00691630i
$960$		0			0
$961$	−67681.6	+	117228.i	−0.0732865	+	0.126936i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	55740.7	+	32181.9i	0.0598574	+	0.0345587i
$966$		0			0
$967$	620154.	+	1.07414e6i	0.663203	+	1.14870i	0.979769	+	0.200131i	$0.0641369\pi$
$967$	620154.	+	1.07414e6i	0.663203	+	1.14870i	−0.316566	+	0.948571i	$0.602530\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$		−	1.27298e6i		−	1.35015i	−0.737748	−	0.675076i	$-0.764111\pi$
$971$		−	1.27298e6i		−	1.35015i	0.737748	−	0.675076i	$-0.235889\pi$
$972$		0			0
$973$	−133673.			−0.141194
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−1.19918e6	+	692344.i	−1.25630	+	0.725325i	−0.972353	−	0.233515i	$-0.924977\pi$
$977$	−1.19918e6	+	692344.i	−1.25630	+	0.725325i	−0.283947	+	0.958840i	$0.591644\pi$
$978$		0			0
$979$	454273.	−	786824.i	0.473971	−	0.820942i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	146384.	+	84514.9i	0.151491	+	0.0874633i	0.573829	−	0.818975i	$-0.305457\pi$
$983$	146384.	+	84514.9i	0.151491	+	0.0874633i	−0.422338	+	0.906438i	$0.638791\pi$
$984$		0			0
$985$	260508.	+	451213.i	0.268503	+	0.465061i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		−	534602.i		−	0.546560i
$990$		0			0
$991$	−1.57481e6			−1.60354			−0.801772	−	0.597630i	$-0.796109\pi$
$991$	−1.57481e6			−1.60354			−0.801772	+	0.597630i	$0.796109\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−332601.	+	192027.i	−0.335952	+	0.193962i
$996$		0			0
$997$	−285374.	+	494282.i	−0.287094	+	0.497261i	−0.973115	−	0.230321i	$-0.926022\pi$
$997$	−285374.	+	494282.i	−0.287094	+	0.497261i	0.686021	+	0.727582i	$0.259356\pi$
$998$		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.89.2		8
3.2	odd	2		36.5.g.a.29.4	yes	8
4.3	odd	2		432.5.q.c.305.2		8
9.2	odd	6		324.5.c.a.161.6		8
9.4	even	3		36.5.g.a.5.4	✓	8
9.5	odd	6	inner	108.5.g.a.17.2		8
9.7	even	3		324.5.c.a.161.3		8
12.11	even	2		144.5.q.c.65.1		8
36.7	odd	6		1296.5.e.g.161.3		8
36.11	even	6		1296.5.e.g.161.6		8
36.23	even	6		432.5.q.c.17.2		8
36.31	odd	6		144.5.q.c.113.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.5.g.a.5.4	✓	8	9.4	even	3
36.5.g.a.29.4	yes	8	3.2	odd	2
108.5.g.a.17.2		8	9.5	odd	6	inner
108.5.g.a.89.2		8	1.1	even	1	trivial
144.5.q.c.65.1		8	12.11	even	2
144.5.q.c.113.1		8	36.31	odd	6
324.5.c.a.161.3		8	9.7	even	3
324.5.c.a.161.6		8	9.2	odd	6
432.5.q.c.17.2		8	36.23	even	6
432.5.q.c.305.2		8	4.3	odd	2
1296.5.e.g.161.3		8	36.7	odd	6
1296.5.e.g.161.6		8	36.11	even	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)

\(f(q)\)	\(=\)	\(q+(-10.6364 + 6.14094i) q^{5} +(7.14202 - 12.3703i) q^{7} +O(q^{10})\)	\(q+(-10.6364 + 6.14094i) q^{5} +(7.14202 - 12.3703i) q^{7} +(-90.2145 - 52.0854i) q^{11} +(-37.6173 - 65.1551i) q^{13} -341.998i q^{17} -706.329 q^{19} +(516.421 - 298.156i) q^{23} +(-237.078 + 410.630i) q^{25} +(-1127.90 - 651.194i) q^{29} +(-514.510 - 891.158i) q^{31} +175.435i q^{35} +563.132 q^{37} +(-85.8619 + 49.5724i) q^{41} +(448.257 - 776.404i) q^{43} +(-372.885 - 215.285i) q^{47} +(1098.48 + 1902.63i) q^{49} +5271.47i q^{53} +1279.41 q^{55} +(4883.74 - 2819.63i) q^{59} +(-565.626 + 979.693i) q^{61} +(800.227 + 462.012i) q^{65} +(676.412 + 1171.58i) q^{67} +5681.42i q^{71} +4236.54 q^{73} +(-1288.63 + 743.990i) q^{77} +(3067.71 - 5313.43i) q^{79} +(-6503.75 - 3754.94i) q^{83} +(2100.19 + 3637.64i) q^{85} +8721.70i q^{89} -1074.65 q^{91} +(7512.81 - 4337.53i) q^{95} +(-2720.65 + 4712.31i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 9 q^{5} + 13 q^{7}+O(q^{10}) \) 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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