LMFDB - Embedded newform 108.5.g.a.89.3

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			89.3
Root			$3.72537 + 4.42407i$ of defining polynomial
Character	$\chi$	$=$	108.89
Dual form			108.5.g.a.17.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(7.67992 - 4.43400i) q^{5} +(-30.9381 + 53.5864i) q^{7} +O(q^{10})$	$q+(7.67992 - 4.43400i) q^{5} +(-30.9381 + 53.5864i) q^{7} +(-94.7648 - 54.7125i) q^{11} +(77.8628 + 134.862i) q^{13} +395.955i q^{17} +140.350 q^{19} +(-802.818 + 463.507i) q^{23} +(-273.179 + 473.160i) q^{25} +(-323.853 - 186.976i) q^{29} +(521.830 + 903.837i) q^{31} +548.719i q^{35} -194.990 q^{37} +(2344.14 - 1353.39i) q^{41} +(-167.963 + 290.920i) q^{43} +(-2468.76 - 1425.34i) q^{47} +(-713.836 - 1236.40i) q^{49} +2765.43i q^{53} -970.381 q^{55} +(4354.55 - 2514.10i) q^{59} +(3523.59 - 6103.03i) q^{61} +(1195.96 + 690.488i) q^{65} +(-3439.96 - 5958.19i) q^{67} -821.812i q^{71} +4091.53 q^{73} +(5863.69 - 3385.40i) q^{77} +(-3783.56 + 6553.32i) q^{79} +(-6777.78 - 3913.15i) q^{83} +(1755.67 + 3040.90i) q^{85} +1283.28i q^{89} -9635.72 q^{91} +(1077.88 - 622.313i) q^{95} +(1890.33 - 3274.14i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	7.67992	−	4.43400i	0.307197	−	0.177360i	−0.338475	−	0.940976i	$-0.609911\pi$
$5$	7.67992	−	4.43400i	0.307197	−	0.177360i	0.645671	+	0.763615i	$0.276578\pi$
$6$		0			0
$7$	−30.9381	+	53.5864i	−0.631390	+	1.09360i	0.355877	+	0.934533i	$0.384182\pi$
$7$	−30.9381	+	53.5864i	−0.631390	+	1.09360i	−0.987268	+	0.159068i	$0.949151\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−94.7648	−	54.7125i	−0.783180	−	0.452169i	0.0543761	−	0.998521i	$-0.482683\pi$
$11$	−94.7648	−	54.7125i	−0.783180	−	0.452169i	−0.837556	+	0.546351i	$0.816016\pi$
$12$		0			0
$13$	77.8628	+	134.862i	0.460727	+	0.798002i	0.998997	−	0.0447702i	$-0.0142556\pi$
$13$	77.8628	+	134.862i	0.460727	+	0.798002i	−0.538271	+	0.842772i	$0.680922\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$			395.955i			1.37009i	0.728502	+	0.685044i	$0.240217\pi$
$17$			395.955i			1.37009i	−0.728502	+	0.685044i	$0.759783\pi$
$18$		0			0
$19$	140.350			0.388782			0.194391	−	0.980924i	$-0.437727\pi$
$19$	140.350			0.388782			0.194391	+	0.980924i	$0.437727\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−802.818	+	463.507i	−1.51761	+	0.876195i	−0.517829	+	0.855484i	$0.673260\pi$
$23$	−802.818	+	463.507i	−1.51761	+	0.876195i	−0.999785	+	0.0207115i	$0.993407\pi$
$24$		0			0
$25$	−273.179	+	473.160i	−0.437087	+	0.757056i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−323.853	−	186.976i	−0.385080	−	0.222326i	0.294946	−	0.955514i	$-0.404698\pi$
$29$	−323.853	−	186.976i	−0.385080	−	0.222326i	−0.680026	+	0.733188i	$0.738032\pi$
$30$		0			0
$31$	521.830	+	903.837i	0.543008	+	0.940517i	0.998729	+	0.0503946i	$0.0160479\pi$
$31$	521.830	+	903.837i	0.543008	+	0.940517i	−0.455722	+	0.890122i	$0.650619\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$			548.719i			0.447934i
$36$		0			0
$37$	−194.990			−0.142432			−0.0712162	−	0.997461i	$-0.522688\pi$
$37$	−194.990			−0.142432			−0.0712162	+	0.997461i	$0.522688\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	2344.14	−	1353.39i	1.39449	−	0.805110i	0.400682	−	0.916217i	$-0.368773\pi$
$41$	2344.14	−	1353.39i	1.39449	−	0.805110i	0.993808	+	0.111108i	$0.0354398\pi$
$42$		0			0
$43$	−167.963	+	290.920i	−0.0908397	+	0.157339i	−0.907865	−	0.419263i	$-0.862288\pi$
$43$	−167.963	+	290.920i	−0.0908397	+	0.157339i	0.817025	+	0.576602i	$0.195622\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−2468.76	−	1425.34i	−1.11759	−	0.645241i	−0.176805	−	0.984246i	$-0.556576\pi$
$47$	−2468.76	−	1425.34i	−1.11759	−	0.645241i	−0.940785	+	0.339005i	$0.889910\pi$
$48$		0			0
$49$	−713.836	−	1236.40i	−0.297308	−	0.514952i
$50$		0			0
$51$		0			0
$52$		0			0
$53$			2765.43i			0.984490i	0.870457	+	0.492245i	$0.163824\pi$
$53$			2765.43i			0.984490i	−0.870457	+	0.492245i	$0.836176\pi$
$54$		0			0
$55$	−970.381			−0.320787
$56$		0			0
$57$		0			0
$58$		0			0
$59$	4354.55	−	2514.10i	1.25095	−	0.722236i	0.279651	−	0.960102i	$-0.409781\pi$
$59$	4354.55	−	2514.10i	1.25095	−	0.722236i	0.971298	+	0.237866i	$0.0764479\pi$
$60$		0			0
$61$	3523.59	−	6103.03i	0.946947	−	1.64016i	0.195140	−	0.980775i	$-0.437484\pi$
$61$	3523.59	−	6103.03i	0.946947	−	1.64016i	0.751806	−	0.659384i	$-0.229183\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	1195.96	+	690.488i	0.283067	+	0.163429i
$66$		0			0
$67$	−3439.96	−	5958.19i	−0.766309	−	1.32729i	−0.939551	−	0.342408i	$-0.888758\pi$
$67$	−3439.96	−	5958.19i	−0.766309	−	1.32729i	0.173242	−	0.984879i	$-0.444576\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	821.812i		−	0.163026i	−0.996672	−	0.0815128i	$-0.974025\pi$
$71$		−	821.812i		−	0.163026i	0.996672	−	0.0815128i	$-0.0259752\pi$
$72$		0			0
$73$	4091.53			0.767786			0.383893	−	0.923378i	$-0.374583\pi$
$73$	4091.53			0.767786			0.383893	+	0.923378i	$0.374583\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	5863.69	−	3385.40i	0.988985	−	0.570991i
$78$		0			0
$79$	−3783.56	+	6553.32i	−0.606243	+	1.05004i	0.385611	+	0.922661i	$0.373991\pi$
$79$	−3783.56	+	6553.32i	−0.606243	+	1.05004i	−0.991854	+	0.127382i	$0.959343\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−6777.78	−	3913.15i	−0.983855	−	0.568029i	−0.0804236	−	0.996761i	$-0.525627\pi$
$83$	−6777.78	−	3913.15i	−0.983855	−	0.568029i	−0.903432	+	0.428732i	$0.858961\pi$
$84$		0			0
$85$	1755.67	+	3040.90i	0.242999	+	0.420886i
$86$		0			0
$87$		0			0
$88$		0			0
$89$			1283.28i			0.162010i	0.996714	+	0.0810051i	$0.0258130\pi$
$89$			1283.28i			0.162010i	−0.996714	+	0.0810051i	$0.974187\pi$
$90$		0			0
$91$	−9635.72			−1.16359
$92$		0			0
$93$		0			0
$94$		0			0
$95$	1077.88	−	622.313i	0.119432	−	0.0689544i
$96$		0			0
$97$	1890.33	−	3274.14i	0.200906	−	0.347979i	−0.747915	−	0.663795i	$-0.768945\pi$
$97$	1890.33	−	3274.14i	0.200906	−	0.347979i	0.948821	+	0.315816i	$0.102278\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	1034.99	+	597.553i	0.101460	+	0.0585779i	0.549871	−	0.835249i	$-0.314677\pi$
$101$	1034.99	+	597.553i	0.101460	+	0.0585779i	−0.448411	+	0.893827i	$0.648010\pi$
$102$		0			0
$103$	6767.50	+	11721.6i	0.637901	+	1.10488i	0.985892	+	0.167380i	$0.0535306\pi$
$103$	6767.50	+	11721.6i	0.637901	+	1.10488i	−0.347991	+	0.937498i	$0.613136\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			18095.0i			1.58049i	0.612792	+	0.790244i	$0.290046\pi$
$107$			18095.0i			1.58049i	−0.612792	+	0.790244i	$0.709954\pi$
$108$		0			0
$109$	10676.5			0.898621			0.449311	−	0.893376i	$-0.351670\pi$
$109$	10676.5			0.898621			0.449311	+	0.893376i	$0.351670\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−11083.8	+	6399.21i	−0.868021	+	0.501152i	−0.866690	−	0.498847i	$-0.833757\pi$
$113$	−11083.8	+	6399.21i	−0.868021	+	0.501152i	−0.00133098	+	0.999999i	$0.500424\pi$
$114$		0			0
$115$	−4110.39	+	7119.40i	−0.310804	+	0.538329i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−21217.8	−	12250.1i	−1.49833	−	0.865060i
$120$		0			0
$121$	−1333.59	−	2309.85i	−0.0910861	−	0.157766i
$122$		0			0
$123$		0			0
$124$		0			0
$125$			10387.6i			0.664807i
$126$		0			0
$127$	449.363			0.0278606			0.0139303	−	0.999903i	$-0.495566\pi$
$127$	449.363			0.0278606			0.0139303	+	0.999903i	$0.495566\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−10075.4	+	5817.06i	−0.587113	+	0.338970i	−0.763955	−	0.645270i	$-0.776745\pi$
$131$	−10075.4	+	5817.06i	−0.587113	+	0.338970i	0.176842	+	0.984239i	$0.443412\pi$
$132$		0			0
$133$	−4342.17	+	7520.86i	−0.245473	+	0.425172i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	24400.6	+	14087.7i	1.30005	+	0.750584i	0.980412	−	0.196956i	$-0.0631055\pi$
$137$	24400.6	+	14087.7i	1.30005	+	0.750584i	0.319637	+	0.947540i	$0.396439\pi$
$138$		0			0
$139$	4747.58	+	8223.05i	0.245721	+	0.425602i	0.962334	−	0.271869i	$-0.0876419\pi$
$139$	4747.58	+	8223.05i	0.245721	+	0.425602i	−0.716613	+	0.697471i	$0.754309\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		−	17040.3i		−	0.833305i
$144$		0			0
$145$	−3316.22			−0.157727
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−1730.39	+	999.043i	−0.0779422	+	0.0449999i	−0.538465	−	0.842648i	$-0.680995\pi$
$149$	−1730.39	+	999.043i	−0.0779422	+	0.0449999i	0.460522	+	0.887648i	$0.347662\pi$
$150$		0			0
$151$	1855.61	−	3214.02i	0.0813830	−	0.140959i	−0.822461	−	0.568821i	$-0.807400\pi$
$151$	1855.61	−	3214.02i	0.0813830	−	0.140959i	0.903844	+	0.427862i	$0.140733\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	8015.23	+	4627.59i	0.333620	+	0.192616i
$156$		0			0
$157$	−1458.43	−	2526.07i	−0.0591679	−	0.102482i	0.834924	−	0.550365i	$-0.185511\pi$
$157$	−1458.43	−	2526.07i	−0.0591679	−	0.102482i	−0.894092	+	0.447883i	$0.852178\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		−	57360.2i		−	2.21289i
$162$		0			0
$163$	−5975.21			−0.224894			−0.112447	−	0.993658i	$-0.535869\pi$
$163$	−5975.21			−0.224894			−0.112447	+	0.993658i	$0.535869\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	3610.95	−	2084.78i	0.129476	−	0.0747529i	−0.433863	−	0.900979i	$-0.642850\pi$
$167$	3610.95	−	2084.78i	0.129476	−	0.0747529i	0.563339	+	0.826226i	$0.309517\pi$
$168$		0			0
$169$	2155.27	−	3733.05i	0.0754622	−	0.130704i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	26710.3	+	15421.2i	0.892455	+	0.515259i	0.874745	−	0.484584i	$-0.161029\pi$
$173$	26710.3	+	15421.2i	0.892455	+	0.515259i	0.0177101	+	0.999843i	$0.494362\pi$
$174$		0			0
$175$	−16903.3	−	29277.4i	−0.551945	−	0.955996i
$176$		0			0
$177$		0			0
$178$		0			0
$179$		−	5977.90i		−	0.186570i	−0.995639	−	0.0932852i	$-0.970263\pi$
$179$		−	5977.90i		−	0.186570i	0.995639	−	0.0932852i	$-0.0297368\pi$
$180$		0			0
$181$	−6456.49			−0.197079			−0.0985393	−	0.995133i	$-0.531417\pi$
$181$	−6456.49			−0.197079			−0.0985393	+	0.995133i	$0.531417\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−1497.51	+	864.586i	−0.0437548	+	0.0252618i
$186$		0			0
$187$	21663.7	−	37522.6i	0.619511	−	1.07302i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	20643.3	+	11918.4i	0.565865	+	0.326703i	0.755496	−	0.655153i	$-0.227396\pi$
$191$	20643.3	+	11918.4i	0.565865	+	0.326703i	−0.189631	+	0.981855i	$0.560729\pi$
$192$		0			0
$193$	−20081.7	−	34782.5i	−0.539121	−	0.933784i	−0.998952	−	0.0457779i	$-0.985423\pi$
$193$	−20081.7	−	34782.5i	−0.539121	−	0.933784i	0.459831	−	0.888006i	$-0.347910\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			3622.11i			0.0933318i	0.998911	+	0.0466659i	$0.0148596\pi$
$197$			3622.11i			0.0933318i	−0.998911	+	0.0466659i	$0.985140\pi$
$198$		0			0
$199$	46416.3			1.17210			0.586049	−	0.810276i	$-0.300683\pi$
$199$	46416.3			1.17210			0.586049	+	0.810276i	$0.300683\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	20038.8	−	11569.4i	0.486272	−	0.280749i
$204$		0			0
$205$	12001.9	−	20787.8i	0.285589	−	0.494654i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−13300.3	−	7678.91i	−0.304486	−	0.175795i
$210$		0			0
$211$	764.093	+	1323.45i	0.0171625	+	0.0297264i	0.874479	−	0.485063i	$-0.161203\pi$
$211$	764.093	+	1323.45i	0.0171625	+	0.0297264i	−0.857317	+	0.514790i	$0.827870\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$			2978.99i			0.0644453i
$216$		0			0
$217$	−64577.8			−1.37140
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−53399.4	+	30830.2i	−1.09333	+	0.631235i
$222$		0			0
$223$	−13741.4	+	23800.8i	−0.276326	+	0.478610i	−0.970469	−	0.241227i	$-0.922450\pi$
$223$	−13741.4	+	23800.8i	−0.276326	+	0.478610i	0.694143	+	0.719837i	$0.255784\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	39178.5	+	22619.7i	0.760319	+	0.438970i	0.829410	−	0.558640i	$-0.188677\pi$
$227$	39178.5	+	22619.7i	0.760319	+	0.438970i	−0.0690916	+	0.997610i	$0.522010\pi$
$228$		0			0
$229$	40074.3	+	69410.7i	0.764178	+	1.32360i	0.940680	+	0.339295i	$0.110189\pi$
$229$	40074.3	+	69410.7i	0.764178	+	1.32360i	−0.176502	+	0.984300i	$0.556478\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	90756.0i		−	1.67172i	−0.548942	−	0.835860i	$-0.684969\pi$
$233$		−	90756.0i		−	1.67172i	0.548942	−	0.835860i	$-0.315031\pi$
$234$		0			0
$235$	−25279.8			−0.457760
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−708.324	+	408.951i	−0.0124004	+	0.00715938i	−0.506187	−	0.862424i	$-0.668946\pi$
$239$	−708.324	+	408.951i	−0.0124004	+	0.00715938i	0.493787	+	0.869583i	$0.335612\pi$
$240$		0			0
$241$	−37158.1	+	64359.7i	−0.639764	+	1.10810i	0.345721	+	0.938337i	$0.387634\pi$
$241$	−37158.1	+	64359.7i	−0.639764	+	1.10810i	−0.985484	+	0.169766i	$0.945699\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−10964.4	−	6330.30i	−0.182664	−	0.105461i
$246$		0			0
$247$	10928.1	+	18928.0i	0.179122	+	0.310249i
$248$		0			0
$249$		0			0
$250$		0			0
$251$			16304.4i			0.258796i	0.991593	+	0.129398i	$0.0413045\pi$
$251$			16304.4i			0.258796i	−0.991593	+	0.129398i	$0.958695\pi$
$252$		0			0
$253$	101439.			1.58475
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−108732.	+	62776.2i	−1.64623	+	0.950449i	−0.667673	+	0.744454i	$0.732710\pi$
$257$	−108732.	+	62776.2i	−1.64623	+	0.950449i	−0.978553	+	0.205995i	$0.933957\pi$
$258$		0			0
$259$	6032.63	−	10448.8i	0.0899305	−	0.155764i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	13971.9	+	8066.67i	0.201996	+	0.116623i	0.597586	−	0.801805i	$-0.296127\pi$
$263$	13971.9	+	8066.67i	0.201996	+	0.116623i	−0.395590	+	0.918427i	$0.629460\pi$
$264$		0			0
$265$	12261.9	+	21238.3i	0.174609	+	0.302432i
$266$		0			0
$267$		0			0
$268$		0			0
$269$			75561.0i			1.04422i	0.852877	+	0.522112i	$0.174856\pi$
$269$			75561.0i			1.04422i	−0.852877	+	0.522112i	$0.825144\pi$
$270$		0			0
$271$	−14842.2			−0.202097			−0.101049	−	0.994881i	$-0.532220\pi$
$271$	−14842.2			−0.202097			−0.101049	+	0.994881i	$0.532220\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	51775.5	−	29892.6i	0.684635	−	0.395274i
$276$		0			0
$277$	−40381.1	+	69942.2i	−0.526283	+	0.911548i	0.473248	+	0.880929i	$0.343081\pi$
$277$	−40381.1	+	69942.2i	−0.526283	+	0.911548i	−0.999531	+	0.0306193i	$0.990252\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−57384.8	−	33131.1i	−0.726749	−	0.419589i	0.0904828	−	0.995898i	$-0.471159\pi$
$281$	−57384.8	−	33131.1i	−0.726749	−	0.419589i	−0.817232	+	0.576309i	$0.804492\pi$
$282$		0			0
$283$	−7288.93	−	12624.8i	−0.0910104	−	0.157635i	0.816926	−	0.576742i	$-0.195676\pi$
$283$	−7288.93	−	12624.8i	−0.0910104	−	0.157635i	−0.907937	+	0.419108i	$0.862343\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			167485.i			2.03335i
$288$		0			0
$289$	−73259.5			−0.877139
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−65027.8	+	37543.8i	−0.757467	+	0.437324i	−0.828386	−	0.560158i	$-0.810740\pi$
$293$	−65027.8	+	37543.8i	−0.757467	+	0.437324i	0.0709185	+	0.997482i	$0.477407\pi$
$294$		0			0
$295$	22295.1	−	38616.2i	0.256192	−	0.443737i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−125019.	−	72179.9i	−1.39841	−	0.807373i
$300$		0			0
$301$	−10392.9	−	18001.0i	−0.114711	−	0.198685i
$302$		0			0
$303$		0			0
$304$		0			0
$305$		−	62494.4i		−	0.671802i
$306$		0			0
$307$	146994.			1.55963			0.779817	−	0.626007i	$-0.215312\pi$
$307$	146994.			1.55963			0.779817	+	0.626007i	$0.215312\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	126237.	−	72882.7i	1.30516	−	0.753536i	0.323878	−	0.946099i	$-0.395013\pi$
$311$	126237.	−	72882.7i	1.30516	−	0.753536i	0.981285	+	0.192563i	$0.0616800\pi$
$312$		0			0
$313$	37866.9	−	65587.3i	0.386519	−	0.669470i	−0.605460	−	0.795876i	$-0.707011\pi$
$313$	37866.9	−	65587.3i	0.386519	−	0.669470i	0.991979	+	0.126406i	$0.0403441\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	80308.7	+	46366.3i	0.799179	+	0.461406i	0.843184	−	0.537625i	$-0.180678\pi$
$317$	80308.7	+	46366.3i	0.799179	+	0.461406i	−0.0440049	+	0.999031i	$0.514012\pi$
$318$		0			0
$319$	20459.9	+	35437.6i	0.201058	+	0.348243i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			55572.4i			0.532665i
$324$		0			0
$325$	−85082.0			−0.805510
$326$		0			0
$327$		0			0
$328$		0			0
$329$	152757.	−	88194.5i	1.41127	−	0.814798i
$330$		0			0
$331$	−5404.90	+	9361.56i	−0.0493323	+	0.0854461i	−0.889637	−	0.456668i	$-0.849043\pi$
$331$	−5404.90	+	9361.56i	−0.0493323	+	0.0854461i	0.840305	+	0.542114i	$0.182376\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−52837.3	−	30505.6i	−0.470816	−	0.271825i
$336$		0			0
$337$	−65323.7	−	113144.i	−0.575190	−	0.996258i	−0.996021	−	0.0891187i	$-0.971595\pi$
$337$	−65323.7	−	113144.i	−0.575190	−	0.996258i	0.420831	−	0.907139i	$-0.361738\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		−	114203.i		−	0.982125i
$342$		0			0
$343$	−60225.9			−0.511912
$344$		0			0
$345$		0			0
$346$		0			0
$347$	141648.	−	81780.7i	1.17639	−	0.679191i	0.221216	−	0.975225i	$-0.428997\pi$
$347$	141648.	−	81780.7i	1.17639	−	0.679191i	0.955177	+	0.296034i	$0.0956641\pi$
$348$		0			0
$349$	−7232.92	+	12527.8i	−0.0593831	+	0.102855i	−0.894189	−	0.447690i	$-0.852247\pi$
$349$	−7232.92	+	12527.8i	−0.0593831	+	0.102855i	0.834806	+	0.550545i	$0.185580\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	8348.17	+	4819.82i	0.0669949	+	0.0386795i	0.533123	−	0.846038i	$-0.321018\pi$
$353$	8348.17	+	4819.82i	0.0669949	+	0.0386795i	−0.466128	+	0.884717i	$0.654352\pi$
$354$		0			0
$355$	−3643.92	−	6311.45i	−0.0289143	−	0.0500810i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			56543.7i			0.438728i	0.975643	+	0.219364i	$0.0703982\pi$
$359$			56543.7i			0.438728i	−0.975643	+	0.219364i	$0.929602\pi$
$360$		0			0
$361$	−110623.			−0.848849
$362$		0			0
$363$		0			0
$364$		0			0
$365$	31422.6	−	18141.9i	0.235861	−	0.136175i
$366$		0			0
$367$	79981.5	−	138532.i	0.593824	−	1.02853i	−0.399888	−	0.916564i	$-0.630951\pi$
$367$	79981.5	−	138532.i	0.593824	−	1.02853i	0.993712	−	0.111969i	$-0.0357157\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−148190.	−	85557.3i	−1.07664	−	0.621598i
$372$		0			0
$373$	52486.5	+	90909.4i	0.377251	+	0.653418i	0.990661	−	0.136347i	$-0.0435361\pi$
$373$	52486.5	+	90909.4i	0.377251	+	0.653418i	−0.613410	+	0.789764i	$0.710203\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	58234.0i		−	0.409727i
$378$		0			0
$379$	25050.7			0.174398			0.0871989	−	0.996191i	$-0.472208\pi$
$379$	25050.7			0.174398			0.0871989	+	0.996191i	$0.472208\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−45503.9	+	26271.7i	−0.310207	+	0.179098i	−0.647019	−	0.762474i	$-0.723985\pi$
$383$	−45503.9	+	26271.7i	−0.310207	+	0.179098i	0.336812	+	0.941572i	$0.390651\pi$
$384$		0			0
$385$	30021.8	−	51999.2i	0.202542	−	0.350813i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	175082.	+	101084.i	1.15702	+	0.668008i	0.950589	−	0.310452i	$-0.100480\pi$
$389$	175082.	+	101084.i	1.15702	+	0.668008i	0.206435	+	0.978460i	$0.433814\pi$
$390$		0			0
$391$	−183528.	−	317880.i	−1.20046	−	2.07926i
$392$		0			0
$393$		0			0
$394$		0			0
$395$			67105.3i			0.430093i
$396$		0			0
$397$	303603.			1.92631			0.963154	−	0.268951i	$-0.0866770\pi$
$397$	303603.			1.92631			0.963154	+	0.268951i	$0.0866770\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	102431.	−	59138.8i	0.637007	−	0.367776i	−0.146453	−	0.989218i	$-0.546786\pi$
$401$	102431.	−	59138.8i	0.637007	−	0.367776i	0.783461	+	0.621441i	$0.213453\pi$
$402$		0			0
$403$	−81262.3	+	140750.i	−0.500356	+	0.866642i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	18478.2	+	10668.4i	0.111550	+	0.0644036i
$408$		0			0
$409$	−20533.2	−	35564.6i	−0.122747	−	0.212604i	0.798103	−	0.602521i	$-0.205837\pi$
$409$	−20533.2	−	35564.6i	−0.122747	−	0.212604i	−0.920850	+	0.389917i	$0.872504\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$			311127.i			1.82405i
$414$		0			0
$415$	−69403.7			−0.402983
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−86655.8	+	50030.8i	−0.493594	+	0.284976i	−0.726064	−	0.687627i	$-0.758652\pi$
$419$	−86655.8	+	50030.8i	−0.493594	+	0.284976i	0.232470	+	0.972603i	$0.425319\pi$
$420$		0			0
$421$	110257.	−	190971.i	0.622074	−	1.07746i	−0.367024	−	0.930211i	$-0.619623\pi$
$421$	110257.	−	190971.i	0.622074	−	1.07746i	0.989099	−	0.147253i	$-0.0470432\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−187350.	−	108167.i	−1.03723	−	0.598847i
$426$		0			0
$427$	218026.	+	377633.i	1.19579	+	2.07116i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		−	211457.i		−	1.13833i	−0.822224	−	0.569163i	$-0.807267\pi$
$431$		−	211457.i		−	1.13833i	0.822224	−	0.569163i	$-0.192733\pi$
$432$		0			0
$433$	−106655.			−0.568859			−0.284430	−	0.958697i	$-0.591804\pi$
$433$	−106655.			−0.568859			−0.284430	+	0.958697i	$0.591804\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−112676.	+	65053.4i	−0.590021	+	0.340649i
$438$		0			0
$439$	−107195.	+	185667.i	−0.556218	+	0.963397i	0.441590	+	0.897217i	$0.354415\pi$
$439$	−107195.	+	185667.i	−0.556218	+	0.963397i	−0.997808	+	0.0661804i	$0.978919\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−174614.	−	100814.i	−0.889759	−	0.513703i	−0.0158954	−	0.999874i	$-0.505060\pi$
$443$	−174614.	−	100814.i	−0.889759	−	0.513703i	−0.873864	+	0.486171i	$0.838393\pi$
$444$		0			0
$445$	5690.08	+	9855.50i	0.0287341	+	0.0497690i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			136895.i			0.679039i	0.940599	+	0.339519i	$0.110264\pi$
$449$			136895.i			0.679039i	−0.940599	+	0.339519i	$0.889736\pi$
$450$		0			0
$451$	−296189.			−1.45618
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−74001.5	+	42724.8i	−0.357452	+	0.206375i
$456$		0			0
$457$	−183338.	+	317551.i	−0.877850	+	1.52048i	−0.0241542	+	0.999708i	$0.507689\pi$
$457$	−183338.	+	317551.i	−0.877850	+	1.52048i	−0.853696	+	0.520772i	$0.825644\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	42379.8	+	24468.0i	0.199415	+	0.115132i	0.596382	−	0.802700i	$-0.296604\pi$
$461$	42379.8	+	24468.0i	0.199415	+	0.115132i	−0.396968	+	0.917833i	$0.629938\pi$
$462$		0			0
$463$	143514.	+	248574.i	0.669472	+	1.15956i	0.978052	+	0.208361i	$0.0668128\pi$
$463$	143514.	+	248574.i	0.669472	+	1.15956i	−0.308580	+	0.951198i	$0.599854\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			43613.3i			0.199979i	0.994988	+	0.0999896i	$0.0318809\pi$
$467$			43613.3i			0.199979i	−0.994988	+	0.0999896i	$0.968119\pi$
$468$		0			0
$469$	425704.			1.93536
$470$		0			0
$471$		0			0
$472$		0			0
$473$	31833.9	−	18379.3i	0.142288	−	0.0821498i
$474$		0			0
$475$	−38340.8	+	66408.2i	−0.169931	+	0.294330i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	199073.	+	114935.i	0.867642	+	0.500933i	0.866564	−	0.499066i	$-0.166324\pi$
$479$	199073.	+	114935.i	0.867642	+	0.500933i	0.00107799	+	0.999999i	$0.499657\pi$
$480$		0			0
$481$	−15182.5	−	26296.8i	−0.0656224	−	0.113661i
$482$		0			0
$483$		0			0
$484$		0			0
$485$		−	33526.8i		−	0.142531i
$486$		0			0
$487$	−15921.9			−0.0671330			−0.0335665	−	0.999436i	$-0.510687\pi$
$487$	−15921.9			−0.0671330			−0.0335665	+	0.999436i	$0.510687\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−145540.	+	84027.8i	−0.603699	+	0.348546i	−0.770496	−	0.637445i	$-0.779991\pi$
$491$	−145540.	+	84027.8i	−0.603699	+	0.348546i	0.166796	+	0.985991i	$0.446658\pi$
$492$		0			0
$493$	74034.3	−	128231.i	0.304606	−	0.527594i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	44038.0	+	25425.3i	0.178285	+	0.102933i
$498$		0			0
$499$	−178029.	−	308355.i	−0.714971	−	1.23837i	−0.962971	−	0.269607i	$-0.913106\pi$
$499$	−178029.	−	308355.i	−0.714971	−	1.23837i	0.247999	−	0.968760i	$-0.420227\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		−	180472.i		−	0.713301i	−0.934238	−	0.356651i	$-0.883919\pi$
$503$		−	180472.i		−	0.713301i	0.934238	−	0.356651i	$-0.116081\pi$
$504$		0			0
$505$	10598.2			0.0415575
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−345324.	+	199373.i	−1.33288	+	0.769540i	−0.985740	−	0.168273i	$-0.946181\pi$
$509$	−345324.	+	199373.i	−1.33288	+	0.769540i	−0.347142	+	0.937813i	$0.612848\pi$
$510$		0			0
$511$	−126584.	+	219250.i	−0.484772	+	0.839651i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	103948.	+	60014.2i	0.391922	+	0.226277i
$516$		0			0
$517$	155967.	+	270143.i	0.583516	+	1.01068i
$518$		0			0
$519$		0			0
$520$		0			0
$521$		−	485387.i		−	1.78819i	−0.447880	−	0.894094i	$-0.647821\pi$
$521$		−	485387.i		−	1.78819i	0.447880	−	0.894094i	$-0.352179\pi$
$522$		0			0
$523$	80589.4			0.294628			0.147314	−	0.989090i	$-0.452937\pi$
$523$	80589.4			0.294628			0.147314	+	0.989090i	$0.452937\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−357879.	+	206621.i	−1.28859	+	0.743968i
$528$		0			0
$529$	289758.	−	501875.i	1.03544	−	1.79343i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	365042.	+	210757.i	1.28496	+	0.741871i
$534$		0			0
$535$	80233.3	+	138968.i	0.280316	+	0.485521i
$536$		0			0
$537$		0			0
$538$		0			0
$539$			156223.i			0.537734i
$540$		0			0
$541$	−446700.			−1.52623			−0.763117	−	0.646260i	$-0.776332\pi$
$541$	−446700.			−1.52623			−0.763117	+	0.646260i	$0.776332\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	81994.8	−	47339.7i	0.276053	−	0.159380i
$546$		0			0
$547$	126958.	−	219898.i	0.424312	−	0.734931i	−0.572043	−	0.820223i	$-0.693849\pi$
$547$	126958.	−	219898.i	0.424312	−	0.734931i	0.996356	+	0.0852925i	$0.0271825\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−45452.8	−	26242.2i	−0.149712	−	0.0864364i
$552$		0			0
$553$	−234113.	−	405495.i	−0.765552	−	1.32597i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			49265.2i			0.158792i	0.996843	+	0.0793962i	$0.0252992\pi$
$557$			49265.2i			0.158792i	−0.996843	+	0.0793962i	$0.974701\pi$
$558$		0			0
$559$	−52312.1			−0.167409
$560$		0			0
$561$		0			0
$562$		0			0
$563$	342365.	−	197665.i	1.08012	−	0.623608i	0.149192	−	0.988808i	$-0.452333\pi$
$563$	342365.	−	197665.i	1.08012	−	0.623608i	0.930929	+	0.365200i	$0.118999\pi$
$564$		0			0
$565$	−56748.3	+	98290.9i	−0.177769	+	0.307905i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	224474.	+	129600.i	0.693332	+	0.400296i	0.804859	−	0.593466i	$-0.202241\pi$
$569$	224474.	+	129600.i	0.693332	+	0.400296i	−0.111527	+	0.993761i	$0.535574\pi$
$570$		0			0
$571$	−226228.	−	391839.i	−0.693864	−	1.20181i	−0.970562	−	0.240851i	$-0.922573\pi$
$571$	−226228.	−	391839.i	−0.693864	−	1.20181i	0.276697	−	0.960957i	$-0.410760\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	506482.i		−	1.53189i
$576$		0			0
$577$	499076.			1.49905			0.749523	−	0.661978i	$-0.230283\pi$
$577$	499076.			1.49905			0.749523	+	0.661978i	$0.230283\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	419384.	−	242131.i	1.24239	−	0.717296i
$582$		0			0
$583$	151304.	−	262066.i	0.445156	−	0.771033i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−238.906	−	137.932i	−0.000693347	−	0.000400304i	0.499653	−	0.866225i	$-0.333461\pi$
$587$	−238.906	−	137.932i	−0.000693347	−	0.000400304i	−0.500347	+	0.865825i	$0.666794\pi$
$588$		0			0
$589$	73239.0	+	126854.i	0.211111	+	0.365656i
$590$		0			0
$591$		0			0
$592$		0			0
$593$			10939.7i			0.0311096i	0.999879	+	0.0155548i	$0.00495145\pi$
$593$			10939.7i			0.0311096i	−0.999879	+	0.0155548i	$0.995049\pi$
$594$		0			0
$595$	−217268.			−0.613708
$596$		0			0
$597$		0			0
$598$		0			0
$599$	13902.7	−	8026.70i	0.0387475	−	0.0223709i	−0.480501	−	0.876994i	$-0.659545\pi$
$599$	13902.7	−	8026.70i	0.0387475	−	0.0223709i	0.519249	+	0.854623i	$0.326212\pi$
$600$		0			0
$601$	−267567.	+	463439.i	−0.740769	+	1.28305i	0.211376	+	0.977405i	$0.432205\pi$
$601$	−267567.	+	463439.i	−0.740769	+	1.28305i	−0.952145	+	0.305645i	$0.901128\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−20483.7	−	11826.3i	−0.0559627	−	0.0323101i
$606$		0			0
$607$	37897.7	+	65640.8i	0.102858	+	0.178154i	0.912861	−	0.408271i	$-0.133868\pi$
$607$	37897.7	+	65640.8i	0.102858	+	0.178154i	−0.810003	+	0.586425i	$0.800535\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		−	443923.i		−	1.18912i
$612$		0			0
$613$	−279865.			−0.744778			−0.372389	−	0.928077i	$-0.621461\pi$
$613$	−279865.			−0.744778			−0.372389	+	0.928077i	$0.621461\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−1881.09	+	1086.05i	−0.00494128	+	0.00285285i	−0.502469	−	0.864595i	$-0.667575\pi$
$617$	−1881.09	+	1086.05i	−0.00494128	+	0.00285285i	0.497527	+	0.867448i	$0.334241\pi$
$618$		0			0
$619$	−3964.87	+	6867.36i	−0.0103478	+	0.0179229i	−0.871153	−	0.491012i	$-0.836627\pi$
$619$	−3964.87	+	6867.36i	−0.0103478	+	0.0179229i	0.860805	+	0.508935i	$0.169961\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−68766.5	−	39702.4i	−0.177174	−	0.102292i
$624$		0			0
$625$	−124678.	−	215949.i	−0.319176	−	0.552830i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		−	77207.3i		−	0.195145i
$630$		0			0
$631$	546257.			1.37195			0.685975	−	0.727625i	$-0.259376\pi$
$631$	546257.			1.37195			0.685975	+	0.727625i	$0.259376\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	3451.07	−	1992.48i	0.00855868	−	0.00494135i
$636$		0			0
$637$	111162.	−	192539.i	0.273955	−	0.474504i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−181888.	−	105013.i	−0.442677	−	0.255580i	0.262055	−	0.965053i	$-0.415600\pi$
$641$	−181888.	−	105013.i	−0.442677	−	0.255580i	−0.704733	+	0.709473i	$0.748933\pi$
$642$		0			0
$643$	39984.7	+	69255.6i	0.0967101	+	0.167507i	0.910321	−	0.413903i	$-0.135835\pi$
$643$	39984.7	+	69255.6i	0.0967101	+	0.167507i	−0.813611	+	0.581410i	$0.802501\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			247483.i			0.591203i	0.955311	+	0.295601i	$0.0955200\pi$
$647$			247483.i			0.591203i	−0.955311	+	0.295601i	$0.904480\pi$
$648$		0			0
$649$	−550211.			−1.30629
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−35706.7	+	20615.3i	−0.0837382	+	0.0483463i	−0.541284	−	0.840840i	$-0.682062\pi$
$653$	−35706.7	+	20615.3i	−0.0837382	+	0.0483463i	0.457546	+	0.889186i	$0.348728\pi$
$654$		0			0
$655$	−51585.7	+	89349.1i	−0.120239	+	0.208261i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	709817.	+	409813.i	1.63446	+	0.943659i	0.982693	+	0.185244i	$0.0593074\pi$
$659$	709817.	+	409813.i	1.63446	+	0.943659i	0.651772	+	0.758415i	$0.274026\pi$
$660$		0			0
$661$	−120074.	−	207974.i	−0.274818	−	0.475999i	0.695271	−	0.718747i	$-0.255284\pi$
$661$	−120074.	−	207974.i	−0.274818	−	0.475999i	−0.970089	+	0.242749i	$0.921951\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$			77012.8i			0.174149i
$666$		0			0
$667$	346660.			0.779205
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−667824.	+	385568.i	−1.48326	+	0.856360i
$672$		0			0
$673$	101639.	−	176044.i	0.224404	−	0.388679i	−0.731737	−	0.681587i	$-0.761290\pi$
$673$	101639.	−	176044.i	0.224404	−	0.388679i	0.956140	+	0.292909i	$0.0946233\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−295368.	−	170531.i	−0.644446	−	0.372071i	0.141879	−	0.989884i	$-0.454686\pi$
$677$	−295368.	−	170531.i	−0.644446	−	0.372071i	−0.786325	+	0.617813i	$0.788019\pi$
$678$		0			0
$679$	116966.	+	202591.i	0.253700	+	0.439422i
$680$		0			0
$681$		0			0
$682$		0			0
$683$			753067.i			1.61433i	0.590326	+	0.807165i	$0.298999\pi$
$683$			753067.i			1.61433i	−0.590326	+	0.807165i	$0.701001\pi$
$684$		0			0
$685$	249860.			0.532495
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−372953.	+	215324.i	−0.785625	+	0.453581i
$690$		0			0
$691$	202444.	−	350643.i	0.423983	−	0.734361i	−0.572341	−	0.820015i	$-0.693965\pi$
$691$	202444.	−	350643.i	0.423983	−	0.734361i	0.996325	+	0.0856546i	$0.0272981\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	72922.0	+	42101.6i	0.150970	+	0.0871623i
$696$		0			0
$697$	535881.	+	928174.i	1.10307	+	1.91057i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			62736.6i			0.127669i	0.997961	+	0.0638344i	$0.0203329\pi$
$701$			62736.6i			0.127669i	−0.997961	+	0.0638344i	$0.979667\pi$
$702$		0			0
$703$	−27366.9			−0.0553751
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−64041.4	+	36974.3i	−0.128122	+	0.0739710i
$708$		0			0
$709$	−478518.	+	828817.i	−0.951931	+	1.64879i	−0.210692	+	0.977553i	$0.567572\pi$
$709$	−478518.	+	828817.i	−0.951931	+	1.64879i	−0.741240	+	0.671241i	$0.765762\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−837870.	−	483744.i	−1.64815	−	0.951562i
$714$		0			0
$715$	−75556.6	−	130868.i	−0.147795	−	0.255989i
$716$		0			0
$717$		0			0
$718$		0			0
$719$		−	109853.i		−	0.212498i	−0.994340	−	0.106249i	$-0.966116\pi$
$719$		−	109853.i		−	0.212498i	0.994340	−	0.106249i	$-0.0338841\pi$
$720$		0			0
$721$	−837495.			−1.61106
$722$		0			0
$723$		0			0
$724$		0			0
$725$	176940.	−	102156.i	0.336627	−	0.194352i
$726$		0			0
$727$	−112227.	+	194383.i	−0.212339	+	0.367781i	−0.952446	−	0.304707i	$-0.901441\pi$
$727$	−112227.	+	194383.i	−0.212339	+	0.367781i	0.740107	+	0.672489i	$0.234775\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−115191.	−	66505.6i	−0.215568	−	0.124458i
$732$		0			0
$733$	−26396.8	−	45720.6i	−0.0491296	−	0.0850950i	0.840415	−	0.541944i	$-0.182311\pi$
$733$	−26396.8	−	45720.6i	−0.0491296	−	0.0850950i	−0.889544	+	0.456849i	$0.848978\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			752836.i			1.38601i
$738$		0			0
$739$	639035.			1.17013			0.585067	−	0.810985i	$-0.301068\pi$
$739$	639035.			1.17013			0.585067	+	0.810985i	$0.301068\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	647838.	−	374029.i	1.17351	−	0.677529i	0.219009	−	0.975723i	$-0.429718\pi$
$743$	647838.	−	374029.i	1.17351	−	0.677529i	0.954505	+	0.298194i	$0.0963842\pi$
$744$		0			0
$745$	−8859.52	+	15345.1i	−0.0159624	+	0.0276477i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−969646.	−	559826.i	−1.72842	−	0.997905i
$750$		0			0
$751$	177786.	+	307935.i	0.315223	+	0.545983i	0.979485	−	0.201518i	$-0.0645873\pi$
$751$	177786.	+	307935.i	0.315223	+	0.545983i	−0.664262	+	0.747500i	$0.731254\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		−	32911.2i		−	0.0577364i
$756$		0			0
$757$	173106.			0.302079			0.151040	−	0.988528i	$-0.451738\pi$
$757$	173106.			0.302079			0.151040	+	0.988528i	$0.451738\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	173520.	−	100182.i	0.299626	−	0.172989i	−0.342649	−	0.939463i	$-0.611324\pi$
$761$	173520.	−	100182.i	0.299626	−	0.172989i	0.642275	+	0.766475i	$0.277991\pi$
$762$		0			0
$763$	−330311.	+	572116.i	−0.567381	+	0.982732i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	678115.	+	391510.i	1.15269	+	0.665506i
$768$		0			0
$769$	200920.	+	348003.i	0.339758	+	0.588478i	0.984387	−	0.176018i	$-0.0563216\pi$
$769$	200920.	+	348003.i	0.339758	+	0.588478i	−0.644629	+	0.764495i	$0.722988\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$			817430.i			1.36802i	0.729474	+	0.684009i	$0.239765\pi$
$773$			817430.i			1.36802i	−0.729474	+	0.684009i	$0.760235\pi$
$774$		0			0
$775$	−570213.			−0.949366
$776$		0			0
$777$		0			0
$778$		0			0
$779$	329000.	−	189948.i	0.542153	−	0.313012i
$780$		0			0
$781$	−44963.4	+	77878.9i	−0.0737152	+	0.127678i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−22401.2	−	12933.4i	−0.0363524	−	0.0209881i
$786$		0			0
$787$	−49202.8	−	85221.7i	−0.0794402	−	0.137594i	0.823568	−	0.567217i	$-0.191980\pi$
$787$	−49202.8	−	85221.7i	−0.0794402	−	0.137594i	−0.903009	+	0.429623i	$0.858647\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		−	791919.i		−	1.26569i
$792$		0			0
$793$	1.09743e6			1.74513
$794$		0			0
$795$		0			0
$796$		0			0
$797$	287305.	−	165876.i	0.452300	−	0.261136i	−0.256501	−	0.966544i	$-0.582570\pi$
$797$	287305.	−	165876.i	0.452300	−	0.261136i	0.708801	+	0.705408i	$0.249236\pi$
$798$		0			0
$799$	564370.	−	977517.i	0.884036	−	1.53120i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−387733.	−	223858.i	−0.601314	−	0.347169i
$804$		0			0
$805$	−254335.	−	440522.i	−0.392478	−	0.679791i
$806$		0			0
$807$		0			0
$808$		0			0
$809$			317676.i			0.485387i	0.970103	+	0.242693i	$0.0780309\pi$
$809$			317676.i			0.485387i	−0.970103	+	0.242693i	$0.921969\pi$
$810$		0			0
$811$	−1.02772e6			−1.56255			−0.781274	−	0.624188i	$-0.785430\pi$
$811$	−1.02772e6			−1.56255			−0.781274	+	0.624188i	$0.785430\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−45889.1	+	26494.1i	−0.0690867	+	0.0398872i
$816$		0			0
$817$	−23573.6	+	40830.6i	−0.0353168	+	0.0611705i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−1.00344e6	−	579339.i	−1.48870	−	0.859501i	−0.488783	−	0.872406i	$-0.662559\pi$
$821$	−1.00344e6	−	579339.i	−1.48870	−	0.859501i	−0.999917	+	0.0129047i	$0.995892\pi$
$822$		0			0
$823$	−442071.	−	765690.i	−0.652669	−	1.13046i	−0.982473	−	0.186406i	$-0.940316\pi$
$823$	−442071.	−	765690.i	−0.652669	−	1.13046i	0.329804	−	0.944049i	$-0.393017\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			772574.i			1.12961i	0.825224	+	0.564806i	$0.191049\pi$
$827$			772574.i			1.12961i	−0.825224	+	0.564806i	$0.808951\pi$
$828$		0			0
$829$	−83501.8			−0.121503			−0.0607515	−	0.998153i	$-0.519350\pi$
$829$	−83501.8			−0.121503			−0.0607515	+	0.998153i	$0.519350\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	489559.	−	282647.i	0.705529	−	0.407337i
$834$		0			0
$835$	18487.9	−	32021.9i	0.0265164	−	0.0459277i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	652813.	+	376902.i	0.927395	+	0.535432i	0.885987	−	0.463711i	$-0.153482\pi$
$839$	652813.	+	376902.i	0.927395	+	0.535432i	0.0414082	+	0.999142i	$0.486816\pi$
$840$		0			0
$841$	−283720.	−	491418.i	−0.401142	−	0.694798i
$842$		0			0
$843$		0			0
$844$		0			0
$845$		−	38226.0i		−	0.0535359i
$846$		0			0
$847$	165035.			0.230043
$848$		0			0
$849$		0			0
$850$		0			0
$851$	156542.	−	90379.3i	0.216158	−	0.124799i
$852$		0			0
$853$	194125.	−	336234.i	0.266798	−	0.462108i	−0.701235	−	0.712930i	$-0.747368\pi$
$853$	194125.	−	336234.i	0.266798	−	0.462108i	0.968033	+	0.250822i	$0.0807010\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	1.01655e6	+	586903.i	1.38409	+	0.799106i	0.992641	−	0.121092i	$-0.0386397\pi$
$857$	1.01655e6	+	586903.i	1.38409	+	0.799106i	0.391452	+	0.920199i	$0.371973\pi$
$858$		0			0
$859$	260195.	+	450672.i	0.352625	+	0.610765i	0.986709	−	0.162500i	$-0.0519558\pi$
$859$	260195.	+	450672.i	0.352625	+	0.610765i	−0.634083	+	0.773265i	$0.718622\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	387934.i		−	0.520878i	−0.965490	−	0.260439i	$-0.916133\pi$
$863$		−	387934.i		−	0.520878i	0.965490	−	0.260439i	$-0.0838673\pi$
$864$		0			0
$865$	273510.			0.365546
$866$		0			0
$867$		0			0
$868$		0			0
$869$	717096.	−	414016.i	0.949594	−	0.548248i
$870$		0			0
$871$	535690.	−	927843.i	0.706118	−	1.22303i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−556635.	−	321373.i	−0.727033	−	0.419753i
$876$		0			0
$877$	−596348.	−	1.03290e6i	−0.775355	−	1.34295i	−0.934595	−	0.355714i	$-0.884238\pi$
$877$	−596348.	−	1.03290e6i	−0.775355	−	1.34295i	0.159240	−	0.987240i	$-0.449096\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	563606.i		−	0.726146i	−0.931761	−	0.363073i	$-0.881728\pi$
$881$		−	563606.i		−	0.726146i	0.931761	−	0.363073i	$-0.118272\pi$
$882$		0			0
$883$	886399.			1.13686			0.568431	−	0.822731i	$-0.307551\pi$
$883$	886399.			1.13686			0.568431	+	0.822731i	$0.307551\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−191045.	+	110300.i	−0.242822	+	0.140193i	−0.616473	−	0.787376i	$-0.711439\pi$
$887$	−191045.	+	110300.i	−0.242822	+	0.140193i	0.373651	+	0.927569i	$0.378106\pi$
$888$		0			0
$889$	−13902.5	+	24079.8i	−0.0175909	+	0.0304683i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−346490.	−	200046.i	−0.434499	−	0.250858i
$894$		0			0
$895$	−26506.0	−	45909.8i	−0.0330901	−	0.0573138i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		−	390280.i		−	0.482900i
$900$		0			0
$901$	−1.09499e6			−1.34884
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−49585.4	+	28628.1i	−0.0605419	+	0.0349539i
$906$		0			0
$907$	142861.	−	247443.i	0.173660	−	0.300788i	−0.766037	−	0.642797i	$-0.777774\pi$
$907$	142861.	−	247443.i	0.173660	−	0.300788i	0.939697	+	0.342009i	$0.111107\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	1.17520e6	+	678500.i	1.41603	+	0.817547i	0.995947	−	0.0899368i	$-0.0286665\pi$
$911$	1.17520e6	+	678500.i	1.41603	+	0.817547i	0.420086	+	0.907484i	$0.362000\pi$
$912$		0			0
$913$	428197.	+	741658.i	0.513691	+	0.889738i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		−	719876.i		−	0.856089i
$918$		0			0
$919$	−185850.			−0.220055			−0.110028	−	0.993929i	$-0.535094\pi$
$919$	−185850.			−0.220055			−0.110028	+	0.993929i	$0.535094\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	110832.	−	63988.6i	0.130095	−	0.0751103i
$924$		0			0
$925$	53267.2	−	92261.6i	0.0622553	−	0.107829i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	346728.	+	200183.i	0.401751	+	0.231951i	0.687239	−	0.726431i	$-0.258822\pi$
$929$	346728.	+	200183.i	0.401751	+	0.231951i	−0.285488	+	0.958382i	$0.592156\pi$
$930$		0			0
$931$	−100187.	−	173529.i	−0.115588	−	0.200204i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		−	384227.i		−	0.439506i
$936$		0			0
$937$	−351423.			−0.400268			−0.200134	−	0.979769i	$-0.564138\pi$
$937$	−351423.			−0.400268			−0.200134	+	0.979769i	$0.564138\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	902928.	−	521306.i	1.01970	−	0.588726i	0.105686	−	0.994400i	$-0.466296\pi$
$941$	902928.	−	521306.i	1.01970	−	0.588726i	0.914018	+	0.405673i	$0.132963\pi$
$942$		0			0
$943$	−1.25461e6	+	2.17305e6i	−1.41087	+	2.44369i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−972731.	−	561606.i	−1.08466	−	0.626227i	−0.152509	−	0.988302i	$-0.548735\pi$
$947$	−972731.	−	561606.i	−1.08466	−	0.626227i	−0.932149	+	0.362075i	$0.882069\pi$
$948$		0			0
$949$	318578.	+	551793.i	0.353739	+	0.612694i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			1.20759e6i			1.32964i	0.747005	+	0.664819i	$0.231491\pi$
$953$			1.20759e6i			1.32964i	−0.747005	+	0.664819i	$0.768509\pi$
$954$		0			0
$955$	211385.			0.231776
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−1.50982e6	+	871695.i	−1.64168	+	0.947823i
$960$		0			0
$961$	−82853.4	+	143506.i	−0.0897146	+	0.155390i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−308452.	−	178085.i	−0.331232	−	0.191237i
$966$		0			0
$967$	−226893.	−	392990.i	−0.242643	−	0.420270i	0.718823	−	0.695193i	$-0.244681\pi$
$967$	−226893.	−	392990.i	−0.242643	−	0.420270i	−0.961466	+	0.274923i	$0.911348\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$		−	35561.3i		−	0.0377171i	−0.999822	−	0.0188586i	$-0.993997\pi$
$971$		−	35561.3i		−	0.0377171i	0.999822	−	0.0188586i	$-0.00600322\pi$
$972$		0			0
$973$	−587525.			−0.620584
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−572069.	+	330284.i	−0.599321	+	0.346018i	−0.768774	−	0.639520i	$-0.779133\pi$
$977$	−572069.	+	330284.i	−0.599321	+	0.346018i	0.169453	+	0.985538i	$0.445800\pi$
$978$		0			0
$979$	70211.6	−	121610.i	0.0732560	−	0.126883i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−344484.	−	198888.i	−0.356502	−	0.205826i	0.311043	−	0.950396i	$-0.399322\pi$
$983$	−344484.	−	198888.i	−0.356502	−	0.205826i	−0.667545	+	0.744569i	$0.732655\pi$
$984$		0			0
$985$	16060.5	+	27817.5i	0.0165533	+	0.0286712i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		−	311407.i		−	0.318373i
$990$		0			0
$991$	910142.			0.926748			0.463374	−	0.886163i	$-0.346639\pi$
$991$	910142.			0.926748			0.463374	+	0.886163i	$0.346639\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	356473.	−	205810.i	0.360065	−	0.207884i
$996$		0			0
$997$	478202.	−	828270.i	0.481084	−	0.833262i	−0.518680	−	0.854968i	$-0.673577\pi$
$997$	478202.	−	828270.i	0.481084	−	0.833262i	0.999764	+	0.0217063i	$0.00690988\pi$
$998$		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.89.3		8
3.2	odd	2		36.5.g.a.29.3	yes	8
4.3	odd	2		432.5.q.c.305.3		8
9.2	odd	6		324.5.c.a.161.4		8
9.4	even	3		36.5.g.a.5.3	✓	8
9.5	odd	6	inner	108.5.g.a.17.3		8
9.7	even	3		324.5.c.a.161.5		8
12.11	even	2		144.5.q.c.65.2		8
36.7	odd	6		1296.5.e.g.161.5		8
36.11	even	6		1296.5.e.g.161.4		8
36.23	even	6		432.5.q.c.17.3		8
36.31	odd	6		144.5.q.c.113.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.5.g.a.5.3	✓	8	9.4	even	3
36.5.g.a.29.3	yes	8	3.2	odd	2
108.5.g.a.17.3		8	9.5	odd	6	inner
108.5.g.a.89.3		8	1.1	even	1	trivial
144.5.q.c.65.2		8	12.11	even	2
144.5.q.c.113.2		8	36.31	odd	6
324.5.c.a.161.4		8	9.2	odd	6
324.5.c.a.161.5		8	9.7	even	3
432.5.q.c.17.3		8	36.23	even	6
432.5.q.c.305.3		8	4.3	odd	2
1296.5.e.g.161.4		8	36.11	even	6
1296.5.e.g.161.5		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)

\(f(q)\)	\(=\)	\(q+(7.67992 - 4.43400i) q^{5} +(-30.9381 + 53.5864i) q^{7} +O(q^{10})\)	\(q+(7.67992 - 4.43400i) q^{5} +(-30.9381 + 53.5864i) q^{7} +(-94.7648 - 54.7125i) q^{11} +(77.8628 + 134.862i) q^{13} +395.955i q^{17} +140.350 q^{19} +(-802.818 + 463.507i) q^{23} +(-273.179 + 473.160i) q^{25} +(-323.853 - 186.976i) q^{29} +(521.830 + 903.837i) q^{31} +548.719i q^{35} -194.990 q^{37} +(2344.14 - 1353.39i) q^{41} +(-167.963 + 290.920i) q^{43} +(-2468.76 - 1425.34i) q^{47} +(-713.836 - 1236.40i) q^{49} +2765.43i q^{53} -970.381 q^{55} +(4354.55 - 2514.10i) q^{59} +(3523.59 - 6103.03i) q^{61} +(1195.96 + 690.488i) q^{65} +(-3439.96 - 5958.19i) q^{67} -821.812i q^{71} +4091.53 q^{73} +(5863.69 - 3385.40i) q^{77} +(-3783.56 + 6553.32i) q^{79} +(-6777.78 - 3913.15i) q^{83} +(1755.67 + 3040.90i) q^{85} +1283.28i q^{89} -9635.72 q^{91} +(1077.88 - 622.313i) q^{95} +(1890.33 - 3274.14i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 9 q^{5} + 13 q^{7}+O(q^{10}) \) 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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