LMFDB - Embedded newform 504.4.s.j.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,4,Mod(289,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("504.289");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	504.s (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$29.7369626429$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 173x^{6} + 9457x^{4} + 168048x^{2} + 746496 $ x^8 + 173x^6 + 9457x^4 + 168048*x^2 + 746496
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{6}\cdot 7 $
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.1
Root			$-4.63878i$ of defining polynomial
Character	$\chi$	$=$	504.361
Dual form			504.4.s.j.289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.90648 - 13.6944i) q^{5} +(15.2050 + 10.5739i) q^{7} +O(q^{10})$	$q+(-7.90648 - 13.6944i) q^{5} +(15.2050 + 10.5739i) q^{7} +(-15.1240 + 26.1955i) q^{11} -61.6298 q^{13} +(28.0724 - 48.6228i) q^{17} +(69.7002 + 120.724i) q^{19} +(-4.07240 - 7.05360i) q^{23} +(-62.5247 + 108.296i) q^{25} +0.217857 q^{29} +(-88.2903 + 152.923i) q^{31} +(24.5855 - 291.826i) q^{35} +(-105.540 - 182.801i) q^{37} +293.305 q^{41} +434.591 q^{43} +(241.698 + 418.633i) q^{47} +(119.385 + 321.553i) q^{49} +(10.2536 - 17.7598i) q^{53} +478.309 q^{55} +(-115.674 + 200.353i) q^{59} +(419.351 + 726.337i) q^{61} +(487.274 + 843.984i) q^{65} +(312.020 - 540.435i) q^{67} -227.106 q^{71} +(-21.5247 + 37.2819i) q^{73} +(-506.949 + 238.383i) q^{77} +(154.530 + 267.654i) q^{79} -1233.99 q^{83} -887.815 q^{85} +(572.179 + 991.042i) q^{89} +(-937.082 - 651.668i) q^{91} +(1102.17 - 1909.01i) q^{95} +1688.12 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{5} + 18 q^{7}+O(q^{10}) $ 8 * q + 4 * q^5 + 18 * q^7	$ 8 q + 4 q^{5} + 18 q^{7} + 14 q^{11} + 44 q^{13} + 96 q^{17} + 26 q^{19} + 96 q^{23} - 110 q^{25} + 152 q^{29} - 238 q^{31} - 152 q^{35} - 562 q^{37} - 856 q^{41} - 516 q^{43} - 80 q^{47} + 156 q^{49} + 2952 q^{55} + 262 q^{59} + 276 q^{61} + 2196 q^{65} - 150 q^{67} + 1696 q^{71} + 218 q^{73} + 764 q^{77} - 1762 q^{79} - 6900 q^{83} + 2904 q^{85} - 344 q^{89} - 2806 q^{91} + 2004 q^{95} - 1244 q^{97}+O(q^{100}) $ 8 * q + 4 * q^5 + 18 * q^7 + 14 * q^11 + 44 * q^13 + 96 * q^17 + 26 * q^19 + 96 * q^23 - 110 * q^25 + 152 * q^29 - 238 * q^31 - 152 * q^35 - 562 * q^37 - 856 * q^41 - 516 * q^43 - 80 * q^47 + 156 * q^49 + 2952 * q^55 + 262 * q^59 + 276 * q^61 + 2196 * q^65 - 150 * q^67 + 1696 * q^71 + 218 * q^73 + 764 * q^77 - 1762 * q^79 - 6900 * q^83 + 2904 * q^85 - 344 * q^89 - 2806 * q^91 + 2004 * q^95 - 1244 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$1$

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
$5$	−7.90648	−	13.6944i	−0.707177	−	1.22487i	−0.965900	−	0.258915i	$-0.916635\pi$
$5$	−7.90648	−	13.6944i	−0.707177	−	1.22487i	0.258724	−	0.965951i	$-0.416698\pi$
$6$		0			0
$7$	15.2050	+	10.5739i	0.820993	+	0.570938i
$7$	15.2050	+	10.5739i	0.820993	+	0.570938i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−15.1240	+	26.1955i	−0.414550	+	0.718021i	−0.995381	−	0.0960028i	$-0.969394\pi$
$11$	−15.1240	+	26.1955i	−0.414550	+	0.718021i	0.580831	+	0.814024i	$0.302728\pi$
$12$		0			0
$13$	−61.6298			−1.31485			−0.657424	−	0.753521i	$-0.728354\pi$
$13$	−61.6298			−1.31485			−0.657424	+	0.753521i	$0.728354\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	28.0724	−	48.6228i	0.400503	−	0.693692i	−0.593283	−	0.804994i	$-0.702169\pi$
$17$	28.0724	−	48.6228i	0.400503	−	0.693692i	0.993787	+	0.111302i	$0.0355020\pi$
$18$		0			0
$19$	69.7002	+	120.724i	0.841596	+	1.45769i	0.888544	+	0.458790i	$0.151717\pi$
$19$	69.7002	+	120.724i	0.841596	+	1.45769i	−0.0469481	+	0.998897i	$0.514950\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−4.07240	−	7.05360i	−0.0369197	−	0.0639469i	0.846975	−	0.531633i	$-0.178421\pi$
$23$	−4.07240	−	7.05360i	−0.0369197	−	0.0639469i	−0.883895	+	0.467686i	$0.845088\pi$
$24$		0			0
$25$	−62.5247	+	108.296i	−0.500198	+	0.866368i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	0.217857			0.00139500			0.000697500	−	1.00000i	$-0.499778\pi$
$29$	0.217857			0.00139500			0.000697500		1.00000i	$0.499778\pi$
$30$		0			0
$31$	−88.2903	+	152.923i	−0.511529	+	0.885994i	0.488382	+	0.872630i	$0.337587\pi$
$31$	−88.2903	+	152.923i	−0.511529	+	0.885994i	−0.999911	+	0.0133642i	$0.995746\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	24.5855	−	291.826i	0.118735	−	1.40936i
$36$		0			0
$37$	−105.540	−	182.801i	−0.468937	−	0.812223i	0.530432	−	0.847727i	$-0.322030\pi$
$37$	−105.540	−	182.801i	−0.468937	−	0.812223i	−0.999370	+	0.0355042i	$0.988696\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	293.305			1.11723			0.558616	−	0.829427i	$-0.311333\pi$
$41$	293.305			1.11723			0.558616	+	0.829427i	$0.311333\pi$
$42$		0			0
$43$	434.591			1.54127			0.770634	−	0.637278i	$-0.219940\pi$
$43$	434.591			1.54127			0.770634	+	0.637278i	$0.219940\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	241.698	+	418.633i	0.750112	+	1.29923i	0.947768	+	0.318960i	$0.103334\pi$
$47$	241.698	+	418.633i	0.750112	+	1.29923i	−0.197657	+	0.980271i	$0.563333\pi$
$48$		0			0
$49$	119.385	+	321.553i	0.348060	+	0.937472i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	10.2536	−	17.7598i	0.0265745	−	0.0460283i	−0.852432	−	0.522838i	$-0.824873\pi$
$53$	10.2536	−	17.7598i	0.0265745	−	0.0460283i	0.879007	+	0.476809i	$0.158207\pi$
$54$		0			0
$55$	478.309			1.17264
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−115.674	+	200.353i	−0.255245	+	0.442097i	−0.964962	−	0.262390i	$-0.915489\pi$
$59$	−115.674	+	200.353i	−0.255245	+	0.442097i	0.709717	+	0.704487i	$0.248823\pi$
$60$		0			0
$61$	419.351	+	726.337i	0.880203	+	1.52456i	0.851115	+	0.524979i	$0.175927\pi$
$61$	419.351	+	726.337i	0.880203	+	1.52456i	0.0290872	+	0.999577i	$0.490740\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	487.274	+	843.984i	0.929830	+	1.61051i
$66$		0			0
$67$	312.020	−	540.435i	0.568945	−	0.985442i	−0.427726	−	0.903909i	$-0.640685\pi$
$67$	312.020	−	540.435i	0.568945	−	0.985442i	0.996671	−	0.0815332i	$-0.0259817\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−227.106			−0.379613			−0.189806	−	0.981822i	$-0.560786\pi$
$71$	−227.106			−0.379613			−0.189806	+	0.981822i	$0.560786\pi$
$72$		0			0
$73$	−21.5247	+	37.2819i	−0.0345107	+	0.0597742i	−0.882765	−	0.469815i	$-0.844321\pi$
$73$	−21.5247	+	37.2819i	−0.0345107	+	0.0597742i	0.848254	+	0.529589i	$0.177654\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−506.949	+	238.383i	−0.750288	+	0.352809i
$78$		0			0
$79$	154.530	+	267.654i	0.220076	+	0.381183i	0.954831	−	0.297150i	$-0.0960362\pi$
$79$	154.530	+	267.654i	0.220076	+	0.381183i	−0.734755	+	0.678333i	$0.762703\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−1233.99			−1.63190			−0.815951	−	0.578122i	$-0.803786\pi$
$83$	−1233.99			−1.63190			−0.815951	+	0.578122i	$0.803786\pi$
$84$		0			0
$85$	−887.815			−1.13291
$86$		0			0
$87$		0			0
$88$		0			0
$89$	572.179	+	991.042i	0.681470	+	1.18034i	0.974532	+	0.224247i	$0.0719922\pi$
$89$	572.179	+	991.042i	0.681470	+	1.18034i	−0.293063	+	0.956093i	$0.594674\pi$
$90$		0			0
$91$	−937.082	−	651.668i	−1.07948	−	0.750696i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	1102.17	−	1909.01i	1.19031	−	2.06169i
$96$		0			0
$97$	1688.12			1.76704			0.883520	−	0.468394i	$-0.155167\pi$
$97$	1688.12			1.76704			0.883520	+	0.468394i	$0.155167\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−743.930	+	1288.52i	−0.732909	+	1.26944i	0.222726	+	0.974881i	$0.428504\pi$
$101$	−743.930	+	1288.52i	−0.732909	+	1.26944i	−0.955635	+	0.294554i	$0.904829\pi$
$102$		0			0
$103$	389.204	+	674.121i	0.372324	+	0.644884i	0.989923	−	0.141609i	$-0.0452276\pi$
$103$	389.204	+	674.121i	0.372324	+	0.644884i	−0.617598	+	0.786494i	$0.711894\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	651.040	+	1127.63i	0.588209	+	1.01881i	0.994467	+	0.105050i	$0.0335001\pi$
$107$	651.040	+	1127.63i	0.588209	+	1.01881i	−0.406258	+	0.913758i	$0.633167\pi$
$108$		0			0
$109$	−234.541	+	406.237i	−0.206100	+	0.356976i	−0.950483	−	0.310777i	$-0.899411\pi$
$109$	−234.541	+	406.237i	−0.206100	+	0.356976i	0.744382	+	0.667754i	$0.232744\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−1653.86			−1.37684			−0.688418	−	0.725314i	$-0.741694\pi$
$113$	−1653.86			−1.37684			−0.688418	+	0.725314i	$0.741694\pi$
$114$		0			0
$115$	−64.3966	+	111.538i	−0.0522175	+	0.0904434i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	940.975	−	442.475i	0.724866	−	0.340854i
$120$		0			0
$121$	208.032	+	360.321i	0.156297	+	0.270715i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	0.781685			0.000559328
$126$		0			0
$127$	163.760			0.114420			0.0572100	−	0.998362i	$-0.481780\pi$
$127$	163.760			0.114420			0.0572100	+	0.998362i	$0.481780\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−260.947	−	451.973i	−0.174038	−	0.301443i	0.765790	−	0.643091i	$-0.222348\pi$
$131$	−260.947	−	451.973i	−0.174038	−	0.301443i	−0.939828	+	0.341648i	$0.889015\pi$
$132$		0			0
$133$	−216.736	+	2572.62i	−0.141304	+	1.67725i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	1338.44	−	2318.25i	0.834679	−	1.44571i	−0.0596120	−	0.998222i	$-0.518986\pi$
$137$	1338.44	−	2318.25i	0.834679	−	1.44571i	0.894291	−	0.447485i	$-0.147680\pi$
$138$		0			0
$139$	853.692			0.520930			0.260465	−	0.965483i	$-0.416124\pi$
$139$	853.692			0.520930			0.260465	+	0.965483i	$0.416124\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	932.087	−	1614.42i	0.545070	−	0.944089i
$144$		0			0
$145$	−1.72248	−	2.98342i	−0.000986512	−	0.00170869i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	278.843	+	482.970i	0.153313	+	0.265547i	0.932444	−	0.361316i	$-0.117672\pi$
$149$	278.843	+	482.970i	0.153313	+	0.265547i	−0.779130	+	0.626862i	$0.784339\pi$
$150$		0			0
$151$	−884.674	+	1532.30i	−0.476780	+	0.825807i	−0.999646	−	0.0266077i	$-0.991530\pi$
$151$	−884.674	+	1532.30i	−0.476780	+	0.825807i	0.522866	+	0.852415i	$0.324863\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	2792.26			1.44697
$156$		0			0
$157$	1202.45	−	2082.70i	0.611247	−	1.05871i	−0.379784	−	0.925075i	$-0.624002\pi$
$157$	1202.45	−	2082.70i	0.611247	−	1.05871i	0.991031	−	0.133635i	$-0.0426651\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	12.6633	−	150.311i	0.00619881	−	0.0735788i
$162$		0			0
$163$	−1689.40	−	2926.12i	−0.811802	−	1.40608i	−0.911601	−	0.411075i	$-0.865153\pi$
$163$	−1689.40	−	2926.12i	−0.811802	−	1.40608i	0.0997991	−	0.995008i	$-0.468180\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	805.900			0.373428			0.186714	−	0.982414i	$-0.440216\pi$
$167$	805.900			0.373428			0.186714	+	0.982414i	$0.440216\pi$
$168$		0			0
$169$	1601.23			0.728826
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−420.252	−	727.898i	−0.184689	−	0.319890i	0.758783	−	0.651344i	$-0.225794\pi$
$173$	−420.252	−	727.898i	−0.184689	−	0.319890i	−0.943472	+	0.331453i	$0.892461\pi$
$174$		0			0
$175$	−2095.80	+	985.511i	−0.905301	+	0.425701i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	802.305	−	1389.63i	0.335012	−	0.580258i	−0.648475	−	0.761236i	$-0.724593\pi$
$179$	802.305	−	1389.63i	0.335012	−	0.580258i	0.983487	+	0.180978i	$0.0579263\pi$
$180$		0			0
$181$	−3779.43			−1.55206			−0.776029	−	0.630697i	$-0.782769\pi$
$181$	−3779.43			−1.55206			−0.776029	+	0.630697i	$0.782769\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−1668.90	+	2890.62i	−0.663243	+	1.14877i
$186$		0			0
$187$	849.132	+	1470.74i	0.332057	+	0.575140i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−924.798	−	1601.80i	−0.350346	−	0.606816i	0.635964	−	0.771718i	$-0.280603\pi$
$191$	−924.798	−	1601.80i	−0.350346	−	0.606816i	−0.986310	+	0.164902i	$0.947269\pi$
$192$		0			0
$193$	176.501	−	305.709i	0.0658282	−	0.114018i	−0.831233	−	0.555924i	$-0.812364\pi$
$193$	176.501	−	305.709i	0.0658282	−	0.114018i	0.897061	+	0.441907i	$0.145698\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−4448.22			−1.60874			−0.804372	−	0.594125i	$-0.797498\pi$
$197$	−4448.22			−1.60874			−0.804372	+	0.594125i	$0.797498\pi$
$198$		0			0
$199$	1120.08	−	1940.03i	0.398995	−	0.691080i	−0.594607	−	0.804017i	$-0.702692\pi$
$199$	1120.08	−	1940.03i	0.398995	−	0.691080i	0.993602	+	0.112936i	$0.0360256\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	3.31252	+	2.30360i	0.00114529	+	0.000796458i
$204$		0			0
$205$	−2319.01	−	4016.64i	−0.790080	−	1.36846i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−4216.58			−1.39553
$210$		0			0
$211$	1224.34			0.399463			0.199732	−	0.979851i	$-0.435993\pi$
$211$	1224.34			0.399463			0.199732	+	0.979851i	$0.435993\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−3436.08	−	5951.47i	−1.08995	−	1.88785i
$216$		0			0
$217$	−2959.45	+	1391.63i	−0.925810	+	0.435344i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−1730.10	+	2996.61i	−0.526601	+	0.912100i
$222$		0			0
$223$	−3457.37			−1.03822			−0.519108	−	0.854708i	$-0.673736\pi$
$223$	−3457.37			−1.03822			−0.519108	+	0.854708i	$0.673736\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−2589.11	+	4484.47i	−0.757027	+	1.31121i	0.187333	+	0.982296i	$0.440016\pi$
$227$	−2589.11	+	4484.47i	−0.757027	+	1.31121i	−0.944360	+	0.328913i	$0.893318\pi$
$228$		0			0
$229$	−1155.94	−	2002.15i	−0.333567	−	0.577755i	0.649642	−	0.760241i	$-0.274919\pi$
$229$	−1155.94	−	2002.15i	−0.333567	−	0.577755i	−0.983208	+	0.182486i	$0.941586\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	2371.49	+	4107.54i	0.666787	+	1.15491i	0.978798	+	0.204830i	$0.0656641\pi$
$233$	2371.49	+	4107.54i	0.666787	+	1.15491i	−0.312011	+	0.950078i	$0.601003\pi$
$234$		0			0
$235$	3821.95	−	6619.82i	1.06092	−	1.83757i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	1412.59			0.382313			0.191157	−	0.981560i	$-0.438776\pi$
$239$	1412.59			0.382313			0.191157	+	0.981560i	$0.438776\pi$
$240$		0			0
$241$	940.577	−	1629.13i	0.251402	−	0.435441i	−0.712510	−	0.701662i	$-0.752442\pi$
$241$	940.577	−	1629.13i	0.251402	−	0.435441i	0.963912	+	0.266221i	$0.0857750\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	3459.57	−	4177.25i	0.902138	−	1.08929i
$246$		0			0
$247$	−4295.61	−	7440.22i	−1.10657	−	1.91664i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−4519.64			−1.13656			−0.568281	−	0.822834i	$-0.692391\pi$
$251$	−4519.64			−1.13656			−0.568281	+	0.822834i	$0.692391\pi$
$252$		0			0
$253$	246.363			0.0612202
$254$		0			0
$255$		0			0
$256$		0			0
$257$	3956.33	+	6852.56i	0.960268	+	1.66323i	0.721824	+	0.692077i	$0.243304\pi$
$257$	3956.33	+	6852.56i	0.960268	+	1.66323i	0.238445	+	0.971156i	$0.423362\pi$
$258$		0			0
$259$	328.182	−	3895.46i	0.0787344	−	0.934564i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−1715.58	+	2971.47i	−0.402233	+	0.696688i	−0.993995	−	0.109425i	$-0.965099\pi$
$263$	−1715.58	+	2971.47i	−0.402233	+	0.696688i	0.591762	+	0.806113i	$0.298432\pi$
$264$		0			0
$265$	−324.281			−0.0751714
$266$		0			0
$267$		0			0
$268$		0			0
$269$	4149.60	−	7187.31i	0.940540	−	1.62906i	0.176097	−	0.984373i	$-0.443653\pi$
$269$	4149.60	−	7187.31i	0.940540	−	1.62906i	0.764443	−	0.644691i	$-0.223014\pi$
$270$		0			0
$271$	2962.24	+	5130.75i	0.663998	+	1.15008i	0.979556	+	0.201172i	$0.0644749\pi$
$271$	2962.24	+	5130.75i	0.663998	+	1.15008i	−0.315558	+	0.948906i	$0.602192\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−1891.24	−	3275.73i	−0.414714	−	0.718305i
$276$		0			0
$277$	−760.300	+	1316.88i	−0.164917	+	0.285645i	−0.936626	−	0.350331i	$-0.886069\pi$
$277$	−760.300	+	1316.88i	−0.164917	+	0.285645i	0.771709	+	0.635976i	$0.219402\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	352.333			0.0747986			0.0373993	−	0.999300i	$-0.488093\pi$
$281$	352.333			0.0747986			0.0373993	+	0.999300i	$0.488093\pi$
$282$		0			0
$283$	−2144.24	+	3713.94i	−0.450396	+	0.780109i	−0.998411	−	0.0563599i	$-0.982051\pi$
$283$	−2144.24	+	3713.94i	−0.450396	+	0.780109i	0.548014	+	0.836469i	$0.315384\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	4459.70	+	3101.38i	0.917239	+	0.637869i
$288$		0			0
$289$	880.381	+	1524.86i	0.179194	+	0.310373i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−2661.99			−0.530767			−0.265384	−	0.964143i	$-0.585499\pi$
$293$	−2661.99			−0.530767			−0.265384	+	0.964143i	$0.585499\pi$
$294$		0			0
$295$	3658.29			0.722013
$296$		0			0
$297$		0			0
$298$		0			0
$299$	250.981	+	434.712i	0.0485438	+	0.0840804i
$300$		0			0
$301$	6607.96	+	4595.33i	1.26537	+	0.879968i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	6631.17	−	11485.5i	1.24492	−	2.15626i
$306$		0			0
$307$	145.970			0.0271366			0.0135683	−	0.999908i	$-0.495681\pi$
$307$	145.970			0.0271366			0.0135683	+	0.999908i	$0.495681\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	1708.26	−	2958.79i	0.311467	−	0.539477i	−0.667213	−	0.744867i	$-0.732513\pi$
$311$	1708.26	−	2958.79i	0.311467	−	0.539477i	0.978680	+	0.205390i	$0.0658462\pi$
$312$		0			0
$313$	−1841.18	−	3189.01i	−0.332490	−	0.575890i	0.650509	−	0.759498i	$-0.274555\pi$
$313$	−1841.18	−	3189.01i	−0.332490	−	0.575890i	−0.982999	+	0.183608i	$0.941222\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−688.389	−	1192.32i	−0.121968	−	0.211254i	0.798576	−	0.601894i	$-0.205587\pi$
$317$	−688.389	−	1192.32i	−0.121968	−	0.211254i	−0.920544	+	0.390640i	$0.872254\pi$
$318$		0			0
$319$	−3.29486	+	5.70686i	−0.000578297	+	0.00100164i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	7826.61			1.34825
$324$		0			0
$325$	3853.38	−	6674.26i	0.657684	−	1.13914i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−751.570	+	8921.01i	−0.125943	+	1.49493i
$330$		0			0
$331$	−1087.46	−	1883.54i	−0.180581	−	0.312776i	0.761497	−	0.648168i	$-0.224465\pi$
$331$	−1087.46	−	1883.54i	−0.180581	−	0.312776i	−0.942079	+	0.335392i	$0.891131\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−9867.92			−1.60938
$336$		0			0
$337$	−6321.14			−1.02176			−0.510882	−	0.859651i	$-0.670681\pi$
$337$	−6321.14			−1.02176			−0.510882	+	0.859651i	$0.670681\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−2670.60	−	4625.61i	−0.424108	−	0.734577i
$342$		0			0
$343$	−1584.83	+	6151.58i	−0.249483	+	0.968379i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−5812.21	+	10067.0i	−0.899181	+	1.55743i	−0.0706381	+	0.997502i	$0.522504\pi$
$347$	−5812.21	+	10067.0i	−0.899181	+	1.55743i	−0.828543	+	0.559925i	$0.810830\pi$
$348$		0			0
$349$	−9841.79			−1.50951			−0.754755	−	0.656007i	$-0.772244\pi$
$349$	−9841.79			−1.50951			−0.754755	+	0.656007i	$0.772244\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	2265.94	−	3924.73i	0.341654	−	0.591762i	−0.643086	−	0.765794i	$-0.722346\pi$
$353$	2265.94	−	3924.73i	0.341654	−	0.591762i	0.984740	+	0.174032i	$0.0556795\pi$
$354$		0			0
$355$	1795.61	+	3110.08i	0.268453	+	0.464975i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−1140.05	−	1974.63i	−0.167603	−	0.290298i	0.769973	−	0.638076i	$-0.220269\pi$
$359$	−1140.05	−	1974.63i	−0.167603	−	0.290298i	−0.937577	+	0.347779i	$0.886936\pi$
$360$		0			0
$361$	−6286.75	+	10889.0i	−0.916569	+	1.58754i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	680.739			0.0976205
$366$		0			0
$367$	−3168.76	+	5488.45i	−0.450702	+	0.780639i	−0.998430	−	0.0560176i	$-0.982160\pi$
$367$	−3168.76	+	5488.45i	−0.450702	+	0.780639i	0.547728	+	0.836657i	$0.315493\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	343.698	−	161.617i	0.0480968	−	0.0226166i
$372$		0			0
$373$	1812.48	+	3139.31i	0.251600	+	0.435783i	0.963966	−	0.266024i	$-0.0857100\pi$
$373$	1812.48	+	3139.31i	0.251600	+	0.435783i	−0.712367	+	0.701807i	$0.752377\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−13.4265			−0.00183421
$378$		0			0
$379$	268.622			0.0364068			0.0182034	−	0.999834i	$-0.494205\pi$
$379$	268.622			0.0364068			0.0182034	+	0.999834i	$0.494205\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−1068.70	−	1851.03i	−0.142579	−	0.246954i	0.785888	−	0.618369i	$-0.212206\pi$
$383$	−1068.70	−	1851.03i	−0.142579	−	0.246954i	−0.928467	+	0.371415i	$0.878873\pi$
$384$		0			0
$385$	7272.69	+	5057.60i	0.962729	+	0.669504i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	731.615	−	1267.19i	0.0953583	−	0.165165i	−0.814400	−	0.580304i	$-0.802934\pi$
$389$	731.615	−	1267.19i	0.0953583	−	0.165165i	0.909758	+	0.415139i	$0.136267\pi$
$390$		0			0
$391$	−457.288			−0.0591459
$392$		0			0
$393$		0			0
$394$		0			0
$395$	2443.58	−	4232.40i	0.311265	−	0.539127i
$396$		0			0
$397$	618.718	+	1071.65i	0.0782180	+	0.135478i	0.902481	−	0.430729i	$-0.141744\pi$
$397$	618.718	+	1071.65i	0.0782180	+	0.135478i	−0.824263	+	0.566207i	$0.808410\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−3089.94	−	5351.94i	−0.384799	−	0.666492i	0.606942	−	0.794746i	$-0.292396\pi$
$401$	−3089.94	−	5351.94i	−0.384799	−	0.666492i	−0.991741	+	0.128254i	$0.959063\pi$
$402$		0			0
$403$	5441.31	−	9424.63i	0.672583	−	1.16495i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	6384.73			0.777591
$408$		0			0
$409$	1127.49	−	1952.87i	0.136310	−	0.236096i	−0.789787	−	0.613381i	$-0.789809\pi$
$409$	1127.49	−	1952.87i	0.136310	−	0.236096i	0.926097	+	0.377285i	$0.123142\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−3877.34	+	1823.24i	−0.461964	+	0.217230i
$414$		0			0
$415$	9756.50	+	16898.7i	1.15404	+	1.99886i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	1404.53			0.163761			0.0818806	−	0.996642i	$-0.473907\pi$
$419$	1404.53			0.163761			0.0818806	+	0.996642i	$0.473907\pi$
$420$		0			0
$421$	13068.1			1.51283			0.756414	−	0.654094i	$-0.226950\pi$
$421$	13068.1			1.51283			0.756414	+	0.654094i	$0.226950\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	3510.44	+	6080.26i	0.400662	+	0.693966i
$426$		0			0
$427$	−1303.99	+	15478.1i	−0.147786	+	1.75419i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−2681.39	+	4644.31i	−0.299671	+	0.519046i	−0.976061	−	0.217499i	$-0.930210\pi$
$431$	−2681.39	+	4644.31i	−0.299671	+	0.519046i	0.676390	+	0.736544i	$0.263544\pi$
$432$		0			0
$433$	−2495.82			−0.277001			−0.138501	−	0.990362i	$-0.544228\pi$
$433$	−2495.82			−0.277001			−0.138501	+	0.990362i	$0.544228\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	567.694	−	983.275i	0.0621430	−	0.107635i
$438$		0			0
$439$	−1881.06	−	3258.09i	−0.204506	−	0.354215i	0.745469	−	0.666540i	$-0.232225\pi$
$439$	−1881.06	−	3258.09i	−0.204506	−	0.354215i	−0.949975	+	0.312325i	$0.898892\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	5722.63	+	9911.88i	0.613748	+	1.06304i	0.990603	+	0.136770i	$0.0436721\pi$
$443$	5722.63	+	9911.88i	0.613748	+	1.06304i	−0.376855	+	0.926272i	$0.622995\pi$
$444$		0			0
$445$	9047.83	−	15671.3i	0.963839	−	1.66942i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	9420.02			0.990107			0.495054	−	0.868862i	$-0.335148\pi$
$449$	9420.02			0.990107			0.495054	+	0.868862i	$0.335148\pi$
$450$		0			0
$451$	−4435.93	+	7683.25i	−0.463148	+	0.802196i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−1515.20	+	17985.2i	−0.156118	+	1.85310i
$456$		0			0
$457$	−5731.98	−	9928.08i	−0.586719	−	1.01623i	−0.994659	−	0.103219i	$-0.967086\pi$
$457$	−5731.98	−	9928.08i	−0.586719	−	1.01623i	0.407939	−	0.913009i	$-0.366247\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	9751.10			0.985149			0.492575	−	0.870270i	$-0.336056\pi$
$461$	9751.10			0.985149			0.492575	+	0.870270i	$0.336056\pi$
$462$		0			0
$463$	2182.03			0.219023			0.109512	−	0.993986i	$-0.465071\pi$
$463$	2182.03			0.219023			0.109512	+	0.993986i	$0.465071\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	1598.17	+	2768.11i	0.158361	+	0.274289i	0.934278	−	0.356546i	$-0.116046\pi$
$467$	1598.17	+	2768.11i	0.158361	+	0.274289i	−0.775917	+	0.630835i	$0.782712\pi$
$468$		0			0
$469$	10458.8	−	4918.04i	1.02973	−	0.484209i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−6572.74	+	11384.3i	−0.638932	+	1.10666i
$474$		0			0
$475$	−17432.0			−1.68386
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−6071.79	+	10516.7i	−0.579180	+	1.00317i	0.416394	+	0.909184i	$0.363294\pi$
$479$	−6071.79	+	10516.7i	−0.579180	+	1.00317i	−0.995574	+	0.0939849i	$0.970039\pi$
$480$		0			0
$481$	6504.41	+	11266.0i	0.616581	+	1.06795i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−13347.1	−	23117.9i	−1.24961	−	2.16439i
$486$		0			0
$487$	10151.2	−	17582.5i	0.944551	−	1.63601i	0.187905	−	0.982187i	$-0.439830\pi$
$487$	10151.2	−	17582.5i	0.944551	−	1.63601i	0.756647	−	0.653824i	$-0.226836\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−2562.41			−0.235519			−0.117760	−	0.993042i	$-0.537571\pi$
$491$	−2562.41			−0.235519			−0.117760	+	0.993042i	$0.537571\pi$
$492$		0			0
$493$	6.11577	−	10.5928i	0.000558702	−	0.000967701i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−3453.15	−	2401.40i	−0.311660	−	0.216735i
$498$		0			0
$499$	5828.05	+	10094.5i	0.522844	+	0.905592i	0.999647	+	0.0265820i	$0.00846232\pi$
$499$	5828.05	+	10094.5i	0.522844	+	0.905592i	−0.476803	+	0.879010i	$0.658204\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	18532.8			1.64281			0.821407	−	0.570342i	$-0.193189\pi$
$503$	18532.8			1.64281			0.821407	+	0.570342i	$0.193189\pi$
$504$		0			0
$505$	23527.5			2.07318
$506$		0			0
$507$		0			0
$508$		0			0
$509$	9366.05	+	16222.5i	0.815605	+	1.41267i	0.908893	+	0.417030i	$0.136929\pi$
$509$	9366.05	+	16222.5i	0.815605	+	1.41267i	−0.0932881	+	0.995639i	$0.529738\pi$
$510$		0			0
$511$	−721.499	+	339.271i	−0.0624604	+	0.0293708i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	6154.46	−	10659.8i	0.526598	−	0.912094i
$516$		0			0
$517$	−14621.7			−1.24383
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−1661.63	+	2878.02i	−0.139726	+	0.242012i	−0.927393	−	0.374089i	$-0.877955\pi$
$521$	−1661.63	+	2878.02i	−0.139726	+	0.242012i	0.787667	+	0.616101i	$0.211289\pi$
$522$		0			0
$523$	11648.7	+	20176.2i	0.973925	+	1.68689i	0.683437	+	0.730010i	$0.260484\pi$
$523$	11648.7	+	20176.2i	0.973925	+	1.68689i	0.290489	+	0.956878i	$0.406182\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	4957.04	+	8585.84i	0.409738	+	0.709687i
$528$		0			0
$529$	6050.33	−	10479.5i	0.497274	−	0.861304i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−18076.3			−1.46899
$534$		0			0
$535$	10294.9	−	17831.2i	0.831936	−	1.44095i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−10228.8	−	1735.82i	−0.817413	−	0.138714i
$540$		0			0
$541$	−4525.01	−	7837.54i	−0.359603	−	0.622851i	0.628292	−	0.777978i	$-0.283755\pi$
$541$	−4525.01	−	7837.54i	−0.359603	−	0.622851i	−0.987894	+	0.155127i	$0.950421\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	7417.56			0.582997
$546$		0			0
$547$	−12316.7			−0.962749			−0.481374	−	0.876515i	$-0.659862\pi$
$547$	−12316.7			−0.962749			−0.481374	+	0.876515i	$0.659862\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	15.1847	+	26.3006i	0.00117403	+	0.00203347i
$552$		0			0
$553$	−480.518	+	5703.67i	−0.0369507	+	0.438598i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	12452.0	−	21567.6i	0.947236	−	1.64066i	0.196024	−	0.980599i	$-0.437197\pi$
$557$	12452.0	−	21567.6i	0.947236	−	1.64066i	0.751212	−	0.660061i	$-0.229470\pi$
$558$		0			0
$559$	−26783.8			−2.02653
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−2073.30	+	3591.06i	−0.155203	+	0.268819i	−0.933133	−	0.359532i	$-0.882936\pi$
$563$	−2073.30	+	3591.06i	−0.155203	+	0.268819i	0.777930	+	0.628351i	$0.216270\pi$
$564$		0			0
$565$	13076.2	+	22648.7i	0.973666	+	1.68644i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	3648.74	+	6319.80i	0.268828	+	0.465624i	0.968559	−	0.248782i	$-0.0800303\pi$
$569$	3648.74	+	6319.80i	0.268828	+	0.465624i	−0.699731	+	0.714406i	$0.746697\pi$
$570$		0			0
$571$	5782.45	−	10015.5i	0.423797	−	0.734037i	−0.572511	−	0.819897i	$-0.694030\pi$
$571$	5782.45	−	10015.5i	0.423797	−	0.734037i	0.996307	+	0.0858600i	$0.0273638\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	1018.50			0.0738687
$576$		0			0
$577$	−4736.72	+	8204.25i	−0.341755	+	0.591936i	−0.984759	−	0.173926i	$-0.944354\pi$
$577$	−4736.72	+	8204.25i	−0.341755	+	0.591936i	0.643004	+	0.765863i	$0.277688\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−18762.8	−	13048.1i	−1.33978	−	0.931714i
$582$		0			0
$583$	310.152	+	537.198i	0.0220329	+	0.0381620i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−7336.02			−0.515826			−0.257913	−	0.966168i	$-0.583035\pi$
$587$	−7336.02			−0.515826			−0.257913	+	0.966168i	$0.583035\pi$
$588$		0			0
$589$	−24615.4			−1.72200
$590$		0			0
$591$		0			0
$592$		0			0
$593$	9040.73	+	15659.0i	0.626068	+	1.08438i	0.988333	+	0.152307i	$0.0486702\pi$
$593$	9040.73	+	15659.0i	0.626068	+	1.08438i	−0.362265	+	0.932075i	$0.617996\pi$
$594$		0			0
$595$	−13499.2	−	9387.68i	−0.930109	−	0.646819i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−96.2165	+	166.652i	−0.00656310	+	0.0113676i	−0.869288	−	0.494305i	$-0.835422\pi$
$599$	−96.2165	+	166.652i	−0.00656310	+	0.0113676i	0.862725	+	0.505673i	$0.168756\pi$
$600$		0			0
$601$	−5055.76			−0.343143			−0.171571	−	0.985172i	$-0.554884\pi$
$601$	−5055.76			−0.343143			−0.171571	+	0.985172i	$0.554884\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	3289.59	−	5697.74i	0.221059	−	0.382886i
$606$		0			0
$607$	−10117.9	−	17524.7i	−0.676560	−	1.17184i	−0.976010	−	0.217724i	$-0.930137\pi$
$607$	−10117.9	−	17524.7i	−0.676560	−	1.17184i	0.299451	−	0.954112i	$-0.403197\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−14895.8	−	25800.2i	−0.986283	−	1.70829i
$612$		0			0
$613$	1920.25	−	3325.98i	0.126523	−	0.219143i	−0.795805	−	0.605554i	$-0.792952\pi$
$613$	1920.25	−	3325.98i	0.126523	−	0.219143i	0.922327	+	0.386410i	$0.126285\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	5720.89			0.373281			0.186641	−	0.982428i	$-0.440240\pi$
$617$	5720.89			0.373281			0.186641	+	0.982428i	$0.440240\pi$
$618$		0			0
$619$	−11470.1	+	19866.8i	−0.744787	+	1.29001i	0.205507	+	0.978656i	$0.434116\pi$
$619$	−11470.1	+	19866.8i	−0.744787	+	1.29001i	−0.950294	+	0.311354i	$0.899218\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−1779.22	+	21119.0i	−0.114419	+	1.35813i
$624$		0			0
$625$	7809.41	+	13526.3i	0.499802	+	0.865683i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−11851.0			−0.751244
$630$		0			0
$631$	7634.81			0.481675			0.240837	−	0.970565i	$-0.422578\pi$
$631$	7634.81			0.481675			0.240837	+	0.970565i	$0.422578\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−1294.76	−	2242.60i	−0.0809152	−	0.140149i
$636$		0			0
$637$	−7357.65	−	19817.2i	−0.457646	−	1.23263i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−1389.80	+	2407.20i	−0.0856376	+	0.148329i	−0.905663	−	0.423999i	$-0.860626\pi$
$641$	−1389.80	+	2407.20i	−0.0856376	+	0.148329i	0.820025	+	0.572328i	$0.193959\pi$
$642$		0			0
$643$	18304.5			1.12264			0.561322	−	0.827598i	$-0.310293\pi$
$643$	18304.5			1.12264			0.561322	+	0.827598i	$0.310293\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	3276.27	−	5674.66i	0.199078	−	0.344813i	−0.749152	−	0.662398i	$-0.769539\pi$
$647$	3276.27	−	5674.66i	0.199078	−	0.344813i	0.948230	+	0.317585i	$0.102872\pi$
$648$		0			0
$649$	−3498.89	−	6060.26i	−0.211623	−	0.366542i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−15993.0	−	27700.8i	−0.958432	−	1.66005i	−0.726312	−	0.687365i	$-0.758767\pi$
$653$	−15993.0	−	27700.8i	−0.958432	−	1.66005i	−0.232120	−	0.972687i	$-0.574566\pi$
$654$		0			0
$655$	−4126.34	+	7147.03i	−0.246152	+	0.426348i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−517.327			−0.0305799			−0.0152900	−	0.999883i	$-0.504867\pi$
$659$	−517.327			−0.0305799			−0.0152900	+	0.999883i	$0.504867\pi$
$660$		0			0
$661$	−9828.40	+	17023.3i	−0.578336	+	1.00171i	0.417334	+	0.908753i	$0.362965\pi$
$661$	−9828.40	+	17023.3i	−0.578336	+	1.00171i	−0.995670	+	0.0929549i	$0.970369\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	36944.1	−	17372.3i	2.15433	−	1.01303i
$666$		0			0
$667$	−0.887200	−	1.53668i	−5.15030e−5	−	8.92059e-5i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−25369.0			−1.45955
$672$		0			0
$673$	25836.1			1.47981			0.739904	−	0.672713i	$-0.234871\pi$
$673$	25836.1			1.47981			0.739904	+	0.672713i	$0.234871\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	13263.1	+	22972.4i	0.752944	+	1.30414i	0.946390	+	0.323026i	$0.104700\pi$
$677$	13263.1	+	22972.4i	0.752944	+	1.30414i	−0.193447	+	0.981111i	$0.561967\pi$
$678$		0			0
$679$	25667.9	+	17850.1i	1.45073	+	1.00887i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	16939.4	−	29339.9i	0.949002	−	1.64372i	0.201470	−	0.979495i	$-0.435428\pi$
$683$	16939.4	−	29339.9i	0.949002	−	1.64372i	0.747532	−	0.664225i	$-0.231239\pi$
$684$		0			0
$685$	−42329.5			−2.36106
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−631.930	+	1094.53i	−0.0349414	+	0.0605203i
$690$		0			0
$691$	500.631	+	867.119i	0.0275614	+	0.0477377i	0.879477	−	0.475941i	$-0.157892\pi$
$691$	500.631	+	867.119i	0.0275614	+	0.0477377i	−0.851916	+	0.523679i	$0.824559\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−6749.70	−	11690.8i	−0.368389	−	0.638069i
$696$		0			0
$697$	8233.76	−	14261.3i	0.447455	−	0.775015i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−7713.38			−0.415592			−0.207796	−	0.978172i	$-0.566629\pi$
$701$	−7713.38			−0.415592			−0.207796	+	0.978172i	$0.566629\pi$
$702$		0			0
$703$	14712.3	−	25482.5i	0.789312	−	1.36713i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−24936.2	+	11725.8i	−1.32648	+	0.623753i
$708$		0			0
$709$	−5017.56	−	8690.67i	−0.265781	−	0.460346i	0.701987	−	0.712190i	$-0.252296\pi$
$709$	−5017.56	−	8690.67i	−0.265781	−	0.460346i	−0.967768	+	0.251844i	$0.918963\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	1438.21			0.0755421
$714$		0			0
$715$	−29478.1			−1.54184
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−10059.7	−	17423.9i	−0.521785	−	0.903758i	−0.999679	−	0.0253401i	$-0.991933\pi$
$719$	−10059.7	−	17423.9i	−0.521785	−	0.903758i	0.477894	−	0.878417i	$-0.341400\pi$
$720$		0			0
$721$	−1210.25	+	14365.4i	−0.0625131	+	0.742020i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−13.6214	+	23.5930i	−0.000697776	+	0.00120858i
$726$		0			0
$727$	−7567.09			−0.386035			−0.193018	−	0.981195i	$-0.561827\pi$
$727$	−7567.09			−0.386035			−0.193018	+	0.981195i	$0.561827\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	12200.0	−	21131.0i	0.617283	−	1.06917i
$732$		0			0
$733$	−15400.0	−	26673.6i	−0.776006	−	1.34408i	−0.934228	−	0.356678i	$-0.883909\pi$
$733$	−15400.0	−	26673.6i	−0.776006	−	1.34408i	0.158222	−	0.987404i	$-0.449424\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	9437.96	+	16347.0i	0.471712	+	0.817029i
$738$		0			0
$739$	6659.66	−	11534.9i	0.331501	−	0.574177i	−0.651305	−	0.758816i	$-0.725778\pi$
$739$	6659.66	−	11534.9i	0.331501	−	0.574177i	0.982806	+	0.184639i	$0.0591115\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	10747.7			0.530682			0.265341	−	0.964155i	$-0.414516\pi$
$743$	10747.7			0.530682			0.265341	+	0.964155i	$0.414516\pi$
$744$		0			0
$745$	4409.33	−	7637.18i	0.216839	−	0.375577i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−2024.44	+	24029.7i	−0.0987601	+	1.17227i
$750$		0			0
$751$	−6106.70	−	10577.1i	−0.296720	−	0.513934i	0.678664	−	0.734449i	$-0.262559\pi$
$751$	−6106.70	−	10577.1i	−0.296720	−	0.513934i	−0.975383	+	0.220515i	$0.929226\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	27978.6			1.34867
$756$		0			0
$757$	−30173.2			−1.44870			−0.724349	−	0.689434i	$-0.757860\pi$
$757$	−30173.2			−1.44870			−0.724349	+	0.689434i	$0.757860\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	7603.67	+	13169.9i	0.362198	+	0.627346i	0.988322	−	0.152378i	$-0.0486930\pi$
$761$	7603.67	+	13169.9i	0.362198	+	0.627346i	−0.626124	+	0.779723i	$0.715360\pi$
$762$		0			0
$763$	−7861.71	+	3696.82i	−0.373018	+	0.175405i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	7128.95	−	12347.7i	0.335608	−	0.581290i
$768$		0			0
$769$	−9368.65			−0.439327			−0.219663	−	0.975576i	$-0.570496\pi$
$769$	−9368.65			−0.439327			−0.219663	+	0.975576i	$0.570496\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	16258.2	−	28159.9i	0.756488	−	1.31028i	−0.188143	−	0.982142i	$-0.560247\pi$
$773$	16258.2	−	28159.9i	0.756488	−	1.31028i	0.944631	−	0.328134i	$-0.106420\pi$
$774$		0			0
$775$	−11040.6	−	19123.0i	−0.511731	−	0.886345i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	20443.4	+	35409.0i	0.940258	+	1.62857i
$780$		0			0
$781$	3434.74	−	5949.15i	0.157368	−	0.272570i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−38028.5			−1.72904
$786$		0			0
$787$	20125.1	−	34857.8i	0.911542	−	1.57884i	0.0996552	−	0.995022i	$-0.468226\pi$
$787$	20125.1	−	34857.8i	0.911542	−	1.57884i	0.811887	−	0.583815i	$-0.198441\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−25147.0	−	17487.8i	−1.13037	−	0.786087i
$792$		0			0
$793$	−25844.5	−	44764.0i	−1.15733	−	2.00456i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−21387.5			−0.950544			−0.475272	−	0.879839i	$-0.657650\pi$
$797$	−21387.5			−0.950544			−0.475272	+	0.879839i	$0.657650\pi$
$798$		0			0
$799$	27140.1			1.20169
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−651.078	−	1127.70i	−0.0286128	−	0.0495587i
$804$		0			0
$805$	−2158.55	+	1015.02i	−0.0945078	+	0.0444405i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−9817.06	+	17003.6i	−0.426637	+	0.738957i	−0.996572	−	0.0827330i	$-0.973635\pi$
$809$	−9817.06	+	17003.6i	−0.426637	+	0.738957i	0.569935	+	0.821690i	$0.306968\pi$
$810$		0			0
$811$	35238.1			1.52574			0.762872	−	0.646549i	$-0.223789\pi$
$811$	35238.1			1.52574			0.762872	+	0.646549i	$0.223789\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−26714.4	+	46270.6i	−1.14818	+	1.98870i
$816$		0			0
$817$	30291.1	+	52465.7i	1.29713	+	2.24669i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−3527.40	−	6109.63i	−0.149948	−	0.259717i	0.781260	−	0.624205i	$-0.214577\pi$
$821$	−3527.40	−	6109.63i	−0.149948	−	0.259717i	−0.931208	+	0.364488i	$0.881244\pi$
$822$		0			0
$823$	−3094.16	+	5359.25i	−0.131052	+	0.226989i	−0.924082	−	0.382193i	$-0.875169\pi$
$823$	−3094.16	+	5359.25i	−0.131052	+	0.226989i	0.793030	+	0.609182i	$0.208502\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	24000.0			1.00915			0.504573	−	0.863369i	$-0.331650\pi$
$827$	24000.0			1.00915			0.504573	+	0.863369i	$0.331650\pi$
$828$		0			0
$829$	4354.43	−	7542.09i	0.182431	−	0.315980i	−0.760277	−	0.649599i	$-0.774937\pi$
$829$	4354.43	−	7542.09i	0.182431	−	0.315980i	0.942708	+	0.333619i	$0.108270\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	18986.2	+	3221.94i	0.789716	+	0.134014i
$834$		0			0
$835$	−6371.83	−	11036.3i	−0.264079	−	0.457399i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−7820.46			−0.321802			−0.160901	−	0.986971i	$-0.551440\pi$
$839$	−7820.46			−0.321802			−0.160901	+	0.986971i	$0.551440\pi$
$840$		0			0
$841$	−24389.0			−0.999998
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−12660.1	−	21927.9i	−0.515409	−	0.892714i
$846$		0			0
$847$	−646.884	+	7678.39i	−0.0262422	+	0.311491i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−859.602	+	1488.87i	−0.0346261	+	0.0599741i
$852$		0			0
$853$	31176.8			1.25143			0.625717	−	0.780050i	$-0.284807\pi$
$853$	31176.8			1.25143			0.625717	+	0.780050i	$0.284807\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	447.864	−	775.724i	0.0178515	−	0.0309197i	−0.856962	−	0.515380i	$-0.827651\pi$
$857$	447.864	−	775.724i	0.0178515	−	0.0309197i	0.874813	+	0.484460i	$0.160984\pi$
$858$		0			0
$859$	−4557.51	−	7893.83i	−0.181025	−	0.313544i	0.761205	−	0.648511i	$-0.224608\pi$
$859$	−4557.51	−	7893.83i	−0.181025	−	0.313544i	−0.942230	+	0.334967i	$0.891275\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−10563.3	−	18296.2i	−0.416662	−	0.721680i	0.578939	−	0.815371i	$-0.303467\pi$
$863$	−10563.3	−	18296.2i	−0.416662	−	0.721680i	−0.995601	+	0.0936906i	$0.970134\pi$
$864$		0			0
$865$	−6645.42	+	11510.2i	−0.261215	+	0.452438i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−9348.43			−0.364930
$870$		0			0
$871$	−19229.7	+	33306.9i	−0.748076	+	1.29571i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	11.8855	+	8.26547i	0.000459205	+	0.000319342i
$876$		0			0
$877$	9374.72	+	16237.5i	0.360960	+	0.625201i	0.988119	−	0.153690i	$-0.0491158\pi$
$877$	9374.72	+	16237.5i	0.360960	+	0.625201i	−0.627159	+	0.778891i	$0.715782\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−37000.3			−1.41495			−0.707475	−	0.706739i	$-0.750166\pi$
$881$	−37000.3			−1.41495			−0.707475	+	0.706739i	$0.750166\pi$
$882$		0			0
$883$	21618.3			0.823913			0.411956	−	0.911204i	$-0.364846\pi$
$883$	21618.3			0.823913			0.411956	+	0.911204i	$0.364846\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	4151.85	+	7191.21i	0.157165	+	0.272218i	0.933845	−	0.357677i	$-0.116431\pi$
$887$	4151.85	+	7191.21i	0.157165	+	0.272218i	−0.776680	+	0.629895i	$0.783098\pi$
$888$		0			0
$889$	2489.97	+	1731.58i	0.0939381	+	0.0653267i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−33692.8	+	58357.6i	−1.26258	+	2.18686i
$894$		0			0
$895$	−25373.6			−0.947650
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−19.2346	+	33.3154i	−0.000713583	+	0.00123596i
$900$		0			0
$901$	−575.689	−	997.122i	−0.0212863	−	0.0368690i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	29881.9	+	51757.0i	1.09758	+	1.90106i
$906$		0			0
$907$	17272.2	−	29916.4i	0.632321	−	1.09521i	−0.354755	−	0.934959i	$-0.615436\pi$
$907$	17272.2	−	29916.4i	0.632321	−	1.09521i	0.987076	−	0.160253i	$-0.0512310\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	10505.3			0.382059			0.191030	−	0.981584i	$-0.438817\pi$
$911$	10505.3			0.382059			0.191030	+	0.981584i	$0.438817\pi$
$912$		0			0
$913$	18662.8	−	32324.9i	0.676504	−	1.17174i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	811.426	−	9631.49i	0.0292210	−	0.346848i
$918$		0			0
$919$	−16100.8	−	27887.4i	−0.577929	−	1.00100i	−0.995717	−	0.0924578i	$-0.970528\pi$
$919$	−16100.8	−	27887.4i	−0.577929	−	1.00100i	0.417787	−	0.908545i	$-0.362806\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	13996.5			0.499133
$924$		0			0
$925$	26395.4			0.938245
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−18517.4	−	32073.1i	−0.653968	−	1.13271i	−0.982151	−	0.188092i	$-0.939770\pi$
$929$	−18517.4	−	32073.1i	−0.653968	−	1.13271i	0.328183	−	0.944614i	$-0.393564\pi$
$930$		0			0
$931$	−30498.1	+	36825.0i	−1.07362	+	1.29634i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	13427.3	−	23256.7i	0.469646	−	0.813451i
$936$		0			0
$937$	−7207.18			−0.251279			−0.125639	−	0.992076i	$-0.540098\pi$
$937$	−7207.18			−0.251279			−0.125639	+	0.992076i	$0.540098\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−10859.4	+	18809.1i	−0.376203	+	0.651603i	−0.990506	−	0.137467i	$-0.956104\pi$
$941$	−10859.4	+	18809.1i	−0.376203	+	0.651603i	0.614303	+	0.789070i	$0.289437\pi$
$942$		0			0
$943$	−1194.45	−	2068.85i	−0.0412479	−	0.0714434i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−65.6714	−	113.746i	−0.00225347	−	0.00390312i	0.864896	−	0.501950i	$-0.167384\pi$
$947$	−65.6714	−	113.746i	−0.00225347	−	0.00390312i	−0.867150	+	0.498047i	$0.834051\pi$
$948$		0			0
$949$	1326.56	−	2297.68i	0.0453763	−	0.0785940i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	39810.0			1.35317			0.676586	−	0.736363i	$-0.263459\pi$
$953$	39810.0			1.35317			0.676586	+	0.736363i	$0.263459\pi$
$954$		0			0
$955$	−14623.8	+	25329.1i	−0.495512	+	0.858253i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	44864.1	−	21096.5i	1.51067	−	0.710366i
$960$		0			0
$961$	−694.846	−	1203.51i	−0.0233240	−	0.0403984i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−5582.01			−0.186209
$966$		0			0
$967$	18858.5			0.627145			0.313573	−	0.949564i	$-0.398474\pi$
$967$	18858.5			0.627145			0.313573	+	0.949564i	$0.398474\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−24177.5	−	41876.7i	−0.799067	−	1.38402i	−0.920225	−	0.391391i	$-0.871994\pi$
$971$	−24177.5	−	41876.7i	−0.799067	−	1.38402i	0.121158	−	0.992633i	$-0.461339\pi$
$972$		0			0
$973$	12980.4	+	9026.87i	0.427680	+	0.297418i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−2542.86	+	4404.36i	−0.0832685	+	0.144225i	−0.904652	−	0.426151i	$-0.859869\pi$
$977$	−2542.86	+	4404.36i	−0.0832685	+	0.144225i	0.821384	+	0.570376i	$0.193203\pi$
$978$		0			0
$979$	−34614.4			−1.13001
$980$		0			0
$981$		0			0
$982$		0			0
$983$	24308.9	−	42104.2i	0.788741	−	1.36614i	−0.137998	−	0.990433i	$-0.544067\pi$
$983$	24308.9	−	42104.2i	0.788741	−	1.36614i	0.926739	−	0.375707i	$-0.122600\pi$
$984$		0			0
$985$	35169.8	+	60915.8i	1.13767	+	1.97050i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−1769.83	−	3065.43i	−0.0569032	−	0.0985592i
$990$		0			0
$991$	−17500.0	+	30310.9i	−0.560955	+	0.971603i	0.436458	+	0.899725i	$0.356233\pi$
$991$	−17500.0	+	30310.9i	−0.560955	+	0.971603i	−0.997413	+	0.0718786i	$0.977101\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−35423.4			−1.12864
$996$		0			0
$997$	−16403.9	+	28412.4i	−0.521081	+	0.902539i	0.478618	+	0.878023i	$0.341138\pi$
$997$	−16403.9	+	28412.4i	−0.521081	+	0.902539i	−0.999699	+	0.0245157i	$0.992196\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.4.s.j.361.1		8
3.2	odd	2		168.4.q.f.25.4	✓	8
7.2	even	3	inner	504.4.s.j.289.1		8
12.11	even	2		336.4.q.m.193.4		8
21.2	odd	6		168.4.q.f.121.4	yes	8
21.11	odd	6		1176.4.a.bd.1.1		4
21.17	even	6		1176.4.a.ba.1.4		4
84.11	even	6		2352.4.a.cm.1.1		4
84.23	even	6		336.4.q.m.289.4		8
84.59	odd	6		2352.4.a.cp.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.4.q.f.25.4	✓	8	3.2	odd	2
168.4.q.f.121.4	yes	8	21.2	odd	6
336.4.q.m.193.4		8	12.11	even	2
336.4.q.m.289.4		8	84.23	even	6
504.4.s.j.289.1		8	7.2	even	3	inner
504.4.s.j.361.1		8	1.1	even	1	trivial
1176.4.a.ba.1.4		4	21.17	even	6
1176.4.a.bd.1.1		4	21.11	odd	6
2352.4.a.cm.1.1		4	84.11	even	6
2352.4.a.cp.1.4		4	84.59	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	504.s (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.90648 - 13.6944i) q^{5} +(15.2050 + 10.5739i) q^{7} +O(q^{10})\)	\(q+(-7.90648 - 13.6944i) q^{5} +(15.2050 + 10.5739i) q^{7} +(-15.1240 + 26.1955i) q^{11} -61.6298 q^{13} +(28.0724 - 48.6228i) q^{17} +(69.7002 + 120.724i) q^{19} +(-4.07240 - 7.05360i) q^{23} +(-62.5247 + 108.296i) q^{25} +0.217857 q^{29} +(-88.2903 + 152.923i) q^{31} +(24.5855 - 291.826i) q^{35} +(-105.540 - 182.801i) q^{37} +293.305 q^{41} +434.591 q^{43} +(241.698 + 418.633i) q^{47} +(119.385 + 321.553i) q^{49} +(10.2536 - 17.7598i) q^{53} +478.309 q^{55} +(-115.674 + 200.353i) q^{59} +(419.351 + 726.337i) q^{61} +(487.274 + 843.984i) q^{65} +(312.020 - 540.435i) q^{67} -227.106 q^{71} +(-21.5247 + 37.2819i) q^{73} +(-506.949 + 238.383i) q^{77} +(154.530 + 267.654i) q^{79} -1233.99 q^{83} -887.815 q^{85} +(572.179 + 991.042i) q^{89} +(-937.082 - 651.668i) q^{91} +(1102.17 - 1909.01i) q^{95} +1688.12 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{5} + 18 q^{7}+O(q^{10}) \) 8 * q + 4 * q^5 + 18 * q^7	\( 8 q + 4 q^{5} + 18 q^{7} + 14 q^{11} + 44 q^{13} + 96 q^{17} + 26 q^{19} + 96 q^{23} - 110 q^{25} + 152 q^{29} - 238 q^{31} - 152 q^{35} - 562 q^{37} - 856 q^{41} - 516 q^{43} - 80 q^{47} + 156 q^{49} + 2952 q^{55} + 262 q^{59} + 276 q^{61} + 2196 q^{65} - 150 q^{67} + 1696 q^{71} + 218 q^{73} + 764 q^{77} - 1762 q^{79} - 6900 q^{83} + 2904 q^{85} - 344 q^{89} - 2806 q^{91} + 2004 q^{95} - 1244 q^{97}+O(q^{100}) \) 8 * q + 4 * q^5 + 18 * q^7 + 14 * q^11 + 44 * q^13 + 96 * q^17 + 26 * q^19 + 96 * q^23 - 110 * q^25 + 152 * q^29 - 238 * q^31 - 152 * q^35 - 562 * q^37 - 856 * q^41 - 516 * q^43 - 80 * q^47 + 156 * q^49 + 2952 * q^55 + 262 * q^59 + 276 * q^61 + 2196 * q^65 - 150 * q^67 + 1696 * q^71 + 218 * q^73 + 764 * q^77 - 1762 * q^79 - 6900 * q^83 + 2904 * q^85 - 344 * q^89 - 2806 * q^91 + 2004 * q^95 - 1244 * q^97

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