LMFDB - Embedded newform 60.5.b.a.29.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,5,Mod(29,60)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

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

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

chi := DirichletCharacter("60.29");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	60.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.20219778503$
Analytic rank:	$0$
Dimension:	$8$
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} + 110x^{6} + 2705x^{4} + 17000x^{2} + 25600 $ x^8 + 110x^6 + 2705x^4 + 17000*x^2 + 25600
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{7}\cdot 3^{2}\cdot 5^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			29.5
Root			$1.49058i$ of defining polynomial
Character	$\chi$	$=$	60.29
Dual form			60.5.b.a.29.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.64318 - 8.60312i) q^{3} +(23.0886 - 9.58741i) q^{5} +11.6269i q^{7} +(-67.0272 - 45.4792i) q^{9} +O(q^{10})$	\(q+(2.64318 - 8.60312i) q^{3} +(23.0886 - 9.58741i) q^{5} +11.6269i q^{7} +(-67.0272 - 45.4792i) q^{9} -177.001i q^{11} -16.7381i q^{13} +(-21.4544 - 223.975i) q^{15} +294.322 q^{17} -390.163 q^{19} +(100.027 + 30.7319i) q^{21} +414.194 q^{23} +(441.163 - 442.719i) q^{25} +(-568.427 + 456.433i) q^{27} +1106.25i q^{29} +250.163 q^{31} +(-1522.76 - 467.845i) q^{33} +(111.471 + 268.447i) q^{35} +2261.90i q^{37} +(-144.000 - 44.2419i) q^{39} +2293.62i q^{41} -990.978i q^{43} +(-1983.59 - 407.431i) q^{45} +3163.39 q^{47} +2265.82 q^{49} +(777.946 - 2532.09i) q^{51} +1253.30 q^{53} +(-1696.98 - 4086.70i) q^{55} +(-1031.27 + 3356.62i) q^{57} -4484.01i q^{59} -4439.14 q^{61} +(528.780 - 779.316i) q^{63} +(-160.475 - 386.459i) q^{65} +8074.48i q^{67} +(1094.79 - 3563.36i) q^{69} -4395.49i q^{71} -5593.47i q^{73} +(-2642.69 - 4965.56i) q^{75} +2057.96 q^{77} +569.510 q^{79} +(2424.29 + 6096.68i) q^{81} -5253.93 q^{83} +(6795.47 - 2821.78i) q^{85} +(9517.17 + 2924.01i) q^{87} +7050.54i q^{89} +194.612 q^{91} +(661.226 - 2152.18i) q^{93} +(-9008.31 + 3740.65i) q^{95} +7364.12i q^{97} +(-8049.85 + 11863.9i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 52 q^{9}+O(q^{10}) $ 8 * q + 52 * q^9	$ 8 q + 52 q^{9} - 100 q^{15} + 408 q^{19} + 212 q^{21} - 1528 q^{31} - 1152 q^{39} - 2900 q^{45} + 480 q^{49} + 7400 q^{51} + 7600 q^{55} - 10808 q^{61} - 8300 q^{69} - 14000 q^{75} + 15144 q^{79} + 34688 q^{81} + 22600 q^{85} - 54912 q^{91} - 24400 q^{99}+O(q^{100}) $ 8 * q + 52 * q^9 - 100 * q^15 + 408 * q^19 + 212 * q^21 - 1528 * q^31 - 1152 * q^39 - 2900 * q^45 + 480 * q^49 + 7400 * q^51 + 7600 * q^55 - 10808 * q^61 - 8300 * q^69 - 14000 * q^75 + 15144 * q^79 + 34688 * q^81 + 22600 * q^85 - 54912 * q^91 - 24400 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$41$
$\chi(n)$	$1$	$-1$	$-1$

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
$3$	2.64318	−	8.60312i	0.293687	−	0.955902i
$3$	2.64318	−	8.60312i	0.293687	−	0.955902i
$4$		0			0
$5$	23.0886	−	9.58741i	0.923542	−	0.383496i
$5$	23.0886	−	9.58741i	0.923542	−	0.383496i
$6$		0			0
$7$			11.6269i			0.237283i	0.992937	+	0.118641i	$0.0378539\pi$
$7$			11.6269i			0.237283i	−0.992937	+	0.118641i	$0.962146\pi$
$8$		0			0
$9$	−67.0272	−	45.4792i	−0.827496	−	0.561471i
$10$		0			0
$11$		−	177.001i		−	1.46282i	−0.681940	−	0.731409i	$-0.738863\pi$
$11$		−	177.001i		−	1.46282i	0.681940	−	0.731409i	$-0.261137\pi$
$12$		0			0
$13$		−	16.7381i		−	0.0990421i	−0.998773	−	0.0495211i	$-0.984231\pi$
$13$		−	16.7381i		−	0.0990421i	0.998773	−	0.0495211i	$-0.0157695\pi$
$14$		0			0
$15$	−21.4544	−	223.975i	−0.0953528	−	0.995444i
$16$		0			0
$17$	294.322			1.01841			0.509207	−	0.860644i	$-0.329939\pi$
$17$	294.322			1.01841			0.509207	+	0.860644i	$0.329939\pi$
$18$		0			0
$19$	−390.163			−1.08078			−0.540392	−	0.841413i	$-0.681724\pi$
$19$	−390.163			−1.08078			−0.540392	+	0.841413i	$0.681724\pi$
$20$		0			0
$21$	100.027	+	30.7319i	0.226819	+	0.0696868i
$22$		0			0
$23$	414.194			0.782975			0.391488	−	0.920183i	$-0.371961\pi$
$23$	414.194			0.782975			0.391488	+	0.920183i	$0.371961\pi$
$24$		0			0
$25$	441.163	−	442.719i	0.705861	−	0.708350i
$26$		0			0
$27$	−568.427	+	456.433i	−0.779736	+	0.626109i
$28$		0			0
$29$			1106.25i			1.31539i	0.753282	+	0.657697i	$0.228469\pi$
$29$			1106.25i			1.31539i	−0.753282	+	0.657697i	$0.771531\pi$
$30$		0			0
$31$	250.163			0.260316			0.130158	−	0.991493i	$-0.458452\pi$
$31$	250.163			0.260316			0.130158	+	0.991493i	$0.458452\pi$
$32$		0			0
$33$	−1522.76	−	467.845i	−1.39831	−	0.429610i
$34$		0			0
$35$	111.471	+	268.447i	0.0909971	+	0.219141i
$36$		0			0
$37$			2261.90i			1.65223i	0.563504	+	0.826113i	$0.309453\pi$
$37$			2261.90i			1.65223i	−0.563504	+	0.826113i	$0.690547\pi$
$38$		0			0
$39$	−144.000	−	44.2419i	−0.0946746	−	0.0290873i
$40$		0			0
$41$			2293.62i			1.36444i	0.731148	+	0.682219i	$0.238985\pi$
$41$			2293.62i			1.36444i	−0.731148	+	0.682219i	$0.761015\pi$
$42$		0			0
$43$		−	990.978i		−	0.535953i	−0.963425	−	0.267977i	$-0.913645\pi$
$43$		−	990.978i		−	0.535953i	0.963425	−	0.267977i	$-0.0863550\pi$
$44$		0			0
$45$	−1983.59	−	407.431i	−0.979550	−	0.201201i
$46$		0			0
$47$	3163.39			1.43205			0.716023	−	0.698077i	$-0.245961\pi$
$47$	3163.39			1.43205			0.716023	+	0.698077i	$0.245961\pi$
$48$		0			0
$49$	2265.82			0.943697
$50$		0			0
$51$	777.946	−	2532.09i	0.299095	−	0.973505i
$52$		0			0
$53$	1253.30			0.446172			0.223086	−	0.974799i	$-0.428387\pi$
$53$	1253.30			0.446172			0.223086	+	0.974799i	$0.428387\pi$
$54$		0			0
$55$	−1696.98	−	4086.70i	−0.560985	−	1.35097i
$56$		0			0
$57$	−1031.27	+	3356.62i	−0.317412	+	1.03312i
$58$		0			0
$59$		−	4484.01i		−	1.28814i	−0.764967	−	0.644069i	$-0.777245\pi$
$59$		−	4484.01i		−	1.28814i	0.764967	−	0.644069i	$-0.222755\pi$
$60$		0			0
$61$	−4439.14			−1.19300			−0.596499	−	0.802614i	$-0.703442\pi$
$61$	−4439.14			−1.19300			−0.596499	+	0.802614i	$0.703442\pi$
$62$		0			0
$63$	528.780	−	779.316i	0.133227	−	0.196351i
$64$		0			0
$65$	−160.475	−	386.459i	−0.0379823	−	0.0914696i
$66$		0			0
$67$			8074.48i			1.79873i	0.437203	+	0.899363i	$0.355969\pi$
$67$			8074.48i			1.79873i	−0.437203	+	0.899363i	$0.644031\pi$
$68$		0			0
$69$	1094.79	−	3563.36i	0.229949	−	0.748448i
$70$		0			0
$71$		−	4395.49i		−	0.871949i	−0.899959	−	0.435974i	$-0.856404\pi$
$71$		−	4395.49i		−	0.871949i	0.899959	−	0.435974i	$-0.143596\pi$
$72$		0			0
$73$		−	5593.47i		−	1.04963i	−0.851217	−	0.524814i	$-0.824135\pi$
$73$		−	5593.47i		−	1.04963i	0.851217	−	0.524814i	$-0.175865\pi$
$74$		0			0
$75$	−2642.69	−	4965.56i	−0.469811	−	0.882767i
$76$		0			0
$77$	2057.96			0.347101
$78$		0			0
$79$	569.510			0.0912531			0.0456265	−	0.998959i	$-0.485472\pi$
$79$	569.510			0.0912531			0.0456265	+	0.998959i	$0.485472\pi$
$80$		0			0
$81$	2424.29	+	6096.68i	0.369500	+	0.929231i
$82$		0			0
$83$	−5253.93			−0.762655			−0.381328	−	0.924440i	$-0.624533\pi$
$83$	−5253.93			−0.762655			−0.381328	+	0.924440i	$0.624533\pi$
$84$		0			0
$85$	6795.47	−	2821.78i	0.940549	−	0.390558i
$86$		0			0
$87$	9517.17	+	2924.01i	1.25739	+	0.386314i
$88$		0			0
$89$			7050.54i			0.890107i	0.895504	+	0.445054i	$0.146815\pi$
$89$			7050.54i			0.890107i	−0.895504	+	0.445054i	$0.853185\pi$
$90$		0			0
$91$	194.612			0.0235010
$92$		0			0
$93$	661.226	−	2152.18i	0.0764512	−	0.248836i
$94$		0			0
$95$	−9008.31	+	3740.65i	−0.998150	+	0.414477i
$96$		0			0
$97$			7364.12i			0.782667i	0.920249	+	0.391334i	$0.127986\pi$
$97$			7364.12i			0.782667i	−0.920249	+	0.391334i	$0.872014\pi$
$98$		0			0
$99$	−8049.85	+	11863.9i	−0.821329	+	1.21048i
$100$		0			0
$101$		−	280.265i		−	0.0274743i	−0.999906	−	0.0137371i	$-0.995627\pi$
$101$		−	280.265i		−	0.0274743i	0.999906	−	0.0137371i	$-0.00437281\pi$
$102$		0			0
$103$			4121.46i			0.388487i	0.980953	+	0.194244i	$0.0622252\pi$
$103$			4121.46i			0.388487i	−0.980953	+	0.194244i	$0.937775\pi$
$104$		0			0
$105$	2604.12	−	249.447i	0.236202	−	0.0226256i
$106$		0			0
$107$	−18817.9			−1.64363			−0.821814	−	0.569756i	$-0.807038\pi$
$107$	−18817.9			−1.64363			−0.821814	+	0.569756i	$0.807038\pi$
$108$		0			0
$109$	−3096.45			−0.260622			−0.130311	−	0.991473i	$-0.541598\pi$
$109$	−3096.45			−0.260622			−0.130311	+	0.991473i	$0.541598\pi$
$110$		0			0
$111$	19459.4	+	5978.60i	1.57937	+	0.485237i
$112$		0			0
$113$	−8644.49			−0.676990			−0.338495	−	0.940968i	$-0.609918\pi$
$113$	−8644.49			−0.676990			−0.338495	+	0.940968i	$0.609918\pi$
$114$		0			0
$115$	9563.14	−	3971.05i	0.723111	−	0.300268i
$116$		0			0
$117$	−761.236	+	1121.91i	−0.0556093	+	0.0819570i
$118$		0			0
$119$			3422.04i			0.241652i
$120$		0			0
$121$	−16688.3			−1.13983
$122$		0			0
$123$	19732.3	+	6062.45i	1.30427	+	0.400717i
$124$		0			0
$125$	5941.30	−	14451.4i	0.380243	−	0.924887i
$126$		0			0
$127$		−	16001.4i		−	0.992089i	−0.868297	−	0.496044i	$-0.834785\pi$
$127$		−	16001.4i		−	0.992089i	0.868297	−	0.496044i	$-0.165215\pi$
$128$		0			0
$129$	−8525.50	−	2619.33i	−0.512319	−	0.157402i
$130$		0			0
$131$		−	1297.86i		−	0.0756285i	−0.999285	−	0.0378143i	$-0.987960\pi$
$131$		−	1297.86i		−	0.0756285i	0.999285	−	0.0378143i	$-0.0120395\pi$
$132$		0			0
$133$		−	4536.37i		−	0.256452i
$134$		0			0
$135$	−8748.16	+	15988.1i	−0.480009	+	0.877264i
$136$		0			0
$137$	18427.4			0.981801			0.490900	−	0.871216i	$-0.336668\pi$
$137$	18427.4			0.981801			0.490900	+	0.871216i	$0.336668\pi$
$138$		0			0
$139$	9241.84			0.478331			0.239166	−	0.970979i	$-0.423126\pi$
$139$	9241.84			0.478331			0.239166	+	0.970979i	$0.423126\pi$
$140$		0			0
$141$	8361.40	−	27215.0i	0.420573	−	1.36889i
$142$		0			0
$143$	−2962.66			−0.144881
$144$		0			0
$145$	10606.0	+	25541.7i	0.504449	+	1.21482i
$146$		0			0
$147$	5988.96	−	19493.1i	0.277151	−	0.902081i
$148$		0			0
$149$		−	36705.5i		−	1.65333i	−0.562696	−	0.826664i	$-0.690236\pi$
$149$		−	36705.5i		−	1.65333i	0.562696	−	0.826664i	$-0.309764\pi$
$150$		0			0
$151$	−29223.8			−1.28169			−0.640845	−	0.767671i	$-0.721416\pi$
$151$	−29223.8			−1.28169			−0.640845	+	0.767671i	$0.721416\pi$
$152$		0			0
$153$	−19727.6	−	13385.5i	−0.842735	−	0.571811i
$154$		0			0
$155$	5775.91	−	2398.42i	0.240412	−	0.0998300i
$156$		0			0
$157$		−	28009.5i		−	1.13633i	−0.822914	−	0.568166i	$-0.807653\pi$
$157$		−	28009.5i		−	1.13633i	0.822914	−	0.568166i	$-0.192347\pi$
$158$		0			0
$159$	3312.69	−	10782.3i	0.131035	−	0.426497i
$160$		0			0
$161$			4815.77i			0.185787i
$162$		0			0
$163$			39685.6i			1.49368i	0.665004	+	0.746840i	$0.268430\pi$
$163$			39685.6i			1.49368i	−0.665004	+	0.746840i	$0.731570\pi$
$164$		0			0
$165$	−39643.7	+	3797.44i	−1.45615	+	0.139484i
$166$		0			0
$167$	−26386.5			−0.946126			−0.473063	−	0.881029i	$-0.656852\pi$
$167$	−26386.5			−0.946126			−0.473063	+	0.881029i	$0.656852\pi$
$168$		0			0
$169$	28280.8			0.990191
$170$		0			0
$171$	26151.6	+	17744.3i	0.894345	+	0.606829i
$172$		0			0
$173$	55622.9			1.85849			0.929247	−	0.369459i	$-0.120457\pi$
$173$	55622.9			1.85849			0.929247	+	0.369459i	$0.120457\pi$
$174$		0			0
$175$	5147.43	+	5129.34i	0.168079	+	0.167489i
$176$		0			0
$177$	−38576.5	−	11852.0i	−1.23133	−	0.378309i
$178$		0			0
$179$			25045.7i			0.781676i	0.920460	+	0.390838i	$0.127815\pi$
$179$			25045.7i			0.781676i	−0.920460	+	0.390838i	$0.872185\pi$
$180$		0			0
$181$	−31678.3			−0.966952			−0.483476	−	0.875358i	$-0.660626\pi$
$181$	−31678.3			−0.966952			−0.483476	+	0.875358i	$0.660626\pi$
$182$		0			0
$183$	−11733.5	+	38190.5i	−0.350367	+	1.14039i
$184$		0			0
$185$	21685.7	+	52224.0i	0.633623	+	1.52590i
$186$		0			0
$187$		−	52095.2i		−	1.48975i
$188$		0			0
$189$	−5306.88	−	6609.02i	−0.148565	−	0.185018i
$190$		0			0
$191$			17906.2i			0.490837i	0.969417	+	0.245418i	$0.0789253\pi$
$191$			17906.2i			0.490837i	−0.969417	+	0.245418i	$0.921075\pi$
$192$		0			0
$193$		−	26498.7i		−	0.711393i	−0.934602	−	0.355696i	$-0.884244\pi$
$193$		−	26498.7i		−	0.711393i	0.934602	−	0.355696i	$-0.115756\pi$
$194$		0			0
$195$	−3748.92	+	359.106i	−0.0985909	+	0.00944394i
$196$		0			0
$197$	17018.7			0.438524			0.219262	−	0.975666i	$-0.429635\pi$
$197$	17018.7			0.438524			0.219262	+	0.975666i	$0.429635\pi$
$198$		0			0
$199$	38402.7			0.969739			0.484870	−	0.874586i	$-0.338867\pi$
$199$	38402.7			0.969739			0.484870	+	0.874586i	$0.338867\pi$
$200$		0			0
$201$	69465.7	+	21342.3i	1.71941	+	0.528262i
$202$		0			0
$203$	−12862.2			−0.312121
$204$		0			0
$205$	21989.9	+	52956.4i	0.523257	+	1.26012i
$206$		0			0
$207$	−27762.3	−	18837.2i	−0.647909	−	0.439618i
$208$		0			0
$209$			69059.2i			1.58099i
$210$		0			0
$211$	−50216.1			−1.12792			−0.563960	−	0.825802i	$-0.690723\pi$
$211$	−50216.1			−1.12792			−0.563960	+	0.825802i	$0.690723\pi$
$212$		0			0
$213$	−37814.9	−	11618.1i	−0.833497	−	0.256080i
$214$		0			0
$215$	−9500.91	−	22880.2i	−0.205536	−	0.494976i
$216$		0			0
$217$			2908.61i			0.0617684i
$218$		0			0
$219$	−48121.2	−	14784.5i	−1.00334	−	0.308262i
$220$		0			0
$221$		−	4926.40i		−	0.100866i
$222$		0			0
$223$			49997.2i			1.00539i	0.864463	+	0.502696i	$0.167659\pi$
$223$			49997.2i			1.00539i	−0.864463	+	0.502696i	$0.832341\pi$
$224$		0			0
$225$	−49704.4	+	9610.48i	−0.981816	+	0.189837i
$226$		0			0
$227$	41601.3			0.807337			0.403669	−	0.914905i	$-0.367735\pi$
$227$	41601.3			0.807337			0.403669	+	0.914905i	$0.367735\pi$
$228$		0			0
$229$	−42178.2			−0.804299			−0.402149	−	0.915574i	$-0.631737\pi$
$229$	−42178.2			−0.804299			−0.402149	+	0.915574i	$0.631737\pi$
$230$		0			0
$231$	5439.57	−	17704.9i	0.101939	−	0.331795i
$232$		0			0
$233$	−30326.6			−0.558614			−0.279307	−	0.960202i	$-0.590105\pi$
$233$	−30326.6			−0.558614			−0.279307	+	0.960202i	$0.590105\pi$
$234$		0			0
$235$	73038.1	−	30328.7i	1.32255	−	0.549184i
$236$		0			0
$237$	1505.32	−	4899.56i	0.0267998	−	0.0872290i
$238$		0			0
$239$		−	60416.0i		−	1.05768i	−0.848720	−	0.528842i	$-0.822626\pi$
$239$		−	60416.0i		−	1.05768i	0.848720	−	0.528842i	$-0.177374\pi$
$240$		0			0
$241$	8045.10			0.138515			0.0692576	−	0.997599i	$-0.477937\pi$
$241$	8045.10			0.138515			0.0692576	+	0.997599i	$0.477937\pi$
$242$		0			0
$243$	58858.3	−	4741.85i	0.996770	−	0.0803036i
$244$		0			0
$245$	52314.4	−	21723.3i	0.871544	−	0.361904i
$246$		0			0
$247$			6530.60i			0.107043i
$248$		0			0
$249$	−13887.1	+	45200.2i	−0.223982	+	0.729024i
$250$		0			0
$251$		−	48910.7i		−	0.776348i	−0.921586	−	0.388174i	$-0.873106\pi$
$251$		−	48910.7i		−	0.776348i	0.921586	−	0.388174i	$-0.126894\pi$
$252$		0			0
$253$		−	73312.7i		−	1.14535i
$254$		0			0
$255$	−6314.49	−	65920.7i	−0.0971087	−	1.01377i
$256$		0			0
$257$	−51287.5			−0.776507			−0.388253	−	0.921553i	$-0.626921\pi$
$257$	−51287.5			−0.776507			−0.388253	+	0.921553i	$0.626921\pi$
$258$		0			0
$259$	−26298.8			−0.392045
$260$		0			0
$261$	50311.2	−	74148.6i	0.738556	−	1.08848i
$262$		0			0
$263$	102945.			1.48830			0.744152	−	0.668010i	$-0.232854\pi$
$263$	102945.			1.48830			0.744152	+	0.668010i	$0.232854\pi$
$264$		0			0
$265$	28936.9	−	12015.9i	0.412059	−	0.171105i
$266$		0			0
$267$	60656.6	+	18635.8i	0.850855	+	0.261413i
$268$		0			0
$269$		−	27899.4i		−	0.385558i	−0.981242	−	0.192779i	$-0.938250\pi$
$269$		−	27899.4i		−	0.385558i	0.981242	−	0.192779i	$-0.0617500\pi$
$270$		0			0
$271$	−91164.7			−1.24133			−0.620666	−	0.784075i	$-0.713138\pi$
$271$	−91164.7			−1.24133			−0.620666	+	0.784075i	$0.713138\pi$
$272$		0			0
$273$	514.394	−	1674.27i	0.00690193	−	0.0224646i
$274$		0			0
$275$	−78361.6	−	78086.3i	−1.03619	−	1.03255i
$276$		0			0
$277$			83010.4i			1.08186i	0.841066	+	0.540932i	$0.181928\pi$
$277$			83010.4i			1.08186i	−0.841066	+	0.540932i	$0.818072\pi$
$278$		0			0
$279$	−16767.7	−	11377.2i	−0.215410	−	0.146160i
$280$		0			0
$281$			37059.2i			0.469336i	0.972076	+	0.234668i	$0.0754003\pi$
$281$			37059.2i			0.469336i	−0.972076	+	0.234668i	$0.924600\pi$
$282$		0			0
$283$			40545.4i			0.506254i	0.967433	+	0.253127i	$0.0814591\pi$
$283$			40545.4i			0.506254i	−0.967433	+	0.253127i	$0.918541\pi$
$284$		0			0
$285$	8370.71	+	87386.7i	0.103056	+	1.07586i
$286$		0			0
$287$	−26667.6			−0.323758
$288$		0			0
$289$	3104.39			0.0371689
$290$		0			0
$291$	63354.3	+	19464.7i	0.748153	+	0.229859i
$292$		0			0
$293$	−162610.			−1.89414			−0.947068	−	0.321032i	$-0.895970\pi$
$293$	−162610.			−1.89414			−0.947068	+	0.321032i	$0.895970\pi$
$294$		0			0
$295$	−42990.0	−	103529.i	−0.493996	−	1.18965i
$296$		0			0
$297$	80789.1	+	100612.i	0.915883	+	1.14061i
$298$		0			0
$299$		−	6932.83i		−	0.0775476i
$300$		0			0
$301$	11522.0			0.127173
$302$		0			0
$303$	−2411.15	−	740.791i	−0.0262627	−	0.00806883i
$304$		0			0
$305$	−102493.	+	42559.9i	−1.10178	+	0.457510i
$306$		0			0
$307$			50365.0i			0.534383i	0.963643	+	0.267191i	$0.0860956\pi$
$307$			50365.0i			0.534383i	−0.963643	+	0.267191i	$0.913904\pi$
$308$		0			0
$309$	35457.4	+	10893.8i	0.371356	+	0.114094i
$310$		0			0
$311$			29441.4i			0.304395i	0.988350	+	0.152198i	$0.0486350\pi$
$311$			29441.4i			0.304395i	−0.988350	+	0.152198i	$0.951365\pi$
$312$		0			0
$313$		−	108346.i		−	1.10592i	−0.833207	−	0.552962i	$-0.813497\pi$
$313$		−	108346.i		−	1.10592i	0.833207	−	0.552962i	$-0.186503\pi$
$314$		0			0
$315$	4737.14	−	23062.9i	0.0477414	−	0.232430i
$316$		0			0
$317$	68136.9			0.678054			0.339027	−	0.940777i	$-0.389902\pi$
$317$	68136.9			0.678054			0.339027	+	0.940777i	$0.389902\pi$
$318$		0			0
$319$	195807.			1.92418
$320$		0			0
$321$	−49739.1	+	161892.i	−0.482711	+	1.57115i
$322$		0			0
$323$	−114834.			−1.10069
$324$		0			0
$325$	−7410.28	−	7384.24i	−0.0701565	−	0.0699100i
$326$		0			0
$327$	−8184.47	+	26639.1i	−0.0765412	+	0.249129i
$328$		0			0
$329$			36780.3i			0.339800i
$330$		0			0
$331$	−31817.4			−0.290408			−0.145204	−	0.989402i	$-0.546384\pi$
$331$	−31817.4			−0.290408			−0.145204	+	0.989402i	$0.546384\pi$
$332$		0			0
$333$	102869.	−	151609.i	0.927677	−	1.36721i
$334$		0			0
$335$	77413.3	+	186428.i	0.689805	+	1.66120i
$336$		0			0
$337$			217789.i			1.91768i	0.283942	+	0.958842i	$0.408358\pi$
$337$			217789.i			1.91768i	−0.283942	+	0.958842i	$0.591642\pi$
$338$		0			0
$339$	−22848.9	+	74369.6i	−0.198823	+	0.647136i
$340$		0			0
$341$		−	44279.1i		−	0.380794i
$342$		0			0
$343$			54260.4i			0.461206i
$344$		0			0
$345$	−8886.27	−	92769.0i	−0.0746589	−	0.779408i
$346$		0			0
$347$	−108878.			−0.904234			−0.452117	−	0.891959i	$-0.649331\pi$
$347$	−108878.			−0.904234			−0.452117	+	0.891959i	$0.649331\pi$
$348$		0			0
$349$	27193.2			0.223259			0.111630	−	0.993750i	$-0.464393\pi$
$349$	27193.2			0.223259			0.111630	+	0.993750i	$0.464393\pi$
$350$		0			0
$351$	7639.84	+	9514.41i	0.0620111	+	0.0772267i
$352$		0			0
$353$	53685.5			0.430832			0.215416	−	0.976522i	$-0.430889\pi$
$353$	53685.5			0.430832			0.215416	+	0.976522i	$0.430889\pi$
$354$		0			0
$355$	−42141.4	−	101486.i	−0.334389	−	0.805282i
$356$		0			0
$357$	29440.2	+	9045.06i	0.230996	+	0.0709701i
$358$		0			0
$359$		−	63041.9i		−	0.489148i	−0.969631	−	0.244574i	$-0.921352\pi$
$359$		−	63041.9i		−	0.489148i	0.969631	−	0.244574i	$-0.0786482\pi$
$360$		0			0
$361$	21906.4			0.168095
$362$		0			0
$363$	−44110.2	+	143571.i	−0.334754	+	1.08957i
$364$		0			0
$365$	−53626.9	−	129145.i	−0.402528	−	0.969376i
$366$		0			0
$367$			18291.7i			0.135807i	0.997692	+	0.0679035i	$0.0216310\pi$
$367$			18291.7i			0.135807i	−0.997692	+	0.0679035i	$0.978369\pi$
$368$		0			0
$369$	104312.	−	153735.i	0.766093	−	1.12907i
$370$		0			0
$371$			14571.9i			0.105869i
$372$		0			0
$373$		−	75846.7i		−	0.545153i	−0.962134	−	0.272577i	$-0.912124\pi$
$373$		−	75846.7i		−	0.545153i	0.962134	−	0.272577i	$-0.0878759\pi$
$374$		0			0
$375$	−108623.	−	89311.2i	−0.772428	−	0.635102i
$376$		0			0
$377$	18516.5			0.130280
$378$		0			0
$379$	−180877.			−1.25923			−0.629616	−	0.776907i	$-0.716788\pi$
$379$	−180877.			−1.25923			−0.629616	+	0.776907i	$0.716788\pi$
$380$		0			0
$381$	−137662.	−	42294.6i	−0.948340	−	0.291363i
$382$		0			0
$383$	83812.2			0.571360			0.285680	−	0.958325i	$-0.407781\pi$
$383$	83812.2			0.571360			0.285680	+	0.958325i	$0.407781\pi$
$384$		0			0
$385$	47515.4	−	19730.5i	0.320563	−	0.133112i
$386$		0			0
$387$	−45068.8	+	66422.5i	−0.300922	+	0.443499i
$388$		0			0
$389$		−	48698.1i		−	0.321820i	−0.986969	−	0.160910i	$-0.948557\pi$
$389$		−	48698.1i		−	0.321820i	0.986969	−	0.160910i	$-0.0514429\pi$
$390$		0			0
$391$	121906.			0.797394
$392$		0			0
$393$	−11165.7	−	3430.48i	−0.0722935	−	0.0222111i
$394$		0			0
$395$	13149.2	−	5460.13i	0.0842761	−	0.0349952i
$396$		0			0
$397$		−	92676.0i		−	0.588012i	−0.955804	−	0.294006i	$-0.905011\pi$
$397$		−	92676.0i		−	0.588012i	0.955804	−	0.294006i	$-0.0949886\pi$
$398$		0			0
$399$	−39026.9	−	11990.4i	−0.245143	−	0.0753164i
$400$		0			0
$401$		−	251104.i		−	1.56158i	−0.624791	−	0.780792i	$-0.714816\pi$
$401$		−	251104.i		−	1.56158i	0.624791	−	0.780792i	$-0.285184\pi$
$402$		0			0
$403$		−	4187.26i		−	0.0257822i
$404$		0			0
$405$	114425.	+	117521.i	0.697606	+	0.716482i
$406$		0			0
$407$	400358.			2.41691
$408$		0			0
$409$	−230500.			−1.37792			−0.688960	−	0.724799i	$-0.741932\pi$
$409$	−230500.			−1.37792			−0.688960	+	0.724799i	$0.741932\pi$
$410$		0			0
$411$	48707.0	−	158533.i	0.288342	−	0.938505i
$412$		0			0
$413$	52135.0			0.305653
$414$		0			0
$415$	−121306.	+	50371.6i	−0.704345	+	0.292476i
$416$		0			0
$417$	24427.8	−	79508.6i	0.140479	−	0.457238i
$418$		0			0
$419$			220779.i			1.25756i	0.777583	+	0.628781i	$0.216446\pi$
$419$			220779.i			1.25756i	−0.777583	+	0.628781i	$0.783554\pi$
$420$		0			0
$421$	−14062.0			−0.0793382			−0.0396691	−	0.999213i	$-0.512630\pi$
$421$	−14062.0			−0.0793382			−0.0396691	+	0.999213i	$0.512630\pi$
$422$		0			0
$423$	−212033.	−	143868.i	−1.18501	−	0.804052i
$424$		0			0
$425$	129844.	−	130302.i	0.718860	−	0.721394i
$426$		0			0
$427$		−	51613.3i		−	0.283078i
$428$		0			0
$429$	−7830.85	+	25488.1i	−0.0425495	+	0.138492i
$430$		0			0
$431$			222578.i			1.19819i	0.800677	+	0.599097i	$0.204473\pi$
$431$			222578.i			1.19819i	−0.800677	+	0.599097i	$0.795527\pi$
$432$		0			0
$433$		−	26766.9i		−	0.142765i	−0.997449	−	0.0713827i	$-0.977259\pi$
$433$		−	26766.9i		−	0.142765i	0.997449	−	0.0713827i	$-0.0227411\pi$
$434$		0			0
$435$	247771.	−	23733.8i	1.30940	−	0.125427i
$436$		0			0
$437$	−161603.			−0.846228
$438$		0			0
$439$	95907.3			0.497648			0.248824	−	0.968549i	$-0.419956\pi$
$439$	95907.3			0.497648			0.248824	+	0.968549i	$0.419956\pi$
$440$		0			0
$441$	−151871.	−	103047.i	−0.780906	−	0.529858i
$442$		0			0
$443$	277148.			1.41223			0.706113	−	0.708099i	$-0.250447\pi$
$443$	277148.			1.41223			0.706113	+	0.708099i	$0.250447\pi$
$444$		0			0
$445$	67596.4	+	162787.i	0.341353	+	0.822052i
$446$		0			0
$447$	−315782.	−	97019.3i	−1.58042	−	0.485560i
$448$		0			0
$449$		−	151594.i		−	0.751950i	−0.926630	−	0.375975i	$-0.877308\pi$
$449$		−	151594.i		−	0.751950i	0.926630	−	0.375975i	$-0.122692\pi$
$450$		0			0
$451$	405973.			1.99592
$452$		0			0
$453$	−77243.7	+	251416.i	−0.376415	+	1.22517i
$454$		0			0
$455$	4493.31	−	1865.82i	0.0217042	−	0.00901255i
$456$		0			0
$457$		−	132213.i		−	0.633057i	−0.948583	−	0.316528i	$-0.897483\pi$
$457$		−	132213.i		−	0.633057i	0.948583	−	0.316528i	$-0.102517\pi$
$458$		0			0
$459$	−167301.	+	134338.i	−0.794095	+	0.637638i
$460$		0			0
$461$			399652.i			1.88053i	0.340446	+	0.940264i	$0.389422\pi$
$461$			399652.i			1.88053i	−0.340446	+	0.940264i	$0.610578\pi$
$462$		0			0
$463$			99054.1i			0.462073i	0.972945	+	0.231036i	$0.0742117\pi$
$463$			99054.1i			0.462073i	−0.972945	+	0.231036i	$0.925788\pi$
$464$		0			0
$465$	−5367.10	−	56030.3i	−0.0248218	−	0.259129i
$466$		0			0
$467$	−198490.			−0.910134			−0.455067	−	0.890457i	$-0.650385\pi$
$467$	−198490.			−0.910134			−0.455067	+	0.890457i	$0.650385\pi$
$468$		0			0
$469$	−93880.8			−0.426807
$470$		0			0
$471$	−240969.	−	74034.0i	−1.08622	−	0.333726i
$472$		0			0
$473$	−175404.			−0.784002
$474$		0			0
$475$	−172126.	+	172733.i	−0.762884	+	0.765574i
$476$		0			0
$477$	−84005.1	−	56999.0i	−0.369206	−	0.250513i
$478$		0			0
$479$			289423.i			1.26143i	0.776016	+	0.630713i	$0.217238\pi$
$479$			289423.i			1.26143i	−0.776016	+	0.630713i	$0.782762\pi$
$480$		0			0
$481$	37859.9			0.163640
$482$		0			0
$483$	41430.7	+	12729.0i	0.177594	+	0.0545630i
$484$		0			0
$485$	70602.8	+	170027.i	0.300150	+	0.722826i
$486$		0			0
$487$		−	141256.i		−	0.595593i	−0.954629	−	0.297796i	$-0.903748\pi$
$487$		−	141256.i		−	0.595593i	0.954629	−	0.297796i	$-0.0962516\pi$
$488$		0			0
$489$	341420.	+	104896.i	1.42781	+	0.438674i
$490$		0			0
$491$		−	132986.i		−	0.551622i	−0.961212	−	0.275811i	$-0.911054\pi$
$491$		−	132986.i		−	0.551622i	0.961212	−	0.275811i	$-0.0889463\pi$
$492$		0			0
$493$			325593.i			1.33962i
$494$		0			0
$495$	−72115.7	+	351097.i	−0.294320	+	1.43290i
$496$		0			0
$497$	51105.8			0.206898
$498$		0			0
$499$	107327.			0.431031			0.215515	−	0.976500i	$-0.430857\pi$
$499$	107327.			0.431031			0.215515	+	0.976500i	$0.430857\pi$
$500$		0			0
$501$	−69744.3	+	227006.i	−0.277865	+	0.904404i
$502$		0			0
$503$	8472.66			0.0334876			0.0167438	−	0.999860i	$-0.494670\pi$
$503$	8472.66			0.0334876			0.0167438	+	0.999860i	$0.494670\pi$
$504$		0			0
$505$	−2687.02	−	6470.92i	−0.0105363	−	0.0253737i
$506$		0			0
$507$	74751.3	−	243303.i	0.290806	−	0.946525i
$508$		0			0
$509$			98517.0i			0.380256i	0.981759	+	0.190128i	$0.0608902\pi$
$509$			98517.0i			0.380256i	−0.981759	+	0.190128i	$0.939110\pi$
$510$		0			0
$511$	65034.5			0.249059
$512$		0			0
$513$	221779.	−	178083.i	0.842726	−	0.676689i
$514$		0			0
$515$	39514.1	+	95158.6i	0.148983	+	0.358785i
$516$		0			0
$517$		−	559922.i		−	2.09482i
$518$		0			0
$519$	147021.	−	478530.i	0.545815	−	1.77654i
$520$		0			0
$521$		−	93249.9i		−	0.343536i	−0.985137	−	0.171768i	$-0.945052\pi$
$521$		−	93249.9i		−	0.343536i	0.985137	−	0.171768i	$-0.0549480\pi$
$522$		0			0
$523$		−	64242.3i		−	0.234865i	−0.993081	−	0.117432i	$-0.962534\pi$
$523$		−	64242.3i		−	0.234865i	0.993081	−	0.117432i	$-0.0374663\pi$
$524$		0			0
$525$	57733.9	−	30726.2i	0.209465	−	0.111478i
$526$		0			0
$527$	73628.5			0.265109
$528$		0			0
$529$	−108284.			−0.386950
$530$		0			0
$531$	−203929.	+	300551.i	−0.723253	+	1.06593i
$532$		0			0
$533$	38390.9			0.135137
$534$		0			0
$535$	−434478.	+	180415.i	−1.51796	+	0.630325i
$536$		0			0
$537$	215471.	+	66200.2i	0.747205	+	0.229568i
$538$		0			0
$539$		−	401051.i		−	1.38046i
$540$		0			0
$541$	370186.			1.26481			0.632406	−	0.774638i	$-0.282068\pi$
$541$	370186.			1.26481			0.632406	+	0.774638i	$0.282068\pi$
$542$		0			0
$543$	−83731.5	+	272532.i	−0.283981	+	0.924311i
$544$		0			0
$545$	−71492.5	+	29686.9i	−0.240695	+	0.0999475i
$546$		0			0
$547$		−	120927.i		−	0.404155i	−0.979370	−	0.202077i	$-0.935231\pi$
$547$		−	120927.i		−	0.404155i	0.979370	−	0.202077i	$-0.0647692\pi$
$548$		0			0
$549$	297543.	+	201888.i	0.987201	+	0.669833i
$550$		0			0
$551$		−	431617.i		−	1.42166i
$552$		0			0
$553$			6621.62i			0.0216528i
$554$		0			0
$555$	506608.	−	48527.6i	1.64470	−	0.157544i
$556$		0			0
$557$	−416965.			−1.34397			−0.671985	−	0.740565i	$-0.734558\pi$
$557$	−416965.			−1.34397			−0.671985	+	0.740565i	$0.734558\pi$
$558$		0			0
$559$	−16587.1			−0.0530820
$560$		0			0
$561$	−448181.	−	137697.i	−1.42406	−	0.437521i
$562$		0			0
$563$	−244647.			−0.771832			−0.385916	−	0.922534i	$-0.626115\pi$
$563$	−244647.			−0.771832			−0.385916	+	0.922534i	$0.626115\pi$
$564$		0			0
$565$	−199589.	+	82878.3i	−0.625229	+	0.259623i
$566$		0			0
$567$	−70885.3	+	28186.9i	−0.220490	+	0.0876761i
$568$		0			0
$569$		−	379067.i		−	1.17082i	−0.810736	−	0.585412i	$-0.800933\pi$
$569$		−	379067.i		−	1.17082i	0.810736	−	0.585412i	$-0.199067\pi$
$570$		0			0
$571$	−231722.			−0.710714			−0.355357	−	0.934731i	$-0.615641\pi$
$571$	−231722.			−0.710714			−0.355357	+	0.934731i	$0.615641\pi$
$572$		0			0
$573$	154049.	+	47329.3i	0.469192	+	0.144152i
$574$		0			0
$575$	182727.	−	183371.i	0.552672	−	0.554621i
$576$		0			0
$577$			266901.i			0.801675i	0.916149	+	0.400837i	$0.131281\pi$
$577$			266901.i			0.801675i	−0.916149	+	0.400837i	$0.868719\pi$
$578$		0			0
$579$	−227971.	−	70040.7i	−0.680021	−	0.208926i
$580$		0			0
$581$		−	61086.7i		−	0.180965i
$582$		0			0
$583$		−	221835.i		−	0.652669i
$584$		0			0
$585$	−6819.63	+	33201.6i	−0.0199273	+	0.0970167i
$586$		0			0
$587$	−149752.			−0.434605			−0.217303	−	0.976104i	$-0.569726\pi$
$587$	−149752.			−0.434605			−0.217303	+	0.976104i	$0.569726\pi$
$588$		0			0
$589$	−97604.5			−0.281345
$590$		0			0
$591$	44983.4	−	146414.i	0.128789	−	0.419186i
$592$		0			0
$593$	83211.3			0.236632			0.118316	−	0.992976i	$-0.462250\pi$
$593$	83211.3			0.236632			0.118316	+	0.992976i	$0.462250\pi$
$594$		0			0
$595$	32808.5	+	79010.0i	0.0926728	+	0.223176i
$596$		0			0
$597$	101505.	−	330382.i	0.284799	−	0.926976i
$598$		0			0
$599$		−	223787.i		−	0.623709i	−0.950130	−	0.311854i	$-0.899050\pi$
$599$		−	223787.i		−	0.623709i	0.950130	−	0.311854i	$-0.100950\pi$
$600$		0			0
$601$	523744.			1.45001			0.725004	−	0.688745i	$-0.241838\pi$
$601$	523744.			1.45001			0.725004	+	0.688745i	$0.241838\pi$
$602$		0			0
$603$	367221.	−	541210.i	1.00993	−	1.48844i
$604$		0			0
$605$	−385309.	+	159998.i	−1.05268	+	0.437122i
$606$		0			0
$607$		−	52257.0i		−	0.141830i	−0.997482	−	0.0709148i	$-0.977408\pi$
$607$		−	52257.0i		−	0.141830i	0.997482	−	0.0709148i	$-0.0225918\pi$
$608$		0			0
$609$	−33997.0	+	110655.i	−0.0916656	+	0.298357i
$610$		0			0
$611$		−	52949.2i		−	0.141833i
$612$		0			0
$613$			563838.i			1.50049i	0.661159	+	0.750246i	$0.270065\pi$
$613$			563838.i			1.50049i	−0.661159	+	0.750246i	$0.729935\pi$
$614$		0			0
$615$	513713.	−	49208.2i	1.35822	−	0.130103i
$616$		0			0
$617$	45450.6			0.119390			0.0596952	−	0.998217i	$-0.480987\pi$
$617$	45450.6			0.119390			0.0596952	+	0.998217i	$0.480987\pi$
$618$		0			0
$619$	371405.			0.969318			0.484659	−	0.874703i	$-0.338944\pi$
$619$	371405.			0.969318			0.484659	+	0.874703i	$0.338944\pi$
$620$		0			0
$621$	−235439.	+	189052.i	−0.610514	+	0.490228i
$622$		0			0
$623$	−81975.6			−0.211207
$624$		0			0
$625$	−1375.00	−	390623.i	−0.00352000	−	0.999994i
$626$		0			0
$627$	594125.	+	182536.i	1.51127	+	0.464316i
$628$		0			0
$629$			665726.i			1.68265i
$630$		0			0
$631$	−146982.			−0.369152			−0.184576	−	0.982818i	$-0.559091\pi$
$631$	−146982.			−0.369152			−0.184576	+	0.982818i	$0.559091\pi$
$632$		0			0
$633$	−132730.	+	432015.i	−0.331255	+	1.07818i
$634$		0			0
$635$	−153412.	−	369449.i	−0.380462	−	0.916236i
$636$		0			0
$637$		−	37925.5i		−	0.0934658i
$638$		0			0
$639$	−199903.	+	294618.i	−0.489574	+	0.721534i
$640$		0			0
$641$			270894.i			0.659301i	0.944103	+	0.329651i	$0.106931\pi$
$641$			270894.i			0.659301i	−0.944103	+	0.329651i	$0.893069\pi$
$642$		0			0
$643$		−	269824.i		−	0.652617i	−0.945263	−	0.326308i	$-0.894195\pi$
$643$		−	269824.i		−	0.652617i	0.945263	−	0.326308i	$-0.105805\pi$
$644$		0			0
$645$	−221954.	+	21260.8i	−0.533511	+	0.0511046i
$646$		0			0
$647$	72190.9			0.172454			0.0862271	−	0.996276i	$-0.472519\pi$
$647$	72190.9			0.172454			0.0862271	+	0.996276i	$0.472519\pi$
$648$		0			0
$649$	−793674.			−1.88431
$650$		0			0
$651$	25023.1	+	7687.98i	0.0590445	+	0.0181406i
$652$		0			0
$653$	−58611.2			−0.137453			−0.0687265	−	0.997636i	$-0.521894\pi$
$653$	−58611.2			−0.137453			−0.0687265	+	0.997636i	$0.521894\pi$
$654$		0			0
$655$	−12443.1	−	29965.8i	−0.0290033	−	0.0698462i
$656$		0			0
$657$	−254386.	+	374915.i	−0.589336	+	0.868563i
$658$		0			0
$659$			247655.i			0.570264i	0.958488	+	0.285132i	$0.0920374\pi$
$659$			247655.i			0.570264i	−0.958488	+	0.285132i	$0.907963\pi$
$660$		0			0
$661$	630440.			1.44292			0.721458	−	0.692458i	$-0.243472\pi$
$661$	630440.			1.44292			0.721458	+	0.692458i	$0.243472\pi$
$662$		0			0
$663$	−42382.4	−	13021.3i	−0.0964180	−	0.0296230i
$664$		0			0
$665$	−43492.1	−	104738.i	−0.0983482	−	0.236844i
$666$		0			0
$667$			458201.i			1.02992i
$668$		0			0
$669$	430131.	+	132151.i	0.961057	+	0.295270i
$670$		0			0
$671$			785732.i			1.74514i
$672$		0			0
$673$		−	233258.i		−	0.515000i	−0.966278	−	0.257500i	$-0.917101\pi$
$673$		−	233258.i		−	0.515000i	0.966278	−	0.257500i	$-0.0828987\pi$
$674$		0			0
$675$	−48697.6	+	453015.i	−0.106881	+	0.994272i
$676$		0			0
$677$	−139465.			−0.304289			−0.152145	−	0.988358i	$-0.548618\pi$
$677$	−139465.			−0.304289			−0.152145	+	0.988358i	$0.548618\pi$
$678$		0			0
$679$	−85621.5			−0.185713
$680$		0			0
$681$	109960.	−	357901.i	0.237104	−	0.771735i
$682$		0			0
$683$	−667760.			−1.43146			−0.715730	−	0.698377i	$-0.753906\pi$
$683$	−667760.			−1.43146			−0.715730	+	0.698377i	$0.753906\pi$
$684$		0			0
$685$	425463.	−	176671.i	0.906735	−	0.376517i
$686$		0			0
$687$	−111485.	+	362864.i	−0.236212	+	0.768831i
$688$		0			0
$689$		−	20977.9i		−	0.0441899i
$690$		0			0
$691$	−146022.			−0.305816			−0.152908	−	0.988240i	$-0.548864\pi$
$691$	−146022.			−0.305816			−0.152908	+	0.988240i	$0.548864\pi$
$692$		0			0
$693$	−137940.	−	93594.5i	−0.287225	−	0.194887i
$694$		0			0
$695$	213381.	−	88605.3i	0.441759	−	0.183438i
$696$		0			0
$697$			675063.i			1.38956i
$698$		0			0
$699$	−80158.6	+	260903.i	−0.164057	+	0.533980i
$700$		0			0
$701$		−	336887.i		−	0.685564i	−0.939415	−	0.342782i	$-0.888631\pi$
$701$		−	336887.i		−	0.685564i	0.939415	−	0.342782i	$-0.111369\pi$
$702$		0			0
$703$		−	882510.i		−	1.78570i
$704$		0			0
$705$	−67868.5	−	708519.i	−0.136549	−	1.42552i
$706$		0			0
$707$	3258.60			0.00651918
$708$		0			0
$709$	−363926.			−0.723970			−0.361985	−	0.932184i	$-0.617901\pi$
$709$	−363926.			−0.723970			−0.361985	+	0.932184i	$0.617901\pi$
$710$		0			0
$711$	−38172.7	−	25900.8i	−0.0755116	−	0.0512359i
$712$		0			0
$713$	103616.			0.203821
$714$		0			0
$715$	−68403.6	+	28404.2i	−0.133803	+	0.0555611i
$716$		0			0
$717$	−519766.	−	159690.i	−1.01104	−	0.310628i
$718$		0			0
$719$			214672.i			0.415259i	0.978208	+	0.207629i	$0.0665748\pi$
$719$			214672.i			0.415259i	−0.978208	+	0.207629i	$0.933425\pi$
$720$		0			0
$721$	−47919.7			−0.0921814
$722$		0			0
$723$	21264.6	−	69212.9i	0.0406800	−	0.132407i
$724$		0			0
$725$	489756.	+	488036.i	0.931760	+	0.928486i
$726$		0			0
$727$			929982.i			1.75957i	0.475374	+	0.879784i	$0.342313\pi$
$727$			929982.i			1.75957i	−0.475374	+	0.879784i	$0.657687\pi$
$728$		0			0
$729$	114778.	−	518898.i	0.215976	−	0.976399i
$730$		0			0
$731$		−	291666.i		−	0.545823i
$732$		0			0
$733$			459420.i			0.855070i	0.903999	+	0.427535i	$0.140618\pi$
$733$			459420.i			0.855070i	−0.903999	+	0.427535i	$0.859382\pi$
$734$		0			0
$735$	−48611.7	−	507486.i	−0.0899841	−	0.939397i
$736$		0			0
$737$	1.42919e6			2.63121
$738$		0			0
$739$	422731.			0.774061			0.387030	−	0.922067i	$-0.373501\pi$
$739$	422731.			0.774061			0.387030	+	0.922067i	$0.373501\pi$
$740$		0			0
$741$	56183.5	+	17261.5i	0.102323	+	0.0314372i
$742$		0			0
$743$	777990.			1.40928			0.704639	−	0.709566i	$-0.251109\pi$
$743$	777990.			1.40928			0.704639	+	0.709566i	$0.251109\pi$
$744$		0			0
$745$	−351911.	−	847478.i	−0.634045	−	1.52692i
$746$		0			0
$747$	352156.	+	238944.i	0.631095	+	0.428209i
$748$		0			0
$749$		−	218793.i		−	0.390005i
$750$		0			0
$751$	35629.1			0.0631720			0.0315860	−	0.999501i	$-0.489944\pi$
$751$	35629.1			0.0631720			0.0315860	+	0.999501i	$0.489944\pi$
$752$		0			0
$753$	−420785.	−	129280.i	−0.742113	−	0.228003i
$754$		0			0
$755$	−674735.	+	280180.i	−1.18369	+	0.491523i
$756$		0			0
$757$		−	654607.i		−	1.14232i	−0.820838	−	0.571161i	$-0.806493\pi$
$757$		−	654607.i		−	1.14232i	0.820838	−	0.571161i	$-0.193507\pi$
$758$		0			0
$759$	−630718.	−	193779.i	−1.09484	−	0.336374i
$760$		0			0
$761$		−	302702.i		−	0.522693i	−0.965245	−	0.261346i	$-0.915834\pi$
$761$		−	302702.i		−	0.522693i	0.965245	−	0.261346i	$-0.0841665\pi$
$762$		0			0
$763$		−	36002.0i		−	0.0618411i
$764$		0			0
$765$	−583814.	−	119916.i	−0.997588	−	0.204906i
$766$		0			0
$767$	−75053.9			−0.127580
$768$		0			0
$769$	538991.			0.911442			0.455721	−	0.890123i	$-0.349382\pi$
$769$	538991.			0.911442			0.455721	+	0.890123i	$0.349382\pi$
$770$		0			0
$771$	−135562.	+	441232.i	−0.228050	+	0.742264i
$772$		0			0
$773$	1.15999e6			1.94131			0.970655	−	0.240476i	$-0.0773035\pi$
$773$	1.15999e6			1.94131			0.970655	+	0.240476i	$0.0773035\pi$
$774$		0			0
$775$	110363.	−	110752.i	0.183747	−	0.184395i
$776$		0			0
$777$	−69512.4	+	226251.i	−0.115138	+	0.374757i
$778$		0			0
$779$		−	894887.i		−	1.47466i
$780$		0			0
$781$	−778006.			−1.27550
$782$		0			0
$783$	−504928.	−	628821.i	−0.823580	−	1.02566i
$784$		0			0
$785$	−268538.	−	646698.i	−0.435779	−	1.04945i
$786$		0			0
$787$			575186.i			0.928664i	0.885661	+	0.464332i	$0.153706\pi$
$787$			575186.i			0.928664i	−0.885661	+	0.464332i	$0.846294\pi$
$788$		0			0
$789$	272101.	−	885644.i	0.437095	−	1.42267i
$790$		0			0
$791$		−	100508.i		−	0.160638i
$792$		0			0
$793$			74302.9i			0.118157i
$794$		0			0
$795$	−26888.7	−	280707.i	−0.0425438	−	0.444140i
$796$		0			0
$797$	534494.			0.841446			0.420723	−	0.907189i	$-0.361776\pi$
$797$	534494.			0.841446			0.420723	+	0.907189i	$0.361776\pi$
$798$		0			0
$799$	931054.			1.45842
$800$		0			0
$801$	320653.	−	472578.i	0.499770	−	0.736561i
$802$		0			0
$803$	−990049.			−1.53541
$804$		0			0
$805$	46170.8	+	111189.i	0.0712485	+	0.171582i
$806$		0			0
$807$	−240021.	−	73743.0i	−0.368555	−	0.113233i
$808$		0			0
$809$			399046.i			0.609713i	0.952398	+	0.304857i	$0.0986085\pi$
$809$			399046.i			0.609713i	−0.952398	+	0.304857i	$0.901391\pi$
$810$		0			0
$811$	−613273.			−0.932421			−0.466211	−	0.884674i	$-0.654381\pi$
$811$	−613273.			−0.932421			−0.466211	+	0.884674i	$0.654381\pi$
$812$		0			0
$813$	−240965.	+	784300.i	−0.364563	+	1.18659i
$814$		0			0
$815$	380482.	+	916283.i	0.572820	+	1.37948i
$816$		0			0
$817$			386643.i			0.579250i
$818$		0			0
$819$	−13044.3	−	8850.78i	−0.0194470	−	0.0131951i
$820$		0			0
$821$		−	425411.i		−	0.631135i	−0.948903	−	0.315568i	$-0.897805\pi$
$821$		−	425411.i		−	0.631135i	0.948903	−	0.315568i	$-0.102195\pi$
$822$		0			0
$823$		−	286394.i		−	0.422829i	−0.977397	−	0.211414i	$-0.932193\pi$
$823$		−	286394.i		−	0.422829i	0.977397	−	0.211414i	$-0.0678069\pi$
$824$		0			0
$825$	−878909.	+	467758.i	−1.29133	+	0.687248i
$826$		0			0
$827$	−167100.			−0.244324			−0.122162	−	0.992510i	$-0.538983\pi$
$827$	−167100.			−0.244324			−0.122162	+	0.992510i	$0.538983\pi$
$828$		0			0
$829$	−872623.			−1.26975			−0.634874	−	0.772616i	$-0.718948\pi$
$829$	−872623.			−1.26975			−0.634874	+	0.772616i	$0.718948\pi$
$830$		0			0
$831$	714148.	+	219411.i	1.03416	+	0.317729i
$832$		0			0
$833$	666879.			0.961075
$834$		0			0
$835$	−609227.	+	252978.i	−0.873788	+	0.362836i
$836$		0			0
$837$	−142200.	+	114183.i	−0.202977	+	0.162986i
$838$		0			0
$839$			428726.i			0.609053i	0.952504	+	0.304527i	$0.0984983\pi$
$839$			428726.i			0.609053i	−0.952504	+	0.304527i	$0.901502\pi$
$840$		0			0
$841$	−516502.			−0.730264
$842$		0			0
$843$	318825.	+	97954.2i	0.448639	+	0.137838i
$844$		0			0
$845$	652964.	−	271140.i	0.914483	−	0.379734i
$846$		0			0
$847$		−	194033.i		−	0.270463i
$848$		0			0
$849$	348817.	+	107169.i	0.483929	+	0.148680i
$850$		0			0
$851$			936865.i			1.29365i
$852$		0			0
$853$		−	199001.i		−	0.273500i	−0.990606	−	0.136750i	$-0.956334\pi$
$853$		−	199001.i		−	0.273500i	0.990606	−	0.136750i	$-0.0436657\pi$
$854$		0			0
$855$	773923.	+	158965.i	1.05868	+	0.217454i
$856$		0			0
$857$	−1.10063e6			−1.49858			−0.749288	−	0.662244i	$-0.769604\pi$
$857$	−1.10063e6			−1.49858			−0.749288	+	0.662244i	$0.769604\pi$
$858$		0			0
$859$	900672.			1.22062			0.610310	−	0.792163i	$-0.291045\pi$
$859$	900672.			1.22062			0.610310	+	0.792163i	$0.291045\pi$
$860$		0			0
$861$	−70487.3	+	229424.i	−0.0950833	+	0.309481i
$862$		0			0
$863$	−330953.			−0.444370			−0.222185	−	0.975004i	$-0.571319\pi$
$863$	−330953.			−0.444370			−0.222185	+	0.975004i	$0.571319\pi$
$864$		0			0
$865$	1.28425e6	−	533279.i	1.71640	−	0.712725i
$866$		0			0
$867$	8205.45	−	26707.4i	0.0109160	−	0.0355298i
$868$		0			0
$869$		−	100804.i		−	0.133487i
$870$		0			0
$871$	135152.			0.178150
$872$		0			0
$873$	334914.	−	493596.i	0.439445	−	0.647654i
$874$		0			0
$875$	168024.	+	69078.6i	0.219460	+	0.0902251i
$876$		0			0
$877$		−	635350.i		−	0.826065i	−0.910716	−	0.413032i	$-0.864470\pi$
$877$		−	635350.i		−	0.826065i	0.910716	−	0.413032i	$-0.135530\pi$
$878$		0			0
$879$	−429807.	+	1.39895e6i	−0.556282	+	1.81061i
$880$		0			0
$881$			1.39000e6i			1.79087i	0.445194	+	0.895434i	$0.353135\pi$
$881$			1.39000e6i			1.79087i	−0.445194	+	0.895434i	$0.646865\pi$
$882$		0			0
$883$			87356.3i			0.112040i	0.998430	+	0.0560200i	$0.0178410\pi$
$883$			87356.3i			0.112040i	−0.998430	+	0.0560200i	$0.982159\pi$
$884$		0			0
$885$	−1.00431e6	+	96201.6i	−1.28227	+	0.122828i
$886$		0			0
$887$	450532.			0.572636			0.286318	−	0.958135i	$-0.407569\pi$
$887$	450532.			0.572636			0.286318	+	0.958135i	$0.407569\pi$
$888$		0			0
$889$	186046.			0.235406
$890$		0			0
$891$	1.07912e6	−	429102.i	1.35929	−	0.540512i
$892$		0			0
$893$	−1.23424e6			−1.54773
$894$		0			0
$895$	240123.	+	578269.i	0.299770	+	0.721911i
$896$		0			0
$897$	−59643.9	−	18324.7i	−0.0741278	−	0.0227747i
$898$		0			0
$899$			276742.i			0.342418i
$900$		0			0
$901$	368873.			0.454389
$902$		0			0
$903$	30454.6	−	99124.7i	0.0373489	−	0.121564i
$904$		0			0
$905$	−731407.	+	303713.i	−0.893022	+	0.370823i
$906$		0			0
$907$		−	1.38725e6i		−	1.68632i	−0.537665	−	0.843158i	$-0.680694\pi$
$907$		−	1.38725e6i		−	1.68632i	0.537665	−	0.843158i	$-0.319306\pi$
$908$		0			0
$909$	−12746.2	+	18785.4i	−0.0154260	+	0.0227349i
$910$		0			0
$911$		−	482647.i		−	0.581558i	−0.956790	−	0.290779i	$-0.906086\pi$
$911$		−	482647.i		−	0.581558i	0.956790	−	0.290779i	$-0.0939144\pi$
$912$		0			0
$913$			929951.i			1.11563i
$914$		0			0
$915$	95239.0	+	994256.i	0.113756	+	1.18756i
$916$		0			0
$917$	15090.1			0.0179454
$918$		0			0
$919$	−1.22708e6			−1.45292			−0.726461	−	0.687207i	$-0.758836\pi$
$919$	−1.22708e6			−1.45292			−0.726461	+	0.687207i	$0.758836\pi$
$920$		0			0
$921$	433296.	+	133124.i	0.510817	+	0.156941i
$922$		0			0
$923$	−73572.3			−0.0863597
$924$		0			0
$925$	1.00139e6	+	997866.i	1.17036	+	1.16624i
$926$		0			0
$927$	187441.	−	276250.i	0.218124	−	0.321472i
$928$		0			0
$929$		−	24692.2i		−	0.0286107i	−0.999898	−	0.0143053i	$-0.995446\pi$
$929$		−	24692.2i		−	0.0286107i	0.999898	−	0.0143053i	$-0.00455368\pi$
$930$		0			0
$931$	−884038.			−1.01993
$932$		0			0
$933$	253288.	+	77818.9i	0.290972	+	0.0893968i
$934$		0			0
$935$	−499458.	−	1.20280e6i	−0.571315	−	1.37585i
$936$		0			0
$937$			955822.i			1.08867i	0.838867	+	0.544337i	$0.183219\pi$
$937$			955822.i			1.08867i	−0.838867	+	0.544337i	$0.816781\pi$
$938$		0			0
$939$	−932115.	−	286379.i	−1.05715	−	0.324795i
$940$		0			0
$941$		−	286579.i		−	0.323642i	−0.986820	−	0.161821i	$-0.948263\pi$
$941$		−	286579.i		−	0.323642i	0.986820	−	0.161821i	$-0.0517367\pi$
$942$		0			0
$943$			950004.i			1.06832i
$944$		0			0
$945$	−185892.	−	101714.i	−0.208160	−	0.113898i
$946$		0			0
$947$	−1.28493e6			−1.43278			−0.716388	−	0.697702i	$-0.754206\pi$
$947$	−1.28493e6			−1.43278			−0.716388	+	0.697702i	$0.754206\pi$
$948$		0			0
$949$	−93624.1			−0.103957
$950$		0			0
$951$	180098.	−	586190.i	0.199135	−	0.648153i
$952$		0			0
$953$	130389.			0.143567			0.0717836	−	0.997420i	$-0.477131\pi$
$953$	130389.			0.143567			0.0717836	+	0.997420i	$0.477131\pi$
$954$		0			0
$955$	171674.	+	413429.i	0.188234	+	0.453309i
$956$		0			0
$957$	517552.	−	1.68455e6i	0.565106	−	1.83933i
$958$		0			0
$959$			214253.i			0.232964i
$960$		0			0
$961$	−860939.			−0.932236
$962$		0			0
$963$	1.26131e6	+	855822.i	1.36010	+	0.922849i
$964$		0			0
$965$	−254053.	−	611816.i	−0.272816	−	0.657001i
$966$		0			0
$967$		−	1.28463e6i		−	1.37381i	−0.726749	−	0.686904i	$-0.758969\pi$
$967$		−	1.28463e6i		−	1.37381i	0.726749	−	0.686904i	$-0.241031\pi$
$968$		0			0
$969$	−303526.	+	987927.i	−0.323257	+	1.05215i
$970$		0			0
$971$		−	1.31697e6i		−	1.39681i	−0.715705	−	0.698403i	$-0.753894\pi$
$971$		−	1.31697e6i		−	1.39681i	0.715705	−	0.698403i	$-0.246106\pi$
$972$		0			0
$973$			107454.i			0.113500i
$974$		0			0
$975$	−83114.2	+	44233.6i	−0.0874311	+	0.0465311i
$976$		0			0
$977$	−346834.			−0.363357			−0.181678	−	0.983358i	$-0.558153\pi$
$977$	−346834.			−0.363357			−0.181678	+	0.983358i	$0.558153\pi$
$978$		0			0
$979$	1.24795e6			1.30206
$980$		0			0
$981$	207546.	+	140824.i	0.215664	+	0.146332i
$982$		0			0
$983$	310815.			0.321658			0.160829	−	0.986982i	$-0.448583\pi$
$983$	310815.			0.321658			0.160829	+	0.986982i	$0.448583\pi$
$984$		0			0
$985$	392937.	−	163165.i	0.404996	−	0.168172i
$986$		0			0
$987$	316425.	+	97216.8i	0.324815	+	0.0997946i
$988$		0			0
$989$		−	410457.i		−	0.419638i
$990$		0			0
$991$	162102.			0.165059			0.0825296	−	0.996589i	$-0.473700\pi$
$991$	162102.			0.165059			0.0825296	+	0.996589i	$0.473700\pi$
$992$		0			0
$993$	−84099.2	+	273729.i	−0.0852890	+	0.277602i
$994$		0			0
$995$	886662.	−	368182.i	0.895595	−	0.371891i
$996$		0			0
$997$		−	1.80197e6i		−	1.81283i	−0.422388	−	0.906415i	$-0.638808\pi$
$997$		−	1.80197e6i		−	1.81283i	0.422388	−	0.906415i	$-0.361192\pi$
$998$		0			0
$999$	−1.03241e6	−	1.28572e6i	−1.03447	−	1.28830i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.5.b.a.29.5	yes	8
3.2	odd	2	inner	60.5.b.a.29.3	✓	8
4.3	odd	2		240.5.c.e.209.4		8
5.2	odd	4		300.5.g.h.101.1		8
5.3	odd	4		300.5.g.h.101.8		8
5.4	even	2	inner	60.5.b.a.29.4	yes	8
12.11	even	2		240.5.c.e.209.6		8
15.2	even	4		300.5.g.h.101.2		8
15.8	even	4		300.5.g.h.101.7		8
15.14	odd	2	inner	60.5.b.a.29.6	yes	8
20.19	odd	2		240.5.c.e.209.5		8
60.59	even	2		240.5.c.e.209.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.5.b.a.29.3	✓	8	3.2	odd	2	inner
60.5.b.a.29.4	yes	8	5.4	even	2	inner
60.5.b.a.29.5	yes	8	1.1	even	1	trivial
60.5.b.a.29.6	yes	8	15.14	odd	2	inner
240.5.c.e.209.3		8	60.59	even	2
240.5.c.e.209.4		8	4.3	odd	2
240.5.c.e.209.5		8	20.19	odd	2
240.5.c.e.209.6		8	12.11	even	2
300.5.g.h.101.1		8	5.2	odd	4
300.5.g.h.101.2		8	15.2	even	4
300.5.g.h.101.7		8	15.8	even	4
300.5.g.h.101.8		8	5.3	odd	4

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:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	60.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(2.64318 - 8.60312i) q^{3} +(23.0886 - 9.58741i) q^{5} +11.6269i q^{7} +(-67.0272 - 45.4792i) q^{9} +O(q^{10})\)	\(q+(2.64318 - 8.60312i) q^{3} +(23.0886 - 9.58741i) q^{5} +11.6269i q^{7} +(-67.0272 - 45.4792i) q^{9} -177.001i q^{11} -16.7381i q^{13} +(-21.4544 - 223.975i) q^{15} +294.322 q^{17} -390.163 q^{19} +(100.027 + 30.7319i) q^{21} +414.194 q^{23} +(441.163 - 442.719i) q^{25} +(-568.427 + 456.433i) q^{27} +1106.25i q^{29} +250.163 q^{31} +(-1522.76 - 467.845i) q^{33} +(111.471 + 268.447i) q^{35} +2261.90i q^{37} +(-144.000 - 44.2419i) q^{39} +2293.62i q^{41} -990.978i q^{43} +(-1983.59 - 407.431i) q^{45} +3163.39 q^{47} +2265.82 q^{49} +(777.946 - 2532.09i) q^{51} +1253.30 q^{53} +(-1696.98 - 4086.70i) q^{55} +(-1031.27 + 3356.62i) q^{57} -4484.01i q^{59} -4439.14 q^{61} +(528.780 - 779.316i) q^{63} +(-160.475 - 386.459i) q^{65} +8074.48i q^{67} +(1094.79 - 3563.36i) q^{69} -4395.49i q^{71} -5593.47i q^{73} +(-2642.69 - 4965.56i) q^{75} +2057.96 q^{77} +569.510 q^{79} +(2424.29 + 6096.68i) q^{81} -5253.93 q^{83} +(6795.47 - 2821.78i) q^{85} +(9517.17 + 2924.01i) q^{87} +7050.54i q^{89} +194.612 q^{91} +(661.226 - 2152.18i) q^{93} +(-9008.31 + 3740.65i) q^{95} +7364.12i q^{97} +(-8049.85 + 11863.9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 52 q^{9}+O(q^{10}) \) 8 * q + 52 * q^9	\( 8 q + 52 q^{9} - 100 q^{15} + 408 q^{19} + 212 q^{21} - 1528 q^{31} - 1152 q^{39} - 2900 q^{45} + 480 q^{49} + 7400 q^{51} + 7600 q^{55} - 10808 q^{61} - 8300 q^{69} - 14000 q^{75} + 15144 q^{79} + 34688 q^{81} + 22600 q^{85} - 54912 q^{91} - 24400 q^{99}+O(q^{100}) \) 8 * q + 52 * q^9 - 100 * q^15 + 408 * q^19 + 212 * q^21 - 1528 * q^31 - 1152 * q^39 - 2900 * q^45 + 480 * q^49 + 7400 * q^51 + 7600 * q^55 - 10808 * q^61 - 8300 * q^69 - 14000 * q^75 + 15144 * q^79 + 34688 * q^81 + 22600 * q^85 - 54912 * q^91 - 24400 * q^99

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