LMFDB - Embedded newform 6027.2.a.y.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6027,2,Mod(1,6027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6027, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("6027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6027 = 3 \cdot 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6027.a (trivial)

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:	yes
Analytic conductor:	$48.1258372982$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 6x^{5} + 16x^{4} + 14x^{3} - 20x^{2} - 10x + 4 $ x^7 - 3x^6 - 6x^5 + 16x^4 + 14x^3 - 20x^2 - 10x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 861)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.35311$ of defining polynomial
Character	$\chi$	$=$	6027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.35311 q^{2} -1.00000 q^{3} -0.169102 q^{4} -1.31916 q^{5} +1.35311 q^{6} +2.93503 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.35311 q^{2} -1.00000 q^{3} -0.169102 q^{4} -1.31916 q^{5} +1.35311 q^{6} +2.93503 q^{8} +1.00000 q^{9} +1.78497 q^{10} -4.13524 q^{11} +0.169102 q^{12} +1.21233 q^{13} +1.31916 q^{15} -3.63320 q^{16} -7.63049 q^{17} -1.35311 q^{18} -6.01351 q^{19} +0.223073 q^{20} +5.59543 q^{22} +3.53357 q^{23} -2.93503 q^{24} -3.25981 q^{25} -1.64041 q^{26} -1.00000 q^{27} -3.42745 q^{29} -1.78497 q^{30} +1.20879 q^{31} -0.953947 q^{32} +4.13524 q^{33} +10.3249 q^{34} -0.169102 q^{36} +1.76018 q^{37} +8.13692 q^{38} -1.21233 q^{39} -3.87178 q^{40} -1.00000 q^{41} -7.13254 q^{43} +0.699279 q^{44} -1.31916 q^{45} -4.78130 q^{46} -12.3718 q^{47} +3.63320 q^{48} +4.41087 q^{50} +7.63049 q^{51} -0.205007 q^{52} +9.78151 q^{53} +1.35311 q^{54} +5.45506 q^{55} +6.01351 q^{57} +4.63770 q^{58} -12.0106 q^{59} -0.223073 q^{60} +9.75390 q^{61} -1.63562 q^{62} +8.55719 q^{64} -1.59926 q^{65} -5.59543 q^{66} +3.28779 q^{67} +1.29033 q^{68} -3.53357 q^{69} -5.17222 q^{71} +2.93503 q^{72} -11.1296 q^{73} -2.38172 q^{74} +3.25981 q^{75} +1.01690 q^{76} +1.64041 q^{78} -4.53670 q^{79} +4.79278 q^{80} +1.00000 q^{81} +1.35311 q^{82} -16.9034 q^{83} +10.0659 q^{85} +9.65109 q^{86} +3.42745 q^{87} -12.1371 q^{88} +10.3639 q^{89} +1.78497 q^{90} -0.597535 q^{92} -1.20879 q^{93} +16.7404 q^{94} +7.93279 q^{95} +0.953947 q^{96} +6.82267 q^{97} -4.13524 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 4 q^{2} - 7 q^{3} + 8 q^{4} - q^{5} - 4 q^{6} + 12 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q + 4 * q^2 - 7 * q^3 + 8 * q^4 - q^5 - 4 * q^6 + 12 * q^8 + 7 * q^9	$ 7 q + 4 q^{2} - 7 q^{3} + 8 q^{4} - q^{5} - 4 q^{6} + 12 q^{8} + 7 q^{9} + 3 q^{10} + 11 q^{11} - 8 q^{12} + 7 q^{13} + q^{15} + 6 q^{16} - 11 q^{17} + 4 q^{18} - 4 q^{19} + 7 q^{20} + 6 q^{22} + 7 q^{23} - 12 q^{24} + 2 q^{25} + 13 q^{26} - 7 q^{27} + 4 q^{29} - 3 q^{30} + 7 q^{31} + 18 q^{32} - 11 q^{33} + 20 q^{34} + 8 q^{36} - 4 q^{38} - 7 q^{39} + 9 q^{40} - 7 q^{41} + q^{43} + 18 q^{44} - q^{45} - 17 q^{46} - 14 q^{47} - 6 q^{48} + 19 q^{50} + 11 q^{51} + 27 q^{52} + 23 q^{53} - 4 q^{54} + 30 q^{55} + 4 q^{57} - 3 q^{58} - 8 q^{59} - 7 q^{60} + 3 q^{61} + 16 q^{62} + 6 q^{64} + 15 q^{65} - 6 q^{66} + 3 q^{67} - 7 q^{69} + 7 q^{71} + 12 q^{72} + 11 q^{73} - 13 q^{74} - 2 q^{75} + 40 q^{76} - 13 q^{78} - q^{79} + 43 q^{80} + 7 q^{81} - 4 q^{82} - 10 q^{85} - 12 q^{86} - 4 q^{87} + 10 q^{88} - 32 q^{89} + 3 q^{90} - 19 q^{92} - 7 q^{93} - 21 q^{94} - 8 q^{95} - 18 q^{96} + 25 q^{97} + 11 q^{99}+O(q^{100}) $ 7 * q + 4 * q^2 - 7 * q^3 + 8 * q^4 - q^5 - 4 * q^6 + 12 * q^8 + 7 * q^9 + 3 * q^10 + 11 * q^11 - 8 * q^12 + 7 * q^13 + q^15 + 6 * q^16 - 11 * q^17 + 4 * q^18 - 4 * q^19 + 7 * q^20 + 6 * q^22 + 7 * q^23 - 12 * q^24 + 2 * q^25 + 13 * q^26 - 7 * q^27 + 4 * q^29 - 3 * q^30 + 7 * q^31 + 18 * q^32 - 11 * q^33 + 20 * q^34 + 8 * q^36 - 4 * q^38 - 7 * q^39 + 9 * q^40 - 7 * q^41 + q^43 + 18 * q^44 - q^45 - 17 * q^46 - 14 * q^47 - 6 * q^48 + 19 * q^50 + 11 * q^51 + 27 * q^52 + 23 * q^53 - 4 * q^54 + 30 * q^55 + 4 * q^57 - 3 * q^58 - 8 * q^59 - 7 * q^60 + 3 * q^61 + 16 * q^62 + 6 * q^64 + 15 * q^65 - 6 * q^66 + 3 * q^67 - 7 * q^69 + 7 * q^71 + 12 * q^72 + 11 * q^73 - 13 * q^74 - 2 * q^75 + 40 * q^76 - 13 * q^78 - q^79 + 43 * q^80 + 7 * q^81 - 4 * q^82 - 10 * q^85 - 12 * q^86 - 4 * q^87 + 10 * q^88 - 32 * q^89 + 3 * q^90 - 19 * q^92 - 7 * q^93 - 21 * q^94 - 8 * q^95 - 18 * q^96 + 25 * q^97 + 11 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−1.35311	−0.956791	−0.478395	−	0.878145i	$-0.658781\pi$
$2$	−1.35311	−0.956791	−0.478395	+	0.878145i	$0.658781\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.169102	−0.0845512
$5$	−1.31916	−0.589947	−0.294974	−	0.955505i	$-0.595311\pi$
$5$	−1.31916	−0.589947	−0.294974	+	0.955505i	$0.595311\pi$
$6$	1.35311	0.552403
$7$	0	0
$7$	0	0
$8$	2.93503	1.03769
$9$	1.00000	0.333333
$10$	1.78497	0.564456
$11$	−4.13524	−1.24682	−0.623412	−	0.781894i	$-0.714254\pi$
$11$	−4.13524	−1.24682	−0.623412	+	0.781894i	$0.714254\pi$
$12$	0.169102	0.0488156
$13$	1.21233	0.336239	0.168119	−	0.985767i	$-0.446231\pi$
$13$	1.21233	0.336239	0.168119	+	0.985767i	$0.446231\pi$
$14$	0	0
$15$	1.31916	0.340606
$16$	−3.63320	−0.908300
$17$	−7.63049	−1.85067	−0.925333	−	0.379155i	$-0.876215\pi$
$17$	−7.63049	−1.85067	−0.925333	+	0.379155i	$0.876215\pi$
$18$	−1.35311	−0.318930
$19$	−6.01351	−1.37959	−0.689797	−	0.724003i	$-0.742300\pi$
$19$	−6.01351	−1.37959	−0.689797	+	0.724003i	$0.742300\pi$
$20$	0.223073	0.0498807
$21$	0	0
$22$	5.59543	1.19295
$23$	3.53357	0.736801	0.368400	−	0.929667i	$-0.379906\pi$
$23$	3.53357	0.736801	0.368400	+	0.929667i	$0.379906\pi$
$24$	−2.93503	−0.599110
$25$	−3.25981	−0.651962
$26$	−1.64041	−0.321710
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−3.42745	−0.636461	−0.318230	−	0.948013i	$-0.603089\pi$
$29$	−3.42745	−0.636461	−0.318230	+	0.948013i	$0.603089\pi$
$30$	−1.78497	−0.325889
$31$	1.20879	0.217105	0.108552	−	0.994091i	$-0.465379\pi$
$31$	1.20879	0.217105	0.108552	+	0.994091i	$0.465379\pi$
$32$	−0.953947	−0.168636
$33$	4.13524	0.719854
$34$	10.3249	1.77070
$35$	0	0
$36$	−0.169102	−0.0281837
$37$	1.76018	0.289373	0.144686	−	0.989478i	$-0.453783\pi$
$37$	1.76018	0.289373	0.144686	+	0.989478i	$0.453783\pi$
$38$	8.13692	1.31998
$39$	−1.21233	−0.194128
$40$	−3.87178	−0.612182
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	−7.13254	−1.08770	−0.543851	−	0.839182i	$-0.683034\pi$
$43$	−7.13254	−1.08770	−0.543851	+	0.839182i	$0.683034\pi$
$44$	0.699279	0.105420
$45$	−1.31916	−0.196649
$46$	−4.78130	−0.704964
$47$	−12.3718	−1.80462	−0.902308	−	0.431092i	$-0.858129\pi$
$47$	−12.3718	−1.80462	−0.902308	+	0.431092i	$0.858129\pi$
$48$	3.63320	0.524407
$49$	0	0
$50$	4.41087	0.623792
$51$	7.63049	1.06848
$52$	−0.205007	−0.0284294
$53$	9.78151	1.34359	0.671797	−	0.740735i	$-0.265523\pi$
$53$	9.78151	1.34359	0.671797	+	0.740735i	$0.265523\pi$
$54$	1.35311	0.184134
$55$	5.45506	0.735560
$56$	0	0
$57$	6.01351	0.796508
$58$	4.63770	0.608960
$59$	−12.0106	−1.56364	−0.781821	−	0.623503i	$-0.785709\pi$
$59$	−12.0106	−1.56364	−0.781821	+	0.623503i	$0.785709\pi$
$60$	−0.223073	−0.0287986
$61$	9.75390	1.24886	0.624430	−	0.781081i	$-0.285331\pi$
$61$	9.75390	1.24886	0.624430	+	0.781081i	$0.285331\pi$
$62$	−1.63562	−0.207724
$63$	0	0
$64$	8.55719	1.06965
$65$	−1.59926	−0.198363
$66$	−5.59543	−0.688749
$67$	3.28779	0.401667	0.200834	−	0.979625i	$-0.435635\pi$
$67$	3.28779	0.401667	0.200834	+	0.979625i	$0.435635\pi$
$68$	1.29033	0.156476
$69$	−3.53357	−0.425392
$70$	0	0
$71$	−5.17222	−0.613830	−0.306915	−	0.951737i	$-0.599297\pi$
$71$	−5.17222	−0.613830	−0.306915	+	0.951737i	$0.599297\pi$
$72$	2.93503	0.345896
$73$	−11.1296	−1.30262	−0.651310	−	0.758812i	$-0.725780\pi$
$73$	−11.1296	−1.30262	−0.651310	+	0.758812i	$0.725780\pi$
$74$	−2.38172	−0.276869
$75$	3.25981	0.376411
$76$	1.01690	0.116646
$77$	0	0
$78$	1.64041	0.185740
$79$	−4.53670	−0.510419	−0.255209	−	0.966886i	$-0.582144\pi$
$79$	−4.53670	−0.510419	−0.255209	+	0.966886i	$0.582144\pi$
$80$	4.79278	0.535849
$81$	1.00000	0.111111
$82$	1.35311	0.149426
$83$	−16.9034	−1.85539	−0.927695	−	0.373340i	$-0.878213\pi$
$83$	−16.9034	−1.85539	−0.927695	+	0.373340i	$0.878213\pi$
$84$	0	0
$85$	10.0659	1.09180
$86$	9.65109	1.04070
$87$	3.42745	0.367461
$88$	−12.1371	−1.29381
$89$	10.3639	1.09857	0.549284	−	0.835636i	$-0.314900\pi$
$89$	10.3639	1.09857	0.549284	+	0.835636i	$0.314900\pi$
$90$	1.78497	0.188152
$91$	0	0
$92$	−0.597535	−0.0622973
$93$	−1.20879	−0.125345
$94$	16.7404	1.72664
$95$	7.93279	0.813887
$96$	0.953947	0.0973618
$97$	6.82267	0.692738	0.346369	−	0.938098i	$-0.387415\pi$
$97$	6.82267	0.692738	0.346369	+	0.938098i	$0.387415\pi$
$98$	0	0
$99$	−4.13524	−0.415608
$100$	0.551242	0.0551242
$101$	−7.85345	−0.781447	−0.390724	−	0.920508i	$-0.627775\pi$
$101$	−7.85345	−0.781447	−0.390724	+	0.920508i	$0.627775\pi$
$102$	−10.3249	−1.02231
$103$	−14.8276	−1.46101	−0.730504	−	0.682909i	$-0.760715\pi$
$103$	−14.8276	−1.46101	−0.730504	+	0.682909i	$0.760715\pi$
$104$	3.55821	0.348911
$105$	0	0
$106$	−13.2354	−1.28554
$107$	15.6391	1.51189	0.755945	−	0.654635i	$-0.227178\pi$
$107$	15.6391	1.51189	0.755945	+	0.654635i	$0.227178\pi$
$108$	0.169102	0.0162719
$109$	2.48326	0.237853	0.118926	−	0.992903i	$-0.462055\pi$
$109$	2.48326	0.237853	0.118926	+	0.992903i	$0.462055\pi$
$110$	−7.38128	−0.703777
$111$	−1.76018	−0.167069
$112$	0	0
$113$	−8.27480	−0.778428	−0.389214	−	0.921147i	$-0.627253\pi$
$113$	−8.27480	−0.778428	−0.389214	+	0.921147i	$0.627253\pi$
$114$	−8.13692	−0.762092
$115$	−4.66135	−0.434673
$116$	0.579589	0.0538135
$117$	1.21233	0.112080
$118$	16.2516	1.49608
$119$	0	0
$120$	3.87178	0.353443
$121$	6.10025	0.554568
$122$	−13.1981	−1.19490
$123$	1.00000	0.0901670
$124$	−0.204409	−0.0183564
$125$	10.8960	0.974571
$126$	0	0
$127$	−15.0645	−1.33676	−0.668379	−	0.743821i	$-0.733012\pi$
$127$	−15.0645	−1.33676	−0.668379	+	0.743821i	$0.733012\pi$
$128$	−9.67090	−0.854795
$129$	7.13254	0.627985
$130$	2.16396	0.189792
$131$	−15.2644	−1.33366	−0.666830	−	0.745210i	$-0.732349\pi$
$131$	−15.2644	−1.33366	−0.666830	+	0.745210i	$0.732349\pi$
$132$	−0.699279	−0.0608645
$133$	0	0
$134$	−4.44873	−0.384312
$135$	1.31916	0.113535
$136$	−22.3957	−1.92042
$137$	−2.70544	−0.231142	−0.115571	−	0.993299i	$-0.536870\pi$
$137$	−2.70544	−0.231142	−0.115571	+	0.993299i	$0.536870\pi$
$138$	4.78130	0.407011
$139$	12.9107	1.09507	0.547535	−	0.836783i	$-0.315566\pi$
$139$	12.9107	1.09507	0.547535	+	0.836783i	$0.315566\pi$
$140$	0	0
$141$	12.3718	1.04190
$142$	6.99857	0.587307
$143$	−5.01327	−0.419230
$144$	−3.63320	−0.302767
$145$	4.52136	0.375478
$146$	15.0595	1.24634
$147$	0	0
$148$	−0.297651	−0.0244668
$149$	−22.4356	−1.83800	−0.918998	−	0.394261i	$-0.871001\pi$
$149$	−22.4356	−1.83800	−0.918998	+	0.394261i	$0.871001\pi$
$150$	−4.41087	−0.360146
$151$	3.55734	0.289492	0.144746	−	0.989469i	$-0.453763\pi$
$151$	3.55734	0.289492	0.144746	+	0.989469i	$0.453763\pi$
$152$	−17.6498	−1.43159
$153$	−7.63049	−0.616889
$154$	0	0
$155$	−1.59459	−0.128080
$156$	0.205007	0.0164137
$157$	7.44432	0.594121	0.297061	−	0.954859i	$-0.403994\pi$
$157$	7.44432	0.594121	0.297061	+	0.954859i	$0.403994\pi$
$158$	6.13864	0.488364
$159$	−9.78151	−0.775725
$160$	1.25841	0.0994861
$161$	0	0
$162$	−1.35311	−0.106310
$163$	−2.97250	−0.232824	−0.116412	−	0.993201i	$-0.537139\pi$
$163$	−2.97250	−0.232824	−0.116412	+	0.993201i	$0.537139\pi$
$164$	0.169102	0.0132047
$165$	−5.45506	−0.424676
$166$	22.8721	1.77522
$167$	18.1220	1.40232	0.701162	−	0.713002i	$-0.252665\pi$
$167$	18.1220	1.40232	0.701162	+	0.713002i	$0.252665\pi$
$168$	0	0
$169$	−11.5303	−0.886943
$170$	−13.6202	−1.04462
$171$	−6.01351	−0.459864
$172$	1.20613	0.0919665
$173$	−21.3159	−1.62062	−0.810308	−	0.586004i	$-0.800700\pi$
$173$	−21.3159	−1.62062	−0.810308	+	0.586004i	$0.800700\pi$
$174$	−4.63770	−0.351583
$175$	0	0
$176$	15.0242	1.13249
$177$	12.0106	0.902769
$178$	−14.0234	−1.05110
$179$	−18.4854	−1.38166	−0.690831	−	0.723016i	$-0.742755\pi$
$179$	−18.4854	−1.38166	−0.690831	+	0.723016i	$0.742755\pi$
$180$	0.223073	0.0166269
$181$	−14.2517	−1.05932	−0.529662	−	0.848209i	$-0.677681\pi$
$181$	−14.2517	−1.05932	−0.529662	+	0.848209i	$0.677681\pi$
$182$	0	0
$183$	−9.75390	−0.721029
$184$	10.3711	0.764570
$185$	−2.32197	−0.170715
$186$	1.63562	0.119929
$187$	31.5540	2.30745
$188$	2.09210	0.152582
$189$	0	0
$190$	−10.7339	−0.778720
$191$	−5.62090	−0.406714	−0.203357	−	0.979105i	$-0.565185\pi$
$191$	−5.62090	−0.406714	−0.203357	+	0.979105i	$0.565185\pi$
$192$	−8.55719	−0.617562
$193$	−24.1490	−1.73828	−0.869141	−	0.494564i	$-0.835328\pi$
$193$	−24.1490	−1.73828	−0.869141	+	0.494564i	$0.835328\pi$
$194$	−9.23181	−0.662805
$195$	1.59926	0.114525
$196$	0	0
$197$	−7.33306	−0.522459	−0.261229	−	0.965277i	$-0.584128\pi$
$197$	−7.33306	−0.522459	−0.261229	+	0.965277i	$0.584128\pi$
$198$	5.59543	0.397650
$199$	18.0592	1.28019	0.640093	−	0.768297i	$-0.278896\pi$
$199$	18.0592	1.28019	0.640093	+	0.768297i	$0.278896\pi$
$200$	−9.56763	−0.676534
$201$	−3.28779	−0.231903
$202$	10.6266	0.747682
$203$	0	0
$204$	−1.29033	−0.0903415
$205$	1.31916	0.0921343
$206$	20.0633	1.39788
$207$	3.53357	0.245600
$208$	−4.40462	−0.305406
$209$	24.8673	1.72011
$210$	0	0
$211$	19.4143	1.33654	0.668268	−	0.743920i	$-0.267036\pi$
$211$	19.4143	1.33654	0.668268	+	0.743920i	$0.267036\pi$
$212$	−1.65408	−0.113602
$213$	5.17222	0.354395
$214$	−21.1614	−1.44656
$215$	9.40897	0.641687
$216$	−2.93503	−0.199703
$217$	0	0
$218$	−3.36011	−0.227576
$219$	11.1296	0.752068
$220$	−0.922463	−0.0621924
$221$	−9.25065	−0.622266
$222$	2.38172	0.159850
$223$	−4.73950	−0.317380	−0.158690	−	0.987328i	$-0.550727\pi$
$223$	−4.73950	−0.317380	−0.158690	+	0.987328i	$0.550727\pi$
$224$	0	0
$225$	−3.25981	−0.217321
$226$	11.1967	0.744793
$227$	−5.22879	−0.347047	−0.173523	−	0.984830i	$-0.555515\pi$
$227$	−5.22879	−0.347047	−0.173523	+	0.984830i	$0.555515\pi$
$228$	−1.01690	−0.0673457
$229$	−18.6808	−1.23446	−0.617232	−	0.786781i	$-0.711746\pi$
$229$	−18.6808	−1.23446	−0.617232	+	0.786781i	$0.711746\pi$
$230$	6.30731	0.415892
$231$	0	0
$232$	−10.0596	−0.660448
$233$	−22.5430	−1.47684	−0.738421	−	0.674340i	$-0.764428\pi$
$233$	−22.5430	−1.47684	−0.738421	+	0.674340i	$0.764428\pi$
$234$	−1.64041	−0.107237
$235$	16.3204	1.06463
$236$	2.03101	0.132208
$237$	4.53670	0.294690
$238$	0	0
$239$	−13.9984	−0.905478	−0.452739	−	0.891643i	$-0.649553\pi$
$239$	−13.9984	−0.905478	−0.452739	+	0.891643i	$0.649553\pi$
$240$	−4.79278	−0.309373
$241$	11.2619	0.725441	0.362720	−	0.931898i	$-0.381848\pi$
$241$	11.2619	0.725441	0.362720	+	0.931898i	$0.381848\pi$
$242$	−8.25429	−0.530606
$243$	−1.00000	−0.0641500
$244$	−1.64941	−0.105592
$245$	0	0
$246$	−1.35311	−0.0862709
$247$	−7.29033	−0.463873
$248$	3.54782	0.225287
$249$	16.9034	1.07121
$250$	−14.7435	−0.932460
$251$	15.3946	0.971696	0.485848	−	0.874043i	$-0.338511\pi$
$251$	15.3946	0.971696	0.485848	+	0.874043i	$0.338511\pi$
$252$	0	0
$253$	−14.6122	−0.918660
$254$	20.3839	1.27900
$255$	−10.0659	−0.630348
$256$	−4.02862	−0.251789
$257$	18.0611	1.12662	0.563311	−	0.826245i	$-0.309527\pi$
$257$	18.0611	1.12662	0.563311	+	0.826245i	$0.309527\pi$
$258$	−9.65109	−0.600850
$259$	0	0
$260$	0.270438	0.0167718
$261$	−3.42745	−0.212154
$262$	20.6544	1.27603
$263$	−5.44028	−0.335462	−0.167731	−	0.985833i	$-0.553644\pi$
$263$	−5.44028	−0.335462	−0.167731	+	0.985833i	$0.553644\pi$
$264$	12.1371	0.746984
$265$	−12.9034	−0.792650
$266$	0	0
$267$	−10.3639	−0.634259
$268$	−0.555973	−0.0339614
$269$	−1.51928	−0.0926320	−0.0463160	−	0.998927i	$-0.514748\pi$
$269$	−1.51928	−0.0926320	−0.0463160	+	0.998927i	$0.514748\pi$
$270$	−1.78497	−0.108630
$271$	−1.16103	−0.0705275	−0.0352638	−	0.999378i	$-0.511227\pi$
$271$	−1.16103	−0.0705275	−0.0352638	+	0.999378i	$0.511227\pi$
$272$	27.7231	1.68096
$273$	0	0
$274$	3.66075	0.221154
$275$	13.4801	0.812882
$276$	0.597535	0.0359674
$277$	10.9612	0.658593	0.329297	−	0.944226i	$-0.393188\pi$
$277$	10.9612	0.658593	0.329297	+	0.944226i	$0.393188\pi$
$278$	−17.4695	−1.04775
$279$	1.20879	0.0723682
$280$	0	0
$281$	30.1018	1.79572	0.897861	−	0.440280i	$-0.145121\pi$
$281$	30.1018	1.79572	0.897861	+	0.440280i	$0.145121\pi$
$282$	−16.7404	−0.996876
$283$	−0.416444	−0.0247550	−0.0123775	−	0.999923i	$-0.503940\pi$
$283$	−0.416444	−0.0247550	−0.0123775	+	0.999923i	$0.503940\pi$
$284$	0.874635	0.0519000
$285$	−7.93279	−0.469898
$286$	6.78348	0.401116
$287$	0	0
$288$	−0.953947	−0.0562119
$289$	41.2244	2.42497
$290$	−6.11788	−0.359254
$291$	−6.82267	−0.399952
$292$	1.88204	0.110138
$293$	12.4827	0.729249	0.364625	−	0.931155i	$-0.381197\pi$
$293$	12.4827	0.729249	0.364625	+	0.931155i	$0.381197\pi$
$294$	0	0
$295$	15.8439	0.922466
$296$	5.16619	0.300279
$297$	4.13524	0.239951
$298$	30.3578	1.75858
$299$	4.28384	0.247741
$300$	−0.551242	−0.0318260
$301$	0	0
$302$	−4.81346	−0.276984
$303$	7.85345	0.451169
$304$	21.8483	1.25308
$305$	−12.8670	−0.736761
$306$	10.3249	0.590234
$307$	24.2680	1.38505	0.692524	−	0.721395i	$-0.256499\pi$
$307$	24.2680	1.38505	0.692524	+	0.721395i	$0.256499\pi$
$308$	0	0
$309$	14.8276	0.843513
$310$	2.15764	0.122546
$311$	14.7110	0.834183	0.417091	−	0.908865i	$-0.363050\pi$
$311$	14.7110	0.834183	0.417091	+	0.908865i	$0.363050\pi$
$312$	−3.55821	−0.201444
$313$	−6.74545	−0.381275	−0.190638	−	0.981660i	$-0.561056\pi$
$313$	−6.74545	−0.381275	−0.190638	+	0.981660i	$0.561056\pi$
$314$	−10.0730	−0.568450
$315$	0	0
$316$	0.767166	0.0431565
$317$	9.54316	0.535997	0.267999	−	0.963419i	$-0.413638\pi$
$317$	9.54316	0.535997	0.267999	+	0.963419i	$0.413638\pi$
$318$	13.2354	0.742206
$319$	14.1733	0.793554
$320$	−11.2883	−0.631036
$321$	−15.6391	−0.872890
$322$	0	0
$323$	45.8860	2.55317
$324$	−0.169102	−0.00939457
$325$	−3.95196	−0.219215
$326$	4.02211	0.222764
$327$	−2.48326	−0.137324
$328$	−2.93503	−0.162060
$329$	0	0
$330$	7.38128	0.406326
$331$	21.5662	1.18538	0.592692	−	0.805429i	$-0.298065\pi$
$331$	21.5662	1.18538	0.592692	+	0.805429i	$0.298065\pi$
$332$	2.85840	0.156875
$333$	1.76018	0.0964575
$334$	−24.5210	−1.34173
$335$	−4.33713	−0.236962
$336$	0	0
$337$	−18.1135	−0.986705	−0.493353	−	0.869829i	$-0.664229\pi$
$337$	−18.1135	−0.986705	−0.493353	+	0.869829i	$0.664229\pi$
$338$	15.6017	0.848619
$339$	8.27480	0.449425
$340$	−1.70216	−0.0923126
$341$	−4.99863	−0.270691
$342$	8.13692	0.439994
$343$	0	0
$344$	−20.9342	−1.12870
$345$	4.66135	0.250959
$346$	28.8427	1.55059
$347$	5.91793	0.317691	0.158846	−	0.987303i	$-0.449223\pi$
$347$	5.91793	0.317691	0.158846	+	0.987303i	$0.449223\pi$
$348$	−0.579589	−0.0310692
$349$	10.6866	0.572041	0.286021	−	0.958223i	$-0.407667\pi$
$349$	10.6866	0.572041	0.286021	+	0.958223i	$0.407667\pi$
$350$	0	0
$351$	−1.21233	−0.0647092
$352$	3.94480	0.210259
$353$	10.6294	0.565747	0.282874	−	0.959157i	$-0.408712\pi$
$353$	10.6294	0.565747	0.282874	+	0.959157i	$0.408712\pi$
$354$	−16.2516	−0.863761
$355$	6.82300	0.362127
$356$	−1.75255	−0.0928852
$357$	0	0
$358$	25.0127	1.32196
$359$	−8.46027	−0.446516	−0.223258	−	0.974759i	$-0.571669\pi$
$359$	−8.46027	−0.446516	−0.223258	+	0.974759i	$0.571669\pi$
$360$	−3.87178	−0.204061
$361$	17.1623	0.903277
$362$	19.2841	1.01355
$363$	−6.10025	−0.320180
$364$	0	0
$365$	14.6817	0.768477
$366$	13.1981	0.689874
$367$	8.70112	0.454195	0.227097	−	0.973872i	$-0.427076\pi$
$367$	8.70112	0.454195	0.227097	+	0.973872i	$0.427076\pi$
$368$	−12.8382	−0.669236
$369$	−1.00000	−0.0520579
$370$	3.14187	0.163338
$371$	0	0
$372$	0.204409	0.0105981
$373$	−3.07218	−0.159071	−0.0795357	−	0.996832i	$-0.525344\pi$
$373$	−3.07218	−0.159071	−0.0795357	+	0.996832i	$0.525344\pi$
$374$	−42.6959	−2.20775
$375$	−10.8960	−0.562669
$376$	−36.3116	−1.87263
$377$	−4.15518	−0.214003
$378$	0	0
$379$	−7.43781	−0.382055	−0.191027	−	0.981585i	$-0.561182\pi$
$379$	−7.43781	−0.382055	−0.191027	+	0.981585i	$0.561182\pi$
$380$	−1.34145	−0.0688151
$381$	15.0645	0.771778
$382$	7.60568	0.389140
$383$	9.19067	0.469621	0.234811	−	0.972041i	$-0.424553\pi$
$383$	9.19067	0.469621	0.234811	+	0.972041i	$0.424553\pi$
$384$	9.67090	0.493516
$385$	0	0
$386$	32.6762	1.66317
$387$	−7.13254	−0.362567
$388$	−1.15373	−0.0585718
$389$	−36.7201	−1.86178	−0.930891	−	0.365298i	$-0.880967\pi$
$389$	−36.7201	−1.86178	−0.930891	+	0.365298i	$0.880967\pi$
$390$	−2.16396	−0.109577
$391$	−26.9629	−1.36357
$392$	0	0
$393$	15.2644	0.769989
$394$	9.92241	0.499884
$395$	5.98464	0.301120
$396$	0.699279	0.0351401
$397$	31.7045	1.59120	0.795602	−	0.605820i	$-0.207155\pi$
$397$	31.7045	1.59120	0.795602	+	0.605820i	$0.207155\pi$
$398$	−24.4361	−1.22487
$399$	0	0
$400$	11.8435	0.592177
$401$	−4.51534	−0.225485	−0.112743	−	0.993624i	$-0.535964\pi$
$401$	−4.51534	−0.225485	−0.112743	+	0.993624i	$0.535964\pi$
$402$	4.44873	0.221882
$403$	1.46544	0.0729990
$404$	1.32804	0.0660723
$405$	−1.31916	−0.0655497
$406$	0	0
$407$	−7.27879	−0.360796
$408$	22.3957	1.10875
$409$	27.9794	1.38349	0.691746	−	0.722141i	$-0.256842\pi$
$409$	27.9794	1.38349	0.691746	+	0.722141i	$0.256842\pi$
$410$	−1.78497	−0.0881532
$411$	2.70544	0.133450
$412$	2.50738	0.123530
$413$	0	0
$414$	−4.78130	−0.234988
$415$	22.2983	1.09458
$416$	−1.15649	−0.0567018
$417$	−12.9107	−0.632239
$418$	−33.6481	−1.64578
$419$	−13.3188	−0.650664	−0.325332	−	0.945600i	$-0.605476\pi$
$419$	−13.3188	−0.650664	−0.325332	+	0.945600i	$0.605476\pi$
$420$	0	0
$421$	−4.78745	−0.233326	−0.116663	−	0.993172i	$-0.537220\pi$
$421$	−4.78745	−0.233326	−0.116663	+	0.993172i	$0.537220\pi$
$422$	−26.2696	−1.27879
$423$	−12.3718	−0.601539
$424$	28.7090	1.39423
$425$	24.8740	1.20656
$426$	−6.99857	−0.339082
$427$	0	0
$428$	−2.64461	−0.127832
$429$	5.01327	0.242043
$430$	−12.7313	−0.613960
$431$	−18.7726	−0.904246	−0.452123	−	0.891956i	$-0.649333\pi$
$431$	−18.7726	−0.904246	−0.452123	+	0.891956i	$0.649333\pi$
$432$	3.63320	0.174802
$433$	−1.21306	−0.0582958	−0.0291479	−	0.999575i	$-0.509279\pi$
$433$	−1.21306	−0.0582958	−0.0291479	+	0.999575i	$0.509279\pi$
$434$	0	0
$435$	−4.52136	−0.216782
$436$	−0.419925	−0.0201107
$437$	−21.2492	−1.01649
$438$	−15.0595	−0.719572
$439$	−5.68678	−0.271415	−0.135708	−	0.990749i	$-0.543331\pi$
$439$	−5.68678	−0.271415	−0.135708	+	0.990749i	$0.543331\pi$
$440$	16.0107	0.763282
$441$	0	0
$442$	12.5171	0.595378
$443$	−36.0080	−1.71079	−0.855397	−	0.517974i	$-0.826687\pi$
$443$	−36.0080	−1.71079	−0.855397	+	0.517974i	$0.826687\pi$
$444$	0.297651	0.0141259
$445$	−13.6716	−0.648097
$446$	6.41304	0.303666
$447$	22.4356	1.06117
$448$	0	0
$449$	18.3922	0.867983	0.433991	−	0.900917i	$-0.357105\pi$
$449$	18.3922	0.867983	0.433991	+	0.900917i	$0.357105\pi$
$450$	4.41087	0.207931
$451$	4.13524	0.194721
$452$	1.39929	0.0658170
$453$	−3.55734	−0.167139
$454$	7.07511	0.332051
$455$	0	0
$456$	17.6498	0.826528
$457$	4.17893	0.195482	0.0977410	−	0.995212i	$-0.468838\pi$
$457$	4.17893	0.195482	0.0977410	+	0.995212i	$0.468838\pi$
$458$	25.2771	1.18112
$459$	7.63049	0.356161
$460$	0.788246	0.0367521
$461$	−18.4750	−0.860467	−0.430233	−	0.902718i	$-0.641569\pi$
$461$	−18.4750	−0.860467	−0.430233	+	0.902718i	$0.641569\pi$
$462$	0	0
$463$	14.2999	0.664573	0.332287	−	0.943178i	$-0.392180\pi$
$463$	14.2999	0.664573	0.332287	+	0.943178i	$0.392180\pi$
$464$	12.4526	0.578097
$465$	1.59459	0.0739472
$466$	30.5031	1.41303
$467$	−24.0941	−1.11494	−0.557471	−	0.830196i	$-0.688228\pi$
$467$	−24.0941	−1.11494	−0.557471	+	0.830196i	$0.688228\pi$
$468$	−0.205007	−0.00947646
$469$	0	0
$470$	−22.0833	−1.01863
$471$	−7.44432	−0.343016
$472$	−35.2513	−1.62257
$473$	29.4948	1.35617
$474$	−6.13864	−0.281957
$475$	19.6029	0.899443
$476$	0	0
$477$	9.78151	0.447865
$478$	18.9413	0.866353
$479$	−17.9242	−0.818977	−0.409489	−	0.912315i	$-0.634293\pi$
$479$	−17.9242	−0.818977	−0.409489	+	0.912315i	$0.634293\pi$
$480$	−1.25841	−0.0574383
$481$	2.13392	0.0972983
$482$	−15.2385	−0.694095
$483$	0	0
$484$	−1.03157	−0.0468894
$485$	−9.00021	−0.408679
$486$	1.35311	0.0613782
$487$	7.14141	0.323608	0.161804	−	0.986823i	$-0.448269\pi$
$487$	7.14141	0.323608	0.161804	+	0.986823i	$0.448269\pi$
$488$	28.6280	1.29593
$489$	2.97250	0.134421
$490$	0	0
$491$	27.0923	1.22266	0.611328	−	0.791377i	$-0.290636\pi$
$491$	27.0923	1.22266	0.611328	+	0.791377i	$0.290636\pi$
$492$	−0.169102	−0.00762372
$493$	26.1531	1.17788
$494$	9.86460	0.443829
$495$	5.45506	0.245187
$496$	−4.39176	−0.197196
$497$	0	0
$498$	−22.8721	−1.02492
$499$	44.1879	1.97812	0.989061	−	0.147510i	$-0.0471259\pi$
$499$	44.1879	1.97812	0.989061	+	0.147510i	$0.0471259\pi$
$500$	−1.84254	−0.0824011
$501$	−18.1220	−0.809632
$502$	−20.8305	−0.929710
$503$	1.40040	0.0624408	0.0312204	−	0.999513i	$-0.490061\pi$
$503$	1.40040	0.0624408	0.0312204	+	0.999513i	$0.490061\pi$
$504$	0	0
$505$	10.3600	0.461013
$506$	19.7718	0.878966
$507$	11.5303	0.512077
$508$	2.54744	0.113024
$509$	8.82748	0.391271	0.195636	−	0.980677i	$-0.437323\pi$
$509$	8.82748	0.391271	0.195636	+	0.980677i	$0.437323\pi$
$510$	13.6202	0.603112
$511$	0	0
$512$	24.7930	1.09570
$513$	6.01351	0.265503
$514$	−24.4386	−1.07794
$515$	19.5600	0.861917
$516$	−1.20613	−0.0530969
$517$	51.1605	2.25004
$518$	0	0
$519$	21.3159	0.935663
$520$	−4.69386	−0.205839
$521$	6.83755	0.299558	0.149779	−	0.988719i	$-0.452144\pi$
$521$	6.83755	0.299558	0.149779	+	0.988719i	$0.452144\pi$
$522$	4.63770	0.202987
$523$	−33.9846	−1.48604	−0.743022	−	0.669267i	$-0.766608\pi$
$523$	−33.9846	−1.48604	−0.743022	+	0.669267i	$0.766608\pi$
$524$	2.58125	0.112763
$525$	0	0
$526$	7.36127	0.320967
$527$	−9.22364	−0.401788
$528$	−15.0242	−0.653843
$529$	−10.5139	−0.457125
$530$	17.4597	0.758400
$531$	−12.0106	−0.521214
$532$	0	0
$533$	−1.21233	−0.0525117
$534$	14.0234	0.606853
$535$	−20.6305	−0.891935
$536$	9.64975	0.416806
$537$	18.4854	0.797703
$538$	2.05574	0.0886294
$539$	0	0
$540$	−0.223073	−0.00959955
$541$	24.3280	1.04594	0.522972	−	0.852350i	$-0.324823\pi$
$541$	24.3280	1.04594	0.522972	+	0.852350i	$0.324823\pi$
$542$	1.57100	0.0674801
$543$	14.2517	0.611601
$544$	7.27908	0.312088
$545$	−3.27582	−0.140321
$546$	0	0
$547$	12.3801	0.529335	0.264668	−	0.964340i	$-0.414738\pi$
$547$	12.3801	0.529335	0.264668	+	0.964340i	$0.414738\pi$
$548$	0.457496	0.0195433
$549$	9.75390	0.416286
$550$	−18.2400	−0.777758
$551$	20.6110	0.878057
$552$	−10.3711	−0.441424
$553$	0	0
$554$	−14.8316	−0.630136
$555$	2.32197	0.0985621
$556$	−2.18323	−0.0925894
$557$	43.6036	1.84754	0.923772	−	0.382943i	$-0.125089\pi$
$557$	43.6036	1.84754	0.923772	+	0.382943i	$0.125089\pi$
$558$	−1.63562	−0.0692412
$559$	−8.64697	−0.365728
$560$	0	0
$561$	−31.5540	−1.33221
$562$	−40.7309	−1.71813
$563$	−31.1035	−1.31086	−0.655429	−	0.755257i	$-0.727512\pi$
$563$	−31.1035	−1.31086	−0.655429	+	0.755257i	$0.727512\pi$
$564$	−2.09210	−0.0880935
$565$	10.9158	0.459231
$566$	0.563494	0.0236854
$567$	0	0
$568$	−15.1806	−0.636964
$569$	−23.4948	−0.984952	−0.492476	−	0.870326i	$-0.663908\pi$
$569$	−23.4948	−0.984952	−0.492476	+	0.870326i	$0.663908\pi$
$570$	10.7339	0.449594
$571$	38.2439	1.60046	0.800229	−	0.599694i	$-0.204711\pi$
$571$	38.2439	1.60046	0.800229	+	0.599694i	$0.204711\pi$
$572$	0.847755	0.0354464
$573$	5.62090	0.234817
$574$	0	0
$575$	−11.5188	−0.480366
$576$	8.55719	0.356550
$577$	28.1043	1.17000	0.584999	−	0.811034i	$-0.301095\pi$
$577$	28.1043	1.17000	0.584999	+	0.811034i	$0.301095\pi$
$578$	−55.7810	−2.32019
$579$	24.1490	1.00360
$580$	−0.764572	−0.0317471
$581$	0	0
$582$	9.23181	0.382671
$583$	−40.4490	−1.67522
$584$	−32.6656	−1.35171
$585$	−1.59926	−0.0661211
$586$	−16.8905	−0.697739
$587$	1.51683	0.0626061	0.0313031	−	0.999510i	$-0.490034\pi$
$587$	1.51683	0.0626061	0.0313031	+	0.999510i	$0.490034\pi$
$588$	0	0
$589$	−7.26905	−0.299516
$590$	−21.4385	−0.882607
$591$	7.33306	0.301642
$592$	−6.39510	−0.262837
$593$	26.2559	1.07820	0.539100	−	0.842242i	$-0.318765\pi$
$593$	26.2559	1.07820	0.539100	+	0.842242i	$0.318765\pi$
$594$	−5.59543	−0.229583
$595$	0	0
$596$	3.79391	0.155405
$597$	−18.0592	−0.739116
$598$	−5.79650	−0.237036
$599$	6.83178	0.279139	0.139569	−	0.990212i	$-0.455428\pi$
$599$	6.83178	0.279139	0.139569	+	0.990212i	$0.455428\pi$
$600$	9.56763	0.390597
$601$	2.08541	0.0850656	0.0425328	−	0.999095i	$-0.486457\pi$
$601$	2.08541	0.0850656	0.0425328	+	0.999095i	$0.486457\pi$
$602$	0	0
$603$	3.28779	0.133889
$604$	−0.601555	−0.0244769
$605$	−8.04722	−0.327166
$606$	−10.6266	−0.431674
$607$	−7.94144	−0.322333	−0.161166	−	0.986927i	$-0.551526\pi$
$607$	−7.94144	−0.322333	−0.161166	+	0.986927i	$0.551526\pi$
$608$	5.73657	0.232648
$609$	0	0
$610$	17.4104	0.704926
$611$	−14.9987	−0.606782
$612$	1.29033	0.0521587
$613$	−20.5806	−0.831244	−0.415622	−	0.909537i	$-0.636436\pi$
$613$	−20.5806	−0.831244	−0.415622	+	0.909537i	$0.636436\pi$
$614$	−32.8372	−1.32520
$615$	−1.31916	−0.0531937
$616$	0	0
$617$	−8.93578	−0.359741	−0.179870	−	0.983690i	$-0.557568\pi$
$617$	−8.93578	−0.359741	−0.179870	+	0.983690i	$0.557568\pi$
$618$	−20.0633	−0.807066
$619$	18.3129	0.736058	0.368029	−	0.929814i	$-0.380033\pi$
$619$	18.3129	0.736058	0.368029	+	0.929814i	$0.380033\pi$
$620$	0.269648	0.0108293
$621$	−3.53357	−0.141797
$622$	−19.9055	−0.798138
$623$	0	0
$624$	4.40462	0.176326
$625$	1.92543	0.0770171
$626$	9.12732	0.364801
$627$	−24.8673	−0.993105
$628$	−1.25885	−0.0502336
$629$	−13.4311	−0.535532
$630$	0	0
$631$	−39.2195	−1.56131	−0.780653	−	0.624965i	$-0.785113\pi$
$631$	−39.2195	−1.56131	−0.780653	+	0.624965i	$0.785113\pi$
$632$	−13.3153	−0.529656
$633$	−19.4143	−0.771650
$634$	−12.9129	−0.512838
$635$	19.8725	0.788617
$636$	1.65408	0.0655884
$637$	0	0
$638$	−19.1780	−0.759265
$639$	−5.17222	−0.204610
$640$	12.7575	0.504284
$641$	36.2325	1.43110	0.715548	−	0.698563i	$-0.246177\pi$
$641$	36.2325	1.43110	0.715548	+	0.698563i	$0.246177\pi$
$642$	21.1614	0.835173
$643$	33.0515	1.30342	0.651712	−	0.758467i	$-0.274051\pi$
$643$	33.0515	1.30342	0.651712	+	0.758467i	$0.274051\pi$
$644$	0	0
$645$	−9.40897	−0.370478
$646$	−62.0887	−2.44285
$647$	−20.5881	−0.809402	−0.404701	−	0.914449i	$-0.632624\pi$
$647$	−20.5881	−0.809402	−0.404701	+	0.914449i	$0.632624\pi$
$648$	2.93503	0.115299
$649$	49.6666	1.94958
$650$	5.34742	0.209743
$651$	0	0
$652$	0.502656	0.0196855
$653$	31.6370	1.23805	0.619025	−	0.785371i	$-0.287528\pi$
$653$	31.6370	1.23805	0.619025	+	0.785371i	$0.287528\pi$
$654$	3.36011	0.131391
$655$	20.1363	0.786789
$656$	3.63320	0.141853
$657$	−11.1296	−0.434207
$658$	0	0
$659$	2.92227	0.113836	0.0569178	−	0.998379i	$-0.481873\pi$
$659$	2.92227	0.113836	0.0569178	+	0.998379i	$0.481873\pi$
$660$	0.922463	0.0359068
$661$	35.9959	1.40008	0.700038	−	0.714105i	$-0.253166\pi$
$661$	35.9959	1.40008	0.700038	+	0.714105i	$0.253166\pi$
$662$	−29.1813	−1.13417
$663$	9.25065	0.359265
$664$	−49.6119	−1.92532
$665$	0	0
$666$	−2.38172	−0.0922897
$667$	−12.1111	−0.468945
$668$	−3.06447	−0.118568
$669$	4.73950	0.183240
$670$	5.86859	0.226724
$671$	−40.3348	−1.55711
$672$	0	0
$673$	−12.3452	−0.475873	−0.237936	−	0.971281i	$-0.576471\pi$
$673$	−12.3452	−0.475873	−0.237936	+	0.971281i	$0.576471\pi$
$674$	24.5095	0.944071
$675$	3.25981	0.125470
$676$	1.94979	0.0749921
$677$	−15.4048	−0.592056	−0.296028	−	0.955179i	$-0.595662\pi$
$677$	−15.4048	−0.592056	−0.296028	+	0.955179i	$0.595662\pi$
$678$	−11.1967	−0.430006
$679$	0	0
$680$	29.5436	1.13294
$681$	5.22879	0.200368
$682$	6.76368	0.258995
$683$	−11.8482	−0.453360	−0.226680	−	0.973969i	$-0.572787\pi$
$683$	−11.8482	−0.453360	−0.226680	+	0.973969i	$0.572787\pi$
$684$	1.01690	0.0388821
$685$	3.56892	0.136361
$686$	0	0
$687$	18.6808	0.712718
$688$	25.9139	0.987960
$689$	11.8584	0.451769
$690$	−6.30731	−0.240115
$691$	−4.45399	−0.169438	−0.0847189	−	0.996405i	$-0.526999\pi$
$691$	−4.45399	−0.169438	−0.0847189	+	0.996405i	$0.526999\pi$
$692$	3.60457	0.137025
$693$	0	0
$694$	−8.00760	−0.303964
$695$	−17.0313	−0.646033
$696$	10.0596	0.381310
$697$	7.63049	0.289026
$698$	−14.4601	−0.547324
$699$	22.5430	0.852655
$700$	0	0
$701$	−48.6204	−1.83637	−0.918183	−	0.396155i	$-0.870344\pi$
$701$	−48.6204	−1.83637	−0.918183	+	0.396155i	$0.870344\pi$
$702$	1.64041	0.0619132
$703$	−10.5849	−0.399216
$704$	−35.3861	−1.33366
$705$	−16.3204	−0.614663
$706$	−14.3827	−0.541302
$707$	0	0
$708$	−2.03101	−0.0763302
$709$	−18.8664	−0.708544	−0.354272	−	0.935143i	$-0.615271\pi$
$709$	−18.8664	−0.708544	−0.354272	+	0.935143i	$0.615271\pi$
$710$	−9.23225	−0.346480
$711$	−4.53670	−0.170140
$712$	30.4182	1.13997
$713$	4.27134	0.159963
$714$	0	0
$715$	6.61331	0.247324
$716$	3.12592	0.116821
$717$	13.9984	0.522778
$718$	11.4477	0.427223
$719$	−28.7532	−1.07231	−0.536156	−	0.844119i	$-0.680124\pi$
$719$	−28.7532	−1.07231	−0.536156	+	0.844119i	$0.680124\pi$
$720$	4.79278	0.178616
$721$	0	0
$722$	−23.2224	−0.864247
$723$	−11.2619	−0.418833
$724$	2.41000	0.0895670
$725$	11.1728	0.414948
$726$	8.25429	0.306345
$727$	14.1780	0.525833	0.262917	−	0.964819i	$-0.415316\pi$
$727$	14.1780	0.525833	0.262917	+	0.964819i	$0.415316\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−19.8660	−0.735272
$731$	54.4248	2.01297
$732$	1.64941	0.0609639
$733$	−39.5706	−1.46157	−0.730786	−	0.682607i	$-0.760846\pi$
$733$	−39.5706	−1.46157	−0.730786	+	0.682607i	$0.760846\pi$
$734$	−11.7735	−0.434569
$735$	0	0
$736$	−3.37084	−0.124251
$737$	−13.5958	−0.500808
$738$	1.35311	0.0498085
$739$	2.50728	0.0922319	0.0461159	−	0.998936i	$-0.485316\pi$
$739$	2.50728	0.0922319	0.0461159	+	0.998936i	$0.485316\pi$
$740$	0.392650	0.0144341
$741$	7.29033	0.267817
$742$	0	0
$743$	−6.99904	−0.256770	−0.128385	−	0.991724i	$-0.540979\pi$
$743$	−6.99904	−0.256770	−0.128385	+	0.991724i	$0.540979\pi$
$744$	−3.54782	−0.130069
$745$	29.5962	1.08432
$746$	4.15699	0.152198
$747$	−16.9034	−0.618463
$748$	−5.33585	−0.195098
$749$	0	0
$750$	14.7435	0.538356
$751$	−2.55120	−0.0930948	−0.0465474	−	0.998916i	$-0.514822\pi$
$751$	−2.55120	−0.0930948	−0.0465474	+	0.998916i	$0.514822\pi$
$752$	44.9493	1.63913
$753$	−15.3946	−0.561009
$754$	5.62241	0.204756
$755$	−4.69271	−0.170785
$756$	0	0
$757$	−2.21284	−0.0804269	−0.0402135	−	0.999191i	$-0.512804\pi$
$757$	−2.21284	−0.0804269	−0.0402135	+	0.999191i	$0.512804\pi$
$758$	10.0642	0.365546
$759$	14.6122	0.530389
$760$	23.2830	0.844561
$761$	−32.3515	−1.17274	−0.586370	−	0.810043i	$-0.699444\pi$
$761$	−32.3515	−1.17274	−0.586370	+	0.810043i	$0.699444\pi$
$762$	−20.3839	−0.738430
$763$	0	0
$764$	0.950507	0.0343882
$765$	10.0659	0.363932
$766$	−12.4360	−0.449329
$767$	−14.5607	−0.525757
$768$	4.02862	0.145370
$769$	−24.5951	−0.886922	−0.443461	−	0.896294i	$-0.646250\pi$
$769$	−24.5951	−0.886922	−0.443461	+	0.896294i	$0.646250\pi$
$770$	0	0
$771$	−18.0611	−0.650455
$772$	4.08365	0.146974
$773$	48.9111	1.75921	0.879605	−	0.475704i	$-0.157807\pi$
$773$	48.9111	1.75921	0.879605	+	0.475704i	$0.157807\pi$
$774$	9.65109	0.346901
$775$	−3.94042	−0.141544
$776$	20.0247	0.718846
$777$	0	0
$778$	49.6862	1.78134
$779$	6.01351	0.215456
$780$	−0.270438	−0.00968323
$781$	21.3884	0.765337
$782$	36.4837	1.30465
$783$	3.42745	0.122487
$784$	0	0
$785$	−9.82026	−0.350500
$786$	−20.6544	−0.736719
$787$	30.3303	1.08116	0.540579	−	0.841293i	$-0.318205\pi$
$787$	30.3303	1.08116	0.540579	+	0.841293i	$0.318205\pi$
$788$	1.24004	0.0441745
$789$	5.44028	0.193679
$790$	−8.09786	−0.288109
$791$	0	0
$792$	−12.1371	−0.431271
$793$	11.8249	0.419915
$794$	−42.8996	−1.52245
$795$	12.9034	0.457637
$796$	−3.05386	−0.108241
$797$	34.4648	1.22081	0.610403	−	0.792091i	$-0.291008\pi$
$797$	34.4648	1.22081	0.610403	+	0.792091i	$0.291008\pi$
$798$	0	0
$799$	94.4031	3.33974
$800$	3.10969	0.109944
$801$	10.3639	0.366189
$802$	6.10974	0.215742
$803$	46.0236	1.62414
$804$	0.555973	0.0196076
$805$	0	0
$806$	−1.98290	−0.0698448
$807$	1.51928	0.0534811
$808$	−23.0501	−0.810899
$809$	1.24184	0.0436607	0.0218303	−	0.999762i	$-0.493051\pi$
$809$	1.24184	0.0436607	0.0218303	+	0.999762i	$0.493051\pi$
$810$	1.78497	0.0627173
$811$	−41.2628	−1.44893	−0.724466	−	0.689311i	$-0.757914\pi$
$811$	−41.2628	−1.44893	−0.724466	+	0.689311i	$0.757914\pi$
$812$	0	0
$813$	1.16103	0.0407191
$814$	9.84898	0.345207
$815$	3.92121	0.137354
$816$	−27.7231	−0.970503
$817$	42.8916	1.50059
$818$	−37.8591	−1.32371
$819$	0	0
$820$	−0.223073	−0.00779006
$821$	−53.2123	−1.85712	−0.928561	−	0.371179i	$-0.878954\pi$
$821$	−53.2123	−1.85712	−0.928561	+	0.371179i	$0.878954\pi$
$822$	−3.66075	−0.127683
$823$	22.1657	0.772647	0.386324	−	0.922363i	$-0.373745\pi$
$823$	22.1657	0.772647	0.386324	+	0.922363i	$0.373745\pi$
$824$	−43.5194	−1.51607
$825$	−13.4801	−0.469317
$826$	0	0
$827$	−9.34066	−0.324807	−0.162403	−	0.986724i	$-0.551925\pi$
$827$	−9.34066	−0.324807	−0.162403	+	0.986724i	$0.551925\pi$
$828$	−0.597535	−0.0207658
$829$	39.9571	1.38777	0.693883	−	0.720088i	$-0.255899\pi$
$829$	39.9571	1.38777	0.693883	+	0.720088i	$0.255899\pi$
$830$	−30.1720	−1.04729
$831$	−10.9612	−0.380239
$832$	10.3741	0.359658
$833$	0	0
$834$	17.4695	0.604920
$835$	−23.9059	−0.827297
$836$	−4.20512	−0.145437
$837$	−1.20879	−0.0417818
$838$	18.0217	0.622549
$839$	−42.8317	−1.47871	−0.739356	−	0.673314i	$-0.764870\pi$
$839$	−42.8317	−1.47871	−0.739356	+	0.673314i	$0.764870\pi$
$840$	0	0
$841$	−17.2526	−0.594918
$842$	6.47793	0.223244
$843$	−30.1018	−1.03676
$844$	−3.28301	−0.113006
$845$	15.2103	0.523250
$846$	16.7404	0.575547
$847$	0	0
$848$	−35.5382	−1.22039
$849$	0.416444	0.0142923
$850$	−33.6571	−1.15443
$851$	6.21974	0.213210
$852$	−0.874635	−0.0299645
$853$	32.5731	1.11528	0.557641	−	0.830082i	$-0.311707\pi$
$853$	32.5731	1.11528	0.557641	+	0.830082i	$0.311707\pi$
$854$	0	0
$855$	7.93279	0.271296
$856$	45.9012	1.56887
$857$	−3.19940	−0.109290	−0.0546448	−	0.998506i	$-0.517403\pi$
$857$	−3.19940	−0.109290	−0.0546448	+	0.998506i	$0.517403\pi$
$858$	−6.78348	−0.231584
$859$	35.1926	1.20076	0.600379	−	0.799716i	$-0.295017\pi$
$859$	35.1926	1.20076	0.600379	+	0.799716i	$0.295017\pi$
$860$	−1.59108	−0.0542554
$861$	0	0
$862$	25.4014	0.865174
$863$	−13.2842	−0.452199	−0.226099	−	0.974104i	$-0.572597\pi$
$863$	−13.2842	−0.452199	−0.226099	+	0.974104i	$0.572597\pi$
$864$	0.953947	0.0324539
$865$	28.1191	0.956078
$866$	1.64140	0.0557769
$867$	−41.2244	−1.40005
$868$	0	0
$869$	18.7604	0.636402
$870$	6.11788	0.207416
$871$	3.98587	0.135056
$872$	7.28843	0.246817
$873$	6.82267	0.230913
$874$	28.7524	0.972564
$875$	0	0
$876$	−1.88204	−0.0635882
$877$	21.1466	0.714070	0.357035	−	0.934091i	$-0.383788\pi$
$877$	21.1466	0.714070	0.357035	+	0.934091i	$0.383788\pi$
$878$	7.69482	0.259688
$879$	−12.4827	−0.421032
$880$	−19.8193	−0.668109
$881$	−41.0838	−1.38415	−0.692074	−	0.721827i	$-0.743303\pi$
$881$	−41.0838	−1.38415	−0.692074	+	0.721827i	$0.743303\pi$
$882$	0	0
$883$	7.09721	0.238840	0.119420	−	0.992844i	$-0.461896\pi$
$883$	7.09721	0.238840	0.119420	+	0.992844i	$0.461896\pi$
$884$	1.56431	0.0526133
$885$	−15.8439	−0.532586
$886$	48.7227	1.63687
$887$	27.5771	0.925948	0.462974	−	0.886372i	$-0.346782\pi$
$887$	27.5771	0.925948	0.462974	+	0.886372i	$0.346782\pi$
$888$	−5.16619	−0.173366
$889$	0	0
$890$	18.4992	0.620094
$891$	−4.13524	−0.138536
$892$	0.801460	0.0268349
$893$	74.3981	2.48964
$894$	−30.3578	−1.01532
$895$	24.3852	0.815107
$896$	0	0
$897$	−4.28384	−0.143033
$898$	−24.8866	−0.830478
$899$	−4.14305	−0.138179
$900$	0.551242	0.0183747
$901$	−74.6378	−2.48655
$902$	−5.59543	−0.186307
$903$	0	0
$904$	−24.2868	−0.807766
$905$	18.8004	0.624945
$906$	4.81346	0.159917
$907$	−32.9302	−1.09343	−0.546715	−	0.837318i	$-0.684122\pi$
$907$	−32.9302	−1.09343	−0.546715	+	0.837318i	$0.684122\pi$
$908$	0.884200	0.0293432
$909$	−7.85345	−0.260482
$910$	0	0
$911$	46.6376	1.54517	0.772586	−	0.634910i	$-0.218963\pi$
$911$	46.6376	1.54517	0.772586	+	0.634910i	$0.218963\pi$
$912$	−21.8483	−0.723469
$913$	69.8997	2.31334
$914$	−5.65454	−0.187035
$915$	12.8670	0.425369
$916$	3.15897	0.104375
$917$	0	0
$918$	−10.3249	−0.340772
$919$	23.9661	0.790568	0.395284	−	0.918559i	$-0.370646\pi$
$919$	23.9661	0.790568	0.395284	+	0.918559i	$0.370646\pi$
$920$	−13.6812	−0.451056
$921$	−24.2680	−0.799658
$922$	24.9987	0.823287
$923$	−6.27042	−0.206393
$924$	0	0
$925$	−5.73787	−0.188660
$926$	−19.3493	−0.635858
$927$	−14.8276	−0.487002
$928$	3.26960	0.107330
$929$	20.8024	0.682505	0.341252	−	0.939972i	$-0.389149\pi$
$929$	20.8024	0.682505	0.341252	+	0.939972i	$0.389149\pi$
$930$	−2.15764	−0.0707520
$931$	0	0
$932$	3.81207	0.124869
$933$	−14.7110	−0.481616
$934$	32.6019	1.06677
$935$	−41.6248	−1.36128
$936$	3.55821	0.116304
$937$	−12.1738	−0.397702	−0.198851	−	0.980030i	$-0.563721\pi$
$937$	−12.1738	−0.397702	−0.198851	+	0.980030i	$0.563721\pi$
$938$	0	0
$939$	6.74545	0.220129
$940$	−2.75982	−0.0900156
$941$	−32.3488	−1.05454	−0.527270	−	0.849698i	$-0.676784\pi$
$941$	−32.3488	−1.05454	−0.527270	+	0.849698i	$0.676784\pi$
$942$	10.0730	0.328195
$943$	−3.53357	−0.115069
$944$	43.6368	1.42026
$945$	0	0
$946$	−39.9096	−1.29757
$947$	−13.7273	−0.446078	−0.223039	−	0.974810i	$-0.571598\pi$
$947$	−13.7273	−0.446078	−0.223039	+	0.974810i	$0.571598\pi$
$948$	−0.767166	−0.0249164
$949$	−13.4927	−0.437992
$950$	−26.5248	−0.860579
$951$	−9.54316	−0.309458
$952$	0	0
$953$	5.34700	0.173206	0.0866031	−	0.996243i	$-0.472399\pi$
$953$	5.34700	0.173206	0.0866031	+	0.996243i	$0.472399\pi$
$954$	−13.2354	−0.428513
$955$	7.41488	0.239940
$956$	2.36715	0.0765592
$957$	−14.1733	−0.458159
$958$	24.2533	0.783590
$959$	0	0
$960$	11.2883	0.364329
$961$	−29.5388	−0.952866
$962$	−2.88742	−0.0930941
$963$	15.6391	0.503963
$964$	−1.90441	−0.0613368
$965$	31.8564	1.02549
$966$	0	0
$967$	−21.8543	−0.702786	−0.351393	−	0.936228i	$-0.614292\pi$
$967$	−21.8543	−0.702786	−0.351393	+	0.936228i	$0.614292\pi$
$968$	17.9044	0.575469
$969$	−45.8860	−1.47407
$970$	12.1782	0.391020
$971$	−43.0619	−1.38192	−0.690962	−	0.722891i	$-0.742813\pi$
$971$	−43.0619	−1.38192	−0.690962	+	0.722891i	$0.742813\pi$
$972$	0.169102	0.00542396
$973$	0	0
$974$	−9.66309	−0.309626
$975$	3.95196	0.126564
$976$	−35.4379	−1.13434
$977$	46.7460	1.49554	0.747768	−	0.663960i	$-0.231125\pi$
$977$	46.7460	1.49554	0.747768	+	0.663960i	$0.231125\pi$
$978$	−4.02211	−0.128613
$979$	−42.8571	−1.36972
$980$	0	0
$981$	2.48326	0.0792843
$982$	−36.6587	−1.16983
$983$	−7.90305	−0.252068	−0.126034	−	0.992026i	$-0.540225\pi$
$983$	−7.90305	−0.252068	−0.126034	+	0.992026i	$0.540225\pi$
$984$	2.93503	0.0935652
$985$	9.67349	0.308223
$986$	−35.3879	−1.12698
$987$	0	0
$988$	1.23281	0.0392210
$989$	−25.2033	−0.801419
$990$	−7.38128	−0.234592
$991$	−49.2242	−1.56366	−0.781829	−	0.623492i	$-0.785713\pi$
$991$	−49.2242	−1.56366	−0.781829	+	0.623492i	$0.785713\pi$
$992$	−1.15312	−0.0366115
$993$	−21.5662	−0.684382
$994$	0	0
$995$	−23.8231	−0.755242
$996$	−2.85840	−0.0905720
$997$	−10.9194	−0.345821	−0.172910	−	0.984938i	$-0.555317\pi$
$997$	−10.9194	−0.345821	−0.172910	+	0.984938i	$0.555317\pi$
$998$	−59.7909	−1.89265
$999$	−1.76018	−0.0556898

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.y.1.2		7
7.6	odd	2		861.2.a.m.1.2	✓	7
21.20	even	2		2583.2.a.u.1.6		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
861.2.a.m.1.2	✓	7	7.6	odd	2
2583.2.a.u.1.6		7	21.20	even	2
6027.2.a.y.1.2		7	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6027.a (trivial)

\(f(q)\)	\(=\)	\(q-1.35311 q^{2} -1.00000 q^{3} -0.169102 q^{4} -1.31916 q^{5} +1.35311 q^{6} +2.93503 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.35311 q^{2} -1.00000 q^{3} -0.169102 q^{4} -1.31916 q^{5} +1.35311 q^{6} +2.93503 q^{8} +1.00000 q^{9} +1.78497 q^{10} -4.13524 q^{11} +0.169102 q^{12} +1.21233 q^{13} +1.31916 q^{15} -3.63320 q^{16} -7.63049 q^{17} -1.35311 q^{18} -6.01351 q^{19} +0.223073 q^{20} +5.59543 q^{22} +3.53357 q^{23} -2.93503 q^{24} -3.25981 q^{25} -1.64041 q^{26} -1.00000 q^{27} -3.42745 q^{29} -1.78497 q^{30} +1.20879 q^{31} -0.953947 q^{32} +4.13524 q^{33} +10.3249 q^{34} -0.169102 q^{36} +1.76018 q^{37} +8.13692 q^{38} -1.21233 q^{39} -3.87178 q^{40} -1.00000 q^{41} -7.13254 q^{43} +0.699279 q^{44} -1.31916 q^{45} -4.78130 q^{46} -12.3718 q^{47} +3.63320 q^{48} +4.41087 q^{50} +7.63049 q^{51} -0.205007 q^{52} +9.78151 q^{53} +1.35311 q^{54} +5.45506 q^{55} +6.01351 q^{57} +4.63770 q^{58} -12.0106 q^{59} -0.223073 q^{60} +9.75390 q^{61} -1.63562 q^{62} +8.55719 q^{64} -1.59926 q^{65} -5.59543 q^{66} +3.28779 q^{67} +1.29033 q^{68} -3.53357 q^{69} -5.17222 q^{71} +2.93503 q^{72} -11.1296 q^{73} -2.38172 q^{74} +3.25981 q^{75} +1.01690 q^{76} +1.64041 q^{78} -4.53670 q^{79} +4.79278 q^{80} +1.00000 q^{81} +1.35311 q^{82} -16.9034 q^{83} +10.0659 q^{85} +9.65109 q^{86} +3.42745 q^{87} -12.1371 q^{88} +10.3639 q^{89} +1.78497 q^{90} -0.597535 q^{92} -1.20879 q^{93} +16.7404 q^{94} +7.93279 q^{95} +0.953947 q^{96} +6.82267 q^{97} -4.13524 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 4 q^{2} - 7 q^{3} + 8 q^{4} - q^{5} - 4 q^{6} + 12 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q + 4 * q^2 - 7 * q^3 + 8 * q^4 - q^5 - 4 * q^6 + 12 * q^8 + 7 * q^9	\( 7 q + 4 q^{2} - 7 q^{3} + 8 q^{4} - q^{5} - 4 q^{6} + 12 q^{8} + 7 q^{9} + 3 q^{10} + 11 q^{11} - 8 q^{12} + 7 q^{13} + q^{15} + 6 q^{16} - 11 q^{17} + 4 q^{18} - 4 q^{19} + 7 q^{20} + 6 q^{22} + 7 q^{23} - 12 q^{24} + 2 q^{25} + 13 q^{26} - 7 q^{27} + 4 q^{29} - 3 q^{30} + 7 q^{31} + 18 q^{32} - 11 q^{33} + 20 q^{34} + 8 q^{36} - 4 q^{38} - 7 q^{39} + 9 q^{40} - 7 q^{41} + q^{43} + 18 q^{44} - q^{45} - 17 q^{46} - 14 q^{47} - 6 q^{48} + 19 q^{50} + 11 q^{51} + 27 q^{52} + 23 q^{53} - 4 q^{54} + 30 q^{55} + 4 q^{57} - 3 q^{58} - 8 q^{59} - 7 q^{60} + 3 q^{61} + 16 q^{62} + 6 q^{64} + 15 q^{65} - 6 q^{66} + 3 q^{67} - 7 q^{69} + 7 q^{71} + 12 q^{72} + 11 q^{73} - 13 q^{74} - 2 q^{75} + 40 q^{76} - 13 q^{78} - q^{79} + 43 q^{80} + 7 q^{81} - 4 q^{82} - 10 q^{85} - 12 q^{86} - 4 q^{87} + 10 q^{88} - 32 q^{89} + 3 q^{90} - 19 q^{92} - 7 q^{93} - 21 q^{94} - 8 q^{95} - 18 q^{96} + 25 q^{97} + 11 q^{99}+O(q^{100}) \) 7 * q + 4 * q^2 - 7 * q^3 + 8 * q^4 - q^5 - 4 * q^6 + 12 * q^8 + 7 * q^9 + 3 * q^10 + 11 * q^11 - 8 * q^12 + 7 * q^13 + q^15 + 6 * q^16 - 11 * q^17 + 4 * q^18 - 4 * q^19 + 7 * q^20 + 6 * q^22 + 7 * q^23 - 12 * q^24 + 2 * q^25 + 13 * q^26 - 7 * q^27 + 4 * q^29 - 3 * q^30 + 7 * q^31 + 18 * q^32 - 11 * q^33 + 20 * q^34 + 8 * q^36 - 4 * q^38 - 7 * q^39 + 9 * q^40 - 7 * q^41 + q^43 + 18 * q^44 - q^45 - 17 * q^46 - 14 * q^47 - 6 * q^48 + 19 * q^50 + 11 * q^51 + 27 * q^52 + 23 * q^53 - 4 * q^54 + 30 * q^55 + 4 * q^57 - 3 * q^58 - 8 * q^59 - 7 * q^60 + 3 * q^61 + 16 * q^62 + 6 * q^64 + 15 * q^65 - 6 * q^66 + 3 * q^67 - 7 * q^69 + 7 * q^71 + 12 * q^72 + 11 * q^73 - 13 * q^74 - 2 * q^75 + 40 * q^76 - 13 * q^78 - q^79 + 43 * q^80 + 7 * q^81 - 4 * q^82 - 10 * q^85 - 12 * q^86 - 4 * q^87 + 10 * q^88 - 32 * q^89 + 3 * q^90 - 19 * q^92 - 7 * q^93 - 21 * q^94 - 8 * q^95 - 18 * q^96 + 25 * q^97 + 11 * q^99

Introduction

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