LMFDB - Embedded newform 6027.2.a.bk.1.1

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:	$1$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} - 19 x^{12} + 36 x^{11} + 134 x^{10} - 237 x^{9} - 438 x^{8} + 716 x^{7} + 662 x^{6} + \cdots + 16 $ x^14 - 2x^13 - 19x^12 + 36x^11 + 134x^10 - 237x^9 - 438x^8 + 716x^7 + 662x^6 - 1007x^5 - 384x^4 + 579x^3 + 44x^2 - 112*x + 16
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			1.1
Root			$2.73044$ 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)

$f(q)$	$=$	$q-2.73044 q^{2} +1.00000 q^{3} +5.45531 q^{4} -3.67975 q^{5} -2.73044 q^{6} -9.43451 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.73044 q^{2} +1.00000 q^{3} +5.45531 q^{4} -3.67975 q^{5} -2.73044 q^{6} -9.43451 q^{8} +1.00000 q^{9} +10.0473 q^{10} -5.55413 q^{11} +5.45531 q^{12} -1.35125 q^{13} -3.67975 q^{15} +14.8498 q^{16} +5.33017 q^{17} -2.73044 q^{18} +3.13095 q^{19} -20.0742 q^{20} +15.1652 q^{22} +6.55809 q^{23} -9.43451 q^{24} +8.54056 q^{25} +3.68952 q^{26} +1.00000 q^{27} -8.35577 q^{29} +10.0473 q^{30} -3.83202 q^{31} -21.6774 q^{32} -5.55413 q^{33} -14.5537 q^{34} +5.45531 q^{36} +0.883409 q^{37} -8.54886 q^{38} -1.35125 q^{39} +34.7166 q^{40} -1.00000 q^{41} -3.78313 q^{43} -30.2995 q^{44} -3.67975 q^{45} -17.9065 q^{46} -2.25564 q^{47} +14.8498 q^{48} -23.3195 q^{50} +5.33017 q^{51} -7.37151 q^{52} +4.13650 q^{53} -2.73044 q^{54} +20.4378 q^{55} +3.13095 q^{57} +22.8149 q^{58} +4.43498 q^{59} -20.0742 q^{60} -4.50628 q^{61} +10.4631 q^{62} +29.4893 q^{64} +4.97228 q^{65} +15.1652 q^{66} -9.88169 q^{67} +29.0777 q^{68} +6.55809 q^{69} +3.25222 q^{71} -9.43451 q^{72} +6.37270 q^{73} -2.41210 q^{74} +8.54056 q^{75} +17.0803 q^{76} +3.68952 q^{78} +4.67377 q^{79} -54.6434 q^{80} +1.00000 q^{81} +2.73044 q^{82} +0.851113 q^{83} -19.6137 q^{85} +10.3296 q^{86} -8.35577 q^{87} +52.4005 q^{88} +9.60988 q^{89} +10.0473 q^{90} +35.7764 q^{92} -3.83202 q^{93} +6.15889 q^{94} -11.5211 q^{95} -21.6774 q^{96} -13.7839 q^{97} -5.55413 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 2 q^{2} + 14 q^{3} + 14 q^{4} - 10 q^{5} - 2 q^{6} - 6 q^{8} + 14 q^{9}+O(q^{10}) $ 14 * q - 2 * q^2 + 14 * q^3 + 14 * q^4 - 10 * q^5 - 2 * q^6 - 6 * q^8 + 14 * q^9	$ 14 q - 2 q^{2} + 14 q^{3} + 14 q^{4} - 10 q^{5} - 2 q^{6} - 6 q^{8} + 14 q^{9} - 3 q^{10} - 16 q^{11} + 14 q^{12} - 21 q^{13} - 10 q^{15} + 22 q^{16} - 12 q^{17} - 2 q^{18} - 2 q^{19} - 40 q^{20} + q^{22} - 7 q^{23} - 6 q^{24} + 22 q^{25} - 2 q^{26} + 14 q^{27} - 16 q^{29} - 3 q^{30} - 8 q^{31} - 19 q^{32} - 16 q^{33} - 33 q^{34} + 14 q^{36} + q^{37} - 32 q^{38} - 21 q^{39} + 13 q^{40} - 14 q^{41} + 14 q^{43} - 36 q^{44} - 10 q^{45} - 12 q^{46} - 12 q^{47} + 22 q^{48} - q^{50} - 12 q^{51} - 60 q^{52} - 20 q^{53} - 2 q^{54} + 11 q^{55} - 2 q^{57} + 21 q^{58} - 25 q^{59} - 40 q^{60} - 26 q^{61} + 33 q^{62} + 42 q^{64} - 8 q^{65} + q^{66} - 22 q^{67} - 15 q^{68} - 7 q^{69} - 36 q^{71} - 6 q^{72} - 31 q^{73} - 65 q^{74} + 22 q^{75} + 2 q^{76} - 2 q^{78} + 12 q^{79} - 112 q^{80} + 14 q^{81} + 2 q^{82} - 20 q^{83} + 40 q^{85} - 9 q^{86} - 16 q^{87} - 54 q^{88} - 39 q^{89} - 3 q^{90} + 63 q^{92} - 8 q^{93} - 14 q^{94} - 55 q^{95} - 19 q^{96} - 18 q^{97} - 16 q^{99}+O(q^{100}) $ 14 * q - 2 * q^2 + 14 * q^3 + 14 * q^4 - 10 * q^5 - 2 * q^6 - 6 * q^8 + 14 * q^9 - 3 * q^10 - 16 * q^11 + 14 * q^12 - 21 * q^13 - 10 * q^15 + 22 * q^16 - 12 * q^17 - 2 * q^18 - 2 * q^19 - 40 * q^20 + q^22 - 7 * q^23 - 6 * q^24 + 22 * q^25 - 2 * q^26 + 14 * q^27 - 16 * q^29 - 3 * q^30 - 8 * q^31 - 19 * q^32 - 16 * q^33 - 33 * q^34 + 14 * q^36 + q^37 - 32 * q^38 - 21 * q^39 + 13 * q^40 - 14 * q^41 + 14 * q^43 - 36 * q^44 - 10 * q^45 - 12 * q^46 - 12 * q^47 + 22 * q^48 - q^50 - 12 * q^51 - 60 * q^52 - 20 * q^53 - 2 * q^54 + 11 * q^55 - 2 * q^57 + 21 * q^58 - 25 * q^59 - 40 * q^60 - 26 * q^61 + 33 * q^62 + 42 * q^64 - 8 * q^65 + q^66 - 22 * q^67 - 15 * q^68 - 7 * q^69 - 36 * q^71 - 6 * q^72 - 31 * q^73 - 65 * q^74 + 22 * q^75 + 2 * q^76 - 2 * q^78 + 12 * q^79 - 112 * q^80 + 14 * q^81 + 2 * q^82 - 20 * q^83 + 40 * q^85 - 9 * q^86 - 16 * q^87 - 54 * q^88 - 39 * q^89 - 3 * q^90 + 63 * q^92 - 8 * q^93 - 14 * q^94 - 55 * q^95 - 19 * q^96 - 18 * q^97 - 16 * 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 $

$2$	−2.73044	−1.93071	−0.965357	−	0.260934i	$-0.915969\pi$
$2$	−2.73044	−1.93071	−0.965357	+	0.260934i	$0.915969\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	5.45531	2.72765
$5$	−3.67975	−1.64563	−0.822817	−	0.568306i	$-0.807599\pi$
$5$	−3.67975	−1.64563	−0.822817	+	0.568306i	$0.807599\pi$
$6$	−2.73044	−1.11470
$7$	0	0
$7$	0	0
$8$	−9.43451	−3.33560
$9$	1.00000	0.333333
$10$	10.0473	3.17725
$11$	−5.55413	−1.67463	−0.837316	−	0.546718i	$-0.815877\pi$
$11$	−5.55413	−1.67463	−0.837316	+	0.546718i	$0.815877\pi$
$12$	5.45531	1.57481
$13$	−1.35125	−0.374770	−0.187385	−	0.982287i	$-0.560001\pi$
$13$	−1.35125	−0.374770	−0.187385	+	0.982287i	$0.560001\pi$
$14$	0	0
$15$	−3.67975	−0.950107
$16$	14.8498	3.71244
$17$	5.33017	1.29276	0.646378	−	0.763017i	$-0.276283\pi$
$17$	5.33017	1.29276	0.646378	+	0.763017i	$0.276283\pi$
$18$	−2.73044	−0.643571
$19$	3.13095	0.718288	0.359144	−	0.933282i	$-0.383069\pi$
$19$	3.13095	0.718288	0.359144	+	0.933282i	$0.383069\pi$
$20$	−20.0742	−4.48872
$21$	0	0
$22$	15.1652	3.23324
$23$	6.55809	1.36746	0.683728	−	0.729737i	$-0.260357\pi$
$23$	6.55809	1.36746	0.683728	+	0.729737i	$0.260357\pi$
$24$	−9.43451	−1.92581
$25$	8.54056	1.70811
$26$	3.68952	0.723574
$27$	1.00000	0.192450
$28$	0	0
$29$	−8.35577	−1.55163	−0.775814	−	0.630962i	$-0.782660\pi$
$29$	−8.35577	−1.55163	−0.775814	+	0.630962i	$0.782660\pi$
$30$	10.0473	1.83438
$31$	−3.83202	−0.688252	−0.344126	−	0.938924i	$-0.611825\pi$
$31$	−3.83202	−0.688252	−0.344126	+	0.938924i	$0.611825\pi$
$32$	−21.6774	−3.83206
$33$	−5.55413	−0.966850
$34$	−14.5537	−2.49594
$35$	0	0
$36$	5.45531	0.909218
$37$	0.883409	0.145232	0.0726158	−	0.997360i	$-0.476865\pi$
$37$	0.883409	0.145232	0.0726158	+	0.997360i	$0.476865\pi$
$38$	−8.54886	−1.38681
$39$	−1.35125	−0.216374
$40$	34.7166	5.48918
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	−3.78313	−0.576922	−0.288461	−	0.957492i	$-0.593144\pi$
$43$	−3.78313	−0.576922	−0.288461	+	0.957492i	$0.593144\pi$
$44$	−30.2995	−4.56782
$45$	−3.67975	−0.548545
$46$	−17.9065	−2.64017
$47$	−2.25564	−0.329019	−0.164509	−	0.986376i	$-0.552604\pi$
$47$	−2.25564	−0.329019	−0.164509	+	0.986376i	$0.552604\pi$
$48$	14.8498	2.14338
$49$	0	0
$50$	−23.3195	−3.29787
$51$	5.33017	0.746373
$52$	−7.37151	−1.02224
$53$	4.13650	0.568192	0.284096	−	0.958796i	$-0.408307\pi$
$53$	4.13650	0.568192	0.284096	+	0.958796i	$0.408307\pi$
$54$	−2.73044	−0.371566
$55$	20.4378	2.75583
$56$	0	0
$57$	3.13095	0.414704
$58$	22.8149	2.99575
$59$	4.43498	0.577386	0.288693	−	0.957422i	$-0.406779\pi$
$59$	4.43498	0.577386	0.288693	+	0.957422i	$0.406779\pi$
$60$	−20.0742	−2.59156
$61$	−4.50628	−0.576971	−0.288485	−	0.957484i	$-0.593152\pi$
$61$	−4.50628	−0.576971	−0.288485	+	0.957484i	$0.593152\pi$
$62$	10.4631	1.32882
$63$	0	0
$64$	29.4893	3.68616
$65$	4.97228	0.616735
$66$	15.1652	1.86671
$67$	−9.88169	−1.20724	−0.603620	−	0.797272i	$-0.706276\pi$
$67$	−9.88169	−1.20724	−0.603620	+	0.797272i	$0.706276\pi$
$68$	29.0777	3.52619
$69$	6.55809	0.789501
$70$	0	0
$71$	3.25222	0.385968	0.192984	−	0.981202i	$-0.438183\pi$
$71$	3.25222	0.385968	0.192984	+	0.981202i	$0.438183\pi$
$72$	−9.43451	−1.11187
$73$	6.37270	0.745868	0.372934	−	0.927858i	$-0.378352\pi$
$73$	6.37270	0.745868	0.372934	+	0.927858i	$0.378352\pi$
$74$	−2.41210	−0.280400
$75$	8.54056	0.986179
$76$	17.0803	1.95924
$77$	0	0
$78$	3.68952	0.417756
$79$	4.67377	0.525840	0.262920	−	0.964818i	$-0.415314\pi$
$79$	4.67377	0.525840	0.262920	+	0.964818i	$0.415314\pi$
$80$	−54.6434	−6.10932
$81$	1.00000	0.111111
$82$	2.73044	0.301527
$83$	0.851113	0.0934218	0.0467109	−	0.998908i	$-0.485126\pi$
$83$	0.851113	0.0934218	0.0467109	+	0.998908i	$0.485126\pi$
$84$	0	0
$85$	−19.6137	−2.12740
$86$	10.3296	1.11387
$87$	−8.35577	−0.895833
$88$	52.4005	5.58591
$89$	9.60988	1.01865	0.509323	−	0.860576i	$-0.329896\pi$
$89$	9.60988	1.01865	0.509323	+	0.860576i	$0.329896\pi$
$90$	10.0473	1.05908
$91$	0	0
$92$	35.7764	3.72995
$93$	−3.83202	−0.397362
$94$	6.15889	0.635241
$95$	−11.5211	−1.18204
$96$	−21.6774	−2.21244
$97$	−13.7839	−1.39955	−0.699774	−	0.714364i	$-0.746716\pi$
$97$	−13.7839	−1.39955	−0.699774	+	0.714364i	$0.746716\pi$
$98$	0	0
$99$	−5.55413	−0.558211
$100$	46.5914	4.65914
$101$	2.22327	0.221224	0.110612	−	0.993864i	$-0.464719\pi$
$101$	2.22327	0.221224	0.110612	+	0.993864i	$0.464719\pi$
$102$	−14.5537	−1.44103
$103$	2.67624	0.263698	0.131849	−	0.991270i	$-0.457909\pi$
$103$	2.67624	0.263698	0.131849	+	0.991270i	$0.457909\pi$
$104$	12.7484	1.25009
$105$	0	0
$106$	−11.2945	−1.09702
$107$	9.72726	0.940370	0.470185	−	0.882568i	$-0.344187\pi$
$107$	9.72726	0.940370	0.470185	+	0.882568i	$0.344187\pi$
$108$	5.45531	0.524937
$109$	19.4402	1.86203	0.931015	−	0.364982i	$-0.118925\pi$
$109$	19.4402	1.86203	0.931015	+	0.364982i	$0.118925\pi$
$110$	−55.8042	−5.32072
$111$	0.883409	0.0838495
$112$	0	0
$113$	5.24038	0.492973	0.246487	−	0.969146i	$-0.420724\pi$
$113$	5.24038	0.492973	0.246487	+	0.969146i	$0.420724\pi$
$114$	−8.54886	−0.800674
$115$	−24.1321	−2.25033
$116$	−45.5833	−4.23230
$117$	−1.35125	−0.124923
$118$	−12.1095	−1.11477
$119$	0	0
$120$	34.7166	3.16918
$121$	19.8484	1.80440
$122$	12.3041	1.11396
$123$	−1.00000	−0.0901670
$124$	−20.9049	−1.87731
$125$	−13.0284	−1.16529
$126$	0	0
$127$	11.1551	0.989854	0.494927	−	0.868935i	$-0.335195\pi$
$127$	11.1551	0.989854	0.494927	+	0.868935i	$0.335195\pi$
$128$	−37.1640	−3.28486
$129$	−3.78313	−0.333086
$130$	−13.5765	−1.19074
$131$	−1.22298	−0.106853	−0.0534263	−	0.998572i	$-0.517014\pi$
$131$	−1.22298	−0.106853	−0.0534263	+	0.998572i	$0.517014\pi$
$132$	−30.2995	−2.63723
$133$	0	0
$134$	26.9814	2.33084
$135$	−3.67975	−0.316702
$136$	−50.2875	−4.31212
$137$	14.7954	1.26406	0.632029	−	0.774944i	$-0.282222\pi$
$137$	14.7954	1.26406	0.632029	+	0.774944i	$0.282222\pi$
$138$	−17.9065	−1.52430
$139$	5.54637	0.470437	0.235219	−	0.971942i	$-0.424419\pi$
$139$	5.54637	0.470437	0.235219	+	0.971942i	$0.424419\pi$
$140$	0	0
$141$	−2.25564	−0.189959
$142$	−8.88000	−0.745193
$143$	7.50504	0.627603
$144$	14.8498	1.23748
$145$	30.7471	2.55341
$146$	−17.4003	−1.44006
$147$	0	0
$148$	4.81927	0.396141
$149$	3.94934	0.323542	0.161771	−	0.986828i	$-0.448279\pi$
$149$	3.94934	0.323542	0.161771	+	0.986828i	$0.448279\pi$
$150$	−23.3195	−1.90403
$151$	16.4925	1.34214	0.671072	−	0.741393i	$-0.265834\pi$
$151$	16.4925	1.34214	0.671072	+	0.741393i	$0.265834\pi$
$152$	−29.5390	−2.39593
$153$	5.33017	0.430919
$154$	0	0
$155$	14.1009	1.13261
$156$	−7.37151	−0.590193
$157$	−11.0722	−0.883662	−0.441831	−	0.897098i	$-0.645671\pi$
$157$	−11.0722	−0.883662	−0.441831	+	0.897098i	$0.645671\pi$
$158$	−12.7614	−1.01525
$159$	4.13650	0.328046
$160$	79.7673	6.30616
$161$	0	0
$162$	−2.73044	−0.214524
$163$	−6.41011	−0.502079	−0.251039	−	0.967977i	$-0.580772\pi$
$163$	−6.41011	−0.502079	−0.251039	+	0.967977i	$0.580772\pi$
$164$	−5.45531	−0.425988
$165$	20.4378	1.59108
$166$	−2.32391	−0.180371
$167$	−9.75464	−0.754837	−0.377418	−	0.926043i	$-0.623188\pi$
$167$	−9.75464	−0.754837	−0.377418	+	0.926043i	$0.623188\pi$
$168$	0	0
$169$	−11.1741	−0.859547
$170$	53.5540	4.10741
$171$	3.13095	0.239429
$172$	−20.6381	−1.57364
$173$	−6.97623	−0.530393	−0.265197	−	0.964194i	$-0.585437\pi$
$173$	−6.97623	−0.530393	−0.265197	+	0.964194i	$0.585437\pi$
$174$	22.8149	1.72960
$175$	0	0
$176$	−82.4775	−6.21698
$177$	4.43498	0.333354
$178$	−26.2392	−1.96671
$179$	−2.84611	−0.212728	−0.106364	−	0.994327i	$-0.533921\pi$
$179$	−2.84611	−0.212728	−0.106364	+	0.994327i	$0.533921\pi$
$180$	−20.0742	−1.49624
$181$	−25.8260	−1.91963	−0.959814	−	0.280636i	$-0.909455\pi$
$181$	−25.8260	−1.91963	−0.959814	+	0.280636i	$0.909455\pi$
$182$	0	0
$183$	−4.50628	−0.333114
$184$	−61.8724	−4.56129
$185$	−3.25072	−0.238998
$186$	10.4631	0.767193
$187$	−29.6044	−2.16489
$188$	−12.3052	−0.897449
$189$	0	0
$190$	31.4577	2.28218
$191$	−21.6988	−1.57007	−0.785037	−	0.619449i	$-0.787356\pi$
$191$	−21.6988	−1.57007	−0.785037	+	0.619449i	$0.787356\pi$
$192$	29.4893	2.12820
$193$	3.38989	0.244009	0.122005	−	0.992530i	$-0.461068\pi$
$193$	3.38989	0.244009	0.122005	+	0.992530i	$0.461068\pi$
$194$	37.6363	2.70213
$195$	4.97228	0.356072
$196$	0	0
$197$	20.6945	1.47442	0.737211	−	0.675663i	$-0.236142\pi$
$197$	20.6945	1.47442	0.737211	+	0.675663i	$0.236142\pi$
$198$	15.1652	1.07775
$199$	23.0318	1.63268	0.816340	−	0.577572i	$-0.196000\pi$
$199$	23.0318	1.63268	0.816340	+	0.577572i	$0.196000\pi$
$200$	−80.5760	−5.69758
$201$	−9.88169	−0.697001
$202$	−6.07050	−0.427119
$203$	0	0
$204$	29.0777	2.03585
$205$	3.67975	0.257005
$206$	−7.30732	−0.509125
$207$	6.55809	0.455819
$208$	−20.0658	−1.39131
$209$	−17.3897	−1.20287
$210$	0	0
$211$	−1.90091	−0.130864	−0.0654322	−	0.997857i	$-0.520843\pi$
$211$	−1.90091	−0.130864	−0.0654322	+	0.997857i	$0.520843\pi$
$212$	22.5659	1.54983
$213$	3.25222	0.222839
$214$	−26.5597	−1.81558
$215$	13.9210	0.949403
$216$	−9.43451	−0.641937
$217$	0	0
$218$	−53.0802	−3.59504
$219$	6.37270	0.430627
$220$	111.495	7.51696
$221$	−7.20241	−0.484487
$222$	−2.41210	−0.161889
$223$	−20.1422	−1.34882	−0.674410	−	0.738357i	$-0.735602\pi$
$223$	−20.1422	−1.34882	−0.674410	+	0.738357i	$0.735602\pi$
$224$	0	0
$225$	8.54056	0.569371
$226$	−14.3085	−0.951790
$227$	12.3852	0.822032	0.411016	−	0.911628i	$-0.365174\pi$
$227$	12.3852	0.822032	0.411016	+	0.911628i	$0.365174\pi$
$228$	17.0803	1.13117
$229$	−22.6986	−1.49997	−0.749984	−	0.661456i	$-0.769939\pi$
$229$	−22.6986	−1.49997	−0.749984	+	0.661456i	$0.769939\pi$
$230$	65.8914	4.34475
$231$	0	0
$232$	78.8326	5.17562
$233$	−10.4318	−0.683409	−0.341704	−	0.939808i	$-0.611004\pi$
$233$	−10.4318	−0.683409	−0.341704	+	0.939808i	$0.611004\pi$
$234$	3.68952	0.241191
$235$	8.30019	0.541445
$236$	24.1942	1.57491
$237$	4.67377	0.303594
$238$	0	0
$239$	−18.7536	−1.21307	−0.606535	−	0.795057i	$-0.707441\pi$
$239$	−18.7536	−1.21307	−0.606535	+	0.795057i	$0.707441\pi$
$240$	−54.6434	−3.52722
$241$	19.4561	1.25327	0.626637	−	0.779311i	$-0.284431\pi$
$241$	19.4561	1.25327	0.626637	+	0.779311i	$0.284431\pi$
$242$	−54.1947	−3.48377
$243$	1.00000	0.0641500
$244$	−24.5832	−1.57378
$245$	0	0
$246$	2.73044	0.174087
$247$	−4.23070	−0.269193
$248$	36.1533	2.29573
$249$	0.851113	0.0539371
$250$	35.5732	2.24985
$251$	4.46572	0.281874	0.140937	−	0.990019i	$-0.454989\pi$
$251$	4.46572	0.281874	0.140937	+	0.990019i	$0.454989\pi$
$252$	0	0
$253$	−36.4245	−2.28999
$254$	−30.4583	−1.91112
$255$	−19.6137	−1.22826
$256$	42.4954	2.65596
$257$	−15.8522	−0.988830	−0.494415	−	0.869226i	$-0.664618\pi$
$257$	−15.8522	−0.988830	−0.494415	+	0.869226i	$0.664618\pi$
$258$	10.3296	0.643094
$259$	0	0
$260$	27.1253	1.68224
$261$	−8.35577	−0.517209
$262$	3.33929	0.206302
$263$	−17.0228	−1.04967	−0.524836	−	0.851203i	$-0.675873\pi$
$263$	−17.0228	−1.04967	−0.524836	+	0.851203i	$0.675873\pi$
$264$	52.4005	3.22503
$265$	−15.2213	−0.935037
$266$	0	0
$267$	9.60988	0.588115
$268$	−53.9077	−3.29294
$269$	−15.1029	−0.920838	−0.460419	−	0.887702i	$-0.652301\pi$
$269$	−15.1029	−0.920838	−0.460419	+	0.887702i	$0.652301\pi$
$270$	10.0473	0.611462
$271$	−14.8353	−0.901183	−0.450591	−	0.892730i	$-0.648787\pi$
$271$	−14.8353	−0.901183	−0.450591	+	0.892730i	$0.648787\pi$
$272$	79.1518	4.79928
$273$	0	0
$274$	−40.3980	−2.44054
$275$	−47.4354	−2.86046
$276$	35.7764	2.15349
$277$	−5.78658	−0.347682	−0.173841	−	0.984774i	$-0.555618\pi$
$277$	−5.78658	−0.347682	−0.173841	+	0.984774i	$0.555618\pi$
$278$	−15.1440	−0.908279
$279$	−3.83202	−0.229417
$280$	0	0
$281$	−10.7954	−0.644000	−0.322000	−	0.946740i	$-0.604355\pi$
$281$	−10.7954	−0.644000	−0.322000	+	0.946740i	$0.604355\pi$
$282$	6.15889	0.366757
$283$	−14.1172	−0.839178	−0.419589	−	0.907714i	$-0.637826\pi$
$283$	−14.1172	−0.839178	−0.419589	+	0.907714i	$0.637826\pi$
$284$	17.7419	1.05279
$285$	−11.5211	−0.682451
$286$	−20.4921	−1.21172
$287$	0	0
$288$	−21.6774	−1.27735
$289$	11.4107	0.671218
$290$	−83.9533	−4.92991
$291$	−13.7839	−0.808029
$292$	34.7650	2.03447
$293$	−31.9086	−1.86412	−0.932061	−	0.362300i	$-0.881991\pi$
$293$	−31.9086	−1.86412	−0.932061	+	0.362300i	$0.881991\pi$
$294$	0	0
$295$	−16.3196	−0.950166
$296$	−8.33453	−0.484435
$297$	−5.55413	−0.322283
$298$	−10.7834	−0.624668
$299$	−8.86165	−0.512482
$300$	46.5914	2.68995
$301$	0	0
$302$	−45.0319	−2.59129
$303$	2.22327	0.127723
$304$	46.4938	2.66660
$305$	16.5820	0.949483
$306$	−14.5537	−0.831980
$307$	−20.8950	−1.19254	−0.596271	−	0.802783i	$-0.703352\pi$
$307$	−20.8950	−1.19254	−0.596271	+	0.802783i	$0.703352\pi$
$308$	0	0
$309$	2.67624	0.152246
$310$	−38.5016	−2.18675
$311$	22.2101	1.25942	0.629709	−	0.776831i	$-0.283174\pi$
$311$	22.2101	1.25942	0.629709	+	0.776831i	$0.283174\pi$
$312$	12.7484	0.721737
$313$	7.85546	0.444017	0.222008	−	0.975045i	$-0.428739\pi$
$313$	7.85546	0.444017	0.222008	+	0.975045i	$0.428739\pi$
$314$	30.2321	1.70610
$315$	0	0
$316$	25.4968	1.43431
$317$	24.1210	1.35477	0.677386	−	0.735628i	$-0.263113\pi$
$317$	24.1210	1.35477	0.677386	+	0.735628i	$0.263113\pi$
$318$	−11.2945	−0.633363
$319$	46.4090	2.59841
$320$	−108.513	−6.06607
$321$	9.72726	0.542923
$322$	0	0
$323$	16.6885	0.928571
$324$	5.45531	0.303073
$325$	−11.5405	−0.640150
$326$	17.5024	0.969370
$327$	19.4402	1.07504
$328$	9.43451	0.520934
$329$	0	0
$330$	−55.8042	−3.07192
$331$	28.2994	1.55548	0.777738	−	0.628588i	$-0.216367\pi$
$331$	28.2994	1.55548	0.777738	+	0.628588i	$0.216367\pi$
$332$	4.64308	0.254822
$333$	0.883409	0.0484105
$334$	26.6345	1.45737
$335$	36.3622	1.98668
$336$	0	0
$337$	29.6052	1.61270	0.806348	−	0.591441i	$-0.201441\pi$
$337$	29.6052	1.61270	0.806348	+	0.591441i	$0.201441\pi$
$338$	30.5103	1.65954
$339$	5.24038	0.284618
$340$	−106.999	−5.80282
$341$	21.2835	1.15257
$342$	−8.54886	−0.462270
$343$	0	0
$344$	35.6920	1.92438
$345$	−24.1321	−1.29923
$346$	19.0482	1.02404
$347$	−8.17662	−0.438944	−0.219472	−	0.975619i	$-0.570433\pi$
$347$	−8.17662	−0.438944	−0.219472	+	0.975619i	$0.570433\pi$
$348$	−45.5833	−2.44352
$349$	−12.5666	−0.672675	−0.336338	−	0.941741i	$-0.609188\pi$
$349$	−12.5666	−0.672675	−0.336338	+	0.941741i	$0.609188\pi$
$350$	0	0
$351$	−1.35125	−0.0721246
$352$	120.399	6.41729
$353$	−26.5257	−1.41182	−0.705911	−	0.708301i	$-0.749462\pi$
$353$	−26.5257	−1.41182	−0.705911	+	0.708301i	$0.749462\pi$
$354$	−12.1095	−0.643611
$355$	−11.9674	−0.635162
$356$	52.4248	2.77851
$357$	0	0
$358$	7.77114	0.410717
$359$	21.3802	1.12841	0.564203	−	0.825636i	$-0.309184\pi$
$359$	21.3802	1.12841	0.564203	+	0.825636i	$0.309184\pi$
$360$	34.7166	1.82973
$361$	−9.19718	−0.484062
$362$	70.5163	3.70625
$363$	19.8484	1.04177
$364$	0	0
$365$	−23.4499	−1.22743
$366$	12.3041	0.643148
$367$	−18.2387	−0.952051	−0.476026	−	0.879431i	$-0.657923\pi$
$367$	−18.2387	−0.952051	−0.476026	+	0.879431i	$0.657923\pi$
$368$	97.3861	5.07660
$369$	−1.00000	−0.0520579
$370$	8.87591	0.461437
$371$	0	0
$372$	−20.9049	−1.08387
$373$	−20.4799	−1.06041	−0.530205	−	0.847870i	$-0.677885\pi$
$373$	−20.4799	−1.06041	−0.530205	+	0.847870i	$0.677885\pi$
$374$	80.8332	4.17978
$375$	−13.0284	−0.672782
$376$	21.2809	1.09748
$377$	11.2908	0.581504
$378$	0	0
$379$	−21.2995	−1.09408	−0.547040	−	0.837106i	$-0.684246\pi$
$379$	−21.2995	−1.09408	−0.547040	+	0.837106i	$0.684246\pi$
$380$	−62.8511	−3.22420
$381$	11.1551	0.571492
$382$	59.2474	3.03136
$383$	4.25583	0.217463	0.108731	−	0.994071i	$-0.465321\pi$
$383$	4.25583	0.217463	0.108731	+	0.994071i	$0.465321\pi$
$384$	−37.1640	−1.89652
$385$	0	0
$386$	−9.25589	−0.471112
$387$	−3.78313	−0.192307
$388$	−75.1957	−3.81748
$389$	1.64453	0.0833810	0.0416905	−	0.999131i	$-0.486726\pi$
$389$	1.64453	0.0833810	0.0416905	+	0.999131i	$0.486726\pi$
$390$	−13.5765	−0.687473
$391$	34.9557	1.76779
$392$	0	0
$393$	−1.22298	−0.0616914
$394$	−56.5051	−2.84669
$395$	−17.1983	−0.865340
$396$	−30.2995	−1.52261
$397$	−22.7752	−1.14306	−0.571528	−	0.820582i	$-0.693649\pi$
$397$	−22.7752	−1.14306	−0.571528	+	0.820582i	$0.693649\pi$
$398$	−62.8869	−3.15224
$399$	0	0
$400$	126.825	6.34126
$401$	−39.5907	−1.97706	−0.988532	−	0.151015i	$-0.951746\pi$
$401$	−39.5907	−1.97706	−0.988532	+	0.151015i	$0.951746\pi$
$402$	26.9814	1.34571
$403$	5.17804	0.257936
$404$	12.1286	0.603421
$405$	−3.67975	−0.182848
$406$	0	0
$407$	−4.90657	−0.243209
$408$	−50.2875	−2.48960
$409$	17.2670	0.853800	0.426900	−	0.904299i	$-0.359606\pi$
$409$	17.2670	0.853800	0.426900	+	0.904299i	$0.359606\pi$
$410$	−10.0473	−0.496203
$411$	14.7954	0.729805
$412$	14.5997	0.719277
$413$	0	0
$414$	−17.9065	−0.880055
$415$	−3.13188	−0.153738
$416$	29.2916	1.43614
$417$	5.54637	0.271607
$418$	47.4815	2.32240
$419$	25.4768	1.24462	0.622312	−	0.782769i	$-0.286193\pi$
$419$	25.4768	1.24462	0.622312	+	0.782769i	$0.286193\pi$
$420$	0	0
$421$	19.0527	0.928572	0.464286	−	0.885685i	$-0.346311\pi$
$421$	19.0527	0.928572	0.464286	+	0.885685i	$0.346311\pi$
$422$	5.19033	0.252662
$423$	−2.25564	−0.109673
$424$	−39.0259	−1.89526
$425$	45.5226	2.20817
$426$	−8.88000	−0.430237
$427$	0	0
$428$	53.0652	2.56500
$429$	7.50504	0.362347
$430$	−38.0104	−1.83302
$431$	−7.72119	−0.371917	−0.185958	−	0.982558i	$-0.559539\pi$
$431$	−7.72119	−0.371917	−0.185958	+	0.982558i	$0.559539\pi$
$432$	14.8498	0.714460
$433$	−20.3059	−0.975839	−0.487919	−	0.872889i	$-0.662244\pi$
$433$	−20.3059	−0.975839	−0.487919	+	0.872889i	$0.662244\pi$
$434$	0	0
$435$	30.7471	1.47421
$436$	106.052	5.07897
$437$	20.5330	0.982228
$438$	−17.4003	−0.831418
$439$	−14.4835	−0.691261	−0.345630	−	0.938371i	$-0.612335\pi$
$439$	−14.4835	−0.691261	−0.345630	+	0.938371i	$0.612335\pi$
$440$	−192.821	−9.19237
$441$	0	0
$442$	19.6658	0.935405
$443$	25.0987	1.19247	0.596237	−	0.802809i	$-0.296662\pi$
$443$	25.0987	1.19247	0.596237	+	0.802809i	$0.296662\pi$
$444$	4.81927	0.228712
$445$	−35.3620	−1.67632
$446$	54.9970	2.60418
$447$	3.94934	0.186797
$448$	0	0
$449$	25.3481	1.19625	0.598126	−	0.801402i	$-0.295912\pi$
$449$	25.3481	1.19625	0.598126	+	0.801402i	$0.295912\pi$
$450$	−23.3195	−1.09929
$451$	5.55413	0.261534
$452$	28.5879	1.34466
$453$	16.4925	0.774887
$454$	−33.8169	−1.58711
$455$	0	0
$456$	−29.5390	−1.38329
$457$	−16.3052	−0.762726	−0.381363	−	0.924425i	$-0.624545\pi$
$457$	−16.3052	−0.762726	−0.381363	+	0.924425i	$0.624545\pi$
$458$	61.9773	2.89601
$459$	5.33017	0.248791
$460$	−131.648	−6.13813
$461$	−2.12664	−0.0990473	−0.0495237	−	0.998773i	$-0.515770\pi$
$461$	−2.12664	−0.0990473	−0.0495237	+	0.998773i	$0.515770\pi$
$462$	0	0
$463$	−38.8841	−1.80710	−0.903549	−	0.428485i	$-0.859048\pi$
$463$	−38.8841	−1.80710	−0.903549	+	0.428485i	$0.859048\pi$
$464$	−124.081	−5.76033
$465$	14.1009	0.653913
$466$	28.4834	1.31947
$467$	−16.8086	−0.777809	−0.388904	−	0.921278i	$-0.627146\pi$
$467$	−16.8086	−0.777809	−0.388904	+	0.921278i	$0.627146\pi$
$468$	−7.37151	−0.340748
$469$	0	0
$470$	−22.6632	−1.04537
$471$	−11.0722	−0.510182
$472$	−41.8419	−1.92593
$473$	21.0120	0.966133
$474$	−12.7614	−0.586153
$475$	26.7400	1.22692
$476$	0	0
$477$	4.13650	0.189397
$478$	51.2056	2.34209
$479$	11.4663	0.523909	0.261954	−	0.965080i	$-0.415633\pi$
$479$	11.4663	0.523909	0.261954	+	0.965080i	$0.415633\pi$
$480$	79.7673	3.64086
$481$	−1.19371	−0.0544285
$482$	−53.1236	−2.41971
$483$	0	0
$484$	108.279	4.92177
$485$	50.7215	2.30314
$486$	−2.73044	−0.123855
$487$	−15.9414	−0.722373	−0.361187	−	0.932494i	$-0.617628\pi$
$487$	−15.9414	−0.722373	−0.361187	+	0.932494i	$0.617628\pi$
$488$	42.5146	1.92455
$489$	−6.41011	−0.289875
$490$	0	0
$491$	−16.1502	−0.728850	−0.364425	−	0.931233i	$-0.618734\pi$
$491$	−16.1502	−0.728850	−0.364425	+	0.931233i	$0.618734\pi$
$492$	−5.45531	−0.245944
$493$	−44.5377	−2.00588
$494$	11.5517	0.519735
$495$	20.4378	0.918611
$496$	−56.9046	−2.55509
$497$	0	0
$498$	−2.32391	−0.104137
$499$	7.64664	0.342311	0.171155	−	0.985244i	$-0.445250\pi$
$499$	7.64664	0.342311	0.171155	+	0.985244i	$0.445250\pi$
$500$	−71.0738	−3.17852
$501$	−9.75464	−0.435805
$502$	−12.1934	−0.544217
$503$	−27.8382	−1.24124	−0.620621	−	0.784111i	$-0.713120\pi$
$503$	−27.8382	−1.24124	−0.620621	+	0.784111i	$0.713120\pi$
$504$	0	0
$505$	−8.18107	−0.364053
$506$	99.4549	4.42131
$507$	−11.1741	−0.496260
$508$	60.8544	2.69998
$509$	−36.9734	−1.63882	−0.819408	−	0.573211i	$-0.805698\pi$
$509$	−36.9734	−1.63882	−0.819408	+	0.573211i	$0.805698\pi$
$510$	53.5540	2.37141
$511$	0	0
$512$	−41.7034	−1.84305
$513$	3.13095	0.138235
$514$	43.2834	1.90915
$515$	−9.84790	−0.433950
$516$	−20.6381	−0.908544
$517$	12.5281	0.550986
$518$	0	0
$519$	−6.97623	−0.306223
$520$	−46.9110	−2.05718
$521$	−4.43422	−0.194267	−0.0971333	−	0.995271i	$-0.530967\pi$
$521$	−4.43422	−0.194267	−0.0971333	+	0.995271i	$0.530967\pi$
$522$	22.8149	0.998583
$523$	−17.3405	−0.758246	−0.379123	−	0.925346i	$-0.623774\pi$
$523$	−17.3405	−0.758246	−0.379123	+	0.925346i	$0.623774\pi$
$524$	−6.67176	−0.291457
$525$	0	0
$526$	46.4798	2.02662
$527$	−20.4253	−0.889741
$528$	−82.4775	−3.58937
$529$	20.0086	0.869937
$530$	41.5608	1.80529
$531$	4.43498	0.192462
$532$	0	0
$533$	1.35125	0.0585293
$534$	−26.2392	−1.13548
$535$	−35.7939	−1.54750
$536$	93.2290	4.02688
$537$	−2.84611	−0.122819
$538$	41.2375	1.77787
$539$	0	0
$540$	−20.0742	−0.863855
$541$	−42.0364	−1.80728	−0.903642	−	0.428288i	$-0.859117\pi$
$541$	−42.0364	−1.80728	−0.903642	+	0.428288i	$0.859117\pi$
$542$	40.5070	1.73993
$543$	−25.8260	−1.10830
$544$	−115.544	−4.95391
$545$	−71.5349	−3.06422
$546$	0	0
$547$	12.9805	0.555004	0.277502	−	0.960725i	$-0.410493\pi$
$547$	12.9805	0.555004	0.277502	+	0.960725i	$0.410493\pi$
$548$	80.7136	3.44792
$549$	−4.50628	−0.192324
$550$	129.519	5.52273
$551$	−26.1615	−1.11452
$552$	−61.8724	−2.63346
$553$	0	0
$554$	15.7999	0.671275
$555$	−3.25072	−0.137986
$556$	30.2572	1.28319
$557$	4.30459	0.182391	0.0911957	−	0.995833i	$-0.470931\pi$
$557$	4.30459	0.182391	0.0911957	+	0.995833i	$0.470931\pi$
$558$	10.4631	0.442939
$559$	5.11197	0.216213
$560$	0	0
$561$	−29.6044	−1.24990
$562$	29.4762	1.24338
$563$	−20.1598	−0.849634	−0.424817	−	0.905279i	$-0.639662\pi$
$563$	−20.1598	−0.849634	−0.424817	+	0.905279i	$0.639662\pi$
$564$	−12.3052	−0.518143
$565$	−19.2833	−0.811254
$566$	38.5461	1.62021
$567$	0	0
$568$	−30.6831	−1.28744
$569$	−14.3572	−0.601887	−0.300943	−	0.953642i	$-0.597301\pi$
$569$	−14.3572	−0.601887	−0.300943	+	0.953642i	$0.597301\pi$
$570$	31.4577	1.31762
$571$	9.18316	0.384303	0.192152	−	0.981365i	$-0.438453\pi$
$571$	9.18316	0.384303	0.192152	+	0.981365i	$0.438453\pi$
$572$	40.9423	1.71188
$573$	−21.6988	−0.906482
$574$	0	0
$575$	56.0098	2.33577
$576$	29.4893	1.22872
$577$	17.0124	0.708235	0.354117	−	0.935201i	$-0.384781\pi$
$577$	17.0124	0.708235	0.354117	+	0.935201i	$0.384781\pi$
$578$	−31.1562	−1.29593
$579$	3.38989	0.140879
$580$	167.735	6.96482
$581$	0	0
$582$	37.6363	1.56007
$583$	−22.9747	−0.951513
$584$	−60.1233	−2.48792
$585$	4.97228	0.205578
$586$	87.1247	3.59909
$587$	−9.69119	−0.399998	−0.199999	−	0.979796i	$-0.564094\pi$
$587$	−9.69119	−0.399998	−0.199999	+	0.979796i	$0.564094\pi$
$588$	0	0
$589$	−11.9979	−0.494363
$590$	44.5598	1.83450
$591$	20.6945	0.851258
$592$	13.1184	0.539163
$593$	−5.02658	−0.206417	−0.103208	−	0.994660i	$-0.532911\pi$
$593$	−5.02658	−0.206417	−0.103208	+	0.994660i	$0.532911\pi$
$594$	15.1652	0.622237
$595$	0	0
$596$	21.5449	0.882512
$597$	23.0318	0.942628
$598$	24.1962	0.989456
$599$	2.15715	0.0881389	0.0440694	−	0.999028i	$-0.485968\pi$
$599$	2.15715	0.0881389	0.0440694	+	0.999028i	$0.485968\pi$
$600$	−80.5760	−3.28950
$601$	7.95644	0.324550	0.162275	−	0.986746i	$-0.448117\pi$
$601$	7.95644	0.324550	0.162275	+	0.986746i	$0.448117\pi$
$602$	0	0
$603$	−9.88169	−0.402414
$604$	89.9718	3.66090
$605$	−73.0370	−2.96937
$606$	−6.07050	−0.246597
$607$	44.2143	1.79460	0.897302	−	0.441418i	$-0.145524\pi$
$607$	44.2143	1.79460	0.897302	+	0.441418i	$0.145524\pi$
$608$	−67.8707	−2.75252
$609$	0	0
$610$	−45.2762	−1.83318
$611$	3.04794	0.123307
$612$	29.0777	1.17540
$613$	−4.98381	−0.201294	−0.100647	−	0.994922i	$-0.532091\pi$
$613$	−4.98381	−0.201294	−0.100647	+	0.994922i	$0.532091\pi$
$614$	57.0526	2.30246
$615$	3.67975	0.148382
$616$	0	0
$617$	−17.4210	−0.701344	−0.350672	−	0.936498i	$-0.614047\pi$
$617$	−17.4210	−0.701344	−0.350672	+	0.936498i	$0.614047\pi$
$618$	−7.30732	−0.293944
$619$	10.6621	0.428547	0.214274	−	0.976774i	$-0.431262\pi$
$619$	10.6621	0.428547	0.214274	+	0.976774i	$0.431262\pi$
$620$	76.9247	3.08937
$621$	6.55809	0.263167
$622$	−60.6433	−2.43158
$623$	0	0
$624$	−20.0658	−0.803275
$625$	5.23835	0.209534
$626$	−21.4489	−0.857269
$627$	−17.3897	−0.694477
$628$	−60.4025	−2.41032
$629$	4.70872	0.187749
$630$	0	0
$631$	−9.76022	−0.388548	−0.194274	−	0.980947i	$-0.562235\pi$
$631$	−9.76022	−0.388548	−0.194274	+	0.980947i	$0.562235\pi$
$632$	−44.0947	−1.75399
$633$	−1.90091	−0.0755546
$634$	−65.8611	−2.61568
$635$	−41.0479	−1.62894
$636$	22.5659	0.894796
$637$	0	0
$638$	−126.717	−5.01678
$639$	3.25222	0.128656
$640$	136.754	5.40568
$641$	−21.8459	−0.862863	−0.431431	−	0.902146i	$-0.641991\pi$
$641$	−21.8459	−0.862863	−0.431431	+	0.902146i	$0.641991\pi$
$642$	−26.5597	−1.04823
$643$	11.0414	0.435430	0.217715	−	0.976012i	$-0.430140\pi$
$643$	11.0414	0.435430	0.217715	+	0.976012i	$0.430140\pi$
$644$	0	0
$645$	13.9210	0.548138
$646$	−45.5669	−1.79281
$647$	−31.7070	−1.24653	−0.623266	−	0.782010i	$-0.714194\pi$
$647$	−31.7070	−1.24653	−0.623266	+	0.782010i	$0.714194\pi$
$648$	−9.43451	−0.370623
$649$	−24.6325	−0.966909
$650$	31.5106	1.23595
$651$	0	0
$652$	−34.9691	−1.36950
$653$	9.21123	0.360463	0.180232	−	0.983624i	$-0.442315\pi$
$653$	9.21123	0.360463	0.180232	+	0.983624i	$0.442315\pi$
$654$	−53.0802	−2.07560
$655$	4.50028	0.175840
$656$	−14.8498	−0.579786
$657$	6.37270	0.248623
$658$	0	0
$659$	0.175225	0.00682579	0.00341289	−	0.999994i	$-0.498914\pi$
$659$	0.175225	0.00682579	0.00341289	+	0.999994i	$0.498914\pi$
$660$	111.495	4.33992
$661$	3.12750	0.121646	0.0608229	−	0.998149i	$-0.480628\pi$
$661$	3.12750	0.121646	0.0608229	+	0.998149i	$0.480628\pi$
$662$	−77.2699	−3.00318
$663$	−7.20241	−0.279719
$664$	−8.02983	−0.311618
$665$	0	0
$666$	−2.41210	−0.0934668
$667$	−54.7979	−2.12178
$668$	−53.2145	−2.05893
$669$	−20.1422	−0.778742
$670$	−99.2847	−3.83570
$671$	25.0285	0.966214
$672$	0	0
$673$	−7.59268	−0.292676	−0.146338	−	0.989235i	$-0.546749\pi$
$673$	−7.59268	−0.292676	−0.146338	+	0.989235i	$0.546749\pi$
$674$	−80.8352	−3.11365
$675$	8.54056	0.328726
$676$	−60.9582	−2.34455
$677$	4.91162	0.188769	0.0943844	−	0.995536i	$-0.469912\pi$
$677$	4.91162	0.188769	0.0943844	+	0.995536i	$0.469912\pi$
$678$	−14.3085	−0.549516
$679$	0	0
$680$	185.046	7.09617
$681$	12.3852	0.474600
$682$	−58.1135	−2.22528
$683$	−17.7094	−0.677632	−0.338816	−	0.940853i	$-0.610026\pi$
$683$	−17.7094	−0.677632	−0.338816	+	0.940853i	$0.610026\pi$
$684$	17.0803	0.653081
$685$	−54.4435	−2.08018
$686$	0	0
$687$	−22.6986	−0.866007
$688$	−56.1786	−2.14179
$689$	−5.58947	−0.212942
$690$	65.8914	2.50844
$691$	−37.6487	−1.43223	−0.716113	−	0.697985i	$-0.754080\pi$
$691$	−37.6487	−1.43223	−0.716113	+	0.697985i	$0.754080\pi$
$692$	−38.0575	−1.44673
$693$	0	0
$694$	22.3258	0.847475
$695$	−20.4093	−0.774167
$696$	78.8326	2.98814
$697$	−5.33017	−0.201895
$698$	34.3124	1.29874
$699$	−10.4318	−0.394566
$700$	0	0
$701$	44.1615	1.66796	0.833979	−	0.551796i	$-0.186057\pi$
$701$	44.1615	1.66796	0.833979	+	0.551796i	$0.186057\pi$
$702$	3.68952	0.139252
$703$	2.76591	0.104318
$704$	−163.787	−6.17296
$705$	8.30019	0.312603
$706$	72.4269	2.72582
$707$	0	0
$708$	24.1942	0.909274
$709$	27.0428	1.01561	0.507806	−	0.861471i	$-0.330457\pi$
$709$	27.0428	1.01561	0.507806	+	0.861471i	$0.330457\pi$
$710$	32.6762	1.22632
$711$	4.67377	0.175280
$712$	−90.6645	−3.39780
$713$	−25.1308	−0.941154
$714$	0	0
$715$	−27.6167	−1.03280
$716$	−15.5264	−0.580249
$717$	−18.7536	−0.700367
$718$	−58.3774	−2.17863
$719$	−21.4573	−0.800223	−0.400112	−	0.916466i	$-0.631029\pi$
$719$	−21.4573	−0.800223	−0.400112	+	0.916466i	$0.631029\pi$
$720$	−54.6434	−2.03644
$721$	0	0
$722$	25.1123	0.934585
$723$	19.4561	0.723578
$724$	−140.889	−5.23608
$725$	−71.3630	−2.65035
$726$	−54.1947	−2.01136
$727$	31.0064	1.14996	0.574982	−	0.818166i	$-0.305009\pi$
$727$	31.0064	1.14996	0.574982	+	0.818166i	$0.305009\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	64.0287	2.36981
$731$	−20.1647	−0.745819
$732$	−24.5832	−0.908620
$733$	−33.7922	−1.24814	−0.624071	−	0.781368i	$-0.714522\pi$
$733$	−33.7922	−1.24814	−0.624071	+	0.781368i	$0.714522\pi$
$734$	49.7996	1.83814
$735$	0	0
$736$	−142.162	−5.24017
$737$	54.8842	2.02169
$738$	2.73044	0.100509
$739$	10.6144	0.390458	0.195229	−	0.980758i	$-0.437455\pi$
$739$	10.6144	0.390458	0.195229	+	0.980758i	$0.437455\pi$
$740$	−17.7337	−0.651904
$741$	−4.23070	−0.155419
$742$	0	0
$743$	−19.6192	−0.719759	−0.359879	−	0.932999i	$-0.617182\pi$
$743$	−19.6192	−0.719759	−0.359879	+	0.932999i	$0.617182\pi$
$744$	36.1533	1.32544
$745$	−14.5326	−0.532432
$746$	55.9192	2.04735
$747$	0.851113	0.0311406
$748$	−161.501	−5.90507
$749$	0	0
$750$	35.5732	1.29895
$751$	−7.30875	−0.266700	−0.133350	−	0.991069i	$-0.542573\pi$
$751$	−7.30875	−0.266700	−0.133350	+	0.991069i	$0.542573\pi$
$752$	−33.4957	−1.22146
$753$	4.46572	0.162740
$754$	−30.8288	−1.12272
$755$	−60.6884	−2.20868
$756$	0	0
$757$	26.3503	0.957719	0.478860	−	0.877891i	$-0.341050\pi$
$757$	26.3503	0.957719	0.478860	+	0.877891i	$0.341050\pi$
$758$	58.1570	2.11236
$759$	−36.4245	−1.32213
$760$	108.696	3.94282
$761$	22.3112	0.808779	0.404390	−	0.914587i	$-0.367484\pi$
$761$	22.3112	0.808779	0.404390	+	0.914587i	$0.367484\pi$
$762$	−30.4583	−1.10339
$763$	0	0
$764$	−118.374	−4.28262
$765$	−19.6137	−0.709134
$766$	−11.6203	−0.419858
$767$	−5.99279	−0.216387
$768$	42.4954	1.53342
$769$	54.2290	1.95555	0.977774	−	0.209663i	$-0.0672368\pi$
$769$	54.2290	1.95555	0.977774	+	0.209663i	$0.0672368\pi$
$770$	0	0
$771$	−15.8522	−0.570902
$772$	18.4929	0.665573
$773$	−34.4225	−1.23809	−0.619046	−	0.785354i	$-0.712481\pi$
$773$	−34.4225	−1.23809	−0.619046	+	0.785354i	$0.712481\pi$
$774$	10.3296	0.371290
$775$	−32.7276	−1.17561
$776$	130.045	4.66834
$777$	0	0
$778$	−4.49029	−0.160985
$779$	−3.13095	−0.112178
$780$	27.1253	0.971242
$781$	−18.0633	−0.646354
$782$	−95.4446	−3.41309
$783$	−8.35577	−0.298611
$784$	0	0
$785$	40.7431	1.45418
$786$	3.33929	0.119108
$787$	−27.4575	−0.978753	−0.489376	−	0.872073i	$-0.662776\pi$
$787$	−27.4575	−0.978753	−0.489376	+	0.872073i	$0.662776\pi$
$788$	112.895	4.02171
$789$	−17.0228	−0.606029
$790$	46.9589	1.67072
$791$	0	0
$792$	52.4005	1.86197
$793$	6.08914	0.216232
$794$	62.1865	2.20692
$795$	−15.2213	−0.539844
$796$	125.645	4.45338
$797$	−6.82635	−0.241802	−0.120901	−	0.992665i	$-0.538578\pi$
$797$	−6.82635	−0.241802	−0.120901	+	0.992665i	$0.538578\pi$
$798$	0	0
$799$	−12.0229	−0.425341
$800$	−185.137	−6.54558
$801$	9.60988	0.339548
$802$	108.100	3.81714
$803$	−35.3948	−1.24906
$804$	−53.9077	−1.90118
$805$	0	0
$806$	−14.1383	−0.498001
$807$	−15.1029	−0.531646
$808$	−20.9755	−0.737914
$809$	8.61638	0.302936	0.151468	−	0.988462i	$-0.451600\pi$
$809$	8.61638	0.302936	0.151468	+	0.988462i	$0.451600\pi$
$810$	10.0473	0.353028
$811$	1.71360	0.0601727	0.0300863	−	0.999547i	$-0.490422\pi$
$811$	1.71360	0.0601727	0.0300863	+	0.999547i	$0.490422\pi$
$812$	0	0
$813$	−14.8353	−0.520298
$814$	13.3971	0.469568
$815$	23.5876	0.826238
$816$	79.1518	2.77087
$817$	−11.8448	−0.414396
$818$	−47.1466	−1.64844
$819$	0	0
$820$	20.0742	0.701020
$821$	40.5547	1.41537	0.707685	−	0.706528i	$-0.249740\pi$
$821$	40.5547	1.41537	0.707685	+	0.706528i	$0.249740\pi$
$822$	−40.3980	−1.40904
$823$	−50.4076	−1.75710	−0.878550	−	0.477651i	$-0.841489\pi$
$823$	−50.4076	−1.75710	−0.878550	+	0.477651i	$0.841489\pi$
$824$	−25.2490	−0.879592
$825$	−47.4354	−1.65149
$826$	0	0
$827$	−55.9884	−1.94691	−0.973454	−	0.228883i	$-0.926493\pi$
$827$	−55.9884	−1.94691	−0.973454	+	0.228883i	$0.926493\pi$
$828$	35.7764	1.24332
$829$	35.2244	1.22339	0.611697	−	0.791092i	$-0.290487\pi$
$829$	35.2244	1.22339	0.611697	+	0.791092i	$0.290487\pi$
$830$	8.55142	0.296824
$831$	−5.78658	−0.200734
$832$	−39.8475	−1.38146
$833$	0	0
$834$	−15.1440	−0.524395
$835$	35.8946	1.24218
$836$	−94.8660	−3.28101
$837$	−3.83202	−0.132454
$838$	−69.5630	−2.40301
$839$	6.15670	0.212553	0.106276	−	0.994337i	$-0.466107\pi$
$839$	6.15670	0.212553	0.106276	+	0.994337i	$0.466107\pi$
$840$	0	0
$841$	40.8189	1.40755
$842$	−52.0223	−1.79281
$843$	−10.7954	−0.371814
$844$	−10.3701	−0.356953
$845$	41.1179	1.41450
$846$	6.15889	0.211747
$847$	0	0
$848$	61.4261	2.10938
$849$	−14.1172	−0.484500
$850$	−124.297	−4.26335
$851$	5.79348	0.198598
$852$	17.7419	0.607826
$853$	−31.1759	−1.06744	−0.533722	−	0.845660i	$-0.679207\pi$
$853$	−31.1759	−1.06744	−0.533722	+	0.845660i	$0.679207\pi$
$854$	0	0
$855$	−11.5211	−0.394013
$856$	−91.7720	−3.13670
$857$	−50.4433	−1.72311	−0.861555	−	0.507664i	$-0.830509\pi$
$857$	−50.4433	−1.72311	−0.861555	+	0.507664i	$0.830509\pi$
$858$	−20.4921	−0.699588
$859$	33.3703	1.13858	0.569290	−	0.822137i	$-0.307218\pi$
$859$	33.3703	1.13858	0.569290	+	0.822137i	$0.307218\pi$
$860$	75.9432	2.58964
$861$	0	0
$862$	21.0823	0.718064
$863$	−16.6210	−0.565786	−0.282893	−	0.959151i	$-0.591294\pi$
$863$	−16.6210	−0.565786	−0.282893	+	0.959151i	$0.591294\pi$
$864$	−21.6774	−0.737479
$865$	25.6708	0.872833
$866$	55.4440	1.88406
$867$	11.4107	0.387528
$868$	0	0
$869$	−25.9587	−0.880589
$870$	−83.9533	−2.84628
$871$	13.3527	0.452438
$872$	−183.408	−6.21099
$873$	−13.7839	−0.466516
$874$	−56.0642	−1.89640
$875$	0	0
$876$	34.7650	1.17460
$877$	−19.4275	−0.656020	−0.328010	−	0.944674i	$-0.606378\pi$
$877$	−19.4275	−0.656020	−0.328010	+	0.944674i	$0.606378\pi$
$878$	39.5464	1.33463
$879$	−31.9086	−1.07625
$880$	303.497	10.2309
$881$	24.7456	0.833702	0.416851	−	0.908975i	$-0.363134\pi$
$881$	24.7456	0.833702	0.416851	+	0.908975i	$0.363134\pi$
$882$	0	0
$883$	−9.21151	−0.309992	−0.154996	−	0.987915i	$-0.549536\pi$
$883$	−9.21151	−0.309992	−0.154996	+	0.987915i	$0.549536\pi$
$884$	−39.2914	−1.32151
$885$	−16.3196	−0.548578
$886$	−68.5304	−2.30232
$887$	27.3860	0.919532	0.459766	−	0.888040i	$-0.347933\pi$
$887$	27.3860	0.919532	0.459766	+	0.888040i	$0.347933\pi$
$888$	−8.33453	−0.279689
$889$	0	0
$890$	96.5537	3.23649
$891$	−5.55413	−0.186070
$892$	−109.882	−3.67911
$893$	−7.06229	−0.236330
$894$	−10.7834	−0.360652
$895$	10.4730	0.350073
$896$	0	0
$897$	−8.86165	−0.295882
$898$	−69.2116	−2.30962
$899$	32.0195	1.06791
$900$	46.5914	1.55305
$901$	22.0483	0.734534
$902$	−15.1652	−0.504947
$903$	0	0
$904$	−49.4404	−1.64436
$905$	95.0331	3.15901
$906$	−45.0319	−1.49608
$907$	1.19783	0.0397734	0.0198867	−	0.999802i	$-0.493669\pi$
$907$	1.19783	0.0397734	0.0198867	+	0.999802i	$0.493669\pi$
$908$	67.5648	2.24222
$909$	2.22327	0.0737412
$910$	0	0
$911$	−52.9657	−1.75483	−0.877416	−	0.479730i	$-0.840734\pi$
$911$	−52.9657	−1.75483	−0.877416	+	0.479730i	$0.840734\pi$
$912$	46.4938	1.53956
$913$	−4.72719	−0.156447
$914$	44.5204	1.47260
$915$	16.5820	0.548184
$916$	−123.828	−4.09139
$917$	0	0
$918$	−14.5537	−0.480344
$919$	24.4543	0.806672	0.403336	−	0.915052i	$-0.367851\pi$
$919$	24.4543	0.806672	0.403336	+	0.915052i	$0.367851\pi$
$920$	227.675	7.50622
$921$	−20.8950	−0.688514
$922$	5.80665	0.191232
$923$	−4.39458	−0.144649
$924$	0	0
$925$	7.54480	0.248072
$926$	106.171	3.48899
$927$	2.67624	0.0878993
$928$	181.131	5.94592
$929$	3.18991	0.104657	0.0523287	−	0.998630i	$-0.483336\pi$
$929$	3.18991	0.104657	0.0523287	+	0.998630i	$0.483336\pi$
$930$	−38.5016	−1.26252
$931$	0	0
$932$	−56.9086	−1.86410
$933$	22.2101	0.727126
$934$	45.8949	1.50173
$935$	108.937	3.56262
$936$	12.7484	0.416695
$937$	22.6297	0.739279	0.369640	−	0.929175i	$-0.379481\pi$
$937$	22.6297	0.739279	0.369640	+	0.929175i	$0.379481\pi$
$938$	0	0
$939$	7.85546	0.256353
$940$	45.2801	1.47687
$941$	−24.5821	−0.801353	−0.400677	−	0.916220i	$-0.631225\pi$
$941$	−24.5821	−0.801353	−0.400677	+	0.916220i	$0.631225\pi$
$942$	30.2321	0.985016
$943$	−6.55809	−0.213561
$944$	65.8585	2.14351
$945$	0	0
$946$	−57.3720	−1.86533
$947$	56.2875	1.82910	0.914550	−	0.404474i	$-0.132545\pi$
$947$	56.2875	1.82910	0.914550	+	0.404474i	$0.132545\pi$
$948$	25.4968	0.828099
$949$	−8.61114	−0.279529
$950$	−73.0121	−2.36882
$951$	24.1210	0.782178
$952$	0	0
$953$	41.0106	1.32847	0.664233	−	0.747526i	$-0.268758\pi$
$953$	41.0106	1.32847	0.664233	+	0.747526i	$0.268758\pi$
$954$	−11.2945	−0.365672
$955$	79.8463	2.58377
$956$	−102.307	−3.30884
$957$	46.4090	1.50019
$958$	−31.3081	−1.01152
$959$	0	0
$960$	−108.513	−3.50225
$961$	−16.3156	−0.526310
$962$	3.25935	0.105086
$963$	9.72726	0.313457
$964$	106.139	3.41850
$965$	−12.4739	−0.401550
$966$	0	0
$967$	5.56198	0.178861	0.0894306	−	0.995993i	$-0.471495\pi$
$967$	5.56198	0.178861	0.0894306	+	0.995993i	$0.471495\pi$
$968$	−187.260	−6.01875
$969$	16.6885	0.536111
$970$	−138.492	−4.44671
$971$	4.71602	0.151344	0.0756722	−	0.997133i	$-0.475890\pi$
$971$	4.71602	0.151344	0.0756722	+	0.997133i	$0.475890\pi$
$972$	5.45531	0.174979
$973$	0	0
$974$	43.5270	1.39470
$975$	−11.5405	−0.369591
$976$	−66.9173	−2.14197
$977$	−17.3670	−0.555620	−0.277810	−	0.960636i	$-0.589609\pi$
$977$	−17.3670	−0.555620	−0.277810	+	0.960636i	$0.589609\pi$
$978$	17.5024	0.559666
$979$	−53.3745	−1.70586
$980$	0	0
$981$	19.4402	0.620676
$982$	44.0972	1.40720
$983$	−1.97887	−0.0631162	−0.0315581	−	0.999502i	$-0.510047\pi$
$983$	−1.97887	−0.0631162	−0.0315581	+	0.999502i	$0.510047\pi$
$984$	9.43451	0.300761
$985$	−76.1506	−2.42636
$986$	121.607	3.87277
$987$	0	0
$988$	−23.0798	−0.734266
$989$	−24.8101	−0.788916
$990$	−55.8042	−1.77357
$991$	2.04528	0.0649704	0.0324852	−	0.999472i	$-0.489658\pi$
$991$	2.04528	0.0649704	0.0324852	+	0.999472i	$0.489658\pi$
$992$	83.0682	2.63742
$993$	28.2994	0.898055
$994$	0	0
$995$	−84.7512	−2.68679
$996$	4.64308	0.147122
$997$	−40.9434	−1.29669	−0.648345	−	0.761346i	$-0.724539\pi$
$997$	−40.9434	−1.29669	−0.648345	+	0.761346i	$0.724539\pi$
$998$	−20.8787	−0.660904
$999$	0.883409	0.0279498

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.bk.1.1		14
7.3	odd	6		861.2.i.g.247.14	✓	28
7.5	odd	6		861.2.i.g.739.14	yes	28
7.6	odd	2		6027.2.a.bj.1.1		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
861.2.i.g.247.14	✓	28	7.3	odd	6
861.2.i.g.739.14	yes	28	7.5	odd	6
6027.2.a.bj.1.1		14	7.6	odd	2
6027.2.a.bk.1.1		14	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)

\(f(q)\)	\(=\)	\(q-2.73044 q^{2} +1.00000 q^{3} +5.45531 q^{4} -3.67975 q^{5} -2.73044 q^{6} -9.43451 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.73044 q^{2} +1.00000 q^{3} +5.45531 q^{4} -3.67975 q^{5} -2.73044 q^{6} -9.43451 q^{8} +1.00000 q^{9} +10.0473 q^{10} -5.55413 q^{11} +5.45531 q^{12} -1.35125 q^{13} -3.67975 q^{15} +14.8498 q^{16} +5.33017 q^{17} -2.73044 q^{18} +3.13095 q^{19} -20.0742 q^{20} +15.1652 q^{22} +6.55809 q^{23} -9.43451 q^{24} +8.54056 q^{25} +3.68952 q^{26} +1.00000 q^{27} -8.35577 q^{29} +10.0473 q^{30} -3.83202 q^{31} -21.6774 q^{32} -5.55413 q^{33} -14.5537 q^{34} +5.45531 q^{36} +0.883409 q^{37} -8.54886 q^{38} -1.35125 q^{39} +34.7166 q^{40} -1.00000 q^{41} -3.78313 q^{43} -30.2995 q^{44} -3.67975 q^{45} -17.9065 q^{46} -2.25564 q^{47} +14.8498 q^{48} -23.3195 q^{50} +5.33017 q^{51} -7.37151 q^{52} +4.13650 q^{53} -2.73044 q^{54} +20.4378 q^{55} +3.13095 q^{57} +22.8149 q^{58} +4.43498 q^{59} -20.0742 q^{60} -4.50628 q^{61} +10.4631 q^{62} +29.4893 q^{64} +4.97228 q^{65} +15.1652 q^{66} -9.88169 q^{67} +29.0777 q^{68} +6.55809 q^{69} +3.25222 q^{71} -9.43451 q^{72} +6.37270 q^{73} -2.41210 q^{74} +8.54056 q^{75} +17.0803 q^{76} +3.68952 q^{78} +4.67377 q^{79} -54.6434 q^{80} +1.00000 q^{81} +2.73044 q^{82} +0.851113 q^{83} -19.6137 q^{85} +10.3296 q^{86} -8.35577 q^{87} +52.4005 q^{88} +9.60988 q^{89} +10.0473 q^{90} +35.7764 q^{92} -3.83202 q^{93} +6.15889 q^{94} -11.5211 q^{95} -21.6774 q^{96} -13.7839 q^{97} -5.55413 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 2 q^{2} + 14 q^{3} + 14 q^{4} - 10 q^{5} - 2 q^{6} - 6 q^{8} + 14 q^{9}+O(q^{10}) \) 14 * q - 2 * q^2 + 14 * q^3 + 14 * q^4 - 10 * q^5 - 2 * q^6 - 6 * q^8 + 14 * q^9	\( 14 q - 2 q^{2} + 14 q^{3} + 14 q^{4} - 10 q^{5} - 2 q^{6} - 6 q^{8} + 14 q^{9} - 3 q^{10} - 16 q^{11} + 14 q^{12} - 21 q^{13} - 10 q^{15} + 22 q^{16} - 12 q^{17} - 2 q^{18} - 2 q^{19} - 40 q^{20} + q^{22} - 7 q^{23} - 6 q^{24} + 22 q^{25} - 2 q^{26} + 14 q^{27} - 16 q^{29} - 3 q^{30} - 8 q^{31} - 19 q^{32} - 16 q^{33} - 33 q^{34} + 14 q^{36} + q^{37} - 32 q^{38} - 21 q^{39} + 13 q^{40} - 14 q^{41} + 14 q^{43} - 36 q^{44} - 10 q^{45} - 12 q^{46} - 12 q^{47} + 22 q^{48} - q^{50} - 12 q^{51} - 60 q^{52} - 20 q^{53} - 2 q^{54} + 11 q^{55} - 2 q^{57} + 21 q^{58} - 25 q^{59} - 40 q^{60} - 26 q^{61} + 33 q^{62} + 42 q^{64} - 8 q^{65} + q^{66} - 22 q^{67} - 15 q^{68} - 7 q^{69} - 36 q^{71} - 6 q^{72} - 31 q^{73} - 65 q^{74} + 22 q^{75} + 2 q^{76} - 2 q^{78} + 12 q^{79} - 112 q^{80} + 14 q^{81} + 2 q^{82} - 20 q^{83} + 40 q^{85} - 9 q^{86} - 16 q^{87} - 54 q^{88} - 39 q^{89} - 3 q^{90} + 63 q^{92} - 8 q^{93} - 14 q^{94} - 55 q^{95} - 19 q^{96} - 18 q^{97} - 16 q^{99}+O(q^{100}) \) 14 * q - 2 * q^2 + 14 * q^3 + 14 * q^4 - 10 * q^5 - 2 * q^6 - 6 * q^8 + 14 * q^9 - 3 * q^10 - 16 * q^11 + 14 * q^12 - 21 * q^13 - 10 * q^15 + 22 * q^16 - 12 * q^17 - 2 * q^18 - 2 * q^19 - 40 * q^20 + q^22 - 7 * q^23 - 6 * q^24 + 22 * q^25 - 2 * q^26 + 14 * q^27 - 16 * q^29 - 3 * q^30 - 8 * q^31 - 19 * q^32 - 16 * q^33 - 33 * q^34 + 14 * q^36 + q^37 - 32 * q^38 - 21 * q^39 + 13 * q^40 - 14 * q^41 + 14 * q^43 - 36 * q^44 - 10 * q^45 - 12 * q^46 - 12 * q^47 + 22 * q^48 - q^50 - 12 * q^51 - 60 * q^52 - 20 * q^53 - 2 * q^54 + 11 * q^55 - 2 * q^57 + 21 * q^58 - 25 * q^59 - 40 * q^60 - 26 * q^61 + 33 * q^62 + 42 * q^64 - 8 * q^65 + q^66 - 22 * q^67 - 15 * q^68 - 7 * q^69 - 36 * q^71 - 6 * q^72 - 31 * q^73 - 65 * q^74 + 22 * q^75 + 2 * q^76 - 2 * q^78 + 12 * q^79 - 112 * q^80 + 14 * q^81 + 2 * q^82 - 20 * q^83 + 40 * q^85 - 9 * q^86 - 16 * q^87 - 54 * q^88 - 39 * q^89 - 3 * q^90 + 63 * q^92 - 8 * q^93 - 14 * q^94 - 55 * q^95 - 19 * q^96 - 18 * q^97 - 16 * q^99

Introduction

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Modular forms

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