LMFDB - Embedded newform 7942.2.a.bj.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7942,2,Mod(1,7942)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7942, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("7942.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7942 = 2 \cdot 11 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7942.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:	$63.4171892853$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.1940.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 8x - 2 $ x^3 - 8*x - 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 418)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.94600$ of defining polynomial
Character	$\chi$	$=$	7942.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +2.94600 q^{3} +1.00000 q^{4} +2.00000 q^{5} +2.94600 q^{6} +4.94600 q^{7} +1.00000 q^{8} +5.67889 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.94600 q^{3} +1.00000 q^{4} +2.00000 q^{5} +2.94600 q^{6} +4.94600 q^{7} +1.00000 q^{8} +5.67889 q^{9} +2.00000 q^{10} +1.00000 q^{11} +2.94600 q^{12} -5.67889 q^{13} +4.94600 q^{14} +5.89199 q^{15} +1.00000 q^{16} +3.73289 q^{17} +5.67889 q^{18} +2.00000 q^{20} +14.5709 q^{21} +1.00000 q^{22} -1.89199 q^{23} +2.94600 q^{24} -1.00000 q^{25} -5.67889 q^{26} +7.89199 q^{27} +4.94600 q^{28} +1.00000 q^{29} +5.89199 q^{30} -3.21310 q^{31} +1.00000 q^{32} +2.94600 q^{33} +3.73289 q^{34} +9.89199 q^{35} +5.67889 q^{36} +4.15910 q^{37} -16.7300 q^{39} +2.00000 q^{40} -9.62488 q^{41} +14.5709 q^{42} -4.62488 q^{43} +1.00000 q^{44} +11.3578 q^{45} -1.89199 q^{46} -7.41178 q^{47} +2.94600 q^{48} +17.4629 q^{49} -1.00000 q^{50} +10.9971 q^{51} -5.67889 q^{52} -11.7840 q^{53} +7.89199 q^{54} +2.00000 q^{55} +4.94600 q^{56} +1.00000 q^{58} +5.89199 q^{60} -5.57088 q^{61} -3.21310 q^{62} +28.0878 q^{63} +1.00000 q^{64} -11.3578 q^{65} +2.94600 q^{66} -8.83799 q^{67} +3.73289 q^{68} -5.57379 q^{69} +9.89199 q^{70} -4.62488 q^{71} +5.67889 q^{72} -3.62488 q^{73} +4.15910 q^{74} -2.94600 q^{75} +4.94600 q^{77} -16.7300 q^{78} +6.83799 q^{79} +2.00000 q^{80} +6.21310 q^{81} -9.62488 q^{82} +14.5169 q^{83} +14.5709 q^{84} +7.46579 q^{85} -4.62488 q^{86} +2.94600 q^{87} +1.00000 q^{88} +0.465785 q^{89} +11.3578 q^{90} -28.0878 q^{91} -1.89199 q^{92} -9.46579 q^{93} -7.41178 q^{94} +2.94600 q^{96} +1.53421 q^{97} +17.4629 q^{98} +5.67889 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} + 3 q^{4} + 6 q^{5} + 6 q^{7} + 3 q^{8} + 7 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 + 3 * q^4 + 6 * q^5 + 6 * q^7 + 3 * q^8 + 7 * q^9	$ 3 q + 3 q^{2} + 3 q^{4} + 6 q^{5} + 6 q^{7} + 3 q^{8} + 7 q^{9} + 6 q^{10} + 3 q^{11} - 7 q^{13} + 6 q^{14} + 3 q^{16} + 10 q^{17} + 7 q^{18} + 6 q^{20} + 16 q^{21} + 3 q^{22} + 12 q^{23} - 3 q^{25} - 7 q^{26} + 6 q^{27} + 6 q^{28} + 3 q^{29} - 2 q^{31} + 3 q^{32} + 10 q^{34} + 12 q^{35} + 7 q^{36} - 4 q^{37} - 6 q^{39} + 6 q^{40} - 10 q^{41} + 16 q^{42} + 5 q^{43} + 3 q^{44} + 14 q^{45} + 12 q^{46} - 11 q^{47} + 7 q^{49} - 3 q^{50} - 10 q^{51} - 7 q^{52} + 6 q^{54} + 6 q^{55} + 6 q^{56} + 3 q^{58} + 11 q^{61} - 2 q^{62} + 20 q^{63} + 3 q^{64} - 14 q^{65} + 10 q^{68} - 32 q^{69} + 12 q^{70} + 5 q^{71} + 7 q^{72} + 8 q^{73} - 4 q^{74} + 6 q^{77} - 6 q^{78} - 6 q^{79} + 6 q^{80} + 11 q^{81} - 10 q^{82} + 7 q^{83} + 16 q^{84} + 20 q^{85} + 5 q^{86} + 3 q^{88} - q^{89} + 14 q^{90} - 20 q^{91} + 12 q^{92} - 26 q^{93} - 11 q^{94} + 7 q^{97} + 7 q^{98} + 7 q^{99}+O(q^{100}) $ 3 * q + 3 * q^2 + 3 * q^4 + 6 * q^5 + 6 * q^7 + 3 * q^8 + 7 * q^9 + 6 * q^10 + 3 * q^11 - 7 * q^13 + 6 * q^14 + 3 * q^16 + 10 * q^17 + 7 * q^18 + 6 * q^20 + 16 * q^21 + 3 * q^22 + 12 * q^23 - 3 * q^25 - 7 * q^26 + 6 * q^27 + 6 * q^28 + 3 * q^29 - 2 * q^31 + 3 * q^32 + 10 * q^34 + 12 * q^35 + 7 * q^36 - 4 * q^37 - 6 * q^39 + 6 * q^40 - 10 * q^41 + 16 * q^42 + 5 * q^43 + 3 * q^44 + 14 * q^45 + 12 * q^46 - 11 * q^47 + 7 * q^49 - 3 * q^50 - 10 * q^51 - 7 * q^52 + 6 * q^54 + 6 * q^55 + 6 * q^56 + 3 * q^58 + 11 * q^61 - 2 * q^62 + 20 * q^63 + 3 * q^64 - 14 * q^65 + 10 * q^68 - 32 * q^69 + 12 * q^70 + 5 * q^71 + 7 * q^72 + 8 * q^73 - 4 * q^74 + 6 * q^77 - 6 * q^78 - 6 * q^79 + 6 * q^80 + 11 * q^81 - 10 * q^82 + 7 * q^83 + 16 * q^84 + 20 * q^85 + 5 * q^86 + 3 * q^88 - q^89 + 14 * q^90 - 20 * q^91 + 12 * q^92 - 26 * q^93 - 11 * q^94 + 7 * q^97 + 7 * q^98 + 7 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	2.94600	1.70087	0.850436	−	0.526079i	$-0.176338\pi$
$3$	2.94600	1.70087	0.850436	+	0.526079i	$0.176338\pi$
$4$	1.00000	0.500000
$5$	2.00000	0.894427	0.447214	−	0.894427i	$-0.352416\pi$
$5$	2.00000	0.894427	0.447214	+	0.894427i	$0.352416\pi$
$6$	2.94600	1.20270
$7$	4.94600	1.86941	0.934705	−	0.355424i	$-0.115663\pi$
$7$	4.94600	1.86941	0.934705	+	0.355424i	$0.115663\pi$
$8$	1.00000	0.353553
$9$	5.67889	1.89296
$10$	2.00000	0.632456
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	2.94600	0.850436
$13$	−5.67889	−1.57504	−0.787520	−	0.616289i	$-0.788635\pi$
$13$	−5.67889	−1.57504	−0.787520	+	0.616289i	$0.788635\pi$
$14$	4.94600	1.32187
$15$	5.89199	1.52131
$16$	1.00000	0.250000
$17$	3.73289	0.905359	0.452680	−	0.891673i	$-0.350468\pi$
$17$	3.73289	0.905359	0.452680	+	0.891673i	$0.350468\pi$
$18$	5.67889	1.33853
$19$	0	0
$19$	0	0
$20$	2.00000	0.447214
$21$	14.5709	3.17963
$22$	1.00000	0.213201
$23$	−1.89199	−0.394507	−0.197254	−	0.980352i	$-0.563202\pi$
$23$	−1.89199	−0.394507	−0.197254	+	0.980352i	$0.563202\pi$
$24$	2.94600	0.601349
$25$	−1.00000	−0.200000
$26$	−5.67889	−1.11372
$27$	7.89199	1.51881
$28$	4.94600	0.934705
$29$	1.00000	0.185695	0.0928477	−	0.995680i	$-0.470403\pi$
$29$	1.00000	0.185695	0.0928477	+	0.995680i	$0.470403\pi$
$30$	5.89199	1.07573
$31$	−3.21310	−0.577090	−0.288545	−	0.957466i	$-0.593172\pi$
$31$	−3.21310	−0.577090	−0.288545	+	0.957466i	$0.593172\pi$
$32$	1.00000	0.176777
$33$	2.94600	0.512832
$34$	3.73289	0.640186
$35$	9.89199	1.67205
$36$	5.67889	0.946481
$37$	4.15910	0.683751	0.341876	−	0.939745i	$-0.388938\pi$
$37$	4.15910	0.683751	0.341876	+	0.939745i	$0.388938\pi$
$38$	0	0
$39$	−16.7300	−2.67894
$40$	2.00000	0.316228
$41$	−9.62488	−1.50315	−0.751577	−	0.659645i	$-0.770707\pi$
$41$	−9.62488	−1.50315	−0.751577	+	0.659645i	$0.770707\pi$
$42$	14.5709	2.24834
$43$	−4.62488	−0.705288	−0.352644	−	0.935758i	$-0.614717\pi$
$43$	−4.62488	−0.705288	−0.352644	+	0.935758i	$0.614717\pi$
$44$	1.00000	0.150756
$45$	11.3578	1.69312
$46$	−1.89199	−0.278959
$47$	−7.41178	−1.08112	−0.540560	−	0.841306i	$-0.681787\pi$
$47$	−7.41178	−1.08112	−0.540560	+	0.841306i	$0.681787\pi$
$48$	2.94600	0.425218
$49$	17.4629	2.49470
$50$	−1.00000	−0.141421
$51$	10.9971	1.53990
$52$	−5.67889	−0.787520
$53$	−11.7840	−1.61865	−0.809327	−	0.587358i	$-0.800168\pi$
$53$	−11.7840	−1.61865	−0.809327	+	0.587358i	$0.800168\pi$
$54$	7.89199	1.07396
$55$	2.00000	0.269680
$56$	4.94600	0.660936
$57$	0	0
$58$	1.00000	0.131306
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	5.89199	0.760653
$61$	−5.57088	−0.713278	−0.356639	−	0.934242i	$-0.616077\pi$
$61$	−5.57088	−0.713278	−0.356639	+	0.934242i	$0.616077\pi$
$62$	−3.21310	−0.408064
$63$	28.0878	3.53872
$64$	1.00000	0.125000
$65$	−11.3578	−1.40876
$66$	2.94600	0.362627
$67$	−8.83799	−1.07973	−0.539866	−	0.841751i	$-0.681525\pi$
$67$	−8.83799	−1.07973	−0.539866	+	0.841751i	$0.681525\pi$
$68$	3.73289	0.452680
$69$	−5.57379	−0.671006
$70$	9.89199	1.18232
$71$	−4.62488	−0.548873	−0.274436	−	0.961605i	$-0.588491\pi$
$71$	−4.62488	−0.548873	−0.274436	+	0.961605i	$0.588491\pi$
$72$	5.67889	0.669263
$73$	−3.62488	−0.424260	−0.212130	−	0.977241i	$-0.568040\pi$
$73$	−3.62488	−0.424260	−0.212130	+	0.977241i	$0.568040\pi$
$74$	4.15910	0.483485
$75$	−2.94600	−0.340174
$76$	0	0
$77$	4.94600	0.563648
$78$	−16.7300	−1.89430
$79$	6.83799	0.769333	0.384667	−	0.923056i	$-0.374316\pi$
$79$	6.83799	0.769333	0.384667	+	0.923056i	$0.374316\pi$
$80$	2.00000	0.223607
$81$	6.21310	0.690345
$82$	−9.62488	−1.06289
$83$	14.5169	1.59343	0.796717	−	0.604353i	$-0.206568\pi$
$83$	14.5169	1.59343	0.796717	+	0.604353i	$0.206568\pi$
$84$	14.5709	1.58981
$85$	7.46579	0.809778
$86$	−4.62488	−0.498714
$87$	2.94600	0.315844
$88$	1.00000	0.106600
$89$	0.465785	0.0493731	0.0246866	−	0.999695i	$-0.492141\pi$
$89$	0.465785	0.0493731	0.0246866	+	0.999695i	$0.492141\pi$
$90$	11.3578	1.19721
$91$	−28.0878	−2.94440
$92$	−1.89199	−0.197254
$93$	−9.46579	−0.981556
$94$	−7.41178	−0.764467
$95$	0	0
$96$	2.94600	0.300674
$97$	1.53421	0.155776	0.0778880	−	0.996962i	$-0.475182\pi$
$97$	1.53421	0.155776	0.0778880	+	0.996962i	$0.475182\pi$
$98$	17.4629	1.76402
$99$	5.67889	0.570750
$100$	−1.00000	−0.100000
$101$	−1.67889	−0.167056	−0.0835278	−	0.996505i	$-0.526619\pi$
$101$	−1.67889	−0.167056	−0.0835278	+	0.996505i	$0.526619\pi$
$102$	10.9971	1.08887
$103$	7.41178	0.730304	0.365152	−	0.930948i	$-0.381017\pi$
$103$	7.41178	0.730304	0.365152	+	0.930948i	$0.381017\pi$
$104$	−5.67889	−0.556861
$105$	29.1418	2.84394
$106$	−11.7840	−1.14456
$107$	−16.3722	−1.58276	−0.791380	−	0.611324i	$-0.790637\pi$
$107$	−16.3722	−1.58276	−0.791380	+	0.611324i	$0.790637\pi$
$108$	7.89199	0.759407
$109$	−17.4629	−1.67264	−0.836320	−	0.548242i	$-0.815297\pi$
$109$	−17.4629	−1.67264	−0.836320	+	0.548242i	$0.815297\pi$
$110$	2.00000	0.190693
$111$	12.2527	1.16297
$112$	4.94600	0.467353
$113$	3.53421	0.332471	0.166235	−	0.986086i	$-0.446839\pi$
$113$	3.53421	0.332471	0.166235	+	0.986086i	$0.446839\pi$
$114$	0	0
$115$	−3.78398	−0.352858
$116$	1.00000	0.0928477
$117$	−32.2498	−2.98149
$118$	0	0
$119$	18.4629	1.69249
$120$	5.89199	0.537863
$121$	1.00000	0.0909091
$122$	−5.57088	−0.504364
$123$	−28.3549	−2.55667
$124$	−3.21310	−0.288545
$125$	−12.0000	−1.07331
$126$	28.0878	2.50226
$127$	5.35778	0.475426	0.237713	−	0.971335i	$-0.423602\pi$
$127$	5.35778	0.475426	0.237713	+	0.971335i	$0.423602\pi$
$128$	1.00000	0.0883883
$129$	−13.6249	−1.19960
$130$	−11.3578	−0.996143
$131$	10.3722	0.906223	0.453112	−	0.891454i	$-0.350314\pi$
$131$	10.3722	0.906223	0.453112	+	0.891454i	$0.350314\pi$
$132$	2.94600	0.256416
$133$	0	0
$134$	−8.83799	−0.763486
$135$	15.7840	1.35847
$136$	3.73289	0.320093
$137$	14.1051	1.20508	0.602540	−	0.798089i	$-0.294156\pi$
$137$	14.1051	1.20508	0.602540	+	0.798089i	$0.294156\pi$
$138$	−5.57379	−0.474473
$139$	−13.6760	−1.15998	−0.579990	−	0.814623i	$-0.696944\pi$
$139$	−13.6760	−1.15998	−0.579990	+	0.814623i	$0.696944\pi$
$140$	9.89199	0.836026
$141$	−21.8351	−1.83884
$142$	−4.62488	−0.388112
$143$	−5.67889	−0.474892
$144$	5.67889	0.473241
$145$	2.00000	0.166091
$146$	−3.62488	−0.299997
$147$	51.4455	4.24316
$148$	4.15910	0.341876
$149$	18.9971	1.55630	0.778151	−	0.628077i	$-0.216158\pi$
$149$	18.9971	1.55630	0.778151	+	0.628077i	$0.216158\pi$
$150$	−2.94600	−0.240540
$151$	23.6615	1.92555	0.962775	−	0.270305i	$-0.0871246\pi$
$151$	23.6615	1.92555	0.962775	+	0.270305i	$0.0871246\pi$
$152$	0	0
$153$	21.1987	1.71381
$154$	4.94600	0.398560
$155$	−6.42621	−0.516165
$156$	−16.7300	−1.33947
$157$	−11.7840	−0.940464	−0.470232	−	0.882543i	$-0.655830\pi$
$157$	−11.7840	−0.940464	−0.470232	+	0.882543i	$0.655830\pi$
$158$	6.83799	0.544001
$159$	−34.7156	−2.75312
$160$	2.00000	0.158114
$161$	−9.35778	−0.737496
$162$	6.21310	0.488147
$163$	−10.8236	−0.847767	−0.423883	−	0.905717i	$-0.639333\pi$
$163$	−10.8236	−0.847767	−0.423883	+	0.905717i	$0.639333\pi$
$164$	−9.62488	−0.751577
$165$	5.89199	0.458691
$166$	14.5169	1.12673
$167$	−4.01443	−0.310646	−0.155323	−	0.987864i	$-0.549642\pi$
$167$	−4.01443	−0.310646	−0.155323	+	0.987864i	$0.549642\pi$
$168$	14.5709	1.12417
$169$	19.2498	1.48075
$170$	7.46579	0.572600
$171$	0	0
$172$	−4.62488	−0.352644
$173$	7.21310	0.548402	0.274201	−	0.961672i	$-0.411587\pi$
$173$	7.21310	0.548402	0.274201	+	0.961672i	$0.411587\pi$
$174$	2.94600	0.223335
$175$	−4.94600	−0.373882
$176$	1.00000	0.0753778
$177$	0	0
$178$	0.465785	0.0349121
$179$	−4.10801	−0.307047	−0.153524	−	0.988145i	$-0.549062\pi$
$179$	−4.10801	−0.307047	−0.153524	+	0.988145i	$0.549062\pi$
$180$	11.3578	0.846559
$181$	−15.4089	−1.14533	−0.572666	−	0.819789i	$-0.694091\pi$
$181$	−15.4089	−1.14533	−0.572666	+	0.819789i	$0.694091\pi$
$182$	−28.0878	−2.08200
$183$	−16.4118	−1.21319
$184$	−1.89199	−0.139479
$185$	8.31820	0.611566
$186$	−9.46579	−0.694065
$187$	3.73289	0.272976
$188$	−7.41178	−0.540560
$189$	39.0337	2.83929
$190$	0	0
$191$	10.5882	0.766137	0.383068	−	0.923720i	$-0.374867\pi$
$191$	10.5882	0.766137	0.383068	+	0.923720i	$0.374867\pi$
$192$	2.94600	0.212609
$193$	5.51687	0.397113	0.198557	−	0.980089i	$-0.436375\pi$
$193$	5.51687	0.397113	0.198557	+	0.980089i	$0.436375\pi$
$194$	1.53421	0.110150
$195$	−33.4600	−2.39612
$196$	17.4629	1.24735
$197$	−9.53421	−0.679285	−0.339642	−	0.940555i	$-0.610306\pi$
$197$	−9.53421	−0.679285	−0.339642	+	0.940555i	$0.610306\pi$
$198$	5.67889	0.403581
$199$	20.6249	1.46206	0.731030	−	0.682346i	$-0.239040\pi$
$199$	20.6249	1.46206	0.731030	+	0.682346i	$0.239040\pi$
$200$	−1.00000	−0.0707107
$201$	−26.0367	−1.83648
$202$	−1.67889	−0.118126
$203$	4.94600	0.347141
$204$	10.9971	0.769950
$205$	−19.2498	−1.34446
$206$	7.41178	0.516403
$207$	−10.7444	−0.746787
$208$	−5.67889	−0.393760
$209$	0	0
$210$	29.1418	2.01097
$211$	25.6760	1.76761	0.883803	−	0.467859i	$-0.154974\pi$
$211$	25.6760	1.76761	0.883803	+	0.467859i	$0.154974\pi$
$212$	−11.7840	−0.809327
$213$	−13.6249	−0.933562
$214$	−16.3722	−1.11918
$215$	−9.24977	−0.630829
$216$	7.89199	0.536982
$217$	−15.8920	−1.07882
$218$	−17.4629	−1.18273
$219$	−10.6789	−0.721612
$220$	2.00000	0.134840
$221$	−21.1987	−1.42598
$222$	12.2527	0.822346
$223$	7.37512	0.493874	0.246937	−	0.969031i	$-0.420576\pi$
$223$	7.37512	0.493874	0.246937	+	0.969031i	$0.420576\pi$
$224$	4.94600	0.330468
$225$	−5.67889	−0.378593
$226$	3.53421	0.235092
$227$	28.3549	1.88198	0.940989	−	0.338437i	$-0.109898\pi$
$227$	28.3549	1.88198	0.940989	+	0.338437i	$0.109898\pi$
$228$	0	0
$229$	−4.98266	−0.329263	−0.164632	−	0.986355i	$-0.552644\pi$
$229$	−4.98266	−0.329263	−0.164632	+	0.986355i	$0.552644\pi$
$230$	−3.78398	−0.249508
$231$	14.5709	0.958693
$232$	1.00000	0.0656532
$233$	22.4484	1.47065	0.735323	−	0.677717i	$-0.237030\pi$
$233$	22.4484	1.47065	0.735323	+	0.677717i	$0.237030\pi$
$234$	−32.2498	−2.10823
$235$	−14.8236	−0.966982
$236$	0	0
$237$	20.1447	1.30854
$238$	18.4629	1.19677
$239$	−23.7840	−1.53846	−0.769229	−	0.638973i	$-0.779359\pi$
$239$	−23.7840	−1.53846	−0.769229	+	0.638973i	$0.779359\pi$
$240$	5.89199	0.380326
$241$	21.1418	1.36186	0.680930	−	0.732348i	$-0.261576\pi$
$241$	21.1418	1.36186	0.680930	+	0.732348i	$0.261576\pi$
$242$	1.00000	0.0642824
$243$	−5.37220	−0.344627
$244$	−5.57088	−0.356639
$245$	34.9257	2.23132
$246$	−28.3549	−1.80784
$247$	0	0
$248$	−3.21310	−0.204032
$249$	42.7666	2.71023
$250$	−12.0000	−0.758947
$251$	0.519790	0.0328088	0.0164044	−	0.999865i	$-0.494778\pi$
$251$	0.519790	0.0328088	0.0164044	+	0.999865i	$0.494778\pi$
$252$	28.0878	1.76936
$253$	−1.89199	−0.118948
$254$	5.35778	0.336177
$255$	21.9942	1.37733
$256$	1.00000	0.0625000
$257$	10.8236	0.675155	0.337578	−	0.941298i	$-0.390392\pi$
$257$	10.8236	0.675155	0.337578	+	0.941298i	$0.390392\pi$
$258$	−13.6249	−0.848248
$259$	20.5709	1.27821
$260$	−11.3578	−0.704379
$261$	5.67889	0.351514
$262$	10.3722	0.640797
$263$	−13.0337	−0.803695	−0.401848	−	0.915707i	$-0.631632\pi$
$263$	−13.0337	−0.803695	−0.401848	+	0.915707i	$0.631632\pi$
$264$	2.94600	0.181313
$265$	−23.5680	−1.44777
$266$	0	0
$267$	1.37220	0.0839773
$268$	−8.83799	−0.539866
$269$	5.73289	0.349541	0.174770	−	0.984609i	$-0.444082\pi$
$269$	5.73289	0.349541	0.174770	+	0.984609i	$0.444082\pi$
$270$	15.7840	0.960582
$271$	−12.0000	−0.728948	−0.364474	−	0.931214i	$-0.618751\pi$
$271$	−12.0000	−0.728948	−0.364474	+	0.931214i	$0.618751\pi$
$272$	3.73289	0.226340
$273$	−82.7464	−5.00804
$274$	14.1051	0.852120
$275$	−1.00000	−0.0603023
$276$	−5.57379	−0.335503
$277$	13.5709	0.815395	0.407698	−	0.913117i	$-0.366332\pi$
$277$	13.5709	0.815395	0.407698	+	0.913117i	$0.366332\pi$
$278$	−13.6760	−0.820230
$279$	−18.2468	−1.09241
$280$	9.89199	0.591159
$281$	−1.19868	−0.0715071	−0.0357536	−	0.999361i	$-0.511383\pi$
$281$	−1.19868	−0.0715071	−0.0357536	+	0.999361i	$0.511383\pi$
$282$	−21.8351	−1.30026
$283$	−4.82356	−0.286731	−0.143365	−	0.989670i	$-0.545792\pi$
$283$	−4.82356	−0.286731	−0.143365	+	0.989670i	$0.545792\pi$
$284$	−4.62488	−0.274436
$285$	0	0
$286$	−5.67889	−0.335800
$287$	−47.6046	−2.81001
$288$	5.67889	0.334632
$289$	−3.06551	−0.180324
$290$	2.00000	0.117444
$291$	4.51979	0.264955
$292$	−3.62488	−0.212130
$293$	−1.21602	−0.0710406	−0.0355203	−	0.999369i	$-0.511309\pi$
$293$	−1.21602	−0.0710406	−0.0355203	+	0.999369i	$0.511309\pi$
$294$	51.4455	3.00036
$295$	0	0
$296$	4.15910	0.241743
$297$	7.89199	0.457940
$298$	18.9971	1.10047
$299$	10.7444	0.621365
$300$	−2.94600	−0.170087
$301$	−22.8746	−1.31847
$302$	23.6615	1.36157
$303$	−4.94600	−0.284140
$304$	0	0
$305$	−11.1418	−0.637975
$306$	21.1987	1.21185
$307$	−32.0482	−1.82909	−0.914543	−	0.404489i	$-0.867449\pi$
$307$	−32.0482	−1.82909	−0.914543	+	0.404489i	$0.867449\pi$
$308$	4.94600	0.281824
$309$	21.8351	1.24215
$310$	−6.42621	−0.364984
$311$	−18.3722	−1.04179	−0.520896	−	0.853620i	$-0.674402\pi$
$311$	−18.3722	−1.04179	−0.520896	+	0.853620i	$0.674402\pi$
$312$	−16.7300	−0.947148
$313$	1.14467	0.0647007	0.0323504	−	0.999477i	$-0.489701\pi$
$313$	1.14467	0.0647007	0.0323504	+	0.999477i	$0.489701\pi$
$314$	−11.7840	−0.665009
$315$	56.1755	3.16513
$316$	6.83799	0.384667
$317$	−24.4484	−1.37316	−0.686581	−	0.727054i	$-0.740889\pi$
$317$	−24.4484	−1.37316	−0.686581	+	0.727054i	$0.740889\pi$
$318$	−34.7156	−1.94675
$319$	1.00000	0.0559893
$320$	2.00000	0.111803
$321$	−48.2324	−2.69207
$322$	−9.35778	−0.521488
$323$	0	0
$324$	6.21310	0.345172
$325$	5.67889	0.315008
$326$	−10.8236	−0.599462
$327$	−51.4455	−2.84494
$328$	−9.62488	−0.531445
$329$	−36.6586	−2.02106
$330$	5.89199	0.324343
$331$	6.30377	0.346487	0.173243	−	0.984879i	$-0.444575\pi$
$331$	6.30377	0.346487	0.173243	+	0.984879i	$0.444575\pi$
$332$	14.5169	0.796717
$333$	23.6190	1.29432
$334$	−4.01443	−0.219660
$335$	−17.6760	−0.965741
$336$	14.5709	0.794907
$337$	10.2893	0.560496	0.280248	−	0.959928i	$-0.409583\pi$
$337$	10.2893	0.560496	0.280248	+	0.959928i	$0.409583\pi$
$338$	19.2498	1.04705
$339$	10.4118	0.565490
$340$	7.46579	0.404889
$341$	−3.21310	−0.173999
$342$	0	0
$343$	51.7493	2.79420
$344$	−4.62488	−0.249357
$345$	−11.1476	−0.600166
$346$	7.21310	0.387779
$347$	−19.1958	−1.03048	−0.515241	−	0.857045i	$-0.672298\pi$
$347$	−19.1958	−1.03048	−0.515241	+	0.857045i	$0.672298\pi$
$348$	2.94600	0.157922
$349$	32.9653	1.76459	0.882296	−	0.470694i	$-0.155996\pi$
$349$	32.9653	1.76459	0.882296	+	0.470694i	$0.155996\pi$
$350$	−4.94600	−0.264375
$351$	−44.8177	−2.39219
$352$	1.00000	0.0533002
$353$	33.2835	1.77150	0.885751	−	0.464160i	$-0.153644\pi$
$353$	33.2835	1.77150	0.885751	+	0.464160i	$0.153644\pi$
$354$	0	0
$355$	−9.24977	−0.490927
$356$	0.465785	0.0246866
$357$	54.3915	2.87870
$358$	−4.10801	−0.217115
$359$	5.68180	0.299874	0.149937	−	0.988696i	$-0.452093\pi$
$359$	5.68180	0.299874	0.149937	+	0.988696i	$0.452093\pi$
$360$	11.3578	0.598607
$361$	0	0
$362$	−15.4089	−0.809872
$363$	2.94600	0.154625
$364$	−28.0878	−1.47220
$365$	−7.24977	−0.379470
$366$	−16.4118	−0.857857
$367$	17.6933	0.923583	0.461792	−	0.886988i	$-0.347207\pi$
$367$	17.6933	0.923583	0.461792	+	0.886988i	$0.347207\pi$
$368$	−1.89199	−0.0986268
$369$	−54.6586	−2.84541
$370$	8.31820	0.432442
$371$	−58.2835	−3.02593
$372$	−9.46579	−0.490778
$373$	37.1051	1.92123	0.960614	−	0.277885i	$-0.0896333\pi$
$373$	37.1051	1.92123	0.960614	+	0.277885i	$0.0896333\pi$
$374$	3.73289	0.193023
$375$	−35.3519	−1.82557
$376$	−7.41178	−0.382233
$377$	−5.67889	−0.292478
$378$	39.0337	2.00768
$379$	−13.5535	−0.696198	−0.348099	−	0.937458i	$-0.613173\pi$
$379$	−13.5535	−0.696198	−0.348099	+	0.937458i	$0.613173\pi$
$380$	0	0
$381$	15.7840	0.808638
$382$	10.5882	0.541740
$383$	−9.67597	−0.494419	−0.247210	−	0.968962i	$-0.579514\pi$
$383$	−9.67597	−0.494419	−0.247210	+	0.968962i	$0.579514\pi$
$384$	2.94600	0.150337
$385$	9.89199	0.504143
$386$	5.51687	0.280801
$387$	−26.2642	−1.33508
$388$	1.53421	0.0778880
$389$	12.8013	0.649053	0.324526	−	0.945877i	$-0.394795\pi$
$389$	12.8013	0.649053	0.324526	+	0.945877i	$0.394795\pi$
$390$	−33.4600	−1.69431
$391$	−7.06260	−0.357171
$392$	17.4629	0.882008
$393$	30.5565	1.54137
$394$	−9.53421	−0.480327
$395$	13.6760	0.688113
$396$	5.67889	0.285375
$397$	−18.1591	−0.911379	−0.455689	−	0.890139i	$-0.650607\pi$
$397$	−18.1591	−0.911379	−0.455689	+	0.890139i	$0.650607\pi$
$398$	20.6249	1.03383
$399$	0	0
$400$	−1.00000	−0.0500000
$401$	7.82064	0.390544	0.195272	−	0.980749i	$-0.437441\pi$
$401$	7.82064	0.390544	0.195272	+	0.980749i	$0.437441\pi$
$402$	−26.0367	−1.29859
$403$	18.2468	0.908940
$404$	−1.67889	−0.0835278
$405$	12.4262	0.617463
$406$	4.94600	0.245466
$407$	4.15910	0.206159
$408$	10.9971	0.544437
$409$	21.0115	1.03895	0.519476	−	0.854485i	$-0.326127\pi$
$409$	21.0115	1.03895	0.519476	+	0.854485i	$0.326127\pi$
$410$	−19.2498	−0.950678
$411$	41.5535	2.04968
$412$	7.41178	0.365152
$413$	0	0
$414$	−10.7444	−0.528059
$415$	29.0337	1.42521
$416$	−5.67889	−0.278430
$417$	−40.2893	−1.97298
$418$	0	0
$419$	−11.0540	−0.540023	−0.270012	−	0.962857i	$-0.587028\pi$
$419$	−11.0540	−0.540023	−0.270012	+	0.962857i	$0.587028\pi$
$420$	29.1418	1.42197
$421$	−4.48313	−0.218494	−0.109247	−	0.994015i	$-0.534844\pi$
$421$	−4.48313	−0.218494	−0.109247	+	0.994015i	$0.534844\pi$
$422$	25.6760	1.24989
$423$	−42.0907	−2.04652
$424$	−11.7840	−0.572281
$425$	−3.73289	−0.181072
$426$	−13.6249	−0.660128
$427$	−27.5535	−1.33341
$428$	−16.3722	−0.791380
$429$	−16.7300	−0.807731
$430$	−9.24977	−0.446063
$431$	−2.19576	−0.105766	−0.0528830	−	0.998601i	$-0.516841\pi$
$431$	−2.19576	−0.105766	−0.0528830	+	0.998601i	$0.516841\pi$
$432$	7.89199	0.379704
$433$	31.8602	1.53110	0.765552	−	0.643374i	$-0.222466\pi$
$433$	31.8602	1.53110	0.765552	+	0.643374i	$0.222466\pi$
$434$	−15.8920	−0.762840
$435$	5.89199	0.282499
$436$	−17.4629	−0.836320
$437$	0	0
$438$	−10.6789	−0.510257
$439$	10.6422	0.507926	0.253963	−	0.967214i	$-0.418266\pi$
$439$	10.6422	0.507926	0.253963	+	0.967214i	$0.418266\pi$
$440$	2.00000	0.0953463
$441$	99.1697	4.72237
$442$	−21.1987	−1.00832
$443$	31.4455	1.49402	0.747011	−	0.664812i	$-0.231488\pi$
$443$	31.4455	1.49402	0.747011	+	0.664812i	$0.231488\pi$
$444$	12.2527	0.581487
$445$	0.931570	0.0441607
$446$	7.37512	0.349222
$447$	55.9653	2.64707
$448$	4.94600	0.233676
$449$	−13.8553	−0.653873	−0.326937	−	0.945046i	$-0.606016\pi$
$449$	−13.8553	−0.653873	−0.326937	+	0.945046i	$0.606016\pi$
$450$	−5.67889	−0.267705
$451$	−9.62488	−0.453218
$452$	3.53421	0.166235
$453$	69.7068	3.27511
$454$	28.3549	1.33076
$455$	−56.1755	−2.63355
$456$	0	0
$457$	−15.7329	−0.735954	−0.367977	−	0.929835i	$-0.619949\pi$
$457$	−15.7329	−0.735954	−0.367977	+	0.929835i	$0.619949\pi$
$458$	−4.98266	−0.232824
$459$	29.4600	1.37507
$460$	−3.78398	−0.176429
$461$	−20.7126	−0.964684	−0.482342	−	0.875983i	$-0.660214\pi$
$461$	−20.7126	−0.964684	−0.482342	+	0.875983i	$0.660214\pi$
$462$	14.5709	0.677899
$463$	−14.3722	−0.667933	−0.333966	−	0.942585i	$-0.608387\pi$
$463$	−14.3722	−0.667933	−0.333966	+	0.942585i	$0.608387\pi$
$464$	1.00000	0.0464238
$465$	−18.9316	−0.877931
$466$	22.4484	1.03990
$467$	−10.3038	−0.476802	−0.238401	−	0.971167i	$-0.576623\pi$
$467$	−10.3038	−0.476802	−0.238401	+	0.971167i	$0.576623\pi$
$468$	−32.2498	−1.49075
$469$	−43.7126	−2.01846
$470$	−14.8236	−0.683760
$471$	−34.7156	−1.59961
$472$	0	0
$473$	−4.62488	−0.212652
$474$	20.1447	0.925275
$475$	0	0
$476$	18.4629	0.846244
$477$	−66.9199	−3.06405
$478$	−23.7840	−1.08785
$479$	7.58822	0.346715	0.173357	−	0.984859i	$-0.444538\pi$
$479$	7.58822	0.346715	0.173357	+	0.984859i	$0.444538\pi$
$480$	5.89199	0.268931
$481$	−23.6190	−1.07694
$482$	21.1418	0.962981
$483$	−27.5680	−1.25439
$484$	1.00000	0.0454545
$485$	3.06843	0.139330
$486$	−5.37220	−0.243688
$487$	0.414697	0.0187917	0.00939585	−	0.999956i	$-0.497009\pi$
$487$	0.414697	0.0187917	0.00939585	+	0.999956i	$0.497009\pi$
$488$	−5.57088	−0.252182
$489$	−31.8862	−1.44194
$490$	34.9257	1.57778
$491$	−0.823561	−0.0371668	−0.0185834	−	0.999827i	$-0.505916\pi$
$491$	−0.823561	−0.0371668	−0.0185834	+	0.999827i	$0.505916\pi$
$492$	−28.3549	−1.27834
$493$	3.73289	0.168121
$494$	0	0
$495$	11.3578	0.510494
$496$	−3.21310	−0.144273
$497$	−22.8746	−1.02607
$498$	42.7666	1.91642
$499$	5.35778	0.239847	0.119923	−	0.992783i	$-0.461735\pi$
$499$	5.35778	0.239847	0.119923	+	0.992783i	$0.461735\pi$
$500$	−12.0000	−0.536656
$501$	−11.8265	−0.528368
$502$	0.519790	0.0231994
$503$	5.57379	0.248523	0.124262	−	0.992249i	$-0.460344\pi$
$503$	5.57379	0.248523	0.124262	+	0.992249i	$0.460344\pi$
$504$	28.0878	1.25113
$505$	−3.35778	−0.149419
$506$	−1.89199	−0.0841092
$507$	56.7097	2.51857
$508$	5.35778	0.237713
$509$	18.4262	0.816727	0.408364	−	0.912819i	$-0.366100\pi$
$509$	18.4262	0.816727	0.408364	+	0.912819i	$0.366100\pi$
$510$	21.9942	0.973918
$511$	−17.9287	−0.793117
$512$	1.00000	0.0441942
$513$	0	0
$514$	10.8236	0.477407
$515$	14.8236	0.653204
$516$	−13.6249	−0.599802
$517$	−7.41178	−0.325970
$518$	20.5709	0.903832
$519$	21.2498	0.932761
$520$	−11.3578	−0.498071
$521$	9.24685	0.405112	0.202556	−	0.979271i	$-0.435075\pi$
$521$	9.24685	0.405112	0.202556	+	0.979271i	$0.435075\pi$
$522$	5.67889	0.248558
$523$	19.4118	0.848818	0.424409	−	0.905471i	$-0.360482\pi$
$523$	19.4118	0.848818	0.424409	+	0.905471i	$0.360482\pi$
$524$	10.3722	0.453112
$525$	−14.5709	−0.635925
$526$	−13.0337	−0.568298
$527$	−11.9942	−0.522474
$528$	2.94600	0.128208
$529$	−19.4204	−0.844364
$530$	−23.5680	−1.02373
$531$	0	0
$532$	0	0
$533$	54.6586	2.36753
$534$	1.37220	0.0593809
$535$	−32.7444	−1.41566
$536$	−8.83799	−0.381743
$537$	−12.1022	−0.522247
$538$	5.73289	0.247163
$539$	17.4629	0.752179
$540$	15.7840	0.679234
$541$	19.6046	0.842869	0.421434	−	0.906859i	$-0.361527\pi$
$541$	19.6046	0.842869	0.421434	+	0.906859i	$0.361527\pi$
$542$	−12.0000	−0.515444
$543$	−45.3944	−1.94806
$544$	3.73289	0.160046
$545$	−34.9257	−1.49605
$546$	−82.7464	−3.54122
$547$	4.62488	0.197746	0.0988729	−	0.995100i	$-0.468476\pi$
$547$	4.62488	0.197746	0.0988729	+	0.995100i	$0.468476\pi$
$548$	14.1051	0.602540
$549$	−31.6364	−1.35021
$550$	−1.00000	−0.0426401
$551$	0	0
$552$	−5.57379	−0.237236
$553$	33.8206	1.43820
$554$	13.5709	0.576571
$555$	24.5054	1.04019
$556$	−13.6760	−0.579990
$557$	22.3211	0.945776	0.472888	−	0.881123i	$-0.343212\pi$
$557$	22.3211	0.945776	0.472888	+	0.881123i	$0.343212\pi$
$558$	−18.2468	−0.772451
$559$	26.2642	1.11086
$560$	9.89199	0.418013
$561$	10.9971	0.464297
$562$	−1.19868	−0.0505632
$563$	−29.6760	−1.25069	−0.625347	−	0.780347i	$-0.715042\pi$
$563$	−29.6760	−1.25069	−0.625347	+	0.780347i	$0.715042\pi$
$564$	−21.8351	−0.919422
$565$	7.06843	0.297371
$566$	−4.82356	−0.202749
$567$	30.7300	1.29054
$568$	−4.62488	−0.194056
$569$	34.0733	1.42843	0.714214	−	0.699927i	$-0.246784\pi$
$569$	34.0733	1.42843	0.714214	+	0.699927i	$0.246784\pi$
$570$	0	0
$571$	16.3722	0.685155	0.342578	−	0.939490i	$-0.388700\pi$
$571$	16.3722	0.685155	0.342578	+	0.939490i	$0.388700\pi$
$572$	−5.67889	−0.237446
$573$	31.1928	1.30310
$574$	−47.6046	−1.98698
$575$	1.89199	0.0789015
$576$	5.67889	0.236620
$577$	23.2864	0.969427	0.484713	−	0.874673i	$-0.338924\pi$
$577$	23.2864	0.969427	0.484713	+	0.874673i	$0.338924\pi$
$578$	−3.06551	−0.127509
$579$	16.2527	0.675438
$580$	2.00000	0.0830455
$581$	71.8004	2.97878
$582$	4.51979	0.187351
$583$	−11.7840	−0.488043
$584$	−3.62488	−0.149999
$585$	−64.4995	−2.66673
$586$	−1.21602	−0.0502333
$587$	19.0540	0.786443	0.393221	−	0.919444i	$-0.371361\pi$
$587$	19.0540	0.786443	0.393221	+	0.919444i	$0.371361\pi$
$588$	51.4455	2.12158
$589$	0	0
$590$	0	0
$591$	−28.0878	−1.15538
$592$	4.15910	0.170938
$593$	1.57379	0.0646280	0.0323140	−	0.999478i	$-0.489712\pi$
$593$	1.57379	0.0646280	0.0323140	+	0.999478i	$0.489712\pi$
$594$	7.89199	0.323812
$595$	36.9257	1.51381
$596$	18.9971	0.778151
$597$	60.7608	2.48677
$598$	10.7444	0.439371
$599$	22.7329	0.928841	0.464420	−	0.885615i	$-0.346263\pi$
$599$	22.7329	0.928841	0.464420	+	0.885615i	$0.346263\pi$
$600$	−2.94600	−0.120270
$601$	−10.8524	−0.442679	−0.221340	−	0.975197i	$-0.571043\pi$
$601$	−10.8524	−0.442679	−0.221340	+	0.975197i	$0.571043\pi$
$602$	−22.8746	−0.932301
$603$	−50.1899	−2.04389
$604$	23.6615	0.962775
$605$	2.00000	0.0813116
$606$	−4.94600	−0.200917
$607$	12.3038	0.499395	0.249697	−	0.968324i	$-0.419669\pi$
$607$	12.3038	0.499395	0.249697	+	0.968324i	$0.419669\pi$
$608$	0	0
$609$	14.5709	0.590442
$610$	−11.1418	−0.451117
$611$	42.0907	1.70281
$612$	21.1987	0.856906
$613$	45.0308	1.81878	0.909389	−	0.415947i	$-0.136550\pi$
$613$	45.0308	1.81878	0.909389	+	0.415947i	$0.136550\pi$
$614$	−32.0482	−1.29336
$615$	−56.7097	−2.28676
$616$	4.94600	0.199280
$617$	21.4629	0.864063	0.432031	−	0.901859i	$-0.357797\pi$
$617$	21.4629	0.864063	0.432031	+	0.901859i	$0.357797\pi$
$618$	21.8351	0.878335
$619$	6.96625	0.279997	0.139999	−	0.990152i	$-0.455290\pi$
$619$	6.96625	0.279997	0.139999	+	0.990152i	$0.455290\pi$
$620$	−6.42621	−0.258083
$621$	−14.9316	−0.599183
$622$	−18.3722	−0.736658
$623$	2.30377	0.0922986
$624$	−16.7300	−0.669735
$625$	−19.0000	−0.760000
$626$	1.14467	0.0457503
$627$	0	0
$628$	−11.7840	−0.470232
$629$	15.5255	0.619041
$630$	56.1755	2.23809
$631$	−40.4089	−1.60865	−0.804326	−	0.594189i	$-0.797473\pi$
$631$	−40.4089	−1.60865	−0.804326	+	0.594189i	$0.797473\pi$
$632$	6.83799	0.272000
$633$	75.6413	3.00647
$634$	−24.4484	−0.970972
$635$	10.7156	0.425234
$636$	−34.7156	−1.37656
$637$	−99.1697	−3.92925
$638$	1.00000	0.0395904
$639$	−26.2642	−1.03900
$640$	2.00000	0.0790569
$641$	26.7840	1.05790	0.528952	−	0.848652i	$-0.322585\pi$
$641$	26.7840	1.05790	0.528952	+	0.848652i	$0.322585\pi$
$642$	−48.2324	−1.90358
$643$	−3.26419	−0.128727	−0.0643636	−	0.997927i	$-0.520502\pi$
$643$	−3.26419	−0.128727	−0.0643636	+	0.997927i	$0.520502\pi$
$644$	−9.35778	−0.368748
$645$	−27.2498	−1.07296
$646$	0	0
$647$	−10.3355	−0.406332	−0.203166	−	0.979144i	$-0.565123\pi$
$647$	−10.3355	−0.406332	−0.203166	+	0.979144i	$0.565123\pi$
$648$	6.21310	0.244074
$649$	0	0
$650$	5.67889	0.222744
$651$	−46.8177	−1.83493
$652$	−10.8236	−0.423883
$653$	16.5853	0.649033	0.324517	−	0.945880i	$-0.394798\pi$
$653$	16.5853	0.649033	0.324517	+	0.945880i	$0.394798\pi$
$654$	−51.4455	−2.01168
$655$	20.7444	0.810551
$656$	−9.62488	−0.375789
$657$	−20.5853	−0.803109
$658$	−36.6586	−1.42910
$659$	33.4118	1.30154	0.650769	−	0.759276i	$-0.274447\pi$
$659$	33.4118	1.30154	0.650769	+	0.759276i	$0.274447\pi$
$660$	5.89199	0.229345
$661$	10.2671	0.399344	0.199672	−	0.979863i	$-0.436012\pi$
$661$	10.2671	0.399344	0.199672	+	0.979863i	$0.436012\pi$
$662$	6.30377	0.245003
$663$	−62.4512	−2.42540
$664$	14.5169	0.563364
$665$	0	0
$666$	23.6190	0.915220
$667$	−1.89199	−0.0732582
$668$	−4.01443	−0.155323
$669$	21.7271	0.840017
$670$	−17.6760	−0.682882
$671$	−5.57088	−0.215061
$672$	14.5709	0.562084
$673$	−47.6190	−1.83558	−0.917790	−	0.397067i	$-0.870028\pi$
$673$	−47.6190	−1.83558	−0.917790	+	0.397067i	$0.870028\pi$
$674$	10.2893	0.396331
$675$	−7.89199	−0.303763
$676$	19.2498	0.740376
$677$	−6.64514	−0.255394	−0.127697	−	0.991813i	$-0.540758\pi$
$677$	−6.64514	−0.255394	−0.127697	+	0.991813i	$0.540758\pi$
$678$	10.4118	0.399862
$679$	7.58822	0.291209
$680$	7.46579	0.286300
$681$	83.5333	3.20100
$682$	−3.21310	−0.123036
$683$	−21.7984	−0.834093	−0.417046	−	0.908885i	$-0.636935\pi$
$683$	−21.7984	−0.834093	−0.417046	+	0.908885i	$0.636935\pi$
$684$	0	0
$685$	28.2102	1.07786
$686$	51.7493	1.97580
$687$	−14.6789	−0.560034
$688$	−4.62488	−0.176322
$689$	66.9199	2.54945
$690$	−11.1476	−0.424381
$691$	−13.2700	−0.504816	−0.252408	−	0.967621i	$-0.581222\pi$
$691$	−13.2700	−0.504816	−0.252408	+	0.967621i	$0.581222\pi$
$692$	7.21310	0.274201
$693$	28.0878	1.06697
$694$	−19.1958	−0.728661
$695$	−27.3519	−1.03752
$696$	2.94600	0.111668
$697$	−35.9287	−1.36089
$698$	32.9653	1.24776
$699$	66.1330	2.50138
$700$	−4.94600	−0.186941
$701$	12.6818	0.478985	0.239493	−	0.970898i	$-0.423019\pi$
$701$	12.6818	0.478985	0.239493	+	0.970898i	$0.423019\pi$
$702$	−44.8177	−1.69154
$703$	0	0
$704$	1.00000	0.0376889
$705$	−43.6701	−1.64471
$706$	33.2835	1.25264
$707$	−8.30377	−0.312295
$708$	0	0
$709$	37.5680	1.41089	0.705447	−	0.708762i	$-0.250746\pi$
$709$	37.5680	1.41089	0.705447	+	0.708762i	$0.250746\pi$
$710$	−9.24977	−0.347138
$711$	38.8322	1.45632
$712$	0.465785	0.0174560
$713$	6.07916	0.227666
$714$	54.3915	2.03555
$715$	−11.3578	−0.424757
$716$	−4.10801	−0.153524
$717$	−70.0675	−2.61672
$718$	5.68180	0.212043
$719$	−2.94308	−0.109758	−0.0548792	−	0.998493i	$-0.517477\pi$
$719$	−2.94308	−0.109758	−0.0548792	+	0.998493i	$0.517477\pi$
$720$	11.3578	0.423279
$721$	36.6586	1.36524
$722$	0	0
$723$	62.2835	2.31635
$724$	−15.4089	−0.572666
$725$	−1.00000	−0.0371391
$726$	2.94600	0.109336
$727$	27.5506	1.02180	0.510898	−	0.859641i	$-0.329313\pi$
$727$	27.5506	1.02180	0.510898	+	0.859641i	$0.329313\pi$
$728$	−28.0878	−1.04100
$729$	−34.4658	−1.27651
$730$	−7.24977	−0.268326
$731$	−17.2642	−0.638539
$732$	−16.4118	−0.606597
$733$	37.6393	1.39024	0.695120	−	0.718894i	$-0.255351\pi$
$733$	37.6393	1.39024	0.695120	+	0.718894i	$0.255351\pi$
$734$	17.6933	0.653072
$735$	102.891	3.79519
$736$	−1.89199	−0.0697397
$737$	−8.83799	−0.325551
$738$	−54.6586	−2.01201
$739$	5.19576	0.191129	0.0955646	−	0.995423i	$-0.469534\pi$
$739$	5.19576	0.191129	0.0955646	+	0.995423i	$0.469534\pi$
$740$	8.31820	0.305783
$741$	0	0
$742$	−58.2835	−2.13966
$743$	1.97974	0.0726297	0.0363148	−	0.999340i	$-0.488438\pi$
$743$	1.97974	0.0726297	0.0363148	+	0.999340i	$0.488438\pi$
$744$	−9.46579	−0.347033
$745$	37.9942	1.39200
$746$	37.1051	1.35851
$747$	82.4397	3.01631
$748$	3.73289	0.136488
$749$	−80.9768	−2.95883
$750$	−35.3519	−1.29087
$751$	3.34043	0.121894	0.0609471	−	0.998141i	$-0.480588\pi$
$751$	3.34043	0.121894	0.0609471	+	0.998141i	$0.480588\pi$
$752$	−7.41178	−0.270280
$753$	1.53130	0.0558036
$754$	−5.67889	−0.206813
$755$	47.3231	1.72226
$756$	39.0337	1.41964
$757$	−42.7097	−1.55231	−0.776156	−	0.630541i	$-0.782833\pi$
$757$	−42.7097	−1.55231	−0.776156	+	0.630541i	$0.782833\pi$
$758$	−13.5535	−0.492287
$759$	−5.57379	−0.202316
$760$	0	0
$761$	−10.5054	−0.380819	−0.190410	−	0.981705i	$-0.560982\pi$
$761$	−10.5054	−0.380819	−0.190410	+	0.981705i	$0.560982\pi$
$762$	15.7840	0.571793
$763$	−86.3713	−3.12685
$764$	10.5882	0.383068
$765$	42.3974	1.53288
$766$	−9.67597	−0.349607
$767$	0	0
$768$	2.94600	0.106304
$769$	−3.07426	−0.110861	−0.0554304	−	0.998463i	$-0.517653\pi$
$769$	−3.07426	−0.110861	−0.0554304	+	0.998463i	$0.517653\pi$
$770$	9.89199	0.356483
$771$	31.8862	1.14835
$772$	5.51687	0.198557
$773$	−5.44355	−0.195791	−0.0978954	−	0.995197i	$-0.531211\pi$
$773$	−5.44355	−0.195791	−0.0978954	+	0.995197i	$0.531211\pi$
$774$	−26.2642	−0.944047
$775$	3.21310	0.115418
$776$	1.53421	0.0550751
$777$	60.6017	2.17407
$778$	12.8013	0.458950
$779$	0	0
$780$	−33.4600	−1.19806
$781$	−4.62488	−0.165491
$782$	−7.06260	−0.252558
$783$	7.89199	0.282037
$784$	17.4629	0.623674
$785$	−23.5680	−0.841177
$786$	30.5565	1.08991
$787$	4.22753	0.150695	0.0753475	−	0.997157i	$-0.475993\pi$
$787$	4.22753	0.150695	0.0753475	+	0.997157i	$0.475993\pi$
$788$	−9.53421	−0.339642
$789$	−38.3974	−1.36698
$790$	13.6760	0.486569
$791$	17.4802	0.621525
$792$	5.67889	0.201790
$793$	31.6364	1.12344
$794$	−18.1591	−0.644442
$795$	−69.4311	−2.46247
$796$	20.6249	0.731030
$797$	1.44355	0.0511331	0.0255665	−	0.999673i	$-0.491861\pi$
$797$	1.44355	0.0511331	0.0255665	+	0.999673i	$0.491861\pi$
$798$	0	0
$799$	−27.6674	−0.978802
$800$	−1.00000	−0.0353553
$801$	2.64514	0.0934615
$802$	7.82064	0.276157
$803$	−3.62488	−0.127919
$804$	−26.0367	−0.918242
$805$	−18.7156	−0.659636
$806$	18.2468	0.642718
$807$	16.8891	0.594524
$808$	−1.67889	−0.0590631
$809$	−28.7378	−1.01037	−0.505183	−	0.863012i	$-0.668575\pi$
$809$	−28.7378	−1.01037	−0.505183	+	0.863012i	$0.668575\pi$
$810$	12.4262	0.436612
$811$	25.4484	0.893616	0.446808	−	0.894630i	$-0.352561\pi$
$811$	25.4484	0.893616	0.446808	+	0.894630i	$0.352561\pi$
$812$	4.94600	0.173570
$813$	−35.3519	−1.23985
$814$	4.15910	0.145776
$815$	−21.6471	−0.758266
$816$	10.9971	0.384975
$817$	0	0
$818$	21.0115	0.734650
$819$	−159.507	−5.57363
$820$	−19.2498	−0.672231
$821$	−27.5024	−0.959842	−0.479921	−	0.877312i	$-0.659335\pi$
$821$	−27.5024	−0.959842	−0.479921	+	0.877312i	$0.659335\pi$
$822$	41.5535	1.44935
$823$	17.5486	0.611707	0.305854	−	0.952079i	$-0.401058\pi$
$823$	17.5486	0.611707	0.305854	+	0.952079i	$0.401058\pi$
$824$	7.41178	0.258202
$825$	−2.94600	−0.102566
$826$	0	0
$827$	33.2324	1.15560	0.577802	−	0.816177i	$-0.303910\pi$
$827$	33.2324	1.15560	0.577802	+	0.816177i	$0.303910\pi$
$828$	−10.7444	−0.373394
$829$	−31.8062	−1.10468	−0.552338	−	0.833620i	$-0.686264\pi$
$829$	−31.8062	−1.10468	−0.552338	+	0.833620i	$0.686264\pi$
$830$	29.0337	1.00778
$831$	39.9797	1.38688
$832$	−5.67889	−0.196880
$833$	65.1870	2.25860
$834$	−40.2893	−1.39511
$835$	−8.02885	−0.277850
$836$	0	0
$837$	−25.3578	−0.876493
$838$	−11.0540	−0.381854
$839$	2.33554	0.0806317	0.0403159	−	0.999187i	$-0.487164\pi$
$839$	2.33554	0.0806317	0.0403159	+	0.999187i	$0.487164\pi$
$840$	29.1418	1.00549
$841$	−28.0000	−0.965517
$842$	−4.48313	−0.154499
$843$	−3.53130	−0.121624
$844$	25.6760	0.883803
$845$	38.4995	1.32442
$846$	−42.0907	−1.44711
$847$	4.94600	0.169946
$848$	−11.7840	−0.404664
$849$	−14.2102	−0.487692
$850$	−3.73289	−0.128037
$851$	−7.86897	−0.269745
$852$	−13.6249	−0.466781
$853$	−5.03177	−0.172284	−0.0861422	−	0.996283i	$-0.527454\pi$
$853$	−5.03177	−0.172284	−0.0861422	+	0.996283i	$0.527454\pi$
$854$	−27.5535	−0.942863
$855$	0	0
$856$	−16.3722	−0.559590
$857$	−9.30085	−0.317711	−0.158856	−	0.987302i	$-0.550780\pi$
$857$	−9.30085	−0.317711	−0.158856	+	0.987302i	$0.550780\pi$
$858$	−16.7300	−0.571152
$859$	−33.5391	−1.14434	−0.572170	−	0.820135i	$-0.693898\pi$
$859$	−33.5391	−1.14434	−0.572170	+	0.820135i	$0.693898\pi$
$860$	−9.24977	−0.315414
$861$	−140.243	−4.77947
$862$	−2.19576	−0.0747879
$863$	−52.6557	−1.79242	−0.896211	−	0.443629i	$-0.853691\pi$
$863$	−52.6557	−1.79242	−0.896211	+	0.443629i	$0.853691\pi$
$864$	7.89199	0.268491
$865$	14.4262	0.490506
$866$	31.8602	1.08265
$867$	−9.03099	−0.306708
$868$	−15.8920	−0.539409
$869$	6.83799	0.231963
$870$	5.89199	0.199757
$871$	50.1899	1.70062
$872$	−17.4629	−0.591367
$873$	8.71263	0.294878
$874$	0	0
$875$	−59.3519	−2.00646
$876$	−10.6789	−0.360806
$877$	−11.2844	−0.381049	−0.190524	−	0.981682i	$-0.561019\pi$
$877$	−11.2844	−0.381049	−0.190524	+	0.981682i	$0.561019\pi$
$878$	10.6422	0.359158
$879$	−3.58239	−0.120831
$880$	2.00000	0.0674200
$881$	−21.6105	−0.728075	−0.364037	−	0.931384i	$-0.618602\pi$
$881$	−21.6105	−0.728075	−0.364037	+	0.931384i	$0.618602\pi$
$882$	99.1697	3.33922
$883$	16.9402	0.570082	0.285041	−	0.958515i	$-0.407993\pi$
$883$	16.9402	0.570082	0.285041	+	0.958515i	$0.407993\pi$
$884$	−21.1987	−0.712989
$885$	0	0
$886$	31.4455	1.05643
$887$	44.5873	1.49709	0.748547	−	0.663081i	$-0.230752\pi$
$887$	44.5873	1.49709	0.748547	+	0.663081i	$0.230752\pi$
$888$	12.2527	0.411173
$889$	26.4995	0.888766
$890$	0.931570	0.0312263
$891$	6.21310	0.208147
$892$	7.37512	0.246937
$893$	0	0
$894$	55.9653	1.87176
$895$	−8.21602	−0.274631
$896$	4.94600	0.165234
$897$	31.6530	1.05686
$898$	−13.8553	−0.462358
$899$	−3.21310	−0.107163
$900$	−5.67889	−0.189296
$901$	−43.9883	−1.46546
$902$	−9.62488	−0.320474
$903$	−67.3886	−2.24255
$904$	3.53421	0.117546
$905$	−30.8177	−1.02442
$906$	69.7068	2.31585
$907$	−34.8969	−1.15873	−0.579366	−	0.815067i	$-0.696700\pi$
$907$	−34.8969	−1.15873	−0.579366	+	0.815067i	$0.696700\pi$
$908$	28.3549	0.940989
$909$	−9.53421	−0.316230
$910$	−56.1755	−1.86220
$911$	−21.8631	−0.724358	−0.362179	−	0.932109i	$-0.617967\pi$
$911$	−21.8631	−0.724358	−0.362179	+	0.932109i	$0.617967\pi$
$912$	0	0
$913$	14.5169	0.480438
$914$	−15.7329	−0.520398
$915$	−32.8236	−1.08511
$916$	−4.98266	−0.164632
$917$	51.3009	1.69410
$918$	29.4600	0.972323
$919$	31.9509	1.05396	0.526981	−	0.849877i	$-0.323324\pi$
$919$	31.9509	1.05396	0.526981	+	0.849877i	$0.323324\pi$
$920$	−3.78398	−0.124754
$921$	−94.4138	−3.11104
$922$	−20.7126	−0.682134
$923$	26.2642	0.864496
$924$	14.5709	0.479347
$925$	−4.15910	−0.136750
$926$	−14.3722	−0.472300
$927$	42.0907	1.38244
$928$	1.00000	0.0328266
$929$	20.0684	0.658424	0.329212	−	0.944256i	$-0.393217\pi$
$929$	20.0684	0.658424	0.329212	+	0.944256i	$0.393217\pi$
$930$	−18.9316	−0.620791
$931$	0	0
$932$	22.4484	0.735323
$933$	−54.1244	−1.77195
$934$	−10.3038	−0.337150
$935$	7.46579	0.244157
$936$	−32.2498	−1.05412
$937$	−45.1359	−1.47453	−0.737263	−	0.675606i	$-0.763882\pi$
$937$	−45.1359	−1.47453	−0.737263	+	0.675606i	$0.763882\pi$
$938$	−43.7126	−1.42727
$939$	3.37220	0.110048
$940$	−14.8236	−0.483491
$941$	−34.0020	−1.10843	−0.554216	−	0.832373i	$-0.686982\pi$
$941$	−34.0020	−1.10843	−0.554216	+	0.832373i	$0.686982\pi$
$942$	−34.7156	−1.13109
$943$	18.2102	0.593005
$944$	0	0
$945$	78.0675	2.53954
$946$	−4.62488	−0.150368
$947$	−52.8177	−1.71635	−0.858173	−	0.513361i	$-0.828400\pi$
$947$	−52.8177	−1.71635	−0.858173	+	0.513361i	$0.828400\pi$
$948$	20.1447	0.654269
$949$	20.5853	0.668227
$950$	0	0
$951$	−72.0250	−2.33557
$952$	18.4629	0.598385
$953$	12.7156	0.411897	0.205949	−	0.978563i	$-0.433972\pi$
$953$	12.7156	0.411897	0.205949	+	0.978563i	$0.433972\pi$
$954$	−66.9199	−2.16661
$955$	21.1764	0.685253
$956$	−23.7840	−0.769229
$957$	2.94600	0.0952305
$958$	7.58822	0.245164
$959$	69.7637	2.25279
$960$	5.89199	0.190163
$961$	−20.6760	−0.666967
$962$	−23.6190	−0.761509
$963$	−92.9759	−2.99611
$964$	21.1418	0.680930
$965$	11.0337	0.355189
$966$	−27.5680	−0.886985
$967$	−9.46579	−0.304399	−0.152200	−	0.988350i	$-0.548636\pi$
$967$	−9.46579	−0.304399	−0.152200	+	0.988350i	$0.548636\pi$
$968$	1.00000	0.0321412
$969$	0	0
$970$	3.06843	0.0985213
$971$	29.1215	0.934553	0.467277	−	0.884111i	$-0.345235\pi$
$971$	29.1215	0.934553	0.467277	+	0.884111i	$0.345235\pi$
$972$	−5.37220	−0.172313
$973$	−67.6413	−2.16848
$974$	0.414697	0.0132877
$975$	16.7300	0.535788
$976$	−5.57088	−0.178319
$977$	1.75023	0.0559950	0.0279975	−	0.999608i	$-0.491087\pi$
$977$	1.75023	0.0559950	0.0279975	+	0.999608i	$0.491087\pi$
$978$	−31.8862	−1.01961
$979$	0.465785	0.0148866
$980$	34.9257	1.11566
$981$	−99.1697	−3.16624
$982$	−0.823561	−0.0262809
$983$	24.0115	0.765848	0.382924	−	0.923780i	$-0.374917\pi$
$983$	24.0115	0.765848	0.382924	+	0.923780i	$0.374917\pi$
$984$	−28.3549	−0.903920
$985$	−19.0684	−0.607571
$986$	3.73289	0.118880
$987$	−107.996	−3.43756
$988$	0	0
$989$	8.75023	0.278241
$990$	11.3578	0.360974
$991$	−45.8033	−1.45499	−0.727495	−	0.686113i	$-0.759316\pi$
$991$	−45.8033	−1.45499	−0.727495	+	0.686113i	$0.759316\pi$
$992$	−3.21310	−0.102016
$993$	18.5709	0.589329
$994$	−22.8746	−0.725540
$995$	41.2498	1.30771
$996$	42.7666	1.35511
$997$	5.14759	0.163026	0.0815129	−	0.996672i	$-0.474025\pi$
$997$	5.14759	0.163026	0.0815129	+	0.996672i	$0.474025\pi$
$998$	5.35778	0.169597
$999$	32.8236	1.03849

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7942.2.a.bj.1.3		3
19.8	odd	6		418.2.e.i.45.3	✓	6
19.12	odd	6		418.2.e.i.353.3	yes	6
19.18	odd	2		7942.2.a.bd.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.e.i.45.3	✓	6	19.8	odd	6
418.2.e.i.353.3	yes	6	19.12	odd	6
7942.2.a.bd.1.1		3	19.18	odd	2
7942.2.a.bj.1.3		3	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:	\( N \)	\(=\)	\( 7942 = 2 \cdot 11 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7942.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.94600 q^{3} +1.00000 q^{4} +2.00000 q^{5} +2.94600 q^{6} +4.94600 q^{7} +1.00000 q^{8} +5.67889 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.94600 q^{3} +1.00000 q^{4} +2.00000 q^{5} +2.94600 q^{6} +4.94600 q^{7} +1.00000 q^{8} +5.67889 q^{9} +2.00000 q^{10} +1.00000 q^{11} +2.94600 q^{12} -5.67889 q^{13} +4.94600 q^{14} +5.89199 q^{15} +1.00000 q^{16} +3.73289 q^{17} +5.67889 q^{18} +2.00000 q^{20} +14.5709 q^{21} +1.00000 q^{22} -1.89199 q^{23} +2.94600 q^{24} -1.00000 q^{25} -5.67889 q^{26} +7.89199 q^{27} +4.94600 q^{28} +1.00000 q^{29} +5.89199 q^{30} -3.21310 q^{31} +1.00000 q^{32} +2.94600 q^{33} +3.73289 q^{34} +9.89199 q^{35} +5.67889 q^{36} +4.15910 q^{37} -16.7300 q^{39} +2.00000 q^{40} -9.62488 q^{41} +14.5709 q^{42} -4.62488 q^{43} +1.00000 q^{44} +11.3578 q^{45} -1.89199 q^{46} -7.41178 q^{47} +2.94600 q^{48} +17.4629 q^{49} -1.00000 q^{50} +10.9971 q^{51} -5.67889 q^{52} -11.7840 q^{53} +7.89199 q^{54} +2.00000 q^{55} +4.94600 q^{56} +1.00000 q^{58} +5.89199 q^{60} -5.57088 q^{61} -3.21310 q^{62} +28.0878 q^{63} +1.00000 q^{64} -11.3578 q^{65} +2.94600 q^{66} -8.83799 q^{67} +3.73289 q^{68} -5.57379 q^{69} +9.89199 q^{70} -4.62488 q^{71} +5.67889 q^{72} -3.62488 q^{73} +4.15910 q^{74} -2.94600 q^{75} +4.94600 q^{77} -16.7300 q^{78} +6.83799 q^{79} +2.00000 q^{80} +6.21310 q^{81} -9.62488 q^{82} +14.5169 q^{83} +14.5709 q^{84} +7.46579 q^{85} -4.62488 q^{86} +2.94600 q^{87} +1.00000 q^{88} +0.465785 q^{89} +11.3578 q^{90} -28.0878 q^{91} -1.89199 q^{92} -9.46579 q^{93} -7.41178 q^{94} +2.94600 q^{96} +1.53421 q^{97} +17.4629 q^{98} +5.67889 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} + 3 q^{4} + 6 q^{5} + 6 q^{7} + 3 q^{8} + 7 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 + 3 * q^4 + 6 * q^5 + 6 * q^7 + 3 * q^8 + 7 * q^9	\( 3 q + 3 q^{2} + 3 q^{4} + 6 q^{5} + 6 q^{7} + 3 q^{8} + 7 q^{9} + 6 q^{10} + 3 q^{11} - 7 q^{13} + 6 q^{14} + 3 q^{16} + 10 q^{17} + 7 q^{18} + 6 q^{20} + 16 q^{21} + 3 q^{22} + 12 q^{23} - 3 q^{25} - 7 q^{26} + 6 q^{27} + 6 q^{28} + 3 q^{29} - 2 q^{31} + 3 q^{32} + 10 q^{34} + 12 q^{35} + 7 q^{36} - 4 q^{37} - 6 q^{39} + 6 q^{40} - 10 q^{41} + 16 q^{42} + 5 q^{43} + 3 q^{44} + 14 q^{45} + 12 q^{46} - 11 q^{47} + 7 q^{49} - 3 q^{50} - 10 q^{51} - 7 q^{52} + 6 q^{54} + 6 q^{55} + 6 q^{56} + 3 q^{58} + 11 q^{61} - 2 q^{62} + 20 q^{63} + 3 q^{64} - 14 q^{65} + 10 q^{68} - 32 q^{69} + 12 q^{70} + 5 q^{71} + 7 q^{72} + 8 q^{73} - 4 q^{74} + 6 q^{77} - 6 q^{78} - 6 q^{79} + 6 q^{80} + 11 q^{81} - 10 q^{82} + 7 q^{83} + 16 q^{84} + 20 q^{85} + 5 q^{86} + 3 q^{88} - q^{89} + 14 q^{90} - 20 q^{91} + 12 q^{92} - 26 q^{93} - 11 q^{94} + 7 q^{97} + 7 q^{98} + 7 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 + 3 * q^4 + 6 * q^5 + 6 * q^7 + 3 * q^8 + 7 * q^9 + 6 * q^10 + 3 * q^11 - 7 * q^13 + 6 * q^14 + 3 * q^16 + 10 * q^17 + 7 * q^18 + 6 * q^20 + 16 * q^21 + 3 * q^22 + 12 * q^23 - 3 * q^25 - 7 * q^26 + 6 * q^27 + 6 * q^28 + 3 * q^29 - 2 * q^31 + 3 * q^32 + 10 * q^34 + 12 * q^35 + 7 * q^36 - 4 * q^37 - 6 * q^39 + 6 * q^40 - 10 * q^41 + 16 * q^42 + 5 * q^43 + 3 * q^44 + 14 * q^45 + 12 * q^46 - 11 * q^47 + 7 * q^49 - 3 * q^50 - 10 * q^51 - 7 * q^52 + 6 * q^54 + 6 * q^55 + 6 * q^56 + 3 * q^58 + 11 * q^61 - 2 * q^62 + 20 * q^63 + 3 * q^64 - 14 * q^65 + 10 * q^68 - 32 * q^69 + 12 * q^70 + 5 * q^71 + 7 * q^72 + 8 * q^73 - 4 * q^74 + 6 * q^77 - 6 * q^78 - 6 * q^79 + 6 * q^80 + 11 * q^81 - 10 * q^82 + 7 * q^83 + 16 * q^84 + 20 * q^85 + 5 * q^86 + 3 * q^88 - q^89 + 14 * q^90 - 20 * q^91 + 12 * q^92 - 26 * q^93 - 11 * q^94 + 7 * q^97 + 7 * q^98 + 7 * q^99

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