LMFDB - Embedded newform 1862.2.a.r.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1862,2,Mod(1,1862)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1862, 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("1862.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1862 = 2 \cdot 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1862.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:	$14.8681448564$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.469.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 5x + 4 $ x^3 - x^2 - 5*x + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 266)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.39138$ of defining polynomial
Character	$\chi$	$=$	1862.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.71871 q^{3} +1.00000 q^{4} +0.391382 q^{5} -1.71871 q^{6} +1.00000 q^{8} -0.0460370 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.71871 q^{3} +1.00000 q^{4} +0.391382 q^{5} -1.71871 q^{6} +1.00000 q^{8} -0.0460370 q^{9} +0.391382 q^{10} +3.06406 q^{11} -1.71871 q^{12} -2.78276 q^{13} -0.672673 q^{15} +1.00000 q^{16} +6.22018 q^{17} -0.0460370 q^{18} +1.00000 q^{19} +0.391382 q^{20} +3.06406 q^{22} -4.78276 q^{23} -1.71871 q^{24} -4.84682 q^{25} -2.78276 q^{26} +5.23525 q^{27} +7.82880 q^{29} -0.672673 q^{30} -1.34535 q^{31} +1.00000 q^{32} -5.26622 q^{33} +6.22018 q^{34} -0.0460370 q^{36} -3.82880 q^{37} +1.00000 q^{38} +4.78276 q^{39} +0.391382 q^{40} +4.39138 q^{41} +5.82880 q^{43} +3.06406 q^{44} -0.0180181 q^{45} -4.78276 q^{46} +5.71871 q^{47} -1.71871 q^{48} -4.84682 q^{50} -10.6907 q^{51} -2.78276 q^{52} +7.15613 q^{53} +5.23525 q^{54} +1.19922 q^{55} -1.71871 q^{57} +7.82880 q^{58} +7.17415 q^{59} -0.672673 q^{60} -8.50147 q^{61} -1.34535 q^{62} +1.00000 q^{64} -1.08913 q^{65} -5.26622 q^{66} +12.2202 q^{67} +6.22018 q^{68} +8.22018 q^{69} +0.935945 q^{71} -0.0460370 q^{72} +4.12811 q^{73} -3.82880 q^{74} +8.33028 q^{75} +1.00000 q^{76} +4.78276 q^{78} +2.95396 q^{79} +0.391382 q^{80} -8.85977 q^{81} +4.39138 q^{82} +13.5655 q^{83} +2.43447 q^{85} +5.82880 q^{86} -13.4554 q^{87} +3.06406 q^{88} -1.06406 q^{89} -0.0180181 q^{90} -4.78276 q^{92} +2.31226 q^{93} +5.71871 q^{94} +0.391382 q^{95} -1.71871 q^{96} -4.50147 q^{97} -0.141060 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} + q^{3} + 3 q^{4} - 5 q^{5} + q^{6} + 3 q^{8} + 6 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 + q^3 + 3 * q^4 - 5 * q^5 + q^6 + 3 * q^8 + 6 * q^9	$ 3 q + 3 q^{2} + q^{3} + 3 q^{4} - 5 q^{5} + q^{6} + 3 q^{8} + 6 q^{9} - 5 q^{10} + 3 q^{11} + q^{12} + 4 q^{13} - 2 q^{15} + 3 q^{16} - 6 q^{17} + 6 q^{18} + 3 q^{19} - 5 q^{20} + 3 q^{22} - 2 q^{23} + q^{24} + 4 q^{25} + 4 q^{26} + 28 q^{27} + 5 q^{29} - 2 q^{30} - 4 q^{31} + 3 q^{32} + 15 q^{33} - 6 q^{34} + 6 q^{36} + 7 q^{37} + 3 q^{38} + 2 q^{39} - 5 q^{40} + 7 q^{41} - q^{43} + 3 q^{44} - 2 q^{46} + 11 q^{47} + q^{48} + 4 q^{50} - 32 q^{51} + 4 q^{52} + 3 q^{53} + 28 q^{54} + 16 q^{55} + q^{57} + 5 q^{58} + 3 q^{59} - 2 q^{60} - 7 q^{61} - 4 q^{62} + 3 q^{64} - 28 q^{65} + 15 q^{66} + 12 q^{67} - 6 q^{68} + 9 q^{71} + 6 q^{72} + 7 q^{74} - 12 q^{75} + 3 q^{76} + 2 q^{78} + 15 q^{79} - 5 q^{80} + 35 q^{81} + 7 q^{82} + 16 q^{83} + 32 q^{85} - q^{86} - 28 q^{87} + 3 q^{88} + 3 q^{89} - 2 q^{92} - 30 q^{93} + 11 q^{94} - 5 q^{95} + q^{96} + 5 q^{97} + 55 q^{99}+O(q^{100}) $ 3 * q + 3 * q^2 + q^3 + 3 * q^4 - 5 * q^5 + q^6 + 3 * q^8 + 6 * q^9 - 5 * q^10 + 3 * q^11 + q^12 + 4 * q^13 - 2 * q^15 + 3 * q^16 - 6 * q^17 + 6 * q^18 + 3 * q^19 - 5 * q^20 + 3 * q^22 - 2 * q^23 + q^24 + 4 * q^25 + 4 * q^26 + 28 * q^27 + 5 * q^29 - 2 * q^30 - 4 * q^31 + 3 * q^32 + 15 * q^33 - 6 * q^34 + 6 * q^36 + 7 * q^37 + 3 * q^38 + 2 * q^39 - 5 * q^40 + 7 * q^41 - q^43 + 3 * q^44 - 2 * q^46 + 11 * q^47 + q^48 + 4 * q^50 - 32 * q^51 + 4 * q^52 + 3 * q^53 + 28 * q^54 + 16 * q^55 + q^57 + 5 * q^58 + 3 * q^59 - 2 * q^60 - 7 * q^61 - 4 * q^62 + 3 * q^64 - 28 * q^65 + 15 * q^66 + 12 * q^67 - 6 * q^68 + 9 * q^71 + 6 * q^72 + 7 * q^74 - 12 * q^75 + 3 * q^76 + 2 * q^78 + 15 * q^79 - 5 * q^80 + 35 * q^81 + 7 * q^82 + 16 * q^83 + 32 * q^85 - q^86 - 28 * q^87 + 3 * q^88 + 3 * q^89 - 2 * q^92 - 30 * q^93 + 11 * q^94 - 5 * q^95 + q^96 + 5 * q^97 + 55 * 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
$3$	−1.71871	−0.992298	−0.496149	−	0.868238i	$-0.665253\pi$
$3$	−1.71871	−0.992298	−0.496149	+	0.868238i	$0.665253\pi$
$4$	1.00000	0.500000
$5$	0.391382	0.175032	0.0875158	−	0.996163i	$-0.472107\pi$
$5$	0.391382	0.175032	0.0875158	+	0.996163i	$0.472107\pi$
$6$	−1.71871	−0.701660
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	−0.0460370	−0.0153457
$10$	0.391382	0.123766
$11$	3.06406	0.923847	0.461924	−	0.886920i	$-0.347159\pi$
$11$	3.06406	0.923847	0.461924	+	0.886920i	$0.347159\pi$
$12$	−1.71871	−0.496149
$13$	−2.78276	−0.771800	−0.385900	−	0.922541i	$-0.626109\pi$
$13$	−2.78276	−0.771800	−0.385900	+	0.922541i	$0.626109\pi$
$14$	0	0
$15$	−0.672673	−0.173683
$16$	1.00000	0.250000
$17$	6.22018	1.50862	0.754308	−	0.656521i	$-0.227972\pi$
$17$	6.22018	1.50862	0.754308	+	0.656521i	$0.227972\pi$
$18$	−0.0460370	−0.0108510
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	0.391382	0.0875158
$21$	0	0
$22$	3.06406	0.653259
$23$	−4.78276	−0.997275	−0.498638	−	0.866811i	$-0.666166\pi$
$23$	−4.78276	−0.997275	−0.498638	+	0.866811i	$0.666166\pi$
$24$	−1.71871	−0.350830
$25$	−4.84682	−0.969364
$26$	−2.78276	−0.545745
$27$	5.23525	1.00752
$28$	0	0
$29$	7.82880	1.45377	0.726886	−	0.686758i	$-0.240967\pi$
$29$	7.82880	1.45377	0.726886	+	0.686758i	$0.240967\pi$
$30$	−0.672673	−0.122813
$31$	−1.34535	−0.241631	−0.120816	−	0.992675i	$-0.538551\pi$
$31$	−1.34535	−0.241631	−0.120816	+	0.992675i	$0.538551\pi$
$32$	1.00000	0.176777
$33$	−5.26622	−0.916731
$34$	6.22018	1.06675
$35$	0	0
$36$	−0.0460370	−0.00767283
$37$	−3.82880	−0.629451	−0.314726	−	0.949183i	$-0.601912\pi$
$37$	−3.82880	−0.629451	−0.314726	+	0.949183i	$0.601912\pi$
$38$	1.00000	0.162221
$39$	4.78276	0.765855
$40$	0.391382	0.0618830
$41$	4.39138	0.685819	0.342909	−	0.939368i	$-0.388588\pi$
$41$	4.39138	0.685819	0.342909	+	0.939368i	$0.388588\pi$
$42$	0	0
$43$	5.82880	0.888884	0.444442	−	0.895808i	$-0.353402\pi$
$43$	5.82880	0.888884	0.444442	+	0.895808i	$0.353402\pi$
$44$	3.06406	0.461924
$45$	−0.0180181	−0.00268598
$46$	−4.78276	−0.705180
$47$	5.71871	0.834160	0.417080	−	0.908870i	$-0.363054\pi$
$47$	5.71871	0.834160	0.417080	+	0.908870i	$0.363054\pi$
$48$	−1.71871	−0.248074
$49$	0	0
$50$	−4.84682	−0.685444
$51$	−10.6907	−1.49700
$52$	−2.78276	−0.385900
$53$	7.15613	0.982970	0.491485	−	0.870886i	$-0.336454\pi$
$53$	7.15613	0.982970	0.491485	+	0.870886i	$0.336454\pi$
$54$	5.23525	0.712428
$55$	1.19922	0.161702
$56$	0	0
$57$	−1.71871	−0.227649
$58$	7.82880	1.02797
$59$	7.17415	0.933994	0.466997	−	0.884259i	$-0.345336\pi$
$59$	7.17415	0.933994	0.466997	+	0.884259i	$0.345336\pi$
$60$	−0.672673	−0.0868417
$61$	−8.50147	−1.08850	−0.544251	−	0.838922i	$-0.683186\pi$
$61$	−8.50147	−1.08850	−0.544251	+	0.838922i	$0.683186\pi$
$62$	−1.34535	−0.170859
$63$	0	0
$64$	1.00000	0.125000
$65$	−1.08913	−0.135089
$66$	−5.26622	−0.648227
$67$	12.2202	1.49293	0.746467	−	0.665423i	$-0.231749\pi$
$67$	12.2202	1.49293	0.746467	+	0.665423i	$0.231749\pi$
$68$	6.22018	0.754308
$69$	8.22018	0.989594
$70$	0	0
$71$	0.935945	0.111076	0.0555381	−	0.998457i	$-0.482313\pi$
$71$	0.935945	0.111076	0.0555381	+	0.998457i	$0.482313\pi$
$72$	−0.0460370	−0.00542551
$73$	4.12811	0.483159	0.241579	−	0.970381i	$-0.422335\pi$
$73$	4.12811	0.483159	0.241579	+	0.970381i	$0.422335\pi$
$74$	−3.82880	−0.445089
$75$	8.33028	0.961897
$76$	1.00000	0.114708
$77$	0	0
$78$	4.78276	0.541541
$79$	2.95396	0.332347	0.166173	−	0.986097i	$-0.446859\pi$
$79$	2.95396	0.332347	0.166173	+	0.986097i	$0.446859\pi$
$80$	0.391382	0.0437579
$81$	−8.85977	−0.984419
$82$	4.39138	0.484947
$83$	13.5655	1.48901	0.744505	−	0.667617i	$-0.232685\pi$
$83$	13.5655	1.48901	0.744505	+	0.667617i	$0.232685\pi$
$84$	0	0
$85$	2.43447	0.264055
$86$	5.82880	0.628536
$87$	−13.4554	−1.44257
$88$	3.06406	0.326629
$89$	−1.06406	−0.112790	−0.0563948	−	0.998409i	$-0.517961\pi$
$89$	−1.06406	−0.112790	−0.0563948	+	0.998409i	$0.517961\pi$
$90$	−0.0180181	−0.00189927
$91$	0	0
$92$	−4.78276	−0.498638
$93$	2.31226	0.239770
$94$	5.71871	0.589840
$95$	0.391382	0.0401550
$96$	−1.71871	−0.175415
$97$	−4.50147	−0.457055	−0.228528	−	0.973537i	$-0.573391\pi$
$97$	−4.50147	−0.457055	−0.228528	+	0.973537i	$0.573391\pi$
$98$	0	0
$99$	−0.141060	−0.0141771
$100$	−4.84682	−0.484682
$101$	−17.1311	−1.70460	−0.852302	−	0.523050i	$-0.824794\pi$
$101$	−17.1311	−1.70460	−0.852302	+	0.523050i	$0.824794\pi$
$102$	−10.6907	−1.05854
$103$	2.09207	0.206138	0.103069	−	0.994674i	$-0.467134\pi$
$103$	2.09207	0.206138	0.103069	+	0.994674i	$0.467134\pi$
$104$	−2.78276	−0.272873
$105$	0	0
$106$	7.15613	0.695065
$107$	−14.0921	−1.36233	−0.681166	−	0.732129i	$-0.738527\pi$
$107$	−14.0921	−1.36233	−0.681166	+	0.732129i	$0.738527\pi$
$108$	5.23525	0.503762
$109$	15.1561	1.45169	0.725847	−	0.687856i	$-0.241448\pi$
$109$	15.1561	1.45169	0.725847	+	0.687856i	$0.241448\pi$
$110$	1.19922	0.114341
$111$	6.58060	0.624603
$112$	0	0
$113$	19.7857	1.86128	0.930642	−	0.365932i	$-0.119250\pi$
$113$	19.7857	1.86128	0.930642	+	0.365932i	$0.119250\pi$
$114$	−1.71871	−0.160972
$115$	−1.87189	−0.174555
$116$	7.82880	0.726886
$117$	0.128110	0.0118438
$118$	7.17415	0.660434
$119$	0	0
$120$	−0.672673	−0.0614063
$121$	−1.61157	−0.146506
$122$	−8.50147	−0.769687
$123$	−7.54751	−0.680536
$124$	−1.34535	−0.120816
$125$	−3.85387	−0.344701
$126$	0	0
$127$	2.50147	0.221970	0.110985	−	0.993822i	$-0.464599\pi$
$127$	2.50147	0.221970	0.110985	+	0.993822i	$0.464599\pi$
$128$	1.00000	0.0883883
$129$	−10.0180	−0.882037
$130$	−1.08913	−0.0955226
$131$	15.4374	1.34877	0.674387	−	0.738378i	$-0.264408\pi$
$131$	15.4374	1.34877	0.674387	+	0.738378i	$0.264408\pi$
$132$	−5.26622	−0.458366
$133$	0	0
$134$	12.2202	1.05566
$135$	2.04899	0.176349
$136$	6.22018	0.533376
$137$	13.9209	1.18934	0.594670	−	0.803970i	$-0.297283\pi$
$137$	13.9209	1.18934	0.594670	+	0.803970i	$0.297283\pi$
$138$	8.22018	0.699749
$139$	−10.8748	−0.922392	−0.461196	−	0.887298i	$-0.652579\pi$
$139$	−10.8748	−0.922392	−0.461196	+	0.887298i	$0.652579\pi$
$140$	0	0
$141$	−9.82880	−0.827734
$142$	0.935945	0.0785428
$143$	−8.52654	−0.713025
$144$	−0.0460370	−0.00383642
$145$	3.06406	0.254456
$146$	4.12811	0.341645
$147$	0	0
$148$	−3.82880	−0.314726
$149$	−1.77982	−0.145808	−0.0729041	−	0.997339i	$-0.523227\pi$
$149$	−1.77982	−0.145808	−0.0729041	+	0.997339i	$0.523227\pi$
$150$	8.33028	0.680164
$151$	5.30931	0.432065	0.216033	−	0.976386i	$-0.430688\pi$
$151$	5.30931	0.432065	0.216033	+	0.976386i	$0.430688\pi$
$152$	1.00000	0.0811107
$153$	−0.286359	−0.0231507
$154$	0	0
$155$	−0.526544	−0.0422931
$156$	4.78276	0.382928
$157$	−15.3763	−1.22716	−0.613582	−	0.789631i	$-0.710272\pi$
$157$	−15.3763	−1.22716	−0.613582	+	0.789631i	$0.710272\pi$
$158$	2.95396	0.235005
$159$	−12.2993	−0.975399
$160$	0.391382	0.0309415
$161$	0	0
$162$	−8.85977	−0.696089
$163$	17.9389	1.40508	0.702541	−	0.711643i	$-0.252049\pi$
$163$	17.9389	1.40508	0.702541	+	0.711643i	$0.252049\pi$
$164$	4.39138	0.342909
$165$	−2.06111	−0.160457
$166$	13.5655	1.05289
$167$	13.5295	1.04694	0.523472	−	0.852043i	$-0.324637\pi$
$167$	13.5295	1.04694	0.523472	+	0.852043i	$0.324637\pi$
$168$	0	0
$169$	−5.25622	−0.404325
$170$	2.43447	0.186715
$171$	−0.0460370	−0.00352054
$172$	5.82880	0.444442
$173$	8.12811	0.617969	0.308984	−	0.951067i	$-0.400011\pi$
$173$	8.12811	0.617969	0.308984	+	0.951067i	$0.400011\pi$
$174$	−13.4554	−1.02005
$175$	0	0
$176$	3.06406	0.230962
$177$	−12.3303	−0.926800
$178$	−1.06406	−0.0797543
$179$	−11.4735	−0.857566	−0.428783	−	0.903407i	$-0.641058\pi$
$179$	−11.4735	−0.857566	−0.428783	+	0.903407i	$0.641058\pi$
$180$	−0.0180181	−0.00134299
$181$	−16.3123	−1.21248	−0.606240	−	0.795282i	$-0.707323\pi$
$181$	−16.3123	−1.21248	−0.606240	+	0.795282i	$0.707323\pi$
$182$	0	0
$183$	14.6116	1.08012
$184$	−4.78276	−0.352590
$185$	−1.49853	−0.110174
$186$	2.31226	0.169543
$187$	19.0590	1.39373
$188$	5.71871	0.417080
$189$	0	0
$190$	0.391382	0.0283939
$191$	−15.4735	−1.11962	−0.559810	−	0.828621i	$-0.689126\pi$
$191$	−15.4735	−1.11962	−0.559810	+	0.828621i	$0.689126\pi$
$192$	−1.71871	−0.124037
$193$	7.00295	0.504083	0.252042	−	0.967716i	$-0.418898\pi$
$193$	7.00295	0.504083	0.252042	+	0.967716i	$0.418898\pi$
$194$	−4.50147	−0.323187
$195$	1.87189	0.134049
$196$	0	0
$197$	−10.4404	−0.743845	−0.371923	−	0.928264i	$-0.621301\pi$
$197$	−10.4404	−0.743845	−0.371923	+	0.928264i	$0.621301\pi$
$198$	−0.141060	−0.0100247
$199$	6.83175	0.484290	0.242145	−	0.970240i	$-0.422149\pi$
$199$	6.83175	0.484290	0.242145	+	0.970240i	$0.422149\pi$
$200$	−4.84682	−0.342722
$201$	−21.0029	−1.48143
$202$	−17.1311	−1.20534
$203$	0	0
$204$	−10.6907	−0.748498
$205$	1.71871	0.120040
$206$	2.09207	0.145762
$207$	0.220184	0.0153039
$208$	−2.78276	−0.192950
$209$	3.06406	0.211945
$210$	0	0
$211$	−9.30931	−0.640879	−0.320440	−	0.947269i	$-0.603831\pi$
$211$	−9.30931	−0.640879	−0.320440	+	0.947269i	$0.603831\pi$
$212$	7.15613	0.491485
$213$	−1.60862	−0.110221
$214$	−14.0921	−0.963314
$215$	2.28129	0.155583
$216$	5.23525	0.356214
$217$	0	0
$218$	15.1561	1.02650
$219$	−7.09502	−0.479437
$220$	1.19922	0.0808512
$221$	−17.3093	−1.16435
$222$	6.58060	0.441661
$223$	2.31226	0.154840	0.0774201	−	0.996999i	$-0.475332\pi$
$223$	2.31226	0.154840	0.0774201	+	0.996999i	$0.475332\pi$
$224$	0	0
$225$	0.223133	0.0148755
$226$	19.7857	1.31613
$227$	−12.4404	−0.825696	−0.412848	−	0.910800i	$-0.635466\pi$
$227$	−12.4404	−0.825696	−0.412848	+	0.910800i	$0.635466\pi$
$228$	−1.71871	−0.113824
$229$	−15.6086	−1.03145	−0.515723	−	0.856755i	$-0.672477\pi$
$229$	−15.6086	−1.03145	−0.515723	+	0.856755i	$0.672477\pi$
$230$	−1.87189	−0.123429
$231$	0	0
$232$	7.82880	0.513986
$233$	−5.28424	−0.346182	−0.173091	−	0.984906i	$-0.555375\pi$
$233$	−5.28424	−0.346182	−0.173091	+	0.984906i	$0.555375\pi$
$234$	0.128110	0.00837482
$235$	2.23820	0.146004
$236$	7.17415	0.466997
$237$	−5.07700	−0.329787
$238$	0	0
$239$	1.87189	0.121082	0.0605412	−	0.998166i	$-0.480717\pi$
$239$	1.87189	0.121082	0.0605412	+	0.998166i	$0.480717\pi$
$240$	−0.672673	−0.0434208
$241$	22.4835	1.44829	0.724143	−	0.689649i	$-0.242235\pi$
$241$	22.4835	1.44829	0.724143	+	0.689649i	$0.242235\pi$
$242$	−1.61157	−0.103595
$243$	−0.478388	−0.0306886
$244$	−8.50147	−0.544251
$245$	0	0
$246$	−7.54751	−0.481212
$247$	−2.78276	−0.177063
$248$	−1.34535	−0.0854295
$249$	−23.3152	−1.47754
$250$	−3.85387	−0.243740
$251$	−11.6936	−0.738096	−0.369048	−	0.929410i	$-0.620316\pi$
$251$	−11.6936	−0.738096	−0.369048	+	0.929410i	$0.620316\pi$
$252$	0	0
$253$	−14.6547	−0.921330
$254$	2.50147	0.156956
$255$	−4.18415	−0.262022
$256$	1.00000	0.0625000
$257$	2.82585	0.176272	0.0881359	−	0.996108i	$-0.471909\pi$
$257$	2.82585	0.176272	0.0881359	+	0.996108i	$0.471909\pi$
$258$	−10.0180	−0.623695
$259$	0	0
$260$	−1.08913	−0.0675447
$261$	−0.360415	−0.0223091
$262$	15.4374	0.953727
$263$	−29.4433	−1.81555	−0.907776	−	0.419455i	$-0.862221\pi$
$263$	−29.4433	−1.81555	−0.907776	+	0.419455i	$0.862221\pi$
$264$	−5.26622	−0.324114
$265$	2.80078	0.172051
$266$	0	0
$267$	1.82880	0.111921
$268$	12.2202	0.746467
$269$	10.4404	0.636560	0.318280	−	0.947997i	$-0.396895\pi$
$269$	10.4404	0.636560	0.318280	+	0.947997i	$0.396895\pi$
$270$	2.04899	0.124697
$271$	4.29931	0.261164	0.130582	−	0.991437i	$-0.458315\pi$
$271$	4.29931	0.261164	0.130582	+	0.991437i	$0.458315\pi$
$272$	6.22018	0.377154
$273$	0	0
$274$	13.9209	0.840991
$275$	−14.8509	−0.895544
$276$	8.22018	0.494797
$277$	−28.7526	−1.72758	−0.863789	−	0.503854i	$-0.831915\pi$
$277$	−28.7526	−1.72758	−0.863789	+	0.503854i	$0.831915\pi$
$278$	−10.8748	−0.652229
$279$	0.0619357	0.00370799
$280$	0	0
$281$	−20.6547	−1.23215	−0.616077	−	0.787686i	$-0.711279\pi$
$281$	−20.6547	−1.23215	−0.616077	+	0.787686i	$0.711279\pi$
$282$	−9.82880	−0.585297
$283$	9.30931	0.553381	0.276690	−	0.960959i	$-0.410762\pi$
$283$	9.30931	0.553381	0.276690	+	0.960959i	$0.410762\pi$
$284$	0.935945	0.0555381
$285$	−0.672673	−0.0398457
$286$	−8.52654	−0.504185
$287$	0	0
$288$	−0.0460370	−0.00271276
$289$	21.6907	1.27592
$290$	3.06406	0.179928
$291$	7.73673	0.453535
$292$	4.12811	0.241579
$293$	−1.65760	−0.0968382	−0.0484191	−	0.998827i	$-0.515418\pi$
$293$	−1.65760	−0.0968382	−0.0484191	+	0.998827i	$0.515418\pi$
$294$	0	0
$295$	2.80783	0.163478
$296$	−3.82880	−0.222545
$297$	16.0411	0.930799
$298$	−1.77982	−0.103102
$299$	13.3093	0.769697
$300$	8.33028	0.480949
$301$	0	0
$302$	5.30931	0.305516
$303$	29.4433	1.69147
$304$	1.00000	0.0573539
$305$	−3.32733	−0.190522
$306$	−0.286359	−0.0163700
$307$	31.0880	1.77428	0.887142	−	0.461496i	$-0.152687\pi$
$307$	31.0880	1.77428	0.887142	+	0.461496i	$0.152687\pi$
$308$	0	0
$309$	−3.59567	−0.204550
$310$	−0.526544	−0.0299057
$311$	−11.8468	−0.671772	−0.335886	−	0.941903i	$-0.609036\pi$
$311$	−11.8468	−0.671772	−0.335886	+	0.941903i	$0.609036\pi$
$312$	4.78276	0.270771
$313$	−34.6606	−1.95913	−0.979565	−	0.201127i	$-0.935540\pi$
$313$	−34.6606	−1.95913	−0.979565	+	0.201127i	$0.935540\pi$
$314$	−15.3763	−0.867736
$315$	0	0
$316$	2.95396	0.166173
$317$	−16.4654	−0.924791	−0.462396	−	0.886674i	$-0.653010\pi$
$317$	−16.4654	−0.924791	−0.462396	+	0.886674i	$0.653010\pi$
$318$	−12.2993	−0.689711
$319$	23.9879	1.34306
$320$	0.391382	0.0218789
$321$	24.2202	1.35184
$322$	0	0
$323$	6.22018	0.346100
$324$	−8.85977	−0.492209
$325$	13.4876	0.748155
$326$	17.9389	0.993543
$327$	−26.0490	−1.44051
$328$	4.39138	0.242474
$329$	0	0
$330$	−2.06111	−0.113460
$331$	−3.09502	−0.170118	−0.0850589	−	0.996376i	$-0.527108\pi$
$331$	−3.09502	−0.170118	−0.0850589	+	0.996376i	$0.527108\pi$
$332$	13.5655	0.744505
$333$	0.176267	0.00965935
$334$	13.5295	0.740301
$335$	4.78276	0.261310
$336$	0	0
$337$	−24.5324	−1.33637	−0.668184	−	0.743996i	$-0.732928\pi$
$337$	−24.5324	−1.33637	−0.668184	+	0.743996i	$0.732928\pi$
$338$	−5.25622	−0.285901
$339$	−34.0059	−1.84695
$340$	2.43447	0.132028
$341$	−4.12221	−0.223230
$342$	−0.0460370	−0.00248940
$343$	0	0
$344$	5.82880	0.314268
$345$	3.21724	0.173210
$346$	8.12811	0.436970
$347$	5.56553	0.298773	0.149387	−	0.988779i	$-0.452270\pi$
$347$	5.56553	0.298773	0.149387	+	0.988779i	$0.452270\pi$
$348$	−13.4554	−0.721287
$349$	−25.1311	−1.34523	−0.672617	−	0.739990i	$-0.734830\pi$
$349$	−25.1311	−1.34523	−0.672617	+	0.739990i	$0.734830\pi$
$350$	0	0
$351$	−14.5685	−0.777608
$352$	3.06406	0.163315
$353$	3.52949	0.187856	0.0939280	−	0.995579i	$-0.470058\pi$
$353$	3.52949	0.187856	0.0939280	+	0.995579i	$0.470058\pi$
$354$	−12.3303	−0.655347
$355$	0.366312	0.0194418
$356$	−1.06406	−0.0563948
$357$	0	0
$358$	−11.4735	−0.606391
$359$	24.9669	1.31770	0.658852	−	0.752273i	$-0.271042\pi$
$359$	24.9669	1.31770	0.658852	+	0.752273i	$0.271042\pi$
$360$	−0.0180181	−0.000949636 0
$361$	1.00000	0.0526316
$362$	−16.3123	−0.857353
$363$	2.76981	0.145378
$364$	0	0
$365$	1.61567	0.0845680
$366$	14.6116	0.763759
$367$	15.2842	0.797831	0.398915	−	0.916988i	$-0.369387\pi$
$367$	15.2842	0.797831	0.398915	+	0.916988i	$0.369387\pi$
$368$	−4.78276	−0.249319
$369$	−0.202166	−0.0105243
$370$	−1.49853	−0.0779046
$371$	0	0
$372$	2.31226	0.119885
$373$	−17.0519	−0.882916	−0.441458	−	0.897282i	$-0.645539\pi$
$373$	−17.0519	−0.882916	−0.441458	+	0.897282i	$0.645539\pi$
$374$	19.0590	0.985517
$375$	6.62369	0.342046
$376$	5.71871	0.294920
$377$	−21.7857	−1.12202
$378$	0	0
$379$	17.0029	0.873383	0.436691	−	0.899611i	$-0.356150\pi$
$379$	17.0029	0.873383	0.436691	+	0.899611i	$0.356150\pi$
$380$	0.391382	0.0200775
$381$	−4.29931	−0.220260
$382$	−15.4735	−0.791691
$383$	−29.2231	−1.49323	−0.746616	−	0.665255i	$-0.768323\pi$
$383$	−29.2231	−1.49323	−0.746616	+	0.665255i	$0.768323\pi$
$384$	−1.71871	−0.0877075
$385$	0	0
$386$	7.00295	0.356441
$387$	−0.268341	−0.0136405
$388$	−4.50147	−0.228528
$389$	−26.4404	−1.34058	−0.670290	−	0.742099i	$-0.733830\pi$
$389$	−26.4404	−1.34058	−0.670290	+	0.742099i	$0.733830\pi$
$390$	1.87189	0.0947868
$391$	−29.7497	−1.50451
$392$	0	0
$393$	−26.5324	−1.33838
$394$	−10.4404	−0.525978
$395$	1.15613	0.0581712
$396$	−0.141060	−0.00708853
$397$	−18.5074	−0.928858	−0.464429	−	0.885610i	$-0.653740\pi$
$397$	−18.5074	−0.928858	−0.464429	+	0.885610i	$0.653740\pi$
$398$	6.83175	0.342445
$399$	0	0
$400$	−4.84682	−0.242341
$401$	−32.2261	−1.60929	−0.804647	−	0.593754i	$-0.797645\pi$
$401$	−32.2261	−1.60929	−0.804647	+	0.593754i	$0.797645\pi$
$402$	−21.0029	−1.04753
$403$	3.74378	0.186491
$404$	−17.1311	−0.852302
$405$	−3.46756	−0.172304
$406$	0	0
$407$	−11.7317	−0.581517
$408$	−10.6907	−0.529268
$409$	−19.3763	−0.958097	−0.479049	−	0.877788i	$-0.659018\pi$
$409$	−19.3763	−0.958097	−0.479049	+	0.877788i	$0.659018\pi$
$410$	1.71871	0.0848810
$411$	−23.9259	−1.18018
$412$	2.09207	0.103069
$413$	0	0
$414$	0.220184	0.0108215
$415$	5.30931	0.260624
$416$	−2.78276	−0.136436
$417$	18.6907	0.915287
$418$	3.06406	0.149868
$419$	−27.5354	−1.34519	−0.672596	−	0.740010i	$-0.734821\pi$
$419$	−27.5354	−1.34519	−0.672596	+	0.740010i	$0.734821\pi$
$420$	0	0
$421$	−16.4345	−0.800967	−0.400484	−	0.916304i	$-0.631158\pi$
$421$	−16.4345	−0.800967	−0.400484	+	0.916304i	$0.631158\pi$
$422$	−9.30931	−0.453170
$423$	−0.263272	−0.0128007
$424$	7.15613	0.347532
$425$	−30.1481	−1.46240
$426$	−1.60862	−0.0779378
$427$	0	0
$428$	−14.0921	−0.681166
$429$	14.6547	0.707533
$430$	2.28129	0.110014
$431$	40.9979	1.97480	0.987399	−	0.158249i	$-0.0505849\pi$
$431$	40.9979	1.97480	0.987399	+	0.158249i	$0.0505849\pi$
$432$	5.23525	0.251881
$433$	22.4835	1.08049	0.540243	−	0.841509i	$-0.318332\pi$
$433$	22.4835	1.08049	0.540243	+	0.841509i	$0.318332\pi$
$434$	0	0
$435$	−5.26622	−0.252496
$436$	15.1561	0.725847
$437$	−4.78276	−0.228791
$438$	−7.09502	−0.339013
$439$	18.9109	0.902567	0.451283	−	0.892381i	$-0.350966\pi$
$439$	18.9109	0.902567	0.451283	+	0.892381i	$0.350966\pi$
$440$	1.19922	0.0571704
$441$	0	0
$442$	−17.3093	−0.823320
$443$	−10.0850	−0.479154	−0.239577	−	0.970877i	$-0.577009\pi$
$443$	−10.0850	−0.479154	−0.239577	+	0.970877i	$0.577009\pi$
$444$	6.58060	0.312301
$445$	−0.416452	−0.0197417
$446$	2.31226	0.109489
$447$	3.05899	0.144685
$448$	0	0
$449$	17.9138	0.845406	0.422703	−	0.906268i	$-0.361081\pi$
$449$	17.9138	0.845406	0.422703	+	0.906268i	$0.361081\pi$
$450$	0.223133	0.0105186
$451$	13.4554	0.633592
$452$	19.7857	0.930642
$453$	−9.12516	−0.428737
$454$	−12.4404	−0.583855
$455$	0	0
$456$	−1.71871	−0.0804860
$457$	23.8527	1.11578	0.557892	−	0.829914i	$-0.311611\pi$
$457$	23.8527	1.11578	0.557892	+	0.829914i	$0.311611\pi$
$458$	−15.6086	−0.729343
$459$	32.5642	1.51997
$460$	−1.87189	−0.0872773
$461$	−22.2512	−1.03634	−0.518170	−	0.855278i	$-0.673386\pi$
$461$	−22.2512	−1.03634	−0.518170	+	0.855278i	$0.673386\pi$
$462$	0	0
$463$	27.8778	1.29559	0.647795	−	0.761814i	$-0.275691\pi$
$463$	27.8778	1.29559	0.647795	+	0.761814i	$0.275691\pi$
$464$	7.82880	0.363443
$465$	0.904977	0.0419673
$466$	−5.28424	−0.244788
$467$	24.0980	1.11512	0.557561	−	0.830136i	$-0.311737\pi$
$467$	24.0980	1.11512	0.557561	+	0.830136i	$0.311737\pi$
$468$	0.128110	0.00592189
$469$	0	0
$470$	2.23820	0.103241
$471$	26.4274	1.21771
$472$	7.17415	0.330217
$473$	17.8598	0.821193
$474$	−5.07700	−0.233195
$475$	−4.84682	−0.222387
$476$	0	0
$477$	−0.329447	−0.0150843
$478$	1.87189	0.0856182
$479$	8.92382	0.407740	0.203870	−	0.978998i	$-0.434648\pi$
$479$	8.92382	0.407740	0.203870	+	0.978998i	$0.434648\pi$
$480$	−0.672673	−0.0307032
$481$	10.6547	0.485810
$482$	22.4835	1.02409
$483$	0	0
$484$	−1.61157	−0.0732530
$485$	−1.76180	−0.0799991
$486$	−0.478388	−0.0217001
$487$	−41.0578	−1.86051	−0.930254	−	0.366916i	$-0.880414\pi$
$487$	−41.0578	−1.86051	−0.930254	+	0.366916i	$0.880414\pi$
$488$	−8.50147	−0.384844
$489$	−30.8318	−1.39426
$490$	0	0
$491$	−20.8807	−0.942334	−0.471167	−	0.882044i	$-0.656167\pi$
$491$	−20.8807	−0.942334	−0.471167	+	0.882044i	$0.656167\pi$
$492$	−7.54751	−0.340268
$493$	48.6966	2.19318
$494$	−2.78276	−0.125203
$495$	−0.0552084	−0.00248143
$496$	−1.34535	−0.0604078
$497$	0	0
$498$	−23.3152	−1.04478
$499$	12.8619	0.575777	0.287889	−	0.957664i	$-0.407047\pi$
$499$	12.8619	0.575777	0.287889	+	0.957664i	$0.407047\pi$
$500$	−3.85387	−0.172350
$501$	−23.2533	−1.03888
$502$	−11.6936	−0.521913
$503$	22.9179	1.02186	0.510930	−	0.859622i	$-0.329301\pi$
$503$	22.9179	1.02186	0.510930	+	0.859622i	$0.329301\pi$
$504$	0	0
$505$	−6.70479	−0.298359
$506$	−14.6547	−0.651479
$507$	9.03392	0.401210
$508$	2.50147	0.110985
$509$	17.6936	0.784257	0.392128	−	0.919910i	$-0.371739\pi$
$509$	17.6936	0.784257	0.392128	+	0.919910i	$0.371739\pi$
$510$	−4.18415	−0.185277
$511$	0	0
$512$	1.00000	0.0441942
$513$	5.23525	0.231142
$514$	2.82585	0.124643
$515$	0.818801	0.0360807
$516$	−10.0180	−0.441019
$517$	17.5224	0.770636
$518$	0	0
$519$	−13.9699	−0.613209
$520$	−1.08913	−0.0477613
$521$	13.3152	0.583350	0.291675	−	0.956518i	$-0.405787\pi$
$521$	13.3152	0.583350	0.291675	+	0.956518i	$0.405787\pi$
$522$	−0.360415	−0.0157749
$523$	44.4404	1.94324	0.971621	−	0.236544i	$-0.0760147\pi$
$523$	44.4404	1.94324	0.971621	+	0.236544i	$0.0760147\pi$
$524$	15.4374	0.674387
$525$	0	0
$526$	−29.4433	−1.28379
$527$	−8.36830	−0.364529
$528$	−5.26622	−0.229183
$529$	−0.125161	−0.00544179
$530$	2.80078	0.121658
$531$	−0.330276	−0.0143328
$532$	0	0
$533$	−12.2202	−0.529315
$534$	1.82880	0.0791400
$535$	−5.51539	−0.238451
$536$	12.2202	0.527832
$537$	19.7195	0.850961
$538$	10.4404	0.450116
$539$	0	0
$540$	2.04899	0.0881743
$541$	18.5626	0.798068	0.399034	−	0.916936i	$-0.369346\pi$
$541$	18.5626	0.798068	0.399034	+	0.916936i	$0.369346\pi$
$542$	4.29931	0.184671
$543$	28.0360	1.20314
$544$	6.22018	0.266688
$545$	5.93184	0.254092
$546$	0	0
$547$	−26.2762	−1.12349	−0.561745	−	0.827310i	$-0.689870\pi$
$547$	−26.2762	−1.12349	−0.561745	+	0.827310i	$0.689870\pi$
$548$	13.9209	0.594670
$549$	0.391382	0.0167038
$550$	−14.8509	−0.633245
$551$	7.82880	0.333518
$552$	8.22018	0.349874
$553$	0	0
$554$	−28.7526	−1.22158
$555$	2.57553	0.109325
$556$	−10.8748	−0.461196
$557$	32.6045	1.38150	0.690749	−	0.723095i	$-0.257281\pi$
$557$	32.6045	1.38150	0.690749	+	0.723095i	$0.257281\pi$
$558$	0.0619357	0.00262195
$559$	−16.2202	−0.686041
$560$	0	0
$561$	−32.7569	−1.38300
$562$	−20.6547	−0.871264
$563$	−35.4182	−1.49270	−0.746351	−	0.665553i	$-0.768196\pi$
$563$	−35.4182	−1.49270	−0.746351	+	0.665553i	$0.768196\pi$
$564$	−9.82880	−0.413867
$565$	7.74378	0.325783
$566$	9.30931	0.391299
$567$	0	0
$568$	0.935945	0.0392714
$569$	−13.6936	−0.574067	−0.287034	−	0.957921i	$-0.592669\pi$
$569$	−13.6936	−0.574067	−0.287034	+	0.957921i	$0.592669\pi$
$570$	−0.672673	−0.0281752
$571$	−17.9389	−0.750719	−0.375360	−	0.926879i	$-0.622481\pi$
$571$	−17.9389	−0.750719	−0.375360	+	0.926879i	$0.622481\pi$
$572$	−8.52654	−0.356513
$573$	26.5944	1.11100
$574$	0	0
$575$	23.1812	0.966723
$576$	−0.0460370	−0.00191821
$577$	45.3873	1.88950	0.944749	−	0.327796i	$-0.106306\pi$
$577$	45.3873	1.88950	0.944749	+	0.327796i	$0.106306\pi$
$578$	21.6907	0.902214
$579$	−12.0360	−0.500201
$580$	3.06406	0.127228
$581$	0	0
$582$	7.73673	0.320698
$583$	21.9268	0.908114
$584$	4.12811	0.170822
$585$	0.0501401	0.00207304
$586$	−1.65760	−0.0684750
$587$	34.3483	1.41771	0.708853	−	0.705356i	$-0.249213\pi$
$587$	34.3483	1.41771	0.708853	+	0.705356i	$0.249213\pi$
$588$	0	0
$589$	−1.34535	−0.0554340
$590$	2.80783	0.115597
$591$	17.9440	0.738116
$592$	−3.82880	−0.157363
$593$	−6.56258	−0.269493	−0.134746	−	0.990880i	$-0.543022\pi$
$593$	−6.56258	−0.269493	−0.134746	+	0.990880i	$0.543022\pi$
$594$	16.0411	0.658174
$595$	0	0
$596$	−1.77982	−0.0729041
$597$	−11.7418	−0.480560
$598$	13.3093	0.544258
$599$	−8.62958	−0.352595	−0.176298	−	0.984337i	$-0.556412\pi$
$599$	−8.62958	−0.352595	−0.176298	+	0.984337i	$0.556412\pi$
$600$	8.33028	0.340082
$601$	−10.4404	−0.425872	−0.212936	−	0.977066i	$-0.568303\pi$
$601$	−10.4404	−0.425872	−0.212936	+	0.977066i	$0.568303\pi$
$602$	0	0
$603$	−0.562581	−0.0229101
$604$	5.30931	0.216033
$605$	−0.630739	−0.0256432
$606$	29.4433	1.19605
$607$	1.43152	0.0581037	0.0290518	−	0.999578i	$-0.490751\pi$
$607$	1.43152	0.0581037	0.0290518	+	0.999578i	$0.490751\pi$
$608$	1.00000	0.0405554
$609$	0	0
$610$	−3.32733	−0.134720
$611$	−15.9138	−0.643804
$612$	−0.286359	−0.0115754
$613$	−41.0950	−1.65981	−0.829906	−	0.557903i	$-0.811606\pi$
$613$	−41.0950	−1.65981	−0.829906	+	0.557903i	$0.811606\pi$
$614$	31.0880	1.25461
$615$	−2.95396	−0.119115
$616$	0	0
$617$	27.1440	1.09278	0.546388	−	0.837532i	$-0.316002\pi$
$617$	27.1440	1.09278	0.546388	+	0.837532i	$0.316002\pi$
$618$	−3.59567	−0.144639
$619$	−1.83585	−0.0737892	−0.0368946	−	0.999319i	$-0.511747\pi$
$619$	−1.83585	−0.0737892	−0.0368946	+	0.999319i	$0.511747\pi$
$620$	−0.526544	−0.0211465
$621$	−25.0390	−1.00478
$622$	−11.8468	−0.475014
$623$	0	0
$624$	4.78276	0.191464
$625$	22.7258	0.909030
$626$	−34.6606	−1.38531
$627$	−5.26622	−0.210313
$628$	−15.3763	−0.613582
$629$	−23.8159	−0.949600
$630$	0	0
$631$	43.5714	1.73455	0.867276	−	0.497828i	$-0.165869\pi$
$631$	43.5714	1.73455	0.867276	+	0.497828i	$0.165869\pi$
$632$	2.95396	0.117502
$633$	16.0000	0.635943
$634$	−16.4654	−0.653926
$635$	0.979033	0.0388517
$636$	−12.2993	−0.487699
$637$	0	0
$638$	23.9879	0.949689
$639$	−0.0430881	−0.00170454
$640$	0.391382	0.0154707
$641$	43.6275	1.72318	0.861591	−	0.507604i	$-0.169469\pi$
$641$	43.6275	1.72318	0.861591	+	0.507604i	$0.169469\pi$
$642$	24.2202	0.955894
$643$	−14.6907	−0.579344	−0.289672	−	0.957126i	$-0.593546\pi$
$643$	−14.6907	−0.579344	−0.289672	+	0.957126i	$0.593546\pi$
$644$	0	0
$645$	−3.92088	−0.154384
$646$	6.22018	0.244730
$647$	−19.6145	−0.771126	−0.385563	−	0.922681i	$-0.625993\pi$
$647$	−19.6145	−0.771126	−0.385563	+	0.922681i	$0.625993\pi$
$648$	−8.85977	−0.348045
$649$	21.9820	0.862868
$650$	13.4876	0.529026
$651$	0	0
$652$	17.9389	0.702541
$653$	42.1700	1.65024	0.825121	−	0.564957i	$-0.191107\pi$
$653$	42.1700	1.65024	0.825121	+	0.564957i	$0.191107\pi$
$654$	−26.0490	−1.01860
$655$	6.04193	0.236078
$656$	4.39138	0.171455
$657$	−0.190046	−0.00741439
$658$	0	0
$659$	34.1900	1.33186	0.665928	−	0.746016i	$-0.268036\pi$
$659$	34.1900	1.33186	0.665928	+	0.746016i	$0.268036\pi$
$660$	−2.06111	−0.0802284
$661$	31.1370	1.21109	0.605544	−	0.795812i	$-0.292956\pi$
$661$	31.1370	1.21109	0.605544	+	0.795812i	$0.292956\pi$
$662$	−3.09502	−0.120291
$663$	29.7497	1.15538
$664$	13.5655	0.526445
$665$	0	0
$666$	0.176267	0.00683019
$667$	−37.4433	−1.44981
$668$	13.5295	0.523472
$669$	−3.97410	−0.153648
$670$	4.78276	0.184774
$671$	−26.0490	−1.00561
$672$	0	0
$673$	−48.6045	−1.87357	−0.936783	−	0.349910i	$-0.886212\pi$
$673$	−48.6045	−1.87357	−0.936783	+	0.349910i	$0.886212\pi$
$674$	−24.5324	−0.944954
$675$	−25.3743	−0.976658
$676$	−5.25622	−0.202162
$677$	−9.81585	−0.377254	−0.188627	−	0.982049i	$-0.560404\pi$
$677$	−9.81585	−0.377254	−0.188627	+	0.982049i	$0.560404\pi$
$678$	−34.0059	−1.30599
$679$	0	0
$680$	2.43447	0.0933577
$681$	21.3814	0.819336
$682$	−4.12221	−0.157848
$683$	−12.6606	−0.484443	−0.242221	−	0.970221i	$-0.577876\pi$
$683$	−12.6606	−0.484443	−0.242221	+	0.970221i	$0.577876\pi$
$684$	−0.0460370	−0.00176027
$685$	5.44839	0.208172
$686$	0	0
$687$	26.8267	1.02350
$688$	5.82880	0.222221
$689$	−19.9138	−0.758656
$690$	3.21724	0.122478
$691$	−45.4073	−1.72737	−0.863687	−	0.504028i	$-0.831851\pi$
$691$	−45.4073	−1.72737	−0.863687	+	0.504028i	$0.831851\pi$
$692$	8.12811	0.308984
$693$	0	0
$694$	5.56553	0.211265
$695$	−4.25622	−0.161448
$696$	−13.4554	−0.510027
$697$	27.3152	1.03464
$698$	−25.1311	−0.951225
$699$	9.08207	0.343516
$700$	0	0
$701$	−11.1871	−0.422531	−0.211265	−	0.977429i	$-0.567758\pi$
$701$	−11.1871	−0.422531	−0.211265	+	0.977429i	$0.567758\pi$
$702$	−14.5685	−0.549852
$703$	−3.82880	−0.144406
$704$	3.06406	0.115481
$705$	−3.84682	−0.144880
$706$	3.52949	0.132834
$707$	0	0
$708$	−12.3303	−0.463400
$709$	13.4014	0.503300	0.251650	−	0.967818i	$-0.419027\pi$
$709$	13.4014	0.503300	0.251650	+	0.967818i	$0.419027\pi$
$710$	0.366312	0.0137475
$711$	−0.135992	−0.00510008
$712$	−1.06406	−0.0398771
$713$	6.43447	0.240973
$714$	0	0
$715$	−3.33714	−0.124802
$716$	−11.4735	−0.428783
$717$	−3.21724	−0.120150
$718$	24.9669	0.931757
$719$	16.0000	0.596699	0.298350	−	0.954457i	$-0.403564\pi$
$719$	16.0000	0.596699	0.298350	+	0.954457i	$0.403564\pi$
$720$	−0.0180181	−0.000671494 0
$721$	0	0
$722$	1.00000	0.0372161
$723$	−38.6425	−1.43713
$724$	−16.3123	−0.606240
$725$	−37.9448	−1.40923
$726$	2.76981	0.102797
$727$	42.4153	1.57310	0.786548	−	0.617529i	$-0.211866\pi$
$727$	42.4153	1.57310	0.786548	+	0.617529i	$0.211866\pi$
$728$	0	0
$729$	27.4015	1.01487
$730$	1.61567	0.0597986
$731$	36.2562	1.34098
$732$	14.6116	0.540059
$733$	43.9628	1.62380	0.811902	−	0.583794i	$-0.198432\pi$
$733$	43.9628	1.62380	0.811902	+	0.583794i	$0.198432\pi$
$734$	15.2842	0.564152
$735$	0	0
$736$	−4.78276	−0.176295
$737$	37.4433	1.37924
$738$	−0.202166	−0.00744184
$739$	1.57258	0.0578483	0.0289242	−	0.999582i	$-0.490792\pi$
$739$	1.57258	0.0578483	0.0289242	+	0.999582i	$0.490792\pi$
$740$	−1.49853	−0.0550869
$741$	4.78276	0.175699
$742$	0	0
$743$	37.0460	1.35909	0.679544	−	0.733635i	$-0.262178\pi$
$743$	37.0460	1.35909	0.679544	+	0.733635i	$0.262178\pi$
$744$	2.31226	0.0847715
$745$	−0.696589	−0.0255210
$746$	−17.0519	−0.624316
$747$	−0.624516	−0.0228499
$748$	19.0590	0.696866
$749$	0	0
$750$	6.62369	0.241863
$751$	15.7367	0.574241	0.287121	−	0.957894i	$-0.407302\pi$
$751$	15.7367	0.574241	0.287121	+	0.957894i	$0.407302\pi$
$752$	5.71871	0.208540
$753$	20.0980	0.732411
$754$	−21.7857	−0.793389
$755$	2.07797	0.0756251
$756$	0	0
$757$	33.3512	1.21217	0.606086	−	0.795399i	$-0.292739\pi$
$757$	33.3512	1.21217	0.606086	+	0.795399i	$0.292739\pi$
$758$	17.0029	0.617575
$759$	25.1871	0.914234
$760$	0.391382	0.0141969
$761$	−20.0059	−0.725213	−0.362607	−	0.931942i	$-0.618113\pi$
$761$	−20.0059	−0.725213	−0.362607	+	0.931942i	$0.618113\pi$
$762$	−4.29931	−0.155748
$763$	0	0
$764$	−15.4735	−0.559810
$765$	−0.112076	−0.00405211
$766$	−29.2231	−1.05587
$767$	−19.9640	−0.720857
$768$	−1.71871	−0.0620186
$769$	−55.0029	−1.98346	−0.991729	−	0.128353i	$-0.959031\pi$
$769$	−55.0029	−1.98346	−0.991729	+	0.128353i	$0.959031\pi$
$770$	0	0
$771$	−4.85682	−0.174914
$772$	7.00295	0.252042
$773$	−32.7526	−1.17803	−0.589015	−	0.808122i	$-0.700484\pi$
$773$	−32.7526	−1.17803	−0.589015	+	0.808122i	$0.700484\pi$
$774$	−0.268341	−0.00964530
$775$	6.52065	0.234229
$776$	−4.50147	−0.161594
$777$	0	0
$778$	−26.4404	−0.947933
$779$	4.39138	0.157338
$780$	1.87189	0.0670244
$781$	2.86779	0.102617
$782$	−29.7497	−1.06385
$783$	40.9858	1.46471
$784$	0	0
$785$	−6.01802	−0.214792
$786$	−26.5324	−0.946381
$787$	−16.2993	−0.581008	−0.290504	−	0.956874i	$-0.593823\pi$
$787$	−16.2993	−0.581008	−0.290504	+	0.956874i	$0.593823\pi$
$788$	−10.4404	−0.371923
$789$	50.6045	1.80157
$790$	1.15613	0.0411332
$791$	0	0
$792$	−0.141060	−0.00501235
$793$	23.6576	0.840106
$794$	−18.5074	−0.656802
$795$	−4.81373	−0.170726
$796$	6.83175	0.242145
$797$	−9.50949	−0.336843	−0.168422	−	0.985715i	$-0.553867\pi$
$797$	−9.50949	−0.336843	−0.168422	+	0.985715i	$0.553867\pi$
$798$	0	0
$799$	35.5714	1.25843
$800$	−4.84682	−0.171361
$801$	0.0489859	0.00173083
$802$	−32.2261	−1.13794
$803$	12.6488	0.446365
$804$	−21.0029	−0.740717
$805$	0	0
$806$	3.74378	0.131869
$807$	−17.9440	−0.631657
$808$	−17.1311	−0.602669
$809$	−20.0129	−0.703618	−0.351809	−	0.936072i	$-0.614433\pi$
$809$	−20.0129	−0.703618	−0.351809	+	0.936072i	$0.614433\pi$
$810$	−3.46756	−0.121838
$811$	−49.8527	−1.75057	−0.875283	−	0.483611i	$-0.839325\pi$
$811$	−49.8527	−1.75057	−0.875283	+	0.483611i	$0.839325\pi$
$812$	0	0
$813$	−7.38926	−0.259153
$814$	−11.7317	−0.411194
$815$	7.02097	0.245934
$816$	−10.6907	−0.374249
$817$	5.82880	0.203924
$818$	−19.3763	−0.677477
$819$	0	0
$820$	1.71871	0.0600199
$821$	−2.68479	−0.0936999	−0.0468500	−	0.998902i	$-0.514918\pi$
$821$	−2.68479	−0.0936999	−0.0468500	+	0.998902i	$0.514918\pi$
$822$	−23.9259	−0.834513
$823$	−28.4764	−0.992625	−0.496313	−	0.868144i	$-0.665313\pi$
$823$	−28.4764	−0.992625	−0.496313	+	0.868144i	$0.665313\pi$
$824$	2.09207	0.0728809
$825$	25.5244	0.888646
$826$	0	0
$827$	−29.0390	−1.00978	−0.504892	−	0.863182i	$-0.668468\pi$
$827$	−29.0390	−1.00978	−0.504892	+	0.863182i	$0.668468\pi$
$828$	0.220184	0.00765193
$829$	19.7136	0.684683	0.342342	−	0.939576i	$-0.388780\pi$
$829$	19.7136	0.684683	0.342342	+	0.939576i	$0.388780\pi$
$830$	5.30931	0.184289
$831$	49.4174	1.71427
$832$	−2.78276	−0.0964750
$833$	0	0
$834$	18.6907	0.647206
$835$	5.29521	0.183248
$836$	3.06406	0.105973
$837$	−7.04322	−0.243449
$838$	−27.5354	−0.951194
$839$	18.9109	0.652876	0.326438	−	0.945219i	$-0.394152\pi$
$839$	18.9109	0.652876	0.326438	+	0.945219i	$0.394152\pi$
$840$	0	0
$841$	32.2901	1.11345
$842$	−16.4345	−0.566369
$843$	35.4994	1.22266
$844$	−9.30931	−0.320440
$845$	−2.05719	−0.0707696
$846$	−0.263272	−0.00905149
$847$	0	0
$848$	7.15613	0.245742
$849$	−16.0000	−0.549119
$850$	−30.1481	−1.03407
$851$	18.3123	0.627736
$852$	−1.60862	−0.0551103
$853$	23.7928	0.814649	0.407324	−	0.913284i	$-0.366462\pi$
$853$	23.7928	0.814649	0.407324	+	0.913284i	$0.366462\pi$
$854$	0	0
$855$	−0.0180181	−0.000616205 0
$856$	−14.0921	−0.481657
$857$	−10.0000	−0.341593	−0.170797	−	0.985306i	$-0.554634\pi$
$857$	−10.0000	−0.341593	−0.170797	+	0.985306i	$0.554634\pi$
$858$	14.6547	0.500302
$859$	12.9669	0.442425	0.221213	−	0.975226i	$-0.428999\pi$
$859$	12.9669	0.442425	0.221213	+	0.975226i	$0.428999\pi$
$860$	2.28129	0.0777914
$861$	0	0
$862$	40.9979	1.39639
$863$	23.0519	0.784697	0.392348	−	0.919817i	$-0.371663\pi$
$863$	23.0519	0.784697	0.392348	+	0.919817i	$0.371663\pi$
$864$	5.23525	0.178107
$865$	3.18120	0.108164
$866$	22.4835	0.764019
$867$	−37.2800	−1.26610
$868$	0	0
$869$	9.05111	0.307038
$870$	−5.26622	−0.178542
$871$	−34.0059	−1.15225
$872$	15.1561	0.513251
$873$	0.207234	0.00701382
$874$	−4.78276	−0.161779
$875$	0	0
$876$	−7.09502	−0.239719
$877$	17.8468	0.602644	0.301322	−	0.953522i	$-0.402572\pi$
$877$	17.8468	0.602644	0.301322	+	0.953522i	$0.402572\pi$
$878$	18.9109	0.638211
$879$	2.84894	0.0960923
$880$	1.19922	0.0404256
$881$	−6.71069	−0.226089	−0.113044	−	0.993590i	$-0.536060\pi$
$881$	−6.71069	−0.226089	−0.113044	+	0.993590i	$0.536060\pi$
$882$	0	0
$883$	13.3144	0.448064	0.224032	−	0.974582i	$-0.428078\pi$
$883$	13.3144	0.448064	0.224032	+	0.974582i	$0.428078\pi$
$884$	−17.3093	−0.582175
$885$	−4.82585	−0.162219
$886$	−10.0850	−0.338813
$887$	−17.2733	−0.579980	−0.289990	−	0.957030i	$-0.593652\pi$
$887$	−17.2733	−0.579980	−0.289990	+	0.957030i	$0.593652\pi$
$888$	6.58060	0.220830
$889$	0	0
$890$	−0.416452	−0.0139595
$891$	−27.1468	−0.909453
$892$	2.31226	0.0774201
$893$	5.71871	0.191369
$894$	3.05899	0.102308
$895$	−4.49051	−0.150101
$896$	0	0
$897$	−22.8748	−0.763769
$898$	17.9138	0.597792
$899$	−10.5324	−0.351277
$900$	0.223133	0.00743777
$901$	44.5124	1.48292
$902$	13.4554	0.448017
$903$	0	0
$904$	19.7857	0.658063
$905$	−6.38433	−0.212222
$906$	−9.12516	−0.303163
$907$	6.99705	0.232333	0.116167	−	0.993230i	$-0.462939\pi$
$907$	6.99705	0.232333	0.116167	+	0.993230i	$0.462939\pi$
$908$	−12.4404	−0.412848
$909$	0.788663	0.0261583
$910$	0	0
$911$	24.1050	0.798635	0.399318	−	0.916813i	$-0.369247\pi$
$911$	24.1050	0.798635	0.399318	+	0.916813i	$0.369247\pi$
$912$	−1.71871	−0.0569122
$913$	41.5655	1.37562
$914$	23.8527	0.788978
$915$	5.71871	0.189055
$916$	−15.6086	−0.515723
$917$	0	0
$918$	32.5642	1.07478
$919$	−55.3011	−1.82422	−0.912108	−	0.409951i	$-0.865546\pi$
$919$	−55.3011	−1.82422	−0.912108	+	0.409951i	$0.865546\pi$
$920$	−1.87189	−0.0617144
$921$	−53.4312	−1.76062
$922$	−22.2512	−0.732803
$923$	−2.60451	−0.0857286
$924$	0	0
$925$	18.5575	0.610167
$926$	27.8778	0.916121
$927$	−0.0963128	−0.00316333
$928$	7.82880	0.256993
$929$	−4.60451	−0.151069	−0.0755346	−	0.997143i	$-0.524066\pi$
$929$	−4.60451	−0.151069	−0.0755346	+	0.997143i	$0.524066\pi$
$930$	0.904977	0.0296754
$931$	0	0
$932$	−5.28424	−0.173091
$933$	20.3612	0.666597
$934$	24.0980	0.788510
$935$	7.45935	0.243947
$936$	0.128110	0.00418741
$937$	−45.7195	−1.49359	−0.746796	−	0.665053i	$-0.768409\pi$
$937$	−45.7195	−1.49359	−0.746796	+	0.665053i	$0.768409\pi$
$938$	0	0
$939$	59.5714	1.94404
$940$	2.23820	0.0730021
$941$	−32.5324	−1.06053	−0.530264	−	0.847833i	$-0.677907\pi$
$941$	−32.5324	−1.06053	−0.530264	+	0.847833i	$0.677907\pi$
$942$	26.4274	0.861052
$943$	−21.0029	−0.683950
$944$	7.17415	0.233499
$945$	0	0
$946$	17.8598	0.580671
$947$	−35.0641	−1.13943	−0.569714	−	0.821843i	$-0.692946\pi$
$947$	−35.0641	−1.13943	−0.569714	+	0.821843i	$0.692946\pi$
$948$	−5.07700	−0.164893
$949$	−11.4876	−0.372902
$950$	−4.84682	−0.157252
$951$	28.2993	0.917668
$952$	0	0
$953$	15.9941	0.518100	0.259050	−	0.965864i	$-0.416591\pi$
$953$	15.9941	0.518100	0.259050	+	0.965864i	$0.416591\pi$
$954$	−0.329447	−0.0106662
$955$	−6.05604	−0.195969
$956$	1.87189	0.0605412
$957$	−41.2282	−1.33272
$958$	8.92382	0.288316
$959$	0	0
$960$	−0.672673	−0.0217104
$961$	−29.1900	−0.941614
$962$	10.6547	0.343520
$963$	0.648757	0.0209059
$964$	22.4835	0.724143
$965$	2.74083	0.0882305
$966$	0	0
$967$	16.0721	0.516843	0.258422	−	0.966032i	$-0.416798\pi$
$967$	16.0721	0.516843	0.258422	+	0.966032i	$0.416798\pi$
$968$	−1.61157	−0.0517977
$969$	−10.6907	−0.343434
$970$	−1.76180	−0.0565679
$971$	−34.6715	−1.11266	−0.556331	−	0.830961i	$-0.687791\pi$
$971$	−34.6715	−1.11266	−0.556331	+	0.830961i	$0.687791\pi$
$972$	−0.478388	−0.0153443
$973$	0	0
$974$	−41.0578	−1.31558
$975$	−23.1812	−0.742393
$976$	−8.50147	−0.272126
$977$	−12.5685	−0.402101	−0.201051	−	0.979581i	$-0.564436\pi$
$977$	−12.5685	−0.402101	−0.201051	+	0.979581i	$0.564436\pi$
$978$	−30.8318	−0.985891
$979$	−3.26032	−0.104200
$980$	0	0
$981$	−0.697743	−0.0222772
$982$	−20.8807	−0.666331
$983$	−1.56553	−0.0499326	−0.0249663	−	0.999688i	$-0.507948\pi$
$983$	−1.56553	−0.0499326	−0.0249663	+	0.999688i	$0.507948\pi$
$984$	−7.54751	−0.240606
$985$	−4.08618	−0.130196
$986$	48.6966	1.55082
$987$	0	0
$988$	−2.78276	−0.0885315
$989$	−27.8778	−0.886462
$990$	−0.0552084	−0.00175464
$991$	−42.6355	−1.35436	−0.677180	−	0.735817i	$-0.736798\pi$
$991$	−42.6355	−1.35436	−0.677180	+	0.735817i	$0.736798\pi$
$992$	−1.34535	−0.0427148
$993$	5.31945	0.168808
$994$	0	0
$995$	2.67383	0.0847660
$996$	−23.3152	−0.738771
$997$	−61.2721	−1.94051	−0.970254	−	0.242090i	$-0.922167\pi$
$997$	−61.2721	−1.94051	−0.970254	+	0.242090i	$0.922167\pi$
$998$	12.8619	0.407136
$999$	−20.0447	−0.634188

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1862.2.a.r.1.1		3
7.6	odd	2		266.2.a.d.1.3	✓	3
21.20	even	2		2394.2.a.ba.1.3		3
28.27	even	2		2128.2.a.s.1.1		3
35.34	odd	2		6650.2.a.cd.1.1		3
56.13	odd	2		8512.2.a.bm.1.1		3
56.27	even	2		8512.2.a.bj.1.3		3
133.132	even	2		5054.2.a.r.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
266.2.a.d.1.3	✓	3	7.6	odd	2
1862.2.a.r.1.1		3	1.1	even	1	trivial
2128.2.a.s.1.1		3	28.27	even	2
2394.2.a.ba.1.3		3	21.20	even	2
5054.2.a.r.1.1		3	133.132	even	2
6650.2.a.cd.1.1		3	35.34	odd	2
8512.2.a.bj.1.3		3	56.27	even	2
8512.2.a.bm.1.1		3	56.13	odd	2

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:	\( N \)	\(=\)	\( 1862 = 2 \cdot 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1862.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.71871 q^{3} +1.00000 q^{4} +0.391382 q^{5} -1.71871 q^{6} +1.00000 q^{8} -0.0460370 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.71871 q^{3} +1.00000 q^{4} +0.391382 q^{5} -1.71871 q^{6} +1.00000 q^{8} -0.0460370 q^{9} +0.391382 q^{10} +3.06406 q^{11} -1.71871 q^{12} -2.78276 q^{13} -0.672673 q^{15} +1.00000 q^{16} +6.22018 q^{17} -0.0460370 q^{18} +1.00000 q^{19} +0.391382 q^{20} +3.06406 q^{22} -4.78276 q^{23} -1.71871 q^{24} -4.84682 q^{25} -2.78276 q^{26} +5.23525 q^{27} +7.82880 q^{29} -0.672673 q^{30} -1.34535 q^{31} +1.00000 q^{32} -5.26622 q^{33} +6.22018 q^{34} -0.0460370 q^{36} -3.82880 q^{37} +1.00000 q^{38} +4.78276 q^{39} +0.391382 q^{40} +4.39138 q^{41} +5.82880 q^{43} +3.06406 q^{44} -0.0180181 q^{45} -4.78276 q^{46} +5.71871 q^{47} -1.71871 q^{48} -4.84682 q^{50} -10.6907 q^{51} -2.78276 q^{52} +7.15613 q^{53} +5.23525 q^{54} +1.19922 q^{55} -1.71871 q^{57} +7.82880 q^{58} +7.17415 q^{59} -0.672673 q^{60} -8.50147 q^{61} -1.34535 q^{62} +1.00000 q^{64} -1.08913 q^{65} -5.26622 q^{66} +12.2202 q^{67} +6.22018 q^{68} +8.22018 q^{69} +0.935945 q^{71} -0.0460370 q^{72} +4.12811 q^{73} -3.82880 q^{74} +8.33028 q^{75} +1.00000 q^{76} +4.78276 q^{78} +2.95396 q^{79} +0.391382 q^{80} -8.85977 q^{81} +4.39138 q^{82} +13.5655 q^{83} +2.43447 q^{85} +5.82880 q^{86} -13.4554 q^{87} +3.06406 q^{88} -1.06406 q^{89} -0.0180181 q^{90} -4.78276 q^{92} +2.31226 q^{93} +5.71871 q^{94} +0.391382 q^{95} -1.71871 q^{96} -4.50147 q^{97} -0.141060 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} + q^{3} + 3 q^{4} - 5 q^{5} + q^{6} + 3 q^{8} + 6 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 + q^3 + 3 * q^4 - 5 * q^5 + q^6 + 3 * q^8 + 6 * q^9	\( 3 q + 3 q^{2} + q^{3} + 3 q^{4} - 5 q^{5} + q^{6} + 3 q^{8} + 6 q^{9} - 5 q^{10} + 3 q^{11} + q^{12} + 4 q^{13} - 2 q^{15} + 3 q^{16} - 6 q^{17} + 6 q^{18} + 3 q^{19} - 5 q^{20} + 3 q^{22} - 2 q^{23} + q^{24} + 4 q^{25} + 4 q^{26} + 28 q^{27} + 5 q^{29} - 2 q^{30} - 4 q^{31} + 3 q^{32} + 15 q^{33} - 6 q^{34} + 6 q^{36} + 7 q^{37} + 3 q^{38} + 2 q^{39} - 5 q^{40} + 7 q^{41} - q^{43} + 3 q^{44} - 2 q^{46} + 11 q^{47} + q^{48} + 4 q^{50} - 32 q^{51} + 4 q^{52} + 3 q^{53} + 28 q^{54} + 16 q^{55} + q^{57} + 5 q^{58} + 3 q^{59} - 2 q^{60} - 7 q^{61} - 4 q^{62} + 3 q^{64} - 28 q^{65} + 15 q^{66} + 12 q^{67} - 6 q^{68} + 9 q^{71} + 6 q^{72} + 7 q^{74} - 12 q^{75} + 3 q^{76} + 2 q^{78} + 15 q^{79} - 5 q^{80} + 35 q^{81} + 7 q^{82} + 16 q^{83} + 32 q^{85} - q^{86} - 28 q^{87} + 3 q^{88} + 3 q^{89} - 2 q^{92} - 30 q^{93} + 11 q^{94} - 5 q^{95} + q^{96} + 5 q^{97} + 55 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 + q^3 + 3 * q^4 - 5 * q^5 + q^6 + 3 * q^8 + 6 * q^9 - 5 * q^10 + 3 * q^11 + q^12 + 4 * q^13 - 2 * q^15 + 3 * q^16 - 6 * q^17 + 6 * q^18 + 3 * q^19 - 5 * q^20 + 3 * q^22 - 2 * q^23 + q^24 + 4 * q^25 + 4 * q^26 + 28 * q^27 + 5 * q^29 - 2 * q^30 - 4 * q^31 + 3 * q^32 + 15 * q^33 - 6 * q^34 + 6 * q^36 + 7 * q^37 + 3 * q^38 + 2 * q^39 - 5 * q^40 + 7 * q^41 - q^43 + 3 * q^44 - 2 * q^46 + 11 * q^47 + q^48 + 4 * q^50 - 32 * q^51 + 4 * q^52 + 3 * q^53 + 28 * q^54 + 16 * q^55 + q^57 + 5 * q^58 + 3 * q^59 - 2 * q^60 - 7 * q^61 - 4 * q^62 + 3 * q^64 - 28 * q^65 + 15 * q^66 + 12 * q^67 - 6 * q^68 + 9 * q^71 + 6 * q^72 + 7 * q^74 - 12 * q^75 + 3 * q^76 + 2 * q^78 + 15 * q^79 - 5 * q^80 + 35 * q^81 + 7 * q^82 + 16 * q^83 + 32 * q^85 - q^86 - 28 * q^87 + 3 * q^88 + 3 * q^89 - 2 * q^92 - 30 * q^93 + 11 * q^94 - 5 * q^95 + q^96 + 5 * q^97 + 55 * q^99

Introduction

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