LMFDB - Embedded newform 2842.2.a.r.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2842,2,Mod(1,2842)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2842, 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("2842.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2842 = 2 \cdot 7^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2842.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:	$22.6934842544$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.11348.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 5x^{2} + x + 2 $ x^4 - x^3 - 5*x^2 + x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 406)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.77571$ of defining polynomial
Character	$\chi$	$=$	2842.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.12631 q^{3} +1.00000 q^{4} -0.153156 q^{5} -1.12631 q^{6} +1.00000 q^{8} -1.73143 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.12631 q^{3} +1.00000 q^{4} -0.153156 q^{5} -1.12631 q^{6} +1.00000 q^{8} -1.73143 q^{9} -0.153156 q^{10} +0.873692 q^{11} -1.12631 q^{12} -5.00339 q^{13} +0.172501 q^{15} +1.00000 q^{16} +1.27946 q^{17} -1.73143 q^{18} +3.55143 q^{19} -0.153156 q^{20} +0.873692 q^{22} +5.55143 q^{23} -1.12631 q^{24} -4.97654 q^{25} -5.00339 q^{26} +5.32905 q^{27} +1.00000 q^{29} +0.172501 q^{30} +7.95720 q^{31} +1.00000 q^{32} -0.984046 q^{33} +1.27946 q^{34} -1.73143 q^{36} -5.29881 q^{37} +3.55143 q^{38} +5.63536 q^{39} -0.153156 q^{40} -0.666840 q^{41} +2.73143 q^{43} +0.873692 q^{44} +0.265179 q^{45} +5.55143 q^{46} +0.854347 q^{47} -1.12631 q^{48} -4.97654 q^{50} -1.44107 q^{51} -5.00339 q^{52} +6.98405 q^{53} +5.32905 q^{54} -0.133811 q^{55} -4.00000 q^{57} +1.00000 q^{58} +7.68113 q^{59} +0.172501 q^{60} +11.6051 q^{61} +7.95720 q^{62} +1.00000 q^{64} +0.766300 q^{65} -0.984046 q^{66} +11.4479 q^{67} +1.27946 q^{68} -6.25262 q^{69} -14.1171 q^{71} -1.73143 q^{72} +14.4360 q^{73} -5.29881 q^{74} +5.60512 q^{75} +3.55143 q^{76} +5.63536 q^{78} +12.3932 q^{79} -0.153156 q^{80} -0.807862 q^{81} -0.666840 q^{82} -14.2787 q^{83} -0.195958 q^{85} +2.73143 q^{86} -1.12631 q^{87} +0.873692 q^{88} +1.58578 q^{89} +0.265179 q^{90} +5.55143 q^{92} -8.96226 q^{93} +0.854347 q^{94} -0.543923 q^{95} -1.12631 q^{96} +0.666840 q^{97} -1.51274 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - q^{3} + 4 q^{4} + q^{5} - q^{6} + 4 q^{8} + 9 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 - q^3 + 4 * q^4 + q^5 - q^6 + 4 * q^8 + 9 * q^9	$ 4 q + 4 q^{2} - q^{3} + 4 q^{4} + q^{5} - q^{6} + 4 q^{8} + 9 q^{9} + q^{10} + 7 q^{11} - q^{12} + 7 q^{13} - 5 q^{15} + 4 q^{16} + 9 q^{18} - 2 q^{19} + q^{20} + 7 q^{22} + 6 q^{23} - q^{24} + 9 q^{25} + 7 q^{26} - 13 q^{27} + 4 q^{29} - 5 q^{30} + 7 q^{31} + 4 q^{32} + 19 q^{33} + 9 q^{36} - 12 q^{37} - 2 q^{38} - 15 q^{39} + q^{40} - 4 q^{41} - 5 q^{43} + 7 q^{44} + 44 q^{45} + 6 q^{46} + 11 q^{47} - q^{48} + 9 q^{50} - 16 q^{51} + 7 q^{52} + 5 q^{53} - 13 q^{54} - 3 q^{55} - 16 q^{57} + 4 q^{58} - 16 q^{59} - 5 q^{60} + 34 q^{61} + 7 q^{62} + 4 q^{64} - q^{65} + 19 q^{66} + 2 q^{67} - 18 q^{69} + 24 q^{71} + 9 q^{72} + 24 q^{73} - 12 q^{74} + 10 q^{75} - 2 q^{76} - 15 q^{78} - 9 q^{79} + q^{80} + 40 q^{81} - 4 q^{82} + 8 q^{83} - 24 q^{85} - 5 q^{86} - q^{87} + 7 q^{88} - 2 q^{89} + 44 q^{90} + 6 q^{92} - 55 q^{93} + 11 q^{94} + 20 q^{95} - q^{96} + 4 q^{97} + 2 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 - q^3 + 4 * q^4 + q^5 - q^6 + 4 * q^8 + 9 * q^9 + q^10 + 7 * q^11 - q^12 + 7 * q^13 - 5 * q^15 + 4 * q^16 + 9 * q^18 - 2 * q^19 + q^20 + 7 * q^22 + 6 * q^23 - q^24 + 9 * q^25 + 7 * q^26 - 13 * q^27 + 4 * q^29 - 5 * q^30 + 7 * q^31 + 4 * q^32 + 19 * q^33 + 9 * q^36 - 12 * q^37 - 2 * q^38 - 15 * q^39 + q^40 - 4 * q^41 - 5 * q^43 + 7 * q^44 + 44 * q^45 + 6 * q^46 + 11 * q^47 - q^48 + 9 * q^50 - 16 * q^51 + 7 * q^52 + 5 * q^53 - 13 * q^54 - 3 * q^55 - 16 * q^57 + 4 * q^58 - 16 * q^59 - 5 * q^60 + 34 * q^61 + 7 * q^62 + 4 * q^64 - q^65 + 19 * q^66 + 2 * q^67 - 18 * q^69 + 24 * q^71 + 9 * q^72 + 24 * q^73 - 12 * q^74 + 10 * q^75 - 2 * q^76 - 15 * q^78 - 9 * q^79 + q^80 + 40 * q^81 - 4 * q^82 + 8 * q^83 - 24 * q^85 - 5 * q^86 - q^87 + 7 * q^88 - 2 * q^89 + 44 * q^90 + 6 * q^92 - 55 * q^93 + 11 * q^94 + 20 * q^95 - q^96 + 4 * q^97 + 2 * 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
$3$	−1.12631	−0.650274	−0.325137	−	0.945667i	$-0.605410\pi$
$3$	−1.12631	−0.650274	−0.325137	+	0.945667i	$0.605410\pi$
$4$	1.00000	0.500000
$5$	−0.153156	−0.0684935	−0.0342468	−	0.999413i	$-0.510903\pi$
$5$	−0.153156	−0.0684935	−0.0342468	+	0.999413i	$0.510903\pi$
$6$	−1.12631	−0.459813
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	−1.73143	−0.577143
$10$	−0.153156	−0.0484322
$11$	0.873692	0.263428	0.131714	−	0.991288i	$-0.457952\pi$
$11$	0.873692	0.263428	0.131714	+	0.991288i	$0.457952\pi$
$12$	−1.12631	−0.325137
$13$	−5.00339	−1.38769	−0.693846	−	0.720124i	$-0.744085\pi$
$13$	−5.00339	−1.38769	−0.693846	+	0.720124i	$0.744085\pi$
$14$	0	0
$15$	0.172501	0.0445396
$16$	1.00000	0.250000
$17$	1.27946	0.310316	0.155158	−	0.987890i	$-0.450411\pi$
$17$	1.27946	0.310316	0.155158	+	0.987890i	$0.450411\pi$
$18$	−1.73143	−0.408102
$19$	3.55143	0.814753	0.407376	−	0.913260i	$-0.366444\pi$
$19$	3.55143	0.814753	0.407376	+	0.913260i	$0.366444\pi$
$20$	−0.153156	−0.0342468
$21$	0	0
$22$	0.873692	0.186272
$23$	5.55143	1.15755	0.578776	−	0.815486i	$-0.303531\pi$
$23$	5.55143	1.15755	0.578776	+	0.815486i	$0.303531\pi$
$24$	−1.12631	−0.229907
$25$	−4.97654	−0.995309
$26$	−5.00339	−0.981246
$27$	5.32905	1.02558
$28$	0	0
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	0.172501	0.0314942
$31$	7.95720	1.42916	0.714578	−	0.699556i	$-0.246619\pi$
$31$	7.95720	1.42916	0.714578	+	0.699556i	$0.246619\pi$
$32$	1.00000	0.176777
$33$	−0.984046	−0.171300
$34$	1.27946	0.219426
$35$	0	0
$36$	−1.73143	−0.288572
$37$	−5.29881	−0.871119	−0.435559	−	0.900160i	$-0.643449\pi$
$37$	−5.29881	−0.871119	−0.435559	+	0.900160i	$0.643449\pi$
$38$	3.55143	0.576117
$39$	5.63536	0.902380
$40$	−0.153156	−0.0242161
$41$	−0.666840	−0.104143	−0.0520714	−	0.998643i	$-0.516582\pi$
$41$	−0.666840	−0.104143	−0.0520714	+	0.998643i	$0.516582\pi$
$42$	0	0
$43$	2.73143	0.416539	0.208270	−	0.978071i	$-0.433217\pi$
$43$	2.73143	0.416539	0.208270	+	0.978071i	$0.433217\pi$
$44$	0.873692	0.131714
$45$	0.265179	0.0395306
$46$	5.55143	0.818513
$47$	0.854347	0.124619	0.0623097	−	0.998057i	$-0.480153\pi$
$47$	0.854347	0.124619	0.0623097	+	0.998057i	$0.480153\pi$
$48$	−1.12631	−0.162569
$49$	0	0
$50$	−4.97654	−0.703789
$51$	−1.44107	−0.201790
$52$	−5.00339	−0.693846
$53$	6.98405	0.959333	0.479666	−	0.877451i	$-0.340758\pi$
$53$	6.98405	0.959333	0.479666	+	0.877451i	$0.340758\pi$
$54$	5.32905	0.725192
$55$	−0.133811	−0.0180431
$56$	0	0
$57$	−4.00000	−0.529813
$58$	1.00000	0.131306
$59$	7.68113	0.999997	0.499999	−	0.866026i	$-0.333334\pi$
$59$	7.68113	0.999997	0.499999	+	0.866026i	$0.333334\pi$
$60$	0.172501	0.0222698
$61$	11.6051	1.48588	0.742942	−	0.669356i	$-0.233430\pi$
$61$	11.6051	1.48588	0.742942	+	0.669356i	$0.233430\pi$
$62$	7.95720	1.01057
$63$	0	0
$64$	1.00000	0.125000
$65$	0.766300	0.0950478
$66$	−0.984046	−0.121128
$67$	11.4479	1.39858	0.699289	−	0.714839i	$-0.253500\pi$
$67$	11.4479	1.39858	0.699289	+	0.714839i	$0.253500\pi$
$68$	1.27946	0.155158
$69$	−6.25262	−0.752727
$70$	0	0
$71$	−14.1171	−1.67540	−0.837698	−	0.546134i	$-0.816099\pi$
$71$	−14.1171	−1.67540	−0.837698	+	0.546134i	$0.816099\pi$
$72$	−1.73143	−0.204051
$73$	14.4360	1.68961	0.844804	−	0.535076i	$-0.179717\pi$
$73$	14.4360	1.68961	0.844804	+	0.535076i	$0.179717\pi$
$74$	−5.29881	−0.615974
$75$	5.60512	0.647224
$76$	3.55143	0.407376
$77$	0	0
$78$	5.63536	0.638079
$79$	12.3932	1.39435	0.697173	−	0.716903i	$-0.254441\pi$
$79$	12.3932	1.39435	0.697173	+	0.716903i	$0.254441\pi$
$80$	−0.153156	−0.0171234
$81$	−0.807862	−0.0897624
$82$	−0.666840	−0.0736401
$83$	−14.2787	−1.56730	−0.783648	−	0.621205i	$-0.786643\pi$
$83$	−14.2787	−1.56730	−0.783648	+	0.621205i	$0.786643\pi$
$84$	0	0
$85$	−0.195958	−0.0212546
$86$	2.73143	0.294538
$87$	−1.12631	−0.120753
$88$	0.873692	0.0931359
$89$	1.58578	0.168092	0.0840460	−	0.996462i	$-0.473216\pi$
$89$	1.58578	0.168092	0.0840460	+	0.996462i	$0.473216\pi$
$90$	0.265179	0.0279523
$91$	0	0
$92$	5.55143	0.578776
$93$	−8.96226	−0.929343
$94$	0.854347	0.0881192
$95$	−0.543923	−0.0558053
$96$	−1.12631	−0.114953
$97$	0.666840	0.0677073	0.0338537	−	0.999427i	$-0.489222\pi$
$97$	0.666840	0.0677073	0.0338537	+	0.999427i	$0.489222\pi$
$98$	0	0
$99$	−1.51274	−0.152036
$100$	−4.97654	−0.497654
$101$	−1.85774	−0.184852	−0.0924259	−	0.995720i	$-0.529462\pi$
$101$	−1.85774	−0.184852	−0.0924259	+	0.995720i	$0.529462\pi$
$102$	−1.44107	−0.142687
$103$	4.65131	0.458308	0.229154	−	0.973390i	$-0.426404\pi$
$103$	4.65131	0.458308	0.229154	+	0.973390i	$0.426404\pi$
$104$	−5.00339	−0.490623
$105$	0	0
$106$	6.98405	0.678351
$107$	−0.850235	−0.0821953	−0.0410977	−	0.999155i	$-0.513085\pi$
$107$	−0.850235	−0.0821953	−0.0410977	+	0.999155i	$0.513085\pi$
$108$	5.32905	0.512788
$109$	−7.83428	−0.750388	−0.375194	−	0.926946i	$-0.622424\pi$
$109$	−7.83428	−0.750388	−0.375194	+	0.926946i	$0.622424\pi$
$110$	−0.133811	−0.0127584
$111$	5.96809	0.566466
$112$	0	0
$113$	6.81155	0.640776	0.320388	−	0.947286i	$-0.396187\pi$
$113$	6.81155	0.640776	0.320388	+	0.947286i	$0.396187\pi$
$114$	−4.00000	−0.374634
$115$	−0.850235	−0.0792848
$116$	1.00000	0.0928477
$117$	8.66302	0.800897
$118$	7.68113	0.707105
$119$	0	0
$120$	0.172501	0.0157471
$121$	−10.2367	−0.930606
$122$	11.6051	1.05068
$123$	0.751067	0.0677214
$124$	7.95720	0.714578
$125$	1.52797	0.136666
$126$	0	0
$127$	5.44107	0.482817	0.241408	−	0.970424i	$-0.422391\pi$
$127$	5.44107	0.482817	0.241408	+	0.970424i	$0.422391\pi$
$128$	1.00000	0.0883883
$129$	−3.07643	−0.270865
$130$	0.766300	0.0672090
$131$	−11.2669	−0.984394	−0.492197	−	0.870484i	$-0.663806\pi$
$131$	−11.2669	−0.984394	−0.492197	+	0.870484i	$0.663806\pi$
$132$	−0.984046	−0.0856502
$133$	0	0
$134$	11.4479	0.988944
$135$	−0.816176	−0.0702453
$136$	1.27946	0.109713
$137$	13.7542	1.17510	0.587549	−	0.809189i	$-0.300093\pi$
$137$	13.7542	1.17510	0.587549	+	0.809189i	$0.300093\pi$
$138$	−6.25262	−0.532258
$139$	−14.8309	−1.25794	−0.628970	−	0.777430i	$-0.716523\pi$
$139$	−14.8309	−1.25794	−0.628970	+	0.777430i	$0.716523\pi$
$140$	0	0
$141$	−0.962258	−0.0810367
$142$	−14.1171	−1.18468
$143$	−4.37142	−0.365557
$144$	−1.73143	−0.144286
$145$	−0.153156	−0.0127189
$146$	14.4360	1.19473
$147$	0	0
$148$	−5.29881	−0.435559
$149$	−4.93035	−0.403910	−0.201955	−	0.979395i	$-0.564729\pi$
$149$	−4.93035	−0.403910	−0.201955	+	0.979395i	$0.564729\pi$
$150$	5.60512	0.457656
$151$	0.433568	0.0352833	0.0176416	−	0.999844i	$-0.494384\pi$
$151$	0.433568	0.0352833	0.0176416	+	0.999844i	$0.494384\pi$
$152$	3.55143	0.288059
$153$	−2.21530	−0.179097
$154$	0	0
$155$	−1.21869	−0.0978878
$156$	5.63536	0.451190
$157$	13.8964	1.10906	0.554528	−	0.832165i	$-0.312899\pi$
$157$	13.8964	1.10906	0.554528	+	0.832165i	$0.312899\pi$
$158$	12.3932	0.985951
$159$	−7.86619	−0.623829
$160$	−0.153156	−0.0121081
$161$	0	0
$162$	−0.807862	−0.0634716
$163$	−1.21869	−0.0954555	−0.0477277	−	0.998860i	$-0.515198\pi$
$163$	−1.21869	−0.0954555	−0.0477277	+	0.998860i	$0.515198\pi$
$164$	−0.666840	−0.0520714
$165$	0.150713	0.0117330
$166$	−14.2787	−1.10825
$167$	−19.4310	−1.50361	−0.751806	−	0.659384i	$-0.770817\pi$
$167$	−19.4310	−1.50361	−0.751806	+	0.659384i	$0.770817\pi$
$168$	0	0
$169$	12.0339	0.925686
$170$	−0.195958	−0.0150293
$171$	−6.14904	−0.470229
$172$	2.73143	0.208270
$173$	24.7840	1.88429	0.942145	−	0.335204i	$-0.108805\pi$
$173$	24.7840	1.88429	0.942145	+	0.335204i	$0.108805\pi$
$174$	−1.12631	−0.0853852
$175$	0	0
$176$	0.873692	0.0658570
$177$	−8.65131	−0.650273
$178$	1.58578	0.118859
$179$	14.5976	1.09108	0.545539	−	0.838086i	$-0.316325\pi$
$179$	14.5976	1.09108	0.545539	+	0.838086i	$0.316325\pi$
$180$	0.265179	0.0197653
$181$	−5.00339	−0.371899	−0.185950	−	0.982559i	$-0.559536\pi$
$181$	−5.00339	−0.371899	−0.185950	+	0.982559i	$0.559536\pi$
$182$	0	0
$183$	−13.0709	−0.966232
$184$	5.55143	0.409257
$185$	0.811545	0.0596660
$186$	−8.96226	−0.657145
$187$	1.11786	0.0817458
$188$	0.854347	0.0623097
$189$	0	0
$190$	−0.543923	−0.0394603
$191$	−0.651314	−0.0471275	−0.0235637	−	0.999722i	$-0.507501\pi$
$191$	−0.651314	−0.0471275	−0.0235637	+	0.999722i	$0.507501\pi$
$192$	−1.12631	−0.0812843
$193$	24.5120	1.76441	0.882207	−	0.470862i	$-0.156057\pi$
$193$	24.5120	1.76441	0.882207	+	0.470862i	$0.156057\pi$
$194$	0.666840	0.0478763
$195$	−0.863090	−0.0618072
$196$	0	0
$197$	22.7646	1.62191	0.810956	−	0.585107i	$-0.198947\pi$
$197$	22.7646	1.62191	0.810956	+	0.585107i	$0.198947\pi$
$198$	−1.51274	−0.107505
$199$	1.94630	0.137970	0.0689849	−	0.997618i	$-0.478024\pi$
$199$	1.94630	0.137970	0.0689849	+	0.997618i	$0.478024\pi$
$200$	−4.97654	−0.351895
$201$	−12.8938	−0.909459
$202$	−1.85774	−0.130710
$203$	0	0
$204$	−1.44107	−0.100895
$205$	0.102131	0.00713311
$206$	4.65131	0.324072
$207$	−9.61190	−0.668073
$208$	−5.00339	−0.346923
$209$	3.10285	0.214629
$210$	0	0
$211$	12.9371	0.890629	0.445314	−	0.895374i	$-0.353092\pi$
$211$	12.9371	0.890629	0.445314	+	0.895374i	$0.353092\pi$
$212$	6.98405	0.479666
$213$	15.9002	1.08947
$214$	−0.850235	−0.0581209
$215$	−0.418335	−0.0285302
$216$	5.32905	0.362596
$217$	0	0
$218$	−7.83428	−0.530604
$219$	−16.2594	−1.09871
$220$	−0.133811	−0.00902155
$221$	−6.40166	−0.430622
$222$	5.96809	0.400552
$223$	−13.1565	−0.881028	−0.440514	−	0.897746i	$-0.645204\pi$
$223$	−13.1565	−0.881028	−0.440514	+	0.897746i	$0.645204\pi$
$224$	0	0
$225$	8.61654	0.574436
$226$	6.81155	0.453097
$227$	−8.60006	−0.570806	−0.285403	−	0.958408i	$-0.592127\pi$
$227$	−8.60006	−0.570806	−0.285403	+	0.958408i	$0.592127\pi$
$228$	−4.00000	−0.264906
$229$	3.45904	0.228580	0.114290	−	0.993447i	$-0.463541\pi$
$229$	3.45904	0.228580	0.114290	+	0.993447i	$0.463541\pi$
$230$	−0.850235	−0.0560628
$231$	0	0
$232$	1.00000	0.0656532
$233$	16.9690	1.11168	0.555839	−	0.831290i	$-0.312397\pi$
$233$	16.9690	1.11168	0.555839	+	0.831290i	$0.312397\pi$
$234$	8.66302	0.566319
$235$	−0.130848	−0.00853561
$236$	7.68113	0.499999
$237$	−13.9586	−0.906707
$238$	0	0
$239$	26.5338	1.71633	0.858165	−	0.513375i	$-0.171605\pi$
$239$	26.5338	1.71633	0.858165	+	0.513375i	$0.171605\pi$
$240$	0.172501	0.0111349
$241$	−0.999052	−0.0643546	−0.0321773	−	0.999482i	$-0.510244\pi$
$241$	−0.999052	−0.0643546	−0.0321773	+	0.999482i	$0.510244\pi$
$242$	−10.2367	−0.658038
$243$	−15.0772	−0.967206
$244$	11.6051	0.742942
$245$	0	0
$246$	0.751067	0.0478863
$247$	−17.7692	−1.13063
$248$	7.95720	0.505283
$249$	16.0823	1.01917
$250$	1.52797	0.0966372
$251$	7.13309	0.450237	0.225118	−	0.974331i	$-0.427723\pi$
$251$	7.13309	0.450237	0.225118	+	0.974331i	$0.427723\pi$
$252$	0	0
$253$	4.85023	0.304932
$254$	5.44107	0.341403
$255$	0.220709	0.0138213
$256$	1.00000	0.0625000
$257$	3.18297	0.198548	0.0992740	−	0.995060i	$-0.468348\pi$
$257$	3.18297	0.198548	0.0992740	+	0.995060i	$0.468348\pi$
$258$	−3.07643	−0.191530
$259$	0	0
$260$	0.766300	0.0475239
$261$	−1.73143	−0.107173
$262$	−11.2669	−0.696072
$263$	8.15560	0.502896	0.251448	−	0.967871i	$-0.419093\pi$
$263$	8.15560	0.502896	0.251448	+	0.967871i	$0.419093\pi$
$264$	−0.984046	−0.0605639
$265$	−1.06965	−0.0657081
$266$	0	0
$267$	−1.78607	−0.109306
$268$	11.4479	0.699289
$269$	−18.3630	−1.11961	−0.559805	−	0.828624i	$-0.689124\pi$
$269$	−18.3630	−1.11961	−0.559805	+	0.828624i	$0.689124\pi$
$270$	−0.816176	−0.0496709
$271$	15.4738	0.939964	0.469982	−	0.882676i	$-0.344260\pi$
$271$	15.4738	0.939964	0.469982	+	0.882676i	$0.344260\pi$
$272$	1.27946	0.0775789
$273$	0	0
$274$	13.7542	0.830920
$275$	−4.34796	−0.262192
$276$	−6.25262	−0.376363
$277$	−18.1520	−1.09065	−0.545324	−	0.838225i	$-0.683593\pi$
$277$	−18.1520	−1.09065	−0.545324	+	0.838225i	$0.683593\pi$
$278$	−14.8309	−0.889498
$279$	−13.7773	−0.824827
$280$	0	0
$281$	−13.5846	−0.810391	−0.405195	−	0.914230i	$-0.632797\pi$
$281$	−13.5846	−0.810391	−0.405195	+	0.914230i	$0.632797\pi$
$282$	−0.962258	−0.0573016
$283$	1.20780	0.0717962	0.0358981	−	0.999355i	$-0.488571\pi$
$283$	1.20780	0.0717962	0.0358981	+	0.999355i	$0.488571\pi$
$284$	−14.1171	−0.837698
$285$	0.612625	0.0362887
$286$	−4.37142	−0.258488
$287$	0	0
$288$	−1.73143	−0.102025
$289$	−15.3630	−0.903704
$290$	−0.153156	−0.00899364
$291$	−0.751067	−0.0440283
$292$	14.4360	0.844804
$293$	16.7617	0.979227	0.489614	−	0.871940i	$-0.337138\pi$
$293$	16.7617	0.979227	0.489614	+	0.871940i	$0.337138\pi$
$294$	0	0
$295$	−1.17641	−0.0684933
$296$	−5.29881	−0.307987
$297$	4.65595	0.270165
$298$	−4.93035	−0.285608
$299$	−27.7760	−1.60632
$300$	5.60512	0.323612
$301$	0	0
$302$	0.433568	0.0249490
$303$	2.09239	0.120204
$304$	3.55143	0.203688
$305$	−1.77740	−0.101773
$306$	−2.21530	−0.126640
$307$	−0.276073	−0.0157563	−0.00787817	−	0.999969i	$-0.502508\pi$
$307$	−0.276073	−0.0157563	−0.00787817	+	0.999969i	$0.502508\pi$
$308$	0	0
$309$	−5.23881	−0.298026
$310$	−1.21869	−0.0692172
$311$	−26.0760	−1.47863	−0.739317	−	0.673357i	$-0.764852\pi$
$311$	−26.0760	−1.47863	−0.739317	+	0.673357i	$0.764852\pi$
$312$	5.63536	0.319039
$313$	−7.77380	−0.439401	−0.219701	−	0.975567i	$-0.570508\pi$
$313$	−7.77380	−0.439401	−0.219701	+	0.975567i	$0.570508\pi$
$314$	13.8964	0.784221
$315$	0	0
$316$	12.3932	0.697173
$317$	−18.3281	−1.02941	−0.514704	−	0.857368i	$-0.672098\pi$
$317$	−18.3281	−1.02941	−0.514704	+	0.857368i	$0.672098\pi$
$318$	−7.86619	−0.441114
$319$	0.873692	0.0489173
$320$	−0.153156	−0.00856169
$321$	0.957627	0.0534495
$322$	0	0
$323$	4.54392	0.252831
$324$	−0.807862	−0.0448812
$325$	24.8996	1.38118
$326$	−1.21869	−0.0674972
$327$	8.82382	0.487958
$328$	−0.666840	−0.0368201
$329$	0	0
$330$	0.150713	0.00829646
$331$	6.44691	0.354354	0.177177	−	0.984179i	$-0.443303\pi$
$331$	6.44691	0.354354	0.177177	+	0.984179i	$0.443303\pi$
$332$	−14.2787	−0.783648
$333$	9.17452	0.502760
$334$	−19.4310	−1.06321
$335$	−1.75331	−0.0957935
$336$	0	0
$337$	−24.3131	−1.32442	−0.662209	−	0.749319i	$-0.730381\pi$
$337$	−24.3131	−1.32442	−0.662209	+	0.749319i	$0.730381\pi$
$338$	12.0339	0.654559
$339$	−7.67190	−0.416680
$340$	−0.195958	−0.0106273
$341$	6.95214	0.376479
$342$	−6.14904	−0.332502
$343$	0	0
$344$	2.73143	0.147269
$345$	0.957627	0.0515569
$346$	24.7840	1.33239
$347$	−26.0068	−1.39612	−0.698059	−	0.716041i	$-0.745953\pi$
$347$	−26.0068	−1.39612	−0.698059	+	0.716041i	$0.745953\pi$
$348$	−1.12631	−0.0603765
$349$	−0.00707471	−0.000378701 0	−0.000189350	−	1.00000i	$-0.500060\pi$
$349$	−0.00707471	−0.000378701 0	−0.000189350		1.00000i	$0.500060\pi$
$350$	0	0
$351$	−26.6633	−1.42318
$352$	0.873692	0.0465679
$353$	1.10285	0.0586989	0.0293494	−	0.999569i	$-0.490656\pi$
$353$	1.10285	0.0586989	0.0293494	+	0.999569i	$0.490656\pi$
$354$	−8.65131	−0.459812
$355$	2.16213	0.114754
$356$	1.58578	0.0840460
$357$	0	0
$358$	14.5976	0.771508
$359$	21.2904	1.12366	0.561831	−	0.827252i	$-0.310097\pi$
$359$	21.2904	1.12366	0.561831	+	0.827252i	$0.310097\pi$
$360$	0.265179	0.0139762
$361$	−6.38738	−0.336178
$362$	−5.00339	−0.262972
$363$	11.5296	0.605149
$364$	0	0
$365$	−2.21096	−0.115727
$366$	−13.0709	−0.683229
$367$	−2.68863	−0.140345	−0.0701726	−	0.997535i	$-0.522355\pi$
$367$	−2.68863	−0.140345	−0.0701726	+	0.997535i	$0.522355\pi$
$368$	5.55143	0.289388
$369$	1.15459	0.0601054
$370$	0.811545	0.0421902
$371$	0	0
$372$	−8.96226	−0.464671
$373$	−33.2585	−1.72206	−0.861029	−	0.508556i	$-0.830179\pi$
$373$	−33.2585	−1.72206	−0.861029	+	0.508556i	$0.830179\pi$
$374$	1.11786	0.0578030
$375$	−1.72096	−0.0888702
$376$	0.854347	0.0440596
$377$	−5.00339	−0.257688
$378$	0	0
$379$	−37.0240	−1.90180	−0.950898	−	0.309503i	$-0.899837\pi$
$379$	−37.0240	−1.90180	−0.950898	+	0.309503i	$0.899837\pi$
$380$	−0.543923	−0.0279026
$381$	−6.12832	−0.313964
$382$	−0.651314	−0.0333241
$383$	21.3555	1.09121	0.545607	−	0.838041i	$-0.316299\pi$
$383$	21.3555	1.09121	0.545607	+	0.838041i	$0.316299\pi$
$384$	−1.12631	−0.0574767
$385$	0	0
$386$	24.5120	1.24763
$387$	−4.72928	−0.240403
$388$	0.666840	0.0338537
$389$	−11.5514	−0.585681	−0.292840	−	0.956161i	$-0.594600\pi$
$389$	−11.5514	−0.585681	−0.292840	+	0.956161i	$0.594600\pi$
$390$	−0.863090	−0.0437043
$391$	7.10285	0.359207
$392$	0	0
$393$	12.6900	0.640126
$394$	22.7646	1.14687
$395$	−1.89810	−0.0955036
$396$	−1.51274	−0.0760178
$397$	−29.2377	−1.46740	−0.733698	−	0.679476i	$-0.762207\pi$
$397$	−29.2377	−1.46740	−0.733698	+	0.679476i	$0.762207\pi$
$398$	1.94630	0.0975594
$399$	0	0
$400$	−4.97654	−0.248827
$401$	19.3121	0.964403	0.482201	−	0.876060i	$-0.339837\pi$
$401$	19.3121	0.964403	0.482201	+	0.876060i	$0.339837\pi$
$402$	−12.8938	−0.643085
$403$	−39.8130	−1.98323
$404$	−1.85774	−0.0924259
$405$	0.123729	0.00614814
$406$	0	0
$407$	−4.62953	−0.229477
$408$	−1.44107	−0.0713437
$409$	13.1721	0.651317	0.325659	−	0.945487i	$-0.394414\pi$
$409$	13.1721	0.651317	0.325659	+	0.945487i	$0.394414\pi$
$410$	0.102131	0.00504387
$411$	−15.4914	−0.764136
$412$	4.65131	0.229154
$413$	0	0
$414$	−9.61190	−0.472399
$415$	2.18688	0.107350
$416$	−5.00339	−0.245311
$417$	16.7042	0.818006
$418$	3.10285	0.151765
$419$	24.8377	1.21340	0.606700	−	0.794931i	$-0.292493\pi$
$419$	24.8377	1.21340	0.606700	+	0.794931i	$0.292493\pi$
$420$	0	0
$421$	−18.3093	−0.892339	−0.446170	−	0.894948i	$-0.647212\pi$
$421$	−18.3093	−0.892339	−0.446170	+	0.894948i	$0.647212\pi$
$422$	12.9371	0.629770
$423$	−1.47924	−0.0719232
$424$	6.98405	0.339175
$425$	−6.36731	−0.308860
$426$	15.9002	0.770369
$427$	0	0
$428$	−0.850235	−0.0410977
$429$	4.92357	0.237712
$430$	−0.418335	−0.0201739
$431$	−36.4114	−1.75388	−0.876938	−	0.480604i	$-0.840418\pi$
$431$	−36.4114	−1.75388	−0.876938	+	0.480604i	$0.840418\pi$
$432$	5.32905	0.256394
$433$	−6.74232	−0.324015	−0.162008	−	0.986789i	$-0.551797\pi$
$433$	−6.74232	−0.324015	−0.162008	+	0.986789i	$0.551797\pi$
$434$	0	0
$435$	0.172501	0.00827079
$436$	−7.83428	−0.375194
$437$	19.7155	0.943119
$438$	−16.2594	−0.776904
$439$	−19.4479	−0.928195	−0.464098	−	0.885784i	$-0.653621\pi$
$439$	−19.4479	−0.928195	−0.464098	+	0.885784i	$0.653621\pi$
$440$	−0.133811	−0.00637920
$441$	0	0
$442$	−6.40166	−0.304496
$443$	19.8427	0.942757	0.471378	−	0.881931i	$-0.343757\pi$
$443$	19.8427	0.942757	0.471378	+	0.881931i	$0.343757\pi$
$444$	5.96809	0.283233
$445$	−0.242871	−0.0115132
$446$	−13.1565	−0.622981
$447$	5.55309	0.262652
$448$	0	0
$449$	27.1783	1.28262	0.641312	−	0.767280i	$-0.278390\pi$
$449$	27.1783	1.28262	0.641312	+	0.767280i	$0.278390\pi$
$450$	8.61654	0.406187
$451$	−0.582612	−0.0274341
$452$	6.81155	0.320388
$453$	−0.488331	−0.0229438
$454$	−8.60006	−0.403621
$455$	0	0
$456$	−4.00000	−0.187317
$457$	−23.4658	−1.09768	−0.548842	−	0.835926i	$-0.684931\pi$
$457$	−23.4658	−1.09768	−0.548842	+	0.835926i	$0.684931\pi$
$458$	3.45904	0.161630
$459$	6.81833	0.318252
$460$	−0.850235	−0.0396424
$461$	1.74442	0.0812458	0.0406229	−	0.999175i	$-0.487066\pi$
$461$	1.74442	0.0812458	0.0406229	+	0.999175i	$0.487066\pi$
$462$	0	0
$463$	−8.52406	−0.396147	−0.198073	−	0.980187i	$-0.563468\pi$
$463$	−8.52406	−0.396147	−0.198073	+	0.980187i	$0.563468\pi$
$464$	1.00000	0.0464238
$465$	1.37262	0.0636540
$466$	16.9690	0.786076
$467$	13.2724	0.614173	0.307086	−	0.951682i	$-0.400646\pi$
$467$	13.2724	0.614173	0.307086	+	0.951682i	$0.400646\pi$
$468$	8.66302	0.400448
$469$	0	0
$470$	−0.130848	−0.00603559
$471$	−15.6517	−0.721190
$472$	7.68113	0.353552
$473$	2.38643	0.109728
$474$	−13.9586	−0.641139
$475$	−17.6738	−0.810931
$476$	0	0
$477$	−12.0924	−0.553672
$478$	26.5338	1.21363
$479$	16.7000	0.763044	0.381522	−	0.924360i	$-0.375400\pi$
$479$	16.7000	0.763044	0.381522	+	0.924360i	$0.375400\pi$
$480$	0.172501	0.00787356
$481$	26.5120	1.20884
$482$	−0.999052	−0.0455056
$483$	0	0
$484$	−10.2367	−0.465303
$485$	−0.102131	−0.00463751
$486$	−15.0772	−0.683918
$487$	21.8079	0.988209	0.494104	−	0.869403i	$-0.335496\pi$
$487$	21.8079	0.988209	0.494104	+	0.869403i	$0.335496\pi$
$488$	11.6051	0.525339
$489$	1.37262	0.0620722
$490$	0	0
$491$	−19.8493	−0.895786	−0.447893	−	0.894087i	$-0.647825\pi$
$491$	−19.8493	−0.895786	−0.447893	+	0.894087i	$0.647825\pi$
$492$	0.751067	0.0338607
$493$	1.27946	0.0576242
$494$	−17.7692	−0.799473
$495$	0.231685	0.0104135
$496$	7.95720	0.357289
$497$	0	0
$498$	16.0823	0.720664
$499$	−10.3300	−0.462434	−0.231217	−	0.972902i	$-0.574271\pi$
$499$	−10.3300	−0.462434	−0.231217	+	0.972902i	$0.574271\pi$
$500$	1.52797	0.0683328
$501$	21.8852	0.977760
$502$	7.13309	0.318365
$503$	25.6659	1.14439	0.572193	−	0.820119i	$-0.306093\pi$
$503$	25.6659	1.14439	0.572193	+	0.820119i	$0.306093\pi$
$504$	0	0
$505$	0.284524	0.0126612
$506$	4.85023	0.215619
$507$	−13.5539	−0.601950
$508$	5.44107	0.241408
$509$	−8.36898	−0.370948	−0.185474	−	0.982649i	$-0.559382\pi$
$509$	−8.36898	−0.370948	−0.185474	+	0.982649i	$0.559382\pi$
$510$	0.220709	0.00977316
$511$	0	0
$512$	1.00000	0.0441942
$513$	18.9257	0.835591
$514$	3.18297	0.140395
$515$	−0.712377	−0.0313911
$516$	−3.07643	−0.135432
$517$	0.746436	0.0328282
$518$	0	0
$519$	−27.9144	−1.22531
$520$	0.766300	0.0336045
$521$	−20.4856	−0.897490	−0.448745	−	0.893660i	$-0.648129\pi$
$521$	−20.4856	−0.897490	−0.448745	+	0.893660i	$0.648129\pi$
$522$	−1.73143	−0.0757826
$523$	−35.7416	−1.56287	−0.781436	−	0.623986i	$-0.785512\pi$
$523$	−35.7416	−1.56287	−0.781436	+	0.623986i	$0.785512\pi$
$524$	−11.2669	−0.492197
$525$	0	0
$526$	8.15560	0.355601
$527$	10.1810	0.443489
$528$	−0.984046	−0.0428251
$529$	7.81833	0.339927
$530$	−1.06965	−0.0464626
$531$	−13.2993	−0.577142
$532$	0	0
$533$	3.33646	0.144518
$534$	−1.78607	−0.0772910
$535$	0.130219	0.00562985
$536$	11.4479	0.494472
$537$	−16.4414	−0.709500
$538$	−18.3630	−0.791684
$539$	0	0
$540$	−0.816176	−0.0351226
$541$	−17.8457	−0.767246	−0.383623	−	0.923490i	$-0.625324\pi$
$541$	−17.8457	−0.767246	−0.383623	+	0.923490i	$0.625324\pi$
$542$	15.4738	0.664655
$543$	5.63536	0.241836
$544$	1.27946	0.0548566
$545$	1.19987	0.0513967
$546$	0	0
$547$	−2.32132	−0.0992524	−0.0496262	−	0.998768i	$-0.515803\pi$
$547$	−2.32132	−0.0992524	−0.0496262	+	0.998768i	$0.515803\pi$
$548$	13.7542	0.587549
$549$	−20.0935	−0.857568
$550$	−4.34796	−0.185398
$551$	3.55143	0.151296
$552$	−6.25262	−0.266129
$553$	0	0
$554$	−18.1520	−0.771205
$555$	−0.914050	−0.0387993
$556$	−14.8309	−0.628970
$557$	5.21024	0.220765	0.110383	−	0.993889i	$-0.464792\pi$
$557$	5.21024	0.220765	0.110383	+	0.993889i	$0.464792\pi$
$558$	−13.7773	−0.583241
$559$	−13.6664	−0.578028
$560$	0	0
$561$	−1.25905	−0.0531572
$562$	−13.5846	−0.573033
$563$	−37.0483	−1.56140	−0.780701	−	0.624905i	$-0.785138\pi$
$563$	−37.0483	−1.56140	−0.780701	+	0.624905i	$0.785138\pi$
$564$	−0.962258	−0.0405184
$565$	−1.04323	−0.0438890
$566$	1.20780	0.0507676
$567$	0	0
$568$	−14.1171	−0.592342
$569$	34.4414	1.44386	0.721930	−	0.691966i	$-0.243255\pi$
$569$	34.4414	1.44386	0.721930	+	0.691966i	$0.243255\pi$
$570$	0.612625	0.0256600
$571$	−33.9430	−1.42047	−0.710234	−	0.703965i	$-0.751411\pi$
$571$	−33.9430	−1.42047	−0.710234	+	0.703965i	$0.751411\pi$
$572$	−4.37142	−0.182778
$573$	0.733581	0.0306458
$574$	0	0
$575$	−27.6269	−1.15212
$576$	−1.73143	−0.0721429
$577$	−23.5456	−0.980218	−0.490109	−	0.871661i	$-0.663043\pi$
$577$	−23.5456	−0.980218	−0.490109	+	0.871661i	$0.663043\pi$
$578$	−15.3630	−0.639015
$579$	−27.6081	−1.14735
$580$	−0.153156	−0.00635946
$581$	0	0
$582$	−0.751067	−0.0311327
$583$	6.10190	0.252715
$584$	14.4360	0.597366
$585$	−1.32679	−0.0548562
$586$	16.7617	0.692418
$587$	31.6642	1.30692	0.653461	−	0.756960i	$-0.273316\pi$
$587$	31.6642	1.30692	0.653461	+	0.756960i	$0.273316\pi$
$588$	0	0
$589$	28.2594	1.16441
$590$	−1.17641	−0.0484321
$591$	−25.6400	−1.05469
$592$	−5.29881	−0.217780
$593$	−21.1293	−0.867675	−0.433838	−	0.900991i	$-0.642841\pi$
$593$	−21.1293	−0.867675	−0.433838	+	0.900991i	$0.642841\pi$
$594$	4.65595	0.191036
$595$	0	0
$596$	−4.93035	−0.201955
$597$	−2.19214	−0.0897183
$598$	−27.7760	−1.13584
$599$	9.29036	0.379594	0.189797	−	0.981823i	$-0.439217\pi$
$599$	9.29036	0.379594	0.189797	+	0.981823i	$0.439217\pi$
$600$	5.60512	0.228828
$601$	−39.3854	−1.60656	−0.803282	−	0.595599i	$-0.796915\pi$
$601$	−39.3854	−1.60656	−0.803282	+	0.595599i	$0.796915\pi$
$602$	0	0
$603$	−19.8212	−0.807180
$604$	0.433568	0.0176416
$605$	1.56781	0.0637405
$606$	2.09239	0.0849974
$607$	44.7823	1.81766	0.908829	−	0.417169i	$-0.136978\pi$
$607$	44.7823	1.81766	0.908829	+	0.417169i	$0.136978\pi$
$608$	3.55143	0.144029
$609$	0	0
$610$	−1.77740	−0.0719646
$611$	−4.27463	−0.172933
$612$	−2.21530	−0.0895483
$613$	22.7382	0.918388	0.459194	−	0.888336i	$-0.348138\pi$
$613$	22.7382	0.918388	0.459194	+	0.888336i	$0.348138\pi$
$614$	−0.276073	−0.0111414
$615$	−0.115031	−0.00463848
$616$	0	0
$617$	−35.9817	−1.44857	−0.724283	−	0.689502i	$-0.757829\pi$
$617$	−35.9817	−1.44857	−0.724283	+	0.689502i	$0.757829\pi$
$618$	−5.23881	−0.210736
$619$	−10.8050	−0.434289	−0.217145	−	0.976139i	$-0.569674\pi$
$619$	−10.8050	−0.434289	−0.217145	+	0.976139i	$0.569674\pi$
$620$	−1.21869	−0.0489439
$621$	29.5838	1.18716
$622$	−26.0760	−1.04555
$623$	0	0
$624$	5.63536	0.225595
$625$	24.6487	0.985948
$626$	−7.77380	−0.310704
$627$	−3.49477	−0.139568
$628$	13.8964	0.554528
$629$	−6.77964	−0.270322
$630$	0	0
$631$	6.91808	0.275404	0.137702	−	0.990474i	$-0.456028\pi$
$631$	6.91808	0.275404	0.137702	+	0.990474i	$0.456028\pi$
$632$	12.3932	0.492975
$633$	−14.5712	−0.579153
$634$	−18.3281	−0.727902
$635$	−0.833334	−0.0330698
$636$	−7.86619	−0.311915
$637$	0	0
$638$	0.873692	0.0345898
$639$	24.4428	0.966943
$640$	−0.153156	−0.00605403
$641$	−6.13022	−0.242129	−0.121065	−	0.992645i	$-0.538631\pi$
$641$	−6.13022	−0.242129	−0.121065	+	0.992645i	$0.538631\pi$
$642$	0.957627	0.0377945
$643$	8.73028	0.344289	0.172144	−	0.985072i	$-0.444930\pi$
$643$	8.73028	0.344289	0.172144	+	0.985072i	$0.444930\pi$
$644$	0	0
$645$	0.471174	0.0185525
$646$	4.54392	0.178778
$647$	12.3368	0.485009	0.242504	−	0.970150i	$-0.422031\pi$
$647$	12.3368	0.485009	0.242504	+	0.970150i	$0.422031\pi$
$648$	−0.807862	−0.0317358
$649$	6.71094	0.263427
$650$	24.8996	0.976642
$651$	0	0
$652$	−1.21869	−0.0477277
$653$	6.26762	0.245271	0.122636	−	0.992452i	$-0.460865\pi$
$653$	6.26762	0.245271	0.122636	+	0.992452i	$0.460865\pi$
$654$	8.82382	0.345038
$655$	1.72560	0.0674246
$656$	−0.666840	−0.0260357
$657$	−24.9949	−0.975145
$658$	0	0
$659$	10.6211	0.413738	0.206869	−	0.978369i	$-0.433673\pi$
$659$	10.6211	0.413738	0.206869	+	0.978369i	$0.433673\pi$
$660$	0.150713	0.00586648
$661$	−14.5096	−0.564357	−0.282178	−	0.959362i	$-0.591057\pi$
$661$	−14.5096	−0.564357	−0.282178	+	0.959362i	$0.591057\pi$
$662$	6.44691	0.250566
$663$	7.21024	0.280023
$664$	−14.2787	−0.554123
$665$	0	0
$666$	9.17452	0.355505
$667$	5.55143	0.214952
$668$	−19.4310	−0.751806
$669$	14.8183	0.572910
$670$	−1.75331	−0.0677362
$671$	10.1393	0.391423
$672$	0	0
$673$	36.6875	1.41420	0.707099	−	0.707114i	$-0.250003\pi$
$673$	36.6875	1.41420	0.707099	+	0.707114i	$0.250003\pi$
$674$	−24.3131	−0.936505
$675$	−26.5202	−1.02076
$676$	12.0339	0.462843
$677$	21.0293	0.808221	0.404111	−	0.914710i	$-0.367581\pi$
$677$	21.0293	0.808221	0.404111	+	0.914710i	$0.367581\pi$
$678$	−7.67190	−0.294638
$679$	0	0
$680$	−0.195958	−0.00751464
$681$	9.68632	0.371181
$682$	6.95214	0.266211
$683$	−6.52024	−0.249490	−0.124745	−	0.992189i	$-0.539811\pi$
$683$	−6.52024	−0.249490	−0.124745	+	0.992189i	$0.539811\pi$
$684$	−6.14904	−0.235115
$685$	−2.10654	−0.0804866
$686$	0	0
$687$	−3.89595	−0.148640
$688$	2.73143	0.104135
$689$	−34.9439	−1.33126
$690$	0.957627	0.0364562
$691$	27.2641	1.03717	0.518587	−	0.855025i	$-0.326458\pi$
$691$	27.2641	1.03717	0.518587	+	0.855025i	$0.326458\pi$
$692$	24.7840	0.942145
$693$	0	0
$694$	−26.0068	−0.987204
$695$	2.27144	0.0861607
$696$	−1.12631	−0.0426926
$697$	−0.853198	−0.0323172
$698$	−0.00707471	−0.000267782 0
$699$	−19.1124	−0.722896
$700$	0	0
$701$	38.0787	1.43821	0.719106	−	0.694901i	$-0.244552\pi$
$701$	38.0787	1.43821	0.719106	+	0.694901i	$0.244552\pi$
$702$	−26.6633	−1.00634
$703$	−18.8183	−0.709747
$704$	0.873692	0.0329285
$705$	0.147376	0.00555049
$706$	1.10285	0.0415064
$707$	0	0
$708$	−8.65131	−0.325136
$709$	40.8583	1.53447	0.767233	−	0.641368i	$-0.221633\pi$
$709$	40.8583	1.53447	0.767233	+	0.641368i	$0.221633\pi$
$710$	2.16213	0.0811432
$711$	−21.4580	−0.804737
$712$	1.58578	0.0594295
$713$	44.1738	1.65432
$714$	0	0
$715$	0.669510	0.0250383
$716$	14.5976	0.545539
$717$	−29.8852	−1.11608
$718$	21.2904	0.794549
$719$	−27.7373	−1.03443	−0.517213	−	0.855857i	$-0.673030\pi$
$719$	−27.7373	−1.03443	−0.517213	+	0.855857i	$0.673030\pi$
$720$	0.265179	0.00988264
$721$	0	0
$722$	−6.38738	−0.237713
$723$	1.12524	0.0418482
$724$	−5.00339	−0.185950
$725$	−4.97654	−0.184824
$726$	11.5296	0.427905
$727$	−32.2817	−1.19726	−0.598631	−	0.801025i	$-0.704288\pi$
$727$	−32.2817	−1.19726	−0.598631	+	0.801025i	$0.704288\pi$
$728$	0	0
$729$	19.4052	0.718711
$730$	−2.21096	−0.0818314
$731$	3.49477	0.129259
$732$	−13.0709	−0.483116
$733$	17.9047	0.661323	0.330662	−	0.943749i	$-0.392728\pi$
$733$	17.9047	0.661323	0.330662	+	0.943749i	$0.392728\pi$
$734$	−2.68863	−0.0992391
$735$	0	0
$736$	5.55143	0.204628
$737$	10.0019	0.368425
$738$	1.15459	0.0425009
$739$	0.194289	0.00714705	0.00357352	−	0.999994i	$-0.498863\pi$
$739$	0.194289	0.00714705	0.00357352	+	0.999994i	$0.498863\pi$
$740$	0.811545	0.0298330
$741$	20.0136	0.735217
$742$	0	0
$743$	−26.4205	−0.969274	−0.484637	−	0.874715i	$-0.661048\pi$
$743$	−26.4205	−0.969274	−0.484637	+	0.874715i	$0.661048\pi$
$744$	−8.96226	−0.328572
$745$	0.755113	0.0276652
$746$	−33.2585	−1.21768
$747$	24.7226	0.904554
$748$	1.11786	0.0408729
$749$	0	0
$750$	−1.72096	−0.0628407
$751$	17.5157	0.639157	0.319578	−	0.947560i	$-0.396459\pi$
$751$	17.5157	0.639157	0.319578	+	0.947560i	$0.396459\pi$
$752$	0.854347	0.0311548
$753$	−8.03406	−0.292777
$754$	−5.00339	−0.182213
$755$	−0.0664036	−0.00241668
$756$	0	0
$757$	−34.5905	−1.25721	−0.628606	−	0.777724i	$-0.716374\pi$
$757$	−34.5905	−1.25721	−0.628606	+	0.777724i	$0.716374\pi$
$758$	−37.0240	−1.34477
$759$	−5.46286	−0.198289
$760$	−0.543923	−0.0197301
$761$	−15.4798	−0.561141	−0.280570	−	0.959833i	$-0.590524\pi$
$761$	−15.4798	−0.561141	−0.280570	+	0.959833i	$0.590524\pi$
$762$	−6.12832	−0.222006
$763$	0	0
$764$	−0.651314	−0.0235637
$765$	0.339287	0.0122670
$766$	21.3555	0.771604
$767$	−38.4317	−1.38769
$768$	−1.12631	−0.0406421
$769$	29.9057	1.07843	0.539213	−	0.842170i	$-0.318722\pi$
$769$	29.9057	1.07843	0.539213	+	0.842170i	$0.318722\pi$
$770$	0	0
$771$	−3.58500	−0.129111
$772$	24.5120	0.882207
$773$	18.5091	0.665724	0.332862	−	0.942975i	$-0.391986\pi$
$773$	18.5091	0.665724	0.332862	+	0.942975i	$0.391986\pi$
$774$	−4.72928	−0.169990
$775$	−39.5993	−1.42245
$776$	0.666840	0.0239382
$777$	0	0
$778$	−11.5514	−0.414139
$779$	−2.36823	−0.0848507
$780$	−0.863090	−0.0309036
$781$	−12.3340	−0.441346
$782$	7.10285	0.253997
$783$	5.32905	0.190445
$784$	0	0
$785$	−2.12832	−0.0759631
$786$	12.6900	0.452637
$787$	17.3042	0.616829	0.308414	−	0.951252i	$-0.400202\pi$
$787$	17.3042	0.616829	0.308414	+	0.951252i	$0.400202\pi$
$788$	22.7646	0.810956
$789$	−9.18572	−0.327020
$790$	−1.89810	−0.0675312
$791$	0	0
$792$	−1.51274	−0.0537527
$793$	−58.0650	−2.06195
$794$	−29.2377	−1.03761
$795$	1.20476	0.0427283
$796$	1.94630	0.0689849
$797$	38.1231	1.35039	0.675194	−	0.737640i	$-0.264060\pi$
$797$	38.1231	1.35039	0.675194	+	0.737640i	$0.264060\pi$
$798$	0	0
$799$	1.09311	0.0386713
$800$	−4.97654	−0.175947
$801$	−2.74566	−0.0970132
$802$	19.3121	0.681936
$803$	12.6126	0.445090
$804$	−12.8938	−0.454730
$805$	0	0
$806$	−39.8130	−1.40235
$807$	20.6824	0.728054
$808$	−1.85774	−0.0653550
$809$	−0.666320	−0.0234266	−0.0117133	−	0.999931i	$-0.503729\pi$
$809$	−0.666320	−0.0234266	−0.0117133	+	0.999931i	$0.503729\pi$
$810$	0.123729	0.00434739
$811$	22.3692	0.785490	0.392745	−	0.919647i	$-0.371525\pi$
$811$	22.3692	0.785490	0.392745	+	0.919647i	$0.371525\pi$
$812$	0	0
$813$	−17.4282	−0.611234
$814$	−4.62953	−0.162265
$815$	0.186650	0.00653808
$816$	−1.44107	−0.0504476
$817$	9.70047	0.339376
$818$	13.1721	0.460551
$819$	0	0
$820$	0.102131	0.00356656
$821$	−2.68596	−0.0937406	−0.0468703	−	0.998901i	$-0.514925\pi$
$821$	−2.68596	−0.0937406	−0.0468703	+	0.998901i	$0.514925\pi$
$822$	−15.4914	−0.540326
$823$	49.4295	1.72300	0.861502	−	0.507754i	$-0.169524\pi$
$823$	49.4295	1.72300	0.861502	+	0.507754i	$0.169524\pi$
$824$	4.65131	0.162036
$825$	4.89715	0.170497
$826$	0	0
$827$	−16.6420	−0.578699	−0.289350	−	0.957223i	$-0.593439\pi$
$827$	−16.6420	−0.578699	−0.289350	+	0.957223i	$0.593439\pi$
$828$	−9.61190	−0.334037
$829$	29.6506	1.02981	0.514904	−	0.857248i	$-0.327828\pi$
$829$	29.6506	1.02981	0.514904	+	0.857248i	$0.327828\pi$
$830$	2.18688	0.0759076
$831$	20.4448	0.709221
$832$	−5.00339	−0.173461
$833$	0	0
$834$	16.7042	0.578418
$835$	2.97597	0.102988
$836$	3.10285	0.107314
$837$	42.4043	1.46571
$838$	24.8377	0.858003
$839$	5.42828	0.187405	0.0937025	−	0.995600i	$-0.470130\pi$
$839$	5.42828	0.187405	0.0937025	+	0.995600i	$0.470130\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	−18.3093	−0.630979
$843$	15.3005	0.526976
$844$	12.9371	0.445314
$845$	−1.84307	−0.0634035
$846$	−1.47924	−0.0508574
$847$	0	0
$848$	6.98405	0.239833
$849$	−1.36035	−0.0466873
$850$	−6.36731	−0.218397
$851$	−29.4159	−1.00837
$852$	15.9002	0.544733
$853$	6.60058	0.226000	0.113000	−	0.993595i	$-0.463954\pi$
$853$	6.60058	0.226000	0.113000	+	0.993595i	$0.463954\pi$
$854$	0	0
$855$	0.941764	0.0322076
$856$	−0.850235	−0.0290604
$857$	52.0250	1.77714	0.888570	−	0.458742i	$-0.151700\pi$
$857$	52.0250	1.77714	0.888570	+	0.458742i	$0.151700\pi$
$858$	4.92357	0.168088
$859$	−12.8418	−0.438156	−0.219078	−	0.975707i	$-0.570305\pi$
$859$	−12.8418	−0.438156	−0.219078	+	0.975707i	$0.570305\pi$
$860$	−0.418335	−0.0142651
$861$	0	0
$862$	−36.4114	−1.24018
$863$	15.1745	0.516547	0.258273	−	0.966072i	$-0.416847\pi$
$863$	15.1745	0.516547	0.258273	+	0.966072i	$0.416847\pi$
$864$	5.32905	0.181298
$865$	−3.79582	−0.129062
$866$	−6.74232	−0.229113
$867$	17.3034	0.587656
$868$	0	0
$869$	10.8278	0.367310
$870$	0.172501	0.00584833
$871$	−57.2781	−1.94079
$872$	−7.83428	−0.265302
$873$	−1.15459	−0.0390768
$874$	19.7155	0.666886
$875$	0	0
$876$	−16.2594	−0.549354
$877$	−48.8137	−1.64832	−0.824161	−	0.566356i	$-0.808353\pi$
$877$	−48.8137	−1.64832	−0.824161	+	0.566356i	$0.808353\pi$
$878$	−19.4479	−0.656333
$879$	−18.8788	−0.636766
$880$	−0.133811	−0.00451078
$881$	−28.4177	−0.957416	−0.478708	−	0.877974i	$-0.658895\pi$
$881$	−28.4177	−0.957416	−0.478708	+	0.877974i	$0.658895\pi$
$882$	0	0
$883$	5.24215	0.176412	0.0882062	−	0.996102i	$-0.471887\pi$
$883$	5.24215	0.176412	0.0882062	+	0.996102i	$0.471887\pi$
$884$	−6.40166	−0.215311
$885$	1.32500	0.0445395
$886$	19.8427	0.666630
$887$	33.4670	1.12371	0.561855	−	0.827235i	$-0.310088\pi$
$887$	33.4670	1.12371	0.561855	+	0.827235i	$0.310088\pi$
$888$	5.96809	0.200276
$889$	0	0
$890$	−0.242871	−0.00814107
$891$	−0.705822	−0.0236459
$892$	−13.1565	−0.440514
$893$	3.03415	0.101534
$894$	5.55309	0.185723
$895$	−2.23571	−0.0747317
$896$	0	0
$897$	31.2843	1.04455
$898$	27.1783	0.906953
$899$	7.95720	0.265387
$900$	8.61654	0.287218
$901$	8.93584	0.297696
$902$	−0.582612	−0.0193989
$903$	0	0
$904$	6.81155	0.226549
$905$	0.766300	0.0254727
$906$	−0.488331	−0.0162237
$907$	2.57775	0.0855929	0.0427965	−	0.999084i	$-0.486373\pi$
$907$	2.57775	0.0855929	0.0427965	+	0.999084i	$0.486373\pi$
$908$	−8.60006	−0.285403
$909$	3.21654	0.106686
$910$	0	0
$911$	−32.1256	−1.06437	−0.532184	−	0.846629i	$-0.678629\pi$
$911$	−32.1256	−1.06437	−0.532184	+	0.846629i	$0.678629\pi$
$912$	−4.00000	−0.132453
$913$	−12.4752	−0.412870
$914$	−23.4658	−0.776180
$915$	2.00190	0.0661806
$916$	3.45904	0.114290
$917$	0	0
$918$	6.81833	0.225038
$919$	−9.26690	−0.305687	−0.152843	−	0.988250i	$-0.548843\pi$
$919$	−9.26690	−0.305687	−0.152843	+	0.988250i	$0.548843\pi$
$920$	−0.850235	−0.0280314
$921$	0.310944	0.0102459
$922$	1.74442	0.0574494
$923$	70.6336	2.32493
$924$	0	0
$925$	26.3698	0.867032
$926$	−8.52406	−0.280118
$927$	−8.05342	−0.264509
$928$	1.00000	0.0328266
$929$	25.5083	0.836901	0.418451	−	0.908240i	$-0.362573\pi$
$929$	25.5083	0.836901	0.418451	+	0.908240i	$0.362573\pi$
$930$	1.37262	0.0450101
$931$	0	0
$932$	16.9690	0.555839
$933$	29.3696	0.961518
$934$	13.2724	0.434286
$935$	−0.171207	−0.00559906
$936$	8.66302	0.283160
$937$	−54.8033	−1.79035	−0.895173	−	0.445718i	$-0.852948\pi$
$937$	−54.8033	−1.79035	−0.895173	+	0.445718i	$0.852948\pi$
$938$	0	0
$939$	8.75570	0.285731
$940$	−0.130848	−0.00426781
$941$	−8.97293	−0.292509	−0.146255	−	0.989247i	$-0.546722\pi$
$941$	−8.97293	−0.292509	−0.146255	+	0.989247i	$0.546722\pi$
$942$	−15.6517	−0.509959
$943$	−3.70191	−0.120551
$944$	7.68113	0.249999
$945$	0	0
$946$	2.38643	0.0775895
$947$	31.1428	1.01201	0.506003	−	0.862532i	$-0.331122\pi$
$947$	31.1428	1.01201	0.506003	+	0.862532i	$0.331122\pi$
$948$	−13.9586	−0.453353
$949$	−72.2290	−2.34465
$950$	−17.6738	−0.573415
$951$	20.6431	0.669398
$952$	0	0
$953$	−13.1868	−0.427162	−0.213581	−	0.976925i	$-0.568513\pi$
$953$	−13.1868	−0.427162	−0.213581	+	0.976925i	$0.568513\pi$
$954$	−12.0924	−0.391505
$955$	0.0997528	0.00322792
$956$	26.5338	0.858165
$957$	−0.984046	−0.0318097
$958$	16.7000	0.539554
$959$	0	0
$960$	0.172501	0.00556745
$961$	32.3170	1.04248
$962$	26.5120	0.854782
$963$	1.47212	0.0474385
$964$	−0.999052	−0.0321773
$965$	−3.75417	−0.120851
$966$	0	0
$967$	14.7281	0.473624	0.236812	−	0.971556i	$-0.423898\pi$
$967$	14.7281	0.473624	0.236812	+	0.971556i	$0.423898\pi$
$968$	−10.2367	−0.329019
$969$	−5.11786	−0.164409
$970$	−0.102131	−0.00327922
$971$	−21.8510	−0.701231	−0.350615	−	0.936520i	$-0.614028\pi$
$971$	−21.8510	−0.701231	−0.350615	+	0.936520i	$0.614028\pi$
$972$	−15.0772	−0.483603
$973$	0	0
$974$	21.8079	0.698769
$975$	−28.0446	−0.898146
$976$	11.6051	0.371471
$977$	42.8932	1.37227	0.686137	−	0.727472i	$-0.259305\pi$
$977$	42.8932	1.37227	0.686137	+	0.727472i	$0.259305\pi$
$978$	1.37262	0.0438917
$979$	1.38548	0.0442801
$980$	0	0
$981$	13.5645	0.433081
$982$	−19.8493	−0.633416
$983$	38.7145	1.23480	0.617400	−	0.786650i	$-0.288186\pi$
$983$	38.7145	1.23480	0.617400	+	0.786650i	$0.288186\pi$
$984$	0.751067	0.0239431
$985$	−3.48654	−0.111091
$986$	1.27946	0.0407464
$987$	0	0
$988$	−17.7692	−0.565313
$989$	15.1633	0.482166
$990$	0.231685	0.00736343
$991$	48.2948	1.53413	0.767067	−	0.641567i	$-0.221716\pi$
$991$	48.2948	1.53413	0.767067	+	0.641567i	$0.221716\pi$
$992$	7.95720	0.252641
$993$	−7.26120	−0.230427
$994$	0	0
$995$	−0.298088	−0.00945004
$996$	16.0823	0.509586
$997$	59.2568	1.87668	0.938341	−	0.345712i	$-0.112363\pi$
$997$	59.2568	1.87668	0.938341	+	0.345712i	$0.112363\pi$
$998$	−10.3300	−0.326990
$999$	−28.2376	−0.893398

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2842.2.a.r.1.2		4
7.6	odd	2		406.2.a.g.1.3	✓	4
21.20	even	2		3654.2.a.bg.1.2		4
28.27	even	2		3248.2.a.x.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
406.2.a.g.1.3	✓	4	7.6	odd	2
2842.2.a.r.1.2		4	1.1	even	1	trivial
3248.2.a.x.1.2		4	28.27	even	2
3654.2.a.bg.1.2		4	21.20	even	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:	\( N \)	\(=\)	\( 2842 = 2 \cdot 7^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2842.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.12631 q^{3} +1.00000 q^{4} -0.153156 q^{5} -1.12631 q^{6} +1.00000 q^{8} -1.73143 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.12631 q^{3} +1.00000 q^{4} -0.153156 q^{5} -1.12631 q^{6} +1.00000 q^{8} -1.73143 q^{9} -0.153156 q^{10} +0.873692 q^{11} -1.12631 q^{12} -5.00339 q^{13} +0.172501 q^{15} +1.00000 q^{16} +1.27946 q^{17} -1.73143 q^{18} +3.55143 q^{19} -0.153156 q^{20} +0.873692 q^{22} +5.55143 q^{23} -1.12631 q^{24} -4.97654 q^{25} -5.00339 q^{26} +5.32905 q^{27} +1.00000 q^{29} +0.172501 q^{30} +7.95720 q^{31} +1.00000 q^{32} -0.984046 q^{33} +1.27946 q^{34} -1.73143 q^{36} -5.29881 q^{37} +3.55143 q^{38} +5.63536 q^{39} -0.153156 q^{40} -0.666840 q^{41} +2.73143 q^{43} +0.873692 q^{44} +0.265179 q^{45} +5.55143 q^{46} +0.854347 q^{47} -1.12631 q^{48} -4.97654 q^{50} -1.44107 q^{51} -5.00339 q^{52} +6.98405 q^{53} +5.32905 q^{54} -0.133811 q^{55} -4.00000 q^{57} +1.00000 q^{58} +7.68113 q^{59} +0.172501 q^{60} +11.6051 q^{61} +7.95720 q^{62} +1.00000 q^{64} +0.766300 q^{65} -0.984046 q^{66} +11.4479 q^{67} +1.27946 q^{68} -6.25262 q^{69} -14.1171 q^{71} -1.73143 q^{72} +14.4360 q^{73} -5.29881 q^{74} +5.60512 q^{75} +3.55143 q^{76} +5.63536 q^{78} +12.3932 q^{79} -0.153156 q^{80} -0.807862 q^{81} -0.666840 q^{82} -14.2787 q^{83} -0.195958 q^{85} +2.73143 q^{86} -1.12631 q^{87} +0.873692 q^{88} +1.58578 q^{89} +0.265179 q^{90} +5.55143 q^{92} -8.96226 q^{93} +0.854347 q^{94} -0.543923 q^{95} -1.12631 q^{96} +0.666840 q^{97} -1.51274 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - q^{3} + 4 q^{4} + q^{5} - q^{6} + 4 q^{8} + 9 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 - q^3 + 4 * q^4 + q^5 - q^6 + 4 * q^8 + 9 * q^9	\( 4 q + 4 q^{2} - q^{3} + 4 q^{4} + q^{5} - q^{6} + 4 q^{8} + 9 q^{9} + q^{10} + 7 q^{11} - q^{12} + 7 q^{13} - 5 q^{15} + 4 q^{16} + 9 q^{18} - 2 q^{19} + q^{20} + 7 q^{22} + 6 q^{23} - q^{24} + 9 q^{25} + 7 q^{26} - 13 q^{27} + 4 q^{29} - 5 q^{30} + 7 q^{31} + 4 q^{32} + 19 q^{33} + 9 q^{36} - 12 q^{37} - 2 q^{38} - 15 q^{39} + q^{40} - 4 q^{41} - 5 q^{43} + 7 q^{44} + 44 q^{45} + 6 q^{46} + 11 q^{47} - q^{48} + 9 q^{50} - 16 q^{51} + 7 q^{52} + 5 q^{53} - 13 q^{54} - 3 q^{55} - 16 q^{57} + 4 q^{58} - 16 q^{59} - 5 q^{60} + 34 q^{61} + 7 q^{62} + 4 q^{64} - q^{65} + 19 q^{66} + 2 q^{67} - 18 q^{69} + 24 q^{71} + 9 q^{72} + 24 q^{73} - 12 q^{74} + 10 q^{75} - 2 q^{76} - 15 q^{78} - 9 q^{79} + q^{80} + 40 q^{81} - 4 q^{82} + 8 q^{83} - 24 q^{85} - 5 q^{86} - q^{87} + 7 q^{88} - 2 q^{89} + 44 q^{90} + 6 q^{92} - 55 q^{93} + 11 q^{94} + 20 q^{95} - q^{96} + 4 q^{97} + 2 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - q^3 + 4 * q^4 + q^5 - q^6 + 4 * q^8 + 9 * q^9 + q^10 + 7 * q^11 - q^12 + 7 * q^13 - 5 * q^15 + 4 * q^16 + 9 * q^18 - 2 * q^19 + q^20 + 7 * q^22 + 6 * q^23 - q^24 + 9 * q^25 + 7 * q^26 - 13 * q^27 + 4 * q^29 - 5 * q^30 + 7 * q^31 + 4 * q^32 + 19 * q^33 + 9 * q^36 - 12 * q^37 - 2 * q^38 - 15 * q^39 + q^40 - 4 * q^41 - 5 * q^43 + 7 * q^44 + 44 * q^45 + 6 * q^46 + 11 * q^47 - q^48 + 9 * q^50 - 16 * q^51 + 7 * q^52 + 5 * q^53 - 13 * q^54 - 3 * q^55 - 16 * q^57 + 4 * q^58 - 16 * q^59 - 5 * q^60 + 34 * q^61 + 7 * q^62 + 4 * q^64 - q^65 + 19 * q^66 + 2 * q^67 - 18 * q^69 + 24 * q^71 + 9 * q^72 + 24 * q^73 - 12 * q^74 + 10 * q^75 - 2 * q^76 - 15 * q^78 - 9 * q^79 + q^80 + 40 * q^81 - 4 * q^82 + 8 * q^83 - 24 * q^85 - 5 * q^86 - q^87 + 7 * q^88 - 2 * q^89 + 44 * q^90 + 6 * q^92 - 55 * q^93 + 11 * q^94 + 20 * q^95 - q^96 + 4 * q^97 + 2 * q^99

Introduction

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