LMFDB - Embedded newform 4018.2.a.br.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4018,2,Mod(1,4018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4018, 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("4018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4018 = 2 \cdot 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4018.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:	$32.0838915322$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 17x^{8} + 36x^{7} + 75x^{6} - 174x^{5} - 69x^{4} + 260x^{3} - 104x^{2} - 24x + 14 $ x^10 - 2x^9 - 17x^8 + 36x^7 + 75x^6 - 174x^5 - 69x^4 + 260x^3 - 104x^2 - 24*x + 14
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$0.835626$ of defining polynomial
Character	$\chi$	$=$	4018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.96764 q^{3} +1.00000 q^{4} +1.63790 q^{5} -1.96764 q^{6} -1.00000 q^{8} +0.871591 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.96764 q^{3} +1.00000 q^{4} +1.63790 q^{5} -1.96764 q^{6} -1.00000 q^{8} +0.871591 q^{9} -1.63790 q^{10} +0.177275 q^{11} +1.96764 q^{12} -5.66555 q^{13} +3.22280 q^{15} +1.00000 q^{16} -6.01783 q^{17} -0.871591 q^{18} -5.54550 q^{19} +1.63790 q^{20} -0.177275 q^{22} +6.91394 q^{23} -1.96764 q^{24} -2.31728 q^{25} +5.66555 q^{26} -4.18793 q^{27} +6.25278 q^{29} -3.22280 q^{30} +2.73897 q^{31} -1.00000 q^{32} +0.348812 q^{33} +6.01783 q^{34} +0.871591 q^{36} -11.1237 q^{37} +5.54550 q^{38} -11.1477 q^{39} -1.63790 q^{40} -1.00000 q^{41} +0.629518 q^{43} +0.177275 q^{44} +1.42758 q^{45} -6.91394 q^{46} +11.3556 q^{47} +1.96764 q^{48} +2.31728 q^{50} -11.8409 q^{51} -5.66555 q^{52} -5.94858 q^{53} +4.18793 q^{54} +0.290359 q^{55} -10.9115 q^{57} -6.25278 q^{58} -4.39184 q^{59} +3.22280 q^{60} -4.01461 q^{61} -2.73897 q^{62} +1.00000 q^{64} -9.27962 q^{65} -0.348812 q^{66} -0.178449 q^{67} -6.01783 q^{68} +13.6041 q^{69} +10.7556 q^{71} -0.871591 q^{72} -10.0193 q^{73} +11.1237 q^{74} -4.55956 q^{75} -5.54550 q^{76} +11.1477 q^{78} -15.2553 q^{79} +1.63790 q^{80} -10.8551 q^{81} +1.00000 q^{82} -13.4114 q^{83} -9.85662 q^{85} -0.629518 q^{86} +12.3032 q^{87} -0.177275 q^{88} -11.9326 q^{89} -1.42758 q^{90} +6.91394 q^{92} +5.38930 q^{93} -11.3556 q^{94} -9.08298 q^{95} -1.96764 q^{96} +16.4196 q^{97} +0.154511 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{2} - 4 q^{3} + 10 q^{4} - 4 q^{5} + 4 q^{6} - 10 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q - 10 * q^2 - 4 * q^3 + 10 * q^4 - 4 * q^5 + 4 * q^6 - 10 * q^8 + 10 * q^9	$ 10 q - 10 q^{2} - 4 q^{3} + 10 q^{4} - 4 q^{5} + 4 q^{6} - 10 q^{8} + 10 q^{9} + 4 q^{10} + 4 q^{11} - 4 q^{12} - 4 q^{13} + 4 q^{15} + 10 q^{16} - 20 q^{17} - 10 q^{18} - 4 q^{20} - 4 q^{22} + 4 q^{23} + 4 q^{24} + 6 q^{25} + 4 q^{26} - 16 q^{27} - 4 q^{29} - 4 q^{30} + 4 q^{31} - 10 q^{32} - 36 q^{33} + 20 q^{34} + 10 q^{36} - 16 q^{37} + 20 q^{39} + 4 q^{40} - 10 q^{41} - 8 q^{43} + 4 q^{44} - 4 q^{45} - 4 q^{46} - 24 q^{47} - 4 q^{48} - 6 q^{50} + 20 q^{51} - 4 q^{52} - 4 q^{53} + 16 q^{54} - 20 q^{55} - 4 q^{57} + 4 q^{58} + 4 q^{60} - 4 q^{62} + 10 q^{64} - 12 q^{65} + 36 q^{66} + 8 q^{67} - 20 q^{68} + 4 q^{71} - 10 q^{72} + 24 q^{73} + 16 q^{74} - 48 q^{75} - 20 q^{78} + 24 q^{79} - 4 q^{80} - 18 q^{81} + 10 q^{82} - 48 q^{83} + 8 q^{85} + 8 q^{86} - 4 q^{87} - 4 q^{88} - 20 q^{89} + 4 q^{90} + 4 q^{92} + 4 q^{93} + 24 q^{94} - 4 q^{95} + 4 q^{96} - 4 q^{97} + 32 q^{99}+O(q^{100}) $ 10 * q - 10 * q^2 - 4 * q^3 + 10 * q^4 - 4 * q^5 + 4 * q^6 - 10 * q^8 + 10 * q^9 + 4 * q^10 + 4 * q^11 - 4 * q^12 - 4 * q^13 + 4 * q^15 + 10 * q^16 - 20 * q^17 - 10 * q^18 - 4 * q^20 - 4 * q^22 + 4 * q^23 + 4 * q^24 + 6 * q^25 + 4 * q^26 - 16 * q^27 - 4 * q^29 - 4 * q^30 + 4 * q^31 - 10 * q^32 - 36 * q^33 + 20 * q^34 + 10 * q^36 - 16 * q^37 + 20 * q^39 + 4 * q^40 - 10 * q^41 - 8 * q^43 + 4 * q^44 - 4 * q^45 - 4 * q^46 - 24 * q^47 - 4 * q^48 - 6 * q^50 + 20 * q^51 - 4 * q^52 - 4 * q^53 + 16 * q^54 - 20 * q^55 - 4 * q^57 + 4 * q^58 + 4 * q^60 - 4 * q^62 + 10 * q^64 - 12 * q^65 + 36 * q^66 + 8 * q^67 - 20 * q^68 + 4 * q^71 - 10 * q^72 + 24 * q^73 + 16 * q^74 - 48 * q^75 - 20 * q^78 + 24 * q^79 - 4 * q^80 - 18 * q^81 + 10 * q^82 - 48 * q^83 + 8 * q^85 + 8 * q^86 - 4 * q^87 - 4 * q^88 - 20 * q^89 + 4 * q^90 + 4 * q^92 + 4 * q^93 + 24 * q^94 - 4 * q^95 + 4 * q^96 - 4 * q^97 + 32 * 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
$3$	1.96764	1.13602	0.568008	−	0.823023i	$-0.307714\pi$
$3$	1.96764	1.13602	0.568008	+	0.823023i	$0.307714\pi$
$4$	1.00000	0.500000
$5$	1.63790	0.732492	0.366246	−	0.930518i	$-0.380643\pi$
$5$	1.63790	0.732492	0.366246	+	0.930518i	$0.380643\pi$
$6$	−1.96764	−0.803284
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	0.871591	0.290530
$10$	−1.63790	−0.517950
$11$	0.177275	0.0534503	0.0267252	−	0.999643i	$-0.491492\pi$
$11$	0.177275	0.0534503	0.0267252	+	0.999643i	$0.491492\pi$
$12$	1.96764	0.568008
$13$	−5.66555	−1.57134	−0.785671	−	0.618645i	$-0.787682\pi$
$13$	−5.66555	−1.57134	−0.785671	+	0.618645i	$0.787682\pi$
$14$	0	0
$15$	3.22280	0.832122
$16$	1.00000	0.250000
$17$	−6.01783	−1.45954	−0.729770	−	0.683693i	$-0.760373\pi$
$17$	−6.01783	−1.45954	−0.729770	+	0.683693i	$0.760373\pi$
$18$	−0.871591	−0.205436
$19$	−5.54550	−1.27222	−0.636112	−	0.771597i	$-0.719458\pi$
$19$	−5.54550	−1.27222	−0.636112	+	0.771597i	$0.719458\pi$
$20$	1.63790	0.366246
$21$	0	0
$22$	−0.177275	−0.0377951
$23$	6.91394	1.44166	0.720828	−	0.693114i	$-0.243762\pi$
$23$	6.91394	1.44166	0.720828	+	0.693114i	$0.243762\pi$
$24$	−1.96764	−0.401642
$25$	−2.31728	−0.463455
$26$	5.66555	1.11111
$27$	−4.18793	−0.805968
$28$	0	0
$29$	6.25278	1.16111	0.580556	−	0.814220i	$-0.302835\pi$
$29$	6.25278	1.16111	0.580556	+	0.814220i	$0.302835\pi$
$30$	−3.22280	−0.588399
$31$	2.73897	0.491934	0.245967	−	0.969278i	$-0.420895\pi$
$31$	2.73897	0.491934	0.245967	+	0.969278i	$0.420895\pi$
$32$	−1.00000	−0.176777
$33$	0.348812	0.0607204
$34$	6.01783	1.03205
$35$	0	0
$36$	0.871591	0.145265
$37$	−11.1237	−1.82873	−0.914363	−	0.404895i	$-0.867308\pi$
$37$	−11.1237	−1.82873	−0.914363	+	0.404895i	$0.867308\pi$
$38$	5.54550	0.899598
$39$	−11.1477	−1.78507
$40$	−1.63790	−0.258975
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	0.629518	0.0960006	0.0480003	−	0.998847i	$-0.484715\pi$
$43$	0.629518	0.0960006	0.0480003	+	0.998847i	$0.484715\pi$
$44$	0.177275	0.0267252
$45$	1.42758	0.212811
$46$	−6.91394	−1.01940
$47$	11.3556	1.65638	0.828189	−	0.560449i	$-0.189371\pi$
$47$	11.3556	1.65638	0.828189	+	0.560449i	$0.189371\pi$
$48$	1.96764	0.284004
$49$	0	0
$50$	2.31728	0.327712
$51$	−11.8409	−1.65806
$52$	−5.66555	−0.785671
$53$	−5.94858	−0.817100	−0.408550	−	0.912736i	$-0.633966\pi$
$53$	−5.94858	−0.817100	−0.408550	+	0.912736i	$0.633966\pi$
$54$	4.18793	0.569906
$55$	0.290359	0.0391519
$56$	0	0
$57$	−10.9115	−1.44527
$58$	−6.25278	−0.821031
$59$	−4.39184	−0.571768	−0.285884	−	0.958264i	$-0.592287\pi$
$59$	−4.39184	−0.571768	−0.285884	+	0.958264i	$0.592287\pi$
$60$	3.22280	0.416061
$61$	−4.01461	−0.514018	−0.257009	−	0.966409i	$-0.582737\pi$
$61$	−4.01461	−0.514018	−0.257009	+	0.966409i	$0.582737\pi$
$62$	−2.73897	−0.347850
$63$	0	0
$64$	1.00000	0.125000
$65$	−9.27962	−1.15100
$66$	−0.348812	−0.0429358
$67$	−0.178449	−0.0218010	−0.0109005	−	0.999941i	$-0.503470\pi$
$67$	−0.178449	−0.0218010	−0.0109005	+	0.999941i	$0.503470\pi$
$68$	−6.01783	−0.729770
$69$	13.6041	1.63774
$70$	0	0
$71$	10.7556	1.27646	0.638228	−	0.769847i	$-0.279668\pi$
$71$	10.7556	1.27646	0.638228	+	0.769847i	$0.279668\pi$
$72$	−0.871591	−0.102718
$73$	−10.0193	−1.17267	−0.586336	−	0.810068i	$-0.699430\pi$
$73$	−10.0193	−1.17267	−0.586336	+	0.810068i	$0.699430\pi$
$74$	11.1237	1.29310
$75$	−4.55956	−0.526492
$76$	−5.54550	−0.636112
$77$	0	0
$78$	11.1477	1.26223
$79$	−15.2553	−1.71635	−0.858176	−	0.513356i	$-0.828402\pi$
$79$	−15.2553	−1.71635	−0.858176	+	0.513356i	$0.828402\pi$
$80$	1.63790	0.183123
$81$	−10.8551	−1.20612
$82$	1.00000	0.110432
$83$	−13.4114	−1.47209	−0.736047	−	0.676931i	$-0.763310\pi$
$83$	−13.4114	−1.47209	−0.736047	+	0.676931i	$0.763310\pi$
$84$	0	0
$85$	−9.85662	−1.06910
$86$	−0.629518	−0.0678827
$87$	12.3032	1.31904
$88$	−0.177275	−0.0188975
$89$	−11.9326	−1.26485	−0.632427	−	0.774620i	$-0.717941\pi$
$89$	−11.9326	−1.26485	−0.632427	+	0.774620i	$0.717941\pi$
$90$	−1.42758	−0.150480
$91$	0	0
$92$	6.91394	0.720828
$93$	5.38930	0.558844
$94$	−11.3556	−1.17124
$95$	−9.08298	−0.931894
$96$	−1.96764	−0.200821
$97$	16.4196	1.66716	0.833580	−	0.552398i	$-0.186287\pi$
$97$	16.4196	1.66716	0.833580	+	0.552398i	$0.186287\pi$
$98$	0	0
$99$	0.154511	0.0155289
$100$	−2.31728	−0.231728
$101$	−3.50222	−0.348484	−0.174242	−	0.984703i	$-0.555747\pi$
$101$	−3.50222	−0.348484	−0.174242	+	0.984703i	$0.555747\pi$
$102$	11.8409	1.17242
$103$	−8.33782	−0.821550	−0.410775	−	0.911737i	$-0.634742\pi$
$103$	−8.33782	−0.821550	−0.410775	+	0.911737i	$0.634742\pi$
$104$	5.66555	0.555553
$105$	0	0
$106$	5.94858	0.577777
$107$	3.76438	0.363916	0.181958	−	0.983306i	$-0.441757\pi$
$107$	3.76438	0.363916	0.181958	+	0.983306i	$0.441757\pi$
$108$	−4.18793	−0.402984
$109$	13.1640	1.26088	0.630440	−	0.776238i	$-0.282874\pi$
$109$	13.1640	1.26088	0.630440	+	0.776238i	$0.282874\pi$
$110$	−0.290359	−0.0276846
$111$	−21.8874	−2.07746
$112$	0	0
$113$	−8.87708	−0.835086	−0.417543	−	0.908657i	$-0.637109\pi$
$113$	−8.87708	−0.835086	−0.417543	+	0.908657i	$0.637109\pi$
$114$	10.9115	1.02196
$115$	11.3244	1.05600
$116$	6.25278	0.580556
$117$	−4.93804	−0.456522
$118$	4.39184	0.404301
$119$	0	0
$120$	−3.22280	−0.294200
$121$	−10.9686	−0.997143
$122$	4.01461	0.363466
$123$	−1.96764	−0.177416
$124$	2.73897	0.245967
$125$	−11.9850	−1.07197
$126$	0	0
$127$	10.3589	0.919202	0.459601	−	0.888125i	$-0.347992\pi$
$127$	10.3589	0.919202	0.459601	+	0.888125i	$0.347992\pi$
$128$	−1.00000	−0.0883883
$129$	1.23866	0.109058
$130$	9.27962	0.813877
$131$	8.20512	0.716884	0.358442	−	0.933552i	$-0.383308\pi$
$131$	8.20512	0.716884	0.358442	+	0.933552i	$0.383308\pi$
$132$	0.348812	0.0303602
$133$	0	0
$134$	0.178449	0.0154156
$135$	−6.85943	−0.590366
$136$	6.01783	0.516025
$137$	−8.55185	−0.730634	−0.365317	−	0.930883i	$-0.619039\pi$
$137$	−8.55185	−0.730634	−0.365317	+	0.930883i	$0.619039\pi$
$138$	−13.6041	−1.15806
$139$	13.8387	1.17378	0.586890	−	0.809667i	$-0.300352\pi$
$139$	13.8387	1.17378	0.586890	+	0.809667i	$0.300352\pi$
$140$	0	0
$141$	22.3436	1.88167
$142$	−10.7556	−0.902591
$143$	−1.00436	−0.0839887
$144$	0.871591	0.0726326
$145$	10.2414	0.850506
$146$	10.0193	0.829204
$147$	0	0
$148$	−11.1237	−0.914363
$149$	−23.8739	−1.95583	−0.977914	−	0.209010i	$-0.932976\pi$
$149$	−23.8739	−1.95583	−0.977914	+	0.209010i	$0.932976\pi$
$150$	4.55956	0.372286
$151$	10.3706	0.843948	0.421974	−	0.906608i	$-0.361337\pi$
$151$	10.3706	0.843948	0.421974	+	0.906608i	$0.361337\pi$
$152$	5.54550	0.449799
$153$	−5.24509	−0.424040
$154$	0	0
$155$	4.48617	0.360338
$156$	−11.1477	−0.892534
$157$	−3.13165	−0.249933	−0.124967	−	0.992161i	$-0.539882\pi$
$157$	−3.13165	−0.249933	−0.124967	+	0.992161i	$0.539882\pi$
$158$	15.2553	1.21364
$159$	−11.7046	−0.928238
$160$	−1.63790	−0.129488
$161$	0	0
$162$	10.8551	0.852857
$163$	6.23464	0.488335	0.244167	−	0.969733i	$-0.421485\pi$
$163$	6.23464	0.488335	0.244167	+	0.969733i	$0.421485\pi$
$164$	−1.00000	−0.0780869
$165$	0.571320	0.0444772
$166$	13.4114	1.04093
$167$	−22.8968	−1.77180	−0.885902	−	0.463872i	$-0.846460\pi$
$167$	−22.8968	−1.77180	−0.885902	+	0.463872i	$0.846460\pi$
$168$	0	0
$169$	19.0985	1.46912
$170$	9.85662	0.755969
$171$	−4.83340	−0.369619
$172$	0.629518	0.0480003
$173$	−23.1258	−1.75822	−0.879111	−	0.476617i	$-0.841863\pi$
$173$	−23.1258	−1.75822	−0.879111	+	0.476617i	$0.841863\pi$
$174$	−12.3032	−0.932703
$175$	0	0
$176$	0.177275	0.0133626
$177$	−8.64153	−0.649537
$178$	11.9326	0.894387
$179$	−3.06162	−0.228836	−0.114418	−	0.993433i	$-0.536500\pi$
$179$	−3.06162	−0.228836	−0.114418	+	0.993433i	$0.536500\pi$
$180$	1.42758	0.106406
$181$	16.4580	1.22331	0.611655	−	0.791125i	$-0.290504\pi$
$181$	16.4580	1.22331	0.611655	+	0.791125i	$0.290504\pi$
$182$	0	0
$183$	−7.89929	−0.583933
$184$	−6.91394	−0.509702
$185$	−18.2195	−1.33953
$186$	−5.38930	−0.395163
$187$	−1.06681	−0.0780128
$188$	11.3556	0.828189
$189$	0	0
$190$	9.08298	0.658949
$191$	20.1912	1.46099	0.730494	−	0.682919i	$-0.239290\pi$
$191$	20.1912	1.46099	0.730494	+	0.682919i	$0.239290\pi$
$192$	1.96764	0.142002
$193$	−19.2974	−1.38906	−0.694529	−	0.719464i	$-0.744387\pi$
$193$	−19.2974	−1.38906	−0.694529	+	0.719464i	$0.744387\pi$
$194$	−16.4196	−1.17886
$195$	−18.2589	−1.30755
$196$	0	0
$197$	21.2438	1.51356	0.756778	−	0.653672i	$-0.226773\pi$
$197$	21.2438	1.51356	0.756778	+	0.653672i	$0.226773\pi$
$198$	−0.154511	−0.0109806
$199$	6.38436	0.452575	0.226288	−	0.974061i	$-0.427341\pi$
$199$	6.38436	0.452575	0.226288	+	0.974061i	$0.427341\pi$
$200$	2.31728	0.163856
$201$	−0.351122	−0.0247662
$202$	3.50222	0.246415
$203$	0	0
$204$	−11.8409	−0.829029
$205$	−1.63790	−0.114396
$206$	8.33782	0.580923
$207$	6.02612	0.418845
$208$	−5.66555	−0.392835
$209$	−0.983076	−0.0680008
$210$	0	0
$211$	−21.3974	−1.47305	−0.736527	−	0.676408i	$-0.763536\pi$
$211$	−21.3974	−1.47305	−0.736527	+	0.676408i	$0.763536\pi$
$212$	−5.94858	−0.408550
$213$	21.1631	1.45007
$214$	−3.76438	−0.257327
$215$	1.03109	0.0703197
$216$	4.18793	0.284953
$217$	0	0
$218$	−13.1640	−0.891577
$219$	−19.7144	−1.33217
$220$	0.290359	0.0195760
$221$	34.0944	2.29344
$222$	21.8874	1.46899
$223$	−11.2650	−0.754362	−0.377181	−	0.926140i	$-0.623107\pi$
$223$	−11.2650	−0.754362	−0.377181	+	0.926140i	$0.623107\pi$
$224$	0	0
$225$	−2.01972	−0.134648
$226$	8.87708	0.590495
$227$	2.91446	0.193439	0.0967196	−	0.995312i	$-0.469165\pi$
$227$	2.91446	0.193439	0.0967196	+	0.995312i	$0.469165\pi$
$228$	−10.9115	−0.722633
$229$	17.7384	1.17219	0.586094	−	0.810243i	$-0.300665\pi$
$229$	17.7384	1.17219	0.586094	+	0.810243i	$0.300665\pi$
$230$	−11.3244	−0.746706
$231$	0	0
$232$	−6.25278	−0.410515
$233$	7.87787	0.516096	0.258048	−	0.966132i	$-0.416921\pi$
$233$	7.87787	0.516096	0.258048	+	0.966132i	$0.416921\pi$
$234$	4.93804	0.322810
$235$	18.5993	1.21328
$236$	−4.39184	−0.285884
$237$	−30.0168	−1.94980
$238$	0	0
$239$	18.4862	1.19577	0.597885	−	0.801582i	$-0.296008\pi$
$239$	18.4862	1.19577	0.597885	+	0.801582i	$0.296008\pi$
$240$	3.22280	0.208031
$241$	−15.9168	−1.02529	−0.512647	−	0.858600i	$-0.671335\pi$
$241$	−15.9168	−1.02529	−0.512647	+	0.858600i	$0.671335\pi$
$242$	10.9686	0.705087
$243$	−8.79508	−0.564205
$244$	−4.01461	−0.257009
$245$	0	0
$246$	1.96764	0.125452
$247$	31.4183	1.99910
$248$	−2.73897	−0.173925
$249$	−26.3888	−1.67232
$250$	11.9850	0.757997
$251$	5.76205	0.363697	0.181849	−	0.983327i	$-0.441792\pi$
$251$	5.76205	0.363697	0.181849	+	0.983327i	$0.441792\pi$
$252$	0	0
$253$	1.22567	0.0770570
$254$	−10.3589	−0.649974
$255$	−19.3942	−1.21451
$256$	1.00000	0.0625000
$257$	3.00362	0.187361	0.0936803	−	0.995602i	$-0.470137\pi$
$257$	3.00362	0.187361	0.0936803	+	0.995602i	$0.470137\pi$
$258$	−1.23866	−0.0771157
$259$	0	0
$260$	−9.27962	−0.575498
$261$	5.44987	0.337338
$262$	−8.20512	−0.506914
$263$	−4.36208	−0.268978	−0.134489	−	0.990915i	$-0.542939\pi$
$263$	−4.36208	−0.268978	−0.134489	+	0.990915i	$0.542939\pi$
$264$	−0.348812	−0.0214679
$265$	−9.74319	−0.598520
$266$	0	0
$267$	−23.4790	−1.43689
$268$	−0.178449	−0.0109005
$269$	18.7718	1.14453	0.572267	−	0.820067i	$-0.306064\pi$
$269$	18.7718	1.14453	0.572267	+	0.820067i	$0.306064\pi$
$270$	6.85943	0.417451
$271$	−5.71415	−0.347110	−0.173555	−	0.984824i	$-0.555525\pi$
$271$	−5.71415	−0.347110	−0.173555	+	0.984824i	$0.555525\pi$
$272$	−6.01783	−0.364885
$273$	0	0
$274$	8.55185	0.516636
$275$	−0.410794	−0.0247718
$276$	13.6041	0.818871
$277$	8.75478	0.526024	0.263012	−	0.964793i	$-0.415284\pi$
$277$	8.75478	0.526024	0.263012	+	0.964793i	$0.415284\pi$
$278$	−13.8387	−0.829988
$279$	2.38726	0.142922
$280$	0	0
$281$	1.66552	0.0993567	0.0496784	−	0.998765i	$-0.484180\pi$
$281$	1.66552	0.0993567	0.0496784	+	0.998765i	$0.484180\pi$
$282$	−22.3436	−1.33054
$283$	11.3174	0.672747	0.336373	−	0.941729i	$-0.390800\pi$
$283$	11.3174	0.672747	0.336373	+	0.941729i	$0.390800\pi$
$284$	10.7556	0.638228
$285$	−17.8720	−1.05865
$286$	1.00436	0.0593890
$287$	0	0
$288$	−0.871591	−0.0513590
$289$	19.2143	1.13025
$290$	−10.2414	−0.601398
$291$	32.3079	1.89392
$292$	−10.0193	−0.586336
$293$	25.7888	1.50660	0.753299	−	0.657679i	$-0.228462\pi$
$293$	25.7888	1.50660	0.753299	+	0.657679i	$0.228462\pi$
$294$	0	0
$295$	−7.19340	−0.418816
$296$	11.1237	0.646552
$297$	−0.742415	−0.0430793
$298$	23.8739	1.38298
$299$	−39.1713	−2.26533
$300$	−4.55956	−0.263246
$301$	0	0
$302$	−10.3706	−0.596762
$303$	−6.89109	−0.395883
$304$	−5.54550	−0.318056
$305$	−6.57554	−0.376514
$306$	5.24509	0.299842
$307$	15.3267	0.874744	0.437372	−	0.899281i	$-0.355909\pi$
$307$	15.3267	0.874744	0.437372	+	0.899281i	$0.355909\pi$
$308$	0	0
$309$	−16.4058	−0.933293
$310$	−4.48617	−0.254797
$311$	0.331235	0.0187826	0.00939131	−	0.999956i	$-0.497011\pi$
$311$	0.331235	0.0187826	0.00939131	+	0.999956i	$0.497011\pi$
$312$	11.1477	0.631117
$313$	−30.1295	−1.70302	−0.851510	−	0.524339i	$-0.824313\pi$
$313$	−30.1295	−1.70302	−0.851510	+	0.524339i	$0.824313\pi$
$314$	3.13165	0.176730
$315$	0	0
$316$	−15.2553	−0.858176
$317$	10.4528	0.587085	0.293543	−	0.955946i	$-0.405166\pi$
$317$	10.4528	0.587085	0.293543	+	0.955946i	$0.405166\pi$
$318$	11.7046	0.656364
$319$	1.10846	0.0620618
$320$	1.63790	0.0915615
$321$	7.40692	0.413414
$322$	0	0
$323$	33.3719	1.85686
$324$	−10.8551	−0.603061
$325$	13.1287	0.728247
$326$	−6.23464	−0.345305
$327$	25.9019	1.43238
$328$	1.00000	0.0552158
$329$	0	0
$330$	−0.571320	−0.0314501
$331$	11.8302	0.650246	0.325123	−	0.945672i	$-0.394594\pi$
$331$	11.8302	0.650246	0.325123	+	0.945672i	$0.394594\pi$
$332$	−13.4114	−0.736047
$333$	−9.69532	−0.531300
$334$	22.8968	1.25285
$335$	−0.292281	−0.0159690
$336$	0	0
$337$	9.48420	0.516637	0.258319	−	0.966060i	$-0.416832\pi$
$337$	9.48420	0.516637	0.258319	+	0.966060i	$0.416832\pi$
$338$	−19.0985	−1.03882
$339$	−17.4669	−0.948670
$340$	−9.85662	−0.534550
$341$	0.485550	0.0262940
$342$	4.83340	0.261360
$343$	0	0
$344$	−0.629518	−0.0339413
$345$	22.2822	1.19963
$346$	23.1258	1.24325
$347$	11.3079	0.607037	0.303519	−	0.952825i	$-0.401839\pi$
$347$	11.3079	0.607037	0.303519	+	0.952825i	$0.401839\pi$
$348$	12.3032	0.659521
$349$	23.3758	1.25128	0.625640	−	0.780112i	$-0.284838\pi$
$349$	23.3758	1.25128	0.625640	+	0.780112i	$0.284838\pi$
$350$	0	0
$351$	23.7270	1.26645
$352$	−0.177275	−0.00944877
$353$	−12.9156	−0.687427	−0.343713	−	0.939075i	$-0.611685\pi$
$353$	−12.9156	−0.687427	−0.343713	+	0.939075i	$0.611685\pi$
$354$	8.64153	0.459292
$355$	17.6166	0.934995
$356$	−11.9326	−0.632427
$357$	0	0
$358$	3.06162	0.161812
$359$	20.8069	1.09815	0.549074	−	0.835774i	$-0.314981\pi$
$359$	20.8069	1.09815	0.549074	+	0.835774i	$0.314981\pi$
$360$	−1.42758	−0.0752401
$361$	11.7525	0.618553
$362$	−16.4580	−0.865011
$363$	−21.5822	−1.13277
$364$	0	0
$365$	−16.4107	−0.858973
$366$	7.89929	0.412903
$367$	−2.54674	−0.132939	−0.0664694	−	0.997788i	$-0.521173\pi$
$367$	−2.54674	−0.132939	−0.0664694	+	0.997788i	$0.521173\pi$
$368$	6.91394	0.360414
$369$	−0.871591	−0.0453732
$370$	18.2195	0.947189
$371$	0	0
$372$	5.38930	0.279422
$373$	1.80837	0.0936341	0.0468170	−	0.998903i	$-0.485092\pi$
$373$	1.80837	0.0936341	0.0468170	+	0.998903i	$0.485092\pi$
$374$	1.06681	0.0551634
$375$	−23.5821	−1.21777
$376$	−11.3556	−0.585618
$377$	−35.4255	−1.82450
$378$	0	0
$379$	11.5711	0.594367	0.297183	−	0.954820i	$-0.403953\pi$
$379$	11.5711	0.594367	0.297183	+	0.954820i	$0.403953\pi$
$380$	−9.08298	−0.465947
$381$	20.3825	1.04423
$382$	−20.1912	−1.03307
$383$	−25.6567	−1.31100	−0.655498	−	0.755197i	$-0.727541\pi$
$383$	−25.6567	−1.31100	−0.655498	+	0.755197i	$0.727541\pi$
$384$	−1.96764	−0.100410
$385$	0	0
$386$	19.2974	0.982213
$387$	0.548682	0.0278911
$388$	16.4196	0.833580
$389$	−8.66594	−0.439380	−0.219690	−	0.975570i	$-0.570505\pi$
$389$	−8.66594	−0.439380	−0.219690	+	0.975570i	$0.570505\pi$
$390$	18.2589	0.924576
$391$	−41.6069	−2.10415
$392$	0	0
$393$	16.1447	0.814391
$394$	−21.2438	−1.07025
$395$	−24.9866	−1.25721
$396$	0.154511	0.00776447
$397$	8.37199	0.420178	0.210089	−	0.977682i	$-0.432625\pi$
$397$	8.37199	0.420178	0.210089	+	0.977682i	$0.432625\pi$
$398$	−6.38436	−0.320019
$399$	0	0
$400$	−2.31728	−0.115864
$401$	−14.6173	−0.729954	−0.364977	−	0.931017i	$-0.618923\pi$
$401$	−14.6173	−0.729954	−0.364977	+	0.931017i	$0.618923\pi$
$402$	0.351122	0.0175124
$403$	−15.5178	−0.772996
$404$	−3.50222	−0.174242
$405$	−17.7796	−0.883475
$406$	0	0
$407$	−1.97195	−0.0977460
$408$	11.8409	0.586212
$409$	18.0146	0.890767	0.445383	−	0.895340i	$-0.353067\pi$
$409$	18.0146	0.890767	0.445383	+	0.895340i	$0.353067\pi$
$410$	1.63790	0.0808902
$411$	−16.8269	−0.830011
$412$	−8.33782	−0.410775
$413$	0	0
$414$	−6.02612	−0.296168
$415$	−21.9666	−1.07830
$416$	5.66555	0.277777
$417$	27.2294	1.33343
$418$	0.983076	0.0480838
$419$	−4.16997	−0.203717	−0.101858	−	0.994799i	$-0.532479\pi$
$419$	−4.16997	−0.203717	−0.101858	+	0.994799i	$0.532479\pi$
$420$	0	0
$421$	−30.6346	−1.49304	−0.746520	−	0.665363i	$-0.768277\pi$
$421$	−30.6346	−1.49304	−0.746520	+	0.665363i	$0.768277\pi$
$422$	21.3974	1.04161
$423$	9.89740	0.481228
$424$	5.94858	0.288889
$425$	13.9450	0.676431
$426$	−21.1631	−1.02536
$427$	0	0
$428$	3.76438	0.181958
$429$	−1.97621	−0.0954125
$430$	−1.03109	−0.0497235
$431$	−27.0936	−1.30506	−0.652528	−	0.757765i	$-0.726291\pi$
$431$	−27.0936	−1.30506	−0.652528	+	0.757765i	$0.726291\pi$
$432$	−4.18793	−0.201492
$433$	−6.78324	−0.325982	−0.162991	−	0.986628i	$-0.552114\pi$
$433$	−6.78324	−0.325982	−0.162991	+	0.986628i	$0.552114\pi$
$434$	0	0
$435$	20.1514	0.966188
$436$	13.1640	0.630440
$437$	−38.3412	−1.83411
$438$	19.7144	0.941989
$439$	−31.0069	−1.47988	−0.739938	−	0.672675i	$-0.765145\pi$
$439$	−31.0069	−1.47988	−0.739938	+	0.672675i	$0.765145\pi$
$440$	−0.290359	−0.0138423
$441$	0	0
$442$	−34.0944	−1.62170
$443$	−17.3504	−0.824341	−0.412170	−	0.911107i	$-0.635229\pi$
$443$	−17.3504	−0.824341	−0.412170	+	0.911107i	$0.635229\pi$
$444$	−21.8874	−1.03873
$445$	−19.5445	−0.926496
$446$	11.2650	0.533414
$447$	−46.9752	−2.22185
$448$	0	0
$449$	4.98443	0.235230	0.117615	−	0.993059i	$-0.462475\pi$
$449$	4.98443	0.235230	0.117615	+	0.993059i	$0.462475\pi$
$450$	2.01972	0.0952103
$451$	−0.177275	−0.00834754
$452$	−8.87708	−0.417543
$453$	20.4056	0.958738
$454$	−2.91446	−0.136782
$455$	0	0
$456$	10.9115	0.510978
$457$	14.0769	0.658489	0.329245	−	0.944245i	$-0.393206\pi$
$457$	14.0769	0.658489	0.329245	+	0.944245i	$0.393206\pi$
$458$	−17.7384	−0.828862
$459$	25.2023	1.17634
$460$	11.3244	0.528001
$461$	−19.4172	−0.904347	−0.452173	−	0.891930i	$-0.649351\pi$
$461$	−19.4172	−0.904347	−0.452173	+	0.891930i	$0.649351\pi$
$462$	0	0
$463$	1.97910	0.0919766	0.0459883	−	0.998942i	$-0.485356\pi$
$463$	1.97910	0.0919766	0.0459883	+	0.998942i	$0.485356\pi$
$464$	6.25278	0.290278
$465$	8.82715	0.409349
$466$	−7.87787	−0.364935
$467$	1.81488	0.0839827	0.0419914	−	0.999118i	$-0.486630\pi$
$467$	1.81488	0.0839827	0.0419914	+	0.999118i	$0.486630\pi$
$468$	−4.93804	−0.228261
$469$	0	0
$470$	−18.5993	−0.857921
$471$	−6.16196	−0.283928
$472$	4.39184	0.202151
$473$	0.111598	0.00513126
$474$	30.0168	1.37872
$475$	12.8504	0.589619
$476$	0	0
$477$	−5.18473	−0.237392
$478$	−18.4862	−0.845537
$479$	−25.5131	−1.16572	−0.582861	−	0.812572i	$-0.698067\pi$
$479$	−25.5131	−1.16572	−0.582861	+	0.812572i	$0.698067\pi$
$480$	−3.22280	−0.147100
$481$	63.0220	2.87355
$482$	15.9168	0.724992
$483$	0	0
$484$	−10.9686	−0.498572
$485$	26.8937	1.22118
$486$	8.79508	0.398953
$487$	2.48616	0.112659	0.0563293	−	0.998412i	$-0.482060\pi$
$487$	2.48616	0.112659	0.0563293	+	0.998412i	$0.482060\pi$
$488$	4.01461	0.181733
$489$	12.2675	0.554756
$490$	0	0
$491$	−15.5577	−0.702111	−0.351055	−	0.936355i	$-0.614177\pi$
$491$	−15.5577	−0.702111	−0.351055	+	0.936355i	$0.614177\pi$
$492$	−1.96764	−0.0887079
$493$	−37.6282	−1.69469
$494$	−31.4183	−1.41358
$495$	0.253074	0.0113748
$496$	2.73897	0.122983
$497$	0	0
$498$	26.3888	1.18251
$499$	22.9520	1.02747	0.513736	−	0.857948i	$-0.328261\pi$
$499$	22.9520	1.02747	0.513736	+	0.857948i	$0.328261\pi$
$500$	−11.9850	−0.535985
$501$	−45.0525	−2.01280
$502$	−5.76205	−0.257173
$503$	20.4397	0.911359	0.455680	−	0.890144i	$-0.349396\pi$
$503$	20.4397	0.911359	0.455680	+	0.890144i	$0.349396\pi$
$504$	0	0
$505$	−5.73629	−0.255262
$506$	−1.22567	−0.0544875
$507$	37.5789	1.66894
$508$	10.3589	0.459601
$509$	41.4484	1.83717	0.918583	−	0.395228i	$-0.129334\pi$
$509$	41.4484	1.83717	0.918583	+	0.395228i	$0.129334\pi$
$510$	19.3942	0.858792
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	23.2242	1.02537
$514$	−3.00362	−0.132484
$515$	−13.6565	−0.601779
$516$	1.23866	0.0545291
$517$	2.01305	0.0885339
$518$	0	0
$519$	−45.5032	−1.99737
$520$	9.27962	0.406938
$521$	−33.0173	−1.44652	−0.723258	−	0.690578i	$-0.757356\pi$
$521$	−33.0173	−1.44652	−0.723258	+	0.690578i	$0.757356\pi$
$522$	−5.44987	−0.238534
$523$	−33.9483	−1.48445	−0.742227	−	0.670148i	$-0.766231\pi$
$523$	−33.9483	−1.48445	−0.742227	+	0.670148i	$0.766231\pi$
$524$	8.20512	0.358442
$525$	0	0
$526$	4.36208	0.190196
$527$	−16.4827	−0.717997
$528$	0.348812	0.0151801
$529$	24.8025	1.07837
$530$	9.74319	0.423217
$531$	−3.82788	−0.166116
$532$	0	0
$533$	5.66555	0.245402
$534$	23.4790	1.01604
$535$	6.16568	0.266566
$536$	0.178449	0.00770780
$537$	−6.02416	−0.259962
$538$	−18.7718	−0.809308
$539$	0	0
$540$	−6.85943	−0.295183
$541$	−7.95936	−0.342200	−0.171100	−	0.985254i	$-0.554732\pi$
$541$	−7.95936	−0.342200	−0.171100	+	0.985254i	$0.554732\pi$
$542$	5.71415	0.245444
$543$	32.3833	1.38970
$544$	6.01783	0.258012
$545$	21.5613	0.923585
$546$	0	0
$547$	39.8890	1.70553	0.852766	−	0.522293i	$-0.174923\pi$
$547$	39.8890	1.70553	0.852766	+	0.522293i	$0.174923\pi$
$548$	−8.55185	−0.365317
$549$	−3.49910	−0.149338
$550$	0.410794	0.0175163
$551$	−34.6748	−1.47720
$552$	−13.6041	−0.579030
$553$	0	0
$554$	−8.75478	−0.371955
$555$	−35.8494	−1.52172
$556$	13.8387	0.586890
$557$	−20.2013	−0.855955	−0.427978	−	0.903789i	$-0.640774\pi$
$557$	−20.2013	−0.855955	−0.427978	+	0.903789i	$0.640774\pi$
$558$	−2.38726	−0.101061
$559$	−3.56657	−0.150850
$560$	0	0
$561$	−2.09909	−0.0886237
$562$	−1.66552	−0.0702558
$563$	−23.6160	−0.995296	−0.497648	−	0.867379i	$-0.665803\pi$
$563$	−23.6160	−0.995296	−0.497648	+	0.867379i	$0.665803\pi$
$564$	22.3436	0.940835
$565$	−14.5398	−0.611694
$566$	−11.3174	−0.475704
$567$	0	0
$568$	−10.7556	−0.451296
$569$	20.9943	0.880128	0.440064	−	0.897966i	$-0.354956\pi$
$569$	20.9943	0.880128	0.440064	+	0.897966i	$0.354956\pi$
$570$	17.8720	0.748576
$571$	−39.0075	−1.63241	−0.816206	−	0.577761i	$-0.803927\pi$
$571$	−39.0075	−1.63241	−0.816206	+	0.577761i	$0.803927\pi$
$572$	−1.00436	−0.0419944
$573$	39.7290	1.65970
$574$	0	0
$575$	−16.0215	−0.668143
$576$	0.871591	0.0363163
$577$	−29.6407	−1.23396	−0.616980	−	0.786979i	$-0.711644\pi$
$577$	−29.6407	−1.23396	−0.616980	+	0.786979i	$0.711644\pi$
$578$	−19.2143	−0.799210
$579$	−37.9703	−1.57799
$580$	10.2414	0.425253
$581$	0	0
$582$	−32.3079	−1.33920
$583$	−1.05453	−0.0436743
$584$	10.0193	0.414602
$585$	−8.08803	−0.334399
$586$	−25.7888	−1.06533
$587$	45.8635	1.89299	0.946494	−	0.322722i	$-0.104598\pi$
$587$	45.8635	1.89299	0.946494	+	0.322722i	$0.104598\pi$
$588$	0	0
$589$	−15.1890	−0.625850
$590$	7.19340	0.296148
$591$	41.8000	1.71942
$592$	−11.1237	−0.457182
$593$	7.16697	0.294312	0.147156	−	0.989113i	$-0.452988\pi$
$593$	7.16697	0.294312	0.147156	+	0.989113i	$0.452988\pi$
$594$	0.742415	0.0304616
$595$	0	0
$596$	−23.8739	−0.977914
$597$	12.5621	0.514132
$598$	39.1713	1.60183
$599$	−6.80357	−0.277986	−0.138993	−	0.990293i	$-0.544387\pi$
$599$	−6.80357	−0.277986	−0.138993	+	0.990293i	$0.544387\pi$
$600$	4.55956	0.186143
$601$	44.5788	1.81841	0.909205	−	0.416350i	$-0.136691\pi$
$601$	44.5788	1.81841	0.909205	+	0.416350i	$0.136691\pi$
$602$	0	0
$603$	−0.155534	−0.00633384
$604$	10.3706	0.421974
$605$	−17.9655	−0.730400
$606$	6.89109	0.279931
$607$	−10.1672	−0.412674	−0.206337	−	0.978481i	$-0.566154\pi$
$607$	−10.1672	−0.412674	−0.206337	+	0.978481i	$0.566154\pi$
$608$	5.54550	0.224900
$609$	0	0
$610$	6.57554	0.266236
$611$	−64.3355	−2.60274
$612$	−5.24509	−0.212020
$613$	7.26147	0.293288	0.146644	−	0.989189i	$-0.453153\pi$
$613$	7.26147	0.293288	0.146644	+	0.989189i	$0.453153\pi$
$614$	−15.3267	−0.618537
$615$	−3.22280	−0.129956
$616$	0	0
$617$	−9.99114	−0.402228	−0.201114	−	0.979568i	$-0.564456\pi$
$617$	−9.99114	−0.402228	−0.201114	+	0.979568i	$0.564456\pi$
$618$	16.4058	0.659938
$619$	−12.9193	−0.519270	−0.259635	−	0.965707i	$-0.583602\pi$
$619$	−12.9193	−0.519270	−0.259635	+	0.965707i	$0.583602\pi$
$620$	4.48617	0.180169
$621$	−28.9551	−1.16193
$622$	−0.331235	−0.0132813
$623$	0	0
$624$	−11.1477	−0.446267
$625$	−8.04385	−0.321754
$626$	30.1295	1.20422
$627$	−1.93433	−0.0772499
$628$	−3.13165	−0.124967
$629$	66.9406	2.66910
$630$	0	0
$631$	−17.1186	−0.681483	−0.340741	−	0.940157i	$-0.610678\pi$
$631$	−17.1186	−0.681483	−0.340741	+	0.940157i	$0.610678\pi$
$632$	15.2553	0.606822
$633$	−42.1022	−1.67341
$634$	−10.4528	−0.415132
$635$	16.9668	0.673308
$636$	−11.7046	−0.464119
$637$	0	0
$638$	−1.10846	−0.0438843
$639$	9.37449	0.370849
$640$	−1.63790	−0.0647438
$641$	9.87731	0.390130	0.195065	−	0.980790i	$-0.437508\pi$
$641$	9.87731	0.390130	0.195065	+	0.980790i	$0.437508\pi$
$642$	−7.40692	−0.292328
$643$	16.0916	0.634591	0.317296	−	0.948327i	$-0.397225\pi$
$643$	16.0916	0.634591	0.317296	+	0.948327i	$0.397225\pi$
$644$	0	0
$645$	2.02881	0.0798842
$646$	−33.3719	−1.31300
$647$	−21.5016	−0.845315	−0.422657	−	0.906290i	$-0.638903\pi$
$647$	−21.5016	−0.845315	−0.422657	+	0.906290i	$0.638903\pi$
$648$	10.8551	0.426429
$649$	−0.778561	−0.0305612
$650$	−13.1287	−0.514948
$651$	0	0
$652$	6.23464	0.244167
$653$	4.01033	0.156936	0.0784681	−	0.996917i	$-0.474997\pi$
$653$	4.01033	0.156936	0.0784681	+	0.996917i	$0.474997\pi$
$654$	−25.9019	−1.01284
$655$	13.4392	0.525112
$656$	−1.00000	−0.0390434
$657$	−8.73274	−0.340697
$658$	0	0
$659$	7.54395	0.293871	0.146935	−	0.989146i	$-0.453059\pi$
$659$	7.54395	0.293871	0.146935	+	0.989146i	$0.453059\pi$
$660$	0.571320	0.0222386
$661$	−49.9000	−1.94088	−0.970442	−	0.241335i	$-0.922415\pi$
$661$	−49.9000	−1.94088	−0.970442	+	0.241335i	$0.922415\pi$
$662$	−11.8302	−0.459794
$663$	67.0853	2.60538
$664$	13.4114	0.520464
$665$	0	0
$666$	9.69532	0.375686
$667$	43.2314	1.67392
$668$	−22.8968	−0.885902
$669$	−22.1655	−0.856967
$670$	0.292281	0.0112918
$671$	−0.711689	−0.0274744
$672$	0	0
$673$	−7.51344	−0.289622	−0.144811	−	0.989459i	$-0.546257\pi$
$673$	−7.51344	−0.289622	−0.144811	+	0.989459i	$0.546257\pi$
$674$	−9.48420	−0.365318
$675$	9.70460	0.373530
$676$	19.0985	0.734558
$677$	−29.1170	−1.11906	−0.559528	−	0.828812i	$-0.689017\pi$
$677$	−29.1170	−1.11906	−0.559528	+	0.828812i	$0.689017\pi$
$678$	17.4669	0.670811
$679$	0	0
$680$	9.85662	0.377984
$681$	5.73459	0.219750
$682$	−0.485550	−0.0185927
$683$	29.2285	1.11840	0.559199	−	0.829034i	$-0.311109\pi$
$683$	29.2285	1.11840	0.559199	+	0.829034i	$0.311109\pi$
$684$	−4.83340	−0.184810
$685$	−14.0071	−0.535184
$686$	0	0
$687$	34.9028	1.33162
$688$	0.629518	0.0240001
$689$	33.7020	1.28394
$690$	−22.2822	−0.848269
$691$	10.0748	0.383264	0.191632	−	0.981467i	$-0.438622\pi$
$691$	10.0748	0.383264	0.191632	+	0.981467i	$0.438622\pi$
$692$	−23.1258	−0.879111
$693$	0	0
$694$	−11.3079	−0.429240
$695$	22.6664	0.859784
$696$	−12.3032	−0.466352
$697$	6.01783	0.227942
$698$	−23.3758	−0.884789
$699$	15.5008	0.586293
$700$	0	0
$701$	−9.77989	−0.369381	−0.184691	−	0.982797i	$-0.559128\pi$
$701$	−9.77989	−0.369381	−0.184691	+	0.982797i	$0.559128\pi$
$702$	−23.7270	−0.895517
$703$	61.6865	2.32655
$704$	0.177275	0.00668129
$705$	36.5966	1.37831
$706$	12.9156	0.486084
$707$	0	0
$708$	−8.64153	−0.324769
$709$	44.2489	1.66180	0.830901	−	0.556421i	$-0.187826\pi$
$709$	44.2489	1.66180	0.830901	+	0.556421i	$0.187826\pi$
$710$	−17.6166	−0.661141
$711$	−13.2963	−0.498652
$712$	11.9326	0.447194
$713$	18.9371	0.709199
$714$	0	0
$715$	−1.64504	−0.0615211
$716$	−3.06162	−0.114418
$717$	36.3740	1.35841
$718$	−20.8069	−0.776508
$719$	−13.5586	−0.505650	−0.252825	−	0.967512i	$-0.581360\pi$
$719$	−13.5586	−0.505650	−0.252825	+	0.967512i	$0.581360\pi$
$720$	1.42758	0.0532028
$721$	0	0
$722$	−11.7525	−0.437383
$723$	−31.3185	−1.16475
$724$	16.4580	0.611655
$725$	−14.4894	−0.538124
$726$	21.5822	0.800989
$727$	13.9968	0.519111	0.259555	−	0.965728i	$-0.416424\pi$
$727$	13.9968	0.519111	0.259555	+	0.965728i	$0.416424\pi$
$728$	0	0
$729$	15.2598	0.565177
$730$	16.4107	0.607386
$731$	−3.78833	−0.140117
$732$	−7.89929	−0.291966
$733$	−23.4260	−0.865259	−0.432629	−	0.901572i	$-0.642414\pi$
$733$	−23.4260	−0.865259	−0.432629	+	0.901572i	$0.642414\pi$
$734$	2.54674	0.0940019
$735$	0	0
$736$	−6.91394	−0.254851
$737$	−0.0316344	−0.00116527
$738$	0.871591	0.0320837
$739$	16.3710	0.602217	0.301109	−	0.953590i	$-0.402643\pi$
$739$	16.3710	0.602217	0.301109	+	0.953590i	$0.402643\pi$
$740$	−18.2195	−0.669764
$741$	61.8198	2.27101
$742$	0	0
$743$	−29.3717	−1.07754	−0.538772	−	0.842452i	$-0.681111\pi$
$743$	−29.3717	−1.07754	−0.538772	+	0.842452i	$0.681111\pi$
$744$	−5.38930	−0.197581
$745$	−39.1031	−1.43263
$746$	−1.80837	−0.0662093
$747$	−11.6893	−0.427688
$748$	−1.06681	−0.0390064
$749$	0	0
$750$	23.5821	0.861096
$751$	22.1157	0.807012	0.403506	−	0.914977i	$-0.367791\pi$
$751$	22.1157	0.807012	0.403506	+	0.914977i	$0.367791\pi$
$752$	11.3556	0.414094
$753$	11.3376	0.413165
$754$	35.4255	1.29012
$755$	16.9860	0.618186
$756$	0	0
$757$	−0.120559	−0.00438179	−0.00219089	−	0.999998i	$-0.500697\pi$
$757$	−0.120559	−0.00438179	−0.00219089	+	0.999998i	$0.500697\pi$
$758$	−11.5711	−0.420281
$759$	2.41166	0.0875379
$760$	9.08298	0.329474
$761$	21.2463	0.770177	0.385088	−	0.922880i	$-0.374171\pi$
$761$	21.2463	0.770177	0.385088	+	0.922880i	$0.374171\pi$
$762$	−20.3825	−0.738380
$763$	0	0
$764$	20.1912	0.730494
$765$	−8.59094	−0.310606
$766$	25.6567	0.927014
$767$	24.8822	0.898444
$768$	1.96764	0.0710009
$769$	−3.27848	−0.118225	−0.0591126	−	0.998251i	$-0.518827\pi$
$769$	−3.27848	−0.118225	−0.0591126	+	0.998251i	$0.518827\pi$
$770$	0	0
$771$	5.91003	0.212844
$772$	−19.2974	−0.694529
$773$	2.48173	0.0892616	0.0446308	−	0.999004i	$-0.485789\pi$
$773$	2.48173	0.0892616	0.0446308	+	0.999004i	$0.485789\pi$
$774$	−0.548682	−0.0197220
$775$	−6.34695	−0.227989
$776$	−16.4196	−0.589430
$777$	0	0
$778$	8.66594	0.310689
$779$	5.54550	0.198688
$780$	−18.2589	−0.653774
$781$	1.90670	0.0682270
$782$	41.6069	1.48786
$783$	−26.1862	−0.935820
$784$	0	0
$785$	−5.12934	−0.183074
$786$	−16.1447	−0.575862
$787$	−27.7447	−0.988993	−0.494497	−	0.869180i	$-0.664648\pi$
$787$	−27.7447	−0.988993	−0.494497	+	0.869180i	$0.664648\pi$
$788$	21.2438	0.756778
$789$	−8.58299	−0.305563
$790$	24.9866	0.888984
$791$	0	0
$792$	−0.154511	−0.00549031
$793$	22.7450	0.807699
$794$	−8.37199	−0.297111
$795$	−19.1711	−0.679927
$796$	6.38436	0.226288
$797$	3.86374	0.136861	0.0684304	−	0.997656i	$-0.478201\pi$
$797$	3.86374	0.136861	0.0684304	+	0.997656i	$0.478201\pi$
$798$	0	0
$799$	−68.3358	−2.41755
$800$	2.31728	0.0819281
$801$	−10.4004	−0.367478
$802$	14.6173	0.516155
$803$	−1.77617	−0.0626797
$804$	−0.351122	−0.0123831
$805$	0	0
$806$	15.5178	0.546591
$807$	36.9360	1.30021
$808$	3.50222	0.123208
$809$	−8.09210	−0.284503	−0.142252	−	0.989831i	$-0.545434\pi$
$809$	−8.09210	−0.284503	−0.142252	+	0.989831i	$0.545434\pi$
$810$	17.7796	0.624711
$811$	29.3509	1.03065	0.515325	−	0.856995i	$-0.327671\pi$
$811$	29.3509	1.03065	0.515325	+	0.856995i	$0.327671\pi$
$812$	0	0
$813$	−11.2434	−0.394322
$814$	1.97195	0.0691169
$815$	10.2117	0.357701
$816$	−11.8409	−0.414515
$817$	−3.49099	−0.122134
$818$	−18.0146	−0.629867
$819$	0	0
$820$	−1.63790	−0.0571980
$821$	−34.0010	−1.18664	−0.593322	−	0.804965i	$-0.702184\pi$
$821$	−34.0010	−1.18664	−0.593322	+	0.804965i	$0.702184\pi$
$822$	16.8269	0.586907
$823$	−2.34110	−0.0816058	−0.0408029	−	0.999167i	$-0.512992\pi$
$823$	−2.34110	−0.0816058	−0.0408029	+	0.999167i	$0.512992\pi$
$824$	8.33782	0.290462
$825$	−0.808294	−0.0281412
$826$	0	0
$827$	34.0918	1.18549	0.592744	−	0.805391i	$-0.298045\pi$
$827$	34.0918	1.18549	0.592744	+	0.805391i	$0.298045\pi$
$828$	6.02612	0.209422
$829$	−1.33376	−0.0463235	−0.0231617	−	0.999732i	$-0.507373\pi$
$829$	−1.33376	−0.0463235	−0.0231617	+	0.999732i	$0.507373\pi$
$830$	21.9666	0.762471
$831$	17.2262	0.597571
$832$	−5.66555	−0.196418
$833$	0	0
$834$	−27.2294	−0.942878
$835$	−37.5027	−1.29783
$836$	−0.983076	−0.0340004
$837$	−11.4706	−0.396483
$838$	4.16997	0.144049
$839$	−1.96043	−0.0676815	−0.0338407	−	0.999427i	$-0.510774\pi$
$839$	−1.96043	−0.0676815	−0.0338407	+	0.999427i	$0.510774\pi$
$840$	0	0
$841$	10.0973	0.348182
$842$	30.6346	1.05574
$843$	3.27714	0.112871
$844$	−21.3974	−0.736527
$845$	31.2815	1.07612
$846$	−9.89740	−0.340279
$847$	0	0
$848$	−5.94858	−0.204275
$849$	22.2684	0.764251
$850$	−13.9450	−0.478309
$851$	−76.9086	−2.63639
$852$	21.1631	0.725037
$853$	31.9896	1.09530	0.547651	−	0.836707i	$-0.315522\pi$
$853$	31.9896	1.09530	0.547651	+	0.836707i	$0.315522\pi$
$854$	0	0
$855$	−7.91664	−0.270743
$856$	−3.76438	−0.128664
$857$	−7.39043	−0.252452	−0.126226	−	0.992001i	$-0.540287\pi$
$857$	−7.39043	−0.252452	−0.126226	+	0.992001i	$0.540287\pi$
$858$	1.97621	0.0674668
$859$	−20.3825	−0.695441	−0.347720	−	0.937598i	$-0.613044\pi$
$859$	−20.3825	−0.695441	−0.347720	+	0.937598i	$0.613044\pi$
$860$	1.03109	0.0351598
$861$	0	0
$862$	27.0936	0.922813
$863$	−15.9668	−0.543516	−0.271758	−	0.962366i	$-0.587605\pi$
$863$	−15.9668	−0.543516	−0.271758	+	0.962366i	$0.587605\pi$
$864$	4.18793	0.142476
$865$	−37.8778	−1.28788
$866$	6.78324	0.230504
$867$	37.8068	1.28399
$868$	0	0
$869$	−2.70437	−0.0917395
$870$	−20.1514	−0.683198
$871$	1.01101	0.0342568
$872$	−13.1640	−0.445788
$873$	14.3112	0.484361
$874$	38.3412	1.29691
$875$	0	0
$876$	−19.7144	−0.666087
$877$	−3.76891	−0.127267	−0.0636335	−	0.997973i	$-0.520269\pi$
$877$	−3.76891	−0.127267	−0.0636335	+	0.997973i	$0.520269\pi$
$878$	31.0069	1.04643
$879$	50.7429	1.71152
$880$	0.290359	0.00978799
$881$	−20.4422	−0.688716	−0.344358	−	0.938839i	$-0.611903\pi$
$881$	−20.4422	−0.688716	−0.344358	+	0.938839i	$0.611903\pi$
$882$	0	0
$883$	52.3948	1.76323	0.881614	−	0.471972i	$-0.156458\pi$
$883$	52.3948	1.76323	0.881614	+	0.471972i	$0.156458\pi$
$884$	34.0944	1.14672
$885$	−14.1540	−0.475781
$886$	17.3504	0.582897
$887$	9.42935	0.316607	0.158303	−	0.987391i	$-0.449398\pi$
$887$	9.42935	0.316607	0.158303	+	0.987391i	$0.449398\pi$
$888$	21.8874	0.734493
$889$	0	0
$890$	19.5445	0.655132
$891$	−1.92433	−0.0644676
$892$	−11.2650	−0.377181
$893$	−62.9722	−2.10728
$894$	46.9752	1.57108
$895$	−5.01464	−0.167621
$896$	0	0
$897$	−77.0748	−2.57345
$898$	−4.98443	−0.166332
$899$	17.1262	0.571191
$900$	−2.01972	−0.0673239
$901$	35.7976	1.19259
$902$	0.177275	0.00590260
$903$	0	0
$904$	8.87708	0.295247
$905$	26.9565	0.896065
$906$	−20.4056	−0.677930
$907$	−6.70609	−0.222672	−0.111336	−	0.993783i	$-0.535513\pi$
$907$	−6.70609	−0.222672	−0.111336	+	0.993783i	$0.535513\pi$
$908$	2.91446	0.0967196
$909$	−3.05250	−0.101245
$910$	0	0
$911$	52.8691	1.75163	0.875816	−	0.482644i	$-0.160324\pi$
$911$	52.8691	1.75163	0.875816	+	0.482644i	$0.160324\pi$
$912$	−10.9115	−0.361316
$913$	−2.37750	−0.0786839
$914$	−14.0769	−0.465622
$915$	−12.9383	−0.427726
$916$	17.7384	0.586094
$917$	0	0
$918$	−25.2023	−0.831800
$919$	−32.1374	−1.06012	−0.530058	−	0.847962i	$-0.677830\pi$
$919$	−32.1374	−1.06012	−0.530058	+	0.847962i	$0.677830\pi$
$920$	−11.3244	−0.373353
$921$	30.1575	0.993722
$922$	19.4172	0.639470
$923$	−60.9365	−2.00575
$924$	0	0
$925$	25.7767	0.847533
$926$	−1.97910	−0.0650373
$927$	−7.26716	−0.238685
$928$	−6.25278	−0.205258
$929$	−20.8754	−0.684899	−0.342449	−	0.939536i	$-0.611257\pi$
$929$	−20.8754	−0.684899	−0.342449	+	0.939536i	$0.611257\pi$
$930$	−8.82715	−0.289454
$931$	0	0
$932$	7.87787	0.258048
$933$	0.651750	0.0213373
$934$	−1.81488	−0.0593847
$935$	−1.74733	−0.0571438
$936$	4.93804	0.161405
$937$	4.24881	0.138803	0.0694013	−	0.997589i	$-0.477891\pi$
$937$	4.24881	0.138803	0.0694013	+	0.997589i	$0.477891\pi$
$938$	0	0
$939$	−59.2839	−1.93466
$940$	18.5993	0.606642
$941$	25.5947	0.834363	0.417181	−	0.908823i	$-0.363018\pi$
$941$	25.5947	0.834363	0.417181	+	0.908823i	$0.363018\pi$
$942$	6.16196	0.200767
$943$	−6.91394	−0.225149
$944$	−4.39184	−0.142942
$945$	0	0
$946$	−0.111598	−0.00362835
$947$	52.9567	1.72086	0.860431	−	0.509567i	$-0.170194\pi$
$947$	52.9567	1.72086	0.860431	+	0.509567i	$0.170194\pi$
$948$	−30.0168	−0.974900
$949$	56.7650	1.84267
$950$	−12.8504	−0.416923
$951$	20.5672	0.666938
$952$	0	0
$953$	26.3196	0.852574	0.426287	−	0.904588i	$-0.359821\pi$
$953$	26.3196	0.852574	0.426287	+	0.904588i	$0.359821\pi$
$954$	5.18473	0.167862
$955$	33.0713	1.07016
$956$	18.4862	0.597885
$957$	2.18105	0.0705032
$958$	25.5131	0.824290
$959$	0	0
$960$	3.22280	0.104015
$961$	−23.4980	−0.758001
$962$	−63.0220	−2.03191
$963$	3.28100	0.105729
$964$	−15.9168	−0.512647
$965$	−31.6073	−1.01747
$966$	0	0
$967$	−34.3868	−1.10581	−0.552903	−	0.833246i	$-0.686480\pi$
$967$	−34.3868	−1.10581	−0.552903	+	0.833246i	$0.686480\pi$
$968$	10.9686	0.352543
$969$	65.6637	2.10942
$970$	−26.8937	−0.863506
$971$	4.37886	0.140524	0.0702621	−	0.997529i	$-0.477616\pi$
$971$	4.37886	0.140524	0.0702621	+	0.997529i	$0.477616\pi$
$972$	−8.79508	−0.282102
$973$	0	0
$974$	−2.48616	−0.0796617
$975$	25.8324	0.827299
$976$	−4.01461	−0.128505
$977$	−32.4690	−1.03878	−0.519388	−	0.854539i	$-0.673840\pi$
$977$	−32.4690	−1.03878	−0.519388	+	0.854539i	$0.673840\pi$
$978$	−12.2675	−0.392271
$979$	−2.11535	−0.0676069
$980$	0	0
$981$	11.4736	0.366324
$982$	15.5577	0.496467
$983$	−44.0499	−1.40498	−0.702488	−	0.711696i	$-0.747927\pi$
$983$	−44.0499	−1.40498	−0.702488	+	0.711696i	$0.747927\pi$
$984$	1.96764	0.0627259
$985$	34.7952	1.10867
$986$	37.6282	1.19833
$987$	0	0
$988$	31.4183	0.999549
$989$	4.35245	0.138400
$990$	−0.253074	−0.00804321
$991$	21.5109	0.683315	0.341658	−	0.939824i	$-0.389012\pi$
$991$	21.5109	0.683315	0.341658	+	0.939824i	$0.389012\pi$
$992$	−2.73897	−0.0869624
$993$	23.2775	0.738690
$994$	0	0
$995$	10.4570	0.331508
$996$	−26.3888	−0.836160
$997$	−23.0566	−0.730211	−0.365106	−	0.930966i	$-0.618967\pi$
$997$	−23.0566	−0.730211	−0.365106	+	0.930966i	$0.618967\pi$
$998$	−22.9520	−0.726532
$999$	46.5854	1.47390

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4018.2.a.br.1.8	✓	10
7.6	odd	2		4018.2.a.bs.1.3	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4018.2.a.br.1.8	✓	10	1.1	even	1	trivial
4018.2.a.bs.1.3	yes	10	7.6	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:	\( N \)	\(=\)	\( 4018 = 2 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.96764 q^{3} +1.00000 q^{4} +1.63790 q^{5} -1.96764 q^{6} -1.00000 q^{8} +0.871591 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.96764 q^{3} +1.00000 q^{4} +1.63790 q^{5} -1.96764 q^{6} -1.00000 q^{8} +0.871591 q^{9} -1.63790 q^{10} +0.177275 q^{11} +1.96764 q^{12} -5.66555 q^{13} +3.22280 q^{15} +1.00000 q^{16} -6.01783 q^{17} -0.871591 q^{18} -5.54550 q^{19} +1.63790 q^{20} -0.177275 q^{22} +6.91394 q^{23} -1.96764 q^{24} -2.31728 q^{25} +5.66555 q^{26} -4.18793 q^{27} +6.25278 q^{29} -3.22280 q^{30} +2.73897 q^{31} -1.00000 q^{32} +0.348812 q^{33} +6.01783 q^{34} +0.871591 q^{36} -11.1237 q^{37} +5.54550 q^{38} -11.1477 q^{39} -1.63790 q^{40} -1.00000 q^{41} +0.629518 q^{43} +0.177275 q^{44} +1.42758 q^{45} -6.91394 q^{46} +11.3556 q^{47} +1.96764 q^{48} +2.31728 q^{50} -11.8409 q^{51} -5.66555 q^{52} -5.94858 q^{53} +4.18793 q^{54} +0.290359 q^{55} -10.9115 q^{57} -6.25278 q^{58} -4.39184 q^{59} +3.22280 q^{60} -4.01461 q^{61} -2.73897 q^{62} +1.00000 q^{64} -9.27962 q^{65} -0.348812 q^{66} -0.178449 q^{67} -6.01783 q^{68} +13.6041 q^{69} +10.7556 q^{71} -0.871591 q^{72} -10.0193 q^{73} +11.1237 q^{74} -4.55956 q^{75} -5.54550 q^{76} +11.1477 q^{78} -15.2553 q^{79} +1.63790 q^{80} -10.8551 q^{81} +1.00000 q^{82} -13.4114 q^{83} -9.85662 q^{85} -0.629518 q^{86} +12.3032 q^{87} -0.177275 q^{88} -11.9326 q^{89} -1.42758 q^{90} +6.91394 q^{92} +5.38930 q^{93} -11.3556 q^{94} -9.08298 q^{95} -1.96764 q^{96} +16.4196 q^{97} +0.154511 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} - 4 q^{3} + 10 q^{4} - 4 q^{5} + 4 q^{6} - 10 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q - 10 * q^2 - 4 * q^3 + 10 * q^4 - 4 * q^5 + 4 * q^6 - 10 * q^8 + 10 * q^9	\( 10 q - 10 q^{2} - 4 q^{3} + 10 q^{4} - 4 q^{5} + 4 q^{6} - 10 q^{8} + 10 q^{9} + 4 q^{10} + 4 q^{11} - 4 q^{12} - 4 q^{13} + 4 q^{15} + 10 q^{16} - 20 q^{17} - 10 q^{18} - 4 q^{20} - 4 q^{22} + 4 q^{23} + 4 q^{24} + 6 q^{25} + 4 q^{26} - 16 q^{27} - 4 q^{29} - 4 q^{30} + 4 q^{31} - 10 q^{32} - 36 q^{33} + 20 q^{34} + 10 q^{36} - 16 q^{37} + 20 q^{39} + 4 q^{40} - 10 q^{41} - 8 q^{43} + 4 q^{44} - 4 q^{45} - 4 q^{46} - 24 q^{47} - 4 q^{48} - 6 q^{50} + 20 q^{51} - 4 q^{52} - 4 q^{53} + 16 q^{54} - 20 q^{55} - 4 q^{57} + 4 q^{58} + 4 q^{60} - 4 q^{62} + 10 q^{64} - 12 q^{65} + 36 q^{66} + 8 q^{67} - 20 q^{68} + 4 q^{71} - 10 q^{72} + 24 q^{73} + 16 q^{74} - 48 q^{75} - 20 q^{78} + 24 q^{79} - 4 q^{80} - 18 q^{81} + 10 q^{82} - 48 q^{83} + 8 q^{85} + 8 q^{86} - 4 q^{87} - 4 q^{88} - 20 q^{89} + 4 q^{90} + 4 q^{92} + 4 q^{93} + 24 q^{94} - 4 q^{95} + 4 q^{96} - 4 q^{97} + 32 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 - 4 * q^3 + 10 * q^4 - 4 * q^5 + 4 * q^6 - 10 * q^8 + 10 * q^9 + 4 * q^10 + 4 * q^11 - 4 * q^12 - 4 * q^13 + 4 * q^15 + 10 * q^16 - 20 * q^17 - 10 * q^18 - 4 * q^20 - 4 * q^22 + 4 * q^23 + 4 * q^24 + 6 * q^25 + 4 * q^26 - 16 * q^27 - 4 * q^29 - 4 * q^30 + 4 * q^31 - 10 * q^32 - 36 * q^33 + 20 * q^34 + 10 * q^36 - 16 * q^37 + 20 * q^39 + 4 * q^40 - 10 * q^41 - 8 * q^43 + 4 * q^44 - 4 * q^45 - 4 * q^46 - 24 * q^47 - 4 * q^48 - 6 * q^50 + 20 * q^51 - 4 * q^52 - 4 * q^53 + 16 * q^54 - 20 * q^55 - 4 * q^57 + 4 * q^58 + 4 * q^60 - 4 * q^62 + 10 * q^64 - 12 * q^65 + 36 * q^66 + 8 * q^67 - 20 * q^68 + 4 * q^71 - 10 * q^72 + 24 * q^73 + 16 * q^74 - 48 * q^75 - 20 * q^78 + 24 * q^79 - 4 * q^80 - 18 * q^81 + 10 * q^82 - 48 * q^83 + 8 * q^85 + 8 * q^86 - 4 * q^87 - 4 * q^88 - 20 * q^89 + 4 * q^90 + 4 * q^92 + 4 * q^93 + 24 * q^94 - 4 * q^95 + 4 * q^96 - 4 * q^97 + 32 * q^99

Introduction

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