LMFDB - Embedded newform 4018.2.a.bt.1.3

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:	$0$
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} - x^{9} - 23x^{8} + 19x^{7} + 181x^{6} - 109x^{5} - 579x^{4} + 231x^{3} + 608x^{2} - 204x - 12 $ x^10 - x^9 - 23x^8 + 19x^7 + 181x^6 - 109x^5 - 579x^4 + 231x^3 + 608x^2 - 204x - 12
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 574)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.41684$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -2.41684 q^{3} +1.00000 q^{4} -2.64605 q^{5} -2.41684 q^{6} +1.00000 q^{8} +2.84113 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.41684 q^{3} +1.00000 q^{4} -2.64605 q^{5} -2.41684 q^{6} +1.00000 q^{8} +2.84113 q^{9} -2.64605 q^{10} +5.04427 q^{11} -2.41684 q^{12} +4.59598 q^{13} +6.39509 q^{15} +1.00000 q^{16} -4.48718 q^{17} +2.84113 q^{18} -1.98701 q^{19} -2.64605 q^{20} +5.04427 q^{22} +3.40377 q^{23} -2.41684 q^{24} +2.00158 q^{25} +4.59598 q^{26} +0.383968 q^{27} -5.50369 q^{29} +6.39509 q^{30} -0.322934 q^{31} +1.00000 q^{32} -12.1912 q^{33} -4.48718 q^{34} +2.84113 q^{36} -8.69590 q^{37} -1.98701 q^{38} -11.1078 q^{39} -2.64605 q^{40} -1.00000 q^{41} -8.64711 q^{43} +5.04427 q^{44} -7.51777 q^{45} +3.40377 q^{46} +10.6158 q^{47} -2.41684 q^{48} +2.00158 q^{50} +10.8448 q^{51} +4.59598 q^{52} +2.26081 q^{53} +0.383968 q^{54} -13.3474 q^{55} +4.80230 q^{57} -5.50369 q^{58} +5.74214 q^{59} +6.39509 q^{60} +9.18440 q^{61} -0.322934 q^{62} +1.00000 q^{64} -12.1612 q^{65} -12.1912 q^{66} +2.97394 q^{67} -4.48718 q^{68} -8.22637 q^{69} -10.8685 q^{71} +2.84113 q^{72} -2.17500 q^{73} -8.69590 q^{74} -4.83751 q^{75} -1.98701 q^{76} -11.1078 q^{78} +14.0168 q^{79} -2.64605 q^{80} -9.45137 q^{81} -1.00000 q^{82} -0.927339 q^{83} +11.8733 q^{85} -8.64711 q^{86} +13.3015 q^{87} +5.04427 q^{88} -5.92692 q^{89} -7.51777 q^{90} +3.40377 q^{92} +0.780481 q^{93} +10.6158 q^{94} +5.25774 q^{95} -2.41684 q^{96} +12.6828 q^{97} +14.3314 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 10 q^{2} - q^{3} + 10 q^{4} + 2 q^{5} - q^{6} + 10 q^{8} + 17 q^{9}+O(q^{10}) $ 10 * q + 10 * q^2 - q^3 + 10 * q^4 + 2 * q^5 - q^6 + 10 * q^8 + 17 * q^9	$ 10 q + 10 q^{2} - q^{3} + 10 q^{4} + 2 q^{5} - q^{6} + 10 q^{8} + 17 q^{9} + 2 q^{10} + 11 q^{11} - q^{12} - 4 q^{13} + 4 q^{15} + 10 q^{16} - 5 q^{17} + 17 q^{18} + q^{19} + 2 q^{20} + 11 q^{22} + 9 q^{23} - q^{24} + 24 q^{25} - 4 q^{26} - 7 q^{27} + 23 q^{29} + 4 q^{30} + 5 q^{31} + 10 q^{32} + 5 q^{33} - 5 q^{34} + 17 q^{36} + 16 q^{37} + q^{38} - 7 q^{39} + 2 q^{40} - 10 q^{41} + 20 q^{43} + 11 q^{44} + 42 q^{45} + 9 q^{46} + 16 q^{47} - q^{48} + 24 q^{50} + 13 q^{51} - 4 q^{52} + 26 q^{53} - 7 q^{54} - 7 q^{55} + 37 q^{57} + 23 q^{58} + 10 q^{59} + 4 q^{60} + 5 q^{62} + 10 q^{64} + 18 q^{65} + 5 q^{66} + 7 q^{67} - 5 q^{68} - 39 q^{69} + 5 q^{71} + 17 q^{72} + 13 q^{73} + 16 q^{74} - 19 q^{75} + q^{76} - 7 q^{78} - q^{79} + 2 q^{80} + 18 q^{81} - 10 q^{82} - 21 q^{83} + 34 q^{85} + 20 q^{86} - 2 q^{87} + 11 q^{88} - 6 q^{89} + 42 q^{90} + 9 q^{92} - 5 q^{93} + 16 q^{94} + 24 q^{95} - q^{96} - 29 q^{97} + 48 q^{99}+O(q^{100}) $ 10 * q + 10 * q^2 - q^3 + 10 * q^4 + 2 * q^5 - q^6 + 10 * q^8 + 17 * q^9 + 2 * q^10 + 11 * q^11 - q^12 - 4 * q^13 + 4 * q^15 + 10 * q^16 - 5 * q^17 + 17 * q^18 + q^19 + 2 * q^20 + 11 * q^22 + 9 * q^23 - q^24 + 24 * q^25 - 4 * q^26 - 7 * q^27 + 23 * q^29 + 4 * q^30 + 5 * q^31 + 10 * q^32 + 5 * q^33 - 5 * q^34 + 17 * q^36 + 16 * q^37 + q^38 - 7 * q^39 + 2 * q^40 - 10 * q^41 + 20 * q^43 + 11 * q^44 + 42 * q^45 + 9 * q^46 + 16 * q^47 - q^48 + 24 * q^50 + 13 * q^51 - 4 * q^52 + 26 * q^53 - 7 * q^54 - 7 * q^55 + 37 * q^57 + 23 * q^58 + 10 * q^59 + 4 * q^60 + 5 * q^62 + 10 * q^64 + 18 * q^65 + 5 * q^66 + 7 * q^67 - 5 * q^68 - 39 * q^69 + 5 * q^71 + 17 * q^72 + 13 * q^73 + 16 * q^74 - 19 * q^75 + q^76 - 7 * q^78 - q^79 + 2 * q^80 + 18 * q^81 - 10 * q^82 - 21 * q^83 + 34 * q^85 + 20 * q^86 - 2 * q^87 + 11 * q^88 - 6 * q^89 + 42 * q^90 + 9 * q^92 - 5 * q^93 + 16 * q^94 + 24 * q^95 - q^96 - 29 * q^97 + 48 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.41684	−1.39536	−0.697682	−	0.716407i	$-0.745785\pi$
$3$	−2.41684	−1.39536	−0.697682	+	0.716407i	$0.745785\pi$
$4$	1.00000	0.500000
$5$	−2.64605	−1.18335	−0.591675	−	0.806177i	$-0.701533\pi$
$5$	−2.64605	−1.18335	−0.591675	+	0.806177i	$0.701533\pi$
$6$	−2.41684	−0.986672
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	2.84113	0.947043
$10$	−2.64605	−0.836755
$11$	5.04427	1.52091	0.760453	−	0.649393i	$-0.224977\pi$
$11$	5.04427	1.52091	0.760453	+	0.649393i	$0.224977\pi$
$12$	−2.41684	−0.697682
$13$	4.59598	1.27470	0.637348	−	0.770576i	$-0.280031\pi$
$13$	4.59598	1.27470	0.637348	+	0.770576i	$0.280031\pi$
$14$	0	0
$15$	6.39509	1.65120
$16$	1.00000	0.250000
$17$	−4.48718	−1.08830	−0.544150	−	0.838988i	$-0.683148\pi$
$17$	−4.48718	−1.08830	−0.544150	+	0.838988i	$0.683148\pi$
$18$	2.84113	0.669660
$19$	−1.98701	−0.455852	−0.227926	−	0.973678i	$-0.573194\pi$
$19$	−1.98701	−0.455852	−0.227926	+	0.973678i	$0.573194\pi$
$20$	−2.64605	−0.591675
$21$	0	0
$22$	5.04427	1.07544
$23$	3.40377	0.709734	0.354867	−	0.934917i	$-0.384526\pi$
$23$	3.40377	0.709734	0.354867	+	0.934917i	$0.384526\pi$
$24$	−2.41684	−0.493336
$25$	2.00158	0.400317
$26$	4.59598	0.901346
$27$	0.383968	0.0738946
$28$	0	0
$29$	−5.50369	−1.02201	−0.511004	−	0.859578i	$-0.670726\pi$
$29$	−5.50369	−1.02201	−0.511004	+	0.859578i	$0.670726\pi$
$30$	6.39509	1.16758
$31$	−0.322934	−0.0580007	−0.0290003	−	0.999579i	$-0.509232\pi$
$31$	−0.322934	−0.0580007	−0.0290003	+	0.999579i	$0.509232\pi$
$32$	1.00000	0.176777
$33$	−12.1912	−2.12222
$34$	−4.48718	−0.769545
$35$	0	0
$36$	2.84113	0.473521
$37$	−8.69590	−1.42960	−0.714799	−	0.699330i	$-0.753482\pi$
$37$	−8.69590	−1.42960	−0.714799	+	0.699330i	$0.753482\pi$
$38$	−1.98701	−0.322336
$39$	−11.1078	−1.77867
$40$	−2.64605	−0.418377
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	−8.64711	−1.31867	−0.659336	−	0.751849i	$-0.729162\pi$
$43$	−8.64711	−1.31867	−0.659336	+	0.751849i	$0.729162\pi$
$44$	5.04427	0.760453
$45$	−7.51777	−1.12068
$46$	3.40377	0.501858
$47$	10.6158	1.54848	0.774238	−	0.632895i	$-0.218133\pi$
$47$	10.6158	1.54848	0.774238	+	0.632895i	$0.218133\pi$
$48$	−2.41684	−0.348841
$49$	0	0
$50$	2.00158	0.283067
$51$	10.8448	1.51858
$52$	4.59598	0.637348
$53$	2.26081	0.310546	0.155273	−	0.987872i	$-0.450374\pi$
$53$	2.26081	0.310546	0.155273	+	0.987872i	$0.450374\pi$
$54$	0.383968	0.0522514
$55$	−13.3474	−1.79976
$56$	0	0
$57$	4.80230	0.636080
$58$	−5.50369	−0.722669
$59$	5.74214	0.747562	0.373781	−	0.927517i	$-0.378061\pi$
$59$	5.74214	0.747562	0.373781	+	0.927517i	$0.378061\pi$
$60$	6.39509	0.825602
$61$	9.18440	1.17594	0.587971	−	0.808882i	$-0.299927\pi$
$61$	9.18440	1.17594	0.587971	+	0.808882i	$0.299927\pi$
$62$	−0.322934	−0.0410127
$63$	0	0
$64$	1.00000	0.125000
$65$	−12.1612	−1.50841
$66$	−12.1912	−1.50063
$67$	2.97394	0.363324	0.181662	−	0.983361i	$-0.441852\pi$
$67$	2.97394	0.363324	0.181662	+	0.983361i	$0.441852\pi$
$68$	−4.48718	−0.544150
$69$	−8.22637	−0.990338
$70$	0	0
$71$	−10.8685	−1.28985	−0.644924	−	0.764246i	$-0.723111\pi$
$71$	−10.8685	−1.28985	−0.644924	+	0.764246i	$0.723111\pi$
$72$	2.84113	0.334830
$73$	−2.17500	−0.254564	−0.127282	−	0.991867i	$-0.540625\pi$
$73$	−2.17500	−0.254564	−0.127282	+	0.991867i	$0.540625\pi$
$74$	−8.69590	−1.01088
$75$	−4.83751	−0.558588
$76$	−1.98701	−0.227926
$77$	0	0
$78$	−11.1078	−1.25771
$79$	14.0168	1.57702	0.788509	−	0.615023i	$-0.210853\pi$
$79$	14.0168	1.57702	0.788509	+	0.615023i	$0.210853\pi$
$80$	−2.64605	−0.295837
$81$	−9.45137	−1.05015
$82$	−1.00000	−0.110432
$83$	−0.927339	−0.101789	−0.0508944	−	0.998704i	$-0.516207\pi$
$83$	−0.927339	−0.101789	−0.0508944	+	0.998704i	$0.516207\pi$
$84$	0	0
$85$	11.8733	1.28784
$86$	−8.64711	−0.932441
$87$	13.3015	1.42608
$88$	5.04427	0.537721
$89$	−5.92692	−0.628252	−0.314126	−	0.949381i	$-0.601711\pi$
$89$	−5.92692	−0.628252	−0.314126	+	0.949381i	$0.601711\pi$
$90$	−7.51777	−0.792442
$91$	0	0
$92$	3.40377	0.354867
$93$	0.780481	0.0809321
$94$	10.6158	1.09494
$95$	5.25774	0.539433
$96$	−2.41684	−0.246668
$97$	12.6828	1.28774	0.643871	−	0.765134i	$-0.277327\pi$
$97$	12.6828	1.28774	0.643871	+	0.765134i	$0.277327\pi$
$98$	0	0
$99$	14.3314	1.44036
$100$	2.00158	0.200158
$101$	9.05154	0.900662	0.450331	−	0.892862i	$-0.351306\pi$
$101$	9.05154	0.900662	0.450331	+	0.892862i	$0.351306\pi$
$102$	10.8448	1.07380
$103$	−12.0375	−1.18609	−0.593047	−	0.805168i	$-0.702075\pi$
$103$	−12.0375	−1.18609	−0.593047	+	0.805168i	$0.702075\pi$
$104$	4.59598	0.450673
$105$	0	0
$106$	2.26081	0.219589
$107$	6.47535	0.625995	0.312998	−	0.949754i	$-0.398667\pi$
$107$	6.47535	0.625995	0.312998	+	0.949754i	$0.398667\pi$
$108$	0.383968	0.0369473
$109$	17.1162	1.63943	0.819716	−	0.572770i	$-0.194131\pi$
$109$	17.1162	1.63943	0.819716	+	0.572770i	$0.194131\pi$
$110$	−13.3474	−1.27262
$111$	21.0166	1.99481
$112$	0	0
$113$	9.15755	0.861470	0.430735	−	0.902479i	$-0.358254\pi$
$113$	9.15755	0.861470	0.430735	+	0.902479i	$0.358254\pi$
$114$	4.80230	0.449777
$115$	−9.00654	−0.839864
$116$	−5.50369	−0.511004
$117$	13.0578	1.20719
$118$	5.74214	0.528607
$119$	0	0
$120$	6.39509	0.583789
$121$	14.4447	1.31315
$122$	9.18440	0.831517
$123$	2.41684	0.217919
$124$	−0.322934	−0.0290003
$125$	7.93396	0.709635
$126$	0	0
$127$	16.4292	1.45785	0.728927	−	0.684591i	$-0.240019\pi$
$127$	16.4292	1.45785	0.728927	+	0.684591i	$0.240019\pi$
$128$	1.00000	0.0883883
$129$	20.8987	1.84003
$130$	−12.1612	−1.06661
$131$	−6.17602	−0.539602	−0.269801	−	0.962916i	$-0.586958\pi$
$131$	−6.17602	−0.539602	−0.269801	+	0.962916i	$0.586958\pi$
$132$	−12.1912	−1.06111
$133$	0	0
$134$	2.97394	0.256909
$135$	−1.01600	−0.0874432
$136$	−4.48718	−0.384772
$137$	18.6232	1.59109	0.795546	−	0.605894i	$-0.207184\pi$
$137$	18.6232	1.59109	0.795546	+	0.605894i	$0.207184\pi$
$138$	−8.22637	−0.700275
$139$	−10.7699	−0.913493	−0.456746	−	0.889597i	$-0.650985\pi$
$139$	−10.7699	−0.913493	−0.456746	+	0.889597i	$0.650985\pi$
$140$	0	0
$141$	−25.6568	−2.16069
$142$	−10.8685	−0.912061
$143$	23.1834	1.93869
$144$	2.84113	0.236761
$145$	14.5630	1.20939
$146$	−2.17500	−0.180004
$147$	0	0
$148$	−8.69590	−0.714799
$149$	−20.5100	−1.68025	−0.840124	−	0.542395i	$-0.817518\pi$
$149$	−20.5100	−1.68025	−0.840124	+	0.542395i	$0.817518\pi$
$150$	−4.83751	−0.394981
$151$	−8.16877	−0.664765	−0.332383	−	0.943145i	$-0.607853\pi$
$151$	−8.16877	−0.664765	−0.332383	+	0.943145i	$0.607853\pi$
$152$	−1.98701	−0.161168
$153$	−12.7487	−1.03067
$154$	0	0
$155$	0.854500	0.0686351
$156$	−11.1078	−0.889333
$157$	8.39021	0.669611	0.334806	−	0.942287i	$-0.391329\pi$
$157$	8.39021	0.669611	0.334806	+	0.942287i	$0.391329\pi$
$158$	14.0168	1.11512
$159$	−5.46403	−0.433326
$160$	−2.64605	−0.209189
$161$	0	0
$162$	−9.45137	−0.742570
$163$	10.7381	0.841074	0.420537	−	0.907275i	$-0.361842\pi$
$163$	10.7381	0.841074	0.420537	+	0.907275i	$0.361842\pi$
$164$	−1.00000	−0.0780869
$165$	32.2586	2.51133
$166$	−0.927339	−0.0719755
$167$	−0.343329	−0.0265676	−0.0132838	−	0.999912i	$-0.504228\pi$
$167$	−0.343329	−0.0265676	−0.0132838	+	0.999912i	$0.504228\pi$
$168$	0	0
$169$	8.12305	0.624850
$170$	11.8733	0.910641
$171$	−5.64536	−0.431712
$172$	−8.64711	−0.659336
$173$	24.8890	1.89228	0.946140	−	0.323759i	$-0.104947\pi$
$173$	24.8890	1.89228	0.946140	+	0.323759i	$0.104947\pi$
$174$	13.3015	1.00839
$175$	0	0
$176$	5.04427	0.380226
$177$	−13.8778	−1.04312
$178$	−5.92692	−0.444241
$179$	9.59343	0.717047	0.358523	−	0.933521i	$-0.383280\pi$
$179$	9.59343	0.717047	0.358523	+	0.933521i	$0.383280\pi$
$180$	−7.51777	−0.560341
$181$	−17.8164	−1.32428	−0.662141	−	0.749379i	$-0.730352\pi$
$181$	−17.8164	−1.32428	−0.662141	+	0.749379i	$0.730352\pi$
$182$	0	0
$183$	−22.1973	−1.64087
$184$	3.40377	0.250929
$185$	23.0098	1.69171
$186$	0.780481	0.0572277
$187$	−22.6346	−1.65520
$188$	10.6158	0.774238
$189$	0	0
$190$	5.25774	0.381437
$191$	4.58649	0.331867	0.165933	−	0.986137i	$-0.446936\pi$
$191$	4.58649	0.331867	0.165933	+	0.986137i	$0.446936\pi$
$192$	−2.41684	−0.174421
$193$	−24.0620	−1.73202	−0.866012	−	0.500023i	$-0.833325\pi$
$193$	−24.0620	−1.73202	−0.866012	+	0.500023i	$0.833325\pi$
$194$	12.6828	0.910572
$195$	29.3917	2.10478
$196$	0	0
$197$	19.8386	1.41344	0.706722	−	0.707492i	$-0.250173\pi$
$197$	19.8386	1.41344	0.706722	+	0.707492i	$0.250173\pi$
$198$	14.3314	1.01849
$199$	0.567519	0.0402303	0.0201152	−	0.999798i	$-0.493597\pi$
$199$	0.567519	0.0402303	0.0201152	+	0.999798i	$0.493597\pi$
$200$	2.00158	0.141533
$201$	−7.18754	−0.506970
$202$	9.05154	0.636864
$203$	0	0
$204$	10.8448	0.759288
$205$	2.64605	0.184808
$206$	−12.0375	−0.838696
$207$	9.67054	0.672149
$208$	4.59598	0.318674
$209$	−10.0230	−0.693309
$210$	0	0
$211$	10.5505	0.726326	0.363163	−	0.931726i	$-0.381697\pi$
$211$	10.5505	0.726326	0.363163	+	0.931726i	$0.381697\pi$
$212$	2.26081	0.155273
$213$	26.2674	1.79981
$214$	6.47535	0.442646
$215$	22.8807	1.56045
$216$	0.383968	0.0261257
$217$	0	0
$218$	17.1162	1.15925
$219$	5.25662	0.355210
$220$	−13.3474	−0.899882
$221$	−20.6230	−1.38725
$222$	21.0166	1.41054
$223$	3.02871	0.202818	0.101409	−	0.994845i	$-0.467665\pi$
$223$	3.02871	0.202818	0.101409	+	0.994845i	$0.467665\pi$
$224$	0	0
$225$	5.68675	0.379117
$226$	9.15755	0.609151
$227$	5.68454	0.377296	0.188648	−	0.982045i	$-0.439589\pi$
$227$	5.68454	0.377296	0.188648	+	0.982045i	$0.439589\pi$
$228$	4.80230	0.318040
$229$	7.22455	0.477412	0.238706	−	0.971092i	$-0.423277\pi$
$229$	7.22455	0.477412	0.238706	+	0.971092i	$0.423277\pi$
$230$	−9.00654	−0.593873
$231$	0	0
$232$	−5.50369	−0.361335
$233$	24.4785	1.60364	0.801818	−	0.597568i	$-0.203866\pi$
$233$	24.4785	1.60364	0.801818	+	0.597568i	$0.203866\pi$
$234$	13.0578	0.853613
$235$	−28.0900	−1.83239
$236$	5.74214	0.373781
$237$	−33.8765	−2.20052
$238$	0	0
$239$	−3.87772	−0.250829	−0.125414	−	0.992104i	$-0.540026\pi$
$239$	−3.87772	−0.250829	−0.125414	+	0.992104i	$0.540026\pi$
$240$	6.39509	0.412801
$241$	28.5369	1.83823	0.919113	−	0.393994i	$-0.128907\pi$
$241$	28.5369	1.83823	0.919113	+	0.393994i	$0.128907\pi$
$242$	14.4447	0.928540
$243$	21.6906	1.39145
$244$	9.18440	0.587971
$245$	0	0
$246$	2.41684	0.154092
$247$	−9.13228	−0.581073
$248$	−0.322934	−0.0205063
$249$	2.24123	0.142032
$250$	7.93396	0.501788
$251$	5.49129	0.346607	0.173303	−	0.984868i	$-0.444556\pi$
$251$	5.49129	0.346607	0.173303	+	0.984868i	$0.444556\pi$
$252$	0	0
$253$	17.1695	1.07944
$254$	16.4292	1.03086
$255$	−28.6959	−1.79701
$256$	1.00000	0.0625000
$257$	8.42680	0.525649	0.262825	−	0.964844i	$-0.415346\pi$
$257$	8.42680	0.525649	0.262825	+	0.964844i	$0.415346\pi$
$258$	20.8987	1.30110
$259$	0	0
$260$	−12.1612	−0.754206
$261$	−15.6367	−0.967886
$262$	−6.17602	−0.381556
$263$	−4.64029	−0.286133	−0.143066	−	0.989713i	$-0.545696\pi$
$263$	−4.64029	−0.286133	−0.143066	+	0.989713i	$0.545696\pi$
$264$	−12.1912	−0.750317
$265$	−5.98222	−0.367485
$266$	0	0
$267$	14.3244	0.876641
$268$	2.97394	0.181662
$269$	−1.50132	−0.0915370	−0.0457685	−	0.998952i	$-0.514574\pi$
$269$	−1.50132	−0.0915370	−0.0457685	+	0.998952i	$0.514574\pi$
$270$	−1.01600	−0.0618317
$271$	−17.1813	−1.04369	−0.521845	−	0.853040i	$-0.674756\pi$
$271$	−17.1813	−1.04369	−0.521845	+	0.853040i	$0.674756\pi$
$272$	−4.48718	−0.272075
$273$	0	0
$274$	18.6232	1.12507
$275$	10.0965	0.608844
$276$	−8.22637	−0.495169
$277$	1.78708	0.107375	0.0536877	−	0.998558i	$-0.482902\pi$
$277$	1.78708	0.107375	0.0536877	+	0.998558i	$0.482902\pi$
$278$	−10.7699	−0.645937
$279$	−0.917497	−0.0549291
$280$	0	0
$281$	−19.4465	−1.16008	−0.580041	−	0.814587i	$-0.696964\pi$
$281$	−19.4465	−1.16008	−0.580041	+	0.814587i	$0.696964\pi$
$282$	−25.6568	−1.52784
$283$	−14.8055	−0.880093	−0.440046	−	0.897975i	$-0.645038\pi$
$283$	−14.8055	−0.880093	−0.440046	+	0.897975i	$0.645038\pi$
$284$	−10.8685	−0.644924
$285$	−12.7071	−0.752706
$286$	23.1834	1.37086
$287$	0	0
$288$	2.84113	0.167415
$289$	3.13477	0.184398
$290$	14.5630	0.855171
$291$	−30.6523	−1.79687
$292$	−2.17500	−0.127282
$293$	−8.02652	−0.468914	−0.234457	−	0.972126i	$-0.575331\pi$
$293$	−8.02652	−0.468914	−0.234457	+	0.972126i	$0.575331\pi$
$294$	0	0
$295$	−15.1940	−0.884628
$296$	−8.69590	−0.505439
$297$	1.93684	0.112387
$298$	−20.5100	−1.18811
$299$	15.6436	0.904695
$300$	−4.83751	−0.279294
$301$	0	0
$302$	−8.16877	−0.470060
$303$	−21.8762	−1.25675
$304$	−1.98701	−0.113963
$305$	−24.3024	−1.39155
$306$	−12.7487	−0.728792
$307$	−29.5722	−1.68777	−0.843887	−	0.536521i	$-0.819738\pi$
$307$	−29.5722	−1.68777	−0.843887	+	0.536521i	$0.819738\pi$
$308$	0	0
$309$	29.0929	1.65503
$310$	0.854500	0.0485323
$311$	22.5916	1.28105	0.640527	−	0.767936i	$-0.278716\pi$
$311$	22.5916	1.28105	0.640527	+	0.767936i	$0.278716\pi$
$312$	−11.1078	−0.628853
$313$	6.17339	0.348941	0.174470	−	0.984662i	$-0.444179\pi$
$313$	6.17339	0.348941	0.174470	+	0.984662i	$0.444179\pi$
$314$	8.39021	0.473487
$315$	0	0
$316$	14.0168	0.788509
$317$	5.33383	0.299578	0.149789	−	0.988718i	$-0.452141\pi$
$317$	5.33383	0.299578	0.149789	+	0.988718i	$0.452141\pi$
$318$	−5.46403	−0.306407
$319$	−27.7621	−1.55438
$320$	−2.64605	−0.147919
$321$	−15.6499	−0.873492
$322$	0	0
$323$	8.91609	0.496104
$324$	−9.45137	−0.525076
$325$	9.19924	0.510282
$326$	10.7381	0.594729
$327$	−41.3671	−2.28761
$328$	−1.00000	−0.0552158
$329$	0	0
$330$	32.2586	1.77578
$331$	23.7404	1.30489	0.652445	−	0.757836i	$-0.273743\pi$
$331$	23.7404	1.30489	0.652445	+	0.757836i	$0.273743\pi$
$332$	−0.927339	−0.0508944
$333$	−24.7062	−1.35389
$334$	−0.343329	−0.0187861
$335$	−7.86919	−0.429940
$336$	0	0
$337$	15.2905	0.832929	0.416465	−	0.909152i	$-0.363269\pi$
$337$	15.2905	0.832929	0.416465	+	0.909152i	$0.363269\pi$
$338$	8.12305	0.441835
$339$	−22.1324	−1.20206
$340$	11.8733	0.643920
$341$	−1.62897	−0.0882136
$342$	−5.64536	−0.305266
$343$	0	0
$344$	−8.64711	−0.466221
$345$	21.7674	1.17192
$346$	24.8890	1.33804
$347$	−4.27491	−0.229489	−0.114744	−	0.993395i	$-0.536605\pi$
$347$	−4.27491	−0.229489	−0.114744	+	0.993395i	$0.536605\pi$
$348$	13.3015	0.713038
$349$	4.37307	0.234085	0.117043	−	0.993127i	$-0.462659\pi$
$349$	4.37307	0.234085	0.117043	+	0.993127i	$0.462659\pi$
$350$	0	0
$351$	1.76471	0.0941932
$352$	5.04427	0.268861
$353$	6.07362	0.323266	0.161633	−	0.986851i	$-0.448324\pi$
$353$	6.07362	0.323266	0.161633	+	0.986851i	$0.448324\pi$
$354$	−13.8778	−0.737599
$355$	28.7585	1.52634
$356$	−5.92692	−0.314126
$357$	0	0
$358$	9.59343	0.507029
$359$	−25.3815	−1.33959	−0.669793	−	0.742548i	$-0.733617\pi$
$359$	−25.3815	−1.33959	−0.669793	+	0.742548i	$0.733617\pi$
$360$	−7.51777	−0.396221
$361$	−15.0518	−0.792199
$362$	−17.8164	−0.936409
$363$	−34.9106	−1.83233
$364$	0	0
$365$	5.75515	0.301238
$366$	−22.1973	−1.16027
$367$	37.5359	1.95936	0.979678	−	0.200574i	$-0.0642809\pi$
$367$	37.5359	1.95936	0.979678	+	0.200574i	$0.0642809\pi$
$368$	3.40377	0.177434
$369$	−2.84113	−0.147903
$370$	23.0098	1.19622
$371$	0	0
$372$	0.780481	0.0404661
$373$	−1.41734	−0.0733873	−0.0366936	−	0.999327i	$-0.511683\pi$
$373$	−1.41734	−0.0733873	−0.0366936	+	0.999327i	$0.511683\pi$
$374$	−22.6346	−1.17041
$375$	−19.1751	−0.990200
$376$	10.6158	0.547469
$377$	−25.2948	−1.30275
$378$	0	0
$379$	−10.3076	−0.529464	−0.264732	−	0.964322i	$-0.585284\pi$
$379$	−10.3076	−0.529464	−0.264732	+	0.964322i	$0.585284\pi$
$380$	5.25774	0.269716
$381$	−39.7068	−2.03424
$382$	4.58649	0.234665
$383$	24.3901	1.24628	0.623139	−	0.782111i	$-0.285857\pi$
$383$	24.3901	1.24628	0.623139	+	0.782111i	$0.285857\pi$
$384$	−2.41684	−0.123334
$385$	0	0
$386$	−24.0620	−1.22473
$387$	−24.5675	−1.24884
$388$	12.6828	0.643871
$389$	24.5003	1.24221	0.621107	−	0.783726i	$-0.286683\pi$
$389$	24.5003	1.24221	0.621107	+	0.783726i	$0.286683\pi$
$390$	29.3917	1.48831
$391$	−15.2733	−0.772404
$392$	0	0
$393$	14.9265	0.752941
$394$	19.8386	0.999455
$395$	−37.0893	−1.86616
$396$	14.3314	0.720181
$397$	−2.12627	−0.106714	−0.0533571	−	0.998575i	$-0.516992\pi$
$397$	−2.12627	−0.106714	−0.0533571	+	0.998575i	$0.516992\pi$
$398$	0.567519	0.0284471
$399$	0	0
$400$	2.00158	0.100079
$401$	−15.5745	−0.777752	−0.388876	−	0.921290i	$-0.627137\pi$
$401$	−15.5745	−0.777752	−0.388876	+	0.921290i	$0.627137\pi$
$402$	−7.18754	−0.358482
$403$	−1.48420	−0.0739332
$404$	9.05154	0.450331
$405$	25.0088	1.24270
$406$	0	0
$407$	−43.8645	−2.17428
$408$	10.8448	0.536898
$409$	−3.29331	−0.162844	−0.0814218	−	0.996680i	$-0.525946\pi$
$409$	−3.29331	−0.162844	−0.0814218	+	0.996680i	$0.525946\pi$
$410$	2.64605	0.130679
$411$	−45.0095	−2.22015
$412$	−12.0375	−0.593047
$413$	0	0
$414$	9.67054	0.475281
$415$	2.45379	0.120452
$416$	4.59598	0.225337
$417$	26.0292	1.27466
$418$	−10.0230	−0.490243
$419$	31.1570	1.52212	0.761059	−	0.648682i	$-0.224680\pi$
$419$	31.1570	1.52212	0.761059	+	0.648682i	$0.224680\pi$
$420$	0	0
$421$	34.6534	1.68891	0.844453	−	0.535630i	$-0.179926\pi$
$421$	34.6534	1.68891	0.844453	+	0.535630i	$0.179926\pi$
$422$	10.5505	0.513590
$423$	30.1609	1.46647
$424$	2.26081	0.109795
$425$	−8.98146	−0.435665
$426$	26.2674	1.27266
$427$	0	0
$428$	6.47535	0.312998
$429$	−56.0306	−2.70518
$430$	22.8807	1.10340
$431$	11.7632	0.566612	0.283306	−	0.959030i	$-0.408569\pi$
$431$	11.7632	0.566612	0.283306	+	0.959030i	$0.408569\pi$
$432$	0.383968	0.0184737
$433$	−33.7669	−1.62273	−0.811366	−	0.584539i	$-0.801276\pi$
$433$	−33.7669	−1.62273	−0.811366	+	0.584539i	$0.801276\pi$
$434$	0	0
$435$	−35.1966	−1.68755
$436$	17.1162	0.819716
$437$	−6.76333	−0.323534
$438$	5.25662	0.251171
$439$	−11.6691	−0.556936	−0.278468	−	0.960446i	$-0.589827\pi$
$439$	−11.6691	−0.556936	−0.278468	+	0.960446i	$0.589827\pi$
$440$	−13.3474	−0.636312
$441$	0	0
$442$	−20.6230	−0.980936
$443$	7.24811	0.344368	0.172184	−	0.985065i	$-0.444918\pi$
$443$	7.24811	0.344368	0.172184	+	0.985065i	$0.444918\pi$
$444$	21.0166	0.997405
$445$	15.6829	0.743442
$446$	3.02871	0.143414
$447$	49.5695	2.34456
$448$	0	0
$449$	18.8170	0.888030	0.444015	−	0.896019i	$-0.353554\pi$
$449$	18.8170	0.888030	0.444015	+	0.896019i	$0.353554\pi$
$450$	5.68675	0.268076
$451$	−5.04427	−0.237526
$452$	9.15755	0.430735
$453$	19.7426	0.927590
$454$	5.68454	0.266789
$455$	0	0
$456$	4.80230	0.224888
$457$	−10.5139	−0.491821	−0.245910	−	0.969293i	$-0.579087\pi$
$457$	−10.5139	−0.491821	−0.245910	+	0.969293i	$0.579087\pi$
$458$	7.22455	0.337581
$459$	−1.72293	−0.0804196
$460$	−9.00654	−0.419932
$461$	33.2981	1.55085	0.775424	−	0.631440i	$-0.217536\pi$
$461$	33.2981	1.55085	0.775424	+	0.631440i	$0.217536\pi$
$462$	0	0
$463$	−42.4236	−1.97159	−0.985797	−	0.167943i	$-0.946287\pi$
$463$	−42.4236	−1.97159	−0.985797	+	0.167943i	$0.946287\pi$
$464$	−5.50369	−0.255502
$465$	−2.06519	−0.0957710
$466$	24.4785	1.13394
$467$	15.1474	0.700937	0.350469	−	0.936574i	$-0.386022\pi$
$467$	15.1474	0.700937	0.350469	+	0.936574i	$0.386022\pi$
$468$	13.0578	0.603596
$469$	0	0
$470$	−28.0900	−1.29569
$471$	−20.2778	−0.934352
$472$	5.74214	0.264303
$473$	−43.6184	−2.00557
$474$	−33.8765	−1.55600
$475$	−3.97717	−0.182485
$476$	0	0
$477$	6.42326	0.294101
$478$	−3.87772	−0.177363
$479$	−11.1498	−0.509449	−0.254725	−	0.967014i	$-0.581985\pi$
$479$	−11.1498	−0.509449	−0.254725	+	0.967014i	$0.581985\pi$
$480$	6.39509	0.291894
$481$	−39.9662	−1.82230
$482$	28.5369	1.29982
$483$	0	0
$484$	14.4447	0.656577
$485$	−33.5593	−1.52385
$486$	21.6906	0.983905
$487$	−18.5221	−0.839319	−0.419659	−	0.907682i	$-0.637850\pi$
$487$	−18.5221	−0.839319	−0.419659	+	0.907682i	$0.637850\pi$
$488$	9.18440	0.415758
$489$	−25.9523	−1.17361
$490$	0	0
$491$	2.33023	0.105162	0.0525809	−	0.998617i	$-0.483255\pi$
$491$	2.33023	0.105162	0.0525809	+	0.998617i	$0.483255\pi$
$492$	2.41684	0.108960
$493$	24.6960	1.11225
$494$	−9.13228	−0.410881
$495$	−37.9217	−1.70445
$496$	−0.322934	−0.0145002
$497$	0	0
$498$	2.24123	0.100432
$499$	−3.65730	−0.163723	−0.0818615	−	0.996644i	$-0.526087\pi$
$499$	−3.65730	−0.163723	−0.0818615	+	0.996644i	$0.526087\pi$
$500$	7.93396	0.354818
$501$	0.829771	0.0370714
$502$	5.49129	0.245088
$503$	9.22355	0.411258	0.205629	−	0.978630i	$-0.434076\pi$
$503$	9.22355	0.411258	0.205629	+	0.978630i	$0.434076\pi$
$504$	0	0
$505$	−23.9508	−1.06580
$506$	17.1695	0.763279
$507$	−19.6321	−0.871893
$508$	16.4292	0.728927
$509$	−17.9377	−0.795074	−0.397537	−	0.917586i	$-0.630135\pi$
$509$	−17.9377	−0.795074	−0.397537	+	0.917586i	$0.630135\pi$
$510$	−28.6959	−1.27068
$511$	0	0
$512$	1.00000	0.0441942
$513$	−0.762950	−0.0336850
$514$	8.42680	0.371690
$515$	31.8520	1.40356
$516$	20.8987	0.920014
$517$	53.5491	2.35509
$518$	0	0
$519$	−60.1529	−2.64042
$520$	−12.1612	−0.533304
$521$	−7.64950	−0.335131	−0.167565	−	0.985861i	$-0.553590\pi$
$521$	−7.64950	−0.335131	−0.167565	+	0.985861i	$0.553590\pi$
$522$	−15.6367	−0.684399
$523$	29.1271	1.27364	0.636820	−	0.771012i	$-0.280249\pi$
$523$	29.1271	1.27364	0.636820	+	0.771012i	$0.280249\pi$
$524$	−6.17602	−0.269801
$525$	0	0
$526$	−4.64029	−0.202326
$527$	1.44906	0.0631222
$528$	−12.1912	−0.530555
$529$	−11.4144	−0.496277
$530$	−5.98222	−0.259851
$531$	16.3141	0.707974
$532$	0	0
$533$	−4.59598	−0.199074
$534$	14.3244	0.619879
$535$	−17.1341	−0.740772
$536$	2.97394	0.128455
$537$	−23.1858	−1.00054
$538$	−1.50132	−0.0647264
$539$	0	0
$540$	−1.01600	−0.0437216
$541$	37.7510	1.62304	0.811520	−	0.584324i	$-0.198640\pi$
$541$	37.7510	1.62304	0.811520	+	0.584324i	$0.198640\pi$
$542$	−17.1813	−0.738000
$543$	43.0594	1.84786
$544$	−4.48718	−0.192386
$545$	−45.2903	−1.94002
$546$	0	0
$547$	43.7953	1.87255	0.936275	−	0.351267i	$-0.114249\pi$
$547$	43.7953	1.87255	0.936275	+	0.351267i	$0.114249\pi$
$548$	18.6232	0.795546
$549$	26.0941	1.11367
$550$	10.0965	0.430518
$551$	10.9359	0.465885
$552$	−8.22637	−0.350137
$553$	0	0
$554$	1.78708	0.0759258
$555$	−55.6110	−2.36056
$556$	−10.7699	−0.456746
$557$	34.2396	1.45078	0.725390	−	0.688338i	$-0.241660\pi$
$557$	34.2396	1.45078	0.725390	+	0.688338i	$0.241660\pi$
$558$	−0.917497	−0.0388408
$559$	−39.7419	−1.68091
$560$	0	0
$561$	54.7042	2.30961
$562$	−19.4465	−0.820302
$563$	−40.1298	−1.69127	−0.845635	−	0.533762i	$-0.820778\pi$
$563$	−40.1298	−1.69127	−0.845635	+	0.533762i	$0.820778\pi$
$564$	−25.6568	−1.08034
$565$	−24.2313	−1.01942
$566$	−14.8055	−0.622319
$567$	0	0
$568$	−10.8685	−0.456030
$569$	14.2966	0.599343	0.299672	−	0.954042i	$-0.403123\pi$
$569$	14.2966	0.599343	0.299672	+	0.954042i	$0.403123\pi$
$570$	−12.7071	−0.532243
$571$	−22.4985	−0.941533	−0.470767	−	0.882258i	$-0.656023\pi$
$571$	−22.4985	−0.941533	−0.470767	+	0.882258i	$0.656023\pi$
$572$	23.1834	0.969346
$573$	−11.0848	−0.463075
$574$	0	0
$575$	6.81292	0.284118
$576$	2.84113	0.118380
$577$	−27.8951	−1.16129	−0.580645	−	0.814157i	$-0.697199\pi$
$577$	−27.8951	−1.16129	−0.580645	+	0.814157i	$0.697199\pi$
$578$	3.13477	0.130389
$579$	58.1542	2.41681
$580$	14.5630	0.604697
$581$	0	0
$582$	−30.6523	−1.27058
$583$	11.4042	0.472312
$584$	−2.17500	−0.0900020
$585$	−34.5515	−1.42853
$586$	−8.02652	−0.331572
$587$	35.6416	1.47109	0.735543	−	0.677478i	$-0.236927\pi$
$587$	35.6416	1.47109	0.735543	+	0.677478i	$0.236927\pi$
$588$	0	0
$589$	0.641675	0.0264398
$590$	−15.1940	−0.625526
$591$	−47.9468	−1.97227
$592$	−8.69590	−0.357399
$593$	−22.6188	−0.928843	−0.464421	−	0.885614i	$-0.653738\pi$
$593$	−22.6188	−0.928843	−0.464421	+	0.885614i	$0.653738\pi$
$594$	1.93684	0.0794695
$595$	0	0
$596$	−20.5100	−0.840124
$597$	−1.37160	−0.0561360
$598$	15.6436	0.639716
$599$	1.94862	0.0796183	0.0398092	−	0.999207i	$-0.487325\pi$
$599$	1.94862	0.0796183	0.0398092	+	0.999207i	$0.487325\pi$
$600$	−4.83751	−0.197491
$601$	44.9667	1.83423	0.917114	−	0.398624i	$-0.130512\pi$
$601$	44.9667	1.83423	0.917114	+	0.398624i	$0.130512\pi$
$602$	0	0
$603$	8.44934	0.344084
$604$	−8.16877	−0.332383
$605$	−38.2214	−1.55392
$606$	−21.8762	−0.888658
$607$	−38.9620	−1.58142	−0.790710	−	0.612191i	$-0.790288\pi$
$607$	−38.9620	−1.58142	−0.790710	+	0.612191i	$0.790288\pi$
$608$	−1.98701	−0.0805841
$609$	0	0
$610$	−24.3024	−0.983975
$611$	48.7901	1.97384
$612$	−12.7487	−0.515334
$613$	24.5009	0.989583	0.494792	−	0.869012i	$-0.335244\pi$
$613$	24.5009	0.989583	0.494792	+	0.869012i	$0.335244\pi$
$614$	−29.5722	−1.19344
$615$	−6.39509	−0.257875
$616$	0	0
$617$	32.0385	1.28982	0.644911	−	0.764258i	$-0.276895\pi$
$617$	32.0385	1.28982	0.644911	+	0.764258i	$0.276895\pi$
$618$	29.0929	1.17029
$619$	29.4956	1.18553	0.592765	−	0.805375i	$-0.298036\pi$
$619$	29.4956	1.18553	0.592765	+	0.805375i	$0.298036\pi$
$620$	0.854500	0.0343176
$621$	1.30694	0.0524456
$622$	22.5916	0.905841
$623$	0	0
$624$	−11.1078	−0.444666
$625$	−31.0016	−1.24006
$626$	6.17339	0.246738
$627$	24.2241	0.967418
$628$	8.39021	0.334806
$629$	39.0201	1.55583
$630$	0	0
$631$	−22.8709	−0.910477	−0.455238	−	0.890370i	$-0.650446\pi$
$631$	−22.8709	−0.910477	−0.455238	+	0.890370i	$0.650446\pi$
$632$	14.0168	0.557560
$633$	−25.4989	−1.01349
$634$	5.33383	0.211833
$635$	−43.4725	−1.72515
$636$	−5.46403	−0.216663
$637$	0	0
$638$	−27.7621	−1.09911
$639$	−30.8787	−1.22154
$640$	−2.64605	−0.104594
$641$	36.1376	1.42735	0.713674	−	0.700478i	$-0.247030\pi$
$641$	36.1376	1.42735	0.713674	+	0.700478i	$0.247030\pi$
$642$	−15.6499	−0.617652
$643$	−19.0055	−0.749506	−0.374753	−	0.927125i	$-0.622272\pi$
$643$	−19.0055	−0.749506	−0.374753	+	0.927125i	$0.622272\pi$
$644$	0	0
$645$	−55.2990	−2.17740
$646$	8.91609	0.350799
$647$	−30.3319	−1.19247	−0.596236	−	0.802810i	$-0.703338\pi$
$647$	−30.3319	−1.19247	−0.596236	+	0.802810i	$0.703338\pi$
$648$	−9.45137	−0.371285
$649$	28.9649	1.13697
$650$	9.19924	0.360824
$651$	0	0
$652$	10.7381	0.420537
$653$	42.0165	1.64423	0.822116	−	0.569321i	$-0.192794\pi$
$653$	42.0165	1.64423	0.822116	+	0.569321i	$0.192794\pi$
$654$	−41.3671	−1.61758
$655$	16.3421	0.638538
$656$	−1.00000	−0.0390434
$657$	−6.17944	−0.241083
$658$	0	0
$659$	3.85533	0.150182	0.0750912	−	0.997177i	$-0.476075\pi$
$659$	3.85533	0.150182	0.0750912	+	0.997177i	$0.476075\pi$
$660$	32.2586	1.25566
$661$	9.44963	0.367548	0.183774	−	0.982969i	$-0.441169\pi$
$661$	9.44963	0.367548	0.183774	+	0.982969i	$0.441169\pi$
$662$	23.7404	0.922697
$663$	49.8425	1.93572
$664$	−0.927339	−0.0359877
$665$	0	0
$666$	−24.7062	−0.957345
$667$	−18.7333	−0.725355
$668$	−0.343329	−0.0132838
$669$	−7.31992	−0.283005
$670$	−7.86919	−0.304013
$671$	46.3286	1.78850
$672$	0	0
$673$	−6.14515	−0.236878	−0.118439	−	0.992961i	$-0.537789\pi$
$673$	−6.14515	−0.236878	−0.118439	+	0.992961i	$0.537789\pi$
$674$	15.2905	0.588970
$675$	0.768543	0.0295812
$676$	8.12305	0.312425
$677$	−14.5243	−0.558214	−0.279107	−	0.960260i	$-0.590038\pi$
$677$	−14.5243	−0.558214	−0.279107	+	0.960260i	$0.590038\pi$
$678$	−22.1324	−0.849988
$679$	0	0
$680$	11.8733	0.455320
$681$	−13.7386	−0.526466
$682$	−1.62897	−0.0623764
$683$	10.4611	0.400284	0.200142	−	0.979767i	$-0.435860\pi$
$683$	10.4611	0.400284	0.200142	+	0.979767i	$0.435860\pi$
$684$	−5.64536	−0.215856
$685$	−49.2781	−1.88282
$686$	0	0
$687$	−17.4606	−0.666163
$688$	−8.64711	−0.329668
$689$	10.3907	0.395852
$690$	21.7674	0.828670
$691$	−8.36579	−0.318250	−0.159125	−	0.987258i	$-0.550867\pi$
$691$	−8.36579	−0.318250	−0.159125	+	0.987258i	$0.550867\pi$
$692$	24.8890	0.946140
$693$	0	0
$694$	−4.27491	−0.162273
$695$	28.4978	1.08098
$696$	13.3015	0.504194
$697$	4.48718	0.169964
$698$	4.37307	0.165523
$699$	−59.1606	−2.23766
$700$	0	0
$701$	−45.6187	−1.72299	−0.861497	−	0.507762i	$-0.830473\pi$
$701$	−45.6187	−1.72299	−0.861497	+	0.507762i	$0.830473\pi$
$702$	1.76471	0.0666046
$703$	17.2789	0.651685
$704$	5.04427	0.190113
$705$	67.8891	2.55685
$706$	6.07362	0.228584
$707$	0	0
$708$	−13.8778	−0.521561
$709$	−20.5455	−0.771601	−0.385800	−	0.922582i	$-0.626075\pi$
$709$	−20.5455	−0.771601	−0.385800	+	0.922582i	$0.626075\pi$
$710$	28.7585	1.07929
$711$	39.8237	1.49350
$712$	−5.92692	−0.222121
$713$	−1.09919	−0.0411651
$714$	0	0
$715$	−61.3444	−2.29415
$716$	9.59343	0.358523
$717$	9.37183	0.349997
$718$	−25.3815	−0.947230
$719$	19.8068	0.738667	0.369334	−	0.929297i	$-0.379586\pi$
$719$	19.8068	0.738667	0.369334	+	0.929297i	$0.379586\pi$
$720$	−7.51777	−0.280171
$721$	0	0
$722$	−15.0518	−0.560169
$723$	−68.9693	−2.56500
$724$	−17.8164	−0.662141
$725$	−11.0161	−0.409127
$726$	−34.9106	−1.29565
$727$	−5.14920	−0.190973	−0.0954867	−	0.995431i	$-0.530441\pi$
$727$	−5.14920	−0.190973	−0.0954867	+	0.995431i	$0.530441\pi$
$728$	0	0
$729$	−24.0686	−0.891430
$730$	5.75515	0.213008
$731$	38.8011	1.43511
$732$	−22.1973	−0.820434
$733$	−6.51303	−0.240564	−0.120282	−	0.992740i	$-0.538380\pi$
$733$	−6.51303	−0.240564	−0.120282	+	0.992740i	$0.538380\pi$
$734$	37.5359	1.38547
$735$	0	0
$736$	3.40377	0.125464
$737$	15.0014	0.552582
$738$	−2.84113	−0.104583
$739$	−12.7156	−0.467750	−0.233875	−	0.972267i	$-0.575141\pi$
$739$	−12.7156	−0.467750	−0.233875	+	0.972267i	$0.575141\pi$
$740$	23.0098	0.845857
$741$	22.0713	0.810809
$742$	0	0
$743$	38.2821	1.40444	0.702218	−	0.711962i	$-0.252193\pi$
$743$	38.2821	1.40444	0.702218	+	0.711962i	$0.252193\pi$
$744$	0.780481	0.0286138
$745$	54.2706	1.98832
$746$	−1.41734	−0.0518927
$747$	−2.63469	−0.0963983
$748$	−22.6346	−0.827601
$749$	0	0
$750$	−19.1751	−0.700177
$751$	−13.1814	−0.480994	−0.240497	−	0.970650i	$-0.577310\pi$
$751$	−13.1814	−0.480994	−0.240497	+	0.970650i	$0.577310\pi$
$752$	10.6158	0.387119
$753$	−13.2716	−0.483643
$754$	−25.2948	−0.921184
$755$	21.6150	0.786650
$756$	0	0
$757$	11.8057	0.429084	0.214542	−	0.976715i	$-0.431174\pi$
$757$	11.8057	0.429084	0.214542	+	0.976715i	$0.431174\pi$
$758$	−10.3076	−0.374388
$759$	−41.4960	−1.50621
$760$	5.25774	0.190718
$761$	48.0050	1.74018	0.870090	−	0.492893i	$-0.164061\pi$
$761$	48.0050	1.74018	0.870090	+	0.492893i	$0.164061\pi$
$762$	−39.7068	−1.43842
$763$	0	0
$764$	4.58649	0.165933
$765$	33.7336	1.21964
$766$	24.3901	0.881252
$767$	26.3908	0.952915
$768$	−2.41684	−0.0872103
$769$	−9.51632	−0.343167	−0.171584	−	0.985170i	$-0.554888\pi$
$769$	−9.51632	−0.343167	−0.171584	+	0.985170i	$0.554888\pi$
$770$	0	0
$771$	−20.3662	−0.733472
$772$	−24.0620	−0.866012
$773$	−9.17532	−0.330013	−0.165007	−	0.986292i	$-0.552765\pi$
$773$	−9.17532	−0.330013	−0.165007	+	0.986292i	$0.552765\pi$
$774$	−24.5675	−0.883062
$775$	−0.646379	−0.0232186
$776$	12.6828	0.455286
$777$	0	0
$778$	24.5003	0.878377
$779$	1.98701	0.0711922
$780$	29.3917	1.05239
$781$	−54.8235	−1.96174
$782$	−15.2733	−0.546172
$783$	−2.11324	−0.0755210
$784$	0	0
$785$	−22.2009	−0.792384
$786$	14.9265	0.532410
$787$	−10.5654	−0.376614	−0.188307	−	0.982110i	$-0.560300\pi$
$787$	−10.5654	−0.376614	−0.188307	+	0.982110i	$0.560300\pi$
$788$	19.8386	0.706722
$789$	11.2149	0.399259
$790$	−37.0893	−1.31958
$791$	0	0
$792$	14.3314	0.509245
$793$	42.2113	1.49897
$794$	−2.12627	−0.0754584
$795$	14.4581	0.512776
$796$	0.567519	0.0201152
$797$	40.7660	1.44401	0.722003	−	0.691890i	$-0.243222\pi$
$797$	40.7660	1.44401	0.722003	+	0.691890i	$0.243222\pi$
$798$	0	0
$799$	−47.6351	−1.68521
$800$	2.00158	0.0707666
$801$	−16.8391	−0.594982
$802$	−15.5745	−0.549954
$803$	−10.9713	−0.387168
$804$	−7.18754	−0.253485
$805$	0	0
$806$	−1.48420	−0.0522787
$807$	3.62845	0.127727
$808$	9.05154	0.318432
$809$	−44.6682	−1.57045	−0.785224	−	0.619211i	$-0.787452\pi$
$809$	−44.6682	−1.57045	−0.785224	+	0.619211i	$0.787452\pi$
$810$	25.0088	0.878720
$811$	22.9277	0.805102	0.402551	−	0.915398i	$-0.368124\pi$
$811$	22.9277	0.805102	0.402551	+	0.915398i	$0.368124\pi$
$812$	0	0
$813$	41.5245	1.45633
$814$	−43.8645	−1.53745
$815$	−28.4136	−0.995285
$816$	10.8448	0.379644
$817$	17.1819	0.601120
$818$	−3.29331	−0.115148
$819$	0	0
$820$	2.64605	0.0924041
$821$	0.988588	0.0345020	0.0172510	−	0.999851i	$-0.494509\pi$
$821$	0.988588	0.0345020	0.0172510	+	0.999851i	$0.494509\pi$
$822$	−45.0095	−1.56989
$823$	−18.2329	−0.635560	−0.317780	−	0.948165i	$-0.602937\pi$
$823$	−18.2329	−0.635560	−0.317780	+	0.948165i	$0.602937\pi$
$824$	−12.0375	−0.419348
$825$	−24.4017	−0.849559
$826$	0	0
$827$	10.9527	0.380863	0.190431	−	0.981701i	$-0.439011\pi$
$827$	10.9527	0.380863	0.190431	+	0.981701i	$0.439011\pi$
$828$	9.67054	0.336074
$829$	5.03481	0.174866	0.0874330	−	0.996170i	$-0.472134\pi$
$829$	5.03481	0.174866	0.0874330	+	0.996170i	$0.472134\pi$
$830$	2.45379	0.0851722
$831$	−4.31910	−0.149828
$832$	4.59598	0.159337
$833$	0	0
$834$	26.0292	0.901318
$835$	0.908465	0.0314387
$836$	−10.0230	−0.346654
$837$	−0.123996	−0.00428594
$838$	31.1570	1.07630
$839$	−46.8736	−1.61826	−0.809128	−	0.587633i	$-0.800060\pi$
$839$	−46.8736	−1.61826	−0.809128	+	0.587633i	$0.800060\pi$
$840$	0	0
$841$	1.29056	0.0445020
$842$	34.6534	1.19424
$843$	46.9992	1.61874
$844$	10.5505	0.363163
$845$	−21.4940	−0.739416
$846$	30.1609	1.03695
$847$	0	0
$848$	2.26081	0.0776366
$849$	35.7824	1.22805
$850$	−8.98146	−0.308061
$851$	−29.5988	−1.01463
$852$	26.2674	0.899905
$853$	32.6075	1.11646	0.558229	−	0.829687i	$-0.311481\pi$
$853$	32.6075	1.11646	0.558229	+	0.829687i	$0.311481\pi$
$854$	0	0
$855$	14.9379	0.510866
$856$	6.47535	0.221323
$857$	−39.1448	−1.33716	−0.668581	−	0.743640i	$-0.733098\pi$
$857$	−39.1448	−1.33716	−0.668581	+	0.743640i	$0.733098\pi$
$858$	−56.0306	−1.91285
$859$	−30.1124	−1.02742	−0.513710	−	0.857964i	$-0.671729\pi$
$859$	−30.1124	−1.02742	−0.513710	+	0.857964i	$0.671729\pi$
$860$	22.8807	0.780225
$861$	0	0
$862$	11.7632	0.400655
$863$	−23.7135	−0.807215	−0.403608	−	0.914932i	$-0.632244\pi$
$863$	−23.7135	−0.807215	−0.403608	+	0.914932i	$0.632244\pi$
$864$	0.383968	0.0130628
$865$	−65.8577	−2.23923
$866$	−33.7669	−1.14744
$867$	−7.57625	−0.257303
$868$	0	0
$869$	70.7048	2.39850
$870$	−35.1966	−1.19327
$871$	13.6682	0.463128
$872$	17.1162	0.579627
$873$	36.0335	1.21955
$874$	−6.76333	−0.228773
$875$	0	0
$876$	5.25662	0.177605
$877$	8.24090	0.278276	0.139138	−	0.990273i	$-0.455567\pi$
$877$	8.24090	0.278276	0.139138	+	0.990273i	$0.455567\pi$
$878$	−11.6691	−0.393813
$879$	19.3988	0.654306
$880$	−13.3474	−0.449941
$881$	33.9613	1.14418	0.572092	−	0.820189i	$-0.306132\pi$
$881$	33.9613	1.14418	0.572092	+	0.820189i	$0.306132\pi$
$882$	0	0
$883$	−9.87708	−0.332390	−0.166195	−	0.986093i	$-0.553148\pi$
$883$	−9.87708	−0.332390	−0.166195	+	0.986093i	$0.553148\pi$
$884$	−20.6230	−0.693626
$885$	36.7215	1.23438
$886$	7.24811	0.243505
$887$	−29.9676	−1.00621	−0.503106	−	0.864224i	$-0.667810\pi$
$887$	−29.9676	−1.00621	−0.503106	+	0.864224i	$0.667810\pi$
$888$	21.0166	0.705272
$889$	0	0
$890$	15.6829	0.525693
$891$	−47.6753	−1.59718
$892$	3.02871	0.101409
$893$	−21.0938	−0.705876
$894$	49.5695	1.65785
$895$	−25.3847	−0.848517
$896$	0	0
$897$	−37.8082	−1.26238
$898$	18.8170	0.627932
$899$	1.77733	0.0592772
$900$	5.68675	0.189558
$901$	−10.1447	−0.337968
$902$	−5.04427	−0.167956
$903$	0	0
$904$	9.15755	0.304576
$905$	47.1431	1.56709
$906$	19.7426	0.655905
$907$	37.3034	1.23864	0.619320	−	0.785139i	$-0.287409\pi$
$907$	37.3034	1.23864	0.619320	+	0.785139i	$0.287409\pi$
$908$	5.68454	0.188648
$909$	25.7166	0.852966
$910$	0	0
$911$	−27.4885	−0.910736	−0.455368	−	0.890303i	$-0.650492\pi$
$911$	−27.4885	−0.910736	−0.455368	+	0.890303i	$0.650492\pi$
$912$	4.80230	0.159020
$913$	−4.67775	−0.154811
$914$	−10.5139	−0.347770
$915$	58.7351	1.94172
$916$	7.22455	0.238706
$917$	0	0
$918$	−1.72293	−0.0568652
$919$	20.6875	0.682417	0.341208	−	0.939988i	$-0.389164\pi$
$919$	20.6875	0.682417	0.341208	+	0.939988i	$0.389164\pi$
$920$	−9.00654	−0.296937
$921$	71.4713	2.35506
$922$	33.2981	1.09662
$923$	−49.9512	−1.64417
$924$	0	0
$925$	−17.4056	−0.572291
$926$	−42.4236	−1.39413
$927$	−34.2002	−1.12328
$928$	−5.50369	−0.180667
$929$	−49.4961	−1.62392	−0.811958	−	0.583716i	$-0.801598\pi$
$929$	−49.4961	−1.62392	−0.811958	+	0.583716i	$0.801598\pi$
$930$	−2.06519	−0.0677203
$931$	0	0
$932$	24.4785	0.801818
$933$	−54.6004	−1.78754
$934$	15.1474	0.495637
$935$	59.8922	1.95868
$936$	13.0578	0.426807
$937$	33.4679	1.09335	0.546675	−	0.837345i	$-0.315893\pi$
$937$	33.4679	1.09335	0.546675	+	0.837345i	$0.315893\pi$
$938$	0	0
$939$	−14.9201	−0.486900
$940$	−28.0900	−0.916194
$941$	−5.29493	−0.172610	−0.0863048	−	0.996269i	$-0.527506\pi$
$941$	−5.29493	−0.172610	−0.0863048	+	0.996269i	$0.527506\pi$
$942$	−20.2778	−0.660687
$943$	−3.40377	−0.110842
$944$	5.74214	0.186891
$945$	0	0
$946$	−43.6184	−1.41816
$947$	−3.97381	−0.129131	−0.0645657	−	0.997913i	$-0.520566\pi$
$947$	−3.97381	−0.129131	−0.0645657	+	0.997913i	$0.520566\pi$
$948$	−33.8765	−1.10026
$949$	−9.99624	−0.324492
$950$	−3.97717	−0.129037
$951$	−12.8910	−0.418020
$952$	0	0
$953$	21.1435	0.684906	0.342453	−	0.939535i	$-0.388742\pi$
$953$	21.1435	0.684906	0.342453	+	0.939535i	$0.388742\pi$
$954$	6.42326	0.207961
$955$	−12.1361	−0.392715
$956$	−3.87772	−0.125414
$957$	67.0966	2.16893
$958$	−11.1498	−0.360235
$959$	0	0
$960$	6.39509	0.206401
$961$	−30.8957	−0.996636
$962$	−39.9662	−1.28856
$963$	18.3973	0.592844
$964$	28.5369	0.919113
$965$	63.6694	2.04959
$966$	0	0
$967$	31.0898	0.999782	0.499891	−	0.866088i	$-0.333373\pi$
$967$	31.0898	0.999782	0.499891	+	0.866088i	$0.333373\pi$
$968$	14.4447	0.464270
$969$	−21.5488	−0.692247
$970$	−33.5593	−1.07752
$971$	3.04723	0.0977902	0.0488951	−	0.998804i	$-0.484430\pi$
$971$	3.04723	0.0977902	0.0488951	+	0.998804i	$0.484430\pi$
$972$	21.6906	0.695726
$973$	0	0
$974$	−18.5221	−0.593488
$975$	−22.2331	−0.712029
$976$	9.18440	0.293986
$977$	−20.0083	−0.640121	−0.320060	−	0.947397i	$-0.603703\pi$
$977$	−20.0083	−0.640121	−0.320060	+	0.947397i	$0.603703\pi$
$978$	−25.9523	−0.829864
$979$	−29.8970	−0.955513
$980$	0	0
$981$	48.6292	1.55261
$982$	2.33023	0.0743607
$983$	−4.04016	−0.128861	−0.0644305	−	0.997922i	$-0.520523\pi$
$983$	−4.04016	−0.128861	−0.0644305	+	0.997922i	$0.520523\pi$
$984$	2.41684	0.0770461
$985$	−52.4940	−1.67260
$986$	24.6960	0.786482
$987$	0	0
$988$	−9.13228	−0.290537
$989$	−29.4327	−0.935906
$990$	−37.9217	−1.20523
$991$	−45.2981	−1.43894	−0.719471	−	0.694522i	$-0.755616\pi$
$991$	−45.2981	−1.43894	−0.719471	+	0.694522i	$0.755616\pi$
$992$	−0.322934	−0.0102532
$993$	−57.3768	−1.82080
$994$	0	0
$995$	−1.50168	−0.0476065
$996$	2.24123	0.0710162
$997$	−49.4043	−1.56465	−0.782324	−	0.622871i	$-0.785966\pi$
$997$	−49.4043	−1.56465	−0.782324	+	0.622871i	$0.785966\pi$
$998$	−3.65730	−0.115770
$999$	−3.33895	−0.105640

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4018.2.a.bt.1.3		10
7.2	even	3		574.2.e.h.165.8	✓	20
7.4	even	3		574.2.e.h.247.8	yes	20
7.6	odd	2		4018.2.a.bu.1.8		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
574.2.e.h.165.8	✓	20	7.2	even	3
574.2.e.h.247.8	yes	20	7.4	even	3
4018.2.a.bt.1.3		10	1.1	even	1	trivial
4018.2.a.bu.1.8		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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.41684 q^{3} +1.00000 q^{4} -2.64605 q^{5} -2.41684 q^{6} +1.00000 q^{8} +2.84113 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.41684 q^{3} +1.00000 q^{4} -2.64605 q^{5} -2.41684 q^{6} +1.00000 q^{8} +2.84113 q^{9} -2.64605 q^{10} +5.04427 q^{11} -2.41684 q^{12} +4.59598 q^{13} +6.39509 q^{15} +1.00000 q^{16} -4.48718 q^{17} +2.84113 q^{18} -1.98701 q^{19} -2.64605 q^{20} +5.04427 q^{22} +3.40377 q^{23} -2.41684 q^{24} +2.00158 q^{25} +4.59598 q^{26} +0.383968 q^{27} -5.50369 q^{29} +6.39509 q^{30} -0.322934 q^{31} +1.00000 q^{32} -12.1912 q^{33} -4.48718 q^{34} +2.84113 q^{36} -8.69590 q^{37} -1.98701 q^{38} -11.1078 q^{39} -2.64605 q^{40} -1.00000 q^{41} -8.64711 q^{43} +5.04427 q^{44} -7.51777 q^{45} +3.40377 q^{46} +10.6158 q^{47} -2.41684 q^{48} +2.00158 q^{50} +10.8448 q^{51} +4.59598 q^{52} +2.26081 q^{53} +0.383968 q^{54} -13.3474 q^{55} +4.80230 q^{57} -5.50369 q^{58} +5.74214 q^{59} +6.39509 q^{60} +9.18440 q^{61} -0.322934 q^{62} +1.00000 q^{64} -12.1612 q^{65} -12.1912 q^{66} +2.97394 q^{67} -4.48718 q^{68} -8.22637 q^{69} -10.8685 q^{71} +2.84113 q^{72} -2.17500 q^{73} -8.69590 q^{74} -4.83751 q^{75} -1.98701 q^{76} -11.1078 q^{78} +14.0168 q^{79} -2.64605 q^{80} -9.45137 q^{81} -1.00000 q^{82} -0.927339 q^{83} +11.8733 q^{85} -8.64711 q^{86} +13.3015 q^{87} +5.04427 q^{88} -5.92692 q^{89} -7.51777 q^{90} +3.40377 q^{92} +0.780481 q^{93} +10.6158 q^{94} +5.25774 q^{95} -2.41684 q^{96} +12.6828 q^{97} +14.3314 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{2} - q^{3} + 10 q^{4} + 2 q^{5} - q^{6} + 10 q^{8} + 17 q^{9}+O(q^{10}) \) 10 * q + 10 * q^2 - q^3 + 10 * q^4 + 2 * q^5 - q^6 + 10 * q^8 + 17 * q^9	\( 10 q + 10 q^{2} - q^{3} + 10 q^{4} + 2 q^{5} - q^{6} + 10 q^{8} + 17 q^{9} + 2 q^{10} + 11 q^{11} - q^{12} - 4 q^{13} + 4 q^{15} + 10 q^{16} - 5 q^{17} + 17 q^{18} + q^{19} + 2 q^{20} + 11 q^{22} + 9 q^{23} - q^{24} + 24 q^{25} - 4 q^{26} - 7 q^{27} + 23 q^{29} + 4 q^{30} + 5 q^{31} + 10 q^{32} + 5 q^{33} - 5 q^{34} + 17 q^{36} + 16 q^{37} + q^{38} - 7 q^{39} + 2 q^{40} - 10 q^{41} + 20 q^{43} + 11 q^{44} + 42 q^{45} + 9 q^{46} + 16 q^{47} - q^{48} + 24 q^{50} + 13 q^{51} - 4 q^{52} + 26 q^{53} - 7 q^{54} - 7 q^{55} + 37 q^{57} + 23 q^{58} + 10 q^{59} + 4 q^{60} + 5 q^{62} + 10 q^{64} + 18 q^{65} + 5 q^{66} + 7 q^{67} - 5 q^{68} - 39 q^{69} + 5 q^{71} + 17 q^{72} + 13 q^{73} + 16 q^{74} - 19 q^{75} + q^{76} - 7 q^{78} - q^{79} + 2 q^{80} + 18 q^{81} - 10 q^{82} - 21 q^{83} + 34 q^{85} + 20 q^{86} - 2 q^{87} + 11 q^{88} - 6 q^{89} + 42 q^{90} + 9 q^{92} - 5 q^{93} + 16 q^{94} + 24 q^{95} - q^{96} - 29 q^{97} + 48 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 - q^3 + 10 * q^4 + 2 * q^5 - q^6 + 10 * q^8 + 17 * q^9 + 2 * q^10 + 11 * q^11 - q^12 - 4 * q^13 + 4 * q^15 + 10 * q^16 - 5 * q^17 + 17 * q^18 + q^19 + 2 * q^20 + 11 * q^22 + 9 * q^23 - q^24 + 24 * q^25 - 4 * q^26 - 7 * q^27 + 23 * q^29 + 4 * q^30 + 5 * q^31 + 10 * q^32 + 5 * q^33 - 5 * q^34 + 17 * q^36 + 16 * q^37 + q^38 - 7 * q^39 + 2 * q^40 - 10 * q^41 + 20 * q^43 + 11 * q^44 + 42 * q^45 + 9 * q^46 + 16 * q^47 - q^48 + 24 * q^50 + 13 * q^51 - 4 * q^52 + 26 * q^53 - 7 * q^54 - 7 * q^55 + 37 * q^57 + 23 * q^58 + 10 * q^59 + 4 * q^60 + 5 * q^62 + 10 * q^64 + 18 * q^65 + 5 * q^66 + 7 * q^67 - 5 * q^68 - 39 * q^69 + 5 * q^71 + 17 * q^72 + 13 * q^73 + 16 * q^74 - 19 * q^75 + q^76 - 7 * q^78 - q^79 + 2 * q^80 + 18 * q^81 - 10 * q^82 - 21 * q^83 + 34 * q^85 + 20 * q^86 - 2 * q^87 + 11 * q^88 - 6 * q^89 + 42 * q^90 + 9 * q^92 - 5 * q^93 + 16 * q^94 + 24 * q^95 - q^96 - 29 * q^97 + 48 * q^99

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