LMFDB - Embedded newform 4018.2.a.bu.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:	$0$
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			1.8
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	$-0.254215\pi$
$3$	2.41684	1.39536	0.697682	+	0.716407i	$0.254215\pi$
$4$	1.00000	0.500000
$5$	2.64605	1.18335	0.591675	−	0.806177i	$-0.298467\pi$
$5$	2.64605	1.18335	0.591675	+	0.806177i	$0.298467\pi$
$6$	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	$-0.719969\pi$
$13$	−4.59598	−1.27470	−0.637348	+	0.770576i	$0.719969\pi$
$14$	0	0
$15$	6.39509	1.65120
$16$	1.00000	0.250000
$17$	4.48718	1.08830	0.544150	−	0.838988i	$-0.316852\pi$
$17$	4.48718	1.08830	0.544150	+	0.838988i	$0.316852\pi$
$18$	2.84113	0.669660
$19$	1.98701	0.455852	0.227926	−	0.973678i	$-0.426806\pi$
$19$	1.98701	0.455852	0.227926	+	0.973678i	$0.426806\pi$
$20$	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	$-0.490768\pi$
$31$	0.322934	0.0580007	0.0290003	+	0.999579i	$0.490768\pi$
$32$	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	$-0.781867\pi$
$47$	−10.6158	−1.54848	−0.774238	+	0.632895i	$0.781867\pi$
$48$	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	$-0.621939\pi$
$59$	−5.74214	−0.747562	−0.373781	+	0.927517i	$0.621939\pi$
$60$	6.39509	0.825602
$61$	−9.18440	−1.17594	−0.587971	−	0.808882i	$-0.700073\pi$
$61$	−9.18440	−1.17594	−0.587971	+	0.808882i	$0.700073\pi$
$62$	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	$-0.459375\pi$
$73$	2.17500	0.254564	0.127282	+	0.991867i	$0.459375\pi$
$74$	−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	$-0.483793\pi$
$83$	0.927339	0.101789	0.0508944	+	0.998704i	$0.483793\pi$
$84$	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	$-0.398289\pi$
$89$	5.92692	0.628252	0.314126	+	0.949381i	$0.398289\pi$
$90$	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	$-0.722673\pi$
$97$	−12.6828	−1.28774	−0.643871	+	0.765134i	$0.722673\pi$
$98$	0	0
$99$	14.3314	1.44036
$100$	2.00158	0.200158
$101$	−9.05154	−0.900662	−0.450331	−	0.892862i	$-0.648694\pi$
$101$	−9.05154	−0.900662	−0.450331	+	0.892862i	$0.648694\pi$
$102$	10.8448	1.07380
$103$	12.0375	1.18609	0.593047	−	0.805168i	$-0.297925\pi$
$103$	12.0375	1.18609	0.593047	+	0.805168i	$0.297925\pi$
$104$	−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	$-0.413042\pi$
$131$	6.17602	0.539602	0.269801	+	0.962916i	$0.413042\pi$
$132$	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	$-0.349015\pi$
$139$	10.7699	0.913493	0.456746	+	0.889597i	$0.349015\pi$
$140$	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	$-0.608671\pi$
$157$	−8.39021	−0.669611	−0.334806	+	0.942287i	$0.608671\pi$
$158$	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	$-0.495772\pi$
$167$	0.343329	0.0265676	0.0132838	+	0.999912i	$0.495772\pi$
$168$	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	$-0.895053\pi$
$173$	−24.8890	−1.89228	−0.946140	+	0.323759i	$0.895053\pi$
$174$	−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	$-0.269648\pi$
$181$	17.8164	1.32428	0.662141	+	0.749379i	$0.269648\pi$
$182$	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	$-0.506403\pi$
$199$	−0.567519	−0.0402303	−0.0201152	+	0.999798i	$0.506403\pi$
$200$	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	$-0.532335\pi$
$223$	−3.02871	−0.202818	−0.101409	+	0.994845i	$0.532335\pi$
$224$	0	0
$225$	5.68675	0.379117
$226$	9.15755	0.609151
$227$	−5.68454	−0.377296	−0.188648	−	0.982045i	$-0.560411\pi$
$227$	−5.68454	−0.377296	−0.188648	+	0.982045i	$0.560411\pi$
$228$	4.80230	0.318040
$229$	−7.22455	−0.477412	−0.238706	−	0.971092i	$-0.576723\pi$
$229$	−7.22455	−0.477412	−0.238706	+	0.971092i	$0.576723\pi$
$230$	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	$-0.871093\pi$
$241$	−28.5369	−1.83823	−0.919113	+	0.393994i	$0.871093\pi$
$242$	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	$-0.555444\pi$
$251$	−5.49129	−0.346607	−0.173303	+	0.984868i	$0.555444\pi$
$252$	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	$-0.584654\pi$
$257$	−8.42680	−0.525649	−0.262825	+	0.964844i	$0.584654\pi$
$258$	−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	$-0.485426\pi$
$269$	1.50132	0.0915370	0.0457685	+	0.998952i	$0.485426\pi$
$270$	−1.01600	−0.0618317
$271$	17.1813	1.04369	0.521845	−	0.853040i	$-0.325244\pi$
$271$	17.1813	1.04369	0.521845	+	0.853040i	$0.325244\pi$
$272$	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	$-0.354962\pi$
$283$	14.8055	0.880093	0.440046	+	0.897975i	$0.354962\pi$
$284$	−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	$-0.424669\pi$
$293$	8.02652	0.468914	0.234457	+	0.972126i	$0.424669\pi$
$294$	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	$-0.180262\pi$
$307$	29.5722	1.68777	0.843887	+	0.536521i	$0.180262\pi$
$308$	0	0
$309$	29.0929	1.65503
$310$	0.854500	0.0485323
$311$	−22.5916	−1.28105	−0.640527	−	0.767936i	$-0.721284\pi$
$311$	−22.5916	−1.28105	−0.640527	+	0.767936i	$0.721284\pi$
$312$	−11.1078	−0.628853
$313$	−6.17339	−0.348941	−0.174470	−	0.984662i	$-0.555821\pi$
$313$	−6.17339	−0.348941	−0.174470	+	0.984662i	$0.555821\pi$
$314$	−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	$-0.537341\pi$
$349$	−4.37307	−0.234085	−0.117043	+	0.993127i	$0.537341\pi$
$350$	0	0
$351$	1.76471	0.0941932
$352$	5.04427	0.268861
$353$	−6.07362	−0.323266	−0.161633	−	0.986851i	$-0.551676\pi$
$353$	−6.07362	−0.323266	−0.161633	+	0.986851i	$0.551676\pi$
$354$	−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	$-0.935719\pi$
$367$	−37.5359	−1.95936	−0.979678	+	0.200574i	$0.935719\pi$
$368$	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	$-0.714143\pi$
$383$	−24.3901	−1.24628	−0.623139	+	0.782111i	$0.714143\pi$
$384$	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	$-0.483008\pi$
$397$	2.12627	0.106714	0.0533571	+	0.998575i	$0.483008\pi$
$398$	−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	$-0.474054\pi$
$409$	3.29331	0.162844	0.0814218	+	0.996680i	$0.474054\pi$
$410$	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	$-0.775320\pi$
$419$	−31.1570	−1.52212	−0.761059	+	0.648682i	$0.775320\pi$
$420$	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	$-0.198724\pi$
$433$	33.7669	1.62273	0.811366	+	0.584539i	$0.198724\pi$
$434$	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	$-0.410173\pi$
$439$	11.6691	0.556936	0.278468	+	0.960446i	$0.410173\pi$
$440$	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	$-0.782464\pi$
$461$	−33.2981	−1.55085	−0.775424	+	0.631440i	$0.782464\pi$
$462$	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	$-0.613978\pi$
$467$	−15.1474	−0.700937	−0.350469	+	0.936574i	$0.613978\pi$
$468$	−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	$-0.418015\pi$
$479$	11.1498	0.509449	0.254725	+	0.967014i	$0.418015\pi$
$480$	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	$-0.565924\pi$
$503$	−9.22355	−0.411258	−0.205629	+	0.978630i	$0.565924\pi$
$504$	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	$-0.369865\pi$
$509$	17.9377	0.795074	0.397537	+	0.917586i	$0.369865\pi$
$510$	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	$-0.446410\pi$
$521$	7.64950	0.335131	0.167565	+	0.985861i	$0.446410\pi$
$522$	−15.6367	−0.684399
$523$	−29.1271	−1.27364	−0.636820	−	0.771012i	$-0.719751\pi$
$523$	−29.1271	−1.27364	−0.636820	+	0.771012i	$0.719751\pi$
$524$	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	$-0.179222\pi$
$563$	40.1298	1.69127	0.845635	+	0.533762i	$0.179222\pi$
$564$	−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	$-0.302801\pi$
$577$	27.8951	1.16129	0.580645	+	0.814157i	$0.302801\pi$
$578$	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	$-0.763073\pi$
$587$	−35.6416	−1.47109	−0.735543	+	0.677478i	$0.763073\pi$
$588$	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	$-0.346262\pi$
$593$	22.6188	0.928843	0.464421	+	0.885614i	$0.346262\pi$
$594$	−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	$-0.869488\pi$
$601$	−44.9667	−1.83423	−0.917114	+	0.398624i	$0.869488\pi$
$602$	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	$-0.209712\pi$
$607$	38.9620	1.58142	0.790710	+	0.612191i	$0.209712\pi$
$608$	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	$-0.701964\pi$
$619$	−29.4956	−1.18553	−0.592765	+	0.805375i	$0.701964\pi$
$620$	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	$-0.377728\pi$
$643$	19.0055	0.749506	0.374753	+	0.927125i	$0.377728\pi$
$644$	0	0
$645$	−55.2990	−2.17740
$646$	8.91609	0.350799
$647$	30.3319	1.19247	0.596236	−	0.802810i	$-0.296662\pi$
$647$	30.3319	1.19247	0.596236	+	0.802810i	$0.296662\pi$
$648$	−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	$-0.558831\pi$
$661$	−9.44963	−0.367548	−0.183774	+	0.982969i	$0.558831\pi$
$662$	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	$-0.409962\pi$
$677$	14.5243	0.558214	0.279107	+	0.960260i	$0.409962\pi$
$678$	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	$-0.449133\pi$
$691$	8.36579	0.318250	0.159125	+	0.987258i	$0.449133\pi$
$692$	−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	$-0.620414\pi$
$719$	−19.8068	−0.738667	−0.369334	+	0.929297i	$0.620414\pi$
$720$	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	$-0.469559\pi$
$727$	5.14920	0.190973	0.0954867	+	0.995431i	$0.469559\pi$
$728$	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	$-0.461620\pi$
$733$	6.51303	0.240564	0.120282	+	0.992740i	$0.461620\pi$
$734$	−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	$-0.835939\pi$
$761$	−48.0050	−1.74018	−0.870090	+	0.492893i	$0.835939\pi$
$762$	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	$-0.445112\pi$
$769$	9.51632	0.343167	0.171584	+	0.985170i	$0.445112\pi$
$770$	0	0
$771$	−20.3662	−0.733472
$772$	−24.0620	−0.866012
$773$	9.17532	0.330013	0.165007	−	0.986292i	$-0.447235\pi$
$773$	9.17532	0.330013	0.165007	+	0.986292i	$0.447235\pi$
$774$	−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	$-0.439700\pi$
$787$	10.5654	0.376614	0.188307	+	0.982110i	$0.439700\pi$
$788$	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	$-0.756778\pi$
$797$	−40.7660	−1.44401	−0.722003	+	0.691890i	$0.756778\pi$
$798$	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	$-0.631876\pi$
$811$	−22.9277	−0.805102	−0.402551	+	0.915398i	$0.631876\pi$
$812$	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	$-0.527866\pi$
$829$	−5.03481	−0.174866	−0.0874330	+	0.996170i	$0.527866\pi$
$830$	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	$-0.199940\pi$
$839$	46.8736	1.61826	0.809128	+	0.587633i	$0.199940\pi$
$840$	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	$-0.688519\pi$
$853$	−32.6075	−1.11646	−0.558229	+	0.829687i	$0.688519\pi$
$854$	0	0
$855$	14.9379	0.510866
$856$	6.47535	0.221323
$857$	39.1448	1.33716	0.668581	−	0.743640i	$-0.266902\pi$
$857$	39.1448	1.33716	0.668581	+	0.743640i	$0.266902\pi$
$858$	−56.0306	−1.91285
$859$	30.1124	1.02742	0.513710	−	0.857964i	$-0.328271\pi$
$859$	30.1124	1.02742	0.513710	+	0.857964i	$0.328271\pi$
$860$	−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	$-0.693868\pi$
$881$	−33.9613	−1.14418	−0.572092	+	0.820189i	$0.693868\pi$
$882$	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	$-0.332190\pi$
$887$	29.9676	1.00621	0.503106	+	0.864224i	$0.332190\pi$
$888$	−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	$-0.198402\pi$
$929$	49.4961	1.62392	0.811958	+	0.583716i	$0.198402\pi$
$930$	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	$-0.684107\pi$
$937$	−33.4679	−1.09335	−0.546675	+	0.837345i	$0.684107\pi$
$938$	0	0
$939$	−14.9201	−0.486900
$940$	−28.0900	−0.916194
$941$	5.29493	0.172610	0.0863048	−	0.996269i	$-0.472494\pi$
$941$	5.29493	0.172610	0.0863048	+	0.996269i	$0.472494\pi$
$942$	−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	$-0.515570\pi$
$971$	−3.04723	−0.0977902	−0.0488951	+	0.998804i	$0.515570\pi$
$972$	−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	$-0.479477\pi$
$983$	4.04016	0.128861	0.0644305	+	0.997922i	$0.479477\pi$
$984$	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	$-0.214034\pi$
$997$	49.4043	1.56465	0.782324	+	0.622871i	$0.214034\pi$
$998$	−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.bu.1.8		10
7.3	odd	6		574.2.e.h.247.8	yes	20
7.5	odd	6		574.2.e.h.165.8	✓	20
7.6	odd	2		4018.2.a.bt.1.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
574.2.e.h.165.8	✓	20	7.5	odd	6
574.2.e.h.247.8	yes	20	7.3	odd	6
4018.2.a.bt.1.3		10	7.6	odd	2
4018.2.a.bu.1.8		10	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4018 = 2 \cdot 7^{2} \cdot 41 \)
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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