LMFDB - Embedded newform 4018.2.a.bk.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:	$1$
Dimension:	$4$
Coefficient field:	4.4.113481.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 9x^{2} + 3x + 12 $ x^4 - 2x^3 - 9x^2 + 3*x + 12
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
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			$-1.84745$ of defining polynomial
Character	$\chi$	$=$	4018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.30741 q^{5} -1.00000 q^{6} -1.00000 q^{8} -2.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.30741 q^{5} -1.00000 q^{6} -1.00000 q^{8} -2.00000 q^{9} -2.30741 q^{10} +0.260511 q^{11} +1.00000 q^{12} -4.41536 q^{13} +2.30741 q^{15} +1.00000 q^{16} -7.00230 q^{17} +2.00000 q^{18} +7.80285 q^{19} +2.30741 q^{20} -0.260511 q^{22} -1.45996 q^{23} -1.00000 q^{24} +0.324124 q^{25} +4.41536 q^{26} -5.00000 q^{27} -7.10796 q^{29} -2.30741 q^{30} +4.11026 q^{31} -1.00000 q^{32} +0.260511 q^{33} +7.00230 q^{34} -2.00000 q^{36} +7.54234 q^{37} -7.80285 q^{38} -4.41536 q^{39} -2.30741 q^{40} -1.00000 q^{41} +0.199448 q^{43} +0.260511 q^{44} -4.61481 q^{45} +1.45996 q^{46} -4.95541 q^{47} +1.00000 q^{48} -0.324124 q^{50} -7.00230 q^{51} -4.41536 q^{52} +3.84745 q^{53} +5.00000 q^{54} +0.601104 q^{55} +7.80285 q^{57} +7.10796 q^{58} +7.34290 q^{59} +2.30741 q^{60} -14.8330 q^{61} -4.11026 q^{62} +1.00000 q^{64} -10.1880 q^{65} -0.260511 q^{66} +4.56792 q^{67} -7.00230 q^{68} -1.45996 q^{69} -5.63383 q^{71} +2.00000 q^{72} -12.8029 q^{73} -7.54234 q^{74} +0.324124 q^{75} +7.80285 q^{76} +4.41536 q^{78} -1.27723 q^{79} +2.30741 q^{80} +1.00000 q^{81} +1.00000 q^{82} -17.8521 q^{83} -16.1572 q^{85} -0.199448 q^{86} -7.10796 q^{87} -0.260511 q^{88} +8.80285 q^{89} +4.61481 q^{90} -1.45996 q^{92} +4.11026 q^{93} +4.95541 q^{94} +18.0044 q^{95} -1.00000 q^{96} -6.87763 q^{97} -0.521022 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} + 3 q^{5} - 4 q^{6} - 4 q^{8} - 8 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 + 3 * q^5 - 4 * q^6 - 4 * q^8 - 8 * q^9	$ 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} + 3 q^{5} - 4 q^{6} - 4 q^{8} - 8 q^{9} - 3 q^{10} + 4 q^{12} - q^{13} + 3 q^{15} + 4 q^{16} - 3 q^{17} + 8 q^{18} + 2 q^{19} + 3 q^{20} - 9 q^{23} - 4 q^{24} + 19 q^{25} + q^{26} - 20 q^{27} - 18 q^{29} - 3 q^{30} - 19 q^{31} - 4 q^{32} + 3 q^{34} - 8 q^{36} + 2 q^{37} - 2 q^{38} - q^{39} - 3 q^{40} - 4 q^{41} + 5 q^{43} - 6 q^{45} + 9 q^{46} + 4 q^{48} - 19 q^{50} - 3 q^{51} - q^{52} + 6 q^{53} + 20 q^{54} - 6 q^{55} + 2 q^{57} + 18 q^{58} - 3 q^{59} + 3 q^{60} - q^{61} + 19 q^{62} + 4 q^{64} - 24 q^{65} + 11 q^{67} - 3 q^{68} - 9 q^{69} - 9 q^{71} + 8 q^{72} - 22 q^{73} - 2 q^{74} + 19 q^{75} + 2 q^{76} + q^{78} - 28 q^{79} + 3 q^{80} + 4 q^{81} + 4 q^{82} - 12 q^{83} - 24 q^{85} - 5 q^{86} - 18 q^{87} + 6 q^{89} + 6 q^{90} - 9 q^{92} - 19 q^{93} - 27 q^{95} - 4 q^{96} + 11 q^{97}+O(q^{100}) $ 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 + 3 * q^5 - 4 * q^6 - 4 * q^8 - 8 * q^9 - 3 * q^10 + 4 * q^12 - q^13 + 3 * q^15 + 4 * q^16 - 3 * q^17 + 8 * q^18 + 2 * q^19 + 3 * q^20 - 9 * q^23 - 4 * q^24 + 19 * q^25 + q^26 - 20 * q^27 - 18 * q^29 - 3 * q^30 - 19 * q^31 - 4 * q^32 + 3 * q^34 - 8 * q^36 + 2 * q^37 - 2 * q^38 - q^39 - 3 * q^40 - 4 * q^41 + 5 * q^43 - 6 * q^45 + 9 * q^46 + 4 * q^48 - 19 * q^50 - 3 * q^51 - q^52 + 6 * q^53 + 20 * q^54 - 6 * q^55 + 2 * q^57 + 18 * q^58 - 3 * q^59 + 3 * q^60 - q^61 + 19 * q^62 + 4 * q^64 - 24 * q^65 + 11 * q^67 - 3 * q^68 - 9 * q^69 - 9 * q^71 + 8 * q^72 - 22 * q^73 - 2 * q^74 + 19 * q^75 + 2 * q^76 + q^78 - 28 * q^79 + 3 * q^80 + 4 * q^81 + 4 * q^82 - 12 * q^83 - 24 * q^85 - 5 * q^86 - 18 * q^87 + 6 * q^89 + 6 * q^90 - 9 * q^92 - 19 * q^93 - 27 * q^95 - 4 * q^96 + 11 * q^97

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350	0.288675	−	0.957427i	$-0.406785\pi$
$3$	1.00000	0.577350	0.288675	+	0.957427i	$0.406785\pi$
$4$	1.00000	0.500000
$5$	2.30741	1.03190	0.515952	−	0.856618i	$-0.327438\pi$
$5$	2.30741	1.03190	0.515952	+	0.856618i	$0.327438\pi$
$6$	−1.00000	−0.408248
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	−2.00000	−0.666667
$10$	−2.30741	−0.729666
$11$	0.260511	0.0785470	0.0392735	−	0.999228i	$-0.487496\pi$
$11$	0.260511	0.0785470	0.0392735	+	0.999228i	$0.487496\pi$
$12$	1.00000	0.288675
$13$	−4.41536	−1.22460	−0.612301	−	0.790625i	$-0.709756\pi$
$13$	−4.41536	−1.22460	−0.612301	+	0.790625i	$0.709756\pi$
$14$	0	0
$15$	2.30741	0.595770
$16$	1.00000	0.250000
$17$	−7.00230	−1.69831	−0.849154	−	0.528146i	$-0.822888\pi$
$17$	−7.00230	−1.69831	−0.849154	+	0.528146i	$0.822888\pi$
$18$	2.00000	0.471405
$19$	7.80285	1.79010	0.895049	−	0.445968i	$-0.147141\pi$
$19$	7.80285	1.79010	0.895049	+	0.445968i	$0.147141\pi$
$20$	2.30741	0.515952
$21$	0	0
$22$	−0.260511	−0.0555411
$23$	−1.45996	−0.304422	−0.152211	−	0.988348i	$-0.548639\pi$
$23$	−1.45996	−0.304422	−0.152211	+	0.988348i	$0.548639\pi$
$24$	−1.00000	−0.204124
$25$	0.324124	0.0648248
$26$	4.41536	0.865924
$27$	−5.00000	−0.962250
$28$	0	0
$29$	−7.10796	−1.31991	−0.659957	−	0.751303i	$-0.729426\pi$
$29$	−7.10796	−1.31991	−0.659957	+	0.751303i	$0.729426\pi$
$30$	−2.30741	−0.421273
$31$	4.11026	0.738225	0.369112	−	0.929385i	$-0.379662\pi$
$31$	4.11026	0.738225	0.369112	+	0.929385i	$0.379662\pi$
$32$	−1.00000	−0.176777
$33$	0.260511	0.0453491
$34$	7.00230	1.20088
$35$	0	0
$36$	−2.00000	−0.333333
$37$	7.54234	1.23995	0.619977	−	0.784620i	$-0.287142\pi$
$37$	7.54234	1.23995	0.619977	+	0.784620i	$0.287142\pi$
$38$	−7.80285	−1.26579
$39$	−4.41536	−0.707024
$40$	−2.30741	−0.364833
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	0.199448	0.0304155	0.0152078	−	0.999884i	$-0.495159\pi$
$43$	0.199448	0.0304155	0.0152078	+	0.999884i	$0.495159\pi$
$44$	0.260511	0.0392735
$45$	−4.61481	−0.687936
$46$	1.45996	0.215259
$47$	−4.95541	−0.722820	−0.361410	−	0.932407i	$-0.617705\pi$
$47$	−4.95541	−0.722820	−0.361410	+	0.932407i	$0.617705\pi$
$48$	1.00000	0.144338
$49$	0	0
$50$	−0.324124	−0.0458381
$51$	−7.00230	−0.980518
$52$	−4.41536	−0.612301
$53$	3.84745	0.528488	0.264244	−	0.964456i	$-0.414878\pi$
$53$	3.84745	0.528488	0.264244	+	0.964456i	$0.414878\pi$
$54$	5.00000	0.680414
$55$	0.601104	0.0810529
$56$	0	0
$57$	7.80285	1.03351
$58$	7.10796	0.933321
$59$	7.34290	0.955964	0.477982	−	0.878370i	$-0.341368\pi$
$59$	7.34290	0.955964	0.477982	+	0.878370i	$0.341368\pi$
$60$	2.30741	0.297885
$61$	−14.8330	−1.89918	−0.949588	−	0.313502i	$-0.898498\pi$
$61$	−14.8330	−1.89918	−0.949588	+	0.313502i	$0.898498\pi$
$62$	−4.11026	−0.522004
$63$	0	0
$64$	1.00000	0.125000
$65$	−10.1880	−1.26367
$66$	−0.260511	−0.0320667
$67$	4.56792	0.558060	0.279030	−	0.960282i	$-0.409987\pi$
$67$	4.56792	0.558060	0.279030	+	0.960282i	$0.409987\pi$
$68$	−7.00230	−0.849154
$69$	−1.45996	−0.175758
$70$	0	0
$71$	−5.63383	−0.668613	−0.334306	−	0.942464i	$-0.608502\pi$
$71$	−5.63383	−0.668613	−0.334306	+	0.942464i	$0.608502\pi$
$72$	2.00000	0.235702
$73$	−12.8029	−1.49846	−0.749230	−	0.662309i	$-0.769576\pi$
$73$	−12.8029	−1.49846	−0.749230	+	0.662309i	$0.769576\pi$
$74$	−7.54234	−0.876780
$75$	0.324124	0.0374266
$76$	7.80285	0.895049
$77$	0	0
$78$	4.41536	0.499942
$79$	−1.27723	−0.143699	−0.0718497	−	0.997415i	$-0.522890\pi$
$79$	−1.27723	−0.143699	−0.0718497	+	0.997415i	$0.522890\pi$
$80$	2.30741	0.257976
$81$	1.00000	0.111111
$82$	1.00000	0.110432
$83$	−17.8521	−1.95952	−0.979759	−	0.200183i	$-0.935846\pi$
$83$	−17.8521	−1.95952	−0.979759	+	0.200183i	$0.935846\pi$
$84$	0	0
$85$	−16.1572	−1.75249
$86$	−0.199448	−0.0215070
$87$	−7.10796	−0.762053
$88$	−0.260511	−0.0277705
$89$	8.80285	0.933101	0.466550	−	0.884495i	$-0.345497\pi$
$89$	8.80285	0.933101	0.466550	+	0.884495i	$0.345497\pi$
$90$	4.61481	0.486444
$91$	0	0
$92$	−1.45996	−0.152211
$93$	4.11026	0.426214
$94$	4.95541	0.511111
$95$	18.0044	1.84721
$96$	−1.00000	−0.102062
$97$	−6.87763	−0.698317	−0.349159	−	0.937064i	$-0.613533\pi$
$97$	−6.87763	−0.698317	−0.349159	+	0.937064i	$0.613533\pi$
$98$	0	0
$99$	−0.521022	−0.0523646
$100$	0.324124	0.0324124
$101$	−8.38749	−0.834586	−0.417293	−	0.908772i	$-0.637021\pi$
$101$	−8.38749	−0.834586	−0.417293	+	0.908772i	$0.637021\pi$
$102$	7.00230	0.693331
$103$	−0.396345	−0.0390531	−0.0195265	−	0.999809i	$-0.506216\pi$
$103$	−0.396345	−0.0390531	−0.0195265	+	0.999809i	$0.506216\pi$
$104$	4.41536	0.432962
$105$	0	0
$106$	−3.84745	−0.373697
$107$	−17.9577	−1.73604	−0.868019	−	0.496532i	$-0.834607\pi$
$107$	−17.9577	−1.73604	−0.868019	+	0.496532i	$0.834607\pi$
$108$	−5.00000	−0.481125
$109$	−7.50685	−0.719026	−0.359513	−	0.933140i	$-0.617057\pi$
$109$	−7.50685	−0.719026	−0.359513	+	0.933140i	$0.617057\pi$
$110$	−0.601104	−0.0573131
$111$	7.54234	0.715888
$112$	0	0
$113$	−5.15255	−0.484711	−0.242356	−	0.970187i	$-0.577920\pi$
$113$	−5.15255	−0.484711	−0.242356	+	0.970187i	$0.577920\pi$
$114$	−7.80285	−0.730804
$115$	−3.36872	−0.314135
$116$	−7.10796	−0.659957
$117$	8.83073	0.816401
$118$	−7.34290	−0.675968
$119$	0	0
$120$	−2.30741	−0.210636
$121$	−10.9321	−0.993830
$122$	14.8330	1.34292
$123$	−1.00000	−0.0901670
$124$	4.11026	0.369112
$125$	−10.7891	−0.965011
$126$	0	0
$127$	−8.54004	−0.757806	−0.378903	−	0.925436i	$-0.623699\pi$
$127$	−8.54004	−0.757806	−0.378903	+	0.925436i	$0.623699\pi$
$128$	−1.00000	−0.0883883
$129$	0.199448	0.0175604
$130$	10.1880	0.893550
$131$	10.0912	0.881676	0.440838	−	0.897587i	$-0.354681\pi$
$131$	10.0912	0.881676	0.440838	+	0.897587i	$0.354681\pi$
$132$	0.260511	0.0226746
$133$	0	0
$134$	−4.56792	−0.394608
$135$	−11.5370	−0.992950
$136$	7.00230	0.600442
$137$	−18.0211	−1.53964	−0.769822	−	0.638259i	$-0.779655\pi$
$137$	−18.0211	−1.53964	−0.769822	+	0.638259i	$0.779655\pi$
$138$	1.45996	0.124280
$139$	15.5867	1.32205	0.661023	−	0.750366i	$-0.270123\pi$
$139$	15.5867	1.32205	0.661023	+	0.750366i	$0.270123\pi$
$140$	0	0
$141$	−4.95541	−0.417320
$142$	5.63383	0.472781
$143$	−1.15025	−0.0961888
$144$	−2.00000	−0.166667
$145$	−16.4009	−1.36202
$146$	12.8029	1.05957
$147$	0	0
$148$	7.54234	0.619977
$149$	0.140687	0.0115255	0.00576275	−	0.999983i	$-0.498166\pi$
$149$	0.140687	0.0115255	0.00576275	+	0.999983i	$0.498166\pi$
$150$	−0.324124	−0.0264646
$151$	9.31201	0.757801	0.378900	−	0.925437i	$-0.376302\pi$
$151$	9.31201	0.757801	0.378900	+	0.925437i	$0.376302\pi$
$152$	−7.80285	−0.632895
$153$	14.0046	1.13221
$154$	0	0
$155$	9.48404	0.761777
$156$	−4.41536	−0.353512
$157$	3.63153	0.289828	0.144914	−	0.989444i	$-0.453709\pi$
$157$	3.63153	0.289828	0.144914	+	0.989444i	$0.453709\pi$
$158$	1.27723	0.101611
$159$	3.84745	0.305122
$160$	−2.30741	−0.182416
$161$	0	0
$162$	−1.00000	−0.0785674
$163$	13.9268	1.09083	0.545416	−	0.838165i	$-0.316372\pi$
$163$	13.9268	1.09083	0.545416	+	0.838165i	$0.316372\pi$
$164$	−1.00000	−0.0780869
$165$	0.601104	0.0467959
$166$	17.8521	1.38559
$167$	12.6926	0.982182	0.491091	−	0.871108i	$-0.336598\pi$
$167$	12.6926	0.982182	0.491091	+	0.871108i	$0.336598\pi$
$168$	0	0
$169$	6.49545	0.499650
$170$	16.1572	1.23920
$171$	−15.6057	−1.19340
$172$	0.199448	0.0152078
$173$	17.1825	1.30636	0.653180	−	0.757203i	$-0.273435\pi$
$173$	17.1825	1.30636	0.653180	+	0.757203i	$0.273435\pi$
$174$	7.10796	0.538853
$175$	0	0
$176$	0.260511	0.0196367
$177$	7.34290	0.551926
$178$	−8.80285	−0.659802
$179$	−5.38749	−0.402680	−0.201340	−	0.979521i	$-0.564530\pi$
$179$	−5.38749	−0.402680	−0.201340	+	0.979521i	$0.564530\pi$
$180$	−4.61481	−0.343968
$181$	−0.0777809	−0.00578141	−0.00289070	−	0.999996i	$-0.500920\pi$
$181$	−0.0777809	−0.00578141	−0.00289070	+	0.999996i	$0.500920\pi$
$182$	0	0
$183$	−14.8330	−1.09649
$184$	1.45996	0.107630
$185$	17.4033	1.27951
$186$	−4.11026	−0.301379
$187$	−1.82418	−0.133397
$188$	−4.95541	−0.361410
$189$	0	0
$190$	−18.0044	−1.30617
$191$	2.04690	0.148108	0.0740541	−	0.997254i	$-0.476406\pi$
$191$	2.04690	0.148108	0.0740541	+	0.997254i	$0.476406\pi$
$192$	1.00000	0.0721688
$193$	−17.1404	−1.23380	−0.616898	−	0.787043i	$-0.711611\pi$
$193$	−17.1404	−1.23380	−0.616898	+	0.787043i	$0.711611\pi$
$194$	6.87763	0.493785
$195$	−10.1880	−0.729581
$196$	0	0
$197$	−19.2514	−1.37161	−0.685803	−	0.727787i	$-0.740549\pi$
$197$	−19.2514	−1.37161	−0.685803	+	0.727787i	$0.740549\pi$
$198$	0.521022	0.0370274
$199$	2.93894	0.208336	0.104168	−	0.994560i	$-0.466782\pi$
$199$	2.93894	0.208336	0.104168	+	0.994560i	$0.466782\pi$
$200$	−0.324124	−0.0229190
$201$	4.56792	0.322196
$202$	8.38749	0.590142
$203$	0	0
$204$	−7.00230	−0.490259
$205$	−2.30741	−0.161156
$206$	0.396345	0.0276147
$207$	2.91992	0.202948
$208$	−4.41536	−0.306150
$209$	2.03273	0.140607
$210$	0	0
$211$	21.2294	1.46149	0.730745	−	0.682650i	$-0.239173\pi$
$211$	21.2294	1.46149	0.730745	+	0.682650i	$0.239173\pi$
$212$	3.84745	0.264244
$213$	−5.63383	−0.386024
$214$	17.9577	1.22756
$215$	0.460207	0.0313859
$216$	5.00000	0.340207
$217$	0	0
$218$	7.50685	0.508428
$219$	−12.8029	−0.865137
$220$	0.601104	0.0405264
$221$	30.9177	2.07975
$222$	−7.54234	−0.506209
$223$	−0.398896	−0.0267120	−0.0133560	−	0.999911i	$-0.504251\pi$
$223$	−0.398896	−0.0267120	−0.0133560	+	0.999911i	$0.504251\pi$
$224$	0	0
$225$	−0.648248	−0.0432166
$226$	5.15255	0.342743
$227$	6.49800	0.431287	0.215644	−	0.976472i	$-0.430815\pi$
$227$	6.49800	0.431287	0.215644	+	0.976472i	$0.430815\pi$
$228$	7.80285	0.516757
$229$	−24.5142	−1.61995	−0.809973	−	0.586468i	$-0.800518\pi$
$229$	−24.5142	−1.61995	−0.809973	+	0.586468i	$0.800518\pi$
$230$	3.36872	0.222127
$231$	0	0
$232$	7.10796	0.466660
$233$	7.37537	0.483177	0.241588	−	0.970379i	$-0.422332\pi$
$233$	7.37537	0.483177	0.241588	+	0.970379i	$0.422332\pi$
$234$	−8.83073	−0.577283
$235$	−11.4341	−0.745881
$236$	7.34290	0.477982
$237$	−1.27723	−0.0829649
$238$	0	0
$239$	−5.55651	−0.359421	−0.179710	−	0.983720i	$-0.557516\pi$
$239$	−5.55651	−0.359421	−0.179710	+	0.983720i	$0.557516\pi$
$240$	2.30741	0.148942
$241$	0.614813	0.0396036	0.0198018	−	0.999804i	$-0.493696\pi$
$241$	0.614813	0.0396036	0.0198018	+	0.999804i	$0.493696\pi$
$242$	10.9321	0.702744
$243$	16.0000	1.02640
$244$	−14.8330	−0.949588
$245$	0	0
$246$	1.00000	0.0637577
$247$	−34.4524	−2.19216
$248$	−4.11026	−0.261002
$249$	−17.8521	−1.13133
$250$	10.7891	0.682365
$251$	8.35405	0.527303	0.263652	−	0.964618i	$-0.415073\pi$
$251$	8.35405	0.527303	0.263652	+	0.964618i	$0.415073\pi$
$252$	0	0
$253$	−0.380335	−0.0239115
$254$	8.54004	0.535850
$255$	−16.1572	−1.01180
$256$	1.00000	0.0625000
$257$	22.3807	1.39607	0.698034	−	0.716064i	$-0.254058\pi$
$257$	22.3807	1.39607	0.698034	+	0.716064i	$0.254058\pi$
$258$	−0.199448	−0.0124171
$259$	0	0
$260$	−10.1880	−0.631835
$261$	14.2159	0.879943
$262$	−10.0912	−0.623439
$263$	−2.80285	−0.172831	−0.0864157	−	0.996259i	$-0.527541\pi$
$263$	−2.80285	−0.172831	−0.0864157	+	0.996259i	$0.527541\pi$
$264$	−0.260511	−0.0160333
$265$	8.87763	0.545348
$266$	0	0
$267$	8.80285	0.538726
$268$	4.56792	0.279030
$269$	23.0135	1.40316	0.701578	−	0.712593i	$-0.252479\pi$
$269$	23.0135	1.40316	0.701578	+	0.712593i	$0.252479\pi$
$270$	11.5370	0.702121
$271$	15.8753	0.964357	0.482179	−	0.876073i	$-0.339846\pi$
$271$	15.8753	0.964357	0.482179	+	0.876073i	$0.339846\pi$
$272$	−7.00230	−0.424577
$273$	0	0
$274$	18.0211	1.08869
$275$	0.0844379	0.00509180
$276$	−1.45996	−0.0878792
$277$	−31.1706	−1.87286	−0.936430	−	0.350853i	$-0.885892\pi$
$277$	−31.1706	−1.87286	−0.936430	+	0.350853i	$0.885892\pi$
$278$	−15.5867	−0.934827
$279$	−8.22052	−0.492150
$280$	0	0
$281$	2.83374	0.169047	0.0845234	−	0.996421i	$-0.473063\pi$
$281$	2.83374	0.169047	0.0845234	+	0.996421i	$0.473063\pi$
$282$	4.95541	0.295090
$283$	−29.4413	−1.75010	−0.875052	−	0.484030i	$-0.839173\pi$
$283$	−29.4413	−1.75010	−0.875052	+	0.484030i	$0.839173\pi$
$284$	−5.63383	−0.334306
$285$	18.0044	1.06649
$286$	1.15025	0.0680157
$287$	0	0
$288$	2.00000	0.117851
$289$	32.0322	1.88425
$290$	16.4009	0.963097
$291$	−6.87763	−0.403174
$292$	−12.8029	−0.749230
$293$	3.90196	0.227955	0.113977	−	0.993483i	$-0.463641\pi$
$293$	3.90196	0.227955	0.113977	+	0.993483i	$0.463641\pi$
$294$	0	0
$295$	16.9430	0.986462
$296$	−7.54234	−0.438390
$297$	−1.30255	−0.0755819
$298$	−0.140687	−0.00814976
$299$	6.44625	0.372796
$300$	0.324124	0.0187133
$301$	0	0
$302$	−9.31201	−0.535846
$303$	−8.38749	−0.481849
$304$	7.80285	0.447524
$305$	−34.2258	−1.95977
$306$	−14.0046	−0.800590
$307$	16.7631	0.956721	0.478361	−	0.878163i	$-0.341231\pi$
$307$	16.7631	0.956721	0.478361	+	0.878163i	$0.341231\pi$
$308$	0	0
$309$	−0.396345	−0.0225473
$310$	−9.48404	−0.538657
$311$	4.32618	0.245315	0.122658	−	0.992449i	$-0.460858\pi$
$311$	4.32618	0.245315	0.122658	+	0.992449i	$0.460858\pi$
$312$	4.41536	0.249971
$313$	10.1850	0.575692	0.287846	−	0.957677i	$-0.407061\pi$
$313$	10.1850	0.575692	0.287846	+	0.957677i	$0.407061\pi$
$314$	−3.63153	−0.204939
$315$	0	0
$316$	−1.27723	−0.0718497
$317$	−10.4977	−0.589612	−0.294806	−	0.955557i	$-0.595255\pi$
$317$	−10.4977	−0.589612	−0.294806	+	0.955557i	$0.595255\pi$
$318$	−3.84745	−0.215754
$319$	−1.85170	−0.103675
$320$	2.30741	0.128988
$321$	−17.9577	−1.00230
$322$	0	0
$323$	−54.6379	−3.04014
$324$	1.00000	0.0555556
$325$	−1.43113	−0.0793846
$326$	−13.9268	−0.771335
$327$	−7.50685	−0.415130
$328$	1.00000	0.0552158
$329$	0	0
$330$	−0.601104	−0.0330897
$331$	−28.8209	−1.58414	−0.792070	−	0.610430i	$-0.790997\pi$
$331$	−28.8209	−1.58414	−0.792070	+	0.610430i	$0.790997\pi$
$332$	−17.8521	−0.979759
$333$	−15.0847	−0.826636
$334$	−12.6926	−0.694508
$335$	10.5400	0.575864
$336$	0	0
$337$	22.4666	1.22383	0.611917	−	0.790922i	$-0.290399\pi$
$337$	22.4666	1.22383	0.611917	+	0.790922i	$0.290399\pi$
$338$	−6.49545	−0.353306
$339$	−5.15255	−0.279848
$340$	−16.1572	−0.876245
$341$	1.07077	0.0579853
$342$	15.6057	0.843860
$343$	0	0
$344$	−0.199448	−0.0107535
$345$	−3.36872	−0.181366
$346$	−17.1825	−0.923736
$347$	5.96302	0.320112	0.160056	−	0.987108i	$-0.448833\pi$
$347$	5.96302	0.320112	0.160056	+	0.987108i	$0.448833\pi$
$348$	−7.10796	−0.381027
$349$	−29.4413	−1.57596	−0.787978	−	0.615703i	$-0.788872\pi$
$349$	−29.4413	−1.57596	−0.787978	+	0.615703i	$0.788872\pi$
$350$	0	0
$351$	22.0768	1.17837
$352$	−0.260511	−0.0138853
$353$	1.16697	0.0621115	0.0310557	−	0.999518i	$-0.490113\pi$
$353$	1.16697	0.0621115	0.0310557	+	0.999518i	$0.490113\pi$
$354$	−7.34290	−0.390270
$355$	−12.9995	−0.689944
$356$	8.80285	0.466550
$357$	0	0
$358$	5.38749	0.284738
$359$	−21.6336	−1.14178	−0.570888	−	0.821028i	$-0.693401\pi$
$359$	−21.6336	−1.14178	−0.570888	+	0.821028i	$0.693401\pi$
$360$	4.61481	0.243222
$361$	41.8845	2.20445
$362$	0.0777809	0.00408807
$363$	−10.9321	−0.573788
$364$	0	0
$365$	−29.5414	−1.54627
$366$	14.8330	0.775335
$367$	−4.96001	−0.258910	−0.129455	−	0.991585i	$-0.541323\pi$
$367$	−4.96001	−0.258910	−0.129455	+	0.991585i	$0.541323\pi$
$368$	−1.45996	−0.0761056
$369$	2.00000	0.104116
$370$	−17.4033	−0.904752
$371$	0	0
$372$	4.11026	0.213107
$373$	16.4253	0.850469	0.425234	−	0.905083i	$-0.360192\pi$
$373$	16.4253	0.850469	0.425234	+	0.905083i	$0.360192\pi$
$374$	1.82418	0.0943259
$375$	−10.7891	−0.557149
$376$	4.95541	0.255556
$377$	31.3842	1.61637
$378$	0	0
$379$	−27.2950	−1.40205	−0.701026	−	0.713136i	$-0.747274\pi$
$379$	−27.2950	−1.40205	−0.701026	+	0.713136i	$0.747274\pi$
$380$	18.0044	0.923604
$381$	−8.54004	−0.437520
$382$	−2.04690	−0.104728
$383$	8.04158	0.410906	0.205453	−	0.978667i	$-0.434133\pi$
$383$	8.04158	0.410906	0.205453	+	0.978667i	$0.434133\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	17.1404	0.872425
$387$	−0.398896	−0.0202770
$388$	−6.87763	−0.349159
$389$	−14.4017	−0.730193	−0.365096	−	0.930970i	$-0.618964\pi$
$389$	−14.4017	−0.730193	−0.365096	+	0.930970i	$0.618964\pi$
$390$	10.1880	0.515892
$391$	10.2231	0.517003
$392$	0	0
$393$	10.0912	0.509036
$394$	19.2514	0.969872
$395$	−2.94709	−0.148284
$396$	−0.521022	−0.0261823
$397$	11.2930	0.566779	0.283389	−	0.959005i	$-0.408541\pi$
$397$	11.2930	0.566779	0.283389	+	0.959005i	$0.408541\pi$
$398$	−2.93894	−0.147316
$399$	0	0
$400$	0.324124	0.0162062
$401$	−23.2598	−1.16154	−0.580770	−	0.814068i	$-0.697248\pi$
$401$	−23.2598	−1.16154	−0.580770	+	0.814068i	$0.697248\pi$
$402$	−4.56792	−0.227827
$403$	−18.1483	−0.904031
$404$	−8.38749	−0.417293
$405$	2.30741	0.114656
$406$	0	0
$407$	1.96486	0.0973946
$408$	7.00230	0.346666
$409$	27.3236	1.35107	0.675533	−	0.737330i	$-0.263913\pi$
$409$	27.3236	1.35107	0.675533	+	0.737330i	$0.263913\pi$
$410$	2.30741	0.113955
$411$	−18.0211	−0.888914
$412$	−0.396345	−0.0195265
$413$	0	0
$414$	−2.91992	−0.143506
$415$	−41.1919	−2.02203
$416$	4.41536	0.216481
$417$	15.5867	0.763283
$418$	−2.03273	−0.0994240
$419$	−31.8655	−1.55673	−0.778366	−	0.627811i	$-0.783951\pi$
$419$	−31.8655	−1.55673	−0.778366	+	0.627811i	$0.783951\pi$
$420$	0	0
$421$	25.1595	1.22620	0.613098	−	0.790006i	$-0.289923\pi$
$421$	25.1595	1.22620	0.613098	+	0.790006i	$0.289923\pi$
$422$	−21.2294	−1.03343
$423$	9.91081	0.481880
$424$	−3.84745	−0.186849
$425$	−2.26962	−0.110093
$426$	5.63383	0.272960
$427$	0	0
$428$	−17.9577	−0.868019
$429$	−1.15025	−0.0555346
$430$	−0.460207	−0.0221932
$431$	9.17593	0.441989	0.220994	−	0.975275i	$-0.429070\pi$
$431$	9.17593	0.441989	0.220994	+	0.975275i	$0.429070\pi$
$432$	−5.00000	−0.240563
$433$	7.16141	0.344155	0.172078	−	0.985083i	$-0.444952\pi$
$433$	7.16141	0.344155	0.172078	+	0.985083i	$0.444952\pi$
$434$	0	0
$435$	−16.4009	−0.786365
$436$	−7.50685	−0.359513
$437$	−11.3918	−0.544946
$438$	12.8029	0.611744
$439$	33.2839	1.58855	0.794277	−	0.607556i	$-0.207850\pi$
$439$	33.2839	1.58855	0.794277	+	0.607556i	$0.207850\pi$
$440$	−0.601104	−0.0286565
$441$	0	0
$442$	−30.9177	−1.47061
$443$	−6.62668	−0.314843	−0.157421	−	0.987532i	$-0.550318\pi$
$443$	−6.62668	−0.314843	−0.157421	+	0.987532i	$0.550318\pi$
$444$	7.54234	0.357944
$445$	20.3118	0.962870
$446$	0.398896	0.0188883
$447$	0.140687	0.00665425
$448$	0	0
$449$	−11.9858	−0.565646	−0.282823	−	0.959172i	$-0.591271\pi$
$449$	−11.9858	−0.565646	−0.282823	+	0.959172i	$0.591271\pi$
$450$	0.648248	0.0305587
$451$	−0.260511	−0.0122670
$452$	−5.15255	−0.242356
$453$	9.31201	0.437516
$454$	−6.49800	−0.304966
$455$	0	0
$456$	−7.80285	−0.365402
$457$	27.2461	1.27452	0.637259	−	0.770649i	$-0.280068\pi$
$457$	27.2461	1.27452	0.637259	+	0.770649i	$0.280068\pi$
$458$	24.5142	1.14547
$459$	35.0115	1.63420
$460$	−3.36872	−0.157067
$461$	36.7278	1.71059	0.855293	−	0.518145i	$-0.173377\pi$
$461$	36.7278	1.71059	0.855293	+	0.518145i	$0.173377\pi$
$462$	0	0
$463$	−4.65561	−0.216365	−0.108182	−	0.994131i	$-0.534503\pi$
$463$	−4.65561	−0.216365	−0.108182	+	0.994131i	$0.534503\pi$
$464$	−7.10796	−0.329979
$465$	9.48404	0.439812
$466$	−7.37537	−0.341658
$467$	−18.7225	−0.866375	−0.433188	−	0.901304i	$-0.642611\pi$
$467$	−18.7225	−0.866375	−0.433188	+	0.901304i	$0.642611\pi$
$468$	8.83073	0.408201
$469$	0	0
$470$	11.4341	0.527417
$471$	3.63153	0.167332
$472$	−7.34290	−0.337984
$473$	0.0519583	0.00238905
$474$	1.27723	0.0586651
$475$	2.52909	0.116043
$476$	0	0
$477$	−7.69490	−0.352325
$478$	5.55651	0.254149
$479$	2.65686	0.121395	0.0606974	−	0.998156i	$-0.480668\pi$
$479$	2.65686	0.121395	0.0606974	+	0.998156i	$0.480668\pi$
$480$	−2.30741	−0.105318
$481$	−33.3022	−1.51845
$482$	−0.614813	−0.0280040
$483$	0	0
$484$	−10.9321	−0.496915
$485$	−15.8695	−0.720596
$486$	−16.0000	−0.725775
$487$	−32.9157	−1.49155	−0.745776	−	0.666197i	$-0.767921\pi$
$487$	−32.9157	−1.49155	−0.745776	+	0.666197i	$0.767921\pi$
$488$	14.8330	0.671460
$489$	13.9268	0.629793
$490$	0	0
$491$	−23.9180	−1.07940	−0.539701	−	0.841857i	$-0.681463\pi$
$491$	−23.9180	−1.07940	−0.539701	+	0.841857i	$0.681463\pi$
$492$	−1.00000	−0.0450835
$493$	49.7721	2.24162
$494$	34.4524	1.55009
$495$	−1.20221	−0.0540353
$496$	4.11026	0.184556
$497$	0	0
$498$	17.8521	0.799970
$499$	42.3384	1.89533	0.947663	−	0.319271i	$-0.103438\pi$
$499$	42.3384	1.89533	0.947663	+	0.319271i	$0.103438\pi$
$500$	−10.7891	−0.482505
$501$	12.6926	0.567063
$502$	−8.35405	−0.372860
$503$	−23.5540	−1.05022	−0.525110	−	0.851035i	$-0.675976\pi$
$503$	−23.5540	−1.05022	−0.525110	+	0.851035i	$0.675976\pi$
$504$	0	0
$505$	−19.3533	−0.861213
$506$	0.380335	0.0169080
$507$	6.49545	0.288473
$508$	−8.54004	−0.378903
$509$	1.59809	0.0708343	0.0354172	−	0.999373i	$-0.488724\pi$
$509$	1.59809	0.0708343	0.0354172	+	0.999373i	$0.488724\pi$
$510$	16.1572	0.715451
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	−39.0143	−1.72252
$514$	−22.3807	−0.987170
$515$	−0.914530	−0.0402990
$516$	0.199448	0.00878020
$517$	−1.29094	−0.0567753
$518$	0	0
$519$	17.1825	0.754227
$520$	10.1880	0.446775
$521$	11.3796	0.498551	0.249275	−	0.968433i	$-0.419808\pi$
$521$	11.3796	0.498551	0.249275	+	0.968433i	$0.419808\pi$
$522$	−14.2159	−0.622214
$523$	−17.2795	−0.755581	−0.377791	−	0.925891i	$-0.623316\pi$
$523$	−17.2795	−0.755581	−0.377791	+	0.925891i	$0.623316\pi$
$524$	10.0912	0.440838
$525$	0	0
$526$	2.80285	0.122210
$527$	−28.7813	−1.25373
$528$	0.260511	0.0113373
$529$	−20.8685	−0.907327
$530$	−8.87763	−0.385619
$531$	−14.6858	−0.637309
$532$	0	0
$533$	4.41536	0.191251
$534$	−8.80285	−0.380937
$535$	−41.4357	−1.79142
$536$	−4.56792	−0.197304
$537$	−5.38749	−0.232487
$538$	−23.0135	−0.992181
$539$	0	0
$540$	−11.5370	−0.496475
$541$	14.5983	0.627632	0.313816	−	0.949484i	$-0.398393\pi$
$541$	14.5983	0.627632	0.313816	+	0.949484i	$0.398393\pi$
$542$	−15.8753	−0.681904
$543$	−0.0777809	−0.00333790
$544$	7.00230	0.300221
$545$	−17.3214	−0.741966
$546$	0	0
$547$	20.6942	0.884820	0.442410	−	0.896813i	$-0.354124\pi$
$547$	20.6942	0.884820	0.442410	+	0.896813i	$0.354124\pi$
$548$	−18.0211	−0.769822
$549$	29.6661	1.26612
$550$	−0.0844379	−0.00360044
$551$	−55.4624	−2.36278
$552$	1.45996	0.0621400
$553$	0	0
$554$	31.1706	1.32431
$555$	17.4033	0.738727
$556$	15.5867	0.661023
$557$	38.5158	1.63197	0.815984	−	0.578075i	$-0.196196\pi$
$557$	38.5158	1.63197	0.815984	+	0.578075i	$0.196196\pi$
$558$	8.22052	0.348002
$559$	−0.880635	−0.0372469
$560$	0	0
$561$	−1.82418	−0.0770168
$562$	−2.83374	−0.119534
$563$	8.89434	0.374852	0.187426	−	0.982279i	$-0.439986\pi$
$563$	8.89434	0.374852	0.187426	+	0.982279i	$0.439986\pi$
$564$	−4.95541	−0.208660
$565$	−11.8890	−0.500175
$566$	29.4413	1.23751
$567$	0	0
$568$	5.63383	0.236390
$569$	−37.1192	−1.55612	−0.778059	−	0.628191i	$-0.783796\pi$
$569$	−37.1192	−1.55612	−0.778059	+	0.628191i	$0.783796\pi$
$570$	−18.0044	−0.754119
$571$	−21.8776	−0.915550	−0.457775	−	0.889068i	$-0.651353\pi$
$571$	−21.8776	−0.915550	−0.457775	+	0.889068i	$0.651353\pi$
$572$	−1.15025	−0.0480944
$573$	2.04690	0.0855103
$574$	0	0
$575$	−0.473208	−0.0197341
$576$	−2.00000	−0.0833333
$577$	32.3113	1.34514	0.672569	−	0.740035i	$-0.265191\pi$
$577$	32.3113	1.34514	0.672569	+	0.740035i	$0.265191\pi$
$578$	−32.0322	−1.33237
$579$	−17.1404	−0.712332
$580$	−16.4009	−0.681012
$581$	0	0
$582$	6.87763	0.285087
$583$	1.00230	0.0415111
$584$	12.8029	0.529786
$585$	20.3761	0.842447
$586$	−3.90196	−0.161188
$587$	−46.4826	−1.91854	−0.959272	−	0.282485i	$-0.908841\pi$
$587$	−46.4826	−1.91854	−0.959272	+	0.282485i	$0.908841\pi$
$588$	0	0
$589$	32.0718	1.32149
$590$	−16.9430	−0.697534
$591$	−19.2514	−0.791897
$592$	7.54234	0.309988
$593$	−36.4715	−1.49770	−0.748852	−	0.662737i	$-0.769395\pi$
$593$	−36.4715	−1.49770	−0.748852	+	0.662737i	$0.769395\pi$
$594$	1.30255	0.0534444
$595$	0	0
$596$	0.140687	0.00576275
$597$	2.93894	0.120283
$598$	−6.44625	−0.263607
$599$	−28.9993	−1.18488	−0.592439	−	0.805615i	$-0.701835\pi$
$599$	−28.9993	−1.18488	−0.592439	+	0.805615i	$0.701835\pi$
$600$	−0.324124	−0.0132323
$601$	15.9932	0.652376	0.326188	−	0.945305i	$-0.394236\pi$
$601$	15.9932	0.652376	0.326188	+	0.945305i	$0.394236\pi$
$602$	0	0
$603$	−9.13583	−0.372040
$604$	9.31201	0.378900
$605$	−25.2249	−1.02554
$606$	8.38749	0.340718
$607$	12.4360	0.504761	0.252380	−	0.967628i	$-0.418787\pi$
$607$	12.4360	0.504761	0.252380	+	0.967628i	$0.418787\pi$
$608$	−7.80285	−0.316448
$609$	0	0
$610$	34.2258	1.38576
$611$	21.8799	0.885167
$612$	14.0046	0.566103
$613$	−21.7385	−0.878011	−0.439006	−	0.898484i	$-0.644669\pi$
$613$	−21.7385	−0.878011	−0.439006	+	0.898484i	$0.644669\pi$
$614$	−16.7631	−0.676504
$615$	−2.30741	−0.0930436
$616$	0	0
$617$	25.5328	1.02791	0.513955	−	0.857817i	$-0.328180\pi$
$617$	25.5328	1.02791	0.513955	+	0.857817i	$0.328180\pi$
$618$	0.396345	0.0159433
$619$	40.2598	1.61818	0.809089	−	0.587686i	$-0.199961\pi$
$619$	40.2598	1.61818	0.809089	+	0.587686i	$0.199961\pi$
$620$	9.48404	0.380888
$621$	7.29979	0.292931
$622$	−4.32618	−0.173464
$623$	0	0
$624$	−4.41536	−0.176756
$625$	−26.5156	−1.06062
$626$	−10.1850	−0.407076
$627$	2.03273	0.0811793
$628$	3.63153	0.144914
$629$	−52.8138	−2.10582
$630$	0	0
$631$	27.3429	1.08850	0.544252	−	0.838922i	$-0.316814\pi$
$631$	27.3429	1.08850	0.544252	+	0.838922i	$0.316814\pi$
$632$	1.27723	0.0508054
$633$	21.2294	0.843792
$634$	10.4977	0.416919
$635$	−19.7053	−0.781983
$636$	3.84745	0.152561
$637$	0	0
$638$	1.85170	0.0733095
$639$	11.2677	0.445742
$640$	−2.30741	−0.0912082
$641$	14.3257	0.565832	0.282916	−	0.959145i	$-0.408698\pi$
$641$	14.3257	0.565832	0.282916	+	0.959145i	$0.408698\pi$
$642$	17.9577	0.708734
$643$	−33.3426	−1.31491	−0.657453	−	0.753496i	$-0.728366\pi$
$643$	−33.3426	−1.31491	−0.657453	+	0.753496i	$0.728366\pi$
$644$	0	0
$645$	0.460207	0.0181206
$646$	54.6379	2.14970
$647$	26.3143	1.03452	0.517261	−	0.855828i	$-0.326952\pi$
$647$	26.3143	1.03452	0.517261	+	0.855828i	$0.326952\pi$
$648$	−1.00000	−0.0392837
$649$	1.91290	0.0750880
$650$	1.43113	0.0561334
$651$	0	0
$652$	13.9268	0.545416
$653$	36.1901	1.41623	0.708114	−	0.706098i	$-0.249546\pi$
$653$	36.1901	1.41623	0.708114	+	0.706098i	$0.249546\pi$
$654$	7.50685	0.293541
$655$	23.2846	0.909804
$656$	−1.00000	−0.0390434
$657$	25.6057	0.998974
$658$	0	0
$659$	5.23008	0.203735	0.101868	−	0.994798i	$-0.467518\pi$
$659$	5.23008	0.203735	0.101868	+	0.994798i	$0.467518\pi$
$660$	0.601104	0.0233980
$661$	−20.3079	−0.789884	−0.394942	−	0.918706i	$-0.629235\pi$
$661$	−20.3079	−0.789884	−0.394942	+	0.918706i	$0.629235\pi$
$662$	28.8209	1.12016
$663$	30.9177	1.20074
$664$	17.8521	0.692794
$665$	0	0
$666$	15.0847	0.584520
$667$	10.3773	0.401812
$668$	12.6926	0.491091
$669$	−0.398896	−0.0154222
$670$	−10.5400	−0.407197
$671$	−3.86417	−0.149174
$672$	0	0
$673$	−15.5001	−0.597483	−0.298742	−	0.954334i	$-0.596567\pi$
$673$	−15.5001	−0.597483	−0.298742	+	0.954334i	$0.596567\pi$
$674$	−22.4666	−0.865382
$675$	−1.62062	−0.0623777
$676$	6.49545	0.249825
$677$	−29.9760	−1.15207	−0.576036	−	0.817424i	$-0.695401\pi$
$677$	−29.9760	−1.15207	−0.576036	+	0.817424i	$0.695401\pi$
$678$	5.15255	0.197883
$679$	0	0
$680$	16.1572	0.619599
$681$	6.49800	0.249004
$682$	−1.07077	−0.0410018
$683$	−42.4803	−1.62546	−0.812732	−	0.582637i	$-0.802021\pi$
$683$	−42.4803	−1.62546	−0.812732	+	0.582637i	$0.802021\pi$
$684$	−15.6057	−0.596699
$685$	−41.5819	−1.58876
$686$	0	0
$687$	−24.5142	−0.935276
$688$	0.199448	0.00760388
$689$	−16.9879	−0.647187
$690$	3.36872	0.128245
$691$	18.3974	0.699870	0.349935	−	0.936774i	$-0.386204\pi$
$691$	18.3974	0.699870	0.349935	+	0.936774i	$0.386204\pi$
$692$	17.1825	0.653180
$693$	0	0
$694$	−5.96302	−0.226353
$695$	35.9648	1.36422
$696$	7.10796	0.269426
$697$	7.00230	0.265231
$698$	29.4413	1.11437
$699$	7.37537	0.278962
$700$	0	0
$701$	−10.0137	−0.378213	−0.189106	−	0.981957i	$-0.560559\pi$
$701$	−10.0137	−0.378213	−0.189106	+	0.981957i	$0.560559\pi$
$702$	−22.0768	−0.833236
$703$	58.8518	2.21964
$704$	0.260511	0.00981837
$705$	−11.4341	−0.430634
$706$	−1.16697	−0.0439194
$707$	0	0
$708$	7.34290	0.275963
$709$	6.87001	0.258009	0.129004	−	0.991644i	$-0.458822\pi$
$709$	6.87001	0.258009	0.129004	+	0.991644i	$0.458822\pi$
$710$	12.9995	0.487864
$711$	2.55446	0.0957996
$712$	−8.80285	−0.329901
$713$	−6.00081	−0.224732
$714$	0	0
$715$	−2.65410	−0.0992575
$716$	−5.38749	−0.201340
$717$	−5.55651	−0.207512
$718$	21.6336	0.807358
$719$	28.3356	1.05674	0.528370	−	0.849014i	$-0.322803\pi$
$719$	28.3356	1.05674	0.528370	+	0.849014i	$0.322803\pi$
$720$	−4.61481	−0.171984
$721$	0	0
$722$	−41.8845	−1.55878
$723$	0.614813	0.0228651
$724$	−0.0777809	−0.00289070
$725$	−2.30386	−0.0855633
$726$	10.9321	0.405730
$727$	40.0459	1.48522	0.742611	−	0.669723i	$-0.233587\pi$
$727$	40.0459	1.48522	0.742611	+	0.669723i	$0.233587\pi$
$728$	0	0
$729$	13.0000	0.481481
$730$	29.5414	1.09338
$731$	−1.39659	−0.0516549
$732$	−14.8330	−0.548245
$733$	−6.39730	−0.236290	−0.118145	−	0.992996i	$-0.537695\pi$
$733$	−6.39730	−0.236290	−0.118145	+	0.992996i	$0.537695\pi$
$734$	4.96001	0.183077
$735$	0	0
$736$	1.45996	0.0538148
$737$	1.18999	0.0438339
$738$	−2.00000	−0.0736210
$739$	−11.3234	−0.416539	−0.208269	−	0.978072i	$-0.566783\pi$
$739$	−11.3234	−0.416539	−0.208269	+	0.978072i	$0.566783\pi$
$740$	17.4033	0.639756
$741$	−34.4524	−1.26564
$742$	0	0
$743$	−27.2466	−0.999579	−0.499790	−	0.866147i	$-0.666589\pi$
$743$	−27.2466	−0.999579	−0.499790	+	0.866147i	$0.666589\pi$
$744$	−4.11026	−0.150689
$745$	0.324621	0.0118932
$746$	−16.4253	−0.601372
$747$	35.7041	1.30634
$748$	−1.82418	−0.0666985
$749$	0	0
$750$	10.7891	0.393964
$751$	−15.9980	−0.583777	−0.291889	−	0.956452i	$-0.594284\pi$
$751$	−15.9980	−0.583777	−0.291889	+	0.956452i	$0.594284\pi$
$752$	−4.95541	−0.180705
$753$	8.35405	0.304439
$754$	−31.3842	−1.14295
$755$	21.4866	0.781977
$756$	0	0
$757$	5.32228	0.193442	0.0967208	−	0.995312i	$-0.469165\pi$
$757$	5.32228	0.193442	0.0967208	+	0.995312i	$0.469165\pi$
$758$	27.2950	0.991401
$759$	−0.380335	−0.0138053
$760$	−18.0044	−0.653087
$761$	0.330927	0.0119961	0.00599805	−	0.999982i	$-0.498091\pi$
$761$	0.330927	0.0119961	0.00599805	+	0.999982i	$0.498091\pi$
$762$	8.54004	0.309373
$763$	0	0
$764$	2.04690	0.0740541
$765$	32.3143	1.16833
$766$	−8.04158	−0.290554
$767$	−32.4216	−1.17067
$768$	1.00000	0.0360844
$769$	−4.06787	−0.146691	−0.0733455	−	0.997307i	$-0.523368\pi$
$769$	−4.06787	−0.146691	−0.0733455	+	0.997307i	$0.523368\pi$
$770$	0	0
$771$	22.3807	0.806021
$772$	−17.1404	−0.616898
$773$	11.5732	0.416260	0.208130	−	0.978101i	$-0.433262\pi$
$773$	11.5732	0.416260	0.208130	+	0.978101i	$0.433262\pi$
$774$	0.398896	0.0143380
$775$	1.33223	0.0478553
$776$	6.87763	0.246892
$777$	0	0
$778$	14.4017	0.516324
$779$	−7.80285	−0.279566
$780$	−10.1880	−0.364790
$781$	−1.46767	−0.0525175
$782$	−10.2231	−0.365576
$783$	35.5398	1.27009
$784$	0	0
$785$	8.37942	0.299074
$786$	−10.0912	−0.359943
$787$	−13.1873	−0.470078	−0.235039	−	0.971986i	$-0.575522\pi$
$787$	−13.1873	−0.470078	−0.235039	+	0.971986i	$0.575522\pi$
$788$	−19.2514	−0.685803
$789$	−2.80285	−0.0997842
$790$	2.94709	0.104853
$791$	0	0
$792$	0.521022	0.0185137
$793$	65.4932	2.32573
$794$	−11.2930	−0.400773
$795$	8.87763	0.314857
$796$	2.93894	0.104168
$797$	−3.34846	−0.118608	−0.0593042	−	0.998240i	$-0.518888\pi$
$797$	−3.34846	−0.118608	−0.0593042	+	0.998240i	$0.518888\pi$
$798$	0	0
$799$	34.6993	1.22757
$800$	−0.324124	−0.0114595
$801$	−17.6057	−0.622067
$802$	23.2598	0.821332
$803$	−3.33528	−0.117700
$804$	4.56792	0.161098
$805$	0	0
$806$	18.1483	0.639247
$807$	23.0135	0.810112
$808$	8.38749	0.295071
$809$	−9.18733	−0.323009	−0.161505	−	0.986872i	$-0.551635\pi$
$809$	−9.18733	−0.323009	−0.161505	+	0.986872i	$0.551635\pi$
$810$	−2.30741	−0.0810740
$811$	18.6709	0.655625	0.327812	−	0.944743i	$-0.393689\pi$
$811$	18.6709	0.655625	0.327812	+	0.944743i	$0.393689\pi$
$812$	0	0
$813$	15.8753	0.556772
$814$	−1.96486	−0.0688684
$815$	32.1348	1.12563
$816$	−7.00230	−0.245130
$817$	1.55626	0.0544467
$818$	−27.3236	−0.955348
$819$	0	0
$820$	−2.30741	−0.0805781
$821$	16.4932	0.575618	0.287809	−	0.957688i	$-0.407073\pi$
$821$	16.4932	0.575618	0.287809	+	0.957688i	$0.407073\pi$
$822$	18.0211	0.628557
$823$	38.6238	1.34634	0.673170	−	0.739488i	$-0.264932\pi$
$823$	38.6238	1.34634	0.673170	+	0.739488i	$0.264932\pi$
$824$	0.396345	0.0138073
$825$	0.0844379	0.00293975
$826$	0	0
$827$	−1.46977	−0.0511089	−0.0255545	−	0.999673i	$-0.508135\pi$
$827$	−1.46977	−0.0511089	−0.0255545	+	0.999673i	$0.508135\pi$
$828$	2.91992	0.101474
$829$	21.3826	0.742650	0.371325	−	0.928503i	$-0.378904\pi$
$829$	21.3826	0.742650	0.371325	+	0.928503i	$0.378904\pi$
$830$	41.1919	1.42979
$831$	−31.1706	−1.08130
$832$	−4.41536	−0.153075
$833$	0	0
$834$	−15.5867	−0.539723
$835$	29.2870	1.01352
$836$	2.03273	0.0703034
$837$	−20.5513	−0.710357
$838$	31.8655	1.10078
$839$	−20.1709	−0.696376	−0.348188	−	0.937425i	$-0.613203\pi$
$839$	−20.1709	−0.696376	−0.348188	+	0.937425i	$0.613203\pi$
$840$	0	0
$841$	21.5231	0.742175
$842$	−25.1595	−0.867052
$843$	2.83374	0.0975992
$844$	21.2294	0.730745
$845$	14.9876	0.515590
$846$	−9.91081	−0.340741
$847$	0	0
$848$	3.84745	0.132122
$849$	−29.4413	−1.01042
$850$	2.26962	0.0778472
$851$	−11.0115	−0.377470
$852$	−5.63383	−0.193012
$853$	4.80817	0.164628	0.0823142	−	0.996606i	$-0.473769\pi$
$853$	4.80817	0.164628	0.0823142	+	0.996606i	$0.473769\pi$
$854$	0	0
$855$	−36.0087	−1.23147
$856$	17.9577	0.613782
$857$	15.5877	0.532467	0.266234	−	0.963909i	$-0.414221\pi$
$857$	15.5877	0.532467	0.266234	+	0.963909i	$0.414221\pi$
$858$	1.15025	0.0392689
$859$	50.2958	1.71607	0.858034	−	0.513592i	$-0.171686\pi$
$859$	50.2958	1.71607	0.858034	+	0.513592i	$0.171686\pi$
$860$	0.460207	0.0156929
$861$	0	0
$862$	−9.17593	−0.312533
$863$	27.4945	0.935923	0.467962	−	0.883749i	$-0.344989\pi$
$863$	27.4945	0.935923	0.467962	+	0.883749i	$0.344989\pi$
$864$	5.00000	0.170103
$865$	39.6470	1.34804
$866$	−7.16141	−0.243355
$867$	32.0322	1.08787
$868$	0	0
$869$	−0.332732	−0.0112872
$870$	16.4009	0.556044
$871$	−20.1690	−0.683401
$872$	7.50685	0.254214
$873$	13.7553	0.465545
$874$	11.3918	0.385335
$875$	0	0
$876$	−12.8029	−0.432568
$877$	44.0492	1.48744	0.743718	−	0.668494i	$-0.233061\pi$
$877$	44.0492	1.48744	0.743718	+	0.668494i	$0.233061\pi$
$878$	−33.2839	−1.12328
$879$	3.90196	0.131610
$880$	0.601104	0.0202632
$881$	−4.87787	−0.164340	−0.0821699	−	0.996618i	$-0.526185\pi$
$881$	−4.87787	−0.164340	−0.0821699	+	0.996618i	$0.526185\pi$
$882$	0	0
$883$	−16.1073	−0.542052	−0.271026	−	0.962572i	$-0.587363\pi$
$883$	−16.1073	−0.542052	−0.271026	+	0.962572i	$0.587363\pi$
$884$	30.9177	1.03988
$885$	16.9430	0.569534
$886$	6.62668	0.222628
$887$	28.4590	0.955560	0.477780	−	0.878480i	$-0.341442\pi$
$887$	28.4590	0.955560	0.477780	+	0.878480i	$0.341442\pi$
$888$	−7.54234	−0.253104
$889$	0	0
$890$	−20.3118	−0.680852
$891$	0.260511	0.00872744
$892$	−0.398896	−0.0133560
$893$	−38.6663	−1.29392
$894$	−0.140687	−0.00470526
$895$	−12.4311	−0.415527
$896$	0	0
$897$	6.44625	0.215234
$898$	11.9858	0.399972
$899$	−29.2156	−0.974394
$900$	−0.648248	−0.0216083
$901$	−26.9410	−0.897535
$902$	0.260511	0.00867406
$903$	0	0
$904$	5.15255	0.171371
$905$	−0.179472	−0.00596585
$906$	−9.31201	−0.309371
$907$	−28.7664	−0.955173	−0.477586	−	0.878585i	$-0.658488\pi$
$907$	−28.7664	−0.955173	−0.477586	+	0.878585i	$0.658488\pi$
$908$	6.49800	0.215644
$909$	16.7750	0.556391
$910$	0	0
$911$	−44.3240	−1.46852	−0.734259	−	0.678869i	$-0.762470\pi$
$911$	−44.3240	−1.46852	−0.734259	+	0.678869i	$0.762470\pi$
$912$	7.80285	0.258378
$913$	−4.65065	−0.153914
$914$	−27.2461	−0.901221
$915$	−34.2258	−1.13147
$916$	−24.5142	−0.809973
$917$	0	0
$918$	−35.0115	−1.15555
$919$	15.4977	0.511224	0.255612	−	0.966780i	$-0.417723\pi$
$919$	15.4977	0.511224	0.255612	+	0.966780i	$0.417723\pi$
$920$	3.36872	0.111063
$921$	16.7631	0.552363
$922$	−36.7278	−1.20957
$923$	24.8754	0.818785
$924$	0	0
$925$	2.44466	0.0803798
$926$	4.65561	0.152993
$927$	0.792691	0.0260354
$928$	7.10796	0.233330
$929$	−35.3001	−1.15816	−0.579080	−	0.815271i	$-0.696588\pi$
$929$	−35.3001	−1.15816	−0.579080	+	0.815271i	$0.696588\pi$
$930$	−9.48404	−0.310994
$931$	0	0
$932$	7.37537	0.241588
$933$	4.32618	0.141633
$934$	18.7225	0.612620
$935$	−4.20911	−0.137653
$936$	−8.83073	−0.288641
$937$	8.46021	0.276383	0.138191	−	0.990406i	$-0.455871\pi$
$937$	8.46021	0.276383	0.138191	+	0.990406i	$0.455871\pi$
$938$	0	0
$939$	10.1850	0.332376
$940$	−11.4341	−0.372940
$941$	−3.89920	−0.127110	−0.0635551	−	0.997978i	$-0.520244\pi$
$941$	−3.89920	−0.127110	−0.0635551	+	0.997978i	$0.520244\pi$
$942$	−3.63153	−0.118322
$943$	1.45996	0.0475428
$944$	7.34290	0.238991
$945$	0	0
$946$	−0.0519583	−0.00168931
$947$	16.0840	0.522659	0.261330	−	0.965250i	$-0.415839\pi$
$947$	16.0840	0.522659	0.261330	+	0.965250i	$0.415839\pi$
$948$	−1.27723	−0.0414825
$949$	56.5293	1.83502
$950$	−2.52909	−0.0820546
$951$	−10.4977	−0.340413
$952$	0	0
$953$	23.0576	0.746908	0.373454	−	0.927649i	$-0.378173\pi$
$953$	23.0576	0.746908	0.373454	+	0.927649i	$0.378173\pi$
$954$	7.69490	0.249131
$955$	4.72302	0.152833
$956$	−5.55651	−0.179710
$957$	−1.85170	−0.0598570
$958$	−2.65686	−0.0858391
$959$	0	0
$960$	2.30741	0.0744712
$961$	−14.1058	−0.455024
$962$	33.3022	1.07371
$963$	35.9154	1.15736
$964$	0.614813	0.0198018
$965$	−39.5500	−1.27316
$966$	0	0
$967$	−13.8738	−0.446152	−0.223076	−	0.974801i	$-0.571610\pi$
$967$	−13.8738	−0.446152	−0.223076	+	0.974801i	$0.571610\pi$
$968$	10.9321	0.351372
$969$	−54.6379	−1.75522
$970$	15.8695	0.509538
$971$	53.4464	1.71518	0.857588	−	0.514338i	$-0.171962\pi$
$971$	53.4464	1.71518	0.857588	+	0.514338i	$0.171962\pi$
$972$	16.0000	0.513200
$973$	0	0
$974$	32.9157	1.05469
$975$	−1.43113	−0.0458327
$976$	−14.8330	−0.474794
$977$	54.5787	1.74613	0.873064	−	0.487606i	$-0.162130\pi$
$977$	54.5787	1.74613	0.873064	+	0.487606i	$0.162130\pi$
$978$	−13.9268	−0.445331
$979$	2.29324	0.0732922
$980$	0	0
$981$	15.0137	0.479351
$982$	23.9180	0.763253
$983$	−51.3995	−1.63939	−0.819694	−	0.572802i	$-0.805857\pi$
$983$	−51.3995	−1.63939	−0.819694	+	0.572802i	$0.805857\pi$
$984$	1.00000	0.0318788
$985$	−44.4208	−1.41536
$986$	−49.7721	−1.58507
$987$	0	0
$988$	−34.4524	−1.09608
$989$	−0.291186	−0.00925916
$990$	1.20221	0.0382087
$991$	−24.5609	−0.780202	−0.390101	−	0.920772i	$-0.627560\pi$
$991$	−24.5609	−0.780202	−0.390101	+	0.920772i	$0.627560\pi$
$992$	−4.11026	−0.130501
$993$	−28.8209	−0.914604
$994$	0	0
$995$	6.78132	0.214982
$996$	−17.8521	−0.565664
$997$	12.7838	0.404868	0.202434	−	0.979296i	$-0.435115\pi$
$997$	12.7838	0.404868	0.202434	+	0.979296i	$0.435115\pi$
$998$	−42.3384	−1.34020
$999$	−37.7117	−1.19315

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4018.2.a.bk.1.3		4
7.2	even	3		574.2.e.f.165.2	✓	8
7.4	even	3		574.2.e.f.247.2	yes	8
7.6	odd	2		4018.2.a.bi.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
574.2.e.f.165.2	✓	8	7.2	even	3
574.2.e.f.247.2	yes	8	7.4	even	3
4018.2.a.bi.1.2		4	7.6	odd	2
4018.2.a.bk.1.3		4	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.30741 q^{5} -1.00000 q^{6} -1.00000 q^{8} -2.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.30741 q^{5} -1.00000 q^{6} -1.00000 q^{8} -2.00000 q^{9} -2.30741 q^{10} +0.260511 q^{11} +1.00000 q^{12} -4.41536 q^{13} +2.30741 q^{15} +1.00000 q^{16} -7.00230 q^{17} +2.00000 q^{18} +7.80285 q^{19} +2.30741 q^{20} -0.260511 q^{22} -1.45996 q^{23} -1.00000 q^{24} +0.324124 q^{25} +4.41536 q^{26} -5.00000 q^{27} -7.10796 q^{29} -2.30741 q^{30} +4.11026 q^{31} -1.00000 q^{32} +0.260511 q^{33} +7.00230 q^{34} -2.00000 q^{36} +7.54234 q^{37} -7.80285 q^{38} -4.41536 q^{39} -2.30741 q^{40} -1.00000 q^{41} +0.199448 q^{43} +0.260511 q^{44} -4.61481 q^{45} +1.45996 q^{46} -4.95541 q^{47} +1.00000 q^{48} -0.324124 q^{50} -7.00230 q^{51} -4.41536 q^{52} +3.84745 q^{53} +5.00000 q^{54} +0.601104 q^{55} +7.80285 q^{57} +7.10796 q^{58} +7.34290 q^{59} +2.30741 q^{60} -14.8330 q^{61} -4.11026 q^{62} +1.00000 q^{64} -10.1880 q^{65} -0.260511 q^{66} +4.56792 q^{67} -7.00230 q^{68} -1.45996 q^{69} -5.63383 q^{71} +2.00000 q^{72} -12.8029 q^{73} -7.54234 q^{74} +0.324124 q^{75} +7.80285 q^{76} +4.41536 q^{78} -1.27723 q^{79} +2.30741 q^{80} +1.00000 q^{81} +1.00000 q^{82} -17.8521 q^{83} -16.1572 q^{85} -0.199448 q^{86} -7.10796 q^{87} -0.260511 q^{88} +8.80285 q^{89} +4.61481 q^{90} -1.45996 q^{92} +4.11026 q^{93} +4.95541 q^{94} +18.0044 q^{95} -1.00000 q^{96} -6.87763 q^{97} -0.521022 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} + 3 q^{5} - 4 q^{6} - 4 q^{8} - 8 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 + 3 * q^5 - 4 * q^6 - 4 * q^8 - 8 * q^9	\( 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} + 3 q^{5} - 4 q^{6} - 4 q^{8} - 8 q^{9} - 3 q^{10} + 4 q^{12} - q^{13} + 3 q^{15} + 4 q^{16} - 3 q^{17} + 8 q^{18} + 2 q^{19} + 3 q^{20} - 9 q^{23} - 4 q^{24} + 19 q^{25} + q^{26} - 20 q^{27} - 18 q^{29} - 3 q^{30} - 19 q^{31} - 4 q^{32} + 3 q^{34} - 8 q^{36} + 2 q^{37} - 2 q^{38} - q^{39} - 3 q^{40} - 4 q^{41} + 5 q^{43} - 6 q^{45} + 9 q^{46} + 4 q^{48} - 19 q^{50} - 3 q^{51} - q^{52} + 6 q^{53} + 20 q^{54} - 6 q^{55} + 2 q^{57} + 18 q^{58} - 3 q^{59} + 3 q^{60} - q^{61} + 19 q^{62} + 4 q^{64} - 24 q^{65} + 11 q^{67} - 3 q^{68} - 9 q^{69} - 9 q^{71} + 8 q^{72} - 22 q^{73} - 2 q^{74} + 19 q^{75} + 2 q^{76} + q^{78} - 28 q^{79} + 3 q^{80} + 4 q^{81} + 4 q^{82} - 12 q^{83} - 24 q^{85} - 5 q^{86} - 18 q^{87} + 6 q^{89} + 6 q^{90} - 9 q^{92} - 19 q^{93} - 27 q^{95} - 4 q^{96} + 11 q^{97}+O(q^{100}) \) 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 + 3 * q^5 - 4 * q^6 - 4 * q^8 - 8 * q^9 - 3 * q^10 + 4 * q^12 - q^13 + 3 * q^15 + 4 * q^16 - 3 * q^17 + 8 * q^18 + 2 * q^19 + 3 * q^20 - 9 * q^23 - 4 * q^24 + 19 * q^25 + q^26 - 20 * q^27 - 18 * q^29 - 3 * q^30 - 19 * q^31 - 4 * q^32 + 3 * q^34 - 8 * q^36 + 2 * q^37 - 2 * q^38 - q^39 - 3 * q^40 - 4 * q^41 + 5 * q^43 - 6 * q^45 + 9 * q^46 + 4 * q^48 - 19 * q^50 - 3 * q^51 - q^52 + 6 * q^53 + 20 * q^54 - 6 * q^55 + 2 * q^57 + 18 * q^58 - 3 * q^59 + 3 * q^60 - q^61 + 19 * q^62 + 4 * q^64 - 24 * q^65 + 11 * q^67 - 3 * q^68 - 9 * q^69 - 9 * q^71 + 8 * q^72 - 22 * q^73 - 2 * q^74 + 19 * q^75 + 2 * q^76 + q^78 - 28 * q^79 + 3 * q^80 + 4 * q^81 + 4 * q^82 - 12 * q^83 - 24 * q^85 - 5 * q^86 - 18 * q^87 + 6 * q^89 + 6 * q^90 - 9 * q^92 - 19 * q^93 - 27 * q^95 - 4 * q^96 + 11 * q^97

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