LMFDB - Embedded newform 8018.2.a.j.1.39

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, 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("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.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:	$64.0240523407$
Analytic rank:	$0$
Dimension:	$47$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.39
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +2.64297 q^{3} +1.00000 q^{4} -1.93875 q^{5} +2.64297 q^{6} +1.07051 q^{7} +1.00000 q^{8} +3.98529 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.64297 q^{3} +1.00000 q^{4} -1.93875 q^{5} +2.64297 q^{6} +1.07051 q^{7} +1.00000 q^{8} +3.98529 q^{9} -1.93875 q^{10} +1.90789 q^{11} +2.64297 q^{12} -2.15683 q^{13} +1.07051 q^{14} -5.12406 q^{15} +1.00000 q^{16} +7.78845 q^{17} +3.98529 q^{18} -1.00000 q^{19} -1.93875 q^{20} +2.82932 q^{21} +1.90789 q^{22} -0.222303 q^{23} +2.64297 q^{24} -1.24125 q^{25} -2.15683 q^{26} +2.60408 q^{27} +1.07051 q^{28} -4.69751 q^{29} -5.12406 q^{30} +8.98008 q^{31} +1.00000 q^{32} +5.04250 q^{33} +7.78845 q^{34} -2.07545 q^{35} +3.98529 q^{36} +4.54921 q^{37} -1.00000 q^{38} -5.70045 q^{39} -1.93875 q^{40} -1.79112 q^{41} +2.82932 q^{42} +2.89071 q^{43} +1.90789 q^{44} -7.72647 q^{45} -0.222303 q^{46} -1.39330 q^{47} +2.64297 q^{48} -5.85401 q^{49} -1.24125 q^{50} +20.5846 q^{51} -2.15683 q^{52} +12.5224 q^{53} +2.60408 q^{54} -3.69892 q^{55} +1.07051 q^{56} -2.64297 q^{57} -4.69751 q^{58} +1.99331 q^{59} -5.12406 q^{60} -3.71852 q^{61} +8.98008 q^{62} +4.26628 q^{63} +1.00000 q^{64} +4.18156 q^{65} +5.04250 q^{66} +11.1632 q^{67} +7.78845 q^{68} -0.587541 q^{69} -2.07545 q^{70} +5.43463 q^{71} +3.98529 q^{72} +5.89762 q^{73} +4.54921 q^{74} -3.28059 q^{75} -1.00000 q^{76} +2.04241 q^{77} -5.70045 q^{78} -5.16416 q^{79} -1.93875 q^{80} -5.07335 q^{81} -1.79112 q^{82} -0.230930 q^{83} +2.82932 q^{84} -15.0999 q^{85} +2.89071 q^{86} -12.4154 q^{87} +1.90789 q^{88} +11.9526 q^{89} -7.72647 q^{90} -2.30891 q^{91} -0.222303 q^{92} +23.7341 q^{93} -1.39330 q^{94} +1.93875 q^{95} +2.64297 q^{96} +15.2285 q^{97} -5.85401 q^{98} +7.60349 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9}+O(q^{10}) $ 47 * q + 47 * q^2 + 10 * q^3 + 47 * q^4 + 15 * q^5 + 10 * q^6 + 47 * q^8 + 69 * q^9	\( 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9} + 15 q^{10} + 17 q^{11} + 10 q^{12} + 27 q^{13} + 10 q^{15} + 47 q^{16} + 16 q^{17} + 69 q^{18} - 47 q^{19} + 15 q^{20} + 26 q^{21} + 17 q^{22} + 24 q^{23} + 10 q^{24} + 86 q^{25} + 27 q^{26} + 43 q^{27} + 58 q^{29} + 10 q^{30} + 21 q^{31} + 47 q^{32} + 18 q^{33} + 16 q^{34} + 24 q^{35} + 69 q^{36} + 78 q^{37} - 47 q^{38} - 4 q^{39} + 15 q^{40} + 53 q^{41} + 26 q^{42} + 47 q^{43} + 17 q^{44} + 23 q^{45} + 24 q^{46} + 16 q^{47} + 10 q^{48} + 93 q^{49} + 86 q^{50} + 28 q^{51} + 27 q^{52} + 43 q^{53} + 43 q^{54} + 23 q^{55} - 10 q^{57} + 58 q^{58} + 3 q^{59} + 10 q^{60} + 12 q^{61} + 21 q^{62} - 5 q^{63} + 47 q^{64} + 62 q^{65} + 18 q^{66} + 68 q^{67} + 16 q^{68} + 12 q^{69} + 24 q^{70} - 13 q^{71} + 69 q^{72} + 35 q^{73} + 78 q^{74} + 22 q^{75} - 47 q^{76} + 26 q^{77} - 4 q^{78} + 21 q^{79} + 15 q^{80} + 123 q^{81} + 53 q^{82} + 23 q^{83} + 26 q^{84} + 38 q^{85} + 47 q^{86} + 39 q^{87} + 17 q^{88} + 24 q^{89} + 23 q^{90} + 49 q^{91} + 24 q^{92} + 91 q^{93} + 16 q^{94} - 15 q^{95} + 10 q^{96} + 88 q^{97} + 93 q^{98} + 26 q^{99}+O(q^{100}) \) 47 * q + 47 * q^2 + 10 * q^3 + 47 * q^4 + 15 * q^5 + 10 * q^6 + 47 * q^8 + 69 * q^9 + 15 * q^10 + 17 * q^11 + 10 * q^12 + 27 * q^13 + 10 * q^15 + 47 * q^16 + 16 * q^17 + 69 * q^18 - 47 * q^19 + 15 * q^20 + 26 * q^21 + 17 * q^22 + 24 * q^23 + 10 * q^24 + 86 * q^25 + 27 * q^26 + 43 * q^27 + 58 * q^29 + 10 * q^30 + 21 * q^31 + 47 * q^32 + 18 * q^33 + 16 * q^34 + 24 * q^35 + 69 * q^36 + 78 * q^37 - 47 * q^38 - 4 * q^39 + 15 * q^40 + 53 * q^41 + 26 * q^42 + 47 * q^43 + 17 * q^44 + 23 * q^45 + 24 * q^46 + 16 * q^47 + 10 * q^48 + 93 * q^49 + 86 * q^50 + 28 * q^51 + 27 * q^52 + 43 * q^53 + 43 * q^54 + 23 * q^55 - 10 * q^57 + 58 * q^58 + 3 * q^59 + 10 * q^60 + 12 * q^61 + 21 * q^62 - 5 * q^63 + 47 * q^64 + 62 * q^65 + 18 * q^66 + 68 * q^67 + 16 * q^68 + 12 * q^69 + 24 * q^70 - 13 * q^71 + 69 * q^72 + 35 * q^73 + 78 * q^74 + 22 * q^75 - 47 * q^76 + 26 * q^77 - 4 * q^78 + 21 * q^79 + 15 * q^80 + 123 * q^81 + 53 * q^82 + 23 * q^83 + 26 * q^84 + 38 * q^85 + 47 * q^86 + 39 * q^87 + 17 * q^88 + 24 * q^89 + 23 * q^90 + 49 * q^91 + 24 * q^92 + 91 * q^93 + 16 * q^94 - 15 * q^95 + 10 * q^96 + 88 * q^97 + 93 * q^98 + 26 * 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
$3$	2.64297	1.52592	0.762960	−	0.646446i	$-0.223746\pi$
$3$	2.64297	1.52592	0.762960	+	0.646446i	$0.223746\pi$
$4$	1.00000	0.500000
$5$	−1.93875	−0.867035	−0.433518	−	0.901145i	$-0.642728\pi$
$5$	−1.93875	−0.867035	−0.433518	+	0.901145i	$0.642728\pi$
$6$	2.64297	1.07899
$7$	1.07051	0.404614	0.202307	−	0.979322i	$-0.435156\pi$
$7$	1.07051	0.404614	0.202307	+	0.979322i	$0.435156\pi$
$8$	1.00000	0.353553
$9$	3.98529	1.32843
$10$	−1.93875	−0.613086
$11$	1.90789	0.575251	0.287625	−	0.957743i	$-0.407134\pi$
$11$	1.90789	0.575251	0.287625	+	0.957743i	$0.407134\pi$
$12$	2.64297	0.762960
$13$	−2.15683	−0.598198	−0.299099	−	0.954222i	$-0.596686\pi$
$13$	−2.15683	−0.598198	−0.299099	+	0.954222i	$0.596686\pi$
$14$	1.07051	0.286106
$15$	−5.12406	−1.32303
$16$	1.00000	0.250000
$17$	7.78845	1.88898	0.944489	−	0.328544i	$-0.106558\pi$
$17$	7.78845	1.88898	0.944489	+	0.328544i	$0.106558\pi$
$18$	3.98529	0.939341
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−1.93875	−0.433518
$21$	2.82932	0.617409
$22$	1.90789	0.406764
$23$	−0.222303	−0.0463534	−0.0231767	−	0.999731i	$-0.507378\pi$
$23$	−0.222303	−0.0463534	−0.0231767	+	0.999731i	$0.507378\pi$
$24$	2.64297	0.539494
$25$	−1.24125	−0.248250
$26$	−2.15683	−0.422990
$27$	2.60408	0.501156
$28$	1.07051	0.202307
$29$	−4.69751	−0.872306	−0.436153	−	0.899872i	$-0.643659\pi$
$29$	−4.69751	−0.872306	−0.436153	+	0.899872i	$0.643659\pi$
$30$	−5.12406	−0.935520
$31$	8.98008	1.61287	0.806435	−	0.591323i	$-0.201394\pi$
$31$	8.98008	1.61287	0.806435	+	0.591323i	$0.201394\pi$
$32$	1.00000	0.176777
$33$	5.04250	0.877786
$34$	7.78845	1.33571
$35$	−2.07545	−0.350815
$36$	3.98529	0.664214
$37$	4.54921	0.747886	0.373943	−	0.927452i	$-0.378006\pi$
$37$	4.54921	0.747886	0.373943	+	0.927452i	$0.378006\pi$
$38$	−1.00000	−0.162221
$39$	−5.70045	−0.912802
$40$	−1.93875	−0.306543
$41$	−1.79112	−0.279726	−0.139863	−	0.990171i	$-0.544666\pi$
$41$	−1.79112	−0.279726	−0.139863	+	0.990171i	$0.544666\pi$
$42$	2.82932	0.436574
$43$	2.89071	0.440829	0.220415	−	0.975406i	$-0.429259\pi$
$43$	2.89071	0.440829	0.220415	+	0.975406i	$0.429259\pi$
$44$	1.90789	0.287625
$45$	−7.72647	−1.15179
$46$	−0.222303	−0.0327768
$47$	−1.39330	−0.203234	−0.101617	−	0.994824i	$-0.532402\pi$
$47$	−1.39330	−0.203234	−0.101617	+	0.994824i	$0.532402\pi$
$48$	2.64297	0.381480
$49$	−5.85401	−0.836287
$50$	−1.24125	−0.175539
$51$	20.5846	2.88243
$52$	−2.15683	−0.299099
$53$	12.5224	1.72008	0.860040	−	0.510226i	$-0.170438\pi$
$53$	12.5224	1.72008	0.860040	+	0.510226i	$0.170438\pi$
$54$	2.60408	0.354371
$55$	−3.69892	−0.498763
$56$	1.07051	0.143053
$57$	−2.64297	−0.350070
$58$	−4.69751	−0.616814
$59$	1.99331	0.259507	0.129754	−	0.991546i	$-0.458581\pi$
$59$	1.99331	0.259507	0.129754	+	0.991546i	$0.458581\pi$
$60$	−5.12406	−0.661513
$61$	−3.71852	−0.476108	−0.238054	−	0.971252i	$-0.576510\pi$
$61$	−3.71852	−0.476108	−0.238054	+	0.971252i	$0.576510\pi$
$62$	8.98008	1.14047
$63$	4.26628	0.537501
$64$	1.00000	0.125000
$65$	4.18156	0.518659
$66$	5.04250	0.620688
$67$	11.1632	1.36380	0.681898	−	0.731447i	$-0.261155\pi$
$67$	11.1632	1.36380	0.681898	+	0.731447i	$0.261155\pi$
$68$	7.78845	0.944489
$69$	−0.587541	−0.0707316
$70$	−2.07545	−0.248064
$71$	5.43463	0.644972	0.322486	−	0.946574i	$-0.395481\pi$
$71$	5.43463	0.644972	0.322486	+	0.946574i	$0.395481\pi$
$72$	3.98529	0.469671
$73$	5.89762	0.690264	0.345132	−	0.938554i	$-0.387834\pi$
$73$	5.89762	0.690264	0.345132	+	0.938554i	$0.387834\pi$
$74$	4.54921	0.528835
$75$	−3.28059	−0.378810
$76$	−1.00000	−0.114708
$77$	2.04241	0.232755
$78$	−5.70045	−0.645448
$79$	−5.16416	−0.581014	−0.290507	−	0.956873i	$-0.593824\pi$
$79$	−5.16416	−0.581014	−0.290507	+	0.956873i	$0.593824\pi$
$80$	−1.93875	−0.216759
$81$	−5.07335	−0.563706
$82$	−1.79112	−0.197796
$83$	−0.230930	−0.0253479	−0.0126739	−	0.999920i	$-0.504034\pi$
$83$	−0.230930	−0.0253479	−0.0126739	+	0.999920i	$0.504034\pi$
$84$	2.82932	0.308704
$85$	−15.0999	−1.63781
$86$	2.89071	0.311713
$87$	−12.4154	−1.33107
$88$	1.90789	0.203382
$89$	11.9526	1.26697	0.633487	−	0.773753i	$-0.281623\pi$
$89$	11.9526	1.26697	0.633487	+	0.773753i	$0.281623\pi$
$90$	−7.72647	−0.814442
$91$	−2.30891	−0.242040
$92$	−0.222303	−0.0231767
$93$	23.7341	2.46111
$94$	−1.39330	−0.143708
$95$	1.93875	0.198911
$96$	2.64297	0.269747
$97$	15.2285	1.54622	0.773110	−	0.634272i	$-0.218700\pi$
$97$	15.2285	1.54622	0.773110	+	0.634272i	$0.218700\pi$
$98$	−5.85401	−0.591344
$99$	7.60349	0.764180
$100$	−1.24125	−0.124125
$101$	−10.4351	−1.03833	−0.519164	−	0.854674i	$-0.673757\pi$
$101$	−10.4351	−1.03833	−0.519164	+	0.854674i	$0.673757\pi$
$102$	20.5846	2.03818
$103$	−9.22594	−0.909059	−0.454529	−	0.890732i	$-0.650193\pi$
$103$	−9.22594	−0.909059	−0.454529	+	0.890732i	$0.650193\pi$
$104$	−2.15683	−0.211495
$105$	−5.48535	−0.535315
$106$	12.5224	1.21628
$107$	14.4935	1.40114	0.700568	−	0.713586i	$-0.252930\pi$
$107$	14.4935	1.40114	0.700568	+	0.713586i	$0.252930\pi$
$108$	2.60408	0.250578
$109$	0.377049	0.0361147	0.0180574	−	0.999837i	$-0.494252\pi$
$109$	0.377049	0.0361147	0.0180574	+	0.999837i	$0.494252\pi$
$110$	−3.69892	−0.352678
$111$	12.0234	1.14121
$112$	1.07051	0.101154
$113$	−12.1055	−1.13879	−0.569394	−	0.822065i	$-0.692822\pi$
$113$	−12.1055	−1.13879	−0.569394	+	0.822065i	$0.692822\pi$
$114$	−2.64297	−0.247537
$115$	0.430990	0.0401900
$116$	−4.69751	−0.436153
$117$	−8.59560	−0.794664
$118$	1.99331	0.183499
$119$	8.33761	0.764307
$120$	−5.12406	−0.467760
$121$	−7.35995	−0.669087
$122$	−3.71852	−0.336659
$123$	−4.73387	−0.426839
$124$	8.98008	0.806435
$125$	12.1002	1.08228
$126$	4.26628	0.380071
$127$	−15.0130	−1.33219	−0.666094	−	0.745867i	$-0.732035\pi$
$127$	−15.0130	−1.33219	−0.666094	+	0.745867i	$0.732035\pi$
$128$	1.00000	0.0883883
$129$	7.64006	0.672670
$130$	4.18156	0.366747
$131$	−10.5144	−0.918648	−0.459324	−	0.888269i	$-0.651908\pi$
$131$	−10.5144	−0.918648	−0.459324	+	0.888269i	$0.651908\pi$
$132$	5.04250	0.438893
$133$	−1.07051	−0.0928249
$134$	11.1632	0.964349
$135$	−5.04866	−0.434520
$136$	7.78845	0.667854
$137$	14.1427	1.20829	0.604145	−	0.796875i	$-0.293515\pi$
$137$	14.1427	1.20829	0.604145	+	0.796875i	$0.293515\pi$
$138$	−0.587541	−0.0500148
$139$	8.69796	0.737751	0.368876	−	0.929479i	$-0.379743\pi$
$139$	8.69796	0.737751	0.368876	+	0.929479i	$0.379743\pi$
$140$	−2.07545	−0.175407
$141$	−3.68245	−0.310118
$142$	5.43463	0.456064
$143$	−4.11500	−0.344114
$144$	3.98529	0.332107
$145$	9.10730	0.756320
$146$	5.89762	0.488090
$147$	−15.4720	−1.27611
$148$	4.54921	0.373943
$149$	−15.3415	−1.25683	−0.628414	−	0.777879i	$-0.716295\pi$
$149$	−15.3415	−1.25683	−0.628414	+	0.777879i	$0.716295\pi$
$150$	−3.28059	−0.267859
$151$	−11.3334	−0.922299	−0.461149	−	0.887323i	$-0.652563\pi$
$151$	−11.3334	−0.922299	−0.461149	+	0.887323i	$0.652563\pi$
$152$	−1.00000	−0.0811107
$153$	31.0392	2.50937
$154$	2.04241	0.164582
$155$	−17.4101	−1.39841
$156$	−5.70045	−0.456401
$157$	8.24005	0.657628	0.328814	−	0.944395i	$-0.393351\pi$
$157$	8.24005	0.657628	0.328814	+	0.944395i	$0.393351\pi$
$158$	−5.16416	−0.410839
$159$	33.0963	2.62470
$160$	−1.93875	−0.153272
$161$	−0.237978	−0.0187553
$162$	−5.07335	−0.398600
$163$	4.23457	0.331677	0.165838	−	0.986153i	$-0.446967\pi$
$163$	4.23457	0.331677	0.165838	+	0.986153i	$0.446967\pi$
$164$	−1.79112	−0.139863
$165$	−9.77614	−0.761071
$166$	−0.230930	−0.0179237
$167$	−10.9498	−0.847323	−0.423662	−	0.905821i	$-0.639255\pi$
$167$	−10.9498	−0.847323	−0.423662	+	0.905821i	$0.639255\pi$
$168$	2.82932	0.218287
$169$	−8.34807	−0.642159
$170$	−15.0999	−1.15811
$171$	−3.98529	−0.304762
$172$	2.89071	0.220415
$173$	−23.7408	−1.80498	−0.902491	−	0.430709i	$-0.858264\pi$
$173$	−23.7408	−1.80498	−0.902491	+	0.430709i	$0.858264\pi$
$174$	−12.4154	−0.941208
$175$	−1.32877	−0.100446
$176$	1.90789	0.143813
$177$	5.26826	0.395987
$178$	11.9526	0.895886
$179$	26.0032	1.94357	0.971786	−	0.235863i	$-0.0757916\pi$
$179$	26.0032	1.94357	0.971786	+	0.235863i	$0.0757916\pi$
$180$	−7.72647	−0.575897
$181$	16.8036	1.24900	0.624500	−	0.781025i	$-0.285303\pi$
$181$	16.8036	1.24900	0.624500	+	0.781025i	$0.285303\pi$
$182$	−2.30891	−0.171148
$183$	−9.82794	−0.726503
$184$	−0.222303	−0.0163884
$185$	−8.81979	−0.648444
$186$	23.7341	1.74027
$187$	14.8595	1.08664
$188$	−1.39330	−0.101617
$189$	2.78769	0.202775
$190$	1.93875	0.140652
$191$	20.8257	1.50689	0.753446	−	0.657510i	$-0.228390\pi$
$191$	20.8257	1.50689	0.753446	+	0.657510i	$0.228390\pi$
$192$	2.64297	0.190740
$193$	−21.5824	−1.55354	−0.776768	−	0.629787i	$-0.783142\pi$
$193$	−21.5824	−1.55354	−0.776768	+	0.629787i	$0.783142\pi$
$194$	15.2285	1.09334
$195$	11.0517	0.791431
$196$	−5.85401	−0.418144
$197$	2.70895	0.193005	0.0965024	−	0.995333i	$-0.469234\pi$
$197$	2.70895	0.193005	0.0965024	+	0.995333i	$0.469234\pi$
$198$	7.60349	0.540357
$199$	20.2479	1.43534	0.717668	−	0.696385i	$-0.245210\pi$
$199$	20.2479	1.43534	0.717668	+	0.696385i	$0.245210\pi$
$200$	−1.24125	−0.0877697
$201$	29.5039	2.08104
$202$	−10.4351	−0.734209
$203$	−5.02873	−0.352948
$204$	20.5846	1.44121
$205$	3.47253	0.242532
$206$	−9.22594	−0.642802
$207$	−0.885942	−0.0615772
$208$	−2.15683	−0.149550
$209$	−1.90789	−0.131972
$210$	−5.48535	−0.378525
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	12.5224	0.860040
$213$	14.3636	0.984175
$214$	14.4935	0.990753
$215$	−5.60436	−0.382214
$216$	2.60408	0.177185
$217$	9.61325	0.652590
$218$	0.377049	0.0255370
$219$	15.5872	1.05329
$220$	−3.69892	−0.249381
$221$	−16.7984	−1.12998
$222$	12.0234	0.806960
$223$	−4.85742	−0.325277	−0.162638	−	0.986686i	$-0.552000\pi$
$223$	−4.85742	−0.325277	−0.162638	+	0.986686i	$0.552000\pi$
$224$	1.07051	0.0715264
$225$	−4.94674	−0.329783
$226$	−12.1055	−0.805245
$227$	−26.4589	−1.75614	−0.878068	−	0.478535i	$-0.841168\pi$
$227$	−26.4589	−1.75614	−0.878068	+	0.478535i	$0.841168\pi$
$228$	−2.64297	−0.175035
$229$	−8.43744	−0.557561	−0.278781	−	0.960355i	$-0.589930\pi$
$229$	−8.43744	−0.557561	−0.278781	+	0.960355i	$0.589930\pi$
$230$	0.430990	0.0284187
$231$	5.39804	0.355165
$232$	−4.69751	−0.308407
$233$	1.96091	0.128464	0.0642319	−	0.997935i	$-0.479540\pi$
$233$	1.96091	0.128464	0.0642319	+	0.997935i	$0.479540\pi$
$234$	−8.59560	−0.561912
$235$	2.70126	0.176211
$236$	1.99331	0.129754
$237$	−13.6487	−0.886580
$238$	8.33761	0.540447
$239$	14.5004	0.937952	0.468976	−	0.883211i	$-0.344623\pi$
$239$	14.5004	0.937952	0.468976	+	0.883211i	$0.344623\pi$
$240$	−5.12406	−0.330756
$241$	−1.57763	−0.101624	−0.0508122	−	0.998708i	$-0.516181\pi$
$241$	−1.57763	−0.101624	−0.0508122	+	0.998708i	$0.516181\pi$
$242$	−7.35995	−0.473116
$243$	−21.2210	−1.36132
$244$	−3.71852	−0.238054
$245$	11.3495	0.725090
$246$	−4.73387	−0.301821
$247$	2.15683	0.137236
$248$	8.98008	0.570236
$249$	−0.610341	−0.0386788
$250$	12.1002	0.765285
$251$	−17.5999	−1.11090	−0.555448	−	0.831551i	$-0.687453\pi$
$251$	−17.5999	−1.11090	−0.555448	+	0.831551i	$0.687453\pi$
$252$	4.26628	0.268751
$253$	−0.424130	−0.0266648
$254$	−15.0130	−0.942000
$255$	−39.9085	−2.49916
$256$	1.00000	0.0625000
$257$	17.9776	1.12141	0.560706	−	0.828015i	$-0.310530\pi$
$257$	17.9776	1.12141	0.560706	+	0.828015i	$0.310530\pi$
$258$	7.64006	0.475649
$259$	4.86998	0.302606
$260$	4.18156	0.259329
$261$	−18.7209	−1.15880
$262$	−10.5144	−0.649582
$263$	−17.0382	−1.05062	−0.525311	−	0.850911i	$-0.676051\pi$
$263$	−17.0382	−1.05062	−0.525311	+	0.850911i	$0.676051\pi$
$264$	5.04250	0.310344
$265$	−24.2777	−1.49137
$266$	−1.07051	−0.0656371
$267$	31.5904	1.93330
$268$	11.1632	0.681898
$269$	−7.47418	−0.455709	−0.227854	−	0.973695i	$-0.573171\pi$
$269$	−7.47418	−0.455709	−0.227854	+	0.973695i	$0.573171\pi$
$270$	−5.04866	−0.307252
$271$	−19.1512	−1.16335	−0.581675	−	0.813421i	$-0.697602\pi$
$271$	−19.1512	−1.16335	−0.581675	+	0.813421i	$0.697602\pi$
$272$	7.78845	0.472244
$273$	−6.10238	−0.369333
$274$	14.1427	0.854390
$275$	−2.36817	−0.142806
$276$	−0.587541	−0.0353658
$277$	24.5407	1.47451	0.737255	−	0.675615i	$-0.236122\pi$
$277$	24.5407	1.47451	0.737255	+	0.675615i	$0.236122\pi$
$278$	8.69796	0.521669
$279$	35.7882	2.14258
$280$	−2.07545	−0.124032
$281$	−3.79496	−0.226388	−0.113194	−	0.993573i	$-0.536108\pi$
$281$	−3.79496	−0.226388	−0.113194	+	0.993573i	$0.536108\pi$
$282$	−3.68245	−0.219287
$283$	−27.7902	−1.65196	−0.825978	−	0.563703i	$-0.809376\pi$
$283$	−27.7902	−1.65196	−0.825978	+	0.563703i	$0.809376\pi$
$284$	5.43463	0.322486
$285$	5.12406	0.303523
$286$	−4.11500	−0.243325
$287$	−1.91741	−0.113181
$288$	3.98529	0.234835
$289$	43.6600	2.56823
$290$	9.10730	0.534799
$291$	40.2485	2.35941
$292$	5.89762	0.345132
$293$	−8.48714	−0.495824	−0.247912	−	0.968783i	$-0.579744\pi$
$293$	−8.48714	−0.495824	−0.247912	+	0.968783i	$0.579744\pi$
$294$	−15.4720	−0.902344
$295$	−3.86453	−0.225002
$296$	4.54921	0.264418
$297$	4.96830	0.288290
$298$	−15.3415	−0.888711
$299$	0.479471	0.0277285
$300$	−3.28059	−0.189405
$301$	3.09453	0.178366
$302$	−11.3334	−0.652164
$303$	−27.5796	−1.58441
$304$	−1.00000	−0.0573539
$305$	7.20929	0.412802
$306$	31.0392	1.77439
$307$	4.84857	0.276722	0.138361	−	0.990382i	$-0.455817\pi$
$307$	4.84857	0.276722	0.138361	+	0.990382i	$0.455817\pi$
$308$	2.04241	0.116377
$309$	−24.3839	−1.38715
$310$	−17.4101	−0.988829
$311$	−14.1514	−0.802454	−0.401227	−	0.915979i	$-0.631416\pi$
$311$	−14.1514	−0.802454	−0.401227	+	0.915979i	$0.631416\pi$
$312$	−5.70045	−0.322724
$313$	23.4069	1.32304	0.661519	−	0.749929i	$-0.269912\pi$
$313$	23.4069	1.32304	0.661519	+	0.749929i	$0.269912\pi$
$314$	8.24005	0.465013
$315$	−8.27126	−0.466033
$316$	−5.16416	−0.290507
$317$	−9.51688	−0.534521	−0.267261	−	0.963624i	$-0.586118\pi$
$317$	−9.51688	−0.534521	−0.267261	+	0.963624i	$0.586118\pi$
$318$	33.0963	1.85595
$319$	−8.96234	−0.501795
$320$	−1.93875	−0.108379
$321$	38.3058	2.13802
$322$	−0.237978	−0.0132620
$323$	−7.78845	−0.433361
$324$	−5.07335	−0.281853
$325$	2.67717	0.148503
$326$	4.23457	0.234531
$327$	0.996528	0.0551081
$328$	−1.79112	−0.0988980
$329$	−1.49154	−0.0822313
$330$	−9.77614	−0.538159
$331$	−7.07091	−0.388653	−0.194326	−	0.980937i	$-0.562252\pi$
$331$	−7.07091	−0.388653	−0.194326	+	0.980937i	$0.562252\pi$
$332$	−0.230930	−0.0126739
$333$	18.1299	0.993514
$334$	−10.9498	−0.599148
$335$	−21.6426	−1.18246
$336$	2.82932	0.154352
$337$	−11.6041	−0.632118	−0.316059	−	0.948740i	$-0.602360\pi$
$337$	−11.6041	−0.632118	−0.316059	+	0.948740i	$0.602360\pi$
$338$	−8.34807	−0.454075
$339$	−31.9944	−1.73770
$340$	−15.0999	−0.818905
$341$	17.1330	0.927804
$342$	−3.98529	−0.215500
$343$	−13.7603	−0.742988
$344$	2.89071	0.155857
$345$	1.13909	0.0613268
$346$	−23.7408	−1.27631
$347$	−16.7929	−0.901491	−0.450746	−	0.892652i	$-0.648842\pi$
$347$	−16.7929	−0.901491	−0.450746	+	0.892652i	$0.648842\pi$
$348$	−12.4154	−0.665534
$349$	31.7047	1.69712	0.848558	−	0.529102i	$-0.177471\pi$
$349$	31.7047	1.69712	0.848558	+	0.529102i	$0.177471\pi$
$350$	−1.32877	−0.0710257
$351$	−5.61657	−0.299790
$352$	1.90789	0.101691
$353$	13.6458	0.726290	0.363145	−	0.931733i	$-0.381703\pi$
$353$	13.6458	0.726290	0.363145	+	0.931733i	$0.381703\pi$
$354$	5.26826	0.280005
$355$	−10.5364	−0.559214
$356$	11.9526	0.633487
$357$	22.0360	1.16627
$358$	26.0032	1.37431
$359$	−9.72550	−0.513292	−0.256646	−	0.966505i	$-0.582617\pi$
$359$	−9.72550	−0.513292	−0.256646	+	0.966505i	$0.582617\pi$
$360$	−7.72647	−0.407221
$361$	1.00000	0.0526316
$362$	16.8036	0.883177
$363$	−19.4521	−1.02097
$364$	−2.30891	−0.121020
$365$	−11.4340	−0.598483
$366$	−9.82794	−0.513715
$367$	15.7535	0.822327	0.411164	−	0.911562i	$-0.365122\pi$
$367$	15.7535	0.822327	0.411164	+	0.911562i	$0.365122\pi$
$368$	−0.222303	−0.0115884
$369$	−7.13812	−0.371596
$370$	−8.81979	−0.458519
$371$	13.4053	0.695969
$372$	23.7341	1.23055
$373$	−4.36906	−0.226221	−0.113111	−	0.993582i	$-0.536081\pi$
$373$	−4.36906	−0.226221	−0.113111	+	0.993582i	$0.536081\pi$
$374$	14.8595	0.768367
$375$	31.9805	1.65147
$376$	−1.39330	−0.0718540
$377$	10.1318	0.521812
$378$	2.78769	0.143383
$379$	33.8876	1.74069	0.870344	−	0.492444i	$-0.163896\pi$
$379$	33.8876	1.74069	0.870344	+	0.492444i	$0.163896\pi$
$380$	1.93875	0.0994557
$381$	−39.6789	−2.03281
$382$	20.8257	1.06553
$383$	26.3698	1.34744	0.673718	−	0.738989i	$-0.264696\pi$
$383$	26.3698	1.34744	0.673718	+	0.738989i	$0.264696\pi$
$384$	2.64297	0.134873
$385$	−3.95973	−0.201806
$386$	−21.5824	−1.09852
$387$	11.5203	0.585610
$388$	15.2285	0.773110
$389$	−12.1389	−0.615466	−0.307733	−	0.951473i	$-0.599570\pi$
$389$	−12.1389	−0.615466	−0.307733	+	0.951473i	$0.599570\pi$
$390$	11.0517	0.559626
$391$	−1.73140	−0.0875606
$392$	−5.85401	−0.295672
$393$	−27.7892	−1.40178
$394$	2.70895	0.136475
$395$	10.0120	0.503759
$396$	7.60349	0.382090
$397$	−9.71956	−0.487811	−0.243905	−	0.969799i	$-0.578429\pi$
$397$	−9.71956	−0.487811	−0.243905	+	0.969799i	$0.578429\pi$
$398$	20.2479	1.01494
$399$	−2.82932	−0.141643
$400$	−1.24125	−0.0620625
$401$	−4.73440	−0.236425	−0.118212	−	0.992988i	$-0.537716\pi$
$401$	−4.73440	−0.236425	−0.118212	+	0.992988i	$0.537716\pi$
$402$	29.5039	1.47152
$403$	−19.3685	−0.964816
$404$	−10.4351	−0.519164
$405$	9.83596	0.488753
$406$	−5.02873	−0.249572
$407$	8.67940	0.430222
$408$	20.5846	1.01909
$409$	−25.6040	−1.26604	−0.633019	−	0.774136i	$-0.718184\pi$
$409$	−25.6040	−1.26604	−0.633019	+	0.774136i	$0.718184\pi$
$410$	3.47253	0.171496
$411$	37.3786	1.84375
$412$	−9.22594	−0.454529
$413$	2.13386	0.105000
$414$	−0.885942	−0.0435417
$415$	0.447716	0.0219775
$416$	−2.15683	−0.105747
$417$	22.9884	1.12575
$418$	−1.90789	−0.0933180
$419$	33.0959	1.61684	0.808419	−	0.588607i	$-0.200324\pi$
$419$	33.0959	1.61684	0.808419	+	0.588607i	$0.200324\pi$
$420$	−5.48535	−0.267658
$421$	−12.1072	−0.590067	−0.295033	−	0.955487i	$-0.595331\pi$
$421$	−12.1072	−0.590067	−0.295033	+	0.955487i	$0.595331\pi$
$422$	−1.00000	−0.0486792
$423$	−5.55270	−0.269982
$424$	12.5224	0.608140
$425$	−9.66742	−0.468939
$426$	14.3636	0.695917
$427$	−3.98071	−0.192640
$428$	14.4935	0.700568
$429$	−10.8758	−0.525090
$430$	−5.60436	−0.270266
$431$	34.9672	1.68431	0.842156	−	0.539235i	$-0.181286\pi$
$431$	34.9672	1.68431	0.842156	+	0.539235i	$0.181286\pi$
$432$	2.60408	0.125289
$433$	−13.3544	−0.641770	−0.320885	−	0.947118i	$-0.603980\pi$
$433$	−13.3544	−0.641770	−0.320885	+	0.947118i	$0.603980\pi$
$434$	9.61325	0.461451
$435$	24.0703	1.15408
$436$	0.377049	0.0180574
$437$	0.222303	0.0106342
$438$	15.5872	0.744787
$439$	−16.9041	−0.806791	−0.403396	−	0.915026i	$-0.632170\pi$
$439$	−16.9041	−0.806791	−0.403396	+	0.915026i	$0.632170\pi$
$440$	−3.69892	−0.176339
$441$	−23.3299	−1.11095
$442$	−16.7984	−0.799018
$443$	−16.8731	−0.801666	−0.400833	−	0.916151i	$-0.631279\pi$
$443$	−16.8731	−0.801666	−0.400833	+	0.916151i	$0.631279\pi$
$444$	12.0234	0.570607
$445$	−23.1731	−1.09851
$446$	−4.85742	−0.230005
$447$	−40.5472	−1.91782
$448$	1.07051	0.0505768
$449$	13.0010	0.613557	0.306778	−	0.951781i	$-0.400749\pi$
$449$	13.0010	0.613557	0.306778	+	0.951781i	$0.400749\pi$
$450$	−4.94674	−0.233192
$451$	−3.41726	−0.160912
$452$	−12.1055	−0.569394
$453$	−29.9538	−1.40735
$454$	−26.4589	−1.24178
$455$	4.47640	0.209857
$456$	−2.64297	−0.123768
$457$	−10.9211	−0.510866	−0.255433	−	0.966827i	$-0.582218\pi$
$457$	−10.9211	−0.510866	−0.255433	+	0.966827i	$0.582218\pi$
$458$	−8.43744	−0.394255
$459$	20.2818	0.946672
$460$	0.430990	0.0200950
$461$	−18.2235	−0.848751	−0.424376	−	0.905486i	$-0.639506\pi$
$461$	−18.2235	−0.848751	−0.424376	+	0.905486i	$0.639506\pi$
$462$	5.39804	0.251139
$463$	−0.303308	−0.0140959	−0.00704797	−	0.999975i	$-0.502243\pi$
$463$	−0.303308	−0.0140959	−0.00704797	+	0.999975i	$0.502243\pi$
$464$	−4.69751	−0.218077
$465$	−46.0144	−2.13387
$466$	1.96091	0.0908376
$467$	27.4837	1.27179	0.635896	−	0.771775i	$-0.280631\pi$
$467$	27.4837	1.27179	0.635896	+	0.771775i	$0.280631\pi$
$468$	−8.59560	−0.397332
$469$	11.9503	0.551811
$470$	2.70126	0.124600
$471$	21.7782	1.00349
$472$	1.99331	0.0917496
$473$	5.51516	0.253587
$474$	−13.6487	−0.626907
$475$	1.24125	0.0569525
$476$	8.33761	0.382154
$477$	49.9053	2.28500
$478$	14.5004	0.663232
$479$	9.72959	0.444556	0.222278	−	0.974983i	$-0.428651\pi$
$479$	9.72959	0.444556	0.222278	+	0.974983i	$0.428651\pi$
$480$	−5.12406	−0.233880
$481$	−9.81190	−0.447384
$482$	−1.57763	−0.0718592
$483$	−0.628967	−0.0286190
$484$	−7.35995	−0.334543
$485$	−29.5242	−1.34063
$486$	−21.2210	−0.962602
$487$	−36.9611	−1.67487	−0.837433	−	0.546540i	$-0.815945\pi$
$487$	−36.9611	−1.67487	−0.837433	+	0.546540i	$0.815945\pi$
$488$	−3.71852	−0.168330
$489$	11.1918	0.506112
$490$	11.3495	0.512716
$491$	24.7579	1.11731	0.558654	−	0.829401i	$-0.311318\pi$
$491$	24.7579	1.11731	0.558654	+	0.829401i	$0.311318\pi$
$492$	−4.73387	−0.213419
$493$	−36.5864	−1.64777
$494$	2.15683	0.0970405
$495$	−14.7413	−0.662571
$496$	8.98008	0.403217
$497$	5.81782	0.260965
$498$	−0.610341	−0.0273500
$499$	21.1337	0.946077	0.473038	−	0.881042i	$-0.343157\pi$
$499$	21.1337	0.946077	0.473038	+	0.881042i	$0.343157\pi$
$500$	12.1002	0.541138
$501$	−28.9401	−1.29295
$502$	−17.5999	−0.785522
$503$	−21.1259	−0.941958	−0.470979	−	0.882144i	$-0.656099\pi$
$503$	−21.1259	−0.941958	−0.470979	+	0.882144i	$0.656099\pi$
$504$	4.26628	0.190035
$505$	20.2310	0.900267
$506$	−0.424130	−0.0188549
$507$	−22.0637	−0.979883
$508$	−15.0130	−0.666094
$509$	−36.0002	−1.59568	−0.797840	−	0.602869i	$-0.794024\pi$
$509$	−36.0002	−1.59568	−0.797840	+	0.602869i	$0.794024\pi$
$510$	−39.9085	−1.76718
$511$	6.31345	0.279291
$512$	1.00000	0.0441942
$513$	−2.60408	−0.114973
$514$	17.9776	0.792958
$515$	17.8868	0.788186
$516$	7.64006	0.336335
$517$	−2.65826	−0.116910
$518$	4.86998	0.213974
$519$	−62.7463	−2.75426
$520$	4.18156	0.183374
$521$	−28.5963	−1.25283	−0.626413	−	0.779491i	$-0.715478\pi$
$521$	−28.5963	−1.25283	−0.626413	+	0.779491i	$0.715478\pi$
$522$	−18.7209	−0.819393
$523$	17.3094	0.756886	0.378443	−	0.925625i	$-0.376460\pi$
$523$	17.3094	0.756886	0.378443	+	0.925625i	$0.376460\pi$
$524$	−10.5144	−0.459324
$525$	−3.51190	−0.153272
$526$	−17.0382	−0.742901
$527$	69.9409	3.04667
$528$	5.04250	0.219446
$529$	−22.9506	−0.997851
$530$	−24.2777	−1.05456
$531$	7.94392	0.344737
$532$	−1.07051	−0.0464124
$533$	3.86314	0.167331
$534$	31.5904	1.36705
$535$	−28.0992	−1.21483
$536$	11.1632	0.482175
$537$	68.7257	2.96573
$538$	−7.47418	−0.322235
$539$	−11.1688	−0.481075
$540$	−5.04866	−0.217260
$541$	5.45996	0.234742	0.117371	−	0.993088i	$-0.462553\pi$
$541$	5.45996	0.234742	0.117371	+	0.993088i	$0.462553\pi$
$542$	−19.1512	−0.822613
$543$	44.4114	1.90587
$544$	7.78845	0.333927
$545$	−0.731003	−0.0313127
$546$	−6.10238	−0.261158
$547$	−42.6293	−1.82270	−0.911349	−	0.411636i	$-0.864958\pi$
$547$	−42.6293	−1.82270	−0.911349	+	0.411636i	$0.864958\pi$
$548$	14.1427	0.604145
$549$	−14.8194	−0.632476
$550$	−2.36817	−0.100979
$551$	4.69751	0.200121
$552$	−0.587541	−0.0250074
$553$	−5.52828	−0.235087
$554$	24.5407	1.04264
$555$	−23.3104	−0.989473
$556$	8.69796	0.368876
$557$	−10.1144	−0.428559	−0.214279	−	0.976772i	$-0.568740\pi$
$557$	−10.1144	−0.428559	−0.214279	+	0.976772i	$0.568740\pi$
$558$	35.7882	1.51503
$559$	−6.23478	−0.263703
$560$	−2.07545	−0.0877037
$561$	39.2732	1.65812
$562$	−3.79496	−0.160081
$563$	7.92958	0.334192	0.167096	−	0.985941i	$-0.446561\pi$
$563$	7.92958	0.334192	0.167096	+	0.985941i	$0.446561\pi$
$564$	−3.68245	−0.155059
$565$	23.4695	0.987369
$566$	−27.7902	−1.16811
$567$	−5.43107	−0.228083
$568$	5.43463	0.228032
$569$	41.2622	1.72980	0.864901	−	0.501943i	$-0.167381\pi$
$569$	41.2622	1.72980	0.864901	+	0.501943i	$0.167381\pi$
$570$	5.12406	0.214623
$571$	45.4796	1.90326	0.951631	−	0.307244i	$-0.0994069\pi$
$571$	45.4796	1.90326	0.951631	+	0.307244i	$0.0994069\pi$
$572$	−4.11500	−0.172057
$573$	55.0416	2.29939
$574$	−1.91741	−0.0800311
$575$	0.275934	0.0115072
$576$	3.98529	0.166054
$577$	−22.5006	−0.936710	−0.468355	−	0.883540i	$-0.655153\pi$
$577$	−22.5006	−0.936710	−0.468355	+	0.883540i	$0.655153\pi$
$578$	43.6600	1.81602
$579$	−57.0416	−2.37057
$580$	9.10730	0.378160
$581$	−0.247213	−0.0102561
$582$	40.2485	1.66835
$583$	23.8913	0.989477
$584$	5.89762	0.244045
$585$	16.6647	0.689001
$586$	−8.48714	−0.350601
$587$	−29.2135	−1.20577	−0.602886	−	0.797828i	$-0.705983\pi$
$587$	−29.2135	−1.20577	−0.602886	+	0.797828i	$0.705983\pi$
$588$	−15.4720	−0.638053
$589$	−8.98008	−0.370018
$590$	−3.86453	−0.159100
$591$	7.15968	0.294510
$592$	4.54921	0.186972
$593$	−8.19493	−0.336525	−0.168263	−	0.985742i	$-0.553816\pi$
$593$	−8.19493	−0.336525	−0.168263	+	0.985742i	$0.553816\pi$
$594$	4.96830	0.203852
$595$	−16.1645	−0.662681
$596$	−15.3415	−0.628414
$597$	53.5146	2.19021
$598$	0.479471	0.0196070
$599$	−38.2983	−1.56482	−0.782412	−	0.622761i	$-0.786011\pi$
$599$	−38.2983	−1.56482	−0.782412	+	0.622761i	$0.786011\pi$
$600$	−3.28059	−0.133929
$601$	−17.1501	−0.699569	−0.349784	−	0.936830i	$-0.613745\pi$
$601$	−17.1501	−0.699569	−0.349784	+	0.936830i	$0.613745\pi$
$602$	3.09453	0.126124
$603$	44.4884	1.81171
$604$	−11.3334	−0.461149
$605$	14.2691	0.580122
$606$	−27.5796	−1.12034
$607$	−18.6251	−0.755969	−0.377984	−	0.925812i	$-0.623383\pi$
$607$	−18.6251	−0.755969	−0.377984	+	0.925812i	$0.623383\pi$
$608$	−1.00000	−0.0405554
$609$	−13.2908	−0.538569
$610$	7.20929	0.291895
$611$	3.00512	0.121574
$612$	31.0392	1.25469
$613$	−16.0099	−0.646635	−0.323318	−	0.946290i	$-0.604798\pi$
$613$	−16.0099	−0.646635	−0.323318	+	0.946290i	$0.604798\pi$
$614$	4.84857	0.195672
$615$	9.17779	0.370084
$616$	2.04241	0.0822912
$617$	−39.3744	−1.58516	−0.792578	−	0.609771i	$-0.791261\pi$
$617$	−39.3744	−1.58516	−0.792578	+	0.609771i	$0.791261\pi$
$618$	−24.3839	−0.980863
$619$	14.6375	0.588332	0.294166	−	0.955754i	$-0.404958\pi$
$619$	14.6375	0.588332	0.294166	+	0.955754i	$0.404958\pi$
$620$	−17.4101	−0.699207
$621$	−0.578896	−0.0232303
$622$	−14.1514	−0.567421
$623$	12.7954	0.512636
$624$	−5.70045	−0.228200
$625$	−17.2530	−0.690122
$626$	23.4069	0.935529
$627$	−5.04250	−0.201378
$628$	8.24005	0.328814
$629$	35.4313	1.41274
$630$	−8.27126	−0.329535
$631$	4.28749	0.170682	0.0853412	−	0.996352i	$-0.472802\pi$
$631$	4.28749	0.170682	0.0853412	+	0.996352i	$0.472802\pi$
$632$	−5.16416	−0.205419
$633$	−2.64297	−0.105049
$634$	−9.51688	−0.377964
$635$	29.1065	1.15505
$636$	33.0963	1.31235
$637$	12.6261	0.500265
$638$	−8.96234	−0.354822
$639$	21.6586	0.856800
$640$	−1.93875	−0.0766358
$641$	−33.6974	−1.33097	−0.665485	−	0.746412i	$-0.731775\pi$
$641$	−33.6974	−1.33097	−0.665485	+	0.746412i	$0.731775\pi$
$642$	38.3058	1.51181
$643$	20.2827	0.799871	0.399936	−	0.916543i	$-0.369033\pi$
$643$	20.2827	0.799871	0.399936	+	0.916543i	$0.369033\pi$
$644$	−0.237978	−0.00937763
$645$	−14.8122	−0.583228
$646$	−7.78845	−0.306433
$647$	24.8186	0.975721	0.487861	−	0.872922i	$-0.337777\pi$
$647$	24.8186	0.975721	0.487861	+	0.872922i	$0.337777\pi$
$648$	−5.07335	−0.199300
$649$	3.80302	0.149282
$650$	2.67717	0.105007
$651$	25.4075	0.995800
$652$	4.23457	0.165838
$653$	−12.1289	−0.474641	−0.237320	−	0.971431i	$-0.576269\pi$
$653$	−12.1289	−0.474641	−0.237320	+	0.971431i	$0.576269\pi$
$654$	0.996528	0.0389673
$655$	20.3848	0.796500
$656$	−1.79112	−0.0699314
$657$	23.5037	0.916967
$658$	−1.49154	−0.0581463
$659$	21.7979	0.849127	0.424563	−	0.905398i	$-0.360428\pi$
$659$	21.7979	0.849127	0.424563	+	0.905398i	$0.360428\pi$
$660$	−9.77614	−0.380536
$661$	24.4316	0.950277	0.475139	−	0.879911i	$-0.342398\pi$
$661$	24.4316	0.950277	0.475139	+	0.879911i	$0.342398\pi$
$662$	−7.07091	−0.274819
$663$	−44.3977	−1.72426
$664$	−0.230930	−0.00896183
$665$	2.07545	0.0804824
$666$	18.1299	0.702520
$667$	1.04427	0.0404344
$668$	−10.9498	−0.423662
$669$	−12.8380	−0.496346
$670$	−21.6426	−0.836125
$671$	−7.09454	−0.273882
$672$	2.82932	0.109143
$673$	6.07897	0.234327	0.117164	−	0.993113i	$-0.462620\pi$
$673$	6.07897	0.234327	0.117164	+	0.993113i	$0.462620\pi$
$674$	−11.6041	−0.446975
$675$	−3.23232	−0.124412
$676$	−8.34807	−0.321080
$677$	−43.4319	−1.66922	−0.834612	−	0.550838i	$-0.814308\pi$
$677$	−43.4319	−1.66922	−0.834612	+	0.550838i	$0.814308\pi$
$678$	−31.9944	−1.22874
$679$	16.3022	0.625623
$680$	−15.0999	−0.579053
$681$	−69.9300	−2.67972
$682$	17.1330	0.656057
$683$	−24.7728	−0.947905	−0.473953	−	0.880550i	$-0.657173\pi$
$683$	−24.7728	−0.947905	−0.473953	+	0.880550i	$0.657173\pi$
$684$	−3.98529	−0.152381
$685$	−27.4191	−1.04763
$686$	−13.7603	−0.525372
$687$	−22.2999	−0.850794
$688$	2.89071	0.110207
$689$	−27.0087	−1.02895
$690$	1.13909	0.0433646
$691$	25.4834	0.969433	0.484717	−	0.874671i	$-0.338923\pi$
$691$	25.4834	0.969433	0.484717	+	0.874671i	$0.338923\pi$
$692$	−23.7408	−0.902491
$693$	8.13960	0.309198
$694$	−16.7929	−0.637451
$695$	−16.8632	−0.639656
$696$	−12.4154	−0.470604
$697$	−13.9500	−0.528395
$698$	31.7047	1.20004
$699$	5.18263	0.196025
$700$	−1.32877	−0.0502228
$701$	7.66947	0.289672	0.144836	−	0.989456i	$-0.453735\pi$
$701$	7.66947	0.289672	0.144836	+	0.989456i	$0.453735\pi$
$702$	−5.61657	−0.211984
$703$	−4.54921	−0.171577
$704$	1.90789	0.0719063
$705$	7.13935	0.268883
$706$	13.6458	0.513565
$707$	−11.1708	−0.420123
$708$	5.26826	0.197993
$709$	−16.9499	−0.636567	−0.318284	−	0.947996i	$-0.603106\pi$
$709$	−16.9499	−0.636567	−0.318284	+	0.947996i	$0.603106\pi$
$710$	−10.5364	−0.395424
$711$	−20.5807	−0.771836
$712$	11.9526	0.447943
$713$	−1.99630	−0.0747620
$714$	22.0360	0.824678
$715$	7.97796	0.298359
$716$	26.0032	0.971786
$717$	38.3241	1.43124
$718$	−9.72550	−0.362952
$719$	−29.0463	−1.08325	−0.541623	−	0.840622i	$-0.682190\pi$
$719$	−29.0463	−1.08325	−0.541623	+	0.840622i	$0.682190\pi$
$720$	−7.72647	−0.287949
$721$	−9.87645	−0.367818
$722$	1.00000	0.0372161
$723$	−4.16964	−0.155070
$724$	16.8036	0.624500
$725$	5.83079	0.216550
$726$	−19.4521	−0.721936
$727$	34.3918	1.27552	0.637761	−	0.770234i	$-0.279861\pi$
$727$	34.3918	1.27552	0.637761	+	0.770234i	$0.279861\pi$
$728$	−2.30891	−0.0855739
$729$	−40.8663	−1.51357
$730$	−11.4340	−0.423192
$731$	22.5142	0.832716
$732$	−9.82794	−0.363251
$733$	17.1339	0.632854	0.316427	−	0.948617i	$-0.397517\pi$
$733$	17.1339	0.632854	0.316427	+	0.948617i	$0.397517\pi$
$734$	15.7535	0.581473
$735$	29.9963	1.10643
$736$	−0.222303	−0.00819421
$737$	21.2981	0.784525
$738$	−7.13812	−0.262758
$739$	−19.0020	−0.699001	−0.349501	−	0.936936i	$-0.613649\pi$
$739$	−19.0020	−0.699001	−0.349501	+	0.936936i	$0.613649\pi$
$740$	−8.81979	−0.324222
$741$	5.70045	0.209411
$742$	13.4053	0.492125
$743$	−2.46848	−0.0905598	−0.0452799	−	0.998974i	$-0.514418\pi$
$743$	−2.46848	−0.0905598	−0.0452799	+	0.998974i	$0.514418\pi$
$744$	23.7341	0.870133
$745$	29.7434	1.08971
$746$	−4.36906	−0.159963
$747$	−0.920323	−0.0336728
$748$	14.8595	0.543318
$749$	15.5154	0.566920
$750$	31.9805	1.16776
$751$	−32.6327	−1.19078	−0.595392	−	0.803436i	$-0.703003\pi$
$751$	−32.6327	−1.19078	−0.595392	+	0.803436i	$0.703003\pi$
$752$	−1.39330	−0.0508084
$753$	−46.5160	−1.69514
$754$	10.1318	0.368977
$755$	21.9726	0.799665
$756$	2.78769	0.101387
$757$	−39.1559	−1.42315	−0.711574	−	0.702612i	$-0.752017\pi$
$757$	−39.1559	−1.42315	−0.711574	+	0.702612i	$0.752017\pi$
$758$	33.8876	1.23085
$759$	−1.12096	−0.0406884
$760$	1.93875	0.0703258
$761$	−17.7976	−0.645163	−0.322581	−	0.946542i	$-0.604551\pi$
$761$	−17.7976	−0.645163	−0.322581	+	0.946542i	$0.604551\pi$
$762$	−39.6789	−1.43742
$763$	0.403634	0.0146125
$764$	20.8257	0.753446
$765$	−60.1773	−2.17571
$766$	26.3698	0.952781
$767$	−4.29924	−0.155237
$768$	2.64297	0.0953699
$769$	−29.8223	−1.07542	−0.537709	−	0.843131i	$-0.680710\pi$
$769$	−29.8223	−1.07542	−0.537709	+	0.843131i	$0.680710\pi$
$770$	−3.95973	−0.142699
$771$	47.5143	1.71118
$772$	−21.5824	−0.776768
$773$	−34.1733	−1.22913	−0.614565	−	0.788866i	$-0.710668\pi$
$773$	−34.1733	−1.22913	−0.614565	+	0.788866i	$0.710668\pi$
$774$	11.5203	0.414089
$775$	−11.1465	−0.400395
$776$	15.2285	0.546671
$777$	12.8712	0.461752
$778$	−12.1389	−0.435200
$779$	1.79112	0.0641735
$780$	11.0517	0.395716
$781$	10.3687	0.371021
$782$	−1.73140	−0.0619147
$783$	−12.2327	−0.437161
$784$	−5.85401	−0.209072
$785$	−15.9754	−0.570186
$786$	−27.7892	−0.991209
$787$	47.4957	1.69304	0.846520	−	0.532357i	$-0.178694\pi$
$787$	47.4957	1.69304	0.846520	+	0.532357i	$0.178694\pi$
$788$	2.70895	0.0965024
$789$	−45.0315	−1.60316
$790$	10.0120	0.356212
$791$	−12.9590	−0.460770
$792$	7.60349	0.270178
$793$	8.02024	0.284807
$794$	−9.71956	−0.344934
$795$	−64.1653	−2.27571
$796$	20.2479	0.717668
$797$	9.12693	0.323293	0.161646	−	0.986849i	$-0.448320\pi$
$797$	9.12693	0.323293	0.161646	+	0.986849i	$0.448320\pi$
$798$	−2.82932	−0.100157
$799$	−10.8517	−0.383904
$800$	−1.24125	−0.0438848
$801$	47.6346	1.68309
$802$	−4.73440	−0.167177
$803$	11.2520	0.397075
$804$	29.5039	1.04052
$805$	0.461379	0.0162615
$806$	−19.3685	−0.682228
$807$	−19.7540	−0.695374
$808$	−10.4351	−0.367105
$809$	47.3604	1.66510	0.832552	−	0.553946i	$-0.186879\pi$
$809$	47.3604	1.66510	0.832552	+	0.553946i	$0.186879\pi$
$810$	9.83596	0.345600
$811$	−21.1504	−0.742690	−0.371345	−	0.928495i	$-0.621103\pi$
$811$	−21.1504	−0.742690	−0.371345	+	0.928495i	$0.621103\pi$
$812$	−5.02873	−0.176474
$813$	−50.6159	−1.77518
$814$	8.67940	0.304213
$815$	−8.20977	−0.287576
$816$	20.5846	0.720607
$817$	−2.89071	−0.101133
$818$	−25.6040	−0.895224
$819$	−9.20167	−0.321532
$820$	3.47253	0.121266
$821$	−43.0150	−1.50123	−0.750617	−	0.660738i	$-0.770243\pi$
$821$	−43.0150	−1.50123	−0.750617	+	0.660738i	$0.770243\pi$
$822$	37.3786	1.30373
$823$	−4.43824	−0.154707	−0.0773537	−	0.997004i	$-0.524647\pi$
$823$	−4.43824	−0.154707	−0.0773537	+	0.997004i	$0.524647\pi$
$824$	−9.22594	−0.321401
$825$	−6.25900	−0.217910
$826$	2.13386	0.0742464
$827$	15.4972	0.538891	0.269446	−	0.963016i	$-0.413160\pi$
$827$	15.4972	0.538891	0.269446	+	0.963016i	$0.413160\pi$
$828$	−0.885942	−0.0307886
$829$	−22.4983	−0.781397	−0.390699	−	0.920519i	$-0.627767\pi$
$829$	−22.4983	−0.781397	−0.390699	+	0.920519i	$0.627767\pi$
$830$	0.447716	0.0155404
$831$	64.8604	2.24998
$832$	−2.15683	−0.0747748
$833$	−45.5937	−1.57973
$834$	22.9884	0.796025
$835$	21.2290	0.734659
$836$	−1.90789	−0.0659858
$837$	23.3849	0.808299
$838$	33.0959	1.14328
$839$	−26.7705	−0.924219	−0.462110	−	0.886823i	$-0.652907\pi$
$839$	−26.7705	−0.924219	−0.462110	+	0.886823i	$0.652907\pi$
$840$	−5.48535	−0.189262
$841$	−6.93337	−0.239082
$842$	−12.1072	−0.417240
$843$	−10.0300	−0.345450
$844$	−1.00000	−0.0344214
$845$	16.1848	0.556774
$846$	−5.55270	−0.190906
$847$	−7.87890	−0.270722
$848$	12.5224	0.430020
$849$	−73.4486	−2.52075
$850$	−9.66742	−0.331590
$851$	−1.01131	−0.0346671
$852$	14.3636	0.492088
$853$	−22.4303	−0.767999	−0.384000	−	0.923333i	$-0.625454\pi$
$853$	−22.4303	−0.767999	−0.384000	+	0.923333i	$0.625454\pi$
$854$	−3.98071	−0.136217
$855$	7.72647	0.264240
$856$	14.4935	0.495376
$857$	−53.5167	−1.82810	−0.914048	−	0.405606i	$-0.867061\pi$
$857$	−53.5167	−1.82810	−0.914048	+	0.405606i	$0.867061\pi$
$858$	−10.8758	−0.371295
$859$	27.0441	0.922732	0.461366	−	0.887210i	$-0.347359\pi$
$859$	27.0441	0.922732	0.461366	+	0.887210i	$0.347359\pi$
$860$	−5.60436	−0.191107
$861$	−5.06765	−0.172705
$862$	34.9672	1.19099
$863$	5.19410	0.176809	0.0884046	−	0.996085i	$-0.471823\pi$
$863$	5.19410	0.176809	0.0884046	+	0.996085i	$0.471823\pi$
$864$	2.60408	0.0885927
$865$	46.0275	1.56498
$866$	−13.3544	−0.453800
$867$	115.392	3.91892
$868$	9.61325	0.326295
$869$	−9.85266	−0.334229
$870$	24.0703	0.816060
$871$	−24.0771	−0.815820
$872$	0.377049	0.0127685
$873$	60.6899	2.05404
$874$	0.222303	0.00751952
$875$	12.9534	0.437905
$876$	15.5872	0.526644
$877$	6.53558	0.220691	0.110345	−	0.993893i	$-0.464804\pi$
$877$	6.53558	0.220691	0.110345	+	0.993893i	$0.464804\pi$
$878$	−16.9041	−0.570487
$879$	−22.4313	−0.756588
$880$	−3.69892	−0.124691
$881$	2.04714	0.0689700	0.0344850	−	0.999405i	$-0.489021\pi$
$881$	2.04714	0.0689700	0.0344850	+	0.999405i	$0.489021\pi$
$882$	−23.3299	−0.785559
$883$	−25.2091	−0.848353	−0.424176	−	0.905580i	$-0.639436\pi$
$883$	−25.2091	−0.848353	−0.424176	+	0.905580i	$0.639436\pi$
$884$	−16.7984	−0.564991
$885$	−10.2138	−0.343334
$886$	−16.8731	−0.566863
$887$	−2.64346	−0.0887588	−0.0443794	−	0.999015i	$-0.514131\pi$
$887$	−2.64346	−0.0887588	−0.0443794	+	0.999015i	$0.514131\pi$
$888$	12.0234	0.403480
$889$	−16.0716	−0.539023
$890$	−23.1731	−0.776765
$891$	−9.67940	−0.324272
$892$	−4.85742	−0.162638
$893$	1.39330	0.0466250
$894$	−40.5472	−1.35610
$895$	−50.4137	−1.68515
$896$	1.07051	0.0357632
$897$	1.26723	0.0423115
$898$	13.0010	0.433850
$899$	−42.1840	−1.40692
$900$	−4.94674	−0.164891
$901$	97.5299	3.24919
$902$	−3.41726	−0.113782
$903$	8.17875	0.272172
$904$	−12.1055	−0.402622
$905$	−32.5779	−1.08293
$906$	−29.9538	−0.995149
$907$	−42.4368	−1.40909	−0.704546	−	0.709658i	$-0.748849\pi$
$907$	−42.4368	−1.40909	−0.704546	+	0.709658i	$0.748849\pi$
$908$	−26.4589	−0.878068
$909$	−41.5868	−1.37935
$910$	4.47640	0.148391
$911$	−20.5445	−0.680669	−0.340334	−	0.940304i	$-0.610540\pi$
$911$	−20.5445	−0.680669	−0.340334	+	0.940304i	$0.610540\pi$
$912$	−2.64297	−0.0875175
$913$	−0.440589	−0.0145814
$914$	−10.9211	−0.361237
$915$	19.0539	0.629903
$916$	−8.43744	−0.278781
$917$	−11.2558	−0.371698
$918$	20.2818	0.669398
$919$	−34.6698	−1.14365	−0.571826	−	0.820375i	$-0.693765\pi$
$919$	−34.6698	−1.14365	−0.571826	+	0.820375i	$0.693765\pi$
$920$	0.430990	0.0142093
$921$	12.8146	0.422256
$922$	−18.2235	−0.600158
$923$	−11.7216	−0.385821
$924$	5.39804	0.177582
$925$	−5.64672	−0.185663
$926$	−0.303308	−0.00996733
$927$	−36.7680	−1.20762
$928$	−4.69751	−0.154203
$929$	40.0901	1.31531	0.657657	−	0.753318i	$-0.271548\pi$
$929$	40.0901	1.31531	0.657657	+	0.753318i	$0.271548\pi$
$930$	−46.0144	−1.50887
$931$	5.85401	0.191857
$932$	1.96091	0.0642319
$933$	−37.4018	−1.22448
$934$	27.4837	0.899293
$935$	−28.8089	−0.942151
$936$	−8.59560	−0.280956
$937$	−47.6590	−1.55695	−0.778477	−	0.627674i	$-0.784007\pi$
$937$	−47.6590	−1.55695	−0.778477	+	0.627674i	$0.784007\pi$
$938$	11.9503	0.390190
$939$	61.8638	2.01885
$940$	2.70126	0.0881054
$941$	−1.82234	−0.0594066	−0.0297033	−	0.999559i	$-0.509456\pi$
$941$	−1.82234	−0.0594066	−0.0297033	+	0.999559i	$0.509456\pi$
$942$	21.7782	0.709572
$943$	0.398171	0.0129662
$944$	1.99331	0.0648768
$945$	−5.40464	−0.175813
$946$	5.51516	0.179313
$947$	−27.9604	−0.908591	−0.454296	−	0.890851i	$-0.650109\pi$
$947$	−27.9604	−0.908591	−0.454296	+	0.890851i	$0.650109\pi$
$948$	−13.6487	−0.443290
$949$	−12.7202	−0.412915
$950$	1.24125	0.0402715
$951$	−25.1528	−0.815636
$952$	8.33761	0.270223
$953$	1.91232	0.0619462	0.0309731	−	0.999520i	$-0.490139\pi$
$953$	1.91232	0.0619462	0.0309731	+	0.999520i	$0.490139\pi$
$954$	49.9053	1.61574
$955$	−40.3757	−1.30653
$956$	14.5004	0.468976
$957$	−23.6872	−0.765698
$958$	9.72959	0.314349
$959$	15.1398	0.488891
$960$	−5.12406	−0.165378
$961$	49.6418	1.60135
$962$	−9.81190	−0.316348
$963$	57.7606	1.86131
$964$	−1.57763	−0.0508122
$965$	41.8429	1.34697
$966$	−0.628967	−0.0202367
$967$	−5.75596	−0.185099	−0.0925496	−	0.995708i	$-0.529502\pi$
$967$	−5.75596	−0.185099	−0.0925496	+	0.995708i	$0.529502\pi$
$968$	−7.35995	−0.236558
$969$	−20.5846	−0.661274
$970$	−29.5242	−0.947966
$971$	2.61039	0.0837714	0.0418857	−	0.999122i	$-0.486663\pi$
$971$	2.61039	0.0837714	0.0418857	+	0.999122i	$0.486663\pi$
$972$	−21.2210	−0.680662
$973$	9.31124	0.298505
$974$	−36.9611	−1.18431
$975$	7.07568	0.226603
$976$	−3.71852	−0.119027
$977$	−45.9336	−1.46954	−0.734772	−	0.678314i	$-0.762711\pi$
$977$	−45.9336	−1.46954	−0.734772	+	0.678314i	$0.762711\pi$
$978$	11.1918	0.357875
$979$	22.8043	0.728828
$980$	11.3495	0.362545
$981$	1.50265	0.0479758
$982$	24.7579	0.790056
$983$	−37.6805	−1.20182	−0.600911	−	0.799316i	$-0.705195\pi$
$983$	−37.6805	−1.20182	−0.600911	+	0.799316i	$0.705195\pi$
$984$	−4.73387	−0.150910
$985$	−5.25198	−0.167342
$986$	−36.5864	−1.16515
$987$	−3.94209	−0.125478
$988$	2.15683	0.0686180
$989$	−0.642614	−0.0204339
$990$	−14.7413	−0.468508
$991$	−59.4001	−1.88691	−0.943454	−	0.331504i	$-0.892444\pi$
$991$	−59.4001	−1.88691	−0.943454	+	0.331504i	$0.892444\pi$
$992$	8.98008	0.285118
$993$	−18.6882	−0.593052
$994$	5.81782	0.184530
$995$	−39.2556	−1.24449
$996$	−0.610341	−0.0193394
$997$	−12.1249	−0.383999	−0.192000	−	0.981395i	$-0.561497\pi$
$997$	−12.1249	−0.383999	−0.192000	+	0.981395i	$0.561497\pi$
$998$	21.1337	0.668977
$999$	11.8465	0.374808

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.j.1.39	✓	47

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.j.1.39	✓	47	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:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.64297 q^{3} +1.00000 q^{4} -1.93875 q^{5} +2.64297 q^{6} +1.07051 q^{7} +1.00000 q^{8} +3.98529 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.64297 q^{3} +1.00000 q^{4} -1.93875 q^{5} +2.64297 q^{6} +1.07051 q^{7} +1.00000 q^{8} +3.98529 q^{9} -1.93875 q^{10} +1.90789 q^{11} +2.64297 q^{12} -2.15683 q^{13} +1.07051 q^{14} -5.12406 q^{15} +1.00000 q^{16} +7.78845 q^{17} +3.98529 q^{18} -1.00000 q^{19} -1.93875 q^{20} +2.82932 q^{21} +1.90789 q^{22} -0.222303 q^{23} +2.64297 q^{24} -1.24125 q^{25} -2.15683 q^{26} +2.60408 q^{27} +1.07051 q^{28} -4.69751 q^{29} -5.12406 q^{30} +8.98008 q^{31} +1.00000 q^{32} +5.04250 q^{33} +7.78845 q^{34} -2.07545 q^{35} +3.98529 q^{36} +4.54921 q^{37} -1.00000 q^{38} -5.70045 q^{39} -1.93875 q^{40} -1.79112 q^{41} +2.82932 q^{42} +2.89071 q^{43} +1.90789 q^{44} -7.72647 q^{45} -0.222303 q^{46} -1.39330 q^{47} +2.64297 q^{48} -5.85401 q^{49} -1.24125 q^{50} +20.5846 q^{51} -2.15683 q^{52} +12.5224 q^{53} +2.60408 q^{54} -3.69892 q^{55} +1.07051 q^{56} -2.64297 q^{57} -4.69751 q^{58} +1.99331 q^{59} -5.12406 q^{60} -3.71852 q^{61} +8.98008 q^{62} +4.26628 q^{63} +1.00000 q^{64} +4.18156 q^{65} +5.04250 q^{66} +11.1632 q^{67} +7.78845 q^{68} -0.587541 q^{69} -2.07545 q^{70} +5.43463 q^{71} +3.98529 q^{72} +5.89762 q^{73} +4.54921 q^{74} -3.28059 q^{75} -1.00000 q^{76} +2.04241 q^{77} -5.70045 q^{78} -5.16416 q^{79} -1.93875 q^{80} -5.07335 q^{81} -1.79112 q^{82} -0.230930 q^{83} +2.82932 q^{84} -15.0999 q^{85} +2.89071 q^{86} -12.4154 q^{87} +1.90789 q^{88} +11.9526 q^{89} -7.72647 q^{90} -2.30891 q^{91} -0.222303 q^{92} +23.7341 q^{93} -1.39330 q^{94} +1.93875 q^{95} +2.64297 q^{96} +15.2285 q^{97} -5.85401 q^{98} +7.60349 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9}+O(q^{10}) \) 47 * q + 47 * q^2 + 10 * q^3 + 47 * q^4 + 15 * q^5 + 10 * q^6 + 47 * q^8 + 69 * q^9	\( 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9} + 15 q^{10} + 17 q^{11} + 10 q^{12} + 27 q^{13} + 10 q^{15} + 47 q^{16} + 16 q^{17} + 69 q^{18} - 47 q^{19} + 15 q^{20} + 26 q^{21} + 17 q^{22} + 24 q^{23} + 10 q^{24} + 86 q^{25} + 27 q^{26} + 43 q^{27} + 58 q^{29} + 10 q^{30} + 21 q^{31} + 47 q^{32} + 18 q^{33} + 16 q^{34} + 24 q^{35} + 69 q^{36} + 78 q^{37} - 47 q^{38} - 4 q^{39} + 15 q^{40} + 53 q^{41} + 26 q^{42} + 47 q^{43} + 17 q^{44} + 23 q^{45} + 24 q^{46} + 16 q^{47} + 10 q^{48} + 93 q^{49} + 86 q^{50} + 28 q^{51} + 27 q^{52} + 43 q^{53} + 43 q^{54} + 23 q^{55} - 10 q^{57} + 58 q^{58} + 3 q^{59} + 10 q^{60} + 12 q^{61} + 21 q^{62} - 5 q^{63} + 47 q^{64} + 62 q^{65} + 18 q^{66} + 68 q^{67} + 16 q^{68} + 12 q^{69} + 24 q^{70} - 13 q^{71} + 69 q^{72} + 35 q^{73} + 78 q^{74} + 22 q^{75} - 47 q^{76} + 26 q^{77} - 4 q^{78} + 21 q^{79} + 15 q^{80} + 123 q^{81} + 53 q^{82} + 23 q^{83} + 26 q^{84} + 38 q^{85} + 47 q^{86} + 39 q^{87} + 17 q^{88} + 24 q^{89} + 23 q^{90} + 49 q^{91} + 24 q^{92} + 91 q^{93} + 16 q^{94} - 15 q^{95} + 10 q^{96} + 88 q^{97} + 93 q^{98} + 26 q^{99}+O(q^{100}) \) 47 * q + 47 * q^2 + 10 * q^3 + 47 * q^4 + 15 * q^5 + 10 * q^6 + 47 * q^8 + 69 * q^9 + 15 * q^10 + 17 * q^11 + 10 * q^12 + 27 * q^13 + 10 * q^15 + 47 * q^16 + 16 * q^17 + 69 * q^18 - 47 * q^19 + 15 * q^20 + 26 * q^21 + 17 * q^22 + 24 * q^23 + 10 * q^24 + 86 * q^25 + 27 * q^26 + 43 * q^27 + 58 * q^29 + 10 * q^30 + 21 * q^31 + 47 * q^32 + 18 * q^33 + 16 * q^34 + 24 * q^35 + 69 * q^36 + 78 * q^37 - 47 * q^38 - 4 * q^39 + 15 * q^40 + 53 * q^41 + 26 * q^42 + 47 * q^43 + 17 * q^44 + 23 * q^45 + 24 * q^46 + 16 * q^47 + 10 * q^48 + 93 * q^49 + 86 * q^50 + 28 * q^51 + 27 * q^52 + 43 * q^53 + 43 * q^54 + 23 * q^55 - 10 * q^57 + 58 * q^58 + 3 * q^59 + 10 * q^60 + 12 * q^61 + 21 * q^62 - 5 * q^63 + 47 * q^64 + 62 * q^65 + 18 * q^66 + 68 * q^67 + 16 * q^68 + 12 * q^69 + 24 * q^70 - 13 * q^71 + 69 * q^72 + 35 * q^73 + 78 * q^74 + 22 * q^75 - 47 * q^76 + 26 * q^77 - 4 * q^78 + 21 * q^79 + 15 * q^80 + 123 * q^81 + 53 * q^82 + 23 * q^83 + 26 * q^84 + 38 * q^85 + 47 * q^86 + 39 * q^87 + 17 * q^88 + 24 * q^89 + 23 * q^90 + 49 * q^91 + 24 * q^92 + 91 * q^93 + 16 * q^94 - 15 * q^95 + 10 * q^96 + 88 * q^97 + 93 * q^98 + 26 * q^99

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