LMFDB - Embedded newform 4001.2.a.a.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4001,2,Mod(1,4001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4001, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4001.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:	$31.9481458487$
Analytic rank:	$1$
Dimension:	$149$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	4001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.21148 q^{2} +1.63586 q^{3} +2.89063 q^{4} +1.70947 q^{5} -3.61768 q^{6} +0.528860 q^{7} -1.96961 q^{8} -0.323947 q^{9} +O(q^{10})$	\(q-2.21148 q^{2} +1.63586 q^{3} +2.89063 q^{4} +1.70947 q^{5} -3.61768 q^{6} +0.528860 q^{7} -1.96961 q^{8} -0.323947 q^{9} -3.78045 q^{10} +2.09152 q^{11} +4.72868 q^{12} -0.0678126 q^{13} -1.16956 q^{14} +2.79646 q^{15} -1.42552 q^{16} -4.09383 q^{17} +0.716401 q^{18} -1.35926 q^{19} +4.94144 q^{20} +0.865143 q^{21} -4.62534 q^{22} +1.36811 q^{23} -3.22201 q^{24} -2.07772 q^{25} +0.149966 q^{26} -5.43753 q^{27} +1.52874 q^{28} -5.01120 q^{29} -6.18430 q^{30} -1.79613 q^{31} +7.09172 q^{32} +3.42144 q^{33} +9.05341 q^{34} +0.904069 q^{35} -0.936410 q^{36} +3.68997 q^{37} +3.00598 q^{38} -0.110932 q^{39} -3.36698 q^{40} -8.48459 q^{41} -1.91324 q^{42} -3.01344 q^{43} +6.04580 q^{44} -0.553777 q^{45} -3.02555 q^{46} -10.2582 q^{47} -2.33195 q^{48} -6.72031 q^{49} +4.59483 q^{50} -6.69695 q^{51} -0.196021 q^{52} -0.357071 q^{53} +12.0250 q^{54} +3.57538 q^{55} -1.04165 q^{56} -2.22357 q^{57} +11.0822 q^{58} -3.48263 q^{59} +8.08353 q^{60} +11.2101 q^{61} +3.97209 q^{62} -0.171323 q^{63} -12.8321 q^{64} -0.115923 q^{65} -7.56643 q^{66} -14.4374 q^{67} -11.8337 q^{68} +2.23805 q^{69} -1.99933 q^{70} +7.25260 q^{71} +0.638048 q^{72} -9.84880 q^{73} -8.16029 q^{74} -3.39887 q^{75} -3.92913 q^{76} +1.10612 q^{77} +0.245324 q^{78} +12.2141 q^{79} -2.43688 q^{80} -7.92322 q^{81} +18.7635 q^{82} +6.04296 q^{83} +2.50081 q^{84} -6.99827 q^{85} +6.66416 q^{86} -8.19764 q^{87} -4.11947 q^{88} -11.3801 q^{89} +1.22466 q^{90} -0.0358634 q^{91} +3.95471 q^{92} -2.93822 q^{93} +22.6858 q^{94} -2.32362 q^{95} +11.6011 q^{96} +6.55422 q^{97} +14.8618 q^{98} -0.677540 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 149 q - 6 q^{2} - 28 q^{3} + 116 q^{4} - 19 q^{5} - 31 q^{6} - 47 q^{7} - 15 q^{8} + 115 q^{9}+O(q^{10}) $ 149 * q - 6 * q^2 - 28 * q^3 + 116 * q^4 - 19 * q^5 - 31 * q^6 - 47 * q^7 - 15 * q^8 + 115 * q^9	\( 149 q - 6 q^{2} - 28 q^{3} + 116 q^{4} - 19 q^{5} - 31 q^{6} - 47 q^{7} - 15 q^{8} + 115 q^{9} - 48 q^{10} - 31 q^{11} - 61 q^{12} - 54 q^{13} - 44 q^{14} - 65 q^{15} + 58 q^{16} - 26 q^{17} - 23 q^{18} - 86 q^{19} - 52 q^{20} - 30 q^{21} - 56 q^{22} - 63 q^{23} - 90 q^{24} + 92 q^{25} - 38 q^{26} - 103 q^{27} - 77 q^{28} - 51 q^{29} - 22 q^{30} - 256 q^{31} - 21 q^{32} - 36 q^{33} - 124 q^{34} - 50 q^{35} + 45 q^{36} - 42 q^{37} - 14 q^{38} - 119 q^{39} - 131 q^{40} - 55 q^{41} - 5 q^{42} - 55 q^{43} - 54 q^{44} - 68 q^{45} - 59 q^{46} - 82 q^{47} - 89 q^{48} + 30 q^{49} + 13 q^{50} - 83 q^{51} - 126 q^{52} - 23 q^{53} - 83 q^{54} - 244 q^{55} - 94 q^{56} - 14 q^{57} - 60 q^{58} - 93 q^{59} - 70 q^{60} - 139 q^{61} - 10 q^{62} - 120 q^{63} - 45 q^{64} - 37 q^{65} - 28 q^{66} - 110 q^{67} - 27 q^{68} - 79 q^{69} - 78 q^{70} - 123 q^{71} - 74 q^{73} - 25 q^{74} - 146 q^{75} - 192 q^{76} - q^{77} + 26 q^{78} - 273 q^{79} - 51 q^{80} + 41 q^{81} - 120 q^{82} - 27 q^{83} - 14 q^{84} - 71 q^{85} + 3 q^{86} - 98 q^{87} - 143 q^{88} - 70 q^{89} - 24 q^{90} - 256 q^{91} - 47 q^{92} + 16 q^{93} - 151 q^{94} - 83 q^{95} - 137 q^{96} - 108 q^{97} + 17 q^{98} - 131 q^{99}+O(q^{100}) \) 149 * q - 6 * q^2 - 28 * q^3 + 116 * q^4 - 19 * q^5 - 31 * q^6 - 47 * q^7 - 15 * q^8 + 115 * q^9 - 48 * q^10 - 31 * q^11 - 61 * q^12 - 54 * q^13 - 44 * q^14 - 65 * q^15 + 58 * q^16 - 26 * q^17 - 23 * q^18 - 86 * q^19 - 52 * q^20 - 30 * q^21 - 56 * q^22 - 63 * q^23 - 90 * q^24 + 92 * q^25 - 38 * q^26 - 103 * q^27 - 77 * q^28 - 51 * q^29 - 22 * q^30 - 256 * q^31 - 21 * q^32 - 36 * q^33 - 124 * q^34 - 50 * q^35 + 45 * q^36 - 42 * q^37 - 14 * q^38 - 119 * q^39 - 131 * q^40 - 55 * q^41 - 5 * q^42 - 55 * q^43 - 54 * q^44 - 68 * q^45 - 59 * q^46 - 82 * q^47 - 89 * q^48 + 30 * q^49 + 13 * q^50 - 83 * q^51 - 126 * q^52 - 23 * q^53 - 83 * q^54 - 244 * q^55 - 94 * q^56 - 14 * q^57 - 60 * q^58 - 93 * q^59 - 70 * q^60 - 139 * q^61 - 10 * q^62 - 120 * q^63 - 45 * q^64 - 37 * q^65 - 28 * q^66 - 110 * q^67 - 27 * q^68 - 79 * q^69 - 78 * q^70 - 123 * q^71 - 74 * q^73 - 25 * q^74 - 146 * q^75 - 192 * q^76 - q^77 + 26 * q^78 - 273 * q^79 - 51 * q^80 + 41 * q^81 - 120 * q^82 - 27 * q^83 - 14 * q^84 - 71 * q^85 + 3 * q^86 - 98 * q^87 - 143 * q^88 - 70 * q^89 - 24 * q^90 - 256 * q^91 - 47 * q^92 + 16 * q^93 - 151 * q^94 - 83 * q^95 - 137 * q^96 - 108 * q^97 + 17 * q^98 - 131 * 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 $

$2$	−2.21148	−1.56375	−0.781875	−	0.623435i	$-0.785737\pi$
$2$	−2.21148	−1.56375	−0.781875	+	0.623435i	$0.785737\pi$
$3$	1.63586	0.944467	0.472233	−	0.881474i	$-0.343448\pi$
$3$	1.63586	0.944467	0.472233	+	0.881474i	$0.343448\pi$
$4$	2.89063	1.44532
$5$	1.70947	0.764497	0.382249	−	0.924060i	$-0.375150\pi$
$5$	1.70947	0.764497	0.382249	+	0.924060i	$0.375150\pi$
$6$	−3.61768	−1.47691
$7$	0.528860	0.199890	0.0999451	−	0.994993i	$-0.468133\pi$
$7$	0.528860	0.199890	0.0999451	+	0.994993i	$0.468133\pi$
$8$	−1.96961	−0.696361
$9$	−0.323947	−0.107982
$10$	−3.78045	−1.19548
$11$	2.09152	0.630616	0.315308	−	0.948989i	$-0.397892\pi$
$11$	2.09152	0.630616	0.315308	+	0.948989i	$0.397892\pi$
$12$	4.72868	1.36505
$13$	−0.0678126	−0.0188078	−0.00940391	−	0.999956i	$-0.502993\pi$
$13$	−0.0678126	−0.0188078	−0.00940391	+	0.999956i	$0.502993\pi$
$14$	−1.16956	−0.312579
$15$	2.79646	0.722042
$16$	−1.42552	−0.356380
$17$	−4.09383	−0.992899	−0.496450	−	0.868065i	$-0.665363\pi$
$17$	−4.09383	−0.992899	−0.496450	+	0.868065i	$0.665363\pi$
$18$	0.716401	0.168857
$19$	−1.35926	−0.311837	−0.155918	−	0.987770i	$-0.549834\pi$
$19$	−1.35926	−0.311837	−0.155918	+	0.987770i	$0.549834\pi$
$20$	4.94144	1.10494
$21$	0.865143	0.188790
$22$	−4.62534	−0.986126
$23$	1.36811	0.285272	0.142636	−	0.989775i	$-0.454442\pi$
$23$	1.36811	0.285272	0.142636	+	0.989775i	$0.454442\pi$
$24$	−3.22201	−0.657690
$25$	−2.07772	−0.415544
$26$	0.149966	0.0294107
$27$	−5.43753	−1.04645
$28$	1.52874	0.288904
$29$	−5.01120	−0.930556	−0.465278	−	0.885164i	$-0.654046\pi$
$29$	−5.01120	−0.930556	−0.465278	+	0.885164i	$0.654046\pi$
$30$	−6.18430	−1.12909
$31$	−1.79613	−0.322594	−0.161297	−	0.986906i	$-0.551568\pi$
$31$	−1.79613	−0.322594	−0.161297	+	0.986906i	$0.551568\pi$
$32$	7.09172	1.25365
$33$	3.42144	0.595596
$34$	9.05341	1.55265
$35$	0.904069	0.152816
$36$	−0.936410	−0.156068
$37$	3.68997	0.606628	0.303314	−	0.952891i	$-0.401907\pi$
$37$	3.68997	0.606628	0.303314	+	0.952891i	$0.401907\pi$
$38$	3.00598	0.487634
$39$	−0.110932	−0.0177634
$40$	−3.36698	−0.532366
$41$	−8.48459	−1.32507	−0.662535	−	0.749031i	$-0.730519\pi$
$41$	−8.48459	−1.32507	−0.662535	+	0.749031i	$0.730519\pi$
$42$	−1.91324	−0.295220
$43$	−3.01344	−0.459546	−0.229773	−	0.973244i	$-0.573798\pi$
$43$	−3.01344	−0.459546	−0.229773	+	0.973244i	$0.573798\pi$
$44$	6.04580	0.911439
$45$	−0.553777	−0.0825521
$46$	−3.02555	−0.446093
$47$	−10.2582	−1.49632	−0.748158	−	0.663520i	$-0.769062\pi$
$47$	−10.2582	−1.49632	−0.748158	+	0.663520i	$0.769062\pi$
$48$	−2.33195	−0.336589
$49$	−6.72031	−0.960044
$50$	4.59483	0.649807
$51$	−6.69695	−0.937761
$52$	−0.196021	−0.0271832
$53$	−0.357071	−0.0490475	−0.0245237	−	0.999699i	$-0.507807\pi$
$53$	−0.357071	−0.0490475	−0.0245237	+	0.999699i	$0.507807\pi$
$54$	12.0250	1.63639
$55$	3.57538	0.482104
$56$	−1.04165	−0.139196
$57$	−2.22357	−0.294519
$58$	11.0822	1.45516
$59$	−3.48263	−0.453399	−0.226700	−	0.973965i	$-0.572794\pi$
$59$	−3.48263	−0.453399	−0.226700	+	0.973965i	$0.572794\pi$
$60$	8.08353	1.04358
$61$	11.2101	1.43530	0.717652	−	0.696402i	$-0.245217\pi$
$61$	11.2101	1.43530	0.717652	+	0.696402i	$0.245217\pi$
$62$	3.97209	0.504456
$63$	−0.171323	−0.0215846
$64$	−12.8321	−1.60402
$65$	−0.115923	−0.0143785
$66$	−7.56643	−0.931363
$67$	−14.4374	−1.76380	−0.881902	−	0.471432i	$-0.843737\pi$
$67$	−14.4374	−1.76380	−0.881902	+	0.471432i	$0.843737\pi$
$68$	−11.8337	−1.43505
$69$	2.23805	0.269430
$70$	−1.99933	−0.238965
$71$	7.25260	0.860725	0.430362	−	0.902656i	$-0.358386\pi$
$71$	7.25260	0.860725	0.430362	+	0.902656i	$0.358386\pi$
$72$	0.638048	0.0751947
$73$	−9.84880	−1.15271	−0.576357	−	0.817198i	$-0.695526\pi$
$73$	−9.84880	−1.15271	−0.576357	+	0.817198i	$0.695526\pi$
$74$	−8.16029	−0.948615
$75$	−3.39887	−0.392467
$76$	−3.92913	−0.450702
$77$	1.10612	0.126054
$78$	0.245324	0.0277775
$79$	12.2141	1.37420	0.687098	−	0.726565i	$-0.258884\pi$
$79$	12.2141	1.37420	0.687098	+	0.726565i	$0.258884\pi$
$80$	−2.43688	−0.272451
$81$	−7.92322	−0.880358
$82$	18.7635	2.07208
$83$	6.04296	0.663301	0.331650	−	0.943402i	$-0.392395\pi$
$83$	6.04296	0.663301	0.331650	+	0.943402i	$0.392395\pi$
$84$	2.50081	0.272861
$85$	−6.99827	−0.759069
$86$	6.66416	0.718614
$87$	−8.19764	−0.878880
$88$	−4.11947	−0.439137
$89$	−11.3801	−1.20628	−0.603142	−	0.797634i	$-0.706085\pi$
$89$	−11.3801	−1.20628	−0.603142	+	0.797634i	$0.706085\pi$
$90$	1.22466	0.129091
$91$	−0.0358634	−0.00375950
$92$	3.95471	0.412307
$93$	−2.93822	−0.304679
$94$	22.6858	2.33987
$95$	−2.32362	−0.238398
$96$	11.6011	1.18403
$97$	6.55422	0.665480	0.332740	−	0.943019i	$-0.392027\pi$
$97$	6.55422	0.665480	0.332740	+	0.943019i	$0.392027\pi$
$98$	14.8618	1.50127
$99$	−0.677540	−0.0680953
$100$	−6.00592	−0.600592
$101$	−8.44879	−0.840686	−0.420343	−	0.907365i	$-0.638090\pi$
$101$	−8.44879	−0.840686	−0.420343	+	0.907365i	$0.638090\pi$
$102$	14.8102	1.46642
$103$	−4.29099	−0.422804	−0.211402	−	0.977399i	$-0.567803\pi$
$103$	−4.29099	−0.422804	−0.211402	+	0.977399i	$0.567803\pi$
$104$	0.133564	0.0130970
$105$	1.47893	0.144329
$106$	0.789654	0.0766980
$107$	−3.22842	−0.312103	−0.156051	−	0.987749i	$-0.549877\pi$
$107$	−3.22842	−0.312103	−0.156051	+	0.987749i	$0.549877\pi$
$108$	−15.7179	−1.51245
$109$	−6.15670	−0.589705	−0.294853	−	0.955543i	$-0.595271\pi$
$109$	−6.15670	−0.589705	−0.294853	+	0.955543i	$0.595271\pi$
$110$	−7.90687	−0.753891
$111$	6.03630	0.572940
$112$	−0.753900	−0.0712368
$113$	7.08347	0.666356	0.333178	−	0.942864i	$-0.391879\pi$
$113$	7.08347	0.666356	0.333178	+	0.942864i	$0.391879\pi$
$114$	4.91738	0.460555
$115$	2.33875	0.218089
$116$	−14.4855	−1.34495
$117$	0.0219677	0.00203091
$118$	7.70175	0.709003
$119$	−2.16506	−0.198471
$120$	−5.50793	−0.502803
$121$	−6.62556	−0.602324
$122$	−24.7908	−2.24446
$123$	−13.8796	−1.25148
$124$	−5.19194	−0.466250
$125$	−12.0991	−1.08218
$126$	0.378876	0.0337529
$127$	−17.5829	−1.56023	−0.780113	−	0.625638i	$-0.784839\pi$
$127$	−17.5829	−1.56023	−0.780113	+	0.625638i	$0.784839\pi$
$128$	14.1945	1.25463
$129$	−4.92958	−0.434026
$130$	0.256362	0.0224844
$131$	2.64713	0.231281	0.115640	−	0.993291i	$-0.463108\pi$
$131$	2.64713	0.231281	0.115640	+	0.993291i	$0.463108\pi$
$132$	9.89011	0.860824
$133$	−0.718860	−0.0623331
$134$	31.9279	2.75815
$135$	−9.29528	−0.800010
$136$	8.06324	0.691417
$137$	8.68098	0.741666	0.370833	−	0.928700i	$-0.379072\pi$
$137$	8.68098	0.741666	0.370833	+	0.928700i	$0.379072\pi$
$138$	−4.94939	−0.421320
$139$	−7.69736	−0.652882	−0.326441	−	0.945218i	$-0.605849\pi$
$139$	−7.69736	−0.652882	−0.326441	+	0.945218i	$0.605849\pi$
$140$	2.61333	0.220867
$141$	−16.7811	−1.41322
$142$	−16.0389	−1.34596
$143$	−0.141831	−0.0118605
$144$	0.461792	0.0384827
$145$	−8.56649	−0.711408
$146$	21.7804	1.80256
$147$	−10.9935	−0.906730
$148$	10.6663	0.876769
$149$	18.4007	1.50745	0.753724	−	0.657191i	$-0.228256\pi$
$149$	18.4007	1.50745	0.753724	+	0.657191i	$0.228256\pi$
$150$	7.51652	0.613721
$151$	−1.87902	−0.152913	−0.0764564	−	0.997073i	$-0.524361\pi$
$151$	−1.87902	−0.152913	−0.0764564	+	0.997073i	$0.524361\pi$
$152$	2.67722	0.217151
$153$	1.32618	0.107216
$154$	−2.44616	−0.197117
$155$	−3.07042	−0.246622
$156$	−0.320664	−0.0256737
$157$	18.7523	1.49660	0.748298	−	0.663363i	$-0.230871\pi$
$157$	18.7523	1.49660	0.748298	+	0.663363i	$0.230871\pi$
$158$	−27.0113	−2.14890
$159$	−0.584120	−0.0463237
$160$	12.1231	0.958412
$161$	0.723541	0.0570230
$162$	17.5220	1.37666
$163$	2.30517	0.180555	0.0902773	−	0.995917i	$-0.471225\pi$
$163$	2.30517	0.180555	0.0902773	+	0.995917i	$0.471225\pi$
$164$	−24.5258	−1.91514
$165$	5.84884	0.455331
$166$	−13.3639	−1.03724
$167$	7.94224	0.614589	0.307294	−	0.951614i	$-0.400576\pi$
$167$	7.94224	0.614589	0.307294	+	0.951614i	$0.400576\pi$
$168$	−1.70399	−0.131466
$169$	−12.9954	−0.999646
$170$	15.4765	1.18699
$171$	0.440329	0.0336728
$172$	−8.71074	−0.664188
$173$	−17.5734	−1.33608	−0.668042	−	0.744124i	$-0.732867\pi$
$173$	−17.5734	−1.33608	−0.668042	+	0.744124i	$0.732867\pi$
$174$	18.1289	1.37435
$175$	−1.09882	−0.0830632
$176$	−2.98149	−0.224739
$177$	−5.69711	−0.428221
$178$	25.1667	1.88633
$179$	22.5408	1.68478	0.842389	−	0.538869i	$-0.181148\pi$
$179$	22.5408	1.68478	0.842389	+	0.538869i	$0.181148\pi$
$180$	−1.60076	−0.119314
$181$	−4.41274	−0.327996	−0.163998	−	0.986461i	$-0.552439\pi$
$181$	−4.41274	−0.327996	−0.163998	+	0.986461i	$0.552439\pi$
$182$	0.0793110	0.00587892
$183$	18.3382	1.35560
$184$	−2.69465	−0.198652
$185$	6.30789	0.463765
$186$	6.49781	0.476442
$187$	−8.56231	−0.626138
$188$	−29.6527	−2.16265
$189$	−2.87569	−0.209176
$190$	5.13863	0.372795
$191$	12.0731	0.873580	0.436790	−	0.899563i	$-0.356115\pi$
$191$	12.0731	0.873580	0.436790	+	0.899563i	$0.356115\pi$
$192$	−20.9916	−1.51494
$193$	−9.69792	−0.698071	−0.349036	−	0.937109i	$-0.613491\pi$
$193$	−9.69792	−0.698071	−0.349036	+	0.937109i	$0.613491\pi$
$194$	−14.4945	−1.04064
$195$	−0.189635	−0.0135800
$196$	−19.4259	−1.38757
$197$	4.87977	0.347669	0.173835	−	0.984775i	$-0.444384\pi$
$197$	4.87977	0.347669	0.173835	+	0.984775i	$0.444384\pi$
$198$	1.49836	0.106484
$199$	15.8615	1.12439	0.562195	−	0.827005i	$-0.309957\pi$
$199$	15.8615	1.12439	0.562195	+	0.827005i	$0.309957\pi$
$200$	4.09229	0.289369
$201$	−23.6176	−1.66586
$202$	18.6843	1.31462
$203$	−2.65022	−0.186009
$204$	−19.3584	−1.35536
$205$	−14.5041	−1.01301
$206$	9.48942	0.661159
$207$	−0.443196	−0.0308043
$208$	0.0966680	0.00670272
$209$	−2.84292	−0.196649
$210$	−3.27063	−0.225695
$211$	−2.90778	−0.200180	−0.100090	−	0.994978i	$-0.531913\pi$
$211$	−2.90778	−0.200180	−0.100090	+	0.994978i	$0.531913\pi$
$212$	−1.03216	−0.0708890
$213$	11.8643	0.812926
$214$	7.13957	0.488051
$215$	−5.15138	−0.351321
$216$	10.7098	0.728709
$217$	−0.949899	−0.0644834
$218$	13.6154	0.922151
$219$	−16.1113	−1.08870
$220$	10.3351	0.696792
$221$	0.277613	0.0186743
$222$	−13.3491	−0.895935
$223$	14.1731	0.949104	0.474552	−	0.880227i	$-0.342610\pi$
$223$	14.1731	0.949104	0.474552	+	0.880227i	$0.342610\pi$
$224$	3.75052	0.250592
$225$	0.673071	0.0448714
$226$	−15.6649	−1.04201
$227$	14.9373	0.991423	0.495712	−	0.868487i	$-0.334907\pi$
$227$	14.9373	0.991423	0.495712	+	0.868487i	$0.334907\pi$
$228$	−6.42752	−0.425673
$229$	−6.15553	−0.406769	−0.203384	−	0.979099i	$-0.565194\pi$
$229$	−6.15553	−0.406769	−0.203384	+	0.979099i	$0.565194\pi$
$230$	−5.17209	−0.341037
$231$	1.80946	0.119054
$232$	9.87010	0.648004
$233$	16.3813	1.07317	0.536587	−	0.843845i	$-0.319713\pi$
$233$	16.3813	1.07317	0.536587	+	0.843845i	$0.319713\pi$
$234$	−0.0485810	−0.00317584
$235$	−17.5361	−1.14393
$236$	−10.0670	−0.655305
$237$	19.9807	1.29788
$238$	4.78799	0.310359
$239$	12.8195	0.829227	0.414613	−	0.909998i	$-0.363917\pi$
$239$	12.8195	0.829227	0.414613	+	0.909998i	$0.363917\pi$
$240$	−3.98640	−0.257321
$241$	−19.1038	−1.23059	−0.615293	−	0.788299i	$-0.710962\pi$
$241$	−19.1038	−1.23059	−0.615293	+	0.788299i	$0.710962\pi$
$242$	14.6523	0.941884
$243$	3.35127	0.214984
$244$	32.4042	2.07447
$245$	−11.4881	−0.733951
$246$	30.6945	1.95701
$247$	0.0921752	0.00586497
$248$	3.53766	0.224642
$249$	9.88546	0.626466
$250$	26.7570	1.69226
$251$	7.22538	0.456062	0.228031	−	0.973654i	$-0.426771\pi$
$251$	7.22538	0.456062	0.228031	+	0.973654i	$0.426771\pi$
$252$	−0.495230	−0.0311966
$253$	2.86143	0.179897
$254$	38.8841	2.43980
$255$	−11.4482	−0.716915
$256$	−5.72661	−0.357913
$257$	6.62580	0.413306	0.206653	−	0.978414i	$-0.433743\pi$
$257$	6.62580	0.413306	0.206653	+	0.978414i	$0.433743\pi$
$258$	10.9017	0.678708
$259$	1.95148	0.121259
$260$	−0.335092	−0.0207815
$261$	1.62336	0.100484
$262$	−5.85407	−0.361666
$263$	17.5289	1.08088	0.540439	−	0.841383i	$-0.318258\pi$
$263$	17.5289	1.08088	0.540439	+	0.841383i	$0.318258\pi$
$264$	−6.73889	−0.414750
$265$	−0.610401	−0.0374967
$266$	1.58974	0.0974734
$267$	−18.6162	−1.13929
$268$	−41.7331	−2.54925
$269$	16.6977	1.01808	0.509039	−	0.860743i	$-0.330001\pi$
$269$	16.6977	1.01808	0.509039	+	0.860743i	$0.330001\pi$
$270$	20.5563	1.25102
$271$	20.6629	1.25518	0.627590	−	0.778544i	$-0.284042\pi$
$271$	20.6629	1.25518	0.627590	+	0.778544i	$0.284042\pi$
$272$	5.83583	0.353849
$273$	−0.0586676	−0.00355072
$274$	−19.1978	−1.15978
$275$	−4.34558	−0.262049
$276$	6.46937	0.389411
$277$	9.83948	0.591197	0.295599	−	0.955312i	$-0.404481\pi$
$277$	9.83948	0.591197	0.295599	+	0.955312i	$0.404481\pi$
$278$	17.0225	1.02094
$279$	0.581849	0.0348344
$280$	−1.78066	−0.106415
$281$	4.01330	0.239413	0.119707	−	0.992809i	$-0.461805\pi$
$281$	4.01330	0.239413	0.119707	+	0.992809i	$0.461805\pi$
$282$	37.1110	2.20993
$283$	2.62856	0.156252	0.0781258	−	0.996944i	$-0.475106\pi$
$283$	2.62856	0.156252	0.0781258	+	0.996944i	$0.475106\pi$
$284$	20.9646	1.24402
$285$	−3.80112	−0.225159
$286$	0.313656	0.0185469
$287$	−4.48716	−0.264869
$288$	−2.29734	−0.135372
$289$	−0.240564	−0.0141508
$290$	18.9446	1.11246
$291$	10.7218	0.628524
$292$	−28.4692	−1.66604
$293$	10.0562	0.587490	0.293745	−	0.955884i	$-0.405098\pi$
$293$	10.0562	0.587490	0.293745	+	0.955884i	$0.405098\pi$
$294$	24.3119	1.41790
$295$	−5.95344	−0.346623
$296$	−7.26780	−0.422432
$297$	−11.3727	−0.659910
$298$	−40.6928	−2.35727
$299$	−0.0927753	−0.00536534
$300$	−9.82487	−0.567239
$301$	−1.59369	−0.0918587
$302$	4.15542	0.239117
$303$	−13.8211	−0.794000
$304$	1.93766	0.111132
$305$	19.1633	1.09729
$306$	−2.93282	−0.167658
$307$	−12.9930	−0.741548	−0.370774	−	0.928723i	$-0.620908\pi$
$307$	−12.9930	−0.741548	−0.370774	+	0.928723i	$0.620908\pi$
$308$	3.19738	0.182188
$309$	−7.01947	−0.399324
$310$	6.79016	0.385655
$311$	−6.91246	−0.391970	−0.195985	−	0.980607i	$-0.562790\pi$
$311$	−6.91246	−0.391970	−0.195985	+	0.980607i	$0.562790\pi$
$312$	0.218493	0.0123697
$313$	−22.6108	−1.27804	−0.639019	−	0.769191i	$-0.720659\pi$
$313$	−22.6108	−1.27804	−0.639019	+	0.769191i	$0.720659\pi$
$314$	−41.4703	−2.34030
$315$	−0.292870	−0.0165014
$316$	35.3065	1.98615
$317$	−33.1829	−1.86374	−0.931868	−	0.362798i	$-0.881822\pi$
$317$	−33.1829	−1.86374	−0.931868	+	0.362798i	$0.881822\pi$
$318$	1.29177	0.0724387
$319$	−10.4810	−0.586824
$320$	−21.9361	−1.22627
$321$	−5.28126	−0.294771
$322$	−1.60009	−0.0891697
$323$	5.56459	0.309622
$324$	−22.9031	−1.27239
$325$	0.140895	0.00781548
$326$	−5.09782	−0.282342
$327$	−10.0715	−0.556957
$328$	16.7113	0.922728
$329$	−5.42517	−0.299099
$330$	−12.9346	−0.712025
$331$	−0.0155869	−0.000856733 0	−0.000428367	−	1.00000i	$-0.500136\pi$
$331$	−0.0155869	−0.000856733 0	−0.000428367		1.00000i	$0.500136\pi$
$332$	17.4680	0.958679
$333$	−1.19536	−0.0655051
$334$	−17.5641	−0.961064
$335$	−24.6802	−1.34842
$336$	−1.23328	−0.0672808
$337$	11.2092	0.610602	0.305301	−	0.952256i	$-0.401243\pi$
$337$	11.2092	0.610602	0.305301	+	0.952256i	$0.401243\pi$
$338$	28.7390	1.56320
$339$	11.5876	0.629352
$340$	−20.2294	−1.09709
$341$	−3.75663	−0.203433
$342$	−0.973778	−0.0526559
$343$	−7.25612	−0.391794
$344$	5.93530	0.320010
$345$	3.82587	0.205978
$346$	38.8633	2.08930
$347$	−26.3769	−1.41599	−0.707993	−	0.706220i	$-0.750399\pi$
$347$	−26.3769	−1.41599	−0.707993	+	0.706220i	$0.750399\pi$
$348$	−23.6964	−1.27026
$349$	3.63084	0.194355	0.0971773	−	0.995267i	$-0.469019\pi$
$349$	3.63084	0.194355	0.0971773	+	0.995267i	$0.469019\pi$
$350$	2.43002	0.129890
$351$	0.368733	0.0196815
$352$	14.8324	0.790572
$353$	16.8241	0.895458	0.447729	−	0.894169i	$-0.352233\pi$
$353$	16.8241	0.895458	0.447729	+	0.894169i	$0.352233\pi$
$354$	12.5990	0.669630
$355$	12.3981	0.658022
$356$	−32.8955	−1.74346
$357$	−3.54175	−0.187449
$358$	−49.8485	−2.63457
$359$	27.3323	1.44254	0.721272	−	0.692652i	$-0.243558\pi$
$359$	27.3323	1.44254	0.721272	+	0.692652i	$0.243558\pi$
$360$	1.09072	0.0574861
$361$	−17.1524	−0.902758
$362$	9.75866	0.512904
$363$	−10.8385	−0.568875
$364$	−0.103668	−0.00543366
$365$	−16.8362	−0.881247
$366$	−40.5544	−2.11981
$367$	−24.7248	−1.29062	−0.645311	−	0.763920i	$-0.723272\pi$
$367$	−24.7248	−1.29062	−0.645311	+	0.763920i	$0.723272\pi$
$368$	−1.95027	−0.101665
$369$	2.74856	0.143084
$370$	−13.9498	−0.725213
$371$	−0.188841	−0.00980411
$372$	−8.49331	−0.440357
$373$	37.4253	1.93781	0.968906	−	0.247431i	$-0.0795863\pi$
$373$	37.4253	1.93781	0.968906	+	0.247431i	$0.0795863\pi$
$374$	18.9354	0.979124
$375$	−19.7925	−1.02208
$376$	20.2047	1.04198
$377$	0.339822	0.0175017
$378$	6.35952	0.327099
$379$	−29.0422	−1.49180	−0.745898	−	0.666060i	$-0.767980\pi$
$379$	−29.0422	−1.49180	−0.745898	+	0.666060i	$0.767980\pi$
$380$	−6.71672	−0.344560
$381$	−28.7632	−1.47358
$382$	−26.6994	−1.36606
$383$	−10.6892	−0.546191	−0.273096	−	0.961987i	$-0.588048\pi$
$383$	−10.6892	−0.546191	−0.273096	+	0.961987i	$0.588048\pi$
$384$	23.2203	1.18496
$385$	1.89088	0.0963679
$386$	21.4467	1.09161
$387$	0.976195	0.0496228
$388$	18.9458	0.961828
$389$	−13.5720	−0.688129	−0.344065	−	0.938946i	$-0.611804\pi$
$389$	−13.5720	−0.688129	−0.344065	+	0.938946i	$0.611804\pi$
$390$	0.419373	0.0212358
$391$	−5.60083	−0.283246
$392$	13.2364	0.668538
$393$	4.33035	0.218437
$394$	−10.7915	−0.543668
$395$	20.8797	1.05057
$396$	−1.95852	−0.0984192
$397$	−27.8943	−1.39997	−0.699987	−	0.714156i	$-0.746811\pi$
$397$	−27.8943	−1.39997	−0.699987	+	0.714156i	$0.746811\pi$
$398$	−35.0773	−1.75827
$399$	−1.17596	−0.0588715
$400$	2.96183	0.148091
$401$	−24.0352	−1.20026	−0.600130	−	0.799903i	$-0.704884\pi$
$401$	−24.0352	−1.20026	−0.600130	+	0.799903i	$0.704884\pi$
$402$	52.2297	2.60498
$403$	0.121800	0.00606729
$404$	−24.4223	−1.21506
$405$	−13.5445	−0.673031
$406$	5.86091	0.290872
$407$	7.71764	0.382549
$408$	13.1904	0.653020
$409$	−12.2052	−0.603509	−0.301754	−	0.953386i	$-0.597572\pi$
$409$	−12.2052	−0.603509	−0.301754	+	0.953386i	$0.597572\pi$
$410$	32.0756	1.58410
$411$	14.2009	0.700479
$412$	−12.4037	−0.611084
$413$	−1.84182	−0.0906301
$414$	0.980118	0.0481702
$415$	10.3302	0.507092
$416$	−0.480907	−0.0235784
$417$	−12.5918	−0.616625
$418$	6.28706	0.307510
$419$	1.08847	0.0531753	0.0265876	−	0.999646i	$-0.491536\pi$
$419$	1.08847	0.0531753	0.0265876	+	0.999646i	$0.491536\pi$
$420$	4.27505	0.208601
$421$	8.09208	0.394384	0.197192	−	0.980365i	$-0.436818\pi$
$421$	8.09208	0.394384	0.197192	+	0.980365i	$0.436818\pi$
$422$	6.43049	0.313031
$423$	3.32312	0.161576
$424$	0.703290	0.0341548
$425$	8.50583	0.412593
$426$	−26.2376	−1.27121
$427$	5.92856	0.286903
$428$	−9.33216	−0.451087
$429$	−0.232016	−0.0112019
$430$	11.3922	0.549379
$431$	21.1892	1.02065	0.510324	−	0.859982i	$-0.329525\pi$
$431$	21.1892	1.02065	0.510324	+	0.859982i	$0.329525\pi$
$432$	7.75129	0.372934
$433$	−6.48022	−0.311419	−0.155710	−	0.987803i	$-0.549766\pi$
$433$	−6.48022	−0.311419	−0.155710	+	0.987803i	$0.549766\pi$
$434$	2.10068	0.100836
$435$	−14.0136	−0.671901
$436$	−17.7967	−0.852310
$437$	−1.85963	−0.0889581
$438$	35.6298	1.70246
$439$	25.2191	1.20364	0.601820	−	0.798632i	$-0.294442\pi$
$439$	25.2191	1.20364	0.601820	+	0.798632i	$0.294442\pi$
$440$	−7.04210	−0.335719
$441$	2.17702	0.103668
$442$	−0.613935	−0.0292019
$443$	31.0894	1.47710	0.738551	−	0.674197i	$-0.235510\pi$
$443$	31.0894	1.47710	0.738551	+	0.674197i	$0.235510\pi$
$444$	17.4487	0.828079
$445$	−19.4538	−0.922200
$446$	−31.3436	−1.48416
$447$	30.1011	1.42373
$448$	−6.78640	−0.320627
$449$	−31.8687	−1.50398	−0.751988	−	0.659177i	$-0.770905\pi$
$449$	−31.8687	−1.50398	−0.751988	+	0.659177i	$0.770905\pi$
$450$	−1.48848	−0.0701676
$451$	−17.7457	−0.835610
$452$	20.4757	0.963095
$453$	−3.07383	−0.144421
$454$	−33.0335	−1.55034
$455$	−0.0613072	−0.00287413
$456$	4.37956	0.205092
$457$	8.42073	0.393905	0.196953	−	0.980413i	$-0.436895\pi$
$457$	8.42073	0.393905	0.196953	+	0.980413i	$0.436895\pi$
$458$	13.6128	0.636085
$459$	22.2603	1.03902
$460$	6.76045	0.315208
$461$	−18.7770	−0.874532	−0.437266	−	0.899332i	$-0.644053\pi$
$461$	−18.7770	−0.874532	−0.437266	+	0.899332i	$0.644053\pi$
$462$	−4.00158	−0.186170
$463$	0.206136	0.00957993	0.00478997	−	0.999989i	$-0.498475\pi$
$463$	0.206136	0.00957993	0.00478997	+	0.999989i	$0.498475\pi$
$464$	7.14356	0.331631
$465$	−5.02279	−0.232926
$466$	−36.2269	−1.67818
$467$	−19.7366	−0.913303	−0.456651	−	0.889646i	$-0.650951\pi$
$467$	−19.7366	−0.913303	−0.456651	+	0.889646i	$0.650951\pi$
$468$	0.0635004	0.00293531
$469$	−7.63535	−0.352567
$470$	38.7807	1.78882
$471$	30.6762	1.41348
$472$	6.85941	0.315730
$473$	−6.30266	−0.289797
$474$	−44.1867	−2.02956
$475$	2.82417	0.129582
$476$	−6.25839	−0.286853
$477$	0.115672	0.00529626
$478$	−28.3501	−1.29670
$479$	−32.1610	−1.46948	−0.734738	−	0.678352i	$-0.762695\pi$
$479$	−32.1610	−1.46948	−0.734738	+	0.678352i	$0.762695\pi$
$480$	19.8317	0.905188
$481$	−0.250227	−0.0114094
$482$	42.2477	1.92433
$483$	1.18361	0.0538563
$484$	−19.1520	−0.870547
$485$	11.2042	0.508757
$486$	−7.41125	−0.336181
$487$	14.2981	0.647909	0.323954	−	0.946073i	$-0.394988\pi$
$487$	14.2981	0.647909	0.323954	+	0.946073i	$0.394988\pi$
$488$	−22.0795	−0.999490
$489$	3.77094	0.170528
$490$	25.4058	1.14772
$491$	3.02419	0.136480	0.0682399	−	0.997669i	$-0.478262\pi$
$491$	3.02419	0.136480	0.0682399	+	0.997669i	$0.478262\pi$
$492$	−40.1209	−1.80879
$493$	20.5150	0.923949
$494$	−0.203843	−0.00917134
$495$	−1.15823	−0.0520587
$496$	2.56041	0.114966
$497$	3.83561	0.172051
$498$	−21.8615	−0.979636
$499$	−33.6899	−1.50817	−0.754084	−	0.656778i	$-0.771919\pi$
$499$	−33.6899	−1.50817	−0.754084	+	0.656778i	$0.771919\pi$
$500$	−34.9741	−1.56409
$501$	12.9924	0.580459
$502$	−15.9788	−0.713167
$503$	7.75063	0.345583	0.172792	−	0.984958i	$-0.444721\pi$
$503$	7.75063	0.345583	0.172792	+	0.984958i	$0.444721\pi$
$504$	0.337438	0.0150307
$505$	−14.4429	−0.642702
$506$	−6.32799	−0.281314
$507$	−21.2587	−0.944133
$508$	−50.8255	−2.25502
$509$	14.3739	0.637112	0.318556	−	0.947904i	$-0.396802\pi$
$509$	14.3739	0.637112	0.318556	+	0.947904i	$0.396802\pi$
$510$	25.3175	1.12108
$511$	−5.20863	−0.230416
$512$	−15.7248	−0.694944
$513$	7.39103	0.326322
$514$	−14.6528	−0.646307
$515$	−7.33530	−0.323232
$516$	−14.2496	−0.627304
$517$	−21.4553	−0.943601
$518$	−4.31565	−0.189619
$519$	−28.7478	−1.26189
$520$	0.228324	0.0100127
$521$	−40.7128	−1.78366	−0.891831	−	0.452369i	$-0.850579\pi$
$521$	−40.7128	−1.78366	−0.891831	+	0.452369i	$0.850579\pi$
$522$	−3.59003	−0.157131
$523$	−44.1260	−1.92950	−0.964748	−	0.263176i	$-0.915230\pi$
$523$	−44.1260	−1.92950	−0.964748	+	0.263176i	$0.915230\pi$
$524$	7.65187	0.334274
$525$	−1.79753	−0.0784504
$526$	−38.7647	−1.69022
$527$	7.35303	0.320303
$528$	−4.87732	−0.212258
$529$	−21.1283	−0.918620
$530$	1.34989	0.0586354
$531$	1.12819	0.0489591
$532$	−2.07796	−0.0900910
$533$	0.575362	0.0249217
$534$	41.1693	1.78157
$535$	−5.51888	−0.238602
$536$	28.4359	1.22825
$537$	36.8737	1.59122
$538$	−36.9266	−1.59202
$539$	−14.0556	−0.605419
$540$	−26.8692	−1.15627
$541$	−27.8142	−1.19583	−0.597913	−	0.801561i	$-0.704003\pi$
$541$	−27.8142	−1.19583	−0.597913	+	0.801561i	$0.704003\pi$
$542$	−45.6954	−1.96279
$543$	−7.21864	−0.309781
$544$	−29.0323	−1.24475
$545$	−10.5247	−0.450828
$546$	0.129742	0.00555245
$547$	−10.9784	−0.469402	−0.234701	−	0.972068i	$-0.575411\pi$
$547$	−10.9784	−0.469402	−0.234701	+	0.972068i	$0.575411\pi$
$548$	25.0935	1.07194
$549$	−3.63147	−0.154987
$550$	9.61016	0.409779
$551$	6.81154	0.290181
$552$	−4.40808	−0.187620
$553$	6.45956	0.274688
$554$	−21.7598	−0.924485
$555$	10.3189	0.438011
$556$	−22.2502	−0.943620
$557$	16.0791	0.681293	0.340646	−	0.940192i	$-0.389354\pi$
$557$	16.0791	0.681293	0.340646	+	0.940192i	$0.389354\pi$
$558$	−1.28675	−0.0544723
$559$	0.204349	0.00864305
$560$	−1.28877	−0.0544603
$561$	−14.0068	−0.591367
$562$	−8.87531	−0.374382
$563$	28.8357	1.21528	0.607641	−	0.794212i	$-0.292116\pi$
$563$	28.8357	1.21528	0.607641	+	0.794212i	$0.292116\pi$
$564$	−48.5079	−2.04255
$565$	12.1090	0.509428
$566$	−5.81300	−0.244339
$567$	−4.19027	−0.175975
$568$	−14.2848	−0.599376
$569$	45.2962	1.89892	0.949458	−	0.313895i	$-0.101634\pi$
$569$	45.2962	1.89892	0.949458	+	0.313895i	$0.101634\pi$
$570$	8.40610	0.352093
$571$	−2.74633	−0.114931	−0.0574653	−	0.998348i	$-0.518302\pi$
$571$	−2.74633	−0.114931	−0.0574653	+	0.998348i	$0.518302\pi$
$572$	−0.409981	−0.0171422
$573$	19.7500	0.825068
$574$	9.92325	0.414188
$575$	−2.84256	−0.118543
$576$	4.15693	0.173205
$577$	21.4329	0.892264	0.446132	−	0.894967i	$-0.352801\pi$
$577$	21.4329	0.892264	0.446132	+	0.894967i	$0.352801\pi$
$578$	0.532002	0.0221283
$579$	−15.8645	−0.659305
$580$	−24.7625	−1.02821
$581$	3.19588	0.132587
$582$	−23.7110	−0.982854
$583$	−0.746820	−0.0309301
$584$	19.3983	0.802706
$585$	0.0375530	0.00155263
$586$	−22.2391	−0.918688
$587$	10.5875	0.436992	0.218496	−	0.975838i	$-0.429885\pi$
$587$	10.5875	0.436992	0.218496	+	0.975838i	$0.429885\pi$
$588$	−31.7782	−1.31051
$589$	2.44141	0.100597
$590$	13.1659	0.542031
$591$	7.98264	0.328362
$592$	−5.26012	−0.216190
$593$	21.5063	0.883158	0.441579	−	0.897222i	$-0.354419\pi$
$593$	21.5063	0.883158	0.441579	+	0.897222i	$0.354419\pi$
$594$	25.1504	1.03193
$595$	−3.70110	−0.151730
$596$	53.1897	2.17874
$597$	25.9472	1.06195
$598$	0.205170	0.00839005
$599$	−8.60435	−0.351564	−0.175782	−	0.984429i	$-0.556245\pi$
$599$	−8.60435	−0.351564	−0.175782	+	0.984429i	$0.556245\pi$
$600$	6.69444	0.273299
$601$	25.3050	1.03221	0.516107	−	0.856524i	$-0.327381\pi$
$601$	25.3050	1.03221	0.516107	+	0.856524i	$0.327381\pi$
$602$	3.52441	0.143644
$603$	4.67694	0.190460
$604$	−5.43156	−0.221007
$605$	−11.3262	−0.460475
$606$	30.5650	1.24162
$607$	−46.7828	−1.89886	−0.949428	−	0.313985i	$-0.898336\pi$
$607$	−46.7828	−1.89886	−0.949428	+	0.313985i	$0.898336\pi$
$608$	−9.63951	−0.390934
$609$	−4.33541	−0.175680
$610$	−42.3791	−1.71588
$611$	0.695637	0.0281425
$612$	3.83350	0.154960
$613$	−12.6905	−0.512563	−0.256281	−	0.966602i	$-0.582497\pi$
$613$	−12.6905	−0.512563	−0.256281	+	0.966602i	$0.582497\pi$
$614$	28.7337	1.15960
$615$	−23.7268	−0.956757
$616$	−2.17862	−0.0877792
$617$	−39.0627	−1.57260	−0.786302	−	0.617842i	$-0.788007\pi$
$617$	−39.0627	−1.57260	−0.786302	+	0.617842i	$0.788007\pi$
$618$	15.5234	0.624443
$619$	−45.0791	−1.81188	−0.905941	−	0.423403i	$-0.860835\pi$
$619$	−45.0791	−1.81188	−0.905941	+	0.423403i	$0.860835\pi$
$620$	−8.87545	−0.356447
$621$	−7.43916	−0.298523
$622$	15.2867	0.612943
$623$	−6.01845	−0.241124
$624$	0.158136	0.00633050
$625$	−10.2945	−0.411779
$626$	50.0033	1.99853
$627$	−4.65064	−0.185729
$628$	54.2059	2.16305
$629$	−15.1061	−0.602321
$630$	0.647676	0.0258040
$631$	−2.63415	−0.104864	−0.0524319	−	0.998625i	$-0.516697\pi$
$631$	−2.63415	−0.104864	−0.0524319	+	0.998625i	$0.516697\pi$
$632$	−24.0570	−0.956937
$633$	−4.75673	−0.189063
$634$	73.3832	2.91442
$635$	−30.0573	−1.19279
$636$	−1.68847	−0.0669524
$637$	0.455721	0.0180563
$638$	23.1785	0.917646
$639$	−2.34946	−0.0929430
$640$	24.2651	0.959162
$641$	−40.0694	−1.58265	−0.791323	−	0.611399i	$-0.790607\pi$
$641$	−40.0694	−1.58265	−0.791323	+	0.611399i	$0.790607\pi$
$642$	11.6794	0.460948
$643$	5.98793	0.236141	0.118070	−	0.993005i	$-0.462329\pi$
$643$	5.98793	0.236141	0.118070	+	0.993005i	$0.462329\pi$
$644$	2.09149	0.0824162
$645$	−8.42696	−0.331811
$646$	−12.3060	−0.484172
$647$	15.0193	0.590470	0.295235	−	0.955425i	$-0.404602\pi$
$647$	15.0193	0.590470	0.295235	+	0.955425i	$0.404602\pi$
$648$	15.6056	0.613047
$649$	−7.28397	−0.285921
$650$	−0.311587	−0.0122215
$651$	−1.55391	−0.0609024
$652$	6.66338	0.260958
$653$	24.5928	0.962391	0.481196	−	0.876613i	$-0.340203\pi$
$653$	24.5928	0.962391	0.481196	+	0.876613i	$0.340203\pi$
$654$	22.2730	0.870941
$655$	4.52518	0.176814
$656$	12.0949	0.472228
$657$	3.19049	0.124473
$658$	11.9976	0.467716
$659$	−23.4080	−0.911848	−0.455924	−	0.890019i	$-0.650691\pi$
$659$	−23.4080	−0.911848	−0.455924	+	0.890019i	$0.650691\pi$
$660$	16.9068	0.658097
$661$	47.0434	1.82978	0.914888	−	0.403709i	$-0.132279\pi$
$661$	47.0434	1.82978	0.914888	+	0.403709i	$0.132279\pi$
$662$	0.0344701	0.00133972
$663$	0.454137	0.0176372
$664$	−11.9023	−0.461897
$665$	−1.22887	−0.0476535
$666$	2.64350	0.102434
$667$	−6.85589	−0.265461
$668$	22.9581	0.888275
$669$	23.1853	0.896397
$670$	54.5797	2.10860
$671$	23.4461	0.905125
$672$	6.13535	0.236676
$673$	35.0317	1.35037	0.675187	−	0.737646i	$-0.264063\pi$
$673$	35.0317	1.35037	0.675187	+	0.737646i	$0.264063\pi$
$674$	−24.7888	−0.954829
$675$	11.2977	0.434847
$676$	−37.5649	−1.44480
$677$	−28.9115	−1.11116	−0.555580	−	0.831463i	$-0.687504\pi$
$677$	−28.9115	−1.11116	−0.555580	+	0.831463i	$0.687504\pi$
$678$	−25.6257	−0.984149
$679$	3.46626	0.133023
$680$	13.7838	0.528586
$681$	24.4354	0.936366
$682$	8.30770	0.318118
$683$	37.1720	1.42235	0.711174	−	0.703016i	$-0.248164\pi$
$683$	37.1720	1.42235	0.711174	+	0.703016i	$0.248164\pi$
$684$	1.27283	0.0486678
$685$	14.8399	0.567002
$686$	16.0467	0.612668
$687$	−10.0696	−0.384180
$688$	4.29572	0.163773
$689$	0.0242139	0.000922476 0
$690$	−8.46083	−0.322098
$691$	−34.2544	−1.30310	−0.651550	−	0.758606i	$-0.725881\pi$
$691$	−34.2544	−1.30310	−0.651550	+	0.758606i	$0.725881\pi$
$692$	−50.7983	−1.93106
$693$	−0.358324	−0.0136116
$694$	58.3319	2.21425
$695$	−13.1584	−0.499126
$696$	16.1461	0.612018
$697$	34.7345	1.31566
$698$	−8.02952	−0.303922
$699$	26.7976	1.01358
$700$	−3.17629	−0.120052
$701$	17.9315	0.677262	0.338631	−	0.940919i	$-0.390036\pi$
$701$	17.9315	0.677262	0.338631	+	0.940919i	$0.390036\pi$
$702$	−0.815444	−0.0307769
$703$	−5.01565	−0.189169
$704$	−26.8386	−1.01152
$705$	−28.6867	−1.08040
$706$	−37.2062	−1.40027
$707$	−4.46823	−0.168045
$708$	−16.4682	−0.618914
$709$	−49.6848	−1.86595	−0.932977	−	0.359936i	$-0.882798\pi$
$709$	−49.6848	−1.86595	−0.932977	+	0.359936i	$0.882798\pi$
$710$	−27.4181	−1.02898
$711$	−3.95673	−0.148389
$712$	22.4142	0.840009
$713$	−2.45731	−0.0920268
$714$	7.83250	0.293124
$715$	−0.242456	−0.00906733
$716$	65.1571	2.43504
$717$	20.9710	0.783177
$718$	−60.4447	−2.25578
$719$	−35.9264	−1.33983	−0.669914	−	0.742438i	$-0.733669\pi$
$719$	−35.9264	−1.33983	−0.669914	+	0.742438i	$0.733669\pi$
$720$	0.789419	0.0294199
$721$	−2.26933	−0.0845143
$722$	37.9321	1.41169
$723$	−31.2513	−1.16225
$724$	−12.7556	−0.474058
$725$	10.4119	0.386687
$726$	23.9691	0.889578
$727$	−37.7577	−1.40036	−0.700178	−	0.713969i	$-0.746896\pi$
$727$	−37.7577	−1.40036	−0.700178	+	0.713969i	$0.746896\pi$
$728$	0.0706367	0.00261797
$729$	29.2519	1.08340
$730$	37.2329	1.37805
$731$	12.3365	0.456282
$732$	53.0089	1.95926
$733$	−16.2408	−0.599868	−0.299934	−	0.953960i	$-0.596965\pi$
$733$	−16.2408	−0.599868	−0.299934	+	0.953960i	$0.596965\pi$
$734$	54.6783	2.01821
$735$	−18.7931	−0.693192
$736$	9.70228	0.357631
$737$	−30.1960	−1.11228
$738$	−6.07837	−0.223748
$739$	−3.37565	−0.124175	−0.0620876	−	0.998071i	$-0.519776\pi$
$739$	−3.37565	−0.124175	−0.0620876	+	0.998071i	$0.519776\pi$
$740$	18.2338	0.670287
$741$	0.150786	0.00553927
$742$	0.417617	0.0153312
$743$	−10.7242	−0.393431	−0.196716	−	0.980461i	$-0.563028\pi$
$743$	−10.7242	−0.393431	−0.196716	+	0.980461i	$0.563028\pi$
$744$	5.78714	0.212167
$745$	31.4555	1.15244
$746$	−82.7653	−3.03025
$747$	−1.95760	−0.0716247
$748$	−24.7505	−0.904967
$749$	−1.70738	−0.0623864
$750$	43.7708	1.59828
$751$	15.1395	0.552447	0.276224	−	0.961093i	$-0.410917\pi$
$751$	15.1395	0.552447	0.276224	+	0.961093i	$0.410917\pi$
$752$	14.6233	0.533257
$753$	11.8197	0.430735
$754$	−0.751509	−0.0273684
$755$	−3.21213	−0.116901
$756$	−8.31256	−0.302325
$757$	−18.1303	−0.658957	−0.329478	−	0.944163i	$-0.606873\pi$
$757$	−18.1303	−0.658957	−0.329478	+	0.944163i	$0.606873\pi$
$758$	64.2261	2.33280
$759$	4.68092	0.169907
$760$	4.57662	0.166011
$761$	−31.5947	−1.14531	−0.572654	−	0.819797i	$-0.694086\pi$
$761$	−31.5947	−1.14531	−0.572654	+	0.819797i	$0.694086\pi$
$762$	63.6091	2.30431
$763$	−3.25603	−0.117876
$764$	34.8989	1.26260
$765$	2.26707	0.0819660
$766$	23.6389	0.854106
$767$	0.236166	0.00852745
$768$	−9.36795	−0.338037
$769$	−8.47953	−0.305780	−0.152890	−	0.988243i	$-0.548858\pi$
$769$	−8.47953	−0.305780	−0.152890	+	0.988243i	$0.548858\pi$
$770$	−4.18163	−0.150695
$771$	10.8389	0.390354
$772$	−28.0331	−1.00893
$773$	17.6026	0.633122	0.316561	−	0.948572i	$-0.397472\pi$
$773$	17.6026	0.633122	0.316561	+	0.948572i	$0.397472\pi$
$774$	−2.15883	−0.0775976
$775$	3.73185	0.134052
$776$	−12.9092	−0.463414
$777$	3.19236	0.114525
$778$	30.0142	1.07606
$779$	11.5328	0.413205
$780$	−0.548165	−0.0196274
$781$	15.1689	0.542787
$782$	12.3861	0.442926
$783$	27.2485	0.973783
$784$	9.57992	0.342140
$785$	32.0564	1.14414
$786$	−9.57646	−0.341581
$787$	−23.0361	−0.821147	−0.410574	−	0.911827i	$-0.634672\pi$
$787$	−23.0361	−0.821147	−0.410574	+	0.911827i	$0.634672\pi$
$788$	14.1056	0.502491
$789$	28.6749	1.02085
$790$	−46.1749	−1.64283
$791$	3.74616	0.133198
$792$	1.33449	0.0474190
$793$	−0.760184	−0.0269949
$794$	61.6876	2.18921
$795$	−0.998534	−0.0354144
$796$	45.8497	1.62510
$797$	0.0937095	0.00331936	0.00165968	−	0.999999i	$-0.499472\pi$
$797$	0.0937095	0.00331936	0.00165968	+	0.999999i	$0.499472\pi$
$798$	2.60060	0.0920604
$799$	41.9954	1.48569
$800$	−14.7346	−0.520947
$801$	3.68653	0.130257
$802$	53.1532	1.87691
$803$	−20.5989	−0.726920
$804$	−68.2697	−2.40769
$805$	1.23687	0.0435939
$806$	−0.269358	−0.00948772
$807$	27.3152	0.961542
$808$	16.6408	0.585421
$809$	31.7466	1.11615	0.558075	−	0.829791i	$-0.311540\pi$
$809$	31.7466	1.11615	0.558075	+	0.829791i	$0.311540\pi$
$810$	29.9533	1.05245
$811$	−10.5904	−0.371880	−0.185940	−	0.982561i	$-0.559533\pi$
$811$	−10.5904	−0.371880	−0.185940	+	0.982561i	$0.559533\pi$
$812$	−7.66081	−0.268842
$813$	33.8016	1.18548
$814$	−17.0674	−0.598212
$815$	3.94061	0.138033
$816$	9.54662	0.334199
$817$	4.09606	0.143303
$818$	26.9915	0.943737
$819$	0.0116178	0.000405959 0
$820$	−41.9261	−1.46412
$821$	−23.3414	−0.814620	−0.407310	−	0.913290i	$-0.633533\pi$
$821$	−23.3414	−0.814620	−0.407310	+	0.913290i	$0.633533\pi$
$822$	−31.4050	−1.09537
$823$	−17.8663	−0.622779	−0.311389	−	0.950282i	$-0.600794\pi$
$823$	−17.8663	−0.622779	−0.311389	+	0.950282i	$0.600794\pi$
$824$	8.45156	0.294424
$825$	−7.10879	−0.247496
$826$	4.07315	0.141723
$827$	31.5783	1.09809	0.549043	−	0.835794i	$-0.314992\pi$
$827$	31.5783	1.09809	0.549043	+	0.835794i	$0.314992\pi$
$828$	−1.28112	−0.0445219
$829$	33.8482	1.17560	0.587799	−	0.809007i	$-0.299995\pi$
$829$	33.8482	1.17560	0.587799	+	0.809007i	$0.299995\pi$
$830$	−22.8451	−0.792965
$831$	16.0961	0.558366
$832$	0.870180	0.0301680
$833$	27.5118	0.953227
$834$	27.8466	0.964248
$835$	13.5770	0.469852
$836$	−8.21784	−0.284220
$837$	9.76649	0.337579
$838$	−2.40713	−0.0831529
$839$	−33.0577	−1.14128	−0.570639	−	0.821201i	$-0.693304\pi$
$839$	−33.0577	−1.14128	−0.570639	+	0.821201i	$0.693304\pi$
$840$	−2.91292	−0.100505
$841$	−3.88788	−0.134065
$842$	−17.8955	−0.616718
$843$	6.56521	0.226118
$844$	−8.40531	−0.289323
$845$	−22.2152	−0.764227
$846$	−7.34900	−0.252664
$847$	−3.50399	−0.120399
$848$	0.509011	0.0174795
$849$	4.29997	0.147575
$850$	−18.8104	−0.645193
$851$	5.04831	0.173054
$852$	34.2952	1.17493
$853$	23.5855	0.807552	0.403776	−	0.914858i	$-0.367697\pi$
$853$	23.5855	0.807552	0.403776	+	0.914858i	$0.367697\pi$
$854$	−13.1109	−0.448645
$855$	0.752729	0.0257428
$856$	6.35872	0.217337
$857$	34.1814	1.16762	0.583808	−	0.811892i	$-0.301562\pi$
$857$	34.1814	1.16762	0.583808	+	0.811892i	$0.301562\pi$
$858$	0.513099	0.0175169
$859$	22.9552	0.783221	0.391610	−	0.920131i	$-0.371918\pi$
$859$	22.9552	0.783221	0.391610	+	0.920131i	$0.371918\pi$
$860$	−14.8907	−0.507770
$861$	−7.34039	−0.250160
$862$	−46.8595	−1.59604
$863$	0.0626076	0.00213119	0.00106559	−	0.999999i	$-0.499661\pi$
$863$	0.0626076	0.00213119	0.00106559	+	0.999999i	$0.499661\pi$
$864$	−38.5614	−1.31189
$865$	−30.0412	−1.02143
$866$	14.3309	0.486982
$867$	−0.393530	−0.0133650
$868$	−2.74581	−0.0931988
$869$	25.5460	0.866590
$870$	30.9908	1.05069
$871$	0.979035	0.0331733
$872$	12.1263	0.410648
$873$	−2.12322	−0.0718600
$874$	4.11252	0.139108
$875$	−6.39875	−0.216317
$876$	−46.5718	−1.57352
$877$	33.2169	1.12166	0.560828	−	0.827932i	$-0.310483\pi$
$877$	33.2169	1.12166	0.560828	+	0.827932i	$0.310483\pi$
$878$	−55.7714	−1.88219
$879$	16.4506	0.554865
$880$	−5.09677	−0.171812
$881$	54.7592	1.84488	0.922441	−	0.386137i	$-0.126191\pi$
$881$	54.7592	1.84488	0.922441	+	0.386137i	$0.126191\pi$
$882$	−4.81443	−0.162110
$883$	45.0433	1.51583	0.757914	−	0.652354i	$-0.226219\pi$
$883$	45.0433	1.51583	0.757914	+	0.652354i	$0.226219\pi$
$884$	0.802477	0.0269902
$885$	−9.73902	−0.327374
$886$	−68.7535	−2.30982
$887$	−46.4079	−1.55822	−0.779112	−	0.626885i	$-0.784330\pi$
$887$	−46.4079	−1.55822	−0.779112	+	0.626885i	$0.784330\pi$
$888$	−11.8891	−0.398973
$889$	−9.29887	−0.311874
$890$	43.0217	1.44209
$891$	−16.5715	−0.555168
$892$	40.9693	1.37175
$893$	13.9436	0.466606
$894$	−66.5679	−2.22637
$895$	38.5328	1.28801
$896$	7.50692	0.250788
$897$	−0.151768	−0.00506738
$898$	70.4769	2.35184
$899$	9.00075	0.300192
$900$	1.94560	0.0648533
$901$	1.46179	0.0486992
$902$	39.2441	1.30669
$903$	−2.60706	−0.0867575
$904$	−13.9516	−0.464025
$905$	−7.54343	−0.250752
$906$	6.79770	0.225838
$907$	4.98227	0.165434	0.0827168	−	0.996573i	$-0.473640\pi$
$907$	4.98227	0.165434	0.0827168	+	0.996573i	$0.473640\pi$
$908$	43.1782	1.43292
$909$	2.73696	0.0907792
$910$	0.135580	0.00449442
$911$	−0.959316	−0.0317836	−0.0158918	−	0.999874i	$-0.505059\pi$
$911$	−0.959316	−0.0317836	−0.0158918	+	0.999874i	$0.505059\pi$
$912$	3.16974	0.104961
$913$	12.6389	0.418288
$914$	−18.6223	−0.615969
$915$	31.3485	1.03635
$916$	−17.7934	−0.587909
$917$	1.39996	0.0462308
$918$	−49.2282	−1.62477
$919$	5.57429	0.183879	0.0919394	−	0.995765i	$-0.470693\pi$
$919$	5.57429	0.183879	0.0919394	+	0.995765i	$0.470693\pi$
$920$	−4.60641	−0.151869
$921$	−21.2547	−0.700368
$922$	41.5249	1.36755
$923$	−0.491817	−0.0161884
$924$	5.23048	0.172070
$925$	−7.66673	−0.252081
$926$	−0.455864	−0.0149806
$927$	1.39005	0.0456553
$928$	−35.5380	−1.16659
$929$	48.4908	1.59093	0.795466	−	0.605998i	$-0.207226\pi$
$929$	48.4908	1.59093	0.795466	+	0.605998i	$0.207226\pi$
$930$	11.1078	0.364239
$931$	9.13467	0.299377
$932$	47.3523	1.55108
$933$	−11.3078	−0.370202
$934$	43.6471	1.42818
$935$	−14.6370	−0.478681
$936$	−0.0432677	−0.00141425
$937$	−4.99425	−0.163155	−0.0815776	−	0.996667i	$-0.525996\pi$
$937$	−4.99425	−0.163155	−0.0815776	+	0.996667i	$0.525996\pi$
$938$	16.8854	0.551328
$939$	−36.9882	−1.20706
$940$	−50.6904	−1.65334
$941$	14.2172	0.463468	0.231734	−	0.972779i	$-0.425560\pi$
$941$	14.2172	0.463468	0.231734	+	0.972779i	$0.425560\pi$
$942$	−67.8397	−2.21034
$943$	−11.6079	−0.378005
$944$	4.96455	0.161582
$945$	−4.91590	−0.159914
$946$	13.9382	0.453170
$947$	−41.2555	−1.34062	−0.670311	−	0.742080i	$-0.733839\pi$
$947$	−41.2555	−1.34062	−0.670311	+	0.742080i	$0.733839\pi$
$948$	57.7567	1.87585
$949$	0.667872	0.0216800
$950$	−6.24559	−0.202634
$951$	−54.2827	−1.76024
$952$	4.26432	0.138208
$953$	−44.6756	−1.44718	−0.723592	−	0.690228i	$-0.757510\pi$
$953$	−44.6756	−1.44718	−0.723592	+	0.690228i	$0.757510\pi$
$954$	−0.255806	−0.00828202
$955$	20.6386	0.667850
$956$	37.0565	1.19849
$957$	−17.1455	−0.554236
$958$	71.1234	2.29789
$959$	4.59102	0.148252
$960$	−35.8845	−1.15817
$961$	−27.7739	−0.895933
$962$	0.553370	0.0178414
$963$	1.04584	0.0337016
$964$	−55.2221	−1.77858
$965$	−16.5783	−0.533674
$966$	−2.61754	−0.0842179
$967$	27.2556	0.876482	0.438241	−	0.898858i	$-0.355602\pi$
$967$	27.2556	0.876482	0.438241	+	0.898858i	$0.355602\pi$
$968$	13.0498	0.419435
$969$	9.10292	0.292428
$970$	−24.7779	−0.795570
$971$	46.2234	1.48338	0.741690	−	0.670743i	$-0.234025\pi$
$971$	46.2234	1.48338	0.741690	+	0.670743i	$0.234025\pi$
$972$	9.68728	0.310720
$973$	−4.07083	−0.130505
$974$	−31.6199	−1.01317
$975$	0.230486	0.00738146
$976$	−15.9802	−0.511513
$977$	55.9466	1.78989	0.894944	−	0.446178i	$-0.147215\pi$
$977$	55.9466	1.78989	0.894944	+	0.446178i	$0.147215\pi$
$978$	−8.33934	−0.266663
$979$	−23.8016	−0.760701
$980$	−33.2080	−1.06079
$981$	1.99444	0.0636777
$982$	−6.68793	−0.213420
$983$	20.8757	0.665831	0.332915	−	0.942957i	$-0.391968\pi$
$983$	20.8757	0.665831	0.332915	+	0.942957i	$0.391968\pi$
$984$	27.3374	0.871486
$985$	8.34181	0.265792
$986$	−45.3684	−1.44483
$987$	−8.87484	−0.282489
$988$	0.266444	0.00847672
$989$	−4.12273	−0.131095
$990$	2.56141	0.0814068
$991$	36.3801	1.15565	0.577827	−	0.816160i	$-0.303901\pi$
$991$	36.3801	1.15565	0.577827	+	0.816160i	$0.303901\pi$
$992$	−12.7376	−0.404420
$993$	−0.0254981	−0.000809156 0
$994$	−8.48236	−0.269044
$995$	27.1147	0.859593
$996$	28.5752	0.905440
$997$	8.27389	0.262037	0.131018	−	0.991380i	$-0.458175\pi$
$997$	8.27389	0.262037	0.131018	+	0.991380i	$0.458175\pi$
$998$	74.5045	2.35840
$999$	−20.0643	−0.634807

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4001.2.a.a.1.19	✓	149

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4001.2.a.a.1.19	✓	149	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:	\( N \)	\(=\)	\( 4001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4001.a (trivial)

\(f(q)\)	\(=\)	\(q-2.21148 q^{2} +1.63586 q^{3} +2.89063 q^{4} +1.70947 q^{5} -3.61768 q^{6} +0.528860 q^{7} -1.96961 q^{8} -0.323947 q^{9} +O(q^{10})\)	\(q-2.21148 q^{2} +1.63586 q^{3} +2.89063 q^{4} +1.70947 q^{5} -3.61768 q^{6} +0.528860 q^{7} -1.96961 q^{8} -0.323947 q^{9} -3.78045 q^{10} +2.09152 q^{11} +4.72868 q^{12} -0.0678126 q^{13} -1.16956 q^{14} +2.79646 q^{15} -1.42552 q^{16} -4.09383 q^{17} +0.716401 q^{18} -1.35926 q^{19} +4.94144 q^{20} +0.865143 q^{21} -4.62534 q^{22} +1.36811 q^{23} -3.22201 q^{24} -2.07772 q^{25} +0.149966 q^{26} -5.43753 q^{27} +1.52874 q^{28} -5.01120 q^{29} -6.18430 q^{30} -1.79613 q^{31} +7.09172 q^{32} +3.42144 q^{33} +9.05341 q^{34} +0.904069 q^{35} -0.936410 q^{36} +3.68997 q^{37} +3.00598 q^{38} -0.110932 q^{39} -3.36698 q^{40} -8.48459 q^{41} -1.91324 q^{42} -3.01344 q^{43} +6.04580 q^{44} -0.553777 q^{45} -3.02555 q^{46} -10.2582 q^{47} -2.33195 q^{48} -6.72031 q^{49} +4.59483 q^{50} -6.69695 q^{51} -0.196021 q^{52} -0.357071 q^{53} +12.0250 q^{54} +3.57538 q^{55} -1.04165 q^{56} -2.22357 q^{57} +11.0822 q^{58} -3.48263 q^{59} +8.08353 q^{60} +11.2101 q^{61} +3.97209 q^{62} -0.171323 q^{63} -12.8321 q^{64} -0.115923 q^{65} -7.56643 q^{66} -14.4374 q^{67} -11.8337 q^{68} +2.23805 q^{69} -1.99933 q^{70} +7.25260 q^{71} +0.638048 q^{72} -9.84880 q^{73} -8.16029 q^{74} -3.39887 q^{75} -3.92913 q^{76} +1.10612 q^{77} +0.245324 q^{78} +12.2141 q^{79} -2.43688 q^{80} -7.92322 q^{81} +18.7635 q^{82} +6.04296 q^{83} +2.50081 q^{84} -6.99827 q^{85} +6.66416 q^{86} -8.19764 q^{87} -4.11947 q^{88} -11.3801 q^{89} +1.22466 q^{90} -0.0358634 q^{91} +3.95471 q^{92} -2.93822 q^{93} +22.6858 q^{94} -2.32362 q^{95} +11.6011 q^{96} +6.55422 q^{97} +14.8618 q^{98} -0.677540 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 149 q - 6 q^{2} - 28 q^{3} + 116 q^{4} - 19 q^{5} - 31 q^{6} - 47 q^{7} - 15 q^{8} + 115 q^{9}+O(q^{10}) \) 149 * q - 6 * q^2 - 28 * q^3 + 116 * q^4 - 19 * q^5 - 31 * q^6 - 47 * q^7 - 15 * q^8 + 115 * q^9	\( 149 q - 6 q^{2} - 28 q^{3} + 116 q^{4} - 19 q^{5} - 31 q^{6} - 47 q^{7} - 15 q^{8} + 115 q^{9} - 48 q^{10} - 31 q^{11} - 61 q^{12} - 54 q^{13} - 44 q^{14} - 65 q^{15} + 58 q^{16} - 26 q^{17} - 23 q^{18} - 86 q^{19} - 52 q^{20} - 30 q^{21} - 56 q^{22} - 63 q^{23} - 90 q^{24} + 92 q^{25} - 38 q^{26} - 103 q^{27} - 77 q^{28} - 51 q^{29} - 22 q^{30} - 256 q^{31} - 21 q^{32} - 36 q^{33} - 124 q^{34} - 50 q^{35} + 45 q^{36} - 42 q^{37} - 14 q^{38} - 119 q^{39} - 131 q^{40} - 55 q^{41} - 5 q^{42} - 55 q^{43} - 54 q^{44} - 68 q^{45} - 59 q^{46} - 82 q^{47} - 89 q^{48} + 30 q^{49} + 13 q^{50} - 83 q^{51} - 126 q^{52} - 23 q^{53} - 83 q^{54} - 244 q^{55} - 94 q^{56} - 14 q^{57} - 60 q^{58} - 93 q^{59} - 70 q^{60} - 139 q^{61} - 10 q^{62} - 120 q^{63} - 45 q^{64} - 37 q^{65} - 28 q^{66} - 110 q^{67} - 27 q^{68} - 79 q^{69} - 78 q^{70} - 123 q^{71} - 74 q^{73} - 25 q^{74} - 146 q^{75} - 192 q^{76} - q^{77} + 26 q^{78} - 273 q^{79} - 51 q^{80} + 41 q^{81} - 120 q^{82} - 27 q^{83} - 14 q^{84} - 71 q^{85} + 3 q^{86} - 98 q^{87} - 143 q^{88} - 70 q^{89} - 24 q^{90} - 256 q^{91} - 47 q^{92} + 16 q^{93} - 151 q^{94} - 83 q^{95} - 137 q^{96} - 108 q^{97} + 17 q^{98} - 131 q^{99}+O(q^{100}) \) 149 * q - 6 * q^2 - 28 * q^3 + 116 * q^4 - 19 * q^5 - 31 * q^6 - 47 * q^7 - 15 * q^8 + 115 * q^9 - 48 * q^10 - 31 * q^11 - 61 * q^12 - 54 * q^13 - 44 * q^14 - 65 * q^15 + 58 * q^16 - 26 * q^17 - 23 * q^18 - 86 * q^19 - 52 * q^20 - 30 * q^21 - 56 * q^22 - 63 * q^23 - 90 * q^24 + 92 * q^25 - 38 * q^26 - 103 * q^27 - 77 * q^28 - 51 * q^29 - 22 * q^30 - 256 * q^31 - 21 * q^32 - 36 * q^33 - 124 * q^34 - 50 * q^35 + 45 * q^36 - 42 * q^37 - 14 * q^38 - 119 * q^39 - 131 * q^40 - 55 * q^41 - 5 * q^42 - 55 * q^43 - 54 * q^44 - 68 * q^45 - 59 * q^46 - 82 * q^47 - 89 * q^48 + 30 * q^49 + 13 * q^50 - 83 * q^51 - 126 * q^52 - 23 * q^53 - 83 * q^54 - 244 * q^55 - 94 * q^56 - 14 * q^57 - 60 * q^58 - 93 * q^59 - 70 * q^60 - 139 * q^61 - 10 * q^62 - 120 * q^63 - 45 * q^64 - 37 * q^65 - 28 * q^66 - 110 * q^67 - 27 * q^68 - 79 * q^69 - 78 * q^70 - 123 * q^71 - 74 * q^73 - 25 * q^74 - 146 * q^75 - 192 * q^76 - q^77 + 26 * q^78 - 273 * q^79 - 51 * q^80 + 41 * q^81 - 120 * q^82 - 27 * q^83 - 14 * q^84 - 71 * q^85 + 3 * q^86 - 98 * q^87 - 143 * q^88 - 70 * q^89 - 24 * q^90 - 256 * q^91 - 47 * q^92 + 16 * q^93 - 151 * q^94 - 83 * q^95 - 137 * q^96 - 108 * q^97 + 17 * q^98 - 131 * q^99

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