LMFDB - Embedded newform 8018.2.a.j.1.47

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			1.47
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)

$f(q)$	$=$	$q+1.00000 q^{2} +3.39370 q^{3} +1.00000 q^{4} +3.61831 q^{5} +3.39370 q^{6} -0.821803 q^{7} +1.00000 q^{8} +8.51720 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +3.39370 q^{3} +1.00000 q^{4} +3.61831 q^{5} +3.39370 q^{6} -0.821803 q^{7} +1.00000 q^{8} +8.51720 q^{9} +3.61831 q^{10} -2.67941 q^{11} +3.39370 q^{12} +3.43790 q^{13} -0.821803 q^{14} +12.2794 q^{15} +1.00000 q^{16} -5.28793 q^{17} +8.51720 q^{18} -1.00000 q^{19} +3.61831 q^{20} -2.78895 q^{21} -2.67941 q^{22} -6.30090 q^{23} +3.39370 q^{24} +8.09214 q^{25} +3.43790 q^{26} +18.7237 q^{27} -0.821803 q^{28} +10.4247 q^{29} +12.2794 q^{30} +2.89630 q^{31} +1.00000 q^{32} -9.09312 q^{33} -5.28793 q^{34} -2.97353 q^{35} +8.51720 q^{36} +5.36617 q^{37} -1.00000 q^{38} +11.6672 q^{39} +3.61831 q^{40} -1.79929 q^{41} -2.78895 q^{42} -11.1104 q^{43} -2.67941 q^{44} +30.8178 q^{45} -6.30090 q^{46} +5.22679 q^{47} +3.39370 q^{48} -6.32464 q^{49} +8.09214 q^{50} -17.9456 q^{51} +3.43790 q^{52} +1.96490 q^{53} +18.7237 q^{54} -9.69493 q^{55} -0.821803 q^{56} -3.39370 q^{57} +10.4247 q^{58} -11.1724 q^{59} +12.2794 q^{60} -9.91475 q^{61} +2.89630 q^{62} -6.99946 q^{63} +1.00000 q^{64} +12.4394 q^{65} -9.09312 q^{66} -9.04646 q^{67} -5.28793 q^{68} -21.3834 q^{69} -2.97353 q^{70} -10.4437 q^{71} +8.51720 q^{72} +3.46531 q^{73} +5.36617 q^{74} +27.4623 q^{75} -1.00000 q^{76} +2.20195 q^{77} +11.6672 q^{78} -17.6911 q^{79} +3.61831 q^{80} +37.9911 q^{81} -1.79929 q^{82} -9.03389 q^{83} -2.78895 q^{84} -19.1333 q^{85} -11.1104 q^{86} +35.3782 q^{87} -2.67941 q^{88} -15.1669 q^{89} +30.8178 q^{90} -2.82528 q^{91} -6.30090 q^{92} +9.82918 q^{93} +5.22679 q^{94} -3.61831 q^{95} +3.39370 q^{96} +5.34961 q^{97} -6.32464 q^{98} -22.8211 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	3.39370	1.95935	0.979677	−	0.200583i	$-0.0642835\pi$
$3$	3.39370	1.95935	0.979677	+	0.200583i	$0.0642835\pi$
$4$	1.00000	0.500000
$5$	3.61831	1.61816	0.809078	−	0.587702i	$-0.199967\pi$
$5$	3.61831	1.61816	0.809078	+	0.587702i	$0.199967\pi$
$6$	3.39370	1.38547
$7$	−0.821803	−0.310612	−0.155306	−	0.987866i	$-0.549636\pi$
$7$	−0.821803	−0.310612	−0.155306	+	0.987866i	$0.549636\pi$
$8$	1.00000	0.353553
$9$	8.51720	2.83907
$10$	3.61831	1.14421
$11$	−2.67941	−0.807873	−0.403936	−	0.914787i	$-0.632358\pi$
$11$	−2.67941	−0.807873	−0.403936	+	0.914787i	$0.632358\pi$
$12$	3.39370	0.979677
$13$	3.43790	0.953503	0.476752	−	0.879038i	$-0.341814\pi$
$13$	3.43790	0.953503	0.476752	+	0.879038i	$0.341814\pi$
$14$	−0.821803	−0.219636
$15$	12.2794	3.17054
$16$	1.00000	0.250000
$17$	−5.28793	−1.28251	−0.641255	−	0.767328i	$-0.721586\pi$
$17$	−5.28793	−1.28251	−0.641255	+	0.767328i	$0.721586\pi$
$18$	8.51720	2.00752
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	3.61831	0.809078
$21$	−2.78895	−0.608599
$22$	−2.67941	−0.571252
$23$	−6.30090	−1.31383	−0.656915	−	0.753965i	$-0.728139\pi$
$23$	−6.30090	−1.31383	−0.656915	+	0.753965i	$0.728139\pi$
$24$	3.39370	0.692736
$25$	8.09214	1.61843
$26$	3.43790	0.674229
$27$	18.7237	3.60338
$28$	−0.821803	−0.155306
$29$	10.4247	1.93581	0.967907	−	0.251307i	$-0.0808605\pi$
$29$	10.4247	1.93581	0.967907	+	0.251307i	$0.0808605\pi$
$30$	12.2794	2.24191
$31$	2.89630	0.520191	0.260096	−	0.965583i	$-0.416246\pi$
$31$	2.89630	0.520191	0.260096	+	0.965583i	$0.416246\pi$
$32$	1.00000	0.176777
$33$	−9.09312	−1.58291
$34$	−5.28793	−0.906872
$35$	−2.97353	−0.502619
$36$	8.51720	1.41953
$37$	5.36617	0.882193	0.441096	−	0.897460i	$-0.354590\pi$
$37$	5.36617	0.882193	0.441096	+	0.897460i	$0.354590\pi$
$38$	−1.00000	−0.162221
$39$	11.6672	1.86825
$40$	3.61831	0.572104
$41$	−1.79929	−0.281002	−0.140501	−	0.990081i	$-0.544871\pi$
$41$	−1.79929	−0.281002	−0.140501	+	0.990081i	$0.544871\pi$
$42$	−2.78895	−0.430345
$43$	−11.1104	−1.69432	−0.847161	−	0.531336i	$-0.821690\pi$
$43$	−11.1104	−1.69432	−0.847161	+	0.531336i	$0.821690\pi$
$44$	−2.67941	−0.403936
$45$	30.8178	4.59405
$46$	−6.30090	−0.929018
$47$	5.22679	0.762405	0.381203	−	0.924492i	$-0.375510\pi$
$47$	5.22679	0.762405	0.381203	+	0.924492i	$0.375510\pi$
$48$	3.39370	0.489838
$49$	−6.32464	−0.903520
$50$	8.09214	1.14440
$51$	−17.9456	−2.51289
$52$	3.43790	0.476752
$53$	1.96490	0.269899	0.134950	−	0.990852i	$-0.456913\pi$
$53$	1.96490	0.269899	0.134950	+	0.990852i	$0.456913\pi$
$54$	18.7237	2.54798
$55$	−9.69493	−1.30726
$56$	−0.821803	−0.109818
$57$	−3.39370	−0.449507
$58$	10.4247	1.36883
$59$	−11.1724	−1.45452	−0.727258	−	0.686364i	$-0.759206\pi$
$59$	−11.1724	−1.45452	−0.727258	+	0.686364i	$0.759206\pi$
$60$	12.2794	1.58527
$61$	−9.91475	−1.26945	−0.634727	−	0.772736i	$-0.718887\pi$
$61$	−9.91475	−1.26945	−0.634727	+	0.772736i	$0.718887\pi$
$62$	2.89630	0.367831
$63$	−6.99946	−0.881849
$64$	1.00000	0.125000
$65$	12.4394	1.54292
$66$	−9.09312	−1.11929
$67$	−9.04646	−1.10520	−0.552601	−	0.833446i	$-0.686365\pi$
$67$	−9.04646	−1.10520	−0.552601	+	0.833446i	$0.686365\pi$
$68$	−5.28793	−0.641255
$69$	−21.3834	−2.57426
$70$	−2.97353	−0.355405
$71$	−10.4437	−1.23943	−0.619717	−	0.784825i	$-0.712753\pi$
$71$	−10.4437	−1.23943	−0.619717	+	0.784825i	$0.712753\pi$
$72$	8.51720	1.00376
$73$	3.46531	0.405584	0.202792	−	0.979222i	$-0.434998\pi$
$73$	3.46531	0.405584	0.202792	+	0.979222i	$0.434998\pi$
$74$	5.36617	0.623805
$75$	27.4623	3.17107
$76$	−1.00000	−0.114708
$77$	2.20195	0.250935
$78$	11.6672	1.32105
$79$	−17.6911	−1.99040	−0.995200	−	0.0978656i	$-0.968798\pi$
$79$	−17.6911	−1.99040	−0.995200	+	0.0978656i	$0.968798\pi$
$80$	3.61831	0.404539
$81$	37.9911	4.22123
$82$	−1.79929	−0.198698
$83$	−9.03389	−0.991598	−0.495799	−	0.868437i	$-0.665125\pi$
$83$	−9.03389	−0.991598	−0.495799	+	0.868437i	$0.665125\pi$
$84$	−2.78895	−0.304300
$85$	−19.1333	−2.07530
$86$	−11.1104	−1.19807
$87$	35.3782	3.79295
$88$	−2.67941	−0.285626
$89$	−15.1669	−1.60769	−0.803844	−	0.594840i	$-0.797215\pi$
$89$	−15.1669	−1.60769	−0.803844	+	0.594840i	$0.797215\pi$
$90$	30.8178	3.24848
$91$	−2.82528	−0.296170
$92$	−6.30090	−0.656915
$93$	9.82918	1.01924
$94$	5.22679	0.539102
$95$	−3.61831	−0.371230
$96$	3.39370	0.346368
$97$	5.34961	0.543170	0.271585	−	0.962414i	$-0.412452\pi$
$97$	5.34961	0.543170	0.271585	+	0.962414i	$0.412452\pi$
$98$	−6.32464	−0.638885
$99$	−22.8211	−2.29360
$100$	8.09214	0.809214
$101$	19.8808	1.97822	0.989109	−	0.147186i	$-0.0470215\pi$
$101$	19.8808	1.97822	0.989109	+	0.147186i	$0.0470215\pi$
$102$	−17.9456	−1.77688
$103$	2.02924	0.199947	0.0999733	−	0.994990i	$-0.468124\pi$
$103$	2.02924	0.199947	0.0999733	+	0.994990i	$0.468124\pi$
$104$	3.43790	0.337114
$105$	−10.0913	−0.984808
$106$	1.96490	0.190848
$107$	13.5961	1.31438	0.657190	−	0.753725i	$-0.271745\pi$
$107$	13.5961	1.31438	0.657190	+	0.753725i	$0.271745\pi$
$108$	18.7237	1.80169
$109$	11.3275	1.08498	0.542490	−	0.840062i	$-0.317482\pi$
$109$	11.3275	1.08498	0.542490	+	0.840062i	$0.317482\pi$
$110$	−9.69493	−0.924375
$111$	18.2112	1.72853
$112$	−0.821803	−0.0776531
$113$	−0.00963292	−0.000906189 0	−0.000453095	−	1.00000i	$-0.500144\pi$
$113$	−0.00963292	−0.000906189 0	−0.000453095		1.00000i	$0.500144\pi$
$114$	−3.39370	−0.317849
$115$	−22.7986	−2.12598
$116$	10.4247	0.967907
$117$	29.2813	2.70706
$118$	−11.1724	−1.02850
$119$	4.34563	0.398364
$120$	12.2794	1.12095
$121$	−3.82076	−0.347342
$122$	−9.91475	−0.897640
$123$	−6.10624	−0.550581
$124$	2.89630	0.260096
$125$	11.1883	1.00071
$126$	−6.99946	−0.623561
$127$	3.55676	0.315612	0.157806	−	0.987470i	$-0.449558\pi$
$127$	3.55676	0.315612	0.157806	+	0.987470i	$0.449558\pi$
$128$	1.00000	0.0883883
$129$	−37.7054	−3.31978
$130$	12.4394	1.09101
$131$	−2.36366	−0.206514	−0.103257	−	0.994655i	$-0.532926\pi$
$131$	−2.36366	−0.206514	−0.103257	+	0.994655i	$0.532926\pi$
$132$	−9.09312	−0.791454
$133$	0.821803	0.0712594
$134$	−9.04646	−0.781495
$135$	67.7481	5.83083
$136$	−5.28793	−0.453436
$137$	0.00261632	0.000223527 0	0.000111764	−	1.00000i	$-0.499964\pi$
$137$	0.00261632	0.000223527 0	0.000111764		1.00000i	$0.499964\pi$
$138$	−21.3834	−1.82027
$139$	9.30889	0.789570	0.394785	−	0.918774i	$-0.370819\pi$
$139$	9.30889	0.789570	0.394785	+	0.918774i	$0.370819\pi$
$140$	−2.97353	−0.251310
$141$	17.7381	1.49382
$142$	−10.4437	−0.876412
$143$	−9.21156	−0.770309
$144$	8.51720	0.709767
$145$	37.7197	3.13245
$146$	3.46531	0.286791
$147$	−21.4639	−1.77032
$148$	5.36617	0.441096
$149$	4.82312	0.395126	0.197563	−	0.980290i	$-0.436697\pi$
$149$	4.82312	0.395126	0.197563	+	0.980290i	$0.436697\pi$
$150$	27.4623	2.24229
$151$	5.19709	0.422933	0.211467	−	0.977385i	$-0.432176\pi$
$151$	5.19709	0.422933	0.211467	+	0.977385i	$0.432176\pi$
$152$	−1.00000	−0.0811107
$153$	−45.0383	−3.64113
$154$	2.20195	0.177438
$155$	10.4797	0.841750
$156$	11.6672	0.934125
$157$	15.3551	1.22547	0.612735	−	0.790288i	$-0.290069\pi$
$157$	15.3551	1.22547	0.612735	+	0.790288i	$0.290069\pi$
$158$	−17.6911	−1.40742
$159$	6.66827	0.528828
$160$	3.61831	0.286052
$161$	5.17810	0.408092
$162$	37.9911	2.98486
$163$	10.8267	0.848009	0.424004	−	0.905660i	$-0.360624\pi$
$163$	10.8267	0.848009	0.424004	+	0.905660i	$0.360624\pi$
$164$	−1.79929	−0.140501
$165$	−32.9017	−2.56139
$166$	−9.03389	−0.701166
$167$	−12.8423	−0.993765	−0.496883	−	0.867818i	$-0.665522\pi$
$167$	−12.8423	−0.993765	−0.496883	+	0.867818i	$0.665522\pi$
$168$	−2.78895	−0.215172
$169$	−1.18081	−0.0908318
$170$	−19.1333	−1.46746
$171$	−8.51720	−0.651327
$172$	−11.1104	−0.847161
$173$	1.12124	0.0852464	0.0426232	−	0.999091i	$-0.486429\pi$
$173$	1.12124	0.0852464	0.0426232	+	0.999091i	$0.486429\pi$
$174$	35.3782	2.68202
$175$	−6.65014	−0.502703
$176$	−2.67941	−0.201968
$177$	−37.9156	−2.84991
$178$	−15.1669	−1.13681
$179$	−0.602741	−0.0450510	−0.0225255	−	0.999746i	$-0.507171\pi$
$179$	−0.602741	−0.0450510	−0.0225255	+	0.999746i	$0.507171\pi$
$180$	30.8178	2.29703
$181$	12.7282	0.946081	0.473041	−	0.881041i	$-0.343156\pi$
$181$	12.7282	0.946081	0.473041	+	0.881041i	$0.343156\pi$
$182$	−2.82528	−0.209424
$183$	−33.6477	−2.48731
$184$	−6.30090	−0.464509
$185$	19.4164	1.42753
$186$	9.82918	0.720710
$187$	14.1685	1.03611
$188$	5.22679	0.381203
$189$	−15.3872	−1.11925
$190$	−3.61831	−0.262499
$191$	9.87850	0.714783	0.357391	−	0.933955i	$-0.383666\pi$
$191$	9.87850	0.714783	0.357391	+	0.933955i	$0.383666\pi$
$192$	3.39370	0.244919
$193$	−5.63807	−0.405837	−0.202919	−	0.979196i	$-0.565043\pi$
$193$	−5.63807	−0.405837	−0.202919	+	0.979196i	$0.565043\pi$
$194$	5.34961	0.384079
$195$	42.2156	3.02312
$196$	−6.32464	−0.451760
$197$	−15.1016	−1.07594	−0.537971	−	0.842963i	$-0.680809\pi$
$197$	−15.1016	−1.07594	−0.537971	+	0.842963i	$0.680809\pi$
$198$	−22.8211	−1.62182
$199$	19.3083	1.36873	0.684365	−	0.729140i	$-0.260079\pi$
$199$	19.3083	1.36873	0.684365	+	0.729140i	$0.260079\pi$
$200$	8.09214	0.572200
$201$	−30.7010	−2.16548
$202$	19.8808	1.39881
$203$	−8.56703	−0.601288
$204$	−17.9456	−1.25645
$205$	−6.51037	−0.454704
$206$	2.02924	0.141384
$207$	−53.6661	−3.73005
$208$	3.43790	0.238376
$209$	2.67941	0.185339
$210$	−10.0913	−0.696365
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	1.96490	0.134950
$213$	−35.4426	−2.42849
$214$	13.5961	0.929407
$215$	−40.2009	−2.74168
$216$	18.7237	1.27399
$217$	−2.38019	−0.161578
$218$	11.3275	0.767196
$219$	11.7602	0.794683
$220$	−9.69493	−0.653632
$221$	−18.1794	−1.22288
$222$	18.2112	1.22225
$223$	−9.77419	−0.654528	−0.327264	−	0.944933i	$-0.606127\pi$
$223$	−9.77419	−0.654528	−0.327264	+	0.944933i	$0.606127\pi$
$224$	−0.821803	−0.0549090
$225$	68.9223	4.59482
$226$	−0.00963292	−0.000640773 0
$227$	−7.31728	−0.485665	−0.242832	−	0.970068i	$-0.578076\pi$
$227$	−7.31728	−0.485665	−0.242832	+	0.970068i	$0.578076\pi$
$228$	−3.39370	−0.224753
$229$	−1.04301	−0.0689238	−0.0344619	−	0.999406i	$-0.510972\pi$
$229$	−1.04301	−0.0689238	−0.0344619	+	0.999406i	$0.510972\pi$
$230$	−22.7986	−1.50330
$231$	7.47275	0.491671
$232$	10.4247	0.684414
$233$	−11.2216	−0.735151	−0.367576	−	0.929994i	$-0.619812\pi$
$233$	−11.2216	−0.735151	−0.367576	+	0.929994i	$0.619812\pi$
$234$	29.2813	1.91418
$235$	18.9121	1.23369
$236$	−11.1724	−0.727258
$237$	−60.0381	−3.89990
$238$	4.34563	0.281686
$239$	2.37212	0.153440	0.0767198	−	0.997053i	$-0.475555\pi$
$239$	2.37212	0.153440	0.0767198	+	0.997053i	$0.475555\pi$
$240$	12.2794	0.792635
$241$	6.43715	0.414654	0.207327	−	0.978272i	$-0.433524\pi$
$241$	6.43715	0.414654	0.207327	+	0.978272i	$0.433524\pi$
$242$	−3.82076	−0.245608
$243$	72.7592	4.66751
$244$	−9.91475	−0.634727
$245$	−22.8845	−1.46204
$246$	−6.10624	−0.389320
$247$	−3.43790	−0.218749
$248$	2.89630	0.183915
$249$	−30.6583	−1.94289
$250$	11.1883	0.707610
$251$	−0.637165	−0.0402175	−0.0201088	−	0.999798i	$-0.506401\pi$
$251$	−0.637165	−0.0402175	−0.0201088	+	0.999798i	$0.506401\pi$
$252$	−6.99946	−0.440925
$253$	16.8827	1.06141
$254$	3.55676	0.223171
$255$	−64.9328	−4.06625
$256$	1.00000	0.0625000
$257$	4.81801	0.300539	0.150270	−	0.988645i	$-0.451986\pi$
$257$	4.81801	0.300539	0.150270	+	0.988645i	$0.451986\pi$
$258$	−37.7054	−2.34744
$259$	−4.40993	−0.274020
$260$	12.4394	0.771458
$261$	88.7891	5.49591
$262$	−2.36366	−0.146027
$263$	25.3215	1.56139	0.780697	−	0.624910i	$-0.214864\pi$
$263$	25.3215	1.56139	0.780697	+	0.624910i	$0.214864\pi$
$264$	−9.09312	−0.559643
$265$	7.10960	0.436739
$266$	0.821803	0.0503880
$267$	−51.4719	−3.15003
$268$	−9.04646	−0.552601
$269$	14.6290	0.891945	0.445972	−	0.895047i	$-0.352858\pi$
$269$	14.6290	0.891945	0.445972	+	0.895047i	$0.352858\pi$
$270$	67.7481	4.12302
$271$	26.2978	1.59748	0.798738	−	0.601679i	$-0.205501\pi$
$271$	26.2978	1.59748	0.798738	+	0.601679i	$0.205501\pi$
$272$	−5.28793	−0.320628
$273$	−9.58815	−0.580301
$274$	0.00261632	0.000158057 0
$275$	−21.6822	−1.30748
$276$	−21.3834	−1.28713
$277$	−14.8634	−0.893055	−0.446527	−	0.894770i	$-0.647339\pi$
$277$	−14.8634	−0.893055	−0.446527	+	0.894770i	$0.647339\pi$
$278$	9.30889	0.558310
$279$	24.6684	1.47686
$280$	−2.97353	−0.177703
$281$	8.31622	0.496104	0.248052	−	0.968747i	$-0.420210\pi$
$281$	8.31622	0.496104	0.248052	+	0.968747i	$0.420210\pi$
$282$	17.7381	1.05629
$283$	−28.5201	−1.69534	−0.847672	−	0.530521i	$-0.821996\pi$
$283$	−28.5201	−1.69534	−0.847672	+	0.530521i	$0.821996\pi$
$284$	−10.4437	−0.619717
$285$	−12.2794	−0.727371
$286$	−9.21156	−0.544691
$287$	1.47866	0.0872825
$288$	8.51720	0.501881
$289$	10.9622	0.644833
$290$	37.7197	2.21498
$291$	18.1550	1.06426
$292$	3.46531	0.202792
$293$	−24.4256	−1.42696	−0.713481	−	0.700675i	$-0.752882\pi$
$293$	−24.4256	−1.42696	−0.713481	+	0.700675i	$0.752882\pi$
$294$	−21.4639	−1.25180
$295$	−40.4250	−2.35363
$296$	5.36617	0.311902
$297$	−50.1685	−2.91107
$298$	4.82312	0.279396
$299$	−21.6619	−1.25274
$300$	27.4623	1.58554
$301$	9.13057	0.526277
$302$	5.19709	0.299059
$303$	67.4696	3.87603
$304$	−1.00000	−0.0573539
$305$	−35.8746	−2.05417
$306$	−45.0383	−2.57467
$307$	4.65979	0.265948	0.132974	−	0.991120i	$-0.457547\pi$
$307$	4.65979	0.265948	0.132974	+	0.991120i	$0.457547\pi$
$308$	2.20195	0.125468
$309$	6.88662	0.391766
$310$	10.4797	0.595207
$311$	−19.6399	−1.11368	−0.556838	−	0.830621i	$-0.687986\pi$
$311$	−19.6399	−1.11368	−0.556838	+	0.830621i	$0.687986\pi$
$312$	11.6672	0.660526
$313$	12.6076	0.712625	0.356312	−	0.934367i	$-0.384034\pi$
$313$	12.6076	0.712625	0.356312	+	0.934367i	$0.384034\pi$
$314$	15.3551	0.866538
$315$	−25.3262	−1.42697
$316$	−17.6911	−0.995200
$317$	15.2264	0.855202	0.427601	−	0.903968i	$-0.359359\pi$
$317$	15.2264	0.855202	0.427601	+	0.903968i	$0.359359\pi$
$318$	6.66827	0.373938
$319$	−27.9320	−1.56389
$320$	3.61831	0.202269
$321$	46.1409	2.57534
$322$	5.17810	0.288564
$323$	5.28793	0.294228
$324$	37.9911	2.11062
$325$	27.8200	1.54318
$326$	10.8267	0.599633
$327$	38.4422	2.12586
$328$	−1.79929	−0.0993491
$329$	−4.29539	−0.236812
$330$	−32.9017	−1.81118
$331$	−24.9185	−1.36964	−0.684822	−	0.728710i	$-0.740120\pi$
$331$	−24.9185	−1.36964	−0.684822	+	0.728710i	$0.740120\pi$
$332$	−9.03389	−0.495799
$333$	45.7047	2.50460
$334$	−12.8423	−0.702698
$335$	−32.7329	−1.78839
$336$	−2.78895	−0.152150
$337$	−10.2899	−0.560526	−0.280263	−	0.959923i	$-0.590422\pi$
$337$	−10.2899	−0.560526	−0.280263	+	0.959923i	$0.590422\pi$
$338$	−1.18081	−0.0642278
$339$	−0.0326913	−0.00177555
$340$	−19.1333	−1.03765
$341$	−7.76038	−0.420248
$342$	−8.51720	−0.460557
$343$	10.9502	0.591257
$344$	−11.1104	−0.599033
$345$	−77.3716	−4.16555
$346$	1.12124	0.0602783
$347$	−8.36269	−0.448933	−0.224466	−	0.974482i	$-0.572064\pi$
$347$	−8.36269	−0.448933	−0.224466	+	0.974482i	$0.572064\pi$
$348$	35.3782	1.89647
$349$	14.7239	0.788154	0.394077	−	0.919077i	$-0.371064\pi$
$349$	14.7239	0.788154	0.394077	+	0.919077i	$0.371064\pi$
$350$	−6.65014	−0.355465
$351$	64.3704	3.43584
$352$	−2.67941	−0.142813
$353$	−0.311257	−0.0165666	−0.00828328	−	0.999966i	$-0.502637\pi$
$353$	−0.311257	−0.0165666	−0.00828328	+	0.999966i	$0.502637\pi$
$354$	−37.9156	−2.01519
$355$	−37.7883	−2.00560
$356$	−15.1669	−0.803844
$357$	14.7478	0.780535
$358$	−0.602741	−0.0318559
$359$	−22.5209	−1.18861	−0.594303	−	0.804242i	$-0.702572\pi$
$359$	−22.5209	−1.18861	−0.594303	+	0.804242i	$0.702572\pi$
$360$	30.8178	1.62424
$361$	1.00000	0.0526316
$362$	12.7282	0.668980
$363$	−12.9665	−0.680565
$364$	−2.82528	−0.148085
$365$	12.5386	0.656298
$366$	−33.6477	−1.75879
$367$	−9.03476	−0.471611	−0.235805	−	0.971800i	$-0.575773\pi$
$367$	−9.03476	−0.471611	−0.235805	+	0.971800i	$0.575773\pi$
$368$	−6.30090	−0.328457
$369$	−15.3249	−0.797782
$370$	19.4164	1.00941
$371$	−1.61476	−0.0838340
$372$	9.82918	0.509619
$373$	19.6507	1.01748	0.508738	−	0.860921i	$-0.330112\pi$
$373$	19.6507	1.01748	0.508738	+	0.860921i	$0.330112\pi$
$374$	14.1685	0.732637
$375$	37.9697	1.96075
$376$	5.22679	0.269551
$377$	35.8391	1.84581
$378$	−15.3872	−0.791433
$379$	33.5725	1.72450	0.862251	−	0.506481i	$-0.169054\pi$
$379$	33.5725	1.72450	0.862251	+	0.506481i	$0.169054\pi$
$380$	−3.61831	−0.185615
$381$	12.0706	0.618395
$382$	9.87850	0.505428
$383$	19.0717	0.974518	0.487259	−	0.873258i	$-0.337997\pi$
$383$	19.0717	0.974518	0.487259	+	0.873258i	$0.337997\pi$
$384$	3.39370	0.173184
$385$	7.96732	0.406052
$386$	−5.63807	−0.286970
$387$	−94.6296	−4.81029
$388$	5.34961	0.271585
$389$	−35.4301	−1.79638	−0.898189	−	0.439610i	$-0.855117\pi$
$389$	−35.4301	−1.79638	−0.898189	+	0.439610i	$0.855117\pi$
$390$	42.2156	2.13767
$391$	33.3187	1.68500
$392$	−6.32464	−0.319443
$393$	−8.02154	−0.404633
$394$	−15.1016	−0.760806
$395$	−64.0116	−3.22078
$396$	−22.8211	−1.14680
$397$	−2.09825	−0.105308	−0.0526540	−	0.998613i	$-0.516768\pi$
$397$	−2.09825	−0.105308	−0.0526540	+	0.998613i	$0.516768\pi$
$398$	19.3083	0.967838
$399$	2.78895	0.139622
$400$	8.09214	0.404607
$401$	12.5379	0.626114	0.313057	−	0.949734i	$-0.398647\pi$
$401$	12.5379	0.626114	0.313057	+	0.949734i	$0.398647\pi$
$402$	−30.7010	−1.53123
$403$	9.95721	0.496004
$404$	19.8808	0.989109
$405$	137.463	6.83061
$406$	−8.56703	−0.425175
$407$	−14.3782	−0.712700
$408$	−17.9456	−0.888441
$409$	−20.7742	−1.02722	−0.513610	−	0.858024i	$-0.671692\pi$
$409$	−20.7742	−1.02722	−0.513610	+	0.858024i	$0.671692\pi$
$410$	−6.51037	−0.321524
$411$	0.00887900	0.000437969 0
$412$	2.02924	0.0999733
$413$	9.18147	0.451791
$414$	−53.6661	−2.63754
$415$	−32.6874	−1.60456
$416$	3.43790	0.168557
$417$	31.5916	1.54705
$418$	2.67941	0.131054
$419$	38.1091	1.86175	0.930877	−	0.365334i	$-0.119045\pi$
$419$	38.1091	1.86175	0.930877	+	0.365334i	$0.119045\pi$
$420$	−10.0913	−0.492404
$421$	3.11612	0.151871	0.0759353	−	0.997113i	$-0.475806\pi$
$421$	3.11612	0.151871	0.0759353	+	0.997113i	$0.475806\pi$
$422$	−1.00000	−0.0486792
$423$	44.5176	2.16452
$424$	1.96490	0.0954238
$425$	−42.7906	−2.07565
$426$	−35.4426	−1.71720
$427$	8.14797	0.394308
$428$	13.5961	0.657190
$429$	−31.2613	−1.50931
$430$	−40.2009	−1.93866
$431$	−22.4601	−1.08187	−0.540933	−	0.841066i	$-0.681929\pi$
$431$	−22.4601	−1.08187	−0.540933	+	0.841066i	$0.681929\pi$
$432$	18.7237	0.900845
$433$	−8.09259	−0.388905	−0.194452	−	0.980912i	$-0.562293\pi$
$433$	−8.09259	−0.388905	−0.194452	+	0.980912i	$0.562293\pi$
$434$	−2.38019	−0.114253
$435$	128.009	6.13758
$436$	11.3275	0.542490
$437$	6.30090	0.301413
$438$	11.7602	0.561926
$439$	18.4403	0.880105	0.440053	−	0.897972i	$-0.354960\pi$
$439$	18.4403	0.880105	0.440053	+	0.897972i	$0.354960\pi$
$440$	−9.69493	−0.462188
$441$	−53.8682	−2.56515
$442$	−18.1794	−0.864705
$443$	17.5684	0.834699	0.417349	−	0.908746i	$-0.362959\pi$
$443$	17.5684	0.834699	0.417349	+	0.908746i	$0.362959\pi$
$444$	18.2112	0.864264
$445$	−54.8785	−2.60149
$446$	−9.77419	−0.462821
$447$	16.3682	0.774191
$448$	−0.821803	−0.0388265
$449$	25.9987	1.22696	0.613478	−	0.789712i	$-0.289770\pi$
$449$	25.9987	1.22696	0.613478	+	0.789712i	$0.289770\pi$
$450$	68.9223	3.24903
$451$	4.82103	0.227014
$452$	−0.00963292	−0.000453095 0
$453$	17.6374	0.828675
$454$	−7.31728	−0.343417
$455$	−10.2227	−0.479249
$456$	−3.39370	−0.158925
$457$	20.7697	0.971564	0.485782	−	0.874080i	$-0.338535\pi$
$457$	20.7697	0.971564	0.485782	+	0.874080i	$0.338535\pi$
$458$	−1.04301	−0.0487365
$459$	−99.0097	−4.62138
$460$	−22.7986	−1.06299
$461$	−8.01016	−0.373070	−0.186535	−	0.982448i	$-0.559726\pi$
$461$	−8.01016	−0.373070	−0.186535	+	0.982448i	$0.559726\pi$
$462$	7.47275	0.347664
$463$	18.7273	0.870333	0.435167	−	0.900350i	$-0.356689\pi$
$463$	18.7273	0.870333	0.435167	+	0.900350i	$0.356689\pi$
$464$	10.4247	0.483954
$465$	35.5650	1.64929
$466$	−11.2216	−0.519831
$467$	12.9841	0.600833	0.300417	−	0.953808i	$-0.402874\pi$
$467$	12.9841	0.600833	0.300417	+	0.953808i	$0.402874\pi$
$468$	29.2813	1.35353
$469$	7.43441	0.343289
$470$	18.9121	0.872351
$471$	52.1106	2.40113
$472$	−11.1724	−0.514249
$473$	29.7694	1.36880
$474$	−60.0381	−2.75764
$475$	−8.09214	−0.371293
$476$	4.34563	0.199182
$477$	16.7354	0.766262
$478$	2.37212	0.108498
$479$	−42.6647	−1.94940	−0.974700	−	0.223515i	$-0.928247\pi$
$479$	−42.6647	−1.94940	−0.974700	+	0.223515i	$0.928247\pi$
$480$	12.2794	0.560477
$481$	18.4484	0.841174
$482$	6.43715	0.293204
$483$	17.5729	0.799596
$484$	−3.82076	−0.173671
$485$	19.3565	0.878934
$486$	72.7592	3.30042
$487$	−10.7012	−0.484919	−0.242460	−	0.970162i	$-0.577954\pi$
$487$	−10.7012	−0.484919	−0.242460	+	0.970162i	$0.577954\pi$
$488$	−9.91475	−0.448820
$489$	36.7424	1.66155
$490$	−22.8845	−1.03382
$491$	10.5105	0.474334	0.237167	−	0.971469i	$-0.423781\pi$
$491$	10.5105	0.474334	0.237167	+	0.971469i	$0.423781\pi$
$492$	−6.10624	−0.275291
$493$	−55.1249	−2.48270
$494$	−3.43790	−0.154679
$495$	−82.5736	−3.71141
$496$	2.89630	0.130048
$497$	8.58263	0.384983
$498$	−30.6583	−1.37383
$499$	−27.6284	−1.23682	−0.618408	−	0.785857i	$-0.712222\pi$
$499$	−27.6284	−1.23682	−0.618408	+	0.785857i	$0.712222\pi$
$500$	11.1883	0.500356
$501$	−43.5828	−1.94714
$502$	−0.637165	−0.0284381
$503$	5.18590	0.231228	0.115614	−	0.993294i	$-0.463116\pi$
$503$	5.18590	0.231228	0.115614	+	0.993294i	$0.463116\pi$
$504$	−6.99946	−0.311781
$505$	71.9350	3.20106
$506$	16.8827	0.750528
$507$	−4.00733	−0.177972
$508$	3.55676	0.157806
$509$	17.5729	0.778907	0.389453	−	0.921046i	$-0.372664\pi$
$509$	17.5729	0.778907	0.389453	+	0.921046i	$0.372664\pi$
$510$	−64.9328	−2.87527
$511$	−2.84780	−0.125979
$512$	1.00000	0.0441942
$513$	−18.7237	−0.826672
$514$	4.81801	0.212513
$515$	7.34240	0.323545
$516$	−37.7054	−1.65989
$517$	−14.0047	−0.615926
$518$	−4.40993	−0.193761
$519$	3.80516	0.167028
$520$	12.4394	0.545503
$521$	−20.9843	−0.919339	−0.459670	−	0.888090i	$-0.652032\pi$
$521$	−20.9843	−0.919339	−0.459670	+	0.888090i	$0.652032\pi$
$522$	88.7891	3.88619
$523$	−34.7231	−1.51834	−0.759168	−	0.650895i	$-0.774394\pi$
$523$	−34.7231	−1.51834	−0.759168	+	0.650895i	$0.774394\pi$
$524$	−2.36366	−0.103257
$525$	−22.5686	−0.984974
$526$	25.3215	1.10407
$527$	−15.3154	−0.667151
$528$	−9.09312	−0.395727
$529$	16.7014	0.726148
$530$	7.10960	0.308821
$531$	−95.1572	−4.12947
$532$	0.821803	0.0356297
$533$	−6.18578	−0.267936
$534$	−51.4719	−2.22741
$535$	49.1947	2.12687
$536$	−9.04646	−0.390748
$537$	−2.04552	−0.0882708
$538$	14.6290	0.630700
$539$	16.9463	0.729929
$540$	67.7481	2.91542
$541$	−21.0393	−0.904549	−0.452274	−	0.891879i	$-0.649387\pi$
$541$	−21.0393	−0.904549	−0.452274	+	0.891879i	$0.649387\pi$
$542$	26.2978	1.12959
$543$	43.1958	1.85371
$544$	−5.28793	−0.226718
$545$	40.9864	1.75567
$546$	−9.58815	−0.410335
$547$	−2.73452	−0.116920	−0.0584599	−	0.998290i	$-0.518619\pi$
$547$	−2.73452	−0.116920	−0.0584599	+	0.998290i	$0.518619\pi$
$548$	0.00261632	0.000111764 0
$549$	−84.4459	−3.60406
$550$	−21.6822	−0.924530
$551$	−10.4247	−0.444106
$552$	−21.3834	−0.910137
$553$	14.5386	0.618243
$554$	−14.8634	−0.631485
$555$	65.8936	2.79703
$556$	9.30889	0.394785
$557$	−38.8910	−1.64786	−0.823932	−	0.566689i	$-0.808224\pi$
$557$	−38.8910	−1.64786	−0.823932	+	0.566689i	$0.808224\pi$
$558$	24.6684	1.04430
$559$	−38.1965	−1.61554
$560$	−2.97353	−0.125655
$561$	48.0837	2.03010
$562$	8.31622	0.350799
$563$	10.3419	0.435861	0.217930	−	0.975964i	$-0.430069\pi$
$563$	10.3419	0.435861	0.217930	+	0.975964i	$0.430069\pi$
$564$	17.7381	0.746911
$565$	−0.0348549	−0.00146636
$566$	−28.5201	−1.19879
$567$	−31.2212	−1.31117
$568$	−10.4437	−0.438206
$569$	−19.1793	−0.804038	−0.402019	−	0.915631i	$-0.631691\pi$
$569$	−19.1793	−0.804038	−0.402019	+	0.915631i	$0.631691\pi$
$570$	−12.2794	−0.514329
$571$	27.9592	1.17006	0.585028	−	0.811013i	$-0.301083\pi$
$571$	27.9592	1.17006	0.585028	+	0.811013i	$0.301083\pi$
$572$	−9.21156	−0.385155
$573$	33.5247	1.40051
$574$	1.47866	0.0617181
$575$	−50.9878	−2.12634
$576$	8.51720	0.354883
$577$	−0.921229	−0.0383513	−0.0191756	−	0.999816i	$-0.506104\pi$
$577$	−0.921229	−0.0383513	−0.0191756	+	0.999816i	$0.506104\pi$
$578$	10.9622	0.455966
$579$	−19.1339	−0.795179
$580$	37.7197	1.56622
$581$	7.42408	0.308003
$582$	18.1550	0.752547
$583$	−5.26476	−0.218044
$584$	3.46531	0.143396
$585$	105.949	4.38044
$586$	−24.4256	−1.00901
$587$	−31.1420	−1.28537	−0.642684	−	0.766131i	$-0.722179\pi$
$587$	−31.1420	−1.28537	−0.642684	+	0.766131i	$0.722179\pi$
$588$	−21.4639	−0.885158
$589$	−2.89630	−0.119340
$590$	−40.4250	−1.66427
$591$	−51.2502	−2.10815
$592$	5.36617	0.220548
$593$	−25.6560	−1.05357	−0.526783	−	0.850000i	$-0.676602\pi$
$593$	−25.6560	−1.05357	−0.526783	+	0.850000i	$0.676602\pi$
$594$	−50.1685	−2.05844
$595$	15.7238	0.644614
$596$	4.82312	0.197563
$597$	65.5266	2.68183
$598$	−21.6619	−0.885821
$599$	−29.5251	−1.20636	−0.603181	−	0.797604i	$-0.706100\pi$
$599$	−29.5251	−1.20636	−0.603181	+	0.797604i	$0.706100\pi$
$600$	27.4623	1.12114
$601$	−28.8942	−1.17862	−0.589310	−	0.807907i	$-0.700600\pi$
$601$	−28.8942	−1.17862	−0.589310	+	0.807907i	$0.700600\pi$
$602$	9.13057	0.372134
$603$	−77.0505	−3.13774
$604$	5.19709	0.211467
$605$	−13.8247	−0.562053
$606$	67.4696	2.74077
$607$	−47.9366	−1.94569	−0.972843	−	0.231464i	$-0.925648\pi$
$607$	−47.9366	−1.94569	−0.972843	+	0.231464i	$0.925648\pi$
$608$	−1.00000	−0.0405554
$609$	−29.0739	−1.17814
$610$	−35.8746	−1.45252
$611$	17.9692	0.726956
$612$	−45.0383	−1.82057
$613$	38.4115	1.55143	0.775713	−	0.631086i	$-0.217391\pi$
$613$	38.4115	1.55143	0.775713	+	0.631086i	$0.217391\pi$
$614$	4.65979	0.188054
$615$	−22.0943	−0.890926
$616$	2.20195	0.0887190
$617$	−6.03761	−0.243065	−0.121533	−	0.992587i	$-0.538781\pi$
$617$	−6.03761	−0.243065	−0.121533	+	0.992587i	$0.538781\pi$
$618$	6.88662	0.277021
$619$	24.7241	0.993747	0.496874	−	0.867823i	$-0.334481\pi$
$619$	24.7241	0.993747	0.496874	+	0.867823i	$0.334481\pi$
$620$	10.4797	0.420875
$621$	−117.976	−4.73423
$622$	−19.6399	−0.787488
$623$	12.4642	0.499368
$624$	11.6672	0.467062
$625$	0.0219778	0.000879113 0
$626$	12.6076	0.503902
$627$	9.09312	0.363144
$628$	15.3551	0.612735
$629$	−28.3759	−1.13142
$630$	−25.3262	−1.00902
$631$	−45.1377	−1.79690	−0.898452	−	0.439072i	$-0.855307\pi$
$631$	−45.1377	−1.79690	−0.898452	+	0.439072i	$0.855307\pi$
$632$	−17.6911	−0.703712
$633$	−3.39370	−0.134887
$634$	15.2264	0.604719
$635$	12.8695	0.510709
$636$	6.66827	0.264414
$637$	−21.7435	−0.861509
$638$	−27.9320	−1.10584
$639$	−88.9507	−3.51884
$640$	3.61831	0.143026
$641$	24.7244	0.976557	0.488279	−	0.872688i	$-0.337625\pi$
$641$	24.7244	0.976557	0.488279	+	0.872688i	$0.337625\pi$
$642$	46.1409	1.82104
$643$	4.64353	0.183123	0.0915614	−	0.995799i	$-0.470814\pi$
$643$	4.64353	0.183123	0.0915614	+	0.995799i	$0.470814\pi$
$644$	5.17810	0.204046
$645$	−136.430	−5.37191
$646$	5.28793	0.208051
$647$	42.8506	1.68463	0.842315	−	0.538986i	$-0.181192\pi$
$647$	42.8506	1.68463	0.842315	+	0.538986i	$0.181192\pi$
$648$	37.9911	1.49243
$649$	29.9353	1.17506
$650$	27.8200	1.09119
$651$	−8.07765	−0.316588
$652$	10.8267	0.424004
$653$	11.8102	0.462171	0.231085	−	0.972933i	$-0.425772\pi$
$653$	11.8102	0.462171	0.231085	+	0.972933i	$0.425772\pi$
$654$	38.4422	1.50321
$655$	−8.55243	−0.334171
$656$	−1.79929	−0.0702504
$657$	29.5148	1.15148
$658$	−4.29539	−0.167452
$659$	−20.5983	−0.802394	−0.401197	−	0.915992i	$-0.631406\pi$
$659$	−20.5983	−0.802394	−0.401197	+	0.915992i	$0.631406\pi$
$660$	−32.9017	−1.28070
$661$	7.29360	0.283688	0.141844	−	0.989889i	$-0.454697\pi$
$661$	7.29360	0.283688	0.141844	+	0.989889i	$0.454697\pi$
$662$	−24.9185	−0.968485
$663$	−61.6954	−2.39605
$664$	−9.03389	−0.350583
$665$	2.97353	0.115309
$666$	45.7047	1.77102
$667$	−65.6849	−2.54333
$668$	−12.8423	−0.496883
$669$	−33.1707	−1.28245
$670$	−32.7329	−1.26458
$671$	26.5657	1.02556
$672$	−2.78895	−0.107586
$673$	−38.4483	−1.48207	−0.741036	−	0.671466i	$-0.765665\pi$
$673$	−38.4483	−1.48207	−0.741036	+	0.671466i	$0.765665\pi$
$674$	−10.2899	−0.396352
$675$	151.515	5.83181
$676$	−1.18081	−0.0454159
$677$	28.8586	1.10913	0.554564	−	0.832141i	$-0.312885\pi$
$677$	28.8586	1.10913	0.554564	+	0.832141i	$0.312885\pi$
$678$	−0.0326913	−0.00125550
$679$	−4.39632	−0.168715
$680$	−19.1333	−0.733730
$681$	−24.8326	−0.951589
$682$	−7.76038	−0.297160
$683$	25.6640	0.982006	0.491003	−	0.871158i	$-0.336630\pi$
$683$	25.6640	0.982006	0.491003	+	0.871158i	$0.336630\pi$
$684$	−8.51720	−0.325663
$685$	0.00946663	0.000361702 0
$686$	10.9502	0.418082
$687$	−3.53965	−0.135046
$688$	−11.1104	−0.423580
$689$	6.75513	0.257350
$690$	−77.3716	−2.94549
$691$	12.0811	0.459587	0.229793	−	0.973239i	$-0.426195\pi$
$691$	12.0811	0.459587	0.229793	+	0.973239i	$0.426195\pi$
$692$	1.12124	0.0426232
$693$	18.7544	0.712422
$694$	−8.36269	−0.317443
$695$	33.6824	1.27765
$696$	35.3782	1.34101
$697$	9.51450	0.360387
$698$	14.7239	0.557309
$699$	−38.0827	−1.44042
$700$	−6.65014	−0.251352
$701$	−40.8703	−1.54365	−0.771825	−	0.635835i	$-0.780656\pi$
$701$	−40.8703	−1.54365	−0.771825	+	0.635835i	$0.780656\pi$
$702$	64.3704	2.42950
$703$	−5.36617	−0.202389
$704$	−2.67941	−0.100984
$705$	64.1820	2.41724
$706$	−0.311257	−0.0117143
$707$	−16.3381	−0.614459
$708$	−37.9156	−1.42496
$709$	47.6255	1.78861	0.894307	−	0.447453i	$-0.147669\pi$
$709$	47.6255	1.78861	0.894307	+	0.447453i	$0.147669\pi$
$710$	−37.7883	−1.41817
$711$	−150.678	−5.65088
$712$	−15.1669	−0.568403
$713$	−18.2493	−0.683442
$714$	14.7478	0.551922
$715$	−33.3302	−1.24648
$716$	−0.602741	−0.0225255
$717$	8.05026	0.300642
$718$	−22.5209	−0.840471
$719$	39.0972	1.45808	0.729039	−	0.684472i	$-0.239967\pi$
$719$	39.0972	1.45808	0.729039	+	0.684472i	$0.239967\pi$
$720$	30.8178	1.14851
$721$	−1.66763	−0.0621059
$722$	1.00000	0.0372161
$723$	21.8458	0.812453
$724$	12.7282	0.473041
$725$	84.3579	3.13297
$726$	−12.9665	−0.481232
$727$	31.1620	1.15574	0.577868	−	0.816130i	$-0.303885\pi$
$727$	31.1620	1.15574	0.577868	+	0.816130i	$0.303885\pi$
$728$	−2.82528	−0.104712
$729$	132.950	4.92406
$730$	12.5386	0.464073
$731$	58.7510	2.17299
$732$	−33.6477	−1.24365
$733$	−38.7822	−1.43245	−0.716227	−	0.697867i	$-0.754132\pi$
$733$	−38.7822	−1.43245	−0.716227	+	0.697867i	$0.754132\pi$
$734$	−9.03476	−0.333479
$735$	−77.6631	−2.86465
$736$	−6.30090	−0.232254
$737$	24.2392	0.892862
$738$	−15.3249	−0.564117
$739$	39.7339	1.46163	0.730817	−	0.682573i	$-0.239139\pi$
$739$	39.7339	1.46163	0.730817	+	0.682573i	$0.239139\pi$
$740$	19.4164	0.713763
$741$	−11.6672	−0.428606
$742$	−1.61476	−0.0592796
$743$	6.85173	0.251366	0.125683	−	0.992070i	$-0.459888\pi$
$743$	6.85173	0.251366	0.125683	+	0.992070i	$0.459888\pi$
$744$	9.82918	0.360355
$745$	17.4515	0.639375
$746$	19.6507	0.719464
$747$	−76.9434	−2.81521
$748$	14.1685	0.518053
$749$	−11.1733	−0.408263
$750$	37.9697	1.38646
$751$	37.3739	1.36379	0.681896	−	0.731449i	$-0.261156\pi$
$751$	37.3739	1.36379	0.681896	+	0.731449i	$0.261156\pi$
$752$	5.22679	0.190601
$753$	−2.16235	−0.0788004
$754$	35.8391	1.30518
$755$	18.8047	0.684371
$756$	−15.3872	−0.559627
$757$	18.0132	0.654702	0.327351	−	0.944903i	$-0.393844\pi$
$757$	18.0132	0.654702	0.327351	+	0.944903i	$0.393844\pi$
$758$	33.5725	1.21941
$759$	57.2949	2.07967
$760$	−3.61831	−0.131250
$761$	29.9933	1.08726	0.543628	−	0.839326i	$-0.317050\pi$
$761$	29.9933	1.08726	0.543628	+	0.839326i	$0.317050\pi$
$762$	12.0706	0.437271
$763$	−9.30899	−0.337008
$764$	9.87850	0.357391
$765$	−162.962	−5.89192
$766$	19.0717	0.689088
$767$	−38.4095	−1.38689
$768$	3.39370	0.122460
$769$	14.8232	0.534538	0.267269	−	0.963622i	$-0.413879\pi$
$769$	14.8232	0.534538	0.267269	+	0.963622i	$0.413879\pi$
$770$	7.96732	0.287122
$771$	16.3509	0.588863
$772$	−5.63807	−0.202919
$773$	20.9295	0.752782	0.376391	−	0.926461i	$-0.377165\pi$
$773$	20.9295	0.752782	0.376391	+	0.926461i	$0.377165\pi$
$774$	−94.6296	−3.40139
$775$	23.4373	0.841891
$776$	5.34961	0.192040
$777$	−14.9660	−0.536902
$778$	−35.4301	−1.27023
$779$	1.79929	0.0644662
$780$	42.2156	1.51156
$781$	27.9828	1.00130
$782$	33.3187	1.19148
$783$	195.189	6.97548
$784$	−6.32464	−0.225880
$785$	55.5594	1.98300
$786$	−8.02154	−0.286119
$787$	−8.08036	−0.288034	−0.144017	−	0.989575i	$-0.546002\pi$
$787$	−8.08036	−0.288034	−0.144017	+	0.989575i	$0.546002\pi$
$788$	−15.1016	−0.537971
$789$	85.9337	3.05932
$790$	−64.0116	−2.27743
$791$	0.00791637	0.000281474 0
$792$	−22.8211	−0.810912
$793$	−34.0860	−1.21043
$794$	−2.09825	−0.0744640
$795$	24.1278	0.855726
$796$	19.3083	0.684365
$797$	−1.30134	−0.0460958	−0.0230479	−	0.999734i	$-0.507337\pi$
$797$	−1.30134	−0.0460958	−0.0230479	+	0.999734i	$0.507337\pi$
$798$	2.78895	0.0987279
$799$	−27.6389	−0.977793
$800$	8.09214	0.286100
$801$	−129.179	−4.56433
$802$	12.5379	0.442729
$803$	−9.28500	−0.327660
$804$	−30.7010	−1.08274
$805$	18.7360	0.660356
$806$	9.95721	0.350728
$807$	49.6464	1.74763
$808$	19.8808	0.699406
$809$	1.04833	0.0368574	0.0184287	−	0.999830i	$-0.494134\pi$
$809$	1.04833	0.0368574	0.0184287	+	0.999830i	$0.494134\pi$
$810$	137.463	4.82997
$811$	−44.6491	−1.56784	−0.783921	−	0.620860i	$-0.786784\pi$
$811$	−44.6491	−1.56784	−0.783921	+	0.620860i	$0.786784\pi$
$812$	−8.56703	−0.300644
$813$	89.2468	3.13002
$814$	−14.3782	−0.503955
$815$	39.1741	1.37221
$816$	−17.9456	−0.628223
$817$	11.1104	0.388704
$818$	−20.7742	−0.726354
$819$	−24.0635	−0.840846
$820$	−6.51037	−0.227352
$821$	41.5817	1.45121	0.725606	−	0.688110i	$-0.241559\pi$
$821$	41.5817	1.45121	0.725606	+	0.688110i	$0.241559\pi$
$822$	0.00887900	0.000309691 0
$823$	46.9854	1.63781	0.818904	−	0.573931i	$-0.194582\pi$
$823$	46.9854	1.63781	0.818904	+	0.573931i	$0.194582\pi$
$824$	2.02924	0.0706918
$825$	−73.5827	−2.56182
$826$	9.18147	0.319464
$827$	19.5015	0.678133	0.339067	−	0.940762i	$-0.389889\pi$
$827$	19.5015	0.678133	0.339067	+	0.940762i	$0.389889\pi$
$828$	−53.6661	−1.86502
$829$	11.9443	0.414842	0.207421	−	0.978252i	$-0.433493\pi$
$829$	11.9443	0.414842	0.207421	+	0.978252i	$0.433493\pi$
$830$	−32.6874	−1.13460
$831$	−50.4419	−1.74981
$832$	3.43790	0.119188
$833$	33.4442	1.15877
$834$	31.5916	1.09393
$835$	−46.4673	−1.60807
$836$	2.67941	0.0926694
$837$	54.2295	1.87445
$838$	38.1091	1.31646
$839$	−42.3189	−1.46101	−0.730505	−	0.682908i	$-0.760715\pi$
$839$	−42.3189	−1.46101	−0.730505	+	0.682908i	$0.760715\pi$
$840$	−10.0913	−0.348182
$841$	79.6740	2.74738
$842$	3.11612	0.107389
$843$	28.2228	0.972043
$844$	−1.00000	−0.0344214
$845$	−4.27254	−0.146980
$846$	44.5176	1.53055
$847$	3.13991	0.107889
$848$	1.96490	0.0674748
$849$	−96.7887	−3.32178
$850$	−42.7906	−1.46771
$851$	−33.8117	−1.15905
$852$	−35.4426	−1.21424
$853$	−33.7605	−1.15594	−0.577968	−	0.816059i	$-0.696154\pi$
$853$	−33.7605	−1.15594	−0.577968	+	0.816059i	$0.696154\pi$
$854$	8.14797	0.278818
$855$	−30.8178	−1.05395
$856$	13.5961	0.464704
$857$	−38.2888	−1.30792	−0.653960	−	0.756529i	$-0.726894\pi$
$857$	−38.2888	−1.30792	−0.653960	+	0.756529i	$0.726894\pi$
$858$	−31.2613	−1.06724
$859$	−23.5354	−0.803018	−0.401509	−	0.915855i	$-0.631514\pi$
$859$	−23.5354	−0.803018	−0.401509	+	0.915855i	$0.631514\pi$
$860$	−40.2009	−1.37084
$861$	5.01813	0.171017
$862$	−22.4601	−0.764995
$863$	14.5056	0.493778	0.246889	−	0.969044i	$-0.420592\pi$
$863$	14.5056	0.493778	0.246889	+	0.969044i	$0.420592\pi$
$864$	18.7237	0.636994
$865$	4.05699	0.137942
$866$	−8.09259	−0.274997
$867$	37.2023	1.26346
$868$	−2.38019	−0.0807889
$869$	47.4016	1.60799
$870$	128.009	4.33992
$871$	−31.1009	−1.05381
$872$	11.3275	0.383598
$873$	45.5637	1.54210
$874$	6.30090	0.213131
$875$	−9.19457	−0.310833
$876$	11.7602	0.397341
$877$	−6.68625	−0.225779	−0.112889	−	0.993608i	$-0.536011\pi$
$877$	−6.68625	−0.225779	−0.112889	+	0.993608i	$0.536011\pi$
$878$	18.4403	0.622328
$879$	−82.8933	−2.79592
$880$	−9.69493	−0.326816
$881$	18.2204	0.613862	0.306931	−	0.951732i	$-0.400698\pi$
$881$	18.2204	0.613862	0.306931	+	0.951732i	$0.400698\pi$
$882$	−53.8682	−1.81384
$883$	−44.5911	−1.50061	−0.750304	−	0.661093i	$-0.770093\pi$
$883$	−44.5911	−1.50061	−0.750304	+	0.661093i	$0.770093\pi$
$884$	−18.1794	−0.611439
$885$	−137.190	−4.61160
$886$	17.5684	0.590221
$887$	16.2922	0.547039	0.273520	−	0.961866i	$-0.411812\pi$
$887$	16.2922	0.547039	0.273520	+	0.961866i	$0.411812\pi$
$888$	18.2112	0.611127
$889$	−2.92296	−0.0980329
$890$	−54.8785	−1.83953
$891$	−101.794	−3.41022
$892$	−9.77419	−0.327264
$893$	−5.22679	−0.174908
$894$	16.3682	0.547436
$895$	−2.18090	−0.0728995
$896$	−0.821803	−0.0274545
$897$	−73.5140	−2.45456
$898$	25.9987	0.867589
$899$	30.1930	1.00699
$900$	68.9223	2.29741
$901$	−10.3902	−0.346149
$902$	4.82103	0.160523
$903$	30.9864	1.03116
$904$	−0.00963292	−0.000320386 0
$905$	46.0546	1.53091
$906$	17.6374	0.585962
$907$	38.2769	1.27096	0.635482	−	0.772116i	$-0.280802\pi$
$907$	38.2769	1.27096	0.635482	+	0.772116i	$0.280802\pi$
$908$	−7.31728	−0.242832
$909$	169.329	5.61629
$910$	−10.2227	−0.338880
$911$	−15.3332	−0.508011	−0.254005	−	0.967203i	$-0.581748\pi$
$911$	−15.3332	−0.508011	−0.254005	+	0.967203i	$0.581748\pi$
$912$	−3.39370	−0.112377
$913$	24.2055	0.801085
$914$	20.7697	0.686999
$915$	−121.748	−4.02485
$916$	−1.04301	−0.0344619
$917$	1.94246	0.0641457
$918$	−99.0097	−3.26781
$919$	−8.89859	−0.293538	−0.146769	−	0.989171i	$-0.546887\pi$
$919$	−8.89859	−0.293538	−0.146769	+	0.989171i	$0.546887\pi$
$920$	−22.7986	−0.751648
$921$	15.8139	0.521086
$922$	−8.01016	−0.263801
$923$	−35.9043	−1.18180
$924$	7.47275	0.245835
$925$	43.4238	1.42776
$926$	18.7273	0.615419
$927$	17.2834	0.567662
$928$	10.4247	0.342207
$929$	30.9754	1.01627	0.508135	−	0.861277i	$-0.330335\pi$
$929$	30.9754	1.01627	0.508135	+	0.861277i	$0.330335\pi$
$930$	35.5650	1.16622
$931$	6.32464	0.207282
$932$	−11.2216	−0.367576
$933$	−66.6519	−2.18209
$934$	12.9841	0.424853
$935$	51.2661	1.67658
$936$	29.2813	0.957090
$937$	−2.18767	−0.0714680	−0.0357340	−	0.999361i	$-0.511377\pi$
$937$	−2.18767	−0.0714680	−0.0357340	+	0.999361i	$0.511377\pi$
$938$	7.43441	0.242742
$939$	42.7865	1.39628
$940$	18.9121	0.616845
$941$	−43.2699	−1.41056	−0.705279	−	0.708930i	$-0.749178\pi$
$941$	−43.2699	−1.41056	−0.705279	+	0.708930i	$0.749178\pi$
$942$	52.1106	1.69785
$943$	11.3371	0.369188
$944$	−11.1724	−0.363629
$945$	−55.6756	−1.81113
$946$	29.7694	0.967885
$947$	20.3511	0.661321	0.330660	−	0.943750i	$-0.392729\pi$
$947$	20.3511	0.661321	0.330660	+	0.943750i	$0.392729\pi$
$948$	−60.0381	−1.94995
$949$	11.9134	0.386726
$950$	−8.09214	−0.262544
$951$	51.6740	1.67564
$952$	4.34563	0.140843
$953$	24.2996	0.787141	0.393570	−	0.919295i	$-0.371240\pi$
$953$	24.2996	0.787141	0.393570	+	0.919295i	$0.371240\pi$
$954$	16.7354	0.541829
$955$	35.7434	1.15663
$956$	2.37212	0.0767198
$957$	−94.7928	−3.06422
$958$	−42.6647	−1.37843
$959$	−0.00215010	−6.94303e−5 0
$960$	12.2794	0.396317
$961$	−22.6114	−0.729401
$962$	18.4484	0.594800
$963$	115.800	3.73161
$964$	6.43715	0.207327
$965$	−20.4003	−0.656708
$966$	17.5729	0.565400
$967$	30.0667	0.966880	0.483440	−	0.875377i	$-0.339387\pi$
$967$	30.0667	0.966880	0.483440	+	0.875377i	$0.339387\pi$
$968$	−3.82076	−0.122804
$969$	17.9456	0.576497
$970$	19.3565	0.621500
$971$	−51.6907	−1.65883	−0.829417	−	0.558631i	$-0.811327\pi$
$971$	−51.6907	−1.65883	−0.829417	+	0.558631i	$0.811327\pi$
$972$	72.7592	2.33375
$973$	−7.65007	−0.245250
$974$	−10.7012	−0.342890
$975$	94.4127	3.02363
$976$	−9.91475	−0.317363
$977$	−1.05997	−0.0339116	−0.0169558	−	0.999856i	$-0.505397\pi$
$977$	−1.05997	−0.0339116	−0.0169558	+	0.999856i	$0.505397\pi$
$978$	36.7424	1.17489
$979$	40.6383	1.29881
$980$	−22.8845	−0.731018
$981$	96.4787	3.08033
$982$	10.5105	0.335405
$983$	−12.5721	−0.400987	−0.200493	−	0.979695i	$-0.564255\pi$
$983$	−12.5721	−0.400987	−0.200493	+	0.979695i	$0.564255\pi$
$984$	−6.10624	−0.194660
$985$	−54.6421	−1.74104
$986$	−55.1249	−1.75554
$987$	−14.5773	−0.463999
$988$	−3.43790	−0.109374
$989$	70.0056	2.22605
$990$	−82.5736	−2.62436
$991$	13.5152	0.429324	0.214662	−	0.976688i	$-0.431135\pi$
$991$	13.5152	0.429324	0.214662	+	0.976688i	$0.431135\pi$
$992$	2.89630	0.0919577
$993$	−84.5659	−2.68362
$994$	8.58263	0.272224
$995$	69.8634	2.21482
$996$	−30.6583	−0.971446
$997$	37.7442	1.19537	0.597685	−	0.801731i	$-0.296087\pi$
$997$	37.7442	1.19537	0.597685	+	0.801731i	$0.296087\pi$
$998$	−27.6284	−0.874561
$999$	100.475	3.17888

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.j.1.47	✓	47

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.j.1.47	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +3.39370 q^{3} +1.00000 q^{4} +3.61831 q^{5} +3.39370 q^{6} -0.821803 q^{7} +1.00000 q^{8} +8.51720 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +3.39370 q^{3} +1.00000 q^{4} +3.61831 q^{5} +3.39370 q^{6} -0.821803 q^{7} +1.00000 q^{8} +8.51720 q^{9} +3.61831 q^{10} -2.67941 q^{11} +3.39370 q^{12} +3.43790 q^{13} -0.821803 q^{14} +12.2794 q^{15} +1.00000 q^{16} -5.28793 q^{17} +8.51720 q^{18} -1.00000 q^{19} +3.61831 q^{20} -2.78895 q^{21} -2.67941 q^{22} -6.30090 q^{23} +3.39370 q^{24} +8.09214 q^{25} +3.43790 q^{26} +18.7237 q^{27} -0.821803 q^{28} +10.4247 q^{29} +12.2794 q^{30} +2.89630 q^{31} +1.00000 q^{32} -9.09312 q^{33} -5.28793 q^{34} -2.97353 q^{35} +8.51720 q^{36} +5.36617 q^{37} -1.00000 q^{38} +11.6672 q^{39} +3.61831 q^{40} -1.79929 q^{41} -2.78895 q^{42} -11.1104 q^{43} -2.67941 q^{44} +30.8178 q^{45} -6.30090 q^{46} +5.22679 q^{47} +3.39370 q^{48} -6.32464 q^{49} +8.09214 q^{50} -17.9456 q^{51} +3.43790 q^{52} +1.96490 q^{53} +18.7237 q^{54} -9.69493 q^{55} -0.821803 q^{56} -3.39370 q^{57} +10.4247 q^{58} -11.1724 q^{59} +12.2794 q^{60} -9.91475 q^{61} +2.89630 q^{62} -6.99946 q^{63} +1.00000 q^{64} +12.4394 q^{65} -9.09312 q^{66} -9.04646 q^{67} -5.28793 q^{68} -21.3834 q^{69} -2.97353 q^{70} -10.4437 q^{71} +8.51720 q^{72} +3.46531 q^{73} +5.36617 q^{74} +27.4623 q^{75} -1.00000 q^{76} +2.20195 q^{77} +11.6672 q^{78} -17.6911 q^{79} +3.61831 q^{80} +37.9911 q^{81} -1.79929 q^{82} -9.03389 q^{83} -2.78895 q^{84} -19.1333 q^{85} -11.1104 q^{86} +35.3782 q^{87} -2.67941 q^{88} -15.1669 q^{89} +30.8178 q^{90} -2.82528 q^{91} -6.30090 q^{92} +9.82918 q^{93} +5.22679 q^{94} -3.61831 q^{95} +3.39370 q^{96} +5.34961 q^{97} -6.32464 q^{98} -22.8211 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9}+O(q^{10}) \) 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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