LMFDB - Embedded newform 8007.2.a.i.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8007,2,Mod(1,8007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8007, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8007 = 3 \cdot 17 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8007.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:	$63.9362168984$
Analytic rank:	$0$
Dimension:	$63$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.58914 q^{2} +1.00000 q^{3} +4.70363 q^{4} -1.26310 q^{5} -2.58914 q^{6} -1.23370 q^{7} -7.00007 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.58914 q^{2} +1.00000 q^{3} +4.70363 q^{4} -1.26310 q^{5} -2.58914 q^{6} -1.23370 q^{7} -7.00007 q^{8} +1.00000 q^{9} +3.27035 q^{10} +0.478341 q^{11} +4.70363 q^{12} +1.76182 q^{13} +3.19421 q^{14} -1.26310 q^{15} +8.71688 q^{16} +1.00000 q^{17} -2.58914 q^{18} -2.88359 q^{19} -5.94118 q^{20} -1.23370 q^{21} -1.23849 q^{22} +5.84495 q^{23} -7.00007 q^{24} -3.40457 q^{25} -4.56158 q^{26} +1.00000 q^{27} -5.80286 q^{28} +7.98301 q^{29} +3.27035 q^{30} +3.38882 q^{31} -8.56905 q^{32} +0.478341 q^{33} -2.58914 q^{34} +1.55829 q^{35} +4.70363 q^{36} -9.33454 q^{37} +7.46602 q^{38} +1.76182 q^{39} +8.84182 q^{40} -0.861734 q^{41} +3.19421 q^{42} -6.69355 q^{43} +2.24994 q^{44} -1.26310 q^{45} -15.1334 q^{46} +7.39214 q^{47} +8.71688 q^{48} -5.47799 q^{49} +8.81489 q^{50} +1.00000 q^{51} +8.28693 q^{52} +12.1165 q^{53} -2.58914 q^{54} -0.604195 q^{55} +8.63597 q^{56} -2.88359 q^{57} -20.6691 q^{58} -6.14116 q^{59} -5.94118 q^{60} -2.39806 q^{61} -8.77412 q^{62} -1.23370 q^{63} +4.75269 q^{64} -2.22536 q^{65} -1.23849 q^{66} +8.37049 q^{67} +4.70363 q^{68} +5.84495 q^{69} -4.03462 q^{70} +8.77677 q^{71} -7.00007 q^{72} +9.60267 q^{73} +24.1684 q^{74} -3.40457 q^{75} -13.5634 q^{76} -0.590128 q^{77} -4.56158 q^{78} +6.09378 q^{79} -11.0103 q^{80} +1.00000 q^{81} +2.23115 q^{82} -11.5956 q^{83} -5.80286 q^{84} -1.26310 q^{85} +17.3305 q^{86} +7.98301 q^{87} -3.34842 q^{88} -5.33225 q^{89} +3.27035 q^{90} -2.17355 q^{91} +27.4925 q^{92} +3.38882 q^{93} -19.1393 q^{94} +3.64228 q^{95} -8.56905 q^{96} -7.31867 q^{97} +14.1833 q^{98} +0.478341 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 63 q + 10 q^{2} + 63 q^{3} + 70 q^{4} + 19 q^{5} + 10 q^{6} + 11 q^{7} + 27 q^{8} + 63 q^{9}+O(q^{10}) $ 63 * q + 10 * q^2 + 63 * q^3 + 70 * q^4 + 19 * q^5 + 10 * q^6 + 11 * q^7 + 27 * q^8 + 63 * q^9	\( 63 q + 10 q^{2} + 63 q^{3} + 70 q^{4} + 19 q^{5} + 10 q^{6} + 11 q^{7} + 27 q^{8} + 63 q^{9} + 4 q^{10} + 23 q^{11} + 70 q^{12} + 10 q^{13} + 18 q^{14} + 19 q^{15} + 72 q^{16} + 63 q^{17} + 10 q^{18} + 6 q^{19} + 48 q^{20} + 11 q^{21} + 21 q^{22} + 44 q^{23} + 27 q^{24} + 110 q^{25} + 41 q^{26} + 63 q^{27} + 26 q^{28} + 35 q^{29} + 4 q^{30} + q^{31} + 54 q^{32} + 23 q^{33} + 10 q^{34} + 47 q^{35} + 70 q^{36} + 40 q^{37} + 38 q^{38} + 10 q^{39} - 10 q^{40} + 35 q^{41} + 18 q^{42} + 27 q^{43} + 46 q^{44} + 19 q^{45} + 8 q^{46} + 29 q^{47} + 72 q^{48} + 114 q^{49} + 27 q^{50} + 63 q^{51} - q^{52} + 75 q^{53} + 10 q^{54} + 5 q^{55} + 24 q^{56} + 6 q^{57} + 41 q^{58} + 105 q^{59} + 48 q^{60} + 5 q^{61} + 22 q^{62} + 11 q^{63} + 61 q^{64} + 49 q^{65} + 21 q^{66} + 4 q^{67} + 70 q^{68} + 44 q^{69} - 16 q^{70} + 16 q^{71} + 27 q^{72} + 39 q^{73} + 54 q^{74} + 110 q^{75} + 6 q^{76} + 88 q^{77} + 41 q^{78} + 16 q^{79} + 102 q^{80} + 63 q^{81} - 29 q^{82} + 73 q^{83} + 26 q^{84} + 19 q^{85} + 46 q^{86} + 35 q^{87} + 18 q^{88} + 88 q^{89} + 4 q^{90} - 15 q^{91} + 110 q^{92} + q^{93} - 8 q^{94} + 28 q^{95} + 54 q^{96} + 70 q^{97} + 33 q^{98} + 23 q^{99}+O(q^{100}) \) 63 * q + 10 * q^2 + 63 * q^3 + 70 * q^4 + 19 * q^5 + 10 * q^6 + 11 * q^7 + 27 * q^8 + 63 * q^9 + 4 * q^10 + 23 * q^11 + 70 * q^12 + 10 * q^13 + 18 * q^14 + 19 * q^15 + 72 * q^16 + 63 * q^17 + 10 * q^18 + 6 * q^19 + 48 * q^20 + 11 * q^21 + 21 * q^22 + 44 * q^23 + 27 * q^24 + 110 * q^25 + 41 * q^26 + 63 * q^27 + 26 * q^28 + 35 * q^29 + 4 * q^30 + q^31 + 54 * q^32 + 23 * q^33 + 10 * q^34 + 47 * q^35 + 70 * q^36 + 40 * q^37 + 38 * q^38 + 10 * q^39 - 10 * q^40 + 35 * q^41 + 18 * q^42 + 27 * q^43 + 46 * q^44 + 19 * q^45 + 8 * q^46 + 29 * q^47 + 72 * q^48 + 114 * q^49 + 27 * q^50 + 63 * q^51 - q^52 + 75 * q^53 + 10 * q^54 + 5 * q^55 + 24 * q^56 + 6 * q^57 + 41 * q^58 + 105 * q^59 + 48 * q^60 + 5 * q^61 + 22 * q^62 + 11 * q^63 + 61 * q^64 + 49 * q^65 + 21 * q^66 + 4 * q^67 + 70 * q^68 + 44 * q^69 - 16 * q^70 + 16 * q^71 + 27 * q^72 + 39 * q^73 + 54 * q^74 + 110 * q^75 + 6 * q^76 + 88 * q^77 + 41 * q^78 + 16 * q^79 + 102 * q^80 + 63 * q^81 - 29 * q^82 + 73 * q^83 + 26 * q^84 + 19 * q^85 + 46 * q^86 + 35 * q^87 + 18 * q^88 + 88 * q^89 + 4 * q^90 - 15 * q^91 + 110 * q^92 + q^93 - 8 * q^94 + 28 * q^95 + 54 * q^96 + 70 * q^97 + 33 * q^98 + 23 * 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 $

$2$	−2.58914	−1.83080	−0.915398	−	0.402550i	$-0.868124\pi$
$2$	−2.58914	−1.83080	−0.915398	+	0.402550i	$0.868124\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.70363	2.35182
$5$	−1.26310	−0.564878	−0.282439	−	0.959285i	$-0.591143\pi$
$5$	−1.26310	−0.564878	−0.282439	+	0.959285i	$0.591143\pi$
$6$	−2.58914	−1.05701
$7$	−1.23370	−0.466294	−0.233147	−	0.972442i	$-0.574902\pi$
$7$	−1.23370	−0.466294	−0.233147	+	0.972442i	$0.574902\pi$
$8$	−7.00007	−2.47490
$9$	1.00000	0.333333
$10$	3.27035	1.03418
$11$	0.478341	0.144225	0.0721127	−	0.997396i	$-0.477026\pi$
$11$	0.478341	0.144225	0.0721127	+	0.997396i	$0.477026\pi$
$12$	4.70363	1.35782
$13$	1.76182	0.488640	0.244320	−	0.969695i	$-0.421435\pi$
$13$	1.76182	0.488640	0.244320	+	0.969695i	$0.421435\pi$
$14$	3.19421	0.853689
$15$	−1.26310	−0.326132
$16$	8.71688	2.17922
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−2.58914	−0.610265
$19$	−2.88359	−0.661541	−0.330771	−	0.943711i	$-0.607309\pi$
$19$	−2.88359	−0.661541	−0.330771	+	0.943711i	$0.607309\pi$
$20$	−5.94118	−1.32849
$21$	−1.23370	−0.269215
$22$	−1.23849	−0.264047
$23$	5.84495	1.21876	0.609378	−	0.792880i	$-0.291419\pi$
$23$	5.84495	1.21876	0.609378	+	0.792880i	$0.291419\pi$
$24$	−7.00007	−1.42888
$25$	−3.40457	−0.680913
$26$	−4.56158	−0.894600
$27$	1.00000	0.192450
$28$	−5.80286	−1.09664
$29$	7.98301	1.48241	0.741204	−	0.671280i	$-0.234255\pi$
$29$	7.98301	1.48241	0.741204	+	0.671280i	$0.234255\pi$
$30$	3.27035	0.597082
$31$	3.38882	0.608650	0.304325	−	0.952568i	$-0.401569\pi$
$31$	3.38882	0.608650	0.304325	+	0.952568i	$0.401569\pi$
$32$	−8.56905	−1.51481
$33$	0.478341	0.0832685
$34$	−2.58914	−0.444033
$35$	1.55829	0.263399
$36$	4.70363	0.783938
$37$	−9.33454	−1.53459	−0.767295	−	0.641295i	$-0.778398\pi$
$37$	−9.33454	−1.53459	−0.767295	+	0.641295i	$0.778398\pi$
$38$	7.46602	1.21115
$39$	1.76182	0.282116
$40$	8.84182	1.39801
$41$	−0.861734	−0.134580	−0.0672902	−	0.997733i	$-0.521435\pi$
$41$	−0.861734	−0.134580	−0.0672902	+	0.997733i	$0.521435\pi$
$42$	3.19421	0.492878
$43$	−6.69355	−1.02076	−0.510379	−	0.859950i	$-0.670495\pi$
$43$	−6.69355	−1.02076	−0.510379	+	0.859950i	$0.670495\pi$
$44$	2.24994	0.339191
$45$	−1.26310	−0.188293
$46$	−15.1334	−2.23129
$47$	7.39214	1.07825	0.539127	−	0.842225i	$-0.318754\pi$
$47$	7.39214	1.07825	0.539127	+	0.842225i	$0.318754\pi$
$48$	8.71688	1.25817
$49$	−5.47799	−0.782570
$50$	8.81489	1.24661
$51$	1.00000	0.140028
$52$	8.28693	1.14919
$53$	12.1165	1.66433	0.832167	−	0.554525i	$-0.187100\pi$
$53$	12.1165	1.66433	0.832167	+	0.554525i	$0.187100\pi$
$54$	−2.58914	−0.352337
$55$	−0.604195	−0.0814697
$56$	8.63597	1.15403
$57$	−2.88359	−0.381941
$58$	−20.6691	−2.71399
$59$	−6.14116	−0.799510	−0.399755	−	0.916622i	$-0.630905\pi$
$59$	−6.14116	−0.799510	−0.399755	+	0.916622i	$0.630905\pi$
$60$	−5.94118	−0.767003
$61$	−2.39806	−0.307040	−0.153520	−	0.988146i	$-0.549061\pi$
$61$	−2.39806	−0.307040	−0.153520	+	0.988146i	$0.549061\pi$
$62$	−8.77412	−1.11431
$63$	−1.23370	−0.155431
$64$	4.75269	0.594086
$65$	−2.22536	−0.276022
$66$	−1.23849	−0.152448
$67$	8.37049	1.02262	0.511309	−	0.859397i	$-0.329161\pi$
$67$	8.37049	1.02262	0.511309	+	0.859397i	$0.329161\pi$
$68$	4.70363	0.570399
$69$	5.84495	0.703649
$70$	−4.03462	−0.482230
$71$	8.77677	1.04161	0.520806	−	0.853675i	$-0.325632\pi$
$71$	8.77677	1.04161	0.520806	+	0.853675i	$0.325632\pi$
$72$	−7.00007	−0.824966
$73$	9.60267	1.12391	0.561954	−	0.827169i	$-0.310050\pi$
$73$	9.60267	1.12391	0.561954	+	0.827169i	$0.310050\pi$
$74$	24.1684	2.80952
$75$	−3.40457	−0.393125
$76$	−13.5634	−1.55582
$77$	−0.590128	−0.0672514
$78$	−4.56158	−0.516497
$79$	6.09378	0.685604	0.342802	−	0.939408i	$-0.388624\pi$
$79$	6.09378	0.685604	0.342802	+	0.939408i	$0.388624\pi$
$80$	−11.0103	−1.23099
$81$	1.00000	0.111111
$82$	2.23115	0.246389
$83$	−11.5956	−1.27278	−0.636390	−	0.771368i	$-0.719573\pi$
$83$	−11.5956	−1.27278	−0.636390	+	0.771368i	$0.719573\pi$
$84$	−5.80286	−0.633144
$85$	−1.26310	−0.137003
$86$	17.3305	1.86880
$87$	7.98301	0.855869
$88$	−3.34842	−0.356943
$89$	−5.33225	−0.565218	−0.282609	−	0.959235i	$-0.591200\pi$
$89$	−5.33225	−0.565218	−0.282609	+	0.959235i	$0.591200\pi$
$90$	3.27035	0.344725
$91$	−2.17355	−0.227850
$92$	27.4925	2.86629
$93$	3.38882	0.351404
$94$	−19.1393	−1.97406
$95$	3.64228	0.373690
$96$	−8.56905	−0.874575
$97$	−7.31867	−0.743098	−0.371549	−	0.928413i	$-0.621173\pi$
$97$	−7.31867	−0.743098	−0.371549	+	0.928413i	$0.621173\pi$
$98$	14.1833	1.43273
$99$	0.478341	0.0480751
$100$	−16.0138	−1.60138
$101$	1.40249	0.139553	0.0697767	−	0.997563i	$-0.477771\pi$
$101$	1.40249	0.139553	0.0697767	+	0.997563i	$0.477771\pi$
$102$	−2.58914	−0.256363
$103$	−15.6730	−1.54430	−0.772151	−	0.635439i	$-0.780819\pi$
$103$	−15.6730	−1.54430	−0.772151	+	0.635439i	$0.780819\pi$
$104$	−12.3328	−1.20933
$105$	1.55829	0.152073
$106$	−31.3714	−3.04706
$107$	3.64527	0.352401	0.176201	−	0.984354i	$-0.443619\pi$
$107$	3.64527	0.352401	0.176201	+	0.984354i	$0.443619\pi$
$108$	4.70363	0.452607
$109$	11.8465	1.13469	0.567343	−	0.823481i	$-0.307971\pi$
$109$	11.8465	1.13469	0.567343	+	0.823481i	$0.307971\pi$
$110$	1.56434	0.149154
$111$	−9.33454	−0.885996
$112$	−10.7540	−1.01616
$113$	12.2287	1.15038	0.575190	−	0.818020i	$-0.304928\pi$
$113$	12.2287	1.15038	0.575190	+	0.818020i	$0.304928\pi$
$114$	7.46602	0.699256
$115$	−7.38278	−0.688448
$116$	37.5491	3.48635
$117$	1.76182	0.162880
$118$	15.9003	1.46374
$119$	−1.23370	−0.113093
$120$	8.84182	0.807144
$121$	−10.7712	−0.979199
$122$	6.20890	0.562127
$123$	−0.861734	−0.0777000
$124$	15.9398	1.43143
$125$	10.6158	0.949510
$126$	3.19421	0.284563
$127$	−5.69221	−0.505102	−0.252551	−	0.967584i	$-0.581270\pi$
$127$	−5.69221	−0.505102	−0.252551	+	0.967584i	$0.581270\pi$
$128$	4.83274	0.427158
$129$	−6.69355	−0.589334
$130$	5.76176	0.505339
$131$	−14.5705	−1.27303	−0.636516	−	0.771264i	$-0.719625\pi$
$131$	−14.5705	−1.27303	−0.636516	+	0.771264i	$0.719625\pi$
$132$	2.24994	0.195832
$133$	3.55748	0.308473
$134$	−21.6724	−1.87221
$135$	−1.26310	−0.108711
$136$	−7.00007	−0.600251
$137$	−2.53894	−0.216916	−0.108458	−	0.994101i	$-0.534591\pi$
$137$	−2.53894	−0.216916	−0.108458	+	0.994101i	$0.534591\pi$
$138$	−15.1334	−1.28824
$139$	19.5250	1.65609	0.828046	−	0.560660i	$-0.189453\pi$
$139$	19.5250	1.65609	0.828046	+	0.560660i	$0.189453\pi$
$140$	7.32962	0.619466
$141$	7.39214	0.622530
$142$	−22.7243	−1.90698
$143$	0.842749	0.0704742
$144$	8.71688	0.726406
$145$	−10.0834	−0.837379
$146$	−24.8626	−2.05765
$147$	−5.47799	−0.451817
$148$	−43.9062	−3.60907
$149$	−15.3798	−1.25996	−0.629982	−	0.776610i	$-0.716938\pi$
$149$	−15.3798	−1.25996	−0.629982	+	0.776610i	$0.716938\pi$
$150$	8.81489	0.719733
$151$	−15.7393	−1.28085	−0.640423	−	0.768023i	$-0.721241\pi$
$151$	−15.7393	−1.28085	−0.640423	+	0.768023i	$0.721241\pi$
$152$	20.1853	1.63725
$153$	1.00000	0.0808452
$154$	1.52792	0.123124
$155$	−4.28044	−0.343813
$156$	8.28693	0.663485
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	−15.7776	−1.25520
$159$	12.1165	0.960904
$160$	10.8236	0.855681
$161$	−7.21090	−0.568298
$162$	−2.58914	−0.203422
$163$	19.0819	1.49461	0.747304	−	0.664483i	$-0.231348\pi$
$163$	19.0819	1.49461	0.747304	+	0.664483i	$0.231348\pi$
$164$	−4.05328	−0.316508
$165$	−0.604195	−0.0470365
$166$	30.0225	2.33020
$167$	−2.51119	−0.194322	−0.0971608	−	0.995269i	$-0.530976\pi$
$167$	−2.51119	−0.194322	−0.0971608	+	0.995269i	$0.530976\pi$
$168$	8.63597	0.666279
$169$	−9.89601	−0.761231
$170$	3.27035	0.250825
$171$	−2.88359	−0.220514
$172$	−31.4840	−2.40063
$173$	−4.69578	−0.357014	−0.178507	−	0.983939i	$-0.557127\pi$
$173$	−4.69578	−0.357014	−0.178507	+	0.983939i	$0.557127\pi$
$174$	−20.6691	−1.56692
$175$	4.20020	0.317506
$176$	4.16964	0.314299
$177$	−6.14116	−0.461598
$178$	13.8059	1.03480
$179$	−11.1901	−0.836385	−0.418193	−	0.908358i	$-0.637336\pi$
$179$	−11.1901	−0.836385	−0.418193	+	0.908358i	$0.637336\pi$
$180$	−5.94118	−0.442829
$181$	23.6455	1.75756	0.878778	−	0.477230i	$-0.158359\pi$
$181$	23.6455	1.75756	0.878778	+	0.477230i	$0.158359\pi$
$182$	5.62761	0.417146
$183$	−2.39806	−0.177269
$184$	−40.9150	−3.01630
$185$	11.7905	0.866855
$186$	−8.77412	−0.643350
$187$	0.478341	0.0349798
$188$	34.7699	2.53585
$189$	−1.23370	−0.0897383
$190$	−9.43036	−0.684150
$191$	−0.863614	−0.0624889	−0.0312445	−	0.999512i	$-0.509947\pi$
$191$	−0.863614	−0.0624889	−0.0312445	+	0.999512i	$0.509947\pi$
$192$	4.75269	0.342996
$193$	−18.1229	−1.30452	−0.652259	−	0.757996i	$-0.726179\pi$
$193$	−18.1229	−1.30452	−0.652259	+	0.757996i	$0.726179\pi$
$194$	18.9490	1.36046
$195$	−2.22536	−0.159361
$196$	−25.7664	−1.84046
$197$	−7.19541	−0.512652	−0.256326	−	0.966590i	$-0.582512\pi$
$197$	−7.19541	−0.512652	−0.256326	+	0.966590i	$0.582512\pi$
$198$	−1.23849	−0.0880157
$199$	27.1446	1.92423	0.962115	−	0.272642i	$-0.0878975\pi$
$199$	27.1446	1.92423	0.962115	+	0.272642i	$0.0878975\pi$
$200$	23.8322	1.68519
$201$	8.37049	0.590409
$202$	−3.63125	−0.255494
$203$	−9.84862	−0.691238
$204$	4.70363	0.329320
$205$	1.08846	0.0760214
$206$	40.5794	2.82730
$207$	5.84495	0.406252
$208$	15.3575	1.06485
$209$	−1.37934	−0.0954110
$210$	−4.03462	−0.278416
$211$	0.536711	0.0369487	0.0184744	−	0.999829i	$-0.494119\pi$
$211$	0.536711	0.0369487	0.0184744	+	0.999829i	$0.494119\pi$
$212$	56.9917	3.91421
$213$	8.77677	0.601375
$214$	−9.43809	−0.645175
$215$	8.45466	0.576603
$216$	−7.00007	−0.476294
$217$	−4.18078	−0.283810
$218$	−30.6722	−2.07738
$219$	9.60267	0.648888
$220$	−2.84191	−0.191602
$221$	1.76182	0.118513
$222$	24.1684	1.62208
$223$	16.5356	1.10731	0.553653	−	0.832747i	$-0.313233\pi$
$223$	16.5356	1.10731	0.553653	+	0.832747i	$0.313233\pi$
$224$	10.5716	0.706346
$225$	−3.40457	−0.226971
$226$	−31.6618	−2.10611
$227$	6.68401	0.443633	0.221817	−	0.975088i	$-0.428801\pi$
$227$	6.68401	0.443633	0.221817	+	0.975088i	$0.428801\pi$
$228$	−13.5634	−0.898255
$229$	6.33203	0.418432	0.209216	−	0.977869i	$-0.432909\pi$
$229$	6.33203	0.418432	0.209216	+	0.977869i	$0.432909\pi$
$230$	19.1150	1.26041
$231$	−0.590128	−0.0388276
$232$	−55.8816	−3.66881
$233$	0.958721	0.0628079	0.0314040	−	0.999507i	$-0.490002\pi$
$233$	0.958721	0.0628079	0.0314040	+	0.999507i	$0.490002\pi$
$234$	−4.56158	−0.298200
$235$	−9.33704	−0.609081
$236$	−28.8857	−1.88030
$237$	6.09378	0.395834
$238$	3.19421	0.207050
$239$	−1.44649	−0.0935655	−0.0467827	−	0.998905i	$-0.514897\pi$
$239$	−1.44649	−0.0935655	−0.0467827	+	0.998905i	$0.514897\pi$
$240$	−11.0103	−0.710714
$241$	−8.22387	−0.529746	−0.264873	−	0.964283i	$-0.585330\pi$
$241$	−8.22387	−0.529746	−0.264873	+	0.964283i	$0.585330\pi$
$242$	27.8881	1.79271
$243$	1.00000	0.0641500
$244$	−11.2796	−0.722101
$245$	6.91928	0.442056
$246$	2.23115	0.142253
$247$	−5.08036	−0.323255
$248$	−23.7220	−1.50635
$249$	−11.5956	−0.734840
$250$	−27.4859	−1.73836
$251$	29.3230	1.85085	0.925427	−	0.378926i	$-0.123706\pi$
$251$	29.3230	1.85085	0.925427	+	0.378926i	$0.123706\pi$
$252$	−5.80286	−0.365546
$253$	2.79588	0.175775
$254$	14.7379	0.924739
$255$	−1.26310	−0.0790987
$256$	−22.0180	−1.37612
$257$	2.67658	0.166960	0.0834802	−	0.996509i	$-0.473396\pi$
$257$	2.67658	0.166960	0.0834802	+	0.996509i	$0.473396\pi$
$258$	17.3305	1.07895
$259$	11.5160	0.715570
$260$	−10.4673	−0.649152
$261$	7.98301	0.494136
$262$	37.7250	2.33066
$263$	18.6026	1.14709	0.573543	−	0.819175i	$-0.305568\pi$
$263$	18.6026	1.14709	0.573543	+	0.819175i	$0.305568\pi$
$264$	−3.34842	−0.206081
$265$	−15.3045	−0.940145
$266$	−9.21080	−0.564751
$267$	−5.33225	−0.326329
$268$	39.3717	2.40501
$269$	−18.1448	−1.10631	−0.553155	−	0.833079i	$-0.686576\pi$
$269$	−18.1448	−1.10631	−0.553155	+	0.833079i	$0.686576\pi$
$270$	3.27035	0.199027
$271$	2.74126	0.166520	0.0832598	−	0.996528i	$-0.473467\pi$
$271$	2.74126	0.166520	0.0832598	+	0.996528i	$0.473467\pi$
$272$	8.71688	0.528538
$273$	−2.17355	−0.131549
$274$	6.57367	0.397130
$275$	−1.62854	−0.0982049
$276$	27.4925	1.65485
$277$	20.1509	1.21075	0.605375	−	0.795941i	$-0.293023\pi$
$277$	20.1509	1.21075	0.605375	+	0.795941i	$0.293023\pi$
$278$	−50.5530	−3.03197
$279$	3.38882	0.202883
$280$	−10.9081	−0.651886
$281$	3.05721	0.182378	0.0911889	−	0.995834i	$-0.470933\pi$
$281$	3.05721	0.182378	0.0911889	+	0.995834i	$0.470933\pi$
$282$	−19.1393	−1.13973
$283$	−0.307420	−0.0182742	−0.00913711	−	0.999958i	$-0.502908\pi$
$283$	−0.307420	−0.0182742	−0.00913711	+	0.999958i	$0.502908\pi$
$284$	41.2827	2.44968
$285$	3.64228	0.215750
$286$	−2.18199	−0.129024
$287$	1.06312	0.0627540
$288$	−8.56905	−0.504936
$289$	1.00000	0.0588235
$290$	26.1073	1.53307
$291$	−7.31867	−0.429028
$292$	45.1674	2.64322
$293$	19.4836	1.13825	0.569123	−	0.822252i	$-0.307283\pi$
$293$	19.4836	1.13825	0.569123	+	0.822252i	$0.307283\pi$
$294$	14.1833	0.827185
$295$	7.75692	0.451626
$296$	65.3424	3.79795
$297$	0.478341	0.0277562
$298$	39.8204	2.30674
$299$	10.2977	0.595533
$300$	−16.0138	−0.924558
$301$	8.25782	0.475973
$302$	40.7512	2.34497
$303$	1.40249	0.0805712
$304$	−25.1359	−1.44164
$305$	3.02900	0.173440
$306$	−2.58914	−0.148011
$307$	25.2629	1.44183	0.720915	−	0.693024i	$-0.243722\pi$
$307$	25.2629	1.44183	0.720915	+	0.693024i	$0.243722\pi$
$308$	−2.77575	−0.158163
$309$	−15.6730	−0.891604
$310$	11.0826	0.629451
$311$	11.1492	0.632212	0.316106	−	0.948724i	$-0.397624\pi$
$311$	11.1492	0.632212	0.316106	+	0.948724i	$0.397624\pi$
$312$	−12.3328	−0.698209
$313$	18.3024	1.03452	0.517258	−	0.855830i	$-0.326953\pi$
$313$	18.3024	1.03452	0.517258	+	0.855830i	$0.326953\pi$
$314$	−2.58914	−0.146113
$315$	1.55829	0.0877996
$316$	28.6629	1.61241
$317$	−24.7351	−1.38926	−0.694631	−	0.719367i	$-0.744432\pi$
$317$	−24.7351	−1.38926	−0.694631	+	0.719367i	$0.744432\pi$
$318$	−31.3714	−1.75922
$319$	3.81860	0.213801
$320$	−6.00314	−0.335586
$321$	3.64527	0.203459
$322$	18.6700	1.04044
$323$	−2.88359	−0.160447
$324$	4.70363	0.261313
$325$	−5.99822	−0.332721
$326$	−49.4056	−2.73632
$327$	11.8465	0.655112
$328$	6.03220	0.333073
$329$	−9.11966	−0.502783
$330$	1.56434	0.0861143
$331$	−15.0508	−0.827268	−0.413634	−	0.910443i	$-0.635741\pi$
$331$	−15.0508	−0.827268	−0.413634	+	0.910443i	$0.635741\pi$
$332$	−54.5413	−2.99334
$333$	−9.33454	−0.511530
$334$	6.50181	0.355763
$335$	−10.5728	−0.577654
$336$	−10.7540	−0.586678
$337$	28.6104	1.55851	0.779255	−	0.626707i	$-0.215598\pi$
$337$	28.6104	1.55851	0.779255	+	0.626707i	$0.215598\pi$
$338$	25.6221	1.39366
$339$	12.2287	0.664172
$340$	−5.94118	−0.322206
$341$	1.62101	0.0877828
$342$	7.46602	0.403716
$343$	15.3941	0.831201
$344$	46.8553	2.52627
$345$	−7.38278	−0.397476
$346$	12.1580	0.653620
$347$	14.1948	0.762018	0.381009	−	0.924571i	$-0.375577\pi$
$347$	14.1948	0.762018	0.381009	+	0.924571i	$0.375577\pi$
$348$	37.5491	2.01284
$349$	−4.44547	−0.237961	−0.118980	−	0.992897i	$-0.537963\pi$
$349$	−4.44547	−0.237961	−0.118980	+	0.992897i	$0.537963\pi$
$350$	−10.8749	−0.581288
$351$	1.76182	0.0940388
$352$	−4.09893	−0.218474
$353$	−3.90583	−0.207886	−0.103943	−	0.994583i	$-0.533146\pi$
$353$	−3.90583	−0.207886	−0.103943	+	0.994583i	$0.533146\pi$
$354$	15.9003	0.845091
$355$	−11.0860	−0.588383
$356$	−25.0809	−1.32929
$357$	−1.23370	−0.0652942
$358$	28.9726	1.53125
$359$	−20.5929	−1.08685	−0.543425	−	0.839458i	$-0.682873\pi$
$359$	−20.5929	−1.08685	−0.543425	+	0.839458i	$0.682873\pi$
$360$	8.84182	0.466005
$361$	−10.6849	−0.562363
$362$	−61.2215	−3.21773
$363$	−10.7712	−0.565341
$364$	−10.2236	−0.535860
$365$	−12.1292	−0.634870
$366$	6.20890	0.324544
$367$	−23.6257	−1.23325	−0.616625	−	0.787257i	$-0.711501\pi$
$367$	−23.6257	−1.23325	−0.616625	+	0.787257i	$0.711501\pi$
$368$	50.9497	2.65594
$369$	−0.861734	−0.0448601
$370$	−30.5272	−1.58704
$371$	−14.9481	−0.776069
$372$	15.9398	0.826438
$373$	18.9975	0.983655	0.491828	−	0.870693i	$-0.336329\pi$
$373$	18.9975	0.983655	0.491828	+	0.870693i	$0.336329\pi$
$374$	−1.23849	−0.0640409
$375$	10.6158	0.548200
$376$	−51.7455	−2.66857
$377$	14.0646	0.724364
$378$	3.19421	0.164293
$379$	3.68411	0.189240	0.0946201	−	0.995513i	$-0.469836\pi$
$379$	3.68411	0.189240	0.0946201	+	0.995513i	$0.469836\pi$
$380$	17.1319	0.878850
$381$	−5.69221	−0.291621
$382$	2.23601	0.114404
$383$	18.1621	0.928039	0.464019	−	0.885825i	$-0.346407\pi$
$383$	18.1621	0.928039	0.464019	+	0.885825i	$0.346407\pi$
$384$	4.83274	0.246620
$385$	0.745394	0.0379888
$386$	46.9228	2.38831
$387$	−6.69355	−0.340252
$388$	−34.4243	−1.74763
$389$	29.6407	1.50284	0.751422	−	0.659822i	$-0.229368\pi$
$389$	29.6407	1.50284	0.751422	+	0.659822i	$0.229368\pi$
$390$	5.76176	0.291758
$391$	5.84495	0.295592
$392$	38.3463	1.93678
$393$	−14.5705	−0.734985
$394$	18.6299	0.938561
$395$	−7.69708	−0.387282
$396$	2.24994	0.113064
$397$	20.2608	1.01686	0.508429	−	0.861104i	$-0.330226\pi$
$397$	20.2608	1.01686	0.508429	+	0.861104i	$0.330226\pi$
$398$	−70.2811	−3.52287
$399$	3.55748	0.178097
$400$	−29.6772	−1.48386
$401$	10.3425	0.516478	0.258239	−	0.966081i	$-0.416858\pi$
$401$	10.3425	0.516478	0.258239	+	0.966081i	$0.416858\pi$
$402$	−21.6724	−1.08092
$403$	5.97048	0.297411
$404$	6.59681	0.328204
$405$	−1.26310	−0.0627642
$406$	25.4994	1.26552
$407$	−4.46510	−0.221327
$408$	−7.00007	−0.346555
$409$	−8.46353	−0.418495	−0.209247	−	0.977863i	$-0.567101\pi$
$409$	−8.46353	−0.418495	−0.209247	+	0.977863i	$0.567101\pi$
$410$	−2.81817	−0.139180
$411$	−2.53894	−0.125237
$412$	−73.7198	−3.63191
$413$	7.57633	0.372807
$414$	−15.1334	−0.743765
$415$	14.6464	0.718965
$416$	−15.0971	−0.740195
$417$	19.5250	0.956145
$418$	3.57130	0.174678
$419$	−24.1798	−1.18126	−0.590630	−	0.806943i	$-0.701121\pi$
$419$	−24.1798	−1.18126	−0.590630	+	0.806943i	$0.701121\pi$
$420$	7.32962	0.357649
$421$	−13.4411	−0.655078	−0.327539	−	0.944838i	$-0.606219\pi$
$421$	−13.4411	−0.655078	−0.327539	+	0.944838i	$0.606219\pi$
$422$	−1.38962	−0.0676456
$423$	7.39214	0.359418
$424$	−84.8166	−4.11906
$425$	−3.40457	−0.165146
$426$	−22.7243	−1.10099
$427$	2.95848	0.143171
$428$	17.1460	0.828782
$429$	0.842749	0.0406883
$430$	−21.8903	−1.05564
$431$	−17.6773	−0.851487	−0.425744	−	0.904844i	$-0.639987\pi$
$431$	−17.6773	−0.851487	−0.425744	+	0.904844i	$0.639987\pi$
$432$	8.71688	0.419391
$433$	20.4221	0.981422	0.490711	−	0.871322i	$-0.336737\pi$
$433$	20.4221	0.981422	0.490711	+	0.871322i	$0.336737\pi$
$434$	10.8246	0.519598
$435$	−10.0834	−0.483461
$436$	55.7215	2.66857
$437$	−16.8544	−0.806258
$438$	−24.8626	−1.18798
$439$	−38.0635	−1.81667	−0.908336	−	0.418241i	$-0.862647\pi$
$439$	−38.0635	−1.81667	−0.908336	+	0.418241i	$0.862647\pi$
$440$	4.22941	0.201629
$441$	−5.47799	−0.260857
$442$	−4.56158	−0.216972
$443$	−26.6302	−1.26524	−0.632620	−	0.774462i	$-0.718020\pi$
$443$	−26.6302	−1.26524	−0.632620	+	0.774462i	$0.718020\pi$
$444$	−43.9062	−2.08370
$445$	6.73519	0.319279
$446$	−42.8130	−2.02725
$447$	−15.3798	−0.727440
$448$	−5.86338	−0.277019
$449$	27.4203	1.29405	0.647023	−	0.762471i	$-0.276014\pi$
$449$	27.4203	1.29405	0.647023	+	0.762471i	$0.276014\pi$
$450$	8.81489	0.415538
$451$	−0.412203	−0.0194099
$452$	57.5193	2.70548
$453$	−15.7393	−0.739496
$454$	−17.3058	−0.812202
$455$	2.74542	0.128707
$456$	20.1853	0.945265
$457$	−4.89404	−0.228934	−0.114467	−	0.993427i	$-0.536516\pi$
$457$	−4.89404	−0.228934	−0.114467	+	0.993427i	$0.536516\pi$
$458$	−16.3945	−0.766064
$459$	1.00000	0.0466760
$460$	−34.7259	−1.61910
$461$	−40.3969	−1.88147	−0.940736	−	0.339140i	$-0.889864\pi$
$461$	−40.3969	−1.88147	−0.940736	+	0.339140i	$0.889864\pi$
$462$	1.52792	0.0710854
$463$	22.7168	1.05574	0.527869	−	0.849326i	$-0.322991\pi$
$463$	22.7168	1.05574	0.527869	+	0.849326i	$0.322991\pi$
$464$	69.5869	3.23049
$465$	−4.28044	−0.198500
$466$	−2.48226	−0.114989
$467$	−41.5613	−1.92323	−0.961614	−	0.274405i	$-0.911519\pi$
$467$	−41.5613	−1.92323	−0.961614	+	0.274405i	$0.911519\pi$
$468$	8.28693	0.383063
$469$	−10.3267	−0.476841
$470$	24.1749	1.11510
$471$	1.00000	0.0460776
$472$	42.9885	1.97871
$473$	−3.20180	−0.147219
$474$	−15.7776	−0.724691
$475$	9.81738	0.450452
$476$	−5.80286	−0.265973
$477$	12.1165	0.554778
$478$	3.74515	0.171299
$479$	36.7338	1.67841	0.839204	−	0.543816i	$-0.183021\pi$
$479$	36.7338	1.67841	0.839204	+	0.543816i	$0.183021\pi$
$480$	10.8236	0.494028
$481$	−16.4457	−0.749861
$482$	21.2927	0.969857
$483$	−7.21090	−0.328107
$484$	−50.6637	−2.30290
$485$	9.24424	0.419759
$486$	−2.58914	−0.117446
$487$	−1.73823	−0.0787668	−0.0393834	−	0.999224i	$-0.512539\pi$
$487$	−1.73823	−0.0787668	−0.0393834	+	0.999224i	$0.512539\pi$
$488$	16.7866	0.759892
$489$	19.0819	0.862912
$490$	−17.9150	−0.809315
$491$	20.0462	0.904671	0.452335	−	0.891848i	$-0.350591\pi$
$491$	20.0462	0.904671	0.452335	+	0.891848i	$0.350591\pi$
$492$	−4.05328	−0.182736
$493$	7.98301	0.359537
$494$	13.1537	0.591815
$495$	−0.604195	−0.0271566
$496$	29.5399	1.32638
$497$	−10.8279	−0.485697
$498$	30.0225	1.34534
$499$	−13.7976	−0.617666	−0.308833	−	0.951116i	$-0.599938\pi$
$499$	−13.7976	−0.617666	−0.308833	+	0.951116i	$0.599938\pi$
$500$	49.9330	2.23307
$501$	−2.51119	−0.112192
$502$	−75.9214	−3.38854
$503$	7.18384	0.320312	0.160156	−	0.987092i	$-0.448800\pi$
$503$	7.18384	0.320312	0.160156	+	0.987092i	$0.448800\pi$
$504$	8.63597	0.384677
$505$	−1.77150	−0.0788306
$506$	−7.23892	−0.321809
$507$	−9.89601	−0.439497
$508$	−26.7741	−1.18791
$509$	−5.01710	−0.222379	−0.111190	−	0.993799i	$-0.535466\pi$
$509$	−5.01710	−0.222379	−0.111190	+	0.993799i	$0.535466\pi$
$510$	3.27035	0.144814
$511$	−11.8468	−0.524071
$512$	47.3421	2.09225
$513$	−2.88359	−0.127314
$514$	−6.93003	−0.305670
$515$	19.7966	0.872342
$516$	−31.4840	−1.38601
$517$	3.53596	0.155512
$518$	−29.8165	−1.31006
$519$	−4.69578	−0.206122
$520$	15.5777	0.683126
$521$	34.8204	1.52551	0.762755	−	0.646688i	$-0.223846\pi$
$521$	34.8204	1.52551	0.762755	+	0.646688i	$0.223846\pi$
$522$	−20.6691	−0.904662
$523$	−31.1735	−1.36312	−0.681562	−	0.731760i	$-0.738699\pi$
$523$	−31.1735	−1.36312	−0.681562	+	0.731760i	$0.738699\pi$
$524$	−68.5343	−2.99393
$525$	4.20020	0.183312
$526$	−48.1647	−2.10008
$527$	3.38882	0.147619
$528$	4.16964	0.181460
$529$	11.1634	0.485366
$530$	39.6253	1.72121
$531$	−6.14116	−0.266503
$532$	16.7331	0.725471
$533$	−1.51822	−0.0657613
$534$	13.8059	0.597441
$535$	−4.60435	−0.199064
$536$	−58.5940	−2.53088
$537$	−11.1901	−0.482887
$538$	46.9794	2.02543
$539$	−2.62035	−0.112866
$540$	−5.94118	−0.255668
$541$	12.8129	0.550870	0.275435	−	0.961320i	$-0.411178\pi$
$541$	12.8129	0.550870	0.275435	+	0.961320i	$0.411178\pi$
$542$	−7.09749	−0.304864
$543$	23.6455	1.01473
$544$	−8.56905	−0.367395
$545$	−14.9633	−0.640959
$546$	5.62761	0.240840
$547$	25.1779	1.07653	0.538264	−	0.842777i	$-0.319080\pi$
$547$	25.1779	1.07653	0.538264	+	0.842777i	$0.319080\pi$
$548$	−11.9422	−0.510147
$549$	−2.39806	−0.102347
$550$	4.21653	0.179793
$551$	−23.0198	−0.980674
$552$	−40.9150	−1.74146
$553$	−7.51788	−0.319693
$554$	−52.1734	−2.21664
$555$	11.7905	0.500479
$556$	91.8385	3.89482
$557$	2.00745	0.0850585	0.0425293	−	0.999095i	$-0.486458\pi$
$557$	2.00745	0.0850585	0.0425293	+	0.999095i	$0.486458\pi$
$558$	−8.77412	−0.371438
$559$	−11.7928	−0.498782
$560$	13.5834	0.574004
$561$	0.478341	0.0201956
$562$	−7.91553	−0.333897
$563$	9.70052	0.408828	0.204414	−	0.978885i	$-0.434471\pi$
$563$	9.70052	0.408828	0.204414	+	0.978885i	$0.434471\pi$
$564$	34.7699	1.46408
$565$	−15.4461	−0.649824
$566$	0.795952	0.0334564
$567$	−1.23370	−0.0518104
$568$	−61.4380	−2.57788
$569$	37.5915	1.57592	0.787958	−	0.615729i	$-0.211138\pi$
$569$	37.5915	1.57592	0.787958	+	0.615729i	$0.211138\pi$
$570$	−9.43036	−0.394994
$571$	−29.4631	−1.23299	−0.616496	−	0.787358i	$-0.711448\pi$
$571$	−29.4631	−1.23299	−0.616496	+	0.787358i	$0.711448\pi$
$572$	3.96398	0.165742
$573$	−0.863614	−0.0360780
$574$	−2.75256	−0.114890
$575$	−19.8995	−0.829867
$576$	4.75269	0.198029
$577$	33.7175	1.40368	0.701840	−	0.712335i	$-0.252362\pi$
$577$	33.7175	1.40368	0.701840	+	0.712335i	$0.252362\pi$
$578$	−2.58914	−0.107694
$579$	−18.1229	−0.753164
$580$	−47.4285	−1.96936
$581$	14.3054	0.593489
$582$	18.9490	0.785463
$583$	5.79584	0.240039
$584$	−67.2194	−2.78156
$585$	−2.22536	−0.0920072
$586$	−50.4458	−2.08390
$587$	1.12987	0.0466346	0.0233173	−	0.999728i	$-0.492577\pi$
$587$	1.12987	0.0466346	0.0233173	+	0.999728i	$0.492577\pi$
$588$	−25.7664	−1.06259
$589$	−9.77198	−0.402647
$590$	−20.0837	−0.826834
$591$	−7.19541	−0.295980
$592$	−81.3681	−3.34421
$593$	3.03057	0.124451	0.0622253	−	0.998062i	$-0.480180\pi$
$593$	3.03057	0.124451	0.0622253	+	0.998062i	$0.480180\pi$
$594$	−1.23849	−0.0508159
$595$	1.55829	0.0638836
$596$	−72.3409	−2.96320
$597$	27.1446	1.11096
$598$	−26.6622	−1.09030
$599$	27.7535	1.13398	0.566989	−	0.823726i	$-0.308108\pi$
$599$	27.7535	1.13398	0.566989	+	0.823726i	$0.308108\pi$
$600$	23.8322	0.972945
$601$	19.5073	0.795720	0.397860	−	0.917446i	$-0.369753\pi$
$601$	19.5073	0.795720	0.397860	+	0.917446i	$0.369753\pi$
$602$	−21.3806	−0.871409
$603$	8.37049	0.340873
$604$	−74.0318	−3.01231
$605$	13.6051	0.553128
$606$	−3.63125	−0.147509
$607$	−40.2145	−1.63226	−0.816129	−	0.577870i	$-0.803884\pi$
$607$	−40.2145	−1.63226	−0.816129	+	0.577870i	$0.803884\pi$
$608$	24.7096	1.00211
$609$	−9.84862	−0.399086
$610$	−7.84249	−0.317533
$611$	13.0236	0.526878
$612$	4.70363	0.190133
$613$	−1.09444	−0.0442041	−0.0221020	−	0.999756i	$-0.507036\pi$
$613$	−1.09444	−0.0442041	−0.0221020	+	0.999756i	$0.507036\pi$
$614$	−65.4091	−2.63970
$615$	1.08846	0.0438910
$616$	4.13094	0.166440
$617$	−29.7018	−1.19575	−0.597876	−	0.801589i	$-0.703988\pi$
$617$	−29.7018	−1.19575	−0.597876	+	0.801589i	$0.703988\pi$
$618$	40.5794	1.63234
$619$	−38.8178	−1.56022	−0.780110	−	0.625642i	$-0.784837\pi$
$619$	−38.8178	−1.56022	−0.780110	+	0.625642i	$0.784837\pi$
$620$	−20.1336	−0.808584
$621$	5.84495	0.234550
$622$	−28.8668	−1.15745
$623$	6.57839	0.263557
$624$	15.3575	0.614793
$625$	3.61390	0.144556
$626$	−47.3875	−1.89399
$627$	−1.37934	−0.0550856
$628$	4.70363	0.187695
$629$	−9.33454	−0.372193
$630$	−4.03462	−0.160743
$631$	−31.8362	−1.26738	−0.633689	−	0.773588i	$-0.718460\pi$
$631$	−31.8362	−1.26738	−0.633689	+	0.773588i	$0.718460\pi$
$632$	−42.6569	−1.69680
$633$	0.536711	0.0213324
$634$	64.0426	2.54345
$635$	7.18986	0.285321
$636$	56.9917	2.25987
$637$	−9.65121	−0.382395
$638$	−9.88689	−0.391426
$639$	8.77677	0.347204
$640$	−6.10426	−0.241292
$641$	23.5205	0.929003	0.464502	−	0.885572i	$-0.346233\pi$
$641$	23.5205	0.929003	0.464502	+	0.885572i	$0.346233\pi$
$642$	−9.43809	−0.372492
$643$	8.22159	0.324228	0.162114	−	0.986772i	$-0.448169\pi$
$643$	8.22159	0.324228	0.162114	+	0.986772i	$0.448169\pi$
$644$	−33.9174	−1.33653
$645$	8.45466	0.332902
$646$	7.46602	0.293746
$647$	15.6215	0.614145	0.307072	−	0.951686i	$-0.400651\pi$
$647$	15.6215	0.614145	0.307072	+	0.951686i	$0.400651\pi$
$648$	−7.00007	−0.274989
$649$	−2.93757	−0.115310
$650$	15.5302	0.609145
$651$	−4.18078	−0.163858
$652$	89.7541	3.51504
$653$	28.3809	1.11063	0.555314	−	0.831641i	$-0.312598\pi$
$653$	28.3809	1.11063	0.555314	+	0.831641i	$0.312598\pi$
$654$	−30.6722	−1.19938
$655$	18.4041	0.719107
$656$	−7.51163	−0.293280
$657$	9.60267	0.374636
$658$	23.6120	0.920493
$659$	49.4007	1.92438	0.962190	−	0.272380i	$-0.0878108\pi$
$659$	49.4007	1.92438	0.962190	+	0.272380i	$0.0878108\pi$
$660$	−2.84191	−0.110621
$661$	25.9869	1.01077	0.505387	−	0.862893i	$-0.331350\pi$
$661$	25.9869	1.01077	0.505387	+	0.862893i	$0.331350\pi$
$662$	38.9687	1.51456
$663$	1.76182	0.0684233
$664$	81.1698	3.15000
$665$	−4.49347	−0.174249
$666$	24.1684	0.936507
$667$	46.6603	1.80669
$668$	−11.8117	−0.457009
$669$	16.5356	0.639304
$670$	27.3745	1.05757
$671$	−1.14709	−0.0442829
$672$	10.5716	0.407809
$673$	1.44563	0.0557251	0.0278625	−	0.999612i	$-0.491130\pi$
$673$	1.44563	0.0557251	0.0278625	+	0.999612i	$0.491130\pi$
$674$	−74.0763	−2.85331
$675$	−3.40457	−0.131042
$676$	−46.5471	−1.79027
$677$	6.16531	0.236952	0.118476	−	0.992957i	$-0.462199\pi$
$677$	6.16531	0.236952	0.118476	+	0.992957i	$0.462199\pi$
$678$	−31.6618	−1.21596
$679$	9.02902	0.346502
$680$	8.84182	0.339068
$681$	6.68401	0.256132
$682$	−4.19702	−0.160712
$683$	6.55442	0.250798	0.125399	−	0.992106i	$-0.459979\pi$
$683$	6.55442	0.250798	0.125399	+	0.992106i	$0.459979\pi$
$684$	−13.5634	−0.518608
$685$	3.20695	0.122531
$686$	−39.8573	−1.52176
$687$	6.33203	0.241582
$688$	−58.3469	−2.22445
$689$	21.3471	0.813260
$690$	19.1150	0.727697
$691$	6.64560	0.252811	0.126405	−	0.991979i	$-0.459656\pi$
$691$	6.64560	0.252811	0.126405	+	0.991979i	$0.459656\pi$
$692$	−22.0872	−0.839631
$693$	−0.590128	−0.0224171
$694$	−36.7524	−1.39510
$695$	−24.6622	−0.935489
$696$	−55.8816	−2.11819
$697$	−0.861734	−0.0326405
$698$	11.5099	0.435658
$699$	0.958721	0.0362622
$700$	19.7562	0.746714
$701$	50.1710	1.89493	0.947466	−	0.319855i	$-0.103634\pi$
$701$	50.1710	1.89493	0.947466	+	0.319855i	$0.103634\pi$
$702$	−4.56158	−0.172166
$703$	26.9170	1.01519
$704$	2.27341	0.0856822
$705$	−9.33704	−0.351653
$706$	10.1127	0.380598
$707$	−1.73025	−0.0650729
$708$	−28.8857	−1.08559
$709$	−39.3899	−1.47932	−0.739660	−	0.672981i	$-0.765014\pi$
$709$	−39.3899	−1.47932	−0.739660	+	0.672981i	$0.765014\pi$
$710$	28.7031	1.07721
$711$	6.09378	0.228535
$712$	37.3261	1.39886
$713$	19.8075	0.741796
$714$	3.19421	0.119540
$715$	−1.06448	−0.0398093
$716$	−52.6340	−1.96702
$717$	−1.44649	−0.0540201
$718$	53.3177	1.98980
$719$	16.3342	0.609162	0.304581	−	0.952486i	$-0.401484\pi$
$719$	16.3342	0.609162	0.304581	+	0.952486i	$0.401484\pi$
$720$	−11.0103	−0.410331
$721$	19.3357	0.720099
$722$	27.6647	1.02957
$723$	−8.22387	−0.305849
$724$	111.220	4.13345
$725$	−27.1787	−1.00939
$726$	27.8881	1.03502
$727$	24.7710	0.918707	0.459353	−	0.888254i	$-0.348081\pi$
$727$	24.7710	0.918707	0.459353	+	0.888254i	$0.348081\pi$
$728$	15.2150	0.563905
$729$	1.00000	0.0370370
$730$	31.4041	1.16232
$731$	−6.69355	−0.247570
$732$	−11.2796	−0.416905
$733$	−15.2401	−0.562908	−0.281454	−	0.959575i	$-0.590817\pi$
$733$	−15.2401	−0.562908	−0.281454	+	0.959575i	$0.590817\pi$
$734$	61.1701	2.25783
$735$	6.91928	0.255221
$736$	−50.0856	−1.84618
$737$	4.00395	0.147487
$738$	2.23115	0.0821297
$739$	−8.17483	−0.300716	−0.150358	−	0.988632i	$-0.548043\pi$
$739$	−8.17483	−0.300716	−0.150358	+	0.988632i	$0.548043\pi$
$740$	55.4582	2.03868
$741$	−5.08036	−0.186632
$742$	38.7028	1.42082
$743$	33.1711	1.21693	0.608465	−	0.793581i	$-0.291786\pi$
$743$	33.1711	1.21693	0.608465	+	0.793581i	$0.291786\pi$
$744$	−23.7220	−0.869690
$745$	19.4263	0.711725
$746$	−49.1872	−1.80087
$747$	−11.5956	−0.424260
$748$	2.24994	0.0822660
$749$	−4.49715	−0.164322
$750$	−27.4859	−1.00364
$751$	2.25197	0.0821755	0.0410877	−	0.999156i	$-0.486918\pi$
$751$	2.25197	0.0821755	0.0410877	+	0.999156i	$0.486918\pi$
$752$	64.4363	2.34975
$753$	29.3230	1.06859
$754$	−36.4152	−1.32616
$755$	19.8804	0.723521
$756$	−5.80286	−0.211048
$757$	41.0825	1.49317	0.746585	−	0.665290i	$-0.231692\pi$
$757$	41.0825	1.49317	0.746585	+	0.665290i	$0.231692\pi$
$758$	−9.53868	−0.346460
$759$	2.79588	0.101484
$760$	−25.4962	−0.924845
$761$	43.2117	1.56642	0.783212	−	0.621754i	$-0.213580\pi$
$761$	43.2117	1.56642	0.783212	+	0.621754i	$0.213580\pi$
$762$	14.7379	0.533899
$763$	−14.6150	−0.529097
$764$	−4.06212	−0.146962
$765$	−1.26310	−0.0456677
$766$	−47.0241	−1.69905
$767$	−10.8196	−0.390673
$768$	−22.0180	−0.794506
$769$	−19.1639	−0.691067	−0.345534	−	0.938406i	$-0.612302\pi$
$769$	−19.1639	−0.691067	−0.345534	+	0.938406i	$0.612302\pi$
$770$	−1.92993	−0.0695498
$771$	2.67658	0.0963946
$772$	−85.2436	−3.06799
$773$	−42.6086	−1.53253	−0.766263	−	0.642527i	$-0.777886\pi$
$773$	−42.6086	−1.53253	−0.766263	+	0.642527i	$0.777886\pi$
$774$	17.3305	0.622933
$775$	−11.5375	−0.414438
$776$	51.2312	1.83909
$777$	11.5160	0.413134
$778$	−76.7438	−2.75140
$779$	2.48489	0.0890305
$780$	−10.4673	−0.374788
$781$	4.19829	0.150227
$782$	−15.1334	−0.541168
$783$	7.98301	0.285290
$784$	−47.7510	−1.70539
$785$	−1.26310	−0.0450821
$786$	37.7250	1.34561
$787$	10.7159	0.381980	0.190990	−	0.981592i	$-0.438830\pi$
$787$	10.7159	0.381980	0.190990	+	0.981592i	$0.438830\pi$
$788$	−33.8446	−1.20566
$789$	18.6026	0.662271
$790$	19.9288	0.709035
$791$	−15.0865	−0.536415
$792$	−3.34842	−0.118981
$793$	−4.22494	−0.150032
$794$	−52.4579	−1.86166
$795$	−15.3045	−0.542793
$796$	127.678	4.52544
$797$	−3.40513	−0.120616	−0.0603079	−	0.998180i	$-0.519208\pi$
$797$	−3.40513	−0.120616	−0.0603079	+	0.998180i	$0.519208\pi$
$798$	−9.21080	−0.326059
$799$	7.39214	0.261515
$800$	29.1739	1.03145
$801$	−5.33225	−0.188406
$802$	−26.7781	−0.945566
$803$	4.59336	0.162096
$804$	39.3717	1.38853
$805$	9.10812	0.321019
$806$	−15.4584	−0.544498
$807$	−18.1448	−0.638728
$808$	−9.81755	−0.345380
$809$	−6.79300	−0.238829	−0.119415	−	0.992844i	$-0.538102\pi$
$809$	−6.79300	−0.238829	−0.119415	+	0.992844i	$0.538102\pi$
$810$	3.27035	0.114908
$811$	−17.9274	−0.629515	−0.314758	−	0.949172i	$-0.601923\pi$
$811$	−17.9274	−0.629515	−0.314758	+	0.949172i	$0.601923\pi$
$812$	−46.3243	−1.62566
$813$	2.74126	0.0961401
$814$	11.5608	0.405204
$815$	−24.1024	−0.844270
$816$	8.71688	0.305152
$817$	19.3015	0.675273
$818$	21.9132	0.766178
$819$	−2.17355	−0.0759499
$820$	5.11972	0.178788
$821$	−27.5880	−0.962829	−0.481414	−	0.876493i	$-0.659877\pi$
$821$	−27.5880	−0.962829	−0.481414	+	0.876493i	$0.659877\pi$
$822$	6.57367	0.229283
$823$	38.2776	1.33427	0.667136	−	0.744936i	$-0.267520\pi$
$823$	38.2776	1.33427	0.667136	+	0.744936i	$0.267520\pi$
$824$	109.712	3.82199
$825$	−1.62854	−0.0566987
$826$	−19.6162	−0.682533
$827$	34.2721	1.19176	0.595879	−	0.803075i	$-0.296804\pi$
$827$	34.2721	1.19176	0.595879	+	0.803075i	$0.296804\pi$
$828$	27.4925	0.955429
$829$	32.0491	1.11311	0.556556	−	0.830810i	$-0.312122\pi$
$829$	32.0491	1.11311	0.556556	+	0.830810i	$0.312122\pi$
$830$	−37.9216	−1.31628
$831$	20.1509	0.699026
$832$	8.37336	0.290294
$833$	−5.47799	−0.189801
$834$	−50.5530	−1.75051
$835$	3.17190	0.109768
$836$	−6.48791	−0.224389
$837$	3.38882	0.117135
$838$	62.6047	2.16264
$839$	44.2217	1.52670	0.763351	−	0.645984i	$-0.223553\pi$
$839$	44.2217	1.52670	0.763351	+	0.645984i	$0.223553\pi$
$840$	−10.9081	−0.376366
$841$	34.7285	1.19753
$842$	34.8008	1.19931
$843$	3.05721	0.105296
$844$	2.52449	0.0868966
$845$	12.4997	0.430002
$846$	−19.1393	−0.658021
$847$	13.2884	0.456594
$848$	105.618	3.62695
$849$	−0.307420	−0.0105506
$850$	8.81489	0.302348
$851$	−54.5599	−1.87029
$852$	41.2827	1.41432
$853$	19.3575	0.662789	0.331394	−	0.943492i	$-0.392481\pi$
$853$	19.3575	0.662789	0.331394	+	0.943492i	$0.392481\pi$
$854$	−7.65990	−0.262116
$855$	3.64228	0.124563
$856$	−25.5171	−0.872157
$857$	39.2095	1.33937	0.669685	−	0.742645i	$-0.266429\pi$
$857$	39.2095	1.33937	0.669685	+	0.742645i	$0.266429\pi$
$858$	−2.18199	−0.0744920
$859$	−29.9777	−1.02282	−0.511412	−	0.859336i	$-0.670877\pi$
$859$	−29.9777	−1.02282	−0.511412	+	0.859336i	$0.670877\pi$
$860$	39.7676	1.35606
$861$	1.06312	0.0362310
$862$	45.7690	1.55890
$863$	49.0944	1.67119	0.835596	−	0.549345i	$-0.185123\pi$
$863$	49.0944	1.67119	0.835596	+	0.549345i	$0.185123\pi$
$864$	−8.56905	−0.291525
$865$	5.93127	0.201669
$866$	−52.8755	−1.79678
$867$	1.00000	0.0339618
$868$	−19.6648	−0.667468
$869$	2.91491	0.0988814
$870$	26.1073	0.885119
$871$	14.7473	0.499692
$872$	−82.9262	−2.80823
$873$	−7.31867	−0.247699
$874$	43.6385	1.47609
$875$	−13.0967	−0.442751
$876$	45.1674	1.52607
$877$	−0.762394	−0.0257442	−0.0128721	−	0.999917i	$-0.504097\pi$
$877$	−0.762394	−0.0257442	−0.0128721	+	0.999917i	$0.504097\pi$
$878$	98.5516	3.32596
$879$	19.4836	0.657167
$880$	−5.26670	−0.177540
$881$	−17.9516	−0.604805	−0.302402	−	0.953180i	$-0.597789\pi$
$881$	−17.9516	−0.604805	−0.302402	+	0.953180i	$0.597789\pi$
$882$	14.1833	0.477575
$883$	−11.1509	−0.375256	−0.187628	−	0.982240i	$-0.560080\pi$
$883$	−11.1509	−0.375256	−0.187628	+	0.982240i	$0.560080\pi$
$884$	8.28693	0.278720
$885$	7.75692	0.260746
$886$	68.9493	2.31640
$887$	30.2719	1.01643	0.508216	−	0.861230i	$-0.330305\pi$
$887$	30.2719	1.01643	0.508216	+	0.861230i	$0.330305\pi$
$888$	65.3424	2.19275
$889$	7.02247	0.235526
$890$	−17.4383	−0.584534
$891$	0.478341	0.0160250
$892$	77.7774	2.60418
$893$	−21.3159	−0.713310
$894$	39.8204	1.33179
$895$	14.1342	0.472455
$896$	−5.96214	−0.199181
$897$	10.2977	0.343831
$898$	−70.9950	−2.36913
$899$	27.0530	0.902268
$900$	−16.0138	−0.533794
$901$	12.1165	0.403660
$902$	1.06725	0.0355356
$903$	8.25782	0.274803
$904$	−85.6018	−2.84707
$905$	−29.8668	−0.992805
$906$	40.7512	1.35387
$907$	37.3746	1.24100	0.620502	−	0.784205i	$-0.286929\pi$
$907$	37.3746	1.24100	0.620502	+	0.784205i	$0.286929\pi$
$908$	31.4391	1.04334
$909$	1.40249	0.0465178
$910$	−7.10826	−0.235637
$911$	−6.55672	−0.217234	−0.108617	−	0.994084i	$-0.534642\pi$
$911$	−6.55672	−0.217234	−0.108617	+	0.994084i	$0.534642\pi$
$912$	−25.1359	−0.832333
$913$	−5.54664	−0.183567
$914$	12.6713	0.419131
$915$	3.02900	0.100136
$916$	29.7835	0.984075
$917$	17.9756	0.593606
$918$	−2.58914	−0.0854543
$919$	−29.9990	−0.989575	−0.494787	−	0.869014i	$-0.664754\pi$
$919$	−29.9990	−0.989575	−0.494787	+	0.869014i	$0.664754\pi$
$920$	51.6800	1.70384
$921$	25.2629	0.832441
$922$	104.593	3.44459
$923$	15.4631	0.508973
$924$	−2.77575	−0.0913153
$925$	31.7801	1.04492
$926$	−58.8169	−1.93284
$927$	−15.6730	−0.514768
$928$	−68.4068	−2.24556
$929$	53.5361	1.75646	0.878230	−	0.478238i	$-0.158724\pi$
$929$	53.5361	1.75646	0.878230	+	0.478238i	$0.158724\pi$
$930$	11.0826	0.363414
$931$	15.7963	0.517703
$932$	4.50947	0.147713
$933$	11.1492	0.365008
$934$	107.608	3.52104
$935$	−0.604195	−0.0197593
$936$	−12.3328	−0.403111
$937$	−48.0366	−1.56929	−0.784643	−	0.619948i	$-0.787154\pi$
$937$	−48.0366	−1.56929	−0.784643	+	0.619948i	$0.787154\pi$
$938$	26.7371	0.872998
$939$	18.3024	0.597278
$940$	−43.9180	−1.43245
$941$	−13.2358	−0.431474	−0.215737	−	0.976452i	$-0.569215\pi$
$941$	−13.2358	−0.431474	−0.215737	+	0.976452i	$0.569215\pi$
$942$	−2.58914	−0.0843586
$943$	−5.03679	−0.164021
$944$	−53.5317	−1.74231
$945$	1.55829	0.0506912
$946$	8.28990	0.269528
$947$	23.0493	0.749001	0.374501	−	0.927227i	$-0.377814\pi$
$947$	23.0493	0.749001	0.374501	+	0.927227i	$0.377814\pi$
$948$	28.6629	0.930927
$949$	16.9181	0.549186
$950$	−25.4185	−0.824686
$951$	−24.7351	−0.802090
$952$	8.63597	0.279893
$953$	28.7577	0.931553	0.465777	−	0.884902i	$-0.345775\pi$
$953$	28.7577	0.931553	0.465777	+	0.884902i	$0.345775\pi$
$954$	−31.3714	−1.01569
$955$	1.09083	0.0352986
$956$	−6.80374	−0.220049
$957$	3.81860	0.123438
$958$	−95.1088	−3.07282
$959$	3.13229	0.101147
$960$	−6.00314	−0.193751
$961$	−19.5159	−0.629545
$962$	42.5803	1.37284
$963$	3.64527	0.117467
$964$	−38.6820	−1.24586
$965$	22.8912	0.736893
$966$	18.6700	0.600697
$967$	−34.5318	−1.11047	−0.555235	−	0.831694i	$-0.687372\pi$
$967$	−34.5318	−1.11047	−0.555235	+	0.831694i	$0.687372\pi$
$968$	75.3991	2.42342
$969$	−2.88359	−0.0926343
$970$	−23.9346	−0.768494
$971$	−60.4207	−1.93899	−0.969496	−	0.245105i	$-0.921177\pi$
$971$	−60.4207	−1.93899	−0.969496	+	0.245105i	$0.921177\pi$
$972$	4.70363	0.150869
$973$	−24.0880	−0.772225
$974$	4.50052	0.144206
$975$	−5.99822	−0.192097
$976$	−20.9036	−0.669107
$977$	54.2457	1.73547	0.867737	−	0.497024i	$-0.165574\pi$
$977$	54.2457	1.73547	0.867737	+	0.497024i	$0.165574\pi$
$978$	−49.4056	−1.57982
$979$	−2.55064	−0.0815187
$980$	32.5457	1.03963
$981$	11.8465	0.378229
$982$	−51.9023	−1.65627
$983$	30.8544	0.984104	0.492052	−	0.870566i	$-0.336247\pi$
$983$	30.8544	0.984104	0.492052	+	0.870566i	$0.336247\pi$
$984$	6.03220	0.192300
$985$	9.08856	0.289586
$986$	−20.6691	−0.658239
$987$	−9.11966	−0.290282
$988$	−23.8961	−0.760237
$989$	−39.1235	−1.24405
$990$	1.56434	0.0497181
$991$	37.7505	1.19918	0.599592	−	0.800306i	$-0.295329\pi$
$991$	37.7505	1.19918	0.599592	+	0.800306i	$0.295329\pi$
$992$	−29.0390	−0.921988
$993$	−15.0508	−0.477624
$994$	28.0349	0.889212
$995$	−34.2865	−1.08696
$996$	−54.5413	−1.72821
$997$	−46.1132	−1.46042	−0.730209	−	0.683224i	$-0.760577\pi$
$997$	−46.1132	−1.46042	−0.730209	+	0.683224i	$0.760577\pi$
$998$	35.7239	1.13082
$999$	−9.33454	−0.295332

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.i.1.3	✓	63

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.i.1.3	✓	63	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:	\( N \)	\(=\)	\( 8007 = 3 \cdot 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8007.a (trivial)

\(f(q)\)	\(=\)	\(q-2.58914 q^{2} +1.00000 q^{3} +4.70363 q^{4} -1.26310 q^{5} -2.58914 q^{6} -1.23370 q^{7} -7.00007 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.58914 q^{2} +1.00000 q^{3} +4.70363 q^{4} -1.26310 q^{5} -2.58914 q^{6} -1.23370 q^{7} -7.00007 q^{8} +1.00000 q^{9} +3.27035 q^{10} +0.478341 q^{11} +4.70363 q^{12} +1.76182 q^{13} +3.19421 q^{14} -1.26310 q^{15} +8.71688 q^{16} +1.00000 q^{17} -2.58914 q^{18} -2.88359 q^{19} -5.94118 q^{20} -1.23370 q^{21} -1.23849 q^{22} +5.84495 q^{23} -7.00007 q^{24} -3.40457 q^{25} -4.56158 q^{26} +1.00000 q^{27} -5.80286 q^{28} +7.98301 q^{29} +3.27035 q^{30} +3.38882 q^{31} -8.56905 q^{32} +0.478341 q^{33} -2.58914 q^{34} +1.55829 q^{35} +4.70363 q^{36} -9.33454 q^{37} +7.46602 q^{38} +1.76182 q^{39} +8.84182 q^{40} -0.861734 q^{41} +3.19421 q^{42} -6.69355 q^{43} +2.24994 q^{44} -1.26310 q^{45} -15.1334 q^{46} +7.39214 q^{47} +8.71688 q^{48} -5.47799 q^{49} +8.81489 q^{50} +1.00000 q^{51} +8.28693 q^{52} +12.1165 q^{53} -2.58914 q^{54} -0.604195 q^{55} +8.63597 q^{56} -2.88359 q^{57} -20.6691 q^{58} -6.14116 q^{59} -5.94118 q^{60} -2.39806 q^{61} -8.77412 q^{62} -1.23370 q^{63} +4.75269 q^{64} -2.22536 q^{65} -1.23849 q^{66} +8.37049 q^{67} +4.70363 q^{68} +5.84495 q^{69} -4.03462 q^{70} +8.77677 q^{71} -7.00007 q^{72} +9.60267 q^{73} +24.1684 q^{74} -3.40457 q^{75} -13.5634 q^{76} -0.590128 q^{77} -4.56158 q^{78} +6.09378 q^{79} -11.0103 q^{80} +1.00000 q^{81} +2.23115 q^{82} -11.5956 q^{83} -5.80286 q^{84} -1.26310 q^{85} +17.3305 q^{86} +7.98301 q^{87} -3.34842 q^{88} -5.33225 q^{89} +3.27035 q^{90} -2.17355 q^{91} +27.4925 q^{92} +3.38882 q^{93} -19.1393 q^{94} +3.64228 q^{95} -8.56905 q^{96} -7.31867 q^{97} +14.1833 q^{98} +0.478341 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 63 q + 10 q^{2} + 63 q^{3} + 70 q^{4} + 19 q^{5} + 10 q^{6} + 11 q^{7} + 27 q^{8} + 63 q^{9}+O(q^{10}) \) 63 * q + 10 * q^2 + 63 * q^3 + 70 * q^4 + 19 * q^5 + 10 * q^6 + 11 * q^7 + 27 * q^8 + 63 * q^9	\( 63 q + 10 q^{2} + 63 q^{3} + 70 q^{4} + 19 q^{5} + 10 q^{6} + 11 q^{7} + 27 q^{8} + 63 q^{9} + 4 q^{10} + 23 q^{11} + 70 q^{12} + 10 q^{13} + 18 q^{14} + 19 q^{15} + 72 q^{16} + 63 q^{17} + 10 q^{18} + 6 q^{19} + 48 q^{20} + 11 q^{21} + 21 q^{22} + 44 q^{23} + 27 q^{24} + 110 q^{25} + 41 q^{26} + 63 q^{27} + 26 q^{28} + 35 q^{29} + 4 q^{30} + q^{31} + 54 q^{32} + 23 q^{33} + 10 q^{34} + 47 q^{35} + 70 q^{36} + 40 q^{37} + 38 q^{38} + 10 q^{39} - 10 q^{40} + 35 q^{41} + 18 q^{42} + 27 q^{43} + 46 q^{44} + 19 q^{45} + 8 q^{46} + 29 q^{47} + 72 q^{48} + 114 q^{49} + 27 q^{50} + 63 q^{51} - q^{52} + 75 q^{53} + 10 q^{54} + 5 q^{55} + 24 q^{56} + 6 q^{57} + 41 q^{58} + 105 q^{59} + 48 q^{60} + 5 q^{61} + 22 q^{62} + 11 q^{63} + 61 q^{64} + 49 q^{65} + 21 q^{66} + 4 q^{67} + 70 q^{68} + 44 q^{69} - 16 q^{70} + 16 q^{71} + 27 q^{72} + 39 q^{73} + 54 q^{74} + 110 q^{75} + 6 q^{76} + 88 q^{77} + 41 q^{78} + 16 q^{79} + 102 q^{80} + 63 q^{81} - 29 q^{82} + 73 q^{83} + 26 q^{84} + 19 q^{85} + 46 q^{86} + 35 q^{87} + 18 q^{88} + 88 q^{89} + 4 q^{90} - 15 q^{91} + 110 q^{92} + q^{93} - 8 q^{94} + 28 q^{95} + 54 q^{96} + 70 q^{97} + 33 q^{98} + 23 q^{99}+O(q^{100}) \) 63 * q + 10 * q^2 + 63 * q^3 + 70 * q^4 + 19 * q^5 + 10 * q^6 + 11 * q^7 + 27 * q^8 + 63 * q^9 + 4 * q^10 + 23 * q^11 + 70 * q^12 + 10 * q^13 + 18 * q^14 + 19 * q^15 + 72 * q^16 + 63 * q^17 + 10 * q^18 + 6 * q^19 + 48 * q^20 + 11 * q^21 + 21 * q^22 + 44 * q^23 + 27 * q^24 + 110 * q^25 + 41 * q^26 + 63 * q^27 + 26 * q^28 + 35 * q^29 + 4 * q^30 + q^31 + 54 * q^32 + 23 * q^33 + 10 * q^34 + 47 * q^35 + 70 * q^36 + 40 * q^37 + 38 * q^38 + 10 * q^39 - 10 * q^40 + 35 * q^41 + 18 * q^42 + 27 * q^43 + 46 * q^44 + 19 * q^45 + 8 * q^46 + 29 * q^47 + 72 * q^48 + 114 * q^49 + 27 * q^50 + 63 * q^51 - q^52 + 75 * q^53 + 10 * q^54 + 5 * q^55 + 24 * q^56 + 6 * q^57 + 41 * q^58 + 105 * q^59 + 48 * q^60 + 5 * q^61 + 22 * q^62 + 11 * q^63 + 61 * q^64 + 49 * q^65 + 21 * q^66 + 4 * q^67 + 70 * q^68 + 44 * q^69 - 16 * q^70 + 16 * q^71 + 27 * q^72 + 39 * q^73 + 54 * q^74 + 110 * q^75 + 6 * q^76 + 88 * q^77 + 41 * q^78 + 16 * q^79 + 102 * q^80 + 63 * q^81 - 29 * q^82 + 73 * q^83 + 26 * q^84 + 19 * q^85 + 46 * q^86 + 35 * q^87 + 18 * q^88 + 88 * q^89 + 4 * q^90 - 15 * q^91 + 110 * q^92 + q^93 - 8 * q^94 + 28 * q^95 + 54 * q^96 + 70 * q^97 + 33 * q^98 + 23 * q^99

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