LMFDB - Embedded newform 8007.2.a.c.1.9

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:	$1$
Dimension:	$39$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
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)

$f(q)$	$=$	$q-1.86416 q^{2} -1.00000 q^{3} +1.47510 q^{4} -3.19016 q^{5} +1.86416 q^{6} +1.30918 q^{7} +0.978494 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.86416 q^{2} -1.00000 q^{3} +1.47510 q^{4} -3.19016 q^{5} +1.86416 q^{6} +1.30918 q^{7} +0.978494 q^{8} +1.00000 q^{9} +5.94698 q^{10} -0.506740 q^{11} -1.47510 q^{12} -3.39426 q^{13} -2.44053 q^{14} +3.19016 q^{15} -4.77428 q^{16} +1.00000 q^{17} -1.86416 q^{18} +0.0170415 q^{19} -4.70581 q^{20} -1.30918 q^{21} +0.944645 q^{22} +3.27852 q^{23} -0.978494 q^{24} +5.17712 q^{25} +6.32746 q^{26} -1.00000 q^{27} +1.93118 q^{28} +6.50923 q^{29} -5.94698 q^{30} -5.41530 q^{31} +6.94304 q^{32} +0.506740 q^{33} -1.86416 q^{34} -4.17650 q^{35} +1.47510 q^{36} -1.52295 q^{37} -0.0317681 q^{38} +3.39426 q^{39} -3.12155 q^{40} -1.68712 q^{41} +2.44053 q^{42} -2.92629 q^{43} -0.747493 q^{44} -3.19016 q^{45} -6.11170 q^{46} +6.03666 q^{47} +4.77428 q^{48} -5.28605 q^{49} -9.65100 q^{50} -1.00000 q^{51} -5.00689 q^{52} -11.2193 q^{53} +1.86416 q^{54} +1.61658 q^{55} +1.28102 q^{56} -0.0170415 q^{57} -12.1343 q^{58} -6.40937 q^{59} +4.70581 q^{60} +6.15883 q^{61} +10.0950 q^{62} +1.30918 q^{63} -3.39441 q^{64} +10.8282 q^{65} -0.944645 q^{66} +15.0829 q^{67} +1.47510 q^{68} -3.27852 q^{69} +7.78567 q^{70} -13.2821 q^{71} +0.978494 q^{72} -0.593766 q^{73} +2.83903 q^{74} -5.17712 q^{75} +0.0251380 q^{76} -0.663414 q^{77} -6.32746 q^{78} +4.20240 q^{79} +15.2307 q^{80} +1.00000 q^{81} +3.14507 q^{82} +13.3428 q^{83} -1.93118 q^{84} -3.19016 q^{85} +5.45507 q^{86} -6.50923 q^{87} -0.495842 q^{88} +8.81822 q^{89} +5.94698 q^{90} -4.44370 q^{91} +4.83616 q^{92} +5.41530 q^{93} -11.2533 q^{94} -0.0543651 q^{95} -6.94304 q^{96} -13.1427 q^{97} +9.85405 q^{98} -0.506740 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q - 4 q^{2} - 39 q^{3} + 30 q^{4} - 3 q^{5} + 4 q^{6} - 5 q^{7} - 3 q^{8} + 39 q^{9}+O(q^{10}) $ 39 * q - 4 * q^2 - 39 * q^3 + 30 * q^4 - 3 * q^5 + 4 * q^6 - 5 * q^7 - 3 * q^8 + 39 * q^9	\( 39 q - 4 q^{2} - 39 q^{3} + 30 q^{4} - 3 q^{5} + 4 q^{6} - 5 q^{7} - 3 q^{8} + 39 q^{9} + 4 q^{10} + q^{11} - 30 q^{12} - 26 q^{13} - 4 q^{14} + 3 q^{15} + 8 q^{16} + 39 q^{17} - 4 q^{18} - 14 q^{19} - 14 q^{20} + 5 q^{21} - 17 q^{22} + 2 q^{23} + 3 q^{24} - 6 q^{25} - 17 q^{26} - 39 q^{27} - 14 q^{28} - 7 q^{29} - 4 q^{30} - q^{31} - 30 q^{32} - q^{33} - 4 q^{34} + q^{35} + 30 q^{36} - 24 q^{37} - 20 q^{38} + 26 q^{39} + 12 q^{40} + q^{41} + 4 q^{42} - 41 q^{43} - 2 q^{44} - 3 q^{45} - 6 q^{46} - 9 q^{47} - 8 q^{48} - 10 q^{49} - 9 q^{50} - 39 q^{51} - 37 q^{52} - 47 q^{53} + 4 q^{54} - 39 q^{55} + 8 q^{56} + 14 q^{57} - 27 q^{58} + 41 q^{59} + 14 q^{60} - 41 q^{61} + 36 q^{62} - 5 q^{63} - 47 q^{64} - 39 q^{65} + 17 q^{66} - 36 q^{67} + 30 q^{68} - 2 q^{69} - 52 q^{70} - 2 q^{71} - 3 q^{72} - 63 q^{73} - 6 q^{74} + 6 q^{75} - 34 q^{76} - 64 q^{77} + 17 q^{78} + 20 q^{79} - 28 q^{80} + 39 q^{81} - 37 q^{82} + 45 q^{83} + 14 q^{84} - 3 q^{85} + 32 q^{86} + 7 q^{87} + 6 q^{88} - 32 q^{89} + 4 q^{90} - 11 q^{91} + 28 q^{92} + q^{93} - 44 q^{94} + 22 q^{95} + 30 q^{96} - 20 q^{97} + 63 q^{98} + q^{99}+O(q^{100}) \) 39 * q - 4 * q^2 - 39 * q^3 + 30 * q^4 - 3 * q^5 + 4 * q^6 - 5 * q^7 - 3 * q^8 + 39 * q^9 + 4 * q^10 + q^11 - 30 * q^12 - 26 * q^13 - 4 * q^14 + 3 * q^15 + 8 * q^16 + 39 * q^17 - 4 * q^18 - 14 * q^19 - 14 * q^20 + 5 * q^21 - 17 * q^22 + 2 * q^23 + 3 * q^24 - 6 * q^25 - 17 * q^26 - 39 * q^27 - 14 * q^28 - 7 * q^29 - 4 * q^30 - q^31 - 30 * q^32 - q^33 - 4 * q^34 + q^35 + 30 * q^36 - 24 * q^37 - 20 * q^38 + 26 * q^39 + 12 * q^40 + q^41 + 4 * q^42 - 41 * q^43 - 2 * q^44 - 3 * q^45 - 6 * q^46 - 9 * q^47 - 8 * q^48 - 10 * q^49 - 9 * q^50 - 39 * q^51 - 37 * q^52 - 47 * q^53 + 4 * q^54 - 39 * q^55 + 8 * q^56 + 14 * q^57 - 27 * q^58 + 41 * q^59 + 14 * q^60 - 41 * q^61 + 36 * q^62 - 5 * q^63 - 47 * q^64 - 39 * q^65 + 17 * q^66 - 36 * q^67 + 30 * q^68 - 2 * q^69 - 52 * q^70 - 2 * q^71 - 3 * q^72 - 63 * q^73 - 6 * q^74 + 6 * q^75 - 34 * q^76 - 64 * q^77 + 17 * q^78 + 20 * q^79 - 28 * q^80 + 39 * q^81 - 37 * q^82 + 45 * q^83 + 14 * q^84 - 3 * q^85 + 32 * q^86 + 7 * q^87 + 6 * q^88 - 32 * q^89 + 4 * q^90 - 11 * q^91 + 28 * q^92 + q^93 - 44 * q^94 + 22 * q^95 + 30 * q^96 - 20 * q^97 + 63 * q^98 + 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 $

$2$	−1.86416	−1.31816	−0.659081	−	0.752072i	$-0.729055\pi$
$2$	−1.86416	−1.31816	−0.659081	+	0.752072i	$0.729055\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.47510	0.737551
$5$	−3.19016	−1.42668	−0.713342	−	0.700816i	$-0.752819\pi$
$5$	−3.19016	−1.42668	−0.713342	+	0.700816i	$0.752819\pi$
$6$	1.86416	0.761041
$7$	1.30918	0.494824	0.247412	−	0.968910i	$-0.420420\pi$
$7$	1.30918	0.494824	0.247412	+	0.968910i	$0.420420\pi$
$8$	0.978494	0.345950
$9$	1.00000	0.333333
$10$	5.94698	1.88060
$11$	−0.506740	−0.152788	−0.0763939	−	0.997078i	$-0.524341\pi$
$11$	−0.506740	−0.152788	−0.0763939	+	0.997078i	$0.524341\pi$
$12$	−1.47510	−0.425825
$13$	−3.39426	−0.941400	−0.470700	−	0.882293i	$-0.655999\pi$
$13$	−3.39426	−0.941400	−0.470700	+	0.882293i	$0.655999\pi$
$14$	−2.44053	−0.652258
$15$	3.19016	0.823696
$16$	−4.77428	−1.19357
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.86416	−0.439387
$19$	0.0170415	0.00390959	0.00195479	−	0.999998i	$-0.499378\pi$
$19$	0.0170415	0.00390959	0.00195479	+	0.999998i	$0.499378\pi$
$20$	−4.70581	−1.05225
$21$	−1.30918	−0.285687
$22$	0.944645	0.201399
$23$	3.27852	0.683619	0.341810	−	0.939769i	$-0.388960\pi$
$23$	3.27852	0.683619	0.341810	+	0.939769i	$0.388960\pi$
$24$	−0.978494	−0.199734
$25$	5.17712	1.03542
$26$	6.32746	1.24092
$27$	−1.00000	−0.192450
$28$	1.93118	0.364958
$29$	6.50923	1.20873	0.604367	−	0.796706i	$-0.293426\pi$
$29$	6.50923	1.20873	0.604367	+	0.796706i	$0.293426\pi$
$30$	−5.94698	−1.08576
$31$	−5.41530	−0.972616	−0.486308	−	0.873787i	$-0.661657\pi$
$31$	−5.41530	−0.972616	−0.486308	+	0.873787i	$0.661657\pi$
$32$	6.94304	1.22737
$33$	0.506740	0.0882121
$34$	−1.86416	−0.319701
$35$	−4.17650	−0.705957
$36$	1.47510	0.245850
$37$	−1.52295	−0.250371	−0.125186	−	0.992133i	$-0.539953\pi$
$37$	−1.52295	−0.250371	−0.125186	+	0.992133i	$0.539953\pi$
$38$	−0.0317681	−0.00515347
$39$	3.39426	0.543517
$40$	−3.12155	−0.493561
$41$	−1.68712	−0.263485	−0.131742	−	0.991284i	$-0.542057\pi$
$41$	−1.68712	−0.263485	−0.131742	+	0.991284i	$0.542057\pi$
$42$	2.44053	0.376581
$43$	−2.92629	−0.446254	−0.223127	−	0.974789i	$-0.571627\pi$
$43$	−2.92629	−0.446254	−0.223127	+	0.974789i	$0.571627\pi$
$44$	−0.747493	−0.112689
$45$	−3.19016	−0.475561
$46$	−6.11170	−0.901121
$47$	6.03666	0.880537	0.440268	−	0.897866i	$-0.354883\pi$
$47$	6.03666	0.880537	0.440268	+	0.897866i	$0.354883\pi$
$48$	4.77428	0.689108
$49$	−5.28605	−0.755150
$50$	−9.65100	−1.36486
$51$	−1.00000	−0.140028
$52$	−5.00689	−0.694331
$53$	−11.2193	−1.54109	−0.770543	−	0.637388i	$-0.780015\pi$
$53$	−11.2193	−1.54109	−0.770543	+	0.637388i	$0.780015\pi$
$54$	1.86416	0.253680
$55$	1.61658	0.217980
$56$	1.28102	0.171184
$57$	−0.0170415	−0.00225720
$58$	−12.1343	−1.59331
$59$	−6.40937	−0.834429	−0.417214	−	0.908808i	$-0.636994\pi$
$59$	−6.40937	−0.834429	−0.417214	+	0.908808i	$0.636994\pi$
$60$	4.70581	0.607518
$61$	6.15883	0.788558	0.394279	−	0.918991i	$-0.370994\pi$
$61$	6.15883	0.788558	0.394279	+	0.918991i	$0.370994\pi$
$62$	10.0950	1.28207
$63$	1.30918	0.164941
$64$	−3.39441	−0.424301
$65$	10.8282	1.34308
$66$	−0.944645	−0.116278
$67$	15.0829	1.84267	0.921336	−	0.388766i	$-0.127099\pi$
$67$	15.0829	1.84267	0.921336	+	0.388766i	$0.127099\pi$
$68$	1.47510	0.178882
$69$	−3.27852	−0.394688
$70$	7.78567	0.930565
$71$	−13.2821	−1.57629	−0.788146	−	0.615488i	$-0.788959\pi$
$71$	−13.2821	−1.57629	−0.788146	+	0.615488i	$0.788959\pi$
$72$	0.978494	0.115317
$73$	−0.593766	−0.0694951	−0.0347475	−	0.999396i	$-0.511063\pi$
$73$	−0.593766	−0.0694951	−0.0347475	+	0.999396i	$0.511063\pi$
$74$	2.83903	0.330030
$75$	−5.17712	−0.597803
$76$	0.0251380	0.00288352
$77$	−0.663414	−0.0756030
$78$	−6.32746	−0.716444
$79$	4.20240	0.472807	0.236403	−	0.971655i	$-0.424031\pi$
$79$	4.20240	0.472807	0.236403	+	0.971655i	$0.424031\pi$
$80$	15.2307	1.70285
$81$	1.00000	0.111111
$82$	3.14507	0.347315
$83$	13.3428	1.46457	0.732283	−	0.681001i	$-0.238455\pi$
$83$	13.3428	1.46457	0.732283	+	0.681001i	$0.238455\pi$
$84$	−1.93118	−0.210709
$85$	−3.19016	−0.346022
$86$	5.45507	0.588236
$87$	−6.50923	−0.697863
$88$	−0.495842	−0.0528569
$89$	8.81822	0.934730	0.467365	−	0.884065i	$-0.345203\pi$
$89$	8.81822	0.934730	0.467365	+	0.884065i	$0.345203\pi$
$90$	5.94698	0.626867
$91$	−4.44370	−0.465827
$92$	4.83616	0.504204
$93$	5.41530	0.561540
$94$	−11.2533	−1.16069
$95$	−0.0543651	−0.00557774
$96$	−6.94304	−0.708621
$97$	−13.1427	−1.33444	−0.667220	−	0.744861i	$-0.732516\pi$
$97$	−13.1427	−1.33444	−0.667220	+	0.744861i	$0.732516\pi$
$98$	9.85405	0.995410
$99$	−0.506740	−0.0509293
$100$	7.63679	0.763679
$101$	13.0416	1.29768	0.648842	−	0.760923i	$-0.275253\pi$
$101$	13.0416	1.29768	0.648842	+	0.760923i	$0.275253\pi$
$102$	1.86416	0.184580
$103$	−7.78054	−0.766640	−0.383320	−	0.923616i	$-0.625219\pi$
$103$	−7.78054	−0.766640	−0.383320	+	0.923616i	$0.625219\pi$
$104$	−3.32127	−0.325677
$105$	4.17650	0.407584
$106$	20.9146	2.03140
$107$	3.40486	0.329160	0.164580	−	0.986364i	$-0.447373\pi$
$107$	3.40486	0.329160	0.164580	+	0.986364i	$0.447373\pi$
$108$	−1.47510	−0.141942
$109$	−2.90866	−0.278599	−0.139300	−	0.990250i	$-0.544485\pi$
$109$	−2.90866	−0.278599	−0.139300	+	0.990250i	$0.544485\pi$
$110$	−3.01357	−0.287333
$111$	1.52295	0.144552
$112$	−6.25039	−0.590606
$113$	3.26641	0.307278	0.153639	−	0.988127i	$-0.450901\pi$
$113$	3.26641	0.307278	0.153639	+	0.988127i	$0.450901\pi$
$114$	0.0317681	0.00297536
$115$	−10.4590	−0.975308
$116$	9.60179	0.891504
$117$	−3.39426	−0.313800
$118$	11.9481	1.09991
$119$	1.30918	0.120012
$120$	3.12155	0.284957
$121$	−10.7432	−0.976656
$122$	−11.4811	−1.03945
$123$	1.68712	0.152123
$124$	−7.98812	−0.717355
$125$	−0.565057	−0.0505402
$126$	−2.44053	−0.217419
$127$	−5.96332	−0.529159	−0.264580	−	0.964364i	$-0.585233\pi$
$127$	−5.96332	−0.529159	−0.264580	+	0.964364i	$0.585233\pi$
$128$	−7.55836	−0.668071
$129$	2.92629	0.257645
$130$	−20.1856	−1.77040
$131$	1.14626	0.100149	0.0500746	−	0.998745i	$-0.484054\pi$
$131$	1.14626	0.100149	0.0500746	+	0.998745i	$0.484054\pi$
$132$	0.747493	0.0650609
$133$	0.0223104	0.00193456
$134$	−28.1170	−2.42894
$135$	3.19016	0.274565
$136$	0.978494	0.0839052
$137$	12.5745	1.07431	0.537154	−	0.843484i	$-0.319499\pi$
$137$	12.5745	1.07431	0.537154	+	0.843484i	$0.319499\pi$
$138$	6.11170	0.520263
$139$	−7.87015	−0.667537	−0.333769	−	0.942655i	$-0.608320\pi$
$139$	−7.87015	−0.667537	−0.333769	+	0.942655i	$0.608320\pi$
$140$	−6.16076	−0.520679
$141$	−6.03666	−0.508378
$142$	24.7600	2.07781
$143$	1.72001	0.143834
$144$	−4.77428	−0.397856
$145$	−20.7655	−1.72448
$146$	1.10688	0.0916058
$147$	5.28605	0.435986
$148$	−2.24651	−0.184662
$149$	2.45781	0.201352	0.100676	−	0.994919i	$-0.467899\pi$
$149$	2.45781	0.201352	0.100676	+	0.994919i	$0.467899\pi$
$150$	9.65100	0.788001
$151$	−8.40740	−0.684185	−0.342092	−	0.939666i	$-0.611136\pi$
$151$	−8.40740	−0.684185	−0.342092	+	0.939666i	$0.611136\pi$
$152$	0.0166750	0.00135252
$153$	1.00000	0.0808452
$154$	1.23671	0.0996570
$155$	17.2757	1.38762
$156$	5.00689	0.400872
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	−7.83395	−0.623236
$159$	11.2193	0.889747
$160$	−22.1494	−1.75107
$161$	4.29218	0.338271
$162$	−1.86416	−0.146462
$163$	−5.55622	−0.435196	−0.217598	−	0.976038i	$-0.569822\pi$
$163$	−5.55622	−0.435196	−0.217598	+	0.976038i	$0.569822\pi$
$164$	−2.48868	−0.194333
$165$	−1.61658	−0.125851
$166$	−24.8732	−1.93053
$167$	10.0190	0.775293	0.387646	−	0.921808i	$-0.373288\pi$
$167$	10.0190	0.775293	0.387646	+	0.921808i	$0.373288\pi$
$168$	−1.28102	−0.0988332
$169$	−1.47897	−0.113767
$170$	5.94698	0.456112
$171$	0.0170415	0.00130320
$172$	−4.31657	−0.329136
$173$	5.27477	0.401033	0.200517	−	0.979690i	$-0.435738\pi$
$173$	5.27477	0.401033	0.200517	+	0.979690i	$0.435738\pi$
$174$	12.1343	0.919897
$175$	6.77779	0.512353
$176$	2.41932	0.182363
$177$	6.40937	0.481758
$178$	−16.4386	−1.23213
$179$	−3.51586	−0.262788	−0.131394	−	0.991330i	$-0.541945\pi$
$179$	−3.51586	−0.262788	−0.131394	+	0.991330i	$0.541945\pi$
$180$	−4.70581	−0.350751
$181$	18.8674	1.40241	0.701203	−	0.712962i	$-0.252647\pi$
$181$	18.8674	1.40241	0.701203	+	0.712962i	$0.252647\pi$
$182$	8.28379	0.614035
$183$	−6.15883	−0.455274
$184$	3.20801	0.236498
$185$	4.85845	0.357201
$186$	−10.0950	−0.740201
$187$	−0.506740	−0.0370565
$188$	8.90469	0.649441
$189$	−1.30918	−0.0952289
$190$	0.101345	0.00735237
$191$	14.6659	1.06119	0.530594	−	0.847626i	$-0.321969\pi$
$191$	14.6659	1.06119	0.530594	+	0.847626i	$0.321969\pi$
$192$	3.39441	0.244970
$193$	13.2123	0.951042	0.475521	−	0.879704i	$-0.342260\pi$
$193$	13.2123	0.951042	0.475521	+	0.879704i	$0.342260\pi$
$194$	24.5001	1.75901
$195$	−10.8282	−0.775427
$196$	−7.79746	−0.556962
$197$	2.93256	0.208936	0.104468	−	0.994528i	$-0.466686\pi$
$197$	2.93256	0.208936	0.104468	+	0.994528i	$0.466686\pi$
$198$	0.944645	0.0671330
$199$	13.4268	0.951802	0.475901	−	0.879499i	$-0.342122\pi$
$199$	13.4268	0.951802	0.475901	+	0.879499i	$0.342122\pi$
$200$	5.06578	0.358205
$201$	−15.0829	−1.06387
$202$	−24.3116	−1.71056
$203$	8.52176	0.598110
$204$	−1.47510	−0.103278
$205$	5.38220	0.375909
$206$	14.5042	1.01056
$207$	3.27852	0.227873
$208$	16.2052	1.12363
$209$	−0.00863560	−0.000597337 0
$210$	−7.78567	−0.537262
$211$	0.892233	0.0614239	0.0307119	−	0.999528i	$-0.490223\pi$
$211$	0.892233	0.0614239	0.0307119	+	0.999528i	$0.490223\pi$
$212$	−16.5496	−1.13663
$213$	13.2821	0.910073
$214$	−6.34721	−0.433886
$215$	9.33532	0.636664
$216$	−0.978494	−0.0665781
$217$	−7.08960	−0.481274
$218$	5.42221	0.367239
$219$	0.593766	0.0401230
$220$	2.38462	0.160771
$221$	−3.39426	−0.228323
$222$	−2.83903	−0.190543
$223$	−13.8327	−0.926304	−0.463152	−	0.886279i	$-0.653282\pi$
$223$	−13.8327	−0.926304	−0.463152	+	0.886279i	$0.653282\pi$
$224$	9.08969	0.607331
$225$	5.17712	0.345142
$226$	−6.08911	−0.405042
$227$	20.9158	1.38823	0.694116	−	0.719863i	$-0.255795\pi$
$227$	20.9158	1.38823	0.694116	+	0.719863i	$0.255795\pi$
$228$	−0.0251380	−0.00166480
$229$	16.6686	1.10149	0.550747	−	0.834672i	$-0.314343\pi$
$229$	16.6686	1.10149	0.550747	+	0.834672i	$0.314343\pi$
$230$	19.4973	1.28561
$231$	0.663414	0.0436494
$232$	6.36925	0.418161
$233$	−19.7496	−1.29384	−0.646920	−	0.762558i	$-0.723943\pi$
$233$	−19.7496	−1.29384	−0.646920	+	0.762558i	$0.723943\pi$
$234$	6.32746	0.413639
$235$	−19.2579	−1.25625
$236$	−9.45448	−0.615434
$237$	−4.20240	−0.272975
$238$	−2.44053	−0.158196
$239$	1.38919	0.0898593	0.0449296	−	0.998990i	$-0.485694\pi$
$239$	1.38919	0.0898593	0.0449296	+	0.998990i	$0.485694\pi$
$240$	−15.2307	−0.983138
$241$	5.65410	0.364213	0.182106	−	0.983279i	$-0.441709\pi$
$241$	5.65410	0.364213	0.182106	+	0.983279i	$0.441709\pi$
$242$	20.0271	1.28739
$243$	−1.00000	−0.0641500
$244$	9.08491	0.581602
$245$	16.8633	1.07736
$246$	−3.14507	−0.200523
$247$	−0.0578433	−0.00368048
$248$	−5.29884	−0.336476
$249$	−13.3428	−0.845567
$250$	1.05336	0.0666202
$251$	27.3223	1.72457	0.862285	−	0.506423i	$-0.169033\pi$
$251$	27.3223	1.72457	0.862285	+	0.506423i	$0.169033\pi$
$252$	1.93118	0.121653
$253$	−1.66136	−0.104449
$254$	11.1166	0.697518
$255$	3.19016	0.199776
$256$	20.8788	1.30493
$257$	−0.349912	−0.0218269	−0.0109135	−	0.999940i	$-0.503474\pi$
$257$	−0.349912	−0.0218269	−0.0109135	+	0.999940i	$0.503474\pi$
$258$	−5.45507	−0.339618
$259$	−1.99382	−0.123890
$260$	15.9728	0.990590
$261$	6.50923	0.402911
$262$	−2.13682	−0.132013
$263$	−12.8481	−0.792246	−0.396123	−	0.918197i	$-0.629645\pi$
$263$	−12.8481	−0.792246	−0.396123	+	0.918197i	$0.629645\pi$
$264$	0.495842	0.0305169
$265$	35.7913	2.19864
$266$	−0.0415902	−0.00255006
$267$	−8.81822	−0.539666
$268$	22.2489	1.35907
$269$	19.7264	1.20274	0.601370	−	0.798970i	$-0.294622\pi$
$269$	19.7264	1.20274	0.601370	+	0.798970i	$0.294622\pi$
$270$	−5.94698	−0.361922
$271$	−10.0051	−0.607767	−0.303884	−	0.952709i	$-0.598283\pi$
$271$	−10.0051	−0.607767	−0.303884	+	0.952709i	$0.598283\pi$
$272$	−4.77428	−0.289483
$273$	4.44370	0.268945
$274$	−23.4408	−1.41611
$275$	−2.62345	−0.158200
$276$	−4.83616	−0.291103
$277$	−9.13375	−0.548794	−0.274397	−	0.961617i	$-0.588478\pi$
$277$	−9.13375	−0.548794	−0.274397	+	0.961617i	$0.588478\pi$
$278$	14.6712	0.879922
$279$	−5.41530	−0.324205
$280$	−4.08668	−0.244226
$281$	14.2755	0.851605	0.425803	−	0.904816i	$-0.359992\pi$
$281$	14.2755	0.851605	0.425803	+	0.904816i	$0.359992\pi$
$282$	11.2533	0.670125
$283$	−4.55362	−0.270685	−0.135342	−	0.990799i	$-0.543213\pi$
$283$	−4.55362	−0.270685	−0.135342	+	0.990799i	$0.543213\pi$
$284$	−19.5924	−1.16260
$285$	0.0543651	0.00322031
$286$	−3.20638	−0.189597
$287$	−2.20875	−0.130378
$288$	6.94304	0.409123
$289$	1.00000	0.0588235
$290$	38.7103	2.27315
$291$	13.1427	0.770439
$292$	−0.875866	−0.0512562
$293$	9.46655	0.553042	0.276521	−	0.961008i	$-0.410818\pi$
$293$	9.46655	0.553042	0.276521	+	0.961008i	$0.410818\pi$
$294$	−9.85405	−0.574700
$295$	20.4469	1.19047
$296$	−1.49020	−0.0866159
$297$	0.506740	0.0294040
$298$	−4.58176	−0.265414
$299$	−11.1282	−0.643559
$300$	−7.63679	−0.440910
$301$	−3.83104	−0.220817
$302$	15.6728	0.901866
$303$	−13.0416	−0.749219
$304$	−0.0813608	−0.00466636
$305$	−19.6477	−1.12502
$306$	−1.86416	−0.106567
$307$	12.8321	0.732369	0.366184	−	0.930542i	$-0.380664\pi$
$307$	12.8321	0.732369	0.366184	+	0.930542i	$0.380664\pi$
$308$	−0.978603	−0.0557611
$309$	7.78054	0.442620
$310$	−32.2047	−1.82910
$311$	18.4875	1.04833	0.524165	−	0.851617i	$-0.324378\pi$
$311$	18.4875	1.04833	0.524165	+	0.851617i	$0.324378\pi$
$312$	3.32127	0.188030
$313$	−34.5376	−1.95218	−0.976091	−	0.217364i	$-0.930254\pi$
$313$	−34.5376	−1.95218	−0.976091	+	0.217364i	$0.930254\pi$
$314$	−1.86416	−0.105201
$315$	−4.17650	−0.235319
$316$	6.19897	0.348719
$317$	7.70783	0.432915	0.216457	−	0.976292i	$-0.430550\pi$
$317$	7.70783	0.432915	0.216457	+	0.976292i	$0.430550\pi$
$318$	−20.9146	−1.17283
$319$	−3.29849	−0.184680
$320$	10.8287	0.605343
$321$	−3.40486	−0.190041
$322$	−8.00132	−0.445896
$323$	0.0170415	0.000948214 0
$324$	1.47510	0.0819502
$325$	−17.5725	−0.974749
$326$	10.3577	0.573659
$327$	2.90866	0.160849
$328$	−1.65084	−0.0911524
$329$	7.90307	0.435710
$330$	3.01357	0.165892
$331$	30.6823	1.68645	0.843225	−	0.537561i	$-0.180654\pi$
$331$	30.6823	1.68645	0.843225	+	0.537561i	$0.180654\pi$
$332$	19.6820	1.08019
$333$	−1.52295	−0.0834571
$334$	−18.6770	−1.02196
$335$	−48.1170	−2.62891
$336$	6.25039	0.340987
$337$	15.1131	0.823264	0.411632	−	0.911350i	$-0.364959\pi$
$337$	15.1131	0.823264	0.411632	+	0.911350i	$0.364959\pi$
$338$	2.75704	0.149963
$339$	−3.26641	−0.177407
$340$	−4.70581	−0.255209
$341$	2.74415	0.148604
$342$	−0.0317681	−0.00171782
$343$	−16.0847	−0.868490
$344$	−2.86335	−0.154382
$345$	10.4590	0.563094
$346$	−9.83302	−0.528627
$347$	−5.66933	−0.304346	−0.152173	−	0.988354i	$-0.548627\pi$
$347$	−5.66933	−0.304346	−0.152173	+	0.988354i	$0.548627\pi$
$348$	−9.60179	−0.514710
$349$	−28.0343	−1.50064	−0.750320	−	0.661074i	$-0.770101\pi$
$349$	−28.0343	−1.50064	−0.750320	+	0.661074i	$0.770101\pi$
$350$	−12.6349	−0.675364
$351$	3.39426	0.181172
$352$	−3.51832	−0.187527
$353$	1.48978	0.0792928	0.0396464	−	0.999214i	$-0.487377\pi$
$353$	1.48978	0.0792928	0.0396464	+	0.999214i	$0.487377\pi$
$354$	−11.9481	−0.635035
$355$	42.3720	2.24887
$356$	13.0078	0.689411
$357$	−1.30918	−0.0692892
$358$	6.55413	0.346397
$359$	−24.8595	−1.31204	−0.656018	−	0.754745i	$-0.727761\pi$
$359$	−24.8595	−1.31204	−0.656018	+	0.754745i	$0.727761\pi$
$360$	−3.12155	−0.164520
$361$	−18.9997	−0.999985
$362$	−35.1720	−1.84860
$363$	10.7432	0.563873
$364$	−6.55492	−0.343571
$365$	1.89421	0.0991474
$366$	11.4811	0.600125
$367$	19.4448	1.01501	0.507504	−	0.861649i	$-0.330568\pi$
$367$	19.4448	1.01501	0.507504	+	0.861649i	$0.330568\pi$
$368$	−15.6526	−0.815947
$369$	−1.68712	−0.0878282
$370$	−9.05695	−0.470848
$371$	−14.6881	−0.762566
$372$	7.98812	0.414165
$373$	32.1737	1.66589	0.832946	−	0.553354i	$-0.186652\pi$
$373$	32.1737	1.66589	0.832946	+	0.553354i	$0.186652\pi$
$374$	0.944645	0.0488464
$375$	0.565057	0.0291794
$376$	5.90683	0.304622
$377$	−22.0941	−1.13790
$378$	2.44053	0.125527
$379$	−7.51881	−0.386215	−0.193108	−	0.981178i	$-0.561857\pi$
$379$	−7.51881	−0.386215	−0.193108	+	0.981178i	$0.561857\pi$
$380$	−0.0801941	−0.00411387
$381$	5.96332	0.305510
$382$	−27.3397	−1.39882
$383$	−27.2878	−1.39434	−0.697172	−	0.716904i	$-0.745559\pi$
$383$	−27.2878	−1.39434	−0.697172	+	0.716904i	$0.745559\pi$
$384$	7.55836	0.385711
$385$	2.11640	0.107862
$386$	−24.6299	−1.25363
$387$	−2.92629	−0.148751
$388$	−19.3868	−0.984218
$389$	−8.15713	−0.413583	−0.206791	−	0.978385i	$-0.566302\pi$
$389$	−8.15713	−0.413583	−0.206791	+	0.978385i	$0.566302\pi$
$390$	20.1856	1.02214
$391$	3.27852	0.165802
$392$	−5.17236	−0.261244
$393$	−1.14626	−0.0578212
$394$	−5.46677	−0.275412
$395$	−13.4063	−0.674545
$396$	−0.747493	−0.0375629
$397$	1.47526	0.0740412	0.0370206	−	0.999315i	$-0.488213\pi$
$397$	1.47526	0.0740412	0.0370206	+	0.999315i	$0.488213\pi$
$398$	−25.0298	−1.25463
$399$	−0.0223104	−0.00111692
$400$	−24.7170	−1.23585
$401$	−20.4140	−1.01943	−0.509714	−	0.860344i	$-0.670249\pi$
$401$	−20.4140	−1.01943	−0.509714	+	0.860344i	$0.670249\pi$
$402$	28.1170	1.40235
$403$	18.3810	0.915621
$404$	19.2377	0.957109
$405$	−3.19016	−0.158520
$406$	−15.8859	−0.788406
$407$	0.771739	0.0382537
$408$	−0.978494	−0.0484427
$409$	15.0794	0.745626	0.372813	−	0.927906i	$-0.378393\pi$
$409$	15.0794	0.745626	0.372813	+	0.927906i	$0.378393\pi$
$410$	−10.0333	−0.495509
$411$	−12.5745	−0.620252
$412$	−11.4771	−0.565436
$413$	−8.39102	−0.412895
$414$	−6.11170	−0.300374
$415$	−42.5658	−2.08947
$416$	−23.5665	−1.15544
$417$	7.87015	0.385403
$418$	0.0160982	0.000787387 0
$419$	16.3053	0.796568	0.398284	−	0.917262i	$-0.369606\pi$
$419$	16.3053	0.796568	0.398284	+	0.917262i	$0.369606\pi$
$420$	6.16076	0.300614
$421$	−4.12556	−0.201068	−0.100534	−	0.994934i	$-0.532055\pi$
$421$	−4.12556	−0.201068	−0.100534	+	0.994934i	$0.532055\pi$
$422$	−1.66327	−0.0809666
$423$	6.03666	0.293512
$424$	−10.9780	−0.533139
$425$	5.17712	0.251127
$426$	−24.7600	−1.19962
$427$	8.06302	0.390197
$428$	5.02252	0.242773
$429$	−1.72001	−0.0830428
$430$	−17.4026	−0.839226
$431$	−19.3921	−0.934086	−0.467043	−	0.884235i	$-0.654681\pi$
$431$	−19.3921	−0.934086	−0.467043	+	0.884235i	$0.654681\pi$
$432$	4.77428	0.229703
$433$	17.6735	0.849335	0.424668	−	0.905349i	$-0.360391\pi$
$433$	17.6735	0.849335	0.424668	+	0.905349i	$0.360391\pi$
$434$	13.2162	0.634397
$435$	20.7655	0.995630
$436$	−4.29057	−0.205481
$437$	0.0558709	0.00267267
$438$	−1.10688	−0.0528886
$439$	−3.11952	−0.148886	−0.0744432	−	0.997225i	$-0.523718\pi$
$439$	−3.11952	−0.148886	−0.0744432	+	0.997225i	$0.523718\pi$
$440$	1.58181	0.0754101
$441$	−5.28605	−0.251717
$442$	6.32746	0.300967
$443$	−27.1713	−1.29095	−0.645474	−	0.763782i	$-0.723340\pi$
$443$	−27.1713	−1.29095	−0.645474	+	0.763782i	$0.723340\pi$
$444$	2.24651	0.106614
$445$	−28.1315	−1.33356
$446$	25.7864	1.22102
$447$	−2.45781	−0.116251
$448$	−4.44389	−0.209954
$449$	−0.616369	−0.0290883	−0.0145441	−	0.999894i	$-0.504630\pi$
$449$	−0.616369	−0.0290883	−0.0145441	+	0.999894i	$0.504630\pi$
$450$	−9.65100	−0.454953
$451$	0.854933	0.0402572
$452$	4.81829	0.226633
$453$	8.40740	0.395014
$454$	−38.9905	−1.82992
$455$	14.1761	0.664587
$456$	−0.0166750	−0.000780878 0
$457$	−4.64355	−0.217216	−0.108608	−	0.994085i	$-0.534639\pi$
$457$	−4.64355	−0.217216	−0.108608	+	0.994085i	$0.534639\pi$
$458$	−31.0730	−1.45195
$459$	−1.00000	−0.0466760
$460$	−15.4281	−0.719340
$461$	30.8834	1.43839	0.719193	−	0.694811i	$-0.244512\pi$
$461$	30.8834	1.43839	0.719193	+	0.694811i	$0.244512\pi$
$462$	−1.23671	−0.0575370
$463$	−2.43456	−0.113143	−0.0565717	−	0.998399i	$-0.518017\pi$
$463$	−2.43456	−0.113143	−0.0565717	+	0.998399i	$0.518017\pi$
$464$	−31.0769	−1.44271
$465$	−17.2757	−0.801140
$466$	36.8165	1.70549
$467$	−23.3816	−1.08197	−0.540986	−	0.841032i	$-0.681949\pi$
$467$	−23.3816	−1.08197	−0.540986	+	0.841032i	$0.681949\pi$
$468$	−5.00689	−0.231444
$469$	19.7463	0.911798
$470$	35.8999	1.65594
$471$	−1.00000	−0.0460776
$472$	−6.27153	−0.288671
$473$	1.48287	0.0681822
$474$	7.83395	0.359825
$475$	0.0882259	0.00404808
$476$	1.93118	0.0885153
$477$	−11.2193	−0.513695
$478$	−2.58968	−0.118449
$479$	11.5708	0.528682	0.264341	−	0.964429i	$-0.414846\pi$
$479$	11.5708	0.528682	0.264341	+	0.964429i	$0.414846\pi$
$480$	22.1494	1.01098
$481$	5.16929	0.235699
$482$	−10.5402	−0.480091
$483$	−4.29218	−0.195301
$484$	−15.8473	−0.720334
$485$	41.9274	1.90382
$486$	1.86416	0.0845601
$487$	−31.7075	−1.43680	−0.718401	−	0.695629i	$-0.755126\pi$
$487$	−31.7075	−1.43680	−0.718401	+	0.695629i	$0.755126\pi$
$488$	6.02638	0.272801
$489$	5.55622	0.251261
$490$	−31.4360	−1.42013
$491$	−30.0154	−1.35458	−0.677288	−	0.735718i	$-0.736845\pi$
$491$	−30.0154	−1.35458	−0.677288	+	0.735718i	$0.736845\pi$
$492$	2.48868	0.112198
$493$	6.50923	0.293161
$494$	0.107829	0.00485147
$495$	1.61658	0.0726599
$496$	25.8541	1.16089
$497$	−17.3886	−0.779987
$498$	24.8732	1.11459
$499$	11.1607	0.499621	0.249810	−	0.968295i	$-0.419632\pi$
$499$	11.1607	0.499621	0.249810	+	0.968295i	$0.419632\pi$
$500$	−0.833517	−0.0372760
$501$	−10.0190	−0.447615
$502$	−50.9333	−2.27326
$503$	26.8395	1.19672	0.598358	−	0.801229i	$-0.295820\pi$
$503$	26.8395	1.19672	0.598358	+	0.801229i	$0.295820\pi$
$504$	1.28102	0.0570614
$505$	−41.6047	−1.85139
$506$	3.09704	0.137680
$507$	1.47897	0.0656833
$508$	−8.79651	−0.390282
$509$	13.1846	0.584399	0.292200	−	0.956357i	$-0.405613\pi$
$509$	13.1846	0.584399	0.292200	+	0.956357i	$0.405613\pi$
$510$	−5.94698	−0.263337
$511$	−0.777347	−0.0343878
$512$	−23.8048	−1.05203
$513$	−0.0170415	−0.000752400 0
$514$	0.652293	0.0287714
$515$	24.8212	1.09375
$516$	4.31657	0.190027
$517$	−3.05901	−0.134535
$518$	3.71680	0.163307
$519$	−5.27477	−0.231537
$520$	10.5954	0.464638
$521$	−28.1598	−1.23370	−0.616851	−	0.787080i	$-0.711592\pi$
$521$	−28.1598	−1.23370	−0.616851	+	0.787080i	$0.711592\pi$
$522$	−12.1343	−0.531103
$523$	−20.2498	−0.885463	−0.442731	−	0.896654i	$-0.645990\pi$
$523$	−20.2498	−0.885463	−0.442731	+	0.896654i	$0.645990\pi$
$524$	1.69085	0.0738653
$525$	−6.77779	−0.295807
$526$	23.9509	1.04431
$527$	−5.41530	−0.235894
$528$	−2.41932	−0.105287
$529$	−12.2513	−0.532665
$530$	−66.7208	−2.89817
$531$	−6.40937	−0.278143
$532$	0.0329101	0.00142683
$533$	5.72655	0.248044
$534$	16.4386	0.711368
$535$	−10.8620	−0.469607
$536$	14.7586	0.637472
$537$	3.51586	0.151720
$538$	−36.7732	−1.58541
$539$	2.67865	0.115378
$540$	4.70581	0.202506
$541$	−12.9286	−0.555843	−0.277921	−	0.960604i	$-0.589645\pi$
$541$	−12.9286	−0.555843	−0.277921	+	0.960604i	$0.589645\pi$
$542$	18.6512	0.801136
$543$	−18.8674	−0.809679
$544$	6.94304	0.297680
$545$	9.27909	0.397473
$546$	−8.28379	−0.354513
$547$	−9.03017	−0.386102	−0.193051	−	0.981189i	$-0.561838\pi$
$547$	−9.03017	−0.386102	−0.193051	+	0.981189i	$0.561838\pi$
$548$	18.5486	0.792358
$549$	6.15883	0.262853
$550$	4.89055	0.208534
$551$	0.110927	0.00472565
$552$	−3.20801	−0.136542
$553$	5.50170	0.233956
$554$	17.0268	0.723399
$555$	−4.85845	−0.206230
$556$	−11.6093	−0.492343
$557$	−39.7016	−1.68221	−0.841106	−	0.540870i	$-0.818095\pi$
$557$	−39.7016	−1.68221	−0.841106	+	0.540870i	$0.818095\pi$
$558$	10.0950	0.427355
$559$	9.93259	0.420104
$560$	19.9397	0.842608
$561$	0.506740	0.0213946
$562$	−26.6119	−1.12255
$563$	−35.1577	−1.48172	−0.740860	−	0.671660i	$-0.765582\pi$
$563$	−35.1577	−1.48172	−0.740860	+	0.671660i	$0.765582\pi$
$564$	−8.90469	−0.374955
$565$	−10.4204	−0.438388
$566$	8.48869	0.356806
$567$	1.30918	0.0549804
$568$	−12.9964	−0.545318
$569$	−29.9375	−1.25505	−0.627523	−	0.778598i	$-0.715931\pi$
$569$	−29.9375	−1.25505	−0.627523	+	0.778598i	$0.715931\pi$
$570$	−0.101345	−0.00424489
$571$	5.42253	0.226926	0.113463	−	0.993542i	$-0.463806\pi$
$571$	5.42253	0.226926	0.113463	+	0.993542i	$0.463806\pi$
$572$	2.53719	0.106085
$573$	−14.6659	−0.612677
$574$	4.11747	0.171860
$575$	16.9733	0.707837
$576$	−3.39441	−0.141434
$577$	−11.6242	−0.483920	−0.241960	−	0.970286i	$-0.577790\pi$
$577$	−11.6242	−0.483920	−0.241960	+	0.970286i	$0.577790\pi$
$578$	−1.86416	−0.0775389
$579$	−13.2123	−0.549084
$580$	−30.6312	−1.27189
$581$	17.4682	0.724702
$582$	−24.5001	−1.01556
$583$	5.68525	0.235459
$584$	−0.580997	−0.0240418
$585$	10.8282	0.447693
$586$	−17.6472	−0.728999
$587$	−12.1711	−0.502356	−0.251178	−	0.967941i	$-0.580818\pi$
$587$	−12.1711	−0.502356	−0.251178	+	0.967941i	$0.580818\pi$
$588$	7.79746	0.321562
$589$	−0.0922848	−0.00380253
$590$	−38.1164	−1.56923
$591$	−2.93256	−0.120629
$592$	7.27098	0.298836
$593$	−18.3743	−0.754541	−0.377270	−	0.926103i	$-0.623137\pi$
$593$	−18.3743	−0.754541	−0.377270	+	0.926103i	$0.623137\pi$
$594$	−0.944645	−0.0387593
$595$	−4.17650	−0.171220
$596$	3.62553	0.148507
$597$	−13.4268	−0.549523
$598$	20.7447	0.848315
$599$	2.17186	0.0887397	0.0443698	−	0.999015i	$-0.485872\pi$
$599$	2.17186	0.0887397	0.0443698	+	0.999015i	$0.485872\pi$
$600$	−5.06578	−0.206810
$601$	−18.6524	−0.760845	−0.380423	−	0.924813i	$-0.624221\pi$
$601$	−18.6524	−0.760845	−0.380423	+	0.924813i	$0.624221\pi$
$602$	7.14168	0.291073
$603$	15.0829	0.614224
$604$	−12.4018	−0.504621
$605$	34.2726	1.39338
$606$	24.3116	0.987592
$607$	−5.07571	−0.206017	−0.103008	−	0.994680i	$-0.532847\pi$
$607$	−5.07571	−0.206017	−0.103008	+	0.994680i	$0.532847\pi$
$608$	0.118320	0.00479850
$609$	−8.52176	−0.345319
$610$	36.6265	1.48296
$611$	−20.4900	−0.828937
$612$	1.47510	0.0596275
$613$	7.04687	0.284620	0.142310	−	0.989822i	$-0.454547\pi$
$613$	7.04687	0.284620	0.142310	+	0.989822i	$0.454547\pi$
$614$	−23.9212	−0.965381
$615$	−5.38220	−0.217031
$616$	−0.649146	−0.0261548
$617$	1.86016	0.0748873	0.0374437	−	0.999299i	$-0.488079\pi$
$617$	1.86016	0.0748873	0.0374437	+	0.999299i	$0.488079\pi$
$618$	−14.5042	−0.583444
$619$	9.57081	0.384683	0.192342	−	0.981328i	$-0.438392\pi$
$619$	9.57081	0.384683	0.192342	+	0.981328i	$0.438392\pi$
$620$	25.4834	1.02344
$621$	−3.27852	−0.131563
$622$	−34.4637	−1.38187
$623$	11.5446	0.462526
$624$	−16.2052	−0.648726
$625$	−24.0830	−0.963320
$626$	64.3837	2.57329
$627$	0.00863560	0.000344873 0
$628$	1.47510	0.0588630
$629$	−1.52295	−0.0607240
$630$	7.78567	0.310188
$631$	10.4518	0.416081	0.208040	−	0.978120i	$-0.433291\pi$
$631$	10.4518	0.416081	0.208040	+	0.978120i	$0.433291\pi$
$632$	4.11202	0.163567
$633$	−0.892233	−0.0354631
$634$	−14.3687	−0.570652
$635$	19.0240	0.754942
$636$	16.5496	0.656234
$637$	17.9422	0.710897
$638$	6.14892	0.243438
$639$	−13.2821	−0.525431
$640$	24.1124	0.953125
$641$	16.9840	0.670827	0.335413	−	0.942071i	$-0.391124\pi$
$641$	16.9840	0.670827	0.335413	+	0.942071i	$0.391124\pi$
$642$	6.34721	0.250504
$643$	−36.7723	−1.45016	−0.725079	−	0.688666i	$-0.758197\pi$
$643$	−36.7723	−1.45016	−0.725079	+	0.688666i	$0.758197\pi$
$644$	6.33140	0.249492
$645$	−9.33532	−0.367578
$646$	−0.0317681	−0.00124990
$647$	0.465603	0.0183047	0.00915237	−	0.999958i	$-0.497087\pi$
$647$	0.465603	0.0183047	0.00915237	+	0.999958i	$0.497087\pi$
$648$	0.978494	0.0384389
$649$	3.24788	0.127491
$650$	32.7581	1.28488
$651$	7.08960	0.277863
$652$	−8.19599	−0.320980
$653$	−26.2785	−1.02836	−0.514179	−	0.857683i	$-0.671903\pi$
$653$	−26.2785	−1.02836	−0.514179	+	0.857683i	$0.671903\pi$
$654$	−5.42221	−0.212025
$655$	−3.65676	−0.142881
$656$	8.05480	0.314487
$657$	−0.593766	−0.0231650
$658$	−14.7326	−0.574337
$659$	−36.2569	−1.41237	−0.706185	−	0.708027i	$-0.749585\pi$
$659$	−36.2569	−1.41237	−0.706185	+	0.708027i	$0.749585\pi$
$660$	−2.38462	−0.0928213
$661$	11.4796	0.446505	0.223253	−	0.974761i	$-0.428332\pi$
$661$	11.4796	0.446505	0.223253	+	0.974761i	$0.428332\pi$
$662$	−57.1967	−2.22301
$663$	3.39426	0.131822
$664$	13.0559	0.506666
$665$	−0.0711737	−0.00276000
$666$	2.83903	0.110010
$667$	21.3407	0.826314
$668$	14.7790	0.571818
$669$	13.8327	0.534802
$670$	89.6978	3.46533
$671$	−3.12093	−0.120482
$672$	−9.08969	−0.350643
$673$	15.4408	0.595200	0.297600	−	0.954691i	$-0.403814\pi$
$673$	15.4408	0.595200	0.297600	+	0.954691i	$0.403814\pi$
$674$	−28.1733	−1.08520
$675$	−5.17712	−0.199268
$676$	−2.18163	−0.0839089
$677$	13.7754	0.529433	0.264716	−	0.964326i	$-0.414722\pi$
$677$	13.7754	0.529433	0.264716	+	0.964326i	$0.414722\pi$
$678$	6.08911	0.233851
$679$	−17.2062	−0.660312
$680$	−3.12155	−0.119706
$681$	−20.9158	−0.801496
$682$	−5.11554	−0.195884
$683$	25.0558	0.958734	0.479367	−	0.877615i	$-0.340866\pi$
$683$	25.0558	0.958734	0.479367	+	0.877615i	$0.340866\pi$
$684$	0.0251380	0.000961174 0
$685$	−40.1146	−1.53270
$686$	29.9844	1.14481
$687$	−16.6686	−0.635948
$688$	13.9709	0.532636
$689$	38.0812	1.45078
$690$	−19.4973	−0.742250
$691$	−39.4249	−1.49979	−0.749897	−	0.661555i	$-0.769897\pi$
$691$	−39.4249	−1.49979	−0.749897	+	0.661555i	$0.769897\pi$
$692$	7.78082	0.295783
$693$	−0.663414	−0.0252010
$694$	10.5686	0.401177
$695$	25.1070	0.952364
$696$	−6.36925	−0.241426
$697$	−1.68712	−0.0639044
$698$	52.2605	1.97809
$699$	19.7496	0.746999
$700$	9.99794	0.377886
$701$	5.71640	0.215905	0.107953	−	0.994156i	$-0.465571\pi$
$701$	5.71640	0.215905	0.107953	+	0.994156i	$0.465571\pi$
$702$	−6.32746	−0.238815
$703$	−0.0259533	−0.000978848 0
$704$	1.72008	0.0648280
$705$	19.2579	0.725295
$706$	−2.77719	−0.104521
$707$	17.0738	0.642125
$708$	9.45448	0.355321
$709$	−17.2511	−0.647880	−0.323940	−	0.946078i	$-0.605008\pi$
$709$	−17.2511	−0.647880	−0.323940	+	0.946078i	$0.605008\pi$
$710$	−78.9882	−2.96438
$711$	4.20240	0.157602
$712$	8.62857	0.323370
$713$	−17.7542	−0.664899
$714$	2.44053	0.0913344
$715$	−5.48710	−0.205206
$716$	−5.18625	−0.193819
$717$	−1.38919	−0.0518803
$718$	46.3422	1.72948
$719$	−1.22950	−0.0458528	−0.0229264	−	0.999737i	$-0.507298\pi$
$719$	−1.22950	−0.0458528	−0.0229264	+	0.999737i	$0.507298\pi$
$720$	15.2307	0.567615
$721$	−10.1861	−0.379351
$722$	35.4186	1.31814
$723$	−5.65410	−0.210278
$724$	27.8314	1.03435
$725$	33.6991	1.25155
$726$	−20.0271	−0.743275
$727$	−33.4970	−1.24234	−0.621168	−	0.783677i	$-0.713342\pi$
$727$	−33.4970	−1.24234	−0.621168	+	0.783677i	$0.713342\pi$
$728$	−4.34814	−0.161153
$729$	1.00000	0.0370370
$730$	−3.53111	−0.130692
$731$	−2.92629	−0.108233
$732$	−9.08491	−0.335788
$733$	27.1209	1.00174	0.500868	−	0.865524i	$-0.333014\pi$
$733$	27.1209	1.00174	0.500868	+	0.865524i	$0.333014\pi$
$734$	−36.2482	−1.33795
$735$	−16.8633	−0.622014
$736$	22.7629	0.839053
$737$	−7.64312	−0.281538
$738$	3.14507	0.115772
$739$	−18.8395	−0.693023	−0.346511	−	0.938046i	$-0.612634\pi$
$739$	−18.8395	−0.693023	−0.346511	+	0.938046i	$0.612634\pi$
$740$	7.16672	0.263454
$741$	0.0578433	0.00212493
$742$	27.3809	1.00519
$743$	−8.04334	−0.295082	−0.147541	−	0.989056i	$-0.547136\pi$
$743$	−8.04334	−0.295082	−0.147541	+	0.989056i	$0.547136\pi$
$744$	5.29884	0.194265
$745$	−7.84082	−0.287265
$746$	−59.9771	−2.19592
$747$	13.3428	0.488188
$748$	−0.747493	−0.0273311
$749$	4.45757	0.162876
$750$	−1.05336	−0.0384632
$751$	−22.9833	−0.838674	−0.419337	−	0.907831i	$-0.637737\pi$
$751$	−22.9833	−0.838674	−0.419337	+	0.907831i	$0.637737\pi$
$752$	−28.8207	−1.05098
$753$	−27.3223	−0.995681
$754$	41.1869	1.49994
$755$	26.8210	0.976115
$756$	−1.93118	−0.0702362
$757$	15.1028	0.548922	0.274461	−	0.961598i	$-0.411501\pi$
$757$	15.1028	0.548922	0.274461	+	0.961598i	$0.411501\pi$
$758$	14.0163	0.509094
$759$	1.66136	0.0603035
$760$	−0.0531959	−0.00192962
$761$	−23.9671	−0.868805	−0.434402	−	0.900719i	$-0.643040\pi$
$761$	−23.9671	−0.868805	−0.434402	+	0.900719i	$0.643040\pi$
$762$	−11.1166	−0.402712
$763$	−3.80796	−0.137857
$764$	21.6337	0.782681
$765$	−3.19016	−0.115341
$766$	50.8690	1.83797
$767$	21.7551	0.785531
$768$	−20.8788	−0.753400
$769$	−32.5435	−1.17355	−0.586774	−	0.809751i	$-0.699602\pi$
$769$	−32.5435	−1.17355	−0.586774	+	0.809751i	$0.699602\pi$
$770$	−3.94531	−0.142179
$771$	0.349912	0.0126018
$772$	19.4895	0.701442
$773$	−17.7617	−0.638844	−0.319422	−	0.947612i	$-0.603489\pi$
$773$	−17.7617	−0.638844	−0.319422	+	0.947612i	$0.603489\pi$
$774$	5.45507	0.196079
$775$	−28.0357	−1.00707
$776$	−12.8601	−0.461649
$777$	1.99382	0.0715277
$778$	15.2062	0.545169
$779$	−0.0287511	−0.00103012
$780$	−15.9728	−0.571917
$781$	6.73056	0.240838
$782$	−6.11170	−0.218554
$783$	−6.50923	−0.232621
$784$	25.2371	0.901323
$785$	−3.19016	−0.113862
$786$	2.13682	0.0762177
$787$	38.3559	1.36724	0.683620	−	0.729838i	$-0.260405\pi$
$787$	38.3559	1.36724	0.683620	+	0.729838i	$0.260405\pi$
$788$	4.32583	0.154101
$789$	12.8481	0.457403
$790$	24.9916	0.889160
$791$	4.27632	0.152048
$792$	−0.495842	−0.0176190
$793$	−20.9047	−0.742348
$794$	−2.75012	−0.0975983
$795$	−35.7913	−1.26939
$796$	19.8059	0.702003
$797$	−1.36758	−0.0484421	−0.0242211	−	0.999707i	$-0.507711\pi$
$797$	−1.36758	−0.0484421	−0.0242211	+	0.999707i	$0.507711\pi$
$798$	0.0415902	0.00147228
$799$	6.03666	0.213562
$800$	35.9450	1.27085
$801$	8.81822	0.311577
$802$	38.0551	1.34377
$803$	0.300885	0.0106180
$804$	−22.2489	−0.784657
$805$	−13.6927	−0.482606
$806$	−34.2651	−1.20694
$807$	−19.7264	−0.694403
$808$	12.7611	0.448934
$809$	13.9848	0.491679	0.245839	−	0.969311i	$-0.420936\pi$
$809$	13.9848	0.491679	0.245839	+	0.969311i	$0.420936\pi$
$810$	5.94698	0.208956
$811$	−20.5133	−0.720318	−0.360159	−	0.932891i	$-0.617278\pi$
$811$	−20.5133	−0.720318	−0.360159	+	0.932891i	$0.617278\pi$
$812$	12.5705	0.441137
$813$	10.0051	0.350895
$814$	−1.43865	−0.0504246
$815$	17.7252	0.620887
$816$	4.77428	0.167133
$817$	−0.0498683	−0.00174467
$818$	−28.1104	−0.982857
$819$	−4.44370	−0.155276
$820$	7.93929	0.277252
$821$	−54.7579	−1.91106	−0.955532	−	0.294887i	$-0.904718\pi$
$821$	−54.7579	−1.91106	−0.955532	+	0.294887i	$0.904718\pi$
$822$	23.4408	0.817593
$823$	−17.6855	−0.616478	−0.308239	−	0.951309i	$-0.599740\pi$
$823$	−17.6855	−0.616478	−0.308239	+	0.951309i	$0.599740\pi$
$824$	−7.61321	−0.265219
$825$	2.62345	0.0913370
$826$	15.6422	0.544263
$827$	24.7445	0.860451	0.430225	−	0.902722i	$-0.358434\pi$
$827$	24.7445	0.860451	0.430225	+	0.902722i	$0.358434\pi$
$828$	4.83616	0.168068
$829$	25.0926	0.871503	0.435751	−	0.900067i	$-0.356483\pi$
$829$	25.0926	0.871503	0.435751	+	0.900067i	$0.356483\pi$
$830$	79.3495	2.75426
$831$	9.13375	0.316846
$832$	11.5215	0.399437
$833$	−5.28605	−0.183151
$834$	−14.6712	−0.508023
$835$	−31.9622	−1.10610
$836$	−0.0127384	−0.000440567 0
$837$	5.41530	0.187180
$838$	−30.3958	−1.05001
$839$	39.6640	1.36935	0.684676	−	0.728847i	$-0.259944\pi$
$839$	39.6640	1.36935	0.684676	+	0.728847i	$0.259944\pi$
$840$	4.08668	0.141004
$841$	13.3701	0.461039
$842$	7.69072	0.265040
$843$	−14.2755	−0.491675
$844$	1.31614	0.0453033
$845$	4.71815	0.162309
$846$	−11.2533	−0.386897
$847$	−14.0648	−0.483272
$848$	53.5639	1.83939
$849$	4.55362	0.156280
$850$	−9.65100	−0.331027
$851$	−4.99303	−0.171159
$852$	19.5924	0.671226
$853$	−3.86483	−0.132329	−0.0661647	−	0.997809i	$-0.521076\pi$
$853$	−3.86483	−0.132329	−0.0661647	+	0.997809i	$0.521076\pi$
$854$	−15.0308	−0.514343
$855$	−0.0543651	−0.00185925
$856$	3.33163	0.113873
$857$	−56.3674	−1.92547	−0.962737	−	0.270440i	$-0.912831\pi$
$857$	−56.3674	−1.92547	−0.962737	+	0.270440i	$0.912831\pi$
$858$	3.20638	0.109464
$859$	45.4424	1.55048	0.775238	−	0.631670i	$-0.217630\pi$
$859$	45.4424	1.55048	0.775238	+	0.631670i	$0.217630\pi$
$860$	13.7706	0.469572
$861$	2.20875	0.0752740
$862$	36.1501	1.23128
$863$	6.51200	0.221671	0.110836	−	0.993839i	$-0.464647\pi$
$863$	6.51200	0.221671	0.110836	+	0.993839i	$0.464647\pi$
$864$	−6.94304	−0.236207
$865$	−16.8274	−0.572147
$866$	−32.9463	−1.11956
$867$	−1.00000	−0.0339618
$868$	−10.4579	−0.354964
$869$	−2.12952	−0.0722391
$870$	−38.7103	−1.31240
$871$	−51.1954	−1.73469
$872$	−2.84611	−0.0963813
$873$	−13.1427	−0.444813
$874$	−0.104153	−0.00352301
$875$	−0.739761	−0.0250085
$876$	0.875866	0.0295928
$877$	5.70880	0.192772	0.0963862	−	0.995344i	$-0.469272\pi$
$877$	5.70880	0.192772	0.0963862	+	0.995344i	$0.469272\pi$
$878$	5.81529	0.196256
$879$	−9.46655	−0.319299
$880$	−7.71801	−0.260174
$881$	−4.54032	−0.152967	−0.0764836	−	0.997071i	$-0.524369\pi$
$881$	−4.54032	−0.152967	−0.0764836	+	0.997071i	$0.524369\pi$
$882$	9.85405	0.331803
$883$	−8.42228	−0.283432	−0.141716	−	0.989907i	$-0.545262\pi$
$883$	−8.42228	−0.283432	−0.141716	+	0.989907i	$0.545262\pi$
$884$	−5.00689	−0.168400
$885$	−20.4469	−0.687316
$886$	50.6518	1.70168
$887$	21.7569	0.730525	0.365263	−	0.930905i	$-0.380979\pi$
$887$	21.7569	0.730525	0.365263	+	0.930905i	$0.380979\pi$
$888$	1.49020	0.0500077
$889$	−7.80706	−0.261840
$890$	52.4418	1.75785
$891$	−0.506740	−0.0169764
$892$	−20.4046	−0.683197
$893$	0.102874	0.00344253
$894$	4.58176	0.153237
$895$	11.2161	0.374915
$896$	−9.89525	−0.330577
$897$	11.1282	0.371559
$898$	1.14901	0.0383431
$899$	−35.2494	−1.17563
$900$	7.63679	0.254560
$901$	−11.2193	−0.373768
$902$	−1.59373	−0.0530655
$903$	3.83104	0.127489
$904$	3.19616	0.106303
$905$	−60.1902	−2.00079
$906$	−15.6728	−0.520693
$907$	−21.8858	−0.726705	−0.363352	−	0.931652i	$-0.618368\pi$
$907$	−21.8858	−0.726705	−0.363352	+	0.931652i	$0.618368\pi$
$908$	30.8530	1.02389
$909$	13.0416	0.432562
$910$	−26.4266	−0.876034
$911$	40.4009	1.33854	0.669270	−	0.743019i	$-0.266607\pi$
$911$	40.4009	1.33854	0.669270	+	0.743019i	$0.266607\pi$
$912$	0.0813608	0.00269413
$913$	−6.76134	−0.223768
$914$	8.65633	0.286326
$915$	19.6477	0.649532
$916$	24.5879	0.812408
$917$	1.50066	0.0495562
$918$	1.86416	0.0615265
$919$	−53.9600	−1.77998	−0.889989	−	0.455982i	$-0.849288\pi$
$919$	−53.9600	−1.77998	−0.889989	+	0.455982i	$0.849288\pi$
$920$	−10.2341	−0.337408
$921$	−12.8321	−0.422833
$922$	−57.5718	−1.89603
$923$	45.0829	1.48392
$924$	0.978603	0.0321937
$925$	−7.88450	−0.259241
$926$	4.53841	0.149141
$927$	−7.78054	−0.255547
$928$	45.1939	1.48356
$929$	25.3157	0.830582	0.415291	−	0.909689i	$-0.363680\pi$
$929$	25.3157	0.830582	0.415291	+	0.909689i	$0.363680\pi$
$930$	32.2047	1.05603
$931$	−0.0900821	−0.00295232
$932$	−29.1327	−0.954274
$933$	−18.4875	−0.605253
$934$	43.5871	1.42621
$935$	1.61658	0.0528679
$936$	−3.32127	−0.108559
$937$	−33.9457	−1.10896	−0.554478	−	0.832198i	$-0.687082\pi$
$937$	−33.9457	−1.10896	−0.554478	+	0.832198i	$0.687082\pi$
$938$	−36.8103	−1.20190
$939$	34.5376	1.12709
$940$	−28.4074	−0.926547
$941$	−15.7188	−0.512419	−0.256210	−	0.966621i	$-0.582474\pi$
$941$	−15.7188	−0.512419	−0.256210	+	0.966621i	$0.582474\pi$
$942$	1.86416	0.0607377
$943$	−5.53128	−0.180123
$944$	30.6001	0.995949
$945$	4.17650	0.135861
$946$	−2.76430	−0.0898752
$947$	−53.6720	−1.74411	−0.872053	−	0.489412i	$-0.837211\pi$
$947$	−53.6720	−1.74411	−0.872053	+	0.489412i	$0.837211\pi$
$948$	−6.19897	−0.201333
$949$	2.01540	0.0654226
$950$	−0.164467	−0.00533603
$951$	−7.70783	−0.249944
$952$	1.28102	0.0415183
$953$	17.3034	0.560512	0.280256	−	0.959925i	$-0.409581\pi$
$953$	17.3034	0.560512	0.280256	+	0.959925i	$0.409581\pi$
$954$	20.9146	0.677134
$955$	−46.7866	−1.51398
$956$	2.04920	0.0662758
$957$	3.29849	0.106625
$958$	−21.5698	−0.696889
$959$	16.4622	0.531593
$960$	−10.8287	−0.349495
$961$	−1.67454	−0.0540175
$962$	−9.63640	−0.310690
$963$	3.40486	0.109720
$964$	8.34038	0.268625
$965$	−42.1494	−1.35684
$966$	8.00132	0.257438
$967$	8.53442	0.274448	0.137224	−	0.990540i	$-0.456182\pi$
$967$	8.53442	0.274448	0.137224	+	0.990540i	$0.456182\pi$
$968$	−10.5122	−0.337874
$969$	−0.0170415	−0.000547452 0
$970$	−78.1594	−2.50955
$971$	−54.4233	−1.74653	−0.873263	−	0.487250i	$-0.838000\pi$
$971$	−54.4233	−1.74653	−0.873263	+	0.487250i	$0.838000\pi$
$972$	−1.47510	−0.0473139
$973$	−10.3034	−0.330313
$974$	59.1079	1.89394
$975$	17.5725	0.562771
$976$	−29.4040	−0.941199
$977$	23.0275	0.736717	0.368358	−	0.929684i	$-0.379920\pi$
$977$	23.0275	0.736717	0.368358	+	0.929684i	$0.379920\pi$
$978$	−10.3577	−0.331202
$979$	−4.46854	−0.142815
$980$	24.8752	0.794608
$981$	−2.90866	−0.0928664
$982$	55.9536	1.78555
$983$	−55.1418	−1.75875	−0.879375	−	0.476129i	$-0.842039\pi$
$983$	−55.1418	−1.75875	−0.879375	+	0.476129i	$0.842039\pi$
$984$	1.65084	0.0526269
$985$	−9.35534	−0.298086
$986$	−12.1343	−0.386434
$987$	−7.90307	−0.251558
$988$	−0.0853249	−0.00271455
$989$	−9.59390	−0.305068
$990$	−3.01357	−0.0957776
$991$	−41.5798	−1.32083	−0.660413	−	0.750902i	$-0.729619\pi$
$991$	−41.5798	−1.32083	−0.660413	+	0.750902i	$0.729619\pi$
$992$	−37.5986	−1.19376
$993$	−30.6823	−0.973672
$994$	32.4152	1.02815
$995$	−42.8337	−1.35792
$996$	−19.6820	−0.623649
$997$	−7.30759	−0.231434	−0.115717	−	0.993282i	$-0.536917\pi$
$997$	−7.30759	−0.231434	−0.115717	+	0.993282i	$0.536917\pi$
$998$	−20.8053	−0.658581
$999$	1.52295	0.0481840

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.c.1.9	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.c.1.9	✓	39	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)

\(f(q)\)	\(=\)	\(q-1.86416 q^{2} -1.00000 q^{3} +1.47510 q^{4} -3.19016 q^{5} +1.86416 q^{6} +1.30918 q^{7} +0.978494 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.86416 q^{2} -1.00000 q^{3} +1.47510 q^{4} -3.19016 q^{5} +1.86416 q^{6} +1.30918 q^{7} +0.978494 q^{8} +1.00000 q^{9} +5.94698 q^{10} -0.506740 q^{11} -1.47510 q^{12} -3.39426 q^{13} -2.44053 q^{14} +3.19016 q^{15} -4.77428 q^{16} +1.00000 q^{17} -1.86416 q^{18} +0.0170415 q^{19} -4.70581 q^{20} -1.30918 q^{21} +0.944645 q^{22} +3.27852 q^{23} -0.978494 q^{24} +5.17712 q^{25} +6.32746 q^{26} -1.00000 q^{27} +1.93118 q^{28} +6.50923 q^{29} -5.94698 q^{30} -5.41530 q^{31} +6.94304 q^{32} +0.506740 q^{33} -1.86416 q^{34} -4.17650 q^{35} +1.47510 q^{36} -1.52295 q^{37} -0.0317681 q^{38} +3.39426 q^{39} -3.12155 q^{40} -1.68712 q^{41} +2.44053 q^{42} -2.92629 q^{43} -0.747493 q^{44} -3.19016 q^{45} -6.11170 q^{46} +6.03666 q^{47} +4.77428 q^{48} -5.28605 q^{49} -9.65100 q^{50} -1.00000 q^{51} -5.00689 q^{52} -11.2193 q^{53} +1.86416 q^{54} +1.61658 q^{55} +1.28102 q^{56} -0.0170415 q^{57} -12.1343 q^{58} -6.40937 q^{59} +4.70581 q^{60} +6.15883 q^{61} +10.0950 q^{62} +1.30918 q^{63} -3.39441 q^{64} +10.8282 q^{65} -0.944645 q^{66} +15.0829 q^{67} +1.47510 q^{68} -3.27852 q^{69} +7.78567 q^{70} -13.2821 q^{71} +0.978494 q^{72} -0.593766 q^{73} +2.83903 q^{74} -5.17712 q^{75} +0.0251380 q^{76} -0.663414 q^{77} -6.32746 q^{78} +4.20240 q^{79} +15.2307 q^{80} +1.00000 q^{81} +3.14507 q^{82} +13.3428 q^{83} -1.93118 q^{84} -3.19016 q^{85} +5.45507 q^{86} -6.50923 q^{87} -0.495842 q^{88} +8.81822 q^{89} +5.94698 q^{90} -4.44370 q^{91} +4.83616 q^{92} +5.41530 q^{93} -11.2533 q^{94} -0.0543651 q^{95} -6.94304 q^{96} -13.1427 q^{97} +9.85405 q^{98} -0.506740 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q - 4 q^{2} - 39 q^{3} + 30 q^{4} - 3 q^{5} + 4 q^{6} - 5 q^{7} - 3 q^{8} + 39 q^{9}+O(q^{10}) \) 39 * q - 4 * q^2 - 39 * q^3 + 30 * q^4 - 3 * q^5 + 4 * q^6 - 5 * q^7 - 3 * q^8 + 39 * q^9	\( 39 q - 4 q^{2} - 39 q^{3} + 30 q^{4} - 3 q^{5} + 4 q^{6} - 5 q^{7} - 3 q^{8} + 39 q^{9} + 4 q^{10} + q^{11} - 30 q^{12} - 26 q^{13} - 4 q^{14} + 3 q^{15} + 8 q^{16} + 39 q^{17} - 4 q^{18} - 14 q^{19} - 14 q^{20} + 5 q^{21} - 17 q^{22} + 2 q^{23} + 3 q^{24} - 6 q^{25} - 17 q^{26} - 39 q^{27} - 14 q^{28} - 7 q^{29} - 4 q^{30} - q^{31} - 30 q^{32} - q^{33} - 4 q^{34} + q^{35} + 30 q^{36} - 24 q^{37} - 20 q^{38} + 26 q^{39} + 12 q^{40} + q^{41} + 4 q^{42} - 41 q^{43} - 2 q^{44} - 3 q^{45} - 6 q^{46} - 9 q^{47} - 8 q^{48} - 10 q^{49} - 9 q^{50} - 39 q^{51} - 37 q^{52} - 47 q^{53} + 4 q^{54} - 39 q^{55} + 8 q^{56} + 14 q^{57} - 27 q^{58} + 41 q^{59} + 14 q^{60} - 41 q^{61} + 36 q^{62} - 5 q^{63} - 47 q^{64} - 39 q^{65} + 17 q^{66} - 36 q^{67} + 30 q^{68} - 2 q^{69} - 52 q^{70} - 2 q^{71} - 3 q^{72} - 63 q^{73} - 6 q^{74} + 6 q^{75} - 34 q^{76} - 64 q^{77} + 17 q^{78} + 20 q^{79} - 28 q^{80} + 39 q^{81} - 37 q^{82} + 45 q^{83} + 14 q^{84} - 3 q^{85} + 32 q^{86} + 7 q^{87} + 6 q^{88} - 32 q^{89} + 4 q^{90} - 11 q^{91} + 28 q^{92} + q^{93} - 44 q^{94} + 22 q^{95} + 30 q^{96} - 20 q^{97} + 63 q^{98} + q^{99}+O(q^{100}) \) 39 * q - 4 * q^2 - 39 * q^3 + 30 * q^4 - 3 * q^5 + 4 * q^6 - 5 * q^7 - 3 * q^8 + 39 * q^9 + 4 * q^10 + q^11 - 30 * q^12 - 26 * q^13 - 4 * q^14 + 3 * q^15 + 8 * q^16 + 39 * q^17 - 4 * q^18 - 14 * q^19 - 14 * q^20 + 5 * q^21 - 17 * q^22 + 2 * q^23 + 3 * q^24 - 6 * q^25 - 17 * q^26 - 39 * q^27 - 14 * q^28 - 7 * q^29 - 4 * q^30 - q^31 - 30 * q^32 - q^33 - 4 * q^34 + q^35 + 30 * q^36 - 24 * q^37 - 20 * q^38 + 26 * q^39 + 12 * q^40 + q^41 + 4 * q^42 - 41 * q^43 - 2 * q^44 - 3 * q^45 - 6 * q^46 - 9 * q^47 - 8 * q^48 - 10 * q^49 - 9 * q^50 - 39 * q^51 - 37 * q^52 - 47 * q^53 + 4 * q^54 - 39 * q^55 + 8 * q^56 + 14 * q^57 - 27 * q^58 + 41 * q^59 + 14 * q^60 - 41 * q^61 + 36 * q^62 - 5 * q^63 - 47 * q^64 - 39 * q^65 + 17 * q^66 - 36 * q^67 + 30 * q^68 - 2 * q^69 - 52 * q^70 - 2 * q^71 - 3 * q^72 - 63 * q^73 - 6 * q^74 + 6 * q^75 - 34 * q^76 - 64 * q^77 + 17 * q^78 + 20 * q^79 - 28 * q^80 + 39 * q^81 - 37 * q^82 + 45 * q^83 + 14 * q^84 - 3 * q^85 + 32 * q^86 + 7 * q^87 + 6 * q^88 - 32 * q^89 + 4 * q^90 - 11 * q^91 + 28 * q^92 + q^93 - 44 * q^94 + 22 * q^95 + 30 * q^96 - 20 * q^97 + 63 * q^98 + q^99

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