LMFDB - Embedded newform 8015.2.a.l.1.31

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8015,2,Mod(1,8015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8015, 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("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.0000972201$
Analytic rank:	$0$
Dimension:	$62$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.31
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.0447957 q^{2} -2.38735 q^{3} -1.99799 q^{4} -1.00000 q^{5} +0.106943 q^{6} -1.00000 q^{7} +0.179093 q^{8} +2.69946 q^{9} +O(q^{10})$	\(q-0.0447957 q^{2} -2.38735 q^{3} -1.99799 q^{4} -1.00000 q^{5} +0.106943 q^{6} -1.00000 q^{7} +0.179093 q^{8} +2.69946 q^{9} +0.0447957 q^{10} +1.58257 q^{11} +4.76992 q^{12} +4.30209 q^{13} +0.0447957 q^{14} +2.38735 q^{15} +3.98796 q^{16} -0.131751 q^{17} -0.120924 q^{18} +5.31805 q^{19} +1.99799 q^{20} +2.38735 q^{21} -0.0708926 q^{22} +4.65052 q^{23} -0.427558 q^{24} +1.00000 q^{25} -0.192715 q^{26} +0.717497 q^{27} +1.99799 q^{28} +3.43161 q^{29} -0.106943 q^{30} +7.13841 q^{31} -0.536830 q^{32} -3.77817 q^{33} +0.00590190 q^{34} +1.00000 q^{35} -5.39350 q^{36} +11.3215 q^{37} -0.238226 q^{38} -10.2706 q^{39} -0.179093 q^{40} -2.91849 q^{41} -0.106943 q^{42} -8.72221 q^{43} -3.16197 q^{44} -2.69946 q^{45} -0.208323 q^{46} +5.61847 q^{47} -9.52068 q^{48} +1.00000 q^{49} -0.0447957 q^{50} +0.314537 q^{51} -8.59555 q^{52} +11.2601 q^{53} -0.0321408 q^{54} -1.58257 q^{55} -0.179093 q^{56} -12.6961 q^{57} -0.153721 q^{58} +12.4882 q^{59} -4.76992 q^{60} -6.94914 q^{61} -0.319770 q^{62} -2.69946 q^{63} -7.95188 q^{64} -4.30209 q^{65} +0.169246 q^{66} +11.4949 q^{67} +0.263239 q^{68} -11.1024 q^{69} -0.0447957 q^{70} +1.19614 q^{71} +0.483454 q^{72} +13.0473 q^{73} -0.507153 q^{74} -2.38735 q^{75} -10.6254 q^{76} -1.58257 q^{77} +0.460079 q^{78} +10.1506 q^{79} -3.98796 q^{80} -9.81130 q^{81} +0.130736 q^{82} -15.3767 q^{83} -4.76992 q^{84} +0.131751 q^{85} +0.390718 q^{86} -8.19246 q^{87} +0.283428 q^{88} +0.726485 q^{89} +0.120924 q^{90} -4.30209 q^{91} -9.29171 q^{92} -17.0419 q^{93} -0.251684 q^{94} -5.31805 q^{95} +1.28160 q^{96} +9.26771 q^{97} -0.0447957 q^{98} +4.27210 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) $ 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9} - 2 q^{10} - 13 q^{11} + 37 q^{12} + 31 q^{13} - 2 q^{14} - 11 q^{15} + 64 q^{16} + 30 q^{17} + 18 q^{18} + 20 q^{19} - 64 q^{20} - 11 q^{21} + 7 q^{22} + 29 q^{24} + 62 q^{25} + 59 q^{27} - 64 q^{28} - 29 q^{29} - 3 q^{30} + 20 q^{31} + 22 q^{32} + 72 q^{33} + 13 q^{34} + 62 q^{35} + 53 q^{36} + 35 q^{37} + 34 q^{38} - 6 q^{39} - 15 q^{40} + 13 q^{41} - 3 q^{42} - 4 q^{43} - 44 q^{44} - 69 q^{45} - 19 q^{46} + 58 q^{47} + 64 q^{48} + 62 q^{49} + 2 q^{50} - 30 q^{51} + 82 q^{52} + 18 q^{53} + 22 q^{54} + 13 q^{55} - 15 q^{56} + 21 q^{57} + 18 q^{58} - 11 q^{59} - 37 q^{60} + 24 q^{61} + 48 q^{62} - 69 q^{63} + 65 q^{64} - 31 q^{65} + 25 q^{66} - 6 q^{67} + 65 q^{68} + 27 q^{69} + 2 q^{70} - 35 q^{71} + 53 q^{72} + 116 q^{73} - 69 q^{74} + 11 q^{75} + 65 q^{76} + 13 q^{77} + 102 q^{78} - 83 q^{79} - 64 q^{80} + 126 q^{81} + 71 q^{82} + 84 q^{83} - 37 q^{84} - 30 q^{85} + 24 q^{86} + 49 q^{87} + 20 q^{88} - 16 q^{89} - 18 q^{90} - 31 q^{91} + 19 q^{92} + 65 q^{93} + 54 q^{94} - 20 q^{95} + 17 q^{96} + 155 q^{97} + 2 q^{98} + 6 q^{99}+O(q^{100}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9 - 2 * q^10 - 13 * q^11 + 37 * q^12 + 31 * q^13 - 2 * q^14 - 11 * q^15 + 64 * q^16 + 30 * q^17 + 18 * q^18 + 20 * q^19 - 64 * q^20 - 11 * q^21 + 7 * q^22 + 29 * q^24 + 62 * q^25 + 59 * q^27 - 64 * q^28 - 29 * q^29 - 3 * q^30 + 20 * q^31 + 22 * q^32 + 72 * q^33 + 13 * q^34 + 62 * q^35 + 53 * q^36 + 35 * q^37 + 34 * q^38 - 6 * q^39 - 15 * q^40 + 13 * q^41 - 3 * q^42 - 4 * q^43 - 44 * q^44 - 69 * q^45 - 19 * q^46 + 58 * q^47 + 64 * q^48 + 62 * q^49 + 2 * q^50 - 30 * q^51 + 82 * q^52 + 18 * q^53 + 22 * q^54 + 13 * q^55 - 15 * q^56 + 21 * q^57 + 18 * q^58 - 11 * q^59 - 37 * q^60 + 24 * q^61 + 48 * q^62 - 69 * q^63 + 65 * q^64 - 31 * q^65 + 25 * q^66 - 6 * q^67 + 65 * q^68 + 27 * q^69 + 2 * q^70 - 35 * q^71 + 53 * q^72 + 116 * q^73 - 69 * q^74 + 11 * q^75 + 65 * q^76 + 13 * q^77 + 102 * q^78 - 83 * q^79 - 64 * q^80 + 126 * q^81 + 71 * q^82 + 84 * q^83 - 37 * q^84 - 30 * q^85 + 24 * q^86 + 49 * q^87 + 20 * q^88 - 16 * q^89 - 18 * q^90 - 31 * q^91 + 19 * q^92 + 65 * q^93 + 54 * q^94 - 20 * q^95 + 17 * q^96 + 155 * q^97 + 2 * q^98 + 6 * 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 $

$2$	−0.0447957	−0.0316754	−0.0158377	−	0.999875i	$-0.505042\pi$
$2$	−0.0447957	−0.0316754	−0.0158377	+	0.999875i	$0.505042\pi$
$3$	−2.38735	−1.37834	−0.689170	−	0.724600i	$-0.742025\pi$
$3$	−2.38735	−1.37834	−0.689170	+	0.724600i	$0.742025\pi$
$4$	−1.99799	−0.998997
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.106943	0.0436594
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	0.179093	0.0633189
$9$	2.69946	0.899820
$10$	0.0447957	0.0141656
$11$	1.58257	0.477164	0.238582	−	0.971122i	$-0.423317\pi$
$11$	1.58257	0.477164	0.238582	+	0.971122i	$0.423317\pi$
$12$	4.76992	1.37696
$13$	4.30209	1.19319	0.596593	−	0.802544i	$-0.296521\pi$
$13$	4.30209	1.19319	0.596593	+	0.802544i	$0.296521\pi$
$14$	0.0447957	0.0119722
$15$	2.38735	0.616412
$16$	3.98796	0.996991
$17$	−0.131751	−0.0319544	−0.0159772	−	0.999872i	$-0.505086\pi$
$17$	−0.131751	−0.0319544	−0.0159772	+	0.999872i	$0.505086\pi$
$18$	−0.120924	−0.0285021
$19$	5.31805	1.22004	0.610022	−	0.792385i	$-0.291161\pi$
$19$	5.31805	1.22004	0.610022	+	0.792385i	$0.291161\pi$
$20$	1.99799	0.446765
$21$	2.38735	0.520963
$22$	−0.0708926	−0.0151143
$23$	4.65052	0.969700	0.484850	−	0.874597i	$-0.338874\pi$
$23$	4.65052	0.969700	0.484850	+	0.874597i	$0.338874\pi$
$24$	−0.427558	−0.0872750
$25$	1.00000	0.200000
$26$	−0.192715	−0.0377946
$27$	0.717497	0.138082
$28$	1.99799	0.377585
$29$	3.43161	0.637233	0.318617	−	0.947884i	$-0.396782\pi$
$29$	3.43161	0.637233	0.318617	+	0.947884i	$0.396782\pi$
$30$	−0.106943	−0.0195251
$31$	7.13841	1.28210	0.641048	−	0.767501i	$-0.278500\pi$
$31$	7.13841	1.28210	0.641048	+	0.767501i	$0.278500\pi$
$32$	−0.536830	−0.0948990
$33$	−3.77817	−0.657694
$34$	0.00590190	0.00101217
$35$	1.00000	0.169031
$36$	−5.39350	−0.898917
$37$	11.3215	1.86124	0.930618	−	0.365991i	$-0.119270\pi$
$37$	11.3215	1.86124	0.930618	+	0.365991i	$0.119270\pi$
$38$	−0.238226	−0.0386453
$39$	−10.2706	−1.64461
$40$	−0.179093	−0.0283171
$41$	−2.91849	−0.455792	−0.227896	−	0.973685i	$-0.573185\pi$
$41$	−2.91849	−0.455792	−0.227896	+	0.973685i	$0.573185\pi$
$42$	−0.106943	−0.0165017
$43$	−8.72221	−1.33012	−0.665062	−	0.746788i	$-0.731595\pi$
$43$	−8.72221	−1.33012	−0.665062	+	0.746788i	$0.731595\pi$
$44$	−3.16197	−0.476685
$45$	−2.69946	−0.402412
$46$	−0.208323	−0.0307156
$47$	5.61847	0.819538	0.409769	−	0.912189i	$-0.365609\pi$
$47$	5.61847	0.819538	0.409769	+	0.912189i	$0.365609\pi$
$48$	−9.52068	−1.37419
$49$	1.00000	0.142857
$50$	−0.0447957	−0.00633507
$51$	0.314537	0.0440440
$52$	−8.59555	−1.19199
$53$	11.2601	1.54669	0.773344	−	0.633986i	$-0.218582\pi$
$53$	11.2601	1.54669	0.773344	+	0.633986i	$0.218582\pi$
$54$	−0.0321408	−0.00437381
$55$	−1.58257	−0.213394
$56$	−0.179093	−0.0239323
$57$	−12.6961	−1.68163
$58$	−0.153721	−0.0201846
$59$	12.4882	1.62583	0.812915	−	0.582383i	$-0.197879\pi$
$59$	12.4882	1.62583	0.812915	+	0.582383i	$0.197879\pi$
$60$	−4.76992	−0.615794
$61$	−6.94914	−0.889747	−0.444873	−	0.895593i	$-0.646751\pi$
$61$	−6.94914	−0.889747	−0.444873	+	0.895593i	$0.646751\pi$
$62$	−0.319770	−0.0406109
$63$	−2.69946	−0.340100
$64$	−7.95188	−0.993985
$65$	−4.30209	−0.533609
$66$	0.169246	0.0208327
$67$	11.4949	1.40432	0.702162	−	0.712017i	$-0.252218\pi$
$67$	11.4949	1.40432	0.702162	+	0.712017i	$0.252218\pi$
$68$	0.263239	0.0319224
$69$	−11.1024	−1.33658
$70$	−0.0447957	−0.00535411
$71$	1.19614	0.141956	0.0709780	−	0.997478i	$-0.477388\pi$
$71$	1.19614	0.141956	0.0709780	+	0.997478i	$0.477388\pi$
$72$	0.483454	0.0569756
$73$	13.0473	1.52708	0.763538	−	0.645763i	$-0.223461\pi$
$73$	13.0473	1.52708	0.763538	+	0.645763i	$0.223461\pi$
$74$	−0.507153	−0.0589553
$75$	−2.38735	−0.275668
$76$	−10.6254	−1.21882
$77$	−1.58257	−0.180351
$78$	0.460079	0.0520937
$79$	10.1506	1.14204	0.571018	−	0.820937i	$-0.306548\pi$
$79$	10.1506	1.14204	0.571018	+	0.820937i	$0.306548\pi$
$80$	−3.98796	−0.445868
$81$	−9.81130	−1.09014
$82$	0.130736	0.0144374
$83$	−15.3767	−1.68781	−0.843905	−	0.536493i	$-0.819749\pi$
$83$	−15.3767	−1.68781	−0.843905	+	0.536493i	$0.819749\pi$
$84$	−4.76992	−0.520441
$85$	0.131751	0.0142905
$86$	0.390718	0.0421322
$87$	−8.19246	−0.878324
$88$	0.283428	0.0302135
$89$	0.726485	0.0770073	0.0385036	−	0.999258i	$-0.487741\pi$
$89$	0.726485	0.0770073	0.0385036	+	0.999258i	$0.487741\pi$
$90$	0.120924	0.0127465
$91$	−4.30209	−0.450982
$92$	−9.29171	−0.968727
$93$	−17.0419	−1.76716
$94$	−0.251684	−0.0259592
$95$	−5.31805	−0.545620
$96$	1.28160	0.130803
$97$	9.26771	0.940993	0.470497	−	0.882402i	$-0.344075\pi$
$97$	9.26771	0.940993	0.470497	+	0.882402i	$0.344075\pi$
$98$	−0.0447957	−0.00452505
$99$	4.27210	0.429362
$100$	−1.99799	−0.199799
$101$	0.448686	0.0446459	0.0223230	−	0.999751i	$-0.492894\pi$
$101$	0.448686	0.0446459	0.0223230	+	0.999751i	$0.492894\pi$
$102$	−0.0140899	−0.00139511
$103$	−8.83920	−0.870952	−0.435476	−	0.900200i	$-0.643420\pi$
$103$	−8.83920	−0.870952	−0.435476	+	0.900200i	$0.643420\pi$
$104$	0.770474	0.0755512
$105$	−2.38735	−0.232982
$106$	−0.504403	−0.0489919
$107$	−13.6818	−1.32267	−0.661333	−	0.750092i	$-0.730009\pi$
$107$	−13.6818	−1.32267	−0.661333	+	0.750092i	$0.730009\pi$
$108$	−1.43355	−0.137944
$109$	−8.47924	−0.812164	−0.406082	−	0.913837i	$-0.633105\pi$
$109$	−8.47924	−0.812164	−0.406082	+	0.913837i	$0.633105\pi$
$110$	0.0708926	0.00675934
$111$	−27.0283	−2.56542
$112$	−3.98796	−0.376827
$113$	0.442889	0.0416635	0.0208318	−	0.999783i	$-0.493369\pi$
$113$	0.442889	0.0416635	0.0208318	+	0.999783i	$0.493369\pi$
$114$	0.568729	0.0532664
$115$	−4.65052	−0.433663
$116$	−6.85633	−0.636594
$117$	11.6133	1.07365
$118$	−0.559419	−0.0514987
$119$	0.131751	0.0120776
$120$	0.427558	0.0390306
$121$	−8.49546	−0.772314
$122$	0.311292	0.0281830
$123$	6.96748	0.628236
$124$	−14.2625	−1.28081
$125$	−1.00000	−0.0894427
$126$	0.120924	0.0107728
$127$	10.8071	0.958972	0.479486	−	0.877549i	$-0.340823\pi$
$127$	10.8071	0.958972	0.479486	+	0.877549i	$0.340823\pi$
$128$	1.42987	0.126384
$129$	20.8230	1.83336
$130$	0.192715	0.0169022
$131$	12.2219	1.06783	0.533917	−	0.845537i	$-0.320719\pi$
$131$	12.2219	1.06783	0.533917	+	0.845537i	$0.320719\pi$
$132$	7.54875	0.657034
$133$	−5.31805	−0.461133
$134$	−0.514922	−0.0444825
$135$	−0.717497	−0.0617523
$136$	−0.0235958	−0.00202332
$137$	−12.2241	−1.04438	−0.522188	−	0.852831i	$-0.674884\pi$
$137$	−12.2241	−1.04438	−0.522188	+	0.852831i	$0.674884\pi$
$138$	0.497342	0.0423365
$139$	4.55663	0.386489	0.193244	−	0.981151i	$-0.438099\pi$
$139$	4.55663	0.386489	0.193244	+	0.981151i	$0.438099\pi$
$140$	−1.99799	−0.168861
$141$	−13.4133	−1.12960
$142$	−0.0535821	−0.00449651
$143$	6.80838	0.569345
$144$	10.7653	0.897112
$145$	−3.43161	−0.284979
$146$	−0.584465	−0.0483706
$147$	−2.38735	−0.196906
$148$	−22.6202	−1.85937
$149$	−17.5863	−1.44072	−0.720362	−	0.693598i	$-0.756024\pi$
$149$	−17.5863	−1.44072	−0.720362	+	0.693598i	$0.756024\pi$
$150$	0.106943	0.00873188
$151$	−9.59414	−0.780760	−0.390380	−	0.920654i	$-0.627656\pi$
$151$	−9.59414	−0.780760	−0.390380	+	0.920654i	$0.627656\pi$
$152$	0.952425	0.0772518
$153$	−0.355658	−0.0287532
$154$	0.0708926	0.00571269
$155$	−7.13841	−0.573371
$156$	20.5206	1.64296
$157$	20.3023	1.62030	0.810151	−	0.586221i	$-0.199385\pi$
$157$	20.3023	1.62030	0.810151	+	0.586221i	$0.199385\pi$
$158$	−0.454705	−0.0361744
$159$	−26.8818	−2.13186
$160$	0.536830	0.0424401
$161$	−4.65052	−0.366512
$162$	0.439504	0.0345307
$163$	9.14773	0.716506	0.358253	−	0.933625i	$-0.383373\pi$
$163$	9.14773	0.716506	0.358253	+	0.933625i	$0.383373\pi$
$164$	5.83113	0.455335
$165$	3.77817	0.294130
$166$	0.688809	0.0534620
$167$	−2.19873	−0.170143	−0.0850713	−	0.996375i	$-0.527112\pi$
$167$	−2.19873	−0.170143	−0.0850713	+	0.996375i	$0.527112\pi$
$168$	0.427558	0.0329868
$169$	5.50798	0.423691
$170$	−0.00590190	−0.000452655 0
$171$	14.3558	1.09782
$172$	17.4269	1.32879
$173$	−2.87001	−0.218203	−0.109101	−	0.994031i	$-0.534797\pi$
$173$	−2.87001	−0.218203	−0.109101	+	0.994031i	$0.534797\pi$
$174$	0.366987	0.0278212
$175$	−1.00000	−0.0755929
$176$	6.31125	0.475728
$177$	−29.8138	−2.24094
$178$	−0.0325434	−0.00243923
$179$	17.4808	1.30657	0.653287	−	0.757110i	$-0.273389\pi$
$179$	17.4808	1.30657	0.653287	+	0.757110i	$0.273389\pi$
$180$	5.39350	0.402008
$181$	17.6474	1.31172	0.655860	−	0.754883i	$-0.272306\pi$
$181$	17.6474	1.31172	0.655860	+	0.754883i	$0.272306\pi$
$182$	0.192715	0.0142850
$183$	16.5901	1.22637
$184$	0.832875	0.0614004
$185$	−11.3215	−0.832370
$186$	0.763405	0.0559756
$187$	−0.208506	−0.0152475
$188$	−11.2257	−0.818716
$189$	−0.717497	−0.0521902
$190$	0.238226	0.0172827
$191$	17.5339	1.26871	0.634356	−	0.773041i	$-0.281265\pi$
$191$	17.5339	1.26871	0.634356	+	0.773041i	$0.281265\pi$
$192$	18.9840	1.37005
$193$	12.5294	0.901883	0.450941	−	0.892554i	$-0.351088\pi$
$193$	12.5294	0.901883	0.450941	+	0.892554i	$0.351088\pi$
$194$	−0.415154	−0.0298063
$195$	10.2706	0.735494
$196$	−1.99799	−0.142714
$197$	27.7307	1.97573	0.987864	−	0.155318i	$-0.0496403\pi$
$197$	27.7307	1.97573	0.987864	+	0.155318i	$0.0496403\pi$
$198$	−0.191372	−0.0136002
$199$	−19.8798	−1.40924	−0.704622	−	0.709583i	$-0.748883\pi$
$199$	−19.8798	−1.40924	−0.704622	+	0.709583i	$0.748883\pi$
$200$	0.179093	0.0126638
$201$	−27.4424	−1.93563
$202$	−0.0200992	−0.00141418
$203$	−3.43161	−0.240852
$204$	−0.628444	−0.0439998
$205$	2.91849	0.203836
$206$	0.395958	0.0275877
$207$	12.5539	0.872556
$208$	17.1566	1.18959
$209$	8.41620	0.582161
$210$	0.106943	0.00737978
$211$	−9.49510	−0.653670	−0.326835	−	0.945081i	$-0.605982\pi$
$211$	−9.49510	−0.653670	−0.326835	+	0.945081i	$0.605982\pi$
$212$	−22.4975	−1.54514
$213$	−2.85562	−0.195664
$214$	0.612885	0.0418959
$215$	8.72221	0.594850
$216$	0.128499	0.00874322
$217$	−7.13841	−0.484587
$218$	0.379834	0.0257256
$219$	−31.1486	−2.10483
$220$	3.16197	0.213180
$221$	−0.566807	−0.0381275
$222$	1.21075	0.0812605
$223$	−8.30400	−0.556077	−0.278038	−	0.960570i	$-0.589684\pi$
$223$	−8.30400	−0.556077	−0.278038	+	0.960570i	$0.589684\pi$
$224$	0.536830	0.0358684
$225$	2.69946	0.179964
$226$	−0.0198395	−0.00131971
$227$	4.06216	0.269615	0.134808	−	0.990872i	$-0.456958\pi$
$227$	4.06216	0.269615	0.134808	+	0.990872i	$0.456958\pi$
$228$	25.3666	1.67995
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	0.208323	0.0137364
$231$	3.77817	0.248585
$232$	0.614577	0.0403489
$233$	17.0263	1.11543	0.557715	−	0.830033i	$-0.311678\pi$
$233$	17.0263	1.11543	0.557715	+	0.830033i	$0.311678\pi$
$234$	−0.520227	−0.0340083
$235$	−5.61847	−0.366509
$236$	−24.9514	−1.62420
$237$	−24.2332	−1.57411
$238$	−0.00590190	−0.000382563 0
$239$	−14.7844	−0.956320	−0.478160	−	0.878273i	$-0.658696\pi$
$239$	−14.7844	−0.956320	−0.478160	+	0.878273i	$0.658696\pi$
$240$	9.52068	0.614557
$241$	29.4672	1.89815	0.949073	−	0.315056i	$-0.102023\pi$
$241$	29.4672	1.89815	0.949073	+	0.315056i	$0.102023\pi$
$242$	0.380560	0.0244633
$243$	21.2705	1.36451
$244$	13.8843	0.888854
$245$	−1.00000	−0.0638877
$246$	−0.312113	−0.0198996
$247$	22.8787	1.45574
$248$	1.27844	0.0811810
$249$	36.7096	2.32637
$250$	0.0447957	0.00283313
$251$	−21.2218	−1.33951	−0.669755	−	0.742582i	$-0.733601\pi$
$251$	−21.2218	−1.33951	−0.669755	+	0.742582i	$0.733601\pi$
$252$	5.39350	0.339759
$253$	7.35979	0.462706
$254$	−0.484110	−0.0303758
$255$	−0.314537	−0.0196971
$256$	15.8397	0.989982
$257$	−16.4599	−1.02674	−0.513370	−	0.858167i	$-0.671603\pi$
$257$	−16.4599	−1.02674	−0.513370	+	0.858167i	$0.671603\pi$
$258$	−0.932781	−0.0580724
$259$	−11.3215	−0.703481
$260$	8.59555	0.533073
$261$	9.26348	0.573395
$262$	−0.547490	−0.0338240
$263$	−20.6340	−1.27235	−0.636173	−	0.771546i	$-0.719484\pi$
$263$	−20.6340	−1.27235	−0.636173	+	0.771546i	$0.719484\pi$
$264$	−0.676643	−0.0416445
$265$	−11.2601	−0.691700
$266$	0.238226	0.0146066
$267$	−1.73438	−0.106142
$268$	−22.9667	−1.40291
$269$	−2.14376	−0.130707	−0.0653536	−	0.997862i	$-0.520818\pi$
$269$	−2.14376	−0.130707	−0.0653536	+	0.997862i	$0.520818\pi$
$270$	0.0321408	0.00195603
$271$	−15.7274	−0.955369	−0.477685	−	0.878531i	$-0.658524\pi$
$271$	−15.7274	−0.955369	−0.477685	+	0.878531i	$0.658524\pi$
$272$	−0.525420	−0.0318583
$273$	10.2706	0.621606
$274$	0.547587	0.0330810
$275$	1.58257	0.0954328
$276$	22.1826	1.33524
$277$	17.2915	1.03894	0.519471	−	0.854488i	$-0.326129\pi$
$277$	17.2915	1.03894	0.519471	+	0.854488i	$0.326129\pi$
$278$	−0.204118	−0.0122422
$279$	19.2699	1.15366
$280$	0.179093	0.0107029
$281$	−5.11865	−0.305353	−0.152677	−	0.988276i	$-0.548789\pi$
$281$	−5.11865	−0.305353	−0.152677	+	0.988276i	$0.548789\pi$
$282$	0.600858	0.0357806
$283$	−18.9392	−1.12582	−0.562909	−	0.826519i	$-0.690318\pi$
$283$	−18.9392	−1.12582	−0.562909	+	0.826519i	$0.690318\pi$
$284$	−2.38989	−0.141814
$285$	12.6961	0.752050
$286$	−0.304986	−0.0180342
$287$	2.91849	0.172273
$288$	−1.44915	−0.0853920
$289$	−16.9826	−0.998979
$290$	0.153721	0.00902682
$291$	−22.1253	−1.29701
$292$	−26.0685	−1.52554
$293$	−8.58792	−0.501712	−0.250856	−	0.968024i	$-0.580712\pi$
$293$	−8.58792	−0.501712	−0.250856	+	0.968024i	$0.580712\pi$
$294$	0.106943	0.00623706
$295$	−12.4882	−0.727093
$296$	2.02759	0.117852
$297$	1.13549	0.0658879
$298$	0.787790	0.0456355
$299$	20.0070	1.15703
$300$	4.76992	0.275391
$301$	8.72221	0.502740
$302$	0.429777	0.0247309
$303$	−1.07117	−0.0615372
$304$	21.2082	1.21637
$305$	6.94914	0.397907
$306$	0.0159319	0.000910768 0
$307$	34.2547	1.95502	0.977510	−	0.210889i	$-0.0676358\pi$
$307$	34.2547	1.95502	0.977510	+	0.210889i	$0.0676358\pi$
$308$	3.16197	0.180170
$309$	21.1023	1.20047
$310$	0.319770	0.0181617
$311$	10.3773	0.588441	0.294221	−	0.955738i	$-0.404940\pi$
$311$	10.3773	0.588441	0.294221	+	0.955738i	$0.404940\pi$
$312$	−1.83939	−0.104135
$313$	26.6713	1.50755	0.753775	−	0.657133i	$-0.228231\pi$
$313$	26.6713	1.50755	0.753775	+	0.657133i	$0.228231\pi$
$314$	−0.909457	−0.0513236
$315$	2.69946	0.152097
$316$	−20.2809	−1.14089
$317$	−9.62408	−0.540542	−0.270271	−	0.962784i	$-0.587113\pi$
$317$	−9.62408	−0.540542	−0.270271	+	0.962784i	$0.587113\pi$
$318$	1.20419	0.0675275
$319$	5.43077	0.304065
$320$	7.95188	0.444524
$321$	32.6632	1.82308
$322$	0.208323	0.0116094
$323$	−0.700660	−0.0389858
$324$	19.6029	1.08905
$325$	4.30209	0.238637
$326$	−0.409779	−0.0226956
$327$	20.2430	1.11944
$328$	−0.522682	−0.0288603
$329$	−5.61847	−0.309756
$330$	−0.169246	−0.00931667
$331$	−19.0463	−1.04688	−0.523439	−	0.852063i	$-0.675351\pi$
$331$	−19.0463	−1.04688	−0.523439	+	0.852063i	$0.675351\pi$
$332$	30.7225	1.68612
$333$	30.5618	1.67478
$334$	0.0984936	0.00538933
$335$	−11.4949	−0.628033
$336$	9.52068	0.519396
$337$	−10.6270	−0.578888	−0.289444	−	0.957195i	$-0.593470\pi$
$337$	−10.6270	−0.578888	−0.289444	+	0.957195i	$0.593470\pi$
$338$	−0.246734	−0.0134206
$339$	−1.05733	−0.0574265
$340$	−0.263239	−0.0142761
$341$	11.2971	0.611770
$342$	−0.643081	−0.0347738
$343$	−1.00000	−0.0539949
$344$	−1.56209	−0.0842221
$345$	11.1024	0.597735
$346$	0.128564	0.00691164
$347$	35.3660	1.89854	0.949272	−	0.314455i	$-0.101822\pi$
$347$	35.3660	1.89854	0.949272	+	0.314455i	$0.101822\pi$
$348$	16.3685	0.877443
$349$	28.5450	1.52798	0.763988	−	0.645230i	$-0.223238\pi$
$349$	28.5450	1.52798	0.763988	+	0.645230i	$0.223238\pi$
$350$	0.0447957	0.00239443
$351$	3.08674	0.164758
$352$	−0.849573	−0.0452824
$353$	−20.8107	−1.10764	−0.553821	−	0.832635i	$-0.686831\pi$
$353$	−20.8107	−1.10764	−0.553821	+	0.832635i	$0.686831\pi$
$354$	1.33553	0.0709827
$355$	−1.19614	−0.0634847
$356$	−1.45151	−0.0769300
$357$	−0.314537	−0.0166471
$358$	−0.783064	−0.0413862
$359$	16.1956	0.854769	0.427384	−	0.904070i	$-0.359435\pi$
$359$	16.1956	0.854769	0.427384	+	0.904070i	$0.359435\pi$
$360$	−0.483454	−0.0254803
$361$	9.28161	0.488506
$362$	−0.790527	−0.0415492
$363$	20.2817	1.06451
$364$	8.59555	0.450529
$365$	−13.0473	−0.682929
$366$	−0.743164	−0.0388458
$367$	0.475455	0.0248185	0.0124093	−	0.999923i	$-0.496050\pi$
$367$	0.475455	0.0248185	0.0124093	+	0.999923i	$0.496050\pi$
$368$	18.5461	0.966783
$369$	−7.87836	−0.410131
$370$	0.507153	0.0263656
$371$	−11.2601	−0.584593
$372$	34.0496	1.76539
$373$	−25.8090	−1.33634	−0.668170	−	0.744009i	$-0.732922\pi$
$373$	−25.8090	−1.33634	−0.668170	+	0.744009i	$0.732922\pi$
$374$	0.00934020	0.000482970 0
$375$	2.38735	0.123282
$376$	1.00623	0.0518923
$377$	14.7631	0.760337
$378$	0.0321408	0.00165314
$379$	−30.8518	−1.58475	−0.792376	−	0.610033i	$-0.791156\pi$
$379$	−30.8518	−1.58475	−0.792376	+	0.610033i	$0.791156\pi$
$380$	10.6254	0.545073
$381$	−25.8003	−1.32179
$382$	−0.785446	−0.0401869
$383$	−11.8981	−0.607967	−0.303983	−	0.952677i	$-0.598317\pi$
$383$	−11.8981	−0.607967	−0.303983	+	0.952677i	$0.598317\pi$
$384$	−3.41360	−0.174200
$385$	1.58257	0.0806555
$386$	−0.561262	−0.0285675
$387$	−23.5453	−1.19687
$388$	−18.5168	−0.940049
$389$	−30.5690	−1.54991	−0.774955	−	0.632016i	$-0.782228\pi$
$389$	−30.5690	−1.54991	−0.774955	+	0.632016i	$0.782228\pi$
$390$	−0.460079	−0.0232970
$391$	−0.612713	−0.0309862
$392$	0.179093	0.00904556
$393$	−29.1781	−1.47184
$394$	−1.24222	−0.0625819
$395$	−10.1506	−0.510734
$396$	−8.53562	−0.428931
$397$	11.6761	0.586007	0.293003	−	0.956111i	$-0.405345\pi$
$397$	11.6761	0.586007	0.293003	+	0.956111i	$0.405345\pi$
$398$	0.890531	0.0446383
$399$	12.6961	0.635598
$400$	3.98796	0.199398
$401$	5.16742	0.258049	0.129024	−	0.991641i	$-0.458815\pi$
$401$	5.16742	0.258049	0.129024	+	0.991641i	$0.458815\pi$
$402$	1.22930	0.0613119
$403$	30.7101	1.52978
$404$	−0.896471	−0.0446011
$405$	9.81130	0.487527
$406$	0.153721	0.00762906
$407$	17.9171	0.888115
$408$	0.0563314	0.00278882
$409$	31.6378	1.56439	0.782194	−	0.623035i	$-0.214101\pi$
$409$	31.6378	1.56439	0.782194	+	0.623035i	$0.214101\pi$
$410$	−0.130736	−0.00645659
$411$	29.1833	1.43950
$412$	17.6607	0.870078
$413$	−12.4882	−0.614506
$414$	−0.562360	−0.0276385
$415$	15.3767	0.754811
$416$	−2.30949	−0.113232
$417$	−10.8783	−0.532712
$418$	−0.377010	−0.0184402
$419$	−10.2940	−0.502896	−0.251448	−	0.967871i	$-0.580907\pi$
$419$	−10.2940	−0.502896	−0.251448	+	0.967871i	$0.580907\pi$
$420$	4.76992	0.232748
$421$	27.6143	1.34584	0.672920	−	0.739715i	$-0.265040\pi$
$421$	27.6143	1.34584	0.672920	+	0.739715i	$0.265040\pi$
$422$	0.425340	0.0207052
$423$	15.1668	0.737437
$424$	2.01660	0.0979347
$425$	−0.131751	−0.00639088
$426$	0.127919	0.00619771
$427$	6.94914	0.336293
$428$	27.3361	1.32134
$429$	−16.2540	−0.784751
$430$	−0.390718	−0.0188421
$431$	−14.4263	−0.694893	−0.347446	−	0.937700i	$-0.612951\pi$
$431$	−14.4263	−0.694893	−0.347446	+	0.937700i	$0.612951\pi$
$432$	2.86135	0.137667
$433$	−24.4376	−1.17439	−0.587197	−	0.809444i	$-0.699769\pi$
$433$	−24.4376	−1.17439	−0.587197	+	0.809444i	$0.699769\pi$
$434$	0.319770	0.0153495
$435$	8.19246	0.392798
$436$	16.9415	0.811349
$437$	24.7317	1.18308
$438$	1.39532	0.0666712
$439$	−4.21055	−0.200958	−0.100479	−	0.994939i	$-0.532038\pi$
$439$	−4.21055	−0.200958	−0.100479	+	0.994939i	$0.532038\pi$
$440$	−0.283428	−0.0135119
$441$	2.69946	0.128546
$442$	0.0253905	0.00120770
$443$	5.39441	0.256296	0.128148	−	0.991755i	$-0.459097\pi$
$443$	5.39441	0.256296	0.128148	+	0.991755i	$0.459097\pi$
$444$	54.0024	2.56284
$445$	−0.726485	−0.0344387
$446$	0.371984	0.0176139
$447$	41.9847	1.98581
$448$	7.95188	0.375691
$449$	−8.52527	−0.402332	−0.201166	−	0.979557i	$-0.564473\pi$
$449$	−8.52527	−0.402332	−0.201166	+	0.979557i	$0.564473\pi$
$450$	−0.120924	−0.00570042
$451$	−4.61873	−0.217488
$452$	−0.884890	−0.0416217
$453$	22.9046	1.07615
$454$	−0.181967	−0.00854016
$455$	4.30209	0.201685
$456$	−2.27377	−0.106479
$457$	−17.1537	−0.802414	−0.401207	−	0.915987i	$-0.631409\pi$
$457$	−17.1537	−0.802414	−0.401207	+	0.915987i	$0.631409\pi$
$458$	−0.0447957	−0.00209317
$459$	−0.0945312	−0.00441234
$460$	9.29171	0.433228
$461$	2.81101	0.130922	0.0654608	−	0.997855i	$-0.479148\pi$
$461$	2.81101	0.130922	0.0654608	+	0.997855i	$0.479148\pi$
$462$	−0.169246	−0.00787402
$463$	3.37771	0.156975	0.0784877	−	0.996915i	$-0.474991\pi$
$463$	3.37771	0.156975	0.0784877	+	0.996915i	$0.474991\pi$
$464$	13.6851	0.635316
$465$	17.0419	0.790300
$466$	−0.762705	−0.0353316
$467$	19.7102	0.912077	0.456039	−	0.889960i	$-0.349268\pi$
$467$	19.7102	0.912077	0.456039	+	0.889960i	$0.349268\pi$
$468$	−23.2033	−1.07257
$469$	−11.4949	−0.530785
$470$	0.251684	0.0116093
$471$	−48.4688	−2.23333
$472$	2.23655	0.102946
$473$	−13.8035	−0.634688
$474$	1.08554	0.0498606
$475$	5.31805	0.244009
$476$	−0.263239	−0.0120655
$477$	30.3961	1.39174
$478$	0.662276	0.0302918
$479$	−17.7879	−0.812751	−0.406375	−	0.913706i	$-0.633207\pi$
$479$	−17.7879	−0.812751	−0.406375	+	0.913706i	$0.633207\pi$
$480$	−1.28160	−0.0584969
$481$	48.7059	2.22080
$482$	−1.32000	−0.0601245
$483$	11.1024	0.505178
$484$	16.9739	0.771539
$485$	−9.26771	−0.420825
$486$	−0.952830	−0.0432212
$487$	3.07983	0.139561	0.0697803	−	0.997562i	$-0.477770\pi$
$487$	3.07983	0.139561	0.0697803	+	0.997562i	$0.477770\pi$
$488$	−1.24454	−0.0563378
$489$	−21.8389	−0.987588
$490$	0.0447957	0.00202366
$491$	−25.1134	−1.13335	−0.566675	−	0.823941i	$-0.691771\pi$
$491$	−25.1134	−1.13335	−0.566675	+	0.823941i	$0.691771\pi$
$492$	−13.9210	−0.627606
$493$	−0.452119	−0.0203624
$494$	−1.02487	−0.0461110
$495$	−4.27210	−0.192016
$496$	28.4677	1.27824
$497$	−1.19614	−0.0536543
$498$	−1.64443	−0.0736887
$499$	30.4339	1.36241	0.681204	−	0.732094i	$-0.261457\pi$
$499$	30.4339	1.36241	0.681204	+	0.732094i	$0.261457\pi$
$500$	1.99799	0.0893530
$501$	5.24914	0.234514
$502$	0.950647	0.0424294
$503$	−14.8887	−0.663854	−0.331927	−	0.943305i	$-0.607699\pi$
$503$	−14.8887	−0.663854	−0.331927	+	0.943305i	$0.607699\pi$
$504$	−0.483454	−0.0215348
$505$	−0.448686	−0.0199663
$506$	−0.329687	−0.0146564
$507$	−13.1495	−0.583990
$508$	−21.5925	−0.958010
$509$	29.0596	1.28804	0.644022	−	0.765007i	$-0.277264\pi$
$509$	29.0596	1.28804	0.644022	+	0.765007i	$0.277264\pi$
$510$	0.0140899	0.000623912 0
$511$	−13.0473	−0.577180
$512$	−3.56929	−0.157742
$513$	3.81568	0.168466
$514$	0.737333	0.0325224
$515$	8.83920	0.389502
$516$	−41.6042	−1.83152
$517$	8.89165	0.391054
$518$	0.507153	0.0222830
$519$	6.85172	0.300757
$520$	−0.770474	−0.0337875
$521$	38.4920	1.68637	0.843183	−	0.537627i	$-0.180679\pi$
$521$	38.4920	1.68637	0.843183	+	0.537627i	$0.180679\pi$
$522$	−0.414964	−0.0181625
$523$	−15.6306	−0.683478	−0.341739	−	0.939795i	$-0.611016\pi$
$523$	−15.6306	−0.683478	−0.341739	+	0.939795i	$0.611016\pi$
$524$	−24.4193	−1.06676
$525$	2.38735	0.104193
$526$	0.924315	0.0403020
$527$	−0.940496	−0.0409686
$528$	−15.0672	−0.655715
$529$	−1.37267	−0.0596813
$530$	0.504403	0.0219099
$531$	33.7115	1.46295
$532$	10.6254	0.460670
$533$	−12.5556	−0.543844
$534$	0.0776927	0.00336209
$535$	13.6818	0.591514
$536$	2.05865	0.0889203
$537$	−41.7328	−1.80090
$538$	0.0960312	0.00414020
$539$	1.58257	0.0681663
$540$	1.43355	0.0616903
$541$	−23.4221	−1.00699	−0.503497	−	0.863997i	$-0.667954\pi$
$541$	−23.4221	−1.00699	−0.503497	+	0.863997i	$0.667954\pi$
$542$	0.704519	0.0302617
$543$	−42.1306	−1.80800
$544$	0.0707281	0.00303244
$545$	8.47924	0.363211
$546$	−0.460079	−0.0196896
$547$	−15.1112	−0.646108	−0.323054	−	0.946381i	$-0.604710\pi$
$547$	−15.1112	−0.646108	−0.323054	+	0.946381i	$0.604710\pi$
$548$	24.4237	1.04333
$549$	−18.7589	−0.800612
$550$	−0.0708926	−0.00302287
$551$	18.2494	0.777452
$552$	−1.98837	−0.0846306
$553$	−10.1506	−0.431649
$554$	−0.774583	−0.0329089
$555$	27.0283	1.14729
$556$	−9.10412	−0.386101
$557$	34.0106	1.44107	0.720537	−	0.693417i	$-0.243895\pi$
$557$	34.0106	1.44107	0.720537	+	0.693417i	$0.243895\pi$
$558$	−0.863207	−0.0365425
$559$	−37.5237	−1.58708
$560$	3.98796	0.168522
$561$	0.497779	0.0210162
$562$	0.229294	0.00967217
$563$	−6.52356	−0.274935	−0.137468	−	0.990506i	$-0.543896\pi$
$563$	−6.52356	−0.274935	−0.137468	+	0.990506i	$0.543896\pi$
$564$	26.7997	1.12847
$565$	−0.442889	−0.0186325
$566$	0.848395	0.0356607
$567$	9.81130	0.412036
$568$	0.214221	0.00898850
$569$	−14.7350	−0.617724	−0.308862	−	0.951107i	$-0.599948\pi$
$569$	−14.7350	−0.617724	−0.308862	+	0.951107i	$0.599948\pi$
$570$	−0.568729	−0.0238214
$571$	−28.2587	−1.18259	−0.591296	−	0.806455i	$-0.701383\pi$
$571$	−28.2587	−1.18259	−0.591296	+	0.806455i	$0.701383\pi$
$572$	−13.6031	−0.568774
$573$	−41.8597	−1.74872
$574$	−0.130736	−0.00545682
$575$	4.65052	0.193940
$576$	−21.4658	−0.894407
$577$	−8.82553	−0.367412	−0.183706	−	0.982981i	$-0.558809\pi$
$577$	−8.82553	−0.367412	−0.183706	+	0.982981i	$0.558809\pi$
$578$	0.760750	0.0316430
$579$	−29.9120	−1.24310
$580$	6.85633	0.284693
$581$	15.3767	0.637932
$582$	0.991119	0.0410832
$583$	17.8199	0.738025
$584$	2.33669	0.0966928
$585$	−11.6133	−0.480152
$586$	0.384702	0.0158919
$587$	28.4393	1.17382	0.586909	−	0.809653i	$-0.300345\pi$
$587$	28.4393	1.17382	0.586909	+	0.809653i	$0.300345\pi$
$588$	4.76992	0.196708
$589$	37.9624	1.56421
$590$	0.559419	0.0230309
$591$	−66.2029	−2.72323
$592$	45.1496	1.85564
$593$	27.0401	1.11041	0.555203	−	0.831715i	$-0.312641\pi$
$593$	27.0401	1.11041	0.555203	+	0.831715i	$0.312641\pi$
$594$	−0.0508652	−0.00208702
$595$	−0.131751	−0.00540128
$596$	35.1373	1.43928
$597$	47.4602	1.94242
$598$	−0.896226	−0.0366494
$599$	−22.2615	−0.909580	−0.454790	−	0.890599i	$-0.650286\pi$
$599$	−22.2615	−0.909580	−0.454790	+	0.890599i	$0.650286\pi$
$600$	−0.427558	−0.0174550
$601$	−15.6646	−0.638974	−0.319487	−	0.947591i	$-0.603511\pi$
$601$	−15.6646	−0.638974	−0.319487	+	0.947591i	$0.603511\pi$
$602$	−0.390718	−0.0159245
$603$	31.0300	1.26364
$604$	19.1690	0.779977
$605$	8.49546	0.345389
$606$	0.0479839	0.00194921
$607$	−12.0908	−0.490752	−0.245376	−	0.969428i	$-0.578911\pi$
$607$	−12.0908	−0.490752	−0.245376	+	0.969428i	$0.578911\pi$
$608$	−2.85488	−0.115781
$609$	8.19246	0.331975
$610$	−0.311292	−0.0126038
$611$	24.1712	0.977861
$612$	0.710602	0.0287244
$613$	−6.44146	−0.260168	−0.130084	−	0.991503i	$-0.541525\pi$
$613$	−6.44146	−0.260168	−0.130084	+	0.991503i	$0.541525\pi$
$614$	−1.53446	−0.0619260
$615$	−6.96748	−0.280956
$616$	−0.283428	−0.0114196
$617$	−7.58935	−0.305536	−0.152768	−	0.988262i	$-0.548819\pi$
$617$	−7.58935	−0.305536	−0.152768	+	0.988262i	$0.548819\pi$
$618$	−0.945293	−0.0380253
$619$	32.3591	1.30062	0.650310	−	0.759669i	$-0.274639\pi$
$619$	32.3591	1.30062	0.650310	+	0.759669i	$0.274639\pi$
$620$	14.2625	0.572796
$621$	3.33673	0.133898
$622$	−0.464858	−0.0186391
$623$	−0.726485	−0.0291060
$624$	−40.9588	−1.63967
$625$	1.00000	0.0400000
$626$	−1.19476	−0.0477522
$627$	−20.0925	−0.802415
$628$	−40.5639	−1.61868
$629$	−1.49162	−0.0594747
$630$	−0.120924	−0.00481774
$631$	−10.0271	−0.399172	−0.199586	−	0.979880i	$-0.563960\pi$
$631$	−10.0271	−0.399172	−0.199586	+	0.979880i	$0.563960\pi$
$632$	1.81791	0.0723126
$633$	22.6682	0.900979
$634$	0.431118	0.0171219
$635$	−10.8071	−0.428865
$636$	53.7096	2.12972
$637$	4.30209	0.170455
$638$	−0.243275	−0.00963136
$639$	3.22894	0.127735
$640$	−1.42987	−0.0565206
$641$	8.01352	0.316515	0.158257	−	0.987398i	$-0.449412\pi$
$641$	8.01352	0.316515	0.158257	+	0.987398i	$0.449412\pi$
$642$	−1.46317	−0.0577468
$643$	−27.2831	−1.07594	−0.537971	−	0.842963i	$-0.680809\pi$
$643$	−27.2831	−1.07594	−0.537971	+	0.842963i	$0.680809\pi$
$644$	9.29171	0.366145
$645$	−20.8230	−0.819905
$646$	0.0313866	0.00123489
$647$	26.0778	1.02523	0.512613	−	0.858620i	$-0.328678\pi$
$647$	26.0778	1.02523	0.512613	+	0.858620i	$0.328678\pi$
$648$	−1.75713	−0.0690268
$649$	19.7636	0.775788
$650$	−0.192715	−0.00755891
$651$	17.0419	0.667925
$652$	−18.2771	−0.715787
$653$	9.61095	0.376105	0.188053	−	0.982159i	$-0.439782\pi$
$653$	9.61095	0.376105	0.188053	+	0.982159i	$0.439782\pi$
$654$	−0.906798	−0.0354586
$655$	−12.2219	−0.477550
$656$	−11.6388	−0.454421
$657$	35.2208	1.37409
$658$	0.251684	0.00981164
$659$	−46.6714	−1.81806	−0.909030	−	0.416732i	$-0.863175\pi$
$659$	−46.6714	−1.81806	−0.909030	+	0.416732i	$0.863175\pi$
$660$	−7.54875	−0.293835
$661$	−49.0933	−1.90951	−0.954753	−	0.297400i	$-0.903881\pi$
$661$	−49.0933	−1.90951	−0.954753	+	0.297400i	$0.903881\pi$
$662$	0.853192	0.0331603
$663$	1.35317	0.0525527
$664$	−2.75385	−0.106870
$665$	5.31805	0.206225
$666$	−1.36904	−0.0530492
$667$	15.9588	0.617925
$668$	4.39304	0.169972
$669$	19.8246	0.766463
$670$	0.514922	0.0198932
$671$	−10.9975	−0.424555
$672$	−1.28160	−0.0494389
$673$	−29.7534	−1.14691	−0.573456	−	0.819237i	$-0.694397\pi$
$673$	−29.7534	−1.14691	−0.573456	+	0.819237i	$0.694397\pi$
$674$	0.476043	0.0183365
$675$	0.717497	0.0276165
$676$	−11.0049	−0.423266
$677$	37.8497	1.45468	0.727340	−	0.686277i	$-0.240756\pi$
$677$	37.8497	1.45468	0.727340	+	0.686277i	$0.240756\pi$
$678$	0.0473640	0.00181900
$679$	−9.26771	−0.355662
$680$	0.0235958	0.000904856 0
$681$	−9.69782	−0.371621
$682$	−0.506060	−0.0193780
$683$	−21.3425	−0.816648	−0.408324	−	0.912837i	$-0.633887\pi$
$683$	−21.3425	−0.816648	−0.408324	+	0.912837i	$0.633887\pi$
$684$	−28.6829	−1.09672
$685$	12.2241	0.467059
$686$	0.0447957	0.00171031
$687$	−2.38735	−0.0910832
$688$	−34.7839	−1.32612
$689$	48.4418	1.84549
$690$	−0.497342	−0.0189335
$691$	−15.5758	−0.592531	−0.296265	−	0.955106i	$-0.595741\pi$
$691$	−15.5758	−0.592531	−0.296265	+	0.955106i	$0.595741\pi$
$692$	5.73425	0.217984
$693$	−4.27210	−0.162283
$694$	−1.58424	−0.0601371
$695$	−4.55663	−0.172843
$696$	−1.46721	−0.0556145
$697$	0.384516	0.0145646
$698$	−1.27869	−0.0483992
$699$	−40.6478	−1.53744
$700$	1.99799	0.0755171
$701$	−19.5113	−0.736931	−0.368466	−	0.929641i	$-0.620117\pi$
$701$	−19.5113	−0.736931	−0.368466	+	0.929641i	$0.620117\pi$
$702$	−0.138273	−0.00521876
$703$	60.2080	2.27079
$704$	−12.5844	−0.474294
$705$	13.4133	0.505173
$706$	0.932231	0.0350850
$707$	−0.448686	−0.0168746
$708$	59.5678	2.23870
$709$	22.2566	0.835864	0.417932	−	0.908478i	$-0.362755\pi$
$709$	22.2566	0.835864	0.417932	+	0.908478i	$0.362755\pi$
$710$	0.0535821	0.00201090
$711$	27.4013	1.02763
$712$	0.130108	0.00487602
$713$	33.1973	1.24325
$714$	0.0140899	0.000527302 0
$715$	−6.80838	−0.254619
$716$	−34.9265	−1.30526
$717$	35.2955	1.31813
$718$	−0.725491	−0.0270751
$719$	43.4834	1.62166	0.810829	−	0.585283i	$-0.199017\pi$
$719$	43.4834	1.62166	0.810829	+	0.585283i	$0.199017\pi$
$720$	−10.7653	−0.401201
$721$	8.83920	0.329189
$722$	−0.415776	−0.0154736
$723$	−70.3485	−2.61629
$724$	−35.2594	−1.31040
$725$	3.43161	0.127447
$726$	−0.908532	−0.0337188
$727$	33.7653	1.25228	0.626142	−	0.779709i	$-0.284633\pi$
$727$	33.7653	1.25228	0.626142	+	0.779709i	$0.284633\pi$
$728$	−0.770474	−0.0285557
$729$	−21.3464	−0.790609
$730$	0.584465	0.0216320
$731$	1.14916	0.0425034
$732$	−33.1468	−1.22514
$733$	−26.0884	−0.963596	−0.481798	−	0.876282i	$-0.660016\pi$
$733$	−26.0884	−0.963596	−0.481798	+	0.876282i	$0.660016\pi$
$734$	−0.0212983	−0.000786136 0
$735$	2.38735	0.0880589
$736$	−2.49654	−0.0920236
$737$	18.1915	0.670093
$738$	0.352917	0.0129910
$739$	7.60255	0.279664	0.139832	−	0.990175i	$-0.455344\pi$
$739$	7.60255	0.279664	0.139832	+	0.990175i	$0.455344\pi$
$740$	22.6202	0.831535
$741$	−54.6196	−2.00650
$742$	0.504403	0.0185172
$743$	−16.1009	−0.590685	−0.295343	−	0.955391i	$-0.595434\pi$
$743$	−16.1009	−0.590685	−0.295343	+	0.955391i	$0.595434\pi$
$744$	−3.05209	−0.111895
$745$	17.5863	0.644312
$746$	1.15613	0.0423290
$747$	−41.5087	−1.51872
$748$	0.416595	0.0152322
$749$	13.6818	0.499921
$750$	−0.106943	−0.00390501
$751$	−44.1925	−1.61261	−0.806304	−	0.591501i	$-0.798535\pi$
$751$	−44.1925	−1.61261	−0.806304	+	0.591501i	$0.798535\pi$
$752$	22.4063	0.817072
$753$	50.6640	1.84630
$754$	−0.661323	−0.0240840
$755$	9.59414	0.349167
$756$	1.43355	0.0521378
$757$	6.38567	0.232091	0.116046	−	0.993244i	$-0.462978\pi$
$757$	6.38567	0.232091	0.116046	+	0.993244i	$0.462978\pi$
$758$	1.38203	0.0501976
$759$	−17.5704	−0.637766
$760$	−0.952425	−0.0345481
$761$	−7.46314	−0.270539	−0.135269	−	0.990809i	$-0.543190\pi$
$761$	−7.46314	−0.270539	−0.135269	+	0.990809i	$0.543190\pi$
$762$	1.15574	0.0418681
$763$	8.47924	0.306969
$764$	−35.0327	−1.26744
$765$	0.355658	0.0128588
$766$	0.532986	0.0192576
$767$	53.7255	1.93992
$768$	−37.8150	−1.36453
$769$	6.07455	0.219054	0.109527	−	0.993984i	$-0.465066\pi$
$769$	6.07455	0.219054	0.109527	+	0.993984i	$0.465066\pi$
$770$	−0.0708926	−0.00255479
$771$	39.2956	1.41520
$772$	−25.0336	−0.900978
$773$	−7.70400	−0.277093	−0.138547	−	0.990356i	$-0.544243\pi$
$773$	−7.70400	−0.277093	−0.138547	+	0.990356i	$0.544243\pi$
$774$	1.05473	0.0379114
$775$	7.13841	0.256419
$776$	1.65978	0.0595827
$777$	27.0283	0.969636
$778$	1.36936	0.0490940
$779$	−15.5207	−0.556086
$780$	−20.5206	−0.734756
$781$	1.89299	0.0677363
$782$	0.0274469	0.000981499 0
$783$	2.46217	0.0879906
$784$	3.98796	0.142427
$785$	−20.3023	−0.724621
$786$	1.30705	0.0466210
$787$	−18.0338	−0.642837	−0.321418	−	0.946937i	$-0.604160\pi$
$787$	−18.0338	−0.642837	−0.321418	+	0.946937i	$0.604160\pi$
$788$	−55.4057	−1.97375
$789$	49.2606	1.75373
$790$	0.454705	0.0161777
$791$	−0.442889	−0.0157473
$792$	0.765102	0.0271867
$793$	−29.8958	−1.06163
$794$	−0.523039	−0.0185620
$795$	26.8818	0.953398
$796$	39.7198	1.40783
$797$	38.2591	1.35521	0.677603	−	0.735428i	$-0.263019\pi$
$797$	38.2591	1.35521	0.677603	+	0.735428i	$0.263019\pi$
$798$	−0.568729	−0.0201328
$799$	−0.740242	−0.0261879
$800$	−0.536830	−0.0189798
$801$	1.96112	0.0692927
$802$	−0.231478	−0.00817379
$803$	20.6484	0.728665
$804$	54.8297	1.93369
$805$	4.65052	0.163909
$806$	−1.37568	−0.0484563
$807$	5.11791	0.180159
$808$	0.0803565	0.00282693
$809$	−22.3576	−0.786052	−0.393026	−	0.919527i	$-0.628572\pi$
$809$	−22.3576	−0.786052	−0.393026	+	0.919527i	$0.628572\pi$
$810$	−0.439504	−0.0154426
$811$	−51.1104	−1.79473	−0.897365	−	0.441290i	$-0.854521\pi$
$811$	−51.1104	−1.79473	−0.897365	+	0.441290i	$0.854521\pi$
$812$	6.85633	0.240610
$813$	37.5468	1.31682
$814$	−0.802607	−0.0281314
$815$	−9.14773	−0.320431
$816$	1.25436	0.0439115
$817$	−46.3851	−1.62281
$818$	−1.41724	−0.0495525
$819$	−11.6133	−0.405802
$820$	−5.83113	−0.203632
$821$	−29.2457	−1.02068	−0.510341	−	0.859972i	$-0.670481\pi$
$821$	−29.2457	−1.02068	−0.510341	+	0.859972i	$0.670481\pi$
$822$	−1.30728	−0.0455968
$823$	56.2610	1.96114	0.980568	−	0.196180i	$-0.0628535\pi$
$823$	56.2610	1.96114	0.980568	+	0.196180i	$0.0628535\pi$
$824$	−1.58304	−0.0551478
$825$	−3.77817	−0.131539
$826$	0.559419	0.0194647
$827$	−42.4840	−1.47731	−0.738656	−	0.674082i	$-0.764539\pi$
$827$	−42.4840	−1.47731	−0.738656	+	0.674082i	$0.764539\pi$
$828$	−25.0826	−0.871680
$829$	10.1327	0.351925	0.175962	−	0.984397i	$-0.443696\pi$
$829$	10.1327	0.351925	0.175962	+	0.984397i	$0.443696\pi$
$830$	−0.688809	−0.0239089
$831$	−41.2808	−1.43202
$832$	−34.2097	−1.18601
$833$	−0.131751	−0.00456492
$834$	0.487301	0.0168739
$835$	2.19873	0.0760901
$836$	−16.8155	−0.581577
$837$	5.12179	0.177035
$838$	0.461128	0.0159294
$839$	17.9616	0.620105	0.310052	−	0.950720i	$-0.399653\pi$
$839$	17.9616	0.620105	0.310052	+	0.950720i	$0.399653\pi$
$840$	−0.427558	−0.0147522
$841$	−17.2241	−0.593934
$842$	−1.23700	−0.0426299
$843$	12.2200	0.420880
$844$	18.9712	0.653014
$845$	−5.50798	−0.189480
$846$	−0.679409	−0.0233586
$847$	8.49546	0.291907
$848$	44.9047	1.54203
$849$	45.2146	1.55176
$850$	0.00590190	0.000202434 0
$851$	52.6507	1.80484
$852$	5.70550	0.195467
$853$	30.4095	1.04120	0.520601	−	0.853800i	$-0.325708\pi$
$853$	30.4095	1.04120	0.520601	+	0.853800i	$0.325708\pi$
$854$	−0.311292	−0.0106522
$855$	−14.3558	−0.490960
$856$	−2.45031	−0.0837498
$857$	−3.29365	−0.112509	−0.0562545	−	0.998416i	$-0.517916\pi$
$857$	−3.29365	−0.112509	−0.0562545	+	0.998416i	$0.517916\pi$
$858$	0.728110	0.0248573
$859$	−49.7394	−1.69709	−0.848543	−	0.529127i	$-0.822520\pi$
$859$	−49.7394	−1.69709	−0.848543	+	0.529127i	$0.822520\pi$
$860$	−17.4269	−0.594253
$861$	−6.96748	−0.237451
$862$	0.646238	0.0220110
$863$	18.8970	0.643262	0.321631	−	0.946865i	$-0.395769\pi$
$863$	18.8970	0.643262	0.321631	+	0.946865i	$0.395769\pi$
$864$	−0.385173	−0.0131039
$865$	2.87001	0.0975831
$866$	1.09470	0.0371994
$867$	40.5436	1.37693
$868$	14.2625	0.484101
$869$	16.0642	0.544939
$870$	−0.366987	−0.0124420
$871$	49.4520	1.67562
$872$	−1.51857	−0.0514254
$873$	25.0178	0.846725
$874$	−1.10787	−0.0374744
$875$	1.00000	0.0338062
$876$	62.2347	2.10272
$877$	29.7300	1.00391	0.501955	−	0.864893i	$-0.332614\pi$
$877$	29.7300	1.00391	0.501955	+	0.864893i	$0.332614\pi$
$878$	0.188614	0.00636543
$879$	20.5024	0.691529
$880$	−6.31125	−0.212752
$881$	0.647171	0.0218038	0.0109019	−	0.999941i	$-0.496530\pi$
$881$	0.647171	0.0218038	0.0109019	+	0.999941i	$0.496530\pi$
$882$	−0.120924	−0.00407173
$883$	−32.2563	−1.08551	−0.542755	−	0.839891i	$-0.682619\pi$
$883$	−32.2563	−1.08551	−0.542755	+	0.839891i	$0.682619\pi$
$884$	1.13248	0.0380893
$885$	29.8138	1.00218
$886$	−0.241646	−0.00811827
$887$	−20.7771	−0.697627	−0.348813	−	0.937192i	$-0.613415\pi$
$887$	−20.7771	−0.697627	−0.348813	+	0.937192i	$0.613415\pi$
$888$	−4.84058	−0.162439
$889$	−10.8071	−0.362457
$890$	0.0325434	0.00109086
$891$	−15.5271	−0.520178
$892$	16.5913	0.555519
$893$	29.8793	0.999872
$894$	−1.88073	−0.0629012
$895$	−17.4808	−0.584318
$896$	−1.42987	−0.0477686
$897$	−47.7637	−1.59478
$898$	0.381895	0.0127440
$899$	24.4962	0.816995
$900$	−5.39350	−0.179783
$901$	−1.48353	−0.0494235
$902$	0.206899	0.00688900
$903$	−20.8230	−0.692946
$904$	0.0793184	0.00263809
$905$	−17.6474	−0.586619
$906$	−1.02603	−0.0340875
$907$	−11.1973	−0.371799	−0.185899	−	0.982569i	$-0.559520\pi$
$907$	−11.1973	−0.371799	−0.185899	+	0.982569i	$0.559520\pi$
$908$	−8.11617	−0.269345
$909$	1.21121	0.0401733
$910$	−0.192715	−0.00638845
$911$	12.4711	0.413186	0.206593	−	0.978427i	$-0.433762\pi$
$911$	12.4711	0.413186	0.206593	+	0.978427i	$0.433762\pi$
$912$	−50.6314	−1.67657
$913$	−24.3347	−0.805362
$914$	0.768410	0.0254167
$915$	−16.5901	−0.548451
$916$	−1.99799	−0.0660156
$917$	−12.2219	−0.403604
$918$	0.00423459	0.000139762 0
$919$	9.46365	0.312177	0.156089	−	0.987743i	$-0.450111\pi$
$919$	9.46365	0.312177	0.156089	+	0.987743i	$0.450111\pi$
$920$	−0.832875	−0.0274591
$921$	−81.7781	−2.69468
$922$	−0.125921	−0.00414699
$923$	5.14591	0.169380
$924$	−7.54875	−0.248336
$925$	11.3215	0.372247
$926$	−0.151307	−0.00497225
$927$	−23.8611	−0.783700
$928$	−1.84219	−0.0604728
$929$	−45.1942	−1.48277	−0.741386	−	0.671079i	$-0.765831\pi$
$929$	−45.1942	−1.48277	−0.741386	+	0.671079i	$0.765831\pi$
$930$	−0.763405	−0.0250330
$931$	5.31805	0.174292
$932$	−34.0184	−1.11431
$933$	−24.7742	−0.811072
$934$	−0.882930	−0.0288904
$935$	0.208506	0.00681889
$936$	2.07986	0.0679825
$937$	−4.10157	−0.133992	−0.0669962	−	0.997753i	$-0.521342\pi$
$937$	−4.10157	−0.133992	−0.0669962	+	0.997753i	$0.521342\pi$
$938$	0.514922	0.0168128
$939$	−63.6738	−2.07792
$940$	11.2257	0.366141
$941$	−13.1563	−0.428884	−0.214442	−	0.976737i	$-0.568793\pi$
$941$	−13.1563	−0.428884	−0.214442	+	0.976737i	$0.568793\pi$
$942$	2.17120	0.0707414
$943$	−13.5725	−0.441982
$944$	49.8026	1.62094
$945$	0.717497	0.0233402
$946$	0.618340	0.0201040
$947$	9.70373	0.315329	0.157664	−	0.987493i	$-0.449604\pi$
$947$	9.70373	0.315329	0.157664	+	0.987493i	$0.449604\pi$
$948$	48.4177	1.57254
$949$	56.1308	1.82208
$950$	−0.238226	−0.00772906
$951$	22.9761	0.745051
$952$	0.0235958	0.000764743 0
$953$	−6.73093	−0.218036	−0.109018	−	0.994040i	$-0.534771\pi$
$953$	−6.73093	−0.218036	−0.109018	+	0.994040i	$0.534771\pi$
$954$	−1.36161	−0.0440839
$955$	−17.5339	−0.567385
$956$	29.5390	0.955361
$957$	−12.9652	−0.419105
$958$	0.796823	0.0257442
$959$	12.2241	0.394737
$960$	−18.9840	−0.612704
$961$	19.9569	0.643771
$962$	−2.18182	−0.0703446
$963$	−36.9334	−1.19016
$964$	−58.8752	−1.89624
$965$	−12.5294	−0.403334
$966$	−0.497342	−0.0160017
$967$	10.8231	0.348048	0.174024	−	0.984741i	$-0.444323\pi$
$967$	10.8231	0.348048	0.174024	+	0.984741i	$0.444323\pi$
$968$	−1.52148	−0.0489021
$969$	1.67272	0.0537356
$970$	0.415154	0.0133298
$971$	−19.0539	−0.611468	−0.305734	−	0.952117i	$-0.598902\pi$
$971$	−19.0539	−0.611468	−0.305734	+	0.952117i	$0.598902\pi$
$972$	−42.4984	−1.36314
$973$	−4.55663	−0.146079
$974$	−0.137963	−0.00442063
$975$	−10.2706	−0.328923
$976$	−27.7129	−0.887070
$977$	−62.3826	−1.99580	−0.997898	−	0.0648026i	$-0.979358\pi$
$977$	−62.3826	−1.99580	−0.997898	+	0.0648026i	$0.979358\pi$
$978$	0.978288	0.0312822
$979$	1.14972	0.0367451
$980$	1.99799	0.0638236
$981$	−22.8894	−0.730802
$982$	1.12497	0.0358993
$983$	−14.7685	−0.471042	−0.235521	−	0.971869i	$-0.575680\pi$
$983$	−14.7685	−0.471042	−0.235521	+	0.971869i	$0.575680\pi$
$984$	1.24783	0.0397793
$985$	−27.7307	−0.883573
$986$	0.0202530	0.000644987 0
$987$	13.4133	0.426950
$988$	−45.7115	−1.45428
$989$	−40.5628	−1.28982
$990$	0.191372	0.00608219
$991$	−6.92792	−0.220073	−0.110036	−	0.993928i	$-0.535097\pi$
$991$	−6.92792	−0.220073	−0.110036	+	0.993928i	$0.535097\pi$
$992$	−3.83211	−0.121670
$993$	45.4702	1.44295
$994$	0.0535821	0.00169952
$995$	19.8798	0.630233
$996$	−73.3455	−2.32404
$997$	−20.7116	−0.655942	−0.327971	−	0.944688i	$-0.606365\pi$
$997$	−20.7116	−0.655942	−0.327971	+	0.944688i	$0.606365\pi$
$998$	−1.36331	−0.0431548
$999$	8.12311	0.257004

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.l.1.31	✓	62

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.l.1.31	✓	62	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:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q-0.0447957 q^{2} -2.38735 q^{3} -1.99799 q^{4} -1.00000 q^{5} +0.106943 q^{6} -1.00000 q^{7} +0.179093 q^{8} +2.69946 q^{9} +O(q^{10})\)	\(q-0.0447957 q^{2} -2.38735 q^{3} -1.99799 q^{4} -1.00000 q^{5} +0.106943 q^{6} -1.00000 q^{7} +0.179093 q^{8} +2.69946 q^{9} +0.0447957 q^{10} +1.58257 q^{11} +4.76992 q^{12} +4.30209 q^{13} +0.0447957 q^{14} +2.38735 q^{15} +3.98796 q^{16} -0.131751 q^{17} -0.120924 q^{18} +5.31805 q^{19} +1.99799 q^{20} +2.38735 q^{21} -0.0708926 q^{22} +4.65052 q^{23} -0.427558 q^{24} +1.00000 q^{25} -0.192715 q^{26} +0.717497 q^{27} +1.99799 q^{28} +3.43161 q^{29} -0.106943 q^{30} +7.13841 q^{31} -0.536830 q^{32} -3.77817 q^{33} +0.00590190 q^{34} +1.00000 q^{35} -5.39350 q^{36} +11.3215 q^{37} -0.238226 q^{38} -10.2706 q^{39} -0.179093 q^{40} -2.91849 q^{41} -0.106943 q^{42} -8.72221 q^{43} -3.16197 q^{44} -2.69946 q^{45} -0.208323 q^{46} +5.61847 q^{47} -9.52068 q^{48} +1.00000 q^{49} -0.0447957 q^{50} +0.314537 q^{51} -8.59555 q^{52} +11.2601 q^{53} -0.0321408 q^{54} -1.58257 q^{55} -0.179093 q^{56} -12.6961 q^{57} -0.153721 q^{58} +12.4882 q^{59} -4.76992 q^{60} -6.94914 q^{61} -0.319770 q^{62} -2.69946 q^{63} -7.95188 q^{64} -4.30209 q^{65} +0.169246 q^{66} +11.4949 q^{67} +0.263239 q^{68} -11.1024 q^{69} -0.0447957 q^{70} +1.19614 q^{71} +0.483454 q^{72} +13.0473 q^{73} -0.507153 q^{74} -2.38735 q^{75} -10.6254 q^{76} -1.58257 q^{77} +0.460079 q^{78} +10.1506 q^{79} -3.98796 q^{80} -9.81130 q^{81} +0.130736 q^{82} -15.3767 q^{83} -4.76992 q^{84} +0.131751 q^{85} +0.390718 q^{86} -8.19246 q^{87} +0.283428 q^{88} +0.726485 q^{89} +0.120924 q^{90} -4.30209 q^{91} -9.29171 q^{92} -17.0419 q^{93} -0.251684 q^{94} -5.31805 q^{95} +1.28160 q^{96} +9.26771 q^{97} -0.0447957 q^{98} +4.27210 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9} - 2 q^{10} - 13 q^{11} + 37 q^{12} + 31 q^{13} - 2 q^{14} - 11 q^{15} + 64 q^{16} + 30 q^{17} + 18 q^{18} + 20 q^{19} - 64 q^{20} - 11 q^{21} + 7 q^{22} + 29 q^{24} + 62 q^{25} + 59 q^{27} - 64 q^{28} - 29 q^{29} - 3 q^{30} + 20 q^{31} + 22 q^{32} + 72 q^{33} + 13 q^{34} + 62 q^{35} + 53 q^{36} + 35 q^{37} + 34 q^{38} - 6 q^{39} - 15 q^{40} + 13 q^{41} - 3 q^{42} - 4 q^{43} - 44 q^{44} - 69 q^{45} - 19 q^{46} + 58 q^{47} + 64 q^{48} + 62 q^{49} + 2 q^{50} - 30 q^{51} + 82 q^{52} + 18 q^{53} + 22 q^{54} + 13 q^{55} - 15 q^{56} + 21 q^{57} + 18 q^{58} - 11 q^{59} - 37 q^{60} + 24 q^{61} + 48 q^{62} - 69 q^{63} + 65 q^{64} - 31 q^{65} + 25 q^{66} - 6 q^{67} + 65 q^{68} + 27 q^{69} + 2 q^{70} - 35 q^{71} + 53 q^{72} + 116 q^{73} - 69 q^{74} + 11 q^{75} + 65 q^{76} + 13 q^{77} + 102 q^{78} - 83 q^{79} - 64 q^{80} + 126 q^{81} + 71 q^{82} + 84 q^{83} - 37 q^{84} - 30 q^{85} + 24 q^{86} + 49 q^{87} + 20 q^{88} - 16 q^{89} - 18 q^{90} - 31 q^{91} + 19 q^{92} + 65 q^{93} + 54 q^{94} - 20 q^{95} + 17 q^{96} + 155 q^{97} + 2 q^{98} + 6 q^{99}+O(q^{100}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9 - 2 * q^10 - 13 * q^11 + 37 * q^12 + 31 * q^13 - 2 * q^14 - 11 * q^15 + 64 * q^16 + 30 * q^17 + 18 * q^18 + 20 * q^19 - 64 * q^20 - 11 * q^21 + 7 * q^22 + 29 * q^24 + 62 * q^25 + 59 * q^27 - 64 * q^28 - 29 * q^29 - 3 * q^30 + 20 * q^31 + 22 * q^32 + 72 * q^33 + 13 * q^34 + 62 * q^35 + 53 * q^36 + 35 * q^37 + 34 * q^38 - 6 * q^39 - 15 * q^40 + 13 * q^41 - 3 * q^42 - 4 * q^43 - 44 * q^44 - 69 * q^45 - 19 * q^46 + 58 * q^47 + 64 * q^48 + 62 * q^49 + 2 * q^50 - 30 * q^51 + 82 * q^52 + 18 * q^53 + 22 * q^54 + 13 * q^55 - 15 * q^56 + 21 * q^57 + 18 * q^58 - 11 * q^59 - 37 * q^60 + 24 * q^61 + 48 * q^62 - 69 * q^63 + 65 * q^64 - 31 * q^65 + 25 * q^66 - 6 * q^67 + 65 * q^68 + 27 * q^69 + 2 * q^70 - 35 * q^71 + 53 * q^72 + 116 * q^73 - 69 * q^74 + 11 * q^75 + 65 * q^76 + 13 * q^77 + 102 * q^78 - 83 * q^79 - 64 * q^80 + 126 * q^81 + 71 * q^82 + 84 * q^83 - 37 * q^84 - 30 * q^85 + 24 * q^86 + 49 * q^87 + 20 * q^88 - 16 * q^89 - 18 * q^90 - 31 * q^91 + 19 * q^92 + 65 * q^93 + 54 * q^94 - 20 * q^95 + 17 * q^96 + 155 * q^97 + 2 * q^98 + 6 * q^99

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