LMFDB - Embedded newform 6015.2.a.f.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6015,2,Mod(1,6015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6015, 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("6015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6015 = 3 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6015.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:	$48.0300168158$
Analytic rank:	$1$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	6015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.139206 q^{2} -1.00000 q^{3} -1.98062 q^{4} -1.00000 q^{5} +0.139206 q^{6} -3.46594 q^{7} +0.554125 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.139206 q^{2} -1.00000 q^{3} -1.98062 q^{4} -1.00000 q^{5} +0.139206 q^{6} -3.46594 q^{7} +0.554125 q^{8} +1.00000 q^{9} +0.139206 q^{10} +1.14060 q^{11} +1.98062 q^{12} +2.00508 q^{13} +0.482479 q^{14} +1.00000 q^{15} +3.88411 q^{16} +0.449203 q^{17} -0.139206 q^{18} -7.45784 q^{19} +1.98062 q^{20} +3.46594 q^{21} -0.158778 q^{22} -3.71040 q^{23} -0.554125 q^{24} +1.00000 q^{25} -0.279119 q^{26} -1.00000 q^{27} +6.86471 q^{28} -7.06308 q^{29} -0.139206 q^{30} +9.74719 q^{31} -1.64894 q^{32} -1.14060 q^{33} -0.0625316 q^{34} +3.46594 q^{35} -1.98062 q^{36} -9.44954 q^{37} +1.03817 q^{38} -2.00508 q^{39} -0.554125 q^{40} +5.26961 q^{41} -0.482479 q^{42} +10.1590 q^{43} -2.25909 q^{44} -1.00000 q^{45} +0.516509 q^{46} +11.5459 q^{47} -3.88411 q^{48} +5.01273 q^{49} -0.139206 q^{50} -0.449203 q^{51} -3.97131 q^{52} +2.48188 q^{53} +0.139206 q^{54} -1.14060 q^{55} -1.92057 q^{56} +7.45784 q^{57} +0.983222 q^{58} +3.76373 q^{59} -1.98062 q^{60} +10.6609 q^{61} -1.35687 q^{62} -3.46594 q^{63} -7.53867 q^{64} -2.00508 q^{65} +0.158778 q^{66} -2.31617 q^{67} -0.889700 q^{68} +3.71040 q^{69} -0.482479 q^{70} +2.65392 q^{71} +0.554125 q^{72} -9.32609 q^{73} +1.31543 q^{74} -1.00000 q^{75} +14.7712 q^{76} -3.95324 q^{77} +0.279119 q^{78} -4.78534 q^{79} -3.88411 q^{80} +1.00000 q^{81} -0.733560 q^{82} -3.53744 q^{83} -6.86471 q^{84} -0.449203 q^{85} -1.41420 q^{86} +7.06308 q^{87} +0.632034 q^{88} +12.1941 q^{89} +0.139206 q^{90} -6.94949 q^{91} +7.34889 q^{92} -9.74719 q^{93} -1.60725 q^{94} +7.45784 q^{95} +1.64894 q^{96} +9.30304 q^{97} -0.697801 q^{98} +1.14060 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 7 q^{2} - 36 q^{3} + 45 q^{4} - 36 q^{5} + 7 q^{6} + 2 q^{7} - 24 q^{8} + 36 q^{9}+O(q^{10}) $ 36 * q - 7 * q^2 - 36 * q^3 + 45 * q^4 - 36 * q^5 + 7 * q^6 + 2 * q^7 - 24 * q^8 + 36 * q^9	\( 36 q - 7 q^{2} - 36 q^{3} + 45 q^{4} - 36 q^{5} + 7 q^{6} + 2 q^{7} - 24 q^{8} + 36 q^{9} + 7 q^{10} - q^{11} - 45 q^{12} - 8 q^{13} - 4 q^{14} + 36 q^{15} + 63 q^{16} - 50 q^{17} - 7 q^{18} + 15 q^{19} - 45 q^{20} - 2 q^{21} + 7 q^{22} - 32 q^{23} + 24 q^{24} + 36 q^{25} - 12 q^{26} - 36 q^{27} - 10 q^{28} + 7 q^{29} - 7 q^{30} + 7 q^{31} - 50 q^{32} + q^{33} + 8 q^{34} - 2 q^{35} + 45 q^{36} - 10 q^{37} - 48 q^{38} + 8 q^{39} + 24 q^{40} - 31 q^{41} + 4 q^{42} + 27 q^{43} - 9 q^{44} - 36 q^{45} + 23 q^{46} - 46 q^{47} - 63 q^{48} + 48 q^{49} - 7 q^{50} + 50 q^{51} - 14 q^{52} - 39 q^{53} + 7 q^{54} + q^{55} - 29 q^{56} - 15 q^{57} - 26 q^{58} - 9 q^{59} + 45 q^{60} + 5 q^{61} - 65 q^{62} + 2 q^{63} + 90 q^{64} + 8 q^{65} - 7 q^{66} + 18 q^{67} - 128 q^{68} + 32 q^{69} + 4 q^{70} + 4 q^{71} - 24 q^{72} - 45 q^{73} - 22 q^{74} - 36 q^{75} + 26 q^{76} - 38 q^{77} + 12 q^{78} + 25 q^{79} - 63 q^{80} + 36 q^{81} - 5 q^{82} - 71 q^{83} + 10 q^{84} + 50 q^{85} + 3 q^{86} - 7 q^{87} - 9 q^{88} - 39 q^{89} + 7 q^{90} + 19 q^{91} - 95 q^{92} - 7 q^{93} + 16 q^{94} - 15 q^{95} + 50 q^{96} - 61 q^{97} - 76 q^{98} - q^{99}+O(q^{100}) \) 36 * q - 7 * q^2 - 36 * q^3 + 45 * q^4 - 36 * q^5 + 7 * q^6 + 2 * q^7 - 24 * q^8 + 36 * q^9 + 7 * q^10 - q^11 - 45 * q^12 - 8 * q^13 - 4 * q^14 + 36 * q^15 + 63 * q^16 - 50 * q^17 - 7 * q^18 + 15 * q^19 - 45 * q^20 - 2 * q^21 + 7 * q^22 - 32 * q^23 + 24 * q^24 + 36 * q^25 - 12 * q^26 - 36 * q^27 - 10 * q^28 + 7 * q^29 - 7 * q^30 + 7 * q^31 - 50 * q^32 + q^33 + 8 * q^34 - 2 * q^35 + 45 * q^36 - 10 * q^37 - 48 * q^38 + 8 * q^39 + 24 * q^40 - 31 * q^41 + 4 * q^42 + 27 * q^43 - 9 * q^44 - 36 * q^45 + 23 * q^46 - 46 * q^47 - 63 * q^48 + 48 * q^49 - 7 * q^50 + 50 * q^51 - 14 * q^52 - 39 * q^53 + 7 * q^54 + q^55 - 29 * q^56 - 15 * q^57 - 26 * q^58 - 9 * q^59 + 45 * q^60 + 5 * q^61 - 65 * q^62 + 2 * q^63 + 90 * q^64 + 8 * q^65 - 7 * q^66 + 18 * q^67 - 128 * q^68 + 32 * q^69 + 4 * q^70 + 4 * q^71 - 24 * q^72 - 45 * q^73 - 22 * q^74 - 36 * q^75 + 26 * q^76 - 38 * q^77 + 12 * q^78 + 25 * q^79 - 63 * q^80 + 36 * q^81 - 5 * q^82 - 71 * q^83 + 10 * q^84 + 50 * q^85 + 3 * q^86 - 7 * q^87 - 9 * q^88 - 39 * q^89 + 7 * q^90 + 19 * q^91 - 95 * q^92 - 7 * q^93 + 16 * q^94 - 15 * q^95 + 50 * q^96 - 61 * q^97 - 76 * 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 $

$2$	−0.139206	−0.0984333	−0.0492167	−	0.998788i	$-0.515672\pi$
$2$	−0.139206	−0.0984333	−0.0492167	+	0.998788i	$0.515672\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.98062	−0.990311
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.139206	0.0568305
$7$	−3.46594	−1.31000	−0.655001	−	0.755628i	$-0.727332\pi$
$7$	−3.46594	−1.31000	−0.655001	+	0.755628i	$0.727332\pi$
$8$	0.554125	0.195913
$9$	1.00000	0.333333
$10$	0.139206	0.0440207
$11$	1.14060	0.343903	0.171951	−	0.985105i	$-0.444993\pi$
$11$	1.14060	0.343903	0.171951	+	0.985105i	$0.444993\pi$
$12$	1.98062	0.571756
$13$	2.00508	0.556110	0.278055	−	0.960565i	$-0.410310\pi$
$13$	2.00508	0.556110	0.278055	+	0.960565i	$0.410310\pi$
$14$	0.482479	0.128948
$15$	1.00000	0.258199
$16$	3.88411	0.971027
$17$	0.449203	0.108948	0.0544738	−	0.998515i	$-0.482652\pi$
$17$	0.449203	0.108948	0.0544738	+	0.998515i	$0.482652\pi$
$18$	−0.139206	−0.0328111
$19$	−7.45784	−1.71095	−0.855473	−	0.517847i	$-0.826734\pi$
$19$	−7.45784	−1.71095	−0.855473	+	0.517847i	$0.826734\pi$
$20$	1.98062	0.442880
$21$	3.46594	0.756330
$22$	−0.158778	−0.0338515
$23$	−3.71040	−0.773671	−0.386836	−	0.922149i	$-0.626432\pi$
$23$	−3.71040	−0.773671	−0.386836	+	0.922149i	$0.626432\pi$
$24$	−0.554125	−0.113110
$25$	1.00000	0.200000
$26$	−0.279119	−0.0547397
$27$	−1.00000	−0.192450
$28$	6.86471	1.29731
$29$	−7.06308	−1.31158	−0.655791	−	0.754943i	$-0.727665\pi$
$29$	−7.06308	−1.31158	−0.655791	+	0.754943i	$0.727665\pi$
$30$	−0.139206	−0.0254154
$31$	9.74719	1.75065	0.875324	−	0.483537i	$-0.160648\pi$
$31$	9.74719	1.75065	0.875324	+	0.483537i	$0.160648\pi$
$32$	−1.64894	−0.291494
$33$	−1.14060	−0.198552
$34$	−0.0625316	−0.0107241
$35$	3.46594	0.585851
$36$	−1.98062	−0.330104
$37$	−9.44954	−1.55349	−0.776747	−	0.629813i	$-0.783132\pi$
$37$	−9.44954	−1.55349	−0.776747	+	0.629813i	$0.783132\pi$
$38$	1.03817	0.168414
$39$	−2.00508	−0.321070
$40$	−0.554125	−0.0876149
$41$	5.26961	0.822974	0.411487	−	0.911416i	$-0.365010\pi$
$41$	5.26961	0.822974	0.411487	+	0.911416i	$0.365010\pi$
$42$	−0.482479	−0.0744481
$43$	10.1590	1.54924	0.774620	−	0.632427i	$-0.217941\pi$
$43$	10.1590	1.54924	0.774620	+	0.632427i	$0.217941\pi$
$44$	−2.25909	−0.340571
$45$	−1.00000	−0.149071
$46$	0.516509	0.0761550
$47$	11.5459	1.68414	0.842069	−	0.539370i	$-0.181338\pi$
$47$	11.5459	1.68414	0.842069	+	0.539370i	$0.181338\pi$
$48$	−3.88411	−0.560622
$49$	5.01273	0.716105
$50$	−0.139206	−0.0196867
$51$	−0.449203	−0.0629009
$52$	−3.97131	−0.550721
$53$	2.48188	0.340913	0.170456	−	0.985365i	$-0.445476\pi$
$53$	2.48188	0.340913	0.170456	+	0.985365i	$0.445476\pi$
$54$	0.139206	0.0189435
$55$	−1.14060	−0.153798
$56$	−1.92057	−0.256646
$57$	7.45784	0.987816
$58$	0.983222	0.129103
$59$	3.76373	0.489996	0.244998	−	0.969524i	$-0.421213\pi$
$59$	3.76373	0.489996	0.244998	+	0.969524i	$0.421213\pi$
$60$	−1.98062	−0.255697
$61$	10.6609	1.36499	0.682497	−	0.730888i	$-0.260894\pi$
$61$	10.6609	1.36499	0.682497	+	0.730888i	$0.260894\pi$
$62$	−1.35687	−0.172322
$63$	−3.46594	−0.436667
$64$	−7.53867	−0.942334
$65$	−2.00508	−0.248700
$66$	0.158778	0.0195442
$67$	−2.31617	−0.282965	−0.141482	−	0.989941i	$-0.545187\pi$
$67$	−2.31617	−0.282965	−0.141482	+	0.989941i	$0.545187\pi$
$68$	−0.889700	−0.107892
$69$	3.71040	0.446679
$70$	−0.482479	−0.0576672
$71$	2.65392	0.314963	0.157481	−	0.987522i	$-0.449663\pi$
$71$	2.65392	0.314963	0.157481	+	0.987522i	$0.449663\pi$
$72$	0.554125	0.0653043
$73$	−9.32609	−1.09154	−0.545768	−	0.837936i	$-0.683762\pi$
$73$	−9.32609	−1.09154	−0.545768	+	0.837936i	$0.683762\pi$
$74$	1.31543	0.152916
$75$	−1.00000	−0.115470
$76$	14.7712	1.69437
$77$	−3.95324	−0.450513
$78$	0.279119	0.0316040
$79$	−4.78534	−0.538392	−0.269196	−	0.963085i	$-0.586758\pi$
$79$	−4.78534	−0.538392	−0.269196	+	0.963085i	$0.586758\pi$
$80$	−3.88411	−0.434256
$81$	1.00000	0.111111
$82$	−0.733560	−0.0810081
$83$	−3.53744	−0.388284	−0.194142	−	0.980973i	$-0.562192\pi$
$83$	−3.53744	−0.388284	−0.194142	+	0.980973i	$0.562192\pi$
$84$	−6.86471	−0.749002
$85$	−0.449203	−0.0487229
$86$	−1.41420	−0.152497
$87$	7.06308	0.757242
$88$	0.632034	0.0673750
$89$	12.1941	1.29257	0.646287	−	0.763095i	$-0.276321\pi$
$89$	12.1941	1.29257	0.646287	+	0.763095i	$0.276321\pi$
$90$	0.139206	0.0146736
$91$	−6.94949	−0.728505
$92$	7.34889	0.766175
$93$	−9.74719	−1.01074
$94$	−1.60725	−0.165775
$95$	7.45784	0.765159
$96$	1.64894	0.168294
$97$	9.30304	0.944580	0.472290	−	0.881443i	$-0.343427\pi$
$97$	9.30304	0.944580	0.472290	+	0.881443i	$0.343427\pi$
$98$	−0.697801	−0.0704886
$99$	1.14060	0.114634
$100$	−1.98062	−0.198062
$101$	13.2398	1.31741	0.658704	−	0.752402i	$-0.271105\pi$
$101$	13.2398	1.31741	0.658704	+	0.752402i	$0.271105\pi$
$102$	0.0625316	0.00619155
$103$	11.8188	1.16454	0.582269	−	0.812996i	$-0.302165\pi$
$103$	11.8188	1.16454	0.582269	+	0.812996i	$0.302165\pi$
$104$	1.11107	0.108949
$105$	−3.46594	−0.338241
$106$	−0.345492	−0.0335572
$107$	13.6498	1.31957	0.659787	−	0.751452i	$-0.270646\pi$
$107$	13.6498	1.31957	0.659787	+	0.751452i	$0.270646\pi$
$108$	1.98062	0.190585
$109$	−10.8952	−1.04357	−0.521784	−	0.853078i	$-0.674733\pi$
$109$	−10.8952	−1.04357	−0.521784	+	0.853078i	$0.674733\pi$
$110$	0.158778	0.0151388
$111$	9.44954	0.896910
$112$	−13.4621	−1.27205
$113$	−0.792157	−0.0745199	−0.0372599	−	0.999306i	$-0.511863\pi$
$113$	−0.792157	−0.0745199	−0.0372599	+	0.999306i	$0.511863\pi$
$114$	−1.03817	−0.0972340
$115$	3.71040	0.345996
$116$	13.9893	1.29887
$117$	2.00508	0.185370
$118$	−0.523933	−0.0482319
$119$	−1.55691	−0.142722
$120$	0.554125	0.0505845
$121$	−9.69904	−0.881731
$122$	−1.48406	−0.134361
$123$	−5.26961	−0.475144
$124$	−19.3055	−1.73369
$125$	−1.00000	−0.0894427
$126$	0.482479	0.0429826
$127$	2.40394	0.213315	0.106658	−	0.994296i	$-0.465985\pi$
$127$	2.40394	0.213315	0.106658	+	0.994296i	$0.465985\pi$
$128$	4.34731	0.384251
$129$	−10.1590	−0.894454
$130$	0.279119	0.0244804
$131$	−8.46442	−0.739540	−0.369770	−	0.929123i	$-0.620563\pi$
$131$	−8.46442	−0.739540	−0.369770	+	0.929123i	$0.620563\pi$
$132$	2.25909	0.196629
$133$	25.8484	2.24134
$134$	0.322424	0.0278532
$135$	1.00000	0.0860663
$136$	0.248915	0.0213442
$137$	−5.24312	−0.447950	−0.223975	−	0.974595i	$-0.571903\pi$
$137$	−5.24312	−0.447950	−0.223975	+	0.974595i	$0.571903\pi$
$138$	−0.516509	−0.0439681
$139$	17.2030	1.45914	0.729572	−	0.683904i	$-0.239719\pi$
$139$	17.2030	1.45914	0.729572	+	0.683904i	$0.239719\pi$
$140$	−6.86471	−0.580174
$141$	−11.5459	−0.972337
$142$	−0.369441	−0.0310028
$143$	2.28699	0.191248
$144$	3.88411	0.323676
$145$	7.06308	0.586557
$146$	1.29824	0.107444
$147$	−5.01273	−0.413443
$148$	18.7160	1.53844
$149$	20.9518	1.71644	0.858219	−	0.513284i	$-0.171571\pi$
$149$	20.9518	1.71644	0.858219	+	0.513284i	$0.171571\pi$
$150$	0.139206	0.0113661
$151$	−19.6538	−1.59940	−0.799701	−	0.600399i	$-0.795009\pi$
$151$	−19.6538	−1.59940	−0.799701	+	0.600399i	$0.795009\pi$
$152$	−4.13258	−0.335197
$153$	0.449203	0.0363159
$154$	0.550313	0.0443455
$155$	−9.74719	−0.782913
$156$	3.97131	0.317959
$157$	−8.33762	−0.665414	−0.332707	−	0.943030i	$-0.607962\pi$
$157$	−8.33762	−0.665414	−0.332707	+	0.943030i	$0.607962\pi$
$158$	0.666146	0.0529958
$159$	−2.48188	−0.196826
$160$	1.64894	0.130360
$161$	12.8600	1.01351
$162$	−0.139206	−0.0109370
$163$	−14.5483	−1.13951	−0.569754	−	0.821815i	$-0.692962\pi$
$163$	−14.5483	−1.13951	−0.569754	+	0.821815i	$0.692962\pi$
$164$	−10.4371	−0.815000
$165$	1.14060	0.0887953
$166$	0.492431	0.0382201
$167$	−10.0698	−0.779223	−0.389612	−	0.920979i	$-0.627391\pi$
$167$	−10.0698	−0.779223	−0.389612	+	0.920979i	$0.627391\pi$
$168$	1.92057	0.148175
$169$	−8.97965	−0.690742
$170$	0.0625316	0.00479595
$171$	−7.45784	−0.570316
$172$	−20.1212	−1.53423
$173$	−20.3844	−1.54979	−0.774897	−	0.632088i	$-0.782198\pi$
$173$	−20.3844	−1.54979	−0.774897	+	0.632088i	$0.782198\pi$
$174$	−0.983222	−0.0745378
$175$	−3.46594	−0.262000
$176$	4.43020	0.333939
$177$	−3.76373	−0.282899
$178$	−1.69749	−0.127232
$179$	−6.03127	−0.450798	−0.225399	−	0.974267i	$-0.572369\pi$
$179$	−6.03127	−0.450798	−0.225399	+	0.974267i	$0.572369\pi$
$180$	1.98062	0.147627
$181$	15.5132	1.15309	0.576543	−	0.817067i	$-0.304401\pi$
$181$	15.5132	1.15309	0.576543	+	0.817067i	$0.304401\pi$
$182$	0.967409	0.0717091
$183$	−10.6609	−0.788080
$184$	−2.05603	−0.151572
$185$	9.44954	0.694744
$186$	1.35687	0.0994902
$187$	0.512359	0.0374674
$188$	−22.8680	−1.66782
$189$	3.46594	0.252110
$190$	−1.03817	−0.0753171
$191$	−21.3457	−1.54452	−0.772261	−	0.635306i	$-0.780874\pi$
$191$	−21.3457	−1.54452	−0.772261	+	0.635306i	$0.780874\pi$
$192$	7.53867	0.544057
$193$	−15.0517	−1.08344	−0.541721	−	0.840558i	$-0.682227\pi$
$193$	−15.0517	−1.08344	−0.541721	+	0.840558i	$0.682227\pi$
$194$	−1.29504	−0.0929782
$195$	2.00508	0.143587
$196$	−9.92833	−0.709166
$197$	−11.2019	−0.798100	−0.399050	−	0.916929i	$-0.630660\pi$
$197$	−11.2019	−0.798100	−0.399050	+	0.916929i	$0.630660\pi$
$198$	−0.158778	−0.0112838
$199$	4.06383	0.288078	0.144039	−	0.989572i	$-0.453991\pi$
$199$	4.06383	0.288078	0.144039	+	0.989572i	$0.453991\pi$
$200$	0.554125	0.0391826
$201$	2.31617	0.163370
$202$	−1.84306	−0.129677
$203$	24.4802	1.71817
$204$	0.889700	0.0622915
$205$	−5.26961	−0.368045
$206$	−1.64524	−0.114629
$207$	−3.71040	−0.257890
$208$	7.78795	0.539997
$209$	−8.50639	−0.588399
$210$	0.482479	0.0332942
$211$	3.65063	0.251320	0.125660	−	0.992073i	$-0.459895\pi$
$211$	3.65063	0.251320	0.125660	+	0.992073i	$0.459895\pi$
$212$	−4.91567	−0.337609
$213$	−2.65392	−0.181844
$214$	−1.90013	−0.129890
$215$	−10.1590	−0.692841
$216$	−0.554125	−0.0377035
$217$	−33.7832	−2.29335
$218$	1.51667	0.102722
$219$	9.32609	0.630198
$220$	2.25909	0.152308
$221$	0.900688	0.0605868
$222$	−1.31543	−0.0882859
$223$	−1.17181	−0.0784705	−0.0392352	−	0.999230i	$-0.512492\pi$
$223$	−1.17181	−0.0784705	−0.0392352	+	0.999230i	$0.512492\pi$
$224$	5.71513	0.381858
$225$	1.00000	0.0666667
$226$	0.110273	0.00733524
$227$	0.938845	0.0623133	0.0311567	−	0.999515i	$-0.490081\pi$
$227$	0.938845	0.0623133	0.0311567	+	0.999515i	$0.490081\pi$
$228$	−14.7712	−0.978244
$229$	0.720654	0.0476222	0.0238111	−	0.999716i	$-0.492420\pi$
$229$	0.720654	0.0476222	0.0238111	+	0.999716i	$0.492420\pi$
$230$	−0.516509	−0.0340576
$231$	3.95324	0.260104
$232$	−3.91383	−0.256956
$233$	−15.6787	−1.02715	−0.513574	−	0.858045i	$-0.671679\pi$
$233$	−15.6787	−1.02715	−0.513574	+	0.858045i	$0.671679\pi$
$234$	−0.279119	−0.0182466
$235$	−11.5459	−0.753169
$236$	−7.45452	−0.485248
$237$	4.78534	0.310841
$238$	0.216731	0.0140486
$239$	1.33373	0.0862717	0.0431358	−	0.999069i	$-0.486265\pi$
$239$	1.33373	0.0862717	0.0431358	+	0.999069i	$0.486265\pi$
$240$	3.88411	0.250718
$241$	−13.4726	−0.867848	−0.433924	−	0.900950i	$-0.642871\pi$
$241$	−13.4726	−0.867848	−0.433924	+	0.900950i	$0.642871\pi$
$242$	1.35016	0.0867917
$243$	−1.00000	−0.0641500
$244$	−21.1153	−1.35177
$245$	−5.01273	−0.320252
$246$	0.733560	0.0467701
$247$	−14.9536	−0.951474
$248$	5.40117	0.342974
$249$	3.53744	0.224176
$250$	0.139206	0.00880415
$251$	0.447003	0.0282146	0.0141073	−	0.999900i	$-0.495509\pi$
$251$	0.447003	0.0282146	0.0141073	+	0.999900i	$0.495509\pi$
$252$	6.86471	0.432436
$253$	−4.23207	−0.266068
$254$	−0.334643	−0.0209974
$255$	0.449203	0.0281302
$256$	14.4722	0.904511
$257$	−13.5504	−0.845254	−0.422627	−	0.906304i	$-0.638892\pi$
$257$	−13.5504	−0.845254	−0.422627	+	0.906304i	$0.638892\pi$
$258$	1.41420	0.0880441
$259$	32.7515	2.03508
$260$	3.97131	0.246290
$261$	−7.06308	−0.437194
$262$	1.17830	0.0727954
$263$	−2.40696	−0.148420	−0.0742098	−	0.997243i	$-0.523643\pi$
$263$	−2.40696	−0.148420	−0.0742098	+	0.997243i	$0.523643\pi$
$264$	−0.632034	−0.0388990
$265$	−2.48188	−0.152461
$266$	−3.59825	−0.220623
$267$	−12.1941	−0.746267
$268$	4.58745	0.280223
$269$	21.2390	1.29496	0.647482	−	0.762081i	$-0.275822\pi$
$269$	21.2390	1.29496	0.647482	+	0.762081i	$0.275822\pi$
$270$	−0.139206	−0.00847179
$271$	18.3939	1.11735	0.558676	−	0.829386i	$-0.311310\pi$
$271$	18.3939	1.11735	0.558676	+	0.829386i	$0.311310\pi$
$272$	1.74475	0.105791
$273$	6.94949	0.420602
$274$	0.729872	0.0440932
$275$	1.14060	0.0687805
$276$	−7.34889	−0.442351
$277$	−7.84720	−0.471493	−0.235746	−	0.971815i	$-0.575753\pi$
$277$	−7.84720	−0.471493	−0.235746	+	0.971815i	$0.575753\pi$
$278$	−2.39476	−0.143628
$279$	9.74719	0.583549
$280$	1.92057	0.114776
$281$	−7.18305	−0.428505	−0.214252	−	0.976778i	$-0.568732\pi$
$281$	−7.18305	−0.428505	−0.214252	+	0.976778i	$0.568732\pi$
$282$	1.60725	0.0957104
$283$	−5.59063	−0.332328	−0.166164	−	0.986098i	$-0.553138\pi$
$283$	−5.59063	−0.332328	−0.166164	+	0.986098i	$0.553138\pi$
$284$	−5.25642	−0.311911
$285$	−7.45784	−0.441765
$286$	−0.318362	−0.0188251
$287$	−18.2641	−1.07810
$288$	−1.64894	−0.0971648
$289$	−16.7982	−0.988130
$290$	−0.983222	−0.0577368
$291$	−9.30304	−0.545354
$292$	18.4714	1.08096
$293$	−33.7066	−1.96916	−0.984579	−	0.174940i	$-0.944027\pi$
$293$	−33.7066	−1.96916	−0.984579	+	0.174940i	$0.944027\pi$
$294$	0.697801	0.0406966
$295$	−3.76373	−0.219133
$296$	−5.23623	−0.304350
$297$	−1.14060	−0.0661841
$298$	−2.91661	−0.168955
$299$	−7.43965	−0.430246
$300$	1.98062	0.114351
$301$	−35.2106	−2.02951
$302$	2.73592	0.157434
$303$	−13.2398	−0.760606
$304$	−28.9671	−1.66137
$305$	−10.6609	−0.610444
$306$	−0.0625316	−0.00357469
$307$	13.3899	0.764200	0.382100	−	0.924121i	$-0.375201\pi$
$307$	13.3899	0.764200	0.382100	+	0.924121i	$0.375201\pi$
$308$	7.82987	0.446148
$309$	−11.8188	−0.672346
$310$	1.35687	0.0770648
$311$	−32.9144	−1.86640	−0.933201	−	0.359354i	$-0.882997\pi$
$311$	−32.9144	−1.86640	−0.933201	+	0.359354i	$0.882997\pi$
$312$	−1.11107	−0.0629018
$313$	−25.2191	−1.42547	−0.712735	−	0.701433i	$-0.752544\pi$
$313$	−25.2191	−1.42547	−0.712735	+	0.701433i	$0.752544\pi$
$314$	1.16064	0.0654990
$315$	3.46594	0.195284
$316$	9.47794	0.533176
$317$	−4.10381	−0.230493	−0.115247	−	0.993337i	$-0.536766\pi$
$317$	−4.10381	−0.230493	−0.115247	+	0.993337i	$0.536766\pi$
$318$	0.345492	0.0193742
$319$	−8.05612	−0.451056
$320$	7.53867	0.421424
$321$	−13.6498	−0.761857
$322$	−1.79019	−0.0997632
$323$	−3.35008	−0.186404
$324$	−1.98062	−0.110035
$325$	2.00508	0.111222
$326$	2.02520	0.112166
$327$	10.8952	0.602504
$328$	2.92002	0.161231
$329$	−40.0173	−2.20622
$330$	−0.158778	−0.00874042
$331$	27.7168	1.52346	0.761728	−	0.647897i	$-0.224351\pi$
$331$	27.7168	1.52346	0.761728	+	0.647897i	$0.224351\pi$
$332$	7.00632	0.384522
$333$	−9.44954	−0.517831
$334$	1.40177	0.0767016
$335$	2.31617	0.126546
$336$	13.4621	0.734416
$337$	−2.12125	−0.115552	−0.0577759	−	0.998330i	$-0.518401\pi$
$337$	−2.12125	−0.115552	−0.0577759	+	0.998330i	$0.518401\pi$
$338$	1.25002	0.0679920
$339$	0.792157	0.0430241
$340$	0.889700	0.0482508
$341$	11.1176	0.602052
$342$	1.03817	0.0561381
$343$	6.88775	0.371904
$344$	5.62938	0.303516
$345$	−3.71040	−0.199761
$346$	2.83762	0.152551
$347$	21.7815	1.16929	0.584647	−	0.811288i	$-0.301233\pi$
$347$	21.7815	1.16929	0.584647	+	0.811288i	$0.301233\pi$
$348$	−13.9893	−0.749905
$349$	26.6643	1.42731	0.713653	−	0.700500i	$-0.247040\pi$
$349$	26.6643	1.42731	0.713653	+	0.700500i	$0.247040\pi$
$350$	0.482479	0.0257896
$351$	−2.00508	−0.107023
$352$	−1.88078	−0.100246
$353$	−12.0633	−0.642063	−0.321031	−	0.947069i	$-0.604030\pi$
$353$	−12.0633	−0.642063	−0.321031	+	0.947069i	$0.604030\pi$
$354$	0.523933	0.0278467
$355$	−2.65392	−0.140856
$356$	−24.1519	−1.28005
$357$	1.55691	0.0824003
$358$	0.839588	0.0443736
$359$	−20.3507	−1.07407	−0.537035	−	0.843560i	$-0.680456\pi$
$359$	−20.3507	−1.07407	−0.537035	+	0.843560i	$0.680456\pi$
$360$	−0.554125	−0.0292050
$361$	36.6194	1.92734
$362$	−2.15953	−0.113502
$363$	9.69904	0.509068
$364$	13.7643	0.721446
$365$	9.32609	0.488150
$366$	1.48406	0.0775733
$367$	16.2471	0.848091	0.424046	−	0.905641i	$-0.360610\pi$
$367$	16.2471	0.848091	0.424046	+	0.905641i	$0.360610\pi$
$368$	−14.4116	−0.751255
$369$	5.26961	0.274325
$370$	−1.31543	−0.0683859
$371$	−8.60205	−0.446596
$372$	19.3055	1.00094
$373$	−8.10162	−0.419486	−0.209743	−	0.977757i	$-0.567263\pi$
$373$	−8.10162	−0.419486	−0.209743	+	0.977757i	$0.567263\pi$
$374$	−0.0713233	−0.00368804
$375$	1.00000	0.0516398
$376$	6.39786	0.329944
$377$	−14.1621	−0.729383
$378$	−0.482479	−0.0248160
$379$	13.2787	0.682079	0.341040	−	0.940049i	$-0.389221\pi$
$379$	13.2787	0.682079	0.341040	+	0.940049i	$0.389221\pi$
$380$	−14.7712	−0.757745
$381$	−2.40394	−0.123158
$382$	2.97145	0.152032
$383$	12.5219	0.639841	0.319921	−	0.947444i	$-0.396344\pi$
$383$	12.5219	0.639841	0.319921	+	0.947444i	$0.396344\pi$
$384$	−4.34731	−0.221848
$385$	3.95324	0.201476
$386$	2.09528	0.106647
$387$	10.1590	0.516413
$388$	−18.4258	−0.935428
$389$	−5.73853	−0.290955	−0.145478	−	0.989362i	$-0.546472\pi$
$389$	−5.73853	−0.290955	−0.145478	+	0.989362i	$0.546472\pi$
$390$	−0.279119	−0.0141337
$391$	−1.66672	−0.0842896
$392$	2.77768	0.140294
$393$	8.46442	0.426974
$394$	1.55936	0.0785597
$395$	4.78534	0.240776
$396$	−2.25909	−0.113524
$397$	18.5450	0.930746	0.465373	−	0.885115i	$-0.345920\pi$
$397$	18.5450	0.930746	0.465373	+	0.885115i	$0.345920\pi$
$398$	−0.565709	−0.0283564
$399$	−25.8484	−1.29404
$400$	3.88411	0.194205
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	−0.322424	−0.0160810
$403$	19.5439	0.973552
$404$	−26.2230	−1.30464
$405$	−1.00000	−0.0496904
$406$	−3.40779	−0.169126
$407$	−10.7781	−0.534251
$408$	−0.248915	−0.0123231
$409$	12.3008	0.608235	0.304117	−	0.952635i	$-0.401638\pi$
$409$	12.3008	0.608235	0.304117	+	0.952635i	$0.401638\pi$
$410$	0.733560	0.0362279
$411$	5.24312	0.258624
$412$	−23.4085	−1.15325
$413$	−13.0449	−0.641895
$414$	0.516509	0.0253850
$415$	3.53744	0.173646
$416$	−3.30626	−0.162103
$417$	−17.2030	−0.842437
$418$	1.18414	0.0579181
$419$	−2.34259	−0.114443	−0.0572216	−	0.998362i	$-0.518224\pi$
$419$	−2.34259	−0.114443	−0.0572216	+	0.998362i	$0.518224\pi$
$420$	6.86471	0.334964
$421$	−30.5260	−1.48775	−0.743874	−	0.668320i	$-0.767014\pi$
$421$	−30.5260	−1.48775	−0.743874	+	0.668320i	$0.767014\pi$
$422$	−0.508189	−0.0247383
$423$	11.5459	0.561379
$424$	1.37527	0.0667892
$425$	0.449203	0.0217895
$426$	0.369441	0.0178995
$427$	−36.9502	−1.78814
$428$	−27.0351	−1.30679
$429$	−2.28699	−0.110417
$430$	1.41420	0.0681986
$431$	25.5258	1.22953	0.614767	−	0.788709i	$-0.289250\pi$
$431$	25.5258	1.22953	0.614767	+	0.788709i	$0.289250\pi$
$432$	−3.88411	−0.186874
$433$	−3.29015	−0.158114	−0.0790572	−	0.996870i	$-0.525191\pi$
$433$	−3.29015	−0.158114	−0.0790572	+	0.996870i	$0.525191\pi$
$434$	4.70281	0.225742
$435$	−7.06308	−0.338649
$436$	21.5792	1.03346
$437$	27.6716	1.32371
$438$	−1.29824	−0.0620325
$439$	14.0837	0.672179	0.336090	−	0.941830i	$-0.390895\pi$
$439$	14.0837	0.672179	0.336090	+	0.941830i	$0.390895\pi$
$440$	−0.632034	−0.0301310
$441$	5.01273	0.238702
$442$	−0.125381	−0.00596376
$443$	37.6091	1.78686	0.893430	−	0.449202i	$-0.148292\pi$
$443$	37.6091	1.78686	0.893430	+	0.449202i	$0.148292\pi$
$444$	−18.7160	−0.888220
$445$	−12.1941	−0.578056
$446$	0.163123	0.00772411
$447$	−20.9518	−0.990986
$448$	26.1286	1.23446
$449$	2.31112	0.109068	0.0545342	−	0.998512i	$-0.482633\pi$
$449$	2.31112	0.109068	0.0545342	+	0.998512i	$0.482633\pi$
$450$	−0.139206	−0.00656222
$451$	6.01049	0.283023
$452$	1.56896	0.0737979
$453$	19.6538	0.923415
$454$	−0.130693	−0.00613371
$455$	6.94949	0.325797
$456$	4.13258	0.193526
$457$	−16.2912	−0.762070	−0.381035	−	0.924561i	$-0.624432\pi$
$457$	−16.2912	−0.762070	−0.381035	+	0.924561i	$0.624432\pi$
$458$	−0.100319	−0.00468761
$459$	−0.449203	−0.0209670
$460$	−7.34889	−0.342644
$461$	18.9316	0.881732	0.440866	−	0.897573i	$-0.354671\pi$
$461$	18.9316	0.881732	0.440866	+	0.897573i	$0.354671\pi$
$462$	−0.550313	−0.0256029
$463$	39.5473	1.83792	0.918959	−	0.394353i	$-0.129031\pi$
$463$	39.5473	1.83792	0.918959	+	0.394353i	$0.129031\pi$
$464$	−27.4338	−1.27358
$465$	9.74719	0.452015
$466$	2.18257	0.101106
$467$	−1.80896	−0.0837085	−0.0418543	−	0.999124i	$-0.513327\pi$
$467$	−1.80896	−0.0837085	−0.0418543	+	0.999124i	$0.513327\pi$
$468$	−3.97131	−0.183574
$469$	8.02770	0.370685
$470$	1.60725	0.0741370
$471$	8.33762	0.384177
$472$	2.08558	0.0959965
$473$	11.5874	0.532788
$474$	−0.666146	−0.0305971
$475$	−7.45784	−0.342189
$476$	3.08365	0.141339
$477$	2.48188	0.113638
$478$	−0.185663	−0.00849201
$479$	−29.0507	−1.32736	−0.663681	−	0.748016i	$-0.731007\pi$
$479$	−29.0507	−1.32736	−0.663681	+	0.748016i	$0.731007\pi$
$480$	−1.64894	−0.0752635
$481$	−18.9471	−0.863913
$482$	1.87547	0.0854251
$483$	−12.8600	−0.585151
$484$	19.2101	0.873188
$485$	−9.30304	−0.422429
$486$	0.139206	0.00631450
$487$	−5.58992	−0.253303	−0.126652	−	0.991947i	$-0.540423\pi$
$487$	−5.58992	−0.253303	−0.126652	+	0.991947i	$0.540423\pi$
$488$	5.90750	0.267420
$489$	14.5483	0.657895
$490$	0.697801	0.0315234
$491$	20.6290	0.930975	0.465487	−	0.885054i	$-0.345879\pi$
$491$	20.6290	0.930975	0.465487	+	0.885054i	$0.345879\pi$
$492$	10.4371	0.470541
$493$	−3.17275	−0.142894
$494$	2.08163	0.0936568
$495$	−1.14060	−0.0512660
$496$	37.8591	1.69993
$497$	−9.19833	−0.412602
$498$	−0.492431	−0.0220664
$499$	−5.20447	−0.232984	−0.116492	−	0.993192i	$-0.537165\pi$
$499$	−5.20447	−0.232984	−0.116492	+	0.993192i	$0.537165\pi$
$500$	1.98062	0.0885761
$501$	10.0698	0.449885
$502$	−0.0622254	−0.00277725
$503$	−2.43248	−0.108459	−0.0542296	−	0.998528i	$-0.517270\pi$
$503$	−2.43248	−0.108459	−0.0542296	+	0.998528i	$0.517270\pi$
$504$	−1.92057	−0.0855488
$505$	−13.2398	−0.589163
$506$	0.589128	0.0261899
$507$	8.97965	0.398800
$508$	−4.76130	−0.211249
$509$	−8.97355	−0.397746	−0.198873	−	0.980025i	$-0.563728\pi$
$509$	−8.97355	−0.397746	−0.198873	+	0.980025i	$0.563728\pi$
$510$	−0.0625316	−0.00276895
$511$	32.3236	1.42991
$512$	−10.7092	−0.473285
$513$	7.45784	0.329272
$514$	1.88630	0.0832011
$515$	−11.8188	−0.520797
$516$	20.1212	0.885787
$517$	13.1692	0.579179
$518$	−4.55920	−0.200320
$519$	20.3844	0.894774
$520$	−1.11107	−0.0487235
$521$	−22.3938	−0.981089	−0.490545	−	0.871416i	$-0.663202\pi$
$521$	−22.3938	−0.981089	−0.490545	+	0.871416i	$0.663202\pi$
$522$	0.983222	0.0430344
$523$	−10.2211	−0.446940	−0.223470	−	0.974711i	$-0.571738\pi$
$523$	−10.2211	−0.446940	−0.223470	+	0.974711i	$0.571738\pi$
$524$	16.7648	0.732374
$525$	3.46594	0.151266
$526$	0.335063	0.0146094
$527$	4.37846	0.190729
$528$	−4.43020	−0.192800
$529$	−9.23296	−0.401433
$530$	0.345492	0.0150072
$531$	3.76373	0.163332
$532$	−51.1960	−2.21963
$533$	10.5660	0.457664
$534$	1.69749	0.0734576
$535$	−13.6498	−0.590132
$536$	−1.28345	−0.0554365
$537$	6.03127	0.260269
$538$	−2.95659	−0.127468
$539$	5.71750	0.246270
$540$	−1.98062	−0.0852324
$541$	8.01155	0.344444	0.172222	−	0.985058i	$-0.444905\pi$
$541$	8.01155	0.344444	0.172222	+	0.985058i	$0.444905\pi$
$542$	−2.56054	−0.109985
$543$	−15.5132	−0.665735
$544$	−0.740708	−0.0317576
$545$	10.8952	0.466698
$546$	−0.967409	−0.0414013
$547$	22.2080	0.949547	0.474774	−	0.880108i	$-0.342530\pi$
$547$	22.2080	0.949547	0.474774	+	0.880108i	$0.342530\pi$
$548$	10.3846	0.443609
$549$	10.6609	0.454998
$550$	−0.158778	−0.00677030
$551$	52.6753	2.24405
$552$	2.05603	0.0875103
$553$	16.5857	0.705295
$554$	1.09238	0.0464106
$555$	−9.44954	−0.401110
$556$	−34.0727	−1.44501
$557$	8.11912	0.344018	0.172009	−	0.985095i	$-0.444974\pi$
$557$	8.11912	0.344018	0.172009	+	0.985095i	$0.444974\pi$
$558$	−1.35687	−0.0574407
$559$	20.3697	0.861547
$560$	13.4621	0.568876
$561$	−0.512359	−0.0216318
$562$	0.999922	0.0421792
$563$	−44.1571	−1.86100	−0.930499	−	0.366294i	$-0.880626\pi$
$563$	−44.1571	−1.86100	−0.930499	+	0.366294i	$0.880626\pi$
$564$	22.8680	0.962916
$565$	0.792157	0.0333263
$566$	0.778248	0.0327122
$567$	−3.46594	−0.145556
$568$	1.47061	0.0617052
$569$	13.1454	0.551085	0.275542	−	0.961289i	$-0.411143\pi$
$569$	13.1454	0.551085	0.275542	+	0.961289i	$0.411143\pi$
$570$	1.03817	0.0434844
$571$	−29.0965	−1.21765	−0.608826	−	0.793304i	$-0.708359\pi$
$571$	−29.0965	−1.21765	−0.608826	+	0.793304i	$0.708359\pi$
$572$	−4.52966	−0.189395
$573$	21.3457	0.891730
$574$	2.54247	0.106121
$575$	−3.71040	−0.154734
$576$	−7.53867	−0.314111
$577$	−16.2508	−0.676531	−0.338265	−	0.941051i	$-0.609840\pi$
$577$	−16.2508	−0.676531	−0.338265	+	0.941051i	$0.609840\pi$
$578$	2.33841	0.0972650
$579$	15.0517	0.625526
$580$	−13.9893	−0.580874
$581$	12.2605	0.508653
$582$	1.29504	0.0536810
$583$	2.83082	0.117241
$584$	−5.16782	−0.213846
$585$	−2.00508	−0.0828999
$586$	4.69215	0.193831
$587$	−11.4729	−0.473538	−0.236769	−	0.971566i	$-0.576089\pi$
$587$	−11.4729	−0.473538	−0.236769	+	0.971566i	$0.576089\pi$
$588$	9.92833	0.409437
$589$	−72.6930	−2.99526
$590$	0.523933	0.0215700
$591$	11.2019	0.460783
$592$	−36.7030	−1.50848
$593$	−28.7424	−1.18031	−0.590154	−	0.807291i	$-0.700933\pi$
$593$	−28.7424	−1.18031	−0.590154	+	0.807291i	$0.700933\pi$
$594$	0.158778	0.00651472
$595$	1.55691	0.0638270
$596$	−41.4976	−1.69981
$597$	−4.06383	−0.166322
$598$	1.03564	0.0423506
$599$	−26.7816	−1.09427	−0.547134	−	0.837045i	$-0.684281\pi$
$599$	−26.7816	−1.09427	−0.547134	+	0.837045i	$0.684281\pi$
$600$	−0.554125	−0.0226221
$601$	−23.1014	−0.942326	−0.471163	−	0.882046i	$-0.656166\pi$
$601$	−23.1014	−0.942326	−0.471163	+	0.882046i	$0.656166\pi$
$602$	4.90152	0.199771
$603$	−2.31617	−0.0943217
$604$	38.9267	1.58390
$605$	9.69904	0.394322
$606$	1.84306	0.0748690
$607$	−14.5809	−0.591821	−0.295911	−	0.955216i	$-0.595623\pi$
$607$	−14.5809	−0.591821	−0.295911	+	0.955216i	$0.595623\pi$
$608$	12.2975	0.498731
$609$	−24.4802	−0.991988
$610$	1.48406	0.0600880
$611$	23.1504	0.936565
$612$	−0.889700	−0.0359640
$613$	8.81807	0.356158	0.178079	−	0.984016i	$-0.443012\pi$
$613$	8.81807	0.356158	0.178079	+	0.984016i	$0.443012\pi$
$614$	−1.86395	−0.0752228
$615$	5.26961	0.212491
$616$	−2.19059	−0.0882614
$617$	−29.5084	−1.18796	−0.593981	−	0.804479i	$-0.702445\pi$
$617$	−29.5084	−1.18796	−0.593981	+	0.804479i	$0.702445\pi$
$618$	1.64524	0.0661813
$619$	12.8294	0.515658	0.257829	−	0.966191i	$-0.416993\pi$
$619$	12.8294	0.515658	0.257829	+	0.966191i	$0.416993\pi$
$620$	19.3055	0.775328
$621$	3.71040	0.148893
$622$	4.58187	0.183716
$623$	−42.2640	−1.69327
$624$	−7.78795	−0.311768
$625$	1.00000	0.0400000
$626$	3.51065	0.140314
$627$	8.50639	0.339712
$628$	16.5137	0.658967
$629$	−4.24476	−0.169249
$630$	−0.482479	−0.0192224
$631$	14.8507	0.591195	0.295598	−	0.955313i	$-0.404481\pi$
$631$	14.8507	0.591195	0.295598	+	0.955313i	$0.404481\pi$
$632$	−2.65168	−0.105478
$633$	−3.65063	−0.145100
$634$	0.571274	0.0226882
$635$	−2.40394	−0.0953976
$636$	4.91567	0.194919
$637$	10.0509	0.398233
$638$	1.12146	0.0443990
$639$	2.65392	0.104988
$640$	−4.34731	−0.171842
$641$	13.4116	0.529725	0.264862	−	0.964286i	$-0.414673\pi$
$641$	13.4116	0.529725	0.264862	+	0.964286i	$0.414673\pi$
$642$	1.90013	0.0749921
$643$	−29.2354	−1.15293	−0.576465	−	0.817122i	$-0.695568\pi$
$643$	−29.2354	−1.15293	−0.576465	+	0.817122i	$0.695568\pi$
$644$	−25.4708	−1.00369
$645$	10.1590	0.400012
$646$	0.466351	0.0183483
$647$	−32.5624	−1.28016	−0.640080	−	0.768308i	$-0.721099\pi$
$647$	−32.5624	−1.28016	−0.640080	+	0.768308i	$0.721099\pi$
$648$	0.554125	0.0217681
$649$	4.29289	0.168511
$650$	−0.279119	−0.0109479
$651$	33.7832	1.32407
$652$	28.8146	1.12847
$653$	−28.6081	−1.11952	−0.559761	−	0.828654i	$-0.689107\pi$
$653$	−28.6081	−1.11952	−0.559761	+	0.828654i	$0.689107\pi$
$654$	−1.51667	−0.0593065
$655$	8.46442	0.330732
$656$	20.4677	0.799130
$657$	−9.32609	−0.363845
$658$	5.57063	0.217166
$659$	−25.7770	−1.00413	−0.502064	−	0.864830i	$-0.667426\pi$
$659$	−25.7770	−1.00413	−0.502064	+	0.864830i	$0.667426\pi$
$660$	−2.25909	−0.0879350
$661$	20.1322	0.783050	0.391525	−	0.920167i	$-0.371948\pi$
$661$	20.1322	0.783050	0.391525	+	0.920167i	$0.371948\pi$
$662$	−3.85834	−0.149959
$663$	−0.900688	−0.0349798
$664$	−1.96018	−0.0760699
$665$	−25.8484	−1.00236
$666$	1.31543	0.0509719
$667$	26.2068	1.01473
$668$	19.9444	0.771673
$669$	1.17181	0.0453049
$670$	−0.322424	−0.0124563
$671$	12.1598	0.469425
$672$	−5.71513	−0.220466
$673$	−8.55034	−0.329591	−0.164796	−	0.986328i	$-0.552696\pi$
$673$	−8.55034	−0.329591	−0.164796	+	0.986328i	$0.552696\pi$
$674$	0.295290	0.0113742
$675$	−1.00000	−0.0384900
$676$	17.7853	0.684049
$677$	−36.9428	−1.41983	−0.709913	−	0.704289i	$-0.751266\pi$
$677$	−36.9428	−1.41983	−0.709913	+	0.704289i	$0.751266\pi$
$678$	−0.110273	−0.00423500
$679$	−32.2438	−1.23740
$680$	−0.248915	−0.00954544
$681$	−0.938845	−0.0359766
$682$	−1.54764	−0.0592620
$683$	37.4069	1.43134	0.715668	−	0.698441i	$-0.246122\pi$
$683$	37.4069	1.43134	0.715668	+	0.698441i	$0.246122\pi$
$684$	14.7712	0.564790
$685$	5.24312	0.200329
$686$	−0.958815	−0.0366077
$687$	−0.720654	−0.0274947
$688$	39.4588	1.50435
$689$	4.97637	0.189585
$690$	0.516509	0.0196631
$691$	−20.2141	−0.768982	−0.384491	−	0.923129i	$-0.625623\pi$
$691$	−20.2141	−0.768982	−0.384491	+	0.923129i	$0.625623\pi$
$692$	40.3737	1.53478
$693$	−3.95324	−0.150171
$694$	−3.03212	−0.115098
$695$	−17.2030	−0.652549
$696$	3.91383	0.148353
$697$	2.36712	0.0896611
$698$	−3.71182	−0.140494
$699$	15.6787	0.593025
$700$	6.86471	0.259462
$701$	−33.3549	−1.25980	−0.629899	−	0.776677i	$-0.716904\pi$
$701$	−33.3549	−1.25980	−0.629899	+	0.776677i	$0.716904\pi$
$702$	0.279119	0.0105347
$703$	70.4732	2.65795
$704$	−8.59858	−0.324071
$705$	11.5459	0.434842
$706$	1.67928	0.0632004
$707$	−45.8883	−1.72581
$708$	7.45452	0.280158
$709$	5.72013	0.214824	0.107412	−	0.994215i	$-0.465744\pi$
$709$	5.72013	0.214824	0.107412	+	0.994215i	$0.465744\pi$
$710$	0.369441	0.0138649
$711$	−4.78534	−0.179464
$712$	6.75707	0.253232
$713$	−36.1660	−1.35443
$714$	−0.216731	−0.00811094
$715$	−2.28699	−0.0855285
$716$	11.9457	0.446430
$717$	−1.33373	−0.0498090
$718$	2.83294	0.105724
$719$	4.28423	0.159775	0.0798874	−	0.996804i	$-0.474544\pi$
$719$	4.28423	0.159775	0.0798874	+	0.996804i	$0.474544\pi$
$720$	−3.88411	−0.144752
$721$	−40.9631	−1.52555
$722$	−5.09764	−0.189714
$723$	13.4726	0.501052
$724$	−30.7258	−1.14191
$725$	−7.06308	−0.262316
$726$	−1.35016	−0.0501092
$727$	−8.63728	−0.320339	−0.160169	−	0.987090i	$-0.551204\pi$
$727$	−8.63728	−0.320339	−0.160169	+	0.987090i	$0.551204\pi$
$728$	−3.85089	−0.142723
$729$	1.00000	0.0370370
$730$	−1.29824	−0.0480502
$731$	4.56347	0.168786
$732$	21.1153	0.780444
$733$	−3.00697	−0.111065	−0.0555326	−	0.998457i	$-0.517686\pi$
$733$	−3.00697	−0.111065	−0.0555326	+	0.998457i	$0.517686\pi$
$734$	−2.26169	−0.0834805
$735$	5.01273	0.184897
$736$	6.11823	0.225521
$737$	−2.64181	−0.0973124
$738$	−0.733560	−0.0270027
$739$	−35.8375	−1.31830	−0.659151	−	0.752010i	$-0.729084\pi$
$739$	−35.8375	−1.31830	−0.659151	+	0.752010i	$0.729084\pi$
$740$	−18.7160	−0.688012
$741$	14.9536	0.549334
$742$	1.19745	0.0439599
$743$	30.2841	1.11102	0.555508	−	0.831511i	$-0.312524\pi$
$743$	30.2841	1.11102	0.555508	+	0.831511i	$0.312524\pi$
$744$	−5.40117	−0.198016
$745$	−20.9518	−0.767614
$746$	1.12779	0.0412914
$747$	−3.53744	−0.129428
$748$	−1.01479	−0.0371044
$749$	−47.3093	−1.72865
$750$	−0.139206	−0.00508308
$751$	0.345976	0.0126249	0.00631243	−	0.999980i	$-0.497991\pi$
$751$	0.345976	0.0126249	0.00631243	+	0.999980i	$0.497991\pi$
$752$	44.8454	1.63534
$753$	−0.447003	−0.0162897
$754$	1.97144	0.0717956
$755$	19.6538	0.715274
$756$	−6.86471	−0.249667
$757$	−13.1917	−0.479462	−0.239731	−	0.970839i	$-0.577059\pi$
$757$	−13.1917	−0.479462	−0.239731	+	0.970839i	$0.577059\pi$
$758$	−1.84847	−0.0671393
$759$	4.23207	0.153614
$760$	4.13258	0.149904
$761$	−7.54441	−0.273485	−0.136742	−	0.990607i	$-0.543663\pi$
$761$	−7.54441	−0.273485	−0.136742	+	0.990607i	$0.543663\pi$
$762$	0.334643	0.0121228
$763$	37.7620	1.36708
$764$	42.2778	1.52956
$765$	−0.449203	−0.0162410
$766$	−1.74313	−0.0629817
$767$	7.54658	0.272491
$768$	−14.4722	−0.522219
$769$	40.6928	1.46742	0.733709	−	0.679463i	$-0.237787\pi$
$769$	40.6928	1.46742	0.733709	+	0.679463i	$0.237787\pi$
$770$	−0.550313	−0.0198319
$771$	13.5504	0.488007
$772$	29.8117	1.07295
$773$	30.4229	1.09424	0.547118	−	0.837056i	$-0.315725\pi$
$773$	30.4229	1.09424	0.547118	+	0.837056i	$0.315725\pi$
$774$	−1.41420	−0.0508323
$775$	9.74719	0.350129
$776$	5.15505	0.185055
$777$	−32.7515	−1.17495
$778$	0.798837	0.0286397
$779$	−39.2999	−1.40807
$780$	−3.97131	−0.142196
$781$	3.02705	0.108316
$782$	0.232017	0.00829691
$783$	7.06308	0.252414
$784$	19.4700	0.695356
$785$	8.33762	0.297582
$786$	−1.17830	−0.0420284
$787$	15.6941	0.559435	0.279718	−	0.960082i	$-0.409759\pi$
$787$	15.6941	0.559435	0.279718	+	0.960082i	$0.409759\pi$
$788$	22.1867	0.790367
$789$	2.40696	0.0856900
$790$	−0.666146	−0.0237004
$791$	2.74557	0.0976212
$792$	0.632034	0.0224583
$793$	21.3761	0.759086
$794$	−2.58157	−0.0916164
$795$	2.48188	0.0880232
$796$	−8.04892	−0.285286
$797$	−4.73105	−0.167583	−0.0837913	−	0.996483i	$-0.526703\pi$
$797$	−4.73105	−0.167583	−0.0837913	+	0.996483i	$0.526703\pi$
$798$	3.59825	0.127377
$799$	5.18643	0.183483
$800$	−1.64894	−0.0582989
$801$	12.1941	0.430858
$802$	0.139206	0.00491553
$803$	−10.6373	−0.375382
$804$	−4.58745	−0.161787
$805$	−12.8600	−0.453256
$806$	−2.72063	−0.0958300
$807$	−21.2390	−0.747648
$808$	7.33651	0.258097
$809$	30.4907	1.07200	0.535998	−	0.844219i	$-0.319935\pi$
$809$	30.4907	1.07200	0.535998	+	0.844219i	$0.319935\pi$
$810$	0.139206	0.00489119
$811$	11.2827	0.396189	0.198095	−	0.980183i	$-0.436525\pi$
$811$	11.2827	0.396189	0.198095	+	0.980183i	$0.436525\pi$
$812$	−48.4860	−1.70153
$813$	−18.3939	−0.645103
$814$	1.50037	0.0525881
$815$	14.5483	0.509604
$816$	−1.74475	−0.0610785
$817$	−75.7645	−2.65067
$818$	−1.71234	−0.0598706
$819$	−6.94949	−0.242835
$820$	10.4371	0.364479
$821$	19.1566	0.668568	0.334284	−	0.942472i	$-0.391505\pi$
$821$	19.1566	0.668568	0.334284	+	0.942472i	$0.391505\pi$
$822$	−0.729872	−0.0254572
$823$	−6.64808	−0.231737	−0.115869	−	0.993265i	$-0.536965\pi$
$823$	−6.64808	−0.231737	−0.115869	+	0.993265i	$0.536965\pi$
$824$	6.54908	0.228148
$825$	−1.14060	−0.0397105
$826$	1.81592	0.0631839
$827$	−46.1250	−1.60392	−0.801961	−	0.597376i	$-0.796210\pi$
$827$	−46.1250	−1.60392	−0.801961	+	0.597376i	$0.796210\pi$
$828$	7.34889	0.255392
$829$	21.0605	0.731462	0.365731	−	0.930721i	$-0.380819\pi$
$829$	21.0605	0.731462	0.365731	+	0.930721i	$0.380819\pi$
$830$	−0.492431	−0.0170925
$831$	7.84720	0.272216
$832$	−15.1156	−0.524041
$833$	2.25173	0.0780179
$834$	2.39476	0.0829239
$835$	10.0698	0.348479
$836$	16.8479	0.582698
$837$	−9.74719	−0.336912
$838$	0.326103	0.0112650
$839$	31.7167	1.09498	0.547491	−	0.836812i	$-0.315583\pi$
$839$	31.7167	1.09498	0.547491	+	0.836812i	$0.315583\pi$
$840$	−1.92057	−0.0662658
$841$	20.8871	0.720245
$842$	4.24940	0.146444
$843$	7.18305	0.247397
$844$	−7.23052	−0.248885
$845$	8.97965	0.308909
$846$	−1.60725	−0.0552584
$847$	33.6163	1.15507
$848$	9.63989	0.331035
$849$	5.59063	0.191870
$850$	−0.0625316	−0.00214482
$851$	35.0615	1.20189
$852$	5.25642	0.180082
$853$	27.3859	0.937675	0.468837	−	0.883285i	$-0.344673\pi$
$853$	27.3859	0.937675	0.468837	+	0.883285i	$0.344673\pi$
$854$	5.14368	0.176013
$855$	7.45784	0.255053
$856$	7.56369	0.258522
$857$	−30.2193	−1.03227	−0.516136	−	0.856507i	$-0.672630\pi$
$857$	−30.2193	−1.03227	−0.516136	+	0.856507i	$0.672630\pi$
$858$	0.318362	0.0108687
$859$	−16.0014	−0.545962	−0.272981	−	0.962019i	$-0.588010\pi$
$859$	−16.0014	−0.545962	−0.272981	+	0.962019i	$0.588010\pi$
$860$	20.1212	0.686128
$861$	18.2641	0.622440
$862$	−3.55333	−0.121027
$863$	27.7280	0.943871	0.471936	−	0.881633i	$-0.343555\pi$
$863$	27.7280	0.943871	0.471936	+	0.881633i	$0.343555\pi$
$864$	1.64894	0.0560981
$865$	20.3844	0.693089
$866$	0.458008	0.0155637
$867$	16.7982	0.570497
$868$	66.9117	2.27113
$869$	−5.45814	−0.185155
$870$	0.983222	0.0333343
$871$	−4.64411	−0.157360
$872$	−6.03729	−0.204448
$873$	9.30304	0.314860
$874$	−3.85204	−0.130297
$875$	3.46594	0.117170
$876$	−18.4714	−0.624092
$877$	−32.5665	−1.09969	−0.549846	−	0.835266i	$-0.685314\pi$
$877$	−32.5665	−1.09969	−0.549846	+	0.835266i	$0.685314\pi$
$878$	−1.96054	−0.0661649
$879$	33.7066	1.13689
$880$	−4.43020	−0.149342
$881$	−6.18608	−0.208414	−0.104207	−	0.994556i	$-0.533231\pi$
$881$	−6.18608	−0.208414	−0.104207	+	0.994556i	$0.533231\pi$
$882$	−0.697801	−0.0234962
$883$	7.58013	0.255092	0.127546	−	0.991833i	$-0.459290\pi$
$883$	7.58013	0.255092	0.127546	+	0.991833i	$0.459290\pi$
$884$	−1.78392	−0.0599998
$885$	3.76373	0.126516
$886$	−5.23540	−0.175887
$887$	−30.2045	−1.01417	−0.507083	−	0.861897i	$-0.669276\pi$
$887$	−30.2045	−1.01417	−0.507083	+	0.861897i	$0.669276\pi$
$888$	5.23623	0.175716
$889$	−8.33192	−0.279444
$890$	1.69749	0.0569000
$891$	1.14060	0.0382114
$892$	2.32092	0.0777101
$893$	−86.1073	−2.88147
$894$	2.91661	0.0975460
$895$	6.03127	0.201603
$896$	−15.0675	−0.503370
$897$	7.43965	0.248403
$898$	−0.321721	−0.0107360
$899$	−68.8452	−2.29612
$900$	−1.98062	−0.0660207
$901$	1.11487	0.0371416
$902$	−0.836695	−0.0278589
$903$	35.2106	1.17174
$904$	−0.438955	−0.0145994
$905$	−15.5132	−0.515676
$906$	−2.73592	−0.0908948
$907$	27.8313	0.924125	0.462062	−	0.886847i	$-0.347110\pi$
$907$	27.8313	0.924125	0.462062	+	0.886847i	$0.347110\pi$
$908$	−1.85950	−0.0617096
$909$	13.2398	0.439136
$910$	−0.967409	−0.0320693
$911$	−26.3115	−0.871739	−0.435869	−	0.900010i	$-0.643559\pi$
$911$	−26.3115	−0.871739	−0.435869	+	0.900010i	$0.643559\pi$
$912$	28.9671	0.959195
$913$	−4.03479	−0.133532
$914$	2.26783	0.0750131
$915$	10.6609	0.352440
$916$	−1.42734	−0.0471607
$917$	29.3372	0.968799
$918$	0.0625316	0.00206385
$919$	33.3291	1.09943	0.549713	−	0.835353i	$-0.314737\pi$
$919$	33.3291	1.09943	0.549713	+	0.835353i	$0.314737\pi$
$920$	2.05603	0.0677852
$921$	−13.3899	−0.441211
$922$	−2.63539	−0.0867918
$923$	5.32133	0.175154
$924$	−7.82987	−0.257584
$925$	−9.44954	−0.310699
$926$	−5.50521	−0.180912
$927$	11.8188	0.388179
$928$	11.6466	0.382318
$929$	−20.7636	−0.681232	−0.340616	−	0.940203i	$-0.610636\pi$
$929$	−20.7636	−0.681232	−0.340616	+	0.940203i	$0.610636\pi$
$930$	−1.35687	−0.0444934
$931$	−37.3842	−1.22522
$932$	31.0537	1.01720
$933$	32.9144	1.07757
$934$	0.251817	0.00823971
$935$	−0.512359	−0.0167559
$936$	1.11107	0.0363164
$937$	−4.51002	−0.147336	−0.0736679	−	0.997283i	$-0.523470\pi$
$937$	−4.51002	−0.147336	−0.0736679	+	0.997283i	$0.523470\pi$
$938$	−1.11750	−0.0364877
$939$	25.2191	0.822996
$940$	22.8680	0.745872
$941$	−32.7155	−1.06649	−0.533247	−	0.845960i	$-0.679028\pi$
$941$	−32.7155	−1.06649	−0.533247	+	0.845960i	$0.679028\pi$
$942$	−1.16064	−0.0378158
$943$	−19.5523	−0.636711
$944$	14.6187	0.475799
$945$	−3.46594	−0.112747
$946$	−1.61303	−0.0524441
$947$	−31.8851	−1.03613	−0.518063	−	0.855343i	$-0.673347\pi$
$947$	−31.8851	−1.03613	−0.518063	+	0.855343i	$0.673347\pi$
$948$	−9.47794	−0.307829
$949$	−18.6996	−0.607014
$950$	1.03817	0.0336828
$951$	4.10381	0.133075
$952$	−0.862723	−0.0279610
$953$	27.7838	0.900007	0.450004	−	0.893027i	$-0.351423\pi$
$953$	27.7838	0.900007	0.450004	+	0.893027i	$0.351423\pi$
$954$	−0.345492	−0.0111857
$955$	21.3457	0.690731
$956$	−2.64161	−0.0854358
$957$	8.05612	0.260418
$958$	4.04403	0.130657
$959$	18.1723	0.586815
$960$	−7.53867	−0.243310
$961$	64.0078	2.06477
$962$	2.63754	0.0850378
$963$	13.6498	0.439858
$964$	26.6842	0.859439
$965$	15.0517	0.484530
$966$	1.79019	0.0575983
$967$	13.0893	0.420925	0.210462	−	0.977602i	$-0.432503\pi$
$967$	13.0893	0.420925	0.210462	+	0.977602i	$0.432503\pi$
$968$	−5.37449	−0.172742
$969$	3.35008	0.107620
$970$	1.29504	0.0415811
$971$	−48.6271	−1.56052	−0.780258	−	0.625457i	$-0.784912\pi$
$971$	−48.6271	−1.56052	−0.780258	+	0.625457i	$0.784912\pi$
$972$	1.98062	0.0635285
$973$	−59.6247	−1.91148
$974$	0.778149	0.0249335
$975$	−2.00508	−0.0642140
$976$	41.4082	1.32545
$977$	−32.5797	−1.04232	−0.521159	−	0.853460i	$-0.674500\pi$
$977$	−32.5797	−1.04232	−0.521159	+	0.853460i	$0.674500\pi$
$978$	−2.02520	−0.0647588
$979$	13.9086	0.444519
$980$	9.92833	0.317149
$981$	−10.8952	−0.347856
$982$	−2.87168	−0.0916390
$983$	−32.6970	−1.04287	−0.521435	−	0.853291i	$-0.674603\pi$
$983$	−32.6970	−1.04287	−0.521435	+	0.853291i	$0.674603\pi$
$984$	−2.92002	−0.0930869
$985$	11.2019	0.356921
$986$	0.441666	0.0140655
$987$	40.0173	1.27376
$988$	29.6174	0.942255
$989$	−37.6941	−1.19860
$990$	0.158778	0.00504628
$991$	41.3304	1.31290	0.656451	−	0.754368i	$-0.272057\pi$
$991$	41.3304	1.31290	0.656451	+	0.754368i	$0.272057\pi$
$992$	−16.0725	−0.510304
$993$	−27.7168	−0.879567
$994$	1.28046	0.0406137
$995$	−4.06383	−0.128832
$996$	−7.00632	−0.222004
$997$	−4.04586	−0.128134	−0.0640669	−	0.997946i	$-0.520407\pi$
$997$	−4.04586	−0.128134	−0.0640669	+	0.997946i	$0.520407\pi$
$998$	0.724493	0.0229334
$999$	9.44954	0.298970

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.f.1.19	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.f.1.19	✓	36	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:	\( N \)	\(=\)	\( 6015 = 3 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6015.a (trivial)

\(f(q)\)	\(=\)	\(q-0.139206 q^{2} -1.00000 q^{3} -1.98062 q^{4} -1.00000 q^{5} +0.139206 q^{6} -3.46594 q^{7} +0.554125 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.139206 q^{2} -1.00000 q^{3} -1.98062 q^{4} -1.00000 q^{5} +0.139206 q^{6} -3.46594 q^{7} +0.554125 q^{8} +1.00000 q^{9} +0.139206 q^{10} +1.14060 q^{11} +1.98062 q^{12} +2.00508 q^{13} +0.482479 q^{14} +1.00000 q^{15} +3.88411 q^{16} +0.449203 q^{17} -0.139206 q^{18} -7.45784 q^{19} +1.98062 q^{20} +3.46594 q^{21} -0.158778 q^{22} -3.71040 q^{23} -0.554125 q^{24} +1.00000 q^{25} -0.279119 q^{26} -1.00000 q^{27} +6.86471 q^{28} -7.06308 q^{29} -0.139206 q^{30} +9.74719 q^{31} -1.64894 q^{32} -1.14060 q^{33} -0.0625316 q^{34} +3.46594 q^{35} -1.98062 q^{36} -9.44954 q^{37} +1.03817 q^{38} -2.00508 q^{39} -0.554125 q^{40} +5.26961 q^{41} -0.482479 q^{42} +10.1590 q^{43} -2.25909 q^{44} -1.00000 q^{45} +0.516509 q^{46} +11.5459 q^{47} -3.88411 q^{48} +5.01273 q^{49} -0.139206 q^{50} -0.449203 q^{51} -3.97131 q^{52} +2.48188 q^{53} +0.139206 q^{54} -1.14060 q^{55} -1.92057 q^{56} +7.45784 q^{57} +0.983222 q^{58} +3.76373 q^{59} -1.98062 q^{60} +10.6609 q^{61} -1.35687 q^{62} -3.46594 q^{63} -7.53867 q^{64} -2.00508 q^{65} +0.158778 q^{66} -2.31617 q^{67} -0.889700 q^{68} +3.71040 q^{69} -0.482479 q^{70} +2.65392 q^{71} +0.554125 q^{72} -9.32609 q^{73} +1.31543 q^{74} -1.00000 q^{75} +14.7712 q^{76} -3.95324 q^{77} +0.279119 q^{78} -4.78534 q^{79} -3.88411 q^{80} +1.00000 q^{81} -0.733560 q^{82} -3.53744 q^{83} -6.86471 q^{84} -0.449203 q^{85} -1.41420 q^{86} +7.06308 q^{87} +0.632034 q^{88} +12.1941 q^{89} +0.139206 q^{90} -6.94949 q^{91} +7.34889 q^{92} -9.74719 q^{93} -1.60725 q^{94} +7.45784 q^{95} +1.64894 q^{96} +9.30304 q^{97} -0.697801 q^{98} +1.14060 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 7 q^{2} - 36 q^{3} + 45 q^{4} - 36 q^{5} + 7 q^{6} + 2 q^{7} - 24 q^{8} + 36 q^{9}+O(q^{10}) \) 36 * q - 7 * q^2 - 36 * q^3 + 45 * q^4 - 36 * q^5 + 7 * q^6 + 2 * q^7 - 24 * q^8 + 36 * q^9	\( 36 q - 7 q^{2} - 36 q^{3} + 45 q^{4} - 36 q^{5} + 7 q^{6} + 2 q^{7} - 24 q^{8} + 36 q^{9} + 7 q^{10} - q^{11} - 45 q^{12} - 8 q^{13} - 4 q^{14} + 36 q^{15} + 63 q^{16} - 50 q^{17} - 7 q^{18} + 15 q^{19} - 45 q^{20} - 2 q^{21} + 7 q^{22} - 32 q^{23} + 24 q^{24} + 36 q^{25} - 12 q^{26} - 36 q^{27} - 10 q^{28} + 7 q^{29} - 7 q^{30} + 7 q^{31} - 50 q^{32} + q^{33} + 8 q^{34} - 2 q^{35} + 45 q^{36} - 10 q^{37} - 48 q^{38} + 8 q^{39} + 24 q^{40} - 31 q^{41} + 4 q^{42} + 27 q^{43} - 9 q^{44} - 36 q^{45} + 23 q^{46} - 46 q^{47} - 63 q^{48} + 48 q^{49} - 7 q^{50} + 50 q^{51} - 14 q^{52} - 39 q^{53} + 7 q^{54} + q^{55} - 29 q^{56} - 15 q^{57} - 26 q^{58} - 9 q^{59} + 45 q^{60} + 5 q^{61} - 65 q^{62} + 2 q^{63} + 90 q^{64} + 8 q^{65} - 7 q^{66} + 18 q^{67} - 128 q^{68} + 32 q^{69} + 4 q^{70} + 4 q^{71} - 24 q^{72} - 45 q^{73} - 22 q^{74} - 36 q^{75} + 26 q^{76} - 38 q^{77} + 12 q^{78} + 25 q^{79} - 63 q^{80} + 36 q^{81} - 5 q^{82} - 71 q^{83} + 10 q^{84} + 50 q^{85} + 3 q^{86} - 7 q^{87} - 9 q^{88} - 39 q^{89} + 7 q^{90} + 19 q^{91} - 95 q^{92} - 7 q^{93} + 16 q^{94} - 15 q^{95} + 50 q^{96} - 61 q^{97} - 76 q^{98} - q^{99}+O(q^{100}) \) 36 * q - 7 * q^2 - 36 * q^3 + 45 * q^4 - 36 * q^5 + 7 * q^6 + 2 * q^7 - 24 * q^8 + 36 * q^9 + 7 * q^10 - q^11 - 45 * q^12 - 8 * q^13 - 4 * q^14 + 36 * q^15 + 63 * q^16 - 50 * q^17 - 7 * q^18 + 15 * q^19 - 45 * q^20 - 2 * q^21 + 7 * q^22 - 32 * q^23 + 24 * q^24 + 36 * q^25 - 12 * q^26 - 36 * q^27 - 10 * q^28 + 7 * q^29 - 7 * q^30 + 7 * q^31 - 50 * q^32 + q^33 + 8 * q^34 - 2 * q^35 + 45 * q^36 - 10 * q^37 - 48 * q^38 + 8 * q^39 + 24 * q^40 - 31 * q^41 + 4 * q^42 + 27 * q^43 - 9 * q^44 - 36 * q^45 + 23 * q^46 - 46 * q^47 - 63 * q^48 + 48 * q^49 - 7 * q^50 + 50 * q^51 - 14 * q^52 - 39 * q^53 + 7 * q^54 + q^55 - 29 * q^56 - 15 * q^57 - 26 * q^58 - 9 * q^59 + 45 * q^60 + 5 * q^61 - 65 * q^62 + 2 * q^63 + 90 * q^64 + 8 * q^65 - 7 * q^66 + 18 * q^67 - 128 * q^68 + 32 * q^69 + 4 * q^70 + 4 * q^71 - 24 * q^72 - 45 * q^73 - 22 * q^74 - 36 * q^75 + 26 * q^76 - 38 * q^77 + 12 * q^78 + 25 * q^79 - 63 * q^80 + 36 * q^81 - 5 * q^82 - 71 * q^83 + 10 * q^84 + 50 * q^85 + 3 * q^86 - 7 * q^87 - 9 * q^88 - 39 * q^89 + 7 * q^90 + 19 * q^91 - 95 * q^92 - 7 * q^93 + 16 * q^94 - 15 * q^95 + 50 * q^96 - 61 * q^97 - 76 * q^98 - q^99

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