LMFDB - Embedded newform 8018.2.a.g.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$64.0240523407$
Analytic rank:	$1$
Dimension:	$34$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +0.0912120 q^{3} +1.00000 q^{4} -2.07635 q^{5} -0.0912120 q^{6} -4.23935 q^{7} -1.00000 q^{8} -2.99168 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.0912120 q^{3} +1.00000 q^{4} -2.07635 q^{5} -0.0912120 q^{6} -4.23935 q^{7} -1.00000 q^{8} -2.99168 q^{9} +2.07635 q^{10} +1.21964 q^{11} +0.0912120 q^{12} +5.34883 q^{13} +4.23935 q^{14} -0.189388 q^{15} +1.00000 q^{16} -4.79706 q^{17} +2.99168 q^{18} +1.00000 q^{19} -2.07635 q^{20} -0.386679 q^{21} -1.21964 q^{22} -8.70007 q^{23} -0.0912120 q^{24} -0.688757 q^{25} -5.34883 q^{26} -0.546513 q^{27} -4.23935 q^{28} +8.96834 q^{29} +0.189388 q^{30} +7.97914 q^{31} -1.00000 q^{32} +0.111246 q^{33} +4.79706 q^{34} +8.80238 q^{35} -2.99168 q^{36} -2.39320 q^{37} -1.00000 q^{38} +0.487878 q^{39} +2.07635 q^{40} +0.101215 q^{41} +0.386679 q^{42} +1.70148 q^{43} +1.21964 q^{44} +6.21179 q^{45} +8.70007 q^{46} +12.3700 q^{47} +0.0912120 q^{48} +10.9721 q^{49} +0.688757 q^{50} -0.437550 q^{51} +5.34883 q^{52} +8.36886 q^{53} +0.546513 q^{54} -2.53240 q^{55} +4.23935 q^{56} +0.0912120 q^{57} -8.96834 q^{58} +11.5637 q^{59} -0.189388 q^{60} -8.14747 q^{61} -7.97914 q^{62} +12.6828 q^{63} +1.00000 q^{64} -11.1061 q^{65} -0.111246 q^{66} -12.6501 q^{67} -4.79706 q^{68} -0.793551 q^{69} -8.80238 q^{70} -11.5797 q^{71} +2.99168 q^{72} -12.2343 q^{73} +2.39320 q^{74} -0.0628229 q^{75} +1.00000 q^{76} -5.17047 q^{77} -0.487878 q^{78} +14.7156 q^{79} -2.07635 q^{80} +8.92519 q^{81} -0.101215 q^{82} +4.68674 q^{83} -0.386679 q^{84} +9.96040 q^{85} -1.70148 q^{86} +0.818020 q^{87} -1.21964 q^{88} -2.86593 q^{89} -6.21179 q^{90} -22.6756 q^{91} -8.70007 q^{92} +0.727794 q^{93} -12.3700 q^{94} -2.07635 q^{95} -0.0912120 q^{96} -4.23561 q^{97} -10.9721 q^{98} -3.64877 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 34 q^{2} - 6 q^{3} + 34 q^{4} + q^{5} + 6 q^{6} - 22 q^{7} - 34 q^{8} + 30 q^{9}+O(q^{10}) $ 34 * q - 34 * q^2 - 6 * q^3 + 34 * q^4 + q^5 + 6 * q^6 - 22 * q^7 - 34 * q^8 + 30 * q^9	\( 34 q - 34 q^{2} - 6 q^{3} + 34 q^{4} + q^{5} + 6 q^{6} - 22 q^{7} - 34 q^{8} + 30 q^{9} - q^{10} + 7 q^{11} - 6 q^{12} - 11 q^{13} + 22 q^{14} - 18 q^{15} + 34 q^{16} - 10 q^{17} - 30 q^{18} + 34 q^{19} + q^{20} + 14 q^{21} - 7 q^{22} - 30 q^{23} + 6 q^{24} + 11 q^{25} + 11 q^{26} - 21 q^{27} - 22 q^{28} + 12 q^{29} + 18 q^{30} - 13 q^{31} - 34 q^{32} - 4 q^{33} + 10 q^{34} - 16 q^{35} + 30 q^{36} - 46 q^{37} - 34 q^{38} - 36 q^{39} - q^{40} + 25 q^{41} - 14 q^{42} - 51 q^{43} + 7 q^{44} - 17 q^{45} + 30 q^{46} - 20 q^{47} - 6 q^{48} - 2 q^{49} - 11 q^{50} + 4 q^{51} - 11 q^{52} - 7 q^{53} + 21 q^{54} - 39 q^{55} + 22 q^{56} - 6 q^{57} - 12 q^{58} + 19 q^{59} - 18 q^{60} - 26 q^{61} + 13 q^{62} - 57 q^{63} + 34 q^{64} + 20 q^{65} + 4 q^{66} - 54 q^{67} - 10 q^{68} + 16 q^{70} + 9 q^{71} - 30 q^{72} - 57 q^{73} + 46 q^{74} + 26 q^{75} + 34 q^{76} + 2 q^{77} + 36 q^{78} - 7 q^{79} + q^{80} + 22 q^{81} - 25 q^{82} - 15 q^{83} + 14 q^{84} - 30 q^{85} + 51 q^{86} - 37 q^{87} - 7 q^{88} + 78 q^{89} + 17 q^{90} - 31 q^{91} - 30 q^{92} - 43 q^{93} + 20 q^{94} + q^{95} + 6 q^{96} - 38 q^{97} + 2 q^{98} + 2 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 - 6 * q^3 + 34 * q^4 + q^5 + 6 * q^6 - 22 * q^7 - 34 * q^8 + 30 * q^9 - q^10 + 7 * q^11 - 6 * q^12 - 11 * q^13 + 22 * q^14 - 18 * q^15 + 34 * q^16 - 10 * q^17 - 30 * q^18 + 34 * q^19 + q^20 + 14 * q^21 - 7 * q^22 - 30 * q^23 + 6 * q^24 + 11 * q^25 + 11 * q^26 - 21 * q^27 - 22 * q^28 + 12 * q^29 + 18 * q^30 - 13 * q^31 - 34 * q^32 - 4 * q^33 + 10 * q^34 - 16 * q^35 + 30 * q^36 - 46 * q^37 - 34 * q^38 - 36 * q^39 - q^40 + 25 * q^41 - 14 * q^42 - 51 * q^43 + 7 * q^44 - 17 * q^45 + 30 * q^46 - 20 * q^47 - 6 * q^48 - 2 * q^49 - 11 * q^50 + 4 * q^51 - 11 * q^52 - 7 * q^53 + 21 * q^54 - 39 * q^55 + 22 * q^56 - 6 * q^57 - 12 * q^58 + 19 * q^59 - 18 * q^60 - 26 * q^61 + 13 * q^62 - 57 * q^63 + 34 * q^64 + 20 * q^65 + 4 * q^66 - 54 * q^67 - 10 * q^68 + 16 * q^70 + 9 * q^71 - 30 * q^72 - 57 * q^73 + 46 * q^74 + 26 * q^75 + 34 * q^76 + 2 * q^77 + 36 * q^78 - 7 * q^79 + q^80 + 22 * q^81 - 25 * q^82 - 15 * q^83 + 14 * q^84 - 30 * q^85 + 51 * q^86 - 37 * q^87 - 7 * q^88 + 78 * q^89 + 17 * q^90 - 31 * q^91 - 30 * q^92 - 43 * q^93 + 20 * q^94 + q^95 + 6 * q^96 - 38 * q^97 + 2 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	0.0912120	0.0526613	0.0263306	−	0.999653i	$-0.491618\pi$
$3$	0.0912120	0.0526613	0.0263306	+	0.999653i	$0.491618\pi$
$4$	1.00000	0.500000
$5$	−2.07635	−0.928573	−0.464287	−	0.885685i	$-0.653689\pi$
$5$	−2.07635	−0.928573	−0.464287	+	0.885685i	$0.653689\pi$
$6$	−0.0912120	−0.0372371
$7$	−4.23935	−1.60232	−0.801161	−	0.598449i	$-0.795784\pi$
$7$	−4.23935	−1.60232	−0.801161	+	0.598449i	$0.795784\pi$
$8$	−1.00000	−0.353553
$9$	−2.99168	−0.997227
$10$	2.07635	0.656601
$11$	1.21964	0.367735	0.183867	−	0.982951i	$-0.441138\pi$
$11$	1.21964	0.367735	0.183867	+	0.982951i	$0.441138\pi$
$12$	0.0912120	0.0263306
$13$	5.34883	1.48350	0.741750	−	0.670677i	$-0.233996\pi$
$13$	5.34883	1.48350	0.741750	+	0.670677i	$0.233996\pi$
$14$	4.23935	1.13301
$15$	−0.189388	−0.0488998
$16$	1.00000	0.250000
$17$	−4.79706	−1.16346	−0.581729	−	0.813382i	$-0.697624\pi$
$17$	−4.79706	−1.16346	−0.581729	+	0.813382i	$0.697624\pi$
$18$	2.99168	0.705146
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−2.07635	−0.464287
$21$	−0.386679	−0.0843803
$22$	−1.21964	−0.260028
$23$	−8.70007	−1.81409	−0.907045	−	0.421033i	$-0.861668\pi$
$23$	−8.70007	−1.81409	−0.907045	+	0.421033i	$0.861668\pi$
$24$	−0.0912120	−0.0186186
$25$	−0.688757	−0.137751
$26$	−5.34883	−1.04899
$27$	−0.546513	−0.105176
$28$	−4.23935	−0.801161
$29$	8.96834	1.66538	0.832690	−	0.553740i	$-0.186800\pi$
$29$	8.96834	1.66538	0.832690	+	0.553740i	$0.186800\pi$
$30$	0.189388	0.0345774
$31$	7.97914	1.43310	0.716548	−	0.697537i	$-0.245721\pi$
$31$	7.97914	1.43310	0.716548	+	0.697537i	$0.245721\pi$
$32$	−1.00000	−0.176777
$33$	0.111246	0.0193654
$34$	4.79706	0.822690
$35$	8.80238	1.48787
$36$	−2.99168	−0.498613
$37$	−2.39320	−0.393440	−0.196720	−	0.980460i	$-0.563029\pi$
$37$	−2.39320	−0.393440	−0.196720	+	0.980460i	$0.563029\pi$
$38$	−1.00000	−0.162221
$39$	0.487878	0.0781229
$40$	2.07635	0.328300
$41$	0.101215	0.0158072	0.00790360	−	0.999969i	$-0.497484\pi$
$41$	0.101215	0.0158072	0.00790360	+	0.999969i	$0.497484\pi$
$42$	0.386679	0.0596659
$43$	1.70148	0.259473	0.129737	−	0.991549i	$-0.458587\pi$
$43$	1.70148	0.259473	0.129737	+	0.991549i	$0.458587\pi$
$44$	1.21964	0.183867
$45$	6.21179	0.925998
$46$	8.70007	1.28276
$47$	12.3700	1.80436	0.902178	−	0.431364i	$-0.141968\pi$
$47$	12.3700	1.80436	0.902178	+	0.431364i	$0.141968\pi$
$48$	0.0912120	0.0131653
$49$	10.9721	1.56744
$50$	0.688757	0.0974050
$51$	−0.437550	−0.0612692
$52$	5.34883	0.741750
$53$	8.36886	1.14955	0.574775	−	0.818311i	$-0.305089\pi$
$53$	8.36886	1.14955	0.574775	+	0.818311i	$0.305089\pi$
$54$	0.546513	0.0743710
$55$	−2.53240	−0.341469
$56$	4.23935	0.566507
$57$	0.0912120	0.0120813
$58$	−8.96834	−1.17760
$59$	11.5637	1.50546	0.752730	−	0.658329i	$-0.228736\pi$
$59$	11.5637	1.50546	0.752730	+	0.658329i	$0.228736\pi$
$60$	−0.189388	−0.0244499
$61$	−8.14747	−1.04318	−0.521588	−	0.853197i	$-0.674660\pi$
$61$	−8.14747	−1.04318	−0.521588	+	0.853197i	$0.674660\pi$
$62$	−7.97914	−1.01335
$63$	12.6828	1.59788
$64$	1.00000	0.125000
$65$	−11.1061	−1.37754
$66$	−0.111246	−0.0136934
$67$	−12.6501	−1.54546	−0.772730	−	0.634735i	$-0.781109\pi$
$67$	−12.6501	−1.54546	−0.772730	+	0.634735i	$0.781109\pi$
$68$	−4.79706	−0.581729
$69$	−0.793551	−0.0955323
$70$	−8.80238	−1.05209
$71$	−11.5797	−1.37426	−0.687131	−	0.726534i	$-0.741130\pi$
$71$	−11.5797	−1.37426	−0.687131	+	0.726534i	$0.741130\pi$
$72$	2.99168	0.352573
$73$	−12.2343	−1.43192	−0.715959	−	0.698143i	$-0.754010\pi$
$73$	−12.2343	−1.43192	−0.715959	+	0.698143i	$0.754010\pi$
$74$	2.39320	0.278204
$75$	−0.0628229	−0.00725417
$76$	1.00000	0.114708
$77$	−5.17047	−0.589230
$78$	−0.487878	−0.0552413
$79$	14.7156	1.65564	0.827818	−	0.560997i	$-0.189582\pi$
$79$	14.7156	1.65564	0.827818	+	0.560997i	$0.189582\pi$
$80$	−2.07635	−0.232143
$81$	8.92519	0.991688
$82$	−0.101215	−0.0111774
$83$	4.68674	0.514436	0.257218	−	0.966353i	$-0.417194\pi$
$83$	4.68674	0.514436	0.257218	+	0.966353i	$0.417194\pi$
$84$	−0.386679	−0.0421902
$85$	9.96040	1.08036
$86$	−1.70148	−0.183475
$87$	0.818020	0.0877010
$88$	−1.21964	−0.130014
$89$	−2.86593	−0.303788	−0.151894	−	0.988397i	$-0.548537\pi$
$89$	−2.86593	−0.303788	−0.151894	+	0.988397i	$0.548537\pi$
$90$	−6.21179	−0.654780
$91$	−22.6756	−2.37704
$92$	−8.70007	−0.907045
$93$	0.727794	0.0754687
$94$	−12.3700	−1.27587
$95$	−2.07635	−0.213029
$96$	−0.0912120	−0.00930928
$97$	−4.23561	−0.430061	−0.215031	−	0.976607i	$-0.568985\pi$
$97$	−4.23561	−0.430061	−0.215031	+	0.976607i	$0.568985\pi$
$98$	−10.9721	−1.10835
$99$	−3.64877	−0.366715
$100$	−0.688757	−0.0688757
$101$	15.9324	1.58533	0.792667	−	0.609655i	$-0.208692\pi$
$101$	15.9324	1.58533	0.792667	+	0.609655i	$0.208692\pi$
$102$	0.437550	0.0433239
$103$	−7.76664	−0.765270	−0.382635	−	0.923900i	$-0.624983\pi$
$103$	−7.76664	−0.765270	−0.382635	+	0.923900i	$0.624983\pi$
$104$	−5.34883	−0.524496
$105$	0.802883	0.0783533
$106$	−8.36886	−0.812855
$107$	19.5495	1.88992	0.944960	−	0.327185i	$-0.106100\pi$
$107$	19.5495	1.88992	0.944960	+	0.327185i	$0.106100\pi$
$108$	−0.546513	−0.0525882
$109$	5.07532	0.486127	0.243064	−	0.970010i	$-0.421848\pi$
$109$	5.07532	0.486127	0.243064	+	0.970010i	$0.421848\pi$
$110$	2.53240	0.241455
$111$	−0.218288	−0.0207190
$112$	−4.23935	−0.400581
$113$	−7.78427	−0.732283	−0.366141	−	0.930559i	$-0.619321\pi$
$113$	−7.78427	−0.732283	−0.366141	+	0.930559i	$0.619321\pi$
$114$	−0.0912120	−0.00854279
$115$	18.0644	1.68452
$116$	8.96834	0.832690
$117$	−16.0020	−1.47939
$118$	−11.5637	−1.06452
$119$	20.3364	1.86424
$120$	0.189388	0.0172887
$121$	−9.51248	−0.864771
$122$	8.14747	0.737637
$123$	0.00923206	0.000832427 0
$124$	7.97914	0.716548
$125$	11.8119	1.05649
$126$	−12.6828	−1.12987
$127$	−13.4531	−1.19377	−0.596886	−	0.802326i	$-0.703596\pi$
$127$	−13.4531	−1.19377	−0.596886	+	0.802326i	$0.703596\pi$
$128$	−1.00000	−0.0883883
$129$	0.155195	0.0136642
$130$	11.1061	0.974066
$131$	−7.69475	−0.672293	−0.336147	−	0.941810i	$-0.609124\pi$
$131$	−7.69475	−0.672293	−0.336147	+	0.941810i	$0.609124\pi$
$132$	0.111246	0.00968269
$133$	−4.23935	−0.367598
$134$	12.6501	1.09281
$135$	1.13475	0.0976641
$136$	4.79706	0.411345
$137$	13.4367	1.14797	0.573987	−	0.818865i	$-0.305396\pi$
$137$	13.4367	1.14797	0.573987	+	0.818865i	$0.305396\pi$
$138$	0.793551	0.0675515
$139$	−3.94533	−0.334639	−0.167319	−	0.985903i	$-0.553511\pi$
$139$	−3.94533	−0.334639	−0.167319	+	0.985903i	$0.553511\pi$
$140$	8.80238	0.743937
$141$	1.12830	0.0950196
$142$	11.5797	0.971749
$143$	6.52364	0.545534
$144$	−2.99168	−0.249307
$145$	−18.6214	−1.54643
$146$	12.2343	1.01252
$147$	1.00078	0.0825432
$148$	−2.39320	−0.196720
$149$	5.53069	0.453091	0.226546	−	0.974001i	$-0.427257\pi$
$149$	5.53069	0.453091	0.226546	+	0.974001i	$0.427257\pi$
$150$	0.0628229	0.00512947
$151$	9.14129	0.743908	0.371954	−	0.928251i	$-0.378688\pi$
$151$	9.14129	0.743908	0.371954	+	0.928251i	$0.378688\pi$
$152$	−1.00000	−0.0811107
$153$	14.3513	1.16023
$154$	5.17047	0.416648
$155$	−16.5675	−1.33074
$156$	0.487878	0.0390615
$157$	23.4943	1.87505	0.937524	−	0.347920i	$-0.113112\pi$
$157$	23.4943	1.87505	0.937524	+	0.347920i	$0.113112\pi$
$158$	−14.7156	−1.17071
$159$	0.763340	0.0605368
$160$	2.07635	0.164150
$161$	36.8826	2.90676
$162$	−8.92519	−0.701229
$163$	−22.7799	−1.78426	−0.892129	−	0.451782i	$-0.850789\pi$
$163$	−22.7799	−1.78426	−0.892129	+	0.451782i	$0.850789\pi$
$164$	0.101215	0.00790360
$165$	−0.230985	−0.0179822
$166$	−4.68674	−0.363761
$167$	−3.05270	−0.236225	−0.118112	−	0.993000i	$-0.537684\pi$
$167$	−3.05270	−0.236225	−0.118112	+	0.993000i	$0.537684\pi$
$168$	0.386679	0.0298330
$169$	15.6100	1.20077
$170$	−9.96040	−0.763928
$171$	−2.99168	−0.228780
$172$	1.70148	0.129737
$173$	−16.9306	−1.28721	−0.643603	−	0.765359i	$-0.722561\pi$
$173$	−16.9306	−1.28721	−0.643603	+	0.765359i	$0.722561\pi$
$174$	−0.818020	−0.0620140
$175$	2.91988	0.220722
$176$	1.21964	0.0919337
$177$	1.05474	0.0792795
$178$	2.86593	0.214811
$179$	0.00190612	0.000142470 0	7.12352e−5	−	1.00000i	$-0.499977\pi$
$179$	0.00190612	0.000142470 0	7.12352e−5		1.00000i	$0.499977\pi$
$180$	6.21179	0.462999
$181$	−16.2480	−1.20770	−0.603851	−	0.797097i	$-0.706368\pi$
$181$	−16.2480	−1.20770	−0.603851	+	0.797097i	$0.706368\pi$
$182$	22.6756	1.68082
$183$	−0.743147	−0.0549350
$184$	8.70007	0.641378
$185$	4.96913	0.365338
$186$	−0.727794	−0.0533644
$187$	−5.85068	−0.427844
$188$	12.3700	0.902178
$189$	2.31686	0.168527
$190$	2.07635	0.150634
$191$	6.33124	0.458112	0.229056	−	0.973413i	$-0.426436\pi$
$191$	6.33124	0.458112	0.229056	+	0.973413i	$0.426436\pi$
$192$	0.0912120	0.00658266
$193$	8.73126	0.628490	0.314245	−	0.949342i	$-0.398249\pi$
$193$	8.73126	0.628490	0.314245	+	0.949342i	$0.398249\pi$
$194$	4.23561	0.304099
$195$	−1.01301	−0.0725429
$196$	10.9721	0.783719
$197$	−8.99074	−0.640563	−0.320282	−	0.947322i	$-0.603778\pi$
$197$	−8.99074	−0.640563	−0.320282	+	0.947322i	$0.603778\pi$
$198$	3.64877	0.259307
$199$	0.827906	0.0586887	0.0293443	−	0.999569i	$-0.490658\pi$
$199$	0.827906	0.0586887	0.0293443	+	0.999569i	$0.490658\pi$
$200$	0.688757	0.0487025
$201$	−1.15384	−0.0813859
$202$	−15.9324	−1.12100
$203$	−38.0199	−2.66848
$204$	−0.437550	−0.0306346
$205$	−0.210159	−0.0146781
$206$	7.76664	0.541128
$207$	26.0278	1.80906
$208$	5.34883	0.370875
$209$	1.21964	0.0843641
$210$	−0.802883	−0.0554042
$211$	1.00000	0.0688428
$211$	1.00000	0.0688428
$212$	8.36886	0.574775
$213$	−1.05621	−0.0723703
$214$	−19.5495	−1.33638
$215$	−3.53287	−0.240940
$216$	0.546513	0.0371855
$217$	−33.8264	−2.29628
$218$	−5.07532	−0.343744
$219$	−1.11592	−0.0754066
$220$	−2.53240	−0.170734
$221$	−25.6587	−1.72599
$222$	0.218288	0.0146506
$223$	−16.2370	−1.08731	−0.543656	−	0.839308i	$-0.682960\pi$
$223$	−16.2370	−1.08731	−0.543656	+	0.839308i	$0.682960\pi$
$224$	4.23935	0.283253
$225$	2.06054	0.137369
$226$	7.78427	0.517802
$227$	−12.6885	−0.842165	−0.421083	−	0.907022i	$-0.638350\pi$
$227$	−12.6885	−0.842165	−0.421083	+	0.907022i	$0.638350\pi$
$228$	0.0912120	0.00604066
$229$	18.4194	1.21719	0.608593	−	0.793482i	$-0.291734\pi$
$229$	18.4194	1.21719	0.608593	+	0.793482i	$0.291734\pi$
$230$	−18.0644	−1.19113
$231$	−0.471609	−0.0310296
$232$	−8.96834	−0.588801
$233$	−1.30500	−0.0854935	−0.0427467	−	0.999086i	$-0.513611\pi$
$233$	−1.30500	−0.0854935	−0.0427467	+	0.999086i	$0.513611\pi$
$234$	16.0020	1.04608
$235$	−25.6846	−1.67548
$236$	11.5637	0.752730
$237$	1.34224	0.0871879
$238$	−20.3364	−1.31821
$239$	−0.257089	−0.0166297	−0.00831484	−	0.999965i	$-0.502647\pi$
$239$	−0.257089	−0.0166297	−0.00831484	+	0.999965i	$0.502647\pi$
$240$	−0.189388	−0.0122250
$241$	−3.23468	−0.208364	−0.104182	−	0.994558i	$-0.533222\pi$
$241$	−3.23468	−0.208364	−0.104182	+	0.994558i	$0.533222\pi$
$242$	9.51248	0.611486
$243$	2.45362	0.157400
$244$	−8.14747	−0.521588
$245$	−22.7819	−1.45548
$246$	−0.00923206	−0.000588615 0
$247$	5.34883	0.340338
$248$	−7.97914	−0.506676
$249$	0.427487	0.0270909
$250$	−11.8119	−0.747048
$251$	−23.8467	−1.50519	−0.752596	−	0.658482i	$-0.771199\pi$
$251$	−23.8467	−1.50519	−0.752596	+	0.658482i	$0.771199\pi$
$252$	12.6828	0.798939
$253$	−10.6109	−0.667104
$254$	13.4531	0.844125
$255$	0.908508	0.0568930
$256$	1.00000	0.0625000
$257$	25.1492	1.56877	0.784383	−	0.620277i	$-0.212980\pi$
$257$	25.1492	1.56877	0.784383	+	0.620277i	$0.212980\pi$
$258$	−0.155195	−0.00966203
$259$	10.1456	0.630417
$260$	−11.1061	−0.688769
$261$	−26.8304	−1.66076
$262$	7.69475	0.475383
$263$	11.9521	0.736998	0.368499	−	0.929628i	$-0.379872\pi$
$263$	11.9521	0.736998	0.368499	+	0.929628i	$0.379872\pi$
$264$	−0.111246	−0.00684669
$265$	−17.3767	−1.06744
$266$	4.23935	0.259931
$267$	−0.261408	−0.0159979
$268$	−12.6501	−0.772730
$269$	−17.8042	−1.08554	−0.542771	−	0.839880i	$-0.682625\pi$
$269$	−17.8042	−1.08554	−0.542771	+	0.839880i	$0.682625\pi$
$270$	−1.13475	−0.0690589
$271$	−3.41956	−0.207723	−0.103862	−	0.994592i	$-0.533120\pi$
$271$	−3.41956	−0.207723	−0.103862	+	0.994592i	$0.533120\pi$
$272$	−4.79706	−0.290865
$273$	−2.06828	−0.125178
$274$	−13.4367	−0.811740
$275$	−0.840035	−0.0506560
$276$	−0.793551	−0.0477661
$277$	−27.3190	−1.64144	−0.820719	−	0.571333i	$-0.806427\pi$
$277$	−27.3190	−1.64144	−0.820719	+	0.571333i	$0.806427\pi$
$278$	3.94533	0.236625
$279$	−23.8710	−1.42912
$280$	−8.80238	−0.526043
$281$	18.5751	1.10810	0.554049	−	0.832484i	$-0.313082\pi$
$281$	18.5751	1.10810	0.554049	+	0.832484i	$0.313082\pi$
$282$	−1.12830	−0.0671890
$283$	3.98303	0.236767	0.118383	−	0.992968i	$-0.462229\pi$
$283$	3.98303	0.236767	0.118383	+	0.992968i	$0.462229\pi$
$284$	−11.5797	−0.687131
$285$	−0.189388	−0.0112184
$286$	−6.52364	−0.385751
$287$	−0.429087	−0.0253282
$288$	2.99168	0.176286
$289$	6.01181	0.353636
$290$	18.6214	1.09349
$291$	−0.386339	−0.0226476
$292$	−12.2343	−0.715959
$293$	−8.07523	−0.471760	−0.235880	−	0.971782i	$-0.575797\pi$
$293$	−8.07523	−0.471760	−0.235880	+	0.971782i	$0.575797\pi$
$294$	−1.00078	−0.0583669
$295$	−24.0102	−1.39793
$296$	2.39320	0.139102
$297$	−0.666548	−0.0386770
$298$	−5.53069	−0.320384
$299$	−46.5352	−2.69120
$300$	−0.0628229	−0.00362708
$301$	−7.21316	−0.415760
$302$	−9.14129	−0.526022
$303$	1.45323	0.0834857
$304$	1.00000	0.0573539
$305$	16.9170	0.968666
$306$	−14.3513	−0.820408
$307$	−29.7517	−1.69802	−0.849009	−	0.528378i	$-0.822800\pi$
$307$	−29.7517	−1.69802	−0.849009	+	0.528378i	$0.822800\pi$
$308$	−5.17047	−0.294615
$309$	−0.708411	−0.0403001
$310$	16.5675	0.940972
$311$	−21.5960	−1.22460	−0.612299	−	0.790626i	$-0.709755\pi$
$311$	−21.5960	−1.22460	−0.612299	+	0.790626i	$0.709755\pi$
$312$	−0.487878	−0.0276206
$313$	26.0174	1.47059	0.735294	−	0.677748i	$-0.237044\pi$
$313$	26.0174	1.47059	0.735294	+	0.677748i	$0.237044\pi$
$314$	−23.4943	−1.32586
$315$	−26.3339	−1.48375
$316$	14.7156	0.827818
$317$	12.5030	0.702240	0.351120	−	0.936330i	$-0.385801\pi$
$317$	12.5030	0.702240	0.351120	+	0.936330i	$0.385801\pi$
$318$	−0.763340	−0.0428060
$319$	10.9381	0.612418
$320$	−2.07635	−0.116072
$321$	1.78315	0.0995256
$322$	−36.8826	−2.05539
$323$	−4.79706	−0.266916
$324$	8.92519	0.495844
$325$	−3.68405	−0.204354
$326$	22.7799	1.26166
$327$	0.462930	0.0256001
$328$	−0.101215	−0.00558869
$329$	−52.4409	−2.89116
$330$	0.230985	0.0127153
$331$	15.1788	0.834301	0.417151	−	0.908837i	$-0.363029\pi$
$331$	15.1788	0.834301	0.417151	+	0.908837i	$0.363029\pi$
$332$	4.68674	0.257218
$333$	7.15969	0.392348
$334$	3.05270	0.167036
$335$	26.2662	1.43507
$336$	−0.386679	−0.0210951
$337$	−10.4858	−0.571199	−0.285600	−	0.958349i	$-0.592193\pi$
$337$	−10.4858	−0.571199	−0.285600	+	0.958349i	$0.592193\pi$
$338$	−15.6100	−0.849073
$339$	−0.710019	−0.0385629
$340$	9.96040	0.540178
$341$	9.73167	0.526999
$342$	2.99168	0.161772
$343$	−16.8389	−0.909217
$344$	−1.70148	−0.0917376
$345$	1.64769	0.0887087
$346$	16.9306	0.910192
$347$	8.37828	0.449770	0.224885	−	0.974385i	$-0.427799\pi$
$347$	8.37828	0.449770	0.224885	+	0.974385i	$0.427799\pi$
$348$	0.818020	0.0438505
$349$	−26.3939	−1.41283	−0.706417	−	0.707796i	$-0.749690\pi$
$349$	−26.3939	−1.41283	−0.706417	+	0.707796i	$0.749690\pi$
$350$	−2.91988	−0.156074
$351$	−2.92321	−0.156029
$352$	−1.21964	−0.0650069
$353$	−15.1382	−0.805727	−0.402863	−	0.915260i	$-0.631985\pi$
$353$	−15.1382	−0.805727	−0.402863	+	0.915260i	$0.631985\pi$
$354$	−1.05474	−0.0560590
$355$	24.0436	1.27610
$356$	−2.86593	−0.151894
$357$	1.85492	0.0981730
$358$	−0.00190612	−0.000100742 0
$359$	−8.52061	−0.449701	−0.224850	−	0.974393i	$-0.572189\pi$
$359$	−8.52061	−0.449701	−0.224850	+	0.974393i	$0.572189\pi$
$360$	−6.21179	−0.327390
$361$	1.00000	0.0526316
$362$	16.2480	0.853975
$363$	−0.867652	−0.0455399
$364$	−22.6756	−1.18852
$365$	25.4027	1.32964
$366$	0.743147	0.0388449
$367$	15.9441	0.832276	0.416138	−	0.909301i	$-0.363383\pi$
$367$	15.9441	0.832276	0.416138	+	0.909301i	$0.363383\pi$
$368$	−8.70007	−0.453523
$369$	−0.302804	−0.0157634
$370$	−4.96913	−0.258333
$371$	−35.4785	−1.84195
$372$	0.727794	0.0377343
$373$	−13.5204	−0.700059	−0.350029	−	0.936739i	$-0.613828\pi$
$373$	−13.5204	−0.700059	−0.350029	+	0.936739i	$0.613828\pi$
$374$	5.85068	0.302532
$375$	1.07738	0.0556359
$376$	−12.3700	−0.637936
$377$	47.9702	2.47059
$378$	−2.31686	−0.119166
$379$	26.6929	1.37112	0.685561	−	0.728015i	$-0.259557\pi$
$379$	26.6929	1.37112	0.685561	+	0.728015i	$0.259557\pi$
$380$	−2.07635	−0.106515
$381$	−1.22709	−0.0628656
$382$	−6.33124	−0.323934
$383$	36.3905	1.85947	0.929733	−	0.368234i	$-0.120037\pi$
$383$	36.3905	1.85947	0.929733	+	0.368234i	$0.120037\pi$
$384$	−0.0912120	−0.00465464
$385$	10.7357	0.547143
$386$	−8.73126	−0.444409
$387$	−5.09028	−0.258753
$388$	−4.23561	−0.215031
$389$	29.6921	1.50545	0.752725	−	0.658335i	$-0.228739\pi$
$389$	29.6921	1.50545	0.752725	+	0.658335i	$0.228739\pi$
$390$	1.01301	0.0512956
$391$	41.7348	2.11062
$392$	−10.9721	−0.554173
$393$	−0.701853	−0.0354038
$394$	8.99074	0.452947
$395$	−30.5548	−1.53738
$396$	−3.64877	−0.183357
$397$	−29.9634	−1.50382	−0.751909	−	0.659266i	$-0.770867\pi$
$397$	−29.9634	−1.50382	−0.751909	+	0.659266i	$0.770867\pi$
$398$	−0.827906	−0.0414992
$399$	−0.386679	−0.0193582
$400$	−0.688757	−0.0344379
$401$	−4.03064	−0.201281	−0.100640	−	0.994923i	$-0.532089\pi$
$401$	−4.03064	−0.201281	−0.100640	+	0.994923i	$0.532089\pi$
$402$	1.15384	0.0575485
$403$	42.6791	2.12600
$404$	15.9324	0.792667
$405$	−18.5319	−0.920855
$406$	38.0199	1.88690
$407$	−2.91884	−0.144681
$408$	0.437550	0.0216619
$409$	−2.10997	−0.104331	−0.0521657	−	0.998638i	$-0.516612\pi$
$409$	−2.10997	−0.104331	−0.0521657	+	0.998638i	$0.516612\pi$
$410$	0.210159	0.0103790
$411$	1.22559	0.0604537
$412$	−7.76664	−0.382635
$413$	−49.0224	−2.41223
$414$	−26.0278	−1.27920
$415$	−9.73132	−0.477692
$416$	−5.34883	−0.262248
$417$	−0.359861	−0.0176225
$418$	−1.21964	−0.0596544
$419$	−13.3365	−0.651532	−0.325766	−	0.945450i	$-0.605622\pi$
$419$	−13.3365	−0.651532	−0.325766	+	0.945450i	$0.605622\pi$
$420$	0.802883	0.0391767
$421$	9.41060	0.458645	0.229322	−	0.973351i	$-0.426349\pi$
$421$	9.41060	0.458645	0.229322	+	0.973351i	$0.426349\pi$
$422$	−1.00000	−0.0486792
$423$	−37.0072	−1.79935
$424$	−8.36886	−0.406428
$425$	3.30401	0.160268
$426$	1.05621	0.0511735
$427$	34.5400	1.67151
$428$	19.5495	0.944960
$429$	0.595034	0.0287285
$430$	3.53287	0.170370
$431$	−9.07209	−0.436987	−0.218494	−	0.975838i	$-0.570114\pi$
$431$	−9.07209	−0.436987	−0.218494	+	0.975838i	$0.570114\pi$
$432$	−0.546513	−0.0262941
$433$	−17.1920	−0.826195	−0.413098	−	0.910687i	$-0.635553\pi$
$433$	−17.1920	−0.826195	−0.413098	+	0.910687i	$0.635553\pi$
$434$	33.8264	1.62372
$435$	−1.69850	−0.0814368
$436$	5.07532	0.243064
$437$	−8.70007	−0.416181
$438$	1.11592	0.0533205
$439$	−26.1492	−1.24803	−0.624016	−	0.781412i	$-0.714500\pi$
$439$	−26.1492	−1.24803	−0.624016	+	0.781412i	$0.714500\pi$
$440$	2.53240	0.120727
$441$	−32.8249	−1.56309
$442$	25.6587	1.22046
$443$	−34.7100	−1.64912	−0.824561	−	0.565773i	$-0.808578\pi$
$443$	−34.7100	−1.64912	−0.824561	+	0.565773i	$0.808578\pi$
$444$	−0.218288	−0.0103595
$445$	5.95069	0.282090
$446$	16.2370	0.768845
$447$	0.504465	0.0238604
$448$	−4.23935	−0.200290
$449$	−10.5327	−0.497068	−0.248534	−	0.968623i	$-0.579949\pi$
$449$	−10.5327	−0.497068	−0.248534	+	0.968623i	$0.579949\pi$
$450$	−2.06054	−0.0971349
$451$	0.123446	0.00581286
$452$	−7.78427	−0.366141
$453$	0.833795	0.0391751
$454$	12.6885	0.595501
$455$	47.0825	2.20726
$456$	−0.0912120	−0.00427139
$457$	−21.0851	−0.986320	−0.493160	−	0.869939i	$-0.664158\pi$
$457$	−21.0851	−0.986320	−0.493160	+	0.869939i	$0.664158\pi$
$458$	−18.4194	−0.860681
$459$	2.62166	0.122369
$460$	18.0644	0.842258
$461$	−18.9973	−0.884794	−0.442397	−	0.896819i	$-0.645872\pi$
$461$	−18.9973	−0.884794	−0.442397	+	0.896819i	$0.645872\pi$
$462$	0.471609	0.0219412
$463$	−41.6892	−1.93746	−0.968731	−	0.248115i	$-0.920189\pi$
$463$	−41.6892	−1.93746	−0.968731	+	0.248115i	$0.920189\pi$
$464$	8.96834	0.416345
$465$	−1.51116	−0.0700782
$466$	1.30500	0.0604530
$467$	17.1981	0.795833	0.397917	−	0.917422i	$-0.369733\pi$
$467$	17.1981	0.795833	0.397917	+	0.917422i	$0.369733\pi$
$468$	−16.0020	−0.739693
$469$	53.6283	2.47633
$470$	25.6846	1.18474
$471$	2.14296	0.0987424
$472$	−11.5637	−0.532261
$473$	2.07519	0.0954173
$474$	−1.34224	−0.0616512
$475$	−0.688757	−0.0316024
$476$	20.3364	0.932118
$477$	−25.0369	−1.14636
$478$	0.257089	0.0117590
$479$	−34.0805	−1.55718	−0.778588	−	0.627535i	$-0.784064\pi$
$479$	−34.0805	−1.55718	−0.778588	+	0.627535i	$0.784064\pi$
$480$	0.189388	0.00864435
$481$	−12.8008	−0.583667
$482$	3.23468	0.147336
$483$	3.36414	0.153074
$484$	−9.51248	−0.432386
$485$	8.79463	0.399343
$486$	−2.45362	−0.111299
$487$	−10.0896	−0.457204	−0.228602	−	0.973520i	$-0.573415\pi$
$487$	−10.0896	−0.457204	−0.228602	+	0.973520i	$0.573415\pi$
$488$	8.14747	0.368819
$489$	−2.07780	−0.0939612
$490$	22.7819	1.02918
$491$	2.79930	0.126331	0.0631653	−	0.998003i	$-0.479880\pi$
$491$	2.79930	0.126331	0.0631653	+	0.998003i	$0.479880\pi$
$492$	0.00923206	0.000416213 0
$493$	−43.0217	−1.93760
$494$	−5.34883	−0.240655
$495$	7.57613	0.340522
$496$	7.97914	0.358274
$497$	49.0905	2.20201
$498$	−0.427487	−0.0191561
$499$	−27.4951	−1.23085	−0.615425	−	0.788196i	$-0.711016\pi$
$499$	−27.4951	−1.23085	−0.615425	+	0.788196i	$0.711016\pi$
$500$	11.8119	0.528243
$501$	−0.278443	−0.0124399
$502$	23.8467	1.06433
$503$	14.9562	0.666862	0.333431	−	0.942775i	$-0.391794\pi$
$503$	14.9562	0.666862	0.333431	+	0.942775i	$0.391794\pi$
$504$	−12.6828	−0.564935
$505$	−33.0813	−1.47210
$506$	10.6109	0.471714
$507$	1.42382	0.0632341
$508$	−13.4531	−0.596886
$509$	18.8182	0.834100	0.417050	−	0.908883i	$-0.363064\pi$
$509$	18.8182	0.834100	0.417050	+	0.908883i	$0.363064\pi$
$510$	−0.908508	−0.0402294
$511$	51.8655	2.29439
$512$	−1.00000	−0.0441942
$513$	−0.546513	−0.0241291
$514$	−25.1492	−1.10928
$515$	16.1263	0.710609
$516$	0.155195	0.00683209
$517$	15.0870	0.663524
$518$	−10.1456	−0.445772
$519$	−1.54427	−0.0677859
$520$	11.1061	0.487033
$521$	22.8484	1.00101	0.500503	−	0.865735i	$-0.333149\pi$
$521$	22.8484	1.00101	0.500503	+	0.865735i	$0.333149\pi$
$522$	26.8304	1.17434
$523$	24.2461	1.06021	0.530103	−	0.847933i	$-0.322153\pi$
$523$	24.2461	1.06021	0.530103	+	0.847933i	$0.322153\pi$
$524$	−7.69475	−0.336147
$525$	0.266328	0.0116235
$526$	−11.9521	−0.521136
$527$	−38.2765	−1.66735
$528$	0.111246	0.00484134
$529$	52.6913	2.29092
$530$	17.3767	0.754796
$531$	−34.5948	−1.50129
$532$	−4.23935	−0.183799
$533$	0.541384	0.0234500
$534$	0.261408	0.0113122
$535$	−40.5916	−1.75493
$536$	12.6501	0.546403
$537$	0.000173861 0	7.50267e−6 0
$538$	17.8042	0.767595
$539$	13.3819	0.576401
$540$	1.13475	0.0488320
$541$	1.17409	0.0504781	0.0252391	−	0.999681i	$-0.491965\pi$
$541$	1.17409	0.0504781	0.0252391	+	0.999681i	$0.491965\pi$
$542$	3.41956	0.146883
$543$	−1.48201	−0.0635992
$544$	4.79706	0.205672
$545$	−10.5382	−0.451405
$546$	2.06828	0.0885143
$547$	−7.77135	−0.332279	−0.166139	−	0.986102i	$-0.553130\pi$
$547$	−7.77135	−0.332279	−0.166139	+	0.986102i	$0.553130\pi$
$548$	13.4367	0.573987
$549$	24.3746	1.04028
$550$	0.840035	0.0358192
$551$	8.96834	0.382064
$552$	0.793551	0.0337758
$553$	−62.3846	−2.65286
$554$	27.3190	1.16067
$555$	0.453244	0.0192391
$556$	−3.94533	−0.167319
$557$	−5.39441	−0.228568	−0.114284	−	0.993448i	$-0.536457\pi$
$557$	−5.39441	−0.228568	−0.114284	+	0.993448i	$0.536457\pi$
$558$	23.8710	1.01054
$559$	9.10092	0.384928
$560$	8.80238	0.371968
$561$	−0.533652	−0.0225308
$562$	−18.5751	−0.783543
$563$	26.9032	1.13383	0.566917	−	0.823775i	$-0.308136\pi$
$563$	26.9032	1.13383	0.566917	+	0.823775i	$0.308136\pi$
$564$	1.12830	0.0475098
$565$	16.1629	0.679978
$566$	−3.98303	−0.167419
$567$	−37.8370	−1.58900
$568$	11.5797	0.485875
$569$	21.9243	0.919113	0.459557	−	0.888148i	$-0.348008\pi$
$569$	21.9243	0.919113	0.459557	+	0.888148i	$0.348008\pi$
$570$	0.189388	0.00793260
$571$	14.2092	0.594638	0.297319	−	0.954778i	$-0.403908\pi$
$571$	14.2092	0.594638	0.297319	+	0.954778i	$0.403908\pi$
$572$	6.52364	0.272767
$573$	0.577485	0.0241248
$574$	0.429087	0.0179098
$575$	5.99224	0.249894
$576$	−2.99168	−0.124653
$577$	21.0861	0.877827	0.438913	−	0.898529i	$-0.355364\pi$
$577$	21.0861	0.877827	0.438913	+	0.898529i	$0.355364\pi$
$578$	−6.01181	−0.250059
$579$	0.796395	0.0330971
$580$	−18.6214	−0.773214
$581$	−19.8687	−0.824293
$582$	0.386339	0.0160142
$583$	10.2070	0.422730
$584$	12.2343	0.506259
$585$	33.2258	1.37372
$586$	8.07523	0.333585
$587$	−5.44772	−0.224852	−0.112426	−	0.993660i	$-0.535862\pi$
$587$	−5.44772	−0.224852	−0.112426	+	0.993660i	$0.535862\pi$
$588$	1.00078	0.0412716
$589$	7.97914	0.328775
$590$	24.0102	0.988486
$591$	−0.820063	−0.0337329
$592$	−2.39320	−0.0983599
$593$	−22.5447	−0.925800	−0.462900	−	0.886410i	$-0.653191\pi$
$593$	−22.5447	−0.925800	−0.462900	+	0.886410i	$0.653191\pi$
$594$	0.666548	0.0273488
$595$	−42.2256	−1.73108
$596$	5.53069	0.226546
$597$	0.0755149	0.00309062
$598$	46.5352	1.90297
$599$	−19.6018	−0.800907	−0.400453	−	0.916317i	$-0.631147\pi$
$599$	−19.6018	−0.800907	−0.400453	+	0.916317i	$0.631147\pi$
$600$	0.0628229	0.00256474
$601$	37.7146	1.53841	0.769206	−	0.639001i	$-0.220652\pi$
$601$	37.7146	1.53841	0.769206	+	0.639001i	$0.220652\pi$
$602$	7.21316	0.293986
$603$	37.8452	1.54117
$604$	9.14129	0.371954
$605$	19.7513	0.803003
$606$	−1.45323	−0.0590333
$607$	2.84017	0.115279	0.0576394	−	0.998337i	$-0.481643\pi$
$607$	2.84017	0.115279	0.0576394	+	0.998337i	$0.481643\pi$
$608$	−1.00000	−0.0405554
$609$	−3.46787	−0.140525
$610$	−16.9170	−0.684950
$611$	66.1653	2.67676
$612$	14.3513	0.580116
$613$	−24.9095	−1.00609	−0.503043	−	0.864262i	$-0.667786\pi$
$613$	−24.9095	−1.00609	−0.503043	+	0.864262i	$0.667786\pi$
$614$	29.7517	1.20068
$615$	−0.0191690	−0.000772970 0
$616$	5.17047	0.208324
$617$	19.4771	0.784120	0.392060	−	0.919940i	$-0.371763\pi$
$617$	19.4771	0.784120	0.392060	+	0.919940i	$0.371763\pi$
$618$	0.708411	0.0284965
$619$	−21.9109	−0.880673	−0.440336	−	0.897833i	$-0.645141\pi$
$619$	−21.9109	−0.880673	−0.440336	+	0.897833i	$0.645141\pi$
$620$	−16.5675	−0.665368
$621$	4.75470	0.190800
$622$	21.5960	0.865922
$623$	12.1497	0.486767
$624$	0.487878	0.0195307
$625$	−21.0818	−0.843273
$626$	−26.0174	−1.03986
$627$	0.111246	0.00444272
$628$	23.4943	0.937524
$629$	11.4803	0.457751
$630$	26.3339	1.04917
$631$	19.5260	0.777318	0.388659	−	0.921382i	$-0.372938\pi$
$631$	19.5260	0.777318	0.388659	+	0.921382i	$0.372938\pi$
$632$	−14.7156	−0.585356
$633$	0.0912120	0.00362535
$634$	−12.5030	−0.496559
$635$	27.9335	1.10851
$636$	0.763340	0.0302684
$637$	58.6877	2.32529
$638$	−10.9381	−0.433045
$639$	34.6429	1.37045
$640$	2.07635	0.0820751
$641$	−1.51964	−0.0600222	−0.0300111	−	0.999550i	$-0.509554\pi$
$641$	−1.51964	−0.0600222	−0.0300111	+	0.999550i	$0.509554\pi$
$642$	−1.78315	−0.0703752
$643$	35.7182	1.40859	0.704294	−	0.709908i	$-0.251264\pi$
$643$	35.7182	1.40859	0.704294	+	0.709908i	$0.251264\pi$
$644$	36.8826	1.45338
$645$	−0.322240	−0.0126882
$646$	4.79706	0.188738
$647$	−20.0570	−0.788523	−0.394261	−	0.918998i	$-0.629000\pi$
$647$	−20.0570	−0.788523	−0.394261	+	0.918998i	$0.629000\pi$
$648$	−8.92519	−0.350615
$649$	14.1035	0.553610
$650$	3.68405	0.144500
$651$	−3.08537	−0.120925
$652$	−22.7799	−0.892129
$653$	17.7150	0.693241	0.346620	−	0.938006i	$-0.387329\pi$
$653$	17.7150	0.693241	0.346620	+	0.938006i	$0.387329\pi$
$654$	−0.462930	−0.0181020
$655$	15.9770	0.624274
$656$	0.101215	0.00395180
$657$	36.6011	1.42795
$658$	52.4409	2.04436
$659$	−15.7179	−0.612281	−0.306141	−	0.951986i	$-0.599038\pi$
$659$	−15.7179	−0.612281	−0.306141	+	0.951986i	$0.599038\pi$
$660$	−0.230985	−0.00899109
$661$	−40.8550	−1.58908	−0.794538	−	0.607214i	$-0.792287\pi$
$661$	−40.8550	−1.58908	−0.794538	+	0.607214i	$0.792287\pi$
$662$	−15.1788	−0.589940
$663$	−2.34038	−0.0908928
$664$	−4.68674	−0.181881
$665$	8.80238	0.341342
$666$	−7.15969	−0.277432
$667$	−78.0252	−3.02115
$668$	−3.05270	−0.118112
$669$	−1.48101	−0.0572592
$670$	−26.2662	−1.01475
$671$	−9.93697	−0.383612
$672$	0.386679	0.0149165
$673$	3.64478	0.140496	0.0702480	−	0.997530i	$-0.477621\pi$
$673$	3.64478	0.140496	0.0702480	+	0.997530i	$0.477621\pi$
$674$	10.4858	0.403899
$675$	0.376415	0.0144882
$676$	15.6100	0.600385
$677$	−48.3591	−1.85859	−0.929295	−	0.369338i	$-0.879584\pi$
$677$	−48.3591	−1.85859	−0.929295	+	0.369338i	$0.879584\pi$
$678$	0.710019	0.0272681
$679$	17.9562	0.689097
$680$	−9.96040	−0.381964
$681$	−1.15734	−0.0443495
$682$	−9.73167	−0.372645
$683$	−20.0805	−0.768360	−0.384180	−	0.923258i	$-0.625516\pi$
$683$	−20.0805	−0.768360	−0.384180	+	0.923258i	$0.625516\pi$
$684$	−2.99168	−0.114390
$685$	−27.8993	−1.06598
$686$	16.8389	0.642914
$687$	1.68007	0.0640986
$688$	1.70148	0.0648683
$689$	44.7636	1.70536
$690$	−1.64769	−0.0627266
$691$	0.276436	0.0105161	0.00525807	−	0.999986i	$-0.498326\pi$
$691$	0.276436	0.0105161	0.00525807	+	0.999986i	$0.498326\pi$
$692$	−16.9306	−0.643603
$693$	15.4684	0.587596
$694$	−8.37828	−0.318035
$695$	8.19190	0.310736
$696$	−0.818020	−0.0310070
$697$	−0.485537	−0.0183910
$698$	26.3939	0.999025
$699$	−0.119032	−0.00450219
$700$	2.91988	0.110361
$701$	2.56755	0.0969750	0.0484875	−	0.998824i	$-0.484560\pi$
$701$	2.56755	0.0969750	0.0484875	+	0.998824i	$0.484560\pi$
$702$	2.92321	0.110329
$703$	−2.39320	−0.0902612
$704$	1.21964	0.0459668
$705$	−2.34274	−0.0882327
$706$	15.1382	0.569735
$707$	−67.5430	−2.54022
$708$	1.05474	0.0396397
$709$	−7.36075	−0.276439	−0.138219	−	0.990402i	$-0.544138\pi$
$709$	−7.36075	−0.276439	−0.138219	+	0.990402i	$0.544138\pi$
$710$	−24.0436	−0.902341
$711$	−44.0244	−1.65104
$712$	2.86593	0.107405
$713$	−69.4191	−2.59977
$714$	−1.85492	−0.0694188
$715$	−13.5454	−0.506568
$716$	0.00190612	7.12352e−5 0
$717$	−0.0234496	−0.000875740 0
$718$	8.52061	0.317986
$719$	−29.1615	−1.08754	−0.543770	−	0.839234i	$-0.683004\pi$
$719$	−29.1615	−1.08754	−0.543770	+	0.839234i	$0.683004\pi$
$720$	6.21179	0.231500
$721$	32.9255	1.22621
$722$	−1.00000	−0.0372161
$723$	−0.295041	−0.0109727
$724$	−16.2480	−0.603851
$725$	−6.17701	−0.229409
$726$	0.867652	0.0322016
$727$	−18.3774	−0.681581	−0.340791	−	0.940139i	$-0.610695\pi$
$727$	−18.3774	−0.681581	−0.340791	+	0.940139i	$0.610695\pi$
$728$	22.6756	0.840412
$729$	−26.5518	−0.983399
$730$	−25.4027	−0.940198
$731$	−8.16210	−0.301886
$732$	−0.743147	−0.0274675
$733$	−16.4009	−0.605782	−0.302891	−	0.953025i	$-0.597952\pi$
$733$	−16.4009	−0.605782	−0.302891	+	0.953025i	$0.597952\pi$
$734$	−15.9441	−0.588508
$735$	−2.07798	−0.0766474
$736$	8.70007	0.320689
$737$	−15.4286	−0.568319
$738$	0.302804	0.0111464
$739$	35.4368	1.30357	0.651783	−	0.758406i	$-0.274021\pi$
$739$	35.4368	1.30357	0.651783	+	0.758406i	$0.274021\pi$
$740$	4.96913	0.182669
$741$	0.487878	0.0179226
$742$	35.4785	1.30246
$743$	−42.9116	−1.57427	−0.787136	−	0.616779i	$-0.788437\pi$
$743$	−42.9116	−1.57427	−0.787136	+	0.616779i	$0.788437\pi$
$744$	−0.727794	−0.0266822
$745$	−11.4837	−0.420729
$746$	13.5204	0.495016
$747$	−14.0212	−0.513010
$748$	−5.85068	−0.213922
$749$	−82.8771	−3.02826
$750$	−1.07738	−0.0393405
$751$	9.62699	0.351294	0.175647	−	0.984453i	$-0.443798\pi$
$751$	9.62699	0.351294	0.175647	+	0.984453i	$0.443798\pi$
$752$	12.3700	0.451089
$753$	−2.17511	−0.0792654
$754$	−47.9702	−1.74697
$755$	−18.9806	−0.690773
$756$	2.31686	0.0842633
$757$	−7.95010	−0.288951	−0.144476	−	0.989508i	$-0.546150\pi$
$757$	−7.95010	−0.288951	−0.144476	+	0.989508i	$0.546150\pi$
$758$	−26.6929	−0.969530
$759$	−0.967845	−0.0351305
$760$	2.07635	0.0753172
$761$	−21.2352	−0.769774	−0.384887	−	0.922964i	$-0.625760\pi$
$761$	−21.2352	−0.769774	−0.384887	+	0.922964i	$0.625760\pi$
$762$	1.22709	0.0444527
$763$	−21.5160	−0.778933
$764$	6.33124	0.229056
$765$	−29.7983	−1.07736
$766$	−36.3905	−1.31484
$767$	61.8521	2.23335
$768$	0.0912120	0.00329133
$769$	−40.1948	−1.44946	−0.724731	−	0.689032i	$-0.758036\pi$
$769$	−40.1948	−1.44946	−0.724731	+	0.689032i	$0.758036\pi$
$770$	−10.7357	−0.386888
$771$	2.29391	0.0826132
$772$	8.73126	0.314245
$773$	22.5975	0.812775	0.406388	−	0.913701i	$-0.366788\pi$
$773$	22.5975	0.812775	0.406388	+	0.913701i	$0.366788\pi$
$774$	5.09028	0.182966
$775$	−5.49570	−0.197411
$776$	4.23561	0.152050
$777$	0.925401	0.0331986
$778$	−29.6921	−1.06451
$779$	0.101215	0.00362642
$780$	−1.01301	−0.0362714
$781$	−14.1231	−0.505364
$782$	−41.7348	−1.49243
$783$	−4.90132	−0.175159
$784$	10.9721	0.391859
$785$	−48.7824	−1.74112
$786$	0.701853	0.0250343
$787$	−21.1772	−0.754885	−0.377443	−	0.926033i	$-0.623196\pi$
$787$	−21.1772	−0.754885	−0.377443	+	0.926033i	$0.623196\pi$
$788$	−8.99074	−0.320282
$789$	1.09017	0.0388112
$790$	30.5548	1.08709
$791$	33.0002	1.17335
$792$	3.64877	0.129653
$793$	−43.5795	−1.54755
$794$	29.9634	1.06336
$795$	−1.58496	−0.0562129
$796$	0.827906	0.0293443
$797$	31.1198	1.10232	0.551160	−	0.834399i	$-0.314185\pi$
$797$	31.1198	1.10232	0.551160	+	0.834399i	$0.314185\pi$
$798$	0.386679	0.0136883
$799$	−59.3399	−2.09929
$800$	0.688757	0.0243513
$801$	8.57396	0.302946
$802$	4.03064	0.142327
$803$	−14.9214	−0.526566
$804$	−1.15384	−0.0406930
$805$	−76.5813	−2.69914
$806$	−42.6791	−1.50331
$807$	−1.62396	−0.0571661
$808$	−15.9324	−0.560500
$809$	−39.5765	−1.39143	−0.695717	−	0.718316i	$-0.744913\pi$
$809$	−39.5765	−1.39143	−0.695717	+	0.718316i	$0.744913\pi$
$810$	18.5319	0.651143
$811$	9.20757	0.323321	0.161661	−	0.986846i	$-0.448315\pi$
$811$	9.20757	0.323321	0.161661	+	0.986846i	$0.448315\pi$
$812$	−38.0199	−1.33424
$813$	−0.311905	−0.0109390
$814$	2.91884	0.102305
$815$	47.2991	1.65681
$816$	−0.437550	−0.0153173
$817$	1.70148	0.0595272
$818$	2.10997	0.0737735
$819$	67.8380	2.37045
$820$	−0.210159	−0.00733907
$821$	30.6845	1.07090	0.535449	−	0.844568i	$-0.320142\pi$
$821$	30.6845	1.07090	0.535449	+	0.844568i	$0.320142\pi$
$822$	−1.22559	−0.0427473
$823$	20.7117	0.721964	0.360982	−	0.932573i	$-0.382442\pi$
$823$	20.7117	0.721964	0.360982	+	0.932573i	$0.382442\pi$
$824$	7.76664	0.270564
$825$	−0.0766212	−0.00266761
$826$	49.0224	1.70571
$827$	−18.8551	−0.655656	−0.327828	−	0.944737i	$-0.606317\pi$
$827$	−18.8551	−0.655656	−0.327828	+	0.944737i	$0.606317\pi$
$828$	26.0278	0.904530
$829$	−46.7486	−1.62365	−0.811823	−	0.583903i	$-0.801525\pi$
$829$	−46.7486	−1.62365	−0.811823	+	0.583903i	$0.801525\pi$
$830$	9.73132	0.337779
$831$	−2.49182	−0.0864402
$832$	5.34883	0.185437
$833$	−52.6337	−1.82365
$834$	0.359861	0.0124610
$835$	6.33848	0.219352
$836$	1.21964	0.0421821
$837$	−4.36071	−0.150728
$838$	13.3365	0.460703
$839$	−45.2240	−1.56131	−0.780653	−	0.624964i	$-0.785114\pi$
$839$	−45.2240	−1.56131	−0.780653	+	0.624964i	$0.785114\pi$
$840$	−0.802883	−0.0277021
$841$	51.4312	1.77349
$842$	−9.41060	−0.324311
$843$	1.69427	0.0583538
$844$	1.00000	0.0344214
$845$	−32.4119	−1.11500
$846$	37.0072	1.27233
$847$	40.3267	1.38564
$848$	8.36886	0.287388
$849$	0.363300	0.0124684
$850$	−3.30401	−0.113327
$851$	20.8210	0.713735
$852$	−1.05621	−0.0361852
$853$	−7.32286	−0.250730	−0.125365	−	0.992111i	$-0.540010\pi$
$853$	−7.32286	−0.250730	−0.125365	+	0.992111i	$0.540010\pi$
$854$	−34.5400	−1.18193
$855$	6.21179	0.212439
$856$	−19.5495	−0.668188
$857$	−11.5583	−0.394825	−0.197413	−	0.980321i	$-0.563254\pi$
$857$	−11.5583	−0.394825	−0.197413	+	0.980321i	$0.563254\pi$
$858$	−0.595034	−0.0203141
$859$	32.6188	1.11294	0.556470	−	0.830868i	$-0.312155\pi$
$859$	32.6188	1.11294	0.556470	+	0.830868i	$0.312155\pi$
$860$	−3.53287	−0.120470
$861$	−0.0391379	−0.00133382
$862$	9.07209	0.308997
$863$	−0.910913	−0.0310079	−0.0155039	−	0.999880i	$-0.504935\pi$
$863$	−0.910913	−0.0310079	−0.0155039	+	0.999880i	$0.504935\pi$
$864$	0.546513	0.0185928
$865$	35.1538	1.19527
$866$	17.1920	0.584208
$867$	0.548350	0.0186229
$868$	−33.8264	−1.14814
$869$	17.9477	0.608835
$870$	1.69850	0.0575845
$871$	−67.6635	−2.29269
$872$	−5.07532	−0.171872
$873$	12.6716	0.428869
$874$	8.70007	0.294284
$875$	−50.0746	−1.69283
$876$	−1.11592	−0.0377033
$877$	40.7571	1.37627	0.688135	−	0.725583i	$-0.258430\pi$
$877$	40.7571	1.37627	0.688135	+	0.725583i	$0.258430\pi$
$878$	26.1492	0.882491
$879$	−0.736558	−0.0248435
$880$	−2.53240	−0.0853672
$881$	8.02643	0.270417	0.135209	−	0.990817i	$-0.456830\pi$
$881$	8.02643	0.270417	0.135209	+	0.990817i	$0.456830\pi$
$882$	32.8249	1.10527
$883$	44.7098	1.50460	0.752302	−	0.658818i	$-0.228943\pi$
$883$	44.7098	1.50460	0.752302	+	0.658818i	$0.228943\pi$
$884$	−25.6587	−0.862995
$885$	−2.19002	−0.0736168
$886$	34.7100	1.16611
$887$	29.1696	0.979421	0.489710	−	0.871885i	$-0.337103\pi$
$887$	29.1696	0.979421	0.489710	+	0.871885i	$0.337103\pi$
$888$	0.218288	0.00732528
$889$	57.0325	1.91281
$890$	−5.95069	−0.199468
$891$	10.8855	0.364678
$892$	−16.2370	−0.543656
$893$	12.3700	0.413948
$894$	−0.504465	−0.0168718
$895$	−0.00395779	−0.000132294 0
$896$	4.23935	0.141627
$897$	−4.24457	−0.141722
$898$	10.5327	0.351480
$899$	71.5597	2.38665
$900$	2.06054	0.0686847
$901$	−40.1459	−1.33745
$902$	−0.123446	−0.00411031
$903$	−0.657926	−0.0218944
$904$	7.78427	0.258901
$905$	33.7365	1.12144
$906$	−0.833795	−0.0277010
$907$	−59.4036	−1.97246	−0.986232	−	0.165366i	$-0.947120\pi$
$907$	−59.4036	−1.97246	−0.986232	+	0.165366i	$0.947120\pi$
$908$	−12.6885	−0.421083
$909$	−47.6647	−1.58094
$910$	−47.0825	−1.56077
$911$	−38.8733	−1.28793	−0.643965	−	0.765055i	$-0.722712\pi$
$911$	−38.8733	−1.28793	−0.643965	+	0.765055i	$0.722712\pi$
$912$	0.0912120	0.00302033
$913$	5.71612	0.189176
$914$	21.0851	0.697433
$915$	1.54304	0.0510112
$916$	18.4194	0.608593
$917$	32.6207	1.07723
$918$	−2.62166	−0.0865276
$919$	−24.1512	−0.796674	−0.398337	−	0.917239i	$-0.630413\pi$
$919$	−24.1512	−0.796674	−0.398337	+	0.917239i	$0.630413\pi$
$920$	−18.0644	−0.595566
$921$	−2.71371	−0.0894198
$922$	18.9973	0.625644
$923$	−61.9380	−2.03872
$924$	−0.471609	−0.0155148
$925$	1.64833	0.0541969
$926$	41.6892	1.36999
$927$	23.2353	0.763148
$928$	−8.96834	−0.294400
$929$	−29.7729	−0.976817	−0.488409	−	0.872615i	$-0.662422\pi$
$929$	−29.7729	−0.976817	−0.488409	+	0.872615i	$0.662422\pi$
$930$	1.51116	0.0495528
$931$	10.9721	0.359595
$932$	−1.30500	−0.0427467
$933$	−1.96982	−0.0644889
$934$	−17.1981	−0.562739
$935$	12.1481	0.397285
$936$	16.0020	0.523042
$937$	30.2249	0.987404	0.493702	−	0.869631i	$-0.335643\pi$
$937$	30.2249	0.987404	0.493702	+	0.869631i	$0.335643\pi$
$938$	−53.6283	−1.75103
$939$	2.37309	0.0774430
$940$	−25.6846	−0.837738
$941$	−16.4484	−0.536202	−0.268101	−	0.963391i	$-0.586396\pi$
$941$	−16.4484	−0.536202	−0.268101	+	0.963391i	$0.586396\pi$
$942$	−2.14296	−0.0698214
$943$	−0.880582	−0.0286757
$944$	11.5637	0.376365
$945$	−4.81062	−0.156489
$946$	−2.07519	−0.0674702
$947$	40.6094	1.31963	0.659815	−	0.751429i	$-0.270635\pi$
$947$	40.6094	1.31963	0.659815	+	0.751429i	$0.270635\pi$
$948$	1.34224	0.0435939
$949$	−65.4393	−2.12425
$950$	0.688757	0.0223462
$951$	1.14043	0.0369809
$952$	−20.3364	−0.659107
$953$	33.0560	1.07079	0.535395	−	0.844602i	$-0.320163\pi$
$953$	33.0560	1.07079	0.535395	+	0.844602i	$0.320163\pi$
$954$	25.0369	0.810601
$955$	−13.1459	−0.425391
$956$	−0.257089	−0.00831484
$957$	0.997689	0.0322507
$958$	34.0805	1.10109
$959$	−56.9628	−1.83942
$960$	−0.189388	−0.00611248
$961$	32.6667	1.05377
$962$	12.8008	0.412715
$963$	−58.4858	−1.88468
$964$	−3.23468	−0.104182
$965$	−18.1292	−0.583599
$966$	−3.36414	−0.108239
$967$	6.38945	0.205471	0.102735	−	0.994709i	$-0.467241\pi$
$967$	6.38945	0.205471	0.102735	+	0.994709i	$0.467241\pi$
$968$	9.51248	0.305743
$969$	−0.437550	−0.0140561
$970$	−8.79463	−0.282378
$971$	−34.3119	−1.10112	−0.550560	−	0.834795i	$-0.685586\pi$
$971$	−34.3119	−1.10112	−0.550560	+	0.834795i	$0.685586\pi$
$972$	2.45362	0.0787000
$973$	16.7256	0.536199
$974$	10.0896	0.323292
$975$	−0.336029	−0.0107616
$976$	−8.14747	−0.260794
$977$	50.0353	1.60077	0.800385	−	0.599487i	$-0.204629\pi$
$977$	50.0353	1.60077	0.800385	+	0.599487i	$0.204629\pi$
$978$	2.07780	0.0664406
$979$	−3.49540	−0.111714
$980$	−22.7819	−0.727740
$981$	−15.1837	−0.484779
$982$	−2.79930	−0.0893292
$983$	1.61431	0.0514886	0.0257443	−	0.999669i	$-0.491804\pi$
$983$	1.61431	0.0514886	0.0257443	+	0.999669i	$0.491804\pi$
$984$	−0.00923206	−0.000294307 0
$985$	18.6679	0.594810
$986$	43.0217	1.37009
$987$	−4.78324	−0.152252
$988$	5.34883	0.170169
$989$	−14.8030	−0.470708
$990$	−7.57613	−0.240785
$991$	46.4038	1.47406	0.737032	−	0.675857i	$-0.236227\pi$
$991$	46.4038	1.47406	0.737032	+	0.675857i	$0.236227\pi$
$992$	−7.97914	−0.253338
$993$	1.38449	0.0439354
$994$	−49.0905	−1.55706
$995$	−1.71902	−0.0544967
$996$	0.427487	0.0135454
$997$	24.4372	0.773935	0.386967	−	0.922093i	$-0.373523\pi$
$997$	24.4372	0.773935	0.386967	+	0.922093i	$0.373523\pi$
$998$	27.4951	0.870342
$999$	1.30791	0.0413806

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.g.1.18	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.g.1.18	✓	34	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.0912120 q^{3} +1.00000 q^{4} -2.07635 q^{5} -0.0912120 q^{6} -4.23935 q^{7} -1.00000 q^{8} -2.99168 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.0912120 q^{3} +1.00000 q^{4} -2.07635 q^{5} -0.0912120 q^{6} -4.23935 q^{7} -1.00000 q^{8} -2.99168 q^{9} +2.07635 q^{10} +1.21964 q^{11} +0.0912120 q^{12} +5.34883 q^{13} +4.23935 q^{14} -0.189388 q^{15} +1.00000 q^{16} -4.79706 q^{17} +2.99168 q^{18} +1.00000 q^{19} -2.07635 q^{20} -0.386679 q^{21} -1.21964 q^{22} -8.70007 q^{23} -0.0912120 q^{24} -0.688757 q^{25} -5.34883 q^{26} -0.546513 q^{27} -4.23935 q^{28} +8.96834 q^{29} +0.189388 q^{30} +7.97914 q^{31} -1.00000 q^{32} +0.111246 q^{33} +4.79706 q^{34} +8.80238 q^{35} -2.99168 q^{36} -2.39320 q^{37} -1.00000 q^{38} +0.487878 q^{39} +2.07635 q^{40} +0.101215 q^{41} +0.386679 q^{42} +1.70148 q^{43} +1.21964 q^{44} +6.21179 q^{45} +8.70007 q^{46} +12.3700 q^{47} +0.0912120 q^{48} +10.9721 q^{49} +0.688757 q^{50} -0.437550 q^{51} +5.34883 q^{52} +8.36886 q^{53} +0.546513 q^{54} -2.53240 q^{55} +4.23935 q^{56} +0.0912120 q^{57} -8.96834 q^{58} +11.5637 q^{59} -0.189388 q^{60} -8.14747 q^{61} -7.97914 q^{62} +12.6828 q^{63} +1.00000 q^{64} -11.1061 q^{65} -0.111246 q^{66} -12.6501 q^{67} -4.79706 q^{68} -0.793551 q^{69} -8.80238 q^{70} -11.5797 q^{71} +2.99168 q^{72} -12.2343 q^{73} +2.39320 q^{74} -0.0628229 q^{75} +1.00000 q^{76} -5.17047 q^{77} -0.487878 q^{78} +14.7156 q^{79} -2.07635 q^{80} +8.92519 q^{81} -0.101215 q^{82} +4.68674 q^{83} -0.386679 q^{84} +9.96040 q^{85} -1.70148 q^{86} +0.818020 q^{87} -1.21964 q^{88} -2.86593 q^{89} -6.21179 q^{90} -22.6756 q^{91} -8.70007 q^{92} +0.727794 q^{93} -12.3700 q^{94} -2.07635 q^{95} -0.0912120 q^{96} -4.23561 q^{97} -10.9721 q^{98} -3.64877 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 34 q^{2} - 6 q^{3} + 34 q^{4} + q^{5} + 6 q^{6} - 22 q^{7} - 34 q^{8} + 30 q^{9}+O(q^{10}) \) 34 * q - 34 * q^2 - 6 * q^3 + 34 * q^4 + q^5 + 6 * q^6 - 22 * q^7 - 34 * q^8 + 30 * q^9	\( 34 q - 34 q^{2} - 6 q^{3} + 34 q^{4} + q^{5} + 6 q^{6} - 22 q^{7} - 34 q^{8} + 30 q^{9} - q^{10} + 7 q^{11} - 6 q^{12} - 11 q^{13} + 22 q^{14} - 18 q^{15} + 34 q^{16} - 10 q^{17} - 30 q^{18} + 34 q^{19} + q^{20} + 14 q^{21} - 7 q^{22} - 30 q^{23} + 6 q^{24} + 11 q^{25} + 11 q^{26} - 21 q^{27} - 22 q^{28} + 12 q^{29} + 18 q^{30} - 13 q^{31} - 34 q^{32} - 4 q^{33} + 10 q^{34} - 16 q^{35} + 30 q^{36} - 46 q^{37} - 34 q^{38} - 36 q^{39} - q^{40} + 25 q^{41} - 14 q^{42} - 51 q^{43} + 7 q^{44} - 17 q^{45} + 30 q^{46} - 20 q^{47} - 6 q^{48} - 2 q^{49} - 11 q^{50} + 4 q^{51} - 11 q^{52} - 7 q^{53} + 21 q^{54} - 39 q^{55} + 22 q^{56} - 6 q^{57} - 12 q^{58} + 19 q^{59} - 18 q^{60} - 26 q^{61} + 13 q^{62} - 57 q^{63} + 34 q^{64} + 20 q^{65} + 4 q^{66} - 54 q^{67} - 10 q^{68} + 16 q^{70} + 9 q^{71} - 30 q^{72} - 57 q^{73} + 46 q^{74} + 26 q^{75} + 34 q^{76} + 2 q^{77} + 36 q^{78} - 7 q^{79} + q^{80} + 22 q^{81} - 25 q^{82} - 15 q^{83} + 14 q^{84} - 30 q^{85} + 51 q^{86} - 37 q^{87} - 7 q^{88} + 78 q^{89} + 17 q^{90} - 31 q^{91} - 30 q^{92} - 43 q^{93} + 20 q^{94} + q^{95} + 6 q^{96} - 38 q^{97} + 2 q^{98} + 2 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 - 6 * q^3 + 34 * q^4 + q^5 + 6 * q^6 - 22 * q^7 - 34 * q^8 + 30 * q^9 - q^10 + 7 * q^11 - 6 * q^12 - 11 * q^13 + 22 * q^14 - 18 * q^15 + 34 * q^16 - 10 * q^17 - 30 * q^18 + 34 * q^19 + q^20 + 14 * q^21 - 7 * q^22 - 30 * q^23 + 6 * q^24 + 11 * q^25 + 11 * q^26 - 21 * q^27 - 22 * q^28 + 12 * q^29 + 18 * q^30 - 13 * q^31 - 34 * q^32 - 4 * q^33 + 10 * q^34 - 16 * q^35 + 30 * q^36 - 46 * q^37 - 34 * q^38 - 36 * q^39 - q^40 + 25 * q^41 - 14 * q^42 - 51 * q^43 + 7 * q^44 - 17 * q^45 + 30 * q^46 - 20 * q^47 - 6 * q^48 - 2 * q^49 - 11 * q^50 + 4 * q^51 - 11 * q^52 - 7 * q^53 + 21 * q^54 - 39 * q^55 + 22 * q^56 - 6 * q^57 - 12 * q^58 + 19 * q^59 - 18 * q^60 - 26 * q^61 + 13 * q^62 - 57 * q^63 + 34 * q^64 + 20 * q^65 + 4 * q^66 - 54 * q^67 - 10 * q^68 + 16 * q^70 + 9 * q^71 - 30 * q^72 - 57 * q^73 + 46 * q^74 + 26 * q^75 + 34 * q^76 + 2 * q^77 + 36 * q^78 - 7 * q^79 + q^80 + 22 * q^81 - 25 * q^82 - 15 * q^83 + 14 * q^84 - 30 * q^85 + 51 * q^86 - 37 * q^87 - 7 * q^88 + 78 * q^89 + 17 * q^90 - 31 * q^91 - 30 * q^92 - 43 * q^93 + 20 * q^94 + q^95 + 6 * q^96 - 38 * q^97 + 2 * q^98 + 2 * q^99

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