LMFDB - Embedded newform 8026.2.a.a.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8026,2,Mod(1,8026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8026, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8026 = 2 \cdot 4013 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8026.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:	$64.0879326623$
Analytic rank:	$1$
Dimension:	$71$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	8026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.02372 q^{3} +1.00000 q^{4} +3.74567 q^{5} -2.02372 q^{6} +1.02525 q^{7} +1.00000 q^{8} +1.09543 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.02372 q^{3} +1.00000 q^{4} +3.74567 q^{5} -2.02372 q^{6} +1.02525 q^{7} +1.00000 q^{8} +1.09543 q^{9} +3.74567 q^{10} -3.56254 q^{11} -2.02372 q^{12} +0.856017 q^{13} +1.02525 q^{14} -7.58017 q^{15} +1.00000 q^{16} -7.78358 q^{17} +1.09543 q^{18} -4.10209 q^{19} +3.74567 q^{20} -2.07481 q^{21} -3.56254 q^{22} -0.878792 q^{23} -2.02372 q^{24} +9.03001 q^{25} +0.856017 q^{26} +3.85431 q^{27} +1.02525 q^{28} -1.17810 q^{29} -7.58017 q^{30} +8.52107 q^{31} +1.00000 q^{32} +7.20958 q^{33} -7.78358 q^{34} +3.84023 q^{35} +1.09543 q^{36} -8.40818 q^{37} -4.10209 q^{38} -1.73234 q^{39} +3.74567 q^{40} -1.59845 q^{41} -2.07481 q^{42} +9.33256 q^{43} -3.56254 q^{44} +4.10311 q^{45} -0.878792 q^{46} +0.295868 q^{47} -2.02372 q^{48} -5.94887 q^{49} +9.03001 q^{50} +15.7518 q^{51} +0.856017 q^{52} +5.45679 q^{53} +3.85431 q^{54} -13.3441 q^{55} +1.02525 q^{56} +8.30147 q^{57} -1.17810 q^{58} -10.3432 q^{59} -7.58017 q^{60} -13.8507 q^{61} +8.52107 q^{62} +1.12308 q^{63} +1.00000 q^{64} +3.20636 q^{65} +7.20958 q^{66} +2.14670 q^{67} -7.78358 q^{68} +1.77843 q^{69} +3.84023 q^{70} +10.3802 q^{71} +1.09543 q^{72} -7.09918 q^{73} -8.40818 q^{74} -18.2742 q^{75} -4.10209 q^{76} -3.65248 q^{77} -1.73234 q^{78} -11.8492 q^{79} +3.74567 q^{80} -11.0863 q^{81} -1.59845 q^{82} -12.1171 q^{83} -2.07481 q^{84} -29.1547 q^{85} +9.33256 q^{86} +2.38415 q^{87} -3.56254 q^{88} +5.16545 q^{89} +4.10311 q^{90} +0.877628 q^{91} -0.878792 q^{92} -17.2442 q^{93} +0.295868 q^{94} -15.3651 q^{95} -2.02372 q^{96} +0.0176862 q^{97} -5.94887 q^{98} -3.90251 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 71 q + 71 q^{2} - 9 q^{3} + 71 q^{4} - 34 q^{5} - 9 q^{6} - 19 q^{7} + 71 q^{8} + 34 q^{9}+O(q^{10}) $ 71 * q + 71 * q^2 - 9 * q^3 + 71 * q^4 - 34 * q^5 - 9 * q^6 - 19 * q^7 + 71 * q^8 + 34 * q^9	\( 71 q + 71 q^{2} - 9 q^{3} + 71 q^{4} - 34 q^{5} - 9 q^{6} - 19 q^{7} + 71 q^{8} + 34 q^{9} - 34 q^{10} - 37 q^{11} - 9 q^{12} - 62 q^{13} - 19 q^{14} - 29 q^{15} + 71 q^{16} - 52 q^{17} + 34 q^{18} - 30 q^{19} - 34 q^{20} - 51 q^{21} - 37 q^{22} - 45 q^{23} - 9 q^{24} + 27 q^{25} - 62 q^{26} - 27 q^{27} - 19 q^{28} - 55 q^{29} - 29 q^{30} - 61 q^{31} + 71 q^{32} - 73 q^{33} - 52 q^{34} - 33 q^{35} + 34 q^{36} - 43 q^{37} - 30 q^{38} - 40 q^{39} - 34 q^{40} - 87 q^{41} - 51 q^{42} - 4 q^{43} - 37 q^{44} - 81 q^{45} - 45 q^{46} - 89 q^{47} - 9 q^{48} - 2 q^{49} + 27 q^{50} - 19 q^{51} - 62 q^{52} - 50 q^{53} - 27 q^{54} - 66 q^{55} - 19 q^{56} - 45 q^{57} - 55 q^{58} - 118 q^{59} - 29 q^{60} - 92 q^{61} - 61 q^{62} - 54 q^{63} + 71 q^{64} - 51 q^{65} - 73 q^{66} - 17 q^{67} - 52 q^{68} - 89 q^{69} - 33 q^{70} - 95 q^{71} + 34 q^{72} - 114 q^{73} - 43 q^{74} - 38 q^{75} - 30 q^{76} - 73 q^{77} - 40 q^{78} - 47 q^{79} - 34 q^{80} - 57 q^{81} - 87 q^{82} - 68 q^{83} - 51 q^{84} - 67 q^{85} - 4 q^{86} - 55 q^{87} - 37 q^{88} - 150 q^{89} - 81 q^{90} - 23 q^{91} - 45 q^{92} - 59 q^{93} - 89 q^{94} - 47 q^{95} - 9 q^{96} - 97 q^{97} - 2 q^{98} - 57 q^{99}+O(q^{100}) \) 71 * q + 71 * q^2 - 9 * q^3 + 71 * q^4 - 34 * q^5 - 9 * q^6 - 19 * q^7 + 71 * q^8 + 34 * q^9 - 34 * q^10 - 37 * q^11 - 9 * q^12 - 62 * q^13 - 19 * q^14 - 29 * q^15 + 71 * q^16 - 52 * q^17 + 34 * q^18 - 30 * q^19 - 34 * q^20 - 51 * q^21 - 37 * q^22 - 45 * q^23 - 9 * q^24 + 27 * q^25 - 62 * q^26 - 27 * q^27 - 19 * q^28 - 55 * q^29 - 29 * q^30 - 61 * q^31 + 71 * q^32 - 73 * q^33 - 52 * q^34 - 33 * q^35 + 34 * q^36 - 43 * q^37 - 30 * q^38 - 40 * q^39 - 34 * q^40 - 87 * q^41 - 51 * q^42 - 4 * q^43 - 37 * q^44 - 81 * q^45 - 45 * q^46 - 89 * q^47 - 9 * q^48 - 2 * q^49 + 27 * q^50 - 19 * q^51 - 62 * q^52 - 50 * q^53 - 27 * q^54 - 66 * q^55 - 19 * q^56 - 45 * q^57 - 55 * q^58 - 118 * q^59 - 29 * q^60 - 92 * q^61 - 61 * q^62 - 54 * q^63 + 71 * q^64 - 51 * q^65 - 73 * q^66 - 17 * q^67 - 52 * q^68 - 89 * q^69 - 33 * q^70 - 95 * q^71 + 34 * q^72 - 114 * q^73 - 43 * q^74 - 38 * q^75 - 30 * q^76 - 73 * q^77 - 40 * q^78 - 47 * q^79 - 34 * q^80 - 57 * q^81 - 87 * q^82 - 68 * q^83 - 51 * q^84 - 67 * q^85 - 4 * q^86 - 55 * q^87 - 37 * q^88 - 150 * q^89 - 81 * q^90 - 23 * q^91 - 45 * q^92 - 59 * q^93 - 89 * q^94 - 47 * q^95 - 9 * q^96 - 97 * q^97 - 2 * q^98 - 57 * 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
$3$	−2.02372	−1.16839	−0.584197	−	0.811612i	$-0.698590\pi$
$3$	−2.02372	−1.16839	−0.584197	+	0.811612i	$0.698590\pi$
$4$	1.00000	0.500000
$5$	3.74567	1.67511	0.837556	−	0.546351i	$-0.183984\pi$
$5$	3.74567	1.67511	0.837556	+	0.546351i	$0.183984\pi$
$6$	−2.02372	−0.826179
$7$	1.02525	0.387506	0.193753	−	0.981050i	$-0.437934\pi$
$7$	1.02525	0.387506	0.193753	+	0.981050i	$0.437934\pi$
$8$	1.00000	0.353553
$9$	1.09543	0.365143
$10$	3.74567	1.18448
$11$	−3.56254	−1.07415	−0.537074	−	0.843535i	$-0.680470\pi$
$11$	−3.56254	−1.07415	−0.537074	+	0.843535i	$0.680470\pi$
$12$	−2.02372	−0.584197
$13$	0.856017	0.237417	0.118708	−	0.992929i	$-0.462125\pi$
$13$	0.856017	0.237417	0.118708	+	0.992929i	$0.462125\pi$
$14$	1.02525	0.274008
$15$	−7.58017	−1.95719
$16$	1.00000	0.250000
$17$	−7.78358	−1.88780	−0.943898	−	0.330237i	$-0.892871\pi$
$17$	−7.78358	−1.88780	−0.943898	+	0.330237i	$0.892871\pi$
$18$	1.09543	0.258195
$19$	−4.10209	−0.941084	−0.470542	−	0.882378i	$-0.655942\pi$
$19$	−4.10209	−0.941084	−0.470542	+	0.882378i	$0.655942\pi$
$20$	3.74567	0.837556
$21$	−2.07481	−0.452760
$22$	−3.56254	−0.759537
$23$	−0.878792	−0.183241	−0.0916204	−	0.995794i	$-0.529205\pi$
$23$	−0.878792	−0.183241	−0.0916204	+	0.995794i	$0.529205\pi$
$24$	−2.02372	−0.413089
$25$	9.03001	1.80600
$26$	0.856017	0.167879
$27$	3.85431	0.741763
$28$	1.02525	0.193753
$29$	−1.17810	−0.218768	−0.109384	−	0.994000i	$-0.534888\pi$
$29$	−1.17810	−0.218768	−0.109384	+	0.994000i	$0.534888\pi$
$30$	−7.58017	−1.38394
$31$	8.52107	1.53043	0.765215	−	0.643775i	$-0.222633\pi$
$31$	8.52107	1.53043	0.765215	+	0.643775i	$0.222633\pi$
$32$	1.00000	0.176777
$33$	7.20958	1.25503
$34$	−7.78358	−1.33487
$35$	3.84023	0.649117
$36$	1.09543	0.182571
$37$	−8.40818	−1.38230	−0.691148	−	0.722713i	$-0.742895\pi$
$37$	−8.40818	−1.38230	−0.691148	+	0.722713i	$0.742895\pi$
$38$	−4.10209	−0.665447
$39$	−1.73234	−0.277396
$40$	3.74567	0.592242
$41$	−1.59845	−0.249636	−0.124818	−	0.992180i	$-0.539835\pi$
$41$	−1.59845	−0.249636	−0.124818	+	0.992180i	$0.539835\pi$
$42$	−2.07481	−0.320149
$43$	9.33256	1.42320	0.711601	−	0.702584i	$-0.247970\pi$
$43$	9.33256	1.42320	0.711601	+	0.702584i	$0.247970\pi$
$44$	−3.56254	−0.537074
$45$	4.10311	0.611655
$46$	−0.878792	−0.129571
$47$	0.295868	0.0431568	0.0215784	−	0.999767i	$-0.493131\pi$
$47$	0.295868	0.0431568	0.0215784	+	0.999767i	$0.493131\pi$
$48$	−2.02372	−0.292098
$49$	−5.94887	−0.849839
$50$	9.03001	1.27704
$51$	15.7518	2.20569
$52$	0.856017	0.118708
$53$	5.45679	0.749548	0.374774	−	0.927116i	$-0.377720\pi$
$53$	5.45679	0.749548	0.374774	+	0.927116i	$0.377720\pi$
$54$	3.85431	0.524505
$55$	−13.3441	−1.79932
$56$	1.02525	0.137004
$57$	8.30147	1.09956
$58$	−1.17810	−0.154693
$59$	−10.3432	−1.34657	−0.673284	−	0.739384i	$-0.735117\pi$
$59$	−10.3432	−1.34657	−0.673284	+	0.739384i	$0.735117\pi$
$60$	−7.58017	−0.978595
$61$	−13.8507	−1.77339	−0.886697	−	0.462350i	$-0.847006\pi$
$61$	−13.8507	−1.77339	−0.886697	+	0.462350i	$0.847006\pi$
$62$	8.52107	1.08218
$63$	1.12308	0.141495
$64$	1.00000	0.125000
$65$	3.20636	0.397699
$66$	7.20958	0.887438
$67$	2.14670	0.262262	0.131131	−	0.991365i	$-0.458139\pi$
$67$	2.14670	0.262262	0.131131	+	0.991365i	$0.458139\pi$
$68$	−7.78358	−0.943898
$69$	1.77843	0.214097
$70$	3.84023	0.458995
$71$	10.3802	1.23191	0.615953	−	0.787783i	$-0.288771\pi$
$71$	10.3802	1.23191	0.615953	+	0.787783i	$0.288771\pi$
$72$	1.09543	0.129098
$73$	−7.09918	−0.830896	−0.415448	−	0.909617i	$-0.636375\pi$
$73$	−7.09918	−0.830896	−0.415448	+	0.909617i	$0.636375\pi$
$74$	−8.40818	−0.977431
$75$	−18.2742	−2.11012
$76$	−4.10209	−0.470542
$77$	−3.65248	−0.416239
$78$	−1.73234	−0.196149
$79$	−11.8492	−1.33314	−0.666570	−	0.745443i	$-0.732238\pi$
$79$	−11.8492	−1.33314	−0.666570	+	0.745443i	$0.732238\pi$
$80$	3.74567	0.418778
$81$	−11.0863	−1.23181
$82$	−1.59845	−0.176519
$83$	−12.1171	−1.33002	−0.665010	−	0.746835i	$-0.731573\pi$
$83$	−12.1171	−1.33002	−0.665010	+	0.746835i	$0.731573\pi$
$84$	−2.07481	−0.226380
$85$	−29.1547	−3.16227
$86$	9.33256	1.00636
$87$	2.38415	0.255607
$88$	−3.56254	−0.379768
$89$	5.16545	0.547536	0.273768	−	0.961796i	$-0.411730\pi$
$89$	5.16545	0.547536	0.273768	+	0.961796i	$0.411730\pi$
$90$	4.10311	0.432506
$91$	0.877628	0.0920004
$92$	−0.878792	−0.0916204
$93$	−17.2442	−1.78814
$94$	0.295868	0.0305165
$95$	−15.3651	−1.57642
$96$	−2.02372	−0.206545
$97$	0.0176862	0.00179577	0.000897883	−	1.00000i	$-0.499714\pi$
$97$	0.0176862	0.00179577	0.000897883		1.00000i	$0.499714\pi$
$98$	−5.94887	−0.600927
$99$	−3.90251	−0.392217
$100$	9.03001	0.903001
$101$	−3.39843	−0.338157	−0.169078	−	0.985603i	$-0.554079\pi$
$101$	−3.39843	−0.338157	−0.169078	+	0.985603i	$0.554079\pi$
$102$	15.7518	1.55966
$103$	−11.0696	−1.09072	−0.545358	−	0.838203i	$-0.683606\pi$
$103$	−11.0696	−1.09072	−0.545358	+	0.838203i	$0.683606\pi$
$104$	0.856017	0.0839394
$105$	−7.77153	−0.758423
$106$	5.45679	0.530010
$107$	−9.27727	−0.896868	−0.448434	−	0.893816i	$-0.648018\pi$
$107$	−9.27727	−0.896868	−0.448434	+	0.893816i	$0.648018\pi$
$108$	3.85431	0.370881
$109$	−7.40078	−0.708866	−0.354433	−	0.935081i	$-0.615326\pi$
$109$	−7.40078	−0.708866	−0.354433	+	0.935081i	$0.615326\pi$
$110$	−13.3441	−1.27231
$111$	17.0158	1.61507
$112$	1.02525	0.0968766
$113$	−9.93481	−0.934589	−0.467294	−	0.884102i	$-0.654771\pi$
$113$	−9.93481	−0.934589	−0.467294	+	0.884102i	$0.654771\pi$
$114$	8.30147	0.777504
$115$	−3.29166	−0.306949
$116$	−1.17810	−0.109384
$117$	0.937706	0.0866910
$118$	−10.3432	−0.952167
$119$	−7.98008	−0.731533
$120$	−7.58017	−0.691971
$121$	1.69172	0.153793
$122$	−13.8507	−1.25398
$123$	3.23481	0.291673
$124$	8.52107	0.765215
$125$	15.0951	1.35014
$126$	1.12308	0.100052
$127$	15.4820	1.37381	0.686904	−	0.726748i	$-0.258969\pi$
$127$	15.4820	1.37381	0.686904	+	0.726748i	$0.258969\pi$
$128$	1.00000	0.0883883
$129$	−18.8865	−1.66286
$130$	3.20636	0.281216
$131$	19.9289	1.74120	0.870598	−	0.491996i	$-0.163732\pi$
$131$	19.9289	1.74120	0.870598	+	0.491996i	$0.163732\pi$
$132$	7.20958	0.627513
$133$	−4.20565	−0.364676
$134$	2.14670	0.185447
$135$	14.4370	1.24254
$136$	−7.78358	−0.667437
$137$	−15.2438	−1.30236	−0.651181	−	0.758922i	$-0.725726\pi$
$137$	−15.2438	−1.30236	−0.651181	+	0.758922i	$0.725726\pi$
$138$	1.77843	0.151390
$139$	8.90629	0.755422	0.377711	−	0.925924i	$-0.376711\pi$
$139$	8.90629	0.755422	0.377711	+	0.925924i	$0.376711\pi$
$140$	3.84023	0.324558
$141$	−0.598753	−0.0504241
$142$	10.3802	0.871089
$143$	−3.04960	−0.255020
$144$	1.09543	0.0912857
$145$	−4.41278	−0.366461
$146$	−7.09918	−0.587532
$147$	12.0388	0.992946
$148$	−8.40818	−0.691148
$149$	21.2685	1.74238	0.871190	−	0.490947i	$-0.163349\pi$
$149$	21.2685	1.74238	0.871190	+	0.490947i	$0.163349\pi$
$150$	−18.2742	−1.49208
$151$	1.84211	0.149909	0.0749543	−	0.997187i	$-0.476119\pi$
$151$	1.84211	0.149909	0.0749543	+	0.997187i	$0.476119\pi$
$152$	−4.10209	−0.332723
$153$	−8.52636	−0.689315
$154$	−3.65248	−0.294325
$155$	31.9171	2.56364
$156$	−1.73234	−0.138698
$157$	15.6269	1.24716	0.623581	−	0.781758i	$-0.285677\pi$
$157$	15.6269	1.24716	0.623581	+	0.781758i	$0.285677\pi$
$158$	−11.8492	−0.942672
$159$	−11.0430	−0.875767
$160$	3.74567	0.296121
$161$	−0.900977	−0.0710069
$162$	−11.0863	−0.871024
$163$	1.92419	0.150714	0.0753572	−	0.997157i	$-0.475990\pi$
$163$	1.92419	0.150714	0.0753572	+	0.997157i	$0.475990\pi$
$164$	−1.59845	−0.124818
$165$	27.0047	2.10231
$166$	−12.1171	−0.940466
$167$	−19.8378	−1.53509	−0.767547	−	0.640993i	$-0.778523\pi$
$167$	−19.8378	−1.53509	−0.767547	+	0.640993i	$0.778523\pi$
$168$	−2.07481	−0.160075
$169$	−12.2672	−0.943633
$170$	−29.1547	−2.23606
$171$	−4.49355	−0.343630
$172$	9.33256	0.711601
$173$	−18.5813	−1.41271	−0.706354	−	0.707859i	$-0.749661\pi$
$173$	−18.5813	−1.41271	−0.706354	+	0.707859i	$0.749661\pi$
$174$	2.38415	0.180742
$175$	9.25797	0.699837
$176$	−3.56254	−0.268537
$177$	20.9317	1.57332
$178$	5.16545	0.387167
$179$	−25.5767	−1.91169	−0.955847	−	0.293866i	$-0.905058\pi$
$179$	−25.5767	−1.91169	−0.955847	+	0.293866i	$0.905058\pi$
$180$	4.10311	0.305828
$181$	12.3649	0.919078	0.459539	−	0.888158i	$-0.348015\pi$
$181$	12.3649	0.919078	0.459539	+	0.888158i	$0.348015\pi$
$182$	0.877628	0.0650541
$183$	28.0298	2.07202
$184$	−0.878792	−0.0647854
$185$	−31.4942	−2.31550
$186$	−17.2442	−1.26441
$187$	27.7294	2.02777
$188$	0.295868	0.0215784
$189$	3.95162	0.287438
$190$	−15.3651	−1.11470
$191$	10.3474	0.748714	0.374357	−	0.927285i	$-0.377863\pi$
$191$	10.3474	0.748714	0.374357	+	0.927285i	$0.377863\pi$
$192$	−2.02372	−0.146049
$193$	23.4583	1.68856	0.844282	−	0.535899i	$-0.180027\pi$
$193$	23.4583	1.68856	0.844282	+	0.535899i	$0.180027\pi$
$194$	0.0176862	0.00126980
$195$	−6.48875	−0.464669
$196$	−5.94887	−0.424919
$197$	−22.7152	−1.61839	−0.809195	−	0.587540i	$-0.800097\pi$
$197$	−22.7152	−1.61839	−0.809195	+	0.587540i	$0.800097\pi$
$198$	−3.90251	−0.277340
$199$	−17.1849	−1.21821	−0.609104	−	0.793090i	$-0.708471\pi$
$199$	−17.1849	−1.21821	−0.609104	+	0.793090i	$0.708471\pi$
$200$	9.03001	0.638518
$201$	−4.34432	−0.306425
$202$	−3.39843	−0.239113
$203$	−1.20784	−0.0847741
$204$	15.7518	1.10284
$205$	−5.98726	−0.418169
$206$	−11.0696	−0.771253
$207$	−0.962654	−0.0669091
$208$	0.856017	0.0593541
$209$	14.6139	1.01086
$210$	−7.77153	−0.536286
$211$	22.7092	1.56337	0.781685	−	0.623674i	$-0.214361\pi$
$211$	22.7092	1.56337	0.781685	+	0.623674i	$0.214361\pi$
$212$	5.45679	0.374774
$213$	−21.0066	−1.43935
$214$	−9.27727	−0.634181
$215$	34.9567	2.38402
$216$	3.85431	0.262253
$217$	8.73619	0.593051
$218$	−7.40078	−0.501244
$219$	14.3667	0.970813
$220$	−13.3441	−0.899659
$221$	−6.66288	−0.448194
$222$	17.0158	1.14202
$223$	−17.1620	−1.14925	−0.574626	−	0.818416i	$-0.694852\pi$
$223$	−17.1620	−1.14925	−0.574626	+	0.818416i	$0.694852\pi$
$224$	1.02525	0.0685021
$225$	9.89173	0.659449
$226$	−9.93481	−0.660854
$227$	0.190868	0.0126683	0.00633417	−	0.999980i	$-0.497984\pi$
$227$	0.190868	0.0126683	0.00633417	+	0.999980i	$0.497984\pi$
$228$	8.30147	0.549778
$229$	−11.7726	−0.777955	−0.388978	−	0.921247i	$-0.627172\pi$
$229$	−11.7726	−0.777955	−0.388978	+	0.921247i	$0.627172\pi$
$230$	−3.29166	−0.217046
$231$	7.39159	0.486331
$232$	−1.17810	−0.0773463
$233$	−6.12202	−0.401067	−0.200533	−	0.979687i	$-0.564268\pi$
$233$	−6.12202	−0.401067	−0.200533	+	0.979687i	$0.564268\pi$
$234$	0.937706	0.0612998
$235$	1.10822	0.0722925
$236$	−10.3432	−0.673284
$237$	23.9794	1.55763
$238$	−7.98008	−0.517272
$239$	−10.1375	−0.655743	−0.327871	−	0.944722i	$-0.606331\pi$
$239$	−10.1375	−0.655743	−0.327871	+	0.944722i	$0.606331\pi$
$240$	−7.58017	−0.489298
$241$	10.7731	0.693956	0.346978	−	0.937873i	$-0.387208\pi$
$241$	10.7731	0.693956	0.346978	+	0.937873i	$0.387208\pi$
$242$	1.69172	0.108748
$243$	10.8726	0.697480
$244$	−13.8507	−0.886697
$245$	−22.2825	−1.42358
$246$	3.23481	0.206244
$247$	−3.51146	−0.223429
$248$	8.52107	0.541088
$249$	24.5215	1.55399
$250$	15.0951	0.954696
$251$	−11.1412	−0.703225	−0.351612	−	0.936146i	$-0.614367\pi$
$251$	−11.1412	−0.703225	−0.351612	+	0.936146i	$0.614367\pi$
$252$	1.12308	0.0707476
$253$	3.13073	0.196828
$254$	15.4820	0.971429
$255$	59.0008	3.69478
$256$	1.00000	0.0625000
$257$	−15.1548	−0.945330	−0.472665	−	0.881242i	$-0.656708\pi$
$257$	−15.1548	−0.945330	−0.472665	+	0.881242i	$0.656708\pi$
$258$	−18.8865	−1.17582
$259$	−8.62045	−0.535649
$260$	3.20636	0.198850
$261$	−1.29053	−0.0798817
$262$	19.9289	1.23121
$263$	12.8736	0.793817	0.396909	−	0.917858i	$-0.370083\pi$
$263$	12.8736	0.793817	0.396909	+	0.917858i	$0.370083\pi$
$264$	7.20958	0.443719
$265$	20.4393	1.25558
$266$	−4.20565	−0.257865
$267$	−10.4534	−0.639738
$268$	2.14670	0.131131
$269$	−0.606507	−0.0369794	−0.0184897	−	0.999829i	$-0.505886\pi$
$269$	−0.606507	−0.0369794	−0.0184897	+	0.999829i	$0.505886\pi$
$270$	14.4370	0.878606
$271$	−29.9069	−1.81672	−0.908359	−	0.418192i	$-0.862664\pi$
$271$	−29.9069	−1.81672	−0.908359	+	0.418192i	$0.862664\pi$
$272$	−7.78358	−0.471949
$273$	−1.77607	−0.107493
$274$	−15.2438	−0.920910
$275$	−32.1698	−1.93991
$276$	1.77843	0.107049
$277$	4.02010	0.241545	0.120772	−	0.992680i	$-0.461463\pi$
$277$	4.02010	0.241545	0.120772	+	0.992680i	$0.461463\pi$
$278$	8.90629	0.534164
$279$	9.33422	0.558825
$280$	3.84023	0.229497
$281$	−1.50139	−0.0895652	−0.0447826	−	0.998997i	$-0.514260\pi$
$281$	−1.50139	−0.0895652	−0.0447826	+	0.998997i	$0.514260\pi$
$282$	−0.598753	−0.0356552
$283$	18.6157	1.10659	0.553293	−	0.832987i	$-0.313371\pi$
$283$	18.6157	1.10659	0.553293	+	0.832987i	$0.313371\pi$
$284$	10.3802	0.615953
$285$	31.0945	1.84188
$286$	−3.04960	−0.180327
$287$	−1.63880	−0.0967356
$288$	1.09543	0.0645488
$289$	43.5841	2.56377
$290$	−4.41278	−0.259127
$291$	−0.0357920	−0.00209816
$292$	−7.09918	−0.415448
$293$	−18.5893	−1.08600	−0.542999	−	0.839733i	$-0.682711\pi$
$293$	−18.5893	−1.08600	−0.542999	+	0.839733i	$0.682711\pi$
$294$	12.0388	0.702119
$295$	−38.7421	−2.25565
$296$	−8.40818	−0.488716
$297$	−13.7312	−0.796763
$298$	21.2685	1.23205
$299$	−0.752261	−0.0435044
$300$	−18.2742	−1.05506
$301$	9.56817	0.551500
$302$	1.84211	0.106001
$303$	6.87747	0.395100
$304$	−4.10209	−0.235271
$305$	−51.8799	−2.97064
$306$	−8.52636	−0.487420
$307$	34.9074	1.99227	0.996134	−	0.0878460i	$-0.0279983\pi$
$307$	34.9074	1.99227	0.996134	+	0.0878460i	$0.0279983\pi$
$308$	−3.65248	−0.208119
$309$	22.4017	1.27439
$310$	31.9171	1.81277
$311$	5.25999	0.298267	0.149133	−	0.988817i	$-0.452352\pi$
$311$	5.25999	0.298267	0.149133	+	0.988817i	$0.452352\pi$
$312$	−1.73234	−0.0980743
$313$	16.3268	0.922848	0.461424	−	0.887180i	$-0.347339\pi$
$313$	16.3268	0.922848	0.461424	+	0.887180i	$0.347339\pi$
$314$	15.6269	0.881877
$315$	4.20669	0.237020
$316$	−11.8492	−0.666570
$317$	−33.3659	−1.87402	−0.937008	−	0.349307i	$-0.886417\pi$
$317$	−33.3659	−1.87402	−0.937008	+	0.349307i	$0.886417\pi$
$318$	−11.0430	−0.619261
$319$	4.19705	0.234989
$320$	3.74567	0.209389
$321$	18.7746	1.04789
$322$	−0.900977	−0.0502095
$323$	31.9290	1.77657
$324$	−11.0863	−0.615907
$325$	7.72985	0.428775
$326$	1.92419	0.106571
$327$	14.9771	0.828234
$328$	−1.59845	−0.0882597
$329$	0.303337	0.0167235
$330$	27.0047	1.48656
$331$	−14.0418	−0.771808	−0.385904	−	0.922539i	$-0.626110\pi$
$331$	−14.0418	−0.771808	−0.385904	+	0.922539i	$0.626110\pi$
$332$	−12.1171	−0.665010
$333$	−9.21056	−0.504736
$334$	−19.8378	−1.08547
$335$	8.04084	0.439318
$336$	−2.07481	−0.113190
$337$	−30.9649	−1.68676	−0.843382	−	0.537314i	$-0.819439\pi$
$337$	−30.9649	−1.68676	−0.843382	+	0.537314i	$0.819439\pi$
$338$	−12.2672	−0.667250
$339$	20.1052	1.09197
$340$	−29.1547	−1.58114
$341$	−30.3567	−1.64391
$342$	−4.49355	−0.242983
$343$	−13.2758	−0.716824
$344$	9.33256	0.503178
$345$	6.66139	0.358637
$346$	−18.5813	−0.998935
$347$	20.2528	1.08723	0.543613	−	0.839336i	$-0.317056\pi$
$347$	20.2528	1.08723	0.543613	+	0.839336i	$0.317056\pi$
$348$	2.38415	0.127804
$349$	0.960901	0.0514359	0.0257179	−	0.999669i	$-0.491813\pi$
$349$	0.960901	0.0514359	0.0257179	+	0.999669i	$0.491813\pi$
$350$	9.25797	0.494859
$351$	3.29936	0.176107
$352$	−3.56254	−0.189884
$353$	−3.89910	−0.207528	−0.103764	−	0.994602i	$-0.533089\pi$
$353$	−3.89910	−0.207528	−0.103764	+	0.994602i	$0.533089\pi$
$354$	20.9317	1.11251
$355$	38.8808	2.06358
$356$	5.16545	0.273768
$357$	16.1494	0.854718
$358$	−25.5767	−1.35177
$359$	19.7537	1.04256	0.521280	−	0.853386i	$-0.325455\pi$
$359$	19.7537	1.04256	0.521280	+	0.853386i	$0.325455\pi$
$360$	4.10311	0.216253
$361$	−2.17285	−0.114361
$362$	12.3649	0.649886
$363$	−3.42356	−0.179691
$364$	0.877628	0.0460002
$365$	−26.5912	−1.39184
$366$	28.0298	1.46514
$367$	15.5764	0.813083	0.406542	−	0.913632i	$-0.366735\pi$
$367$	15.5764	0.813083	0.406542	+	0.913632i	$0.366735\pi$
$368$	−0.878792	−0.0458102
$369$	−1.75099	−0.0911529
$370$	−31.4942	−1.63731
$371$	5.59455	0.290454
$372$	−17.2442	−0.894072
$373$	−31.3049	−1.62091	−0.810454	−	0.585803i	$-0.800779\pi$
$373$	−31.3049	−1.62091	−0.810454	+	0.585803i	$0.800779\pi$
$374$	27.7294	1.43385
$375$	−30.5481	−1.57750
$376$	0.295868	0.0152582
$377$	−1.00848	−0.0519392
$378$	3.95162	0.203249
$379$	11.2930	0.580082	0.290041	−	0.957014i	$-0.406331\pi$
$379$	11.2930	0.580082	0.290041	+	0.957014i	$0.406331\pi$
$380$	−15.3651	−0.788211
$381$	−31.3312	−1.60515
$382$	10.3474	0.529421
$383$	15.8710	0.810972	0.405486	−	0.914101i	$-0.367102\pi$
$383$	15.8710	0.810972	0.405486	+	0.914101i	$0.367102\pi$
$384$	−2.02372	−0.103272
$385$	−13.6810	−0.697247
$386$	23.4583	1.19399
$387$	10.2232	0.519672
$388$	0.0176862	0.000897883 0
$389$	16.7156	0.847515	0.423757	−	0.905776i	$-0.360711\pi$
$389$	16.7156	0.847515	0.423757	+	0.905776i	$0.360711\pi$
$390$	−6.48875	−0.328571
$391$	6.84015	0.345921
$392$	−5.94887	−0.300463
$393$	−40.3304	−2.03440
$394$	−22.7152	−1.14437
$395$	−44.3831	−2.23316
$396$	−3.90251	−0.196109
$397$	−22.6750	−1.13802	−0.569012	−	0.822329i	$-0.692674\pi$
$397$	−22.6750	−1.13802	−0.569012	+	0.822329i	$0.692674\pi$
$398$	−17.1849	−0.861404
$399$	8.51104	0.426085
$400$	9.03001	0.451500
$401$	4.99593	0.249485	0.124742	−	0.992189i	$-0.460190\pi$
$401$	4.99593	0.249485	0.124742	+	0.992189i	$0.460190\pi$
$402$	−4.34432	−0.216675
$403$	7.29418	0.363349
$404$	−3.39843	−0.169078
$405$	−41.5257	−2.06343
$406$	−1.20784	−0.0599443
$407$	29.9545	1.48479
$408$	15.7518	0.779828
$409$	24.5558	1.21421	0.607104	−	0.794622i	$-0.292331\pi$
$409$	24.5558	1.21421	0.607104	+	0.794622i	$0.292331\pi$
$410$	−5.98726	−0.295690
$411$	30.8491	1.52167
$412$	−11.0696	−0.545358
$413$	−10.6043	−0.521803
$414$	−0.962654	−0.0473119
$415$	−45.3864	−2.22793
$416$	0.856017	0.0419697
$417$	−18.0238	−0.882630
$418$	14.6139	0.714788
$419$	−18.9136	−0.923989	−0.461995	−	0.886883i	$-0.652866\pi$
$419$	−18.9136	−0.923989	−0.461995	+	0.886883i	$0.652866\pi$
$420$	−7.77153	−0.379212
$421$	−33.1603	−1.61614	−0.808068	−	0.589090i	$-0.799487\pi$
$421$	−33.1603	−1.61614	−0.808068	+	0.589090i	$0.799487\pi$
$422$	22.7092	1.10547
$423$	0.324103	0.0157584
$424$	5.45679	0.265005
$425$	−70.2858	−3.40936
$426$	−21.0066	−1.01777
$427$	−14.2003	−0.687202
$428$	−9.27727	−0.448434
$429$	6.17153	0.297964
$430$	34.9567	1.68576
$431$	−19.7608	−0.951847	−0.475923	−	0.879487i	$-0.657886\pi$
$431$	−19.7608	−0.951847	−0.475923	+	0.879487i	$0.657886\pi$
$432$	3.85431	0.185441
$433$	5.76290	0.276947	0.138474	−	0.990366i	$-0.455780\pi$
$433$	5.76290	0.276947	0.138474	+	0.990366i	$0.455780\pi$
$434$	8.73619	0.419350
$435$	8.93022	0.428171
$436$	−7.40078	−0.354433
$437$	3.60488	0.172445
$438$	14.3667	0.686469
$439$	−24.7550	−1.18149	−0.590745	−	0.806858i	$-0.701166\pi$
$439$	−24.7550	−1.18149	−0.590745	+	0.806858i	$0.701166\pi$
$440$	−13.3441	−0.636155
$441$	−6.51657	−0.310313
$442$	−6.66288	−0.316921
$443$	17.3781	0.825660	0.412830	−	0.910808i	$-0.364540\pi$
$443$	17.3781	0.825660	0.412830	+	0.910808i	$0.364540\pi$
$444$	17.0158	0.807533
$445$	19.3480	0.917185
$446$	−17.1620	−0.812643
$447$	−43.0413	−2.03578
$448$	1.02525	0.0484383
$449$	32.7701	1.54651	0.773257	−	0.634093i	$-0.218626\pi$
$449$	32.7701	1.54651	0.773257	+	0.634093i	$0.218626\pi$
$450$	9.89173	0.466301
$451$	5.69455	0.268146
$452$	−9.93481	−0.467294
$453$	−3.72790	−0.175152
$454$	0.190868	0.00895787
$455$	3.28730	0.154111
$456$	8.30147	0.388752
$457$	9.06818	0.424192	0.212096	−	0.977249i	$-0.431971\pi$
$457$	9.06818	0.424192	0.212096	+	0.977249i	$0.431971\pi$
$458$	−11.7726	−0.550098
$459$	−30.0004	−1.40030
$460$	−3.29166	−0.153474
$461$	−6.99922	−0.325986	−0.162993	−	0.986627i	$-0.552115\pi$
$461$	−6.99922	−0.325986	−0.162993	+	0.986627i	$0.552115\pi$
$462$	7.39159	0.343888
$463$	33.3097	1.54803	0.774017	−	0.633165i	$-0.218245\pi$
$463$	33.3097	1.54803	0.774017	+	0.633165i	$0.218245\pi$
$464$	−1.17810	−0.0546921
$465$	−64.5911	−2.99534
$466$	−6.12202	−0.283597
$467$	24.0550	1.11313	0.556567	−	0.830803i	$-0.312118\pi$
$467$	24.0550	1.11313	0.556567	+	0.830803i	$0.312118\pi$
$468$	0.937706	0.0433455
$469$	2.20090	0.101628
$470$	1.10822	0.0511185
$471$	−31.6244	−1.45718
$472$	−10.3432	−0.476084
$473$	−33.2477	−1.52873
$474$	23.9794	1.10141
$475$	−37.0419	−1.69960
$476$	−7.98008	−0.365766
$477$	5.97753	0.273692
$478$	−10.1375	−0.463680
$479$	39.7443	1.81597	0.907983	−	0.419008i	$-0.137622\pi$
$479$	39.7443	1.81597	0.907983	+	0.419008i	$0.137622\pi$
$480$	−7.58017	−0.345986
$481$	−7.19755	−0.328180
$482$	10.7731	0.490701
$483$	1.82332	0.0829640
$484$	1.69172	0.0768964
$485$	0.0662468	0.00300811
$486$	10.8726	0.493193
$487$	−25.8312	−1.17052	−0.585261	−	0.810845i	$-0.699008\pi$
$487$	−25.8312	−1.17052	−0.585261	+	0.810845i	$0.699008\pi$
$488$	−13.8507	−0.626990
$489$	−3.89402	−0.176094
$490$	−22.2825	−1.00662
$491$	−13.2715	−0.598935	−0.299468	−	0.954106i	$-0.596809\pi$
$491$	−13.2715	−0.598935	−0.299468	+	0.954106i	$0.596809\pi$
$492$	3.23481	0.145837
$493$	9.16986	0.412990
$494$	−3.51146	−0.157988
$495$	−14.6175	−0.657008
$496$	8.52107	0.382607
$497$	10.6423	0.477371
$498$	24.5215	1.09883
$499$	2.47797	0.110929	0.0554647	−	0.998461i	$-0.482336\pi$
$499$	2.47797	0.110929	0.0554647	+	0.998461i	$0.482336\pi$
$500$	15.0951	0.675072
$501$	40.1460	1.79359
$502$	−11.1412	−0.497255
$503$	−15.1774	−0.676728	−0.338364	−	0.941015i	$-0.609873\pi$
$503$	−15.1774	−0.676728	−0.338364	+	0.941015i	$0.609873\pi$
$504$	1.12308	0.0500261
$505$	−12.7294	−0.566451
$506$	3.13073	0.139178
$507$	24.8254	1.10253
$508$	15.4820	0.686904
$509$	−13.9990	−0.620493	−0.310247	−	0.950656i	$-0.600412\pi$
$509$	−13.9990	−0.620493	−0.310247	+	0.950656i	$0.600412\pi$
$510$	59.0008	2.61260
$511$	−7.27840	−0.321977
$512$	1.00000	0.0441942
$513$	−15.8107	−0.698061
$514$	−15.1548	−0.668449
$515$	−41.4629	−1.82707
$516$	−18.8865	−0.831430
$517$	−1.05404	−0.0463568
$518$	−8.62045	−0.378761
$519$	37.6032	1.65060
$520$	3.20636	0.140608
$521$	21.9574	0.961972	0.480986	−	0.876728i	$-0.340279\pi$
$521$	21.9574	0.961972	0.480986	+	0.876728i	$0.340279\pi$
$522$	−1.29053	−0.0564849
$523$	−1.73590	−0.0759055	−0.0379527	−	0.999280i	$-0.512084\pi$
$523$	−1.73590	−0.0759055	−0.0379527	+	0.999280i	$0.512084\pi$
$524$	19.9289	0.870598
$525$	−18.7355	−0.817685
$526$	12.8736	0.561314
$527$	−66.3244	−2.88914
$528$	7.20958	0.313757
$529$	−22.2277	−0.966423
$530$	20.4393	0.887827
$531$	−11.3302	−0.491690
$532$	−4.20565	−0.182338
$533$	−1.36830	−0.0592677
$534$	−10.4534	−0.452363
$535$	−34.7496	−1.50235
$536$	2.14670	0.0927235
$537$	51.7600	2.23361
$538$	−0.606507	−0.0261484
$539$	21.1931	0.912852
$540$	14.4370	0.621268
$541$	0.845041	0.0363311	0.0181656	−	0.999835i	$-0.494217\pi$
$541$	0.845041	0.0363311	0.0181656	+	0.999835i	$0.494217\pi$
$542$	−29.9069	−1.28461
$543$	−25.0231	−1.07384
$544$	−7.78358	−0.333718
$545$	−27.7208	−1.18743
$546$	−1.77607	−0.0760088
$547$	12.5668	0.537317	0.268659	−	0.963235i	$-0.413420\pi$
$547$	12.5668	0.537317	0.268659	+	0.963235i	$0.413420\pi$
$548$	−15.2438	−0.651181
$549$	−15.1724	−0.647543
$550$	−32.1698	−1.37173
$551$	4.83269	0.205879
$552$	1.77843	0.0756948
$553$	−12.1483	−0.516600
$554$	4.02010	0.170798
$555$	63.7354	2.70542
$556$	8.90629	0.377711
$557$	46.8466	1.98496	0.992478	−	0.122425i	$-0.0390671\pi$
$557$	46.8466	1.98496	0.992478	+	0.122425i	$0.0390671\pi$
$558$	9.33422	0.395149
$559$	7.98884	0.337892
$560$	3.84023	0.162279
$561$	−56.1164	−2.36923
$562$	−1.50139	−0.0633321
$563$	34.6962	1.46227	0.731134	−	0.682234i	$-0.238991\pi$
$563$	34.6962	1.46227	0.731134	+	0.682234i	$0.238991\pi$
$564$	−0.598753	−0.0252121
$565$	−37.2125	−1.56554
$566$	18.6157	0.782474
$567$	−11.3662	−0.477335
$568$	10.3802	0.435544
$569$	−27.9427	−1.17142	−0.585709	−	0.810521i	$-0.699184\pi$
$569$	−27.9427	−1.17142	−0.585709	+	0.810521i	$0.699184\pi$
$570$	31.0945	1.30241
$571$	21.3435	0.893196	0.446598	−	0.894735i	$-0.352635\pi$
$571$	21.3435	0.893196	0.446598	+	0.894735i	$0.352635\pi$
$572$	−3.04960	−0.127510
$573$	−20.9403	−0.874792
$574$	−1.63880	−0.0684024
$575$	−7.93550	−0.330933
$576$	1.09543	0.0456429
$577$	6.92674	0.288364	0.144182	−	0.989551i	$-0.453945\pi$
$577$	6.92674	0.288364	0.144182	+	0.989551i	$0.453945\pi$
$578$	43.5841	1.81286
$579$	−47.4729	−1.97291
$580$	−4.41278	−0.183231
$581$	−12.4230	−0.515391
$582$	−0.0357920	−0.00148362
$583$	−19.4401	−0.805125
$584$	−7.09918	−0.293766
$585$	3.51233	0.145217
$586$	−18.5893	−0.767917
$587$	4.76528	0.196684	0.0983422	−	0.995153i	$-0.468646\pi$
$587$	4.76528	0.196684	0.0983422	+	0.995153i	$0.468646\pi$
$588$	12.0388	0.496473
$589$	−34.9542	−1.44026
$590$	−38.7421	−1.59499
$591$	45.9691	1.89092
$592$	−8.40818	−0.345574
$593$	−27.1815	−1.11621	−0.558105	−	0.829770i	$-0.688471\pi$
$593$	−27.1815	−1.11621	−0.558105	+	0.829770i	$0.688471\pi$
$594$	−13.7312	−0.563396
$595$	−29.8907	−1.22540
$596$	21.2685	0.871190
$597$	34.7775	1.42335
$598$	−0.752261	−0.0307622
$599$	14.8722	0.607662	0.303831	−	0.952726i	$-0.401734\pi$
$599$	14.8722	0.607662	0.303831	+	0.952726i	$0.401734\pi$
$600$	−18.2742	−0.746040
$601$	−0.496788	−0.0202644	−0.0101322	−	0.999949i	$-0.503225\pi$
$601$	−0.496788	−0.0202644	−0.0101322	+	0.999949i	$0.503225\pi$
$602$	9.56817	0.389969
$603$	2.35156	0.0957630
$604$	1.84211	0.0749543
$605$	6.33662	0.257620
$606$	6.87747	0.279378
$607$	−26.6084	−1.08000	−0.540001	−	0.841664i	$-0.681576\pi$
$607$	−26.6084	−1.08000	−0.540001	+	0.841664i	$0.681576\pi$
$608$	−4.10209	−0.166362
$609$	2.44434	0.0990495
$610$	−51.8799	−2.10056
$611$	0.253268	0.0102461
$612$	−8.52636	−0.344658
$613$	23.0538	0.931134	0.465567	−	0.885013i	$-0.345850\pi$
$613$	23.0538	0.931134	0.465567	+	0.885013i	$0.345850\pi$
$614$	34.9074	1.40875
$615$	12.1165	0.488585
$616$	−3.65248	−0.147163
$617$	−36.2971	−1.46126	−0.730632	−	0.682771i	$-0.760775\pi$
$617$	−36.2971	−1.46126	−0.730632	+	0.682771i	$0.760775\pi$
$618$	22.4017	0.901127
$619$	−5.91304	−0.237665	−0.118833	−	0.992914i	$-0.537915\pi$
$619$	−5.91304	−0.237665	−0.118833	+	0.992914i	$0.537915\pi$
$620$	31.9171	1.28182
$621$	−3.38714	−0.135921
$622$	5.25999	0.210906
$623$	5.29585	0.212174
$624$	−1.73234	−0.0693490
$625$	11.3910	0.455641
$626$	16.3268	0.652552
$627$	−29.5743	−1.18109
$628$	15.6269	0.623581
$629$	65.4458	2.60949
$630$	4.20669	0.167599
$631$	−26.5415	−1.05660	−0.528299	−	0.849058i	$-0.677170\pi$
$631$	−26.5415	−1.05660	−0.528299	+	0.849058i	$0.677170\pi$
$632$	−11.8492	−0.471336
$633$	−45.9571	−1.82663
$634$	−33.3659	−1.32513
$635$	57.9905	2.30128
$636$	−11.0430	−0.437883
$637$	−5.09234	−0.201766
$638$	4.19705	0.166163
$639$	11.3708	0.449822
$640$	3.74567	0.148060
$641$	26.0174	1.02763	0.513813	−	0.857902i	$-0.328232\pi$
$641$	26.0174	1.02763	0.513813	+	0.857902i	$0.328232\pi$
$642$	18.7746	0.740973
$643$	−30.1859	−1.19042	−0.595208	−	0.803572i	$-0.702930\pi$
$643$	−30.1859	−1.19042	−0.595208	+	0.803572i	$0.702930\pi$
$644$	−0.900977	−0.0355035
$645$	−70.7424	−2.78548
$646$	31.9290	1.25623
$647$	6.88501	0.270678	0.135339	−	0.990799i	$-0.456788\pi$
$647$	6.88501	0.270678	0.135339	+	0.990799i	$0.456788\pi$
$648$	−11.0863	−0.435512
$649$	36.8480	1.44641
$650$	7.72985	0.303189
$651$	−17.6796	−0.692917
$652$	1.92419	0.0753572
$653$	−22.6524	−0.886458	−0.443229	−	0.896408i	$-0.646167\pi$
$653$	−22.6524	−0.886458	−0.443229	+	0.896408i	$0.646167\pi$
$654$	14.9771	0.585650
$655$	74.6470	2.91670
$656$	−1.59845	−0.0624090
$657$	−7.77665	−0.303396
$658$	0.303337	0.0118253
$659$	19.2684	0.750589	0.375294	−	0.926906i	$-0.377542\pi$
$659$	19.2684	0.750589	0.375294	+	0.926906i	$0.377542\pi$
$660$	27.0047	1.05116
$661$	12.2687	0.477198	0.238599	−	0.971118i	$-0.423312\pi$
$661$	12.2687	0.477198	0.238599	+	0.971118i	$0.423312\pi$
$662$	−14.0418	−0.545751
$663$	13.4838	0.523667
$664$	−12.1171	−0.470233
$665$	−15.7530	−0.610873
$666$	−9.21056	−0.356902
$667$	1.03531	0.0400873
$668$	−19.8378	−0.767547
$669$	34.7310	1.34278
$670$	8.04084	0.310645
$671$	49.3436	1.90489
$672$	−2.07481	−0.0800374
$673$	20.0195	0.771695	0.385848	−	0.922563i	$-0.373909\pi$
$673$	20.0195	0.771695	0.385848	+	0.922563i	$0.373909\pi$
$674$	−30.9649	−1.19272
$675$	34.8045	1.33962
$676$	−12.2672	−0.471817
$677$	28.7097	1.10340	0.551702	−	0.834041i	$-0.313979\pi$
$677$	28.7097	1.10340	0.551702	+	0.834041i	$0.313979\pi$
$678$	20.1052	0.772137
$679$	0.0181327	0.000695871 0
$680$	−29.1547	−1.11803
$681$	−0.386262	−0.0148016
$682$	−30.3567	−1.16242
$683$	−36.2791	−1.38818	−0.694090	−	0.719888i	$-0.744193\pi$
$683$	−36.2791	−1.38818	−0.694090	+	0.719888i	$0.744193\pi$
$684$	−4.49355	−0.171815
$685$	−57.0980	−2.18160
$686$	−13.2758	−0.506871
$687$	23.8244	0.908958
$688$	9.33256	0.355801
$689$	4.67111	0.177955
$690$	6.66139	0.253595
$691$	5.26579	0.200320	0.100160	−	0.994971i	$-0.468065\pi$
$691$	5.26579	0.200320	0.100160	+	0.994971i	$0.468065\pi$
$692$	−18.5813	−0.706354
$693$	−4.00103	−0.151987
$694$	20.2528	0.768785
$695$	33.3600	1.26542
$696$	2.38415	0.0903709
$697$	12.4417	0.471262
$698$	0.960901	0.0363707
$699$	12.3892	0.468604
$700$	9.25797	0.349919
$701$	−6.01867	−0.227322	−0.113661	−	0.993520i	$-0.536258\pi$
$701$	−6.01867	−0.227322	−0.113661	+	0.993520i	$0.536258\pi$
$702$	3.29936	0.124526
$703$	34.4911	1.30086
$704$	−3.56254	−0.134268
$705$	−2.24273	−0.0844661
$706$	−3.89910	−0.146745
$707$	−3.48423	−0.131038
$708$	20.9317	0.786660
$709$	7.24522	0.272100	0.136050	−	0.990702i	$-0.456559\pi$
$709$	7.24522	0.272100	0.136050	+	0.990702i	$0.456559\pi$
$710$	38.8808	1.45917
$711$	−12.9800	−0.486786
$712$	5.16545	0.193583
$713$	−7.48825	−0.280437
$714$	16.1494	0.604377
$715$	−11.4228	−0.427188
$716$	−25.5767	−0.955847
$717$	20.5155	0.766166
$718$	19.7537	0.737201
$719$	−50.1118	−1.86885	−0.934427	−	0.356154i	$-0.884088\pi$
$719$	−50.1118	−1.86885	−0.934427	+	0.356154i	$0.884088\pi$
$720$	4.10311	0.152914
$721$	−11.3490	−0.422660
$722$	−2.17285	−0.0808653
$723$	−21.8017	−0.810813
$724$	12.3649	0.459539
$725$	−10.6383	−0.395096
$726$	−3.42356	−0.127060
$727$	20.9355	0.776456	0.388228	−	0.921563i	$-0.373087\pi$
$727$	20.9355	0.776456	0.388228	+	0.921563i	$0.373087\pi$
$728$	0.877628	0.0325271
$729$	11.2558	0.416883
$730$	−26.5912	−0.984183
$731$	−72.6408	−2.68672
$732$	28.0298	1.03601
$733$	−4.25740	−0.157251	−0.0786253	−	0.996904i	$-0.525053\pi$
$733$	−4.25740	−0.157251	−0.0786253	+	0.996904i	$0.525053\pi$
$734$	15.5764	0.574937
$735$	45.0934	1.66330
$736$	−0.878792	−0.0323927
$737$	−7.64773	−0.281708
$738$	−1.75099	−0.0644548
$739$	−34.7797	−1.27939	−0.639696	−	0.768628i	$-0.720940\pi$
$739$	−34.7797	−1.27939	−0.639696	+	0.768628i	$0.720940\pi$
$740$	−31.4942	−1.15775
$741$	7.10620	0.261053
$742$	5.59455	0.205382
$743$	43.7765	1.60600	0.803001	−	0.595977i	$-0.203235\pi$
$743$	43.7765	1.60600	0.803001	+	0.595977i	$0.203235\pi$
$744$	−17.2442	−0.632204
$745$	79.6645	2.91868
$746$	−31.3049	−1.14615
$747$	−13.2734	−0.485647
$748$	27.7294	1.01389
$749$	−9.51148	−0.347542
$750$	−30.5481	−1.11546
$751$	54.3128	1.98190	0.990950	−	0.134229i	$-0.0428557\pi$
$751$	54.3128	1.98190	0.990950	+	0.134229i	$0.0428557\pi$
$752$	0.295868	0.0107892
$753$	22.5466	0.821643
$754$	−1.00848	−0.0367266
$755$	6.89992	0.251114
$756$	3.95162	0.143719
$757$	−5.99619	−0.217935	−0.108968	−	0.994045i	$-0.534754\pi$
$757$	−5.99619	−0.217935	−0.108968	+	0.994045i	$0.534754\pi$
$758$	11.2930	0.410180
$759$	−6.33572	−0.229972
$760$	−15.3651	−0.557349
$761$	−38.2889	−1.38797	−0.693985	−	0.719989i	$-0.744147\pi$
$761$	−38.2889	−1.38797	−0.693985	+	0.719989i	$0.744147\pi$
$762$	−31.3312	−1.13501
$763$	−7.58761	−0.274690
$764$	10.3474	0.374357
$765$	−31.9369	−1.15468
$766$	15.8710	0.573444
$767$	−8.85394	−0.319697
$768$	−2.02372	−0.0730246
$769$	41.5459	1.49818	0.749092	−	0.662466i	$-0.230490\pi$
$769$	41.5459	1.49818	0.749092	+	0.662466i	$0.230490\pi$
$770$	−13.6810	−0.493028
$771$	30.6690	1.10452
$772$	23.4583	0.844282
$773$	48.5331	1.74561	0.872807	−	0.488065i	$-0.162297\pi$
$773$	48.5331	1.74561	0.872807	+	0.488065i	$0.162297\pi$
$774$	10.2232	0.367464
$775$	76.9453	2.76396
$776$	0.0176862	0.000634899 0
$777$	17.4453	0.625848
$778$	16.7156	0.599284
$779$	6.55699	0.234929
$780$	−6.48875	−0.232335
$781$	−36.9800	−1.32325
$782$	6.84015	0.244603
$783$	−4.54078	−0.162274
$784$	−5.94887	−0.212460
$785$	58.5332	2.08914
$786$	−40.3304	−1.43854
$787$	−37.6125	−1.34074	−0.670371	−	0.742026i	$-0.733865\pi$
$787$	−37.6125	−1.34074	−0.670371	+	0.742026i	$0.733865\pi$
$788$	−22.7152	−0.809195
$789$	−26.0524	−0.927491
$790$	−44.3831	−1.57908
$791$	−10.1856	−0.362159
$792$	−3.90251	−0.138670
$793$	−11.8564	−0.421033
$794$	−22.6750	−0.804705
$795$	−41.3634	−1.46701
$796$	−17.1849	−0.609104
$797$	−15.0067	−0.531564	−0.265782	−	0.964033i	$-0.585630\pi$
$797$	−15.0067	−0.531564	−0.265782	+	0.964033i	$0.585630\pi$
$798$	8.51104	0.301288
$799$	−2.30291	−0.0814713
$800$	9.03001	0.319259
$801$	5.65838	0.199929
$802$	4.99593	0.176413
$803$	25.2911	0.892505
$804$	−4.34432	−0.153212
$805$	−3.37476	−0.118945
$806$	7.29418	0.256927
$807$	1.22740	0.0432065
$808$	−3.39843	−0.119557
$809$	−15.4795	−0.544230	−0.272115	−	0.962265i	$-0.587723\pi$
$809$	−15.4795	−0.544230	−0.272115	+	0.962265i	$0.587723\pi$
$810$	−41.5257	−1.45906
$811$	19.9026	0.698873	0.349437	−	0.936960i	$-0.386373\pi$
$811$	19.9026	0.698873	0.349437	+	0.936960i	$0.386373\pi$
$812$	−1.20784	−0.0423870
$813$	60.5232	2.12264
$814$	29.9545	1.04991
$815$	7.20738	0.252464
$816$	15.7518	0.551422
$817$	−38.2830	−1.33935
$818$	24.5558	0.858575
$819$	0.961379	0.0335933
$820$	−5.98726	−0.209084
$821$	−32.7430	−1.14274	−0.571370	−	0.820693i	$-0.693588\pi$
$821$	−32.7430	−1.14274	−0.571370	+	0.820693i	$0.693588\pi$
$822$	30.8491	1.07598
$823$	9.72566	0.339015	0.169508	−	0.985529i	$-0.445782\pi$
$823$	9.72566	0.339015	0.169508	+	0.985529i	$0.445782\pi$
$824$	−11.0696	−0.385627
$825$	65.1026	2.26658
$826$	−10.6043	−0.368971
$827$	−30.9130	−1.07495	−0.537476	−	0.843279i	$-0.680622\pi$
$827$	−30.9130	−1.07495	−0.537476	+	0.843279i	$0.680622\pi$
$828$	−0.962654	−0.0334545
$829$	−56.1286	−1.94943	−0.974714	−	0.223456i	$-0.928266\pi$
$829$	−56.1286	−1.94943	−0.974714	+	0.223456i	$0.928266\pi$
$830$	−45.3864	−1.57539
$831$	−8.13555	−0.282219
$832$	0.856017	0.0296771
$833$	46.3035	1.60432
$834$	−18.0238	−0.624113
$835$	−74.3057	−2.57145
$836$	14.6139	0.505432
$837$	32.8429	1.13522
$838$	−18.9136	−0.653359
$839$	−14.8702	−0.513377	−0.256688	−	0.966494i	$-0.582631\pi$
$839$	−14.8702	−0.513377	−0.256688	+	0.966494i	$0.582631\pi$
$840$	−7.77153	−0.268143
$841$	−27.6121	−0.952140
$842$	−33.1603	−1.14278
$843$	3.03838	0.104647
$844$	22.7092	0.781685
$845$	−45.9490	−1.58069
$846$	0.324103	0.0111429
$847$	1.73443	0.0595957
$848$	5.45679	0.187387
$849$	−37.6728	−1.29293
$850$	−70.2858	−2.41078
$851$	7.38904	0.253293
$852$	−21.0066	−0.719675
$853$	42.6082	1.45888	0.729439	−	0.684046i	$-0.239781\pi$
$853$	42.6082	1.45888	0.729439	+	0.684046i	$0.239781\pi$
$854$	−14.2003	−0.485925
$855$	−16.8313	−0.575619
$856$	−9.27727	−0.317091
$857$	43.9936	1.50279	0.751396	−	0.659852i	$-0.229381\pi$
$857$	43.9936	1.50279	0.751396	+	0.659852i	$0.229381\pi$
$858$	6.17153	0.210692
$859$	−18.0746	−0.616698	−0.308349	−	0.951273i	$-0.599776\pi$
$859$	−18.0746	−0.616698	−0.308349	+	0.951273i	$0.599776\pi$
$860$	34.9567	1.19201
$861$	3.31648	0.113025
$862$	−19.7608	−0.673057
$863$	−26.7562	−0.910791	−0.455395	−	0.890289i	$-0.650502\pi$
$863$	−26.7562	−0.910791	−0.455395	+	0.890289i	$0.650502\pi$
$864$	3.85431	0.131126
$865$	−69.5992	−2.36644
$866$	5.76290	0.195831
$867$	−88.2020	−2.99550
$868$	8.73619	0.296525
$869$	42.2133	1.43199
$870$	8.93022	0.302763
$871$	1.83762	0.0622653
$872$	−7.40078	−0.250622
$873$	0.0193740	0.000655711 0
$874$	3.60488	0.121937
$875$	15.4761	0.523189
$876$	14.3667	0.485407
$877$	47.6221	1.60808	0.804041	−	0.594574i	$-0.202679\pi$
$877$	47.6221	1.60808	0.804041	+	0.594574i	$0.202679\pi$
$878$	−24.7550	−0.835440
$879$	37.6195	1.26887
$880$	−13.3441	−0.449829
$881$	39.0730	1.31640	0.658201	−	0.752842i	$-0.271318\pi$
$881$	39.0730	1.31640	0.658201	+	0.752842i	$0.271318\pi$
$882$	−6.51657	−0.219424
$883$	−25.8598	−0.870251	−0.435126	−	0.900370i	$-0.643296\pi$
$883$	−25.8598	−0.870251	−0.435126	+	0.900370i	$0.643296\pi$
$884$	−6.66288	−0.224097
$885$	78.4030	2.63549
$886$	17.3781	0.583829
$887$	7.70049	0.258557	0.129279	−	0.991608i	$-0.458734\pi$
$887$	7.70049	0.258557	0.129279	+	0.991608i	$0.458734\pi$
$888$	17.0158	0.571012
$889$	15.8729	0.532359
$890$	19.3480	0.648548
$891$	39.4955	1.32315
$892$	−17.1620	−0.574626
$893$	−1.21368	−0.0406142
$894$	−43.0413	−1.43952
$895$	−95.8018	−3.20230
$896$	1.02525	0.0342510
$897$	1.52236	0.0508302
$898$	32.7701	1.09355
$899$	−10.0387	−0.334809
$900$	9.89173	0.329724
$901$	−42.4734	−1.41499
$902$	5.69455	0.189608
$903$	−19.3633	−0.644369
$904$	−9.93481	−0.330427
$905$	46.3149	1.53956
$906$	−3.72790	−0.123851
$907$	−13.0942	−0.434785	−0.217393	−	0.976084i	$-0.569755\pi$
$907$	−13.0942	−0.434785	−0.217393	+	0.976084i	$0.569755\pi$
$908$	0.190868	0.00633417
$909$	−3.72274	−0.123476
$910$	3.28730	0.108973
$911$	−44.8628	−1.48637	−0.743186	−	0.669085i	$-0.766686\pi$
$911$	−44.8628	−1.48637	−0.743186	+	0.669085i	$0.766686\pi$
$912$	8.30147	0.274889
$913$	43.1676	1.42864
$914$	9.06818	0.299949
$915$	104.990	3.47087
$916$	−11.7726	−0.388978
$917$	20.4320	0.674724
$918$	−30.0004	−0.990159
$919$	29.8260	0.983870	0.491935	−	0.870632i	$-0.336290\pi$
$919$	29.8260	0.983870	0.491935	+	0.870632i	$0.336290\pi$
$920$	−3.29166	−0.108523
$921$	−70.6426	−2.32775
$922$	−6.99922	−0.230507
$923$	8.88565	0.292475
$924$	7.39159	0.243165
$925$	−75.9260	−2.49643
$926$	33.3097	1.09462
$927$	−12.1259	−0.398268
$928$	−1.17810	−0.0386731
$929$	2.16073	0.0708913	0.0354457	−	0.999372i	$-0.488715\pi$
$929$	2.16073	0.0708913	0.0354457	+	0.999372i	$0.488715\pi$
$930$	−64.5911	−2.11803
$931$	24.4028	0.799770
$932$	−6.12202	−0.200533
$933$	−10.6447	−0.348493
$934$	24.0550	0.787105
$935$	103.865	3.39674
$936$	0.937706	0.0306499
$937$	13.7505	0.449208	0.224604	−	0.974450i	$-0.427891\pi$
$937$	13.7505	0.449208	0.224604	+	0.974450i	$0.427891\pi$
$938$	2.20090	0.0718619
$939$	−33.0409	−1.07825
$940$	1.10822	0.0361463
$941$	29.2310	0.952905	0.476452	−	0.879200i	$-0.341922\pi$
$941$	29.2310	0.952905	0.476452	+	0.879200i	$0.341922\pi$
$942$	−31.6244	−1.03038
$943$	1.40471	0.0457435
$944$	−10.3432	−0.336642
$945$	14.8014	0.481490
$946$	−33.2477	−1.08098
$947$	30.0495	0.976479	0.488240	−	0.872710i	$-0.337639\pi$
$947$	30.0495	0.976479	0.488240	+	0.872710i	$0.337639\pi$
$948$	23.9794	0.778815
$949$	−6.07702	−0.197268
$950$	−37.0419	−1.20180
$951$	67.5232	2.18959
$952$	−7.98008	−0.258636
$953$	−15.2520	−0.494061	−0.247031	−	0.969008i	$-0.579455\pi$
$953$	−15.2520	−0.494061	−0.247031	+	0.969008i	$0.579455\pi$
$954$	5.97753	0.193530
$955$	38.7580	1.25418
$956$	−10.1375	−0.327871
$957$	−8.49363	−0.274560
$958$	39.7443	1.28408
$959$	−15.6286	−0.504674
$960$	−7.58017	−0.244649
$961$	41.6086	1.34221
$962$	−7.19755	−0.232058
$963$	−10.1626	−0.327485
$964$	10.7731	0.346978
$965$	87.8669	2.82853
$966$	1.82332	0.0586644
$967$	24.4249	0.785450	0.392725	−	0.919656i	$-0.371532\pi$
$967$	24.4249	0.785450	0.392725	+	0.919656i	$0.371532\pi$
$968$	1.69172	0.0543740
$969$	−64.6152	−2.07574
$970$	0.0662468	0.00212706
$971$	−47.2023	−1.51479	−0.757396	−	0.652956i	$-0.773529\pi$
$971$	−47.2023	−1.51479	−0.757396	+	0.652956i	$0.773529\pi$
$972$	10.8726	0.348740
$973$	9.13113	0.292731
$974$	−25.8312	−0.827684
$975$	−15.6430	−0.500977
$976$	−13.8507	−0.443349
$977$	−6.12326	−0.195900	−0.0979502	−	0.995191i	$-0.531229\pi$
$977$	−6.12326	−0.195900	−0.0979502	+	0.995191i	$0.531229\pi$
$978$	−3.89402	−0.124517
$979$	−18.4021	−0.588135
$980$	−22.2825	−0.711788
$981$	−8.10702	−0.258837
$982$	−13.2715	−0.423511
$983$	32.9376	1.05055	0.525273	−	0.850934i	$-0.323963\pi$
$983$	32.9376	1.05055	0.525273	+	0.850934i	$0.323963\pi$
$984$	3.23481	0.103122
$985$	−85.0835	−2.71099
$986$	9.16986	0.292028
$987$	−0.613869	−0.0195397
$988$	−3.51146	−0.111714
$989$	−8.20138	−0.260789
$990$	−14.6175	−0.464575
$991$	27.1857	0.863582	0.431791	−	0.901974i	$-0.357882\pi$
$991$	27.1857	0.863582	0.431791	+	0.901974i	$0.357882\pi$
$992$	8.52107	0.270544
$993$	28.4167	0.901775
$994$	10.6423	0.337552
$995$	−64.3691	−2.04064
$996$	24.5215	0.776993
$997$	48.4008	1.53287	0.766434	−	0.642323i	$-0.222029\pi$
$997$	48.4008	1.53287	0.766434	+	0.642323i	$0.222029\pi$
$998$	2.47797	0.0784389
$999$	−32.4078	−1.02534

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8026.2.a.a.1.15	✓	71

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8026.2.a.a.1.15	✓	71	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:	\( N \)	\(=\)	\( 8026 = 2 \cdot 4013 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.02372 q^{3} +1.00000 q^{4} +3.74567 q^{5} -2.02372 q^{6} +1.02525 q^{7} +1.00000 q^{8} +1.09543 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.02372 q^{3} +1.00000 q^{4} +3.74567 q^{5} -2.02372 q^{6} +1.02525 q^{7} +1.00000 q^{8} +1.09543 q^{9} +3.74567 q^{10} -3.56254 q^{11} -2.02372 q^{12} +0.856017 q^{13} +1.02525 q^{14} -7.58017 q^{15} +1.00000 q^{16} -7.78358 q^{17} +1.09543 q^{18} -4.10209 q^{19} +3.74567 q^{20} -2.07481 q^{21} -3.56254 q^{22} -0.878792 q^{23} -2.02372 q^{24} +9.03001 q^{25} +0.856017 q^{26} +3.85431 q^{27} +1.02525 q^{28} -1.17810 q^{29} -7.58017 q^{30} +8.52107 q^{31} +1.00000 q^{32} +7.20958 q^{33} -7.78358 q^{34} +3.84023 q^{35} +1.09543 q^{36} -8.40818 q^{37} -4.10209 q^{38} -1.73234 q^{39} +3.74567 q^{40} -1.59845 q^{41} -2.07481 q^{42} +9.33256 q^{43} -3.56254 q^{44} +4.10311 q^{45} -0.878792 q^{46} +0.295868 q^{47} -2.02372 q^{48} -5.94887 q^{49} +9.03001 q^{50} +15.7518 q^{51} +0.856017 q^{52} +5.45679 q^{53} +3.85431 q^{54} -13.3441 q^{55} +1.02525 q^{56} +8.30147 q^{57} -1.17810 q^{58} -10.3432 q^{59} -7.58017 q^{60} -13.8507 q^{61} +8.52107 q^{62} +1.12308 q^{63} +1.00000 q^{64} +3.20636 q^{65} +7.20958 q^{66} +2.14670 q^{67} -7.78358 q^{68} +1.77843 q^{69} +3.84023 q^{70} +10.3802 q^{71} +1.09543 q^{72} -7.09918 q^{73} -8.40818 q^{74} -18.2742 q^{75} -4.10209 q^{76} -3.65248 q^{77} -1.73234 q^{78} -11.8492 q^{79} +3.74567 q^{80} -11.0863 q^{81} -1.59845 q^{82} -12.1171 q^{83} -2.07481 q^{84} -29.1547 q^{85} +9.33256 q^{86} +2.38415 q^{87} -3.56254 q^{88} +5.16545 q^{89} +4.10311 q^{90} +0.877628 q^{91} -0.878792 q^{92} -17.2442 q^{93} +0.295868 q^{94} -15.3651 q^{95} -2.02372 q^{96} +0.0176862 q^{97} -5.94887 q^{98} -3.90251 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 71 q + 71 q^{2} - 9 q^{3} + 71 q^{4} - 34 q^{5} - 9 q^{6} - 19 q^{7} + 71 q^{8} + 34 q^{9}+O(q^{10}) \) 71 * q + 71 * q^2 - 9 * q^3 + 71 * q^4 - 34 * q^5 - 9 * q^6 - 19 * q^7 + 71 * q^8 + 34 * q^9	\( 71 q + 71 q^{2} - 9 q^{3} + 71 q^{4} - 34 q^{5} - 9 q^{6} - 19 q^{7} + 71 q^{8} + 34 q^{9} - 34 q^{10} - 37 q^{11} - 9 q^{12} - 62 q^{13} - 19 q^{14} - 29 q^{15} + 71 q^{16} - 52 q^{17} + 34 q^{18} - 30 q^{19} - 34 q^{20} - 51 q^{21} - 37 q^{22} - 45 q^{23} - 9 q^{24} + 27 q^{25} - 62 q^{26} - 27 q^{27} - 19 q^{28} - 55 q^{29} - 29 q^{30} - 61 q^{31} + 71 q^{32} - 73 q^{33} - 52 q^{34} - 33 q^{35} + 34 q^{36} - 43 q^{37} - 30 q^{38} - 40 q^{39} - 34 q^{40} - 87 q^{41} - 51 q^{42} - 4 q^{43} - 37 q^{44} - 81 q^{45} - 45 q^{46} - 89 q^{47} - 9 q^{48} - 2 q^{49} + 27 q^{50} - 19 q^{51} - 62 q^{52} - 50 q^{53} - 27 q^{54} - 66 q^{55} - 19 q^{56} - 45 q^{57} - 55 q^{58} - 118 q^{59} - 29 q^{60} - 92 q^{61} - 61 q^{62} - 54 q^{63} + 71 q^{64} - 51 q^{65} - 73 q^{66} - 17 q^{67} - 52 q^{68} - 89 q^{69} - 33 q^{70} - 95 q^{71} + 34 q^{72} - 114 q^{73} - 43 q^{74} - 38 q^{75} - 30 q^{76} - 73 q^{77} - 40 q^{78} - 47 q^{79} - 34 q^{80} - 57 q^{81} - 87 q^{82} - 68 q^{83} - 51 q^{84} - 67 q^{85} - 4 q^{86} - 55 q^{87} - 37 q^{88} - 150 q^{89} - 81 q^{90} - 23 q^{91} - 45 q^{92} - 59 q^{93} - 89 q^{94} - 47 q^{95} - 9 q^{96} - 97 q^{97} - 2 q^{98} - 57 q^{99}+O(q^{100}) \) 71 * q + 71 * q^2 - 9 * q^3 + 71 * q^4 - 34 * q^5 - 9 * q^6 - 19 * q^7 + 71 * q^8 + 34 * q^9 - 34 * q^10 - 37 * q^11 - 9 * q^12 - 62 * q^13 - 19 * q^14 - 29 * q^15 + 71 * q^16 - 52 * q^17 + 34 * q^18 - 30 * q^19 - 34 * q^20 - 51 * q^21 - 37 * q^22 - 45 * q^23 - 9 * q^24 + 27 * q^25 - 62 * q^26 - 27 * q^27 - 19 * q^28 - 55 * q^29 - 29 * q^30 - 61 * q^31 + 71 * q^32 - 73 * q^33 - 52 * q^34 - 33 * q^35 + 34 * q^36 - 43 * q^37 - 30 * q^38 - 40 * q^39 - 34 * q^40 - 87 * q^41 - 51 * q^42 - 4 * q^43 - 37 * q^44 - 81 * q^45 - 45 * q^46 - 89 * q^47 - 9 * q^48 - 2 * q^49 + 27 * q^50 - 19 * q^51 - 62 * q^52 - 50 * q^53 - 27 * q^54 - 66 * q^55 - 19 * q^56 - 45 * q^57 - 55 * q^58 - 118 * q^59 - 29 * q^60 - 92 * q^61 - 61 * q^62 - 54 * q^63 + 71 * q^64 - 51 * q^65 - 73 * q^66 - 17 * q^67 - 52 * q^68 - 89 * q^69 - 33 * q^70 - 95 * q^71 + 34 * q^72 - 114 * q^73 - 43 * q^74 - 38 * q^75 - 30 * q^76 - 73 * q^77 - 40 * q^78 - 47 * q^79 - 34 * q^80 - 57 * q^81 - 87 * q^82 - 68 * q^83 - 51 * q^84 - 67 * q^85 - 4 * q^86 - 55 * q^87 - 37 * q^88 - 150 * q^89 - 81 * q^90 - 23 * q^91 - 45 * q^92 - 59 * q^93 - 89 * q^94 - 47 * q^95 - 9 * q^96 - 97 * q^97 - 2 * q^98 - 57 * q^99

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