LMFDB - Embedded newform 6022.2.a.e.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6022,2,Mod(1,6022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6022, 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("6022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6022 = 2 \cdot 3011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6022.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.0859120972$
Analytic rank:	$0$
Dimension:	$68$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	6022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.24505 q^{3} +1.00000 q^{4} -1.17279 q^{5} -2.24505 q^{6} +1.15296 q^{7} +1.00000 q^{8} +2.04026 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.24505 q^{3} +1.00000 q^{4} -1.17279 q^{5} -2.24505 q^{6} +1.15296 q^{7} +1.00000 q^{8} +2.04026 q^{9} -1.17279 q^{10} -1.84251 q^{11} -2.24505 q^{12} -4.34162 q^{13} +1.15296 q^{14} +2.63297 q^{15} +1.00000 q^{16} +1.06843 q^{17} +2.04026 q^{18} +1.56820 q^{19} -1.17279 q^{20} -2.58846 q^{21} -1.84251 q^{22} +0.917320 q^{23} -2.24505 q^{24} -3.62457 q^{25} -4.34162 q^{26} +2.15467 q^{27} +1.15296 q^{28} -1.90545 q^{29} +2.63297 q^{30} -2.15632 q^{31} +1.00000 q^{32} +4.13653 q^{33} +1.06843 q^{34} -1.35218 q^{35} +2.04026 q^{36} +6.20262 q^{37} +1.56820 q^{38} +9.74716 q^{39} -1.17279 q^{40} +3.14882 q^{41} -2.58846 q^{42} -10.5038 q^{43} -1.84251 q^{44} -2.39279 q^{45} +0.917320 q^{46} +0.169073 q^{47} -2.24505 q^{48} -5.67068 q^{49} -3.62457 q^{50} -2.39867 q^{51} -4.34162 q^{52} -1.15052 q^{53} +2.15467 q^{54} +2.16087 q^{55} +1.15296 q^{56} -3.52069 q^{57} -1.90545 q^{58} +3.10768 q^{59} +2.63297 q^{60} +5.20117 q^{61} -2.15632 q^{62} +2.35234 q^{63} +1.00000 q^{64} +5.09180 q^{65} +4.13653 q^{66} -4.91971 q^{67} +1.06843 q^{68} -2.05943 q^{69} -1.35218 q^{70} +3.13817 q^{71} +2.04026 q^{72} +5.73706 q^{73} +6.20262 q^{74} +8.13735 q^{75} +1.56820 q^{76} -2.12435 q^{77} +9.74716 q^{78} +5.14521 q^{79} -1.17279 q^{80} -10.9581 q^{81} +3.14882 q^{82} -12.8584 q^{83} -2.58846 q^{84} -1.25304 q^{85} -10.5038 q^{86} +4.27783 q^{87} -1.84251 q^{88} +2.55750 q^{89} -2.39279 q^{90} -5.00573 q^{91} +0.917320 q^{92} +4.84104 q^{93} +0.169073 q^{94} -1.83917 q^{95} -2.24505 q^{96} +17.1915 q^{97} -5.67068 q^{98} -3.75919 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 68 q^{2} + 25 q^{3} + 68 q^{4} + 20 q^{5} + 25 q^{6} + 29 q^{7} + 68 q^{8} + 87 q^{9}+O(q^{10}) $ 68 * q + 68 * q^2 + 25 * q^3 + 68 * q^4 + 20 * q^5 + 25 * q^6 + 29 * q^7 + 68 * q^8 + 87 * q^9	\( 68 q + 68 q^{2} + 25 q^{3} + 68 q^{4} + 20 q^{5} + 25 q^{6} + 29 q^{7} + 68 q^{8} + 87 q^{9} + 20 q^{10} + 46 q^{11} + 25 q^{12} + 30 q^{13} + 29 q^{14} + 13 q^{15} + 68 q^{16} + 73 q^{17} + 87 q^{18} + 56 q^{19} + 20 q^{20} - 5 q^{21} + 46 q^{22} + 63 q^{23} + 25 q^{24} + 88 q^{25} + 30 q^{26} + 67 q^{27} + 29 q^{28} + 43 q^{29} + 13 q^{30} + 68 q^{31} + 68 q^{32} + 26 q^{33} + 73 q^{34} + 50 q^{35} + 87 q^{36} + 8 q^{37} + 56 q^{38} + 6 q^{39} + 20 q^{40} + 64 q^{41} - 5 q^{42} + 52 q^{43} + 46 q^{44} + 7 q^{45} + 63 q^{46} + 94 q^{47} + 25 q^{48} + 91 q^{49} + 88 q^{50} + 20 q^{51} + 30 q^{52} + 38 q^{53} + 67 q^{54} + 37 q^{55} + 29 q^{56} + 4 q^{57} + 43 q^{58} + 84 q^{59} + 13 q^{60} + 26 q^{61} + 68 q^{62} + 22 q^{63} + 68 q^{64} - 20 q^{65} + 26 q^{66} + 54 q^{67} + 73 q^{68} - 11 q^{69} + 50 q^{70} + 46 q^{71} + 87 q^{72} + 62 q^{73} + 8 q^{74} + 54 q^{75} + 56 q^{76} + 67 q^{77} + 6 q^{78} + 67 q^{79} + 20 q^{80} + 120 q^{81} + 64 q^{82} + 130 q^{83} - 5 q^{84} - 24 q^{85} + 52 q^{86} + 72 q^{87} + 46 q^{88} + 61 q^{89} + 7 q^{90} + 43 q^{91} + 63 q^{92} + 40 q^{93} + 94 q^{94} + 55 q^{95} + 25 q^{96} + 41 q^{97} + 91 q^{98} + 106 q^{99}+O(q^{100}) \) 68 * q + 68 * q^2 + 25 * q^3 + 68 * q^4 + 20 * q^5 + 25 * q^6 + 29 * q^7 + 68 * q^8 + 87 * q^9 + 20 * q^10 + 46 * q^11 + 25 * q^12 + 30 * q^13 + 29 * q^14 + 13 * q^15 + 68 * q^16 + 73 * q^17 + 87 * q^18 + 56 * q^19 + 20 * q^20 - 5 * q^21 + 46 * q^22 + 63 * q^23 + 25 * q^24 + 88 * q^25 + 30 * q^26 + 67 * q^27 + 29 * q^28 + 43 * q^29 + 13 * q^30 + 68 * q^31 + 68 * q^32 + 26 * q^33 + 73 * q^34 + 50 * q^35 + 87 * q^36 + 8 * q^37 + 56 * q^38 + 6 * q^39 + 20 * q^40 + 64 * q^41 - 5 * q^42 + 52 * q^43 + 46 * q^44 + 7 * q^45 + 63 * q^46 + 94 * q^47 + 25 * q^48 + 91 * q^49 + 88 * q^50 + 20 * q^51 + 30 * q^52 + 38 * q^53 + 67 * q^54 + 37 * q^55 + 29 * q^56 + 4 * q^57 + 43 * q^58 + 84 * q^59 + 13 * q^60 + 26 * q^61 + 68 * q^62 + 22 * q^63 + 68 * q^64 - 20 * q^65 + 26 * q^66 + 54 * q^67 + 73 * q^68 - 11 * q^69 + 50 * q^70 + 46 * q^71 + 87 * q^72 + 62 * q^73 + 8 * q^74 + 54 * q^75 + 56 * q^76 + 67 * q^77 + 6 * q^78 + 67 * q^79 + 20 * q^80 + 120 * q^81 + 64 * q^82 + 130 * q^83 - 5 * q^84 - 24 * q^85 + 52 * q^86 + 72 * q^87 + 46 * q^88 + 61 * q^89 + 7 * q^90 + 43 * q^91 + 63 * q^92 + 40 * q^93 + 94 * q^94 + 55 * q^95 + 25 * q^96 + 41 * q^97 + 91 * q^98 + 106 * 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
$3$	−2.24505	−1.29618	−0.648091	−	0.761563i	$-0.724432\pi$
$3$	−2.24505	−1.29618	−0.648091	+	0.761563i	$0.724432\pi$
$4$	1.00000	0.500000
$5$	−1.17279	−0.524486	−0.262243	−	0.965002i	$-0.584462\pi$
$5$	−1.17279	−0.524486	−0.262243	+	0.965002i	$0.584462\pi$
$6$	−2.24505	−0.916538
$7$	1.15296	0.435779	0.217890	−	0.975973i	$-0.430083\pi$
$7$	1.15296	0.435779	0.217890	+	0.975973i	$0.430083\pi$
$8$	1.00000	0.353553
$9$	2.04026	0.680086
$10$	−1.17279	−0.370868
$11$	−1.84251	−0.555537	−0.277769	−	0.960648i	$-0.589595\pi$
$11$	−1.84251	−0.555537	−0.277769	+	0.960648i	$0.589595\pi$
$12$	−2.24505	−0.648091
$13$	−4.34162	−1.20415	−0.602075	−	0.798440i	$-0.705659\pi$
$13$	−4.34162	−1.20415	−0.602075	+	0.798440i	$0.705659\pi$
$14$	1.15296	0.308142
$15$	2.63297	0.679829
$16$	1.00000	0.250000
$17$	1.06843	0.259132	0.129566	−	0.991571i	$-0.458642\pi$
$17$	1.06843	0.259132	0.129566	+	0.991571i	$0.458642\pi$
$18$	2.04026	0.480893
$19$	1.56820	0.359770	0.179885	−	0.983688i	$-0.442427\pi$
$19$	1.56820	0.359770	0.179885	+	0.983688i	$0.442427\pi$
$20$	−1.17279	−0.262243
$21$	−2.58846	−0.564849
$22$	−1.84251	−0.392824
$23$	0.917320	0.191275	0.0956373	−	0.995416i	$-0.469511\pi$
$23$	0.917320	0.191275	0.0956373	+	0.995416i	$0.469511\pi$
$24$	−2.24505	−0.458269
$25$	−3.62457	−0.724914
$26$	−4.34162	−0.851462
$27$	2.15467	0.414667
$28$	1.15296	0.217890
$29$	−1.90545	−0.353833	−0.176916	−	0.984226i	$-0.556612\pi$
$29$	−1.90545	−0.353833	−0.176916	+	0.984226i	$0.556612\pi$
$30$	2.63297	0.480712
$31$	−2.15632	−0.387286	−0.193643	−	0.981072i	$-0.562030\pi$
$31$	−2.15632	−0.387286	−0.193643	+	0.981072i	$0.562030\pi$
$32$	1.00000	0.176777
$33$	4.13653	0.720077
$34$	1.06843	0.183234
$35$	−1.35218	−0.228560
$36$	2.04026	0.340043
$37$	6.20262	1.01970	0.509852	−	0.860262i	$-0.329700\pi$
$37$	6.20262	1.01970	0.509852	+	0.860262i	$0.329700\pi$
$38$	1.56820	0.254396
$39$	9.74716	1.56080
$40$	−1.17279	−0.185434
$41$	3.14882	0.491763	0.245882	−	0.969300i	$-0.420923\pi$
$41$	3.14882	0.491763	0.245882	+	0.969300i	$0.420923\pi$
$42$	−2.58846	−0.399408
$43$	−10.5038	−1.60182	−0.800910	−	0.598785i	$-0.795651\pi$
$43$	−10.5038	−1.60182	−0.800910	+	0.598785i	$0.795651\pi$
$44$	−1.84251	−0.277769
$45$	−2.39279	−0.356696
$46$	0.917320	0.135252
$47$	0.169073	0.0246619	0.0123309	−	0.999924i	$-0.496075\pi$
$47$	0.169073	0.0246619	0.0123309	+	0.999924i	$0.496075\pi$
$48$	−2.24505	−0.324045
$49$	−5.67068	−0.810096
$50$	−3.62457	−0.512592
$51$	−2.39867	−0.335881
$52$	−4.34162	−0.602075
$53$	−1.15052	−0.158037	−0.0790183	−	0.996873i	$-0.525179\pi$
$53$	−1.15052	−0.158037	−0.0790183	+	0.996873i	$0.525179\pi$
$54$	2.15467	0.293214
$55$	2.16087	0.291372
$56$	1.15296	0.154071
$57$	−3.52069	−0.466327
$58$	−1.90545	−0.250197
$59$	3.10768	0.404585	0.202293	−	0.979325i	$-0.435161\pi$
$59$	3.10768	0.404585	0.202293	+	0.979325i	$0.435161\pi$
$60$	2.63297	0.339915
$61$	5.20117	0.665942	0.332971	−	0.942937i	$-0.391949\pi$
$61$	5.20117	0.665942	0.332971	+	0.942937i	$0.391949\pi$
$62$	−2.15632	−0.273853
$63$	2.35234	0.296367
$64$	1.00000	0.125000
$65$	5.09180	0.631560
$66$	4.13653	0.509171
$67$	−4.91971	−0.601039	−0.300519	−	0.953776i	$-0.597160\pi$
$67$	−4.91971	−0.601039	−0.300519	+	0.953776i	$0.597160\pi$
$68$	1.06843	0.129566
$69$	−2.05943	−0.247926
$70$	−1.35218	−0.161617
$71$	3.13817	0.372432	0.186216	−	0.982509i	$-0.440378\pi$
$71$	3.13817	0.372432	0.186216	+	0.982509i	$0.440378\pi$
$72$	2.04026	0.240447
$73$	5.73706	0.671472	0.335736	−	0.941956i	$-0.391015\pi$
$73$	5.73706	0.671472	0.335736	+	0.941956i	$0.391015\pi$
$74$	6.20262	0.721040
$75$	8.13735	0.939620
$76$	1.56820	0.179885
$77$	−2.12435	−0.242092
$78$	9.74716	1.10365
$79$	5.14521	0.578881	0.289441	−	0.957196i	$-0.406531\pi$
$79$	5.14521	0.578881	0.289441	+	0.957196i	$0.406531\pi$
$80$	−1.17279	−0.131122
$81$	−10.9581	−1.21757
$82$	3.14882	0.347729
$83$	−12.8584	−1.41139	−0.705695	−	0.708515i	$-0.749365\pi$
$83$	−12.8584	−1.41139	−0.705695	+	0.708515i	$0.749365\pi$
$84$	−2.58846	−0.282424
$85$	−1.25304	−0.135911
$86$	−10.5038	−1.13266
$87$	4.27783	0.458631
$88$	−1.84251	−0.196412
$89$	2.55750	0.271094	0.135547	−	0.990771i	$-0.456721\pi$
$89$	2.55750	0.271094	0.135547	+	0.990771i	$0.456721\pi$
$90$	−2.39279	−0.252222
$91$	−5.00573	−0.524743
$92$	0.917320	0.0956373
$93$	4.84104	0.501993
$94$	0.169073	0.0174386
$95$	−1.83917	−0.188694
$96$	−2.24505	−0.229135
$97$	17.1915	1.74553	0.872765	−	0.488140i	$-0.162324\pi$
$97$	17.1915	1.74553	0.872765	+	0.488140i	$0.162324\pi$
$98$	−5.67068	−0.572825
$99$	−3.75919	−0.377813
$100$	−3.62457	−0.362457
$101$	1.53880	0.153117	0.0765583	−	0.997065i	$-0.475607\pi$
$101$	1.53880	0.153117	0.0765583	+	0.997065i	$0.475607\pi$
$102$	−2.39867	−0.237504
$103$	5.01961	0.494597	0.247298	−	0.968939i	$-0.420457\pi$
$103$	5.01961	0.494597	0.247298	+	0.968939i	$0.420457\pi$
$104$	−4.34162	−0.425731
$105$	3.03572	0.296256
$106$	−1.15052	−0.111749
$107$	−0.0793806	−0.00767402	−0.00383701	−	0.999993i	$-0.501221\pi$
$107$	−0.0793806	−0.00767402	−0.00383701	+	0.999993i	$0.501221\pi$
$108$	2.15467	0.207334
$109$	18.7308	1.79408	0.897040	−	0.441948i	$-0.145713\pi$
$109$	18.7308	1.79408	0.897040	+	0.441948i	$0.145713\pi$
$110$	2.16087	0.206031
$111$	−13.9252	−1.32172
$112$	1.15296	0.108945
$113$	19.6188	1.84558	0.922791	−	0.385302i	$-0.125903\pi$
$113$	19.6188	1.84558	0.922791	+	0.385302i	$0.125903\pi$
$114$	−3.52069	−0.329743
$115$	−1.07582	−0.100321
$116$	−1.90545	−0.176916
$117$	−8.85802	−0.818924
$118$	3.10768	0.286085
$119$	1.23186	0.112924
$120$	2.63297	0.240356
$121$	−7.60516	−0.691378
$122$	5.20117	0.470892
$123$	−7.06926	−0.637414
$124$	−2.15632	−0.193643
$125$	10.1148	0.904694
$126$	2.35234	0.209563
$127$	21.4303	1.90163	0.950817	−	0.309753i	$-0.100247\pi$
$127$	21.4303	1.90163	0.950817	+	0.309753i	$0.100247\pi$
$128$	1.00000	0.0883883
$129$	23.5817	2.07625
$130$	5.09180	0.446580
$131$	−16.9927	−1.48465	−0.742327	−	0.670037i	$-0.766278\pi$
$131$	−16.9927	−1.48465	−0.742327	+	0.670037i	$0.766278\pi$
$132$	4.13653	0.360038
$133$	1.80808	0.156780
$134$	−4.91971	−0.424999
$135$	−2.52697	−0.217487
$136$	1.06843	0.0916169
$137$	−15.0965	−1.28978	−0.644890	−	0.764276i	$-0.723097\pi$
$137$	−15.0965	−1.28978	−0.644890	+	0.764276i	$0.723097\pi$
$138$	−2.05943	−0.175310
$139$	−8.90659	−0.755447	−0.377724	−	0.925918i	$-0.623293\pi$
$139$	−8.90659	−0.755447	−0.377724	+	0.925918i	$0.623293\pi$
$140$	−1.35218	−0.114280
$141$	−0.379578	−0.0319663
$142$	3.13817	0.263349
$143$	7.99947	0.668950
$144$	2.04026	0.170021
$145$	2.23468	0.185580
$146$	5.73706	0.474802
$147$	12.7310	1.05003
$148$	6.20262	0.509852
$149$	−7.04466	−0.577121	−0.288560	−	0.957462i	$-0.593177\pi$
$149$	−7.04466	−0.577121	−0.288560	+	0.957462i	$0.593177\pi$
$150$	8.13735	0.664412
$151$	5.74961	0.467897	0.233948	−	0.972249i	$-0.424835\pi$
$151$	5.74961	0.467897	0.233948	+	0.972249i	$0.424835\pi$
$152$	1.56820	0.127198
$153$	2.17987	0.176232
$154$	−2.12435	−0.171185
$155$	2.52890	0.203126
$156$	9.74716	0.780398
$157$	−2.53396	−0.202232	−0.101116	−	0.994875i	$-0.532241\pi$
$157$	−2.53396	−0.202232	−0.101116	+	0.994875i	$0.532241\pi$
$158$	5.14521	0.409331
$159$	2.58299	0.204844
$160$	−1.17279	−0.0927170
$161$	1.05764	0.0833535
$162$	−10.9581	−0.860951
$163$	−12.3779	−0.969515	−0.484758	−	0.874649i	$-0.661092\pi$
$163$	−12.3779	−0.969515	−0.484758	+	0.874649i	$0.661092\pi$
$164$	3.14882	0.245882
$165$	−4.85127	−0.377671
$166$	−12.8584	−0.998004
$167$	2.64292	0.204515	0.102258	−	0.994758i	$-0.467393\pi$
$167$	2.64292	0.204515	0.102258	+	0.994758i	$0.467393\pi$
$168$	−2.58846	−0.199704
$169$	5.84968	0.449975
$170$	−1.25304	−0.0961036
$171$	3.19953	0.244674
$172$	−10.5038	−0.800910
$173$	−22.3993	−1.70299	−0.851495	−	0.524363i	$-0.824304\pi$
$173$	−22.3993	−1.70299	−0.851495	+	0.524363i	$0.824304\pi$
$174$	4.27783	0.324301
$175$	−4.17900	−0.315902
$176$	−1.84251	−0.138884
$177$	−6.97690	−0.524416
$178$	2.55750	0.191692
$179$	7.35350	0.549627	0.274813	−	0.961498i	$-0.411384\pi$
$179$	7.35350	0.549627	0.274813	+	0.961498i	$0.411384\pi$
$180$	−2.39279	−0.178348
$181$	3.96329	0.294589	0.147294	−	0.989093i	$-0.452944\pi$
$181$	3.96329	0.294589	0.147294	+	0.989093i	$0.452944\pi$
$182$	−5.00573	−0.371049
$183$	−11.6769	−0.863182
$184$	0.917320	0.0676258
$185$	−7.27435	−0.534821
$186$	4.84104	0.354962
$187$	−1.96859	−0.143957
$188$	0.169073	0.0123309
$189$	2.48426	0.180703
$190$	−1.83917	−0.133427
$191$	8.82914	0.638854	0.319427	−	0.947611i	$-0.396510\pi$
$191$	8.82914	0.638854	0.319427	+	0.947611i	$0.396510\pi$
$192$	−2.24505	−0.162023
$193$	−14.8552	−1.06930	−0.534651	−	0.845073i	$-0.679557\pi$
$193$	−14.8552	−1.06930	−0.534651	+	0.845073i	$0.679557\pi$
$194$	17.1915	1.23428
$195$	−11.4314	−0.818616
$196$	−5.67068	−0.405048
$197$	27.8814	1.98647	0.993235	−	0.116124i	$-0.0370470\pi$
$197$	27.8814	1.98647	0.993235	+	0.116124i	$0.0370470\pi$
$198$	−3.75919	−0.267154
$199$	23.4092	1.65943	0.829715	−	0.558187i	$-0.188503\pi$
$199$	23.4092	1.65943	0.829715	+	0.558187i	$0.188503\pi$
$200$	−3.62457	−0.256296
$201$	11.0450	0.779055
$202$	1.53880	0.108270
$203$	−2.19691	−0.154193
$204$	−2.39867	−0.167941
$205$	−3.69290	−0.257923
$206$	5.01961	0.349733
$207$	1.87157	0.130083
$208$	−4.34162	−0.301037
$209$	−2.88942	−0.199866
$210$	3.03572	0.209484
$211$	17.0517	1.17389	0.586944	−	0.809627i	$-0.300331\pi$
$211$	17.0517	1.17389	0.586944	+	0.809627i	$0.300331\pi$
$212$	−1.15052	−0.0790183
$213$	−7.04534	−0.482739
$214$	−0.0793806	−0.00542635
$215$	12.3188	0.840133
$216$	2.15467	0.146607
$217$	−2.48615	−0.168771
$218$	18.7308	1.26861
$219$	−12.8800	−0.870349
$220$	2.16087	0.145686
$221$	−4.63871	−0.312033
$222$	−13.9252	−0.934598
$223$	17.0033	1.13862	0.569311	−	0.822122i	$-0.307210\pi$
$223$	17.0033	1.13862	0.569311	+	0.822122i	$0.307210\pi$
$224$	1.15296	0.0770356
$225$	−7.39505	−0.493004
$226$	19.6188	1.30502
$227$	28.5454	1.89463	0.947313	−	0.320310i	$-0.103787\pi$
$227$	28.5454	1.89463	0.947313	+	0.320310i	$0.103787\pi$
$228$	−3.52069	−0.233164
$229$	−11.5548	−0.763560	−0.381780	−	0.924253i	$-0.624689\pi$
$229$	−11.5548	−0.763560	−0.381780	+	0.924253i	$0.624689\pi$
$230$	−1.07582	−0.0709376
$231$	4.76926	0.313795
$232$	−1.90545	−0.125099
$233$	−9.24345	−0.605559	−0.302779	−	0.953061i	$-0.597915\pi$
$233$	−9.24345	−0.605559	−0.302779	+	0.953061i	$0.597915\pi$
$234$	−8.85802	−0.579067
$235$	−0.198287	−0.0129348
$236$	3.10768	0.202293
$237$	−11.5513	−0.750335
$238$	1.23186	0.0798495
$239$	2.10864	0.136397	0.0681983	−	0.997672i	$-0.478275\pi$
$239$	2.10864	0.136397	0.0681983	+	0.997672i	$0.478275\pi$
$240$	2.63297	0.169957
$241$	−0.153691	−0.00990012	−0.00495006	−	0.999988i	$-0.501576\pi$
$241$	−0.153691	−0.00990012	−0.00495006	+	0.999988i	$0.501576\pi$
$242$	−7.60516	−0.488878
$243$	18.1375	1.16352
$244$	5.20117	0.332971
$245$	6.65050	0.424885
$246$	−7.06926	−0.450720
$247$	−6.80853	−0.433217
$248$	−2.15632	−0.136926
$249$	28.8677	1.82942
$250$	10.1148	0.639715
$251$	23.7179	1.49706	0.748529	−	0.663102i	$-0.230760\pi$
$251$	23.7179	1.49706	0.748529	+	0.663102i	$0.230760\pi$
$252$	2.35234	0.148184
$253$	−1.69017	−0.106260
$254$	21.4303	1.34466
$255$	2.81313	0.176165
$256$	1.00000	0.0625000
$257$	22.9701	1.43284	0.716419	−	0.697670i	$-0.245780\pi$
$257$	22.9701	1.43284	0.716419	+	0.697670i	$0.245780\pi$
$258$	23.5817	1.46813
$259$	7.15139	0.444366
$260$	5.09180	0.315780
$261$	−3.88760	−0.240636
$262$	−16.9927	−1.04981
$263$	13.4852	0.831536	0.415768	−	0.909471i	$-0.363513\pi$
$263$	13.4852	0.831536	0.415768	+	0.909471i	$0.363513\pi$
$264$	4.13653	0.254586
$265$	1.34932	0.0828881
$266$	1.80808	0.110860
$267$	−5.74171	−0.351387
$268$	−4.91971	−0.300519
$269$	−6.25763	−0.381535	−0.190767	−	0.981635i	$-0.561098\pi$
$269$	−6.25763	−0.381535	−0.190767	+	0.981635i	$0.561098\pi$
$270$	−2.52697	−0.153787
$271$	15.0583	0.914729	0.457365	−	0.889279i	$-0.348793\pi$
$271$	15.0583	0.914729	0.457365	+	0.889279i	$0.348793\pi$
$272$	1.06843	0.0647829
$273$	11.2381	0.680162
$274$	−15.0965	−0.912012
$275$	6.67830	0.402717
$276$	−2.05943	−0.123963
$277$	−4.20331	−0.252552	−0.126276	−	0.991995i	$-0.540303\pi$
$277$	−4.20331	−0.252552	−0.126276	+	0.991995i	$0.540303\pi$
$278$	−8.90659	−0.534182
$279$	−4.39944	−0.263388
$280$	−1.35218	−0.0808083
$281$	7.45926	0.444982	0.222491	−	0.974935i	$-0.428581\pi$
$281$	7.45926	0.444982	0.222491	+	0.974935i	$0.428581\pi$
$282$	−0.379578	−0.0226036
$283$	12.7819	0.759805	0.379902	−	0.925027i	$-0.375958\pi$
$283$	12.7819	0.759805	0.379902	+	0.925027i	$0.375958\pi$
$284$	3.13817	0.186216
$285$	4.12902	0.244582
$286$	7.99947	0.473019
$287$	3.63048	0.214300
$288$	2.04026	0.120223
$289$	−15.8585	−0.932851
$290$	2.23468	0.131225
$291$	−38.5958	−2.26252
$292$	5.73706	0.335736
$293$	4.94554	0.288921	0.144461	−	0.989511i	$-0.453855\pi$
$293$	4.94554	0.288921	0.144461	+	0.989511i	$0.453855\pi$
$294$	12.7310	0.742485
$295$	−3.64465	−0.212200
$296$	6.20262	0.360520
$297$	−3.97000	−0.230363
$298$	−7.04466	−0.408086
$299$	−3.98266	−0.230323
$300$	8.13735	0.469810
$301$	−12.1105	−0.698040
$302$	5.74961	0.330853
$303$	−3.45469	−0.198467
$304$	1.56820	0.0899425
$305$	−6.09987	−0.349278
$306$	2.17987	0.124615
$307$	30.1553	1.72105	0.860526	−	0.509407i	$-0.170135\pi$
$307$	30.1553	1.72105	0.860526	+	0.509407i	$0.170135\pi$
$308$	−2.12435	−0.121046
$309$	−11.2693	−0.641087
$310$	2.52890	0.143632
$311$	−4.92488	−0.279264	−0.139632	−	0.990203i	$-0.544592\pi$
$311$	−4.92488	−0.279264	−0.139632	+	0.990203i	$0.544592\pi$
$312$	9.74716	0.551824
$313$	19.7508	1.11638	0.558191	−	0.829712i	$-0.311495\pi$
$313$	19.7508	1.11638	0.558191	+	0.829712i	$0.311495\pi$
$314$	−2.53396	−0.143000
$315$	−2.75880	−0.155441
$316$	5.14521	0.289441
$317$	28.9281	1.62476	0.812381	−	0.583127i	$-0.198171\pi$
$317$	28.9281	1.62476	0.812381	+	0.583127i	$0.198171\pi$
$318$	2.58299	0.144847
$319$	3.51080	0.196567
$320$	−1.17279	−0.0655608
$321$	0.178214	0.00994692
$322$	1.05764	0.0589398
$323$	1.67551	0.0932278
$324$	−10.9581	−0.608785
$325$	15.7365	0.872905
$326$	−12.3779	−0.685551
$327$	−42.0515	−2.32545
$328$	3.14882	0.173865
$329$	0.194935	0.0107471
$330$	−4.85127	−0.267053
$331$	12.9349	0.710968	0.355484	−	0.934682i	$-0.384316\pi$
$331$	12.9349	0.710968	0.355484	+	0.934682i	$0.384316\pi$
$332$	−12.8584	−0.705695
$333$	12.6549	0.693486
$334$	2.64292	0.144614
$335$	5.76978	0.315237
$336$	−2.58846	−0.141212
$337$	−12.9228	−0.703951	−0.351975	−	0.936009i	$-0.614490\pi$
$337$	−12.9228	−0.703951	−0.351975	+	0.936009i	$0.614490\pi$
$338$	5.84968	0.318180
$339$	−44.0452	−2.39221
$340$	−1.25304	−0.0679555
$341$	3.97303	0.215152
$342$	3.19953	0.173011
$343$	−14.6088	−0.788802
$344$	−10.5038	−0.566329
$345$	2.41528	0.130034
$346$	−22.3993	−1.20420
$347$	10.8871	0.584448	0.292224	−	0.956350i	$-0.405605\pi$
$347$	10.8871	0.584448	0.292224	+	0.956350i	$0.405605\pi$
$348$	4.27783	0.229316
$349$	16.6549	0.891516	0.445758	−	0.895154i	$-0.352934\pi$
$349$	16.6549	0.891516	0.445758	+	0.895154i	$0.352934\pi$
$350$	−4.17900	−0.223377
$351$	−9.35478	−0.499321
$352$	−1.84251	−0.0982060
$353$	−28.9485	−1.54078	−0.770388	−	0.637576i	$-0.779937\pi$
$353$	−28.9485	−1.54078	−0.770388	+	0.637576i	$0.779937\pi$
$354$	−6.97690	−0.370818
$355$	−3.68040	−0.195335
$356$	2.55750	0.135547
$357$	−2.76558	−0.146370
$358$	7.35350	0.388645
$359$	−0.00789570	−0.000416719 0	−0.000208359	−	1.00000i	$-0.500066\pi$
$359$	−0.00789570	−0.000416719 0	−0.000208359		1.00000i	$0.500066\pi$
$360$	−2.39279	−0.126111
$361$	−16.5407	−0.870566
$362$	3.96329	0.208306
$363$	17.0740	0.896152
$364$	−5.00573	−0.262372
$365$	−6.72835	−0.352178
$366$	−11.6769	−0.610362
$367$	4.06499	0.212191	0.106095	−	0.994356i	$-0.466165\pi$
$367$	4.06499	0.212191	0.106095	+	0.994356i	$0.466165\pi$
$368$	0.917320	0.0478186
$369$	6.42440	0.334441
$370$	−7.27435	−0.378176
$371$	−1.32651	−0.0688691
$372$	4.84104	0.250996
$373$	−21.0225	−1.08851	−0.544253	−	0.838921i	$-0.683187\pi$
$373$	−21.0225	−1.08851	−0.544253	+	0.838921i	$0.683187\pi$
$374$	−1.96859	−0.101793
$375$	−22.7082	−1.17265
$376$	0.169073	0.00871929
$377$	8.27273	0.426067
$378$	2.48426	0.127777
$379$	−20.6087	−1.05860	−0.529298	−	0.848436i	$-0.677545\pi$
$379$	−20.6087	−1.05860	−0.529298	+	0.848436i	$0.677545\pi$
$380$	−1.83917	−0.0943472
$381$	−48.1122	−2.46486
$382$	8.82914	0.451738
$383$	29.9187	1.52877	0.764386	−	0.644759i	$-0.223042\pi$
$383$	29.9187	1.52877	0.764386	+	0.644759i	$0.223042\pi$
$384$	−2.24505	−0.114567
$385$	2.49141	0.126974
$386$	−14.8552	−0.756110
$387$	−21.4305	−1.08937
$388$	17.1915	0.872765
$389$	−3.86857	−0.196144	−0.0980721	−	0.995179i	$-0.531268\pi$
$389$	−3.86857	−0.196144	−0.0980721	+	0.995179i	$0.531268\pi$
$390$	−11.4314	−0.578849
$391$	0.980090	0.0495653
$392$	−5.67068	−0.286412
$393$	38.1494	1.92438
$394$	27.8814	1.40465
$395$	−6.03424	−0.303615
$396$	−3.75919	−0.188906
$397$	25.8708	1.29842	0.649210	−	0.760609i	$-0.275100\pi$
$397$	25.8708	1.29842	0.649210	+	0.760609i	$0.275100\pi$
$398$	23.4092	1.17339
$399$	−4.05923	−0.203216
$400$	−3.62457	−0.181228
$401$	−2.12826	−0.106280	−0.0531400	−	0.998587i	$-0.516923\pi$
$401$	−2.12826	−0.106280	−0.0531400	+	0.998587i	$0.516923\pi$
$402$	11.0450	0.550875
$403$	9.36191	0.466350
$404$	1.53880	0.0765583
$405$	12.8515	0.638599
$406$	−2.19691	−0.109031
$407$	−11.4284	−0.566484
$408$	−2.39867	−0.118752
$409$	4.04439	0.199982	0.0999911	−	0.994988i	$-0.468119\pi$
$409$	4.04439	0.199982	0.0999911	+	0.994988i	$0.468119\pi$
$410$	−3.69290	−0.182379
$411$	33.8924	1.67179
$412$	5.01961	0.247298
$413$	3.58304	0.176310
$414$	1.87157	0.0919826
$415$	15.0801	0.740255
$416$	−4.34162	−0.212865
$417$	19.9958	0.979196
$418$	−2.88942	−0.141326
$419$	18.3906	0.898441	0.449220	−	0.893421i	$-0.351702\pi$
$419$	18.3906	0.898441	0.449220	+	0.893421i	$0.351702\pi$
$420$	3.03572	0.148128
$421$	−7.93651	−0.386802	−0.193401	−	0.981120i	$-0.561952\pi$
$421$	−7.93651	−0.386802	−0.193401	+	0.981120i	$0.561952\pi$
$422$	17.0517	0.830065
$423$	0.344953	0.0167722
$424$	−1.15052	−0.0558744
$425$	−3.87259	−0.187848
$426$	−7.04534	−0.341348
$427$	5.99676	0.290204
$428$	−0.0793806	−0.00383701
$429$	−17.9592	−0.867080
$430$	12.3188	0.594064
$431$	18.4308	0.887782	0.443891	−	0.896081i	$-0.353598\pi$
$431$	18.4308	0.887782	0.443891	+	0.896081i	$0.353598\pi$
$432$	2.15467	0.103667
$433$	−8.58629	−0.412631	−0.206315	−	0.978486i	$-0.566147\pi$
$433$	−8.58629	−0.412631	−0.206315	+	0.978486i	$0.566147\pi$
$434$	−2.48615	−0.119339
$435$	−5.01698	−0.240546
$436$	18.7308	0.897040
$437$	1.43854	0.0688148
$438$	−12.8800	−0.615430
$439$	40.7119	1.94307	0.971537	−	0.236887i	$-0.0761271\pi$
$439$	40.7119	1.94307	0.971537	+	0.236887i	$0.0761271\pi$
$440$	2.16087	0.103015
$441$	−11.5696	−0.550935
$442$	−4.63871	−0.220641
$443$	26.6862	1.26790	0.633950	−	0.773374i	$-0.281433\pi$
$443$	26.6862	1.26790	0.633950	+	0.773374i	$0.281433\pi$
$444$	−13.9252	−0.660861
$445$	−2.99940	−0.142185
$446$	17.0033	0.805127
$447$	15.8156	0.748053
$448$	1.15296	0.0544724
$449$	24.2289	1.14343	0.571716	−	0.820452i	$-0.306278\pi$
$449$	24.2289	1.14343	0.571716	+	0.820452i	$0.306278\pi$
$450$	−7.39505	−0.348606
$451$	−5.80173	−0.273193
$452$	19.6188	0.922791
$453$	−12.9082	−0.606479
$454$	28.5454	1.33970
$455$	5.87066	0.275221
$456$	−3.52069	−0.164872
$457$	1.89243	0.0885244	0.0442622	−	0.999020i	$-0.485906\pi$
$457$	1.89243	0.0885244	0.0442622	+	0.999020i	$0.485906\pi$
$458$	−11.5548	−0.539919
$459$	2.30211	0.107453
$460$	−1.07582	−0.0501604
$461$	−27.9857	−1.30342	−0.651711	−	0.758467i	$-0.725949\pi$
$461$	−27.9857	−1.30342	−0.651711	+	0.758467i	$0.725949\pi$
$462$	4.76926	0.221886
$463$	10.4447	0.485405	0.242703	−	0.970101i	$-0.421966\pi$
$463$	10.4447	0.485405	0.242703	+	0.970101i	$0.421966\pi$
$464$	−1.90545	−0.0884581
$465$	−5.67751	−0.263288
$466$	−9.24345	−0.428195
$467$	7.62444	0.352817	0.176409	−	0.984317i	$-0.443552\pi$
$467$	7.62444	0.352817	0.176409	+	0.984317i	$0.443552\pi$
$468$	−8.85802	−0.409462
$469$	−5.67225	−0.261920
$470$	−0.198287	−0.00914630
$471$	5.68888	0.262130
$472$	3.10768	0.143043
$473$	19.3534	0.889871
$474$	−11.5513	−0.530567
$475$	−5.68405	−0.260802
$476$	1.23186	0.0564621
$477$	−2.34737	−0.107478
$478$	2.10864	0.0964469
$479$	−12.2145	−0.558097	−0.279048	−	0.960277i	$-0.590019\pi$
$479$	−12.2145	−0.558097	−0.279048	+	0.960277i	$0.590019\pi$
$480$	2.63297	0.120178
$481$	−26.9294	−1.22788
$482$	−0.153691	−0.00700044
$483$	−2.37445	−0.108041
$484$	−7.60516	−0.345689
$485$	−20.1620	−0.915507
$486$	18.1375	0.822735
$487$	−21.0687	−0.954716	−0.477358	−	0.878709i	$-0.658406\pi$
$487$	−21.0687	−0.954716	−0.477358	+	0.878709i	$0.658406\pi$
$488$	5.20117	0.235446
$489$	27.7891	1.25667
$490$	6.65050	0.300439
$491$	15.5577	0.702110	0.351055	−	0.936355i	$-0.385823\pi$
$491$	15.5577	0.702110	0.351055	+	0.936355i	$0.385823\pi$
$492$	−7.06926	−0.318707
$493$	−2.03583	−0.0916892
$494$	−6.80853	−0.306330
$495$	4.40873	0.198158
$496$	−2.15632	−0.0968215
$497$	3.61819	0.162298
$498$	28.8677	1.29359
$499$	−36.7009	−1.64296	−0.821480	−	0.570238i	$-0.806851\pi$
$499$	−36.7009	−1.64296	−0.821480	+	0.570238i	$0.806851\pi$
$500$	10.1148	0.452347
$501$	−5.93349	−0.265089
$502$	23.7179	1.05858
$503$	7.05268	0.314463	0.157232	−	0.987562i	$-0.449743\pi$
$503$	7.05268	0.314463	0.157232	+	0.987562i	$0.449743\pi$
$504$	2.35234	0.104782
$505$	−1.80469	−0.0803076
$506$	−1.69017	−0.0751373
$507$	−13.1328	−0.583249
$508$	21.4303	0.950817
$509$	26.8264	1.18906	0.594529	−	0.804074i	$-0.297338\pi$
$509$	26.8264	1.18906	0.594529	+	0.804074i	$0.297338\pi$
$510$	2.81313	0.124568
$511$	6.61462	0.292613
$512$	1.00000	0.0441942
$513$	3.37896	0.149185
$514$	22.9701	1.01317
$515$	−5.88693	−0.259409
$516$	23.5817	1.03812
$517$	−0.311519	−0.0137006
$518$	7.15139	0.314214
$519$	50.2877	2.20738
$520$	5.09180	0.223290
$521$	0.638619	0.0279784	0.0139892	−	0.999902i	$-0.495547\pi$
$521$	0.638619	0.0279784	0.0139892	+	0.999902i	$0.495547\pi$
$522$	−3.88760	−0.170156
$523$	7.45301	0.325898	0.162949	−	0.986635i	$-0.447899\pi$
$523$	7.45301	0.325898	0.162949	+	0.986635i	$0.447899\pi$
$524$	−16.9927	−0.742327
$525$	9.38206	0.409467
$526$	13.4852	0.587985
$527$	−2.30387	−0.100358
$528$	4.13653	0.180019
$529$	−22.1585	−0.963414
$530$	1.34932	0.0586107
$531$	6.34046	0.275153
$532$	1.80808	0.0783901
$533$	−13.6710	−0.592156
$534$	−5.74171	−0.248468
$535$	0.0930966	0.00402492
$536$	−4.91971	−0.212499
$537$	−16.5090	−0.712416
$538$	−6.25763	−0.269786
$539$	10.4483	0.450039
$540$	−2.52697	−0.108744
$541$	38.5424	1.65707	0.828533	−	0.559940i	$-0.189176\pi$
$541$	38.5424	1.65707	0.828533	+	0.559940i	$0.189176\pi$
$542$	15.0583	0.646811
$543$	−8.89779	−0.381841
$544$	1.06843	0.0458084
$545$	−21.9672	−0.940971
$546$	11.2381	0.480947
$547$	−30.2867	−1.29496	−0.647482	−	0.762081i	$-0.724178\pi$
$547$	−30.2867	−1.29496	−0.647482	+	0.762081i	$0.724178\pi$
$548$	−15.0965	−0.644890
$549$	10.6117	0.452898
$550$	6.67830	0.284764
$551$	−2.98812	−0.127298
$552$	−2.05943	−0.0876552
$553$	5.93224	0.252265
$554$	−4.20331	−0.178581
$555$	16.3313	0.693225
$556$	−8.90659	−0.377724
$557$	−9.84966	−0.417344	−0.208672	−	0.977986i	$-0.566914\pi$
$557$	−9.84966	−0.417344	−0.208672	+	0.977986i	$0.566914\pi$
$558$	−4.39944	−0.186243
$559$	45.6037	1.92883
$560$	−1.35218	−0.0571401
$561$	4.41958	0.186595
$562$	7.45926	0.314650
$563$	−13.8542	−0.583887	−0.291943	−	0.956436i	$-0.594302\pi$
$563$	−13.8542	−0.583887	−0.291943	+	0.956436i	$0.594302\pi$
$564$	−0.379578	−0.0159831
$565$	−23.0087	−0.967982
$566$	12.7819	0.537263
$567$	−12.6343	−0.530591
$568$	3.13817	0.131675
$569$	37.1021	1.55540	0.777700	−	0.628636i	$-0.216386\pi$
$569$	37.1021	1.55540	0.777700	+	0.628636i	$0.216386\pi$
$570$	4.12902	0.172946
$571$	11.0451	0.462225	0.231112	−	0.972927i	$-0.425764\pi$
$571$	11.0451	0.462225	0.231112	+	0.972927i	$0.425764\pi$
$572$	7.99947	0.334475
$573$	−19.8219	−0.828071
$574$	3.63048	0.151533
$575$	−3.32489	−0.138658
$576$	2.04026	0.0850107
$577$	−15.9074	−0.662235	−0.331117	−	0.943590i	$-0.607426\pi$
$577$	−15.9074	−0.662235	−0.331117	+	0.943590i	$0.607426\pi$
$578$	−15.8585	−0.659625
$579$	33.3507	1.38601
$580$	2.23468	0.0927902
$581$	−14.8252	−0.615055
$582$	−38.5958	−1.59985
$583$	2.11985	0.0877953
$584$	5.73706	0.237401
$585$	10.3886	0.429515
$586$	4.94554	0.204298
$587$	5.10648	0.210767	0.105384	−	0.994432i	$-0.466393\pi$
$587$	5.10648	0.210767	0.105384	+	0.994432i	$0.466393\pi$
$588$	12.7310	0.525016
$589$	−3.38154	−0.139334
$590$	−3.64465	−0.150048
$591$	−62.5952	−2.57482
$592$	6.20262	0.254926
$593$	−25.4248	−1.04407	−0.522035	−	0.852924i	$-0.674827\pi$
$593$	−25.4248	−1.04407	−0.522035	+	0.852924i	$0.674827\pi$
$594$	−3.97000	−0.162891
$595$	−1.44471	−0.0592272
$596$	−7.04466	−0.288560
$597$	−52.5548	−2.15092
$598$	−3.98266	−0.162863
$599$	−8.22501	−0.336065	−0.168032	−	0.985781i	$-0.553741\pi$
$599$	−8.22501	−0.336065	−0.168032	+	0.985781i	$0.553741\pi$
$600$	8.13735	0.332206
$601$	−15.5075	−0.632564	−0.316282	−	0.948665i	$-0.602435\pi$
$601$	−15.5075	−0.632564	−0.316282	+	0.948665i	$0.602435\pi$
$602$	−12.1105	−0.493589
$603$	−10.0375	−0.408758
$604$	5.74961	0.233948
$605$	8.91924	0.362619
$606$	−3.45469	−0.140337
$607$	−24.5990	−0.998443	−0.499222	−	0.866474i	$-0.666381\pi$
$607$	−24.5990	−0.998443	−0.499222	+	0.866474i	$0.666381\pi$
$608$	1.56820	0.0635989
$609$	4.93218	0.199862
$610$	−6.09987	−0.246977
$611$	−0.734053	−0.0296966
$612$	2.17987	0.0881158
$613$	−31.1023	−1.25621	−0.628105	−	0.778129i	$-0.716169\pi$
$613$	−31.1023	−1.25621	−0.628105	+	0.778129i	$0.716169\pi$
$614$	30.1553	1.21697
$615$	8.29074	0.334315
$616$	−2.12435	−0.0855923
$617$	−8.48274	−0.341502	−0.170751	−	0.985314i	$-0.554619\pi$
$617$	−8.48274	−0.341502	−0.170751	+	0.985314i	$0.554619\pi$
$618$	−11.2693	−0.453317
$619$	5.08891	0.204541	0.102270	−	0.994757i	$-0.467389\pi$
$619$	5.08891	0.204541	0.102270	+	0.994757i	$0.467389\pi$
$620$	2.52890	0.101563
$621$	1.97653	0.0793152
$622$	−4.92488	−0.197470
$623$	2.94870	0.118137
$624$	9.74716	0.390199
$625$	6.26036	0.250414
$626$	19.7508	0.789402
$627$	6.48691	0.259062
$628$	−2.53396	−0.101116
$629$	6.62705	0.264238
$630$	−2.75880	−0.109913
$631$	−26.2515	−1.04506	−0.522528	−	0.852622i	$-0.675011\pi$
$631$	−26.2515	−1.04506	−0.522528	+	0.852622i	$0.675011\pi$
$632$	5.14521	0.204666
$633$	−38.2820	−1.52157
$634$	28.9281	1.14888
$635$	−25.1332	−0.997381
$636$	2.58299	0.102422
$637$	24.6199	0.975477
$638$	3.51080	0.138994
$639$	6.40266	0.253285
$640$	−1.17279	−0.0463585
$641$	16.3205	0.644623	0.322311	−	0.946634i	$-0.395540\pi$
$641$	16.3205	0.644623	0.322311	+	0.946634i	$0.395540\pi$
$642$	0.178214	0.00703353
$643$	3.49194	0.137709	0.0688544	−	0.997627i	$-0.478066\pi$
$643$	3.49194	0.137709	0.0688544	+	0.997627i	$0.478066\pi$
$644$	1.05764	0.0416767
$645$	−27.6563	−1.08896
$646$	1.67551	0.0659220
$647$	22.5568	0.886799	0.443399	−	0.896324i	$-0.353772\pi$
$647$	22.5568	0.886799	0.443399	+	0.896324i	$0.353772\pi$
$648$	−10.9581	−0.430476
$649$	−5.72593	−0.224762
$650$	15.7365	0.617237
$651$	5.58155	0.218758
$652$	−12.3779	−0.484758
$653$	−30.5925	−1.19718	−0.598589	−	0.801057i	$-0.704272\pi$
$653$	−30.5925	−1.19718	−0.598589	+	0.801057i	$0.704272\pi$
$654$	−42.0515	−1.64434
$655$	19.9288	0.778681
$656$	3.14882	0.122941
$657$	11.7051	0.456658
$658$	0.194935	0.00759937
$659$	24.0069	0.935176	0.467588	−	0.883946i	$-0.345123\pi$
$659$	24.0069	0.935176	0.467588	+	0.883946i	$0.345123\pi$
$660$	−4.85127	−0.188835
$661$	−42.9661	−1.67119	−0.835594	−	0.549347i	$-0.814876\pi$
$661$	−42.9661	−1.67119	−0.835594	+	0.549347i	$0.814876\pi$
$662$	12.9349	0.502730
$663$	10.4141	0.404451
$664$	−12.8584	−0.499002
$665$	−2.12049	−0.0822291
$666$	12.6549	0.490369
$667$	−1.74791	−0.0676792
$668$	2.64292	0.102258
$669$	−38.1732	−1.47586
$670$	5.76978	0.222906
$671$	−9.58321	−0.369956
$672$	−2.58846	−0.0998521
$673$	−4.34375	−0.167439	−0.0837197	−	0.996489i	$-0.526680\pi$
$673$	−4.34375	−0.167439	−0.0837197	+	0.996489i	$0.526680\pi$
$674$	−12.9228	−0.497768
$675$	−7.80976	−0.300598
$676$	5.84968	0.224988
$677$	−49.4644	−1.90107	−0.950536	−	0.310615i	$-0.899465\pi$
$677$	−49.4644	−1.90107	−0.950536	+	0.310615i	$0.899465\pi$
$678$	−44.0452	−1.69155
$679$	19.8212	0.760666
$680$	−1.25304	−0.0480518
$681$	−64.0859	−2.45578
$682$	3.97303	0.152135
$683$	−7.34354	−0.280993	−0.140496	−	0.990081i	$-0.544870\pi$
$683$	−7.34354	−0.280993	−0.140496	+	0.990081i	$0.544870\pi$
$684$	3.19953	0.122337
$685$	17.7050	0.676472
$686$	−14.6088	−0.557768
$687$	25.9410	0.989712
$688$	−10.5038	−0.400455
$689$	4.99514	0.190300
$690$	2.41528	0.0919480
$691$	−18.3432	−0.697808	−0.348904	−	0.937158i	$-0.613446\pi$
$691$	−18.3432	−0.697808	−0.348904	+	0.937158i	$0.613446\pi$
$692$	−22.3993	−0.851495
$693$	−4.33421	−0.164643
$694$	10.8871	0.413267
$695$	10.4455	0.396222
$696$	4.27783	0.162151
$697$	3.36428	0.127431
$698$	16.6549	0.630397
$699$	20.7520	0.784914
$700$	−4.17900	−0.157951
$701$	−33.8657	−1.27909	−0.639544	−	0.768754i	$-0.720877\pi$
$701$	−33.8657	−1.27909	−0.639544	+	0.768754i	$0.720877\pi$
$702$	−9.35478	−0.353073
$703$	9.72695	0.366859
$704$	−1.84251	−0.0694422
$705$	0.445165	0.0167659
$706$	−28.9485	−1.08949
$707$	1.77418	0.0667250
$708$	−6.97690	−0.262208
$709$	−27.0359	−1.01536	−0.507678	−	0.861547i	$-0.669496\pi$
$709$	−27.0359	−1.01536	−0.507678	+	0.861547i	$0.669496\pi$
$710$	−3.68040	−0.138123
$711$	10.4976	0.393689
$712$	2.55750	0.0958462
$713$	−1.97803	−0.0740779
$714$	−2.76558	−0.103499
$715$	−9.38168	−0.350855
$716$	7.35350	0.274813
$717$	−4.73400	−0.176795
$718$	−0.00789570	−0.000294665 0
$719$	39.2613	1.46420	0.732100	−	0.681197i	$-0.238540\pi$
$719$	39.2613	1.46420	0.732100	+	0.681197i	$0.238540\pi$
$720$	−2.39279	−0.0891739
$721$	5.78743	0.215535
$722$	−16.5407	−0.615583
$723$	0.345045	0.0128324
$724$	3.96329	0.147294
$725$	6.90642	0.256498
$726$	17.0740	0.633675
$727$	−0.542440	−0.0201180	−0.0100590	−	0.999949i	$-0.503202\pi$
$727$	−0.542440	−0.0201180	−0.0100590	+	0.999949i	$0.503202\pi$
$728$	−5.00573	−0.185525
$729$	−7.84533	−0.290568
$730$	−6.72835	−0.249027
$731$	−11.2226	−0.415082
$732$	−11.6769	−0.431591
$733$	−21.0860	−0.778828	−0.389414	−	0.921063i	$-0.627323\pi$
$733$	−21.0860	−0.778828	−0.389414	+	0.921063i	$0.627323\pi$
$734$	4.06499	0.150041
$735$	−14.9307	−0.550727
$736$	0.917320	0.0338129
$737$	9.06461	0.333899
$738$	6.42440	0.236486
$739$	−46.0785	−1.69502	−0.847512	−	0.530777i	$-0.821900\pi$
$739$	−46.0785	−1.69502	−0.847512	+	0.530777i	$0.821900\pi$
$740$	−7.27435	−0.267411
$741$	15.2855	0.561527
$742$	−1.32651	−0.0486978
$743$	25.5608	0.937735	0.468868	−	0.883268i	$-0.344662\pi$
$743$	25.5608	0.937735	0.468868	+	0.883268i	$0.344662\pi$
$744$	4.84104	0.177481
$745$	8.26188	0.302692
$746$	−21.0225	−0.769689
$747$	−26.2344	−0.959866
$748$	−1.96859	−0.0719786
$749$	−0.0915230	−0.00334418
$750$	−22.7082	−0.829187
$751$	−26.3091	−0.960033	−0.480016	−	0.877260i	$-0.659369\pi$
$751$	−26.3091	−0.960033	−0.480016	+	0.877260i	$0.659369\pi$
$752$	0.169073	0.00616547
$753$	−53.2478	−1.94046
$754$	8.27273	0.301275
$755$	−6.74307	−0.245405
$756$	2.48426	0.0903516
$757$	−19.3597	−0.703641	−0.351821	−	0.936067i	$-0.614437\pi$
$757$	−19.3597	−0.703641	−0.351821	+	0.936067i	$0.614437\pi$
$758$	−20.6087	−0.748540
$759$	3.79452	0.137732
$760$	−1.83917	−0.0667136
$761$	9.80805	0.355541	0.177771	−	0.984072i	$-0.443111\pi$
$761$	9.80805	0.355541	0.177771	+	0.984072i	$0.443111\pi$
$762$	−48.1122	−1.74292
$763$	21.5959	0.781823
$764$	8.82914	0.319427
$765$	−2.55652	−0.0924311
$766$	29.9187	1.08101
$767$	−13.4924	−0.487181
$768$	−2.24505	−0.0810113
$769$	44.3354	1.59878	0.799388	−	0.600815i	$-0.205157\pi$
$769$	44.3354	1.59878	0.799388	+	0.600815i	$0.205157\pi$
$770$	2.49141	0.0897840
$771$	−51.5692	−1.85722
$772$	−14.8552	−0.534651
$773$	20.4188	0.734414	0.367207	−	0.930139i	$-0.380314\pi$
$773$	20.4188	0.734414	0.367207	+	0.930139i	$0.380314\pi$
$774$	−21.4305	−0.770304
$775$	7.81572	0.280749
$776$	17.1915	0.617138
$777$	−16.0553	−0.575979
$778$	−3.86857	−0.138695
$779$	4.93798	0.176922
$780$	−11.4314	−0.409308
$781$	−5.78210	−0.206900
$782$	0.980090	0.0350479
$783$	−4.10561	−0.146723
$784$	−5.67068	−0.202524
$785$	2.97180	0.106068
$786$	38.1494	1.36074
$787$	12.8886	0.459430	0.229715	−	0.973258i	$-0.426221\pi$
$787$	12.8886	0.459430	0.229715	+	0.973258i	$0.426221\pi$
$788$	27.8814	0.993235
$789$	−30.2751	−1.07782
$790$	−6.03424	−0.214689
$791$	22.6198	0.804266
$792$	−3.75919	−0.133577
$793$	−22.5815	−0.801894
$794$	25.8708	0.918122
$795$	−3.02929	−0.107438
$796$	23.4092	0.829715
$797$	48.7080	1.72533	0.862663	−	0.505778i	$-0.168795\pi$
$797$	48.7080	1.72533	0.862663	+	0.505778i	$0.168795\pi$
$798$	−4.05923	−0.143695
$799$	0.180643	0.00639067
$800$	−3.62457	−0.128148
$801$	5.21795	0.184367
$802$	−2.12826	−0.0751513
$803$	−10.5706	−0.373027
$804$	11.0450	0.389527
$805$	−1.24038	−0.0437178
$806$	9.36191	0.329759
$807$	14.0487	0.494538
$808$	1.53880	0.0541349
$809$	−21.4042	−0.752530	−0.376265	−	0.926512i	$-0.622792\pi$
$809$	−21.4042	−0.752530	−0.376265	+	0.926512i	$0.622792\pi$
$810$	12.8515	0.451557
$811$	−35.7663	−1.25593	−0.627963	−	0.778243i	$-0.716111\pi$
$811$	−35.7663	−1.25593	−0.627963	+	0.778243i	$0.716111\pi$
$812$	−2.19691	−0.0770964
$813$	−33.8068	−1.18565
$814$	−11.4284	−0.400565
$815$	14.5167	0.508498
$816$	−2.39867	−0.0839704
$817$	−16.4721	−0.576287
$818$	4.04439	0.141409
$819$	−10.2130	−0.356870
$820$	−3.69290	−0.128962
$821$	−22.7390	−0.793598	−0.396799	−	0.917905i	$-0.629879\pi$
$821$	−22.7390	−0.793598	−0.396799	+	0.917905i	$0.629879\pi$
$822$	33.8924	1.18213
$823$	−36.2591	−1.26391	−0.631956	−	0.775005i	$-0.717748\pi$
$823$	−36.2591	−1.26391	−0.631956	+	0.775005i	$0.717748\pi$
$824$	5.01961	0.174866
$825$	−14.9931	−0.521994
$826$	3.58304	0.124670
$827$	31.8316	1.10689	0.553446	−	0.832885i	$-0.313312\pi$
$827$	31.8316	1.10689	0.553446	+	0.832885i	$0.313312\pi$
$828$	1.87157	0.0650415
$829$	−13.1721	−0.457488	−0.228744	−	0.973487i	$-0.573462\pi$
$829$	−13.1721	−0.457488	−0.228744	+	0.973487i	$0.573462\pi$
$830$	15.0801	0.523439
$831$	9.43665	0.327354
$832$	−4.34162	−0.150519
$833$	−6.05870	−0.209922
$834$	19.9958	0.692396
$835$	−3.09958	−0.107265
$836$	−2.88942	−0.0999328
$837$	−4.64616	−0.160595
$838$	18.3906	0.635294
$839$	−51.9753	−1.79439	−0.897193	−	0.441639i	$-0.854397\pi$
$839$	−51.9753	−1.79439	−0.897193	+	0.441639i	$0.854397\pi$
$840$	3.03572	0.104742
$841$	−25.3693	−0.874803
$842$	−7.93651	−0.273510
$843$	−16.7464	−0.576777
$844$	17.0517	0.586944
$845$	−6.86043	−0.236006
$846$	0.344953	0.0118597
$847$	−8.76847	−0.301288
$848$	−1.15052	−0.0395092
$849$	−28.6960	−0.984845
$850$	−3.87259	−0.132829
$851$	5.68979	0.195044
$852$	−7.04534	−0.241370
$853$	−15.3124	−0.524288	−0.262144	−	0.965029i	$-0.584430\pi$
$853$	−15.3124	−0.524288	−0.262144	+	0.965029i	$0.584430\pi$
$854$	5.99676	0.205205
$855$	−3.75237	−0.128328
$856$	−0.0793806	−0.00271317
$857$	42.7285	1.45958	0.729789	−	0.683673i	$-0.239618\pi$
$857$	42.7285	1.45958	0.729789	+	0.683673i	$0.239618\pi$
$858$	−17.9592	−0.613118
$859$	−22.8283	−0.778891	−0.389446	−	0.921049i	$-0.627333\pi$
$859$	−22.8283	−0.778891	−0.389446	+	0.921049i	$0.627333\pi$
$860$	12.3188	0.420066
$861$	−8.15060	−0.277772
$862$	18.4308	0.627757
$863$	−25.5950	−0.871265	−0.435633	−	0.900125i	$-0.643475\pi$
$863$	−25.5950	−0.871265	−0.435633	+	0.900125i	$0.643475\pi$
$864$	2.15467	0.0733035
$865$	26.2697	0.893195
$866$	−8.58629	−0.291774
$867$	35.6031	1.20914
$868$	−2.48615	−0.0843856
$869$	−9.48010	−0.321590
$870$	−5.01698	−0.170092
$871$	21.3595	0.723740
$872$	18.7308	0.634303
$873$	35.0750	1.18711
$874$	1.43854	0.0486594
$875$	11.6620	0.394247
$876$	−12.8800	−0.435174
$877$	−27.1053	−0.915282	−0.457641	−	0.889137i	$-0.651305\pi$
$877$	−27.1053	−0.915282	−0.457641	+	0.889137i	$0.651305\pi$
$878$	40.7119	1.37396
$879$	−11.1030	−0.374494
$880$	2.16087	0.0728429
$881$	−44.1800	−1.48846	−0.744232	−	0.667922i	$-0.767184\pi$
$881$	−44.1800	−1.48846	−0.744232	+	0.667922i	$0.767184\pi$
$882$	−11.5696	−0.389570
$883$	51.4571	1.73167	0.865835	−	0.500330i	$-0.166788\pi$
$883$	51.4571	1.73167	0.865835	+	0.500330i	$0.166788\pi$
$884$	−4.63871	−0.156017
$885$	8.18242	0.275049
$886$	26.6862	0.896540
$887$	15.1835	0.509811	0.254905	−	0.966966i	$-0.417956\pi$
$887$	15.1835	0.509811	0.254905	+	0.966966i	$0.417956\pi$
$888$	−13.9252	−0.467299
$889$	24.7084	0.828693
$890$	−2.99940	−0.100540
$891$	20.1904	0.676405
$892$	17.0033	0.569311
$893$	0.265141	0.00887261
$894$	15.8156	0.528953
$895$	−8.62410	−0.288272
$896$	1.15296	0.0385178
$897$	8.94127	0.298540
$898$	24.2289	0.808529
$899$	4.10875	0.137034
$900$	−7.39505	−0.246502
$901$	−1.22925	−0.0409523
$902$	−5.80173	−0.193176
$903$	27.1888	0.904786
$904$	19.6188	0.652511
$905$	−4.64809	−0.154508
$906$	−12.9082	−0.428845
$907$	−43.1939	−1.43423	−0.717115	−	0.696955i	$-0.754538\pi$
$907$	−43.1939	−1.43423	−0.717115	+	0.696955i	$0.754538\pi$
$908$	28.5454	0.947313
$909$	3.13955	0.104132
$910$	5.87066	0.194610
$911$	−12.3465	−0.409059	−0.204530	−	0.978860i	$-0.565566\pi$
$911$	−12.3465	−0.409059	−0.204530	+	0.978860i	$0.565566\pi$
$912$	−3.52069	−0.116582
$913$	23.6917	0.784080
$914$	1.89243	0.0625962
$915$	13.6945	0.452727
$916$	−11.5548	−0.381780
$917$	−19.5919	−0.646982
$918$	2.30211	0.0759810
$919$	−43.4715	−1.43399	−0.716997	−	0.697077i	$-0.754484\pi$
$919$	−43.4715	−1.43399	−0.716997	+	0.697077i	$0.754484\pi$
$920$	−1.07582	−0.0354688
$921$	−67.7001	−2.23079
$922$	−27.9857	−0.921659
$923$	−13.6247	−0.448463
$924$	4.76926	0.156897
$925$	−22.4818	−0.739198
$926$	10.4447	0.343233
$927$	10.2413	0.336368
$928$	−1.90545	−0.0625493
$929$	35.0616	1.15033	0.575167	−	0.818036i	$-0.304937\pi$
$929$	35.0616	1.15033	0.575167	+	0.818036i	$0.304937\pi$
$930$	−5.67751	−0.186173
$931$	−8.89276	−0.291448
$932$	−9.24345	−0.302779
$933$	11.0566	0.361977
$934$	7.62444	0.249479
$935$	2.30873	0.0755036
$936$	−8.85802	−0.289534
$937$	31.2105	1.01960	0.509802	−	0.860292i	$-0.329719\pi$
$937$	31.2105	1.01960	0.509802	+	0.860292i	$0.329719\pi$
$938$	−5.67225	−0.185206
$939$	−44.3416	−1.44703
$940$	−0.198287	−0.00646741
$941$	5.31344	0.173213	0.0866066	−	0.996243i	$-0.472398\pi$
$941$	5.31344	0.173213	0.0866066	+	0.996243i	$0.472398\pi$
$942$	5.68888	0.185354
$943$	2.88848	0.0940618
$944$	3.10768	0.101146
$945$	−2.91351	−0.0947764
$946$	19.3534	0.629234
$947$	−37.2614	−1.21083	−0.605416	−	0.795909i	$-0.706993\pi$
$947$	−37.2614	−1.21083	−0.605416	+	0.795909i	$0.706993\pi$
$948$	−11.5513	−0.375168
$949$	−24.9081	−0.808552
$950$	−5.68405	−0.184415
$951$	−64.9450	−2.10599
$952$	1.23186	0.0399247
$953$	5.50831	0.178432	0.0892158	−	0.996012i	$-0.471564\pi$
$953$	5.50831	0.178432	0.0892158	+	0.996012i	$0.471564\pi$
$954$	−2.34737	−0.0759988
$955$	−10.3547	−0.335070
$956$	2.10864	0.0681983
$957$	−7.88193	−0.254787
$958$	−12.2145	−0.394634
$959$	−17.4057	−0.562059
$960$	2.63297	0.0849787
$961$	−26.3503	−0.850010
$962$	−26.9294	−0.868240
$963$	−0.161957	−0.00521899
$964$	−0.153691	−0.00495006
$965$	17.4220	0.560834
$966$	−2.37445	−0.0763967
$967$	−44.4184	−1.42840	−0.714201	−	0.699941i	$-0.753210\pi$
$967$	−44.4184	−1.42840	−0.714201	+	0.699941i	$0.753210\pi$
$968$	−7.60516	−0.244439
$969$	−3.76160	−0.120840
$970$	−20.1620	−0.647361
$971$	30.9694	0.993856	0.496928	−	0.867792i	$-0.334461\pi$
$971$	30.9694	0.993856	0.496928	+	0.867792i	$0.334461\pi$
$972$	18.1375	0.581762
$973$	−10.2690	−0.329208
$974$	−21.0687	−0.675086
$975$	−35.3293	−1.13144
$976$	5.20117	0.166486
$977$	38.5053	1.23189	0.615946	−	0.787788i	$-0.288774\pi$
$977$	38.5053	1.23189	0.615946	+	0.787788i	$0.288774\pi$
$978$	27.7891	0.888598
$979$	−4.71221	−0.150603
$980$	6.65050	0.212442
$981$	38.2155	1.22013
$982$	15.5577	0.496467
$983$	47.6098	1.51852	0.759259	−	0.650789i	$-0.225562\pi$
$983$	47.6098	1.51852	0.759259	+	0.650789i	$0.225562\pi$
$984$	−7.06926	−0.225360
$985$	−32.6990	−1.04188
$986$	−2.03583	−0.0648340
$987$	−0.437640	−0.0139302
$988$	−6.80853	−0.216608
$989$	−9.63538	−0.306387
$990$	4.40873	0.140119
$991$	1.40268	0.0445575	0.0222788	−	0.999752i	$-0.492908\pi$
$991$	1.40268	0.0445575	0.0222788	+	0.999752i	$0.492908\pi$
$992$	−2.15632	−0.0684631
$993$	−29.0396	−0.921543
$994$	3.61819	0.114762
$995$	−27.4540	−0.870349
$996$	28.8677	0.914709
$997$	−43.0549	−1.36356	−0.681782	−	0.731556i	$-0.738795\pi$
$997$	−43.0549	−1.36356	−0.681782	+	0.731556i	$0.738795\pi$
$998$	−36.7009	−1.16175
$999$	13.3646	0.422838

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6022.2.a.e.1.14	✓	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6022.2.a.e.1.14	✓	68	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:	\( N \)	\(=\)	\( 6022 = 2 \cdot 3011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6022.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.24505 q^{3} +1.00000 q^{4} -1.17279 q^{5} -2.24505 q^{6} +1.15296 q^{7} +1.00000 q^{8} +2.04026 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.24505 q^{3} +1.00000 q^{4} -1.17279 q^{5} -2.24505 q^{6} +1.15296 q^{7} +1.00000 q^{8} +2.04026 q^{9} -1.17279 q^{10} -1.84251 q^{11} -2.24505 q^{12} -4.34162 q^{13} +1.15296 q^{14} +2.63297 q^{15} +1.00000 q^{16} +1.06843 q^{17} +2.04026 q^{18} +1.56820 q^{19} -1.17279 q^{20} -2.58846 q^{21} -1.84251 q^{22} +0.917320 q^{23} -2.24505 q^{24} -3.62457 q^{25} -4.34162 q^{26} +2.15467 q^{27} +1.15296 q^{28} -1.90545 q^{29} +2.63297 q^{30} -2.15632 q^{31} +1.00000 q^{32} +4.13653 q^{33} +1.06843 q^{34} -1.35218 q^{35} +2.04026 q^{36} +6.20262 q^{37} +1.56820 q^{38} +9.74716 q^{39} -1.17279 q^{40} +3.14882 q^{41} -2.58846 q^{42} -10.5038 q^{43} -1.84251 q^{44} -2.39279 q^{45} +0.917320 q^{46} +0.169073 q^{47} -2.24505 q^{48} -5.67068 q^{49} -3.62457 q^{50} -2.39867 q^{51} -4.34162 q^{52} -1.15052 q^{53} +2.15467 q^{54} +2.16087 q^{55} +1.15296 q^{56} -3.52069 q^{57} -1.90545 q^{58} +3.10768 q^{59} +2.63297 q^{60} +5.20117 q^{61} -2.15632 q^{62} +2.35234 q^{63} +1.00000 q^{64} +5.09180 q^{65} +4.13653 q^{66} -4.91971 q^{67} +1.06843 q^{68} -2.05943 q^{69} -1.35218 q^{70} +3.13817 q^{71} +2.04026 q^{72} +5.73706 q^{73} +6.20262 q^{74} +8.13735 q^{75} +1.56820 q^{76} -2.12435 q^{77} +9.74716 q^{78} +5.14521 q^{79} -1.17279 q^{80} -10.9581 q^{81} +3.14882 q^{82} -12.8584 q^{83} -2.58846 q^{84} -1.25304 q^{85} -10.5038 q^{86} +4.27783 q^{87} -1.84251 q^{88} +2.55750 q^{89} -2.39279 q^{90} -5.00573 q^{91} +0.917320 q^{92} +4.84104 q^{93} +0.169073 q^{94} -1.83917 q^{95} -2.24505 q^{96} +17.1915 q^{97} -5.67068 q^{98} -3.75919 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 68 q^{2} + 25 q^{3} + 68 q^{4} + 20 q^{5} + 25 q^{6} + 29 q^{7} + 68 q^{8} + 87 q^{9}+O(q^{10}) \) 68 * q + 68 * q^2 + 25 * q^3 + 68 * q^4 + 20 * q^5 + 25 * q^6 + 29 * q^7 + 68 * q^8 + 87 * q^9	\( 68 q + 68 q^{2} + 25 q^{3} + 68 q^{4} + 20 q^{5} + 25 q^{6} + 29 q^{7} + 68 q^{8} + 87 q^{9} + 20 q^{10} + 46 q^{11} + 25 q^{12} + 30 q^{13} + 29 q^{14} + 13 q^{15} + 68 q^{16} + 73 q^{17} + 87 q^{18} + 56 q^{19} + 20 q^{20} - 5 q^{21} + 46 q^{22} + 63 q^{23} + 25 q^{24} + 88 q^{25} + 30 q^{26} + 67 q^{27} + 29 q^{28} + 43 q^{29} + 13 q^{30} + 68 q^{31} + 68 q^{32} + 26 q^{33} + 73 q^{34} + 50 q^{35} + 87 q^{36} + 8 q^{37} + 56 q^{38} + 6 q^{39} + 20 q^{40} + 64 q^{41} - 5 q^{42} + 52 q^{43} + 46 q^{44} + 7 q^{45} + 63 q^{46} + 94 q^{47} + 25 q^{48} + 91 q^{49} + 88 q^{50} + 20 q^{51} + 30 q^{52} + 38 q^{53} + 67 q^{54} + 37 q^{55} + 29 q^{56} + 4 q^{57} + 43 q^{58} + 84 q^{59} + 13 q^{60} + 26 q^{61} + 68 q^{62} + 22 q^{63} + 68 q^{64} - 20 q^{65} + 26 q^{66} + 54 q^{67} + 73 q^{68} - 11 q^{69} + 50 q^{70} + 46 q^{71} + 87 q^{72} + 62 q^{73} + 8 q^{74} + 54 q^{75} + 56 q^{76} + 67 q^{77} + 6 q^{78} + 67 q^{79} + 20 q^{80} + 120 q^{81} + 64 q^{82} + 130 q^{83} - 5 q^{84} - 24 q^{85} + 52 q^{86} + 72 q^{87} + 46 q^{88} + 61 q^{89} + 7 q^{90} + 43 q^{91} + 63 q^{92} + 40 q^{93} + 94 q^{94} + 55 q^{95} + 25 q^{96} + 41 q^{97} + 91 q^{98} + 106 q^{99}+O(q^{100}) \) 68 * q + 68 * q^2 + 25 * q^3 + 68 * q^4 + 20 * q^5 + 25 * q^6 + 29 * q^7 + 68 * q^8 + 87 * q^9 + 20 * q^10 + 46 * q^11 + 25 * q^12 + 30 * q^13 + 29 * q^14 + 13 * q^15 + 68 * q^16 + 73 * q^17 + 87 * q^18 + 56 * q^19 + 20 * q^20 - 5 * q^21 + 46 * q^22 + 63 * q^23 + 25 * q^24 + 88 * q^25 + 30 * q^26 + 67 * q^27 + 29 * q^28 + 43 * q^29 + 13 * q^30 + 68 * q^31 + 68 * q^32 + 26 * q^33 + 73 * q^34 + 50 * q^35 + 87 * q^36 + 8 * q^37 + 56 * q^38 + 6 * q^39 + 20 * q^40 + 64 * q^41 - 5 * q^42 + 52 * q^43 + 46 * q^44 + 7 * q^45 + 63 * q^46 + 94 * q^47 + 25 * q^48 + 91 * q^49 + 88 * q^50 + 20 * q^51 + 30 * q^52 + 38 * q^53 + 67 * q^54 + 37 * q^55 + 29 * q^56 + 4 * q^57 + 43 * q^58 + 84 * q^59 + 13 * q^60 + 26 * q^61 + 68 * q^62 + 22 * q^63 + 68 * q^64 - 20 * q^65 + 26 * q^66 + 54 * q^67 + 73 * q^68 - 11 * q^69 + 50 * q^70 + 46 * q^71 + 87 * q^72 + 62 * q^73 + 8 * q^74 + 54 * q^75 + 56 * q^76 + 67 * q^77 + 6 * q^78 + 67 * q^79 + 20 * q^80 + 120 * q^81 + 64 * q^82 + 130 * q^83 - 5 * q^84 - 24 * q^85 + 52 * q^86 + 72 * q^87 + 46 * q^88 + 61 * q^89 + 7 * q^90 + 43 * q^91 + 63 * q^92 + 40 * q^93 + 94 * q^94 + 55 * q^95 + 25 * q^96 + 41 * q^97 + 91 * q^98 + 106 * q^99

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