LMFDB - Embedded newform 8049.2.a.c.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8049,2,Mod(1,8049)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8049, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8049.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8049 = 3 \cdot 2683 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8049.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:	$64.2715885869$
Analytic rank:	$0$
Dimension:	$119$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	8049.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.60392 q^{2} -1.00000 q^{3} +4.78038 q^{4} +3.66153 q^{5} +2.60392 q^{6} -3.52018 q^{7} -7.23988 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.60392 q^{2} -1.00000 q^{3} +4.78038 q^{4} +3.66153 q^{5} +2.60392 q^{6} -3.52018 q^{7} -7.23988 q^{8} +1.00000 q^{9} -9.53431 q^{10} +5.74897 q^{11} -4.78038 q^{12} +2.37776 q^{13} +9.16625 q^{14} -3.66153 q^{15} +9.29129 q^{16} -0.694695 q^{17} -2.60392 q^{18} +6.01967 q^{19} +17.5035 q^{20} +3.52018 q^{21} -14.9699 q^{22} -3.39314 q^{23} +7.23988 q^{24} +8.40678 q^{25} -6.19148 q^{26} -1.00000 q^{27} -16.8278 q^{28} -0.633517 q^{29} +9.53431 q^{30} +2.23947 q^{31} -9.71398 q^{32} -5.74897 q^{33} +1.80893 q^{34} -12.8892 q^{35} +4.78038 q^{36} +10.1069 q^{37} -15.6747 q^{38} -2.37776 q^{39} -26.5090 q^{40} +3.96241 q^{41} -9.16625 q^{42} +11.8026 q^{43} +27.4823 q^{44} +3.66153 q^{45} +8.83546 q^{46} +4.36809 q^{47} -9.29129 q^{48} +5.39164 q^{49} -21.8906 q^{50} +0.694695 q^{51} +11.3666 q^{52} -10.9508 q^{53} +2.60392 q^{54} +21.0500 q^{55} +25.4857 q^{56} -6.01967 q^{57} +1.64963 q^{58} +14.3437 q^{59} -17.5035 q^{60} -2.14448 q^{61} -5.83139 q^{62} -3.52018 q^{63} +6.71180 q^{64} +8.70623 q^{65} +14.9699 q^{66} -15.0663 q^{67} -3.32091 q^{68} +3.39314 q^{69} +33.5625 q^{70} +12.8175 q^{71} -7.23988 q^{72} -6.55787 q^{73} -26.3175 q^{74} -8.40678 q^{75} +28.7763 q^{76} -20.2374 q^{77} +6.19148 q^{78} -0.569661 q^{79} +34.0203 q^{80} +1.00000 q^{81} -10.3178 q^{82} -2.47776 q^{83} +16.8278 q^{84} -2.54365 q^{85} -30.7329 q^{86} +0.633517 q^{87} -41.6219 q^{88} +12.6497 q^{89} -9.53431 q^{90} -8.37013 q^{91} -16.2205 q^{92} -2.23947 q^{93} -11.3741 q^{94} +22.0412 q^{95} +9.71398 q^{96} -4.02220 q^{97} -14.0394 q^{98} +5.74897 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 119 q + 11 q^{2} - 119 q^{3} + 137 q^{4} + 17 q^{5} - 11 q^{6} + 10 q^{7} + 33 q^{8} + 119 q^{9}+O(q^{10}) $ 119 * q + 11 * q^2 - 119 * q^3 + 137 * q^4 + 17 * q^5 - 11 * q^6 + 10 * q^7 + 33 * q^8 + 119 * q^9	\( 119 q + 11 q^{2} - 119 q^{3} + 137 q^{4} + 17 q^{5} - 11 q^{6} + 10 q^{7} + 33 q^{8} + 119 q^{9} - 10 q^{10} + 56 q^{11} - 137 q^{12} - 37 q^{13} + 31 q^{14} - 17 q^{15} + 173 q^{16} + 17 q^{17} + 11 q^{18} + 16 q^{19} + 61 q^{20} - 10 q^{21} - 3 q^{22} + 76 q^{23} - 33 q^{24} + 134 q^{25} + 47 q^{26} - 119 q^{27} - q^{28} + 47 q^{29} + 10 q^{30} + 51 q^{31} + 87 q^{32} - 56 q^{33} + 13 q^{34} + 58 q^{35} + 137 q^{36} - 67 q^{37} + 35 q^{38} + 37 q^{39} - 40 q^{40} + 47 q^{41} - 31 q^{42} + 12 q^{43} + 148 q^{44} + 17 q^{45} + 26 q^{46} + 107 q^{47} - 173 q^{48} + 163 q^{49} + 76 q^{50} - 17 q^{51} - 57 q^{52} + 64 q^{53} - 11 q^{54} + 71 q^{55} + 91 q^{56} - 16 q^{57} + 12 q^{58} + 98 q^{59} - 61 q^{60} - 50 q^{61} + 40 q^{62} + 10 q^{63} + 245 q^{64} + 40 q^{65} + 3 q^{66} + 12 q^{67} + 75 q^{68} - 76 q^{69} - 9 q^{70} + 194 q^{71} + 33 q^{72} - 79 q^{73} + 72 q^{74} - 134 q^{75} + 12 q^{76} + 71 q^{77} - 47 q^{78} + 127 q^{79} + 148 q^{80} + 119 q^{81} - 54 q^{82} + 77 q^{83} + q^{84} - 25 q^{85} + 142 q^{86} - 47 q^{87} + q^{88} + 93 q^{89} - 10 q^{90} + 61 q^{91} + 156 q^{92} - 51 q^{93} + 16 q^{94} + 138 q^{95} - 87 q^{96} - 110 q^{97} + 96 q^{98} + 56 q^{99}+O(q^{100}) \) 119 * q + 11 * q^2 - 119 * q^3 + 137 * q^4 + 17 * q^5 - 11 * q^6 + 10 * q^7 + 33 * q^8 + 119 * q^9 - 10 * q^10 + 56 * q^11 - 137 * q^12 - 37 * q^13 + 31 * q^14 - 17 * q^15 + 173 * q^16 + 17 * q^17 + 11 * q^18 + 16 * q^19 + 61 * q^20 - 10 * q^21 - 3 * q^22 + 76 * q^23 - 33 * q^24 + 134 * q^25 + 47 * q^26 - 119 * q^27 - q^28 + 47 * q^29 + 10 * q^30 + 51 * q^31 + 87 * q^32 - 56 * q^33 + 13 * q^34 + 58 * q^35 + 137 * q^36 - 67 * q^37 + 35 * q^38 + 37 * q^39 - 40 * q^40 + 47 * q^41 - 31 * q^42 + 12 * q^43 + 148 * q^44 + 17 * q^45 + 26 * q^46 + 107 * q^47 - 173 * q^48 + 163 * q^49 + 76 * q^50 - 17 * q^51 - 57 * q^52 + 64 * q^53 - 11 * q^54 + 71 * q^55 + 91 * q^56 - 16 * q^57 + 12 * q^58 + 98 * q^59 - 61 * q^60 - 50 * q^61 + 40 * q^62 + 10 * q^63 + 245 * q^64 + 40 * q^65 + 3 * q^66 + 12 * q^67 + 75 * q^68 - 76 * q^69 - 9 * q^70 + 194 * q^71 + 33 * q^72 - 79 * q^73 + 72 * q^74 - 134 * q^75 + 12 * q^76 + 71 * q^77 - 47 * q^78 + 127 * q^79 + 148 * q^80 + 119 * q^81 - 54 * q^82 + 77 * q^83 + q^84 - 25 * q^85 + 142 * q^86 - 47 * q^87 + q^88 + 93 * q^89 - 10 * q^90 + 61 * q^91 + 156 * q^92 - 51 * q^93 + 16 * q^94 + 138 * q^95 - 87 * q^96 - 110 * q^97 + 96 * q^98 + 56 * 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 $

$2$	−2.60392	−1.84125	−0.920624	−	0.390451i	$-0.872319\pi$
$2$	−2.60392	−1.84125	−0.920624	+	0.390451i	$0.872319\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.78038	2.39019
$5$	3.66153	1.63748	0.818742	−	0.574161i	$-0.194672\pi$
$5$	3.66153	1.63748	0.818742	+	0.574161i	$0.194672\pi$
$6$	2.60392	1.06304
$7$	−3.52018	−1.33050	−0.665251	−	0.746620i	$-0.731675\pi$
$7$	−3.52018	−1.33050	−0.665251	+	0.746620i	$0.731675\pi$
$8$	−7.23988	−2.55969
$9$	1.00000	0.333333
$10$	−9.53431	−3.01501
$11$	5.74897	1.73338	0.866690	−	0.498846i	$-0.166243\pi$
$11$	5.74897	1.73338	0.866690	+	0.498846i	$0.166243\pi$
$12$	−4.78038	−1.37998
$13$	2.37776	0.659472	0.329736	−	0.944073i	$-0.393040\pi$
$13$	2.37776	0.659472	0.329736	+	0.944073i	$0.393040\pi$
$14$	9.16625	2.44978
$15$	−3.66153	−0.945402
$16$	9.29129	2.32282
$17$	−0.694695	−0.168488	−0.0842442	−	0.996445i	$-0.526848\pi$
$17$	−0.694695	−0.168488	−0.0842442	+	0.996445i	$0.526848\pi$
$18$	−2.60392	−0.613749
$19$	6.01967	1.38101	0.690504	−	0.723329i	$-0.257389\pi$
$19$	6.01967	1.38101	0.690504	+	0.723329i	$0.257389\pi$
$20$	17.5035	3.91390
$21$	3.52018	0.768165
$22$	−14.9699	−3.19158
$23$	−3.39314	−0.707519	−0.353760	−	0.935336i	$-0.615097\pi$
$23$	−3.39314	−0.707519	−0.353760	+	0.935336i	$0.615097\pi$
$24$	7.23988	1.47784
$25$	8.40678	1.68136
$26$	−6.19148	−1.21425
$27$	−1.00000	−0.192450
$28$	−16.8278	−3.18015
$29$	−0.633517	−0.117641	−0.0588206	−	0.998269i	$-0.518734\pi$
$29$	−0.633517	−0.117641	−0.0588206	+	0.998269i	$0.518734\pi$
$30$	9.53431	1.74072
$31$	2.23947	0.402220	0.201110	−	0.979569i	$-0.435545\pi$
$31$	2.23947	0.402220	0.201110	+	0.979569i	$0.435545\pi$
$32$	−9.71398	−1.71720
$33$	−5.74897	−1.00077
$34$	1.80893	0.310229
$35$	−12.8892	−2.17868
$36$	4.78038	0.796730
$37$	10.1069	1.66156	0.830782	−	0.556598i	$-0.187893\pi$
$37$	10.1069	1.66156	0.830782	+	0.556598i	$0.187893\pi$
$38$	−15.6747	−2.54278
$39$	−2.37776	−0.380746
$40$	−26.5090	−4.19145
$41$	3.96241	0.618824	0.309412	−	0.950928i	$-0.399868\pi$
$41$	3.96241	0.618824	0.309412	+	0.950928i	$0.399868\pi$
$42$	−9.16625	−1.41438
$43$	11.8026	1.79987	0.899937	−	0.436019i	$-0.143612\pi$
$43$	11.8026	1.79987	0.899937	+	0.436019i	$0.143612\pi$
$44$	27.4823	4.14311
$45$	3.66153	0.545828
$46$	8.83546	1.30272
$47$	4.36809	0.637151	0.318576	−	0.947897i	$-0.396795\pi$
$47$	4.36809	0.637151	0.318576	+	0.947897i	$0.396795\pi$
$48$	−9.29129	−1.34108
$49$	5.39164	0.770235
$50$	−21.8906	−3.09579
$51$	0.694695	0.0972768
$52$	11.3666	1.57626
$53$	−10.9508	−1.50421	−0.752103	−	0.659045i	$-0.770961\pi$
$53$	−10.9508	−1.50421	−0.752103	+	0.659045i	$0.770961\pi$
$54$	2.60392	0.354348
$55$	21.0500	2.83838
$56$	25.4857	3.40567
$57$	−6.01967	−0.797325
$58$	1.64963	0.216607
$59$	14.3437	1.86739	0.933693	−	0.358075i	$-0.116567\pi$
$59$	14.3437	1.86739	0.933693	+	0.358075i	$0.116567\pi$
$60$	−17.5035	−2.25969
$61$	−2.14448	−0.274572	−0.137286	−	0.990531i	$-0.543838\pi$
$61$	−2.14448	−0.274572	−0.137286	+	0.990531i	$0.543838\pi$
$62$	−5.83139	−0.740587
$63$	−3.52018	−0.443501
$64$	6.71180	0.838976
$65$	8.70623	1.07987
$66$	14.9699	1.84266
$67$	−15.0663	−1.84065	−0.920323	−	0.391158i	$-0.872075\pi$
$67$	−15.0663	−1.84065	−0.920323	+	0.391158i	$0.872075\pi$
$68$	−3.32091	−0.402719
$69$	3.39314	0.408487
$70$	33.5625	4.01148
$71$	12.8175	1.52116	0.760581	−	0.649243i	$-0.224914\pi$
$71$	12.8175	1.52116	0.760581	+	0.649243i	$0.224914\pi$
$72$	−7.23988	−0.853228
$73$	−6.55787	−0.767541	−0.383770	−	0.923429i	$-0.625375\pi$
$73$	−6.55787	−0.767541	−0.383770	+	0.923429i	$0.625375\pi$
$74$	−26.3175	−3.05935
$75$	−8.40678	−0.970731
$76$	28.7763	3.30087
$77$	−20.2374	−2.30627
$78$	6.19148	0.701048
$79$	−0.569661	−0.0640919	−0.0320460	−	0.999486i	$-0.510202\pi$
$79$	−0.569661	−0.0640919	−0.0320460	+	0.999486i	$0.510202\pi$
$80$	34.0203	3.80359
$81$	1.00000	0.111111
$82$	−10.3178	−1.13941
$83$	−2.47776	−0.271969	−0.135985	−	0.990711i	$-0.543420\pi$
$83$	−2.47776	−0.271969	−0.135985	+	0.990711i	$0.543420\pi$
$84$	16.8278	1.83606
$85$	−2.54365	−0.275897
$86$	−30.7329	−3.31401
$87$	0.633517	0.0679202
$88$	−41.6219	−4.43691
$89$	12.6497	1.34087	0.670435	−	0.741968i	$-0.266107\pi$
$89$	12.6497	1.34087	0.670435	+	0.741968i	$0.266107\pi$
$90$	−9.53431	−1.00500
$91$	−8.37013	−0.877428
$92$	−16.2205	−1.69111
$93$	−2.23947	−0.232222
$94$	−11.3741	−1.17315
$95$	22.0412	2.26138
$96$	9.71398	0.991428
$97$	−4.02220	−0.408393	−0.204196	−	0.978930i	$-0.565458\pi$
$97$	−4.02220	−0.408393	−0.204196	+	0.978930i	$0.565458\pi$
$98$	−14.0394	−1.41819
$99$	5.74897	0.577794
$100$	40.1876	4.01876
$101$	−3.97186	−0.395215	−0.197608	−	0.980281i	$-0.563317\pi$
$101$	−3.97186	−0.395215	−0.197608	+	0.980281i	$0.563317\pi$
$102$	−1.80893	−0.179111
$103$	−7.06131	−0.695772	−0.347886	−	0.937537i	$-0.613100\pi$
$103$	−7.06131	−0.695772	−0.347886	+	0.937537i	$0.613100\pi$
$104$	−17.2147	−1.68804
$105$	12.8892	1.25786
$106$	28.5149	2.76962
$107$	14.6197	1.41334	0.706671	−	0.707542i	$-0.250196\pi$
$107$	14.6197	1.41334	0.706671	+	0.707542i	$0.250196\pi$
$108$	−4.78038	−0.459992
$109$	−20.5205	−1.96551	−0.982756	−	0.184909i	$-0.940801\pi$
$109$	−20.5205	−1.96551	−0.982756	+	0.184909i	$0.940801\pi$
$110$	−54.8125	−5.22617
$111$	−10.1069	−0.959305
$112$	−32.7070	−3.09052
$113$	−3.35042	−0.315181	−0.157591	−	0.987505i	$-0.550373\pi$
$113$	−3.35042	−0.315181	−0.157591	+	0.987505i	$0.550373\pi$
$114$	15.6747	1.46807
$115$	−12.4241	−1.15855
$116$	−3.02846	−0.281185
$117$	2.37776	0.219824
$118$	−37.3497	−3.43832
$119$	2.44545	0.224174
$120$	26.5090	2.41993
$121$	22.0507	2.00461
$122$	5.58404	0.505555
$123$	−3.96241	−0.357278
$124$	10.7055	0.961383
$125$	12.4740	1.11571
$126$	9.16625	0.816594
$127$	16.3625	1.45194	0.725969	−	0.687727i	$-0.241391\pi$
$127$	16.3625	1.45194	0.725969	+	0.687727i	$0.241391\pi$
$128$	1.95097	0.172443
$129$	−11.8026	−1.03916
$130$	−22.6703	−1.98832
$131$	−10.2045	−0.891572	−0.445786	−	0.895140i	$-0.647076\pi$
$131$	−10.2045	−0.891572	−0.445786	+	0.895140i	$0.647076\pi$
$132$	−27.4823	−2.39203
$133$	−21.1903	−1.83743
$134$	39.2315	3.38909
$135$	−3.66153	−0.315134
$136$	5.02951	0.431277
$137$	8.10121	0.692133	0.346067	−	0.938210i	$-0.387517\pi$
$137$	8.10121	0.692133	0.346067	+	0.938210i	$0.387517\pi$
$138$	−8.83546	−0.752125
$139$	−2.70730	−0.229630	−0.114815	−	0.993387i	$-0.536628\pi$
$139$	−2.70730	−0.229630	−0.114815	+	0.993387i	$0.536628\pi$
$140$	−61.6154	−5.20745
$141$	−4.36809	−0.367860
$142$	−33.3758	−2.80084
$143$	13.6697	1.14312
$144$	9.29129	0.774274
$145$	−2.31964	−0.192636
$146$	17.0761	1.41323
$147$	−5.39164	−0.444695
$148$	48.3149	3.97146
$149$	−13.2765	−1.08765	−0.543827	−	0.839197i	$-0.683025\pi$
$149$	−13.2765	−1.08765	−0.543827	+	0.839197i	$0.683025\pi$
$150$	21.8906	1.78736
$151$	−2.30900	−0.187904	−0.0939520	−	0.995577i	$-0.529950\pi$
$151$	−2.30900	−0.187904	−0.0939520	+	0.995577i	$0.529950\pi$
$152$	−43.5817	−3.53495
$153$	−0.694695	−0.0561628
$154$	52.6965	4.24641
$155$	8.19987	0.658630
$156$	−11.3666	−0.910056
$157$	13.8307	1.10381	0.551904	−	0.833908i	$-0.313901\pi$
$157$	13.8307	1.10381	0.551904	+	0.833908i	$0.313901\pi$
$158$	1.48335	0.118009
$159$	10.9508	0.868454
$160$	−35.5680	−2.81190
$161$	11.9445	0.941356
$162$	−2.60392	−0.204583
$163$	20.2581	1.58674	0.793369	−	0.608741i	$-0.208325\pi$
$163$	20.2581	1.58674	0.793369	+	0.608741i	$0.208325\pi$
$164$	18.9418	1.47911
$165$	−21.0500	−1.63874
$166$	6.45188	0.500763
$167$	−9.16461	−0.709178	−0.354589	−	0.935022i	$-0.615379\pi$
$167$	−9.16461	−0.709178	−0.354589	+	0.935022i	$0.615379\pi$
$168$	−25.4857	−1.96626
$169$	−7.34626	−0.565097
$170$	6.62344	0.507995
$171$	6.01967	0.460336
$172$	56.4208	4.30204
$173$	15.8368	1.20405	0.602024	−	0.798478i	$-0.294361\pi$
$173$	15.8368	1.20405	0.602024	+	0.798478i	$0.294361\pi$
$174$	−1.64963	−0.125058
$175$	−29.5933	−2.23705
$176$	53.4154	4.02634
$177$	−14.3437	−1.07814
$178$	−32.9389	−2.46887
$179$	−14.7123	−1.09965	−0.549823	−	0.835281i	$-0.685305\pi$
$179$	−14.7123	−1.09965	−0.549823	+	0.835281i	$0.685305\pi$
$180$	17.5035	1.30463
$181$	9.36636	0.696196	0.348098	−	0.937458i	$-0.386828\pi$
$181$	9.36636	0.696196	0.348098	+	0.937458i	$0.386828\pi$
$182$	21.7951	1.61556
$183$	2.14448	0.158524
$184$	24.5660	1.81103
$185$	37.0067	2.72079
$186$	5.83139	0.427578
$187$	−3.99379	−0.292055
$188$	20.8811	1.52291
$189$	3.52018	0.256055
$190$	−57.3934	−4.16376
$191$	15.5520	1.12531	0.562653	−	0.826693i	$-0.309781\pi$
$191$	15.5520	1.12531	0.562653	+	0.826693i	$0.309781\pi$
$192$	−6.71180	−0.484383
$193$	−9.26819	−0.667139	−0.333570	−	0.942726i	$-0.608253\pi$
$193$	−9.26819	−0.667139	−0.333570	+	0.942726i	$0.608253\pi$
$194$	10.4735	0.751952
$195$	−8.70623	−0.623466
$196$	25.7741	1.84101
$197$	1.76973	0.126088	0.0630440	−	0.998011i	$-0.479919\pi$
$197$	1.76973	0.126088	0.0630440	+	0.998011i	$0.479919\pi$
$198$	−14.9699	−1.06386
$199$	7.95825	0.564146	0.282073	−	0.959393i	$-0.408978\pi$
$199$	7.95825	0.564146	0.282073	+	0.959393i	$0.408978\pi$
$200$	−60.8641	−4.30374
$201$	15.0663	1.06270
$202$	10.3424	0.727689
$203$	2.23009	0.156522
$204$	3.32091	0.232510
$205$	14.5085	1.01331
$206$	18.3871	1.28109
$207$	−3.39314	−0.235840
$208$	22.0924	1.53184
$209$	34.6069	2.39381
$210$	−33.5625	−2.31603
$211$	−1.82935	−0.125937	−0.0629687	−	0.998015i	$-0.520057\pi$
$211$	−1.82935	−0.125937	−0.0629687	+	0.998015i	$0.520057\pi$
$212$	−52.3490	−3.59534
$213$	−12.8175	−0.878243
$214$	−38.0686	−2.60231
$215$	43.2154	2.94727
$216$	7.23988	0.492612
$217$	−7.88332	−0.535155
$218$	53.4338	3.61899
$219$	6.55787	0.443140
$220$	100.627	6.78428
$221$	−1.65182	−0.111113
$222$	26.3175	1.76632
$223$	0.869974	0.0582578	0.0291289	−	0.999576i	$-0.490727\pi$
$223$	0.869974	0.0582578	0.0291289	+	0.999576i	$0.490727\pi$
$224$	34.1949	2.28474
$225$	8.40678	0.560452
$226$	8.72423	0.580327
$227$	−21.0139	−1.39474	−0.697370	−	0.716711i	$-0.745647\pi$
$227$	−21.0139	−1.39474	−0.697370	+	0.716711i	$0.745647\pi$
$228$	−28.7763	−1.90576
$229$	2.75178	0.181842	0.0909212	−	0.995858i	$-0.471019\pi$
$229$	2.75178	0.181842	0.0909212	+	0.995858i	$0.471019\pi$
$230$	32.3513	2.13318
$231$	20.2374	1.33152
$232$	4.58659	0.301125
$233$	2.97583	0.194953	0.0974764	−	0.995238i	$-0.468923\pi$
$233$	2.97583	0.194953	0.0974764	+	0.995238i	$0.468923\pi$
$234$	−6.19148	−0.404750
$235$	15.9939	1.04333
$236$	68.5682	4.46341
$237$	0.569661	0.0370035
$238$	−6.36775	−0.412760
$239$	18.8290	1.21795	0.608974	−	0.793190i	$-0.291581\pi$
$239$	18.8290	1.21795	0.608974	+	0.793190i	$0.291581\pi$
$240$	−34.0203	−2.19600
$241$	−29.0336	−1.87022	−0.935108	−	0.354363i	$-0.884698\pi$
$241$	−29.0336	−1.87022	−0.935108	+	0.354363i	$0.884698\pi$
$242$	−57.4182	−3.69098
$243$	−1.00000	−0.0641500
$244$	−10.2514	−0.656279
$245$	19.7416	1.26125
$246$	10.3178	0.657838
$247$	14.3133	0.910735
$248$	−16.2135	−1.02956
$249$	2.47776	0.157022
$250$	−32.4813	−2.05430
$251$	−12.5053	−0.789327	−0.394663	−	0.918826i	$-0.629139\pi$
$251$	−12.5053	−0.789327	−0.394663	+	0.918826i	$0.629139\pi$
$252$	−16.8278	−1.06005
$253$	−19.5071	−1.22640
$254$	−42.6066	−2.67338
$255$	2.54365	0.159289
$256$	−18.5038	−1.15649
$257$	12.0846	0.753818	0.376909	−	0.926250i	$-0.376987\pi$
$257$	12.0846	0.753818	0.376909	+	0.926250i	$0.376987\pi$
$258$	30.7329	1.91335
$259$	−35.5781	−2.21071
$260$	41.6191	2.58111
$261$	−0.633517	−0.0392137
$262$	26.5717	1.64160
$263$	−8.12095	−0.500759	−0.250380	−	0.968148i	$-0.580555\pi$
$263$	−8.12095	−0.500759	−0.250380	+	0.968148i	$0.580555\pi$
$264$	41.6219	2.56165
$265$	−40.0966	−2.46312
$266$	55.1778	3.38317
$267$	−12.6497	−0.774152
$268$	−72.0229	−4.39950
$269$	12.5284	0.763869	0.381935	−	0.924189i	$-0.375258\pi$
$269$	12.5284	0.763869	0.381935	+	0.924189i	$0.375258\pi$
$270$	9.53431	0.580240
$271$	−23.4858	−1.42666	−0.713330	−	0.700829i	$-0.752814\pi$
$271$	−23.4858	−1.42666	−0.713330	+	0.700829i	$0.752814\pi$
$272$	−6.45461	−0.391368
$273$	8.37013	0.506583
$274$	−21.0949	−1.27439
$275$	48.3304	2.91443
$276$	16.2205	0.976361
$277$	−8.34987	−0.501695	−0.250848	−	0.968027i	$-0.580709\pi$
$277$	−8.34987	−0.501695	−0.250848	+	0.968027i	$0.580709\pi$
$278$	7.04958	0.422806
$279$	2.23947	0.134073
$280$	93.3165	5.57672
$281$	−16.1862	−0.965587	−0.482794	−	0.875734i	$-0.660378\pi$
$281$	−16.1862	−0.965587	−0.482794	+	0.875734i	$0.660378\pi$
$282$	11.3741	0.677320
$283$	11.1395	0.662173	0.331086	−	0.943600i	$-0.392585\pi$
$283$	11.1395	0.662173	0.331086	+	0.943600i	$0.392585\pi$
$284$	61.2727	3.63587
$285$	−22.0412	−1.30561
$286$	−35.5947	−2.10476
$287$	−13.9484	−0.823346
$288$	−9.71398	−0.572401
$289$	−16.5174	−0.971612
$290$	6.04015	0.354690
$291$	4.02220	0.235786
$292$	−31.3491	−1.83457
$293$	14.3344	0.837424	0.418712	−	0.908119i	$-0.362482\pi$
$293$	14.3344	0.837424	0.418712	+	0.908119i	$0.362482\pi$
$294$	14.0394	0.818794
$295$	52.5197	3.05782
$296$	−73.1728	−4.25308
$297$	−5.74897	−0.333589
$298$	34.5709	2.00264
$299$	−8.06808	−0.466589
$300$	−40.1876	−2.32023
$301$	−41.5471	−2.39474
$302$	6.01245	0.345978
$303$	3.97186	0.228178
$304$	55.9305	3.20784
$305$	−7.85206	−0.449607
$306$	1.80893	0.103410
$307$	2.35813	0.134586	0.0672929	−	0.997733i	$-0.478564\pi$
$307$	2.35813	0.134586	0.0672929	+	0.997733i	$0.478564\pi$
$308$	−96.7425	−5.51242
$309$	7.06131	0.401704
$310$	−21.3518	−1.21270
$311$	28.5697	1.62004	0.810020	−	0.586403i	$-0.199456\pi$
$311$	28.5697	1.62004	0.810020	+	0.586403i	$0.199456\pi$
$312$	17.2147	0.974590
$313$	−17.7585	−1.00377	−0.501884	−	0.864935i	$-0.667360\pi$
$313$	−17.7585	−1.00377	−0.501884	+	0.864935i	$0.667360\pi$
$314$	−36.0139	−2.03238
$315$	−12.8892	−0.726225
$316$	−2.72320	−0.153192
$317$	−13.7767	−0.773774	−0.386887	−	0.922127i	$-0.626450\pi$
$317$	−13.7767	−0.773774	−0.386887	+	0.922127i	$0.626450\pi$
$318$	−28.5149	−1.59904
$319$	−3.64208	−0.203917
$320$	24.5755	1.37381
$321$	−14.6197	−0.815994
$322$	−31.1024	−1.73327
$323$	−4.18184	−0.232684
$324$	4.78038	0.265577
$325$	19.9893	1.10881
$326$	−52.7505	−2.92158
$327$	20.5205	1.13479
$328$	−28.6874	−1.58399
$329$	−15.3764	−0.847731
$330$	54.8125	3.01733
$331$	−27.9196	−1.53460	−0.767299	−	0.641289i	$-0.778400\pi$
$331$	−27.9196	−1.53460	−0.767299	+	0.641289i	$0.778400\pi$
$332$	−11.8446	−0.650059
$333$	10.1069	0.553855
$334$	23.8639	1.30577
$335$	−55.1658	−3.01403
$336$	32.7070	1.78431
$337$	−35.4115	−1.92899	−0.964493	−	0.264108i	$-0.914923\pi$
$337$	−35.4115	−1.92899	−0.964493	+	0.264108i	$0.914923\pi$
$338$	19.1291	1.04048
$339$	3.35042	0.181970
$340$	−12.1596	−0.659447
$341$	12.8746	0.697201
$342$	−15.6747	−0.847592
$343$	5.66170	0.305703
$344$	−85.4492	−4.60711
$345$	12.4241	0.668890
$346$	−41.2376	−2.21695
$347$	15.2423	0.818251	0.409126	−	0.912478i	$-0.365834\pi$
$347$	15.2423	0.818251	0.409126	+	0.912478i	$0.365834\pi$
$348$	3.02846	0.162342
$349$	−18.8637	−1.00975	−0.504875	−	0.863192i	$-0.668461\pi$
$349$	−18.8637	−1.00975	−0.504875	+	0.863192i	$0.668461\pi$
$350$	77.0586	4.11896
$351$	−2.37776	−0.126915
$352$	−55.8454	−2.97657
$353$	26.1318	1.39086	0.695428	−	0.718595i	$-0.255215\pi$
$353$	26.1318	1.39086	0.695428	+	0.718595i	$0.255215\pi$
$354$	37.3497	1.98511
$355$	46.9318	2.49088
$356$	60.4706	3.20494
$357$	−2.44545	−0.129427
$358$	38.3095	2.02472
$359$	10.7921	0.569585	0.284792	−	0.958589i	$-0.408075\pi$
$359$	10.7921	0.569585	0.284792	+	0.958589i	$0.408075\pi$
$360$	−26.5090	−1.39715
$361$	17.2365	0.907183
$362$	−24.3892	−1.28187
$363$	−22.0507	−1.15736
$364$	−40.0124	−2.09722
$365$	−24.0118	−1.25684
$366$	−5.58404	−0.291882
$367$	7.88319	0.411499	0.205750	−	0.978605i	$-0.434037\pi$
$367$	7.88319	0.411499	0.205750	+	0.978605i	$0.434037\pi$
$368$	−31.5267	−1.64344
$369$	3.96241	0.206275
$370$	−96.3624	−5.00964
$371$	38.5487	2.00135
$372$	−10.7055	−0.555055
$373$	−20.8305	−1.07856	−0.539281	−	0.842126i	$-0.681304\pi$
$373$	−20.8305	−1.07856	−0.539281	+	0.842126i	$0.681304\pi$
$374$	10.3995	0.537745
$375$	−12.4740	−0.644155
$376$	−31.6245	−1.63091
$377$	−1.50635	−0.0775810
$378$	−9.16625	−0.471461
$379$	15.4745	0.794871	0.397436	−	0.917630i	$-0.369900\pi$
$379$	15.4745	0.794871	0.397436	+	0.917630i	$0.369900\pi$
$380$	105.365	5.40513
$381$	−16.3625	−0.838277
$382$	−40.4962	−2.07197
$383$	−9.33901	−0.477201	−0.238600	−	0.971118i	$-0.576689\pi$
$383$	−9.33901	−0.477201	−0.238600	+	0.971118i	$0.576689\pi$
$384$	−1.95097	−0.0995600
$385$	−74.0998	−3.77648
$386$	24.1336	1.22837
$387$	11.8026	0.599958
$388$	−19.2277	−0.976136
$389$	15.7546	0.798790	0.399395	−	0.916779i	$-0.369220\pi$
$389$	15.7546	0.798790	0.399395	+	0.916779i	$0.369220\pi$
$390$	22.6703	1.14795
$391$	2.35720	0.119209
$392$	−39.0349	−1.97156
$393$	10.2045	0.514749
$394$	−4.60823	−0.232159
$395$	−2.08583	−0.104950
$396$	27.4823	1.38104
$397$	−31.2319	−1.56749	−0.783743	−	0.621085i	$-0.786692\pi$
$397$	−31.2319	−1.56749	−0.783743	+	0.621085i	$0.786692\pi$
$398$	−20.7226	−1.03873
$399$	21.1903	1.06084
$400$	78.1098	3.90549
$401$	−4.39391	−0.219421	−0.109711	−	0.993964i	$-0.534992\pi$
$401$	−4.39391	−0.219421	−0.109711	+	0.993964i	$0.534992\pi$
$402$	−39.2315	−1.95669
$403$	5.32491	0.265253
$404$	−18.9870	−0.944640
$405$	3.66153	0.181943
$406$	−5.80698	−0.288195
$407$	58.1043	2.88012
$408$	−5.02951	−0.248998
$409$	−17.5229	−0.866451	−0.433225	−	0.901286i	$-0.642625\pi$
$409$	−17.5229	−0.866451	−0.433225	+	0.901286i	$0.642625\pi$
$410$	−37.7788	−1.86576
$411$	−8.10121	−0.399603
$412$	−33.7558	−1.66303
$413$	−50.4922	−2.48456
$414$	8.83546	0.434239
$415$	−9.07238	−0.445346
$416$	−23.0975	−1.13245
$417$	2.70730	0.132577
$418$	−90.1136	−4.40760
$419$	4.45110	0.217450	0.108725	−	0.994072i	$-0.465323\pi$
$419$	4.45110	0.217450	0.108725	+	0.994072i	$0.465323\pi$
$420$	61.6154	3.00652
$421$	−4.30131	−0.209633	−0.104817	−	0.994492i	$-0.533426\pi$
$421$	−4.30131	−0.209633	−0.104817	+	0.994492i	$0.533426\pi$
$422$	4.76347	0.231882
$423$	4.36809	0.212384
$424$	79.2824	3.85030
$425$	−5.84015	−0.283289
$426$	33.3758	1.61706
$427$	7.54893	0.365318
$428$	69.8879	3.37816
$429$	−13.6697	−0.659978
$430$	−112.529	−5.42665
$431$	10.0251	0.482891	0.241445	−	0.970414i	$-0.422379\pi$
$431$	10.0251	0.482891	0.241445	+	0.970414i	$0.422379\pi$
$432$	−9.29129	−0.447027
$433$	19.5863	0.941258	0.470629	−	0.882331i	$-0.344027\pi$
$433$	19.5863	0.941258	0.470629	+	0.882331i	$0.344027\pi$
$434$	20.5275	0.985352
$435$	2.31964	0.111218
$436$	−98.0960	−4.69795
$437$	−20.4256	−0.977090
$438$	−17.0761	−0.815930
$439$	−20.1812	−0.963194	−0.481597	−	0.876393i	$-0.659943\pi$
$439$	−20.1812	−0.963194	−0.481597	+	0.876393i	$0.659943\pi$
$440$	−152.400	−7.26537
$441$	5.39164	0.256745
$442$	4.30120	0.204587
$443$	−25.3314	−1.20353	−0.601765	−	0.798673i	$-0.705536\pi$
$443$	−25.3314	−1.20353	−0.601765	+	0.798673i	$0.705536\pi$
$444$	−48.3149	−2.29292
$445$	46.3174	2.19565
$446$	−2.26534	−0.107267
$447$	13.2765	0.627957
$448$	−23.6267	−1.11626
$449$	−27.2212	−1.28465	−0.642325	−	0.766432i	$-0.722030\pi$
$449$	−27.2212	−1.28465	−0.642325	+	0.766432i	$0.722030\pi$
$450$	−21.8906	−1.03193
$451$	22.7798	1.07266
$452$	−16.0163	−0.753344
$453$	2.30900	0.108486
$454$	54.7184	2.56806
$455$	−30.6475	−1.43677
$456$	43.5817	2.04090
$457$	38.3373	1.79334	0.896672	−	0.442695i	$-0.145978\pi$
$457$	38.3373	1.79334	0.896672	+	0.442695i	$0.145978\pi$
$458$	−7.16539	−0.334817
$459$	0.694695	0.0324256
$460$	−59.3919	−2.76916
$461$	−21.4172	−0.997499	−0.498750	−	0.866746i	$-0.666207\pi$
$461$	−21.4172	−0.997499	−0.498750	+	0.866746i	$0.666207\pi$
$462$	−52.6965	−2.45166
$463$	35.5600	1.65261	0.826307	−	0.563220i	$-0.190437\pi$
$463$	35.5600	1.65261	0.826307	+	0.563220i	$0.190437\pi$
$464$	−5.88619	−0.273260
$465$	−8.19987	−0.380260
$466$	−7.74880	−0.358956
$467$	21.4724	0.993622	0.496811	−	0.867859i	$-0.334504\pi$
$467$	21.4724	0.993622	0.496811	+	0.867859i	$0.334504\pi$
$468$	11.3666	0.525421
$469$	53.0362	2.44898
$470$	−41.6467	−1.92102
$471$	−13.8307	−0.637284
$472$	−103.846	−4.77992
$473$	67.8527	3.11987
$474$	−1.48335	−0.0681326
$475$	50.6061	2.32197
$476$	11.6902	0.535819
$477$	−10.9508	−0.501402
$478$	−49.0292	−2.24254
$479$	−34.4495	−1.57404	−0.787018	−	0.616930i	$-0.788376\pi$
$479$	−34.4495	−1.57404	−0.787018	+	0.616930i	$0.788376\pi$
$480$	35.5680	1.62345
$481$	24.0318	1.09575
$482$	75.6010	3.44353
$483$	−11.9445	−0.543492
$484$	105.411	4.79140
$485$	−14.7274	−0.668737
$486$	2.60392	0.118116
$487$	−37.2483	−1.68788	−0.843942	−	0.536435i	$-0.819771\pi$
$487$	−37.2483	−1.68788	−0.843942	+	0.536435i	$0.819771\pi$
$488$	15.5258	0.702818
$489$	−20.2581	−0.916104
$490$	−51.4056	−2.32227
$491$	7.06818	0.318982	0.159491	−	0.987199i	$-0.449015\pi$
$491$	7.06818	0.318982	0.159491	+	0.987199i	$0.449015\pi$
$492$	−18.9418	−0.853963
$493$	0.440102	0.0198212
$494$	−37.2707	−1.67689
$495$	21.0500	0.946128
$496$	20.8075	0.934286
$497$	−45.1200	−2.02391
$498$	−6.45188	−0.289115
$499$	−14.6277	−0.654824	−0.327412	−	0.944882i	$-0.606176\pi$
$499$	−14.6277	−0.654824	−0.327412	+	0.944882i	$0.606176\pi$
$500$	59.6306	2.66676
$501$	9.16461	0.409444
$502$	32.5627	1.45335
$503$	−19.7674	−0.881384	−0.440692	−	0.897658i	$-0.645267\pi$
$503$	−19.7674	−0.881384	−0.440692	+	0.897658i	$0.645267\pi$
$504$	25.4857	1.13522
$505$	−14.5431	−0.647159
$506$	50.7949	2.25811
$507$	7.34626	0.326259
$508$	78.2191	3.47041
$509$	−8.26719	−0.366437	−0.183218	−	0.983072i	$-0.558652\pi$
$509$	−8.26719	−0.366437	−0.183218	+	0.983072i	$0.558652\pi$
$510$	−6.62344	−0.293291
$511$	23.0849	1.02121
$512$	44.2803	1.95693
$513$	−6.01967	−0.265775
$514$	−31.4674	−1.38797
$515$	−25.8552	−1.13932
$516$	−56.4208	−2.48379
$517$	25.1120	1.10443
$518$	92.6424	4.07047
$519$	−15.8368	−0.695157
$520$	−63.0321	−2.76414
$521$	−8.33446	−0.365139	−0.182570	−	0.983193i	$-0.558442\pi$
$521$	−8.33446	−0.365139	−0.182570	+	0.983193i	$0.558442\pi$
$522$	1.64963	0.0722022
$523$	−11.5973	−0.507114	−0.253557	−	0.967321i	$-0.581600\pi$
$523$	−11.5973	−0.507114	−0.253557	+	0.967321i	$0.581600\pi$
$524$	−48.7814	−2.13103
$525$	29.5933	1.29156
$526$	21.1463	0.922021
$527$	−1.55575	−0.0677694
$528$	−53.4154	−2.32461
$529$	−11.4866	−0.499416
$530$	104.408	4.53520
$531$	14.3437	0.622462
$532$	−101.298	−4.39182
$533$	9.42165	0.408097
$534$	32.9389	1.42540
$535$	53.5305	2.31433
$536$	109.079	4.71148
$537$	14.7123	0.634881
$538$	−32.6229	−1.40647
$539$	30.9964	1.33511
$540$	−17.5035	−0.753231
$541$	25.8483	1.11131	0.555653	−	0.831414i	$-0.312468\pi$
$541$	25.8483	1.11131	0.555653	+	0.831414i	$0.312468\pi$
$542$	61.1550	2.62683
$543$	−9.36636	−0.401949
$544$	6.74825	0.289329
$545$	−75.1365	−3.21849
$546$	−21.7951	−0.932745
$547$	31.9750	1.36715	0.683576	−	0.729879i	$-0.260424\pi$
$547$	31.9750	1.36715	0.683576	+	0.729879i	$0.260424\pi$
$548$	38.7269	1.65433
$549$	−2.14448	−0.0915240
$550$	−125.848	−5.36619
$551$	−3.81357	−0.162463
$552$	−24.5660	−1.04560
$553$	2.00531	0.0852744
$554$	21.7424	0.923745
$555$	−37.0067	−1.57085
$556$	−12.9419	−0.548860
$557$	5.40117	0.228855	0.114427	−	0.993432i	$-0.463497\pi$
$557$	5.40117	0.228855	0.114427	+	0.993432i	$0.463497\pi$
$558$	−5.83139	−0.246862
$559$	28.0637	1.18697
$560$	−119.757	−5.06068
$561$	3.99379	0.168618
$562$	42.1475	1.77789
$563$	20.4551	0.862079	0.431040	−	0.902333i	$-0.358147\pi$
$563$	20.4551	0.862079	0.431040	+	0.902333i	$0.358147\pi$
$564$	−20.8811	−0.879255
$565$	−12.2677	−0.516105
$566$	−29.0063	−1.21922
$567$	−3.52018	−0.147834
$568$	−92.7975	−3.89370
$569$	22.9955	0.964020	0.482010	−	0.876166i	$-0.339907\pi$
$569$	22.9955	0.964020	0.482010	+	0.876166i	$0.339907\pi$
$570$	57.3934	2.40395
$571$	−37.0129	−1.54894	−0.774470	−	0.632610i	$-0.781984\pi$
$571$	−37.0129	−1.54894	−0.774470	+	0.632610i	$0.781984\pi$
$572$	65.3463	2.73226
$573$	−15.5520	−0.649696
$574$	36.3204	1.51598
$575$	−28.5254	−1.18959
$576$	6.71180	0.279659
$577$	−32.8885	−1.36917	−0.684584	−	0.728934i	$-0.740016\pi$
$577$	−32.8885	−1.36917	−0.684584	+	0.728934i	$0.740016\pi$
$578$	43.0099	1.78898
$579$	9.26819	0.385173
$580$	−11.0888	−0.460436
$581$	8.72215	0.361856
$582$	−10.4735	−0.434139
$583$	−62.9558	−2.60736
$584$	47.4782	1.96466
$585$	8.70623	0.359958
$586$	−37.3256	−1.54191
$587$	−29.2744	−1.20828	−0.604141	−	0.796877i	$-0.706484\pi$
$587$	−29.2744	−1.20828	−0.604141	+	0.796877i	$0.706484\pi$
$588$	−25.7741	−1.06291
$589$	13.4809	0.555469
$590$	−136.757	−5.63019
$591$	−1.76973	−0.0727970
$592$	93.9062	3.85952
$593$	12.7632	0.524121	0.262061	−	0.965051i	$-0.415598\pi$
$593$	12.7632	0.524121	0.262061	+	0.965051i	$0.415598\pi$
$594$	14.9699	0.614220
$595$	8.95408	0.367082
$596$	−63.4668	−2.59970
$597$	−7.95825	−0.325710
$598$	21.0086	0.859105
$599$	24.9365	1.01888	0.509438	−	0.860507i	$-0.329853\pi$
$599$	24.9365	1.01888	0.509438	+	0.860507i	$0.329853\pi$
$600$	60.8641	2.48477
$601$	−30.5323	−1.24544	−0.622720	−	0.782445i	$-0.713972\pi$
$601$	−30.5323	−1.24544	−0.622720	+	0.782445i	$0.713972\pi$
$602$	108.185	4.40930
$603$	−15.0663	−0.613549
$604$	−11.0379	−0.449126
$605$	80.7393	3.28252
$606$	−10.3424	−0.420131
$607$	−35.5395	−1.44250	−0.721251	−	0.692674i	$-0.756433\pi$
$607$	−35.5395	−1.44250	−0.721251	+	0.692674i	$0.756433\pi$
$608$	−58.4750	−2.37147
$609$	−2.23009	−0.0903679
$610$	20.4461	0.827838
$611$	10.3863	0.420183
$612$	−3.32091	−0.134240
$613$	29.3120	1.18390	0.591949	−	0.805975i	$-0.298359\pi$
$613$	29.3120	1.18390	0.591949	+	0.805975i	$0.298359\pi$
$614$	−6.14039	−0.247806
$615$	−14.5085	−0.585038
$616$	146.516	5.90332
$617$	−39.8001	−1.60229	−0.801145	−	0.598470i	$-0.795775\pi$
$617$	−39.8001	−1.60229	−0.801145	+	0.598470i	$0.795775\pi$
$618$	−18.3871	−0.739636
$619$	6.37884	0.256387	0.128194	−	0.991749i	$-0.459082\pi$
$619$	6.37884	0.256387	0.128194	+	0.991749i	$0.459082\pi$
$620$	39.1985	1.57425
$621$	3.39314	0.136162
$622$	−74.3931	−2.98289
$623$	−44.5293	−1.78403
$624$	−22.0924	−0.884405
$625$	3.64005	0.145602
$626$	46.2416	1.84819
$627$	−34.6069	−1.38207
$628$	66.1159	2.63831
$629$	−7.02122	−0.279954
$630$	33.5625	1.33716
$631$	37.4451	1.49067	0.745333	−	0.666692i	$-0.232290\pi$
$631$	37.4451	1.49067	0.745333	+	0.666692i	$0.232290\pi$
$632$	4.12428	0.164055
$633$	1.82935	0.0727100
$634$	35.8733	1.42471
$635$	59.9118	2.37753
$636$	52.3490	2.07577
$637$	12.8200	0.507948
$638$	9.48366	0.375462
$639$	12.8175	0.507054
$640$	7.14353	0.282373
$641$	−31.1602	−1.23076	−0.615378	−	0.788233i	$-0.710996\pi$
$641$	−31.1602	−1.23076	−0.615378	+	0.788233i	$0.710996\pi$
$642$	38.0686	1.50245
$643$	−2.80937	−0.110791	−0.0553954	−	0.998464i	$-0.517642\pi$
$643$	−2.80937	−0.110791	−0.0553954	+	0.998464i	$0.517642\pi$
$644$	57.0991	2.25002
$645$	−43.2154	−1.70161
$646$	10.8892	0.428428
$647$	−13.9514	−0.548488	−0.274244	−	0.961660i	$-0.588428\pi$
$647$	−13.9514	−0.548488	−0.274244	+	0.961660i	$0.588428\pi$
$648$	−7.23988	−0.284409
$649$	82.4613	3.23689
$650$	−52.0505	−2.04159
$651$	7.88332	0.308972
$652$	96.8416	3.79261
$653$	14.4074	0.563806	0.281903	−	0.959443i	$-0.409034\pi$
$653$	14.4074	0.563806	0.281903	+	0.959443i	$0.409034\pi$
$654$	−53.4338	−2.08943
$655$	−37.3641	−1.45994
$656$	36.8159	1.43742
$657$	−6.55787	−0.255847
$658$	40.0390	1.56088
$659$	18.1377	0.706546	0.353273	−	0.935520i	$-0.385069\pi$
$659$	18.1377	0.706546	0.353273	+	0.935520i	$0.385069\pi$
$660$	−100.627	−3.91691
$661$	−9.43929	−0.367146	−0.183573	−	0.983006i	$-0.558766\pi$
$661$	−9.43929	−0.367146	−0.183573	+	0.983006i	$0.558766\pi$
$662$	72.7002	2.82557
$663$	1.65182	0.0641513
$664$	17.9387	0.696156
$665$	−77.5889	−3.00877
$666$	−26.3175	−1.01978
$667$	2.14962	0.0832335
$668$	−43.8103	−1.69507
$669$	−0.869974	−0.0336352
$670$	143.647	5.54958
$671$	−12.3285	−0.475938
$672$	−34.1949	−1.31910
$673$	−18.0586	−0.696107	−0.348054	−	0.937475i	$-0.613157\pi$
$673$	−18.0586	−0.696107	−0.348054	+	0.937475i	$0.613157\pi$
$674$	92.2085	3.55174
$675$	−8.40678	−0.323577
$676$	−35.1180	−1.35069
$677$	18.6814	0.717986	0.358993	−	0.933340i	$-0.383120\pi$
$677$	18.6814	0.717986	0.358993	+	0.933340i	$0.383120\pi$
$678$	−8.72423	−0.335052
$679$	14.1589	0.543367
$680$	18.4157	0.706210
$681$	21.0139	0.805253
$682$	−33.5245	−1.28372
$683$	−34.9714	−1.33814	−0.669072	−	0.743198i	$-0.733308\pi$
$683$	−34.9714	−1.33814	−0.669072	+	0.743198i	$0.733308\pi$
$684$	28.7763	1.10029
$685$	29.6628	1.13336
$686$	−14.7426	−0.562875
$687$	−2.75178	−0.104987
$688$	109.661	4.18079
$689$	−26.0383	−0.991982
$690$	−32.3513	−1.23159
$691$	5.01371	0.190730	0.0953652	−	0.995442i	$-0.469598\pi$
$691$	5.01371	0.190730	0.0953652	+	0.995442i	$0.469598\pi$
$692$	75.7058	2.87790
$693$	−20.2374	−0.768755
$694$	−39.6898	−1.50660
$695$	−9.91285	−0.376016
$696$	−4.58659	−0.173854
$697$	−2.75267	−0.104265
$698$	49.1195	1.85920
$699$	−2.97583	−0.112556
$700$	−141.468	−5.34697
$701$	−10.6914	−0.403809	−0.201905	−	0.979405i	$-0.564713\pi$
$701$	−10.6914	−0.403809	−0.201905	+	0.979405i	$0.564713\pi$
$702$	6.19148	0.233683
$703$	60.8403	2.29463
$704$	38.5860	1.45426
$705$	−15.9939	−0.602364
$706$	−68.0451	−2.56091
$707$	13.9817	0.525835
$708$	−68.5682	−2.57695
$709$	−17.3847	−0.652896	−0.326448	−	0.945215i	$-0.605852\pi$
$709$	−17.3847	−0.652896	−0.326448	+	0.945215i	$0.605852\pi$
$710$	−122.206	−4.58632
$711$	−0.569661	−0.0213640
$712$	−91.5827	−3.43221
$713$	−7.59884	−0.284579
$714$	6.36775	0.238307
$715$	50.0519	1.87183
$716$	−70.3302	−2.62836
$717$	−18.8290	−0.703182
$718$	−28.1017	−1.04875
$719$	33.3824	1.24495	0.622477	−	0.782638i	$-0.286126\pi$
$719$	33.3824	1.24495	0.622477	+	0.782638i	$0.286126\pi$
$720$	34.0203	1.26786
$721$	24.8571	0.925726
$722$	−44.8823	−1.67035
$723$	29.0336	1.07977
$724$	44.7748	1.66404
$725$	−5.32584	−0.197797
$726$	57.4182	2.13099
$727$	45.5393	1.68896	0.844479	−	0.535589i	$-0.179910\pi$
$727$	45.5393	1.68896	0.844479	+	0.535589i	$0.179910\pi$
$728$	60.5988	2.24594
$729$	1.00000	0.0370370
$730$	62.5248	2.31415
$731$	−8.19919	−0.303258
$732$	10.2514	0.378903
$733$	3.41554	0.126156	0.0630779	−	0.998009i	$-0.479908\pi$
$733$	3.41554	0.126156	0.0630779	+	0.998009i	$0.479908\pi$
$734$	−20.5272	−0.757672
$735$	−19.7416	−0.728181
$736$	32.9609	1.21496
$737$	−86.6160	−3.19054
$738$	−10.3178	−0.379803
$739$	10.8460	0.398977	0.199488	−	0.979900i	$-0.436072\pi$
$739$	10.8460	0.398977	0.199488	+	0.979900i	$0.436072\pi$
$740$	176.906	6.50320
$741$	−14.3133	−0.525813
$742$	−100.378	−3.68498
$743$	−4.56129	−0.167337	−0.0836687	−	0.996494i	$-0.526664\pi$
$743$	−4.56129	−0.167337	−0.0836687	+	0.996494i	$0.526664\pi$
$744$	16.2135	0.594415
$745$	−48.6123	−1.78102
$746$	54.2409	1.98590
$747$	−2.47776	−0.0906564
$748$	−19.0918	−0.698066
$749$	−51.4640	−1.88045
$750$	32.4813	1.18605
$751$	1.40534	0.0512817	0.0256409	−	0.999671i	$-0.491837\pi$
$751$	1.40534	0.0512817	0.0256409	+	0.999671i	$0.491837\pi$
$752$	40.5852	1.47999
$753$	12.5053	0.455718
$754$	3.92241	0.142846
$755$	−8.45447	−0.307690
$756$	16.8278	0.612021
$757$	32.0777	1.16588	0.582942	−	0.812514i	$-0.301901\pi$
$757$	32.0777	1.16588	0.582942	+	0.812514i	$0.301901\pi$
$758$	−40.2943	−1.46355
$759$	19.5071	0.708063
$760$	−159.576	−5.78842
$761$	−2.19592	−0.0796020	−0.0398010	−	0.999208i	$-0.512672\pi$
$761$	−2.19592	−0.0796020	−0.0398010	+	0.999208i	$0.512672\pi$
$762$	42.6066	1.54348
$763$	72.2359	2.61512
$764$	74.3447	2.68970
$765$	−2.54365	−0.0919657
$766$	24.3180	0.878645
$767$	34.1058	1.23149
$768$	18.5038	0.667697
$769$	44.6901	1.61157	0.805783	−	0.592211i	$-0.201745\pi$
$769$	44.6901	1.61157	0.805783	+	0.592211i	$0.201745\pi$
$770$	192.950	6.95342
$771$	−12.0846	−0.435217
$772$	−44.3055	−1.59459
$773$	28.2824	1.01725	0.508623	−	0.860989i	$-0.330155\pi$
$773$	28.2824	1.01725	0.508623	+	0.860989i	$0.330155\pi$
$774$	−30.7329	−1.10467
$775$	18.8267	0.676275
$776$	29.1203	1.04536
$777$	35.5781	1.27636
$778$	−41.0236	−1.47077
$779$	23.8524	0.854601
$780$	−41.6191	−1.49020
$781$	73.6877	2.63675
$782$	−6.13796	−0.219493
$783$	0.633517	0.0226401
$784$	50.0953	1.78912
$785$	50.6414	1.80747
$786$	−26.5717	−0.947781
$787$	20.9023	0.745086	0.372543	−	0.928015i	$-0.378486\pi$
$787$	20.9023	0.745086	0.372543	+	0.928015i	$0.378486\pi$
$788$	8.45999	0.301375
$789$	8.12095	0.289113
$790$	5.43133	0.193238
$791$	11.7941	0.419349
$792$	−41.6219	−1.47897
$793$	−5.09905	−0.181072
$794$	81.3254	2.88613
$795$	40.0966	1.42208
$796$	38.0435	1.34842
$797$	24.9094	0.882337	0.441168	−	0.897424i	$-0.354564\pi$
$797$	24.9094	0.882337	0.441168	+	0.897424i	$0.354564\pi$
$798$	−55.1778	−1.95327
$799$	−3.03449	−0.107353
$800$	−81.6633	−2.88723
$801$	12.6497	0.446957
$802$	11.4414	0.404009
$803$	−37.7010	−1.33044
$804$	72.0229	2.54005
$805$	43.7350	1.54146
$806$	−13.8656	−0.488396
$807$	−12.5284	−0.441020
$808$	28.7558	1.01163
$809$	37.5719	1.32096	0.660479	−	0.750844i	$-0.270353\pi$
$809$	37.5719	1.32096	0.660479	+	0.750844i	$0.270353\pi$
$810$	−9.53431	−0.335002
$811$	−8.02288	−0.281721	−0.140861	−	0.990029i	$-0.544987\pi$
$811$	−8.02288	−0.281721	−0.140861	+	0.990029i	$0.544987\pi$
$812$	10.6607	0.374117
$813$	23.4858	0.823682
$814$	−151.299	−5.30302
$815$	74.1757	2.59826
$816$	6.45461	0.225957
$817$	71.0476	2.48564
$818$	45.6281	1.59535
$819$	−8.37013	−0.292476
$820$	69.3560	2.42202
$821$	−28.4574	−0.993169	−0.496585	−	0.867988i	$-0.665413\pi$
$821$	−28.4574	−0.993169	−0.496585	+	0.867988i	$0.665413\pi$
$822$	21.0949	0.735769
$823$	17.6555	0.615432	0.307716	−	0.951478i	$-0.400435\pi$
$823$	17.6555	0.615432	0.307716	+	0.951478i	$0.400435\pi$
$824$	51.1231	1.78096
$825$	−48.3304	−1.68265
$826$	131.478	4.57469
$827$	−47.6022	−1.65529	−0.827646	−	0.561251i	$-0.810320\pi$
$827$	−47.6022	−1.65529	−0.827646	+	0.561251i	$0.810320\pi$
$828$	−16.2205	−0.563702
$829$	16.4126	0.570032	0.285016	−	0.958523i	$-0.408001\pi$
$829$	16.4126	0.570032	0.285016	+	0.958523i	$0.408001\pi$
$830$	23.6237	0.819991
$831$	8.34987	0.289654
$832$	15.9591	0.553281
$833$	−3.74555	−0.129776
$834$	−7.04958	−0.244107
$835$	−33.5565	−1.16127
$836$	165.434	5.72167
$837$	−2.23947	−0.0774073
$838$	−11.5903	−0.400380
$839$	54.4945	1.88136	0.940679	−	0.339297i	$-0.110189\pi$
$839$	54.4945	1.88136	0.940679	+	0.339297i	$0.110189\pi$
$840$	−93.3165	−3.21972
$841$	−28.5987	−0.986161
$842$	11.2003	0.385986
$843$	16.1862	0.557482
$844$	−8.74498	−0.301015
$845$	−26.8985	−0.925338
$846$	−11.3741	−0.391051
$847$	−77.6224	−2.66714
$848$	−101.747	−3.49400
$849$	−11.1395	−0.382306
$850$	15.2073	0.521605
$851$	−34.2942	−1.17559
$852$	−61.2727	−2.09917
$853$	14.3509	0.491366	0.245683	−	0.969350i	$-0.420988\pi$
$853$	14.3509	0.491366	0.245683	+	0.969350i	$0.420988\pi$
$854$	−19.6568	−0.672642
$855$	22.0412	0.753793
$856$	−105.845	−3.61771
$857$	9.98540	0.341095	0.170547	−	0.985349i	$-0.445446\pi$
$857$	9.98540	0.341095	0.170547	+	0.985349i	$0.445446\pi$
$858$	35.5947	1.21518
$859$	28.4811	0.971762	0.485881	−	0.874025i	$-0.338499\pi$
$859$	28.4811	0.971762	0.485881	+	0.874025i	$0.338499\pi$
$860$	206.586	7.04453
$861$	13.9484	0.475359
$862$	−26.1045	−0.889121
$863$	−24.7016	−0.840851	−0.420426	−	0.907327i	$-0.638119\pi$
$863$	−24.7016	−0.840851	−0.420426	+	0.907327i	$0.638119\pi$
$864$	9.71398	0.330476
$865$	57.9868	1.97161
$866$	−51.0011	−1.73309
$867$	16.5174	0.560960
$868$	−37.6853	−1.27912
$869$	−3.27497	−0.111096
$870$	−6.04015	−0.204780
$871$	−35.8241	−1.21385
$872$	148.566	5.03109
$873$	−4.02220	−0.136131
$874$	53.1866	1.79906
$875$	−43.9107	−1.48445
$876$	31.3491	1.05919
$877$	−22.1663	−0.748504	−0.374252	−	0.927327i	$-0.622100\pi$
$877$	−22.1663	−0.748504	−0.374252	+	0.927327i	$0.622100\pi$
$878$	52.5501	1.77348
$879$	−14.3344	−0.483487
$880$	195.582	6.59306
$881$	6.64034	0.223719	0.111859	−	0.993724i	$-0.464319\pi$
$881$	6.64034	0.223719	0.111859	+	0.993724i	$0.464319\pi$
$882$	−14.0394	−0.472731
$883$	−5.96750	−0.200822	−0.100411	−	0.994946i	$-0.532016\pi$
$883$	−5.96750	−0.200822	−0.100411	+	0.994946i	$0.532016\pi$
$884$	−7.89632	−0.265582
$885$	−52.5197	−1.76543
$886$	65.9608	2.21600
$887$	−31.4891	−1.05730	−0.528651	−	0.848839i	$-0.677302\pi$
$887$	−31.4891	−1.05730	−0.528651	+	0.848839i	$0.677302\pi$
$888$	73.1728	2.45552
$889$	−57.5989	−1.93181
$890$	−120.607	−4.04274
$891$	5.74897	0.192598
$892$	4.15881	0.139247
$893$	26.2945	0.879911
$894$	−34.5709	−1.15622
$895$	−53.8693	−1.80065
$896$	−6.86776	−0.229436
$897$	8.06808	0.269385
$898$	70.8819	2.36536
$899$	−1.41874	−0.0473177
$900$	40.1876	1.33959
$901$	7.60746	0.253441
$902$	−59.3166	−1.97503
$903$	41.5471	1.38260
$904$	24.2567	0.806765
$905$	34.2952	1.14001
$906$	−6.01245	−0.199750
$907$	−10.0734	−0.334481	−0.167241	−	0.985916i	$-0.553486\pi$
$907$	−10.0734	−0.334481	−0.167241	+	0.985916i	$0.553486\pi$
$908$	−100.454	−3.33369
$909$	−3.97186	−0.131738
$910$	79.8034	2.64546
$911$	53.0562	1.75783	0.878915	−	0.476979i	$-0.158268\pi$
$911$	53.0562	1.75783	0.878915	+	0.476979i	$0.158268\pi$
$912$	−55.9305	−1.85204
$913$	−14.2446	−0.471426
$914$	−99.8272	−3.30199
$915$	7.85206	0.259581
$916$	13.1545	0.434638
$917$	35.9217	1.18624
$918$	−1.80893	−0.0597035
$919$	−4.31723	−0.142412	−0.0712061	−	0.997462i	$-0.522685\pi$
$919$	−4.31723	−0.142412	−0.0712061	+	0.997462i	$0.522685\pi$
$920$	89.9489	2.96553
$921$	−2.35813	−0.0777032
$922$	55.7686	1.83664
$923$	30.4770	1.00316
$924$	96.7425	3.18260
$925$	84.9665	2.79368
$926$	−92.5953	−3.04287
$927$	−7.06131	−0.231924
$928$	6.15397	0.202014
$929$	23.0134	0.755044	0.377522	−	0.926001i	$-0.376776\pi$
$929$	23.0134	0.755044	0.377522	+	0.926001i	$0.376776\pi$
$930$	21.3518	0.700153
$931$	32.4559	1.06370
$932$	14.2256	0.465974
$933$	−28.5697	−0.935330
$934$	−55.9122	−1.82950
$935$	−14.6234	−0.478235
$936$	−17.2147	−0.562680
$937$	42.9894	1.40440	0.702201	−	0.711979i	$-0.252201\pi$
$937$	42.9894	1.40440	0.702201	+	0.711979i	$0.252201\pi$
$938$	−138.102	−4.50918
$939$	17.7585	0.579526
$940$	76.4569	2.49375
$941$	32.2928	1.05271	0.526357	−	0.850264i	$-0.323557\pi$
$941$	32.2928	1.05271	0.526357	+	0.850264i	$0.323557\pi$
$942$	36.0139	1.17340
$943$	−13.4450	−0.437830
$944$	133.271	4.33760
$945$	12.8892	0.419286
$946$	−176.683	−5.74445
$947$	49.0308	1.59329	0.796643	−	0.604451i	$-0.206607\pi$
$947$	49.0308	1.59329	0.796643	+	0.604451i	$0.206607\pi$
$948$	2.72320	0.0884454
$949$	−15.5930	−0.506171
$950$	−131.774	−4.27531
$951$	13.7767	0.446739
$952$	−17.7048	−0.573815
$953$	−1.00783	−0.0326469	−0.0163235	−	0.999867i	$-0.505196\pi$
$953$	−1.00783	−0.0326469	−0.0163235	+	0.999867i	$0.505196\pi$
$954$	28.5149	0.923205
$955$	56.9442	1.84267
$956$	90.0099	2.91113
$957$	3.64208	0.117732
$958$	89.7035	2.89819
$959$	−28.5177	−0.920885
$960$	−24.5755	−0.793169
$961$	−25.9848	−0.838219
$962$	−62.5767	−2.01755
$963$	14.6197	0.471114
$964$	−138.791	−4.47017
$965$	−33.9357	−1.09243
$966$	31.1024	1.00070
$967$	−17.3345	−0.557441	−0.278720	−	0.960372i	$-0.589910\pi$
$967$	−17.3345	−0.557441	−0.278720	+	0.960372i	$0.589910\pi$
$968$	−159.645	−5.13117
$969$	4.18184	0.134340
$970$	38.3489	1.23131
$971$	−13.1490	−0.421971	−0.210986	−	0.977489i	$-0.567667\pi$
$971$	−13.1490	−0.421971	−0.210986	+	0.977489i	$0.567667\pi$
$972$	−4.78038	−0.153331
$973$	9.53017	0.305523
$974$	96.9916	3.10781
$975$	−19.9893	−0.640170
$976$	−19.9249	−0.637782
$977$	6.09281	0.194926	0.0974632	−	0.995239i	$-0.468927\pi$
$977$	6.09281	0.194926	0.0974632	+	0.995239i	$0.468927\pi$
$978$	52.7505	1.68677
$979$	72.7231	2.32424
$980$	94.3726	3.01462
$981$	−20.5205	−0.655170
$982$	−18.4050	−0.587326
$983$	−9.67550	−0.308600	−0.154300	−	0.988024i	$-0.549312\pi$
$983$	−9.67550	−0.308600	−0.154300	+	0.988024i	$0.549312\pi$
$984$	28.6874	0.914520
$985$	6.47992	0.206467
$986$	−1.14599	−0.0364957
$987$	15.3764	0.489438
$988$	68.4232	2.17683
$989$	−40.0478	−1.27345
$990$	−54.8125	−1.74206
$991$	0.399953	0.0127049	0.00635246	−	0.999980i	$-0.497978\pi$
$991$	0.399953	0.0127049	0.00635246	+	0.999980i	$0.497978\pi$
$992$	−21.7541	−0.690694
$993$	27.9196	0.886001
$994$	117.489	3.72652
$995$	29.1394	0.923780
$996$	11.8446	0.375311
$997$	9.24550	0.292808	0.146404	−	0.989225i	$-0.453230\pi$
$997$	9.24550	0.292808	0.146404	+	0.989225i	$0.453230\pi$
$998$	38.0892	1.20569
$999$	−10.1069	−0.319768

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8049.2.a.c.1.8	✓	119

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8049.2.a.c.1.8	✓	119	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:	\( N \)	\(=\)	\( 8049 = 3 \cdot 2683 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8049.a (trivial)

\(f(q)\)	\(=\)	\(q-2.60392 q^{2} -1.00000 q^{3} +4.78038 q^{4} +3.66153 q^{5} +2.60392 q^{6} -3.52018 q^{7} -7.23988 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.60392 q^{2} -1.00000 q^{3} +4.78038 q^{4} +3.66153 q^{5} +2.60392 q^{6} -3.52018 q^{7} -7.23988 q^{8} +1.00000 q^{9} -9.53431 q^{10} +5.74897 q^{11} -4.78038 q^{12} +2.37776 q^{13} +9.16625 q^{14} -3.66153 q^{15} +9.29129 q^{16} -0.694695 q^{17} -2.60392 q^{18} +6.01967 q^{19} +17.5035 q^{20} +3.52018 q^{21} -14.9699 q^{22} -3.39314 q^{23} +7.23988 q^{24} +8.40678 q^{25} -6.19148 q^{26} -1.00000 q^{27} -16.8278 q^{28} -0.633517 q^{29} +9.53431 q^{30} +2.23947 q^{31} -9.71398 q^{32} -5.74897 q^{33} +1.80893 q^{34} -12.8892 q^{35} +4.78038 q^{36} +10.1069 q^{37} -15.6747 q^{38} -2.37776 q^{39} -26.5090 q^{40} +3.96241 q^{41} -9.16625 q^{42} +11.8026 q^{43} +27.4823 q^{44} +3.66153 q^{45} +8.83546 q^{46} +4.36809 q^{47} -9.29129 q^{48} +5.39164 q^{49} -21.8906 q^{50} +0.694695 q^{51} +11.3666 q^{52} -10.9508 q^{53} +2.60392 q^{54} +21.0500 q^{55} +25.4857 q^{56} -6.01967 q^{57} +1.64963 q^{58} +14.3437 q^{59} -17.5035 q^{60} -2.14448 q^{61} -5.83139 q^{62} -3.52018 q^{63} +6.71180 q^{64} +8.70623 q^{65} +14.9699 q^{66} -15.0663 q^{67} -3.32091 q^{68} +3.39314 q^{69} +33.5625 q^{70} +12.8175 q^{71} -7.23988 q^{72} -6.55787 q^{73} -26.3175 q^{74} -8.40678 q^{75} +28.7763 q^{76} -20.2374 q^{77} +6.19148 q^{78} -0.569661 q^{79} +34.0203 q^{80} +1.00000 q^{81} -10.3178 q^{82} -2.47776 q^{83} +16.8278 q^{84} -2.54365 q^{85} -30.7329 q^{86} +0.633517 q^{87} -41.6219 q^{88} +12.6497 q^{89} -9.53431 q^{90} -8.37013 q^{91} -16.2205 q^{92} -2.23947 q^{93} -11.3741 q^{94} +22.0412 q^{95} +9.71398 q^{96} -4.02220 q^{97} -14.0394 q^{98} +5.74897 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 119 q + 11 q^{2} - 119 q^{3} + 137 q^{4} + 17 q^{5} - 11 q^{6} + 10 q^{7} + 33 q^{8} + 119 q^{9}+O(q^{10}) \) 119 * q + 11 * q^2 - 119 * q^3 + 137 * q^4 + 17 * q^5 - 11 * q^6 + 10 * q^7 + 33 * q^8 + 119 * q^9	\( 119 q + 11 q^{2} - 119 q^{3} + 137 q^{4} + 17 q^{5} - 11 q^{6} + 10 q^{7} + 33 q^{8} + 119 q^{9} - 10 q^{10} + 56 q^{11} - 137 q^{12} - 37 q^{13} + 31 q^{14} - 17 q^{15} + 173 q^{16} + 17 q^{17} + 11 q^{18} + 16 q^{19} + 61 q^{20} - 10 q^{21} - 3 q^{22} + 76 q^{23} - 33 q^{24} + 134 q^{25} + 47 q^{26} - 119 q^{27} - q^{28} + 47 q^{29} + 10 q^{30} + 51 q^{31} + 87 q^{32} - 56 q^{33} + 13 q^{34} + 58 q^{35} + 137 q^{36} - 67 q^{37} + 35 q^{38} + 37 q^{39} - 40 q^{40} + 47 q^{41} - 31 q^{42} + 12 q^{43} + 148 q^{44} + 17 q^{45} + 26 q^{46} + 107 q^{47} - 173 q^{48} + 163 q^{49} + 76 q^{50} - 17 q^{51} - 57 q^{52} + 64 q^{53} - 11 q^{54} + 71 q^{55} + 91 q^{56} - 16 q^{57} + 12 q^{58} + 98 q^{59} - 61 q^{60} - 50 q^{61} + 40 q^{62} + 10 q^{63} + 245 q^{64} + 40 q^{65} + 3 q^{66} + 12 q^{67} + 75 q^{68} - 76 q^{69} - 9 q^{70} + 194 q^{71} + 33 q^{72} - 79 q^{73} + 72 q^{74} - 134 q^{75} + 12 q^{76} + 71 q^{77} - 47 q^{78} + 127 q^{79} + 148 q^{80} + 119 q^{81} - 54 q^{82} + 77 q^{83} + q^{84} - 25 q^{85} + 142 q^{86} - 47 q^{87} + q^{88} + 93 q^{89} - 10 q^{90} + 61 q^{91} + 156 q^{92} - 51 q^{93} + 16 q^{94} + 138 q^{95} - 87 q^{96} - 110 q^{97} + 96 q^{98} + 56 q^{99}+O(q^{100}) \) 119 * q + 11 * q^2 - 119 * q^3 + 137 * q^4 + 17 * q^5 - 11 * q^6 + 10 * q^7 + 33 * q^8 + 119 * q^9 - 10 * q^10 + 56 * q^11 - 137 * q^12 - 37 * q^13 + 31 * q^14 - 17 * q^15 + 173 * q^16 + 17 * q^17 + 11 * q^18 + 16 * q^19 + 61 * q^20 - 10 * q^21 - 3 * q^22 + 76 * q^23 - 33 * q^24 + 134 * q^25 + 47 * q^26 - 119 * q^27 - q^28 + 47 * q^29 + 10 * q^30 + 51 * q^31 + 87 * q^32 - 56 * q^33 + 13 * q^34 + 58 * q^35 + 137 * q^36 - 67 * q^37 + 35 * q^38 + 37 * q^39 - 40 * q^40 + 47 * q^41 - 31 * q^42 + 12 * q^43 + 148 * q^44 + 17 * q^45 + 26 * q^46 + 107 * q^47 - 173 * q^48 + 163 * q^49 + 76 * q^50 - 17 * q^51 - 57 * q^52 + 64 * q^53 - 11 * q^54 + 71 * q^55 + 91 * q^56 - 16 * q^57 + 12 * q^58 + 98 * q^59 - 61 * q^60 - 50 * q^61 + 40 * q^62 + 10 * q^63 + 245 * q^64 + 40 * q^65 + 3 * q^66 + 12 * q^67 + 75 * q^68 - 76 * q^69 - 9 * q^70 + 194 * q^71 + 33 * q^72 - 79 * q^73 + 72 * q^74 - 134 * q^75 + 12 * q^76 + 71 * q^77 - 47 * q^78 + 127 * q^79 + 148 * q^80 + 119 * q^81 - 54 * q^82 + 77 * q^83 + q^84 - 25 * q^85 + 142 * q^86 - 47 * q^87 + q^88 + 93 * q^89 - 10 * q^90 + 61 * q^91 + 156 * q^92 - 51 * q^93 + 16 * q^94 + 138 * q^95 - 87 * q^96 - 110 * q^97 + 96 * q^98 + 56 * q^99

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