LMFDB - Embedded newform 8023.2.a.e.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8023,2,Mod(1,8023)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8023, 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("8023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8023 = 71 \cdot 113 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8023.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:	$64.0639775417$
Analytic rank:	$0$
Dimension:	$172$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	8023.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.68206 q^{2} +0.545640 q^{3} +5.19345 q^{4} -2.53261 q^{5} -1.46344 q^{6} -1.66793 q^{7} -8.56503 q^{8} -2.70228 q^{9} +O(q^{10})$	\(q-2.68206 q^{2} +0.545640 q^{3} +5.19345 q^{4} -2.53261 q^{5} -1.46344 q^{6} -1.66793 q^{7} -8.56503 q^{8} -2.70228 q^{9} +6.79262 q^{10} +1.62257 q^{11} +2.83375 q^{12} -1.22667 q^{13} +4.47349 q^{14} -1.38189 q^{15} +12.5850 q^{16} +2.77094 q^{17} +7.24767 q^{18} +7.89446 q^{19} -13.1530 q^{20} -0.910090 q^{21} -4.35182 q^{22} +0.744552 q^{23} -4.67342 q^{24} +1.41413 q^{25} +3.29000 q^{26} -3.11139 q^{27} -8.66232 q^{28} +0.401005 q^{29} +3.70633 q^{30} -7.42019 q^{31} -16.6237 q^{32} +0.885337 q^{33} -7.43183 q^{34} +4.22422 q^{35} -14.0341 q^{36} -6.43776 q^{37} -21.1734 q^{38} -0.669320 q^{39} +21.6919 q^{40} +4.08260 q^{41} +2.44092 q^{42} +2.42635 q^{43} +8.42672 q^{44} +6.84382 q^{45} -1.99693 q^{46} +7.67302 q^{47} +6.86689 q^{48} -4.21801 q^{49} -3.79277 q^{50} +1.51194 q^{51} -6.37065 q^{52} +8.86643 q^{53} +8.34494 q^{54} -4.10933 q^{55} +14.2859 q^{56} +4.30753 q^{57} -1.07552 q^{58} +9.40106 q^{59} -7.17680 q^{60} -8.70008 q^{61} +19.9014 q^{62} +4.50721 q^{63} +19.4159 q^{64} +3.10668 q^{65} -2.37453 q^{66} -8.60662 q^{67} +14.3907 q^{68} +0.406258 q^{69} -11.3296 q^{70} -1.00000 q^{71} +23.1451 q^{72} -8.34498 q^{73} +17.2665 q^{74} +0.771604 q^{75} +40.9995 q^{76} -2.70633 q^{77} +1.79516 q^{78} -8.81396 q^{79} -31.8730 q^{80} +6.40913 q^{81} -10.9498 q^{82} +8.58464 q^{83} -4.72651 q^{84} -7.01772 q^{85} -6.50761 q^{86} +0.218804 q^{87} -13.8973 q^{88} -15.5694 q^{89} -18.3555 q^{90} +2.04600 q^{91} +3.86680 q^{92} -4.04875 q^{93} -20.5795 q^{94} -19.9936 q^{95} -9.07058 q^{96} +17.3216 q^{97} +11.3129 q^{98} -4.38462 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 172 q + 24 q^{2} + 18 q^{3} + 180 q^{4} + 28 q^{5} + 16 q^{6} + 4 q^{7} + 72 q^{8} + 198 q^{9}+O(q^{10}) $ 172 * q + 24 * q^2 + 18 * q^3 + 180 * q^4 + 28 * q^5 + 16 * q^6 + 4 * q^7 + 72 * q^8 + 198 * q^9	\( 172 q + 24 q^{2} + 18 q^{3} + 180 q^{4} + 28 q^{5} + 16 q^{6} + 4 q^{7} + 72 q^{8} + 198 q^{9} + 14 q^{10} + 20 q^{11} + 54 q^{12} + 36 q^{13} + 26 q^{14} + 32 q^{15} + 196 q^{16} + 123 q^{17} + 74 q^{18} + 20 q^{19} + 70 q^{20} + 37 q^{21} + 11 q^{22} + 22 q^{23} + 62 q^{24} + 210 q^{25} + 50 q^{26} + 69 q^{27} + 42 q^{28} + 58 q^{29} + 36 q^{30} + 10 q^{31} + 168 q^{32} + 124 q^{33} + 5 q^{34} + 59 q^{35} + 192 q^{36} + 40 q^{37} + 58 q^{38} + 15 q^{39} + 7 q^{40} + 155 q^{41} - 6 q^{42} + 19 q^{43} + 22 q^{44} + 76 q^{45} + q^{46} + 71 q^{47} + 144 q^{48} + 206 q^{49} + 126 q^{50} + 33 q^{51} + 71 q^{52} + 101 q^{53} + 92 q^{54} - 2 q^{55} + 57 q^{56} + 114 q^{57} + 4 q^{58} + 71 q^{59} + 38 q^{60} + 50 q^{61} + 86 q^{62} + 14 q^{63} + 240 q^{64} + 143 q^{65} + 21 q^{66} + 8 q^{67} + 192 q^{68} + 41 q^{69} - 12 q^{70} - 172 q^{71} + 156 q^{72} + 128 q^{73} + 30 q^{74} + 72 q^{75} + 74 q^{76} + 127 q^{77} + 107 q^{78} + 2 q^{79} + 50 q^{80} + 236 q^{81} + 42 q^{82} + 140 q^{83} + 71 q^{84} + 55 q^{85} + 46 q^{86} + 100 q^{87} - 31 q^{88} + 215 q^{89} - 7 q^{90} + 22 q^{91} - 15 q^{92} + 60 q^{93} + 5 q^{94} + 74 q^{95} + 182 q^{96} + 120 q^{97} + 164 q^{98} + 60 q^{99}+O(q^{100}) \) 172 * q + 24 * q^2 + 18 * q^3 + 180 * q^4 + 28 * q^5 + 16 * q^6 + 4 * q^7 + 72 * q^8 + 198 * q^9 + 14 * q^10 + 20 * q^11 + 54 * q^12 + 36 * q^13 + 26 * q^14 + 32 * q^15 + 196 * q^16 + 123 * q^17 + 74 * q^18 + 20 * q^19 + 70 * q^20 + 37 * q^21 + 11 * q^22 + 22 * q^23 + 62 * q^24 + 210 * q^25 + 50 * q^26 + 69 * q^27 + 42 * q^28 + 58 * q^29 + 36 * q^30 + 10 * q^31 + 168 * q^32 + 124 * q^33 + 5 * q^34 + 59 * q^35 + 192 * q^36 + 40 * q^37 + 58 * q^38 + 15 * q^39 + 7 * q^40 + 155 * q^41 - 6 * q^42 + 19 * q^43 + 22 * q^44 + 76 * q^45 + q^46 + 71 * q^47 + 144 * q^48 + 206 * q^49 + 126 * q^50 + 33 * q^51 + 71 * q^52 + 101 * q^53 + 92 * q^54 - 2 * q^55 + 57 * q^56 + 114 * q^57 + 4 * q^58 + 71 * q^59 + 38 * q^60 + 50 * q^61 + 86 * q^62 + 14 * q^63 + 240 * q^64 + 143 * q^65 + 21 * q^66 + 8 * q^67 + 192 * q^68 + 41 * q^69 - 12 * q^70 - 172 * q^71 + 156 * q^72 + 128 * q^73 + 30 * q^74 + 72 * q^75 + 74 * q^76 + 127 * q^77 + 107 * q^78 + 2 * q^79 + 50 * q^80 + 236 * q^81 + 42 * q^82 + 140 * q^83 + 71 * q^84 + 55 * q^85 + 46 * q^86 + 100 * q^87 - 31 * q^88 + 215 * q^89 - 7 * q^90 + 22 * q^91 - 15 * q^92 + 60 * q^93 + 5 * q^94 + 74 * q^95 + 182 * q^96 + 120 * q^97 + 164 * q^98 + 60 * 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 $

$2$	−2.68206	−1.89650	−0.948252	−	0.317520i	$-0.897150\pi$
$2$	−2.68206	−1.89650	−0.948252	+	0.317520i	$0.897150\pi$
$3$	0.545640	0.315025	0.157513	−	0.987517i	$-0.449652\pi$
$3$	0.545640	0.315025	0.157513	+	0.987517i	$0.449652\pi$
$4$	5.19345	2.59673
$5$	−2.53261	−1.13262	−0.566309	−	0.824193i	$-0.691629\pi$
$5$	−2.53261	−1.13262	−0.566309	+	0.824193i	$0.691629\pi$
$6$	−1.46344	−0.597447
$7$	−1.66793	−0.630419	−0.315209	−	0.949022i	$-0.602075\pi$
$7$	−1.66793	−0.630419	−0.315209	+	0.949022i	$0.602075\pi$
$8$	−8.56503	−3.02819
$9$	−2.70228	−0.900759
$10$	6.79262	2.14802
$11$	1.62257	0.489222	0.244611	−	0.969621i	$-0.421340\pi$
$11$	1.62257	0.489222	0.244611	+	0.969621i	$0.421340\pi$
$12$	2.83375	0.818034
$13$	−1.22667	−0.340217	−0.170109	−	0.985425i	$-0.554412\pi$
$13$	−1.22667	−0.340217	−0.170109	+	0.985425i	$0.554412\pi$
$14$	4.47349	1.19559
$15$	−1.38189	−0.356804
$16$	12.5850	3.14626
$17$	2.77094	0.672051	0.336026	−	0.941853i	$-0.390917\pi$
$17$	2.77094	0.672051	0.336026	+	0.941853i	$0.390917\pi$
$18$	7.24767	1.70829
$19$	7.89446	1.81111	0.905556	−	0.424226i	$-0.139454\pi$
$19$	7.89446	1.81111	0.905556	+	0.424226i	$0.139454\pi$
$20$	−13.1530	−2.94110
$21$	−0.910090	−0.198598
$22$	−4.35182	−0.927811
$23$	0.744552	0.155250	0.0776249	−	0.996983i	$-0.475266\pi$
$23$	0.744552	0.155250	0.0776249	+	0.996983i	$0.475266\pi$
$24$	−4.67342	−0.953958
$25$	1.41413	0.282825
$26$	3.29000	0.645223
$27$	−3.11139	−0.598787
$28$	−8.66232	−1.63702
$29$	0.401005	0.0744647	0.0372323	−	0.999307i	$-0.488146\pi$
$29$	0.401005	0.0744647	0.0372323	+	0.999307i	$0.488146\pi$
$30$	3.70633	0.676679
$31$	−7.42019	−1.33271	−0.666353	−	0.745637i	$-0.732145\pi$
$31$	−7.42019	−1.33271	−0.666353	+	0.745637i	$0.732145\pi$
$32$	−16.6237	−2.93869
$33$	0.885337	0.154117
$34$	−7.43183	−1.27455
$35$	4.22422	0.714024
$36$	−14.0341	−2.33902
$37$	−6.43776	−1.05836	−0.529181	−	0.848509i	$-0.677501\pi$
$37$	−6.43776	−1.05836	−0.529181	+	0.848509i	$0.677501\pi$
$38$	−21.1734	−3.43478
$39$	−0.669320	−0.107177
$40$	21.6919	3.42979
$41$	4.08260	0.637595	0.318797	−	0.947823i	$-0.396721\pi$
$41$	4.08260	0.637595	0.318797	+	0.947823i	$0.396721\pi$
$42$	2.44092	0.376642
$43$	2.42635	0.370015	0.185007	−	0.982737i	$-0.440769\pi$
$43$	2.42635	0.370015	0.185007	+	0.982737i	$0.440769\pi$
$44$	8.42672	1.27038
$45$	6.84382	1.02022
$46$	−1.99693	−0.294432
$47$	7.67302	1.11922	0.559612	−	0.828754i	$-0.310950\pi$
$47$	7.67302	1.11922	0.559612	+	0.828754i	$0.310950\pi$
$48$	6.86689	0.991151
$49$	−4.21801	−0.602572
$50$	−3.79277	−0.536379
$51$	1.51194	0.211713
$52$	−6.37065	−0.883450
$53$	8.86643	1.21790	0.608949	−	0.793209i	$-0.291591\pi$
$53$	8.86643	1.21790	0.608949	+	0.793209i	$0.291591\pi$
$54$	8.34494	1.13560
$55$	−4.10933	−0.554102
$56$	14.2859	1.90903
$57$	4.30753	0.570546
$58$	−1.07552	−0.141223
$59$	9.40106	1.22391	0.611957	−	0.790891i	$-0.290382\pi$
$59$	9.40106	1.22391	0.611957	+	0.790891i	$0.290382\pi$
$60$	−7.17680	−0.926521
$61$	−8.70008	−1.11393	−0.556965	−	0.830536i	$-0.688034\pi$
$61$	−8.70008	−1.11393	−0.556965	+	0.830536i	$0.688034\pi$
$62$	19.9014	2.52748
$63$	4.50721	0.567855
$64$	19.4159	2.42698
$65$	3.10668	0.385336
$66$	−2.37453	−0.292284
$67$	−8.60662	−1.05147	−0.525733	−	0.850650i	$-0.676209\pi$
$67$	−8.60662	−1.05147	−0.525733	+	0.850650i	$0.676209\pi$
$68$	14.3907	1.74513
$69$	0.406258	0.0489077
$70$	−11.3296	−1.35415
$71$	−1.00000	−0.118678
$71$	−1.00000	−0.118678
$72$	23.1451	2.72767
$73$	−8.34498	−0.976706	−0.488353	−	0.872646i	$-0.662402\pi$
$73$	−8.34498	−0.976706	−0.488353	+	0.872646i	$0.662402\pi$
$74$	17.2665	2.00719
$75$	0.771604	0.0890972
$76$	40.9995	4.70296
$77$	−2.70633	−0.308415
$78$	1.79516	0.203262
$79$	−8.81396	−0.991648	−0.495824	−	0.868423i	$-0.665134\pi$
$79$	−8.81396	−0.991648	−0.495824	+	0.868423i	$0.665134\pi$
$80$	−31.8730	−3.56351
$81$	6.40913	0.712126
$82$	−10.9498	−1.20920
$83$	8.58464	0.942287	0.471143	−	0.882057i	$-0.343841\pi$
$83$	8.58464	0.942287	0.471143	+	0.882057i	$0.343841\pi$
$84$	−4.72651	−0.515704
$85$	−7.01772	−0.761178
$86$	−6.50761	−0.701734
$87$	0.218804	0.0234583
$88$	−13.8973	−1.48146
$89$	−15.5694	−1.65035	−0.825177	−	0.564874i	$-0.808925\pi$
$89$	−15.5694	−1.65035	−0.825177	+	0.564874i	$0.808925\pi$
$90$	−18.3555	−1.93484
$91$	2.04600	0.214479
$92$	3.86680	0.403141
$93$	−4.04875	−0.419836
$94$	−20.5795	−2.12261
$95$	−19.9936	−2.05130
$96$	−9.07058	−0.925762
$97$	17.3216	1.75874	0.879369	−	0.476141i	$-0.157965\pi$
$97$	17.3216	1.75874	0.879369	+	0.476141i	$0.157965\pi$
$98$	11.3129	1.14278
$99$	−4.38462	−0.440671
$100$	7.34420	0.734420
$101$	−11.4298	−1.13730	−0.568652	−	0.822578i	$-0.692535\pi$
$101$	−11.4298	−1.13730	−0.568652	+	0.822578i	$0.692535\pi$
$102$	−4.05510	−0.401515
$103$	8.45584	0.833179	0.416589	−	0.909095i	$-0.363225\pi$
$103$	8.45584	0.833179	0.416589	+	0.909095i	$0.363225\pi$
$104$	10.5065	1.03024
$105$	2.30491	0.224936
$106$	−23.7803	−2.30975
$107$	15.9701	1.54389	0.771944	−	0.635690i	$-0.219284\pi$
$107$	15.9701	1.54389	0.771944	+	0.635690i	$0.219284\pi$
$108$	−16.1589	−1.55489
$109$	−19.8939	−1.90549	−0.952745	−	0.303771i	$-0.901754\pi$
$109$	−19.8939	−1.90549	−0.952745	+	0.303771i	$0.901754\pi$
$110$	11.0215	1.05086
$111$	−3.51270	−0.333411
$112$	−20.9910	−1.98346
$113$	1.00000	0.0940721
$113$	1.00000	0.0940721
$114$	−11.5531	−1.08204
$115$	−1.88566	−0.175839
$116$	2.08260	0.193364
$117$	3.31480	0.306454
$118$	−25.2142	−2.32116
$119$	−4.62174	−0.423674
$120$	11.8360	1.08047
$121$	−8.36728	−0.760662
$122$	23.3341	2.11257
$123$	2.22763	0.200858
$124$	−38.5364	−3.46067
$125$	9.08163	0.812285
$126$	−12.0886	−1.07694
$127$	−4.47103	−0.396740	−0.198370	−	0.980127i	$-0.563565\pi$
$127$	−4.47103	−0.396740	−0.198370	+	0.980127i	$0.563565\pi$
$128$	−18.8270	−1.66409
$129$	1.32391	0.116564
$130$	−8.33231	−0.730792
$131$	−16.5459	−1.44563	−0.722813	−	0.691044i	$-0.757151\pi$
$131$	−16.5459	−1.44563	−0.722813	+	0.691044i	$0.757151\pi$
$132$	4.59795	0.400201
$133$	−13.1674	−1.14176
$134$	23.0835	1.99411
$135$	7.87995	0.678198
$136$	−23.7332	−2.03510
$137$	10.9051	0.931688	0.465844	−	0.884867i	$-0.345751\pi$
$137$	10.9051	0.931688	0.465844	+	0.884867i	$0.345751\pi$
$138$	−1.08961	−0.0927535
$139$	−15.0768	−1.27880	−0.639399	−	0.768875i	$-0.720817\pi$
$139$	−15.0768	−1.27880	−0.639399	+	0.768875i	$0.720817\pi$
$140$	21.9383	1.85412
$141$	4.18671	0.352584
$142$	2.68206	0.225074
$143$	−1.99035	−0.166442
$144$	−34.0082	−2.83402
$145$	−1.01559	−0.0843401
$146$	22.3817	1.85233
$147$	−2.30151	−0.189826
$148$	−33.4342	−2.74827
$149$	−1.52398	−0.124849	−0.0624247	−	0.998050i	$-0.519883\pi$
$149$	−1.52398	−0.124849	−0.0624247	+	0.998050i	$0.519883\pi$
$150$	−2.06949	−0.168973
$151$	−1.06390	−0.0865790	−0.0432895	−	0.999063i	$-0.513784\pi$
$151$	−1.06390	−0.0865790	−0.0432895	+	0.999063i	$0.513784\pi$
$152$	−67.6162	−5.48440
$153$	−7.48785	−0.605356
$154$	7.25854	0.584910
$155$	18.7925	1.50945
$156$	−3.47608	−0.278309
$157$	3.81625	0.304570	0.152285	−	0.988337i	$-0.451337\pi$
$157$	3.81625	0.304570	0.152285	+	0.988337i	$0.451337\pi$
$158$	23.6396	1.88066
$159$	4.83788	0.383669
$160$	42.1015	3.32842
$161$	−1.24186	−0.0978724
$162$	−17.1897	−1.35055
$163$	−4.73627	−0.370974	−0.185487	−	0.982647i	$-0.559386\pi$
$163$	−4.73627	−0.370974	−0.185487	+	0.982647i	$0.559386\pi$
$164$	21.2028	1.65566
$165$	−2.24222	−0.174556
$166$	−23.0245	−1.78705
$167$	−5.46862	−0.423175	−0.211587	−	0.977359i	$-0.567863\pi$
$167$	−5.46862	−0.423175	−0.211587	+	0.977359i	$0.567863\pi$
$168$	7.79495	0.601393
$169$	−11.4953	−0.884252
$170$	18.8219	1.44358
$171$	−21.3330	−1.63138
$172$	12.6011	0.960826
$173$	−23.5517	−1.79060	−0.895300	−	0.445463i	$-0.853039\pi$
$173$	−23.5517	−1.79060	−0.895300	+	0.445463i	$0.853039\pi$
$174$	−0.586846	−0.0444887
$175$	−2.35867	−0.178298
$176$	20.4200	1.53922
$177$	5.12960	0.385564
$178$	41.7581	3.12990
$179$	−15.0758	−1.12682	−0.563408	−	0.826179i	$-0.690510\pi$
$179$	−15.0758	−1.12682	−0.563408	+	0.826179i	$0.690510\pi$
$180$	35.5430	2.64922
$181$	7.14238	0.530889	0.265445	−	0.964126i	$-0.414481\pi$
$181$	7.14238	0.530889	0.265445	+	0.964126i	$0.414481\pi$
$182$	−5.48750	−0.406761
$183$	−4.74711	−0.350916
$184$	−6.37711	−0.470127
$185$	16.3044	1.19872
$186$	10.8590	0.796220
$187$	4.49603	0.328782
$188$	39.8494	2.90632
$189$	5.18958	0.377487
$190$	53.6241	3.89030
$191$	−7.34629	−0.531559	−0.265779	−	0.964034i	$-0.585629\pi$
$191$	−7.34629	−0.531559	−0.265779	+	0.964034i	$0.585629\pi$
$192$	10.5941	0.764561
$193$	12.2328	0.880537	0.440269	−	0.897866i	$-0.354883\pi$
$193$	12.2328	0.880537	0.440269	+	0.897866i	$0.354883\pi$
$194$	−46.4575	−3.33545
$195$	1.69513	0.121391
$196$	−21.9060	−1.56471
$197$	−5.52438	−0.393596	−0.196798	−	0.980444i	$-0.563054\pi$
$197$	−5.52438	−0.393596	−0.196798	+	0.980444i	$0.563054\pi$
$198$	11.7598	0.835734
$199$	22.9700	1.62830	0.814150	−	0.580655i	$-0.197203\pi$
$199$	22.9700	1.62830	0.814150	+	0.580655i	$0.197203\pi$
$200$	−12.1120	−0.856450
$201$	−4.69611	−0.331238
$202$	30.6553	2.15690
$203$	−0.668848	−0.0469439
$204$	7.85216	0.549761
$205$	−10.3396	−0.722152
$206$	−22.6791	−1.58013
$207$	−2.01199	−0.139843
$208$	−15.4377	−1.07041
$209$	12.8093	0.886036
$210$	−6.18190	−0.426591
$211$	26.0002	1.78993	0.894964	−	0.446139i	$-0.147201\pi$
$211$	26.0002	1.78993	0.894964	+	0.446139i	$0.147201\pi$
$212$	46.0474	3.16255
$213$	−0.545640	−0.0373866
$214$	−42.8328	−2.92799
$215$	−6.14500	−0.419086
$216$	26.6491	1.81324
$217$	12.3764	0.840162
$218$	53.3567	3.61377
$219$	−4.55336	−0.307687
$220$	−21.3416	−1.43885
$221$	−3.39903	−0.228643
$222$	9.42127	0.632314
$223$	18.1767	1.21720	0.608600	−	0.793477i	$-0.291732\pi$
$223$	18.1767	1.21720	0.608600	+	0.793477i	$0.291732\pi$
$224$	27.7273	1.85261
$225$	−3.82136	−0.254758
$226$	−2.68206	−0.178408
$227$	21.4412	1.42310	0.711551	−	0.702634i	$-0.247993\pi$
$227$	21.4412	1.42310	0.711551	+	0.702634i	$0.247993\pi$
$228$	22.3710	1.48155
$229$	−2.58101	−0.170558	−0.0852791	−	0.996357i	$-0.527178\pi$
$229$	−2.58101	−0.170558	−0.0852791	+	0.996357i	$0.527178\pi$
$230$	5.05746	0.333479
$231$	−1.47668	−0.0971585
$232$	−3.43462	−0.225494
$233$	12.9159	0.846150	0.423075	−	0.906095i	$-0.360951\pi$
$233$	12.9159	0.846150	0.423075	+	0.906095i	$0.360951\pi$
$234$	−8.89050	−0.581190
$235$	−19.4328	−1.26766
$236$	48.8240	3.17817
$237$	−4.80925	−0.312394
$238$	12.3958	0.803499
$239$	14.6094	0.945006	0.472503	−	0.881329i	$-0.343351\pi$
$239$	14.6094	0.945006	0.472503	+	0.881329i	$0.343351\pi$
$240$	−17.3912	−1.12260
$241$	−11.1734	−0.719742	−0.359871	−	0.933002i	$-0.617179\pi$
$241$	−11.1734	−0.719742	−0.359871	+	0.933002i	$0.617179\pi$
$242$	22.4416	1.44260
$243$	12.8313	0.823125
$244$	−45.1834	−2.89257
$245$	10.6826	0.682485
$246$	−5.97463	−0.380929
$247$	−9.68389	−0.616171
$248$	63.5541	4.03569
$249$	4.68412	0.296844
$250$	−24.3575	−1.54050
$251$	−0.693580	−0.0437784	−0.0218892	−	0.999760i	$-0.506968\pi$
$251$	−0.693580	−0.0437784	−0.0218892	+	0.999760i	$0.506968\pi$
$252$	23.4080	1.47456
$253$	1.20809	0.0759517
$254$	11.9916	0.752418
$255$	−3.82915	−0.239790
$256$	11.6635	0.728966
$257$	−12.4626	−0.777398	−0.388699	−	0.921365i	$-0.627075\pi$
$257$	−12.4626	−0.777398	−0.388699	+	0.921365i	$0.627075\pi$
$258$	−3.55081	−0.221064
$259$	10.7377	0.667211
$260$	16.1344	1.00061
$261$	−1.08363	−0.0670747
$262$	44.3772	2.74163
$263$	6.31352	0.389308	0.194654	−	0.980872i	$-0.437642\pi$
$263$	6.31352	0.389308	0.194654	+	0.980872i	$0.437642\pi$
$264$	−7.58294	−0.466697
$265$	−22.4552	−1.37941
$266$	35.3158	2.16535
$267$	−8.49529	−0.519903
$268$	−44.6980	−2.73037
$269$	−11.2962	−0.688740	−0.344370	−	0.938834i	$-0.611908\pi$
$269$	−11.2962	−0.688740	−0.344370	+	0.938834i	$0.611908\pi$
$270$	−21.1345	−1.28620
$271$	−3.62851	−0.220416	−0.110208	−	0.993909i	$-0.535152\pi$
$271$	−3.62851	−0.220416	−0.110208	+	0.993909i	$0.535152\pi$
$272$	34.8723	2.11445
$273$	1.11638	0.0675664
$274$	−29.2482	−1.76695
$275$	2.29451	0.138364
$276$	2.10988	0.127000
$277$	5.20372	0.312661	0.156331	−	0.987705i	$-0.450033\pi$
$277$	5.20372	0.312661	0.156331	+	0.987705i	$0.450033\pi$
$278$	40.4369	2.42524
$279$	20.0514	1.20045
$280$	−36.1806	−2.16220
$281$	−27.0095	−1.61125	−0.805626	−	0.592425i	$-0.798171\pi$
$281$	−27.0095	−1.61125	−0.805626	+	0.592425i	$0.798171\pi$
$282$	−11.2290	−0.668677
$283$	4.84180	0.287815	0.143907	−	0.989591i	$-0.454033\pi$
$283$	4.84180	0.287815	0.143907	+	0.989591i	$0.454033\pi$
$284$	−5.19345	−0.308175
$285$	−10.9093	−0.646212
$286$	5.33825	0.315657
$287$	−6.80949	−0.401951
$288$	44.9220	2.64705
$289$	−9.32190	−0.548347
$290$	2.72387	0.159951
$291$	9.45133	0.554047
$292$	−43.3392	−2.53624
$293$	−13.7725	−0.804599	−0.402300	−	0.915508i	$-0.631789\pi$
$293$	−13.7725	−0.804599	−0.402300	+	0.915508i	$0.631789\pi$
$294$	6.17280	0.360005
$295$	−23.8093	−1.38623
$296$	55.1396	3.20492
$297$	−5.04844	−0.292940
$298$	4.08741	0.236777
$299$	−0.913320	−0.0528187
$300$	4.00729	0.231361
$301$	−4.04698	−0.233264
$302$	2.85345	0.164197
$303$	−6.23654	−0.358280
$304$	99.3519	5.69822
$305$	22.0339	1.26166
$306$	20.0829	1.14806
$307$	−13.8260	−0.789090	−0.394545	−	0.918877i	$-0.629098\pi$
$307$	−13.8260	−0.789090	−0.394545	+	0.918877i	$0.629098\pi$
$308$	−14.0552	−0.800868
$309$	4.61385	0.262472
$310$	−50.4025	−2.86267
$311$	13.9369	0.790287	0.395144	−	0.918619i	$-0.370695\pi$
$311$	13.9369	0.790287	0.395144	+	0.918619i	$0.370695\pi$
$312$	5.73275	0.324553
$313$	−16.4572	−0.930214	−0.465107	−	0.885254i	$-0.653984\pi$
$313$	−16.4572	−0.930214	−0.465107	+	0.885254i	$0.653984\pi$
$314$	−10.2354	−0.577618
$315$	−11.4150	−0.643164
$316$	−45.7749	−2.57504
$317$	1.37402	0.0771729	0.0385864	−	0.999255i	$-0.487715\pi$
$317$	1.37402	0.0771729	0.0385864	+	0.999255i	$0.487715\pi$
$318$	−12.9755	−0.727629
$319$	0.650657	0.0364298
$320$	−49.1728	−2.74884
$321$	8.71393	0.486364
$322$	3.33075	0.185615
$323$	21.8751	1.21716
$324$	33.2855	1.84919
$325$	−1.73467	−0.0962220
$326$	12.7030	0.703553
$327$	−10.8549	−0.600278
$328$	−34.9676	−1.93076
$329$	−12.7981	−0.705580
$330$	6.01376	0.331047
$331$	14.2757	0.784663	0.392332	−	0.919824i	$-0.371669\pi$
$331$	14.2757	0.784663	0.392332	+	0.919824i	$0.371669\pi$
$332$	44.5839	2.44686
$333$	17.3966	0.953328
$334$	14.6672	0.802552
$335$	21.7972	1.19091
$336$	−11.4535	−0.624840
$337$	16.3169	0.888840	0.444420	−	0.895819i	$-0.353410\pi$
$337$	16.3169	0.888840	0.444420	+	0.895819i	$0.353410\pi$
$338$	30.8310	1.67699
$339$	0.545640	0.0296351
$340$	−36.4462	−1.97657
$341$	−12.0397	−0.651989
$342$	57.2164	3.09391
$343$	18.7109	1.01029
$344$	−20.7817	−1.12048
$345$	−1.02889	−0.0553937
$346$	63.1670	3.39588
$347$	8.63799	0.463711	0.231856	−	0.972750i	$-0.425520\pi$
$347$	8.63799	0.463711	0.231856	+	0.972750i	$0.425520\pi$
$348$	1.13635	0.0609147
$349$	19.9558	1.06821	0.534106	−	0.845417i	$-0.320648\pi$
$349$	19.9558	1.06821	0.534106	+	0.845417i	$0.320648\pi$
$350$	6.32609	0.338144
$351$	3.81665	0.203718
$352$	−26.9731	−1.43767
$353$	29.2298	1.55575	0.777873	−	0.628422i	$-0.216299\pi$
$353$	29.2298	1.55575	0.777873	+	0.628422i	$0.216299\pi$
$354$	−13.7579	−0.731224
$355$	2.53261	0.134417
$356$	−80.8590	−4.28552
$357$	−2.52180	−0.133468
$358$	40.4341	2.13701
$359$	15.2481	0.804766	0.402383	−	0.915471i	$-0.368182\pi$
$359$	15.2481	0.804766	0.402383	+	0.915471i	$0.368182\pi$
$360$	−58.6175	−3.08941
$361$	43.3224	2.28013
$362$	−19.1563	−1.00683
$363$	−4.56552	−0.239628
$364$	10.6258	0.556944
$365$	21.1346	1.10624
$366$	12.7320	0.665514
$367$	−14.5165	−0.757754	−0.378877	−	0.925447i	$-0.623690\pi$
$367$	−14.5165	−0.757754	−0.378877	+	0.925447i	$0.623690\pi$
$368$	9.37021	0.488456
$369$	−11.0323	−0.574319
$370$	−43.7293	−2.27338
$371$	−14.7886	−0.767786
$372$	−21.0270	−1.09020
$373$	−25.8301	−1.33743	−0.668716	−	0.743518i	$-0.733156\pi$
$373$	−25.8301	−1.33743	−0.668716	+	0.743518i	$0.733156\pi$
$374$	−12.0586	−0.623537
$375$	4.95530	0.255891
$376$	−65.7196	−3.38923
$377$	−0.491900	−0.0253342
$378$	−13.9188	−0.715905
$379$	23.7007	1.21742	0.608712	−	0.793391i	$-0.291687\pi$
$379$	23.7007	1.21742	0.608712	+	0.793391i	$0.291687\pi$
$380$	−103.836	−5.32666
$381$	−2.43957	−0.124983
$382$	19.7032	1.00810
$383$	−22.4019	−1.14469	−0.572343	−	0.820014i	$-0.693965\pi$
$383$	−22.4019	−1.14469	−0.572343	+	0.820014i	$0.693965\pi$
$384$	−10.2728	−0.524230
$385$	6.85408	0.349316
$386$	−32.8092	−1.66994
$387$	−6.55667	−0.333294
$388$	89.9586	4.56696
$389$	−10.4407	−0.529365	−0.264683	−	0.964336i	$-0.585267\pi$
$389$	−10.4407	−0.529365	−0.264683	+	0.964336i	$0.585267\pi$
$390$	−4.54644	−0.230218
$391$	2.06311	0.104336
$392$	36.1273	1.82471
$393$	−9.02813	−0.455409
$394$	14.8167	0.746456
$395$	22.3224	1.12316
$396$	−22.7713	−1.14430
$397$	26.7782	1.34396	0.671981	−	0.740569i	$-0.265444\pi$
$397$	26.7782	1.34396	0.671981	+	0.740569i	$0.265444\pi$
$398$	−61.6069	−3.08808
$399$	−7.18467	−0.359683
$400$	17.7968	0.889841
$401$	−16.8370	−0.840801	−0.420400	−	0.907339i	$-0.638110\pi$
$401$	−16.8370	−0.840801	−0.420400	+	0.907339i	$0.638110\pi$
$402$	12.5953	0.628195
$403$	9.10212	0.453409
$404$	−59.3599	−2.95327
$405$	−16.2318	−0.806567
$406$	1.79389	0.0890293
$407$	−10.4457	−0.517774
$408$	−12.9498	−0.641109
$409$	18.3003	0.904893	0.452446	−	0.891792i	$-0.350551\pi$
$409$	18.3003	0.904893	0.452446	+	0.891792i	$0.350551\pi$
$410$	27.7315	1.36956
$411$	5.95027	0.293505
$412$	43.9150	2.16354
$413$	−15.6803	−0.771578
$414$	5.39627	0.265212
$415$	−21.7416	−1.06725
$416$	20.3919	0.999793
$417$	−8.22651	−0.402854
$418$	−34.3553	−1.68037
$419$	−15.3045	−0.747671	−0.373836	−	0.927495i	$-0.621958\pi$
$419$	−15.3045	−0.747671	−0.373836	+	0.927495i	$0.621958\pi$
$420$	11.9704	0.584096
$421$	31.5918	1.53969	0.769845	−	0.638231i	$-0.220334\pi$
$421$	31.5918	1.53969	0.769845	+	0.638231i	$0.220334\pi$
$422$	−69.7341	−3.39460
$423$	−20.7346	−1.00815
$424$	−75.9412	−3.68803
$425$	3.91846	0.190073
$426$	1.46344	0.0709039
$427$	14.5111	0.702243
$428$	82.9400	4.00905
$429$	−1.08602	−0.0524334
$430$	16.4813	0.794797
$431$	−24.9362	−1.20113	−0.600566	−	0.799575i	$-0.705058\pi$
$431$	−24.9362	−1.20113	−0.600566	+	0.799575i	$0.705058\pi$
$432$	−39.1569	−1.88394
$433$	−11.5275	−0.553975	−0.276988	−	0.960873i	$-0.589336\pi$
$433$	−11.5275	−0.553975	−0.276988	+	0.960873i	$0.589336\pi$
$434$	−33.1942	−1.59337
$435$	−0.554146	−0.0265693
$436$	−103.318	−4.94803
$437$	5.87784	0.281175
$438$	12.2124	0.583530
$439$	−2.68907	−0.128342	−0.0641711	−	0.997939i	$-0.520440\pi$
$439$	−2.68907	−0.128342	−0.0641711	+	0.997939i	$0.520440\pi$
$440$	35.1965	1.67793
$441$	11.3982	0.542772
$442$	9.11640	0.433623
$443$	24.1553	1.14765	0.573826	−	0.818977i	$-0.305459\pi$
$443$	24.1553	1.14765	0.573826	+	0.818977i	$0.305459\pi$
$444$	−18.2430	−0.865776
$445$	39.4313	1.86922
$446$	−48.7509	−2.30842
$447$	−0.831545	−0.0393307
$448$	−32.3843	−1.53001
$449$	29.7657	1.40473	0.702365	−	0.711817i	$-0.252128\pi$
$449$	29.7657	1.40473	0.702365	+	0.711817i	$0.252128\pi$
$450$	10.2491	0.483149
$451$	6.62428	0.311925
$452$	5.19345	0.244279
$453$	−0.580507	−0.0272746
$454$	−57.5066	−2.69892
$455$	−5.18173	−0.242923
$456$	−36.8941	−1.72773
$457$	19.6205	0.917810	0.458905	−	0.888485i	$-0.348242\pi$
$457$	19.6205	0.917810	0.458905	+	0.888485i	$0.348242\pi$
$458$	6.92244	0.323464
$459$	−8.62147	−0.402416
$460$	−9.79310	−0.456605
$461$	16.2163	0.755268	0.377634	−	0.925955i	$-0.376738\pi$
$461$	16.2163	0.755268	0.377634	+	0.925955i	$0.376738\pi$
$462$	3.96055	0.184261
$463$	−21.0325	−0.977461	−0.488731	−	0.872435i	$-0.662540\pi$
$463$	−21.0325	−0.977461	−0.488731	+	0.872435i	$0.662540\pi$
$464$	5.04665	0.234285
$465$	10.2539	0.475514
$466$	−34.6413	−1.60473
$467$	−0.600130	−0.0277707	−0.0138854	−	0.999904i	$-0.504420\pi$
$467$	−0.600130	−0.0277707	−0.0138854	+	0.999904i	$0.504420\pi$
$468$	17.2153	0.795776
$469$	14.3552	0.662864
$470$	52.1199	2.40411
$471$	2.08230	0.0959473
$472$	−80.5204	−3.70625
$473$	3.93691	0.181019
$474$	12.8987	0.592457
$475$	11.1638	0.512229
$476$	−24.0028	−1.10016
$477$	−23.9596	−1.09703
$478$	−39.1834	−1.79221
$479$	−13.9814	−0.638828	−0.319414	−	0.947615i	$-0.603486\pi$
$479$	−13.9814	−0.638828	−0.319414	+	0.947615i	$0.603486\pi$
$480$	22.9723	1.04854
$481$	7.89701	0.360073
$482$	29.9677	1.36499
$483$	−0.677610	−0.0308323
$484$	−43.4550	−1.97523
$485$	−43.8688	−1.99198
$486$	−34.4142	−1.56106
$487$	21.4166	0.970480	0.485240	−	0.874381i	$-0.338732\pi$
$487$	21.4166	0.970480	0.485240	+	0.874381i	$0.338732\pi$
$488$	74.5164	3.37320
$489$	−2.58430	−0.116866
$490$	−28.6513	−1.29433
$491$	39.0646	1.76296	0.881480	−	0.472221i	$-0.156548\pi$
$491$	39.0646	1.76296	0.881480	+	0.472221i	$0.156548\pi$
$492$	11.5691	0.521574
$493$	1.11116	0.0500441
$494$	25.9728	1.16857
$495$	11.1046	0.499113
$496$	−93.3833	−4.19303
$497$	1.66793	0.0748169
$498$	−12.5631	−0.562966
$499$	37.6203	1.68411	0.842057	−	0.539388i	$-0.181344\pi$
$499$	37.6203	1.68411	0.842057	+	0.539388i	$0.181344\pi$
$500$	47.1650	2.10928
$501$	−2.98390	−0.133311
$502$	1.86022	0.0830258
$503$	27.9648	1.24689	0.623444	−	0.781868i	$-0.285733\pi$
$503$	27.9648	1.24689	0.623444	+	0.781868i	$0.285733\pi$
$504$	−38.6044	−1.71958
$505$	28.9472	1.28813
$506$	−3.24016	−0.144043
$507$	−6.27228	−0.278562
$508$	−23.2201	−1.03022
$509$	26.9297	1.19364	0.596820	−	0.802375i	$-0.296431\pi$
$509$	26.9297	1.19364	0.596820	+	0.802375i	$0.296431\pi$
$510$	10.2700	0.454763
$511$	13.9189	0.615734
$512$	6.37190	0.281601
$513$	−24.5627	−1.08447
$514$	33.4256	1.47434
$515$	−21.4154	−0.943674
$516$	6.87568	0.302685
$517$	12.4500	0.547550
$518$	−28.7993	−1.26537
$519$	−12.8507	−0.564085
$520$	−26.6088	−1.16687
$521$	−34.8852	−1.52835	−0.764175	−	0.645009i	$-0.776854\pi$
$521$	−34.8852	−1.52835	−0.764175	+	0.645009i	$0.776854\pi$
$522$	2.90635	0.127207
$523$	34.9112	1.52656	0.763281	−	0.646067i	$-0.223587\pi$
$523$	34.9112	1.52656	0.763281	+	0.646067i	$0.223587\pi$
$524$	−85.9306	−3.75389
$525$	−1.28698	−0.0561685
$526$	−16.9332	−0.738324
$527$	−20.5609	−0.895646
$528$	11.1420	0.484893
$529$	−22.4456	−0.975897
$530$	60.2263	2.61606
$531$	−25.4043	−1.10245
$532$	−68.3843	−2.96483
$533$	−5.00800	−0.216921
$534$	22.7849	0.985999
$535$	−40.4461	−1.74864
$536$	73.7159	3.18404
$537$	−8.22594	−0.354975
$538$	30.2971	1.30620
$539$	−6.84399	−0.294792
$540$	40.9241	1.76109
$541$	16.2516	0.698711	0.349356	−	0.936990i	$-0.386401\pi$
$541$	16.2516	0.698711	0.349356	+	0.936990i	$0.386401\pi$
$542$	9.73188	0.418020
$543$	3.89717	0.167244
$544$	−46.0634	−1.97495
$545$	50.3835	2.15819
$546$	−2.99420	−0.128140
$547$	−5.71819	−0.244492	−0.122246	−	0.992500i	$-0.539010\pi$
$547$	−5.71819	−0.244492	−0.122246	+	0.992500i	$0.539010\pi$
$548$	56.6352	2.41934
$549$	23.5100	1.00338
$550$	−6.15403	−0.262409
$551$	3.16571	0.134864
$552$	−3.47961	−0.148102
$553$	14.7011	0.625154
$554$	−13.9567	−0.592963
$555$	8.89631	0.377627
$556$	−78.3006	−3.32069
$557$	−10.5175	−0.445640	−0.222820	−	0.974860i	$-0.571526\pi$
$557$	−10.5175	−0.445640	−0.222820	+	0.974860i	$0.571526\pi$
$558$	−53.7791	−2.27665
$559$	−2.97633	−0.125885
$560$	53.1620	2.24650
$561$	2.45322	0.103575
$562$	72.4411	3.05574
$563$	21.2380	0.895073	0.447537	−	0.894266i	$-0.352301\pi$
$563$	21.2380	0.895073	0.447537	+	0.894266i	$0.352301\pi$
$564$	21.7435	0.915564
$565$	−2.53261	−0.106548
$566$	−12.9860	−0.545842
$567$	−10.6900	−0.448937
$568$	8.56503	0.359381
$569$	−7.40250	−0.310329	−0.155164	−	0.987889i	$-0.549591\pi$
$569$	−7.40250	−0.310329	−0.155164	+	0.987889i	$0.549591\pi$
$570$	29.2594	1.22554
$571$	28.8721	1.20826	0.604131	−	0.796885i	$-0.293520\pi$
$571$	28.8721	1.20826	0.604131	+	0.796885i	$0.293520\pi$
$572$	−10.3368	−0.432203
$573$	−4.00843	−0.167455
$574$	18.2635	0.762302
$575$	1.05289	0.0439086
$576$	−52.4670	−2.18613
$577$	−24.3801	−1.01496	−0.507478	−	0.861665i	$-0.669422\pi$
$577$	−24.3801	−1.01496	−0.507478	+	0.861665i	$0.669422\pi$
$578$	25.0019	1.03994
$579$	6.67471	0.277392
$580$	−5.27441	−0.219008
$581$	−14.3186	−0.594035
$582$	−25.3491	−1.05075
$583$	14.3864	0.595823
$584$	71.4750	2.95766
$585$	−8.39511	−0.347095
$586$	36.9387	1.52592
$587$	−6.18685	−0.255358	−0.127679	−	0.991816i	$-0.540753\pi$
$587$	−6.18685	−0.255358	−0.127679	+	0.991816i	$0.540753\pi$
$588$	−11.9528	−0.492925
$589$	−58.5784	−2.41368
$590$	63.8579	2.62899
$591$	−3.01432	−0.123993
$592$	−81.0194	−3.32988
$593$	−33.2301	−1.36460	−0.682298	−	0.731074i	$-0.739019\pi$
$593$	−33.2301	−1.36460	−0.682298	+	0.731074i	$0.739019\pi$
$594$	13.5402	0.555562
$595$	11.7051	0.479861
$596$	−7.91472	−0.324200
$597$	12.5333	0.512956
$598$	2.44958	0.100171
$599$	−41.1304	−1.68054	−0.840271	−	0.542167i	$-0.817604\pi$
$599$	−41.1304	−1.68054	−0.840271	+	0.542167i	$0.817604\pi$
$600$	−6.60881	−0.269804
$601$	38.6292	1.57572	0.787859	−	0.615856i	$-0.211190\pi$
$601$	38.6292	1.57572	0.787859	+	0.615856i	$0.211190\pi$
$602$	10.8543	0.442386
$603$	23.2575	0.947117
$604$	−5.52532	−0.224822
$605$	21.1911	0.861540
$606$	16.7268	0.679479
$607$	−34.6586	−1.40675	−0.703374	−	0.710820i	$-0.748324\pi$
$607$	−34.6586	−1.40675	−0.703374	+	0.710820i	$0.748324\pi$
$608$	−131.235	−5.32230
$609$	−0.364950	−0.0147885
$610$	−59.0963	−2.39274
$611$	−9.41226	−0.380779
$612$	−38.8878	−1.57194
$613$	−41.8591	−1.69067	−0.845336	−	0.534236i	$-0.820600\pi$
$613$	−41.8591	−1.69067	−0.845336	+	0.534236i	$0.820600\pi$
$614$	37.0821	1.49651
$615$	−5.64172	−0.227496
$616$	23.1798	0.933940
$617$	−28.7788	−1.15859	−0.579296	−	0.815117i	$-0.696672\pi$
$617$	−28.7788	−1.15859	−0.579296	+	0.815117i	$0.696672\pi$
$618$	−12.3746	−0.497780
$619$	14.2046	0.570932	0.285466	−	0.958389i	$-0.407852\pi$
$619$	14.2046	0.570932	0.285466	+	0.958389i	$0.407852\pi$
$620$	97.5977	3.91962
$621$	−2.31659	−0.0929617
$622$	−37.3795	−1.49878
$623$	25.9687	1.04041
$624$	−8.42341	−0.337206
$625$	−30.0709	−1.20284
$626$	44.1391	1.76415
$627$	6.98926	0.279124
$628$	19.8195	0.790885
$629$	−17.8386	−0.711273
$630$	30.6158	1.21976
$631$	39.1695	1.55931	0.779656	−	0.626208i	$-0.215394\pi$
$631$	39.1695	1.55931	0.779656	+	0.626208i	$0.215394\pi$
$632$	75.4918	3.00290
$633$	14.1867	0.563873
$634$	−3.68522	−0.146359
$635$	11.3234	0.449355
$636$	25.1253	0.996282
$637$	5.17410	0.205005
$638$	−1.74510	−0.0690892
$639$	2.70228	0.106900
$640$	47.6815	1.88478
$641$	31.6922	1.25177	0.625884	−	0.779916i	$-0.284738\pi$
$641$	31.6922	1.25177	0.625884	+	0.779916i	$0.284738\pi$
$642$	−23.3713	−0.922391
$643$	−23.0163	−0.907674	−0.453837	−	0.891085i	$-0.649945\pi$
$643$	−23.0163	−0.907674	−0.453837	+	0.891085i	$0.649945\pi$
$644$	−6.44955	−0.254148
$645$	−3.35296	−0.132023
$646$	−58.6702	−2.30835
$647$	39.0546	1.53539	0.767697	−	0.640813i	$-0.221402\pi$
$647$	39.0546	1.53539	0.767697	+	0.640813i	$0.221402\pi$
$648$	−54.8944	−2.15646
$649$	15.2538	0.598766
$650$	4.65248	0.182485
$651$	6.75304	0.264672
$652$	−24.5976	−0.963316
$653$	−12.5671	−0.491788	−0.245894	−	0.969297i	$-0.579081\pi$
$653$	−12.5671	−0.491788	−0.245894	+	0.969297i	$0.579081\pi$
$654$	29.1135	1.13843
$655$	41.9045	1.63734
$656$	51.3796	2.00604
$657$	22.5505	0.879777
$658$	34.3252	1.33814
$659$	39.6989	1.54645	0.773224	−	0.634133i	$-0.218643\pi$
$659$	39.6989	1.54645	0.773224	+	0.634133i	$0.218643\pi$
$660$	−11.6448	−0.453275
$661$	−4.73766	−0.184274	−0.0921368	−	0.995746i	$-0.529370\pi$
$661$	−4.73766	−0.184274	−0.0921368	+	0.995746i	$0.529370\pi$
$662$	−38.2883	−1.48812
$663$	−1.85465	−0.0720285
$664$	−73.5277	−2.85343
$665$	33.3479	1.29318
$666$	−46.6588	−1.80799
$667$	0.298569	0.0115606
$668$	−28.4010	−1.09887
$669$	9.91791	0.383449
$670$	−58.4615	−2.25856
$671$	−14.1165	−0.544960
$672$	15.1291	0.583618
$673$	−41.7039	−1.60757	−0.803784	−	0.594922i	$-0.797183\pi$
$673$	−41.7039	−1.60757	−0.803784	+	0.594922i	$0.797183\pi$
$674$	−43.7630	−1.68569
$675$	−4.39990	−0.169352
$676$	−59.7002	−2.29616
$677$	−6.04928	−0.232493	−0.116246	−	0.993220i	$-0.537086\pi$
$677$	−6.04928	−0.232493	−0.116246	+	0.993220i	$0.537086\pi$
$678$	−1.46344	−0.0562031
$679$	−28.8912	−1.10874
$680$	60.1069	2.30500
$681$	11.6992	0.448314
$682$	32.2913	1.23650
$683$	11.5041	0.440192	0.220096	−	0.975478i	$-0.429363\pi$
$683$	11.5041	0.440192	0.220096	+	0.975478i	$0.429363\pi$
$684$	−110.792	−4.23624
$685$	−27.6185	−1.05525
$686$	−50.1837	−1.91602
$687$	−1.40830	−0.0537302
$688$	30.5357	1.16416
$689$	−10.8762	−0.414350
$690$	2.75955	0.105054
$691$	7.16494	0.272567	0.136284	−	0.990670i	$-0.456484\pi$
$691$	7.16494	0.272567	0.136284	+	0.990670i	$0.456484\pi$
$692$	−122.314	−4.64970
$693$	7.31325	0.277807
$694$	−23.1676	−0.879430
$695$	38.1837	1.44839
$696$	−1.87406	−0.0710362
$697$	11.3126	0.428496
$698$	−53.5228	−2.02587
$699$	7.04745	0.266559
$700$	−12.2496	−0.462992
$701$	11.4593	0.432811	0.216405	−	0.976304i	$-0.430567\pi$
$701$	11.4593	0.432811	0.216405	+	0.976304i	$0.430567\pi$
$702$	−10.2365	−0.386351
$703$	−50.8226	−1.91681
$704$	31.5035	1.18733
$705$	−10.6033	−0.399344
$706$	−78.3961	−2.95048
$707$	19.0641	0.716978
$708$	26.6403	1.00120
$709$	11.4104	0.428525	0.214263	−	0.976776i	$-0.431265\pi$
$709$	11.4104	0.428525	0.214263	+	0.976776i	$0.431265\pi$
$710$	−6.79262	−0.254923
$711$	23.8178	0.893236
$712$	133.352	4.99759
$713$	−5.52472	−0.206902
$714$	6.76363	0.253123
$715$	5.04079	0.188515
$716$	−78.2952	−2.92603
$717$	7.97150	0.297701
$718$	−40.8965	−1.52624
$719$	−28.7252	−1.07127	−0.535635	−	0.844450i	$-0.679928\pi$
$719$	−28.7252	−1.07127	−0.535635	+	0.844450i	$0.679928\pi$
$720$	86.1297	3.20986
$721$	−14.1038	−0.525251
$722$	−116.193	−4.32427
$723$	−6.09665	−0.226737
$724$	37.0936	1.37857
$725$	0.567071	0.0210605
$726$	12.2450	0.454455
$727$	−12.1503	−0.450630	−0.225315	−	0.974286i	$-0.572341\pi$
$727$	−12.1503	−0.450630	−0.225315	+	0.974286i	$0.572341\pi$
$728$	−17.5241	−0.649485
$729$	−12.2262	−0.452820
$730$	−56.6843	−2.09798
$731$	6.72326	0.248669
$732$	−24.6539	−0.911234
$733$	−16.1123	−0.595122	−0.297561	−	0.954703i	$-0.596173\pi$
$733$	−16.1123	−0.595122	−0.297561	+	0.954703i	$0.596173\pi$
$734$	38.9341	1.43708
$735$	5.82884	0.215000
$736$	−12.3773	−0.456231
$737$	−13.9648	−0.514400
$738$	29.5893	1.08920
$739$	35.5158	1.30647	0.653234	−	0.757156i	$-0.273412\pi$
$739$	35.5158	1.30647	0.653234	+	0.757156i	$0.273412\pi$
$740$	84.6758	3.11275
$741$	−5.28392	−0.194110
$742$	39.6639	1.45611
$743$	−4.09622	−0.150276	−0.0751379	−	0.997173i	$-0.523940\pi$
$743$	−4.09622	−0.150276	−0.0751379	+	0.997173i	$0.523940\pi$
$744$	34.6777	1.27134
$745$	3.85966	0.141407
$746$	69.2779	2.53644
$747$	−23.1981	−0.848773
$748$	23.3499	0.853758
$749$	−26.6370	−0.973296
$750$	−13.2904	−0.485297
$751$	23.2921	0.849940	0.424970	−	0.905208i	$-0.360285\pi$
$751$	23.2921	0.849940	0.424970	+	0.905208i	$0.360285\pi$
$752$	96.5651	3.52137
$753$	−0.378445	−0.0137913
$754$	1.31931	0.0480463
$755$	2.69445	0.0980610
$756$	26.9519	0.980229
$757$	−0.638497	−0.0232066	−0.0116033	−	0.999933i	$-0.503694\pi$
$757$	−0.638497	−0.0232066	−0.0116033	+	0.999933i	$0.503694\pi$
$758$	−63.5667	−2.30885
$759$	0.659180	0.0239267
$760$	171.246	6.21174
$761$	−36.0156	−1.30557	−0.652783	−	0.757545i	$-0.726399\pi$
$761$	−36.0156	−1.30557	−0.652783	+	0.757545i	$0.726399\pi$
$762$	6.54308	0.237031
$763$	33.1817	1.20126
$764$	−38.1526	−1.38031
$765$	18.9638	0.685638
$766$	60.0834	2.17090
$767$	−11.5320	−0.416397
$768$	6.36405	0.229643
$769$	16.7163	0.602804	0.301402	−	0.953497i	$-0.402545\pi$
$769$	16.7163	0.602804	0.301402	+	0.953497i	$0.402545\pi$
$770$	−18.3831	−0.662480
$771$	−6.80012	−0.244900
$772$	63.5305	2.28651
$773$	47.7286	1.71668	0.858338	−	0.513084i	$-0.171497\pi$
$773$	47.7286	1.71668	0.858338	+	0.513084i	$0.171497\pi$
$774$	17.5854	0.632093
$775$	−10.4931	−0.376923
$776$	−148.360	−5.32580
$777$	5.85894	0.210188
$778$	28.0026	1.00394
$779$	32.2299	1.15476
$780$	8.80357	0.315218
$781$	−1.62257	−0.0580600
$782$	−5.53338	−0.197873
$783$	−1.24768	−0.0445885
$784$	−53.0837	−1.89585
$785$	−9.66509	−0.344962
$786$	24.2140	0.863685
$787$	30.8135	1.09838	0.549192	−	0.835696i	$-0.314936\pi$
$787$	30.8135	1.09838	0.549192	+	0.835696i	$0.314936\pi$
$788$	−28.6906	−1.02206
$789$	3.44491	0.122642
$790$	−59.8699	−2.13008
$791$	−1.66793	−0.0593048
$792$	37.5544	1.33444
$793$	10.6721	0.378978
$794$	−71.8209	−2.54883
$795$	−12.2525	−0.434550
$796$	119.294	4.22825
$797$	20.4234	0.723435	0.361717	−	0.932288i	$-0.382191\pi$
$797$	20.4234	0.723435	0.361717	+	0.932288i	$0.382191\pi$
$798$	19.2697	0.682140
$799$	21.2615	0.752177
$800$	−23.5081	−0.831136
$801$	42.0729	1.48657
$802$	45.1579	1.59458
$803$	−13.5403	−0.477826
$804$	−24.3890	−0.860135
$805$	3.14516	0.110852
$806$	−24.4124	−0.859892
$807$	−6.16365	−0.216971
$808$	97.8962	3.44398
$809$	25.2319	0.887106	0.443553	−	0.896248i	$-0.353718\pi$
$809$	25.2319	0.887106	0.443553	+	0.896248i	$0.353718\pi$
$810$	43.5348	1.52966
$811$	48.9672	1.71947	0.859736	−	0.510740i	$-0.170628\pi$
$811$	48.9672	1.71947	0.859736	+	0.510740i	$0.170628\pi$
$812$	−3.47363	−0.121900
$813$	−1.97986	−0.0694367
$814$	28.0160	0.981960
$815$	11.9951	0.420172
$816$	19.0277	0.666104
$817$	19.1547	0.670138
$818$	−49.0826	−1.71613
$819$	−5.52886	−0.193194
$820$	−53.6984	−1.87523
$821$	16.3424	0.570352	0.285176	−	0.958475i	$-0.407948\pi$
$821$	16.3424	0.570352	0.285176	+	0.958475i	$0.407948\pi$
$822$	−15.9590	−0.556634
$823$	8.22748	0.286792	0.143396	−	0.989665i	$-0.454198\pi$
$823$	8.22748	0.286792	0.143396	+	0.989665i	$0.454198\pi$
$824$	−72.4245	−2.52303
$825$	1.25198	0.0435883
$826$	42.0556	1.46330
$827$	32.1597	1.11830	0.559152	−	0.829065i	$-0.311127\pi$
$827$	32.1597	1.11830	0.559152	+	0.829065i	$0.311127\pi$
$828$	−10.4492	−0.363133
$829$	−13.2995	−0.461912	−0.230956	−	0.972964i	$-0.574185\pi$
$829$	−13.2995	−0.461912	−0.230956	+	0.972964i	$0.574185\pi$
$830$	58.3122	2.02405
$831$	2.83936	0.0984963
$832$	−23.8168	−0.825701
$833$	−11.6878	−0.404960
$834$	22.0640	0.764013
$835$	13.8499	0.479296
$836$	66.5244	2.30079
$837$	23.0871	0.798007
$838$	41.0475	1.41796
$839$	−45.2544	−1.56236	−0.781178	−	0.624309i	$-0.785381\pi$
$839$	−45.2544	−1.56236	−0.781178	+	0.624309i	$0.785381\pi$
$840$	−19.7416	−0.681149
$841$	−28.8392	−0.994455
$842$	−84.7311	−2.92003
$843$	−14.7375	−0.507585
$844$	135.031	4.64795
$845$	29.1131	1.00152
$846$	55.6115	1.91196
$847$	13.9560	0.479535
$848$	111.584	3.83182
$849$	2.64188	0.0906690
$850$	−10.5095	−0.360475
$851$	−4.79325	−0.164310
$852$	−2.83375	−0.0970828
$853$	−24.6680	−0.844616	−0.422308	−	0.906452i	$-0.638780\pi$
$853$	−24.6680	−0.844616	−0.422308	+	0.906452i	$0.638780\pi$
$854$	−38.9197	−1.33181
$855$	54.0282	1.84773
$856$	−136.784	−4.67520
$857$	−20.1744	−0.689144	−0.344572	−	0.938760i	$-0.611976\pi$
$857$	−20.1744	−0.689144	−0.344572	+	0.938760i	$0.611976\pi$
$858$	2.91276	0.0994401
$859$	−36.1604	−1.23378	−0.616889	−	0.787050i	$-0.711607\pi$
$859$	−36.1604	−1.23378	−0.616889	+	0.787050i	$0.711607\pi$
$860$	−31.9138	−1.08825
$861$	−3.71553	−0.126625
$862$	66.8803	2.27795
$863$	48.9318	1.66566	0.832829	−	0.553531i	$-0.186720\pi$
$863$	48.9318	1.66566	0.832829	+	0.553531i	$0.186720\pi$
$864$	51.7230	1.75965
$865$	59.6473	2.02807
$866$	30.9174	1.05062
$867$	−5.08640	−0.172743
$868$	64.2760	2.18167
$869$	−14.3012	−0.485136
$870$	1.48625	0.0503887
$871$	10.5575	0.357727
$872$	170.392	5.77020
$873$	−46.8076	−1.58420
$874$	−15.7647	−0.533249
$875$	−15.1475	−0.512080
$876$	−23.6476	−0.798979
$877$	55.4917	1.87382	0.936911	−	0.349569i	$-0.113672\pi$
$877$	55.4917	1.87382	0.936911	+	0.349569i	$0.113672\pi$
$878$	7.21225	0.243402
$879$	−7.51484	−0.253469
$880$	−51.7160	−1.74335
$881$	−21.1753	−0.713413	−0.356707	−	0.934216i	$-0.616100\pi$
$881$	−21.1753	−0.713413	−0.356707	+	0.934216i	$0.616100\pi$
$882$	−30.5707	−1.02937
$883$	18.6125	0.626359	0.313179	−	0.949694i	$-0.398606\pi$
$883$	18.6125	0.626359	0.313179	+	0.949694i	$0.398606\pi$
$884$	−17.6527	−0.593724
$885$	−12.9913	−0.436697
$886$	−64.7859	−2.17653
$887$	56.9310	1.91156	0.955778	−	0.294090i	$-0.0950167\pi$
$887$	56.9310	1.91156	0.955778	+	0.294090i	$0.0950167\pi$
$888$	30.0864	1.00963
$889$	7.45737	0.250112
$890$	−105.757	−3.54499
$891$	10.3992	0.348388
$892$	94.3996	3.16073
$893$	60.5743	2.02704
$894$	2.23026	0.0745909
$895$	38.1811	1.27625
$896$	31.4021	1.04907
$897$	−0.498344	−0.0166392
$898$	−79.8334	−2.66407
$899$	−2.97553	−0.0992395
$900$	−19.8461	−0.661535
$901$	24.5683	0.818490
$902$	−17.7667	−0.591567
$903$	−2.20820	−0.0734841
$904$	−8.56503	−0.284869
$905$	−18.0889	−0.601295
$906$	1.55695	0.0517263
$907$	−8.45739	−0.280823	−0.140412	−	0.990093i	$-0.544843\pi$
$907$	−8.45739	−0.280823	−0.140412	+	0.990093i	$0.544843\pi$
$908$	111.354	3.69541
$909$	30.8864	1.02444
$910$	13.8977	0.460705
$911$	23.9778	0.794418	0.397209	−	0.917728i	$-0.369979\pi$
$911$	23.9778	0.794418	0.397209	+	0.917728i	$0.369979\pi$
$912$	54.2104	1.79509
$913$	13.9291	0.460987
$914$	−52.6235	−1.74063
$915$	12.0226	0.397455
$916$	−13.4044	−0.442893
$917$	27.5975	0.911350
$918$	23.1233	0.763183
$919$	−5.47669	−0.180659	−0.0903297	−	0.995912i	$-0.528792\pi$
$919$	−5.47669	−0.180659	−0.0903297	+	0.995912i	$0.528792\pi$
$920$	16.1508	0.532475
$921$	−7.54400	−0.248583
$922$	−43.4931	−1.43237
$923$	1.22667	0.0403763
$924$	−7.66907	−0.252294
$925$	−9.10381	−0.299331
$926$	56.4103	1.85376
$927$	−22.8500	−0.750493
$928$	−6.66620	−0.218829
$929$	−30.7578	−1.00913	−0.504565	−	0.863374i	$-0.668347\pi$
$929$	−30.7578	−1.00913	−0.504565	+	0.863374i	$0.668347\pi$
$930$	−27.5016	−0.901814
$931$	−33.2989	−1.09133
$932$	67.0782	2.19722
$933$	7.60451	0.248961
$934$	1.60959	0.0526672
$935$	−11.3867	−0.372385
$936$	−28.3914	−0.928001
$937$	10.0738	0.329096	0.164548	−	0.986369i	$-0.447383\pi$
$937$	10.0738	0.329096	0.164548	+	0.986369i	$0.447383\pi$
$938$	−38.5016	−1.25712
$939$	−8.97969	−0.293041
$940$	−100.923	−3.29175
$941$	21.0783	0.687134	0.343567	−	0.939128i	$-0.388365\pi$
$941$	21.0783	0.687134	0.343567	+	0.939128i	$0.388365\pi$
$942$	−5.58485	−0.181964
$943$	3.03971	0.0989865
$944$	118.313	3.85075
$945$	−13.1432	−0.427549
$946$	−10.5590	−0.343304
$947$	37.5691	1.22083	0.610416	−	0.792081i	$-0.291002\pi$
$947$	37.5691	1.22083	0.610416	+	0.792081i	$0.291002\pi$
$948$	−24.9766	−0.811202
$949$	10.2365	0.332292
$950$	−29.9419	−0.971443
$951$	0.749722	0.0243114
$952$	39.5853	1.28297
$953$	−23.1800	−0.750873	−0.375436	−	0.926848i	$-0.622507\pi$
$953$	−23.1800	−0.750873	−0.375436	+	0.926848i	$0.622507\pi$
$954$	64.2610	2.08053
$955$	18.6053	0.602054
$956$	75.8734	2.45392
$957$	0.355024	0.0114763
$958$	37.4990	1.21154
$959$	−18.1890	−0.587353
$960$	−26.8307	−0.865956
$961$	24.0592	0.776103
$962$	−21.1803	−0.682879
$963$	−43.1557	−1.39067
$964$	−58.0285	−1.86897
$965$	−30.9810	−0.997313
$966$	1.81739	0.0584736
$967$	−55.3423	−1.77969	−0.889844	−	0.456264i	$-0.849187\pi$
$967$	−55.3423	−1.77969	−0.889844	+	0.456264i	$0.849187\pi$
$968$	71.6660	2.30343
$969$	11.9359	0.383437
$970$	117.659	3.77780
$971$	32.0472	1.02844	0.514222	−	0.857657i	$-0.328081\pi$
$971$	32.0472	1.02844	0.514222	+	0.857657i	$0.328081\pi$
$972$	66.6385	2.13743
$973$	25.1471	0.806178
$974$	−57.4407	−1.84052
$975$	−0.946504	−0.0303124
$976$	−109.491	−3.50471
$977$	43.4068	1.38871	0.694354	−	0.719634i	$-0.255690\pi$
$977$	43.4068	1.38871	0.694354	+	0.719634i	$0.255690\pi$
$978$	6.93125	0.221637
$979$	−25.2624	−0.807390
$980$	55.4794	1.77223
$981$	53.7588	1.71639
$982$	−104.774	−3.34346
$983$	50.2716	1.60341	0.801707	−	0.597717i	$-0.203925\pi$
$983$	50.2716	1.60341	0.801707	+	0.597717i	$0.203925\pi$
$984$	−19.0797	−0.608239
$985$	13.9911	0.445794
$986$	−2.98020	−0.0949088
$987$	−6.98314	−0.222276
$988$	−50.2928	−1.60003
$989$	1.80654	0.0574447
$990$	−29.7831	−0.946569
$991$	1.52230	0.0483574	0.0241787	−	0.999708i	$-0.492303\pi$
$991$	1.52230	0.0483574	0.0241787	+	0.999708i	$0.492303\pi$
$992$	123.351	3.91641
$993$	7.78939	0.247189
$994$	−4.47349	−0.141891
$995$	−58.1741	−1.84424
$996$	24.3268	0.770823
$997$	−11.5773	−0.366657	−0.183328	−	0.983052i	$-0.558687\pi$
$997$	−11.5773	−0.366657	−0.183328	+	0.983052i	$0.558687\pi$
$998$	−100.900	−3.19393
$999$	20.0304	0.633733

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8023.2.a.e.1.3	✓	172

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8023.2.a.e.1.3	✓	172	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:	\( N \)	\(=\)	\( 8023 = 71 \cdot 113 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8023.a (trivial)

\(f(q)\)	\(=\)	\(q-2.68206 q^{2} +0.545640 q^{3} +5.19345 q^{4} -2.53261 q^{5} -1.46344 q^{6} -1.66793 q^{7} -8.56503 q^{8} -2.70228 q^{9} +O(q^{10})\)	\(q-2.68206 q^{2} +0.545640 q^{3} +5.19345 q^{4} -2.53261 q^{5} -1.46344 q^{6} -1.66793 q^{7} -8.56503 q^{8} -2.70228 q^{9} +6.79262 q^{10} +1.62257 q^{11} +2.83375 q^{12} -1.22667 q^{13} +4.47349 q^{14} -1.38189 q^{15} +12.5850 q^{16} +2.77094 q^{17} +7.24767 q^{18} +7.89446 q^{19} -13.1530 q^{20} -0.910090 q^{21} -4.35182 q^{22} +0.744552 q^{23} -4.67342 q^{24} +1.41413 q^{25} +3.29000 q^{26} -3.11139 q^{27} -8.66232 q^{28} +0.401005 q^{29} +3.70633 q^{30} -7.42019 q^{31} -16.6237 q^{32} +0.885337 q^{33} -7.43183 q^{34} +4.22422 q^{35} -14.0341 q^{36} -6.43776 q^{37} -21.1734 q^{38} -0.669320 q^{39} +21.6919 q^{40} +4.08260 q^{41} +2.44092 q^{42} +2.42635 q^{43} +8.42672 q^{44} +6.84382 q^{45} -1.99693 q^{46} +7.67302 q^{47} +6.86689 q^{48} -4.21801 q^{49} -3.79277 q^{50} +1.51194 q^{51} -6.37065 q^{52} +8.86643 q^{53} +8.34494 q^{54} -4.10933 q^{55} +14.2859 q^{56} +4.30753 q^{57} -1.07552 q^{58} +9.40106 q^{59} -7.17680 q^{60} -8.70008 q^{61} +19.9014 q^{62} +4.50721 q^{63} +19.4159 q^{64} +3.10668 q^{65} -2.37453 q^{66} -8.60662 q^{67} +14.3907 q^{68} +0.406258 q^{69} -11.3296 q^{70} -1.00000 q^{71} +23.1451 q^{72} -8.34498 q^{73} +17.2665 q^{74} +0.771604 q^{75} +40.9995 q^{76} -2.70633 q^{77} +1.79516 q^{78} -8.81396 q^{79} -31.8730 q^{80} +6.40913 q^{81} -10.9498 q^{82} +8.58464 q^{83} -4.72651 q^{84} -7.01772 q^{85} -6.50761 q^{86} +0.218804 q^{87} -13.8973 q^{88} -15.5694 q^{89} -18.3555 q^{90} +2.04600 q^{91} +3.86680 q^{92} -4.04875 q^{93} -20.5795 q^{94} -19.9936 q^{95} -9.07058 q^{96} +17.3216 q^{97} +11.3129 q^{98} -4.38462 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 172 q + 24 q^{2} + 18 q^{3} + 180 q^{4} + 28 q^{5} + 16 q^{6} + 4 q^{7} + 72 q^{8} + 198 q^{9}+O(q^{10}) \) 172 * q + 24 * q^2 + 18 * q^3 + 180 * q^4 + 28 * q^5 + 16 * q^6 + 4 * q^7 + 72 * q^8 + 198 * q^9	\( 172 q + 24 q^{2} + 18 q^{3} + 180 q^{4} + 28 q^{5} + 16 q^{6} + 4 q^{7} + 72 q^{8} + 198 q^{9} + 14 q^{10} + 20 q^{11} + 54 q^{12} + 36 q^{13} + 26 q^{14} + 32 q^{15} + 196 q^{16} + 123 q^{17} + 74 q^{18} + 20 q^{19} + 70 q^{20} + 37 q^{21} + 11 q^{22} + 22 q^{23} + 62 q^{24} + 210 q^{25} + 50 q^{26} + 69 q^{27} + 42 q^{28} + 58 q^{29} + 36 q^{30} + 10 q^{31} + 168 q^{32} + 124 q^{33} + 5 q^{34} + 59 q^{35} + 192 q^{36} + 40 q^{37} + 58 q^{38} + 15 q^{39} + 7 q^{40} + 155 q^{41} - 6 q^{42} + 19 q^{43} + 22 q^{44} + 76 q^{45} + q^{46} + 71 q^{47} + 144 q^{48} + 206 q^{49} + 126 q^{50} + 33 q^{51} + 71 q^{52} + 101 q^{53} + 92 q^{54} - 2 q^{55} + 57 q^{56} + 114 q^{57} + 4 q^{58} + 71 q^{59} + 38 q^{60} + 50 q^{61} + 86 q^{62} + 14 q^{63} + 240 q^{64} + 143 q^{65} + 21 q^{66} + 8 q^{67} + 192 q^{68} + 41 q^{69} - 12 q^{70} - 172 q^{71} + 156 q^{72} + 128 q^{73} + 30 q^{74} + 72 q^{75} + 74 q^{76} + 127 q^{77} + 107 q^{78} + 2 q^{79} + 50 q^{80} + 236 q^{81} + 42 q^{82} + 140 q^{83} + 71 q^{84} + 55 q^{85} + 46 q^{86} + 100 q^{87} - 31 q^{88} + 215 q^{89} - 7 q^{90} + 22 q^{91} - 15 q^{92} + 60 q^{93} + 5 q^{94} + 74 q^{95} + 182 q^{96} + 120 q^{97} + 164 q^{98} + 60 q^{99}+O(q^{100}) \) 172 * q + 24 * q^2 + 18 * q^3 + 180 * q^4 + 28 * q^5 + 16 * q^6 + 4 * q^7 + 72 * q^8 + 198 * q^9 + 14 * q^10 + 20 * q^11 + 54 * q^12 + 36 * q^13 + 26 * q^14 + 32 * q^15 + 196 * q^16 + 123 * q^17 + 74 * q^18 + 20 * q^19 + 70 * q^20 + 37 * q^21 + 11 * q^22 + 22 * q^23 + 62 * q^24 + 210 * q^25 + 50 * q^26 + 69 * q^27 + 42 * q^28 + 58 * q^29 + 36 * q^30 + 10 * q^31 + 168 * q^32 + 124 * q^33 + 5 * q^34 + 59 * q^35 + 192 * q^36 + 40 * q^37 + 58 * q^38 + 15 * q^39 + 7 * q^40 + 155 * q^41 - 6 * q^42 + 19 * q^43 + 22 * q^44 + 76 * q^45 + q^46 + 71 * q^47 + 144 * q^48 + 206 * q^49 + 126 * q^50 + 33 * q^51 + 71 * q^52 + 101 * q^53 + 92 * q^54 - 2 * q^55 + 57 * q^56 + 114 * q^57 + 4 * q^58 + 71 * q^59 + 38 * q^60 + 50 * q^61 + 86 * q^62 + 14 * q^63 + 240 * q^64 + 143 * q^65 + 21 * q^66 + 8 * q^67 + 192 * q^68 + 41 * q^69 - 12 * q^70 - 172 * q^71 + 156 * q^72 + 128 * q^73 + 30 * q^74 + 72 * q^75 + 74 * q^76 + 127 * q^77 + 107 * q^78 + 2 * q^79 + 50 * q^80 + 236 * q^81 + 42 * q^82 + 140 * q^83 + 71 * q^84 + 55 * q^85 + 46 * q^86 + 100 * q^87 - 31 * q^88 + 215 * q^89 - 7 * q^90 + 22 * q^91 - 15 * q^92 + 60 * q^93 + 5 * q^94 + 74 * q^95 + 182 * q^96 + 120 * q^97 + 164 * q^98 + 60 * q^99

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