LMFDB - Embedded newform 8023.2.a.c.1.12

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:	$1$
Dimension:	$158$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
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)

$f(q)$	$=$	$q-2.54938 q^{2} +0.0117245 q^{3} +4.49933 q^{4} +3.26987 q^{5} -0.0298901 q^{6} -0.929031 q^{7} -6.37175 q^{8} -2.99986 q^{9} +O(q^{10})$	\(q-2.54938 q^{2} +0.0117245 q^{3} +4.49933 q^{4} +3.26987 q^{5} -0.0298901 q^{6} -0.929031 q^{7} -6.37175 q^{8} -2.99986 q^{9} -8.33615 q^{10} -5.56961 q^{11} +0.0527523 q^{12} +3.44304 q^{13} +2.36845 q^{14} +0.0383375 q^{15} +7.24534 q^{16} +1.70770 q^{17} +7.64779 q^{18} +5.28092 q^{19} +14.7123 q^{20} -0.0108924 q^{21} +14.1990 q^{22} -9.41041 q^{23} -0.0747054 q^{24} +5.69208 q^{25} -8.77761 q^{26} -0.0703452 q^{27} -4.18002 q^{28} +1.77199 q^{29} -0.0977369 q^{30} +9.57642 q^{31} -5.72761 q^{32} -0.0653007 q^{33} -4.35358 q^{34} -3.03781 q^{35} -13.4974 q^{36} -7.57145 q^{37} -13.4631 q^{38} +0.0403678 q^{39} -20.8348 q^{40} -8.48628 q^{41} +0.0277688 q^{42} +6.66532 q^{43} -25.0595 q^{44} -9.80917 q^{45} +23.9907 q^{46} +2.35175 q^{47} +0.0849477 q^{48} -6.13690 q^{49} -14.5113 q^{50} +0.0200219 q^{51} +15.4914 q^{52} -6.47642 q^{53} +0.179337 q^{54} -18.2119 q^{55} +5.91955 q^{56} +0.0619160 q^{57} -4.51747 q^{58} +6.35518 q^{59} +0.172493 q^{60} +9.96874 q^{61} -24.4139 q^{62} +2.78696 q^{63} +0.111184 q^{64} +11.2583 q^{65} +0.166476 q^{66} -3.80965 q^{67} +7.68353 q^{68} -0.110332 q^{69} +7.74454 q^{70} -1.00000 q^{71} +19.1144 q^{72} +3.10423 q^{73} +19.3025 q^{74} +0.0667366 q^{75} +23.7606 q^{76} +5.17434 q^{77} -0.102913 q^{78} +10.9911 q^{79} +23.6913 q^{80} +8.99876 q^{81} +21.6347 q^{82} -0.444810 q^{83} -0.0490085 q^{84} +5.58398 q^{85} -16.9924 q^{86} +0.0207756 q^{87} +35.4881 q^{88} -16.2834 q^{89} +25.0073 q^{90} -3.19869 q^{91} -42.3406 q^{92} +0.112278 q^{93} -5.99549 q^{94} +17.2679 q^{95} -0.0671532 q^{96} +1.42351 q^{97} +15.6453 q^{98} +16.7081 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 158 q - 24 q^{2} - 23 q^{3} + 158 q^{4} - 31 q^{5} - 17 q^{6} - 2 q^{7} - 69 q^{8} + 135 q^{9}+O(q^{10}) $ 158 * q - 24 * q^2 - 23 * q^3 + 158 * q^4 - 31 * q^5 - 17 * q^6 - 2 * q^7 - 69 * q^8 + 135 * q^9	\( 158 q - 24 q^{2} - 23 q^{3} + 158 q^{4} - 31 q^{5} - 17 q^{6} - 2 q^{7} - 69 q^{8} + 135 q^{9} - 10 q^{10} - 10 q^{11} - 46 q^{12} - 28 q^{13} - 27 q^{14} - 41 q^{15} + 150 q^{16} - 137 q^{17} - 67 q^{18} - 42 q^{19} - 66 q^{20} - 46 q^{21} - 8 q^{22} - 26 q^{23} - 48 q^{24} + 129 q^{25} - 67 q^{26} - 89 q^{27} - 21 q^{28} - 79 q^{29} - 11 q^{30} + 7 q^{31} - 147 q^{32} - 112 q^{33} - 28 q^{34} - 53 q^{35} + 141 q^{36} - 60 q^{37} - 53 q^{38} - 3 q^{39} - 48 q^{40} - 128 q^{41} + 32 q^{42} - 63 q^{43} - 88 q^{45} - 2 q^{46} - 92 q^{47} - 131 q^{48} + 122 q^{49} - 116 q^{50} - 12 q^{51} - 89 q^{52} - 94 q^{53} - 71 q^{54} - 12 q^{55} - 104 q^{56} - 93 q^{57} - 65 q^{58} - 54 q^{59} - 12 q^{60} + 17 q^{61} - 97 q^{62} - 28 q^{63} + 163 q^{64} - 163 q^{65} - 65 q^{66} - 35 q^{67} - 217 q^{68} - 46 q^{69} - 79 q^{70} - 158 q^{71} - 99 q^{72} - 165 q^{73} - 94 q^{75} - 93 q^{76} - 140 q^{77} + 25 q^{78} - 61 q^{79} - 134 q^{80} + 114 q^{81} + 10 q^{82} - 158 q^{83} - 160 q^{84} + 23 q^{85} - 122 q^{86} - 71 q^{87} - 14 q^{88} - 251 q^{89} - 6 q^{90} - 57 q^{91} - 58 q^{92} - 52 q^{93} - 64 q^{94} - 84 q^{95} - 98 q^{96} - 48 q^{97} - 84 q^{98} + 85 q^{99}+O(q^{100}) \) 158 * q - 24 * q^2 - 23 * q^3 + 158 * q^4 - 31 * q^5 - 17 * q^6 - 2 * q^7 - 69 * q^8 + 135 * q^9 - 10 * q^10 - 10 * q^11 - 46 * q^12 - 28 * q^13 - 27 * q^14 - 41 * q^15 + 150 * q^16 - 137 * q^17 - 67 * q^18 - 42 * q^19 - 66 * q^20 - 46 * q^21 - 8 * q^22 - 26 * q^23 - 48 * q^24 + 129 * q^25 - 67 * q^26 - 89 * q^27 - 21 * q^28 - 79 * q^29 - 11 * q^30 + 7 * q^31 - 147 * q^32 - 112 * q^33 - 28 * q^34 - 53 * q^35 + 141 * q^36 - 60 * q^37 - 53 * q^38 - 3 * q^39 - 48 * q^40 - 128 * q^41 + 32 * q^42 - 63 * q^43 - 88 * q^45 - 2 * q^46 - 92 * q^47 - 131 * q^48 + 122 * q^49 - 116 * q^50 - 12 * q^51 - 89 * q^52 - 94 * q^53 - 71 * q^54 - 12 * q^55 - 104 * q^56 - 93 * q^57 - 65 * q^58 - 54 * q^59 - 12 * q^60 + 17 * q^61 - 97 * q^62 - 28 * q^63 + 163 * q^64 - 163 * q^65 - 65 * q^66 - 35 * q^67 - 217 * q^68 - 46 * q^69 - 79 * q^70 - 158 * q^71 - 99 * q^72 - 165 * q^73 - 94 * q^75 - 93 * q^76 - 140 * q^77 + 25 * q^78 - 61 * q^79 - 134 * q^80 + 114 * q^81 + 10 * q^82 - 158 * q^83 - 160 * q^84 + 23 * q^85 - 122 * q^86 - 71 * q^87 - 14 * q^88 - 251 * q^89 - 6 * q^90 - 57 * q^91 - 58 * q^92 - 52 * q^93 - 64 * q^94 - 84 * q^95 - 98 * q^96 - 48 * q^97 - 84 * q^98 + 85 * 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 $

$2$	−2.54938	−1.80268	−0.901342	−	0.433109i	$-0.857417\pi$
$2$	−2.54938	−1.80268	−0.901342	+	0.433109i	$0.857417\pi$
$3$	0.0117245	0.00676912	0.00338456	−	0.999994i	$-0.498923\pi$
$3$	0.0117245	0.00676912	0.00338456	+	0.999994i	$0.498923\pi$
$4$	4.49933	2.24967
$5$	3.26987	1.46233	0.731166	−	0.682200i	$-0.238976\pi$
$5$	3.26987	1.46233	0.731166	+	0.682200i	$0.238976\pi$
$6$	−0.0298901	−0.0122026
$7$	−0.929031	−0.351141	−0.175570	−	0.984467i	$-0.556177\pi$
$7$	−0.929031	−0.351141	−0.175570	+	0.984467i	$0.556177\pi$
$8$	−6.37175	−2.25275
$9$	−2.99986	−0.999954
$10$	−8.33615	−2.63612
$11$	−5.56961	−1.67930	−0.839650	−	0.543128i	$-0.817240\pi$
$11$	−5.56961	−1.67930	−0.839650	+	0.543128i	$0.817240\pi$
$12$	0.0527523	0.0152283
$13$	3.44304	0.954927	0.477463	−	0.878652i	$-0.341556\pi$
$13$	3.44304	0.954927	0.477463	+	0.878652i	$0.341556\pi$
$14$	2.36845	0.632995
$15$	0.0383375	0.00989871
$16$	7.24534	1.81133
$17$	1.70770	0.414179	0.207090	−	0.978322i	$-0.433601\pi$
$17$	1.70770	0.414179	0.207090	+	0.978322i	$0.433601\pi$
$18$	7.64779	1.80260
$19$	5.28092	1.21153	0.605763	−	0.795645i	$-0.292868\pi$
$19$	5.28092	1.21153	0.605763	+	0.795645i	$0.292868\pi$
$20$	14.7123	3.28976
$21$	−0.0108924	−0.00237691
$22$	14.1990	3.02725
$23$	−9.41041	−1.96221	−0.981103	−	0.193487i	$-0.938020\pi$
$23$	−9.41041	−1.96221	−0.981103	+	0.193487i	$0.938020\pi$
$24$	−0.0747054	−0.0152492
$25$	5.69208	1.13842
$26$	−8.77761	−1.72143
$27$	−0.0703452	−0.0135379
$28$	−4.18002	−0.789949
$29$	1.77199	0.329050	0.164525	−	0.986373i	$-0.447391\pi$
$29$	1.77199	0.329050	0.164525	+	0.986373i	$0.447391\pi$
$30$	−0.0977369	−0.0178442
$31$	9.57642	1.71998	0.859988	−	0.510314i	$-0.170471\pi$
$31$	9.57642	1.71998	0.859988	+	0.510314i	$0.170471\pi$
$32$	−5.72761	−1.01251
$33$	−0.0653007	−0.0113674
$34$	−4.35358	−0.746634
$35$	−3.03781	−0.513484
$36$	−13.4974	−2.24956
$37$	−7.57145	−1.24474	−0.622370	−	0.782723i	$-0.713830\pi$
$37$	−7.57145	−1.24474	−0.622370	+	0.782723i	$0.713830\pi$
$38$	−13.4631	−2.18400
$39$	0.0403678	0.00646402
$40$	−20.8348	−3.29427
$41$	−8.48628	−1.32533	−0.662667	−	0.748914i	$-0.730576\pi$
$41$	−8.48628	−1.32533	−0.662667	+	0.748914i	$0.730576\pi$
$42$	0.0277688	0.00428482
$43$	6.66532	1.01645	0.508226	−	0.861224i	$-0.330302\pi$
$43$	6.66532	1.01645	0.508226	+	0.861224i	$0.330302\pi$
$44$	−25.0595	−3.77787
$45$	−9.80917	−1.46227
$46$	23.9907	3.53724
$47$	2.35175	0.343037	0.171519	−	0.985181i	$-0.445133\pi$
$47$	2.35175	0.343037	0.171519	+	0.985181i	$0.445133\pi$
$48$	0.0849477	0.0122611
$49$	−6.13690	−0.876700
$50$	−14.5113	−2.05220
$51$	0.0200219	0.00280363
$52$	15.4914	2.14827
$53$	−6.47642	−0.889605	−0.444803	−	0.895629i	$-0.646726\pi$
$53$	−6.47642	−0.889605	−0.444803	+	0.895629i	$0.646726\pi$
$54$	0.179337	0.0244046
$55$	−18.2119	−2.45569
$56$	5.91955	0.791033
$57$	0.0619160	0.00820097
$58$	−4.51747	−0.593172
$59$	6.35518	0.827374	0.413687	−	0.910419i	$-0.364241\pi$
$59$	6.35518	0.827374	0.413687	+	0.910419i	$0.364241\pi$
$60$	0.172493	0.0222688
$61$	9.96874	1.27637	0.638183	−	0.769884i	$-0.279686\pi$
$61$	9.96874	1.27637	0.638183	+	0.769884i	$0.279686\pi$
$62$	−24.4139	−3.10057
$63$	2.78696	0.351125
$64$	0.111184	0.0138980
$65$	11.2583	1.39642
$66$	0.166476	0.0204918
$67$	−3.80965	−0.465423	−0.232712	−	0.972546i	$-0.574760\pi$
$67$	−3.80965	−0.465423	−0.232712	+	0.972546i	$0.574760\pi$
$68$	7.68353	0.931765
$69$	−0.110332	−0.0132824
$70$	7.74454	0.925649
$71$	−1.00000	−0.118678
$71$	−1.00000	−0.118678
$72$	19.1144	2.25265
$73$	3.10423	0.363322	0.181661	−	0.983361i	$-0.441853\pi$
$73$	3.10423	0.363322	0.181661	+	0.983361i	$0.441853\pi$
$74$	19.3025	2.24387
$75$	0.0667366	0.00770607
$76$	23.7606	2.72553
$77$	5.17434	0.589670
$78$	−0.102913	−0.0116526
$79$	10.9911	1.23659	0.618295	−	0.785946i	$-0.287824\pi$
$79$	10.9911	1.23659	0.618295	+	0.785946i	$0.287824\pi$
$80$	23.6913	2.64877
$81$	8.99876	0.999863
$82$	21.6347	2.38916
$83$	−0.444810	−0.0488242	−0.0244121	−	0.999702i	$-0.507771\pi$
$83$	−0.444810	−0.0488242	−0.0244121	+	0.999702i	$0.507771\pi$
$84$	−0.0490085	−0.00534727
$85$	5.58398	0.605667
$86$	−16.9924	−1.83234
$87$	0.0207756	0.00222738
$88$	35.4881	3.78305
$89$	−16.2834	−1.72604	−0.863021	−	0.505169i	$-0.831430\pi$
$89$	−16.2834	−1.72604	−0.863021	+	0.505169i	$0.831430\pi$
$90$	25.0073	2.63600
$91$	−3.19869	−0.335314
$92$	−42.3406	−4.41431
$93$	0.112278	0.0116427
$94$	−5.99549	−0.618388
$95$	17.2679	1.77165
$96$	−0.0671532	−0.00685380
$97$	1.42351	0.144536	0.0722678	−	0.997385i	$-0.476976\pi$
$97$	1.42351	0.144536	0.0722678	+	0.997385i	$0.476976\pi$
$98$	15.6453	1.58041
$99$	16.7081	1.67922
$100$	25.6106	2.56106
$101$	3.69311	0.367478	0.183739	−	0.982975i	$-0.441180\pi$
$101$	3.69311	0.367478	0.183739	+	0.982975i	$0.441180\pi$
$102$	−0.0510435	−0.00505406
$103$	−2.27534	−0.224196	−0.112098	−	0.993697i	$-0.535757\pi$
$103$	−2.27534	−0.224196	−0.112098	+	0.993697i	$0.535757\pi$
$104$	−21.9382	−2.15121
$105$	−0.0356167	−0.00347584
$106$	16.5109	1.60368
$107$	4.03121	0.389711	0.194856	−	0.980832i	$-0.437576\pi$
$107$	4.03121	0.389711	0.194856	+	0.980832i	$0.437576\pi$
$108$	−0.316507	−0.0304559
$109$	−11.8856	−1.13843	−0.569216	−	0.822188i	$-0.692753\pi$
$109$	−11.8856	−1.13843	−0.569216	+	0.822188i	$0.692753\pi$
$110$	46.4291	4.42684
$111$	−0.0887713	−0.00842580
$112$	−6.73114	−0.636033
$113$	−1.00000	−0.0940721
$113$	−1.00000	−0.0940721
$114$	−0.157847	−0.0147837
$115$	−30.7708	−2.86940
$116$	7.97276	0.740252
$117$	−10.3286	−0.954883
$118$	−16.2018	−1.49149
$119$	−1.58651	−0.145435
$120$	−0.244277	−0.0222994
$121$	20.0205	1.82005
$122$	−25.4141	−2.30089
$123$	−0.0994971	−0.00897135
$124$	43.0875	3.86937
$125$	2.26300	0.202409
$126$	−7.10503	−0.632966
$127$	14.6142	1.29680	0.648400	−	0.761300i	$-0.275439\pi$
$127$	14.6142	1.29680	0.648400	+	0.761300i	$0.275439\pi$
$128$	11.1718	0.987455
$129$	0.0781473	0.00688048
$130$	−28.7017	−2.51730
$131$	−3.45705	−0.302044	−0.151022	−	0.988530i	$-0.548256\pi$
$131$	−3.45705	−0.302044	−0.151022	+	0.988530i	$0.548256\pi$
$132$	−0.293810	−0.0255728
$133$	−4.90614	−0.425416
$134$	9.71225	0.839010
$135$	−0.230020	−0.0197970
$136$	−10.8811	−0.933043
$137$	5.82743	0.497871	0.248936	−	0.968520i	$-0.419919\pi$
$137$	5.82743	0.497871	0.248936	+	0.968520i	$0.419919\pi$
$138$	0.281278	0.0239440
$139$	−12.2602	−1.03990	−0.519948	−	0.854198i	$-0.674049\pi$
$139$	−12.2602	−1.03990	−0.519948	+	0.854198i	$0.674049\pi$
$140$	−13.6681	−1.15517
$141$	0.0275730	0.00232206
$142$	2.54938	0.213939
$143$	−19.1764	−1.60361
$144$	−21.7350	−1.81125
$145$	5.79417	0.481180
$146$	−7.91385	−0.654955
$147$	−0.0719519	−0.00593449
$148$	−34.0665	−2.80025
$149$	−5.41982	−0.444009	−0.222004	−	0.975046i	$-0.571260\pi$
$149$	−5.41982	−0.444009	−0.222004	+	0.975046i	$0.571260\pi$
$150$	−0.170137	−0.0138916
$151$	−9.47806	−0.771314	−0.385657	−	0.922642i	$-0.626025\pi$
$151$	−9.47806	−0.771314	−0.385657	+	0.922642i	$0.626025\pi$
$152$	−33.6487	−2.72927
$153$	−5.12288	−0.414160
$154$	−13.1913	−1.06299
$155$	31.3137	2.51518
$156$	0.181628	0.0145419
$157$	−9.38842	−0.749277	−0.374639	−	0.927171i	$-0.622233\pi$
$157$	−9.38842	−0.749277	−0.374639	+	0.927171i	$0.622233\pi$
$158$	−28.0204	−2.22918
$159$	−0.0759326	−0.00602185
$160$	−18.7286	−1.48062
$161$	8.74256	0.689010
$162$	−22.9413	−1.80244
$163$	2.88184	0.225723	0.112862	−	0.993611i	$-0.463998\pi$
$163$	2.88184	0.225723	0.112862	+	0.993611i	$0.463998\pi$
$164$	−38.1826	−2.98156
$165$	−0.213525	−0.0166229
$166$	1.13399	0.0880146
$167$	0.473924	0.0366734	0.0183367	−	0.999832i	$-0.494163\pi$
$167$	0.473924	0.0366734	0.0183367	+	0.999832i	$0.494163\pi$
$168$	0.0694036	0.00535460
$169$	−1.14549	−0.0881148
$170$	−14.2357	−1.09183
$171$	−15.8420	−1.21147
$172$	29.9895	2.28668
$173$	−3.24839	−0.246970	−0.123485	−	0.992346i	$-0.539407\pi$
$173$	−3.24839	−0.246970	−0.123485	+	0.992346i	$0.539407\pi$
$174$	−0.0529649	−0.00401526
$175$	−5.28811	−0.399744
$176$	−40.3537	−3.04177
$177$	0.0745111	0.00560060
$178$	41.5127	3.11151
$179$	17.4771	1.30630	0.653150	−	0.757229i	$-0.273447\pi$
$179$	17.4771	1.30630	0.653150	+	0.757229i	$0.273447\pi$
$180$	−44.1347	−3.28961
$181$	16.5353	1.22906	0.614530	−	0.788893i	$-0.289346\pi$
$181$	16.5353	1.22906	0.614530	+	0.788893i	$0.289346\pi$
$182$	8.15467	0.604464
$183$	0.116878	0.00863989
$184$	59.9608	4.42037
$185$	−24.7577	−1.82022
$186$	−0.286240	−0.0209882
$187$	−9.51124	−0.695531
$188$	10.5813	0.771720
$189$	0.0653528	0.00475372
$190$	−44.0225	−3.19373
$191$	−25.2018	−1.82354	−0.911769	−	0.410704i	$-0.865283\pi$
$191$	−25.2018	−1.82354	−0.911769	+	0.410704i	$0.865283\pi$
$192$	0.00130358	9.40775e−5 0
$193$	−18.7587	−1.35028	−0.675139	−	0.737691i	$-0.735916\pi$
$193$	−18.7587	−1.35028	−0.675139	+	0.737691i	$0.735916\pi$
$194$	−3.62907	−0.260552
$195$	0.131998	0.00945254
$196$	−27.6120	−1.97228
$197$	−5.02044	−0.357692	−0.178846	−	0.983877i	$-0.557236\pi$
$197$	−5.02044	−0.357692	−0.178846	+	0.983877i	$0.557236\pi$
$198$	−42.5952	−3.02711
$199$	−25.4114	−1.80136	−0.900682	−	0.434478i	$-0.856933\pi$
$199$	−25.4114	−1.80136	−0.900682	+	0.434478i	$0.856933\pi$
$200$	−36.2685	−2.56457
$201$	−0.0446661	−0.00315051
$202$	−9.41512	−0.662446
$203$	−1.64623	−0.115543
$204$	0.0900853	0.00630723
$205$	−27.7491	−1.93808
$206$	5.80071	0.404154
$207$	28.2299	1.96212
$208$	24.9460	1.72969
$209$	−29.4126	−2.03452
$210$	0.0908006	0.00626584
$211$	−9.95845	−0.685568	−0.342784	−	0.939414i	$-0.611370\pi$
$211$	−9.95845	−0.685568	−0.342784	+	0.939414i	$0.611370\pi$
$212$	−29.1396	−2.00132
$213$	−0.0117245	−0.000803347 0
$214$	−10.2771	−0.702526
$215$	21.7947	1.48639
$216$	0.448222	0.0304976
$217$	−8.89679	−0.603953
$218$	30.3008	2.05223
$219$	0.0363954	0.00245937
$220$	−81.9415	−5.52449
$221$	5.87969	0.395511
$222$	0.226312	0.0151890
$223$	10.8374	0.725725	0.362862	−	0.931843i	$-0.381799\pi$
$223$	10.8374	0.725725	0.362862	+	0.931843i	$0.381799\pi$
$224$	5.32113	0.355533
$225$	−17.0754	−1.13836
$226$	2.54938	0.169582
$227$	−3.82878	−0.254125	−0.127063	−	0.991895i	$-0.540555\pi$
$227$	−3.82878	−0.254125	−0.127063	+	0.991895i	$0.540555\pi$
$228$	0.278581	0.0184494
$229$	4.40440	0.291051	0.145526	−	0.989354i	$-0.453513\pi$
$229$	4.40440	0.291051	0.145526	+	0.989354i	$0.453513\pi$
$230$	78.4466	5.17261
$231$	0.0606663	0.00399155
$232$	−11.2907	−0.741268
$233$	6.40012	0.419286	0.209643	−	0.977778i	$-0.432770\pi$
$233$	6.40012	0.419286	0.209643	+	0.977778i	$0.432770\pi$
$234$	26.3316	1.72135
$235$	7.68991	0.501635
$236$	28.5941	1.86132
$237$	0.128864	0.00837063
$238$	4.04461	0.262173
$239$	16.0555	1.03855	0.519273	−	0.854609i	$-0.326203\pi$
$239$	16.0555	1.03855	0.519273	+	0.854609i	$0.326203\pi$
$240$	0.277768	0.0179299
$241$	−28.5223	−1.83728	−0.918641	−	0.395094i	$-0.870712\pi$
$241$	−28.5223	−1.83728	−0.918641	+	0.395094i	$0.870712\pi$
$242$	−51.0399	−3.28097
$243$	0.316541	0.0203061
$244$	44.8527	2.87140
$245$	−20.0669	−1.28203
$246$	0.253656	0.0161725
$247$	18.1824	1.15692
$248$	−61.0186	−3.87468
$249$	−0.00521516	−0.000330497 0
$250$	−5.76925	−0.364880
$251$	18.0735	1.14079	0.570395	−	0.821371i	$-0.306790\pi$
$251$	18.0735	1.14079	0.570395	+	0.821371i	$0.306790\pi$
$252$	12.5395	0.789913
$253$	52.4123	3.29513
$254$	−37.2571	−2.33772
$255$	0.0654692	0.00409984
$256$	−28.7035	−1.79397
$257$	−28.2394	−1.76153	−0.880764	−	0.473556i	$-0.842970\pi$
$257$	−28.2394	−1.76153	−0.880764	+	0.473556i	$0.842970\pi$
$258$	−0.199227	−0.0124033
$259$	7.03411	0.437079
$260$	50.6548	3.14148
$261$	−5.31572	−0.329035
$262$	8.81334	0.544490
$263$	−19.8293	−1.22273	−0.611364	−	0.791349i	$-0.709379\pi$
$263$	−19.8293	−1.22273	−0.611364	+	0.791349i	$0.709379\pi$
$264$	0.416080	0.0256079
$265$	−21.1771	−1.30090
$266$	12.5076	0.766890
$267$	−0.190915	−0.0116838
$268$	−17.1409	−1.04705
$269$	12.9440	0.789212	0.394606	−	0.918851i	$-0.370881\pi$
$269$	12.9440	0.789212	0.394606	+	0.918851i	$0.370881\pi$
$270$	0.586408	0.0356877
$271$	−19.2483	−1.16925	−0.584625	−	0.811303i	$-0.698758\pi$
$271$	−19.2483	−1.16925	−0.584625	+	0.811303i	$0.698758\pi$
$272$	12.3729	0.750217
$273$	−0.0375029	−0.00226978
$274$	−14.8563	−0.897504
$275$	−31.7026	−1.91174
$276$	−0.496421	−0.0298810
$277$	−27.4561	−1.64967	−0.824837	−	0.565370i	$-0.808733\pi$
$277$	−27.4561	−1.64967	−0.824837	+	0.565370i	$0.808733\pi$
$278$	31.2559	1.87460
$279$	−28.7279	−1.71990
$280$	19.3562	1.15675
$281$	2.25837	0.134723	0.0673616	−	0.997729i	$-0.478542\pi$
$281$	2.25837	0.134723	0.0673616	+	0.997729i	$0.478542\pi$
$282$	−0.0702940	−0.00418594
$283$	−1.49274	−0.0887343	−0.0443671	−	0.999015i	$-0.514127\pi$
$283$	−1.49274	−0.0887343	−0.0443671	+	0.999015i	$0.514127\pi$
$284$	−4.49933	−0.266986
$285$	0.202457	0.0119925
$286$	48.8878	2.89080
$287$	7.88401	0.465379
$288$	17.1821	1.01246
$289$	−14.0837	−0.828456
$290$	−14.7715	−0.867415
$291$	0.0166899	0.000978380 0
$292$	13.9670	0.817354
$293$	9.94664	0.581089	0.290544	−	0.956861i	$-0.406164\pi$
$293$	9.94664	0.581089	0.290544	+	0.956861i	$0.406164\pi$
$294$	0.183433	0.0106980
$295$	20.7806	1.20990
$296$	48.2434	2.80409
$297$	0.391795	0.0227343
$298$	13.8172	0.800407
$299$	−32.4004	−1.87376
$300$	0.300270	0.0173361
$301$	−6.19228	−0.356917
$302$	24.1632	1.39043
$303$	0.0432997	0.00248750
$304$	38.2620	2.19448
$305$	32.5965	1.86647
$306$	13.0602	0.746599
$307$	−26.0517	−1.48685	−0.743425	−	0.668819i	$-0.766800\pi$
$307$	−26.0517	−1.48685	−0.743425	+	0.668819i	$0.766800\pi$
$308$	23.2811	1.32656
$309$	−0.0266772	−0.00151761
$310$	−79.8305	−4.53407
$311$	4.82082	0.273364	0.136682	−	0.990615i	$-0.456356\pi$
$311$	4.82082	0.273364	0.136682	+	0.990615i	$0.456356\pi$
$312$	−0.257213	−0.0145618
$313$	9.44313	0.533757	0.266879	−	0.963730i	$-0.414008\pi$
$313$	9.44313	0.533757	0.266879	+	0.963730i	$0.414008\pi$
$314$	23.9346	1.35071
$315$	9.11302	0.513461
$316$	49.4524	2.78192
$317$	10.8513	0.609470	0.304735	−	0.952437i	$-0.401432\pi$
$317$	10.8513	0.609470	0.304735	+	0.952437i	$0.401432\pi$
$318$	0.193581	0.0108555
$319$	−9.86927	−0.552573
$320$	0.363559	0.0203235
$321$	0.0472638	0.00263801
$322$	−22.2881	−1.24207
$323$	9.01825	0.501789
$324$	40.4884	2.24936
$325$	19.5980	1.08710
$326$	−7.34691	−0.406908
$327$	−0.139352	−0.00770619
$328$	54.0724	2.98565
$329$	−2.18484	−0.120454
$330$	0.544356	0.0299658
$331$	9.31371	0.511928	0.255964	−	0.966686i	$-0.417607\pi$
$331$	9.31371	0.511928	0.255964	+	0.966686i	$0.417607\pi$
$332$	−2.00135	−0.109838
$333$	22.7133	1.24468
$334$	−1.20821	−0.0661104
$335$	−12.4571	−0.680603
$336$	−0.0789191	−0.00430539
$337$	28.4746	1.55111	0.775556	−	0.631279i	$-0.217470\pi$
$337$	28.4746	1.55111	0.775556	+	0.631279i	$0.217470\pi$
$338$	2.92029	0.158843
$339$	−0.0117245	−0.000636786 0
$340$	25.1242	1.36255
$341$	−53.3369	−2.88836
$342$	40.3873	2.18390
$343$	12.2046	0.658986
$344$	−42.4697	−2.28981
$345$	−0.360772	−0.0194233
$346$	8.28137	0.445209
$347$	−32.7256	−1.75680	−0.878401	−	0.477924i	$-0.841389\pi$
$347$	−32.7256	−1.75680	−0.878401	+	0.477924i	$0.841389\pi$
$348$	0.0934763	0.00501086
$349$	−26.3566	−1.41084	−0.705418	−	0.708792i	$-0.749241\pi$
$349$	−26.3566	−1.41084	−0.705418	+	0.708792i	$0.749241\pi$
$350$	13.4814	0.720612
$351$	−0.242201	−0.0129277
$352$	31.9006	1.70031
$353$	−19.1170	−1.01749	−0.508747	−	0.860916i	$-0.669891\pi$
$353$	−19.1170	−1.01749	−0.508747	+	0.860916i	$0.669891\pi$
$354$	−0.189957	−0.0100961
$355$	−3.26987	−0.173547
$356$	−73.2646	−3.88302
$357$	−0.0186010	−0.000984468 0
$358$	−44.5557	−2.35484
$359$	−3.22116	−0.170006	−0.0850031	−	0.996381i	$-0.527090\pi$
$359$	−3.22116	−0.170006	−0.0850031	+	0.996381i	$0.527090\pi$
$360$	62.5016	3.29412
$361$	8.88810	0.467795
$362$	−42.1548	−2.21561
$363$	0.234730	0.0123201
$364$	−14.3920	−0.754344
$365$	10.1504	0.531298
$366$	−0.297967	−0.0155750
$367$	−17.0879	−0.891979	−0.445990	−	0.895038i	$-0.647148\pi$
$367$	−17.0879	−0.891979	−0.445990	+	0.895038i	$0.647148\pi$
$368$	−68.1816	−3.55421
$369$	25.4577	1.32527
$370$	63.1168	3.28128
$371$	6.01680	0.312377
$372$	0.505178	0.0261923
$373$	7.94138	0.411189	0.205595	−	0.978637i	$-0.434087\pi$
$373$	7.94138	0.411189	0.205595	+	0.978637i	$0.434087\pi$
$374$	24.2478	1.25382
$375$	0.0265325	0.00137013
$376$	−14.9847	−0.772779
$377$	6.10102	0.314218
$378$	−0.166609	−0.00856945
$379$	25.9919	1.33511	0.667557	−	0.744559i	$-0.267340\pi$
$379$	25.9919	1.33511	0.667557	+	0.744559i	$0.267340\pi$
$380$	77.6942	3.98563
$381$	0.171344	0.00877820
$382$	64.2489	3.28726
$383$	4.18043	0.213610	0.106805	−	0.994280i	$-0.465938\pi$
$383$	4.18043	0.213610	0.106805	+	0.994280i	$0.465938\pi$
$384$	0.130983	0.00668421
$385$	16.9194	0.862294
$386$	47.8229	2.43412
$387$	−19.9950	−1.01640
$388$	6.40485	0.325157
$389$	−3.59198	−0.182121	−0.0910603	−	0.995845i	$-0.529026\pi$
$389$	−3.59198	−0.182121	−0.0910603	+	0.995845i	$0.529026\pi$
$390$	−0.336512	−0.0170399
$391$	−16.0702	−0.812704
$392$	39.1028	1.97499
$393$	−0.0405321	−0.00204457
$394$	12.7990	0.644805
$395$	35.9394	1.80831
$396$	75.1751	3.77769
$397$	10.3509	0.519499	0.259749	−	0.965676i	$-0.416360\pi$
$397$	10.3509	0.519499	0.259749	+	0.965676i	$0.416360\pi$
$398$	64.7832	3.24729
$399$	−0.0575218	−0.00287969
$400$	41.2410	2.06205
$401$	31.4248	1.56928	0.784640	−	0.619951i	$-0.212848\pi$
$401$	31.4248	1.56928	0.784640	+	0.619951i	$0.212848\pi$
$402$	0.113871	0.00567937
$403$	32.9720	1.64245
$404$	16.6165	0.826702
$405$	29.4248	1.46213
$406$	4.19686	0.208287
$407$	42.1700	2.09029
$408$	−0.127575	−0.00631589
$409$	−8.92108	−0.441119	−0.220560	−	0.975374i	$-0.570788\pi$
$409$	−8.92108	−0.441119	−0.220560	+	0.975374i	$0.570788\pi$
$410$	70.7429	3.49374
$411$	0.0683235	0.00337015
$412$	−10.2375	−0.504366
$413$	−5.90416	−0.290525
$414$	−71.9688	−3.53707
$415$	−1.45447	−0.0713972
$416$	−19.7204	−0.966872
$417$	−0.143744	−0.00703919
$418$	74.9840	3.66759
$419$	5.05826	0.247112	0.123556	−	0.992338i	$-0.460570\pi$
$419$	5.05826	0.247112	0.123556	+	0.992338i	$0.460570\pi$
$420$	−0.160252	−0.00781948
$421$	−37.4612	−1.82575	−0.912873	−	0.408244i	$-0.866141\pi$
$421$	−37.4612	−1.82575	−0.912873	+	0.408244i	$0.866141\pi$
$422$	25.3879	1.23586
$423$	−7.05492	−0.343022
$424$	41.2662	2.00406
$425$	9.72038	0.471508
$426$	0.0298901	0.00144818
$427$	−9.26127	−0.448184
$428$	18.1377	0.876721
$429$	−0.224833	−0.0108550
$430$	−55.5631	−2.67949
$431$	24.5304	1.18159	0.590793	−	0.806823i	$-0.298815\pi$
$431$	24.5304	1.18159	0.590793	+	0.806823i	$0.298815\pi$
$432$	−0.509675	−0.0245217
$433$	−12.0374	−0.578479	−0.289239	−	0.957257i	$-0.593402\pi$
$433$	−12.0374	−0.578479	−0.289239	+	0.957257i	$0.593402\pi$
$434$	22.6813	1.08874
$435$	0.0679336	0.00325717
$436$	−53.4772	−2.56109
$437$	−49.6956	−2.37726
$438$	−0.0927857	−0.00443347
$439$	28.2367	1.34766	0.673831	−	0.738885i	$-0.264648\pi$
$439$	28.2367	1.34766	0.673831	+	0.738885i	$0.264648\pi$
$440$	116.042	5.53207
$441$	18.4099	0.876660
$442$	−14.9896	−0.712980
$443$	12.1710	0.578260	0.289130	−	0.957290i	$-0.406634\pi$
$443$	12.1710	0.578260	0.289130	+	0.957290i	$0.406634\pi$
$444$	−0.399412	−0.0189552
$445$	−53.2448	−2.52405
$446$	−27.6286	−1.30825
$447$	−0.0635445	−0.00300555
$448$	−0.103294	−0.00488016
$449$	7.93731	0.374585	0.187292	−	0.982304i	$-0.440029\pi$
$449$	7.93731	0.374585	0.187292	+	0.982304i	$0.440029\pi$
$450$	43.5318	2.05211
$451$	47.2652	2.22563
$452$	−4.49933	−0.211631
$453$	−0.111125	−0.00522112
$454$	9.76102	0.458107
$455$	−10.4593	−0.490340
$456$	−0.394513	−0.0184748
$457$	−19.2744	−0.901618	−0.450809	−	0.892620i	$-0.648864\pi$
$457$	−19.2744	−0.901618	−0.450809	+	0.892620i	$0.648864\pi$
$458$	−11.2285	−0.524673
$459$	−0.120129	−0.00560713
$460$	−138.448	−6.45519
$461$	−14.5004	−0.675352	−0.337676	−	0.941262i	$-0.609641\pi$
$461$	−14.5004	−0.675352	−0.337676	+	0.941262i	$0.609641\pi$
$462$	−0.154662	−0.00719550
$463$	−16.9131	−0.786019	−0.393010	−	0.919534i	$-0.628566\pi$
$463$	−16.9131	−0.786019	−0.393010	+	0.919534i	$0.628566\pi$
$464$	12.8386	0.596019
$465$	0.367136	0.0170255
$466$	−16.3163	−0.755839
$467$	1.91976	0.0888360	0.0444180	−	0.999013i	$-0.485857\pi$
$467$	1.91976	0.0888360	0.0444180	+	0.999013i	$0.485857\pi$
$468$	−46.4720	−2.14817
$469$	3.53928	0.163429
$470$	−19.6045	−0.904289
$471$	−0.110074	−0.00507195
$472$	−40.4936	−1.86387
$473$	−37.1232	−1.70693
$474$	−0.328524	−0.0150896
$475$	30.0594	1.37922
$476$	−7.13824	−0.327181
$477$	19.4284	0.889565
$478$	−40.9316	−1.87217
$479$	4.59034	0.209738	0.104869	−	0.994486i	$-0.466558\pi$
$479$	4.59034	0.209738	0.104869	+	0.994486i	$0.466558\pi$
$480$	−0.219583	−0.0100225
$481$	−26.0688	−1.18863
$482$	72.7141	3.31204
$483$	0.102502	0.00466399
$484$	90.0790	4.09450
$485$	4.65470	0.211359
$486$	−0.806984	−0.0366055
$487$	22.7328	1.03012	0.515060	−	0.857154i	$-0.327769\pi$
$487$	22.7328	1.03012	0.515060	+	0.857154i	$0.327769\pi$
$488$	−63.5183	−2.87534
$489$	0.0337881	0.00152795
$490$	51.1581	2.31109
$491$	−16.4531	−0.742520	−0.371260	−	0.928529i	$-0.621074\pi$
$491$	−16.4531	−0.742520	−0.371260	+	0.928529i	$0.621074\pi$
$492$	−0.447671	−0.0201826
$493$	3.02603	0.136285
$494$	−46.3538	−2.08556
$495$	54.6332	2.45558
$496$	69.3844	3.11545
$497$	0.929031	0.0416727
$498$	0.0132954	0.000595782 0
$499$	−19.5547	−0.875390	−0.437695	−	0.899124i	$-0.644205\pi$
$499$	−19.5547	−0.875390	−0.437695	+	0.899124i	$0.644205\pi$
$500$	10.1820	0.455353
$501$	0.00555651	0.000248246 0
$502$	−46.0762	−2.05648
$503$	−34.7915	−1.55128	−0.775638	−	0.631178i	$-0.782572\pi$
$503$	−34.7915	−1.55128	−0.775638	+	0.631178i	$0.782572\pi$
$504$	−17.7578	−0.790997
$505$	12.0760	0.537374
$506$	−133.619	−5.94008
$507$	−0.0134303	−0.000596460 0
$508$	65.7541	2.91737
$509$	−11.1044	−0.492193	−0.246097	−	0.969245i	$-0.579148\pi$
$509$	−11.1044	−0.492193	−0.246097	+	0.969245i	$0.579148\pi$
$510$	−0.166906	−0.00739071
$511$	−2.88392	−0.127577
$512$	50.8325	2.24650
$513$	−0.371487	−0.0164016
$514$	71.9930	3.17548
$515$	−7.44008	−0.327849
$516$	0.351611	0.0154788
$517$	−13.0983	−0.576063
$518$	−17.9326	−0.787914
$519$	−0.0380856	−0.00167177
$520$	−71.7351	−3.14579
$521$	−40.2936	−1.76530	−0.882648	−	0.470035i	$-0.844241\pi$
$521$	−40.2936	−1.76530	−0.882648	+	0.470035i	$0.844241\pi$
$522$	13.5518	0.593145
$523$	−25.2861	−1.10568	−0.552841	−	0.833286i	$-0.686456\pi$
$523$	−25.2861	−1.10568	−0.552841	+	0.833286i	$0.686456\pi$
$524$	−15.5544	−0.679498
$525$	−0.0620003	−0.00270592
$526$	50.5524	2.20419
$527$	16.3537	0.712378
$528$	−0.473126	−0.0205901
$529$	65.5558	2.85025
$530$	53.9884	2.34511
$531$	−19.0647	−0.827336
$532$	−22.0743	−0.957044
$533$	−29.2186	−1.26560
$534$	0.486714	0.0210622
$535$	13.1815	0.569888
$536$	24.2741	1.04848
$537$	0.204910	0.00884250
$538$	−32.9992	−1.42270
$539$	34.1801	1.47224
$540$	−1.03494	−0.0445366
$541$	−5.32773	−0.229057	−0.114529	−	0.993420i	$-0.536536\pi$
$541$	−5.32773	−0.229057	−0.114529	+	0.993420i	$0.536536\pi$
$542$	49.0712	2.10779
$543$	0.193868	0.00831966
$544$	−9.78107	−0.419360
$545$	−38.8643	−1.66477
$546$	0.0956091	0.00409169
$547$	−16.1736	−0.691532	−0.345766	−	0.938321i	$-0.612381\pi$
$547$	−16.1736	−0.691532	−0.345766	+	0.938321i	$0.612381\pi$
$548$	26.2196	1.12004
$549$	−29.9049	−1.27631
$550$	80.8220	3.44626
$551$	9.35772	0.398652
$552$	0.703008	0.0299220
$553$	−10.2110	−0.434217
$554$	69.9959	2.97384
$555$	−0.290271	−0.0123213
$556$	−55.1627	−2.33942
$557$	5.62127	0.238181	0.119090	−	0.992883i	$-0.462002\pi$
$557$	5.62127	0.238181	0.119090	+	0.992883i	$0.462002\pi$
$558$	73.2384	3.10043
$559$	22.9489	0.970636
$560$	−22.0100	−0.930092
$561$	−0.111514	−0.00470813
$562$	−5.75745	−0.242863
$563$	−19.2079	−0.809516	−0.404758	−	0.914424i	$-0.632644\pi$
$563$	−19.2079	−0.809516	−0.404758	+	0.914424i	$0.632644\pi$
$564$	0.124060	0.00522387
$565$	−3.26987	−0.137565
$566$	3.80557	0.159960
$567$	−8.36013	−0.351092
$568$	6.37175	0.267353
$569$	−19.5553	−0.819801	−0.409900	−	0.912130i	$-0.634437\pi$
$569$	−19.5553	−0.819801	−0.409900	+	0.912130i	$0.634437\pi$
$570$	−0.516141	−0.0216188
$571$	−18.4863	−0.773626	−0.386813	−	0.922158i	$-0.626424\pi$
$571$	−18.4863	−0.773626	−0.386813	+	0.922158i	$0.626424\pi$
$572$	−86.2809	−3.60759
$573$	−0.295477	−0.0123437
$574$	−20.0993	−0.838930
$575$	−53.5648	−2.23380
$576$	−0.333537	−0.0138974
$577$	−14.8524	−0.618315	−0.309158	−	0.951011i	$-0.600047\pi$
$577$	−14.8524	−0.618315	−0.309158	+	0.951011i	$0.600047\pi$
$578$	35.9048	1.49344
$579$	−0.219935	−0.00914020
$580$	26.0699	1.08249
$581$	0.413242	0.0171442
$582$	−0.0425489	−0.00176371
$583$	36.0711	1.49391
$584$	−19.7794	−0.818476
$585$	−33.7734	−1.39636
$586$	−25.3578	−1.04752
$587$	−25.0986	−1.03593	−0.517965	−	0.855402i	$-0.673310\pi$
$587$	−25.0986	−1.03593	−0.517965	+	0.855402i	$0.673310\pi$
$588$	−0.323736	−0.0133506
$589$	50.5723	2.08380
$590$	−52.9777	−2.18106
$591$	−0.0588620	−0.00242126
$592$	−54.8577	−2.25464
$593$	−47.3392	−1.94399	−0.971995	−	0.235003i	$-0.924490\pi$
$593$	−47.3392	−1.94399	−0.971995	+	0.235003i	$0.924490\pi$
$594$	−0.998834	−0.0409827
$595$	−5.18769	−0.212674
$596$	−24.3856	−0.998872
$597$	−0.297935	−0.0121937
$598$	82.6009	3.37780
$599$	27.0511	1.10528	0.552639	−	0.833421i	$-0.313621\pi$
$599$	27.0511	1.10528	0.552639	+	0.833421i	$0.313621\pi$
$600$	−0.425229	−0.0173599
$601$	31.3381	1.27831	0.639154	−	0.769079i	$-0.279285\pi$
$601$	31.3381	1.27831	0.639154	+	0.769079i	$0.279285\pi$
$602$	15.7865	0.643409
$603$	11.4284	0.465402
$604$	−42.6450	−1.73520
$605$	65.4646	2.66151
$606$	−0.110387	−0.00448418
$607$	16.9699	0.688788	0.344394	−	0.938825i	$-0.388084\pi$
$607$	16.9699	0.688788	0.344394	+	0.938825i	$0.388084\pi$
$608$	−30.2471	−1.22668
$609$	−0.0193012	−0.000782123 0
$610$	−83.1009	−3.36466
$611$	8.09715	0.327576
$612$	−23.0495	−0.931722
$613$	−19.7055	−0.795898	−0.397949	−	0.917407i	$-0.630278\pi$
$613$	−19.7055	−0.795898	−0.397949	+	0.917407i	$0.630278\pi$
$614$	66.4157	2.68032
$615$	−0.325343	−0.0131191
$616$	−32.9696	−1.32838
$617$	−43.7337	−1.76065	−0.880327	−	0.474368i	$-0.842677\pi$
$617$	−43.7337	−1.76065	−0.880327	+	0.474368i	$0.842677\pi$
$618$	0.0680102	0.00273577
$619$	43.5685	1.75117	0.875583	−	0.483068i	$-0.160478\pi$
$619$	43.5685	1.75117	0.875583	+	0.483068i	$0.160478\pi$
$620$	140.891	5.65831
$621$	0.661977	0.0265642
$622$	−12.2901	−0.492788
$623$	15.1278	0.606083
$624$	0.292478	0.0117085
$625$	−21.0606	−0.842426
$626$	−24.0741	−0.962195
$627$	−0.344848	−0.0137719
$628$	−42.2416	−1.68562
$629$	−12.9298	−0.515545
$630$	−23.2326	−0.925607
$631$	42.0877	1.67548	0.837742	−	0.546067i	$-0.183875\pi$
$631$	42.0877	1.67548	0.837742	+	0.546067i	$0.183875\pi$
$632$	−70.0322	−2.78573
$633$	−0.116757	−0.00464069
$634$	−27.6641	−1.09868
$635$	47.7866	1.89635
$636$	−0.341646	−0.0135472
$637$	−21.1296	−0.837185
$638$	25.1605	0.996114
$639$	2.99986	0.118673
$640$	36.5303	1.44399
$641$	−45.8246	−1.80996	−0.904982	−	0.425450i	$-0.860116\pi$
$641$	−45.8246	−1.80996	−0.904982	+	0.425450i	$0.860116\pi$
$642$	−0.120493	−0.00475549
$643$	20.1937	0.796362	0.398181	−	0.917307i	$-0.369642\pi$
$643$	20.1937	0.796362	0.398181	+	0.917307i	$0.369642\pi$
$644$	39.3357	1.55004
$645$	0.255532	0.0100616
$646$	−22.9909	−0.904566
$647$	6.77909	0.266514	0.133257	−	0.991082i	$-0.457456\pi$
$647$	6.77909	0.266514	0.133257	+	0.991082i	$0.457456\pi$
$648$	−57.3379	−2.25244
$649$	−35.3959	−1.38941
$650$	−49.9628	−1.95970
$651$	−0.104310	−0.00408824
$652$	12.9664	0.507802
$653$	−38.1200	−1.49175	−0.745875	−	0.666086i	$-0.767968\pi$
$653$	−38.1200	−1.49175	−0.745875	+	0.666086i	$0.767968\pi$
$654$	0.355261	0.0138918
$655$	−11.3041	−0.441689
$656$	−61.4860	−2.40062
$657$	−9.31226	−0.363306
$658$	5.57000	0.217141
$659$	19.2408	0.749515	0.374758	−	0.927123i	$-0.377726\pi$
$659$	19.2408	0.749515	0.374758	+	0.927123i	$0.377726\pi$
$660$	−0.960720	−0.0373960
$661$	9.01691	0.350717	0.175359	−	0.984505i	$-0.443892\pi$
$661$	9.01691	0.350717	0.175359	+	0.984505i	$0.443892\pi$
$662$	−23.7442	−0.922844
$663$	0.0689362	0.00267726
$664$	2.83422	0.109989
$665$	−16.0424	−0.622099
$666$	−57.9049	−2.24377
$667$	−16.6751	−0.645663
$668$	2.13234	0.0825028
$669$	0.127063	0.00491252
$670$	31.7578	1.22691
$671$	−55.5220	−2.14340
$672$	0.0623874	0.00240665
$673$	−46.1469	−1.77883	−0.889417	−	0.457097i	$-0.848889\pi$
$673$	−46.1469	−1.77883	−0.889417	+	0.457097i	$0.848889\pi$
$674$	−72.5926	−2.79616
$675$	−0.400410	−0.0154118
$676$	−5.15395	−0.198229
$677$	36.0355	1.38496	0.692478	−	0.721439i	$-0.256519\pi$
$677$	36.0355	1.38496	0.692478	+	0.721439i	$0.256519\pi$
$678$	0.0298901	0.00114792
$679$	−1.32249	−0.0507524
$680$	−35.5797	−1.36442
$681$	−0.0448904	−0.00172021
$682$	135.976	5.20679
$683$	9.62920	0.368451	0.184226	−	0.982884i	$-0.441022\pi$
$683$	9.62920	0.368451	0.184226	+	0.982884i	$0.441022\pi$
$684$	−71.2786	−2.72540
$685$	19.0550	0.728053
$686$	−31.1141	−1.18794
$687$	0.0516393	0.00197016
$688$	48.2925	1.84113
$689$	−22.2986	−0.849508
$690$	0.919744	0.0350141
$691$	15.2620	0.580592	0.290296	−	0.956937i	$-0.406246\pi$
$691$	15.2620	0.580592	0.290296	+	0.956937i	$0.406246\pi$
$692$	−14.6156	−0.555601
$693$	−15.5223	−0.589643
$694$	83.4299	3.16696
$695$	−40.0893	−1.52067
$696$	−0.132377	−0.00501773
$697$	−14.4921	−0.548926
$698$	67.1929	2.54329
$699$	0.0750380	0.00283820
$700$	−23.7930	−0.899291
$701$	36.9246	1.39462	0.697312	−	0.716767i	$-0.254379\pi$
$701$	36.9246	1.39462	0.697312	+	0.716767i	$0.254379\pi$
$702$	0.617463	0.0233046
$703$	−39.9842	−1.50803
$704$	−0.619253	−0.0233390
$705$	0.0901602	0.00339563
$706$	48.7364	1.83422
$707$	−3.43101	−0.129036
$708$	0.335250	0.0125995
$709$	−24.3982	−0.916293	−0.458146	−	0.888877i	$-0.651486\pi$
$709$	−24.3982	−0.916293	−0.458146	+	0.888877i	$0.651486\pi$
$710$	8.33615	0.312850
$711$	−32.9716	−1.23653
$712$	103.754	3.88835
$713$	−90.1180	−3.37495
$714$	0.0474209	0.00177468
$715$	−62.7043	−2.34501
$716$	78.6353	2.93874
$717$	0.188242	0.00703004
$718$	8.21196	0.306467
$719$	5.08613	0.189680	0.0948402	−	0.995493i	$-0.469766\pi$
$719$	5.08613	0.189680	0.0948402	+	0.995493i	$0.469766\pi$
$720$	−71.0708	−2.64865
$721$	2.11386	0.0787243
$722$	−22.6591	−0.843286
$723$	−0.334408	−0.0124368
$724$	74.3979	2.76498
$725$	10.0863	0.374595
$726$	−0.598416	−0.0222093
$727$	−27.8236	−1.03192	−0.515960	−	0.856613i	$-0.672565\pi$
$727$	−27.8236	−1.03192	−0.515960	+	0.856613i	$0.672565\pi$
$728$	20.3812	0.755379
$729$	−26.9926	−0.999725
$730$	−25.8773	−0.957762
$731$	11.3824	0.420993
$732$	0.525874	0.0194369
$733$	−37.2228	−1.37486	−0.687428	−	0.726253i	$-0.741260\pi$
$733$	−37.2228	−1.37486	−0.687428	+	0.726253i	$0.741260\pi$
$734$	43.5635	1.60796
$735$	−0.235274	−0.00867820
$736$	53.8992	1.98675
$737$	21.2183	0.781585
$738$	−64.9012	−2.38905
$739$	27.7877	1.02219	0.511093	−	0.859526i	$-0.329241\pi$
$739$	27.7877	1.02219	0.511093	+	0.859526i	$0.329241\pi$
$740$	−111.393	−4.09489
$741$	0.213179	0.00783132
$742$	−15.3391	−0.563116
$743$	−1.49616	−0.0548888	−0.0274444	−	0.999623i	$-0.508737\pi$
$743$	−1.49616	−0.0548888	−0.0274444	+	0.999623i	$0.508737\pi$
$744$	−0.715410	−0.0262282
$745$	−17.7221	−0.649288
$746$	−20.2456	−0.741244
$747$	1.33437	0.0488220
$748$	−42.7943	−1.56471
$749$	−3.74511	−0.136844
$750$	−0.0676414	−0.00246992
$751$	9.83820	0.359001	0.179500	−	0.983758i	$-0.442552\pi$
$751$	9.83820	0.359001	0.179500	+	0.983758i	$0.442552\pi$
$752$	17.0392	0.621356
$753$	0.211902	0.00772215
$754$	−15.5538	−0.566436
$755$	−30.9921	−1.12792
$756$	0.294044	0.0106943
$757$	−41.0354	−1.49146	−0.745728	−	0.666250i	$-0.767898\pi$
$757$	−41.0354	−1.49146	−0.745728	+	0.666250i	$0.767898\pi$
$758$	−66.2632	−2.40679
$759$	0.614506	0.0223052
$760$	−110.027	−3.99110
$761$	11.8831	0.430762	0.215381	−	0.976530i	$-0.430901\pi$
$761$	11.8831	0.430762	0.215381	+	0.976530i	$0.430901\pi$
$762$	−0.436820	−0.0158243
$763$	11.0421	0.399750
$764$	−113.391	−4.10235
$765$	−16.7512	−0.605640
$766$	−10.6575	−0.385071
$767$	21.8811	0.790082
$768$	−0.336533	−0.0121436
$769$	45.9250	1.65610	0.828049	−	0.560656i	$-0.189451\pi$
$769$	45.9250	1.65610	0.828049	+	0.560656i	$0.189451\pi$
$770$	−43.1340	−1.55444
$771$	−0.331092	−0.0119240
$772$	−84.4015	−3.03768
$773$	−0.796653	−0.0286536	−0.0143268	−	0.999897i	$-0.504561\pi$
$773$	−0.796653	−0.0286536	−0.0143268	+	0.999897i	$0.504561\pi$
$774$	50.9749	1.83226
$775$	54.5097	1.95805
$776$	−9.07026	−0.325603
$777$	0.0824712	0.00295864
$778$	9.15732	0.328306
$779$	−44.8153	−1.60568
$780$	0.593901	0.0212651
$781$	5.56961	0.199296
$782$	40.9690	1.46505
$783$	−0.124651	−0.00445465
$784$	−44.4639	−1.58800
$785$	−30.6989	−1.09569
$786$	0.103332	0.00368572
$787$	−37.3664	−1.33197	−0.665983	−	0.745967i	$-0.731988\pi$
$787$	−37.3664	−1.33197	−0.665983	+	0.745967i	$0.731988\pi$
$788$	−22.5886	−0.804687
$789$	−0.232488	−0.00827680
$790$	−91.6230	−3.25980
$791$	0.929031	0.0330325
$792$	−106.460	−3.78288
$793$	34.3228	1.21884
$794$	−26.3885	−0.936491
$795$	−0.248290	−0.00880594
$796$	−114.334	−4.05247
$797$	−7.82125	−0.277043	−0.138521	−	0.990359i	$-0.544235\pi$
$797$	−7.82125	−0.277043	−0.138521	+	0.990359i	$0.544235\pi$
$798$	0.146645	0.00519117
$799$	4.01609	0.142079
$800$	−32.6020	−1.15266
$801$	48.8481	1.72596
$802$	−80.1138	−2.82892
$803$	−17.2893	−0.610127
$804$	−0.200968	−0.00708759
$805$	28.5871	1.00756
$806$	−84.0581	−2.96082
$807$	0.151762	0.00534227
$808$	−23.5315	−0.827837
$809$	13.3569	0.469603	0.234802	−	0.972043i	$-0.424556\pi$
$809$	13.3569	0.469603	0.234802	+	0.972043i	$0.424556\pi$
$810$	−75.0150	−2.63576
$811$	−32.3923	−1.13745	−0.568723	−	0.822529i	$-0.692562\pi$
$811$	−32.3923	−1.13745	−0.568723	+	0.822529i	$0.692562\pi$
$812$	−7.40694	−0.259933
$813$	−0.225676	−0.00791480
$814$	−107.507	−3.76813
$815$	9.42326	0.330082
$816$	0.145066	0.00507831
$817$	35.1990	1.23146
$818$	22.7432	0.795198
$819$	9.59562	0.335298
$820$	−124.852	−4.36003
$821$	−19.9575	−0.696522	−0.348261	−	0.937398i	$-0.613228\pi$
$821$	−19.9575	−0.696522	−0.348261	+	0.937398i	$0.613228\pi$
$822$	−0.174183	−0.00607532
$823$	2.45284	0.0855008	0.0427504	−	0.999086i	$-0.486388\pi$
$823$	2.45284	0.0855008	0.0427504	+	0.999086i	$0.486388\pi$
$824$	14.4979	0.505058
$825$	−0.371696	−0.0129408
$826$	15.0519	0.523724
$827$	10.5398	0.366506	0.183253	−	0.983066i	$-0.441337\pi$
$827$	10.5398	0.366506	0.183253	+	0.983066i	$0.441337\pi$
$828$	127.016	4.41411
$829$	46.3162	1.60863	0.804314	−	0.594204i	$-0.202533\pi$
$829$	46.3162	1.60863	0.804314	+	0.594204i	$0.202533\pi$
$830$	3.70800	0.128707
$831$	−0.321908	−0.0111669
$832$	0.382812	0.0132716
$833$	−10.4800	−0.363111
$834$	0.366459	0.0126894
$835$	1.54967	0.0536286
$836$	−132.337	−4.57698
$837$	−0.673655	−0.0232849
$838$	−12.8954	−0.445465
$839$	12.9920	0.448534	0.224267	−	0.974528i	$-0.428001\pi$
$839$	12.9920	0.448534	0.224267	+	0.974528i	$0.428001\pi$
$840$	0.226941	0.00783021
$841$	−25.8601	−0.891726
$842$	95.5027	3.29124
$843$	0.0264782	0.000911959 0
$844$	−44.8064	−1.54230
$845$	−3.74562	−0.128853
$846$	17.9857	0.618360
$847$	−18.5997	−0.639093
$848$	−46.9239	−1.61137
$849$	−0.0175016	−0.000600653 0
$850$	−24.7809	−0.849979
$851$	71.2505	2.44243
$852$	−0.0527523	−0.00180726
$853$	38.1029	1.30462	0.652310	−	0.757953i	$-0.273800\pi$
$853$	38.1029	1.30462	0.652310	+	0.757953i	$0.273800\pi$
$854$	23.6105	0.807934
$855$	−51.8014	−1.77157
$856$	−25.6858	−0.877924
$857$	24.7332	0.844871	0.422435	−	0.906393i	$-0.361175\pi$
$857$	24.7332	0.844871	0.422435	+	0.906393i	$0.361175\pi$
$858$	0.573184	0.0195682
$859$	21.1804	0.722666	0.361333	−	0.932437i	$-0.382322\pi$
$859$	21.1804	0.722666	0.361333	+	0.932437i	$0.382322\pi$
$860$	98.0618	3.34388
$861$	0.0924359	0.00315021
$862$	−62.5372	−2.13003
$863$	32.9643	1.12212	0.561059	−	0.827776i	$-0.310394\pi$
$863$	32.9643	1.12212	0.561059	+	0.827776i	$0.310394\pi$
$864$	0.402910	0.0137073
$865$	−10.6218	−0.361152
$866$	30.6878	1.04281
$867$	−0.165124	−0.00560792
$868$	−40.0296	−1.35869
$869$	−61.2158	−2.07661
$870$	−0.173188	−0.00587164
$871$	−13.1168	−0.444445
$872$	75.7319	2.56461
$873$	−4.27034	−0.144529
$874$	126.693	4.28545
$875$	−2.10240	−0.0710741
$876$	0.163755	0.00553277
$877$	−12.3822	−0.418116	−0.209058	−	0.977903i	$-0.567040\pi$
$877$	−12.3822	−0.418116	−0.209058	+	0.977903i	$0.567040\pi$
$878$	−71.9859	−2.42941
$879$	0.116619	0.00393346
$880$	−131.951	−4.44808
$881$	22.6066	0.761636	0.380818	−	0.924650i	$-0.375642\pi$
$881$	22.6066	0.761636	0.380818	+	0.924650i	$0.375642\pi$
$882$	−46.9337	−1.58034
$883$	11.6576	0.392309	0.196154	−	0.980573i	$-0.437155\pi$
$883$	11.6576	0.392309	0.196154	+	0.980573i	$0.437155\pi$
$884$	26.4547	0.889767
$885$	0.243642	0.00818993
$886$	−31.0284	−1.04242
$887$	−24.9958	−0.839275	−0.419638	−	0.907692i	$-0.637843\pi$
$887$	−24.9958	−0.839275	−0.419638	+	0.907692i	$0.637843\pi$
$888$	0.565628	0.0189812
$889$	−13.5770	−0.455359
$890$	135.741	4.55005
$891$	−50.1196	−1.67907
$892$	48.7610	1.63264
$893$	12.4194	0.415599
$894$	0.161999	0.00541806
$895$	57.1479	1.91024
$896$	−10.3789	−0.346736
$897$	−0.379877	−0.0126837
$898$	−20.2352	−0.675258
$899$	16.9693	0.565957
$900$	−76.8281	−2.56094
$901$	−11.0598	−0.368456
$902$	−120.497	−4.01211
$903$	−0.0726012	−0.00241602
$904$	6.37175	0.211921
$905$	54.0684	1.79729
$906$	0.283300	0.00941202
$907$	−53.5941	−1.77956	−0.889782	−	0.456387i	$-0.849143\pi$
$907$	−53.5941	−1.77956	−0.889782	+	0.456387i	$0.849143\pi$
$908$	−17.2270	−0.571697
$909$	−11.0788	−0.367461
$910$	26.6647	0.883927
$911$	−28.0838	−0.930457	−0.465228	−	0.885191i	$-0.654028\pi$
$911$	−28.0838	−0.930457	−0.465228	+	0.885191i	$0.654028\pi$
$912$	0.448602	0.0148547
$913$	2.47742	0.0819905
$914$	49.1377	1.62533
$915$	0.382177	0.0126344
$916$	19.8169	0.654768
$917$	3.21171	0.106060
$918$	0.306254	0.0101079
$919$	−14.5367	−0.479520	−0.239760	−	0.970832i	$-0.577069\pi$
$919$	−14.5367	−0.479520	−0.239760	+	0.970832i	$0.577069\pi$
$920$	196.064	6.46404
$921$	−0.305443	−0.0100647
$922$	36.9671	1.21745
$923$	−3.44304	−0.113329
$924$	0.272958	0.00897966
$925$	−43.0973	−1.41703
$926$	43.1180	1.41694
$927$	6.82571	0.224186
$928$	−10.1493	−0.333166
$929$	49.7393	1.63189	0.815947	−	0.578126i	$-0.196216\pi$
$929$	49.7393	1.63189	0.815947	+	0.578126i	$0.196216\pi$
$930$	−0.935970	−0.0306917
$931$	−32.4085	−1.06214
$932$	28.7963	0.943253
$933$	0.0565216	0.00185043
$934$	−4.89420	−0.160143
$935$	−31.1006	−1.01710
$936$	65.8115	2.15112
$937$	1.98083	0.0647108	0.0323554	−	0.999476i	$-0.489699\pi$
$937$	1.98083	0.0647108	0.0323554	+	0.999476i	$0.489699\pi$
$938$	−9.02298	−0.294611
$939$	0.110716	0.00361307
$940$	34.5995	1.12851
$941$	17.7936	0.580054	0.290027	−	0.957019i	$-0.406336\pi$
$941$	17.7936	0.580054	0.290027	+	0.957019i	$0.406336\pi$
$942$	0.280621	0.00914312
$943$	79.8593	2.60058
$944$	46.0454	1.49865
$945$	0.213696	0.00695152
$946$	94.6411	3.07705
$947$	−17.6855	−0.574700	−0.287350	−	0.957826i	$-0.592774\pi$
$947$	−17.6855	−0.574700	−0.287350	+	0.957826i	$0.592774\pi$
$948$	0.579803	0.0188311
$949$	10.6880	0.346946
$950$	−76.6328	−2.48630
$951$	0.127226	0.00412558
$952$	10.1088	0.327629
$953$	33.7874	1.09448	0.547241	−	0.836975i	$-0.315678\pi$
$953$	33.7874	1.09448	0.547241	+	0.836975i	$0.315678\pi$
$954$	−49.5303	−1.60360
$955$	−82.4067	−2.66662
$956$	72.2392	2.33638
$957$	−0.115712	−0.00374044
$958$	−11.7025	−0.378091
$959$	−5.41386	−0.174823
$960$	0.00426253	0.000137573 0
$961$	60.7078	1.95832
$962$	66.4593	2.14273
$963$	−12.0931	−0.389694
$964$	−128.331	−4.13327
$965$	−61.3385	−1.97456
$966$	−0.261316	−0.00840771
$967$	47.5889	1.53036	0.765178	−	0.643818i	$-0.222651\pi$
$967$	47.5889	1.53036	0.765178	+	0.643818i	$0.222651\pi$
$968$	−127.566	−4.10012
$969$	0.105734	0.00339667
$970$	−11.8666	−0.381014
$971$	−9.79537	−0.314349	−0.157174	−	0.987571i	$-0.550238\pi$
$971$	−9.79537	−0.314349	−0.157174	+	0.987571i	$0.550238\pi$
$972$	1.42422	0.0456820
$973$	11.3901	0.365150
$974$	−57.9545	−1.85698
$975$	0.229777	0.00735874
$976$	72.2269	2.31193
$977$	2.58502	0.0827022	0.0413511	−	0.999145i	$-0.486834\pi$
$977$	2.58502	0.0827022	0.0413511	+	0.999145i	$0.486834\pi$
$978$	−0.0861386	−0.00275441
$979$	90.6924	2.89854
$980$	−90.2877	−2.88413
$981$	35.6551	1.13838
$982$	41.9453	1.33853
$983$	−28.4543	−0.907550	−0.453775	−	0.891116i	$-0.649923\pi$
$983$	−28.4543	−0.907550	−0.453775	+	0.891116i	$0.649923\pi$
$984$	0.633971	0.0202102
$985$	−16.4162	−0.523064
$986$	−7.71449	−0.245680
$987$	−0.0256161	−0.000815371 0
$988$	81.8087	2.60268
$989$	−62.7233	−1.99449
$990$	−139.281	−4.42664
$991$	48.4296	1.53842	0.769208	−	0.638999i	$-0.220651\pi$
$991$	48.4296	1.53842	0.769208	+	0.638999i	$0.220651\pi$
$992$	−54.8500	−1.74149
$993$	0.109198	0.00346530
$994$	−2.36845	−0.0751227
$995$	−83.0920	−2.63419
$996$	−0.0234647	−0.000743509 0
$997$	−24.0452	−0.761520	−0.380760	−	0.924674i	$-0.624338\pi$
$997$	−24.0452	−0.761520	−0.380760	+	0.924674i	$0.624338\pi$
$998$	49.8524	1.57805
$999$	0.532615	0.0168512

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8023.2.a.c.1.12	✓	158

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8023.2.a.c.1.12	✓	158	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)

\(f(q)\)	\(=\)	\(q-2.54938 q^{2} +0.0117245 q^{3} +4.49933 q^{4} +3.26987 q^{5} -0.0298901 q^{6} -0.929031 q^{7} -6.37175 q^{8} -2.99986 q^{9} +O(q^{10})\)	\(q-2.54938 q^{2} +0.0117245 q^{3} +4.49933 q^{4} +3.26987 q^{5} -0.0298901 q^{6} -0.929031 q^{7} -6.37175 q^{8} -2.99986 q^{9} -8.33615 q^{10} -5.56961 q^{11} +0.0527523 q^{12} +3.44304 q^{13} +2.36845 q^{14} +0.0383375 q^{15} +7.24534 q^{16} +1.70770 q^{17} +7.64779 q^{18} +5.28092 q^{19} +14.7123 q^{20} -0.0108924 q^{21} +14.1990 q^{22} -9.41041 q^{23} -0.0747054 q^{24} +5.69208 q^{25} -8.77761 q^{26} -0.0703452 q^{27} -4.18002 q^{28} +1.77199 q^{29} -0.0977369 q^{30} +9.57642 q^{31} -5.72761 q^{32} -0.0653007 q^{33} -4.35358 q^{34} -3.03781 q^{35} -13.4974 q^{36} -7.57145 q^{37} -13.4631 q^{38} +0.0403678 q^{39} -20.8348 q^{40} -8.48628 q^{41} +0.0277688 q^{42} +6.66532 q^{43} -25.0595 q^{44} -9.80917 q^{45} +23.9907 q^{46} +2.35175 q^{47} +0.0849477 q^{48} -6.13690 q^{49} -14.5113 q^{50} +0.0200219 q^{51} +15.4914 q^{52} -6.47642 q^{53} +0.179337 q^{54} -18.2119 q^{55} +5.91955 q^{56} +0.0619160 q^{57} -4.51747 q^{58} +6.35518 q^{59} +0.172493 q^{60} +9.96874 q^{61} -24.4139 q^{62} +2.78696 q^{63} +0.111184 q^{64} +11.2583 q^{65} +0.166476 q^{66} -3.80965 q^{67} +7.68353 q^{68} -0.110332 q^{69} +7.74454 q^{70} -1.00000 q^{71} +19.1144 q^{72} +3.10423 q^{73} +19.3025 q^{74} +0.0667366 q^{75} +23.7606 q^{76} +5.17434 q^{77} -0.102913 q^{78} +10.9911 q^{79} +23.6913 q^{80} +8.99876 q^{81} +21.6347 q^{82} -0.444810 q^{83} -0.0490085 q^{84} +5.58398 q^{85} -16.9924 q^{86} +0.0207756 q^{87} +35.4881 q^{88} -16.2834 q^{89} +25.0073 q^{90} -3.19869 q^{91} -42.3406 q^{92} +0.112278 q^{93} -5.99549 q^{94} +17.2679 q^{95} -0.0671532 q^{96} +1.42351 q^{97} +15.6453 q^{98} +16.7081 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 158 q - 24 q^{2} - 23 q^{3} + 158 q^{4} - 31 q^{5} - 17 q^{6} - 2 q^{7} - 69 q^{8} + 135 q^{9}+O(q^{10}) \) 158 * q - 24 * q^2 - 23 * q^3 + 158 * q^4 - 31 * q^5 - 17 * q^6 - 2 * q^7 - 69 * q^8 + 135 * q^9	\( 158 q - 24 q^{2} - 23 q^{3} + 158 q^{4} - 31 q^{5} - 17 q^{6} - 2 q^{7} - 69 q^{8} + 135 q^{9} - 10 q^{10} - 10 q^{11} - 46 q^{12} - 28 q^{13} - 27 q^{14} - 41 q^{15} + 150 q^{16} - 137 q^{17} - 67 q^{18} - 42 q^{19} - 66 q^{20} - 46 q^{21} - 8 q^{22} - 26 q^{23} - 48 q^{24} + 129 q^{25} - 67 q^{26} - 89 q^{27} - 21 q^{28} - 79 q^{29} - 11 q^{30} + 7 q^{31} - 147 q^{32} - 112 q^{33} - 28 q^{34} - 53 q^{35} + 141 q^{36} - 60 q^{37} - 53 q^{38} - 3 q^{39} - 48 q^{40} - 128 q^{41} + 32 q^{42} - 63 q^{43} - 88 q^{45} - 2 q^{46} - 92 q^{47} - 131 q^{48} + 122 q^{49} - 116 q^{50} - 12 q^{51} - 89 q^{52} - 94 q^{53} - 71 q^{54} - 12 q^{55} - 104 q^{56} - 93 q^{57} - 65 q^{58} - 54 q^{59} - 12 q^{60} + 17 q^{61} - 97 q^{62} - 28 q^{63} + 163 q^{64} - 163 q^{65} - 65 q^{66} - 35 q^{67} - 217 q^{68} - 46 q^{69} - 79 q^{70} - 158 q^{71} - 99 q^{72} - 165 q^{73} - 94 q^{75} - 93 q^{76} - 140 q^{77} + 25 q^{78} - 61 q^{79} - 134 q^{80} + 114 q^{81} + 10 q^{82} - 158 q^{83} - 160 q^{84} + 23 q^{85} - 122 q^{86} - 71 q^{87} - 14 q^{88} - 251 q^{89} - 6 q^{90} - 57 q^{91} - 58 q^{92} - 52 q^{93} - 64 q^{94} - 84 q^{95} - 98 q^{96} - 48 q^{97} - 84 q^{98} + 85 q^{99}+O(q^{100}) \) 158 * q - 24 * q^2 - 23 * q^3 + 158 * q^4 - 31 * q^5 - 17 * q^6 - 2 * q^7 - 69 * q^8 + 135 * q^9 - 10 * q^10 - 10 * q^11 - 46 * q^12 - 28 * q^13 - 27 * q^14 - 41 * q^15 + 150 * q^16 - 137 * q^17 - 67 * q^18 - 42 * q^19 - 66 * q^20 - 46 * q^21 - 8 * q^22 - 26 * q^23 - 48 * q^24 + 129 * q^25 - 67 * q^26 - 89 * q^27 - 21 * q^28 - 79 * q^29 - 11 * q^30 + 7 * q^31 - 147 * q^32 - 112 * q^33 - 28 * q^34 - 53 * q^35 + 141 * q^36 - 60 * q^37 - 53 * q^38 - 3 * q^39 - 48 * q^40 - 128 * q^41 + 32 * q^42 - 63 * q^43 - 88 * q^45 - 2 * q^46 - 92 * q^47 - 131 * q^48 + 122 * q^49 - 116 * q^50 - 12 * q^51 - 89 * q^52 - 94 * q^53 - 71 * q^54 - 12 * q^55 - 104 * q^56 - 93 * q^57 - 65 * q^58 - 54 * q^59 - 12 * q^60 + 17 * q^61 - 97 * q^62 - 28 * q^63 + 163 * q^64 - 163 * q^65 - 65 * q^66 - 35 * q^67 - 217 * q^68 - 46 * q^69 - 79 * q^70 - 158 * q^71 - 99 * q^72 - 165 * q^73 - 94 * q^75 - 93 * q^76 - 140 * q^77 + 25 * q^78 - 61 * q^79 - 134 * q^80 + 114 * q^81 + 10 * q^82 - 158 * q^83 - 160 * q^84 + 23 * q^85 - 122 * q^86 - 71 * q^87 - 14 * q^88 - 251 * q^89 - 6 * q^90 - 57 * q^91 - 58 * q^92 - 52 * q^93 - 64 * q^94 - 84 * q^95 - 98 * q^96 - 48 * q^97 - 84 * q^98 + 85 * q^99

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