LMFDB - Embedded newform 8023.2.a.b.1.13

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:	$155$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
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)

$f(q)$	$=$	$q-2.52683 q^{2} +1.49048 q^{3} +4.38485 q^{4} -0.343930 q^{5} -3.76619 q^{6} +0.360206 q^{7} -6.02610 q^{8} -0.778467 q^{9} +O(q^{10})$	\(q-2.52683 q^{2} +1.49048 q^{3} +4.38485 q^{4} -0.343930 q^{5} -3.76619 q^{6} +0.360206 q^{7} -6.02610 q^{8} -0.778467 q^{9} +0.869051 q^{10} +1.14810 q^{11} +6.53553 q^{12} +2.22566 q^{13} -0.910178 q^{14} -0.512621 q^{15} +6.45721 q^{16} -6.77322 q^{17} +1.96705 q^{18} -1.87868 q^{19} -1.50808 q^{20} +0.536880 q^{21} -2.90104 q^{22} +1.85906 q^{23} -8.98179 q^{24} -4.88171 q^{25} -5.62386 q^{26} -5.63173 q^{27} +1.57945 q^{28} -0.349623 q^{29} +1.29530 q^{30} +1.81750 q^{31} -4.26404 q^{32} +1.71122 q^{33} +17.1148 q^{34} -0.123886 q^{35} -3.41346 q^{36} +4.37413 q^{37} +4.74709 q^{38} +3.31731 q^{39} +2.07256 q^{40} +4.78027 q^{41} -1.35660 q^{42} +12.9428 q^{43} +5.03423 q^{44} +0.267738 q^{45} -4.69752 q^{46} +2.93208 q^{47} +9.62435 q^{48} -6.87025 q^{49} +12.3352 q^{50} -10.0954 q^{51} +9.75919 q^{52} -6.55787 q^{53} +14.2304 q^{54} -0.394865 q^{55} -2.17064 q^{56} -2.80013 q^{57} +0.883435 q^{58} +10.5117 q^{59} -2.24777 q^{60} +2.38916 q^{61} -4.59251 q^{62} -0.280408 q^{63} -2.13993 q^{64} -0.765472 q^{65} -4.32395 q^{66} -9.02507 q^{67} -29.6996 q^{68} +2.77089 q^{69} +0.313038 q^{70} +1.00000 q^{71} +4.69112 q^{72} +10.0937 q^{73} -11.0527 q^{74} -7.27610 q^{75} -8.23771 q^{76} +0.413552 q^{77} -8.38226 q^{78} +13.8384 q^{79} -2.22083 q^{80} -6.05859 q^{81} -12.0789 q^{82} -5.26638 q^{83} +2.35414 q^{84} +2.32952 q^{85} -32.7041 q^{86} -0.521106 q^{87} -6.91855 q^{88} -5.90533 q^{89} -0.676528 q^{90} +0.801697 q^{91} +8.15170 q^{92} +2.70895 q^{93} -7.40885 q^{94} +0.646133 q^{95} -6.35547 q^{96} +11.5952 q^{97} +17.3599 q^{98} -0.893755 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 155 q - 21 q^{2} - 16 q^{3} + 151 q^{4} - 26 q^{5} - 10 q^{6} - 40 q^{7} - 57 q^{8} + 135 q^{9}+O(q^{10}) $ 155 * q - 21 * q^2 - 16 * q^3 + 151 * q^4 - 26 * q^5 - 10 * q^6 - 40 * q^7 - 57 * q^8 + 135 * q^9	\( 155 q - 21 q^{2} - 16 q^{3} + 151 q^{4} - 26 q^{5} - 10 q^{6} - 40 q^{7} - 57 q^{8} + 135 q^{9} - 2 q^{10} - 24 q^{11} - 32 q^{12} - 62 q^{13} - 18 q^{14} - 12 q^{15} + 155 q^{16} - 129 q^{17} - 42 q^{18} - 18 q^{19} - 59 q^{20} - 45 q^{21} - 17 q^{22} - 38 q^{23} - 27 q^{24} + 129 q^{25} - 44 q^{26} - 43 q^{27} - 100 q^{28} - 52 q^{29} - 39 q^{30} - 56 q^{31} - 145 q^{32} - 126 q^{33} - q^{34} - 49 q^{35} + 131 q^{36} - 30 q^{37} - 91 q^{38} - 29 q^{39} - 5 q^{40} - 163 q^{41} - 80 q^{42} - 15 q^{43} - 118 q^{44} - 66 q^{45} + 2 q^{46} - 111 q^{47} - 89 q^{48} + 101 q^{49} - 121 q^{50} + 5 q^{51} - 111 q^{52} - 93 q^{53} - 68 q^{54} - 60 q^{55} - 27 q^{56} - 106 q^{57} + 16 q^{58} - 79 q^{59} - 103 q^{60} - 74 q^{61} - 102 q^{62} - 118 q^{63} + 175 q^{64} - 109 q^{65} + 65 q^{66} - 18 q^{67} - 346 q^{68} - 39 q^{69} + 32 q^{70} + 155 q^{71} - 203 q^{72} - 108 q^{73} - 87 q^{74} - 22 q^{75} - 16 q^{76} - 121 q^{77} - 75 q^{78} - 6 q^{79} - 136 q^{80} + 107 q^{81} - 30 q^{82} - 116 q^{83} - 5 q^{84} - 53 q^{85} + 8 q^{86} - 100 q^{87} - 43 q^{88} - 189 q^{89} - 76 q^{90} + 14 q^{91} - 99 q^{92} - 72 q^{93} + 17 q^{94} - 18 q^{95} - 50 q^{96} - 184 q^{97} - 249 q^{98} - 114 q^{99}+O(q^{100}) \) 155 * q - 21 * q^2 - 16 * q^3 + 151 * q^4 - 26 * q^5 - 10 * q^6 - 40 * q^7 - 57 * q^8 + 135 * q^9 - 2 * q^10 - 24 * q^11 - 32 * q^12 - 62 * q^13 - 18 * q^14 - 12 * q^15 + 155 * q^16 - 129 * q^17 - 42 * q^18 - 18 * q^19 - 59 * q^20 - 45 * q^21 - 17 * q^22 - 38 * q^23 - 27 * q^24 + 129 * q^25 - 44 * q^26 - 43 * q^27 - 100 * q^28 - 52 * q^29 - 39 * q^30 - 56 * q^31 - 145 * q^32 - 126 * q^33 - q^34 - 49 * q^35 + 131 * q^36 - 30 * q^37 - 91 * q^38 - 29 * q^39 - 5 * q^40 - 163 * q^41 - 80 * q^42 - 15 * q^43 - 118 * q^44 - 66 * q^45 + 2 * q^46 - 111 * q^47 - 89 * q^48 + 101 * q^49 - 121 * q^50 + 5 * q^51 - 111 * q^52 - 93 * q^53 - 68 * q^54 - 60 * q^55 - 27 * q^56 - 106 * q^57 + 16 * q^58 - 79 * q^59 - 103 * q^60 - 74 * q^61 - 102 * q^62 - 118 * q^63 + 175 * q^64 - 109 * q^65 + 65 * q^66 - 18 * q^67 - 346 * q^68 - 39 * q^69 + 32 * q^70 + 155 * q^71 - 203 * q^72 - 108 * q^73 - 87 * q^74 - 22 * q^75 - 16 * q^76 - 121 * q^77 - 75 * q^78 - 6 * q^79 - 136 * q^80 + 107 * q^81 - 30 * q^82 - 116 * q^83 - 5 * q^84 - 53 * q^85 + 8 * q^86 - 100 * q^87 - 43 * q^88 - 189 * q^89 - 76 * q^90 + 14 * q^91 - 99 * q^92 - 72 * q^93 + 17 * q^94 - 18 * q^95 - 50 * q^96 - 184 * q^97 - 249 * q^98 - 114 * 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 $

$2$	−2.52683	−1.78674	−0.893368	−	0.449326i	$-0.851664\pi$
$2$	−2.52683	−1.78674	−0.893368	+	0.449326i	$0.851664\pi$
$3$	1.49048	0.860530	0.430265	−	0.902703i	$-0.358420\pi$
$3$	1.49048	0.860530	0.430265	+	0.902703i	$0.358420\pi$
$4$	4.38485	2.19242
$5$	−0.343930	−0.153810	−0.0769051	−	0.997038i	$-0.524504\pi$
$5$	−0.343930	−0.153810	−0.0769051	+	0.997038i	$0.524504\pi$
$6$	−3.76619	−1.53754
$7$	0.360206	0.136145	0.0680726	−	0.997680i	$-0.478315\pi$
$7$	0.360206	0.136145	0.0680726	+	0.997680i	$0.478315\pi$
$8$	−6.02610	−2.13055
$9$	−0.778467	−0.259489
$10$	0.869051	0.274818
$11$	1.14810	0.346164	0.173082	−	0.984907i	$-0.444627\pi$
$11$	1.14810	0.346164	0.173082	+	0.984907i	$0.444627\pi$
$12$	6.53553	1.88665
$13$	2.22566	0.617287	0.308644	−	0.951178i	$-0.400125\pi$
$13$	2.22566	0.617287	0.308644	+	0.951178i	$0.400125\pi$
$14$	−0.910178	−0.243255
$15$	−0.512621	−0.132358
$16$	6.45721	1.61430
$17$	−6.77322	−1.64275	−0.821374	−	0.570390i	$-0.806792\pi$
$17$	−6.77322	−1.64275	−0.821374	+	0.570390i	$0.806792\pi$
$18$	1.96705	0.463638
$19$	−1.87868	−0.430998	−0.215499	−	0.976504i	$-0.569138\pi$
$19$	−1.87868	−0.430998	−0.215499	+	0.976504i	$0.569138\pi$
$20$	−1.50808	−0.337217
$21$	0.536880	0.117157
$22$	−2.90104	−0.618504
$23$	1.85906	0.387641	0.193820	−	0.981037i	$-0.437912\pi$
$23$	1.85906	0.387641	0.193820	+	0.981037i	$0.437912\pi$
$24$	−8.98179	−1.83340
$25$	−4.88171	−0.976342
$26$	−5.62386	−1.10293
$27$	−5.63173	−1.08383
$28$	1.57945	0.298488
$29$	−0.349623	−0.0649233	−0.0324616	−	0.999473i	$-0.510335\pi$
$29$	−0.349623	−0.0649233	−0.0324616	+	0.999473i	$0.510335\pi$
$30$	1.29530	0.236489
$31$	1.81750	0.326433	0.163216	−	0.986590i	$-0.447813\pi$
$31$	1.81750	0.326433	0.163216	+	0.986590i	$0.447813\pi$
$32$	−4.26404	−0.753783
$33$	1.71122	0.297885
$34$	17.1148	2.93516
$35$	−0.123886	−0.0209405
$36$	−3.41346	−0.568910
$37$	4.37413	0.719103	0.359551	−	0.933125i	$-0.382930\pi$
$37$	4.37413	0.719103	0.359551	+	0.933125i	$0.382930\pi$
$38$	4.74709	0.770079
$39$	3.31731	0.531194
$40$	2.07256	0.327700
$41$	4.78027	0.746553	0.373276	−	0.927720i	$-0.378234\pi$
$41$	4.78027	0.746553	0.373276	+	0.927720i	$0.378234\pi$
$42$	−1.35660	−0.209328
$43$	12.9428	1.97375	0.986876	−	0.161482i	$-0.0516273\pi$
$43$	12.9428	1.97375	0.986876	+	0.161482i	$0.0516273\pi$
$44$	5.03423	0.758939
$45$	0.267738	0.0399120
$46$	−4.69752	−0.692612
$47$	2.93208	0.427687	0.213844	−	0.976868i	$-0.431402\pi$
$47$	2.93208	0.427687	0.213844	+	0.976868i	$0.431402\pi$
$48$	9.62435	1.38915
$49$	−6.87025	−0.981465
$50$	12.3352	1.74447
$51$	−10.0954	−1.41363
$52$	9.75919	1.35336
$53$	−6.55787	−0.900792	−0.450396	−	0.892829i	$-0.648717\pi$
$53$	−6.55787	−0.900792	−0.450396	+	0.892829i	$0.648717\pi$
$54$	14.2304	1.93651
$55$	−0.394865	−0.0532436
$56$	−2.17064	−0.290064
$57$	−2.80013	−0.370886
$58$	0.883435	0.116001
$59$	10.5117	1.36850	0.684252	−	0.729246i	$-0.260129\pi$
$59$	10.5117	1.36850	0.684252	+	0.729246i	$0.260129\pi$
$60$	−2.24777	−0.290185
$61$	2.38916	0.305901	0.152950	−	0.988234i	$-0.451123\pi$
$61$	2.38916	0.305901	0.152950	+	0.988234i	$0.451123\pi$
$62$	−4.59251	−0.583249
$63$	−0.280408	−0.0353281
$64$	−2.13993	−0.267491
$65$	−0.765472	−0.0949451
$66$	−4.32395	−0.532241
$67$	−9.02507	−1.10259	−0.551294	−	0.834311i	$-0.685866\pi$
$67$	−9.02507	−1.10259	−0.551294	+	0.834311i	$0.685866\pi$
$68$	−29.6996	−3.60160
$69$	2.77089	0.333576
$70$	0.313038	0.0374152
$71$	1.00000	0.118678
$71$	1.00000	0.118678
$72$	4.69112	0.552854
$73$	10.0937	1.18138	0.590688	−	0.806900i	$-0.298856\pi$
$73$	10.0937	1.18138	0.590688	+	0.806900i	$0.298856\pi$
$74$	−11.0527	−1.28485
$75$	−7.27610	−0.840172
$76$	−8.23771	−0.944930
$77$	0.413552	0.0471286
$78$	−8.38226	−0.949104
$79$	13.8384	1.55694	0.778469	−	0.627684i	$-0.215997\pi$
$79$	13.8384	1.55694	0.778469	+	0.627684i	$0.215997\pi$
$80$	−2.22083	−0.248296
$81$	−6.05859	−0.673177
$82$	−12.0789	−1.33389
$83$	−5.26638	−0.578061	−0.289030	−	0.957320i	$-0.593333\pi$
$83$	−5.26638	−0.578061	−0.289030	+	0.957320i	$0.593333\pi$
$84$	2.35414	0.256858
$85$	2.32952	0.252671
$86$	−32.7041	−3.52657
$87$	−0.521106	−0.0558684
$88$	−6.91855	−0.737520
$89$	−5.90533	−0.625964	−0.312982	−	0.949759i	$-0.601328\pi$
$89$	−5.90533	−0.625964	−0.312982	+	0.949759i	$0.601328\pi$
$90$	−0.676528	−0.0713123
$91$	0.801697	0.0840407
$92$	8.15170	0.849874
$93$	2.70895	0.280905
$94$	−7.40885	−0.764165
$95$	0.646133	0.0662918
$96$	−6.35547	−0.648653
$97$	11.5952	1.17731	0.588657	−	0.808383i	$-0.299657\pi$
$97$	11.5952	1.17731	0.588657	+	0.808383i	$0.299657\pi$
$98$	17.3599	1.75362
$99$	−0.893755	−0.0898258
$100$	−21.4056	−2.14056
$101$	−14.7241	−1.46510	−0.732550	−	0.680713i	$-0.761670\pi$
$101$	−14.7241	−1.46510	−0.732550	+	0.680713i	$0.761670\pi$
$102$	25.5092	2.52579
$103$	−11.3235	−1.11574	−0.557869	−	0.829929i	$-0.688381\pi$
$103$	−11.3235	−1.11574	−0.557869	+	0.829929i	$0.688381\pi$
$104$	−13.4121	−1.31516
$105$	−0.184649	−0.0180199
$106$	16.5706	1.60948
$107$	−16.1209	−1.55847	−0.779234	−	0.626733i	$-0.784392\pi$
$107$	−16.1209	−1.55847	−0.779234	+	0.626733i	$0.784392\pi$
$108$	−24.6943	−2.37621
$109$	10.1496	0.972160	0.486080	−	0.873914i	$-0.338426\pi$
$109$	10.1496	0.972160	0.486080	+	0.873914i	$0.338426\pi$
$110$	0.997756	0.0951323
$111$	6.51956	0.618809
$112$	2.32593	0.219779
$113$	1.00000	0.0940721
$113$	1.00000	0.0940721
$114$	7.07544	0.662676
$115$	−0.639387	−0.0596231
$116$	−1.53304	−0.142339
$117$	−1.73260	−0.160179
$118$	−26.5612	−2.44515
$119$	−2.43976	−0.223652
$120$	3.08911	0.281996
$121$	−9.68187	−0.880170
$122$	−6.03699	−0.546563
$123$	7.12490	0.642431
$124$	7.96947	0.715679
$125$	3.39862	0.303982
$126$	0.708543	0.0631221
$127$	−9.37425	−0.831830	−0.415915	−	0.909403i	$-0.636539\pi$
$127$	−9.37425	−0.831830	−0.415915	+	0.909403i	$0.636539\pi$
$128$	13.9353	1.23172
$129$	19.2909	1.69847
$130$	1.93421	0.169642
$131$	−14.4599	−1.26337	−0.631685	−	0.775226i	$-0.717636\pi$
$131$	−14.4599	−1.26337	−0.631685	+	0.775226i	$0.717636\pi$
$132$	7.50343	0.653090
$133$	−0.676710	−0.0586782
$134$	22.8048	1.97003
$135$	1.93692	0.166704
$136$	40.8161	3.49995
$137$	14.4127	1.23136	0.615678	−	0.787998i	$-0.288882\pi$
$137$	14.4127	1.23136	0.615678	+	0.787998i	$0.288882\pi$
$138$	−7.00157	−0.596013
$139$	14.6220	1.24022	0.620111	−	0.784514i	$-0.287087\pi$
$139$	14.6220	1.24022	0.620111	+	0.784514i	$0.287087\pi$
$140$	−0.543220	−0.0459105
$141$	4.37021	0.368038
$142$	−2.52683	−0.212047
$143$	2.55528	0.213683
$144$	−5.02672	−0.418893
$145$	0.120246	0.00998586
$146$	−25.5050	−2.11081
$147$	−10.2400	−0.844579
$148$	19.1799	1.57658
$149$	1.50843	0.123576	0.0617878	−	0.998089i	$-0.480320\pi$
$149$	1.50843	0.123576	0.0617878	+	0.998089i	$0.480320\pi$
$150$	18.3854	1.50116
$151$	−5.31975	−0.432915	−0.216457	−	0.976292i	$-0.569450\pi$
$151$	−5.31975	−0.432915	−0.216457	+	0.976292i	$0.569450\pi$
$152$	11.3211	0.918261
$153$	5.27273	0.426275
$154$	−1.04497	−0.0842063
$155$	−0.625093	−0.0502087
$156$	14.5459	1.16460
$157$	−11.5798	−0.924167	−0.462084	−	0.886836i	$-0.652898\pi$
$157$	−11.5798	−0.924167	−0.462084	+	0.886836i	$0.652898\pi$
$158$	−34.9671	−2.78184
$159$	−9.77437	−0.775158
$160$	1.46653	0.115940
$161$	0.669645	0.0527754
$162$	15.3090	1.20279
$163$	5.49527	0.430422	0.215211	−	0.976568i	$-0.430956\pi$
$163$	5.49527	0.430422	0.215211	+	0.976568i	$0.430956\pi$
$164$	20.9608	1.63676
$165$	−0.588539	−0.0458177
$166$	13.3072	1.03284
$167$	−15.8549	−1.22689	−0.613446	−	0.789737i	$-0.710217\pi$
$167$	−15.8549	−1.22689	−0.613446	+	0.789737i	$0.710217\pi$
$168$	−3.23530	−0.249608
$169$	−8.04643	−0.618956
$170$	−5.88628	−0.451457
$171$	1.46249	0.111839
$172$	56.7520	4.32730
$173$	−3.37867	−0.256876	−0.128438	−	0.991718i	$-0.540996\pi$
$173$	−3.37867	−0.256876	−0.128438	+	0.991718i	$0.540996\pi$
$174$	1.31674	0.0998221
$175$	−1.75842	−0.132924
$176$	7.41350	0.558814
$177$	15.6674	1.17764
$178$	14.9218	1.11843
$179$	−16.0609	−1.20044	−0.600222	−	0.799833i	$-0.704921\pi$
$179$	−16.0609	−1.20044	−0.600222	+	0.799833i	$0.704921\pi$
$180$	1.17399	0.0875041
$181$	−3.29783	−0.245126	−0.122563	−	0.992461i	$-0.539111\pi$
$181$	−3.29783	−0.245126	−0.122563	+	0.992461i	$0.539111\pi$
$182$	−2.02575	−0.150158
$183$	3.56100	0.263236
$184$	−11.2029	−0.825888
$185$	−1.50439	−0.110605
$186$	−6.84505	−0.501903
$187$	−7.77632	−0.568661
$188$	12.8567	0.937673
$189$	−2.02858	−0.147558
$190$	−1.63267	−0.118446
$191$	9.31556	0.674050	0.337025	−	0.941496i	$-0.390579\pi$
$191$	9.31556	0.674050	0.337025	+	0.941496i	$0.390579\pi$
$192$	−3.18952	−0.230184
$193$	−0.282188	−0.0203123	−0.0101562	−	0.999948i	$-0.503233\pi$
$193$	−0.282188	−0.0203123	−0.0101562	+	0.999948i	$0.503233\pi$
$194$	−29.2991	−2.10355
$195$	−1.14092	−0.0817031
$196$	−30.1250	−2.15179
$197$	−11.4964	−0.819083	−0.409542	−	0.912291i	$-0.634311\pi$
$197$	−11.4964	−0.819083	−0.409542	+	0.912291i	$0.634311\pi$
$198$	2.25836	0.160495
$199$	−12.1889	−0.864048	−0.432024	−	0.901862i	$-0.642200\pi$
$199$	−12.1889	−0.864048	−0.432024	+	0.901862i	$0.642200\pi$
$200$	29.4177	2.08014
$201$	−13.4517	−0.948809
$202$	37.2052	2.61775
$203$	−0.125936	−0.00883899
$204$	−44.2666	−3.09929
$205$	−1.64408	−0.114827
$206$	28.6125	1.99353
$207$	−1.44722	−0.100589
$208$	14.3716	0.996488
$209$	−2.15690	−0.149196
$210$	0.466577	0.0321969
$211$	19.2161	1.32289	0.661447	−	0.749992i	$-0.269943\pi$
$211$	19.2161	1.32289	0.661447	+	0.749992i	$0.269943\pi$
$212$	−28.7553	−1.97492
$213$	1.49048	0.102126
$214$	40.7348	2.78457
$215$	−4.45140	−0.303583
$216$	33.9374	2.30915
$217$	0.654675	0.0444422
$218$	−25.6464	−1.73699
$219$	15.0444	1.01661
$220$	−1.73142	−0.116733
$221$	−15.0749	−1.01405
$222$	−16.4738	−1.10565
$223$	−18.3710	−1.23021	−0.615107	−	0.788444i	$-0.710887\pi$
$223$	−18.3710	−1.23021	−0.615107	+	0.788444i	$0.710887\pi$
$224$	−1.53593	−0.102624
$225$	3.80025	0.253350
$226$	−2.52683	−0.168082
$227$	−14.0826	−0.934698	−0.467349	−	0.884073i	$-0.654791\pi$
$227$	−14.0826	−0.934698	−0.467349	+	0.884073i	$0.654791\pi$
$228$	−12.2781	−0.813140
$229$	−1.20005	−0.0793014	−0.0396507	−	0.999214i	$-0.512625\pi$
$229$	−1.20005	−0.0793014	−0.0396507	+	0.999214i	$0.512625\pi$
$230$	1.61562	0.106531
$231$	0.616391	0.0405555
$232$	2.10686	0.138322
$233$	−4.30987	−0.282349	−0.141174	−	0.989985i	$-0.545088\pi$
$233$	−4.30987	−0.282349	−0.141174	+	0.989985i	$0.545088\pi$
$234$	4.37799	0.286198
$235$	−1.00843	−0.0657827
$236$	46.0921	3.00034
$237$	20.6258	1.33979
$238$	6.16484	0.399607
$239$	−21.8504	−1.41339	−0.706693	−	0.707521i	$-0.749814\pi$
$239$	−21.8504	−1.41339	−0.706693	+	0.707521i	$0.749814\pi$
$240$	−3.31010	−0.213666
$241$	−26.4787	−1.70564	−0.852820	−	0.522205i	$-0.825110\pi$
$241$	−26.4787	−1.70564	−0.852820	+	0.522205i	$0.825110\pi$
$242$	24.4644	1.57263
$243$	7.86498	0.504539
$244$	10.4761	0.670664
$245$	2.36289	0.150959
$246$	−18.0034	−1.14785
$247$	−4.18130	−0.266049
$248$	−10.9524	−0.695481
$249$	−7.84944	−0.497438
$250$	−8.58772	−0.543135
$251$	−18.3797	−1.16012	−0.580059	−	0.814575i	$-0.696970\pi$
$251$	−18.3797	−1.16012	−0.580059	+	0.814575i	$0.696970\pi$
$252$	−1.22955	−0.0774543
$253$	2.13438	0.134187
$254$	23.6871	1.48626
$255$	3.47210	0.217431
$256$	−30.9322	−1.93326
$257$	−19.3742	−1.20853	−0.604263	−	0.796785i	$-0.706532\pi$
$257$	−19.3742	−1.20853	−0.604263	+	0.796785i	$0.706532\pi$
$258$	−48.7448	−3.03472
$259$	1.57559	0.0979023
$260$	−3.35648	−0.208160
$261$	0.272169	0.0168469
$262$	36.5377	2.25731
$263$	−30.9943	−1.91119	−0.955596	−	0.294679i	$-0.904787\pi$
$263$	−30.9943	−1.91119	−0.955596	+	0.294679i	$0.904787\pi$
$264$	−10.3120	−0.634658
$265$	2.25545	0.138551
$266$	1.70993	0.104843
$267$	−8.80179	−0.538661
$268$	−39.5736	−2.41734
$269$	0.422229	0.0257437	0.0128719	−	0.999917i	$-0.495903\pi$
$269$	0.422229	0.0257437	0.0128719	+	0.999917i	$0.495903\pi$
$270$	−4.89427	−0.297856
$271$	−25.0648	−1.52258	−0.761290	−	0.648411i	$-0.775434\pi$
$271$	−25.0648	−1.52258	−0.761290	+	0.648411i	$0.775434\pi$
$272$	−43.7361	−2.65189
$273$	1.19491	0.0723195
$274$	−36.4183	−2.20011
$275$	−5.60468	−0.337975
$276$	12.1500	0.731341
$277$	27.3063	1.64068	0.820338	−	0.571878i	$-0.193785\pi$
$277$	27.3063	1.64068	0.820338	+	0.571878i	$0.193785\pi$
$278$	−36.9473	−2.21595
$279$	−1.41486	−0.0847057
$280$	0.746548	0.0446148
$281$	6.51732	0.388790	0.194395	−	0.980923i	$-0.437726\pi$
$281$	6.51732	0.388790	0.194395	+	0.980923i	$0.437726\pi$
$282$	−11.0427	−0.657586
$283$	−28.6007	−1.70014	−0.850068	−	0.526674i	$-0.823439\pi$
$283$	−28.6007	−1.70014	−0.850068	+	0.526674i	$0.823439\pi$
$284$	4.38485	0.260193
$285$	0.963049	0.0570461
$286$	−6.45674	−0.381795
$287$	1.72188	0.101639
$288$	3.31941	0.195598
$289$	28.8766	1.69862
$290$	−0.303840	−0.0178421
$291$	17.2824	1.01311
$292$	44.2593	2.59008
$293$	−22.5870	−1.31955	−0.659773	−	0.751465i	$-0.729348\pi$
$293$	−22.5870	−1.31955	−0.659773	+	0.751465i	$0.729348\pi$
$294$	25.8746	1.50904
$295$	−3.61528	−0.210490
$296$	−26.3589	−1.53208
$297$	−6.46578	−0.375182
$298$	−3.81154	−0.220797
$299$	4.13764	0.239286
$300$	−31.9046	−1.84201
$301$	4.66206	0.268717
$302$	13.4421	0.773504
$303$	−21.9460	−1.26076
$304$	−12.1310	−0.695760
$305$	−0.821704	−0.0470506
$306$	−13.3233	−0.761641
$307$	5.68001	0.324175	0.162088	−	0.986776i	$-0.448177\pi$
$307$	5.68001	0.324175	0.162088	+	0.986776i	$0.448177\pi$
$308$	1.81336	0.103326
$309$	−16.8775	−0.960126
$310$	1.57950	0.0897097
$311$	−10.6587	−0.604402	−0.302201	−	0.953244i	$-0.597721\pi$
$311$	−10.6587	−0.604402	−0.302201	+	0.953244i	$0.597721\pi$
$312$	−19.9904	−1.13173
$313$	30.7499	1.73809	0.869043	−	0.494737i	$-0.164736\pi$
$313$	30.7499	1.73809	0.869043	+	0.494737i	$0.164736\pi$
$314$	29.2601	1.65124
$315$	0.0964409	0.00543383
$316$	60.6791	3.41347
$317$	0.573904	0.0322337	0.0161168	−	0.999870i	$-0.494870\pi$
$317$	0.573904	0.0322337	0.0161168	+	0.999870i	$0.494870\pi$
$318$	24.6981	1.38500
$319$	−0.401401	−0.0224741
$320$	0.735986	0.0411428
$321$	−24.0279	−1.34111
$322$	−1.69208	−0.0942957
$323$	12.7247	0.708021
$324$	−26.5660	−1.47589
$325$	−10.8650	−0.602684
$326$	−13.8856	−0.769051
$327$	15.1279	0.836572
$328$	−28.8064	−1.59057
$329$	1.05615	0.0582276
$330$	1.48714	0.0818641
$331$	21.1845	1.16440	0.582202	−	0.813044i	$-0.302191\pi$
$331$	21.1845	1.16440	0.582202	+	0.813044i	$0.302191\pi$
$332$	−23.0923	−1.26735
$333$	−3.40511	−0.186599
$334$	40.0627	2.19213
$335$	3.10399	0.169589
$336$	3.46675	0.189127
$337$	−8.91065	−0.485394	−0.242697	−	0.970102i	$-0.578032\pi$
$337$	−8.91065	−0.485394	−0.242697	+	0.970102i	$0.578032\pi$
$338$	20.3319	1.10591
$339$	1.49048	0.0809518
$340$	10.2146	0.553963
$341$	2.08667	0.112999
$342$	−3.69545	−0.199827
$343$	−4.99615	−0.269767
$344$	−77.9943	−4.20517
$345$	−0.952994	−0.0513075
$346$	8.53732	0.458969
$347$	20.0011	1.07372	0.536858	−	0.843673i	$-0.319611\pi$
$347$	20.0011	1.07372	0.536858	+	0.843673i	$0.319611\pi$
$348$	−2.28497	−0.122487
$349$	−33.8223	−1.81047	−0.905233	−	0.424915i	$-0.860304\pi$
$349$	−33.8223	−1.81047	−0.905233	+	0.424915i	$0.860304\pi$
$350$	4.44323	0.237501
$351$	−12.5343	−0.669033
$352$	−4.89553	−0.260933
$353$	7.22406	0.384498	0.192249	−	0.981346i	$-0.438422\pi$
$353$	7.22406	0.384498	0.192249	+	0.981346i	$0.438422\pi$
$354$	−39.5889	−2.10413
$355$	−0.343930	−0.0182539
$356$	−25.8940	−1.37238
$357$	−3.63641	−0.192459
$358$	40.5830	2.14488
$359$	10.5988	0.559382	0.279691	−	0.960090i	$-0.409768\pi$
$359$	10.5988	0.559382	0.279691	+	0.960090i	$0.409768\pi$
$360$	−1.61342	−0.0850345
$361$	−15.4706	−0.814241
$362$	8.33305	0.437975
$363$	−14.4306	−0.757413
$364$	3.51532	0.184253
$365$	−3.47152	−0.181708
$366$	−8.99802	−0.470334
$367$	−15.7406	−0.821655	−0.410828	−	0.911713i	$-0.634760\pi$
$367$	−15.7406	−0.821655	−0.410828	+	0.911713i	$0.634760\pi$
$368$	12.0043	0.625770
$369$	−3.72128	−0.193722
$370$	3.80134	0.197622
$371$	−2.36218	−0.122638
$372$	11.8783	0.615863
$373$	−5.30760	−0.274817	−0.137409	−	0.990514i	$-0.543877\pi$
$373$	−5.30760	−0.274817	−0.137409	+	0.990514i	$0.543877\pi$
$374$	19.6494	1.01605
$375$	5.06558	0.261585
$376$	−17.6690	−0.911209
$377$	−0.778141	−0.0400763
$378$	5.12588	0.263647
$379$	18.9216	0.971938	0.485969	−	0.873976i	$-0.338467\pi$
$379$	18.9216	0.971938	0.485969	+	0.873976i	$0.338467\pi$
$380$	2.83320	0.145340
$381$	−13.9721	−0.715815
$382$	−23.5388	−1.20435
$383$	3.94546	0.201604	0.100802	−	0.994907i	$-0.467859\pi$
$383$	3.94546	0.201604	0.100802	+	0.994907i	$0.467859\pi$
$384$	20.7703	1.05993
$385$	−0.142233	−0.00724886
$386$	0.713040	0.0362928
$387$	−10.0755	−0.512166
$388$	50.8432	2.58117
$389$	21.7230	1.10140	0.550699	−	0.834704i	$-0.314361\pi$
$389$	21.7230	1.10140	0.550699	+	0.834704i	$0.314361\pi$
$390$	2.88291	0.145982
$391$	−12.5918	−0.636797
$392$	41.4008	2.09106
$393$	−21.5522	−1.08717
$394$	29.0494	1.46349
$395$	−4.75943	−0.239473
$396$	−3.91898	−0.196936
$397$	22.4909	1.12879	0.564394	−	0.825505i	$-0.309110\pi$
$397$	22.4909	1.12879	0.564394	+	0.825505i	$0.309110\pi$
$398$	30.7992	1.54383
$399$	−1.00862	−0.0504944
$400$	−31.5222	−1.57611
$401$	−21.3337	−1.06535	−0.532677	−	0.846319i	$-0.678814\pi$
$401$	−21.3337	−1.06535	−0.532677	+	0.846319i	$0.678814\pi$
$402$	33.9901	1.69527
$403$	4.04514	0.201503
$404$	−64.5629	−3.21212
$405$	2.08373	0.103541
$406$	0.318219	0.0157929
$407$	5.02193	0.248928
$408$	60.8357	3.01181
$409$	15.7905	0.780790	0.390395	−	0.920648i	$-0.372339\pi$
$409$	15.7905	0.780790	0.390395	+	0.920648i	$0.372339\pi$
$410$	4.15430	0.205166
$411$	21.4818	1.05962
$412$	−49.6519	−2.44617
$413$	3.78637	0.186315
$414$	3.65686	0.179725
$415$	1.81127	0.0889116
$416$	−9.49031	−0.465301
$417$	21.7938	1.06725
$418$	5.45012	0.266574
$419$	0.833080	0.0406986	0.0203493	−	0.999793i	$-0.493522\pi$
$419$	0.833080	0.0406986	0.0203493	+	0.999793i	$0.493522\pi$
$420$	−0.809660	−0.0395073
$421$	−0.870927	−0.0424464	−0.0212232	−	0.999775i	$-0.506756\pi$
$421$	−0.870927	−0.0424464	−0.0212232	+	0.999775i	$0.506756\pi$
$422$	−48.5558	−2.36366
$423$	−2.28252	−0.110980
$424$	39.5184	1.91918
$425$	33.0649	1.60388
$426$	−3.76619	−0.182472
$427$	0.860590	0.0416469
$428$	−70.6878	−3.41683
$429$	3.80859	0.183880
$430$	11.2479	0.542423
$431$	12.3223	0.593546	0.296773	−	0.954948i	$-0.404090\pi$
$431$	12.3223	0.593546	0.296773	+	0.954948i	$0.404090\pi$
$432$	−36.3653	−1.74962
$433$	31.9858	1.53714	0.768569	−	0.639767i	$-0.220969\pi$
$433$	31.9858	1.53714	0.768569	+	0.639767i	$0.220969\pi$
$434$	−1.65425	−0.0794065
$435$	0.179224	0.00859313
$436$	44.5047	2.13139
$437$	−3.49257	−0.167072
$438$	−38.0147	−1.81641
$439$	1.06670	0.0509106	0.0254553	−	0.999676i	$-0.491896\pi$
$439$	1.06670	0.0509106	0.0254553	+	0.999676i	$0.491896\pi$
$440$	2.37950	0.113438
$441$	5.34826	0.254679
$442$	38.0917	1.81184
$443$	−11.8992	−0.565347	−0.282674	−	0.959216i	$-0.591221\pi$
$443$	−11.8992	−0.565347	−0.282674	+	0.959216i	$0.591221\pi$
$444$	28.5873	1.35669
$445$	2.03102	0.0962797
$446$	46.4203	2.19807
$447$	2.24829	0.106340
$448$	−0.770815	−0.0364176
$449$	−36.1936	−1.70808	−0.854041	−	0.520206i	$-0.825855\pi$
$449$	−36.1936	−1.70808	−0.854041	+	0.520206i	$0.825855\pi$
$450$	−9.60257	−0.452669
$451$	5.48821	0.258430
$452$	4.38485	0.206246
$453$	−7.92898	−0.372536
$454$	35.5844	1.67006
$455$	−0.275728	−0.0129263
$456$	16.8739	0.790191
$457$	−15.0325	−0.703191	−0.351595	−	0.936152i	$-0.614361\pi$
$457$	−15.0325	−0.703191	−0.351595	+	0.936152i	$0.614361\pi$
$458$	3.03231	0.141691
$459$	38.1450	1.78046
$460$	−2.80362	−0.130719
$461$	11.4088	0.531360	0.265680	−	0.964061i	$-0.414404\pi$
$461$	11.4088	0.531360	0.265680	+	0.964061i	$0.414404\pi$
$462$	−1.55751	−0.0724620
$463$	−4.43189	−0.205967	−0.102984	−	0.994683i	$-0.532839\pi$
$463$	−4.43189	−0.205967	−0.102984	+	0.994683i	$0.532839\pi$
$464$	−2.25759	−0.104806
$465$	−0.931689	−0.0432061
$466$	10.8903	0.504483
$467$	−6.86316	−0.317589	−0.158795	−	0.987312i	$-0.550761\pi$
$467$	−6.86316	−0.317589	−0.158795	+	0.987312i	$0.550761\pi$
$468$	−7.59720	−0.351181
$469$	−3.25089	−0.150112
$470$	2.54813	0.117536
$471$	−17.2594	−0.795273
$472$	−63.3444	−2.91566
$473$	14.8595	0.683242
$474$	−52.1178	−2.39385
$475$	9.17115	0.420801
$476$	−10.6980	−0.490341
$477$	5.10508	0.233746
$478$	55.2122	2.52535
$479$	−5.30677	−0.242472	−0.121236	−	0.992624i	$-0.538686\pi$
$479$	−5.30677	−0.242472	−0.121236	+	0.992624i	$0.538686\pi$
$480$	2.18584	0.0997694
$481$	9.73533	0.443893
$482$	66.9070	3.04753
$483$	0.998093	0.0454148
$484$	−42.4536	−1.92971
$485$	−3.98794	−0.181083
$486$	−19.8734	−0.901478
$487$	−31.1333	−1.41078	−0.705391	−	0.708818i	$-0.749229\pi$
$487$	−31.1333	−1.41078	−0.705391	+	0.708818i	$0.749229\pi$
$488$	−14.3973	−0.651736
$489$	8.19059	0.370391
$490$	−5.97060	−0.269724
$491$	33.0045	1.48947	0.744736	−	0.667360i	$-0.232576\pi$
$491$	33.0045	1.48947	0.744736	+	0.667360i	$0.232576\pi$
$492$	31.2416	1.40848
$493$	2.36807	0.106653
$494$	10.5654	0.475360
$495$	0.307389	0.0138161
$496$	11.7360	0.526961
$497$	0.360206	0.0161575
$498$	19.8342	0.888791
$499$	0.626211	0.0280331	0.0140165	−	0.999902i	$-0.495538\pi$
$499$	0.626211	0.0280331	0.0140165	+	0.999902i	$0.495538\pi$
$500$	14.9024	0.666457
$501$	−23.6315	−1.05578
$502$	46.4423	2.07282
$503$	−19.3150	−0.861214	−0.430607	−	0.902540i	$-0.641700\pi$
$503$	−19.3150	−0.861214	−0.430607	+	0.902540i	$0.641700\pi$
$504$	1.68977	0.0752683
$505$	5.06405	0.225347
$506$	−5.39321	−0.239758
$507$	−11.9931	−0.532630
$508$	−41.1047	−1.82373
$509$	5.82654	0.258257	0.129129	−	0.991628i	$-0.458782\pi$
$509$	5.82654	0.258257	0.129129	+	0.991628i	$0.458782\pi$
$510$	−8.77339	−0.388492
$511$	3.63581	0.160839
$512$	50.2898	2.22251
$513$	10.5802	0.467127
$514$	48.9551	2.15932
$515$	3.89449	0.171612
$516$	84.5878	3.72377
$517$	3.36631	0.148050
$518$	−3.98124	−0.174926
$519$	−5.03585	−0.221049
$520$	4.61281	0.202285
$521$	18.1488	0.795113	0.397557	−	0.917578i	$-0.369858\pi$
$521$	18.1488	0.795113	0.397557	+	0.917578i	$0.369858\pi$
$522$	−0.687725	−0.0301009
$523$	28.3153	1.23814	0.619071	−	0.785335i	$-0.287509\pi$
$523$	28.3153	1.23814	0.619071	+	0.785335i	$0.287509\pi$
$524$	−63.4046	−2.76984
$525$	−2.62090	−0.114385
$526$	78.3173	3.41480
$527$	−12.3103	−0.536247
$528$	11.0497	0.480876
$529$	−19.5439	−0.849735
$530$	−5.69912	−0.247554
$531$	−8.18299	−0.355111
$532$	−2.96727	−0.128648
$533$	10.6393	0.460838
$534$	22.2406	0.962444
$535$	5.54447	0.239708
$536$	54.3860	2.34912
$537$	−23.9384	−1.03302
$538$	−1.06690	−0.0459972
$539$	−7.88772	−0.339748
$540$	8.49311	0.365485
$541$	13.4486	0.578201	0.289101	−	0.957299i	$-0.406644\pi$
$541$	13.4486	0.578201	0.289101	+	0.957299i	$0.406644\pi$
$542$	63.3345	2.72045
$543$	−4.91536	−0.210938
$544$	28.8813	1.23828
$545$	−3.49077	−0.149528
$546$	−3.01934	−0.129216
$547$	9.50908	0.406579	0.203289	−	0.979119i	$-0.434837\pi$
$547$	9.50908	0.406579	0.203289	+	0.979119i	$0.434837\pi$
$548$	63.1974	2.69966
$549$	−1.85988	−0.0793778
$550$	14.1621	0.603872
$551$	0.656827	0.0279818
$552$	−16.6977	−0.710701
$553$	4.98466	0.211969
$554$	−68.9983	−2.93146
$555$	−2.24227	−0.0951791
$556$	64.1153	2.71910
$557$	−25.8825	−1.09667	−0.548337	−	0.836257i	$-0.684739\pi$
$557$	−25.8825	−1.09667	−0.548337	+	0.836257i	$0.684739\pi$
$558$	3.57511	0.151347
$559$	28.8062	1.21837
$560$	−0.799956	−0.0338043
$561$	−11.5905	−0.489350
$562$	−16.4681	−0.694666
$563$	−12.0739	−0.508852	−0.254426	−	0.967092i	$-0.581887\pi$
$563$	−12.0739	−0.508852	−0.254426	+	0.967092i	$0.581887\pi$
$564$	19.1627	0.806895
$565$	−0.343930	−0.0144692
$566$	72.2690	3.03769
$567$	−2.18234	−0.0916497
$568$	−6.02610	−0.252850
$569$	−6.34645	−0.266057	−0.133029	−	0.991112i	$-0.542470\pi$
$569$	−6.34645	−0.266057	−0.133029	+	0.991112i	$0.542470\pi$
$570$	−2.43346	−0.101926
$571$	−25.4686	−1.06583	−0.532914	−	0.846170i	$-0.678903\pi$
$571$	−25.4686	−1.06583	−0.532914	+	0.846170i	$0.678903\pi$
$572$	11.2045	0.468484
$573$	13.8847	0.580040
$574$	−4.35090	−0.181603
$575$	−9.07540	−0.378470
$576$	1.66586	0.0694109
$577$	−11.7992	−0.491208	−0.245604	−	0.969370i	$-0.578986\pi$
$577$	−11.7992	−0.491208	−0.245604	+	0.969370i	$0.578986\pi$
$578$	−72.9661	−3.03499
$579$	−0.420596	−0.0174794
$580$	0.527259	0.0218933
$581$	−1.89698	−0.0787002
$582$	−43.6697	−1.81017
$583$	−7.52907	−0.311822
$584$	−60.8256	−2.51698
$585$	0.595894	0.0246372
$586$	57.0734	2.35768
$587$	−20.1186	−0.830384	−0.415192	−	0.909734i	$-0.636286\pi$
$587$	−20.1186	−0.830384	−0.415192	+	0.909734i	$0.636286\pi$
$588$	−44.9008	−1.85168
$589$	−3.41449	−0.140692
$590$	9.13519	0.376090
$591$	−17.1351	−0.704845
$592$	28.2447	1.16085
$593$	−28.6875	−1.17805	−0.589027	−	0.808114i	$-0.700489\pi$
$593$	−28.6875	−1.17805	−0.589027	+	0.808114i	$0.700489\pi$
$594$	16.3379	0.670352
$595$	0.839106	0.0344000
$596$	6.61425	0.270930
$597$	−18.1673	−0.743539
$598$	−10.4551	−0.427541
$599$	25.0247	1.02248	0.511241	−	0.859437i	$-0.329186\pi$
$599$	25.0247	1.02248	0.511241	+	0.859437i	$0.329186\pi$
$600$	43.8465	1.79003
$601$	40.5932	1.65583	0.827916	−	0.560852i	$-0.189526\pi$
$601$	40.5932	1.65583	0.827916	+	0.560852i	$0.189526\pi$
$602$	−11.7802	−0.480126
$603$	7.02572	0.286109
$604$	−23.3263	−0.949133
$605$	3.32989	0.135379
$606$	55.4536	2.25265
$607$	−24.1705	−0.981052	−0.490526	−	0.871427i	$-0.663195\pi$
$607$	−24.1705	−0.981052	−0.490526	+	0.871427i	$0.663195\pi$
$608$	8.01075	0.324879
$609$	−0.187705	−0.00760621
$610$	2.07630	0.0840670
$611$	6.52581	0.264006
$612$	23.1201	0.934576
$613$	−34.6042	−1.39765	−0.698824	−	0.715293i	$-0.746293\pi$
$613$	−34.6042	−1.39765	−0.698824	+	0.715293i	$0.746293\pi$
$614$	−14.3524	−0.579215
$615$	−2.45047	−0.0988124
$616$	−2.49210	−0.100410
$617$	−1.86422	−0.0750508	−0.0375254	−	0.999296i	$-0.511948\pi$
$617$	−1.86422	−0.0750508	−0.0375254	+	0.999296i	$0.511948\pi$
$618$	42.6464	1.71549
$619$	−36.6983	−1.47503	−0.737514	−	0.675332i	$-0.764000\pi$
$619$	−36.6983	−1.47503	−0.737514	+	0.675332i	$0.764000\pi$
$620$	−2.74094	−0.110079
$621$	−10.4697	−0.420136
$622$	26.9328	1.07991
$623$	−2.12714	−0.0852220
$624$	21.4205	0.857508
$625$	23.2397	0.929587
$626$	−77.6996	−3.10550
$627$	−3.21482	−0.128388
$628$	−50.7756	−2.02617
$629$	−29.6270	−1.18130
$630$	−0.243689	−0.00970882
$631$	44.5334	1.77285	0.886423	−	0.462875i	$-0.153182\pi$
$631$	44.5334	1.77285	0.886423	+	0.462875i	$0.153182\pi$
$632$	−83.3913	−3.31713
$633$	28.6413	1.13839
$634$	−1.45016	−0.0575931
$635$	3.22409	0.127944
$636$	−42.8592	−1.69948
$637$	−15.2909	−0.605846
$638$	1.01427	0.0401553
$639$	−0.778467	−0.0307957
$640$	−4.79277	−0.189451
$641$	14.5610	0.575123	0.287562	−	0.957762i	$-0.407155\pi$
$641$	14.5610	0.575123	0.287562	+	0.957762i	$0.407155\pi$
$642$	60.7144	2.39621
$643$	24.0198	0.947247	0.473624	−	0.880727i	$-0.342946\pi$
$643$	24.0198	0.947247	0.473624	+	0.880727i	$0.342946\pi$
$644$	2.93629	0.115706
$645$	−6.63473	−0.261242
$646$	−32.1531	−1.26505
$647$	12.2139	0.480179	0.240089	−	0.970751i	$-0.422823\pi$
$647$	12.2139	0.480179	0.240089	+	0.970751i	$0.422823\pi$
$648$	36.5097	1.43424
$649$	12.0684	0.473727
$650$	27.4541	1.07684
$651$	0.975780	0.0382439
$652$	24.0959	0.943669
$653$	34.9427	1.36741	0.683707	−	0.729756i	$-0.260366\pi$
$653$	34.9427	1.36741	0.683707	+	0.729756i	$0.260366\pi$
$654$	−38.2255	−1.49473
$655$	4.97320	0.194319
$656$	30.8672	1.20516
$657$	−7.85760	−0.306554
$658$	−2.66871	−0.104037
$659$	−13.0088	−0.506751	−0.253375	−	0.967368i	$-0.581541\pi$
$659$	−13.0088	−0.506751	−0.253375	+	0.967368i	$0.581541\pi$
$660$	−2.58066	−0.100452
$661$	−37.9925	−1.47774	−0.738868	−	0.673850i	$-0.764639\pi$
$661$	−37.9925	−1.47774	−0.738868	+	0.673850i	$0.764639\pi$
$662$	−53.5295	−2.08048
$663$	−22.4689	−0.872618
$664$	31.7358	1.23159
$665$	0.232741	0.00902531
$666$	8.60413	0.333403
$667$	−0.649969	−0.0251669
$668$	−69.5215	−2.68987
$669$	−27.3816	−1.05863
$670$	−7.84325	−0.303011
$671$	2.74299	0.105892
$672$	−2.28928	−0.0883109
$673$	−12.9524	−0.499277	−0.249639	−	0.968339i	$-0.580312\pi$
$673$	−12.9524	−0.499277	−0.249639	+	0.968339i	$0.580312\pi$
$674$	22.5157	0.867270
$675$	27.4925	1.05819
$676$	−35.2824	−1.35701
$677$	−44.6351	−1.71547	−0.857733	−	0.514095i	$-0.828128\pi$
$677$	−44.6351	−1.71547	−0.857733	+	0.514095i	$0.828128\pi$
$678$	−3.76619	−0.144640
$679$	4.17666	0.160286
$680$	−14.0379	−0.538329
$681$	−20.9899	−0.804335
$682$	−5.27265	−0.201900
$683$	−19.4219	−0.743158	−0.371579	−	0.928401i	$-0.621184\pi$
$683$	−19.4219	−0.743158	−0.371579	+	0.928401i	$0.621184\pi$
$684$	6.41278	0.245199
$685$	−4.95695	−0.189395
$686$	12.6244	0.482002
$687$	−1.78865	−0.0682412
$688$	83.5741	3.18623
$689$	−14.5956	−0.556048
$690$	2.40805	0.0916729
$691$	27.0251	1.02808	0.514041	−	0.857766i	$-0.328148\pi$
$691$	27.0251	1.02808	0.514041	+	0.857766i	$0.328148\pi$
$692$	−14.8150	−0.563181
$693$	−0.321936	−0.0122293
$694$	−50.5393	−1.91845
$695$	−5.02895	−0.190759
$696$	3.14024	0.119030
$697$	−32.3778	−1.22640
$698$	85.4631	3.23483
$699$	−6.42377	−0.242969
$700$	−7.71042	−0.291426
$701$	−1.58226	−0.0597612	−0.0298806	−	0.999553i	$-0.509513\pi$
$701$	−1.58226	−0.0597612	−0.0298806	+	0.999553i	$0.509513\pi$
$702$	31.6721	1.19539
$703$	−8.21757	−0.309932
$704$	−2.45685	−0.0925958
$705$	−1.50305	−0.0566080
$706$	−18.2540	−0.686997
$707$	−5.30370	−0.199466
$708$	68.6994	2.58188
$709$	−2.23161	−0.0838098	−0.0419049	−	0.999122i	$-0.513343\pi$
$709$	−2.23161	−0.0838098	−0.0419049	+	0.999122i	$0.513343\pi$
$710$	0.869051	0.0326149
$711$	−10.7727	−0.404008
$712$	35.5861	1.33365
$713$	3.37884	0.126539
$714$	9.18858	0.343874
$715$	−0.878836	−0.0328666
$716$	−70.4245	−2.63189
$717$	−32.5676	−1.21626
$718$	−26.7812	−0.999467
$719$	53.3818	1.99081	0.995403	−	0.0957714i	$-0.0305318\pi$
$719$	53.3818	1.99081	0.995403	+	0.0957714i	$0.0305318\pi$
$720$	1.72884	0.0644301
$721$	−4.07880	−0.151902
$722$	39.0915	1.45483
$723$	−39.4659	−1.46775
$724$	−14.4605	−0.537420
$725$	1.70676	0.0633873
$726$	36.4637	1.35330
$727$	−6.17327	−0.228954	−0.114477	−	0.993426i	$-0.536519\pi$
$727$	−6.17327	−0.228954	−0.114477	+	0.993426i	$0.536519\pi$
$728$	−4.83111	−0.179053
$729$	29.8984	1.10735
$730$	8.77193	0.324664
$731$	−87.6642	−3.24238
$732$	15.6144	0.577126
$733$	37.4462	1.38311	0.691554	−	0.722325i	$-0.256926\pi$
$733$	37.4462	1.38311	0.691554	+	0.722325i	$0.256926\pi$
$734$	39.7739	1.46808
$735$	3.52184	0.129905
$736$	−7.92711	−0.292197
$737$	−10.3617	−0.381677
$738$	9.40303	0.346130
$739$	3.97245	0.146129	0.0730645	−	0.997327i	$-0.476722\pi$
$739$	3.97245	0.146129	0.0730645	+	0.997327i	$0.476722\pi$
$740$	−6.59655	−0.242494
$741$	−6.23214	−0.228943
$742$	5.96883	0.219123
$743$	20.2045	0.741231	0.370615	−	0.928786i	$-0.379147\pi$
$743$	20.2045	0.741231	0.370615	+	0.928786i	$0.379147\pi$
$744$	−16.3244	−0.598482
$745$	−0.518795	−0.0190072
$746$	13.4114	0.491026
$747$	4.09970	0.150000
$748$	−34.0980	−1.24675
$749$	−5.80686	−0.212178
$750$	−12.7998	−0.467384
$751$	13.9359	0.508529	0.254264	−	0.967135i	$-0.418167\pi$
$751$	13.9359	0.508529	0.254264	+	0.967135i	$0.418167\pi$
$752$	18.9330	0.690417
$753$	−27.3946	−0.998315
$754$	1.96623	0.0716058
$755$	1.82962	0.0665867
$756$	−8.89504	−0.323509
$757$	27.2880	0.991799	0.495900	−	0.868380i	$-0.334838\pi$
$757$	27.2880	0.991799	0.495900	+	0.868380i	$0.334838\pi$
$758$	−47.8116	−1.73660
$759$	3.18126	0.115472
$760$	−3.89366	−0.141238
$761$	17.4837	0.633783	0.316891	−	0.948462i	$-0.397361\pi$
$761$	17.4837	0.633783	0.316891	+	0.948462i	$0.397361\pi$
$762$	35.3052	1.27897
$763$	3.65597	0.132355
$764$	40.8473	1.47780
$765$	−1.81345	−0.0655654
$766$	−9.96950	−0.360213
$767$	23.3954	0.844760
$768$	−46.1039	−1.66363
$769$	14.0581	0.506946	0.253473	−	0.967342i	$-0.418427\pi$
$769$	14.0581	0.506946	0.253473	+	0.967342i	$0.418427\pi$
$770$	0.359398	0.0129518
$771$	−28.8768	−1.03997
$772$	−1.23735	−0.0445333
$773$	9.53350	0.342896	0.171448	−	0.985193i	$-0.445155\pi$
$773$	9.53350	0.342896	0.171448	+	0.985193i	$0.445155\pi$
$774$	25.4590	0.915106
$775$	−8.87251	−0.318710
$776$	−69.8739	−2.50833
$777$	2.34838	0.0842478
$778$	−54.8902	−1.96791
$779$	−8.98057	−0.321762
$780$	−5.00277	−0.179128
$781$	1.14810	0.0410821
$782$	31.8174	1.13779
$783$	1.96898	0.0703656
$784$	−44.3626	−1.58438
$785$	3.98264	0.142146
$786$	54.4587	1.94248
$787$	−22.3843	−0.797913	−0.398956	−	0.916970i	$-0.630628\pi$
$787$	−22.3843	−0.797913	−0.398956	+	0.916970i	$0.630628\pi$
$788$	−50.4099	−1.79578
$789$	−46.1965	−1.64464
$790$	12.0262	0.427875
$791$	0.360206	0.0128075
$792$	5.38586	0.191378
$793$	5.31746	0.188829
$794$	−56.8307	−2.01685
$795$	3.36170	0.119227
$796$	−53.4465	−1.89436
$797$	−0.252787	−0.00895418	−0.00447709	−	0.999990i	$-0.501425\pi$
$797$	−0.252787	−0.00895418	−0.00447709	+	0.999990i	$0.501425\pi$
$798$	2.54862	0.0902201
$799$	−19.8596	−0.702583
$800$	20.8158	0.735950
$801$	4.59711	0.162431
$802$	53.9065	1.90351
$803$	11.5885	0.408951
$804$	−58.9837	−2.08019
$805$	−0.230311	−0.00811740
$806$	−10.2214	−0.360032
$807$	0.629324	0.0221532
$808$	88.7288	3.12147
$809$	5.91385	0.207920	0.103960	−	0.994581i	$-0.466849\pi$
$809$	5.91385	0.207920	0.103960	+	0.994581i	$0.466849\pi$
$810$	−5.26523	−0.185001
$811$	−10.3857	−0.364691	−0.182345	−	0.983235i	$-0.558369\pi$
$811$	−10.3857	−0.364691	−0.182345	+	0.983235i	$0.558369\pi$
$812$	−0.552211	−0.0193788
$813$	−37.3587	−1.31023
$814$	−12.6895	−0.444768
$815$	−1.88999	−0.0662034
$816$	−65.1879	−2.28203
$817$	−24.3152	−0.850682
$818$	−39.8998	−1.39506
$819$	−0.624094	−0.0218076
$820$	−7.20904	−0.251750
$821$	−35.3407	−1.23340	−0.616699	−	0.787199i	$-0.711530\pi$
$821$	−35.3407	−1.23340	−0.616699	+	0.787199i	$0.711530\pi$
$822$	−54.2808	−1.89326
$823$	−46.9031	−1.63494	−0.817469	−	0.575973i	$-0.804623\pi$
$823$	−46.9031	−1.63494	−0.817469	+	0.575973i	$0.804623\pi$
$824$	68.2366	2.37713
$825$	−8.35367	−0.290837
$826$	−9.56750	−0.332896
$827$	−45.7931	−1.59238	−0.796191	−	0.605046i	$-0.793155\pi$
$827$	−45.7931	−1.59238	−0.796191	+	0.605046i	$0.793155\pi$
$828$	−6.34583	−0.220533
$829$	52.6031	1.82698	0.913491	−	0.406859i	$-0.133376\pi$
$829$	52.6031	1.82698	0.913491	+	0.406859i	$0.133376\pi$
$830$	−4.57676	−0.158862
$831$	40.6995	1.41185
$832$	−4.76276	−0.165119
$833$	46.5338	1.61230
$834$	−55.0692	−1.90689
$835$	5.45299	0.188708
$836$	−9.45769	−0.327101
$837$	−10.2357	−0.353797
$838$	−2.10505	−0.0727177
$839$	19.6190	0.677322	0.338661	−	0.940908i	$-0.390026\pi$
$839$	19.6190	0.677322	0.338661	+	0.940908i	$0.390026\pi$
$840$	1.11272	0.0383923
$841$	−28.8778	−0.995785
$842$	2.20068	0.0758405
$843$	9.71394	0.334566
$844$	84.2599	2.90034
$845$	2.76741	0.0952018
$846$	5.76754	0.198292
$847$	−3.48747	−0.119831
$848$	−42.3455	−1.45415
$849$	−42.6288	−1.46302
$850$	−83.5493	−2.86572
$851$	8.13177	0.278754
$852$	6.53553	0.223904
$853$	−48.2858	−1.65327	−0.826637	−	0.562735i	$-0.809749\pi$
$853$	−48.2858	−1.65327	−0.826637	+	0.562735i	$0.809749\pi$
$854$	−2.17456	−0.0744120
$855$	−0.502993	−0.0172020
$856$	97.1463	3.32039
$857$	47.2741	1.61485	0.807427	−	0.589968i	$-0.200860\pi$
$857$	47.2741	1.61485	0.807427	+	0.589968i	$0.200860\pi$
$858$	−9.62364	−0.328546
$859$	−4.88896	−0.166809	−0.0834047	−	0.996516i	$-0.526579\pi$
$859$	−4.88896	−0.166809	−0.0834047	+	0.996516i	$0.526579\pi$
$860$	−19.5187	−0.665583
$861$	2.56643	0.0874638
$862$	−31.1364	−1.06051
$863$	19.4398	0.661737	0.330869	−	0.943677i	$-0.392658\pi$
$863$	19.4398	0.661737	0.330869	+	0.943677i	$0.392658\pi$
$864$	24.0139	0.816971
$865$	1.16203	0.0395101
$866$	−80.8225	−2.74646
$867$	43.0400	1.46171
$868$	2.87065	0.0974362
$869$	15.8878	0.538956
$870$	−0.452868	−0.0153537
$871$	−20.0868	−0.680614
$872$	−61.1628	−2.07123
$873$	−9.02648	−0.305500
$874$	8.82512	0.298514
$875$	1.22420	0.0413856
$876$	65.9677	2.22884
$877$	32.8815	1.11033	0.555165	−	0.831741i	$-0.312655\pi$
$877$	32.8815	1.11033	0.555165	+	0.831741i	$0.312655\pi$
$878$	−2.69535	−0.0909638
$879$	−33.6655	−1.13551
$880$	−2.54973	−0.0859513
$881$	−12.5052	−0.421312	−0.210656	−	0.977560i	$-0.567560\pi$
$881$	−12.5052	−0.421312	−0.210656	+	0.977560i	$0.567560\pi$
$882$	−13.5141	−0.455044
$883$	−50.4346	−1.69726	−0.848629	−	0.528988i	$-0.822572\pi$
$883$	−50.4346	−1.69726	−0.848629	+	0.528988i	$0.822572\pi$
$884$	−66.1012	−2.22322
$885$	−5.38851	−0.181133
$886$	30.0672	1.01013
$887$	49.3710	1.65771	0.828857	−	0.559460i	$-0.188991\pi$
$887$	49.3710	1.65771	0.828857	+	0.559460i	$0.188991\pi$
$888$	−39.2875	−1.31840
$889$	−3.37666	−0.113250
$890$	−5.13204	−0.172026
$891$	−6.95585	−0.233030
$892$	−80.5541	−2.69715
$893$	−5.50842	−0.184332
$894$	−5.68103	−0.190002
$895$	5.52381	0.184641
$896$	5.01958	0.167693
$897$	6.16707	0.205913
$898$	91.4550	3.05189
$899$	−0.635439	−0.0211931
$900$	16.6635	0.555451
$901$	44.4179	1.47977
$902$	−13.8678	−0.461746
$903$	6.94871	0.231239
$904$	−6.02610	−0.200425
$905$	1.13422	0.0377029
$906$	20.0352	0.665623
$907$	56.0875	1.86236	0.931178	−	0.364566i	$-0.118783\pi$
$907$	56.0875	1.86236	0.931178	+	0.364566i	$0.118783\pi$
$908$	−61.7503	−2.04925
$909$	11.4622	0.380177
$910$	0.696716	0.0230959
$911$	1.69364	0.0561128	0.0280564	−	0.999606i	$-0.491068\pi$
$911$	1.69364	0.0561128	0.0280564	+	0.999606i	$0.491068\pi$
$912$	−18.0810	−0.598722
$913$	−6.04632	−0.200104
$914$	37.9845	1.25642
$915$	−1.22473	−0.0404885
$916$	−5.26203	−0.173862
$917$	−5.20855	−0.172002
$918$	−96.3858	−3.18120
$919$	−40.0880	−1.32238	−0.661191	−	0.750217i	$-0.729949\pi$
$919$	−40.0880	−1.32238	−0.661191	+	0.750217i	$0.729949\pi$
$920$	3.85301	0.127030
$921$	8.46594	0.278962
$922$	−28.8280	−0.949399
$923$	2.22566	0.0732585
$924$	2.70278	0.0889150
$925$	−21.3532	−0.702090
$926$	11.1986	0.368009
$927$	8.81497	0.289522
$928$	1.49080	0.0489381
$929$	52.6431	1.72716	0.863581	−	0.504209i	$-0.168216\pi$
$929$	52.6431	1.72716	0.863581	+	0.504209i	$0.168216\pi$
$930$	2.35422	0.0771978
$931$	12.9070	0.423009
$932$	−18.8981	−0.619028
$933$	−15.8867	−0.520106
$934$	17.3420	0.567448
$935$	2.67451	0.0874659
$936$	10.4408	0.341270
$937$	−19.1729	−0.626352	−0.313176	−	0.949695i	$-0.601393\pi$
$937$	−19.1729	−0.626352	−0.313176	+	0.949695i	$0.601393\pi$
$938$	8.21442	0.268210
$939$	45.8321	1.49567
$940$	−4.42181	−0.144224
$941$	−52.0012	−1.69519	−0.847595	−	0.530643i	$-0.821951\pi$
$941$	−52.0012	−1.69519	−0.847595	+	0.530643i	$0.821951\pi$
$942$	43.6116	1.42094
$943$	8.88681	0.289394
$944$	67.8761	2.20918
$945$	0.697691	0.0226959
$946$	−37.5475	−1.22077
$947$	−41.6106	−1.35216	−0.676081	−	0.736827i	$-0.736323\pi$
$947$	−41.6106	−1.35216	−0.676081	+	0.736827i	$0.736323\pi$
$948$	90.4411	2.93739
$949$	22.4651	0.729249
$950$	−23.1739	−0.751861
$951$	0.855393	0.0277380
$952$	14.7022	0.476502
$953$	3.83739	0.124305	0.0621526	−	0.998067i	$-0.480203\pi$
$953$	3.83739	0.124305	0.0621526	+	0.998067i	$0.480203\pi$
$954$	−12.8996	−0.417642
$955$	−3.20390	−0.103676
$956$	−95.8108	−3.09874
$957$	−0.598280	−0.0193396
$958$	13.4093	0.433234
$959$	5.19153	0.167643
$960$	1.09697	0.0354046
$961$	−27.6967	−0.893442
$962$	−24.5995	−0.793120
$963$	12.5496	0.404405
$964$	−116.105	−3.73949
$965$	0.0970529	0.00312424
$966$	−2.52201	−0.0811443
$967$	−40.4074	−1.29942	−0.649708	−	0.760184i	$-0.725109\pi$
$967$	−40.4074	−1.29942	−0.649708	+	0.760184i	$0.725109\pi$
$968$	58.3439	1.87525
$969$	18.9659	0.609273
$970$	10.0768	0.323548
$971$	53.9074	1.72997	0.864985	−	0.501798i	$-0.167328\pi$
$971$	53.9074	1.72997	0.864985	+	0.501798i	$0.167328\pi$
$972$	34.4868	1.10616
$973$	5.26694	0.168850
$974$	78.6683	2.52070
$975$	−16.1941	−0.518627
$976$	15.4273	0.493816
$977$	28.9577	0.926440	0.463220	−	0.886243i	$-0.346694\pi$
$977$	28.9577	0.926440	0.463220	+	0.886243i	$0.346694\pi$
$978$	−20.6962	−0.661791
$979$	−6.77990	−0.216686
$980$	10.3609	0.330967
$981$	−7.90116	−0.252265
$982$	−83.3966	−2.66129
$983$	−23.4696	−0.748563	−0.374281	−	0.927315i	$-0.622111\pi$
$983$	−23.4696	−0.748563	−0.374281	+	0.927315i	$0.622111\pi$
$984$	−42.9354	−1.36873
$985$	3.95395	0.125983
$986$	−5.98371	−0.190560
$987$	1.57417	0.0501065
$988$	−18.3344	−0.583293
$989$	24.0614	0.765107
$990$	−0.776719	−0.0246858
$991$	46.6489	1.48185	0.740926	−	0.671587i	$-0.234387\pi$
$991$	46.6489	1.48185	0.740926	+	0.671587i	$0.234387\pi$
$992$	−7.74990	−0.246059
$993$	31.5751	1.00200
$994$	−0.910178	−0.0288691
$995$	4.19213	0.132899
$996$	−34.4186	−1.09060
$997$	−9.88749	−0.313140	−0.156570	−	0.987667i	$-0.550044\pi$
$997$	−9.88749	−0.313140	−0.156570	+	0.987667i	$0.550044\pi$
$998$	−1.58233	−0.0500877
$999$	−24.6339	−0.779383

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8023.2.a.b.1.13	✓	155

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8023.2.a.b.1.13	✓	155	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)

\(f(q)\)	\(=\)	\(q-2.52683 q^{2} +1.49048 q^{3} +4.38485 q^{4} -0.343930 q^{5} -3.76619 q^{6} +0.360206 q^{7} -6.02610 q^{8} -0.778467 q^{9} +O(q^{10})\)	\(q-2.52683 q^{2} +1.49048 q^{3} +4.38485 q^{4} -0.343930 q^{5} -3.76619 q^{6} +0.360206 q^{7} -6.02610 q^{8} -0.778467 q^{9} +0.869051 q^{10} +1.14810 q^{11} +6.53553 q^{12} +2.22566 q^{13} -0.910178 q^{14} -0.512621 q^{15} +6.45721 q^{16} -6.77322 q^{17} +1.96705 q^{18} -1.87868 q^{19} -1.50808 q^{20} +0.536880 q^{21} -2.90104 q^{22} +1.85906 q^{23} -8.98179 q^{24} -4.88171 q^{25} -5.62386 q^{26} -5.63173 q^{27} +1.57945 q^{28} -0.349623 q^{29} +1.29530 q^{30} +1.81750 q^{31} -4.26404 q^{32} +1.71122 q^{33} +17.1148 q^{34} -0.123886 q^{35} -3.41346 q^{36} +4.37413 q^{37} +4.74709 q^{38} +3.31731 q^{39} +2.07256 q^{40} +4.78027 q^{41} -1.35660 q^{42} +12.9428 q^{43} +5.03423 q^{44} +0.267738 q^{45} -4.69752 q^{46} +2.93208 q^{47} +9.62435 q^{48} -6.87025 q^{49} +12.3352 q^{50} -10.0954 q^{51} +9.75919 q^{52} -6.55787 q^{53} +14.2304 q^{54} -0.394865 q^{55} -2.17064 q^{56} -2.80013 q^{57} +0.883435 q^{58} +10.5117 q^{59} -2.24777 q^{60} +2.38916 q^{61} -4.59251 q^{62} -0.280408 q^{63} -2.13993 q^{64} -0.765472 q^{65} -4.32395 q^{66} -9.02507 q^{67} -29.6996 q^{68} +2.77089 q^{69} +0.313038 q^{70} +1.00000 q^{71} +4.69112 q^{72} +10.0937 q^{73} -11.0527 q^{74} -7.27610 q^{75} -8.23771 q^{76} +0.413552 q^{77} -8.38226 q^{78} +13.8384 q^{79} -2.22083 q^{80} -6.05859 q^{81} -12.0789 q^{82} -5.26638 q^{83} +2.35414 q^{84} +2.32952 q^{85} -32.7041 q^{86} -0.521106 q^{87} -6.91855 q^{88} -5.90533 q^{89} -0.676528 q^{90} +0.801697 q^{91} +8.15170 q^{92} +2.70895 q^{93} -7.40885 q^{94} +0.646133 q^{95} -6.35547 q^{96} +11.5952 q^{97} +17.3599 q^{98} -0.893755 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 155 q - 21 q^{2} - 16 q^{3} + 151 q^{4} - 26 q^{5} - 10 q^{6} - 40 q^{7} - 57 q^{8} + 135 q^{9}+O(q^{10}) \) 155 * q - 21 * q^2 - 16 * q^3 + 151 * q^4 - 26 * q^5 - 10 * q^6 - 40 * q^7 - 57 * q^8 + 135 * q^9	\( 155 q - 21 q^{2} - 16 q^{3} + 151 q^{4} - 26 q^{5} - 10 q^{6} - 40 q^{7} - 57 q^{8} + 135 q^{9} - 2 q^{10} - 24 q^{11} - 32 q^{12} - 62 q^{13} - 18 q^{14} - 12 q^{15} + 155 q^{16} - 129 q^{17} - 42 q^{18} - 18 q^{19} - 59 q^{20} - 45 q^{21} - 17 q^{22} - 38 q^{23} - 27 q^{24} + 129 q^{25} - 44 q^{26} - 43 q^{27} - 100 q^{28} - 52 q^{29} - 39 q^{30} - 56 q^{31} - 145 q^{32} - 126 q^{33} - q^{34} - 49 q^{35} + 131 q^{36} - 30 q^{37} - 91 q^{38} - 29 q^{39} - 5 q^{40} - 163 q^{41} - 80 q^{42} - 15 q^{43} - 118 q^{44} - 66 q^{45} + 2 q^{46} - 111 q^{47} - 89 q^{48} + 101 q^{49} - 121 q^{50} + 5 q^{51} - 111 q^{52} - 93 q^{53} - 68 q^{54} - 60 q^{55} - 27 q^{56} - 106 q^{57} + 16 q^{58} - 79 q^{59} - 103 q^{60} - 74 q^{61} - 102 q^{62} - 118 q^{63} + 175 q^{64} - 109 q^{65} + 65 q^{66} - 18 q^{67} - 346 q^{68} - 39 q^{69} + 32 q^{70} + 155 q^{71} - 203 q^{72} - 108 q^{73} - 87 q^{74} - 22 q^{75} - 16 q^{76} - 121 q^{77} - 75 q^{78} - 6 q^{79} - 136 q^{80} + 107 q^{81} - 30 q^{82} - 116 q^{83} - 5 q^{84} - 53 q^{85} + 8 q^{86} - 100 q^{87} - 43 q^{88} - 189 q^{89} - 76 q^{90} + 14 q^{91} - 99 q^{92} - 72 q^{93} + 17 q^{94} - 18 q^{95} - 50 q^{96} - 184 q^{97} - 249 q^{98} - 114 q^{99}+O(q^{100}) \) 155 * q - 21 * q^2 - 16 * q^3 + 151 * q^4 - 26 * q^5 - 10 * q^6 - 40 * q^7 - 57 * q^8 + 135 * q^9 - 2 * q^10 - 24 * q^11 - 32 * q^12 - 62 * q^13 - 18 * q^14 - 12 * q^15 + 155 * q^16 - 129 * q^17 - 42 * q^18 - 18 * q^19 - 59 * q^20 - 45 * q^21 - 17 * q^22 - 38 * q^23 - 27 * q^24 + 129 * q^25 - 44 * q^26 - 43 * q^27 - 100 * q^28 - 52 * q^29 - 39 * q^30 - 56 * q^31 - 145 * q^32 - 126 * q^33 - q^34 - 49 * q^35 + 131 * q^36 - 30 * q^37 - 91 * q^38 - 29 * q^39 - 5 * q^40 - 163 * q^41 - 80 * q^42 - 15 * q^43 - 118 * q^44 - 66 * q^45 + 2 * q^46 - 111 * q^47 - 89 * q^48 + 101 * q^49 - 121 * q^50 + 5 * q^51 - 111 * q^52 - 93 * q^53 - 68 * q^54 - 60 * q^55 - 27 * q^56 - 106 * q^57 + 16 * q^58 - 79 * q^59 - 103 * q^60 - 74 * q^61 - 102 * q^62 - 118 * q^63 + 175 * q^64 - 109 * q^65 + 65 * q^66 - 18 * q^67 - 346 * q^68 - 39 * q^69 + 32 * q^70 + 155 * q^71 - 203 * q^72 - 108 * q^73 - 87 * q^74 - 22 * q^75 - 16 * q^76 - 121 * q^77 - 75 * q^78 - 6 * q^79 - 136 * q^80 + 107 * q^81 - 30 * q^82 - 116 * q^83 - 5 * q^84 - 53 * q^85 + 8 * q^86 - 100 * q^87 - 43 * q^88 - 189 * q^89 - 76 * q^90 + 14 * q^91 - 99 * q^92 - 72 * q^93 + 17 * q^94 - 18 * q^95 - 50 * q^96 - 184 * q^97 - 249 * q^98 - 114 * q^99

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