LMFDB - Embedded newform 8035.2.a.c.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8035,2,Mod(1,8035)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8035, 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("8035.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8035 = 5 \cdot 1607 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8035.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:	$64.1597980241$
Analytic rank:	$0$
Dimension:	$127$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	8035.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.23096 q^{2} +0.376155 q^{3} +2.97717 q^{4} -1.00000 q^{5} -0.839185 q^{6} -1.46614 q^{7} -2.18003 q^{8} -2.85851 q^{9} +O(q^{10})$	\(q-2.23096 q^{2} +0.376155 q^{3} +2.97717 q^{4} -1.00000 q^{5} -0.839185 q^{6} -1.46614 q^{7} -2.18003 q^{8} -2.85851 q^{9} +2.23096 q^{10} -0.286789 q^{11} +1.11988 q^{12} +2.65048 q^{13} +3.27089 q^{14} -0.376155 q^{15} -1.09078 q^{16} -6.33858 q^{17} +6.37721 q^{18} -5.84820 q^{19} -2.97717 q^{20} -0.551495 q^{21} +0.639814 q^{22} -2.11881 q^{23} -0.820030 q^{24} +1.00000 q^{25} -5.91310 q^{26} -2.20371 q^{27} -4.36495 q^{28} +4.20015 q^{29} +0.839185 q^{30} -7.45015 q^{31} +6.79356 q^{32} -0.107877 q^{33} +14.1411 q^{34} +1.46614 q^{35} -8.51028 q^{36} -4.74921 q^{37} +13.0471 q^{38} +0.996989 q^{39} +2.18003 q^{40} -5.42988 q^{41} +1.23036 q^{42} -5.10150 q^{43} -0.853820 q^{44} +2.85851 q^{45} +4.72699 q^{46} -4.92824 q^{47} -0.410303 q^{48} -4.85044 q^{49} -2.23096 q^{50} -2.38429 q^{51} +7.89093 q^{52} -6.71555 q^{53} +4.91637 q^{54} +0.286789 q^{55} +3.19623 q^{56} -2.19983 q^{57} -9.37036 q^{58} +7.12154 q^{59} -1.11988 q^{60} +7.98944 q^{61} +16.6210 q^{62} +4.19097 q^{63} -12.9746 q^{64} -2.65048 q^{65} +0.240669 q^{66} +11.1862 q^{67} -18.8711 q^{68} -0.797002 q^{69} -3.27089 q^{70} -11.3043 q^{71} +6.23165 q^{72} -14.9306 q^{73} +10.5953 q^{74} +0.376155 q^{75} -17.4111 q^{76} +0.420472 q^{77} -2.22424 q^{78} +1.05457 q^{79} +1.09078 q^{80} +7.74659 q^{81} +12.1138 q^{82} -10.4692 q^{83} -1.64190 q^{84} +6.33858 q^{85} +11.3812 q^{86} +1.57991 q^{87} +0.625209 q^{88} +13.6839 q^{89} -6.37721 q^{90} -3.88596 q^{91} -6.30808 q^{92} -2.80241 q^{93} +10.9947 q^{94} +5.84820 q^{95} +2.55543 q^{96} -3.25877 q^{97} +10.8211 q^{98} +0.819788 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 127 q + 19 q^{2} + 10 q^{3} + 125 q^{4} - 127 q^{5} + 13 q^{7} + 54 q^{8} + 123 q^{9}+O(q^{10}) $ 127 * q + 19 * q^2 + 10 * q^3 + 125 * q^4 - 127 * q^5 + 13 * q^7 + 54 * q^8 + 123 * q^9	\( 127 q + 19 q^{2} + 10 q^{3} + 125 q^{4} - 127 q^{5} + 13 q^{7} + 54 q^{8} + 123 q^{9} - 19 q^{10} + 30 q^{11} + 35 q^{12} + 30 q^{13} + 39 q^{14} - 10 q^{15} + 121 q^{16} + 63 q^{17} + 53 q^{18} - 35 q^{19} - 125 q^{20} + 33 q^{21} + 49 q^{22} + 61 q^{23} - 5 q^{24} + 127 q^{25} + 10 q^{26} + 40 q^{27} + 32 q^{28} + 134 q^{29} - 25 q^{31} + 122 q^{32} + 48 q^{33} - 21 q^{34} - 13 q^{35} + 133 q^{36} + 60 q^{37} + 33 q^{38} + 26 q^{39} - 54 q^{40} + 9 q^{41} + 45 q^{42} + 48 q^{43} + 85 q^{44} - 123 q^{45} - 11 q^{46} + 57 q^{47} + 71 q^{48} + 70 q^{49} + 19 q^{50} + 45 q^{51} + 68 q^{52} + 182 q^{53} - 29 q^{54} - 30 q^{55} + 96 q^{56} + 74 q^{57} + 47 q^{58} + 19 q^{59} - 35 q^{60} + 16 q^{61} + 43 q^{62} + 73 q^{63} + 110 q^{64} - 30 q^{65} + 8 q^{66} + 40 q^{67} + 129 q^{68} + 2 q^{69} - 39 q^{70} + 48 q^{71} + 151 q^{72} + 30 q^{73} + 117 q^{74} + 10 q^{75} - 98 q^{76} + 134 q^{77} + 54 q^{78} + 23 q^{79} - 121 q^{80} + 111 q^{81} + 4 q^{82} + 92 q^{83} + 48 q^{84} - 63 q^{85} + 42 q^{86} + 69 q^{87} + 121 q^{88} + 12 q^{89} - 53 q^{90} - 30 q^{91} + 175 q^{92} + 82 q^{93} - 23 q^{94} + 35 q^{95} + 6 q^{96} + 67 q^{97} + 122 q^{98} + 73 q^{99}+O(q^{100}) \) 127 * q + 19 * q^2 + 10 * q^3 + 125 * q^4 - 127 * q^5 + 13 * q^7 + 54 * q^8 + 123 * q^9 - 19 * q^10 + 30 * q^11 + 35 * q^12 + 30 * q^13 + 39 * q^14 - 10 * q^15 + 121 * q^16 + 63 * q^17 + 53 * q^18 - 35 * q^19 - 125 * q^20 + 33 * q^21 + 49 * q^22 + 61 * q^23 - 5 * q^24 + 127 * q^25 + 10 * q^26 + 40 * q^27 + 32 * q^28 + 134 * q^29 - 25 * q^31 + 122 * q^32 + 48 * q^33 - 21 * q^34 - 13 * q^35 + 133 * q^36 + 60 * q^37 + 33 * q^38 + 26 * q^39 - 54 * q^40 + 9 * q^41 + 45 * q^42 + 48 * q^43 + 85 * q^44 - 123 * q^45 - 11 * q^46 + 57 * q^47 + 71 * q^48 + 70 * q^49 + 19 * q^50 + 45 * q^51 + 68 * q^52 + 182 * q^53 - 29 * q^54 - 30 * q^55 + 96 * q^56 + 74 * q^57 + 47 * q^58 + 19 * q^59 - 35 * q^60 + 16 * q^61 + 43 * q^62 + 73 * q^63 + 110 * q^64 - 30 * q^65 + 8 * q^66 + 40 * q^67 + 129 * q^68 + 2 * q^69 - 39 * q^70 + 48 * q^71 + 151 * q^72 + 30 * q^73 + 117 * q^74 + 10 * q^75 - 98 * q^76 + 134 * q^77 + 54 * q^78 + 23 * q^79 - 121 * q^80 + 111 * q^81 + 4 * q^82 + 92 * q^83 + 48 * q^84 - 63 * q^85 + 42 * q^86 + 69 * q^87 + 121 * q^88 + 12 * q^89 - 53 * q^90 - 30 * q^91 + 175 * q^92 + 82 * q^93 - 23 * q^94 + 35 * q^95 + 6 * q^96 + 67 * q^97 + 122 * q^98 + 73 * 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 $

$2$	−2.23096	−1.57753	−0.788763	−	0.614698i	$-0.789278\pi$
$2$	−2.23096	−1.57753	−0.788763	+	0.614698i	$0.789278\pi$
$3$	0.376155	0.217173	0.108587	−	0.994087i	$-0.465368\pi$
$3$	0.376155	0.217173	0.108587	+	0.994087i	$0.465368\pi$
$4$	2.97717	1.48859
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.839185	−0.342596
$7$	−1.46614	−0.554148	−0.277074	−	0.960849i	$-0.589365\pi$
$7$	−1.46614	−0.554148	−0.277074	+	0.960849i	$0.589365\pi$
$8$	−2.18003	−0.770759
$9$	−2.85851	−0.952836
$10$	2.23096	0.705491
$11$	−0.286789	−0.0864700	−0.0432350	−	0.999065i	$-0.513766\pi$
$11$	−0.286789	−0.0864700	−0.0432350	+	0.999065i	$0.513766\pi$
$12$	1.11988	0.323281
$13$	2.65048	0.735110	0.367555	−	0.930002i	$-0.380195\pi$
$13$	2.65048	0.735110	0.367555	+	0.930002i	$0.380195\pi$
$14$	3.27089	0.874183
$15$	−0.376155	−0.0971227
$16$	−1.09078	−0.272696
$17$	−6.33858	−1.53733	−0.768666	−	0.639650i	$-0.779079\pi$
$17$	−6.33858	−1.53733	−0.768666	+	0.639650i	$0.779079\pi$
$18$	6.37721	1.50312
$19$	−5.84820	−1.34167	−0.670835	−	0.741607i	$-0.734064\pi$
$19$	−5.84820	−1.34167	−0.670835	+	0.741607i	$0.734064\pi$
$20$	−2.97717	−0.665716
$21$	−0.551495	−0.120346
$22$	0.639814	0.136409
$23$	−2.11881	−0.441803	−0.220902	−	0.975296i	$-0.570900\pi$
$23$	−2.11881	−0.441803	−0.220902	+	0.975296i	$0.570900\pi$
$24$	−0.820030	−0.167388
$25$	1.00000	0.200000
$26$	−5.91310	−1.15965
$27$	−2.20371	−0.424103
$28$	−4.36495	−0.824897
$29$	4.20015	0.779949	0.389974	−	0.920826i	$-0.372484\pi$
$29$	4.20015	0.779949	0.389974	+	0.920826i	$0.372484\pi$
$30$	0.839185	0.153214
$31$	−7.45015	−1.33809	−0.669043	−	0.743224i	$-0.733296\pi$
$31$	−7.45015	−1.33809	−0.669043	+	0.743224i	$0.733296\pi$
$32$	6.79356	1.20094
$33$	−0.107877	−0.0187790
$34$	14.1411	2.42518
$35$	1.46614	0.247822
$36$	−8.51028	−1.41838
$37$	−4.74921	−0.780765	−0.390383	−	0.920653i	$-0.627657\pi$
$37$	−4.74921	−0.780765	−0.390383	+	0.920653i	$0.627657\pi$
$38$	13.0471	2.11652
$39$	0.996989	0.159646
$40$	2.18003	0.344694
$41$	−5.42988	−0.848005	−0.424002	−	0.905661i	$-0.639375\pi$
$41$	−5.42988	−0.848005	−0.424002	+	0.905661i	$0.639375\pi$
$42$	1.23036	0.189849
$43$	−5.10150	−0.777971	−0.388986	−	0.921244i	$-0.627174\pi$
$43$	−5.10150	−0.777971	−0.388986	+	0.921244i	$0.627174\pi$
$44$	−0.853820	−0.128718
$45$	2.85851	0.426121
$46$	4.72699	0.696956
$47$	−4.92824	−0.718858	−0.359429	−	0.933172i	$-0.617028\pi$
$47$	−4.92824	−0.718858	−0.359429	+	0.933172i	$0.617028\pi$
$48$	−0.410303	−0.0592221
$49$	−4.85044	−0.692920
$50$	−2.23096	−0.315505
$51$	−2.38429	−0.333867
$52$	7.89093	1.09428
$53$	−6.71555	−0.922451	−0.461226	−	0.887283i	$-0.652590\pi$
$53$	−6.71555	−0.922451	−0.461226	+	0.887283i	$0.652590\pi$
$54$	4.91637	0.669034
$55$	0.286789	0.0386706
$56$	3.19623	0.427114
$57$	−2.19983	−0.291374
$58$	−9.37036	−1.23039
$59$	7.12154	0.927146	0.463573	−	0.886059i	$-0.346567\pi$
$59$	7.12154	0.927146	0.463573	+	0.886059i	$0.346567\pi$
$60$	−1.11988	−0.144576
$61$	7.98944	1.02294	0.511472	−	0.859300i	$-0.329101\pi$
$61$	7.98944	1.02294	0.511472	+	0.859300i	$0.329101\pi$
$62$	16.6210	2.11086
$63$	4.19097	0.528012
$64$	−12.9746	−1.62182
$65$	−2.65048	−0.328751
$66$	0.240669	0.0296243
$67$	11.1862	1.36661	0.683304	−	0.730134i	$-0.260542\pi$
$67$	11.1862	1.36661	0.683304	+	0.730134i	$0.260542\pi$
$68$	−18.8711	−2.28845
$69$	−0.797002	−0.0959478
$70$	−3.27089	−0.390946
$71$	−11.3043	−1.34157	−0.670786	−	0.741651i	$-0.734043\pi$
$71$	−11.3043	−1.34157	−0.670786	+	0.741651i	$0.734043\pi$
$72$	6.23165	0.734407
$73$	−14.9306	−1.74750	−0.873750	−	0.486376i	$-0.838319\pi$
$73$	−14.9306	−1.74750	−0.873750	+	0.486376i	$0.838319\pi$
$74$	10.5953	1.23168
$75$	0.376155	0.0434346
$76$	−17.4111	−1.99719
$77$	0.420472	0.0479172
$78$	−2.22424	−0.251846
$79$	1.05457	0.118649	0.0593243	−	0.998239i	$-0.481105\pi$
$79$	1.05457	0.118649	0.0593243	+	0.998239i	$0.481105\pi$
$80$	1.09078	0.121953
$81$	7.74659	0.860732
$82$	12.1138	1.33775
$83$	−10.4692	−1.14914	−0.574572	−	0.818454i	$-0.694831\pi$
$83$	−10.4692	−1.14914	−0.574572	+	0.818454i	$0.694831\pi$
$84$	−1.64190	−0.179145
$85$	6.33858	0.687516
$86$	11.3812	1.22727
$87$	1.57991	0.169384
$88$	0.625209	0.0666475
$89$	13.6839	1.45049	0.725246	−	0.688489i	$-0.241726\pi$
$89$	13.6839	1.45049	0.725246	+	0.688489i	$0.241726\pi$
$90$	−6.37721	−0.672217
$91$	−3.88596	−0.407360
$92$	−6.30808	−0.657663
$93$	−2.80241	−0.290596
$94$	10.9947	1.13402
$95$	5.84820	0.600013
$96$	2.55543	0.260812
$97$	−3.25877	−0.330878	−0.165439	−	0.986220i	$-0.552904\pi$
$97$	−3.25877	−0.330878	−0.165439	+	0.986220i	$0.552904\pi$
$98$	10.8211	1.09310
$99$	0.819788	0.0823918
$100$	2.97717	0.297717
$101$	4.53203	0.450954	0.225477	−	0.974248i	$-0.427606\pi$
$101$	4.53203	0.450954	0.225477	+	0.974248i	$0.427606\pi$
$102$	5.31925	0.526684
$103$	3.50032	0.344897	0.172448	−	0.985019i	$-0.444832\pi$
$103$	3.50032	0.344897	0.172448	+	0.985019i	$0.444832\pi$
$104$	−5.77813	−0.566592
$105$	0.551495	0.0538204
$106$	14.9821	1.45519
$107$	6.88455	0.665555	0.332777	−	0.943005i	$-0.392014\pi$
$107$	6.88455	0.665555	0.332777	+	0.943005i	$0.392014\pi$
$108$	−6.56081	−0.631315
$109$	−11.2962	−1.08198	−0.540989	−	0.841029i	$-0.681950\pi$
$109$	−11.2962	−1.08198	−0.540989	+	0.841029i	$0.681950\pi$
$110$	−0.639814	−0.0610038
$111$	−1.78644	−0.169561
$112$	1.59924	0.151114
$113$	−5.91086	−0.556047	−0.278023	−	0.960574i	$-0.589679\pi$
$113$	−5.91086	−0.556047	−0.278023	+	0.960574i	$0.589679\pi$
$114$	4.90772	0.459651
$115$	2.11881	0.197580
$116$	12.5046	1.16102
$117$	−7.57641	−0.700439
$118$	−15.8879	−1.46260
$119$	9.29323	0.851909
$120$	0.820030	0.0748582
$121$	−10.9178	−0.992523
$122$	−17.8241	−1.61372
$123$	−2.04247	−0.184164
$124$	−22.1804	−1.99186
$125$	−1.00000	−0.0894427
$126$	−9.34987	−0.832952
$127$	14.4760	1.28454	0.642271	−	0.766478i	$-0.277993\pi$
$127$	14.4760	1.28454	0.642271	+	0.766478i	$0.277993\pi$
$128$	15.3586	1.35752
$129$	−1.91895	−0.168954
$130$	5.91310	0.518613
$131$	−4.87788	−0.426182	−0.213091	−	0.977032i	$-0.568353\pi$
$131$	−4.87788	−0.426182	−0.213091	+	0.977032i	$0.568353\pi$
$132$	−0.321168	−0.0279541
$133$	8.57427	0.743483
$134$	−24.9559	−2.15586
$135$	2.20371	0.189665
$136$	13.8183	1.18491
$137$	11.2309	0.959521	0.479760	−	0.877400i	$-0.340724\pi$
$137$	11.2309	0.959521	0.479760	+	0.877400i	$0.340724\pi$
$138$	1.77808	0.151360
$139$	−15.1145	−1.28199	−0.640996	−	0.767544i	$-0.721479\pi$
$139$	−15.1145	−1.28199	−0.640996	+	0.767544i	$0.721479\pi$
$140$	4.36495	0.368905
$141$	−1.85378	−0.156117
$142$	25.2194	2.11636
$143$	−0.760127	−0.0635650
$144$	3.11801	0.259834
$145$	−4.20015	−0.348804
$146$	33.3096	2.75673
$147$	−1.82452	−0.150484
$148$	−14.1392	−1.16224
$149$	−21.0981	−1.72842	−0.864210	−	0.503131i	$-0.832181\pi$
$149$	−21.0981	−1.72842	−0.864210	+	0.503131i	$0.832181\pi$
$150$	−0.839185	−0.0685192
$151$	−11.0432	−0.898683	−0.449341	−	0.893360i	$-0.648341\pi$
$151$	−11.0432	−0.898683	−0.449341	+	0.893360i	$0.648341\pi$
$152$	12.7493	1.03410
$153$	18.1189	1.46483
$154$	−0.938055	−0.0755906
$155$	7.45015	0.598410
$156$	2.96821	0.237647
$157$	21.6215	1.72559	0.862793	−	0.505557i	$-0.168713\pi$
$157$	21.6215	1.72559	0.862793	+	0.505557i	$0.168713\pi$
$158$	−2.35271	−0.187171
$159$	−2.52609	−0.200332
$160$	−6.79356	−0.537078
$161$	3.10647	0.244824
$162$	−17.2823	−1.35783
$163$	−8.73967	−0.684544	−0.342272	−	0.939601i	$-0.611196\pi$
$163$	−8.73967	−0.684544	−0.342272	+	0.939601i	$0.611196\pi$
$164$	−16.1657	−1.26233
$165$	0.107877	0.00839821
$166$	23.3563	1.81280
$167$	−13.1428	−1.01702	−0.508512	−	0.861055i	$-0.669804\pi$
$167$	−13.1428	−1.01702	−0.508512	+	0.861055i	$0.669804\pi$
$168$	1.20228	0.0927577
$169$	−5.97498	−0.459614
$170$	−14.1411	−1.08457
$171$	16.7171	1.27839
$172$	−15.1881	−1.15808
$173$	16.0704	1.22181	0.610906	−	0.791703i	$-0.290805\pi$
$173$	16.0704	1.22181	0.610906	+	0.791703i	$0.290805\pi$
$174$	−3.52471	−0.267207
$175$	−1.46614	−0.110830
$176$	0.312824	0.0235800
$177$	2.67880	0.201351
$178$	−30.5283	−2.28819
$179$	10.7309	0.802066	0.401033	−	0.916064i	$-0.368651\pi$
$179$	10.7309	0.802066	0.401033	+	0.916064i	$0.368651\pi$
$180$	8.51028	0.634318
$181$	−25.5432	−1.89861	−0.949304	−	0.314359i	$-0.898210\pi$
$181$	−25.5432	−1.89861	−0.949304	+	0.314359i	$0.898210\pi$
$182$	8.66942	0.642620
$183$	3.00527	0.222156
$184$	4.61909	0.340524
$185$	4.74921	0.349169
$186$	6.25206	0.458423
$187$	1.81783	0.132933
$188$	−14.6722	−1.07008
$189$	3.23094	0.235016
$190$	−13.0471	−0.946535
$191$	−12.2801	−0.888554	−0.444277	−	0.895889i	$-0.646539\pi$
$191$	−12.2801	−0.888554	−0.444277	+	0.895889i	$0.646539\pi$
$192$	−4.88045	−0.352216
$193$	1.13260	0.0815264	0.0407632	−	0.999169i	$-0.487021\pi$
$193$	1.13260	0.0815264	0.0407632	+	0.999169i	$0.487021\pi$
$194$	7.27018	0.521968
$195$	−0.996989	−0.0713959
$196$	−14.4406	−1.03147
$197$	2.98432	0.212624	0.106312	−	0.994333i	$-0.466096\pi$
$197$	2.98432	0.212624	0.106312	+	0.994333i	$0.466096\pi$
$198$	−1.82891	−0.129975
$199$	−0.201726	−0.0143000	−0.00714999	−	0.999974i	$-0.502276\pi$
$199$	−0.201726	−0.0143000	−0.00714999	+	0.999974i	$0.502276\pi$
$200$	−2.18003	−0.154152
$201$	4.20773	0.296791
$202$	−10.1108	−0.711391
$203$	−6.15800	−0.432207
$204$	−7.09844	−0.496990
$205$	5.42988	0.379239
$206$	−7.80906	−0.544083
$207$	6.05665	0.420966
$208$	−2.89109	−0.200461
$209$	1.67720	0.116014
$210$	−1.23036	−0.0849030
$211$	−6.79793	−0.467989	−0.233994	−	0.972238i	$-0.575180\pi$
$211$	−6.79793	−0.467989	−0.233994	+	0.972238i	$0.575180\pi$
$212$	−19.9934	−1.37315
$213$	−4.25216	−0.291353
$214$	−15.3591	−1.04993
$215$	5.10150	0.347919
$216$	4.80415	0.326881
$217$	10.9229	0.741498
$218$	25.2013	1.70685
$219$	−5.61623	−0.379510
$220$	0.853820	0.0575645
$221$	−16.8003	−1.13011
$222$	3.98547	0.267487
$223$	−11.4140	−0.764336	−0.382168	−	0.924093i	$-0.624823\pi$
$223$	−11.4140	−0.764336	−0.382168	+	0.924093i	$0.624823\pi$
$224$	−9.96029	−0.665500
$225$	−2.85851	−0.190567
$226$	13.1869	0.877178
$227$	15.6599	1.03939	0.519694	−	0.854353i	$-0.326046\pi$
$227$	15.6599	1.03939	0.519694	+	0.854353i	$0.326046\pi$
$228$	−6.54927	−0.433736
$229$	−2.36008	−0.155958	−0.0779792	−	0.996955i	$-0.524847\pi$
$229$	−2.36008	−0.155958	−0.0779792	+	0.996955i	$0.524847\pi$
$230$	−4.72699	−0.311688
$231$	0.158162	0.0104063
$232$	−9.15648	−0.601152
$233$	25.0390	1.64036	0.820181	−	0.572105i	$-0.193873\pi$
$233$	25.0390	1.64036	0.820181	+	0.572105i	$0.193873\pi$
$234$	16.9026	1.10496
$235$	4.92824	0.321483
$236$	21.2021	1.38014
$237$	0.396682	0.0257673
$238$	−20.7328	−1.34391
$239$	19.3504	1.25167	0.625836	−	0.779955i	$-0.284758\pi$
$239$	19.3504	1.25167	0.625836	+	0.779955i	$0.284758\pi$
$240$	0.410303	0.0264849
$241$	17.1945	1.10759	0.553797	−	0.832652i	$-0.313178\pi$
$241$	17.1945	1.10759	0.553797	+	0.832652i	$0.313178\pi$
$242$	24.3570	1.56573
$243$	9.52503	0.611031
$244$	23.7860	1.52274
$245$	4.85044	0.309883
$246$	4.55668	0.290523
$247$	−15.5005	−0.986274
$248$	16.2416	1.03134
$249$	−3.93804	−0.249563
$250$	2.23096	0.141098
$251$	−23.6093	−1.49021	−0.745103	−	0.666949i	$-0.767600\pi$
$251$	−23.6093	−1.49021	−0.745103	+	0.666949i	$0.767600\pi$
$252$	12.4772	0.785992
$253$	0.607652	0.0382027
$254$	−32.2954	−2.02640
$255$	2.38429	0.149310
$256$	−8.31530	−0.519706
$257$	19.0497	1.18829	0.594144	−	0.804359i	$-0.297491\pi$
$257$	19.0497	1.18829	0.594144	+	0.804359i	$0.297491\pi$
$258$	4.28110	0.266530
$259$	6.96300	0.432660
$260$	−7.89093	−0.489375
$261$	−12.0062	−0.743163
$262$	10.8823	0.672313
$263$	23.8338	1.46966	0.734829	−	0.678253i	$-0.237262\pi$
$263$	23.8338	1.46966	0.734829	+	0.678253i	$0.237262\pi$
$264$	0.235175	0.0144740
$265$	6.71555	0.412533
$266$	−19.1288	−1.17286
$267$	5.14727	0.315008
$268$	33.3032	2.03432
$269$	3.62340	0.220923	0.110461	−	0.993880i	$-0.464767\pi$
$269$	3.62340	0.220923	0.110461	+	0.993880i	$0.464767\pi$
$270$	−4.91637	−0.299201
$271$	12.9217	0.784940	0.392470	−	0.919765i	$-0.371621\pi$
$271$	12.9217	0.784940	0.392470	+	0.919765i	$0.371621\pi$
$272$	6.91401	0.419224
$273$	−1.46172	−0.0884675
$274$	−25.0557	−1.51367
$275$	−0.286789	−0.0172940
$276$	−2.37281	−0.142827
$277$	17.6254	1.05901	0.529505	−	0.848307i	$-0.322378\pi$
$277$	17.6254	1.05901	0.529505	+	0.848307i	$0.322378\pi$
$278$	33.7198	2.02238
$279$	21.2963	1.27498
$280$	−3.19623	−0.191011
$281$	−8.50459	−0.507342	−0.253671	−	0.967291i	$-0.581638\pi$
$281$	−8.50459	−0.507342	−0.253671	+	0.967291i	$0.581638\pi$
$282$	4.13571	0.246278
$283$	−17.0314	−1.01241	−0.506204	−	0.862414i	$-0.668952\pi$
$283$	−17.0314	−1.01241	−0.506204	+	0.862414i	$0.668952\pi$
$284$	−33.6548	−1.99705
$285$	2.19983	0.130307
$286$	1.69581	0.100275
$287$	7.96095	0.469920
$288$	−19.4194	−1.14430
$289$	23.1776	1.36339
$290$	9.37036	0.550247
$291$	−1.22580	−0.0718578
$292$	−44.4511	−2.60131
$293$	−3.10103	−0.181164	−0.0905821	−	0.995889i	$-0.528873\pi$
$293$	−3.10103	−0.181164	−0.0905821	+	0.995889i	$0.528873\pi$
$294$	4.07042	0.237392
$295$	−7.12154	−0.414632
$296$	10.3534	0.601782
$297$	0.631998	0.0366722
$298$	47.0689	2.72663
$299$	−5.61587	−0.324774
$300$	1.11988	0.0646562
$301$	7.47950	0.431111
$302$	24.6369	1.41770
$303$	1.70475	0.0979350
$304$	6.37911	0.365867
$305$	−7.98944	−0.457474
$306$	−40.4225	−2.31080
$307$	−14.7073	−0.839388	−0.419694	−	0.907666i	$-0.637863\pi$
$307$	−14.7073	−0.839388	−0.419694	+	0.907666i	$0.637863\pi$
$308$	1.25182	0.0713289
$309$	1.31666	0.0749023
$310$	−16.6210	−0.944007
$311$	−34.5917	−1.96151	−0.980757	−	0.195233i	$-0.937454\pi$
$311$	−34.5917	−1.96151	−0.980757	+	0.195233i	$0.937454\pi$
$312$	−2.17347	−0.123049
$313$	−11.0665	−0.625517	−0.312758	−	0.949833i	$-0.601253\pi$
$313$	−11.0665	−0.625517	−0.312758	+	0.949833i	$0.601253\pi$
$314$	−48.2367	−2.72216
$315$	−4.19097	−0.236134
$316$	3.13965	0.176619
$317$	31.4186	1.76464	0.882322	−	0.470647i	$-0.155979\pi$
$317$	31.4186	1.76464	0.882322	+	0.470647i	$0.155979\pi$
$318$	5.63559	0.316028
$319$	−1.20456	−0.0674422
$320$	12.9746	0.725301
$321$	2.58966	0.144541
$322$	−6.93041	−0.386217
$323$	37.0693	2.06259
$324$	23.0629	1.28127
$325$	2.65048	0.147022
$326$	19.4978	1.07989
$327$	−4.24912	−0.234977
$328$	11.8373	0.653607
$329$	7.22548	0.398353
$330$	−0.240669	−0.0132484
$331$	−25.8899	−1.42304	−0.711520	−	0.702666i	$-0.751993\pi$
$331$	−25.8899	−1.42304	−0.711520	+	0.702666i	$0.751993\pi$
$332$	−31.1686	−1.71060
$333$	13.5757	0.743941
$334$	29.3211	1.60438
$335$	−11.1862	−0.611166
$336$	0.601560	0.0328178
$337$	−7.90840	−0.430798	−0.215399	−	0.976526i	$-0.569105\pi$
$337$	−7.90840	−0.430798	−0.215399	+	0.976526i	$0.569105\pi$
$338$	13.3299	0.725052
$339$	−2.22340	−0.120758
$340$	18.8711	1.02343
$341$	2.13662	0.115704
$342$	−37.2952	−2.01669
$343$	17.3744	0.938128
$344$	11.1214	0.599628
$345$	0.797002	0.0429091
$346$	−35.8525	−1.92744
$347$	−2.57476	−0.138221	−0.0691103	−	0.997609i	$-0.522016\pi$
$347$	−2.57476	−0.138221	−0.0691103	+	0.997609i	$0.522016\pi$
$348$	4.70366	0.252143
$349$	−24.1004	−1.29006	−0.645031	−	0.764156i	$-0.723156\pi$
$349$	−24.1004	−1.29006	−0.645031	+	0.764156i	$0.723156\pi$
$350$	3.27089	0.174837
$351$	−5.84087	−0.311763
$352$	−1.94832	−0.103846
$353$	28.3621	1.50956	0.754782	−	0.655976i	$-0.227743\pi$
$353$	28.3621	1.50956	0.754782	+	0.655976i	$0.227743\pi$
$354$	−5.97629	−0.317636
$355$	11.3043	0.599969
$356$	40.7394	2.15918
$357$	3.49569	0.185012
$358$	−23.9402	−1.26528
$359$	−28.6235	−1.51069	−0.755346	−	0.655326i	$-0.772531\pi$
$359$	−28.6235	−1.51069	−0.755346	+	0.655326i	$0.772531\pi$
$360$	−6.23165	−0.328437
$361$	15.2014	0.800076
$362$	56.9857	2.99510
$363$	−4.10676	−0.215549
$364$	−11.5692	−0.606390
$365$	14.9306	0.781506
$366$	−6.70462	−0.350456
$367$	−3.09820	−0.161725	−0.0808625	−	0.996725i	$-0.525767\pi$
$367$	−3.09820	−0.161725	−0.0808625	+	0.996725i	$0.525767\pi$
$368$	2.31116	0.120478
$369$	15.5214	0.808009
$370$	−10.5953	−0.550823
$371$	9.84592	0.511175
$372$	−8.34326	−0.432578
$373$	−33.9285	−1.75675	−0.878377	−	0.477969i	$-0.841373\pi$
$373$	−33.9285	−1.75675	−0.878377	+	0.477969i	$0.841373\pi$
$374$	−4.05551	−0.209705
$375$	−0.376155	−0.0194245
$376$	10.7437	0.554066
$377$	11.1324	0.573348
$378$	−7.20808	−0.370744
$379$	−1.80556	−0.0927454	−0.0463727	−	0.998924i	$-0.514766\pi$
$379$	−1.80556	−0.0927454	−0.0463727	+	0.998924i	$0.514766\pi$
$380$	17.4111	0.893171
$381$	5.44523	0.278968
$382$	27.3963	1.40172
$383$	−5.85145	−0.298995	−0.149497	−	0.988762i	$-0.547766\pi$
$383$	−5.85145	−0.298995	−0.149497	+	0.988762i	$0.547766\pi$
$384$	5.77722	0.294818
$385$	−0.420472	−0.0214292
$386$	−2.52679	−0.128610
$387$	14.5827	0.741279
$388$	−9.70192	−0.492541
$389$	−10.3369	−0.524101	−0.262051	−	0.965054i	$-0.584399\pi$
$389$	−10.3369	−0.524101	−0.262051	+	0.965054i	$0.584399\pi$
$390$	2.22424	0.112629
$391$	13.4303	0.679198
$392$	10.5741	0.534074
$393$	−1.83484	−0.0925552
$394$	−6.65789	−0.335420
$395$	−1.05457	−0.0530613
$396$	2.44065	0.122647
$397$	−20.4148	−1.02459	−0.512295	−	0.858810i	$-0.671204\pi$
$397$	−20.4148	−1.02459	−0.512295	+	0.858810i	$0.671204\pi$
$398$	0.450042	0.0225586
$399$	3.22525	0.161465
$400$	−1.09078	−0.0545391
$401$	−0.0820956	−0.00409966	−0.00204983	−	0.999998i	$-0.500652\pi$
$401$	−0.0820956	−0.00409966	−0.00204983	+	0.999998i	$0.500652\pi$
$402$	−9.38727	−0.468195
$403$	−19.7464	−0.983640
$404$	13.4926	0.671284
$405$	−7.74659	−0.384931
$406$	13.7382	0.681818
$407$	1.36202	0.0675128
$408$	5.19783	0.257331
$409$	−2.70564	−0.133786	−0.0668928	−	0.997760i	$-0.521309\pi$
$409$	−2.70564	−0.133786	−0.0668928	+	0.997760i	$0.521309\pi$
$410$	−12.1138	−0.598260
$411$	4.22456	0.208382
$412$	10.4211	0.513409
$413$	−10.4412	−0.513776
$414$	−13.5121	−0.664085
$415$	10.4692	0.513913
$416$	18.0062	0.882825
$417$	−5.68538	−0.278414
$418$	−3.74176	−0.183015
$419$	32.5660	1.59095	0.795477	−	0.605984i	$-0.207220\pi$
$419$	32.5660	1.59095	0.795477	+	0.605984i	$0.207220\pi$
$420$	1.64190	0.0801163
$421$	13.9674	0.680728	0.340364	−	0.940294i	$-0.389450\pi$
$421$	13.9674	0.680728	0.340364	+	0.940294i	$0.389450\pi$
$422$	15.1659	0.738264
$423$	14.0874	0.684953
$424$	14.6401	0.710987
$425$	−6.33858	−0.307466
$426$	9.48639	0.459617
$427$	−11.7136	−0.566862
$428$	20.4965	0.990736
$429$	−0.285925	−0.0138046
$430$	−11.3812	−0.548852
$431$	27.4370	1.32159	0.660796	−	0.750565i	$-0.270219\pi$
$431$	27.4370	1.32159	0.660796	+	0.750565i	$0.270219\pi$
$432$	2.40376	0.115651
$433$	23.7457	1.14114	0.570572	−	0.821247i	$-0.306721\pi$
$433$	23.7457	1.14114	0.570572	+	0.821247i	$0.306721\pi$
$434$	−24.3686	−1.16973
$435$	−1.57991	−0.0757508
$436$	−33.6307	−1.61062
$437$	12.3912	0.592754
$438$	12.5296	0.598686
$439$	21.1810	1.01092	0.505458	−	0.862851i	$-0.331324\pi$
$439$	21.1810	1.01092	0.505458	+	0.862851i	$0.331324\pi$
$440$	−0.625209	−0.0298057
$441$	13.8650	0.660239
$442$	37.4807	1.78277
$443$	−11.0667	−0.525796	−0.262898	−	0.964824i	$-0.584678\pi$
$443$	−11.0667	−0.525796	−0.262898	+	0.964824i	$0.584678\pi$
$444$	−5.31854	−0.252407
$445$	−13.6839	−0.648680
$446$	25.4641	1.20576
$447$	−7.93614	−0.375366
$448$	19.0225	0.898730
$449$	−18.3191	−0.864534	−0.432267	−	0.901746i	$-0.642286\pi$
$449$	−18.3191	−0.864534	−0.432267	+	0.901746i	$0.642286\pi$
$450$	6.37721	0.300625
$451$	1.55723	0.0733270
$452$	−17.5977	−0.827724
$453$	−4.15395	−0.195170
$454$	−34.9367	−1.63966
$455$	3.88596	0.182177
$456$	4.79570	0.224579
$457$	−20.5009	−0.958989	−0.479495	−	0.877545i	$-0.659180\pi$
$457$	−20.5009	−0.958989	−0.479495	+	0.877545i	$0.659180\pi$
$458$	5.26524	0.246028
$459$	13.9684	0.651988
$460$	6.30808	0.294116
$461$	−39.1231	−1.82214	−0.911072	−	0.412248i	$-0.864744\pi$
$461$	−39.1231	−1.82214	−0.911072	+	0.412248i	$0.864744\pi$
$462$	−0.352854	−0.0164162
$463$	11.4040	0.529991	0.264995	−	0.964250i	$-0.414630\pi$
$463$	11.4040	0.529991	0.264995	+	0.964250i	$0.414630\pi$
$464$	−4.58145	−0.212689
$465$	2.80241	0.129959
$466$	−55.8610	−2.58771
$467$	−11.7896	−0.545556	−0.272778	−	0.962077i	$-0.587943\pi$
$467$	−11.7896	−0.545556	−0.272778	+	0.962077i	$0.587943\pi$
$468$	−22.5563	−1.04266
$469$	−16.4005	−0.757303
$470$	−10.9947	−0.507148
$471$	8.13304	0.374751
$472$	−15.5252	−0.714606
$473$	1.46305	0.0672712
$474$	−0.884982	−0.0406486
$475$	−5.84820	−0.268334
$476$	27.6676	1.26814
$477$	19.1964	0.878945
$478$	−43.1699	−1.97455
$479$	−11.5911	−0.529612	−0.264806	−	0.964302i	$-0.585308\pi$
$479$	−11.5911	−0.529612	−0.264806	+	0.964302i	$0.585308\pi$
$480$	−2.55543	−0.116639
$481$	−12.5877	−0.573948
$482$	−38.3602	−1.74726
$483$	1.16851	0.0531692
$484$	−32.5041	−1.47746
$485$	3.25877	0.147973
$486$	−21.2499	−0.963917
$487$	−38.6931	−1.75335	−0.876677	−	0.481080i	$-0.840245\pi$
$487$	−38.6931	−1.75335	−0.876677	+	0.481080i	$0.840245\pi$
$488$	−17.4173	−0.788443
$489$	−3.28747	−0.148664
$490$	−10.8211	−0.488849
$491$	−5.81885	−0.262601	−0.131301	−	0.991343i	$-0.541915\pi$
$491$	−5.81885	−0.262601	−0.131301	+	0.991343i	$0.541915\pi$
$492$	−6.08080	−0.274144
$493$	−26.6230	−1.19904
$494$	34.5810	1.55587
$495$	−0.819788	−0.0368467
$496$	8.12649	0.364890
$497$	16.5736	0.743429
$498$	8.78560	0.393692
$499$	30.7341	1.37585	0.687923	−	0.725784i	$-0.258523\pi$
$499$	30.7341	1.37585	0.687923	+	0.725784i	$0.258523\pi$
$500$	−2.97717	−0.133143
$501$	−4.94374	−0.220870
$502$	52.6714	2.35084
$503$	−35.6934	−1.59149	−0.795745	−	0.605632i	$-0.792920\pi$
$503$	−35.6934	−1.59149	−0.795745	+	0.605632i	$0.792920\pi$
$504$	−9.13645	−0.406970
$505$	−4.53203	−0.201673
$506$	−1.35565	−0.0602658
$507$	−2.24752	−0.0998157
$508$	43.0977	1.91215
$509$	26.0795	1.15595	0.577977	−	0.816053i	$-0.303843\pi$
$509$	26.0795	1.15595	0.577977	+	0.816053i	$0.303843\pi$
$510$	−5.31925	−0.235540
$511$	21.8904	0.968373
$512$	−12.1662	−0.537674
$513$	12.8877	0.569006
$514$	−42.4991	−1.87455
$515$	−3.50032	−0.154242
$516$	−5.71306	−0.251503
$517$	1.41336	0.0621597
$518$	−15.5342	−0.682532
$519$	6.04497	0.265345
$520$	5.77813	0.253388
$521$	−21.7748	−0.953973	−0.476986	−	0.878911i	$-0.658271\pi$
$521$	−21.7748	−0.953973	−0.476986	+	0.878911i	$0.658271\pi$
$522$	26.7853	1.17236
$523$	−11.1448	−0.487328	−0.243664	−	0.969860i	$-0.578349\pi$
$523$	−11.1448	−0.487328	−0.243664	+	0.969860i	$0.578349\pi$
$524$	−14.5223	−0.634409
$525$	−0.551495	−0.0240692
$526$	−53.1723	−2.31842
$527$	47.2234	2.05708
$528$	0.117670	0.00512094
$529$	−18.5106	−0.804810
$530$	−14.9821	−0.650781
$531$	−20.3570	−0.883418
$532$	25.5271	1.10674
$533$	−14.3918	−0.623377
$534$	−11.4833	−0.496933
$535$	−6.88455	−0.297645
$536$	−24.3862	−1.05333
$537$	4.03648	0.174187
$538$	−8.08366	−0.348511
$539$	1.39105	0.0599168
$540$	6.56081	0.282333
$541$	19.1122	0.821697	0.410849	−	0.911704i	$-0.365232\pi$
$541$	19.1122	0.821697	0.410849	+	0.911704i	$0.365232\pi$
$542$	−28.8279	−1.23826
$543$	−9.60818	−0.412327
$544$	−43.0615	−1.84625
$545$	11.2962	0.483876
$546$	3.26104	0.139560
$547$	18.0392	0.771299	0.385650	−	0.922645i	$-0.373977\pi$
$547$	18.0392	0.771299	0.385650	+	0.922645i	$0.373977\pi$
$548$	33.4364	1.42833
$549$	−22.8379	−0.974697
$550$	0.639814	0.0272817
$551$	−24.5633	−1.04643
$552$	1.73749	0.0739526
$553$	−1.54615	−0.0657489
$554$	−39.3216	−1.67061
$555$	1.78644	0.0758301
$556$	−44.9984	−1.90836
$557$	−44.4577	−1.88373	−0.941867	−	0.335987i	$-0.890930\pi$
$557$	−44.4577	−1.88373	−0.941867	+	0.335987i	$0.890930\pi$
$558$	−47.5112	−2.01131
$559$	−13.5214	−0.571894
$560$	−1.59924	−0.0675801
$561$	0.683787	0.0288695
$562$	18.9734	0.800344
$563$	6.00583	0.253116	0.126558	−	0.991959i	$-0.459607\pi$
$563$	6.00583	0.253116	0.126558	+	0.991959i	$0.459607\pi$
$564$	−5.51903	−0.232393
$565$	5.91086	0.248672
$566$	37.9962	1.59710
$567$	−11.3576	−0.476973
$568$	24.6437	1.03403
$569$	22.1660	0.929247	0.464623	−	0.885508i	$-0.346190\pi$
$569$	22.1660	0.929247	0.464623	+	0.885508i	$0.346190\pi$
$570$	−4.90772	−0.205562
$571$	−30.9745	−1.29624	−0.648122	−	0.761536i	$-0.724445\pi$
$571$	−30.9745	−1.29624	−0.648122	+	0.761536i	$0.724445\pi$
$572$	−2.26303	−0.0946220
$573$	−4.61920	−0.192970
$574$	−17.7605	−0.741311
$575$	−2.11881	−0.0883606
$576$	37.0879	1.54533
$577$	28.7939	1.19871	0.599354	−	0.800484i	$-0.295424\pi$
$577$	28.7939	1.19871	0.599354	+	0.800484i	$0.295424\pi$
$578$	−51.7083	−2.15078
$579$	0.426033	0.0177053
$580$	−12.5046	−0.519225
$581$	15.3493	0.636796
$582$	2.73471	0.113357
$583$	1.92594	0.0797644
$584$	32.5493	1.34690
$585$	7.57641	0.313246
$586$	6.91827	0.285791
$587$	46.4061	1.91538	0.957692	−	0.287795i	$-0.0929222\pi$
$587$	46.4061	1.91538	0.957692	+	0.287795i	$0.0929222\pi$
$588$	−5.43190	−0.224008
$589$	43.5700	1.79527
$590$	15.8879	0.654093
$591$	1.12257	0.0461762
$592$	5.18035	0.212911
$593$	41.6147	1.70891	0.854455	−	0.519526i	$-0.173891\pi$
$593$	41.6147	1.70891	0.854455	+	0.519526i	$0.173891\pi$
$594$	−1.40996	−0.0578514
$595$	−9.29323	−0.380985
$596$	−62.8126	−2.57290
$597$	−0.0758802	−0.00310557
$598$	12.5288	0.512339
$599$	23.8099	0.972848	0.486424	−	0.873723i	$-0.338301\pi$
$599$	23.8099	0.972848	0.486424	+	0.873723i	$0.338301\pi$
$600$	−0.820030	−0.0334776
$601$	−20.2594	−0.826397	−0.413199	−	0.910641i	$-0.635588\pi$
$601$	−20.2594	−0.826397	−0.413199	+	0.910641i	$0.635588\pi$
$602$	−16.6864	−0.680089
$603$	−31.9758	−1.30215
$604$	−32.8775	−1.33777
$605$	10.9178	0.443870
$606$	−3.80322	−0.154495
$607$	29.5958	1.20126	0.600628	−	0.799529i	$-0.294917\pi$
$607$	29.5958	1.20126	0.600628	+	0.799529i	$0.294917\pi$
$608$	−39.7301	−1.61127
$609$	−2.31636	−0.0938637
$610$	17.8241	0.721677
$611$	−13.0622	−0.528439
$612$	53.9431	2.18052
$613$	−8.01304	−0.323644	−0.161822	−	0.986820i	$-0.551737\pi$
$613$	−8.01304	−0.323644	−0.161822	+	0.986820i	$0.551737\pi$
$614$	32.8113	1.32416
$615$	2.04247	0.0823605
$616$	−0.916643	−0.0369326
$617$	43.5632	1.75379	0.876894	−	0.480683i	$-0.159611\pi$
$617$	43.5632	1.75379	0.876894	+	0.480683i	$0.159611\pi$
$618$	−2.93742	−0.118160
$619$	11.8824	0.477592	0.238796	−	0.971070i	$-0.423247\pi$
$619$	11.8824	0.477592	0.238796	+	0.971070i	$0.423247\pi$
$620$	22.1804	0.890786
$621$	4.66924	0.187370
$622$	77.1726	3.09434
$623$	−20.0625	−0.803787
$624$	−1.08750	−0.0435348
$625$	1.00000	0.0400000
$626$	24.6890	0.986769
$627$	0.630886	0.0251952
$628$	64.3711	2.56869
$629$	30.1033	1.20030
$630$	9.34987	0.372508
$631$	1.68576	0.0671089	0.0335544	−	0.999437i	$-0.489317\pi$
$631$	1.68576	0.0671089	0.0335544	+	0.999437i	$0.489317\pi$
$632$	−2.29900	−0.0914495
$633$	−2.55707	−0.101635
$634$	−70.0935	−2.78377
$635$	−14.4760	−0.574464
$636$	−7.52060	−0.298211
$637$	−12.8560	−0.509372
$638$	2.68731	0.106392
$639$	32.3134	1.27830
$640$	−15.3586	−0.607103
$641$	21.0381	0.830956	0.415478	−	0.909603i	$-0.363614\pi$
$641$	21.0381	0.830956	0.415478	+	0.909603i	$0.363614\pi$
$642$	−5.77741	−0.228016
$643$	−3.55764	−0.140300	−0.0701498	−	0.997536i	$-0.522348\pi$
$643$	−3.55764	−0.140300	−0.0701498	+	0.997536i	$0.522348\pi$
$644$	9.24851	0.364442
$645$	1.91895	0.0755587
$646$	−82.7001	−3.25379
$647$	−12.0064	−0.472020	−0.236010	−	0.971751i	$-0.575840\pi$
$647$	−12.0064	−0.472020	−0.236010	+	0.971751i	$0.575840\pi$
$648$	−16.8878	−0.663417
$649$	−2.04238	−0.0801703
$650$	−5.91310	−0.231931
$651$	4.10872	0.161033
$652$	−26.0195	−1.01900
$653$	−36.0476	−1.41065	−0.705326	−	0.708883i	$-0.749199\pi$
$653$	−36.0476	−1.41065	−0.705326	+	0.708883i	$0.749199\pi$
$654$	9.47960	0.370682
$655$	4.87788	0.190594
$656$	5.92282	0.231247
$657$	42.6794	1.66508
$658$	−16.1197	−0.628413
$659$	−28.2049	−1.09871	−0.549353	−	0.835591i	$-0.685126\pi$
$659$	−28.2049	−1.09871	−0.549353	+	0.835591i	$0.685126\pi$
$660$	0.321168	0.0125015
$661$	−29.6345	−1.15265	−0.576324	−	0.817221i	$-0.695513\pi$
$661$	−29.6345	−1.15265	−0.576324	+	0.817221i	$0.695513\pi$
$662$	57.7594	2.24488
$663$	−6.31950	−0.245429
$664$	22.8232	0.885712
$665$	−8.57427	−0.332496
$666$	−30.2867	−1.17359
$667$	−8.89934	−0.344584
$668$	−39.1285	−1.51393
$669$	−4.29342	−0.165993
$670$	24.9559	0.964130
$671$	−2.29128	−0.0884540
$672$	−3.74661	−0.144529
$673$	−9.04285	−0.348576	−0.174288	−	0.984695i	$-0.555762\pi$
$673$	−9.04285	−0.348576	−0.174288	+	0.984695i	$0.555762\pi$
$674$	17.6433	0.679595
$675$	−2.20371	−0.0848207
$676$	−17.7885	−0.684175
$677$	38.6675	1.48611	0.743056	−	0.669230i	$-0.233376\pi$
$677$	38.6675	1.48611	0.743056	+	0.669230i	$0.233376\pi$
$678$	4.96031	0.190499
$679$	4.77780	0.183355
$680$	−13.8183	−0.529909
$681$	5.89056	0.225727
$682$	−4.76670	−0.182527
$683$	4.48140	0.171476	0.0857380	−	0.996318i	$-0.472675\pi$
$683$	4.48140	0.171476	0.0857380	+	0.996318i	$0.472675\pi$
$684$	49.7698	1.90300
$685$	−11.2309	−0.429111
$686$	−38.7615	−1.47992
$687$	−0.887755	−0.0338700
$688$	5.56462	0.212149
$689$	−17.7994	−0.678103
$690$	−1.77808	−0.0676903
$691$	22.0777	0.839875	0.419937	−	0.907553i	$-0.362052\pi$
$691$	22.0777	0.839875	0.419937	+	0.907553i	$0.362052\pi$
$692$	47.8445	1.81877
$693$	−1.20192	−0.0456572
$694$	5.74419	0.218047
$695$	15.1145	0.573325
$696$	−3.44425	−0.130554
$697$	34.4177	1.30366
$698$	53.7669	2.03511
$699$	9.41855	0.356242
$700$	−4.36495	−0.164979
$701$	35.4834	1.34019	0.670094	−	0.742276i	$-0.266254\pi$
$701$	35.4834	1.34019	0.670094	+	0.742276i	$0.266254\pi$
$702$	13.0307	0.491813
$703$	27.7743	1.04753
$704$	3.72096	0.140239
$705$	1.85378	0.0698174
$706$	−63.2747	−2.38138
$707$	−6.64458	−0.249895
$708$	7.97526	0.299729
$709$	15.6669	0.588382	0.294191	−	0.955747i	$-0.404950\pi$
$709$	15.6669	0.588382	0.294191	+	0.955747i	$0.404950\pi$
$710$	−25.2194	−0.946466
$711$	−3.01450	−0.113053
$712$	−29.8314	−1.11798
$713$	15.7855	0.591171
$714$	−7.79875	−0.291861
$715$	0.760127	0.0284271
$716$	31.9478	1.19395
$717$	7.27874	0.271829
$718$	63.8579	2.38316
$719$	12.2957	0.458552	0.229276	−	0.973361i	$-0.426364\pi$
$719$	12.2957	0.458552	0.229276	+	0.973361i	$0.426364\pi$
$720$	−3.11801	−0.116201
$721$	−5.13195	−0.191124
$722$	−33.9138	−1.26214
$723$	6.46779	0.240540
$724$	−76.0464	−2.82624
$725$	4.20015	0.155990
$726$	9.16202	0.340034
$727$	−25.5983	−0.949388	−0.474694	−	0.880151i	$-0.657441\pi$
$727$	−25.5983	−0.949388	−0.474694	+	0.880151i	$0.657441\pi$
$728$	8.47153	0.313976
$729$	−19.6569	−0.728033
$730$	−33.3096	−1.23285
$731$	32.3363	1.19600
$732$	8.94720	0.330698
$733$	22.2241	0.820866	0.410433	−	0.911891i	$-0.365378\pi$
$733$	22.2241	0.820866	0.410433	+	0.911891i	$0.365378\pi$
$734$	6.91196	0.255125
$735$	1.82452	0.0672983
$736$	−14.3943	−0.530580
$737$	−3.20807	−0.118171
$738$	−34.6275	−1.27466
$739$	41.6789	1.53318	0.766592	−	0.642134i	$-0.221951\pi$
$739$	41.6789	1.53318	0.766592	+	0.642134i	$0.221951\pi$
$740$	14.1392	0.519768
$741$	−5.83059	−0.214192
$742$	−21.9658	−0.806391
$743$	11.1209	0.407987	0.203994	−	0.978972i	$-0.434608\pi$
$743$	11.1209	0.407987	0.203994	+	0.978972i	$0.434608\pi$
$744$	6.10935	0.223980
$745$	21.0981	0.772973
$746$	75.6932	2.77132
$747$	29.9263	1.09495
$748$	5.41201	0.197883
$749$	−10.0937	−0.368816
$750$	0.839185	0.0306427
$751$	24.7288	0.902366	0.451183	−	0.892432i	$-0.351002\pi$
$751$	24.7288	0.902366	0.451183	+	0.892432i	$0.351002\pi$
$752$	5.37564	0.196029
$753$	−8.88075	−0.323633
$754$	−24.8359	−0.904471
$755$	11.0432	0.401903
$756$	9.61906	0.349842
$757$	−19.7245	−0.716898	−0.358449	−	0.933549i	$-0.616694\pi$
$757$	−19.7245	−0.716898	−0.358449	+	0.933549i	$0.616694\pi$
$758$	4.02813	0.146308
$759$	0.228571	0.00829661
$760$	−12.7493	−0.462465
$761$	−27.3039	−0.989767	−0.494884	−	0.868959i	$-0.664789\pi$
$761$	−27.3039	−0.989767	−0.494884	+	0.868959i	$0.664789\pi$
$762$	−12.1481	−0.440079
$763$	16.5618	0.599576
$764$	−36.5599	−1.32269
$765$	−18.1189	−0.655090
$766$	13.0543	0.471672
$767$	18.8755	0.681554
$768$	−3.12784	−0.112866
$769$	31.3262	1.12965	0.564825	−	0.825211i	$-0.308944\pi$
$769$	31.3262	1.12965	0.564825	+	0.825211i	$0.308944\pi$
$770$	0.938055	0.0338051
$771$	7.16563	0.258064
$772$	3.37195	0.121359
$773$	19.1974	0.690484	0.345242	−	0.938514i	$-0.387797\pi$
$773$	19.1974	0.690484	0.345242	+	0.938514i	$0.387797\pi$
$774$	−32.5333	−1.16939
$775$	−7.45015	−0.267617
$776$	7.10423	0.255027
$777$	2.61916	0.0939620
$778$	23.0612	0.826783
$779$	31.7550	1.13774
$780$	−2.96821	−0.106279
$781$	3.24194	0.116006
$782$	−29.9624	−1.07145
$783$	−9.25590	−0.330779
$784$	5.29077	0.188956
$785$	−21.6215	−0.771706
$786$	4.09344	0.146008
$787$	−4.59736	−0.163878	−0.0819391	−	0.996637i	$-0.526111\pi$
$787$	−4.59736	−0.163878	−0.0819391	+	0.996637i	$0.526111\pi$
$788$	8.88484	0.316509
$789$	8.96521	0.319170
$790$	2.35271	0.0837055
$791$	8.66613	0.308132
$792$	−1.78717	−0.0635042
$793$	21.1758	0.751976
$794$	45.5445	1.61632
$795$	2.52609	0.0895910
$796$	−0.600573	−0.0212868
$797$	−29.7496	−1.05378	−0.526892	−	0.849932i	$-0.676643\pi$
$797$	−29.7496	−1.05378	−0.526892	+	0.849932i	$0.676643\pi$
$798$	−7.19540	−0.254714
$799$	31.2381	1.10512
$800$	6.79356	0.240189
$801$	−39.1156	−1.38208
$802$	0.183152	0.00646732
$803$	4.28194	0.151106
$804$	12.5272	0.441799
$805$	−3.10647	−0.109489
$806$	44.0535	1.55172
$807$	1.36296	0.0479785
$808$	−9.87999	−0.347577
$809$	−16.8242	−0.591508	−0.295754	−	0.955264i	$-0.595571\pi$
$809$	−16.8242	−0.591508	−0.295754	+	0.955264i	$0.595571\pi$
$810$	17.2823	0.607239
$811$	−10.3836	−0.364619	−0.182310	−	0.983241i	$-0.558357\pi$
$811$	−10.3836	−0.364619	−0.182310	+	0.983241i	$0.558357\pi$
$812$	−18.3334	−0.643378
$813$	4.86057	0.170468
$814$	−3.03861	−0.106503
$815$	8.73967	0.306137
$816$	2.60074	0.0910440
$817$	29.8346	1.04378
$818$	6.03618	0.211050
$819$	11.1081	0.388147
$820$	16.1657	0.564531
$821$	−10.8514	−0.378716	−0.189358	−	0.981908i	$-0.560641\pi$
$821$	−10.8514	−0.378716	−0.189358	+	0.981908i	$0.560641\pi$
$822$	−9.42481	−0.328728
$823$	−1.91784	−0.0668517	−0.0334258	−	0.999441i	$-0.510642\pi$
$823$	−1.91784	−0.0668517	−0.0334258	+	0.999441i	$0.510642\pi$
$824$	−7.63082	−0.265832
$825$	−0.107877	−0.00375579
$826$	23.2938	0.810495
$827$	33.3651	1.16022	0.580109	−	0.814539i	$-0.303010\pi$
$827$	33.3651	1.16022	0.580109	+	0.814539i	$0.303010\pi$
$828$	18.0317	0.626645
$829$	−7.33250	−0.254668	−0.127334	−	0.991860i	$-0.540642\pi$
$829$	−7.33250	−0.254668	−0.127334	+	0.991860i	$0.540642\pi$
$830$	−23.3563	−0.810710
$831$	6.62989	0.229988
$832$	−34.3888	−1.19222
$833$	30.7449	1.06525
$834$	12.6838	0.439206
$835$	13.1428	0.454827
$836$	4.99331	0.172697
$837$	16.4179	0.567487
$838$	−72.6534	−2.50977
$839$	34.4191	1.18828	0.594140	−	0.804362i	$-0.297493\pi$
$839$	34.4191	1.18828	0.594140	+	0.804362i	$0.297493\pi$
$840$	−1.20228	−0.0414825
$841$	−11.3587	−0.391680
$842$	−31.1606	−1.07387
$843$	−3.19904	−0.110181
$844$	−20.2386	−0.696642
$845$	5.97498	0.205545
$846$	−31.4284	−1.08053
$847$	16.0069	0.550005
$848$	7.32520	0.251548
$849$	−6.40642	−0.219868
$850$	14.1411	0.485036
$851$	10.0627	0.344945
$852$	−12.6594	−0.433704
$853$	−51.1145	−1.75013	−0.875064	−	0.484007i	$-0.839181\pi$
$853$	−51.1145	−1.75013	−0.875064	+	0.484007i	$0.839181\pi$
$854$	26.1326	0.894239
$855$	−16.7171	−0.571714
$856$	−15.0086	−0.512982
$857$	56.7182	1.93746	0.968729	−	0.248121i	$-0.0798132\pi$
$857$	56.7182	1.93746	0.968729	+	0.248121i	$0.0798132\pi$
$858$	0.637887	0.0217771
$859$	24.4109	0.832890	0.416445	−	0.909161i	$-0.363276\pi$
$859$	24.4109	0.832890	0.416445	+	0.909161i	$0.363276\pi$
$860$	15.1881	0.517908
$861$	2.99455	0.102054
$862$	−61.2107	−2.08485
$863$	46.4152	1.57999	0.789997	−	0.613111i	$-0.210082\pi$
$863$	46.4152	1.57999	0.789997	+	0.613111i	$0.210082\pi$
$864$	−14.9710	−0.509324
$865$	−16.0704	−0.546411
$866$	−52.9756	−1.80018
$867$	8.71837	0.296091
$868$	32.5195	1.10378
$869$	−0.302439	−0.0102596
$870$	3.52471	0.119499
$871$	29.6487	1.00461
$872$	24.6261	0.833944
$873$	9.31522	0.315272
$874$	−27.6444	−0.935084
$875$	1.46614	0.0495645
$876$	−16.7205	−0.564933
$877$	0.0543204	0.00183427	0.000917134	−	1.00000i	$-0.499708\pi$
$877$	0.0543204	0.00183427	0.000917134		1.00000i	$0.499708\pi$
$878$	−47.2540	−1.59474
$879$	−1.16647	−0.0393440
$880$	−0.312824	−0.0105453
$881$	32.3185	1.08884	0.544419	−	0.838813i	$-0.316750\pi$
$881$	32.3185	1.08884	0.544419	+	0.838813i	$0.316750\pi$
$882$	−30.9323	−1.04154
$883$	−13.5204	−0.454996	−0.227498	−	0.973779i	$-0.573055\pi$
$883$	−13.5204	−0.454996	−0.227498	+	0.973779i	$0.573055\pi$
$884$	−50.0173	−1.68226
$885$	−2.67880	−0.0900469
$886$	24.6894	0.829456
$887$	−37.7133	−1.26629	−0.633144	−	0.774034i	$-0.718236\pi$
$887$	−37.7133	−1.26629	−0.633144	+	0.774034i	$0.718236\pi$
$888$	3.89450	0.130691
$889$	−21.2239	−0.711826
$890$	30.5283	1.02331
$891$	−2.22163	−0.0744275
$892$	−33.9814	−1.13778
$893$	28.8213	0.964469
$894$	17.7052	0.592150
$895$	−10.7309	−0.358695
$896$	−22.5179	−0.752269
$897$	−2.11243	−0.0705321
$898$	40.8692	1.36382
$899$	−31.2918	−1.04364
$900$	−8.51028	−0.283676
$901$	42.5671	1.41811
$902$	−3.47411	−0.115675
$903$	2.81345	0.0936257
$904$	12.8859	0.428578
$905$	25.5432	0.849083
$906$	9.26729	0.307885
$907$	−22.8851	−0.759887	−0.379943	−	0.925010i	$-0.624056\pi$
$907$	−22.8851	−0.759887	−0.379943	+	0.925010i	$0.624056\pi$
$908$	46.6224	1.54722
$909$	−12.9548	−0.429685
$910$	−8.66942	−0.287388
$911$	−2.64951	−0.0877822	−0.0438911	−	0.999036i	$-0.513975\pi$
$911$	−2.64951	−0.0877822	−0.0438911	+	0.999036i	$0.513975\pi$
$912$	2.39953	0.0794565
$913$	3.00245	0.0993665
$914$	45.7365	1.51283
$915$	−3.00527	−0.0993511
$916$	−7.02637	−0.232158
$917$	7.15164	0.236168
$918$	−31.1628	−1.02853
$919$	14.5345	0.479450	0.239725	−	0.970841i	$-0.422943\pi$
$919$	14.5345	0.479450	0.239725	+	0.970841i	$0.422943\pi$
$920$	−4.61909	−0.152287
$921$	−5.53220	−0.182292
$922$	87.2819	2.87448
$923$	−29.9617	−0.986202
$924$	0.470877	0.0154907
$925$	−4.74921	−0.156153
$926$	−25.4419	−0.836074
$927$	−10.0057	−0.328630
$928$	28.5340	0.936674
$929$	−44.1873	−1.44974	−0.724869	−	0.688887i	$-0.758100\pi$
$929$	−44.1873	−1.44974	−0.724869	+	0.688887i	$0.758100\pi$
$930$	−6.25206	−0.205013
$931$	28.3663	0.929670
$932$	74.5455	2.44182
$933$	−13.0118	−0.425988
$934$	26.3020	0.860629
$935$	−1.81783	−0.0594495
$936$	16.5168	0.539869
$937$	34.4880	1.12667	0.563336	−	0.826228i	$-0.309518\pi$
$937$	34.4880	1.12667	0.563336	+	0.826228i	$0.309518\pi$
$938$	36.5888	1.19467
$939$	−4.16273	−0.135845
$940$	14.6722	0.478555
$941$	−25.9276	−0.845216	−0.422608	−	0.906313i	$-0.638885\pi$
$941$	−25.9276	−0.845216	−0.422608	+	0.906313i	$0.638885\pi$
$942$	−18.1445	−0.591179
$943$	11.5049	0.374651
$944$	−7.76805	−0.252828
$945$	−3.23094	−0.105102
$946$	−3.26401	−0.106122
$947$	8.84430	0.287401	0.143701	−	0.989621i	$-0.454100\pi$
$947$	8.84430	0.287401	0.143701	+	0.989621i	$0.454100\pi$
$948$	1.18099	0.0383569
$949$	−39.5733	−1.28460
$950$	13.0471	0.423304
$951$	11.8182	0.383233
$952$	−20.2596	−0.656616
$953$	1.98784	0.0643924	0.0321962	−	0.999482i	$-0.489750\pi$
$953$	1.98784	0.0643924	0.0321962	+	0.999482i	$0.489750\pi$
$954$	−42.8265	−1.38656
$955$	12.2801	0.397374
$956$	57.6095	1.86322
$957$	−0.453099	−0.0146466
$958$	25.8593	0.835477
$959$	−16.4660	−0.531716
$960$	4.88045	0.157516
$961$	24.5047	0.790474
$962$	28.0826	0.905418
$963$	−19.6795	−0.634164
$964$	51.1910	1.64875
$965$	−1.13260	−0.0364597
$966$	−2.60691	−0.0838758
$967$	16.3829	0.526838	0.263419	−	0.964682i	$-0.415150\pi$
$967$	16.3829	0.526838	0.263419	+	0.964682i	$0.415150\pi$
$968$	23.8011	0.764996
$969$	13.9438	0.447939
$970$	−7.27018	−0.233431
$971$	57.5157	1.84577	0.922883	−	0.385081i	$-0.125827\pi$
$971$	57.5157	1.84577	0.922883	+	0.385081i	$0.125827\pi$
$972$	28.3577	0.909573
$973$	22.1599	0.710414
$974$	86.3227	2.76596
$975$	0.996989	0.0319292
$976$	−8.71474	−0.278952
$977$	−32.2981	−1.03331	−0.516654	−	0.856194i	$-0.672823\pi$
$977$	−32.2981	−1.03331	−0.516654	+	0.856194i	$0.672823\pi$
$978$	7.33420	0.234522
$979$	−3.92439	−0.125424
$980$	14.4406	0.461288
$981$	32.2902	1.03095
$982$	12.9816	0.414260
$983$	40.4669	1.29069	0.645346	−	0.763890i	$-0.276713\pi$
$983$	40.4669	1.29069	0.645346	+	0.763890i	$0.276713\pi$
$984$	4.45267	0.141946
$985$	−2.98432	−0.0950883
$986$	59.3948	1.89152
$987$	2.71790	0.0865116
$988$	−46.1477	−1.46816
$989$	10.8091	0.343710
$990$	1.82891	0.0581266
$991$	40.4757	1.28575	0.642877	−	0.765970i	$-0.277741\pi$
$991$	40.4757	1.28575	0.642877	+	0.765970i	$0.277741\pi$
$992$	−50.6130	−1.60696
$993$	−9.73863	−0.309046
$994$	−36.9751	−1.17278
$995$	0.201726	0.00639514
$996$	−11.7242	−0.371496
$997$	58.0928	1.83982	0.919908	−	0.392133i	$-0.128263\pi$
$997$	58.0928	1.83982	0.919908	+	0.392133i	$0.128263\pi$
$998$	−68.5664	−2.17043
$999$	10.4659	0.331125

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8035.2.a.c.1.14	✓	127

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8035.2.a.c.1.14	✓	127	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:	\( N \)	\(=\)	\( 8035 = 5 \cdot 1607 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8035.a (trivial)

\(f(q)\)	\(=\)	\(q-2.23096 q^{2} +0.376155 q^{3} +2.97717 q^{4} -1.00000 q^{5} -0.839185 q^{6} -1.46614 q^{7} -2.18003 q^{8} -2.85851 q^{9} +O(q^{10})\)	\(q-2.23096 q^{2} +0.376155 q^{3} +2.97717 q^{4} -1.00000 q^{5} -0.839185 q^{6} -1.46614 q^{7} -2.18003 q^{8} -2.85851 q^{9} +2.23096 q^{10} -0.286789 q^{11} +1.11988 q^{12} +2.65048 q^{13} +3.27089 q^{14} -0.376155 q^{15} -1.09078 q^{16} -6.33858 q^{17} +6.37721 q^{18} -5.84820 q^{19} -2.97717 q^{20} -0.551495 q^{21} +0.639814 q^{22} -2.11881 q^{23} -0.820030 q^{24} +1.00000 q^{25} -5.91310 q^{26} -2.20371 q^{27} -4.36495 q^{28} +4.20015 q^{29} +0.839185 q^{30} -7.45015 q^{31} +6.79356 q^{32} -0.107877 q^{33} +14.1411 q^{34} +1.46614 q^{35} -8.51028 q^{36} -4.74921 q^{37} +13.0471 q^{38} +0.996989 q^{39} +2.18003 q^{40} -5.42988 q^{41} +1.23036 q^{42} -5.10150 q^{43} -0.853820 q^{44} +2.85851 q^{45} +4.72699 q^{46} -4.92824 q^{47} -0.410303 q^{48} -4.85044 q^{49} -2.23096 q^{50} -2.38429 q^{51} +7.89093 q^{52} -6.71555 q^{53} +4.91637 q^{54} +0.286789 q^{55} +3.19623 q^{56} -2.19983 q^{57} -9.37036 q^{58} +7.12154 q^{59} -1.11988 q^{60} +7.98944 q^{61} +16.6210 q^{62} +4.19097 q^{63} -12.9746 q^{64} -2.65048 q^{65} +0.240669 q^{66} +11.1862 q^{67} -18.8711 q^{68} -0.797002 q^{69} -3.27089 q^{70} -11.3043 q^{71} +6.23165 q^{72} -14.9306 q^{73} +10.5953 q^{74} +0.376155 q^{75} -17.4111 q^{76} +0.420472 q^{77} -2.22424 q^{78} +1.05457 q^{79} +1.09078 q^{80} +7.74659 q^{81} +12.1138 q^{82} -10.4692 q^{83} -1.64190 q^{84} +6.33858 q^{85} +11.3812 q^{86} +1.57991 q^{87} +0.625209 q^{88} +13.6839 q^{89} -6.37721 q^{90} -3.88596 q^{91} -6.30808 q^{92} -2.80241 q^{93} +10.9947 q^{94} +5.84820 q^{95} +2.55543 q^{96} -3.25877 q^{97} +10.8211 q^{98} +0.819788 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 127 q + 19 q^{2} + 10 q^{3} + 125 q^{4} - 127 q^{5} + 13 q^{7} + 54 q^{8} + 123 q^{9}+O(q^{10}) \) 127 * q + 19 * q^2 + 10 * q^3 + 125 * q^4 - 127 * q^5 + 13 * q^7 + 54 * q^8 + 123 * q^9	\( 127 q + 19 q^{2} + 10 q^{3} + 125 q^{4} - 127 q^{5} + 13 q^{7} + 54 q^{8} + 123 q^{9} - 19 q^{10} + 30 q^{11} + 35 q^{12} + 30 q^{13} + 39 q^{14} - 10 q^{15} + 121 q^{16} + 63 q^{17} + 53 q^{18} - 35 q^{19} - 125 q^{20} + 33 q^{21} + 49 q^{22} + 61 q^{23} - 5 q^{24} + 127 q^{25} + 10 q^{26} + 40 q^{27} + 32 q^{28} + 134 q^{29} - 25 q^{31} + 122 q^{32} + 48 q^{33} - 21 q^{34} - 13 q^{35} + 133 q^{36} + 60 q^{37} + 33 q^{38} + 26 q^{39} - 54 q^{40} + 9 q^{41} + 45 q^{42} + 48 q^{43} + 85 q^{44} - 123 q^{45} - 11 q^{46} + 57 q^{47} + 71 q^{48} + 70 q^{49} + 19 q^{50} + 45 q^{51} + 68 q^{52} + 182 q^{53} - 29 q^{54} - 30 q^{55} + 96 q^{56} + 74 q^{57} + 47 q^{58} + 19 q^{59} - 35 q^{60} + 16 q^{61} + 43 q^{62} + 73 q^{63} + 110 q^{64} - 30 q^{65} + 8 q^{66} + 40 q^{67} + 129 q^{68} + 2 q^{69} - 39 q^{70} + 48 q^{71} + 151 q^{72} + 30 q^{73} + 117 q^{74} + 10 q^{75} - 98 q^{76} + 134 q^{77} + 54 q^{78} + 23 q^{79} - 121 q^{80} + 111 q^{81} + 4 q^{82} + 92 q^{83} + 48 q^{84} - 63 q^{85} + 42 q^{86} + 69 q^{87} + 121 q^{88} + 12 q^{89} - 53 q^{90} - 30 q^{91} + 175 q^{92} + 82 q^{93} - 23 q^{94} + 35 q^{95} + 6 q^{96} + 67 q^{97} + 122 q^{98} + 73 q^{99}+O(q^{100}) \) 127 * q + 19 * q^2 + 10 * q^3 + 125 * q^4 - 127 * q^5 + 13 * q^7 + 54 * q^8 + 123 * q^9 - 19 * q^10 + 30 * q^11 + 35 * q^12 + 30 * q^13 + 39 * q^14 - 10 * q^15 + 121 * q^16 + 63 * q^17 + 53 * q^18 - 35 * q^19 - 125 * q^20 + 33 * q^21 + 49 * q^22 + 61 * q^23 - 5 * q^24 + 127 * q^25 + 10 * q^26 + 40 * q^27 + 32 * q^28 + 134 * q^29 - 25 * q^31 + 122 * q^32 + 48 * q^33 - 21 * q^34 - 13 * q^35 + 133 * q^36 + 60 * q^37 + 33 * q^38 + 26 * q^39 - 54 * q^40 + 9 * q^41 + 45 * q^42 + 48 * q^43 + 85 * q^44 - 123 * q^45 - 11 * q^46 + 57 * q^47 + 71 * q^48 + 70 * q^49 + 19 * q^50 + 45 * q^51 + 68 * q^52 + 182 * q^53 - 29 * q^54 - 30 * q^55 + 96 * q^56 + 74 * q^57 + 47 * q^58 + 19 * q^59 - 35 * q^60 + 16 * q^61 + 43 * q^62 + 73 * q^63 + 110 * q^64 - 30 * q^65 + 8 * q^66 + 40 * q^67 + 129 * q^68 + 2 * q^69 - 39 * q^70 + 48 * q^71 + 151 * q^72 + 30 * q^73 + 117 * q^74 + 10 * q^75 - 98 * q^76 + 134 * q^77 + 54 * q^78 + 23 * q^79 - 121 * q^80 + 111 * q^81 + 4 * q^82 + 92 * q^83 + 48 * q^84 - 63 * q^85 + 42 * q^86 + 69 * q^87 + 121 * q^88 + 12 * q^89 - 53 * q^90 - 30 * q^91 + 175 * q^92 + 82 * q^93 - 23 * q^94 + 35 * q^95 + 6 * q^96 + 67 * q^97 + 122 * q^98 + 73 * q^99

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