LMFDB - Embedded newform 8015.2.a.o.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8015,2,Mod(1,8015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8015, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.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:	$64.0000972201$
Analytic rank:	$0$
Dimension:	$73$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.84781 q^{2} -2.80168 q^{3} +1.41441 q^{4} +1.00000 q^{5} +5.17697 q^{6} +1.00000 q^{7} +1.08207 q^{8} +4.84939 q^{9} +O(q^{10})$	\(q-1.84781 q^{2} -2.80168 q^{3} +1.41441 q^{4} +1.00000 q^{5} +5.17697 q^{6} +1.00000 q^{7} +1.08207 q^{8} +4.84939 q^{9} -1.84781 q^{10} -1.50470 q^{11} -3.96271 q^{12} +2.64111 q^{13} -1.84781 q^{14} -2.80168 q^{15} -4.82827 q^{16} -5.57678 q^{17} -8.96075 q^{18} +5.28184 q^{19} +1.41441 q^{20} -2.80168 q^{21} +2.78040 q^{22} -7.51259 q^{23} -3.03160 q^{24} +1.00000 q^{25} -4.88028 q^{26} -5.18138 q^{27} +1.41441 q^{28} -7.57023 q^{29} +5.17697 q^{30} -9.14359 q^{31} +6.75759 q^{32} +4.21568 q^{33} +10.3048 q^{34} +1.00000 q^{35} +6.85900 q^{36} +0.716572 q^{37} -9.75984 q^{38} -7.39954 q^{39} +1.08207 q^{40} -8.71600 q^{41} +5.17697 q^{42} -4.01864 q^{43} -2.12826 q^{44} +4.84939 q^{45} +13.8818 q^{46} -9.05205 q^{47} +13.5272 q^{48} +1.00000 q^{49} -1.84781 q^{50} +15.6243 q^{51} +3.73561 q^{52} -4.90340 q^{53} +9.57421 q^{54} -1.50470 q^{55} +1.08207 q^{56} -14.7980 q^{57} +13.9884 q^{58} -1.87071 q^{59} -3.96271 q^{60} +9.51937 q^{61} +16.8956 q^{62} +4.84939 q^{63} -2.83022 q^{64} +2.64111 q^{65} -7.78978 q^{66} -1.93775 q^{67} -7.88784 q^{68} +21.0478 q^{69} -1.84781 q^{70} +8.08335 q^{71} +5.24736 q^{72} -10.5591 q^{73} -1.32409 q^{74} -2.80168 q^{75} +7.47066 q^{76} -1.50470 q^{77} +13.6730 q^{78} +5.21995 q^{79} -4.82827 q^{80} -0.0316184 q^{81} +16.1055 q^{82} -3.94028 q^{83} -3.96271 q^{84} -5.57678 q^{85} +7.42568 q^{86} +21.2093 q^{87} -1.62819 q^{88} +9.39380 q^{89} -8.96075 q^{90} +2.64111 q^{91} -10.6259 q^{92} +25.6174 q^{93} +16.7265 q^{94} +5.28184 q^{95} -18.9326 q^{96} +2.81635 q^{97} -1.84781 q^{98} -7.29687 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 73 q + 7 q^{2} + 14 q^{3} + 95 q^{4} + 73 q^{5} - q^{6} + 73 q^{7} + 18 q^{8} + 111 q^{9}+O(q^{10}) $ 73 * q + 7 * q^2 + 14 * q^3 + 95 * q^4 + 73 * q^5 - q^6 + 73 * q^7 + 18 * q^8 + 111 * q^9	\( 73 q + 7 q^{2} + 14 q^{3} + 95 q^{4} + 73 q^{5} - q^{6} + 73 q^{7} + 18 q^{8} + 111 q^{9} + 7 q^{10} + 27 q^{11} + 21 q^{12} + 21 q^{13} + 7 q^{14} + 14 q^{15} + 135 q^{16} + 23 q^{17} + 41 q^{18} + 26 q^{19} + 95 q^{20} + 14 q^{21} + 48 q^{22} + 16 q^{23} - q^{24} + 73 q^{25} + 7 q^{26} + 44 q^{27} + 95 q^{28} + 66 q^{29} - q^{30} + 23 q^{31} + 3 q^{32} + 77 q^{33} + 29 q^{34} + 73 q^{35} + 142 q^{36} + 66 q^{37} - 12 q^{38} + 53 q^{39} + 18 q^{40} + 50 q^{41} - q^{42} + 43 q^{43} + 37 q^{44} + 111 q^{45} + 65 q^{46} + 28 q^{47} - 20 q^{48} + 73 q^{49} + 7 q^{50} + 71 q^{51} + 29 q^{52} - 7 q^{53} - 16 q^{54} + 27 q^{55} + 18 q^{56} + 33 q^{57} + 48 q^{58} + 16 q^{59} + 21 q^{60} + 42 q^{61} - 3 q^{62} + 111 q^{63} + 216 q^{64} + 21 q^{65} - 53 q^{66} + 48 q^{67} + 13 q^{68} + 73 q^{69} + 7 q^{70} + 68 q^{71} + 18 q^{72} + 65 q^{73} + 4 q^{74} + 14 q^{75} + 37 q^{76} + 27 q^{77} + 60 q^{78} + 116 q^{79} + 135 q^{80} + 177 q^{81} + 20 q^{82} + 40 q^{83} + 21 q^{84} + 23 q^{85} + 35 q^{86} - 14 q^{87} + 47 q^{88} + 59 q^{89} + 41 q^{90} + 21 q^{91} + 3 q^{92} + 37 q^{93} - 11 q^{94} + 26 q^{95} - 23 q^{96} + 70 q^{97} + 7 q^{98} + 49 q^{99}+O(q^{100}) \) 73 * q + 7 * q^2 + 14 * q^3 + 95 * q^4 + 73 * q^5 - q^6 + 73 * q^7 + 18 * q^8 + 111 * q^9 + 7 * q^10 + 27 * q^11 + 21 * q^12 + 21 * q^13 + 7 * q^14 + 14 * q^15 + 135 * q^16 + 23 * q^17 + 41 * q^18 + 26 * q^19 + 95 * q^20 + 14 * q^21 + 48 * q^22 + 16 * q^23 - q^24 + 73 * q^25 + 7 * q^26 + 44 * q^27 + 95 * q^28 + 66 * q^29 - q^30 + 23 * q^31 + 3 * q^32 + 77 * q^33 + 29 * q^34 + 73 * q^35 + 142 * q^36 + 66 * q^37 - 12 * q^38 + 53 * q^39 + 18 * q^40 + 50 * q^41 - q^42 + 43 * q^43 + 37 * q^44 + 111 * q^45 + 65 * q^46 + 28 * q^47 - 20 * q^48 + 73 * q^49 + 7 * q^50 + 71 * q^51 + 29 * q^52 - 7 * q^53 - 16 * q^54 + 27 * q^55 + 18 * q^56 + 33 * q^57 + 48 * q^58 + 16 * q^59 + 21 * q^60 + 42 * q^61 - 3 * q^62 + 111 * q^63 + 216 * q^64 + 21 * q^65 - 53 * q^66 + 48 * q^67 + 13 * q^68 + 73 * q^69 + 7 * q^70 + 68 * q^71 + 18 * q^72 + 65 * q^73 + 4 * q^74 + 14 * q^75 + 37 * q^76 + 27 * q^77 + 60 * q^78 + 116 * q^79 + 135 * q^80 + 177 * q^81 + 20 * q^82 + 40 * q^83 + 21 * q^84 + 23 * q^85 + 35 * q^86 - 14 * q^87 + 47 * q^88 + 59 * q^89 + 41 * q^90 + 21 * q^91 + 3 * q^92 + 37 * q^93 - 11 * q^94 + 26 * q^95 - 23 * q^96 + 70 * q^97 + 7 * q^98 + 49 * 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 $

$2$	−1.84781	−1.30660	−0.653300	−	0.757099i	$-0.726616\pi$
$2$	−1.84781	−1.30660	−0.653300	+	0.757099i	$0.726616\pi$
$3$	−2.80168	−1.61755	−0.808774	−	0.588120i	$-0.799868\pi$
$3$	−2.80168	−1.61755	−0.808774	+	0.588120i	$0.799868\pi$
$4$	1.41441	0.707203
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	5.17697	2.11349
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.08207	0.382568
$9$	4.84939	1.61646
$10$	−1.84781	−0.584329
$11$	−1.50470	−0.453684	−0.226842	−	0.973932i	$-0.572840\pi$
$11$	−1.50470	−0.453684	−0.226842	+	0.973932i	$0.572840\pi$
$12$	−3.96271	−1.14394
$13$	2.64111	0.732513	0.366256	−	0.930514i	$-0.380639\pi$
$13$	2.64111	0.732513	0.366256	+	0.930514i	$0.380639\pi$
$14$	−1.84781	−0.493848
$15$	−2.80168	−0.723389
$16$	−4.82827	−1.20707
$17$	−5.57678	−1.35257	−0.676284	−	0.736641i	$-0.736411\pi$
$17$	−5.57678	−1.35257	−0.676284	+	0.736641i	$0.736411\pi$
$18$	−8.96075	−2.11207
$19$	5.28184	1.21174	0.605868	−	0.795565i	$-0.292826\pi$
$19$	5.28184	1.21174	0.605868	+	0.795565i	$0.292826\pi$
$20$	1.41441	0.316271
$21$	−2.80168	−0.611376
$22$	2.78040	0.592784
$23$	−7.51259	−1.56648	−0.783242	−	0.621717i	$-0.786435\pi$
$23$	−7.51259	−1.56648	−0.783242	+	0.621717i	$0.786435\pi$
$24$	−3.03160	−0.618823
$25$	1.00000	0.200000
$26$	−4.88028	−0.957101
$27$	−5.18138	−0.997157
$28$	1.41441	0.267298
$29$	−7.57023	−1.40576	−0.702878	−	0.711310i	$-0.748102\pi$
$29$	−7.57023	−1.40576	−0.702878	+	0.711310i	$0.748102\pi$
$30$	5.17697	0.945181
$31$	−9.14359	−1.64224	−0.821118	−	0.570758i	$-0.806649\pi$
$31$	−9.14359	−1.64224	−0.821118	+	0.570758i	$0.806649\pi$
$32$	6.75759	1.19459
$33$	4.21568	0.733856
$34$	10.3048	1.76727
$35$	1.00000	0.169031
$36$	6.85900	1.14317
$37$	0.716572	0.117804	0.0589019	−	0.998264i	$-0.481240\pi$
$37$	0.716572	0.117804	0.0589019	+	0.998264i	$0.481240\pi$
$38$	−9.75984	−1.58325
$39$	−7.39954	−1.18487
$40$	1.08207	0.171090
$41$	−8.71600	−1.36121	−0.680605	−	0.732650i	$-0.738283\pi$
$41$	−8.71600	−1.36121	−0.680605	+	0.732650i	$0.738283\pi$
$42$	5.17697	0.798823
$43$	−4.01864	−0.612836	−0.306418	−	0.951897i	$-0.599131\pi$
$43$	−4.01864	−0.612836	−0.306418	+	0.951897i	$0.599131\pi$
$44$	−2.12826	−0.320847
$45$	4.84939	0.722904
$46$	13.8818	2.04677
$47$	−9.05205	−1.32038	−0.660188	−	0.751100i	$-0.729524\pi$
$47$	−9.05205	−1.32038	−0.660188	+	0.751100i	$0.729524\pi$
$48$	13.5272	1.95249
$49$	1.00000	0.142857
$50$	−1.84781	−0.261320
$51$	15.6243	2.18784
$52$	3.73561	0.518035
$53$	−4.90340	−0.673533	−0.336767	−	0.941588i	$-0.609333\pi$
$53$	−4.90340	−0.673533	−0.336767	+	0.941588i	$0.609333\pi$
$54$	9.57421	1.30288
$55$	−1.50470	−0.202894
$56$	1.08207	0.144597
$57$	−14.7980	−1.96004
$58$	13.9884	1.83676
$59$	−1.87071	−0.243545	−0.121773	−	0.992558i	$-0.538858\pi$
$59$	−1.87071	−0.243545	−0.121773	+	0.992558i	$0.538858\pi$
$60$	−3.96271	−0.511583
$61$	9.51937	1.21883	0.609415	−	0.792851i	$-0.291404\pi$
$61$	9.51937	1.21883	0.609415	+	0.792851i	$0.291404\pi$
$62$	16.8956	2.14575
$63$	4.84939	0.610965
$64$	−2.83022	−0.353778
$65$	2.64111	0.327590
$66$	−7.78978	−0.958856
$67$	−1.93775	−0.236734	−0.118367	−	0.992970i	$-0.537766\pi$
$67$	−1.93775	−0.236734	−0.118367	+	0.992970i	$0.537766\pi$
$68$	−7.88784	−0.956541
$69$	21.0478	2.53386
$70$	−1.84781	−0.220856
$71$	8.08335	0.959317	0.479658	−	0.877455i	$-0.340761\pi$
$71$	8.08335	0.959317	0.479658	+	0.877455i	$0.340761\pi$
$72$	5.24736	0.618407
$73$	−10.5591	−1.23585	−0.617926	−	0.786236i	$-0.712027\pi$
$73$	−10.5591	−1.23585	−0.617926	+	0.786236i	$0.712027\pi$
$74$	−1.32409	−0.153922
$75$	−2.80168	−0.323510
$76$	7.47066	0.856944
$77$	−1.50470	−0.171476
$78$	13.6730	1.54816
$79$	5.21995	0.587291	0.293645	−	0.955914i	$-0.405132\pi$
$79$	5.21995	0.587291	0.293645	+	0.955914i	$0.405132\pi$
$80$	−4.82827	−0.539817
$81$	−0.0316184	−0.00351315
$82$	16.1055	1.77856
$83$	−3.94028	−0.432502	−0.216251	−	0.976338i	$-0.569383\pi$
$83$	−3.94028	−0.432502	−0.216251	+	0.976338i	$0.569383\pi$
$84$	−3.96271	−0.432367
$85$	−5.57678	−0.604887
$86$	7.42568	0.800732
$87$	21.2093	2.27388
$88$	−1.62819	−0.173565
$89$	9.39380	0.995740	0.497870	−	0.867252i	$-0.334116\pi$
$89$	9.39380	0.995740	0.497870	+	0.867252i	$0.334116\pi$
$90$	−8.96075	−0.944546
$91$	2.64111	0.276864
$92$	−10.6259	−1.10782
$93$	25.6174	2.65640
$94$	16.7265	1.72520
$95$	5.28184	0.541905
$96$	−18.9326	−1.93230
$97$	2.81635	0.285957	0.142978	−	0.989726i	$-0.454332\pi$
$97$	2.81635	0.285957	0.142978	+	0.989726i	$0.454332\pi$
$98$	−1.84781	−0.186657
$99$	−7.29687	−0.733363
$100$	1.41441	0.141441
$101$	0.859285	0.0855021	0.0427510	−	0.999086i	$-0.486388\pi$
$101$	0.859285	0.0855021	0.0427510	+	0.999086i	$0.486388\pi$
$102$	−28.8708	−2.85864
$103$	1.29693	0.127790	0.0638952	−	0.997957i	$-0.479648\pi$
$103$	1.29693	0.127790	0.0638952	+	0.997957i	$0.479648\pi$
$104$	2.85786	0.280236
$105$	−2.80168	−0.273416
$106$	9.06055	0.880038
$107$	−17.4788	−1.68974	−0.844871	−	0.534970i	$-0.820323\pi$
$107$	−17.4788	−1.68974	−0.844871	+	0.534970i	$0.820323\pi$
$108$	−7.32857	−0.705192
$109$	9.57399	0.917022	0.458511	−	0.888689i	$-0.348383\pi$
$109$	9.57399	0.917022	0.458511	+	0.888689i	$0.348383\pi$
$110$	2.78040	0.265101
$111$	−2.00760	−0.190553
$112$	−4.82827	−0.456228
$113$	−2.39048	−0.224878	−0.112439	−	0.993659i	$-0.535866\pi$
$113$	−2.39048	−0.224878	−0.112439	+	0.993659i	$0.535866\pi$
$114$	27.3439	2.56099
$115$	−7.51259	−0.700553
$116$	−10.7074	−0.994155
$117$	12.8078	1.18408
$118$	3.45671	0.318216
$119$	−5.57678	−0.511223
$120$	−3.03160	−0.276746
$121$	−8.73588	−0.794171
$122$	−17.5900	−1.59252
$123$	24.4194	2.20182
$124$	−12.9327	−1.16140
$125$	1.00000	0.0894427
$126$	−8.96075	−0.798287
$127$	0.245096	0.0217487	0.0108744	−	0.999941i	$-0.496539\pi$
$127$	0.245096	0.0217487	0.0108744	+	0.999941i	$0.496539\pi$
$128$	−8.28547	−0.732339
$129$	11.2589	0.991292
$130$	−4.88028	−0.428029
$131$	−5.46386	−0.477380	−0.238690	−	0.971096i	$-0.576718\pi$
$131$	−5.46386	−0.477380	−0.238690	+	0.971096i	$0.576718\pi$
$132$	5.96269	0.518985
$133$	5.28184	0.457993
$134$	3.58059	0.309316
$135$	−5.18138	−0.445942
$136$	−6.03445	−0.517450
$137$	3.66496	0.313119	0.156559	−	0.987669i	$-0.449960\pi$
$137$	3.66496	0.313119	0.156559	+	0.987669i	$0.449960\pi$
$138$	−38.8924	−3.31074
$139$	15.3650	1.30324	0.651622	−	0.758544i	$-0.274089\pi$
$139$	15.3650	1.30324	0.651622	+	0.758544i	$0.274089\pi$
$140$	1.41441	0.119539
$141$	25.3609	2.13577
$142$	−14.9365	−1.25344
$143$	−3.97408	−0.332329
$144$	−23.4141	−1.95118
$145$	−7.57023	−0.628673
$146$	19.5113	1.61476
$147$	−2.80168	−0.231078
$148$	1.01352	0.0833112
$149$	19.5944	1.60524	0.802618	−	0.596493i	$-0.203440\pi$
$149$	19.5944	1.60524	0.802618	+	0.596493i	$0.203440\pi$
$150$	5.17697	0.422698
$151$	19.5529	1.59119	0.795596	−	0.605828i	$-0.207158\pi$
$151$	19.5529	1.59119	0.795596	+	0.605828i	$0.207158\pi$
$152$	5.71530	0.463572
$153$	−27.0440	−2.18638
$154$	2.78040	0.224051
$155$	−9.14359	−0.734431
$156$	−10.4660	−0.837947
$157$	17.5114	1.39756	0.698780	−	0.715337i	$-0.253727\pi$
$157$	17.5114	1.39756	0.698780	+	0.715337i	$0.253727\pi$
$158$	−9.64549	−0.767354
$159$	13.7377	1.08947
$160$	6.75759	0.534235
$161$	−7.51259	−0.592075
$162$	0.0584248	0.00459029
$163$	11.1884	0.876347	0.438173	−	0.898890i	$-0.355626\pi$
$163$	11.1884	0.876347	0.438173	+	0.898890i	$0.355626\pi$
$164$	−12.3280	−0.962653
$165$	4.21568	0.328190
$166$	7.28090	0.565107
$167$	−20.2741	−1.56885	−0.784427	−	0.620221i	$-0.787043\pi$
$167$	−20.2741	−1.56885	−0.784427	+	0.620221i	$0.787043\pi$
$168$	−3.03160	−0.233893
$169$	−6.02453	−0.463425
$170$	10.3048	0.790345
$171$	25.6137	1.95873
$172$	−5.68399	−0.433400
$173$	15.0656	1.14542	0.572708	−	0.819760i	$-0.305893\pi$
$173$	15.0656	1.14542	0.572708	+	0.819760i	$0.305893\pi$
$174$	−39.1908	−2.97105
$175$	1.00000	0.0755929
$176$	7.26509	0.547627
$177$	5.24111	0.393946
$178$	−17.3580	−1.30103
$179$	−7.73749	−0.578327	−0.289164	−	0.957280i	$-0.593377\pi$
$179$	−7.73749	−0.578327	−0.289164	+	0.957280i	$0.593377\pi$
$180$	6.85900	0.511240
$181$	4.73454	0.351916	0.175958	−	0.984398i	$-0.443698\pi$
$181$	4.73454	0.351916	0.175958	+	0.984398i	$0.443698\pi$
$182$	−4.88028	−0.361750
$183$	−26.6702	−1.97152
$184$	−8.12912	−0.599287
$185$	0.716572	0.0526834
$186$	−47.3361	−3.47085
$187$	8.39139	0.613639
$188$	−12.8033	−0.933775
$189$	−5.18138	−0.376890
$190$	−9.75984	−0.708053
$191$	6.16197	0.445865	0.222932	−	0.974834i	$-0.428437\pi$
$191$	6.16197	0.445865	0.222932	+	0.974834i	$0.428437\pi$
$192$	7.92936	0.572253
$193$	−20.0392	−1.44246	−0.721228	−	0.692698i	$-0.756422\pi$
$193$	−20.0392	−1.44246	−0.721228	+	0.692698i	$0.756422\pi$
$194$	−5.20408	−0.373631
$195$	−7.39954	−0.529892
$196$	1.41441	0.101029
$197$	6.39547	0.455658	0.227829	−	0.973701i	$-0.426837\pi$
$197$	6.39547	0.455658	0.227829	+	0.973701i	$0.426837\pi$
$198$	13.4832	0.958212
$199$	−10.5352	−0.746818	−0.373409	−	0.927667i	$-0.621811\pi$
$199$	−10.5352	−0.746818	−0.373409	+	0.927667i	$0.621811\pi$
$200$	1.08207	0.0765137
$201$	5.42894	0.382928
$202$	−1.58780	−0.111717
$203$	−7.57023	−0.531326
$204$	22.0992	1.54725
$205$	−8.71600	−0.608752
$206$	−2.39648	−0.166971
$207$	−36.4314	−2.53216
$208$	−12.7520	−0.884192
$209$	−7.94758	−0.549746
$210$	5.17697	0.357245
$211$	−11.0595	−0.761371	−0.380685	−	0.924705i	$-0.624312\pi$
$211$	−11.0595	−0.761371	−0.380685	+	0.924705i	$0.624312\pi$
$212$	−6.93539	−0.476325
$213$	−22.6469	−1.55174
$214$	32.2976	2.20782
$215$	−4.01864	−0.274069
$216$	−5.60660	−0.381480
$217$	−9.14359	−0.620707
$218$	−17.6909	−1.19818
$219$	29.5833	1.99905
$220$	−2.12826	−0.143487
$221$	−14.7289	−0.990774
$222$	3.70967	0.248977
$223$	−15.4637	−1.03553	−0.517763	−	0.855524i	$-0.673235\pi$
$223$	−15.4637	−1.03553	−0.517763	+	0.855524i	$0.673235\pi$
$224$	6.75759	0.451511
$225$	4.84939	0.323292
$226$	4.41716	0.293825
$227$	−14.5606	−0.966419	−0.483210	−	0.875505i	$-0.660529\pi$
$227$	−14.5606	−0.966419	−0.483210	+	0.875505i	$0.660529\pi$
$228$	−20.9304	−1.38615
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	13.8818	0.915342
$231$	4.21568	0.277371
$232$	−8.19149	−0.537798
$233$	10.7340	0.703211	0.351605	−	0.936148i	$-0.385636\pi$
$233$	10.7340	0.703211	0.351605	+	0.936148i	$0.385636\pi$
$234$	−23.6663	−1.54712
$235$	−9.05205	−0.590491
$236$	−2.64594	−0.172236
$237$	−14.6246	−0.949971
$238$	10.3048	0.667964
$239$	−3.18115	−0.205772	−0.102886	−	0.994693i	$-0.532808\pi$
$239$	−3.18115	−0.205772	−0.102886	+	0.994693i	$0.532808\pi$
$240$	13.5272	0.873179
$241$	−16.8417	−1.08487	−0.542434	−	0.840098i	$-0.682497\pi$
$241$	−16.8417	−1.08487	−0.542434	+	0.840098i	$0.682497\pi$
$242$	16.1423	1.03766
$243$	15.6327	1.00284
$244$	13.4643	0.861961
$245$	1.00000	0.0638877
$246$	−45.1225	−2.87690
$247$	13.9499	0.887612
$248$	−9.89397	−0.628268
$249$	11.0394	0.699593
$250$	−1.84781	−0.116866
$251$	−6.91680	−0.436585	−0.218292	−	0.975883i	$-0.570049\pi$
$251$	−6.91680	−0.436585	−0.218292	+	0.975883i	$0.570049\pi$
$252$	6.85900	0.432076
$253$	11.3042	0.710689
$254$	−0.452891	−0.0284169
$255$	15.6243	0.978434
$256$	20.9704	1.31065
$257$	2.94231	0.183537	0.0917683	−	0.995780i	$-0.470748\pi$
$257$	2.94231	0.183537	0.0917683	+	0.995780i	$0.470748\pi$
$258$	−20.8044	−1.29522
$259$	0.716572	0.0445256
$260$	3.73561	0.231672
$261$	−36.7110	−2.27235
$262$	10.0962	0.623744
$263$	9.49130	0.585259	0.292629	−	0.956226i	$-0.405470\pi$
$263$	9.49130	0.585259	0.292629	+	0.956226i	$0.405470\pi$
$264$	4.56165	0.280750
$265$	−4.90340	−0.301213
$266$	−9.75984	−0.598414
$267$	−26.3184	−1.61066
$268$	−2.74076	−0.167419
$269$	12.2114	0.744542	0.372271	−	0.928124i	$-0.378579\pi$
$269$	12.2114	0.744542	0.372271	+	0.928124i	$0.378579\pi$
$270$	9.57421	0.582668
$271$	24.1656	1.46796	0.733978	−	0.679173i	$-0.237662\pi$
$271$	24.1656	1.46796	0.733978	+	0.679173i	$0.237662\pi$
$272$	26.9262	1.63264
$273$	−7.39954	−0.447840
$274$	−6.77216	−0.409121
$275$	−1.50470	−0.0907368
$276$	29.7702	1.79196
$277$	−6.50345	−0.390755	−0.195377	−	0.980728i	$-0.562593\pi$
$277$	−6.50345	−0.390755	−0.195377	+	0.980728i	$0.562593\pi$
$278$	−28.3916	−1.70282
$279$	−44.3408	−2.65461
$280$	1.08207	0.0646658
$281$	6.85761	0.409091	0.204545	−	0.978857i	$-0.434428\pi$
$281$	6.85761	0.409091	0.204545	+	0.978857i	$0.434428\pi$
$282$	−46.8622	−2.79060
$283$	−26.4464	−1.57207	−0.786037	−	0.618179i	$-0.787871\pi$
$283$	−26.4464	−1.57207	−0.786037	+	0.618179i	$0.787871\pi$
$284$	11.4331	0.678432
$285$	−14.7980	−0.876557
$286$	7.34335	0.434222
$287$	−8.71600	−0.514489
$288$	32.7702	1.93100
$289$	14.1005	0.829441
$290$	13.9884	0.821424
$291$	−7.89049	−0.462549
$292$	−14.9349	−0.873999
$293$	30.9524	1.80826	0.904128	−	0.427261i	$-0.140522\pi$
$293$	30.9524	1.80826	0.904128	+	0.427261i	$0.140522\pi$
$294$	5.17697	0.301927
$295$	−1.87071	−0.108917
$296$	0.775379	0.0450680
$297$	7.79642	0.452394
$298$	−36.2068	−2.09740
$299$	−19.8416	−1.14747
$300$	−3.96271	−0.228787
$301$	−4.01864	−0.231630
$302$	−36.1300	−2.07905
$303$	−2.40744	−0.138304
$304$	−25.5021	−1.46265
$305$	9.51937	0.545078
$306$	49.9721	2.85672
$307$	24.5961	1.40378	0.701888	−	0.712287i	$-0.252341\pi$
$307$	24.5961	1.40378	0.701888	+	0.712287i	$0.252341\pi$
$308$	−2.12826	−0.121269
$309$	−3.63358	−0.206707
$310$	16.8956	0.959607
$311$	17.1341	0.971583	0.485792	−	0.874075i	$-0.338531\pi$
$311$	17.1341	0.971583	0.485792	+	0.874075i	$0.338531\pi$
$312$	−8.00679	−0.453295
$313$	−22.3590	−1.26381	−0.631903	−	0.775047i	$-0.717726\pi$
$313$	−22.3590	−1.26381	−0.631903	+	0.775047i	$0.717726\pi$
$314$	−32.3577	−1.82605
$315$	4.84939	0.273232
$316$	7.38314	0.415334
$317$	6.81047	0.382514	0.191257	−	0.981540i	$-0.438744\pi$
$317$	6.81047	0.382514	0.191257	+	0.981540i	$0.438744\pi$
$318$	−25.3847	−1.42350
$319$	11.3909	0.637769
$320$	−2.83022	−0.158214
$321$	48.9700	2.73324
$322$	13.8818	0.773605
$323$	−29.4557	−1.63896
$324$	−0.0447213	−0.00248451
$325$	2.64111	0.146503
$326$	−20.6741	−1.14503
$327$	−26.8232	−1.48333
$328$	−9.43130	−0.520756
$329$	−9.05205	−0.499056
$330$	−7.78978	−0.428813
$331$	13.3760	0.735210	0.367605	−	0.929982i	$-0.380178\pi$
$331$	13.3760	0.735210	0.367605	+	0.929982i	$0.380178\pi$
$332$	−5.57316	−0.305867
$333$	3.47493	0.190425
$334$	37.4626	2.04986
$335$	−1.93775	−0.105870
$336$	13.5272	0.737971
$337$	−18.9082	−1.02999	−0.514996	−	0.857192i	$-0.672207\pi$
$337$	−18.9082	−1.02999	−0.514996	+	0.857192i	$0.672207\pi$
$338$	11.1322	0.605511
$339$	6.69736	0.363751
$340$	−7.88784	−0.427778
$341$	13.7584	0.745057
$342$	−47.3292	−2.55927
$343$	1.00000	0.0539949
$344$	−4.34843	−0.234452
$345$	21.0478	1.13318
$346$	−27.8384	−1.49660
$347$	−12.7372	−0.683767	−0.341883	−	0.939742i	$-0.611065\pi$
$347$	−12.7372	−0.683767	−0.341883	+	0.939742i	$0.611065\pi$
$348$	29.9986	1.60809
$349$	5.18065	0.277314	0.138657	−	0.990340i	$-0.455721\pi$
$349$	5.18065	0.277314	0.138657	+	0.990340i	$0.455721\pi$
$350$	−1.84781	−0.0987697
$351$	−13.6846	−0.730430
$352$	−10.1682	−0.541964
$353$	7.94750	0.423003	0.211501	−	0.977378i	$-0.432165\pi$
$353$	7.94750	0.423003	0.211501	+	0.977378i	$0.432165\pi$
$354$	−9.68459	−0.514730
$355$	8.08335	0.429020
$356$	13.2866	0.704191
$357$	15.6243	0.826928
$358$	14.2974	0.755642
$359$	−28.1922	−1.48793	−0.743965	−	0.668219i	$-0.767057\pi$
$359$	−28.1922	−1.48793	−0.743965	+	0.668219i	$0.767057\pi$
$360$	5.24736	0.276560
$361$	8.89779	0.468305
$362$	−8.74854	−0.459813
$363$	24.4751	1.28461
$364$	3.73561	0.195799
$365$	−10.5591	−0.552690
$366$	49.2815	2.57598
$367$	−17.8052	−0.929425	−0.464712	−	0.885462i	$-0.653842\pi$
$367$	−17.8052	−0.929425	−0.464712	+	0.885462i	$0.653842\pi$
$368$	36.2728	1.89085
$369$	−42.2673	−2.20035
$370$	−1.32409	−0.0688362
$371$	−4.90340	−0.254572
$372$	36.2334	1.87861
$373$	−14.0957	−0.729848	−0.364924	−	0.931037i	$-0.618905\pi$
$373$	−14.0957	−0.729848	−0.364924	+	0.931037i	$0.618905\pi$
$374$	−15.5057	−0.801780
$375$	−2.80168	−0.144678
$376$	−9.79492	−0.505134
$377$	−19.9938	−1.02973
$378$	9.57421	0.492444
$379$	−37.7772	−1.94048	−0.970241	−	0.242139i	$-0.922151\pi$
$379$	−37.7772	−1.94048	−0.970241	+	0.242139i	$0.922151\pi$
$380$	7.47066	0.383237
$381$	−0.686679	−0.0351796
$382$	−11.3862	−0.582567
$383$	15.7741	0.806018	0.403009	−	0.915196i	$-0.367964\pi$
$383$	15.7741	0.806018	0.403009	+	0.915196i	$0.367964\pi$
$384$	23.2132	1.18459
$385$	−1.50470	−0.0766866
$386$	37.0287	1.88471
$387$	−19.4879	−0.990627
$388$	3.98346	0.202230
$389$	25.8759	1.31196	0.655979	−	0.754779i	$-0.272256\pi$
$389$	25.8759	1.31196	0.655979	+	0.754779i	$0.272256\pi$
$390$	13.6730	0.692357
$391$	41.8961	2.11878
$392$	1.08207	0.0546526
$393$	15.3080	0.772185
$394$	−11.8176	−0.595363
$395$	5.21995	0.262644
$396$	−10.3207	−0.518637
$397$	7.76158	0.389543	0.194771	−	0.980849i	$-0.437604\pi$
$397$	7.76158	0.389543	0.194771	+	0.980849i	$0.437604\pi$
$398$	19.4670	0.975792
$399$	−14.7980	−0.740826
$400$	−4.82827	−0.241413
$401$	−23.3281	−1.16495	−0.582474	−	0.812849i	$-0.697915\pi$
$401$	−23.3281	−1.16495	−0.582474	+	0.812849i	$0.697915\pi$
$402$	−10.0317	−0.500334
$403$	−24.1492	−1.20296
$404$	1.21538	0.0604673
$405$	−0.0316184	−0.00157113
$406$	13.9884	0.694230
$407$	−1.07823	−0.0534457
$408$	16.9066	0.837000
$409$	−28.7450	−1.42135	−0.710675	−	0.703520i	$-0.751610\pi$
$409$	−28.7450	−1.42135	−0.710675	+	0.703520i	$0.751610\pi$
$410$	16.1055	0.795395
$411$	−10.2680	−0.506485
$412$	1.83439	0.0903738
$413$	−1.87071	−0.0920515
$414$	67.3184	3.30852
$415$	−3.94028	−0.193421
$416$	17.8476	0.875049
$417$	−43.0478	−2.10806
$418$	14.6856	0.718297
$419$	−27.8242	−1.35930	−0.679651	−	0.733536i	$-0.737869\pi$
$419$	−27.8242	−1.35930	−0.679651	+	0.733536i	$0.737869\pi$
$420$	−3.96271	−0.193360
$421$	29.4863	1.43707	0.718536	−	0.695490i	$-0.244813\pi$
$421$	29.4863	1.43707	0.718536	+	0.695490i	$0.244813\pi$
$422$	20.4360	0.994807
$423$	−43.8969	−2.13434
$424$	−5.30580	−0.257672
$425$	−5.57678	−0.270514
$426$	41.8472	2.02750
$427$	9.51937	0.460675
$428$	−24.7222	−1.19499
$429$	11.1341	0.537559
$430$	7.42568	0.358098
$431$	38.0264	1.83167	0.915834	−	0.401558i	$-0.131531\pi$
$431$	38.0264	1.83167	0.915834	+	0.401558i	$0.131531\pi$
$432$	25.0171	1.20363
$433$	19.6289	0.943303	0.471652	−	0.881785i	$-0.343658\pi$
$433$	19.6289	0.943303	0.471652	+	0.881785i	$0.343658\pi$
$434$	16.8956	0.811016
$435$	21.2093	1.01691
$436$	13.5415	0.648521
$437$	−39.6803	−1.89816
$438$	−54.6643	−2.61196
$439$	21.5056	1.02641	0.513204	−	0.858267i	$-0.328459\pi$
$439$	21.5056	1.02641	0.513204	+	0.858267i	$0.328459\pi$
$440$	−1.62819	−0.0776207
$441$	4.84939	0.230923
$442$	27.2162	1.29454
$443$	3.10318	0.147437	0.0737184	−	0.997279i	$-0.476513\pi$
$443$	3.10318	0.147437	0.0737184	+	0.997279i	$0.476513\pi$
$444$	−2.83957	−0.134760
$445$	9.39380	0.445309
$446$	28.5740	1.35302
$447$	−54.8972	−2.59655
$448$	−2.83022	−0.133715
$449$	8.96756	0.423205	0.211603	−	0.977356i	$-0.432132\pi$
$449$	8.96756	0.423205	0.211603	+	0.977356i	$0.432132\pi$
$450$	−8.96075	−0.422414
$451$	13.1150	0.617560
$452$	−3.38112	−0.159034
$453$	−54.7808	−2.57383
$454$	26.9052	1.26272
$455$	2.64111	0.123817
$456$	−16.0124	−0.749850
$457$	12.9612	0.606302	0.303151	−	0.952943i	$-0.401961\pi$
$457$	12.9612	0.606302	0.303151	+	0.952943i	$0.401961\pi$
$458$	−1.84781	−0.0863425
$459$	28.8954	1.34872
$460$	−10.6259	−0.495433
$461$	33.6327	1.56643	0.783215	−	0.621751i	$-0.213578\pi$
$461$	33.6327	1.56643	0.783215	+	0.621751i	$0.213578\pi$
$462$	−7.78978	−0.362414
$463$	34.7930	1.61697	0.808483	−	0.588519i	$-0.200289\pi$
$463$	34.7930	1.61697	0.808483	+	0.588519i	$0.200289\pi$
$464$	36.5511	1.69684
$465$	25.6174	1.18798
$466$	−19.8345	−0.918815
$467$	12.1926	0.564204	0.282102	−	0.959384i	$-0.408968\pi$
$467$	12.1926	0.564204	0.282102	+	0.959384i	$0.408968\pi$
$468$	18.1154	0.837384
$469$	−1.93775	−0.0894769
$470$	16.7265	0.771535
$471$	−49.0612	−2.26062
$472$	−2.02423	−0.0931727
$473$	6.04684	0.278034
$474$	27.0235	1.24123
$475$	5.28184	0.242347
$476$	−7.88784	−0.361538
$477$	−23.7785	−1.08874
$478$	5.87817	0.268861
$479$	35.6433	1.62859	0.814293	−	0.580454i	$-0.197125\pi$
$479$	35.6433	1.62859	0.814293	+	0.580454i	$0.197125\pi$
$480$	−18.9326	−0.864150
$481$	1.89255	0.0862927
$482$	31.1203	1.41749
$483$	21.0478	0.957710
$484$	−12.3561	−0.561640
$485$	2.81635	0.127884
$486$	−28.8863	−1.31031
$487$	1.29251	0.0585694	0.0292847	−	0.999571i	$-0.490677\pi$
$487$	1.29251	0.0585694	0.0292847	+	0.999571i	$0.490677\pi$
$488$	10.3006	0.466286
$489$	−31.3464	−1.41753
$490$	−1.84781	−0.0834756
$491$	24.3304	1.09802	0.549008	−	0.835817i	$-0.315006\pi$
$491$	24.3304	1.09802	0.549008	+	0.835817i	$0.315006\pi$
$492$	34.5390	1.55714
$493$	42.2175	1.90138
$494$	−25.7768	−1.15975
$495$	−7.29687	−0.327970
$496$	44.1477	1.98229
$497$	8.08335	0.362588
$498$	−20.3987	−0.914089
$499$	−7.80369	−0.349341	−0.174671	−	0.984627i	$-0.555886\pi$
$499$	−7.80369	−0.349341	−0.174671	+	0.984627i	$0.555886\pi$
$500$	1.41441	0.0632542
$501$	56.8013	2.53770
$502$	12.7809	0.570441
$503$	16.0703	0.716541	0.358271	−	0.933618i	$-0.383367\pi$
$503$	16.0703	0.716541	0.358271	+	0.933618i	$0.383367\pi$
$504$	5.24736	0.233736
$505$	0.859285	0.0382377
$506$	−20.8880	−0.928586
$507$	16.8788	0.749612
$508$	0.346665	0.0153808
$509$	−6.17149	−0.273546	−0.136773	−	0.990602i	$-0.543673\pi$
$509$	−6.17149	−0.273546	−0.136773	+	0.990602i	$0.543673\pi$
$510$	−28.8708	−1.27842
$511$	−10.5591	−0.467108
$512$	−22.1785	−0.980159
$513$	−27.3672	−1.20829
$514$	−5.43684	−0.239809
$515$	1.29693	0.0571496
$516$	15.9247	0.701045
$517$	13.6206	0.599034
$518$	−1.32409	−0.0581772
$519$	−42.2089	−1.85276
$520$	2.85786	0.125325
$521$	13.8626	0.607330	0.303665	−	0.952779i	$-0.401790\pi$
$521$	13.8626	0.607330	0.303665	+	0.952779i	$0.401790\pi$
$522$	67.8349	2.96905
$523$	−13.8373	−0.605063	−0.302532	−	0.953139i	$-0.597832\pi$
$523$	−13.8373	−0.605063	−0.302532	+	0.953139i	$0.597832\pi$
$524$	−7.72812	−0.337605
$525$	−2.80168	−0.122275
$526$	−17.5381	−0.764699
$527$	50.9918	2.22124
$528$	−20.3544	−0.885813
$529$	33.4390	1.45387
$530$	9.06055	0.393565
$531$	−9.07178	−0.393682
$532$	7.47066	0.323894
$533$	−23.0199	−0.997104
$534$	48.6314	2.10449
$535$	−17.4788	−0.755676
$536$	−2.09677	−0.0905667
$537$	21.6779	0.935472
$538$	−22.5644	−0.972818
$539$	−1.50470	−0.0648120
$540$	−7.32857	−0.315372
$541$	28.5322	1.22669	0.613347	−	0.789814i	$-0.289823\pi$
$541$	28.5322	1.22669	0.613347	+	0.789814i	$0.289823\pi$
$542$	−44.6535	−1.91803
$543$	−13.2647	−0.569241
$544$	−37.6856	−1.61576
$545$	9.57399	0.410105
$546$	13.6730	0.585148
$547$	−18.1568	−0.776328	−0.388164	−	0.921590i	$-0.626891\pi$
$547$	−18.1568	−0.776328	−0.388164	+	0.921590i	$0.626891\pi$
$548$	5.18375	0.221439
$549$	46.1631	1.97019
$550$	2.78040	0.118557
$551$	−39.9847	−1.70341
$552$	22.7752	0.969375
$553$	5.21995	0.221975
$554$	12.0172	0.510560
$555$	−2.00760	−0.0852180
$556$	21.7324	0.921658
$557$	27.7111	1.17416	0.587079	−	0.809529i	$-0.300278\pi$
$557$	27.7111	1.17416	0.587079	+	0.809529i	$0.300278\pi$
$558$	81.9334	3.46852
$559$	−10.6137	−0.448910
$560$	−4.82827	−0.204032
$561$	−23.5099	−0.992590
$562$	−12.6716	−0.534518
$563$	10.4878	0.442007	0.221004	−	0.975273i	$-0.429067\pi$
$563$	10.4878	0.442007	0.221004	+	0.975273i	$0.429067\pi$
$564$	35.8706	1.51043
$565$	−2.39048	−0.100568
$566$	48.8679	2.05407
$567$	−0.0316184	−0.00132785
$568$	8.74672	0.367004
$569$	−8.73017	−0.365988	−0.182994	−	0.983114i	$-0.558579\pi$
$569$	−8.73017	−0.365988	−0.182994	+	0.983114i	$0.558579\pi$
$570$	27.3439	1.14531
$571$	−17.4614	−0.730736	−0.365368	−	0.930863i	$-0.619057\pi$
$571$	−17.4614	−0.730736	−0.365368	+	0.930863i	$0.619057\pi$
$572$	−5.62097	−0.235024
$573$	−17.2638	−0.721207
$574$	16.1055	0.672232
$575$	−7.51259	−0.313297
$576$	−13.7248	−0.571868
$577$	28.6481	1.19264	0.596318	−	0.802749i	$-0.296630\pi$
$577$	28.6481	1.19264	0.596318	+	0.802749i	$0.296630\pi$
$578$	−26.0551	−1.08375
$579$	56.1434	2.33324
$580$	−10.7074	−0.444600
$581$	−3.94028	−0.163471
$582$	14.5801	0.604366
$583$	7.37814	0.305571
$584$	−11.4257	−0.472798
$585$	12.8078	0.529536
$586$	−57.1941	−2.36267
$587$	−28.1539	−1.16203	−0.581017	−	0.813891i	$-0.697345\pi$
$587$	−28.1539	−1.16203	−0.581017	+	0.813891i	$0.697345\pi$
$588$	−3.96271	−0.163419
$589$	−48.2949	−1.98996
$590$	3.45671	0.142311
$591$	−17.9180	−0.737049
$592$	−3.45980	−0.142197
$593$	−15.0159	−0.616631	−0.308315	−	0.951284i	$-0.599765\pi$
$593$	−15.0159	−0.616631	−0.308315	+	0.951284i	$0.599765\pi$
$594$	−14.4063	−0.591098
$595$	−5.57678	−0.228626
$596$	27.7145	1.13523
$597$	29.5161	1.20801
$598$	36.6635	1.49928
$599$	−17.5227	−0.715959	−0.357980	−	0.933729i	$-0.616534\pi$
$599$	−17.5227	−0.715959	−0.357980	+	0.933729i	$0.616534\pi$
$600$	−3.03160	−0.123765
$601$	−16.3683	−0.667676	−0.333838	−	0.942630i	$-0.608344\pi$
$601$	−16.3683	−0.667676	−0.333838	+	0.942630i	$0.608344\pi$
$602$	7.42568	0.302648
$603$	−9.39688	−0.382671
$604$	27.6557	1.12530
$605$	−8.73588	−0.355164
$606$	4.44849	0.180708
$607$	−29.1914	−1.18484	−0.592421	−	0.805628i	$-0.701828\pi$
$607$	−29.1914	−1.18484	−0.592421	+	0.805628i	$0.701828\pi$
$608$	35.6925	1.44752
$609$	21.2093	0.859445
$610$	−17.5900	−0.712199
$611$	−23.9075	−0.967193
$612$	−38.2512	−1.54621
$613$	6.03784	0.243866	0.121933	−	0.992538i	$-0.461091\pi$
$613$	6.03784	0.243866	0.121933	+	0.992538i	$0.461091\pi$
$614$	−45.4490	−1.83417
$615$	24.4194	0.984686
$616$	−1.62819	−0.0656015
$617$	41.3215	1.66354	0.831771	−	0.555118i	$-0.187327\pi$
$617$	41.3215	1.66354	0.831771	+	0.555118i	$0.187327\pi$
$618$	6.71417	0.270083
$619$	−39.4803	−1.58685	−0.793425	−	0.608669i	$-0.791704\pi$
$619$	−39.4803	−1.58685	−0.793425	+	0.608669i	$0.791704\pi$
$620$	−12.9327	−0.519392
$621$	38.9256	1.56203
$622$	−31.6605	−1.26947
$623$	9.39380	0.376354
$624$	35.7270	1.43022
$625$	1.00000	0.0400000
$626$	41.3152	1.65129
$627$	22.2665	0.889240
$628$	24.7682	0.988359
$629$	−3.99617	−0.159338
$630$	−8.96075	−0.357005
$631$	−36.8086	−1.46533	−0.732665	−	0.680590i	$-0.761724\pi$
$631$	−36.8086	−1.46533	−0.732665	+	0.680590i	$0.761724\pi$
$632$	5.64834	0.224679
$633$	30.9853	1.23155
$634$	−12.5845	−0.499793
$635$	0.245096	0.00972633
$636$	19.4307	0.770478
$637$	2.64111	0.104645
$638$	−21.0483	−0.833309
$639$	39.1993	1.55070
$640$	−8.28547	−0.327512
$641$	47.6562	1.88231	0.941154	−	0.337979i	$-0.109743\pi$
$641$	47.6562	1.88231	0.941154	+	0.337979i	$0.109743\pi$
$642$	−90.4873	−3.57125
$643$	−0.999936	−0.0394336	−0.0197168	−	0.999806i	$-0.506276\pi$
$643$	−0.999936	−0.0394336	−0.0197168	+	0.999806i	$0.506276\pi$
$644$	−10.6259	−0.418717
$645$	11.2589	0.443319
$646$	54.4285	2.14146
$647$	−49.2219	−1.93511	−0.967557	−	0.252654i	$-0.918696\pi$
$647$	−49.2219	−1.93511	−0.967557	+	0.252654i	$0.918696\pi$
$648$	−0.0342132	−0.00134402
$649$	2.81485	0.110493
$650$	−4.88028	−0.191420
$651$	25.6174	1.00402
$652$	15.8250	0.619755
$653$	23.4820	0.918920	0.459460	−	0.888198i	$-0.348043\pi$
$653$	23.4820	0.918920	0.459460	+	0.888198i	$0.348043\pi$
$654$	49.5642	1.93811
$655$	−5.46386	−0.213491
$656$	42.0832	1.64307
$657$	−51.2053	−1.99771
$658$	16.7265	0.652066
$659$	2.00359	0.0780487	0.0390243	−	0.999238i	$-0.487575\pi$
$659$	2.00359	0.0780487	0.0390243	+	0.999238i	$0.487575\pi$
$660$	5.96269	0.232097
$661$	41.7029	1.62205	0.811027	−	0.585009i	$-0.198909\pi$
$661$	41.7029	1.62205	0.811027	+	0.585009i	$0.198909\pi$
$662$	−24.7163	−0.960625
$663$	41.2656	1.60262
$664$	−4.26365	−0.165462
$665$	5.28184	0.204821
$666$	−6.42102	−0.248810
$667$	56.8720	2.20209
$668$	−28.6758	−1.10950
$669$	43.3242	1.67501
$670$	3.58059	0.138330
$671$	−14.3238	−0.552964
$672$	−18.9326	−0.730340
$673$	10.5001	0.404747	0.202374	−	0.979308i	$-0.435134\pi$
$673$	10.5001	0.404747	0.202374	+	0.979308i	$0.435134\pi$
$674$	34.9387	1.34579
$675$	−5.18138	−0.199431
$676$	−8.52113	−0.327736
$677$	5.71219	0.219537	0.109769	−	0.993957i	$-0.464989\pi$
$677$	5.71219	0.219537	0.109769	+	0.993957i	$0.464989\pi$
$678$	−12.3755	−0.475277
$679$	2.81635	0.108081
$680$	−6.03445	−0.231411
$681$	40.7940	1.56323
$682$	−25.4228	−0.973491
$683$	−49.9792	−1.91240	−0.956201	−	0.292710i	$-0.905443\pi$
$683$	−49.9792	−1.91240	−0.956201	+	0.292710i	$0.905443\pi$
$684$	36.2281	1.38522
$685$	3.66496	0.140031
$686$	−1.84781	−0.0705498
$687$	−2.80168	−0.106891
$688$	19.4031	0.739734
$689$	−12.9504	−0.493372
$690$	−38.8924	−1.48061
$691$	27.7825	1.05690	0.528448	−	0.848965i	$-0.322774\pi$
$691$	27.7825	1.05690	0.528448	+	0.848965i	$0.322774\pi$
$692$	21.3089	0.810041
$693$	−7.29687	−0.277185
$694$	23.5359	0.893410
$695$	15.3650	0.582828
$696$	22.9499	0.869914
$697$	48.6073	1.84113
$698$	−9.57287	−0.362338
$699$	−30.0733	−1.13748
$700$	1.41441	0.0534595
$701$	17.2609	0.651934	0.325967	−	0.945381i	$-0.394310\pi$
$701$	17.2609	0.651934	0.325967	+	0.945381i	$0.394310\pi$
$702$	25.2866	0.954380
$703$	3.78482	0.142747
$704$	4.25864	0.160503
$705$	25.3609	0.955147
$706$	−14.6855	−0.552695
$707$	0.859285	0.0323167
$708$	7.41306	0.278600
$709$	−7.63149	−0.286607	−0.143303	−	0.989679i	$-0.545772\pi$
$709$	−7.63149	−0.286607	−0.143303	+	0.989679i	$0.545772\pi$
$710$	−14.9365	−0.560557
$711$	25.3136	0.949333
$712$	10.1647	0.380939
$713$	68.6920	2.57254
$714$	−28.8708	−1.08046
$715$	−3.97408	−0.148622
$716$	−10.9440	−0.408995
$717$	8.91255	0.332845
$718$	52.0939	1.94413
$719$	−12.8603	−0.479607	−0.239804	−	0.970821i	$-0.577083\pi$
$719$	−12.8603	−0.479607	−0.239804	+	0.970821i	$0.577083\pi$
$720$	−23.4141	−0.872593
$721$	1.29693	0.0483002
$722$	−16.4414	−0.611887
$723$	47.1849	1.75483
$724$	6.69657	0.248876
$725$	−7.57023	−0.281151
$726$	−45.2254	−1.67847
$727$	39.4100	1.46164	0.730819	−	0.682571i	$-0.239138\pi$
$727$	39.4100	1.46164	0.730819	+	0.682571i	$0.239138\pi$
$728$	2.85786	0.105919
$729$	−43.7029	−1.61863
$730$	19.5113	0.722145
$731$	22.4111	0.828903
$732$	−37.7225	−1.39426
$733$	−11.1567	−0.412083	−0.206041	−	0.978543i	$-0.566058\pi$
$733$	−11.1567	−0.412083	−0.206041	+	0.978543i	$0.566058\pi$
$734$	32.9007	1.21439
$735$	−2.80168	−0.103341
$736$	−50.7670	−1.87130
$737$	2.91573	0.107402
$738$	78.1019	2.87497
$739$	22.0433	0.810877	0.405438	−	0.914122i	$-0.367119\pi$
$739$	22.0433	0.810877	0.405438	+	0.914122i	$0.367119\pi$
$740$	1.01352	0.0372579
$741$	−39.0832	−1.43576
$742$	9.06055	0.332623
$743$	41.3072	1.51541	0.757706	−	0.652596i	$-0.226320\pi$
$743$	41.3072	1.51541	0.757706	+	0.652596i	$0.226320\pi$
$744$	27.7197	1.01625
$745$	19.5944	0.717884
$746$	26.0462	0.953619
$747$	−19.1080	−0.699123
$748$	11.8688	0.433967
$749$	−17.4788	−0.638662
$750$	5.17697	0.189036
$751$	22.0894	0.806053	0.403026	−	0.915188i	$-0.367958\pi$
$751$	22.0894	0.806053	0.403026	+	0.915188i	$0.367958\pi$
$752$	43.7057	1.59378
$753$	19.3786	0.706197
$754$	36.9448	1.34545
$755$	19.5529	0.711602
$756$	−7.32857	−0.266538
$757$	37.8995	1.37748	0.688741	−	0.725008i	$-0.258164\pi$
$757$	37.8995	1.37748	0.688741	+	0.725008i	$0.258164\pi$
$758$	69.8051	2.53543
$759$	−31.6707	−1.14957
$760$	5.71530	0.207316
$761$	−44.2860	−1.60537	−0.802684	−	0.596405i	$-0.796595\pi$
$761$	−44.2860	−1.60537	−0.802684	+	0.596405i	$0.796595\pi$
$762$	1.26885	0.0459657
$763$	9.57399	0.346602
$764$	8.71553	0.315317
$765$	−27.0440	−0.977777
$766$	−29.1475	−1.05314
$767$	−4.94075	−0.178400
$768$	−58.7523	−2.12004
$769$	−16.8764	−0.608580	−0.304290	−	0.952579i	$-0.598419\pi$
$769$	−16.8764	−0.608580	−0.304290	+	0.952579i	$0.598419\pi$
$770$	2.78040	0.100199
$771$	−8.24341	−0.296879
$772$	−28.3436	−1.02011
$773$	−34.0856	−1.22597	−0.612987	−	0.790093i	$-0.710032\pi$
$773$	−34.0856	−1.22597	−0.612987	+	0.790093i	$0.710032\pi$
$774$	36.0100	1.29435
$775$	−9.14359	−0.328447
$776$	3.04748	0.109398
$777$	−2.00760	−0.0720224
$778$	−47.8137	−1.71420
$779$	−46.0365	−1.64943
$780$	−10.4660	−0.374741
$781$	−12.1630	−0.435227
$782$	−77.4160	−2.76839
$783$	39.2242	1.40176
$784$	−4.82827	−0.172438
$785$	17.5114	0.625008
$786$	−28.2862	−1.00894
$787$	2.05249	0.0731635	0.0365818	−	0.999331i	$-0.488353\pi$
$787$	2.05249	0.0731635	0.0365818	+	0.999331i	$0.488353\pi$
$788$	9.04579	0.322243
$789$	−26.5916	−0.946684
$790$	−9.64549	−0.343171
$791$	−2.39048	−0.0849959
$792$	−7.89570	−0.280561
$793$	25.1417	0.892809
$794$	−14.3419	−0.508976
$795$	13.7377	0.487227
$796$	−14.9010	−0.528152
$797$	−56.2629	−1.99293	−0.996466	−	0.0839923i	$-0.973233\pi$
$797$	−56.2629	−1.99293	−0.996466	+	0.0839923i	$0.973233\pi$
$798$	27.3439	0.967963
$799$	50.4813	1.78590
$800$	6.75759	0.238917
$801$	45.5541	1.60958
$802$	43.1059	1.52212
$803$	15.8883	0.560687
$804$	7.67873	0.270808
$805$	−7.51259	−0.264784
$806$	44.6232	1.57179
$807$	−34.2124	−1.20433
$808$	0.929804	0.0327104
$809$	−26.8246	−0.943102	−0.471551	−	0.881839i	$-0.656306\pi$
$809$	−26.8246	−0.943102	−0.471551	+	0.881839i	$0.656306\pi$
$810$	0.0584248	0.00205284
$811$	−24.1795	−0.849059	−0.424529	−	0.905414i	$-0.639560\pi$
$811$	−24.1795	−0.849059	−0.424529	+	0.905414i	$0.639560\pi$
$812$	−10.7074	−0.375755
$813$	−67.7042	−2.37449
$814$	1.99236	0.0698321
$815$	11.1884	0.391914
$816$	−75.4385	−2.64087
$817$	−21.2258	−0.742596
$818$	53.1154	1.85714
$819$	12.8078	0.447540
$820$	−12.3280	−0.430511
$821$	−7.94543	−0.277297	−0.138649	−	0.990342i	$-0.544276\pi$
$821$	−7.94543	−0.277297	−0.138649	+	0.990342i	$0.544276\pi$
$822$	18.9734	0.661773
$823$	0.0691044	0.00240883	0.00120441	−	0.999999i	$-0.499617\pi$
$823$	0.0691044	0.00240883	0.00120441	+	0.999999i	$0.499617\pi$
$824$	1.40337	0.0488886
$825$	4.21568	0.146771
$826$	3.45671	0.120274
$827$	48.1159	1.67315	0.836576	−	0.547850i	$-0.184554\pi$
$827$	48.1159	1.67315	0.836576	+	0.547850i	$0.184554\pi$
$828$	−51.5289	−1.79075
$829$	−20.3884	−0.708119	−0.354060	−	0.935223i	$-0.615199\pi$
$829$	−20.3884	−0.708119	−0.354060	+	0.935223i	$0.615199\pi$
$830$	7.28090	0.252724
$831$	18.2206	0.632064
$832$	−7.47494	−0.259147
$833$	−5.57678	−0.193224
$834$	79.5442	2.75439
$835$	−20.2741	−0.701613
$836$	−11.2411	−0.388782
$837$	47.3764	1.63757
$838$	51.4139	1.77606
$839$	−30.0692	−1.03810	−0.519052	−	0.854743i	$-0.673715\pi$
$839$	−30.0692	−1.03810	−0.519052	+	0.854743i	$0.673715\pi$
$840$	−3.03160	−0.104600
$841$	28.3084	0.976151
$842$	−54.4850	−1.87768
$843$	−19.2128	−0.661724
$844$	−15.6427	−0.538444
$845$	−6.02453	−0.207250
$846$	81.1131	2.78873
$847$	−8.73588	−0.300168
$848$	23.6749	0.812999
$849$	74.0942	2.54291
$850$	10.3048	0.353453
$851$	−5.38331	−0.184538
$852$	−32.0319	−1.09740
$853$	−6.95912	−0.238276	−0.119138	−	0.992878i	$-0.538013\pi$
$853$	−6.95912	−0.238276	−0.119138	+	0.992878i	$0.538013\pi$
$854$	−17.5900	−0.601918
$855$	25.6137	0.875969
$856$	−18.9133	−0.646442
$857$	32.1074	1.09677	0.548384	−	0.836227i	$-0.315243\pi$
$857$	32.1074	1.09677	0.548384	+	0.836227i	$0.315243\pi$
$858$	−20.5737	−0.702374
$859$	25.0190	0.853638	0.426819	−	0.904337i	$-0.359634\pi$
$859$	25.0190	0.853638	0.426819	+	0.904337i	$0.359634\pi$
$860$	−5.68399	−0.193822
$861$	24.4194	0.832211
$862$	−70.2656	−2.39326
$863$	−8.24030	−0.280503	−0.140252	−	0.990116i	$-0.544791\pi$
$863$	−8.24030	−0.280503	−0.140252	+	0.990116i	$0.544791\pi$
$864$	−35.0136	−1.19119
$865$	15.0656	0.512245
$866$	−36.2704	−1.23252
$867$	−39.5050	−1.34166
$868$	−12.9327	−0.438966
$869$	−7.85447	−0.266445
$870$	−39.1908	−1.32869
$871$	−5.11781	−0.173410
$872$	10.3597	0.350824
$873$	13.6576	0.462238
$874$	73.3216	2.48014
$875$	1.00000	0.0338062
$876$	41.8427	1.41374
$877$	53.3104	1.80016	0.900082	−	0.435720i	$-0.143506\pi$
$877$	53.3104	1.80016	0.900082	+	0.435720i	$0.143506\pi$
$878$	−39.7383	−1.34110
$879$	−86.7185	−2.92494
$880$	7.26509	0.244906
$881$	−55.0053	−1.85318	−0.926588	−	0.376079i	$-0.877272\pi$
$881$	−55.0053	−1.85318	−0.926588	+	0.376079i	$0.877272\pi$
$882$	−8.96075	−0.301724
$883$	8.81754	0.296734	0.148367	−	0.988932i	$-0.452598\pi$
$883$	8.81754	0.296734	0.148367	+	0.988932i	$0.452598\pi$
$884$	−20.8327	−0.700678
$885$	5.24111	0.176178
$886$	−5.73410	−0.192641
$887$	−27.2321	−0.914364	−0.457182	−	0.889373i	$-0.651141\pi$
$887$	−27.2321	−0.914364	−0.457182	+	0.889373i	$0.651141\pi$
$888$	−2.17236	−0.0728996
$889$	0.245096	0.00822025
$890$	−17.3580	−0.581840
$891$	0.0475762	0.00159386
$892$	−21.8719	−0.732327
$893$	−47.8114	−1.59995
$894$	101.440	3.39265
$895$	−7.73749	−0.258636
$896$	−8.28547	−0.276798
$897$	55.5897	1.85609
$898$	−16.5703	−0.552960
$899$	69.2191	2.30858
$900$	6.85900	0.228633
$901$	27.3452	0.911000
$902$	−24.2340	−0.806904
$903$	11.2589	0.374673
$904$	−2.58666	−0.0860312
$905$	4.73454	0.157382
$906$	101.225	3.36296
$907$	−7.25001	−0.240733	−0.120366	−	0.992730i	$-0.538407\pi$
$907$	−7.25001	−0.240733	−0.120366	+	0.992730i	$0.538407\pi$
$908$	−20.5946	−0.683455
$909$	4.16700	0.138211
$910$	−4.88028	−0.161780
$911$	9.78287	0.324121	0.162060	−	0.986781i	$-0.448186\pi$
$911$	9.78287	0.324121	0.162060	+	0.986781i	$0.448186\pi$
$912$	71.4487	2.36590
$913$	5.92895	0.196219
$914$	−23.9499	−0.792194
$915$	−26.6702	−0.881689
$916$	1.41441	0.0467333
$917$	−5.46386	−0.180433
$918$	−53.3933	−1.76224
$919$	33.2592	1.09712	0.548559	−	0.836112i	$-0.315176\pi$
$919$	33.2592	1.09712	0.548559	+	0.836112i	$0.315176\pi$
$920$	−8.12912	−0.268009
$921$	−68.9104	−2.27068
$922$	−62.1468	−2.04670
$923$	21.3490	0.702712
$924$	5.96269	0.196158
$925$	0.716572	0.0235608
$926$	−64.2908	−2.11273
$927$	6.28932	0.206568
$928$	−51.1565	−1.67930
$929$	−37.0764	−1.21644	−0.608218	−	0.793770i	$-0.708115\pi$
$929$	−37.0764	−1.21644	−0.608218	+	0.793770i	$0.708115\pi$
$930$	−47.3361	−1.55221
$931$	5.28184	0.173105
$932$	15.1823	0.497313
$933$	−48.0041	−1.57158
$934$	−22.5295	−0.737189
$935$	8.39139	0.274428
$936$	13.8589	0.452991
$937$	−21.8967	−0.715335	−0.357667	−	0.933849i	$-0.616428\pi$
$937$	−21.8967	−0.715335	−0.357667	+	0.933849i	$0.616428\pi$
$938$	3.58059	0.116910
$939$	62.6427	2.04427
$940$	−12.8033	−0.417597
$941$	1.63707	0.0533671	0.0266835	−	0.999644i	$-0.491505\pi$
$941$	1.63707	0.0533671	0.0266835	+	0.999644i	$0.491505\pi$
$942$	90.6558	2.95373
$943$	65.4798	2.13231
$944$	9.03227	0.293975
$945$	−5.18138	−0.168550
$946$	−11.1734	−0.363279
$947$	−7.05454	−0.229242	−0.114621	−	0.993409i	$-0.536565\pi$
$947$	−7.05454	−0.229242	−0.114621	+	0.993409i	$0.536565\pi$
$948$	−20.6852	−0.671823
$949$	−27.8878	−0.905278
$950$	−9.75984	−0.316651
$951$	−19.0807	−0.618735
$952$	−6.03445	−0.195578
$953$	30.6763	0.993703	0.496851	−	0.867836i	$-0.334489\pi$
$953$	30.6763	0.993703	0.496851	+	0.867836i	$0.334489\pi$
$954$	43.9381	1.42255
$955$	6.16197	0.199397
$956$	−4.49944	−0.145522
$957$	−31.9137	−1.03162
$958$	−65.8622	−2.12791
$959$	3.66496	0.118348
$960$	7.92936	0.255919
$961$	52.6052	1.69694
$962$	−3.49707	−0.112750
$963$	−84.7616	−2.73140
$964$	−23.8210	−0.767222
$965$	−20.0392	−0.645086
$966$	−38.8924	−1.25134
$967$	−15.0126	−0.482773	−0.241386	−	0.970429i	$-0.577602\pi$
$967$	−15.0126	−0.482773	−0.241386	+	0.970429i	$0.577602\pi$
$968$	−9.45280	−0.303825
$969$	82.5252	2.65109
$970$	−5.20408	−0.167093
$971$	55.0967	1.76814	0.884069	−	0.467357i	$-0.154794\pi$
$971$	55.0967	1.76814	0.884069	+	0.467357i	$0.154794\pi$
$972$	22.1110	0.709211
$973$	15.3650	0.492580
$974$	−2.38832	−0.0765267
$975$	−7.39954	−0.236975
$976$	−45.9621	−1.47121
$977$	6.87085	0.219818	0.109909	−	0.993942i	$-0.464944\pi$
$977$	6.87085	0.219818	0.109909	+	0.993942i	$0.464944\pi$
$978$	57.9222	1.85215
$979$	−14.1348	−0.451752
$980$	1.41441	0.0451816
$981$	46.4280	1.48233
$982$	−44.9580	−1.43467
$983$	44.7573	1.42754	0.713768	−	0.700382i	$-0.246987\pi$
$983$	44.7573	1.42754	0.713768	+	0.700382i	$0.246987\pi$
$984$	26.4234	0.842348
$985$	6.39547	0.203777
$986$	−78.0100	−2.48434
$987$	25.3609	0.807246
$988$	19.7309	0.627722
$989$	30.1904	0.959998
$990$	13.4832	0.428525
$991$	−3.87009	−0.122938	−0.0614688	−	0.998109i	$-0.519578\pi$
$991$	−3.87009	−0.122938	−0.0614688	+	0.998109i	$0.519578\pi$
$992$	−61.7886	−1.96179
$993$	−37.4751	−1.18924
$994$	−14.9365	−0.473757
$995$	−10.5352	−0.333987
$996$	15.6142	0.494755
$997$	−28.6488	−0.907318	−0.453659	−	0.891175i	$-0.649882\pi$
$997$	−28.6488	−0.907318	−0.453659	+	0.891175i	$0.649882\pi$
$998$	14.4198	0.456449
$999$	−3.71283	−0.117469

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.o.1.16	✓	73

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.o.1.16	✓	73	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:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q-1.84781 q^{2} -2.80168 q^{3} +1.41441 q^{4} +1.00000 q^{5} +5.17697 q^{6} +1.00000 q^{7} +1.08207 q^{8} +4.84939 q^{9} +O(q^{10})\)	\(q-1.84781 q^{2} -2.80168 q^{3} +1.41441 q^{4} +1.00000 q^{5} +5.17697 q^{6} +1.00000 q^{7} +1.08207 q^{8} +4.84939 q^{9} -1.84781 q^{10} -1.50470 q^{11} -3.96271 q^{12} +2.64111 q^{13} -1.84781 q^{14} -2.80168 q^{15} -4.82827 q^{16} -5.57678 q^{17} -8.96075 q^{18} +5.28184 q^{19} +1.41441 q^{20} -2.80168 q^{21} +2.78040 q^{22} -7.51259 q^{23} -3.03160 q^{24} +1.00000 q^{25} -4.88028 q^{26} -5.18138 q^{27} +1.41441 q^{28} -7.57023 q^{29} +5.17697 q^{30} -9.14359 q^{31} +6.75759 q^{32} +4.21568 q^{33} +10.3048 q^{34} +1.00000 q^{35} +6.85900 q^{36} +0.716572 q^{37} -9.75984 q^{38} -7.39954 q^{39} +1.08207 q^{40} -8.71600 q^{41} +5.17697 q^{42} -4.01864 q^{43} -2.12826 q^{44} +4.84939 q^{45} +13.8818 q^{46} -9.05205 q^{47} +13.5272 q^{48} +1.00000 q^{49} -1.84781 q^{50} +15.6243 q^{51} +3.73561 q^{52} -4.90340 q^{53} +9.57421 q^{54} -1.50470 q^{55} +1.08207 q^{56} -14.7980 q^{57} +13.9884 q^{58} -1.87071 q^{59} -3.96271 q^{60} +9.51937 q^{61} +16.8956 q^{62} +4.84939 q^{63} -2.83022 q^{64} +2.64111 q^{65} -7.78978 q^{66} -1.93775 q^{67} -7.88784 q^{68} +21.0478 q^{69} -1.84781 q^{70} +8.08335 q^{71} +5.24736 q^{72} -10.5591 q^{73} -1.32409 q^{74} -2.80168 q^{75} +7.47066 q^{76} -1.50470 q^{77} +13.6730 q^{78} +5.21995 q^{79} -4.82827 q^{80} -0.0316184 q^{81} +16.1055 q^{82} -3.94028 q^{83} -3.96271 q^{84} -5.57678 q^{85} +7.42568 q^{86} +21.2093 q^{87} -1.62819 q^{88} +9.39380 q^{89} -8.96075 q^{90} +2.64111 q^{91} -10.6259 q^{92} +25.6174 q^{93} +16.7265 q^{94} +5.28184 q^{95} -18.9326 q^{96} +2.81635 q^{97} -1.84781 q^{98} -7.29687 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 73 q + 7 q^{2} + 14 q^{3} + 95 q^{4} + 73 q^{5} - q^{6} + 73 q^{7} + 18 q^{8} + 111 q^{9}+O(q^{10}) \) 73 * q + 7 * q^2 + 14 * q^3 + 95 * q^4 + 73 * q^5 - q^6 + 73 * q^7 + 18 * q^8 + 111 * q^9	\( 73 q + 7 q^{2} + 14 q^{3} + 95 q^{4} + 73 q^{5} - q^{6} + 73 q^{7} + 18 q^{8} + 111 q^{9} + 7 q^{10} + 27 q^{11} + 21 q^{12} + 21 q^{13} + 7 q^{14} + 14 q^{15} + 135 q^{16} + 23 q^{17} + 41 q^{18} + 26 q^{19} + 95 q^{20} + 14 q^{21} + 48 q^{22} + 16 q^{23} - q^{24} + 73 q^{25} + 7 q^{26} + 44 q^{27} + 95 q^{28} + 66 q^{29} - q^{30} + 23 q^{31} + 3 q^{32} + 77 q^{33} + 29 q^{34} + 73 q^{35} + 142 q^{36} + 66 q^{37} - 12 q^{38} + 53 q^{39} + 18 q^{40} + 50 q^{41} - q^{42} + 43 q^{43} + 37 q^{44} + 111 q^{45} + 65 q^{46} + 28 q^{47} - 20 q^{48} + 73 q^{49} + 7 q^{50} + 71 q^{51} + 29 q^{52} - 7 q^{53} - 16 q^{54} + 27 q^{55} + 18 q^{56} + 33 q^{57} + 48 q^{58} + 16 q^{59} + 21 q^{60} + 42 q^{61} - 3 q^{62} + 111 q^{63} + 216 q^{64} + 21 q^{65} - 53 q^{66} + 48 q^{67} + 13 q^{68} + 73 q^{69} + 7 q^{70} + 68 q^{71} + 18 q^{72} + 65 q^{73} + 4 q^{74} + 14 q^{75} + 37 q^{76} + 27 q^{77} + 60 q^{78} + 116 q^{79} + 135 q^{80} + 177 q^{81} + 20 q^{82} + 40 q^{83} + 21 q^{84} + 23 q^{85} + 35 q^{86} - 14 q^{87} + 47 q^{88} + 59 q^{89} + 41 q^{90} + 21 q^{91} + 3 q^{92} + 37 q^{93} - 11 q^{94} + 26 q^{95} - 23 q^{96} + 70 q^{97} + 7 q^{98} + 49 q^{99}+O(q^{100}) \) 73 * q + 7 * q^2 + 14 * q^3 + 95 * q^4 + 73 * q^5 - q^6 + 73 * q^7 + 18 * q^8 + 111 * q^9 + 7 * q^10 + 27 * q^11 + 21 * q^12 + 21 * q^13 + 7 * q^14 + 14 * q^15 + 135 * q^16 + 23 * q^17 + 41 * q^18 + 26 * q^19 + 95 * q^20 + 14 * q^21 + 48 * q^22 + 16 * q^23 - q^24 + 73 * q^25 + 7 * q^26 + 44 * q^27 + 95 * q^28 + 66 * q^29 - q^30 + 23 * q^31 + 3 * q^32 + 77 * q^33 + 29 * q^34 + 73 * q^35 + 142 * q^36 + 66 * q^37 - 12 * q^38 + 53 * q^39 + 18 * q^40 + 50 * q^41 - q^42 + 43 * q^43 + 37 * q^44 + 111 * q^45 + 65 * q^46 + 28 * q^47 - 20 * q^48 + 73 * q^49 + 7 * q^50 + 71 * q^51 + 29 * q^52 - 7 * q^53 - 16 * q^54 + 27 * q^55 + 18 * q^56 + 33 * q^57 + 48 * q^58 + 16 * q^59 + 21 * q^60 + 42 * q^61 - 3 * q^62 + 111 * q^63 + 216 * q^64 + 21 * q^65 - 53 * q^66 + 48 * q^67 + 13 * q^68 + 73 * q^69 + 7 * q^70 + 68 * q^71 + 18 * q^72 + 65 * q^73 + 4 * q^74 + 14 * q^75 + 37 * q^76 + 27 * q^77 + 60 * q^78 + 116 * q^79 + 135 * q^80 + 177 * q^81 + 20 * q^82 + 40 * q^83 + 21 * q^84 + 23 * q^85 + 35 * q^86 - 14 * q^87 + 47 * q^88 + 59 * q^89 + 41 * q^90 + 21 * q^91 + 3 * q^92 + 37 * q^93 - 11 * q^94 + 26 * q^95 - 23 * q^96 + 70 * q^97 + 7 * q^98 + 49 * q^99

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