LMFDB - Embedded newform 8015.2.a.j.1.9

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:	$1$
Dimension:	$45$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
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)

$f(q)$	$=$	$q-1.81008 q^{2} -0.874461 q^{3} +1.27639 q^{4} -1.00000 q^{5} +1.58284 q^{6} +1.00000 q^{7} +1.30979 q^{8} -2.23532 q^{9} +O(q^{10})$	\(q-1.81008 q^{2} -0.874461 q^{3} +1.27639 q^{4} -1.00000 q^{5} +1.58284 q^{6} +1.00000 q^{7} +1.30979 q^{8} -2.23532 q^{9} +1.81008 q^{10} -4.01850 q^{11} -1.11615 q^{12} +3.22334 q^{13} -1.81008 q^{14} +0.874461 q^{15} -4.92361 q^{16} +1.62762 q^{17} +4.04611 q^{18} -4.71112 q^{19} -1.27639 q^{20} -0.874461 q^{21} +7.27380 q^{22} +0.483762 q^{23} -1.14536 q^{24} +1.00000 q^{25} -5.83451 q^{26} +4.57808 q^{27} +1.27639 q^{28} -7.46967 q^{29} -1.58284 q^{30} -3.28056 q^{31} +6.29254 q^{32} +3.51402 q^{33} -2.94613 q^{34} -1.00000 q^{35} -2.85314 q^{36} +8.72622 q^{37} +8.52751 q^{38} -2.81869 q^{39} -1.30979 q^{40} +2.50441 q^{41} +1.58284 q^{42} +3.80858 q^{43} -5.12917 q^{44} +2.23532 q^{45} -0.875648 q^{46} +6.39494 q^{47} +4.30550 q^{48} +1.00000 q^{49} -1.81008 q^{50} -1.42329 q^{51} +4.11424 q^{52} +4.28606 q^{53} -8.28669 q^{54} +4.01850 q^{55} +1.30979 q^{56} +4.11969 q^{57} +13.5207 q^{58} +5.68214 q^{59} +1.11615 q^{60} +0.252679 q^{61} +5.93808 q^{62} -2.23532 q^{63} -1.54279 q^{64} -3.22334 q^{65} -6.36065 q^{66} -12.9071 q^{67} +2.07748 q^{68} -0.423031 q^{69} +1.81008 q^{70} +6.03880 q^{71} -2.92780 q^{72} -16.2460 q^{73} -15.7952 q^{74} -0.874461 q^{75} -6.01323 q^{76} -4.01850 q^{77} +5.10205 q^{78} -11.9266 q^{79} +4.92361 q^{80} +2.70260 q^{81} -4.53318 q^{82} +5.95693 q^{83} -1.11615 q^{84} -1.62762 q^{85} -6.89383 q^{86} +6.53193 q^{87} -5.26340 q^{88} +1.33647 q^{89} -4.04611 q^{90} +3.22334 q^{91} +0.617469 q^{92} +2.86872 q^{93} -11.5754 q^{94} +4.71112 q^{95} -5.50258 q^{96} -9.36924 q^{97} -1.81008 q^{98} +8.98262 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 45 q - 6 q^{2} + 34 q^{4} - 45 q^{5} + q^{6} + 45 q^{7} - 15 q^{8} + 29 q^{9}+O(q^{10}) $ 45 * q - 6 * q^2 + 34 * q^4 - 45 * q^5 + q^6 + 45 * q^7 - 15 * q^8 + 29 * q^9	\( 45 q - 6 q^{2} + 34 q^{4} - 45 q^{5} + q^{6} + 45 q^{7} - 15 q^{8} + 29 q^{9} + 6 q^{10} - q^{11} - 3 q^{12} - 21 q^{13} - 6 q^{14} + 8 q^{16} - 7 q^{17} - 36 q^{18} - 20 q^{19} - 34 q^{20} - 34 q^{22} - 22 q^{23} - 11 q^{24} + 45 q^{25} - q^{26} + 12 q^{27} + 34 q^{28} + 10 q^{29} - q^{30} - 27 q^{31} - 26 q^{32} - 39 q^{33} - 13 q^{34} - 45 q^{35} - 3 q^{36} - 72 q^{37} + 2 q^{38} - 37 q^{39} + 15 q^{40} - 4 q^{41} + q^{42} - 49 q^{43} + 5 q^{44} - 29 q^{45} - 67 q^{46} + 2 q^{47} + 8 q^{48} + 45 q^{49} - 6 q^{50} - 49 q^{51} - 47 q^{52} - 35 q^{53} - 12 q^{54} + q^{55} - 15 q^{56} - 77 q^{57} - 50 q^{58} + 4 q^{59} + 3 q^{60} - 36 q^{61} + 17 q^{62} + 29 q^{63} + 5 q^{64} + 21 q^{65} - 8 q^{66} - 80 q^{67} + 27 q^{68} + 9 q^{69} + 6 q^{70} - 12 q^{71} - 97 q^{72} - 55 q^{73} + 32 q^{74} - 37 q^{76} - q^{77} + 20 q^{78} - 94 q^{79} - 8 q^{80} - 19 q^{81} - 36 q^{82} + 24 q^{83} - 3 q^{84} + 7 q^{85} - 3 q^{86} - 4 q^{87} - 95 q^{88} + q^{89} + 36 q^{90} - 21 q^{91} - 65 q^{92} - 71 q^{93} - 53 q^{94} + 20 q^{95} - 13 q^{96} - 110 q^{97} - 6 q^{98} - 27 q^{99}+O(q^{100}) \) 45 * q - 6 * q^2 + 34 * q^4 - 45 * q^5 + q^6 + 45 * q^7 - 15 * q^8 + 29 * q^9 + 6 * q^10 - q^11 - 3 * q^12 - 21 * q^13 - 6 * q^14 + 8 * q^16 - 7 * q^17 - 36 * q^18 - 20 * q^19 - 34 * q^20 - 34 * q^22 - 22 * q^23 - 11 * q^24 + 45 * q^25 - q^26 + 12 * q^27 + 34 * q^28 + 10 * q^29 - q^30 - 27 * q^31 - 26 * q^32 - 39 * q^33 - 13 * q^34 - 45 * q^35 - 3 * q^36 - 72 * q^37 + 2 * q^38 - 37 * q^39 + 15 * q^40 - 4 * q^41 + q^42 - 49 * q^43 + 5 * q^44 - 29 * q^45 - 67 * q^46 + 2 * q^47 + 8 * q^48 + 45 * q^49 - 6 * q^50 - 49 * q^51 - 47 * q^52 - 35 * q^53 - 12 * q^54 + q^55 - 15 * q^56 - 77 * q^57 - 50 * q^58 + 4 * q^59 + 3 * q^60 - 36 * q^61 + 17 * q^62 + 29 * q^63 + 5 * q^64 + 21 * q^65 - 8 * q^66 - 80 * q^67 + 27 * q^68 + 9 * q^69 + 6 * q^70 - 12 * q^71 - 97 * q^72 - 55 * q^73 + 32 * q^74 - 37 * q^76 - q^77 + 20 * q^78 - 94 * q^79 - 8 * q^80 - 19 * q^81 - 36 * q^82 + 24 * q^83 - 3 * q^84 + 7 * q^85 - 3 * q^86 - 4 * q^87 - 95 * q^88 + q^89 + 36 * q^90 - 21 * q^91 - 65 * q^92 - 71 * q^93 - 53 * q^94 + 20 * q^95 - 13 * q^96 - 110 * q^97 - 6 * q^98 - 27 * 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 $

$2$	−1.81008	−1.27992	−0.639960	−	0.768408i	$-0.721049\pi$
$2$	−1.81008	−1.27992	−0.639960	+	0.768408i	$0.721049\pi$
$3$	−0.874461	−0.504870	−0.252435	−	0.967614i	$-0.581231\pi$
$3$	−0.874461	−0.504870	−0.252435	+	0.967614i	$0.581231\pi$
$4$	1.27639	0.638195
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.58284	0.646193
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.30979	0.463081
$9$	−2.23532	−0.745106
$10$	1.81008	0.572398
$11$	−4.01850	−1.21162	−0.605811	−	0.795608i	$-0.707151\pi$
$11$	−4.01850	−1.21162	−0.605811	+	0.795608i	$0.707151\pi$
$12$	−1.11615	−0.322206
$13$	3.22334	0.893994	0.446997	−	0.894535i	$-0.352493\pi$
$13$	3.22334	0.893994	0.446997	+	0.894535i	$0.352493\pi$
$14$	−1.81008	−0.483764
$15$	0.874461	0.225785
$16$	−4.92361	−1.23090
$17$	1.62762	0.394756	0.197378	−	0.980327i	$-0.436757\pi$
$17$	1.62762	0.394756	0.197378	+	0.980327i	$0.436757\pi$
$18$	4.04611	0.953676
$19$	−4.71112	−1.08081	−0.540403	−	0.841407i	$-0.681728\pi$
$19$	−4.71112	−1.08081	−0.540403	+	0.841407i	$0.681728\pi$
$20$	−1.27639	−0.285409
$21$	−0.874461	−0.190823
$22$	7.27380	1.55078
$23$	0.483762	0.100871	0.0504357	−	0.998727i	$-0.483939\pi$
$23$	0.483762	0.100871	0.0504357	+	0.998727i	$0.483939\pi$
$24$	−1.14536	−0.233796
$25$	1.00000	0.200000
$26$	−5.83451	−1.14424
$27$	4.57808	0.881052
$28$	1.27639	0.241215
$29$	−7.46967	−1.38708	−0.693541	−	0.720417i	$-0.743950\pi$
$29$	−7.46967	−1.38708	−0.693541	+	0.720417i	$0.743950\pi$
$30$	−1.58284	−0.288986
$31$	−3.28056	−0.589206	−0.294603	−	0.955620i	$-0.595187\pi$
$31$	−3.28056	−0.589206	−0.294603	+	0.955620i	$0.595187\pi$
$32$	6.29254	1.11237
$33$	3.51402	0.611712
$34$	−2.94613	−0.505256
$35$	−1.00000	−0.169031
$36$	−2.85314	−0.475523
$37$	8.72622	1.43458	0.717291	−	0.696773i	$-0.245382\pi$
$37$	8.72622	1.43458	0.717291	+	0.696773i	$0.245382\pi$
$38$	8.52751	1.38334
$39$	−2.81869	−0.451351
$40$	−1.30979	−0.207096
$41$	2.50441	0.391123	0.195562	−	0.980691i	$-0.437347\pi$
$41$	2.50441	0.391123	0.195562	+	0.980691i	$0.437347\pi$
$42$	1.58284	0.244238
$43$	3.80858	0.580803	0.290401	−	0.956905i	$-0.406211\pi$
$43$	3.80858	0.580803	0.290401	+	0.956905i	$0.406211\pi$
$44$	−5.12917	−0.773251
$45$	2.23532	0.333222
$46$	−0.875648	−0.129107
$47$	6.39494	0.932798	0.466399	−	0.884575i	$-0.345551\pi$
$47$	6.39494	0.932798	0.466399	+	0.884575i	$0.345551\pi$
$48$	4.30550	0.621446
$49$	1.00000	0.142857
$50$	−1.81008	−0.255984
$51$	−1.42329	−0.199301
$52$	4.11424	0.570543
$53$	4.28606	0.588736	0.294368	−	0.955692i	$-0.404891\pi$
$53$	4.28606	0.588736	0.294368	+	0.955692i	$0.404891\pi$
$54$	−8.28669	−1.12768
$55$	4.01850	0.541854
$56$	1.30979	0.175028
$57$	4.11969	0.545666
$58$	13.5207	1.77535
$59$	5.68214	0.739751	0.369876	−	0.929081i	$-0.379400\pi$
$59$	5.68214	0.739751	0.369876	+	0.929081i	$0.379400\pi$
$60$	1.11615	0.144095
$61$	0.252679	0.0323522	0.0161761	−	0.999869i	$-0.494851\pi$
$61$	0.252679	0.0323522	0.0161761	+	0.999869i	$0.494851\pi$
$62$	5.93808	0.754137
$63$	−2.23532	−0.281624
$64$	−1.54279	−0.192848
$65$	−3.22334	−0.399806
$66$	−6.36065	−0.782942
$67$	−12.9071	−1.57686	−0.788428	−	0.615127i	$-0.789105\pi$
$67$	−12.9071	−1.57686	−0.788428	+	0.615127i	$0.789105\pi$
$68$	2.07748	0.251931
$69$	−0.423031	−0.0509269
$70$	1.81008	0.216346
$71$	6.03880	0.716674	0.358337	−	0.933592i	$-0.383344\pi$
$71$	6.03880	0.716674	0.358337	+	0.933592i	$0.383344\pi$
$72$	−2.92780	−0.345045
$73$	−16.2460	−1.90145	−0.950723	−	0.310042i	$-0.899657\pi$
$73$	−16.2460	−1.90145	−0.950723	+	0.310042i	$0.899657\pi$
$74$	−15.7952	−1.83615
$75$	−0.874461	−0.100974
$76$	−6.01323	−0.689764
$77$	−4.01850	−0.457950
$78$	5.10205	0.577693
$79$	−11.9266	−1.34185	−0.670924	−	0.741526i	$-0.734102\pi$
$79$	−11.9266	−1.34185	−0.670924	+	0.741526i	$0.734102\pi$
$80$	4.92361	0.550476
$81$	2.70260	0.300289
$82$	−4.53318	−0.500606
$83$	5.95693	0.653858	0.326929	−	0.945049i	$-0.393986\pi$
$83$	5.95693	0.653858	0.326929	+	0.945049i	$0.393986\pi$
$84$	−1.11615	−0.121782
$85$	−1.62762	−0.176540
$86$	−6.89383	−0.743381
$87$	6.53193	0.700297
$88$	−5.26340	−0.561080
$89$	1.33647	0.141666	0.0708329	−	0.997488i	$-0.477434\pi$
$89$	1.33647	0.141666	0.0708329	+	0.997488i	$0.477434\pi$
$90$	−4.04611	−0.426497
$91$	3.22334	0.337898
$92$	0.617469	0.0643756
$93$	2.86872	0.297473
$94$	−11.5754	−1.19391
$95$	4.71112	0.483351
$96$	−5.50258	−0.561605
$97$	−9.36924	−0.951302	−0.475651	−	0.879634i	$-0.657787\pi$
$97$	−9.36924	−0.951302	−0.475651	+	0.879634i	$0.657787\pi$
$98$	−1.81008	−0.182846
$99$	8.98262	0.902787
$100$	1.27639	0.127639
$101$	−10.7801	−1.07266	−0.536328	−	0.844010i	$-0.680189\pi$
$101$	−10.7801	−1.07266	−0.536328	+	0.844010i	$0.680189\pi$
$102$	2.57627	0.255089
$103$	0.605277	0.0596397	0.0298199	−	0.999555i	$-0.490507\pi$
$103$	0.605277	0.0596397	0.0298199	+	0.999555i	$0.490507\pi$
$104$	4.22191	0.413992
$105$	0.874461	0.0853386
$106$	−7.75812	−0.753535
$107$	16.7024	1.61468	0.807342	−	0.590084i	$-0.200905\pi$
$107$	16.7024	1.61468	0.807342	+	0.590084i	$0.200905\pi$
$108$	5.84342	0.562283
$109$	1.86110	0.178261	0.0891305	−	0.996020i	$-0.471591\pi$
$109$	1.86110	0.178261	0.0891305	+	0.996020i	$0.471591\pi$
$110$	−7.27380	−0.693530
$111$	−7.63074	−0.724278
$112$	−4.92361	−0.465237
$113$	13.5136	1.27125	0.635626	−	0.771998i	$-0.280742\pi$
$113$	13.5136	1.27125	0.635626	+	0.771998i	$0.280742\pi$
$114$	−7.45697	−0.698409
$115$	−0.483762	−0.0451110
$116$	−9.53421	−0.885229
$117$	−7.20520	−0.666121
$118$	−10.2851	−0.946822
$119$	1.62762	0.149204
$120$	1.14536	0.104557
$121$	5.14832	0.468029
$122$	−0.457369	−0.0414083
$123$	−2.19001	−0.197466
$124$	−4.18727	−0.376028
$125$	−1.00000	−0.0894427
$126$	4.04611	0.360456
$127$	11.3810	1.00990	0.504952	−	0.863148i	$-0.331510\pi$
$127$	11.3810	1.00990	0.504952	+	0.863148i	$0.331510\pi$
$128$	−9.79251	−0.865544
$129$	−3.33045	−0.293230
$130$	5.83451	0.511720
$131$	10.6855	0.933599	0.466800	−	0.884363i	$-0.345407\pi$
$131$	10.6855	0.933599	0.466800	+	0.884363i	$0.345407\pi$
$132$	4.48526	0.390391
$133$	−4.71112	−0.408506
$134$	23.3629	2.01825
$135$	−4.57808	−0.394018
$136$	2.13185	0.182804
$137$	7.52657	0.643038	0.321519	−	0.946903i	$-0.395807\pi$
$137$	7.52657	0.643038	0.321519	+	0.946903i	$0.395807\pi$
$138$	0.765720	0.0651824
$139$	16.4712	1.39707	0.698535	−	0.715575i	$-0.253835\pi$
$139$	16.4712	1.39707	0.698535	+	0.715575i	$0.253835\pi$
$140$	−1.27639	−0.107875
$141$	−5.59212	−0.470942
$142$	−10.9307	−0.917285
$143$	−12.9530	−1.08318
$144$	11.0058	0.917153
$145$	7.46967	0.620322
$146$	29.4065	2.43370
$147$	−0.874461	−0.0721243
$148$	11.1381	0.915543
$149$	15.4760	1.26784	0.633921	−	0.773398i	$-0.281445\pi$
$149$	15.4760	1.26784	0.633921	+	0.773398i	$0.281445\pi$
$150$	1.58284	0.129239
$151$	−3.39937	−0.276637	−0.138319	−	0.990388i	$-0.544170\pi$
$151$	−3.39937	−0.276637	−0.138319	+	0.990388i	$0.544170\pi$
$152$	−6.17059	−0.500501
$153$	−3.63825	−0.294135
$154$	7.27380	0.586140
$155$	3.28056	0.263501
$156$	−3.59774	−0.288050
$157$	4.45043	0.355183	0.177592	−	0.984104i	$-0.443169\pi$
$157$	4.45043	0.355183	0.177592	+	0.984104i	$0.443169\pi$
$158$	21.5881	1.71746
$159$	−3.74799	−0.297235
$160$	−6.29254	−0.497469
$161$	0.483762	0.0381258
$162$	−4.89193	−0.384346
$163$	−22.6440	−1.77362	−0.886808	−	0.462139i	$-0.847082\pi$
$163$	−22.6440	−1.77362	−0.886808	+	0.462139i	$0.847082\pi$
$164$	3.19660	0.249613
$165$	−3.51402	−0.273566
$166$	−10.7825	−0.836885
$167$	−7.91185	−0.612237	−0.306119	−	0.951993i	$-0.599030\pi$
$167$	−7.91185	−0.612237	−0.306119	+	0.951993i	$0.599030\pi$
$168$	−1.14536	−0.0883666
$169$	−2.61007	−0.200775
$170$	2.94613	0.225958
$171$	10.5309	0.805315
$172$	4.86123	0.370665
$173$	−13.5017	−1.02652	−0.513258	−	0.858235i	$-0.671561\pi$
$173$	−13.5017	−1.02652	−0.513258	+	0.858235i	$0.671561\pi$
$174$	−11.8233	−0.896323
$175$	1.00000	0.0755929
$176$	19.7855	1.49139
$177$	−4.96880	−0.373478
$178$	−2.41912	−0.181321
$179$	−14.5157	−1.08495	−0.542477	−	0.840071i	$-0.682513\pi$
$179$	−14.5157	−1.08495	−0.542477	+	0.840071i	$0.682513\pi$
$180$	2.85314	0.212660
$181$	5.84697	0.434602	0.217301	−	0.976105i	$-0.430275\pi$
$181$	5.84697	0.434602	0.217301	+	0.976105i	$0.430275\pi$
$182$	−5.83451	−0.432482
$183$	−0.220958	−0.0163337
$184$	0.633628	0.0467117
$185$	−8.72622	−0.641565
$186$	−5.19262	−0.380741
$187$	−6.54059	−0.478296
$188$	8.16244	0.595307
$189$	4.57808	0.333006
$190$	−8.52751	−0.618650
$191$	−0.0232270	−0.00168065	−0.000840325	−	1.00000i	$-0.500267\pi$
$191$	−0.0232270	−0.00168065	−0.000840325		1.00000i	$0.500267\pi$
$192$	1.34911	0.0973634
$193$	2.01336	0.144925	0.0724625	−	0.997371i	$-0.476914\pi$
$193$	2.01336	0.144925	0.0724625	+	0.997371i	$0.476914\pi$
$194$	16.9591	1.21759
$195$	2.81869	0.201850
$196$	1.27639	0.0911707
$197$	6.84003	0.487332	0.243666	−	0.969859i	$-0.421650\pi$
$197$	6.84003	0.487332	0.243666	+	0.969859i	$0.421650\pi$
$198$	−16.2593	−1.15550
$199$	0.129125	0.00915345	0.00457673	−	0.999990i	$-0.498543\pi$
$199$	0.129125	0.00915345	0.00457673	+	0.999990i	$0.498543\pi$
$200$	1.30979	0.0926163
$201$	11.2868	0.796108
$202$	19.5128	1.37291
$203$	−7.46967	−0.524268
$204$	−1.81667	−0.127193
$205$	−2.50441	−0.174916
$206$	−1.09560	−0.0763341
$207$	−1.08136	−0.0751599
$208$	−15.8705	−1.10042
$209$	18.9316	1.30953
$210$	−1.58284	−0.109227
$211$	2.68950	0.185153	0.0925764	−	0.995706i	$-0.470490\pi$
$211$	2.68950	0.185153	0.0925764	+	0.995706i	$0.470490\pi$
$212$	5.47069	0.375728
$213$	−5.28069	−0.361827
$214$	−30.2327	−2.06667
$215$	−3.80858	−0.259743
$216$	5.99633	0.407999
$217$	−3.28056	−0.222699
$218$	−3.36874	−0.228160
$219$	14.2065	0.959983
$220$	5.12917	0.345808
$221$	5.24638	0.352910
$222$	13.8123	0.927018
$223$	25.7005	1.72103	0.860517	−	0.509422i	$-0.170141\pi$
$223$	25.7005	1.72103	0.860517	+	0.509422i	$0.170141\pi$
$224$	6.29254	0.420438
$225$	−2.23532	−0.149021
$226$	−24.4607	−1.62710
$227$	4.55014	0.302003	0.151002	−	0.988534i	$-0.451750\pi$
$227$	4.55014	0.302003	0.151002	+	0.988534i	$0.451750\pi$
$228$	5.25833	0.348241
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	0.875648	0.0577385
$231$	3.51402	0.231205
$232$	−9.78371	−0.642332
$233$	−8.07378	−0.528931	−0.264465	−	0.964395i	$-0.585195\pi$
$233$	−8.07378	−0.528931	−0.264465	+	0.964395i	$0.585195\pi$
$234$	13.0420	0.852581
$235$	−6.39494	−0.417160
$236$	7.25262	0.472105
$237$	10.4294	0.677459
$238$	−2.94613	−0.190969
$239$	2.72101	0.176008	0.0880039	−	0.996120i	$-0.471951\pi$
$239$	2.72101	0.176008	0.0880039	+	0.996120i	$0.471951\pi$
$240$	−4.30550	−0.277919
$241$	−26.1242	−1.68281	−0.841405	−	0.540405i	$-0.818271\pi$
$241$	−26.1242	−1.68281	−0.841405	+	0.540405i	$0.818271\pi$
$242$	−9.31886	−0.599039
$243$	−16.0976	−1.03266
$244$	0.322517	0.0206470
$245$	−1.00000	−0.0638877
$246$	3.96409	0.252741
$247$	−15.1856	−0.966233
$248$	−4.29685	−0.272850
$249$	−5.20910	−0.330113
$250$	1.81008	0.114480
$251$	−10.4049	−0.656752	−0.328376	−	0.944547i	$-0.606501\pi$
$251$	−10.4049	−0.656752	−0.328376	+	0.944547i	$0.606501\pi$
$252$	−2.85314	−0.179731
$253$	−1.94400	−0.122218
$254$	−20.6006	−1.29260
$255$	1.42329	0.0891300
$256$	20.8108	1.30068
$257$	14.4170	0.899306	0.449653	−	0.893203i	$-0.351548\pi$
$257$	14.4170	0.899306	0.449653	+	0.893203i	$0.351548\pi$
$258$	6.02838	0.375311
$259$	8.72622	0.542221
$260$	−4.11424	−0.255154
$261$	16.6971	1.03352
$262$	−19.3417	−1.19493
$263$	17.8752	1.10223	0.551115	−	0.834429i	$-0.314202\pi$
$263$	17.8752	1.10223	0.551115	+	0.834429i	$0.314202\pi$
$264$	4.60263	0.283272
$265$	−4.28606	−0.263291
$266$	8.52751	0.522855
$267$	−1.16869	−0.0715228
$268$	−16.4745	−1.00634
$269$	−22.8377	−1.39244	−0.696219	−	0.717830i	$-0.745136\pi$
$269$	−22.8377	−1.39244	−0.696219	+	0.717830i	$0.745136\pi$
$270$	8.28669	0.504312
$271$	2.25200	0.136799	0.0683997	−	0.997658i	$-0.478211\pi$
$271$	2.25200	0.136799	0.0683997	+	0.997658i	$0.478211\pi$
$272$	−8.01377	−0.485906
$273$	−2.81869	−0.170595
$274$	−13.6237	−0.823037
$275$	−4.01850	−0.242324
$276$	−0.539952	−0.0325013
$277$	8.33479	0.500789	0.250394	−	0.968144i	$-0.419440\pi$
$277$	8.33479	0.500789	0.250394	+	0.968144i	$0.419440\pi$
$278$	−29.8142	−1.78814
$279$	7.33310	0.439021
$280$	−1.30979	−0.0782751
$281$	13.5285	0.807042	0.403521	−	0.914970i	$-0.367786\pi$
$281$	13.5285	0.807042	0.403521	+	0.914970i	$0.367786\pi$
$282$	10.1222	0.602768
$283$	24.5719	1.46065	0.730324	−	0.683101i	$-0.239369\pi$
$283$	24.5719	1.46065	0.730324	+	0.683101i	$0.239369\pi$
$284$	7.70787	0.457378
$285$	−4.11969	−0.244029
$286$	23.4459	1.38639
$287$	2.50441	0.147831
$288$	−14.0658	−0.828837
$289$	−14.3508	−0.844167
$290$	−13.5207	−0.793963
$291$	8.19303	0.480284
$292$	−20.7362	−1.21349
$293$	−0.468510	−0.0273707	−0.0136853	−	0.999906i	$-0.504356\pi$
$293$	−0.468510	−0.0273707	−0.0136853	+	0.999906i	$0.504356\pi$
$294$	1.58284	0.0923133
$295$	−5.68214	−0.330827
$296$	11.4295	0.664329
$297$	−18.3970	−1.06750
$298$	−28.0128	−1.62274
$299$	1.55933	0.0901784
$300$	−1.11615	−0.0644411
$301$	3.80858	0.219523
$302$	6.15314	0.354073
$303$	9.42673	0.541552
$304$	23.1957	1.33037
$305$	−0.252679	−0.0144684
$306$	6.58553	0.376470
$307$	17.6182	1.00553	0.502763	−	0.864424i	$-0.332317\pi$
$307$	17.6182	1.00553	0.502763	+	0.864424i	$0.332317\pi$
$308$	−5.12917	−0.292262
$309$	−0.529291	−0.0301103
$310$	−5.93808	−0.337260
$311$	25.8012	1.46305	0.731527	−	0.681813i	$-0.238808\pi$
$311$	25.8012	1.46305	0.731527	+	0.681813i	$0.238808\pi$
$312$	−3.69189	−0.209012
$313$	−4.60262	−0.260155	−0.130078	−	0.991504i	$-0.541523\pi$
$313$	−4.60262	−0.260155	−0.130078	+	0.991504i	$0.541523\pi$
$314$	−8.05564	−0.454606
$315$	2.23532	0.125946
$316$	−15.2230	−0.856361
$317$	0.0843270	0.00473627	0.00236814	−	0.999997i	$-0.499246\pi$
$317$	0.0843270	0.00473627	0.00236814	+	0.999997i	$0.499246\pi$
$318$	6.78417	0.380437
$319$	30.0168	1.68062
$320$	1.54279	0.0862444
$321$	−14.6056	−0.815205
$322$	−0.875648	−0.0487980
$323$	−7.66792	−0.426655
$324$	3.44958	0.191643
$325$	3.22334	0.178799
$326$	40.9875	2.27009
$327$	−1.62746	−0.0899986
$328$	3.28026	0.181122
$329$	6.39494	0.352564
$330$	6.36065	0.350142
$331$	−7.65590	−0.420806	−0.210403	−	0.977615i	$-0.567478\pi$
$331$	−7.65590	−0.420806	−0.210403	+	0.977615i	$0.567478\pi$
$332$	7.60336	0.417289
$333$	−19.5059	−1.06892
$334$	14.3211	0.783615
$335$	12.9071	0.705192
$336$	4.30550	0.234884
$337$	19.6087	1.06815	0.534077	−	0.845436i	$-0.320659\pi$
$337$	19.6087	1.06815	0.534077	+	0.845436i	$0.320659\pi$
$338$	4.72443	0.256975
$339$	−11.8171	−0.641817
$340$	−2.07748	−0.112667
$341$	13.1829	0.713895
$342$	−19.0617	−1.03074
$343$	1.00000	0.0539949
$344$	4.98844	0.268959
$345$	0.423031	0.0227752
$346$	24.4392	1.31386
$347$	15.6138	0.838194	0.419097	−	0.907942i	$-0.362347\pi$
$347$	15.6138	0.838194	0.419097	+	0.907942i	$0.362347\pi$
$348$	8.33729	0.446926
$349$	−15.6247	−0.836369	−0.418184	−	0.908362i	$-0.637333\pi$
$349$	−15.6247	−0.836369	−0.418184	+	0.908362i	$0.637333\pi$
$350$	−1.81008	−0.0967529
$351$	14.7567	0.787655
$352$	−25.2866	−1.34778
$353$	−28.1925	−1.50053	−0.750267	−	0.661134i	$-0.770075\pi$
$353$	−28.1925	−1.50053	−0.750267	+	0.661134i	$0.770075\pi$
$354$	8.99393	0.478022
$355$	−6.03880	−0.320506
$356$	1.70586	0.0904104
$357$	−1.42329	−0.0753286
$358$	26.2745	1.38865
$359$	21.5247	1.13603	0.568015	−	0.823018i	$-0.307712\pi$
$359$	21.5247	1.13603	0.568015	+	0.823018i	$0.307712\pi$
$360$	2.92780	0.154309
$361$	3.19466	0.168140
$362$	−10.5835	−0.556255
$363$	−4.50200	−0.236294
$364$	4.11424	0.215645
$365$	16.2460	0.850352
$366$	0.399952	0.0209058
$367$	19.1072	0.997388	0.498694	−	0.866778i	$-0.333813\pi$
$367$	19.1072	0.997388	0.498694	+	0.866778i	$0.333813\pi$
$368$	−2.38186	−0.124163
$369$	−5.59815	−0.291428
$370$	15.7952	0.821152
$371$	4.28606	0.222521
$372$	3.66161	0.189845
$373$	−24.2926	−1.25782	−0.628912	−	0.777477i	$-0.716499\pi$
$373$	−24.2926	−1.25782	−0.628912	+	0.777477i	$0.716499\pi$
$374$	11.8390	0.612180
$375$	0.874461	0.0451570
$376$	8.37604	0.431961
$377$	−24.0773	−1.24004
$378$	−8.28669	−0.426221
$379$	−29.2165	−1.50075	−0.750377	−	0.661011i	$-0.770128\pi$
$379$	−29.2165	−1.50075	−0.750377	+	0.661011i	$0.770128\pi$
$380$	6.01323	0.308472
$381$	−9.95227	−0.509870
$382$	0.0420428	0.00215110
$383$	−6.41231	−0.327654	−0.163827	−	0.986489i	$-0.552384\pi$
$383$	−6.41231	−0.327654	−0.163827	+	0.986489i	$0.552384\pi$
$384$	8.56317	0.436987
$385$	4.01850	0.204802
$386$	−3.64434	−0.185492
$387$	−8.51338	−0.432760
$388$	−11.9588	−0.607116
$389$	14.5689	0.738671	0.369336	−	0.929296i	$-0.379585\pi$
$389$	14.5689	0.738671	0.369336	+	0.929296i	$0.379585\pi$
$390$	−5.10205	−0.258352
$391$	0.787382	0.0398196
$392$	1.30979	0.0661545
$393$	−9.34408	−0.471346
$394$	−12.3810	−0.623746
$395$	11.9266	0.600093
$396$	11.4653	0.576154
$397$	−21.7284	−1.09052	−0.545258	−	0.838268i	$-0.683568\pi$
$397$	−21.7284	−1.09052	−0.545258	+	0.838268i	$0.683568\pi$
$398$	−0.233727	−0.0117157
$399$	4.11969	0.206242
$400$	−4.92361	−0.246180
$401$	−20.2231	−1.00989	−0.504946	−	0.863151i	$-0.668488\pi$
$401$	−20.2231	−1.00989	−0.504946	+	0.863151i	$0.668488\pi$
$402$	−20.4300	−1.01895
$403$	−10.5744	−0.526747
$404$	−13.7596	−0.684563
$405$	−2.70260	−0.134293
$406$	13.5207	0.671021
$407$	−35.0663	−1.73817
$408$	−1.86422	−0.0922924
$409$	−25.1107	−1.24164	−0.620822	−	0.783951i	$-0.713201\pi$
$409$	−25.1107	−1.24164	−0.620822	+	0.783951i	$0.713201\pi$
$410$	4.53318	0.223878
$411$	−6.58169	−0.324651
$412$	0.772570	0.0380618
$413$	5.68214	0.279600
$414$	1.95735	0.0961986
$415$	−5.95693	−0.292414
$416$	20.2830	0.994456
$417$	−14.4034	−0.705339
$418$	−34.2678	−1.67609
$419$	−6.11541	−0.298757	−0.149379	−	0.988780i	$-0.547727\pi$
$419$	−6.11541	−0.298757	−0.149379	+	0.988780i	$0.547727\pi$
$420$	1.11615	0.0544627
$421$	22.1431	1.07919	0.539594	−	0.841925i	$-0.318578\pi$
$421$	22.1431	1.07919	0.539594	+	0.841925i	$0.318578\pi$
$422$	−4.86821	−0.236981
$423$	−14.2947	−0.695033
$424$	5.61385	0.272633
$425$	1.62762	0.0789513
$426$	9.55848	0.463110
$427$	0.252679	0.0122280
$428$	21.3188	1.03048
$429$	11.3269	0.546867
$430$	6.89383	0.332450
$431$	18.7639	0.903825	0.451913	−	0.892062i	$-0.350742\pi$
$431$	18.7639	0.903825	0.451913	+	0.892062i	$0.350742\pi$
$432$	−22.5407	−1.08449
$433$	9.41204	0.452314	0.226157	−	0.974091i	$-0.427384\pi$
$433$	9.41204	0.452314	0.226157	+	0.974091i	$0.427384\pi$
$434$	5.93808	0.285037
$435$	−6.53193	−0.313182
$436$	2.37549	0.113765
$437$	−2.27906	−0.109022
$438$	−25.7148	−1.22870
$439$	−2.97633	−0.142052	−0.0710262	−	0.997474i	$-0.522627\pi$
$439$	−2.97633	−0.142052	−0.0710262	+	0.997474i	$0.522627\pi$
$440$	5.26340	0.250923
$441$	−2.23532	−0.106444
$442$	−9.49637	−0.451696
$443$	5.99596	0.284877	0.142438	−	0.989804i	$-0.454506\pi$
$443$	5.99596	0.284877	0.142438	+	0.989804i	$0.454506\pi$
$444$	−9.73980	−0.462230
$445$	−1.33647	−0.0633549
$446$	−46.5200	−2.20278
$447$	−13.5331	−0.640095
$448$	−1.54279	−0.0728898
$449$	2.04036	0.0962906	0.0481453	−	0.998840i	$-0.484669\pi$
$449$	2.04036	0.0962906	0.0481453	+	0.998840i	$0.484669\pi$
$450$	4.04611	0.190735
$451$	−10.0640	−0.473894
$452$	17.2486	0.811306
$453$	2.97262	0.139666
$454$	−8.23611	−0.386540
$455$	−3.22334	−0.151113
$456$	5.39594	0.252688
$457$	−15.6296	−0.731122	−0.365561	−	0.930787i	$-0.619123\pi$
$457$	−15.6296	−0.731122	−0.365561	+	0.930787i	$0.619123\pi$
$458$	−1.81008	−0.0845795
$459$	7.45138	0.347801
$460$	−0.617469	−0.0287896
$461$	−22.7407	−1.05914	−0.529570	−	0.848266i	$-0.677647\pi$
$461$	−22.7407	−1.05914	−0.529570	+	0.848266i	$0.677647\pi$
$462$	−6.36065	−0.295924
$463$	−1.52816	−0.0710194	−0.0355097	−	0.999369i	$-0.511305\pi$
$463$	−1.52816	−0.0710194	−0.0355097	+	0.999369i	$0.511305\pi$
$464$	36.7777	1.70736
$465$	−2.86872	−0.133034
$466$	14.6142	0.676989
$467$	−12.7375	−0.589421	−0.294711	−	0.955587i	$-0.595223\pi$
$467$	−12.7375	−0.589421	−0.294711	+	0.955587i	$0.595223\pi$
$468$	−9.19664	−0.425115
$469$	−12.9071	−0.595996
$470$	11.5754	0.533931
$471$	−3.89173	−0.179321
$472$	7.44242	0.342565
$473$	−15.3048	−0.703713
$474$	−18.8780	−0.867093
$475$	−4.71112	−0.216161
$476$	2.07748	0.0952212
$477$	−9.58072	−0.438671
$478$	−4.92525	−0.225276
$479$	−25.5612	−1.16792	−0.583961	−	0.811782i	$-0.698498\pi$
$479$	−25.5612	−1.16792	−0.583961	+	0.811782i	$0.698498\pi$
$480$	5.50258	0.251157
$481$	28.1276	1.28251
$482$	47.2869	2.15386
$483$	−0.423031	−0.0192486
$484$	6.57126	0.298694
$485$	9.36924	0.425435
$486$	29.1379	1.32172
$487$	41.0269	1.85911	0.929553	−	0.368687i	$-0.120193\pi$
$487$	41.0269	1.85911	0.929553	+	0.368687i	$0.120193\pi$
$488$	0.330957	0.0149817
$489$	19.8013	0.895445
$490$	1.81008	0.0817711
$491$	−29.7183	−1.34117	−0.670584	−	0.741834i	$-0.733956\pi$
$491$	−29.7183	−1.34117	−0.670584	+	0.741834i	$0.733956\pi$
$492$	−2.79530	−0.126022
$493$	−12.1578	−0.547560
$494$	27.4871	1.23670
$495$	−8.98262	−0.403739
$496$	16.1522	0.725255
$497$	6.03880	0.270877
$498$	9.42889	0.422518
$499$	18.3899	0.823243	0.411621	−	0.911355i	$-0.364963\pi$
$499$	18.3899	0.823243	0.411621	+	0.911355i	$0.364963\pi$
$500$	−1.27639	−0.0570819
$501$	6.91860	0.309100
$502$	18.8337	0.840590
$503$	−24.7186	−1.10215	−0.551074	−	0.834456i	$-0.685782\pi$
$503$	−24.7186	−1.10215	−0.551074	+	0.834456i	$0.685782\pi$
$504$	−2.92780	−0.130415
$505$	10.7801	0.479706
$506$	3.51879	0.156429
$507$	2.28240	0.101365
$508$	14.5266	0.644515
$509$	−0.963641	−0.0427126	−0.0213563	−	0.999772i	$-0.506798\pi$
$509$	−0.963641	−0.0427126	−0.0213563	+	0.999772i	$0.506798\pi$
$510$	−2.57627	−0.114079
$511$	−16.2460	−0.718679
$512$	−18.0842	−0.799216
$513$	−21.5679	−0.952246
$514$	−26.0959	−1.15104
$515$	−0.605277	−0.0266717
$516$	−4.25095	−0.187138
$517$	−25.6980	−1.13020
$518$	−15.7952	−0.694000
$519$	11.8067	0.518257
$520$	−4.22191	−0.185143
$521$	5.88228	0.257708	0.128854	−	0.991664i	$-0.458870\pi$
$521$	5.88228	0.257708	0.128854	+	0.991664i	$0.458870\pi$
$522$	−30.2231	−1.32283
$523$	19.9366	0.871768	0.435884	−	0.900003i	$-0.356436\pi$
$523$	19.9366	0.871768	0.435884	+	0.900003i	$0.356436\pi$
$524$	13.6389	0.595818
$525$	−0.874461	−0.0381646
$526$	−32.3555	−1.41077
$527$	−5.33951	−0.232593
$528$	−17.3016	−0.752958
$529$	−22.7660	−0.989825
$530$	7.75812	0.336991
$531$	−12.7014	−0.551193
$532$	−6.01323	−0.260706
$533$	8.07257	0.349662
$534$	2.11543	0.0915435
$535$	−16.7024	−0.722108
$536$	−16.9056	−0.730213
$537$	12.6934	0.547760
$538$	41.3380	1.78221
$539$	−4.01850	−0.173089
$540$	−5.84342	−0.251461
$541$	−21.9643	−0.944320	−0.472160	−	0.881513i	$-0.656526\pi$
$541$	−21.9643	−0.944320	−0.472160	+	0.881513i	$0.656526\pi$
$542$	−4.07631	−0.175092
$543$	−5.11294	−0.219417
$544$	10.2419	0.439117
$545$	−1.86110	−0.0797207
$546$	5.10205	0.218347
$547$	29.6459	1.26757	0.633784	−	0.773510i	$-0.281501\pi$
$547$	29.6459	1.26757	0.633784	+	0.773510i	$0.281501\pi$
$548$	9.60684	0.410384
$549$	−0.564818	−0.0241059
$550$	7.27380	0.310156
$551$	35.1905	1.49917
$552$	−0.554083	−0.0235833
$553$	−11.9266	−0.507171
$554$	−15.0866	−0.640970
$555$	7.63074	0.323907
$556$	21.0237	0.891604
$557$	25.8645	1.09591	0.547957	−	0.836507i	$-0.315406\pi$
$557$	25.8645	1.09591	0.547957	+	0.836507i	$0.315406\pi$
$558$	−13.2735	−0.561912
$559$	12.2763	0.519234
$560$	4.92361	0.208060
$561$	5.71949	0.241477
$562$	−24.4877	−1.03295
$563$	−3.82572	−0.161235	−0.0806175	−	0.996745i	$-0.525689\pi$
$563$	−3.82572	−0.161235	−0.0806175	+	0.996745i	$0.525689\pi$
$564$	−7.13773	−0.300553
$565$	−13.5136	−0.568521
$566$	−44.4771	−1.86951
$567$	2.70260	0.113499
$568$	7.90957	0.331878
$569$	−37.7694	−1.58338	−0.791688	−	0.610926i	$-0.790797\pi$
$569$	−37.7694	−1.58338	−0.791688	+	0.610926i	$0.790797\pi$
$570$	7.45697	0.312338
$571$	−43.8174	−1.83370	−0.916851	−	0.399229i	$-0.869278\pi$
$571$	−43.8174	−1.83370	−0.916851	+	0.399229i	$0.869278\pi$
$572$	−16.5331	−0.691282
$573$	0.0203111	0.000848510 0
$574$	−4.53318	−0.189211
$575$	0.483762	0.0201743
$576$	3.44862	0.143693
$577$	0.255681	0.0106441	0.00532206	−	0.999986i	$-0.498306\pi$
$577$	0.255681	0.0106441	0.00532206	+	0.999986i	$0.498306\pi$
$578$	25.9762	1.08047
$579$	−1.76061	−0.0731683
$580$	9.53421	0.395886
$581$	5.95693	0.247135
$582$	−14.8300	−0.614725
$583$	−17.2235	−0.713326
$584$	−21.2788	−0.880524
$585$	7.20520	0.297898
$586$	0.848041	0.0350322
$587$	−17.8804	−0.738004	−0.369002	−	0.929429i	$-0.620300\pi$
$587$	−17.8804	−0.738004	−0.369002	+	0.929429i	$0.620300\pi$
$588$	−1.11615	−0.0460294
$589$	15.4551	0.636817
$590$	10.2851	0.423432
$591$	−5.98134	−0.246040
$592$	−42.9645	−1.76583
$593$	30.4244	1.24938	0.624690	−	0.780873i	$-0.285225\pi$
$593$	30.4244	1.24938	0.624690	+	0.780873i	$0.285225\pi$
$594$	33.3000	1.36632
$595$	−1.62762	−0.0667260
$596$	19.7534	0.809130
$597$	−0.112915	−0.00462130
$598$	−2.82251	−0.115421
$599$	−37.5196	−1.53301	−0.766504	−	0.642239i	$-0.778006\pi$
$599$	−37.5196	−1.53301	−0.766504	+	0.642239i	$0.778006\pi$
$600$	−1.14536	−0.0467592
$601$	−32.5935	−1.32952	−0.664758	−	0.747058i	$-0.731466\pi$
$601$	−32.5935	−1.32952	−0.664758	+	0.747058i	$0.731466\pi$
$602$	−6.89383	−0.280972
$603$	28.8515	1.17493
$604$	−4.33893	−0.176548
$605$	−5.14832	−0.209309
$606$	−17.0631	−0.693143
$607$	−30.1057	−1.22195	−0.610977	−	0.791649i	$-0.709223\pi$
$607$	−30.1057	−1.22195	−0.610977	+	0.791649i	$0.709223\pi$
$608$	−29.6449	−1.20226
$609$	6.53193	0.264687
$610$	0.457369	0.0185183
$611$	20.6131	0.833916
$612$	−4.64383	−0.187716
$613$	9.94135	0.401527	0.200764	−	0.979640i	$-0.435658\pi$
$613$	9.94135	0.401527	0.200764	+	0.979640i	$0.435658\pi$
$614$	−31.8904	−1.28699
$615$	2.19001	0.0883097
$616$	−5.26340	−0.212068
$617$	9.20764	0.370686	0.185343	−	0.982674i	$-0.440660\pi$
$617$	9.20764	0.370686	0.185343	+	0.982674i	$0.440660\pi$
$618$	0.958059	0.0385388
$619$	30.9441	1.24375	0.621874	−	0.783117i	$-0.286372\pi$
$619$	30.9441	1.24375	0.621874	+	0.783117i	$0.286372\pi$
$620$	4.18727	0.168165
$621$	2.21470	0.0888729
$622$	−46.7023	−1.87259
$623$	1.33647	0.0535446
$624$	13.8781	0.555569
$625$	1.00000	0.0400000
$626$	8.33110	0.332978
$627$	−16.5550	−0.661141
$628$	5.68049	0.226676
$629$	14.2030	0.566310
$630$	−4.04611	−0.161201
$631$	−43.3625	−1.72623	−0.863116	−	0.505005i	$-0.831491\pi$
$631$	−43.3625	−1.72623	−0.863116	+	0.505005i	$0.831491\pi$
$632$	−15.6214	−0.621385
$633$	−2.35186	−0.0934781
$634$	−0.152639	−0.00606205
$635$	−11.3810	−0.451643
$636$	−4.78390	−0.189694
$637$	3.22334	0.127713
$638$	−54.3329	−2.15106
$639$	−13.4986	−0.533998
$640$	9.79251	0.387083
$641$	22.5695	0.891442	0.445721	−	0.895172i	$-0.352947\pi$
$641$	22.5695	0.891442	0.445721	+	0.895172i	$0.352947\pi$
$642$	26.4373	1.04340
$643$	−21.3891	−0.843504	−0.421752	−	0.906711i	$-0.638585\pi$
$643$	−21.3891	−0.843504	−0.421752	+	0.906711i	$0.638585\pi$
$644$	0.617469	0.0243317
$645$	3.33045	0.131136
$646$	13.8796	0.546084
$647$	−28.0615	−1.10321	−0.551606	−	0.834105i	$-0.685985\pi$
$647$	−28.0615	−1.10321	−0.551606	+	0.834105i	$0.685985\pi$
$648$	3.53985	0.139058
$649$	−22.8336	−0.896299
$650$	−5.83451	−0.228848
$651$	2.86872	0.112434
$652$	−28.9026	−1.13191
$653$	−9.42315	−0.368757	−0.184378	−	0.982855i	$-0.559027\pi$
$653$	−9.42315	−0.368757	−0.184378	+	0.982855i	$0.559027\pi$
$654$	2.94583	0.115191
$655$	−10.6855	−0.417518
$656$	−12.3307	−0.481434
$657$	36.3149	1.41678
$658$	−11.5754	−0.451254
$659$	16.7188	0.651271	0.325636	−	0.945495i	$-0.394422\pi$
$659$	16.7188	0.651271	0.325636	+	0.945495i	$0.394422\pi$
$660$	−4.48526	−0.174588
$661$	−26.9389	−1.04780	−0.523900	−	0.851780i	$-0.675524\pi$
$661$	−26.9389	−1.04780	−0.523900	+	0.851780i	$0.675524\pi$
$662$	13.8578	0.538598
$663$	−4.58775	−0.178174
$664$	7.80234	0.302789
$665$	4.71112	0.182689
$666$	35.3072	1.36813
$667$	−3.61354	−0.139917
$668$	−10.0986	−0.390727
$669$	−22.4741	−0.868898
$670$	−23.3629	−0.902589
$671$	−1.01539	−0.0391987
$672$	−5.50258	−0.212267
$673$	12.2961	0.473979	0.236989	−	0.971512i	$-0.423839\pi$
$673$	12.2961	0.473979	0.236989	+	0.971512i	$0.423839\pi$
$674$	−35.4933	−1.36715
$675$	4.57808	0.176210
$676$	−3.33147	−0.128133
$677$	26.4242	1.01556	0.507782	−	0.861486i	$-0.330466\pi$
$677$	26.4242	1.01556	0.507782	+	0.861486i	$0.330466\pi$
$678$	21.3899	0.821474
$679$	−9.36924	−0.359558
$680$	−2.13185	−0.0817526
$681$	−3.97892	−0.152472
$682$	−23.8621	−0.913729
$683$	1.08640	0.0415701	0.0207851	−	0.999784i	$-0.493383\pi$
$683$	1.08640	0.0415701	0.0207851	+	0.999784i	$0.493383\pi$
$684$	13.4415	0.513948
$685$	−7.52657	−0.287575
$686$	−1.81008	−0.0691092
$687$	−0.874461	−0.0333628
$688$	−18.7519	−0.714911
$689$	13.8154	0.526327
$690$	−0.765720	−0.0291505
$691$	43.5881	1.65817	0.829085	−	0.559122i	$-0.188862\pi$
$691$	43.5881	1.65817	0.829085	+	0.559122i	$0.188862\pi$
$692$	−17.2334	−0.655117
$693$	8.98262	0.341222
$694$	−28.2623	−1.07282
$695$	−16.4712	−0.624789
$696$	8.55547	0.324294
$697$	4.07623	0.154398
$698$	28.2819	1.07048
$699$	7.06020	0.267041
$700$	1.27639	0.0482430
$701$	13.6699	0.516304	0.258152	−	0.966104i	$-0.416886\pi$
$701$	13.6699	0.516304	0.258152	+	0.966104i	$0.416886\pi$
$702$	−26.7108	−1.00814
$703$	−41.1103	−1.55050
$704$	6.19969	0.233659
$705$	5.59212	0.210612
$706$	51.0307	1.92056
$707$	−10.7801	−0.405426
$708$	−6.34213	−0.238352
$709$	−16.0697	−0.603509	−0.301754	−	0.953386i	$-0.597572\pi$
$709$	−16.0697	−0.603509	−0.301754	+	0.953386i	$0.597572\pi$
$710$	10.9307	0.410222
$711$	26.6598	0.999820
$712$	1.75050	0.0656028
$713$	−1.58701	−0.0594340
$714$	2.57627	0.0964145
$715$	12.9530	0.484414
$716$	−18.5277	−0.692412
$717$	−2.37942	−0.0888611
$718$	−38.9614	−1.45403
$719$	−41.6365	−1.55278	−0.776389	−	0.630254i	$-0.782951\pi$
$719$	−41.6365	−1.55278	−0.776389	+	0.630254i	$0.782951\pi$
$720$	−11.0058	−0.410163
$721$	0.605277	0.0225417
$722$	−5.78259	−0.215206
$723$	22.8446	0.849600
$724$	7.46301	0.277361
$725$	−7.46967	−0.277417
$726$	8.14898	0.302437
$727$	−23.7643	−0.881371	−0.440685	−	0.897662i	$-0.645265\pi$
$727$	−23.7643	−0.881371	−0.440685	+	0.897662i	$0.645265\pi$
$728$	4.22191	0.156474
$729$	5.96887	0.221069
$730$	−29.4065	−1.08838
$731$	6.19892	0.229275
$732$	−0.282028	−0.0104241
$733$	−25.2499	−0.932628	−0.466314	−	0.884619i	$-0.654418\pi$
$733$	−25.2499	−0.932628	−0.466314	+	0.884619i	$0.654418\pi$
$734$	−34.5856	−1.27658
$735$	0.874461	0.0322550
$736$	3.04409	0.112207
$737$	51.8672	1.91055
$738$	10.1331	0.373005
$739$	−36.6766	−1.34917	−0.674586	−	0.738196i	$-0.735678\pi$
$739$	−36.6766	−1.34917	−0.674586	+	0.738196i	$0.735678\pi$
$740$	−11.1381	−0.409443
$741$	13.2792	0.487822
$742$	−7.75812	−0.284809
$743$	−52.4548	−1.92438	−0.962189	−	0.272382i	$-0.912188\pi$
$743$	−52.4548	−1.92438	−0.962189	+	0.272382i	$0.912188\pi$
$744$	3.75743	0.137754
$745$	−15.4760	−0.566996
$746$	43.9716	1.60991
$747$	−13.3156	−0.487193
$748$	−8.34835	−0.305246
$749$	16.7024	0.610293
$750$	−1.58284	−0.0577973
$751$	−31.3633	−1.14446	−0.572231	−	0.820093i	$-0.693922\pi$
$751$	−31.3633	−1.14446	−0.572231	+	0.820093i	$0.693922\pi$
$752$	−31.4862	−1.14818
$753$	9.09868	0.331574
$754$	43.5818	1.58716
$755$	3.39937	0.123716
$756$	5.84342	0.212523
$757$	−25.4438	−0.924769	−0.462385	−	0.886679i	$-0.653006\pi$
$757$	−25.4438	−0.924769	−0.462385	+	0.886679i	$0.653006\pi$
$758$	52.8843	1.92084
$759$	1.69995	0.0617042
$760$	6.17059	0.223831
$761$	21.4765	0.778522	0.389261	−	0.921127i	$-0.372730\pi$
$761$	21.4765	0.778522	0.389261	+	0.921127i	$0.372730\pi$
$762$	18.0144	0.652593
$763$	1.86110	0.0673763
$764$	−0.0296468	−0.00107258
$765$	3.63825	0.131541
$766$	11.6068	0.419370
$767$	18.3155	0.661333
$768$	−18.1982	−0.656672
$769$	15.4017	0.555399	0.277700	−	0.960668i	$-0.410428\pi$
$769$	15.4017	0.555399	0.277700	+	0.960668i	$0.410428\pi$
$770$	−7.27380	−0.262130
$771$	−12.6071	−0.454033
$772$	2.56983	0.0924903
$773$	−13.0737	−0.470228	−0.235114	−	0.971968i	$-0.575546\pi$
$773$	−13.0737	−0.470228	−0.235114	+	0.971968i	$0.575546\pi$
$774$	15.4099	0.553898
$775$	−3.28056	−0.117841
$776$	−12.2718	−0.440530
$777$	−7.63074	−0.273751
$778$	−26.3708	−0.945440
$779$	−11.7986	−0.422728
$780$	3.59774	0.128820
$781$	−24.2669	−0.868338
$782$	−1.42522	−0.0509659
$783$	−34.1967	−1.22209
$784$	−4.92361	−0.175843
$785$	−4.45043	−0.158843
$786$	16.9135	0.603286
$787$	−10.9963	−0.391975	−0.195988	−	0.980606i	$-0.562791\pi$
$787$	−10.9963	−0.391975	−0.195988	+	0.980606i	$0.562791\pi$
$788$	8.73055	0.311013
$789$	−15.6311	−0.556483
$790$	−21.5881	−0.768071
$791$	13.5136	0.480488
$792$	11.7654	0.418064
$793$	0.814471	0.0289227
$794$	39.3301	1.39577
$795$	3.74799	0.132928
$796$	0.164814	0.00584169
$797$	−49.8523	−1.76586	−0.882929	−	0.469506i	$-0.844432\pi$
$797$	−49.8523	−1.76586	−0.882929	+	0.469506i	$0.844432\pi$
$798$	−7.45697	−0.263974
$799$	10.4085	0.368228
$800$	6.29254	0.222475
$801$	−2.98744	−0.105556
$802$	36.6054	1.29258
$803$	65.2843	2.30383
$804$	14.4063	0.508072
$805$	−0.483762	−0.0170504
$806$	19.1405	0.674194
$807$	19.9706	0.703000
$808$	−14.1196	−0.496727
$809$	−37.1095	−1.30470	−0.652349	−	0.757918i	$-0.726217\pi$
$809$	−37.1095	−1.30470	−0.652349	+	0.757918i	$0.726217\pi$
$810$	4.89193	0.171885
$811$	−21.0538	−0.739301	−0.369650	−	0.929171i	$-0.620523\pi$
$811$	−21.0538	−0.739301	−0.369650	+	0.929171i	$0.620523\pi$
$812$	−9.53421	−0.334585
$813$	−1.96929	−0.0690660
$814$	63.4728	2.22472
$815$	22.6440	0.793185
$816$	7.00773	0.245320
$817$	−17.9427	−0.627734
$818$	45.4524	1.58921
$819$	−7.20520	−0.251770
$820$	−3.19660	−0.111630
$821$	1.74065	0.0607490	0.0303745	−	0.999539i	$-0.490330\pi$
$821$	1.74065	0.0607490	0.0303745	+	0.999539i	$0.490330\pi$
$822$	11.9134	0.415527
$823$	0.644072	0.0224509	0.0112255	−	0.999937i	$-0.496427\pi$
$823$	0.644072	0.0224509	0.0112255	+	0.999937i	$0.496427\pi$
$824$	0.792787	0.0276181
$825$	3.51402	0.122342
$826$	−10.2851	−0.357865
$827$	−16.7081	−0.580997	−0.290498	−	0.956875i	$-0.593821\pi$
$827$	−16.7081	−0.580997	−0.290498	+	0.956875i	$0.593821\pi$
$828$	−1.38024	−0.0479667
$829$	−53.7828	−1.86796	−0.933978	−	0.357331i	$-0.883687\pi$
$829$	−53.7828	−1.86796	−0.933978	+	0.357331i	$0.883687\pi$
$830$	10.7825	0.374267
$831$	−7.28845	−0.252833
$832$	−4.97293	−0.172405
$833$	1.62762	0.0563938
$834$	26.0714	0.902778
$835$	7.91185	0.273801
$836$	24.1641	0.835734
$837$	−15.0187	−0.519121
$838$	11.0694	0.382385
$839$	−19.9394	−0.688384	−0.344192	−	0.938899i	$-0.611847\pi$
$839$	−19.9394	−0.688384	−0.344192	+	0.938899i	$0.611847\pi$
$840$	1.14536	0.0395187
$841$	26.7959	0.923998
$842$	−40.0808	−1.38127
$843$	−11.8301	−0.407451
$844$	3.43285	0.118164
$845$	2.61007	0.0897891
$846$	25.8746	0.889587
$847$	5.14832	0.176898
$848$	−21.1029	−0.724677
$849$	−21.4872	−0.737438
$850$	−2.94613	−0.101051
$851$	4.22142	0.144708
$852$	−6.74023	−0.230916
$853$	13.5344	0.463411	0.231705	−	0.972786i	$-0.425570\pi$
$853$	13.5344	0.463411	0.231705	+	0.972786i	$0.425570\pi$
$854$	−0.457369	−0.0156509
$855$	−10.5309	−0.360148
$856$	21.8767	0.747730
$857$	−46.0991	−1.57471	−0.787357	−	0.616497i	$-0.788551\pi$
$857$	−46.0991	−1.57471	−0.787357	+	0.616497i	$0.788551\pi$
$858$	−20.5026	−0.699946
$859$	42.0983	1.43638	0.718188	−	0.695849i	$-0.244972\pi$
$859$	42.0983	1.43638	0.718188	+	0.695849i	$0.244972\pi$
$860$	−4.86123	−0.165767
$861$	−2.19001	−0.0746353
$862$	−33.9642	−1.15682
$863$	−10.8578	−0.369603	−0.184801	−	0.982776i	$-0.559164\pi$
$863$	−10.8578	−0.369603	−0.184801	+	0.982776i	$0.559164\pi$
$864$	28.8078	0.980060
$865$	13.5017	0.459072
$866$	−17.0365	−0.578925
$867$	12.5493	0.426195
$868$	−4.18727	−0.142125
$869$	47.9270	1.62581
$870$	11.8233	0.400848
$871$	−41.6041	−1.40970
$872$	2.43765	0.0825493
$873$	20.9432	0.708821
$874$	4.12528	0.139540
$875$	−1.00000	−0.0338062
$876$	18.1330	0.612656
$877$	−29.1601	−0.984666	−0.492333	−	0.870407i	$-0.663856\pi$
$877$	−29.1601	−0.984666	−0.492333	+	0.870407i	$0.663856\pi$
$878$	5.38739	0.181816
$879$	0.409694	0.0138186
$880$	−19.7855	−0.666969
$881$	20.8582	0.702729	0.351365	−	0.936239i	$-0.385718\pi$
$881$	20.8582	0.702729	0.351365	+	0.936239i	$0.385718\pi$
$882$	4.04611	0.136239
$883$	−2.75941	−0.0928615	−0.0464307	−	0.998922i	$-0.514785\pi$
$883$	−2.75941	−0.0928615	−0.0464307	+	0.998922i	$0.514785\pi$
$884$	6.69643	0.225225
$885$	4.96880	0.167025
$886$	−10.8532	−0.364620
$887$	47.6256	1.59911	0.799555	−	0.600593i	$-0.205069\pi$
$887$	47.6256	1.59911	0.799555	+	0.600593i	$0.205069\pi$
$888$	−9.99468	−0.335400
$889$	11.3810	0.381708
$890$	2.41912	0.0810892
$891$	−10.8604	−0.363837
$892$	32.8039	1.09835
$893$	−30.1273	−1.00817
$894$	24.4961	0.819271
$895$	14.5157	0.485206
$896$	−9.79251	−0.327145
$897$	−1.36357	−0.0455284
$898$	−3.69322	−0.123244
$899$	24.5047	0.817277
$900$	−2.85314	−0.0951046
$901$	6.97609	0.232407
$902$	18.2166	0.606546
$903$	−3.33045	−0.110830
$904$	17.7000	0.588693
$905$	−5.84697	−0.194360
$906$	−5.38068	−0.178761
$907$	43.7740	1.45349	0.726746	−	0.686906i	$-0.241032\pi$
$907$	43.7740	1.45349	0.726746	+	0.686906i	$0.241032\pi$
$908$	5.80775	0.192737
$909$	24.0969	0.799242
$910$	5.83451	0.193412
$911$	−3.75748	−0.124491	−0.0622455	−	0.998061i	$-0.519826\pi$
$911$	−3.75748	−0.124491	−0.0622455	+	0.998061i	$0.519826\pi$
$912$	−20.2837	−0.671662
$913$	−23.9379	−0.792229
$914$	28.2908	0.935778
$915$	0.220958	0.00730464
$916$	1.27639	0.0421731
$917$	10.6855	0.352867
$918$	−13.4876	−0.445157
$919$	−46.5598	−1.53587	−0.767933	−	0.640530i	$-0.778715\pi$
$919$	−46.5598	−1.53587	−0.767933	+	0.640530i	$0.778715\pi$
$920$	−0.633628	−0.0208901
$921$	−15.4065	−0.507660
$922$	41.1625	1.35561
$923$	19.4651	0.640702
$924$	4.48526	0.147554
$925$	8.72622	0.286916
$926$	2.76609	0.0908992
$927$	−1.35299	−0.0444379
$928$	−47.0032	−1.54296
$929$	20.2741	0.665172	0.332586	−	0.943073i	$-0.392079\pi$
$929$	20.2741	0.665172	0.332586	+	0.943073i	$0.392079\pi$
$930$	5.19262	0.170273
$931$	−4.71112	−0.154401
$932$	−10.3053	−0.337561
$933$	−22.5622	−0.738652
$934$	23.0559	0.754412
$935$	6.54059	0.213900
$936$	−9.43731	−0.308468
$937$	−34.4164	−1.12433	−0.562167	−	0.827023i	$-0.690032\pi$
$937$	−34.4164	−1.12433	−0.562167	+	0.827023i	$0.690032\pi$
$938$	23.3629	0.762827
$939$	4.02481	0.131345
$940$	−8.16244	−0.266229
$941$	32.3669	1.05513	0.527566	−	0.849514i	$-0.323105\pi$
$941$	32.3669	1.05513	0.527566	+	0.849514i	$0.323105\pi$
$942$	7.04434	0.229517
$943$	1.21154	0.0394531
$944$	−27.9766	−0.910561
$945$	−4.57808	−0.148925
$946$	27.7028	0.900697
$947$	12.2905	0.399388	0.199694	−	0.979858i	$-0.436005\pi$
$947$	12.2905	0.399388	0.199694	+	0.979858i	$0.436005\pi$
$948$	13.3119	0.432351
$949$	−52.3663	−1.69988
$950$	8.52751	0.276669
$951$	−0.0737406	−0.00239120
$952$	2.13185	0.0690935
$953$	−14.2159	−0.460497	−0.230248	−	0.973132i	$-0.573954\pi$
$953$	−14.2159	−0.460497	−0.230248	+	0.973132i	$0.573954\pi$
$954$	17.3419	0.561464
$955$	0.0232270	0.000751609 0
$956$	3.47307	0.112327
$957$	−26.2485	−0.848495
$958$	46.2679	1.49485
$959$	7.52657	0.243046
$960$	−1.34911	−0.0435422
$961$	−20.2379	−0.652836
$962$	−50.9132	−1.64151
$963$	−37.3352	−1.20311
$964$	−33.3447	−1.07396
$965$	−2.01336	−0.0648124
$966$	0.765720	0.0246366
$967$	−44.4875	−1.43062	−0.715310	−	0.698807i	$-0.753715\pi$
$967$	−44.4875	−1.43062	−0.715310	+	0.698807i	$0.753715\pi$
$968$	6.74322	0.216735
$969$	6.70530	0.215405
$970$	−16.9591	−0.544523
$971$	−34.5079	−1.10741	−0.553705	−	0.832713i	$-0.686786\pi$
$971$	−34.5079	−1.10741	−0.553705	+	0.832713i	$0.686786\pi$
$972$	−20.5468	−0.659038
$973$	16.4712	0.528043
$974$	−74.2620	−2.37951
$975$	−2.81869	−0.0902702
$976$	−1.24409	−0.0398224
$977$	2.37262	0.0759069	0.0379535	−	0.999280i	$-0.487916\pi$
$977$	2.37262	0.0759069	0.0379535	+	0.999280i	$0.487916\pi$
$978$	−35.8419	−1.14610
$979$	−5.37061	−0.171645
$980$	−1.27639	−0.0407728
$981$	−4.16015	−0.132823
$982$	53.7925	1.71659
$983$	19.7456	0.629788	0.314894	−	0.949127i	$-0.398031\pi$
$983$	19.7456	0.629788	0.314894	+	0.949127i	$0.398031\pi$
$984$	−2.86846	−0.0914430
$985$	−6.84003	−0.217942
$986$	22.0066	0.700832
$987$	−5.59212	−0.177999
$988$	−19.3827	−0.616645
$989$	1.84245	0.0585863
$990$	16.2593	0.516753
$991$	−40.2786	−1.27949	−0.639746	−	0.768586i	$-0.720961\pi$
$991$	−40.2786	−1.27949	−0.639746	+	0.768586i	$0.720961\pi$
$992$	−20.6431	−0.655418
$993$	6.69478	0.212453
$994$	−10.9307	−0.346701
$995$	−0.129125	−0.00409355
$996$	−6.64884	−0.210677
$997$	−43.8545	−1.38889	−0.694443	−	0.719548i	$-0.744349\pi$
$997$	−43.8545	−1.38889	−0.694443	+	0.719548i	$0.744349\pi$
$998$	−33.2871	−1.05368
$999$	39.9494	1.26394

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.j.1.9	✓	45

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.j.1.9	✓	45	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)

\(f(q)\)	\(=\)	\(q-1.81008 q^{2} -0.874461 q^{3} +1.27639 q^{4} -1.00000 q^{5} +1.58284 q^{6} +1.00000 q^{7} +1.30979 q^{8} -2.23532 q^{9} +O(q^{10})\)	\(q-1.81008 q^{2} -0.874461 q^{3} +1.27639 q^{4} -1.00000 q^{5} +1.58284 q^{6} +1.00000 q^{7} +1.30979 q^{8} -2.23532 q^{9} +1.81008 q^{10} -4.01850 q^{11} -1.11615 q^{12} +3.22334 q^{13} -1.81008 q^{14} +0.874461 q^{15} -4.92361 q^{16} +1.62762 q^{17} +4.04611 q^{18} -4.71112 q^{19} -1.27639 q^{20} -0.874461 q^{21} +7.27380 q^{22} +0.483762 q^{23} -1.14536 q^{24} +1.00000 q^{25} -5.83451 q^{26} +4.57808 q^{27} +1.27639 q^{28} -7.46967 q^{29} -1.58284 q^{30} -3.28056 q^{31} +6.29254 q^{32} +3.51402 q^{33} -2.94613 q^{34} -1.00000 q^{35} -2.85314 q^{36} +8.72622 q^{37} +8.52751 q^{38} -2.81869 q^{39} -1.30979 q^{40} +2.50441 q^{41} +1.58284 q^{42} +3.80858 q^{43} -5.12917 q^{44} +2.23532 q^{45} -0.875648 q^{46} +6.39494 q^{47} +4.30550 q^{48} +1.00000 q^{49} -1.81008 q^{50} -1.42329 q^{51} +4.11424 q^{52} +4.28606 q^{53} -8.28669 q^{54} +4.01850 q^{55} +1.30979 q^{56} +4.11969 q^{57} +13.5207 q^{58} +5.68214 q^{59} +1.11615 q^{60} +0.252679 q^{61} +5.93808 q^{62} -2.23532 q^{63} -1.54279 q^{64} -3.22334 q^{65} -6.36065 q^{66} -12.9071 q^{67} +2.07748 q^{68} -0.423031 q^{69} +1.81008 q^{70} +6.03880 q^{71} -2.92780 q^{72} -16.2460 q^{73} -15.7952 q^{74} -0.874461 q^{75} -6.01323 q^{76} -4.01850 q^{77} +5.10205 q^{78} -11.9266 q^{79} +4.92361 q^{80} +2.70260 q^{81} -4.53318 q^{82} +5.95693 q^{83} -1.11615 q^{84} -1.62762 q^{85} -6.89383 q^{86} +6.53193 q^{87} -5.26340 q^{88} +1.33647 q^{89} -4.04611 q^{90} +3.22334 q^{91} +0.617469 q^{92} +2.86872 q^{93} -11.5754 q^{94} +4.71112 q^{95} -5.50258 q^{96} -9.36924 q^{97} -1.81008 q^{98} +8.98262 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 45 q - 6 q^{2} + 34 q^{4} - 45 q^{5} + q^{6} + 45 q^{7} - 15 q^{8} + 29 q^{9}+O(q^{10}) \) 45 * q - 6 * q^2 + 34 * q^4 - 45 * q^5 + q^6 + 45 * q^7 - 15 * q^8 + 29 * q^9	\( 45 q - 6 q^{2} + 34 q^{4} - 45 q^{5} + q^{6} + 45 q^{7} - 15 q^{8} + 29 q^{9} + 6 q^{10} - q^{11} - 3 q^{12} - 21 q^{13} - 6 q^{14} + 8 q^{16} - 7 q^{17} - 36 q^{18} - 20 q^{19} - 34 q^{20} - 34 q^{22} - 22 q^{23} - 11 q^{24} + 45 q^{25} - q^{26} + 12 q^{27} + 34 q^{28} + 10 q^{29} - q^{30} - 27 q^{31} - 26 q^{32} - 39 q^{33} - 13 q^{34} - 45 q^{35} - 3 q^{36} - 72 q^{37} + 2 q^{38} - 37 q^{39} + 15 q^{40} - 4 q^{41} + q^{42} - 49 q^{43} + 5 q^{44} - 29 q^{45} - 67 q^{46} + 2 q^{47} + 8 q^{48} + 45 q^{49} - 6 q^{50} - 49 q^{51} - 47 q^{52} - 35 q^{53} - 12 q^{54} + q^{55} - 15 q^{56} - 77 q^{57} - 50 q^{58} + 4 q^{59} + 3 q^{60} - 36 q^{61} + 17 q^{62} + 29 q^{63} + 5 q^{64} + 21 q^{65} - 8 q^{66} - 80 q^{67} + 27 q^{68} + 9 q^{69} + 6 q^{70} - 12 q^{71} - 97 q^{72} - 55 q^{73} + 32 q^{74} - 37 q^{76} - q^{77} + 20 q^{78} - 94 q^{79} - 8 q^{80} - 19 q^{81} - 36 q^{82} + 24 q^{83} - 3 q^{84} + 7 q^{85} - 3 q^{86} - 4 q^{87} - 95 q^{88} + q^{89} + 36 q^{90} - 21 q^{91} - 65 q^{92} - 71 q^{93} - 53 q^{94} + 20 q^{95} - 13 q^{96} - 110 q^{97} - 6 q^{98} - 27 q^{99}+O(q^{100}) \) 45 * q - 6 * q^2 + 34 * q^4 - 45 * q^5 + q^6 + 45 * q^7 - 15 * q^8 + 29 * q^9 + 6 * q^10 - q^11 - 3 * q^12 - 21 * q^13 - 6 * q^14 + 8 * q^16 - 7 * q^17 - 36 * q^18 - 20 * q^19 - 34 * q^20 - 34 * q^22 - 22 * q^23 - 11 * q^24 + 45 * q^25 - q^26 + 12 * q^27 + 34 * q^28 + 10 * q^29 - q^30 - 27 * q^31 - 26 * q^32 - 39 * q^33 - 13 * q^34 - 45 * q^35 - 3 * q^36 - 72 * q^37 + 2 * q^38 - 37 * q^39 + 15 * q^40 - 4 * q^41 + q^42 - 49 * q^43 + 5 * q^44 - 29 * q^45 - 67 * q^46 + 2 * q^47 + 8 * q^48 + 45 * q^49 - 6 * q^50 - 49 * q^51 - 47 * q^52 - 35 * q^53 - 12 * q^54 + q^55 - 15 * q^56 - 77 * q^57 - 50 * q^58 + 4 * q^59 + 3 * q^60 - 36 * q^61 + 17 * q^62 + 29 * q^63 + 5 * q^64 + 21 * q^65 - 8 * q^66 - 80 * q^67 + 27 * q^68 + 9 * q^69 + 6 * q^70 - 12 * q^71 - 97 * q^72 - 55 * q^73 + 32 * q^74 - 37 * q^76 - q^77 + 20 * q^78 - 94 * q^79 - 8 * q^80 - 19 * q^81 - 36 * q^82 + 24 * q^83 - 3 * q^84 + 7 * q^85 - 3 * q^86 - 4 * q^87 - 95 * q^88 + q^89 + 36 * q^90 - 21 * q^91 - 65 * q^92 - 71 * q^93 - 53 * q^94 + 20 * q^95 - 13 * q^96 - 110 * q^97 - 6 * q^98 - 27 * q^99

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