LMFDB - Embedded newform 2015.4.a.d.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2015,4,Mod(1,2015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2015, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2015.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2015 = 5 \cdot 13 \cdot 31 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2015.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:	$118.888848662$
Analytic rank:	$1$
Dimension:	$40$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	2015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.566764 q^{2} -0.796068 q^{3} -7.67878 q^{4} -5.00000 q^{5} +0.451182 q^{6} -20.1270 q^{7} +8.88617 q^{8} -26.3663 q^{9} +O(q^{10})$	\(q-0.566764 q^{2} -0.796068 q^{3} -7.67878 q^{4} -5.00000 q^{5} +0.451182 q^{6} -20.1270 q^{7} +8.88617 q^{8} -26.3663 q^{9} +2.83382 q^{10} -36.7820 q^{11} +6.11283 q^{12} -13.0000 q^{13} +11.4073 q^{14} +3.98034 q^{15} +56.3939 q^{16} -12.6345 q^{17} +14.9435 q^{18} +135.516 q^{19} +38.3939 q^{20} +16.0225 q^{21} +20.8467 q^{22} -130.470 q^{23} -7.07399 q^{24} +25.0000 q^{25} +7.36793 q^{26} +42.4832 q^{27} +154.551 q^{28} +133.415 q^{29} -2.25591 q^{30} +31.0000 q^{31} -103.051 q^{32} +29.2809 q^{33} +7.16075 q^{34} +100.635 q^{35} +202.461 q^{36} +101.556 q^{37} -76.8054 q^{38} +10.3489 q^{39} -44.4308 q^{40} +79.1020 q^{41} -9.08095 q^{42} -7.44035 q^{43} +282.441 q^{44} +131.831 q^{45} +73.9459 q^{46} +168.148 q^{47} -44.8933 q^{48} +62.0963 q^{49} -14.1691 q^{50} +10.0579 q^{51} +99.8241 q^{52} +126.249 q^{53} -24.0779 q^{54} +183.910 q^{55} -178.852 q^{56} -107.880 q^{57} -75.6146 q^{58} +679.047 q^{59} -30.5641 q^{60} +643.029 q^{61} -17.5697 q^{62} +530.674 q^{63} -392.745 q^{64} +65.0000 q^{65} -16.5954 q^{66} -173.282 q^{67} +97.0172 q^{68} +103.863 q^{69} -57.0363 q^{70} +127.869 q^{71} -234.295 q^{72} -499.610 q^{73} -57.5584 q^{74} -19.9017 q^{75} -1040.60 q^{76} +740.311 q^{77} -5.86537 q^{78} -476.335 q^{79} -281.969 q^{80} +678.070 q^{81} -44.8321 q^{82} -944.154 q^{83} -123.033 q^{84} +63.1723 q^{85} +4.21692 q^{86} -106.207 q^{87} -326.851 q^{88} +541.406 q^{89} -74.7173 q^{90} +261.651 q^{91} +1001.85 q^{92} -24.6781 q^{93} -95.3004 q^{94} -677.579 q^{95} +82.0358 q^{96} -838.704 q^{97} -35.1939 q^{98} +969.803 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 5 q^{2} - 17 q^{3} + 149 q^{4} - 200 q^{5} - 35 q^{6} - 20 q^{7} - 39 q^{8} + 247 q^{9}+O(q^{10}) $ 40 * q - 5 * q^2 - 17 * q^3 + 149 * q^4 - 200 * q^5 - 35 * q^6 - 20 * q^7 - 39 * q^8 + 247 * q^9	\( 40 q - 5 q^{2} - 17 q^{3} + 149 q^{4} - 200 q^{5} - 35 q^{6} - 20 q^{7} - 39 q^{8} + 247 q^{9} + 25 q^{10} + 127 q^{11} - 76 q^{12} - 520 q^{13} + 138 q^{14} + 85 q^{15} + 413 q^{16} - 264 q^{17} - 126 q^{18} - q^{19} - 745 q^{20} + 176 q^{21} - 191 q^{22} - 106 q^{23} + 31 q^{24} + 1000 q^{25} + 65 q^{26} - 344 q^{27} + 255 q^{28} + 107 q^{29} + 175 q^{30} + 1240 q^{31} - 372 q^{32} - 386 q^{33} - 6 q^{34} + 100 q^{35} + 790 q^{36} - 741 q^{37} - 318 q^{38} + 221 q^{39} + 195 q^{40} + 1232 q^{41} - 1180 q^{42} - 615 q^{43} - 152 q^{44} - 1235 q^{45} - 329 q^{46} - 784 q^{47} - 1089 q^{48} - 516 q^{49} - 125 q^{50} - 200 q^{51} - 1937 q^{52} - 1503 q^{53} + 1658 q^{54} - 635 q^{55} + 1518 q^{56} - 1704 q^{57} - 1035 q^{58} - 107 q^{59} + 380 q^{60} - 857 q^{61} - 155 q^{62} - 2636 q^{63} - 215 q^{64} + 2600 q^{65} - 1785 q^{66} - 2689 q^{67} - 2639 q^{68} + 2544 q^{69} - 690 q^{70} + 1554 q^{71} - 420 q^{72} - 1968 q^{73} - 27 q^{74} - 425 q^{75} - 110 q^{76} - 1040 q^{77} + 455 q^{78} - 3182 q^{79} - 2065 q^{80} - 1576 q^{81} - 386 q^{82} + 317 q^{83} - 617 q^{84} + 1320 q^{85} + 347 q^{86} - 216 q^{87} - 4081 q^{88} + 3610 q^{89} + 630 q^{90} + 260 q^{91} - 4965 q^{92} - 527 q^{93} - 2942 q^{94} + 5 q^{95} + 1002 q^{96} - 3318 q^{97} + 1659 q^{98} + 5943 q^{99}+O(q^{100}) \) 40 * q - 5 * q^2 - 17 * q^3 + 149 * q^4 - 200 * q^5 - 35 * q^6 - 20 * q^7 - 39 * q^8 + 247 * q^9 + 25 * q^10 + 127 * q^11 - 76 * q^12 - 520 * q^13 + 138 * q^14 + 85 * q^15 + 413 * q^16 - 264 * q^17 - 126 * q^18 - q^19 - 745 * q^20 + 176 * q^21 - 191 * q^22 - 106 * q^23 + 31 * q^24 + 1000 * q^25 + 65 * q^26 - 344 * q^27 + 255 * q^28 + 107 * q^29 + 175 * q^30 + 1240 * q^31 - 372 * q^32 - 386 * q^33 - 6 * q^34 + 100 * q^35 + 790 * q^36 - 741 * q^37 - 318 * q^38 + 221 * q^39 + 195 * q^40 + 1232 * q^41 - 1180 * q^42 - 615 * q^43 - 152 * q^44 - 1235 * q^45 - 329 * q^46 - 784 * q^47 - 1089 * q^48 - 516 * q^49 - 125 * q^50 - 200 * q^51 - 1937 * q^52 - 1503 * q^53 + 1658 * q^54 - 635 * q^55 + 1518 * q^56 - 1704 * q^57 - 1035 * q^58 - 107 * q^59 + 380 * q^60 - 857 * q^61 - 155 * q^62 - 2636 * q^63 - 215 * q^64 + 2600 * q^65 - 1785 * q^66 - 2689 * q^67 - 2639 * q^68 + 2544 * q^69 - 690 * q^70 + 1554 * q^71 - 420 * q^72 - 1968 * q^73 - 27 * q^74 - 425 * q^75 - 110 * q^76 - 1040 * q^77 + 455 * q^78 - 3182 * q^79 - 2065 * q^80 - 1576 * q^81 - 386 * q^82 + 317 * q^83 - 617 * q^84 + 1320 * q^85 + 347 * q^86 - 216 * q^87 - 4081 * q^88 + 3610 * q^89 + 630 * q^90 + 260 * q^91 - 4965 * q^92 - 527 * q^93 - 2942 * q^94 + 5 * q^95 + 1002 * q^96 - 3318 * q^97 + 1659 * q^98 + 5943 * 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 $

$2$	−0.566764	−0.200381	−0.100191	−	0.994968i	$-0.531945\pi$
$2$	−0.566764	−0.200381	−0.100191	+	0.994968i	$0.531945\pi$
$3$	−0.796068	−0.153203	−0.0766017	−	0.997062i	$-0.524407\pi$
$3$	−0.796068	−0.153203	−0.0766017	+	0.997062i	$0.524407\pi$
$4$	−7.67878	−0.959847
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	0.451182	0.0306991
$7$	−20.1270	−1.08676	−0.543378	−	0.839488i	$-0.682855\pi$
$7$	−20.1270	−1.08676	−0.543378	+	0.839488i	$0.682855\pi$
$8$	8.88617	0.392717
$9$	−26.3663	−0.976529
$10$	2.83382	0.0896132
$11$	−36.7820	−1.00820	−0.504099	−	0.863646i	$-0.668175\pi$
$11$	−36.7820	−1.00820	−0.504099	+	0.863646i	$0.668175\pi$
$12$	6.11283	0.147052
$13$	−13.0000	−0.277350
$13$	−13.0000	−0.277350
$14$	11.4073	0.217766
$15$	3.98034	0.0685146
$16$	56.3939	0.881154
$17$	−12.6345	−0.180253	−0.0901267	−	0.995930i	$-0.528727\pi$
$17$	−12.6345	−0.180253	−0.0901267	+	0.995930i	$0.528727\pi$
$18$	14.9435	0.195678
$19$	135.516	1.63629	0.818143	−	0.575015i	$-0.195004\pi$
$19$	135.516	1.63629	0.818143	+	0.575015i	$0.195004\pi$
$20$	38.3939	0.429257
$21$	16.0225	0.166495
$22$	20.8467	0.202024
$23$	−130.470	−1.18282	−0.591412	−	0.806370i	$-0.701429\pi$
$23$	−130.470	−1.18282	−0.591412	+	0.806370i	$0.701429\pi$
$24$	−7.07399	−0.0601655
$25$	25.0000	0.200000
$26$	7.36793	0.0555758
$27$	42.4832	0.302811
$28$	154.551	1.04312
$29$	133.415	0.854292	0.427146	−	0.904183i	$-0.359519\pi$
$29$	133.415	0.854292	0.427146	+	0.904183i	$0.359519\pi$
$30$	−2.25591	−0.0137290
$31$	31.0000	0.179605
$31$	31.0000	0.179605
$32$	−103.051	−0.569284
$33$	29.2809	0.154459
$34$	7.16075	0.0361194
$35$	100.635	0.486012
$36$	202.461	0.937319
$37$	101.556	0.451236	0.225618	−	0.974216i	$-0.427560\pi$
$37$	101.556	0.451236	0.225618	+	0.974216i	$0.427560\pi$
$38$	−76.8054	−0.327881
$39$	10.3489	0.0424910
$40$	−44.4308	−0.175628
$41$	79.1020	0.301309	0.150654	−	0.988587i	$-0.451862\pi$
$41$	79.1020	0.301309	0.150654	+	0.988587i	$0.451862\pi$
$42$	−9.08095	−0.0333624
$43$	−7.44035	−0.0263870	−0.0131935	−	0.999913i	$-0.504200\pi$
$43$	−7.44035	−0.0263870	−0.0131935	+	0.999913i	$0.504200\pi$
$44$	282.441	0.967716
$45$	131.831	0.436717
$46$	73.9459	0.237016
$47$	168.148	0.521850	0.260925	−	0.965359i	$-0.415972\pi$
$47$	168.148	0.521850	0.260925	+	0.965359i	$0.415972\pi$
$48$	−44.8933	−0.134996
$49$	62.0963	0.181039
$50$	−14.1691	−0.0400763
$51$	10.0579	0.0276154
$52$	99.8241	0.266214
$53$	126.249	0.327201	0.163601	−	0.986527i	$-0.447689\pi$
$53$	126.249	0.327201	0.163601	+	0.986527i	$0.447689\pi$
$54$	−24.0779	−0.0606776
$55$	183.910	0.450880
$56$	−178.852	−0.426787
$57$	−107.880	−0.250685
$58$	−75.6146	−0.171184
$59$	679.047	1.49838	0.749190	−	0.662356i	$-0.230443\pi$
$59$	679.047	1.49838	0.749190	+	0.662356i	$0.230443\pi$
$60$	−30.5641	−0.0657636
$61$	643.029	1.34970	0.674848	−	0.737957i	$-0.264209\pi$
$61$	643.029	1.34970	0.674848	+	0.737957i	$0.264209\pi$
$62$	−17.5697	−0.0359895
$63$	530.674	1.06125
$64$	−392.745	−0.767080
$65$	65.0000	0.124035
$66$	−16.5954	−0.0309508
$67$	−173.282	−0.315966	−0.157983	−	0.987442i	$-0.550499\pi$
$67$	−173.282	−0.315966	−0.157983	+	0.987442i	$0.550499\pi$
$68$	97.0172	0.173016
$69$	103.863	0.181212
$70$	−57.0363	−0.0973877
$71$	127.869	0.213736	0.106868	−	0.994273i	$-0.465918\pi$
$71$	127.869	0.213736	0.106868	+	0.994273i	$0.465918\pi$
$72$	−234.295	−0.383499
$73$	−499.610	−0.801026	−0.400513	−	0.916291i	$-0.631168\pi$
$73$	−499.610	−0.801026	−0.400513	+	0.916291i	$0.631168\pi$
$74$	−57.5584	−0.0904192
$75$	−19.9017	−0.0306407
$76$	−1040.60	−1.57059
$77$	740.311	1.09567
$78$	−5.86537	−0.00851439
$79$	−476.335	−0.678378	−0.339189	−	0.940718i	$-0.610153\pi$
$79$	−476.335	−0.678378	−0.339189	+	0.940718i	$0.610153\pi$
$80$	−281.969	−0.394064
$81$	678.070	0.930137
$82$	−44.8321	−0.0603766
$83$	−944.154	−1.24861	−0.624303	−	0.781182i	$-0.714617\pi$
$83$	−944.154	−1.24861	−0.624303	+	0.781182i	$0.714617\pi$
$84$	−123.033	−0.159809
$85$	63.1723	0.0806117
$86$	4.21692	0.00528747
$87$	−106.207	−0.130880
$88$	−326.851	−0.395936
$89$	541.406	0.644820	0.322410	−	0.946600i	$-0.395507\pi$
$89$	541.406	0.644820	0.322410	+	0.946600i	$0.395507\pi$
$90$	−74.7173	−0.0875099
$91$	261.651	0.301412
$92$	1001.85	1.13533
$93$	−24.6781	−0.0275161
$94$	−95.3004	−0.104569
$95$	−677.579	−0.731770
$96$	82.0358	0.0872161
$97$	−838.704	−0.877912	−0.438956	−	0.898508i	$-0.644652\pi$
$97$	−838.704	−0.877912	−0.438956	+	0.898508i	$0.644652\pi$
$98$	−35.1939	−0.0362768
$99$	969.803	0.984534
$100$	−191.969	−0.191969
$101$	−389.845	−0.384070	−0.192035	−	0.981388i	$-0.561509\pi$
$101$	−389.845	−0.384070	−0.192035	+	0.981388i	$0.561509\pi$
$102$	−5.70045	−0.00553361
$103$	1610.42	1.54058	0.770288	−	0.637696i	$-0.220112\pi$
$103$	1610.42	1.54058	0.770288	+	0.637696i	$0.220112\pi$
$104$	−115.520	−0.108920
$105$	−80.1123	−0.0744587
$106$	−71.5535	−0.0655650
$107$	−179.650	−0.162312	−0.0811562	−	0.996701i	$-0.525861\pi$
$107$	−179.650	−0.162312	−0.0811562	+	0.996701i	$0.525861\pi$
$108$	−326.219	−0.290652
$109$	−2104.04	−1.84890	−0.924451	−	0.381300i	$-0.875476\pi$
$109$	−2104.04	−1.84890	−0.924451	+	0.381300i	$0.875476\pi$
$110$	−104.233	−0.0903479
$111$	−80.8456	−0.0691308
$112$	−1135.04	−0.957600
$113$	170.996	0.142353	0.0711767	−	0.997464i	$-0.477325\pi$
$113$	170.996	0.142353	0.0711767	+	0.997464i	$0.477325\pi$
$114$	61.1423	0.0502325
$115$	652.352	0.528975
$116$	−1024.46	−0.819990
$117$	342.762	0.270840
$118$	−384.859	−0.300247
$119$	254.294	0.195891
$120$	35.3700	0.0269068
$121$	21.9128	0.0164634
$122$	−364.446	−0.270454
$123$	−62.9705	−0.0461615
$124$	−238.042	−0.172394
$125$	−125.000	−0.0894427
$126$	−300.767	−0.212654
$127$	4.65852	0.00325494	0.00162747	−	0.999999i	$-0.499482\pi$
$127$	4.65852	0.00325494	0.00162747	+	0.999999i	$0.499482\pi$
$128$	1047.00	0.722992
$129$	5.92302	0.00404258
$130$	−36.8397	−0.0248542
$131$	617.206	0.411646	0.205823	−	0.978589i	$-0.434013\pi$
$131$	617.206	0.411646	0.205823	+	0.978589i	$0.434013\pi$
$132$	−224.842	−0.148257
$133$	−2727.53	−1.77824
$134$	98.2097	0.0633136
$135$	−212.416	−0.135421
$136$	−112.272	−0.0707885
$137$	1019.38	0.635707	0.317853	−	0.948140i	$-0.397038\pi$
$137$	1019.38	0.635707	0.317853	+	0.948140i	$0.397038\pi$
$138$	−58.8659	−0.0363116
$139$	−631.049	−0.385071	−0.192536	−	0.981290i	$-0.561671\pi$
$139$	−631.049	−0.385071	−0.192536	+	0.981290i	$0.561671\pi$
$140$	−772.754	−0.466497
$141$	−133.857	−0.0799492
$142$	−72.4716	−0.0428287
$143$	478.166	0.279624
$144$	−1486.90	−0.860472
$145$	−667.073	−0.382051
$146$	283.161	0.160511
$147$	−49.4328	−0.0277357
$148$	−779.827	−0.433118
$149$	−306.183	−0.168346	−0.0841729	−	0.996451i	$-0.526825\pi$
$149$	−306.183	−0.168346	−0.0841729	+	0.996451i	$0.526825\pi$
$150$	11.2796	0.00613982
$151$	1435.27	0.773515	0.386757	−	0.922182i	$-0.373595\pi$
$151$	1435.27	0.773515	0.386757	+	0.922182i	$0.373595\pi$
$152$	1204.22	0.642597
$153$	333.124	0.176023
$154$	−419.581	−0.219551
$155$	−155.000	−0.0803219
$156$	−79.4668	−0.0407848
$157$	2042.07	1.03806	0.519030	−	0.854756i	$-0.326293\pi$
$157$	2042.07	1.03806	0.519030	+	0.854756i	$0.326293\pi$
$158$	269.969	0.135934
$159$	−100.503	−0.0501283
$160$	515.257	0.254591
$161$	2625.98	1.28544
$162$	−384.306	−0.186382
$163$	795.416	0.382220	0.191110	−	0.981569i	$-0.438791\pi$
$163$	795.416	0.382220	0.191110	+	0.981569i	$0.438791\pi$
$164$	−607.407	−0.289210
$165$	−146.405	−0.0690763
$166$	535.112	0.250197
$167$	475.150	0.220169	0.110084	−	0.993922i	$-0.464888\pi$
$167$	475.150	0.220169	0.110084	+	0.993922i	$0.464888\pi$
$168$	142.378	0.0653852
$169$	169.000	0.0769231
$170$	−35.8038	−0.0161531
$171$	−3573.05	−1.59788
$172$	57.1328	0.0253275
$173$	2949.97	1.29643	0.648213	−	0.761459i	$-0.275517\pi$
$173$	2949.97	1.29643	0.648213	+	0.761459i	$0.275517\pi$
$174$	60.1943	0.0262260
$175$	−503.175	−0.217351
$176$	−2074.28	−0.888378
$177$	−540.567	−0.229557
$178$	−306.850	−0.129210
$179$	1298.76	0.542310	0.271155	−	0.962536i	$-0.412594\pi$
$179$	1298.76	0.542310	0.271155	+	0.962536i	$0.412594\pi$
$180$	−1012.30	−0.419182
$181$	1021.88	0.419646	0.209823	−	0.977739i	$-0.432711\pi$
$181$	1021.88	0.419646	0.209823	+	0.977739i	$0.432711\pi$
$182$	−148.294	−0.0603973
$183$	−511.895	−0.206778
$184$	−1159.38	−0.464515
$185$	−507.781	−0.201799
$186$	13.9867	0.00551372
$187$	464.720	0.181731
$188$	−1291.17	−0.500896
$189$	−855.059	−0.329081
$190$	384.027	0.146633
$191$	2061.50	0.780968	0.390484	−	0.920610i	$-0.372308\pi$
$191$	2061.50	0.780968	0.390484	+	0.920610i	$0.372308\pi$
$192$	312.652	0.117519
$193$	43.1485	0.0160927	0.00804637	−	0.999968i	$-0.497439\pi$
$193$	43.1485	0.0160927	0.00804637	+	0.999968i	$0.497439\pi$
$194$	475.347	0.175917
$195$	−51.7444	−0.0190025
$196$	−476.823	−0.173769
$197$	−2491.79	−0.901182	−0.450591	−	0.892730i	$-0.648787\pi$
$197$	−2491.79	−0.901182	−0.450591	+	0.892730i	$0.648787\pi$
$198$	−549.650	−0.197282
$199$	−4984.27	−1.77551	−0.887753	−	0.460320i	$-0.847735\pi$
$199$	−4984.27	−1.77551	−0.887753	+	0.460320i	$0.847735\pi$
$200$	222.154	0.0785433
$201$	137.944	0.0484070
$202$	220.950	0.0769604
$203$	−2685.24	−0.928407
$204$	−77.2323	−0.0265066
$205$	−395.510	−0.134749
$206$	−912.728	−0.308703
$207$	3440.02	1.15506
$208$	−733.120	−0.244388
$209$	−4984.53	−1.64970
$210$	45.4048	0.0149201
$211$	4721.70	1.54054	0.770272	−	0.637715i	$-0.220120\pi$
$211$	4721.70	1.54054	0.770272	+	0.637715i	$0.220120\pi$
$212$	−969.439	−0.314063
$213$	−101.793	−0.0327451
$214$	101.819	0.0325244
$215$	37.2017	0.0118006
$216$	377.513	0.118919
$217$	−623.937	−0.195187
$218$	1192.49	0.370485
$219$	397.723	0.122720
$220$	−1412.20	−0.432776
$221$	164.248	0.0499933
$222$	45.8204	0.0138525
$223$	−5325.95	−1.59934	−0.799669	−	0.600442i	$-0.794991\pi$
$223$	−5325.95	−1.59934	−0.799669	+	0.600442i	$0.794991\pi$
$224$	2074.11	0.618672
$225$	−659.157	−0.195306
$226$	−96.9142	−0.0285249
$227$	2520.93	0.737092	0.368546	−	0.929610i	$-0.379856\pi$
$227$	2520.93	0.737092	0.368546	+	0.929610i	$0.379856\pi$
$228$	828.384	0.240619
$229$	−436.059	−0.125832	−0.0629162	−	0.998019i	$-0.520040\pi$
$229$	−436.059	−0.125832	−0.0629162	+	0.998019i	$0.520040\pi$
$230$	−369.729	−0.105997
$231$	−589.338	−0.167860
$232$	1185.54	0.335495
$233$	3593.84	1.01047	0.505237	−	0.862981i	$-0.331405\pi$
$233$	3593.84	1.01047	0.505237	+	0.862981i	$0.331405\pi$
$234$	−194.265	−0.0542713
$235$	−840.742	−0.233378
$236$	−5214.25	−1.43822
$237$	379.195	0.103930
$238$	−144.125	−0.0392530
$239$	−3589.10	−0.971378	−0.485689	−	0.874132i	$-0.661431\pi$
$239$	−3589.10	−0.971378	−0.485689	+	0.874132i	$0.661431\pi$
$240$	224.467	0.0603719
$241$	2411.61	0.644587	0.322293	−	0.946640i	$-0.395546\pi$
$241$	2411.61	0.644587	0.322293	+	0.946640i	$0.395546\pi$
$242$	−12.4194	−0.00329896
$243$	−1686.84	−0.445311
$244$	−4937.68	−1.29550
$245$	−310.481	−0.0809629
$246$	35.6894	0.00924990
$247$	−1761.70	−0.453824
$248$	275.471	0.0705340
$249$	751.610	0.191291
$250$	70.8455	0.0179226
$251$	−7387.40	−1.85772	−0.928861	−	0.370428i	$-0.879211\pi$
$251$	−7387.40	−1.85772	−0.928861	+	0.370428i	$0.879211\pi$
$252$	−4074.93	−1.01864
$253$	4798.95	1.19252
$254$	−2.64028	−0.000652228 0
$255$	−50.2894	−0.0123500
$256$	2548.56	0.622206
$257$	−5135.19	−1.24640	−0.623199	−	0.782063i	$-0.714167\pi$
$257$	−5135.19	−1.24640	−0.623199	+	0.782063i	$0.714167\pi$
$258$	−3.35695	−0.000810058 0
$259$	−2044.02	−0.490383
$260$	−499.121	−0.119054
$261$	−3517.65	−0.834241
$262$	−349.810	−0.0824861
$263$	−2366.90	−0.554941	−0.277471	−	0.960734i	$-0.589496\pi$
$263$	−2366.90	−0.554941	−0.277471	+	0.960734i	$0.589496\pi$
$264$	260.195	0.0606588
$265$	−631.246	−0.146329
$266$	1545.86	0.356327
$267$	−430.996	−0.0987885
$268$	1330.59	0.303279
$269$	−7052.23	−1.59845	−0.799223	−	0.601035i	$-0.794755\pi$
$269$	−7052.23	−1.59845	−0.799223	+	0.601035i	$0.794755\pi$
$270$	120.390	0.0271359
$271$	3308.33	0.741575	0.370788	−	0.928718i	$-0.379088\pi$
$271$	3308.33	0.741575	0.370788	+	0.928718i	$0.379088\pi$
$272$	−712.506	−0.158831
$273$	−208.292	−0.0461773
$274$	−577.750	−0.127384
$275$	−919.549	−0.201640
$276$	−797.543	−0.173936
$277$	−3254.70	−0.705979	−0.352989	−	0.935627i	$-0.614835\pi$
$277$	−3254.70	−0.705979	−0.352989	+	0.935627i	$0.614835\pi$
$278$	357.656	0.0771611
$279$	−817.355	−0.175390
$280$	894.259	0.190865
$281$	3090.71	0.656144	0.328072	−	0.944653i	$-0.393601\pi$
$281$	3090.71	0.656144	0.328072	+	0.944653i	$0.393601\pi$
$282$	75.8656	0.0160203
$283$	−5152.57	−1.08229	−0.541146	−	0.840929i	$-0.682009\pi$
$283$	−5152.57	−1.08229	−0.541146	+	0.840929i	$0.682009\pi$
$284$	−981.879	−0.205154
$285$	539.399	0.112110
$286$	−271.007	−0.0560314
$287$	−1592.09	−0.327449
$288$	2717.08	0.555922
$289$	−4753.37	−0.967509
$290$	378.073	0.0765559
$291$	667.665	0.134499
$292$	3836.39	0.768863
$293$	2277.16	0.454038	0.227019	−	0.973890i	$-0.427102\pi$
$293$	2277.16	0.454038	0.227019	+	0.973890i	$0.427102\pi$
$294$	28.0167	0.00555772
$295$	−3395.23	−0.670096
$296$	902.445	0.177208
$297$	−1562.61	−0.305293
$298$	173.534	0.0337333
$299$	1696.11	0.328056
$300$	152.821	0.0294104
$301$	149.752	0.0286763
$302$	−813.460	−0.154998
$303$	310.343	0.0588408
$304$	7642.26	1.44182
$305$	−3215.15	−0.603602
$306$	−188.802	−0.0352716
$307$	971.994	0.180699	0.0903496	−	0.995910i	$-0.471202\pi$
$307$	971.994	0.180699	0.0903496	+	0.995910i	$0.471202\pi$
$308$	−5684.68	−1.05167
$309$	−1282.00	−0.236021
$310$	87.8484	0.0160950
$311$	9530.01	1.73761	0.868806	−	0.495153i	$-0.164888\pi$
$311$	9530.01	1.73761	0.868806	+	0.495153i	$0.164888\pi$
$312$	91.9619	0.0166869
$313$	2409.11	0.435051	0.217526	−	0.976055i	$-0.430201\pi$
$313$	2409.11	0.435051	0.217526	+	0.976055i	$0.430201\pi$
$314$	−1157.37	−0.208008
$315$	−2653.37	−0.474605
$316$	3657.67	0.651140
$317$	−6033.83	−1.06907	−0.534533	−	0.845148i	$-0.679512\pi$
$317$	−6033.83	−1.06907	−0.534533	+	0.845148i	$0.679512\pi$
$318$	56.9614	0.0100448
$319$	−4907.25	−0.861296
$320$	1963.73	0.343049
$321$	143.014	0.0248668
$322$	−1488.31	−0.257578
$323$	−1712.17	−0.294946
$324$	−5206.75	−0.892790
$325$	−325.000	−0.0554700
$326$	−450.813	−0.0765897
$327$	1674.96	0.283258
$328$	702.913	0.118329
$329$	−3384.32	−0.567124
$330$	82.9769	0.0138416
$331$	−3628.37	−0.602518	−0.301259	−	0.953542i	$-0.597407\pi$
$331$	−3628.37	−0.602518	−0.301259	+	0.953542i	$0.597407\pi$
$332$	7249.95	1.19847
$333$	−2677.66	−0.440645
$334$	−269.298	−0.0441177
$335$	866.408	0.141304
$336$	903.569	0.146707
$337$	7450.21	1.20427	0.602134	−	0.798395i	$-0.294317\pi$
$337$	7450.21	1.20427	0.602134	+	0.798395i	$0.294317\pi$
$338$	−95.7831	−0.0154139
$339$	−136.124	−0.0218090
$340$	−485.086	−0.0773750
$341$	−1140.24	−0.181078
$342$	2025.07	0.320185
$343$	5653.75	0.890011
$344$	−66.1162	−0.0103626
$345$	−519.316	−0.0810407
$346$	−1671.93	−0.259780
$347$	11858.5	1.83458	0.917290	−	0.398220i	$-0.130372\pi$
$347$	11858.5	1.83458	0.917290	+	0.398220i	$0.130372\pi$
$348$	815.541	0.125625
$349$	12484.8	1.91488	0.957441	−	0.288629i	$-0.0931994\pi$
$349$	12484.8	1.91488	0.957441	+	0.288629i	$0.0931994\pi$
$350$	285.181	0.0435531
$351$	−552.281	−0.0839846
$352$	3790.43	0.573951
$353$	−7343.01	−1.10716	−0.553582	−	0.832795i	$-0.686739\pi$
$353$	−7343.01	−1.10716	−0.553582	+	0.832795i	$0.686739\pi$
$354$	306.374	0.0459989
$355$	−639.346	−0.0955858
$356$	−4157.34	−0.618928
$357$	−202.435	−0.0300112
$358$	−736.087	−0.108669
$359$	−3540.74	−0.520537	−0.260269	−	0.965536i	$-0.583811\pi$
$359$	−3540.74	−0.520537	−0.260269	+	0.965536i	$0.583811\pi$
$360$	1171.48	0.171506
$361$	11505.5	1.67743
$362$	−579.166	−0.0840892
$363$	−17.4441	−0.00252225
$364$	−2009.16	−0.289309
$365$	2498.05	0.358230
$366$	290.123	0.0414344
$367$	−6499.15	−0.924394	−0.462197	−	0.886777i	$-0.652939\pi$
$367$	−6499.15	−0.924394	−0.462197	+	0.886777i	$0.652939\pi$
$368$	−7357.73	−1.04225
$369$	−2085.62	−0.294237
$370$	287.792	0.0404367
$371$	−2541.02	−0.355588
$372$	189.498	0.0264113
$373$	−9744.40	−1.35267	−0.676335	−	0.736594i	$-0.736433\pi$
$373$	−9744.40	−1.35267	−0.676335	+	0.736594i	$0.736433\pi$
$374$	−263.387	−0.0364155
$375$	99.5085	0.0137029
$376$	1494.19	0.204939
$377$	−1734.39	−0.236938
$378$	484.617	0.0659418
$379$	−9346.97	−1.26681	−0.633406	−	0.773820i	$-0.718344\pi$
$379$	−9346.97	−1.26681	−0.633406	+	0.773820i	$0.718344\pi$
$380$	5202.98	0.702387
$381$	−3.70850	−0.000498667 0
$382$	−1168.38	−0.156491
$383$	2179.40	0.290763	0.145382	−	0.989376i	$-0.453559\pi$
$383$	2179.40	0.290763	0.145382	+	0.989376i	$0.453559\pi$
$384$	−833.487	−0.110765
$385$	−3701.55	−0.489996
$386$	−24.4550	−0.00322468
$387$	196.174	0.0257677
$388$	6440.22	0.842662
$389$	−5630.83	−0.733919	−0.366959	−	0.930237i	$-0.619601\pi$
$389$	−5630.83	−0.733919	−0.366959	+	0.930237i	$0.619601\pi$
$390$	29.3269	0.00380775
$391$	1648.42	0.213208
$392$	551.798	0.0710969
$393$	−491.338	−0.0630655
$394$	1412.26	0.180580
$395$	2381.68	0.303380
$396$	−7446.91	−0.945003
$397$	−9020.04	−1.14031	−0.570154	−	0.821538i	$-0.693117\pi$
$397$	−9020.04	−1.14031	−0.570154	+	0.821538i	$0.693117\pi$
$398$	2824.91	0.355778
$399$	2171.30	0.272433
$400$	1409.85	0.176231
$401$	−4311.62	−0.536938	−0.268469	−	0.963288i	$-0.586518\pi$
$401$	−4311.62	−0.536938	−0.268469	+	0.963288i	$0.586518\pi$
$402$	−78.1816	−0.00969986
$403$	−403.000	−0.0498135
$404$	2993.54	0.368648
$405$	−3390.35	−0.415970
$406$	1521.90	0.186035
$407$	−3735.43	−0.454935
$408$	89.3760	0.0108450
$409$	8757.38	1.05874	0.529370	−	0.848391i	$-0.322428\pi$
$409$	8757.38	1.05874	0.529370	+	0.848391i	$0.322428\pi$
$410$	224.161	0.0270012
$411$	−811.499	−0.0973924
$412$	−12366.1	−1.47872
$413$	−13667.2	−1.62837
$414$	−1949.68	−0.231453
$415$	4720.77	0.558394
$416$	1339.67	0.157891
$417$	502.358	0.0589942
$418$	2825.05	0.330569
$419$	6091.39	0.710225	0.355112	−	0.934824i	$-0.384443\pi$
$419$	6091.39	0.710225	0.355112	+	0.934824i	$0.384443\pi$
$420$	615.165	0.0714689
$421$	−649.106	−0.0751437	−0.0375718	−	0.999294i	$-0.511962\pi$
$421$	−649.106	−0.0751437	−0.0375718	+	0.999294i	$0.511962\pi$
$422$	−2676.09	−0.308696
$423$	−4433.45	−0.509602
$424$	1121.87	0.128497
$425$	−315.861	−0.0360507
$426$	57.6923	0.00656151
$427$	−12942.2	−1.46679
$428$	1379.49	0.155795
$429$	−380.652	−0.0428393
$430$	−21.0846	−0.00236463
$431$	2116.95	0.236589	0.118294	−	0.992979i	$-0.462257\pi$
$431$	2116.95	0.236589	0.118294	+	0.992979i	$0.462257\pi$
$432$	2395.79	0.266823
$433$	13817.1	1.53351	0.766754	−	0.641941i	$-0.221871\pi$
$433$	13817.1	1.53351	0.766754	+	0.641941i	$0.221871\pi$
$434$	353.625	0.0391119
$435$	531.035	0.0585315
$436$	16156.4	1.77466
$437$	−17680.8	−1.93544
$438$	−225.415	−0.0245908
$439$	−2157.34	−0.234542	−0.117271	−	0.993100i	$-0.537415\pi$
$439$	−2157.34	−0.234542	−0.117271	+	0.993100i	$0.537415\pi$
$440$	1634.25	0.177068
$441$	−1637.25	−0.176789
$442$	−93.0898	−0.0100177
$443$	4096.34	0.439329	0.219665	−	0.975575i	$-0.429504\pi$
$443$	4096.34	0.439329	0.219665	+	0.975575i	$0.429504\pi$
$444$	620.795	0.0663551
$445$	−2707.03	−0.288372
$446$	3018.56	0.320477
$447$	243.743	0.0257911
$448$	7904.78	0.833629
$449$	−2666.77	−0.280295	−0.140148	−	0.990131i	$-0.544758\pi$
$449$	−2666.77	−0.280295	−0.140148	+	0.990131i	$0.544758\pi$
$450$	373.586	0.0391356
$451$	−2909.53	−0.303779
$452$	−1313.04	−0.136637
$453$	−1142.57	−0.118505
$454$	−1428.77	−0.147699
$455$	−1308.26	−0.134795
$456$	−958.637	−0.0984480
$457$	−1933.45	−0.197906	−0.0989531	−	0.995092i	$-0.531549\pi$
$457$	−1933.45	−0.197906	−0.0989531	+	0.995092i	$0.531549\pi$
$458$	247.143	0.0252144
$459$	−536.752	−0.0545826
$460$	−5009.26	−0.507735
$461$	1675.90	0.169316	0.0846578	−	0.996410i	$-0.473020\pi$
$461$	1675.90	0.169316	0.0846578	+	0.996410i	$0.473020\pi$
$462$	334.015	0.0336359
$463$	−1694.19	−0.170055	−0.0850276	−	0.996379i	$-0.527098\pi$
$463$	−1694.19	−0.170055	−0.0850276	+	0.996379i	$0.527098\pi$
$464$	7523.77	0.752763
$465$	123.391	0.0123056
$466$	−2036.86	−0.202480
$467$	−13222.1	−1.31016	−0.655080	−	0.755560i	$-0.727365\pi$
$467$	−13222.1	−1.31016	−0.655080	+	0.755560i	$0.727365\pi$
$468$	−2631.99	−0.259965
$469$	3487.64	0.343378
$470$	476.502	0.0467647
$471$	−1625.63	−0.159034
$472$	6034.12	0.588439
$473$	273.671	0.0266034
$474$	−214.914	−0.0208256
$475$	3387.89	0.327257
$476$	−1952.67	−0.188026
$477$	−3328.72	−0.319521
$478$	2034.17	0.194646
$479$	6297.39	0.600700	0.300350	−	0.953829i	$-0.402897\pi$
$479$	6297.39	0.600700	0.300350	+	0.953829i	$0.402897\pi$
$480$	−410.179	−0.0390042
$481$	−1320.23	−0.125150
$482$	−1366.81	−0.129163
$483$	−2090.46	−0.196934
$484$	−168.264	−0.0158024
$485$	4193.52	0.392614
$486$	956.037	0.0892320
$487$	4253.09	0.395741	0.197871	−	0.980228i	$-0.436597\pi$
$487$	4253.09	0.395741	0.197871	+	0.980228i	$0.436597\pi$
$488$	5714.06	0.530048
$489$	−633.205	−0.0585573
$490$	175.970	0.0162235
$491$	−7760.72	−0.713312	−0.356656	−	0.934236i	$-0.616083\pi$
$491$	−7760.72	−0.713312	−0.356656	+	0.934236i	$0.616083\pi$
$492$	483.537	0.0443080
$493$	−1685.62	−0.153989
$494$	998.470	0.0909379
$495$	−4849.02	−0.440297
$496$	1748.21	0.158260
$497$	−2573.62	−0.232279
$498$	−425.986	−0.0383311
$499$	16122.3	1.44636	0.723180	−	0.690660i	$-0.242680\pi$
$499$	16122.3	1.44636	0.723180	+	0.690660i	$0.242680\pi$
$500$	959.847	0.0858514
$501$	−378.252	−0.0337306
$502$	4186.91	0.372253
$503$	−3222.65	−0.285667	−0.142834	−	0.989747i	$-0.545621\pi$
$503$	−3222.65	−0.285667	−0.142834	+	0.989747i	$0.545621\pi$
$504$	4715.66	0.416770
$505$	1949.23	0.171761
$506$	−2719.87	−0.238959
$507$	−134.535	−0.0117849
$508$	−35.7717	−0.00312424
$509$	−4418.03	−0.384727	−0.192363	−	0.981324i	$-0.561615\pi$
$509$	−4418.03	−0.384727	−0.192363	+	0.981324i	$0.561615\pi$
$510$	28.5022	0.00247471
$511$	10055.6	0.870520
$512$	−9820.47	−0.847671
$513$	5757.14	0.495485
$514$	2910.44	0.249755
$515$	−8052.10	−0.688967
$516$	−45.4816	−0.00388026
$517$	−6184.83	−0.526128
$518$	1158.48	0.0982636
$519$	−2348.37	−0.198617
$520$	577.601	0.0487105
$521$	5728.72	0.481727	0.240864	−	0.970559i	$-0.422569\pi$
$521$	5728.72	0.481727	0.240864	+	0.970559i	$0.422569\pi$
$522$	1993.68	0.167166
$523$	−13711.2	−1.14637	−0.573184	−	0.819427i	$-0.694292\pi$
$523$	−13711.2	−1.14637	−0.573184	+	0.819427i	$0.694292\pi$
$524$	−4739.39	−0.395117
$525$	400.561	0.0332989
$526$	1341.48	0.111200
$527$	−391.668	−0.0323745
$528$	1651.27	0.136102
$529$	4855.50	0.399071
$530$	357.767	0.0293215
$531$	−17903.9	−1.46321
$532$	20944.1	1.70684
$533$	−1028.33	−0.0835680
$534$	244.273	0.0197954
$535$	898.250	0.0725883
$536$	−1539.81	−0.124085
$537$	−1033.90	−0.0830837
$538$	3996.95	0.320299
$539$	−2284.02	−0.182523
$540$	1631.09	0.129984
$541$	14255.9	1.13291	0.566457	−	0.824091i	$-0.308314\pi$
$541$	14255.9	1.13291	0.566457	+	0.824091i	$0.308314\pi$
$542$	−1875.04	−0.148598
$543$	−813.488	−0.0642912
$544$	1302.00	0.102615
$545$	10520.2	0.826854
$546$	118.052	0.00925307
$547$	−10819.2	−0.845693	−0.422846	−	0.906201i	$-0.638969\pi$
$547$	−10819.2	−0.845693	−0.422846	+	0.906201i	$0.638969\pi$
$548$	−7827.62	−0.610181
$549$	−16954.3	−1.31802
$550$	521.167	0.0404048
$551$	18079.8	1.39787
$552$	922.946	0.0711652
$553$	9587.20	0.737232
$554$	1844.65	0.141465
$555$	404.228	0.0309163
$556$	4845.69	0.369610
$557$	3422.11	0.260322	0.130161	−	0.991493i	$-0.458451\pi$
$557$	3422.11	0.260322	0.130161	+	0.991493i	$0.458451\pi$
$558$	463.247	0.0351448
$559$	96.7245	0.00731845
$560$	5675.20	0.428252
$561$	−369.949	−0.0278418
$562$	−1751.71	−0.131479
$563$	22439.3	1.67976	0.839878	−	0.542775i	$-0.182626\pi$
$563$	22439.3	1.67976	0.839878	+	0.542775i	$0.182626\pi$
$564$	1027.86	0.0767390
$565$	−854.979	−0.0636623
$566$	2920.29	0.216871
$567$	−13647.5	−1.01083
$568$	1136.27	0.0839378
$569$	−20348.5	−1.49921	−0.749607	−	0.661883i	$-0.769757\pi$
$569$	−20348.5	−1.49921	−0.749607	+	0.661883i	$0.769757\pi$
$570$	−305.712	−0.0224647
$571$	−3232.80	−0.236932	−0.118466	−	0.992958i	$-0.537798\pi$
$571$	−3232.80	−0.236932	−0.118466	+	0.992958i	$0.537798\pi$
$572$	−3671.73	−0.268396
$573$	−1641.09	−0.119647
$574$	902.337	0.0656146
$575$	−3261.76	−0.236565
$576$	10355.2	0.749076
$577$	9004.93	0.649706	0.324853	−	0.945765i	$-0.394685\pi$
$577$	9004.93	0.649706	0.324853	+	0.945765i	$0.394685\pi$
$578$	2694.04	0.193871
$579$	−34.3492	−0.00246546
$580$	5122.31	0.366711
$581$	19003.0	1.35693
$582$	−378.409	−0.0269511
$583$	−4643.69	−0.329884
$584$	−4439.61	−0.314576
$585$	−1713.81	−0.121123
$586$	−1290.61	−0.0909808
$587$	−23023.7	−1.61889	−0.809447	−	0.587193i	$-0.800233\pi$
$587$	−23023.7	−1.61889	−0.809447	+	0.587193i	$0.800233\pi$
$588$	379.584	0.0266221
$589$	4200.99	0.293886
$590$	1924.30	0.134275
$591$	1983.64	0.138064
$592$	5727.14	0.397608
$593$	−7887.58	−0.546213	−0.273106	−	0.961984i	$-0.588051\pi$
$593$	−7887.58	−0.546213	−0.273106	+	0.961984i	$0.588051\pi$
$594$	885.633	0.0611751
$595$	−1271.47	−0.0876053
$596$	2351.11	0.161586
$597$	3967.82	0.272013
$598$	−961.296	−0.0657363
$599$	12510.1	0.853339	0.426670	−	0.904408i	$-0.359687\pi$
$599$	12510.1	0.853339	0.426670	+	0.904408i	$0.359687\pi$
$600$	−176.850	−0.0120331
$601$	−14335.1	−0.972946	−0.486473	−	0.873696i	$-0.661717\pi$
$601$	−14335.1	−0.972946	−0.486473	+	0.873696i	$0.661717\pi$
$602$	−84.8740	−0.00574619
$603$	4568.79	0.308550
$604$	−11021.1	−0.742456
$605$	−109.564	−0.00736266
$606$	−175.891	−0.0117906
$607$	−13529.8	−0.904710	−0.452355	−	0.891838i	$-0.649416\pi$
$607$	−13529.8	−0.904710	−0.452355	+	0.891838i	$0.649416\pi$
$608$	−13965.1	−0.931511
$609$	2137.63	0.142235
$610$	1822.23	0.120951
$611$	−2185.93	−0.144735
$612$	−2557.98	−0.168955
$613$	422.293	0.0278242	0.0139121	−	0.999903i	$-0.495571\pi$
$613$	422.293	0.0278242	0.0139121	+	0.999903i	$0.495571\pi$
$614$	−550.891	−0.0362087
$615$	314.853	0.0206440
$616$	6578.52	0.430286
$617$	28599.5	1.86608	0.933041	−	0.359770i	$-0.117145\pi$
$617$	28599.5	1.86608	0.933041	+	0.359770i	$0.117145\pi$
$618$	726.593	0.0472943
$619$	−2292.04	−0.148829	−0.0744144	−	0.997227i	$-0.523709\pi$
$619$	−2292.04	−0.148829	−0.0744144	+	0.997227i	$0.523709\pi$
$620$	1190.21	0.0770968
$621$	−5542.79	−0.358172
$622$	−5401.26	−0.348185
$623$	−10896.9	−0.700762
$624$	583.614	0.0374411
$625$	625.000	0.0400000
$626$	−1365.40	−0.0871761
$627$	3968.03	0.252740
$628$	−15680.6	−0.996378
$629$	−1283.11	−0.0813368
$630$	1503.83	0.0951019
$631$	1481.18	0.0934464	0.0467232	−	0.998908i	$-0.485122\pi$
$631$	1481.18	0.0934464	0.0467232	+	0.998908i	$0.485122\pi$
$632$	−4232.79	−0.266410
$633$	−3758.79	−0.236017
$634$	3419.76	0.214221
$635$	−23.2926	−0.00145565
$636$	771.740	0.0481155
$637$	−807.251	−0.0502111
$638$	2781.25	0.172588
$639$	−3371.43	−0.208720
$640$	−5235.02	−0.323332
$641$	26427.6	1.62843	0.814217	−	0.580560i	$-0.197166\pi$
$641$	26427.6	1.62843	0.814217	+	0.580560i	$0.197166\pi$
$642$	−81.0549	−0.00498284
$643$	−5196.30	−0.318697	−0.159348	−	0.987222i	$-0.550939\pi$
$643$	−5196.30	−0.318697	−0.159348	+	0.987222i	$0.550939\pi$
$644$	−20164.3	−1.23383
$645$	−29.6151	−0.00180790
$646$	970.395	0.0591017
$647$	−3306.01	−0.200885	−0.100443	−	0.994943i	$-0.532026\pi$
$647$	−3306.01	−0.200885	−0.100443	+	0.994943i	$0.532026\pi$
$648$	6025.44	0.365280
$649$	−24976.7	−1.51066
$650$	184.198	0.0111152
$651$	496.696	0.0299033
$652$	−6107.83	−0.366873
$653$	8950.71	0.536399	0.268199	−	0.963363i	$-0.413571\pi$
$653$	8950.71	0.536399	0.268199	+	0.963363i	$0.413571\pi$
$654$	−949.306	−0.0567596
$655$	−3086.03	−0.184093
$656$	4460.87	0.265499
$657$	13172.8	0.782225
$658$	1918.11	0.113641
$659$	4969.67	0.293765	0.146882	−	0.989154i	$-0.453076\pi$
$659$	4969.67	0.293765	0.146882	+	0.989154i	$0.453076\pi$
$660$	1124.21	0.0663027
$661$	321.242	0.0189029	0.00945147	−	0.999955i	$-0.496991\pi$
$661$	321.242	0.0189029	0.00945147	+	0.999955i	$0.496991\pi$
$662$	2056.43	0.120733
$663$	−130.753	−0.00765914
$664$	−8389.91	−0.490349
$665$	13637.6	0.795255
$666$	1517.60	0.0882970
$667$	−17406.6	−1.01048
$668$	−3648.57	−0.211329
$669$	4239.82	0.245024
$670$	−491.049	−0.0283147
$671$	−23651.9	−1.36076
$672$	−1651.14	−0.0947827
$673$	−11866.7	−0.679684	−0.339842	−	0.940482i	$-0.610374\pi$
$673$	−11866.7	−0.679684	−0.339842	+	0.940482i	$0.610374\pi$
$674$	−4222.51	−0.241313
$675$	1062.08	0.0605622
$676$	−1297.71	−0.0738344
$677$	−5678.96	−0.322393	−0.161197	−	0.986922i	$-0.551535\pi$
$677$	−5678.96	−0.322393	−0.161197	+	0.986922i	$0.551535\pi$
$678$	77.1503	0.00437012
$679$	16880.6	0.954077
$680$	561.359	0.0316576
$681$	−2006.83	−0.112925
$682$	646.247	0.0362846
$683$	11410.9	0.639276	0.319638	−	0.947540i	$-0.396439\pi$
$683$	11410.9	0.639276	0.319638	+	0.947540i	$0.396439\pi$
$684$	27436.6	1.53372
$685$	−5096.92	−0.284297
$686$	−3204.34	−0.178342
$687$	347.133	0.0192779
$688$	−419.590	−0.0232510
$689$	−1641.24	−0.0907493
$690$	294.330	0.0162390
$691$	−16484.1	−0.907502	−0.453751	−	0.891128i	$-0.649915\pi$
$691$	−16484.1	−0.907502	−0.453751	+	0.891128i	$0.649915\pi$
$692$	−22652.1	−1.24437
$693$	−19519.2	−1.06995
$694$	−6720.98	−0.367615
$695$	3155.25	0.172209
$696$	−943.774	−0.0513989
$697$	−999.411	−0.0543119
$698$	−7075.91	−0.383707
$699$	−2860.94	−0.154808
$700$	3863.77	0.208624
$701$	−2675.05	−0.144130	−0.0720651	−	0.997400i	$-0.522959\pi$
$701$	−2675.05	−0.144130	−0.0720651	+	0.997400i	$0.522959\pi$
$702$	313.013	0.0168289
$703$	13762.5	0.738351
$704$	14445.9	0.773369
$705$	669.287	0.0357544
$706$	4161.75	0.221855
$707$	7846.42	0.417390
$708$	4150.90	0.220339
$709$	20611.2	1.09178	0.545889	−	0.837857i	$-0.316192\pi$
$709$	20611.2	1.09178	0.545889	+	0.837857i	$0.316192\pi$
$710$	362.358	0.0191536
$711$	12559.2	0.662456
$712$	4811.03	0.253231
$713$	−4044.58	−0.212441
$714$	114.733	0.00601368
$715$	−2390.83	−0.125052
$716$	−9972.85	−0.520535
$717$	2857.16	0.148818
$718$	2006.76	0.104306
$719$	31140.1	1.61520	0.807600	−	0.589730i	$-0.200766\pi$
$719$	31140.1	1.61520	0.807600	+	0.589730i	$0.200766\pi$
$720$	7434.48	0.384815
$721$	−32412.9	−1.67423
$722$	−6520.91	−0.336126
$723$	−1919.80	−0.0987528
$724$	−7846.81	−0.402796
$725$	3335.37	0.170858
$726$	9.88667	0.000505412 0
$727$	14345.0	0.731810	0.365905	−	0.930652i	$-0.380760\pi$
$727$	14345.0	0.731810	0.365905	+	0.930652i	$0.380760\pi$
$728$	2325.07	0.118369
$729$	−16965.1	−0.861914
$730$	−1415.80	−0.0717825
$731$	94.0048	0.00475635
$732$	3930.73	0.198475
$733$	24096.8	1.21424	0.607118	−	0.794611i	$-0.292325\pi$
$733$	24096.8	1.21424	0.607118	+	0.794611i	$0.292325\pi$
$734$	3683.48	0.185231
$735$	247.164	0.0124038
$736$	13445.1	0.673362
$737$	6373.64	0.318556
$738$	1182.06	0.0589595
$739$	−2842.78	−0.141507	−0.0707533	−	0.997494i	$-0.522540\pi$
$739$	−2842.78	−0.141507	−0.0707533	+	0.997494i	$0.522540\pi$
$740$	3899.14	0.193696
$741$	1402.44	0.0695274
$742$	1440.16	0.0712531
$743$	32854.1	1.62221	0.811103	−	0.584903i	$-0.198868\pi$
$743$	32854.1	1.62221	0.811103	+	0.584903i	$0.198868\pi$
$744$	−219.294	−0.0108060
$745$	1530.92	0.0752865
$746$	5522.77	0.271050
$747$	24893.8	1.21930
$748$	−3568.48	−0.174434
$749$	3615.82	0.176394
$750$	−56.3978	−0.00274581
$751$	23962.1	1.16430	0.582150	−	0.813081i	$-0.302212\pi$
$751$	23962.1	1.16430	0.582150	+	0.813081i	$0.302212\pi$
$752$	9482.53	0.459830
$753$	5880.87	0.284609
$754$	982.990	0.0474779
$755$	−7176.35	−0.345926
$756$	6565.81	0.315868
$757$	−11128.8	−0.534323	−0.267161	−	0.963652i	$-0.586086\pi$
$757$	−11128.8	−0.534323	−0.267161	+	0.963652i	$0.586086\pi$
$758$	5297.53	0.253845
$759$	−3820.29	−0.182698
$760$	−6021.08	−0.287378
$761$	18610.0	0.886479	0.443240	−	0.896403i	$-0.353829\pi$
$761$	18610.0	0.886479	0.443240	+	0.896403i	$0.353829\pi$
$762$	2.10184	9.99235e−5 0
$763$	42348.0	2.00931
$764$	−15829.8	−0.749610
$765$	−1665.62	−0.0787197
$766$	−1235.21	−0.0582635
$767$	−8827.61	−0.415576
$768$	−2028.82	−0.0953241
$769$	−22386.8	−1.04979	−0.524894	−	0.851168i	$-0.675895\pi$
$769$	−22386.8	−1.04979	−0.524894	+	0.851168i	$0.675895\pi$
$770$	2097.91	0.0981861
$771$	4087.96	0.190952
$772$	−331.328	−0.0154466
$773$	3450.50	0.160551	0.0802754	−	0.996773i	$-0.474420\pi$
$773$	3450.50	0.160551	0.0802754	+	0.996773i	$0.474420\pi$
$774$	−111.184	−0.00516336
$775$	775.000	0.0359211
$776$	−7452.86	−0.344771
$777$	1627.18	0.0751284
$778$	3191.35	0.147064
$779$	10719.6	0.493027
$780$	397.334	0.0182395
$781$	−4703.28	−0.215488
$782$	−934.266	−0.0427229
$783$	5667.88	0.258689
$784$	3501.85	0.159523
$785$	−10210.4	−0.464234
$786$	278.473	0.0126371
$787$	14139.1	0.640411	0.320206	−	0.947348i	$-0.396248\pi$
$787$	14139.1	0.640411	0.320206	+	0.947348i	$0.396248\pi$
$788$	19133.9	0.864997
$789$	1884.22	0.0850188
$790$	−1349.85	−0.0607917
$791$	−3441.63	−0.154703
$792$	8617.83	0.386643
$793$	−8359.38	−0.374338
$794$	5112.23	0.228497
$795$	502.515	0.0224181
$796$	38273.1	1.70421
$797$	−20163.4	−0.896140	−0.448070	−	0.893999i	$-0.647888\pi$
$797$	−20163.4	−0.896140	−0.448070	+	0.893999i	$0.647888\pi$
$798$	−1230.61	−0.0545905
$799$	−2124.46	−0.0940652
$800$	−2576.28	−0.113857
$801$	−14274.9	−0.629685
$802$	2443.67	0.107592
$803$	18376.6	0.807593
$804$	−1059.24	−0.0464634
$805$	−13129.9	−0.574866
$806$	228.406	0.00998170
$807$	5614.05	0.244887
$808$	−3464.23	−0.150831
$809$	11690.7	0.508062	0.254031	−	0.967196i	$-0.418244\pi$
$809$	11690.7	0.508062	0.254031	+	0.967196i	$0.418244\pi$
$810$	1921.53	0.0833526
$811$	−22054.9	−0.954935	−0.477467	−	0.878649i	$-0.658445\pi$
$811$	−22054.9	−0.954935	−0.477467	+	0.878649i	$0.658445\pi$
$812$	20619.3	0.891129
$813$	−2633.66	−0.113612
$814$	2117.11	0.0911605
$815$	−3977.08	−0.170934
$816$	567.203	0.0243334
$817$	−1008.28	−0.0431767
$818$	−4963.37	−0.212152
$819$	−6898.76	−0.294337
$820$	3037.03	0.129339
$821$	−28779.6	−1.22340	−0.611702	−	0.791089i	$-0.709515\pi$
$821$	−28779.6	−1.22340	−0.611702	+	0.791089i	$0.709515\pi$
$822$	459.928	0.0195156
$823$	24220.1	1.02583	0.512916	−	0.858439i	$-0.328565\pi$
$823$	24220.1	1.02583	0.512916	+	0.858439i	$0.328565\pi$
$824$	14310.5	0.605010
$825$	732.023	0.0308919
$826$	7746.06	0.326295
$827$	−4160.28	−0.174930	−0.0874650	−	0.996168i	$-0.527877\pi$
$827$	−4160.28	−0.174930	−0.0874650	+	0.996168i	$0.527877\pi$
$828$	−26415.1	−1.10868
$829$	−40944.6	−1.71540	−0.857699	−	0.514152i	$-0.828107\pi$
$829$	−40944.6	−1.71540	−0.857699	+	0.514152i	$0.828107\pi$
$830$	−2675.56	−0.111892
$831$	2590.96	0.108158
$832$	5105.69	0.212750
$833$	−784.553	−0.0326328
$834$	−284.718	−0.0118213
$835$	−2375.75	−0.0984626
$836$	38275.1	1.58346
$837$	1316.98	0.0543864
$838$	−3452.38	−0.142316
$839$	11169.4	0.459607	0.229803	−	0.973237i	$-0.426192\pi$
$839$	11169.4	0.459607	0.229803	+	0.973237i	$0.426192\pi$
$840$	−711.891	−0.0292412
$841$	−6589.54	−0.270185
$842$	367.890	0.0150574
$843$	−2460.42	−0.100523
$844$	−36256.9	−1.47869
$845$	−845.000	−0.0344010
$846$	2512.72	0.102115
$847$	−441.039	−0.0178917
$848$	7119.68	0.288315
$849$	4101.80	0.165811
$850$	179.019	0.00722388
$851$	−13250.1	−0.533732
$852$	781.642	0.0314303
$853$	−15696.0	−0.630036	−0.315018	−	0.949086i	$-0.602011\pi$
$853$	−15696.0	−0.630036	−0.315018	+	0.949086i	$0.602011\pi$
$854$	7335.20	0.293917
$855$	17865.2	0.714594
$856$	−1596.40	−0.0637428
$857$	−36647.8	−1.46075	−0.730377	−	0.683044i	$-0.760656\pi$
$857$	−36647.8	−1.46075	−0.730377	+	0.683044i	$0.760656\pi$
$858$	215.740	0.00858419
$859$	16999.5	0.675221	0.337611	−	0.941286i	$-0.390381\pi$
$859$	16999.5	0.675221	0.337611	+	0.941286i	$0.390381\pi$
$860$	−285.664	−0.0113268
$861$	1267.41	0.0501663
$862$	−1199.81	−0.0474080
$863$	4032.49	0.159059	0.0795294	−	0.996833i	$-0.474658\pi$
$863$	4032.49	0.159059	0.0795294	+	0.996833i	$0.474658\pi$
$864$	−4377.95	−0.172385
$865$	−14749.8	−0.579779
$866$	−7831.05	−0.307286
$867$	3784.01	0.148226
$868$	4791.07	0.187350
$869$	17520.5	0.683940
$870$	−300.972	−0.0117286
$871$	2252.66	0.0876332
$872$	−18696.8	−0.726095
$873$	22113.5	0.857307
$874$	10020.8	0.387826
$875$	2515.88	0.0972024
$876$	−3054.03	−0.117792
$877$	−15840.7	−0.609922	−0.304961	−	0.952365i	$-0.598643\pi$
$877$	−15840.7	−0.609922	−0.304961	+	0.952365i	$0.598643\pi$
$878$	1222.70	0.0469979
$879$	−1812.78	−0.0695602
$880$	10371.4	0.397295
$881$	−26052.8	−0.996300	−0.498150	−	0.867091i	$-0.665987\pi$
$881$	−26052.8	−0.996300	−0.498150	+	0.867091i	$0.665987\pi$
$882$	927.932	0.0354253
$883$	−36094.1	−1.37561	−0.687804	−	0.725896i	$-0.741425\pi$
$883$	−36094.1	−1.37561	−0.687804	+	0.725896i	$0.741425\pi$
$884$	−1261.22	−0.0479859
$885$	2702.84	0.102661
$886$	−2321.66	−0.0880334
$887$	31304.2	1.18500	0.592498	−	0.805572i	$-0.298142\pi$
$887$	31304.2	1.18500	0.592498	+	0.805572i	$0.298142\pi$
$888$	−718.407	−0.0271488
$889$	−93.7621	−0.00353732
$890$	1534.25	0.0577844
$891$	−24940.7	−0.937762
$892$	40896.8	1.53512
$893$	22786.7	0.853896
$894$	−138.145	−0.00516806
$895$	−6493.78	−0.242528
$896$	−21073.1	−0.785716
$897$	−1350.22	−0.0502593
$898$	1511.43	0.0561659
$899$	4135.85	0.153435
$900$	5061.52	0.187464
$901$	−1595.09	−0.0589791
$902$	1649.01	0.0608716
$903$	−119.213	−0.00439330
$904$	1519.50	0.0559045
$905$	−5109.41	−0.187671
$906$	647.569	0.0237462
$907$	27591.9	1.01012	0.505058	−	0.863085i	$-0.331471\pi$
$907$	27591.9	1.01012	0.505058	+	0.863085i	$0.331471\pi$
$908$	−19357.6	−0.707496
$909$	10278.8	0.375055
$910$	741.472	0.0270105
$911$	166.647	0.00606066	0.00303033	−	0.999995i	$-0.499035\pi$
$911$	166.647	0.00606066	0.00303033	+	0.999995i	$0.499035\pi$
$912$	−6083.75	−0.220892
$913$	34727.8	1.25884
$914$	1095.81	0.0396567
$915$	2559.47	0.0924739
$916$	3348.40	0.120780
$917$	−12422.5	−0.447358
$918$	304.212	0.0109373
$919$	−14362.1	−0.515520	−0.257760	−	0.966209i	$-0.582984\pi$
$919$	−14362.1	−0.515520	−0.257760	+	0.966209i	$0.582984\pi$
$920$	5796.90	0.207737
$921$	−773.773	−0.0276837
$922$	−949.840	−0.0339277
$923$	−1662.30	−0.0592798
$924$	4525.39	0.161120
$925$	2538.90	0.0902472
$926$	960.204	0.0340759
$927$	−42460.8	−1.50442
$928$	−13748.6	−0.486334
$929$	−12045.7	−0.425410	−0.212705	−	0.977116i	$-0.568227\pi$
$929$	−12045.7	−0.425410	−0.212705	+	0.977116i	$0.568227\pi$
$930$	−69.9333	−0.00246581
$931$	8415.02	0.296231
$932$	−27596.3	−0.969900
$933$	−7586.53	−0.266208
$934$	7493.79	0.262531
$935$	−2323.60	−0.0812726
$936$	3045.84	0.106364
$937$	5334.84	0.186000	0.0929999	−	0.995666i	$-0.470354\pi$
$937$	5334.84	0.186000	0.0929999	+	0.995666i	$0.470354\pi$
$938$	−1976.67	−0.0688065
$939$	−1917.82	−0.0666513
$940$	6455.87	0.224008
$941$	48383.4	1.67615	0.838074	−	0.545557i	$-0.183682\pi$
$941$	48383.4	1.67615	0.838074	+	0.545557i	$0.183682\pi$
$942$	921.348	0.0318675
$943$	−10320.5	−0.356395
$944$	38294.1	1.32030
$945$	4275.29	0.147170
$946$	−155.107	−0.00533082
$947$	−12117.7	−0.415812	−0.207906	−	0.978149i	$-0.566665\pi$
$947$	−12117.7	−0.415812	−0.207906	+	0.978149i	$0.566665\pi$
$948$	−2911.75	−0.0997567
$949$	6494.93	0.222165
$950$	−1920.14	−0.0655762
$951$	4803.34	0.163784
$952$	2259.70	0.0769298
$953$	−42025.9	−1.42849	−0.714246	−	0.699895i	$-0.753230\pi$
$953$	−42025.9	−1.42849	−0.714246	+	0.699895i	$0.753230\pi$
$954$	1886.60	0.0640261
$955$	−10307.5	−0.349260
$956$	27559.9	0.932375
$957$	3906.51	0.131953
$958$	−3569.14	−0.120369
$959$	−20517.1	−0.690858
$960$	−1563.26	−0.0525562
$961$	961.000	0.0322581
$962$	748.259	0.0250778
$963$	4736.70	0.158503
$964$	−18518.2	−0.618705
$965$	−215.743	−0.00719689
$966$	1184.79	0.0394618
$967$	−471.826	−0.0156907	−0.00784535	−	0.999969i	$-0.502497\pi$
$967$	−471.826	−0.0156907	−0.00784535	+	0.999969i	$0.502497\pi$
$968$	194.721	0.00646546
$969$	1363.00	0.0451867
$970$	−2376.74	−0.0786726
$971$	39499.4	1.30546	0.652728	−	0.757593i	$-0.273625\pi$
$971$	39499.4	1.30546	0.652728	+	0.757593i	$0.273625\pi$
$972$	12952.8	0.427430
$973$	12701.1	0.418479
$974$	−2410.50	−0.0792991
$975$	258.722	0.00849819
$976$	36262.9	1.18929
$977$	−13550.6	−0.443727	−0.221864	−	0.975078i	$-0.571214\pi$
$977$	−13550.6	−0.443727	−0.221864	+	0.975078i	$0.571214\pi$
$978$	358.878	0.0117338
$979$	−19914.0	−0.650106
$980$	2384.12	0.0777121
$981$	55475.7	1.80551
$982$	4398.49	0.142934
$983$	−19421.2	−0.630152	−0.315076	−	0.949066i	$-0.602030\pi$
$983$	−19421.2	−0.630152	−0.315076	+	0.949066i	$0.602030\pi$
$984$	−559.567	−0.0181284
$985$	12459.0	0.403021
$986$	955.349	0.0308565
$987$	2694.15	0.0868852
$988$	13527.7	0.435602
$989$	970.745	0.0312112
$990$	2748.25	0.0882273
$991$	47166.3	1.51189	0.755947	−	0.654633i	$-0.227177\pi$
$991$	47166.3	1.51189	0.755947	+	0.654633i	$0.227177\pi$
$992$	−3194.59	−0.102246
$993$	2888.43	0.0923077
$994$	1458.64	0.0465444
$995$	24921.4	0.794030
$996$	−5771.45	−0.183610
$997$	22553.5	0.716427	0.358213	−	0.933640i	$-0.383386\pi$
$997$	22553.5	0.716427	0.358213	+	0.933640i	$0.383386\pi$
$998$	−9137.54	−0.289823
$999$	4314.43	0.136639

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2015.4.a.d.1.19	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2015.4.a.d.1.19	✓	40	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:	\( N \)	\(=\)	\( 2015 = 5 \cdot 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2015.a (trivial)

\(f(q)\)	\(=\)	\(q-0.566764 q^{2} -0.796068 q^{3} -7.67878 q^{4} -5.00000 q^{5} +0.451182 q^{6} -20.1270 q^{7} +8.88617 q^{8} -26.3663 q^{9} +O(q^{10})\)	\(q-0.566764 q^{2} -0.796068 q^{3} -7.67878 q^{4} -5.00000 q^{5} +0.451182 q^{6} -20.1270 q^{7} +8.88617 q^{8} -26.3663 q^{9} +2.83382 q^{10} -36.7820 q^{11} +6.11283 q^{12} -13.0000 q^{13} +11.4073 q^{14} +3.98034 q^{15} +56.3939 q^{16} -12.6345 q^{17} +14.9435 q^{18} +135.516 q^{19} +38.3939 q^{20} +16.0225 q^{21} +20.8467 q^{22} -130.470 q^{23} -7.07399 q^{24} +25.0000 q^{25} +7.36793 q^{26} +42.4832 q^{27} +154.551 q^{28} +133.415 q^{29} -2.25591 q^{30} +31.0000 q^{31} -103.051 q^{32} +29.2809 q^{33} +7.16075 q^{34} +100.635 q^{35} +202.461 q^{36} +101.556 q^{37} -76.8054 q^{38} +10.3489 q^{39} -44.4308 q^{40} +79.1020 q^{41} -9.08095 q^{42} -7.44035 q^{43} +282.441 q^{44} +131.831 q^{45} +73.9459 q^{46} +168.148 q^{47} -44.8933 q^{48} +62.0963 q^{49} -14.1691 q^{50} +10.0579 q^{51} +99.8241 q^{52} +126.249 q^{53} -24.0779 q^{54} +183.910 q^{55} -178.852 q^{56} -107.880 q^{57} -75.6146 q^{58} +679.047 q^{59} -30.5641 q^{60} +643.029 q^{61} -17.5697 q^{62} +530.674 q^{63} -392.745 q^{64} +65.0000 q^{65} -16.5954 q^{66} -173.282 q^{67} +97.0172 q^{68} +103.863 q^{69} -57.0363 q^{70} +127.869 q^{71} -234.295 q^{72} -499.610 q^{73} -57.5584 q^{74} -19.9017 q^{75} -1040.60 q^{76} +740.311 q^{77} -5.86537 q^{78} -476.335 q^{79} -281.969 q^{80} +678.070 q^{81} -44.8321 q^{82} -944.154 q^{83} -123.033 q^{84} +63.1723 q^{85} +4.21692 q^{86} -106.207 q^{87} -326.851 q^{88} +541.406 q^{89} -74.7173 q^{90} +261.651 q^{91} +1001.85 q^{92} -24.6781 q^{93} -95.3004 q^{94} -677.579 q^{95} +82.0358 q^{96} -838.704 q^{97} -35.1939 q^{98} +969.803 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 5 q^{2} - 17 q^{3} + 149 q^{4} - 200 q^{5} - 35 q^{6} - 20 q^{7} - 39 q^{8} + 247 q^{9}+O(q^{10}) \) 40 * q - 5 * q^2 - 17 * q^3 + 149 * q^4 - 200 * q^5 - 35 * q^6 - 20 * q^7 - 39 * q^8 + 247 * q^9	\( 40 q - 5 q^{2} - 17 q^{3} + 149 q^{4} - 200 q^{5} - 35 q^{6} - 20 q^{7} - 39 q^{8} + 247 q^{9} + 25 q^{10} + 127 q^{11} - 76 q^{12} - 520 q^{13} + 138 q^{14} + 85 q^{15} + 413 q^{16} - 264 q^{17} - 126 q^{18} - q^{19} - 745 q^{20} + 176 q^{21} - 191 q^{22} - 106 q^{23} + 31 q^{24} + 1000 q^{25} + 65 q^{26} - 344 q^{27} + 255 q^{28} + 107 q^{29} + 175 q^{30} + 1240 q^{31} - 372 q^{32} - 386 q^{33} - 6 q^{34} + 100 q^{35} + 790 q^{36} - 741 q^{37} - 318 q^{38} + 221 q^{39} + 195 q^{40} + 1232 q^{41} - 1180 q^{42} - 615 q^{43} - 152 q^{44} - 1235 q^{45} - 329 q^{46} - 784 q^{47} - 1089 q^{48} - 516 q^{49} - 125 q^{50} - 200 q^{51} - 1937 q^{52} - 1503 q^{53} + 1658 q^{54} - 635 q^{55} + 1518 q^{56} - 1704 q^{57} - 1035 q^{58} - 107 q^{59} + 380 q^{60} - 857 q^{61} - 155 q^{62} - 2636 q^{63} - 215 q^{64} + 2600 q^{65} - 1785 q^{66} - 2689 q^{67} - 2639 q^{68} + 2544 q^{69} - 690 q^{70} + 1554 q^{71} - 420 q^{72} - 1968 q^{73} - 27 q^{74} - 425 q^{75} - 110 q^{76} - 1040 q^{77} + 455 q^{78} - 3182 q^{79} - 2065 q^{80} - 1576 q^{81} - 386 q^{82} + 317 q^{83} - 617 q^{84} + 1320 q^{85} + 347 q^{86} - 216 q^{87} - 4081 q^{88} + 3610 q^{89} + 630 q^{90} + 260 q^{91} - 4965 q^{92} - 527 q^{93} - 2942 q^{94} + 5 q^{95} + 1002 q^{96} - 3318 q^{97} + 1659 q^{98} + 5943 q^{99}+O(q^{100}) \) 40 * q - 5 * q^2 - 17 * q^3 + 149 * q^4 - 200 * q^5 - 35 * q^6 - 20 * q^7 - 39 * q^8 + 247 * q^9 + 25 * q^10 + 127 * q^11 - 76 * q^12 - 520 * q^13 + 138 * q^14 + 85 * q^15 + 413 * q^16 - 264 * q^17 - 126 * q^18 - q^19 - 745 * q^20 + 176 * q^21 - 191 * q^22 - 106 * q^23 + 31 * q^24 + 1000 * q^25 + 65 * q^26 - 344 * q^27 + 255 * q^28 + 107 * q^29 + 175 * q^30 + 1240 * q^31 - 372 * q^32 - 386 * q^33 - 6 * q^34 + 100 * q^35 + 790 * q^36 - 741 * q^37 - 318 * q^38 + 221 * q^39 + 195 * q^40 + 1232 * q^41 - 1180 * q^42 - 615 * q^43 - 152 * q^44 - 1235 * q^45 - 329 * q^46 - 784 * q^47 - 1089 * q^48 - 516 * q^49 - 125 * q^50 - 200 * q^51 - 1937 * q^52 - 1503 * q^53 + 1658 * q^54 - 635 * q^55 + 1518 * q^56 - 1704 * q^57 - 1035 * q^58 - 107 * q^59 + 380 * q^60 - 857 * q^61 - 155 * q^62 - 2636 * q^63 - 215 * q^64 + 2600 * q^65 - 1785 * q^66 - 2689 * q^67 - 2639 * q^68 + 2544 * q^69 - 690 * q^70 + 1554 * q^71 - 420 * q^72 - 1968 * q^73 - 27 * q^74 - 425 * q^75 - 110 * q^76 - 1040 * q^77 + 455 * q^78 - 3182 * q^79 - 2065 * q^80 - 1576 * q^81 - 386 * q^82 + 317 * q^83 - 617 * q^84 + 1320 * q^85 + 347 * q^86 - 216 * q^87 - 4081 * q^88 + 3610 * q^89 + 630 * q^90 + 260 * q^91 - 4965 * q^92 - 527 * q^93 - 2942 * q^94 + 5 * q^95 + 1002 * q^96 - 3318 * q^97 + 1659 * q^98 + 5943 * q^99

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