LMFDB - Embedded newform 2015.4.a.d.1.1

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			1.1
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)

$f(q)$	$=$	$q-5.34747 q^{2} -7.64905 q^{3} +20.5954 q^{4} -5.00000 q^{5} +40.9031 q^{6} -21.7958 q^{7} -67.3535 q^{8} +31.5080 q^{9} +O(q^{10})$	\(q-5.34747 q^{2} -7.64905 q^{3} +20.5954 q^{4} -5.00000 q^{5} +40.9031 q^{6} -21.7958 q^{7} -67.3535 q^{8} +31.5080 q^{9} +26.7373 q^{10} +30.4421 q^{11} -157.535 q^{12} -13.0000 q^{13} +116.552 q^{14} +38.2453 q^{15} +195.407 q^{16} -20.7188 q^{17} -168.488 q^{18} -36.7603 q^{19} -102.977 q^{20} +166.717 q^{21} -162.788 q^{22} -75.7254 q^{23} +515.190 q^{24} +25.0000 q^{25} +69.5171 q^{26} -34.4820 q^{27} -448.892 q^{28} -133.696 q^{29} -204.515 q^{30} +31.0000 q^{31} -506.106 q^{32} -232.853 q^{33} +110.793 q^{34} +108.979 q^{35} +648.920 q^{36} -36.1613 q^{37} +196.575 q^{38} +99.4377 q^{39} +336.767 q^{40} +22.5945 q^{41} -891.513 q^{42} +128.488 q^{43} +626.966 q^{44} -157.540 q^{45} +404.939 q^{46} +103.544 q^{47} -1494.68 q^{48} +132.055 q^{49} -133.687 q^{50} +158.479 q^{51} -267.740 q^{52} -43.9894 q^{53} +184.392 q^{54} -152.210 q^{55} +1468.02 q^{56} +281.182 q^{57} +714.937 q^{58} -349.234 q^{59} +787.677 q^{60} -313.514 q^{61} -165.771 q^{62} -686.741 q^{63} +1143.13 q^{64} +65.0000 q^{65} +1245.17 q^{66} -267.495 q^{67} -426.713 q^{68} +579.227 q^{69} -582.760 q^{70} +698.057 q^{71} -2122.17 q^{72} -373.703 q^{73} +193.372 q^{74} -191.226 q^{75} -757.093 q^{76} -663.508 q^{77} -531.740 q^{78} -1199.79 q^{79} -977.036 q^{80} -586.961 q^{81} -120.823 q^{82} -560.661 q^{83} +3433.60 q^{84} +103.594 q^{85} -687.084 q^{86} +1022.65 q^{87} -2050.38 q^{88} +443.677 q^{89} +842.440 q^{90} +283.345 q^{91} -1559.59 q^{92} -237.121 q^{93} -553.697 q^{94} +183.802 q^{95} +3871.23 q^{96} +904.719 q^{97} -706.160 q^{98} +959.169 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−5.34747	−1.89061	−0.945307	−	0.326181i	$-0.894238\pi$
$2$	−5.34747	−1.89061	−0.945307	+	0.326181i	$0.894238\pi$
$3$	−7.64905	−1.47206	−0.736030	−	0.676948i	$-0.763302\pi$
$3$	−7.64905	−1.47206	−0.736030	+	0.676948i	$0.763302\pi$
$4$	20.5954	2.57442
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	40.9031	2.78310
$7$	−21.7958	−1.17686	−0.588430	−	0.808548i	$-0.700254\pi$
$7$	−21.7958	−1.17686	−0.588430	+	0.808548i	$0.700254\pi$
$8$	−67.3535	−2.97663
$9$	31.5080	1.16696
$10$	26.7373	0.845509
$11$	30.4421	0.834420	0.417210	−	0.908810i	$-0.363008\pi$
$11$	30.4421	0.834420	0.417210	+	0.908810i	$0.363008\pi$
$12$	−157.535	−3.78971
$13$	−13.0000	−0.277350
$13$	−13.0000	−0.277350
$14$	116.552	2.22499
$15$	38.2453	0.658326
$16$	195.407	3.05324
$17$	−20.7188	−0.295591	−0.147796	−	0.989018i	$-0.547218\pi$
$17$	−20.7188	−0.295591	−0.147796	+	0.989018i	$0.547218\pi$
$18$	−168.488	−2.20628
$19$	−36.7603	−0.443863	−0.221931	−	0.975062i	$-0.571236\pi$
$19$	−36.7603	−0.443863	−0.221931	+	0.975062i	$0.571236\pi$
$20$	−102.977	−1.15132
$21$	166.717	1.73241
$22$	−162.788	−1.57757
$23$	−75.7254	−0.686514	−0.343257	−	0.939241i	$-0.611530\pi$
$23$	−75.7254	−0.686514	−0.343257	+	0.939241i	$0.611530\pi$
$24$	515.190	4.38178
$25$	25.0000	0.200000
$26$	69.5171	0.524362
$27$	−34.4820	−0.245780
$28$	−448.892	−3.02974
$29$	−133.696	−0.856096	−0.428048	−	0.903756i	$-0.640799\pi$
$29$	−133.696	−0.856096	−0.428048	+	0.903756i	$0.640799\pi$
$30$	−204.515	−1.24464
$31$	31.0000	0.179605
$31$	31.0000	0.179605
$32$	−506.106	−2.79587
$33$	−232.853	−1.22832
$34$	110.793	0.558850
$35$	108.979	0.526308
$36$	648.920	3.00426
$37$	−36.1613	−0.160673	−0.0803363	−	0.996768i	$-0.525599\pi$
$37$	−36.1613	−0.160673	−0.0803363	+	0.996768i	$0.525599\pi$
$38$	196.575	0.839174
$39$	99.4377	0.408276
$40$	336.767	1.33119
$41$	22.5945	0.0860650	0.0430325	−	0.999074i	$-0.486298\pi$
$41$	22.5945	0.0860650	0.0430325	+	0.999074i	$0.486298\pi$
$42$	−891.513	−3.27532
$43$	128.488	0.455679	0.227840	−	0.973699i	$-0.426834\pi$
$43$	128.488	0.455679	0.227840	+	0.973699i	$0.426834\pi$
$44$	626.966	2.14815
$45$	−157.540	−0.521882
$46$	404.939	1.29793
$47$	103.544	0.321349	0.160674	−	0.987007i	$-0.448633\pi$
$47$	103.544	0.321349	0.160674	+	0.987007i	$0.448633\pi$
$48$	−1494.68	−4.49455
$49$	132.055	0.385000
$50$	−133.687	−0.378123
$51$	158.479	0.435129
$52$	−267.740	−0.714017
$53$	−43.9894	−0.114008	−0.0570039	−	0.998374i	$-0.518155\pi$
$53$	−43.9894	−0.114008	−0.0570039	+	0.998374i	$0.518155\pi$
$54$	184.392	0.464676
$55$	−152.210	−0.373164
$56$	1468.02	3.50308
$57$	281.182	0.653393
$58$	714.937	1.61855
$59$	−349.234	−0.770618	−0.385309	−	0.922788i	$-0.625905\pi$
$59$	−349.234	−0.770618	−0.385309	+	0.922788i	$0.625905\pi$
$60$	787.677	1.69481
$61$	−313.514	−0.658054	−0.329027	−	0.944320i	$-0.606721\pi$
$61$	−313.514	−0.658054	−0.329027	+	0.944320i	$0.606721\pi$
$62$	−165.771	−0.339564
$63$	−686.741	−1.37335
$64$	1143.13	2.23267
$65$	65.0000	0.124035
$66$	1245.17	2.32228
$67$	−267.495	−0.487756	−0.243878	−	0.969806i	$-0.578420\pi$
$67$	−267.495	−0.487756	−0.243878	+	0.969806i	$0.578420\pi$
$68$	−426.713	−0.760978
$69$	579.227	1.01059
$70$	−582.760	−0.995046
$71$	698.057	1.16682	0.583409	−	0.812178i	$-0.301718\pi$
$71$	698.057	1.16682	0.583409	+	0.812178i	$0.301718\pi$
$72$	−2122.17	−3.47362
$73$	−373.703	−0.599159	−0.299579	−	0.954071i	$-0.596846\pi$
$73$	−373.703	−0.599159	−0.299579	+	0.954071i	$0.596846\pi$
$74$	193.372	0.303770
$75$	−191.226	−0.294412
$76$	−757.093	−1.14269
$77$	−663.508	−0.981996
$78$	−531.740	−0.771893
$79$	−1199.79	−1.70869	−0.854345	−	0.519707i	$-0.826041\pi$
$79$	−1199.79	−1.70869	−0.854345	+	0.519707i	$0.826041\pi$
$80$	−977.036	−1.36545
$81$	−586.961	−0.805160
$82$	−120.823	−0.162716
$83$	−560.661	−0.741453	−0.370726	−	0.928742i	$-0.620891\pi$
$83$	−560.661	−0.741453	−0.370726	+	0.928742i	$0.620891\pi$
$84$	3433.60	4.45996
$85$	103.594	0.132193
$86$	−687.084	−0.861514
$87$	1022.65	1.26023
$88$	−2050.38	−2.48376
$89$	443.677	0.528423	0.264211	−	0.964465i	$-0.414888\pi$
$89$	443.677	0.528423	0.264211	+	0.964465i	$0.414888\pi$
$90$	842.440	0.986678
$91$	283.345	0.326402
$92$	−1559.59	−1.76738
$93$	−237.121	−0.264390
$94$	−553.697	−0.607547
$95$	183.802	0.198501
$96$	3871.23	4.11569
$97$	904.719	0.947013	0.473507	−	0.880790i	$-0.342988\pi$
$97$	904.719	0.947013	0.473507	+	0.880790i	$0.342988\pi$
$98$	−706.160	−0.727888
$99$	959.169	0.973738
$100$	514.885	0.514885
$101$	1063.01	1.04726	0.523630	−	0.851946i	$-0.324577\pi$
$101$	1063.01	1.04726	0.523630	+	0.851946i	$0.324577\pi$
$102$	−847.464	−0.822661
$103$	−1090.05	−1.04278	−0.521389	−	0.853319i	$-0.674586\pi$
$103$	−1090.05	−1.04278	−0.521389	+	0.853319i	$0.674586\pi$
$104$	875.595	0.825569
$105$	−833.585	−0.774757
$106$	235.232	0.215545
$107$	−103.688	−0.0936813	−0.0468407	−	0.998902i	$-0.514915\pi$
$107$	−103.688	−0.0936813	−0.0468407	+	0.998902i	$0.514915\pi$
$108$	−710.171	−0.632743
$109$	571.641	0.502323	0.251162	−	0.967945i	$-0.419187\pi$
$109$	571.641	0.502323	0.251162	+	0.967945i	$0.419187\pi$
$110$	813.939	0.705510
$111$	276.600	0.236520
$112$	−4259.05	−3.59324
$113$	776.038	0.646049	0.323024	−	0.946391i	$-0.395300\pi$
$113$	776.038	0.646049	0.323024	+	0.946391i	$0.395300\pi$
$114$	−1503.61	−1.23531
$115$	378.627	0.307019
$116$	−2753.53	−2.20396
$117$	−409.604	−0.323657
$118$	1867.52	1.45694
$119$	451.583	0.347870
$120$	−2575.95	−1.95959
$121$	−404.281	−0.303743
$122$	1676.50	1.24413
$123$	−172.826	−0.126693
$124$	638.457	0.462380
$125$	−125.000	−0.0894427
$126$	3672.33	2.59648
$127$	1572.89	1.09899	0.549493	−	0.835498i	$-0.314821\pi$
$127$	1572.89	1.09899	0.549493	+	0.835498i	$0.314821\pi$
$128$	−2063.98	−1.42525
$129$	−982.810	−0.670788
$130$	−347.585	−0.234502
$131$	1555.83	1.03766	0.518832	−	0.854876i	$-0.326367\pi$
$131$	1555.83	1.03766	0.518832	+	0.854876i	$0.326367\pi$
$132$	−4795.70	−3.16221
$133$	801.219	0.522365
$134$	1430.42	0.922159
$135$	172.410	0.109916
$136$	1395.49	0.879867
$137$	348.141	0.217107	0.108554	−	0.994091i	$-0.465378\pi$
$137$	348.141	0.217107	0.108554	+	0.994091i	$0.465378\pi$
$138$	−3097.40	−1.91064
$139$	1364.06	0.832360	0.416180	−	0.909282i	$-0.363369\pi$
$139$	1364.06	0.832360	0.416180	+	0.909282i	$0.363369\pi$
$140$	2244.46	1.35494
$141$	−792.011	−0.473045
$142$	−3732.84	−2.20600
$143$	−395.747	−0.231427
$144$	6156.89	3.56302
$145$	668.482	0.382858
$146$	1998.36	1.13278
$147$	−1010.10	−0.566744
$148$	−744.757	−0.413640
$149$	1367.29	0.751765	0.375882	−	0.926667i	$-0.377340\pi$
$149$	1367.29	0.751765	0.375882	+	0.926667i	$0.377340\pi$
$150$	1022.58	0.556620
$151$	585.176	0.315371	0.157685	−	0.987489i	$-0.449597\pi$
$151$	585.176	0.315371	0.157685	+	0.987489i	$0.449597\pi$
$152$	2475.93	1.32122
$153$	−652.809	−0.344944
$154$	3548.09	1.85658
$155$	−155.000	−0.0803219
$156$	2047.96	1.05108
$157$	2314.94	1.17676	0.588382	−	0.808583i	$-0.299765\pi$
$157$	2314.94	1.17676	0.588382	+	0.808583i	$0.299765\pi$
$158$	6415.81	3.23047
$159$	336.477	0.167826
$160$	2530.53	1.25035
$161$	1650.49	0.807932
$162$	3138.76	1.52225
$163$	1677.09	0.805889	0.402945	−	0.915224i	$-0.367987\pi$
$163$	1677.09	0.805889	0.402945	+	0.915224i	$0.367987\pi$
$164$	465.343	0.221568
$165$	1164.26	0.549320
$166$	2998.12	1.40180
$167$	1865.05	0.864205	0.432102	−	0.901825i	$-0.357772\pi$
$167$	1865.05	0.864205	0.432102	+	0.901825i	$0.357772\pi$
$168$	−11229.0	−5.15675
$169$	169.000	0.0769231
$170$	−553.966	−0.249925
$171$	−1158.24	−0.517972
$172$	2646.26	1.17311
$173$	3312.53	1.45576	0.727881	−	0.685703i	$-0.240505\pi$
$173$	3312.53	1.45576	0.727881	+	0.685703i	$0.240505\pi$
$174$	−5468.59	−2.38260
$175$	−544.894	−0.235372
$176$	5948.60	2.54768
$177$	2671.31	1.13440
$178$	−2372.55	−0.999044
$179$	−1506.31	−0.628977	−0.314489	−	0.949261i	$-0.601833\pi$
$179$	−1506.31	−0.628977	−0.314489	+	0.949261i	$0.601833\pi$
$180$	−3244.60	−1.34355
$181$	−2113.06	−0.867747	−0.433874	−	0.900974i	$-0.642854\pi$
$181$	−2113.06	−0.867747	−0.433874	+	0.900974i	$0.642854\pi$
$182$	−1515.18	−0.617101
$183$	2398.08	0.968696
$184$	5100.37	2.04350
$185$	180.807	0.0718550
$186$	1267.99	0.499860
$187$	−630.724	−0.246648
$188$	2132.52	0.827289
$189$	751.562	0.289249
$190$	−982.873	−0.375290
$191$	512.991	0.194339	0.0971695	−	0.995268i	$-0.469021\pi$
$191$	512.991	0.194339	0.0971695	+	0.995268i	$0.469021\pi$
$192$	−8743.84	−3.28663
$193$	985.496	0.367552	0.183776	−	0.982968i	$-0.441168\pi$
$193$	985.496	0.367552	0.183776	+	0.982968i	$0.441168\pi$
$194$	−4837.95	−1.79044
$195$	−497.188	−0.182587
$196$	2719.73	0.991155
$197$	−1770.11	−0.640178	−0.320089	−	0.947387i	$-0.603713\pi$
$197$	−1770.11	−0.640178	−0.320089	+	0.947387i	$0.603713\pi$
$198$	−5129.12	−1.84096
$199$	−1862.91	−0.663608	−0.331804	−	0.943348i	$-0.607657\pi$
$199$	−1862.91	−0.663608	−0.331804	+	0.943348i	$0.607657\pi$
$200$	−1683.84	−0.595326
$201$	2046.08	0.718007
$202$	−5684.40	−1.97997
$203$	2914.01	1.00751
$204$	3263.95	1.12021
$205$	−112.972	−0.0384895
$206$	5829.02	1.97149
$207$	−2385.96	−0.801137
$208$	−2540.29	−0.846816
$209$	−1119.06	−0.370368
$210$	4457.57	1.46477
$211$	2986.99	0.974565	0.487282	−	0.873244i	$-0.337988\pi$
$211$	2986.99	0.974565	0.487282	+	0.873244i	$0.337988\pi$
$212$	−905.980	−0.293504
$213$	−5339.47	−1.71763
$214$	554.468	0.177115
$215$	−642.439	−0.203786
$216$	2322.49	0.731598
$217$	−675.669	−0.211370
$218$	−3056.83	−0.949700
$219$	2858.47	0.881999
$220$	−3134.83	−0.960683
$221$	269.345	0.0819823
$222$	−1479.11	−0.447168
$223$	395.263	0.118694	0.0593471	−	0.998237i	$-0.481098\pi$
$223$	395.263	0.118694	0.0593471	+	0.998237i	$0.481098\pi$
$224$	11031.0	3.29035
$225$	787.700	0.233393
$226$	−4149.84	−1.22143
$227$	2303.84	0.673619	0.336809	−	0.941573i	$-0.390652\pi$
$227$	2303.84	0.673619	0.336809	+	0.941573i	$0.390652\pi$
$228$	5791.05	1.68211
$229$	4265.62	1.23092	0.615459	−	0.788169i	$-0.288971\pi$
$229$	4265.62	1.23092	0.615459	+	0.788169i	$0.288971\pi$
$230$	−2024.69	−0.580454
$231$	5075.21	1.44556
$232$	9004.91	2.54828
$233$	2515.59	0.707303	0.353651	−	0.935377i	$-0.384940\pi$
$233$	2515.59	0.707303	0.353651	+	0.935377i	$0.384940\pi$
$234$	2190.34	0.611912
$235$	−517.719	−0.143712
$236$	−7192.62	−1.98390
$237$	9177.23	2.51529
$238$	−2414.82	−0.657688
$239$	5933.86	1.60598	0.802991	−	0.595992i	$-0.203241\pi$
$239$	5933.86	1.60598	0.802991	+	0.595992i	$0.203241\pi$
$240$	7473.40	2.01003
$241$	692.454	0.185083	0.0925413	−	0.995709i	$-0.470501\pi$
$241$	692.454	0.185083	0.0925413	+	0.995709i	$0.470501\pi$
$242$	2161.88	0.574260
$243$	5420.71	1.43102
$244$	−6456.94	−1.69411
$245$	−660.276	−0.172177
$246$	924.184	0.239528
$247$	477.884	0.123105
$248$	−2087.96	−0.534619
$249$	4288.53	1.09146
$250$	668.433	0.169102
$251$	−3959.15	−0.995615	−0.497807	−	0.867288i	$-0.665861\pi$
$251$	−3959.15	−0.995615	−0.497807	+	0.867288i	$0.665861\pi$
$252$	−14143.7	−3.53559
$253$	−2305.24	−0.572842
$254$	−8410.96	−2.07776
$255$	−792.397	−0.194595
$256$	1892.07	0.461932
$257$	6167.72	1.49701	0.748506	−	0.663128i	$-0.230771\pi$
$257$	6167.72	1.49701	0.748506	+	0.663128i	$0.230771\pi$
$258$	5255.54	1.26820
$259$	788.164	0.189089
$260$	1338.70	0.319318
$261$	−4212.51	−0.999033
$262$	−8319.77	−1.96182
$263$	5055.81	1.18538	0.592690	−	0.805431i	$-0.298066\pi$
$263$	5055.81	1.18538	0.592690	+	0.805431i	$0.298066\pi$
$264$	15683.5	3.65625
$265$	219.947	0.0509858
$266$	−4284.49	−0.987590
$267$	−3393.71	−0.777870
$268$	−5509.16	−1.25569
$269$	−3169.74	−0.718448	−0.359224	−	0.933251i	$-0.616959\pi$
$269$	−3169.74	−0.718448	−0.359224	+	0.933251i	$0.616959\pi$
$270$	−921.958	−0.207810
$271$	4336.41	0.972022	0.486011	−	0.873953i	$-0.338451\pi$
$271$	4336.41	0.972022	0.486011	+	0.873953i	$0.338451\pi$
$272$	−4048.61	−0.902511
$273$	−2167.32	−0.480484
$274$	−1861.67	−0.410466
$275$	761.051	0.166884
$276$	11929.4	2.60169
$277$	−1621.41	−0.351701	−0.175850	−	0.984417i	$-0.556268\pi$
$277$	−1621.41	−0.351701	−0.175850	+	0.984417i	$0.556268\pi$
$278$	−7294.26	−1.57367
$279$	976.748	0.209593
$280$	−7340.10	−1.56662
$281$	−2833.59	−0.601557	−0.300779	−	0.953694i	$-0.597247\pi$
$281$	−2833.59	−0.601557	−0.300779	+	0.953694i	$0.597247\pi$
$282$	4235.25	0.894347
$283$	−2975.96	−0.625096	−0.312548	−	0.949902i	$-0.601183\pi$
$283$	−2975.96	−0.625096	−0.312548	+	0.949902i	$0.601183\pi$
$284$	14376.8	3.00389
$285$	−1405.91	−0.292206
$286$	2116.24	0.437539
$287$	−492.464	−0.101287
$288$	−15946.4	−3.26267
$289$	−4483.73	−0.912626
$290$	−3574.68	−0.723837
$291$	−6920.24	−1.39406
$292$	−7696.56	−1.54249
$293$	−1269.05	−0.253034	−0.126517	−	0.991964i	$-0.540380\pi$
$293$	−1269.05	−0.253034	−0.126517	+	0.991964i	$0.540380\pi$
$294$	5401.46	1.07149
$295$	1746.17	0.344631
$296$	2435.59	0.478263
$297$	−1049.70	−0.205084
$298$	−7311.55	−1.42130
$299$	984.430	0.190405
$300$	−3938.38	−0.757942
$301$	−2800.49	−0.536271
$302$	−3129.21	−0.596244
$303$	−8131.01	−1.54163
$304$	−7183.23	−1.35522
$305$	1567.57	0.294291
$306$	3490.88	0.652157
$307$	−705.793	−0.131211	−0.0656054	−	0.997846i	$-0.520898\pi$
$307$	−705.793	−0.131211	−0.0656054	+	0.997846i	$0.520898\pi$
$308$	−13665.2	−2.52808
$309$	8337.87	1.53503
$310$	828.857	0.151858
$311$	−6997.52	−1.27586	−0.637931	−	0.770094i	$-0.720210\pi$
$311$	−6997.52	−1.27586	−0.637931	+	0.770094i	$0.720210\pi$
$312$	−6697.47	−1.21529
$313$	−2759.12	−0.498258	−0.249129	−	0.968470i	$-0.580144\pi$
$313$	−2759.12	−0.498258	−0.249129	+	0.968470i	$0.580144\pi$
$314$	−12379.0	−2.22481
$315$	3433.71	0.614182
$316$	−24710.1	−4.39889
$317$	2810.56	0.497972	0.248986	−	0.968507i	$-0.419903\pi$
$317$	2810.56	0.497972	0.248986	+	0.968507i	$0.419903\pi$
$318$	−1799.30	−0.317295
$319$	−4069.99	−0.714344
$320$	−5715.63	−0.998480
$321$	793.115	0.137905
$322$	−8825.95	−1.52749
$323$	761.631	0.131202
$324$	−12088.7	−2.07282
$325$	−325.000	−0.0554700
$326$	−8968.19	−1.52363
$327$	−4372.51	−0.739451
$328$	−1521.82	−0.256184
$329$	−2256.81	−0.378183
$330$	−6225.87	−1.03855
$331$	1450.45	0.240857	0.120429	−	0.992722i	$-0.461573\pi$
$331$	1450.45	0.240857	0.120429	+	0.992722i	$0.461573\pi$
$332$	−11547.0	−1.90881
$333$	−1139.37	−0.187499
$334$	−9973.31	−1.63388
$335$	1337.47	0.218131
$336$	32577.7	5.28946
$337$	−6281.14	−1.01530	−0.507649	−	0.861564i	$-0.669485\pi$
$337$	−6281.14	−1.01530	−0.507649	+	0.861564i	$0.669485\pi$
$338$	−903.722	−0.145432
$339$	−5935.96	−0.951023
$340$	2133.56	0.340320
$341$	943.704	0.149866
$342$	6193.67	0.979285
$343$	4597.70	0.723769
$344$	−8654.10	−1.35639
$345$	−2896.14	−0.451950
$346$	−17713.6	−2.75229
$347$	1632.12	0.252498	0.126249	−	0.991999i	$-0.459706\pi$
$347$	1632.12	0.252498	0.126249	+	0.991999i	$0.459706\pi$
$348$	21061.9	3.24436
$349$	5836.46	0.895182	0.447591	−	0.894238i	$-0.352282\pi$
$349$	5836.46	0.895182	0.447591	+	0.894238i	$0.352282\pi$
$350$	2913.80	0.444998
$351$	448.267	0.0681672
$352$	−15406.9	−2.33293
$353$	−3215.04	−0.484758	−0.242379	−	0.970182i	$-0.577928\pi$
$353$	−3215.04	−0.484758	−0.242379	+	0.970182i	$0.577928\pi$
$354$	−14284.8	−2.14471
$355$	−3490.28	−0.521817
$356$	9137.70	1.36038
$357$	−3454.18	−0.512086
$358$	8054.94	1.18915
$359$	9815.62	1.44303	0.721516	−	0.692398i	$-0.243446\pi$
$359$	9815.62	1.44303	0.721516	+	0.692398i	$0.243446\pi$
$360$	10610.9	1.55345
$361$	−5507.68	−0.802986
$362$	11299.5	1.64058
$363$	3092.37	0.447128
$364$	5835.60	0.840298
$365$	1868.51	0.267952
$366$	−12823.7	−1.83143
$367$	−1060.74	−0.150872	−0.0754359	−	0.997151i	$-0.524035\pi$
$367$	−1060.74	−0.150872	−0.0754359	+	0.997151i	$0.524035\pi$
$368$	−14797.3	−2.09609
$369$	711.908	0.100435
$370$	−966.858	−0.135850
$371$	958.783	0.134171
$372$	−4883.59	−0.680652
$373$	−11332.2	−1.57308	−0.786540	−	0.617539i	$-0.788130\pi$
$373$	−11332.2	−1.57308	−0.786540	+	0.617539i	$0.788130\pi$
$374$	3372.77	0.466316
$375$	956.132	0.131665
$376$	−6974.03	−0.956537
$377$	1738.05	0.237438
$378$	−4018.95	−0.546859
$379$	3816.06	0.517197	0.258599	−	0.965985i	$-0.416739\pi$
$379$	3816.06	0.517197	0.258599	+	0.965985i	$0.416739\pi$
$380$	3785.47	0.511027
$381$	−12031.1	−1.61777
$382$	−2743.20	−0.367420
$383$	12281.8	1.63856	0.819282	−	0.573391i	$-0.194372\pi$
$383$	12281.8	1.63856	0.819282	+	0.573391i	$0.194372\pi$
$384$	15787.5	2.09806
$385$	3317.54	0.439162
$386$	−5269.91	−0.694899
$387$	4048.40	0.531761
$388$	18633.0	2.43801
$389$	−12091.1	−1.57595	−0.787976	−	0.615706i	$-0.788871\pi$
$389$	−12091.1	−1.57595	−0.787976	+	0.615706i	$0.788871\pi$
$390$	2658.70	0.345201
$391$	1568.94	0.202928
$392$	−8894.37	−1.14600
$393$	−11900.7	−1.52750
$394$	9465.60	1.21033
$395$	5998.93	0.764149
$396$	19754.5	2.50682
$397$	−9794.12	−1.23817	−0.619084	−	0.785325i	$-0.712496\pi$
$397$	−9794.12	−1.23817	−0.619084	+	0.785325i	$0.712496\pi$
$398$	9961.84	1.25463
$399$	−6128.57	−0.768952
$400$	4885.18	0.610648
$401$	−6958.12	−0.866514	−0.433257	−	0.901271i	$-0.642636\pi$
$401$	−6958.12	−0.866514	−0.433257	+	0.901271i	$0.642636\pi$
$402$	−10941.3	−1.35747
$403$	−403.000	−0.0498135
$404$	21893.1	2.69609
$405$	2934.81	0.360078
$406$	−15582.6	−1.90481
$407$	−1100.83	−0.134069
$408$	−10674.1	−1.29522
$409$	−1208.59	−0.146115	−0.0730575	−	0.997328i	$-0.523276\pi$
$409$	−1208.59	−0.146115	−0.0730575	+	0.997328i	$0.523276\pi$
$410$	604.116	0.0727687
$411$	−2662.95	−0.319595
$412$	−22450.1	−2.68455
$413$	7611.83	0.906910
$414$	12758.8	1.51464
$415$	2803.31	0.331588
$416$	6579.38	0.775434
$417$	−10433.8	−1.22528
$418$	5984.13	0.700224
$419$	13569.7	1.58216	0.791078	−	0.611715i	$-0.209520\pi$
$419$	13569.7	1.58216	0.791078	+	0.611715i	$0.209520\pi$
$420$	−17168.0	−1.99455
$421$	−8053.65	−0.932330	−0.466165	−	0.884698i	$-0.654365\pi$
$421$	−8053.65	−0.932330	−0.466165	+	0.884698i	$0.654365\pi$
$422$	−15972.9	−1.84253
$423$	3262.46	0.375003
$424$	2962.84	0.339359
$425$	−517.971	−0.0591183
$426$	28552.7	3.24737
$427$	6833.27	0.774438
$428$	−2135.50	−0.241176
$429$	3027.09	0.340674
$430$	3435.42	0.385281
$431$	−4748.41	−0.530680	−0.265340	−	0.964155i	$-0.585484\pi$
$431$	−4748.41	−0.530680	−0.265340	+	0.964155i	$0.585484\pi$
$432$	−6738.04	−0.750426
$433$	−4176.29	−0.463510	−0.231755	−	0.972774i	$-0.574447\pi$
$433$	−4176.29	−0.463510	−0.231755	+	0.972774i	$0.574447\pi$
$434$	3613.12	0.399620
$435$	−5113.25	−0.563590
$436$	11773.2	1.29319
$437$	2783.69	0.304718
$438$	−15285.6	−1.66752
$439$	7338.41	0.797821	0.398910	−	0.916990i	$-0.369388\pi$
$439$	7338.41	0.797821	0.398910	+	0.916990i	$0.369388\pi$
$440$	10251.9	1.11077
$441$	4160.80	0.449281
$442$	−1440.31	−0.154997
$443$	−7966.74	−0.854428	−0.427214	−	0.904151i	$-0.640505\pi$
$443$	−7966.74	−0.854428	−0.427214	+	0.904151i	$0.640505\pi$
$444$	5696.69	0.608903
$445$	−2218.38	−0.236318
$446$	−2113.66	−0.224405
$447$	−10458.5	−1.10664
$448$	−24915.3	−2.62754
$449$	14455.3	1.51935	0.759673	−	0.650305i	$-0.225359\pi$
$449$	14455.3	1.51935	0.759673	+	0.650305i	$0.225359\pi$
$450$	−4212.20	−0.441256
$451$	687.823	0.0718144
$452$	15982.8	1.66320
$453$	−4476.04	−0.464245
$454$	−12319.7	−1.27355
$455$	−1416.72	−0.145972
$456$	−18938.6	−1.94491
$457$	−13179.6	−1.34905	−0.674527	−	0.738250i	$-0.735652\pi$
$457$	−13179.6	−1.34905	−0.674527	+	0.738250i	$0.735652\pi$
$458$	−22810.3	−2.32719
$459$	714.428	0.0726506
$460$	7797.97	0.790396
$461$	14112.9	1.42582	0.712910	−	0.701255i	$-0.247377\pi$
$461$	14112.9	1.42582	0.712910	+	0.701255i	$0.247377\pi$
$462$	−27139.5	−2.73299
$463$	3090.13	0.310174	0.155087	−	0.987901i	$-0.450434\pi$
$463$	3090.13	0.310174	0.155087	+	0.987901i	$0.450434\pi$
$464$	−26125.2	−2.61387
$465$	1185.60	0.118239
$466$	−13452.0	−1.33724
$467$	9674.31	0.958616	0.479308	−	0.877647i	$-0.340888\pi$
$467$	9674.31	0.958616	0.479308	+	0.877647i	$0.340888\pi$
$468$	−8435.96	−0.833232
$469$	5830.25	0.574021
$470$	2768.48	0.271703
$471$	−17707.1	−1.73227
$472$	23522.2	2.29385
$473$	3911.43	0.380228
$474$	−49074.9	−4.75545
$475$	−919.008	−0.0887726
$476$	9300.53	0.895565
$477$	−1386.02	−0.133043
$478$	−31731.1	−3.03629
$479$	−2020.87	−0.192768	−0.0963841	−	0.995344i	$-0.530728\pi$
$479$	−2020.87	−0.192768	−0.0963841	+	0.995344i	$0.530728\pi$
$480$	−19356.2	−1.84059
$481$	470.097	0.0445626
$482$	−3702.88	−0.349920
$483$	−12624.7	−1.18932
$484$	−8326.34	−0.781962
$485$	−4523.59	−0.423517
$486$	−28987.1	−2.70552
$487$	−6123.95	−0.569820	−0.284910	−	0.958554i	$-0.591964\pi$
$487$	−6123.95	−0.569820	−0.284910	+	0.958554i	$0.591964\pi$
$488$	21116.2	1.95879
$489$	−12828.2	−1.18632
$490$	3530.80	0.325521
$491$	10812.6	0.993816	0.496908	−	0.867803i	$-0.334469\pi$
$491$	10812.6	0.993816	0.496908	+	0.867803i	$0.334469\pi$
$492$	−3559.43	−0.326162
$493$	2770.03	0.253055
$494$	−2555.47	−0.232745
$495$	−4795.84	−0.435469
$496$	6057.63	0.548378
$497$	−15214.7	−1.37318
$498$	−22932.8	−2.06354
$499$	−12405.8	−1.11295	−0.556474	−	0.830865i	$-0.687846\pi$
$499$	−12405.8	−1.11295	−0.556474	+	0.830865i	$0.687846\pi$
$500$	−2574.42	−0.230264
$501$	−14265.9	−1.27216
$502$	21171.4	1.88232
$503$	9638.71	0.854411	0.427205	−	0.904155i	$-0.359498\pi$
$503$	9638.71	0.854411	0.427205	+	0.904155i	$0.359498\pi$
$504$	46254.4	4.08797
$505$	−5315.04	−0.468349
$506$	12327.2	1.08302
$507$	−1292.69	−0.113235
$508$	32394.2	2.82926
$509$	−5616.38	−0.489080	−0.244540	−	0.969639i	$-0.578637\pi$
$509$	−5616.38	−0.489080	−0.244540	+	0.969639i	$0.578637\pi$
$510$	4237.32	0.367905
$511$	8145.14	0.705126
$512$	6394.07	0.551916
$513$	1267.57	0.109093
$514$	−32981.7	−2.83027
$515$	5450.26	0.466344
$516$	−20241.4	−1.72689
$517$	3152.08	0.268140
$518$	−4214.68	−0.357495
$519$	−25337.7	−2.14297
$520$	−4377.98	−0.369206
$521$	−15392.6	−1.29436	−0.647179	−	0.762338i	$-0.724051\pi$
$521$	−15392.6	−1.29436	−0.647179	+	0.762338i	$0.724051\pi$
$522$	22526.2	1.88879
$523$	−12869.5	−1.07599	−0.537996	−	0.842948i	$-0.680818\pi$
$523$	−12869.5	−1.07599	−0.537996	+	0.842948i	$0.680818\pi$
$524$	32043.0	2.67139
$525$	4167.92	0.346482
$526$	−27035.8	−2.24110
$527$	−642.284	−0.0530898
$528$	−45501.1	−3.75035
$529$	−6432.67	−0.528698
$530$	−1176.16	−0.0963945
$531$	−11003.7	−0.899283
$532$	16501.4	1.34479
$533$	−293.728	−0.0238701
$534$	18147.7	1.47065
$535$	518.440	0.0418956
$536$	18016.7	1.45187
$537$	11521.8	0.925893
$538$	16950.1	1.35831
$539$	4020.03	0.321252
$540$	3550.86	0.282971
$541$	−10095.1	−0.802258	−0.401129	−	0.916022i	$-0.631382\pi$
$541$	−10095.1	−0.802258	−0.401129	+	0.916022i	$0.631382\pi$
$542$	−23188.8	−1.83772
$543$	16162.9	1.27738
$544$	10485.9	0.826434
$545$	−2858.20	−0.224646
$546$	11589.7	0.908411
$547$	−2497.10	−0.195189	−0.0975944	−	0.995226i	$-0.531115\pi$
$547$	−2497.10	−0.195189	−0.0975944	+	0.995226i	$0.531115\pi$
$548$	7170.10	0.558926
$549$	−9878.20	−0.767926
$550$	−4069.70	−0.315514
$551$	4914.72	0.379989
$552$	−39013.0	−3.00816
$553$	26150.2	2.01089
$554$	8670.44	0.664931
$555$	−1383.00	−0.105775
$556$	28093.3	2.14285
$557$	23314.3	1.77353	0.886767	−	0.462216i	$-0.152945\pi$
$557$	23314.3	1.77353	0.886767	+	0.462216i	$0.152945\pi$
$558$	−5223.13	−0.396259
$559$	−1670.34	−0.126383
$560$	21295.2	1.60694
$561$	4824.44	0.363080
$562$	15152.5	1.13731
$563$	−21229.4	−1.58919	−0.794595	−	0.607140i	$-0.792317\pi$
$563$	−21229.4	−1.58919	−0.794595	+	0.607140i	$0.792317\pi$
$564$	−16311.8	−1.21782
$565$	−3880.19	−0.288922
$566$	15913.8	1.18182
$567$	12793.3	0.947561
$568$	−47016.6	−3.47319
$569$	22816.9	1.68108	0.840541	−	0.541749i	$-0.182237\pi$
$569$	22816.9	1.68108	0.840541	+	0.541749i	$0.182237\pi$
$570$	7518.04	0.552450
$571$	16255.2	1.19134	0.595672	−	0.803228i	$-0.296886\pi$
$571$	16255.2	1.19134	0.595672	+	0.803228i	$0.296886\pi$
$572$	−8150.56	−0.595790
$573$	−3923.90	−0.286079
$574$	2633.44	0.191494
$575$	−1893.13	−0.137303
$576$	36017.7	2.60544
$577$	−6293.03	−0.454042	−0.227021	−	0.973890i	$-0.572899\pi$
$577$	−6293.03	−0.454042	−0.227021	+	0.973890i	$0.572899\pi$
$578$	23976.6	1.72542
$579$	−7538.11	−0.541059
$580$	13767.6	0.985639
$581$	12220.0	0.872586
$582$	37005.8	2.63563
$583$	−1339.13	−0.0951304
$584$	25170.2	1.78348
$585$	2048.02	0.144744
$586$	6786.22	0.478390
$587$	25226.4	1.77377	0.886885	−	0.461990i	$-0.152864\pi$
$587$	25226.4	1.77377	0.886885	+	0.461990i	$0.152864\pi$
$588$	−20803.3	−1.45904
$589$	−1139.57	−0.0797201
$590$	−9337.60	−0.651564
$591$	13539.7	0.942381
$592$	−7066.19	−0.490572
$593$	−3966.85	−0.274703	−0.137351	−	0.990522i	$-0.543859\pi$
$593$	−3966.85	−0.274703	−0.137351	+	0.990522i	$0.543859\pi$
$594$	5613.26	0.387735
$595$	−2257.91	−0.155572
$596$	28159.9	1.93536
$597$	14249.5	0.976872
$598$	−5264.21	−0.359982
$599$	−20212.3	−1.37871	−0.689357	−	0.724421i	$-0.742107\pi$
$599$	−20212.3	−1.37871	−0.689357	+	0.724421i	$0.742107\pi$
$600$	12879.8	0.876357
$601$	13170.8	0.893921	0.446961	−	0.894554i	$-0.352506\pi$
$601$	13170.8	0.893921	0.446961	+	0.894554i	$0.352506\pi$
$602$	14975.5	1.01388
$603$	−8428.23	−0.569194
$604$	12051.9	0.811898
$605$	2021.41	0.135838
$606$	43480.3	2.91463
$607$	95.8082	0.00640648	0.00320324	−	0.999995i	$-0.498980\pi$
$607$	95.8082	0.00640648	0.00320324	+	0.999995i	$0.498980\pi$
$608$	18604.6	1.24098
$609$	−22289.4	−1.48311
$610$	−8382.52	−0.556391
$611$	−1346.07	−0.0891262
$612$	−13444.9	−0.888034
$613$	−11126.4	−0.733099	−0.366550	−	0.930399i	$-0.619461\pi$
$613$	−11126.4	−0.733099	−0.366550	+	0.930399i	$0.619461\pi$
$614$	3774.20	0.248069
$615$	864.132	0.0566588
$616$	44689.5	2.92304
$617$	−13372.2	−0.872522	−0.436261	−	0.899820i	$-0.643697\pi$
$617$	−13372.2	−0.872522	−0.436261	+	0.899820i	$0.643697\pi$
$618$	−44586.5	−2.90215
$619$	−22593.8	−1.46708	−0.733540	−	0.679646i	$-0.762133\pi$
$619$	−22593.8	−1.46708	−0.733540	+	0.679646i	$0.762133\pi$
$620$	−3192.29	−0.206783
$621$	2611.17	0.168732
$622$	37419.0	2.41216
$623$	−9670.27	−0.621880
$624$	19430.8	1.24656
$625$	625.000	0.0400000
$626$	14754.3	0.942015
$627$	8559.74	0.545204
$628$	47677.1	3.02949
$629$	749.221	0.0474935
$630$	−18361.6	−1.16118
$631$	22887.7	1.44397	0.721984	−	0.691909i	$-0.243230\pi$
$631$	22887.7	1.44397	0.721984	+	0.691909i	$0.243230\pi$
$632$	80809.7	5.08614
$633$	−22847.7	−1.43462
$634$	−15029.4	−0.941473
$635$	−7864.44	−0.491481
$636$	6929.89	0.432056
$637$	−1716.72	−0.106780
$638$	21764.1	1.35055
$639$	21994.4	1.36163
$640$	10319.9	0.637392
$641$	11523.7	0.710074	0.355037	−	0.934852i	$-0.384468\pi$
$641$	11523.7	0.710074	0.355037	+	0.934852i	$0.384468\pi$
$642$	−4241.16	−0.260725
$643$	6763.42	0.414811	0.207405	−	0.978255i	$-0.433498\pi$
$643$	6763.42	0.414811	0.207405	+	0.978255i	$0.433498\pi$
$644$	33992.5	2.07996
$645$	4914.05	0.299985
$646$	−4072.79	−0.248053
$647$	21506.4	1.30681	0.653404	−	0.757009i	$-0.273340\pi$
$647$	21506.4	1.30681	0.653404	+	0.757009i	$0.273340\pi$
$648$	39533.9	2.39666
$649$	−10631.4	−0.643019
$650$	1737.93	0.104872
$651$	5168.22	0.311150
$652$	34540.4	2.07470
$653$	16909.5	1.01335	0.506676	−	0.862137i	$-0.330874\pi$
$653$	16909.5	1.01335	0.506676	+	0.862137i	$0.330874\pi$
$654$	23381.9	1.39802
$655$	−7779.17	−0.464057
$656$	4415.13	0.262777
$657$	−11774.6	−0.699197
$658$	12068.2	0.714998
$659$	1968.99	0.116390	0.0581950	−	0.998305i	$-0.481465\pi$
$659$	1968.99	0.116390	0.0581950	+	0.998305i	$0.481465\pi$
$660$	23978.5	1.41418
$661$	−6801.51	−0.400224	−0.200112	−	0.979773i	$-0.564131\pi$
$661$	−6801.51	−0.400224	−0.200112	+	0.979773i	$0.564131\pi$
$662$	−7756.22	−0.455369
$663$	−2060.23	−0.120683
$664$	37762.5	2.20703
$665$	−4006.09	−0.233609
$666$	6092.75	0.354489
$667$	10124.2	0.587722
$668$	38411.5	2.22483
$669$	−3023.39	−0.174725
$670$	−7152.09	−0.412402
$671$	−9544.00	−0.549094
$672$	−84376.4	−4.84359
$673$	−21389.3	−1.22510	−0.612552	−	0.790430i	$-0.709857\pi$
$673$	−21389.3	−1.22510	−0.612552	+	0.790430i	$0.709857\pi$
$674$	33588.2	1.91954
$675$	−862.051	−0.0491561
$676$	3480.62	0.198033
$677$	−16335.0	−0.927335	−0.463668	−	0.886009i	$-0.653467\pi$
$677$	−16335.0	−0.927335	−0.463668	+	0.886009i	$0.653467\pi$
$678$	31742.3	1.79802
$679$	−19719.0	−1.11450
$680$	−6977.43	−0.393488
$681$	−17622.2	−0.991608
$682$	−5046.42	−0.283340
$683$	−14730.5	−0.825253	−0.412627	−	0.910900i	$-0.635389\pi$
$683$	−14730.5	−0.825253	−0.412627	+	0.910900i	$0.635389\pi$
$684$	−23854.5	−1.33348
$685$	−1740.70	−0.0970933
$686$	−24586.1	−1.36837
$687$	−32628.0	−1.81199
$688$	25107.5	1.39130
$689$	571.862	0.0316201
$690$	15487.0	0.854464
$691$	21758.3	1.19787	0.598933	−	0.800799i	$-0.295591\pi$
$691$	21758.3	1.19787	0.598933	+	0.800799i	$0.295591\pi$
$692$	68222.9	3.74775
$693$	−20905.8	−1.14595
$694$	−8727.72	−0.477377
$695$	−6820.29	−0.372242
$696$	−68879.1	−3.75123
$697$	−468.132	−0.0254401
$698$	−31210.3	−1.69244
$699$	−19241.9	−1.04119
$700$	−11222.3	−0.605948
$701$	−26545.9	−1.43028	−0.715138	−	0.698983i	$-0.753636\pi$
$701$	−26545.9	−1.43028	−0.715138	+	0.698983i	$0.753636\pi$
$702$	−2397.09	−0.128878
$703$	1329.30	0.0713166
$704$	34799.1	1.86299
$705$	3960.06	0.211552
$706$	17192.3	0.916490
$707$	−23169.1	−1.23248
$708$	55016.8	2.92042
$709$	−15470.5	−0.819474	−0.409737	−	0.912204i	$-0.634380\pi$
$709$	−15470.5	−0.819474	−0.409737	+	0.912204i	$0.634380\pi$
$710$	18664.2	0.986555
$711$	−37802.9	−1.99398
$712$	−29883.2	−1.57292
$713$	−2347.49	−0.123302
$714$	18471.1	0.968157
$715$	1978.73	0.103497
$716$	−31023.1	−1.61925
$717$	−45388.4	−2.36410
$718$	−52488.7	−2.72822
$719$	6427.82	0.333403	0.166702	−	0.986007i	$-0.446688\pi$
$719$	6427.82	0.333403	0.166702	+	0.986007i	$0.446688\pi$
$720$	−30784.5	−1.59343
$721$	23758.5	1.22720
$722$	29452.1	1.51814
$723$	−5296.62	−0.272453
$724$	−43519.2	−2.23395
$725$	−3342.41	−0.171219
$726$	−16536.3	−0.845346
$727$	−23551.0	−1.20146	−0.600728	−	0.799453i	$-0.705123\pi$
$727$	−23551.0	−1.20146	−0.600728	+	0.799453i	$0.705123\pi$
$728$	−19084.3	−0.971579
$729$	−25615.4	−1.30140
$730$	−9991.82	−0.506594
$731$	−2662.12	−0.134695
$732$	49389.5	2.49384
$733$	10166.2	0.512273	0.256137	−	0.966641i	$-0.417550\pi$
$733$	10166.2	0.512273	0.256137	+	0.966641i	$0.417550\pi$
$734$	5672.25	0.285240
$735$	5050.48	0.253456
$736$	38325.1	1.91940
$737$	−8143.09	−0.406994
$738$	−3806.90	−0.189883
$739$	−28252.8	−1.40635	−0.703177	−	0.711014i	$-0.748236\pi$
$739$	−28252.8	−1.40635	−0.703177	+	0.711014i	$0.748236\pi$
$740$	3723.79	0.184985
$741$	−3655.36	−0.181219
$742$	−5127.06	−0.253666
$743$	−38436.9	−1.89787	−0.948933	−	0.315479i	$-0.897835\pi$
$743$	−38436.9	−1.89787	−0.948933	+	0.315479i	$0.897835\pi$
$744$	15970.9	0.786991
$745$	−6836.46	−0.336199
$746$	60598.5	2.97409
$747$	−17665.3	−0.865248
$748$	−12990.0	−0.634976
$749$	2259.96	0.110250
$750$	−5112.88	−0.248928
$751$	8154.32	0.396212	0.198106	−	0.980181i	$-0.436521\pi$
$751$	8154.32	0.396212	0.198106	+	0.980181i	$0.436521\pi$
$752$	20233.2	0.981155
$753$	30283.7	1.46561
$754$	−9294.18	−0.448905
$755$	−2925.88	−0.141038
$756$	15478.7	0.744651
$757$	32943.5	1.58171	0.790854	−	0.612005i	$-0.209637\pi$
$757$	32943.5	1.58171	0.790854	+	0.612005i	$0.209637\pi$
$758$	−20406.2	−0.977821
$759$	17632.9	0.843258
$760$	−12379.7	−0.590866
$761$	−650.636	−0.0309928	−0.0154964	−	0.999880i	$-0.504933\pi$
$761$	−650.636	−0.0309928	−0.0154964	+	0.999880i	$0.504933\pi$
$762$	64335.9	3.05859
$763$	−12459.3	−0.591165
$764$	10565.3	0.500311
$765$	3264.05	0.154264
$766$	−65676.4	−3.09789
$767$	4540.05	0.213731
$768$	−14472.6	−0.679992
$769$	13632.7	0.639284	0.319642	−	0.947538i	$-0.396437\pi$
$769$	13632.7	0.639284	0.319642	+	0.947538i	$0.396437\pi$
$770$	−17740.4	−0.830286
$771$	−47177.3	−2.20369
$772$	20296.7	0.946235
$773$	−20561.4	−0.956715	−0.478357	−	0.878165i	$-0.658768\pi$
$773$	−20561.4	−0.956715	−0.478357	+	0.878165i	$0.658768\pi$
$774$	−21648.7	−1.00536
$775$	775.000	0.0359211
$776$	−60935.9	−2.81891
$777$	−6028.71	−0.278351
$778$	64657.0	2.97952
$779$	−830.580	−0.0382011
$780$	−10239.8	−0.470056
$781$	21250.3	0.973617
$782$	−8389.86	−0.383658
$783$	4610.12	0.210412
$784$	25804.5	1.17550
$785$	−11574.7	−0.526265
$786$	63638.4	2.88792
$787$	10953.7	0.496134	0.248067	−	0.968743i	$-0.420205\pi$
$787$	10953.7	0.496134	0.248067	+	0.968743i	$0.420205\pi$
$788$	−36456.1	−1.64809
$789$	−38672.2	−1.74495
$790$	−32079.1	−1.44471
$791$	−16914.3	−0.760309
$792$	−64603.3	−2.89846
$793$	4075.68	0.182511
$794$	52373.7	2.34090
$795$	−1682.39	−0.0750542
$796$	−38367.3	−1.70841
$797$	−181.145	−0.00805082	−0.00402541	−	0.999992i	$-0.501281\pi$
$797$	−181.145	−0.00805082	−0.00402541	+	0.999992i	$0.501281\pi$
$798$	32772.3	1.45379
$799$	−2145.30	−0.0949880
$800$	−12652.7	−0.559173
$801$	13979.4	0.616650
$802$	37208.3	1.63824
$803$	−11376.3	−0.499950
$804$	42139.9	1.84846
$805$	−8252.46	−0.361318
$806$	2155.03	0.0941782
$807$	24245.5	1.05760
$808$	−71597.3	−3.11731
$809$	29389.7	1.27724	0.638619	−	0.769523i	$-0.279506\pi$
$809$	29389.7	1.27724	0.638619	+	0.769523i	$0.279506\pi$
$810$	−15693.8	−0.680770
$811$	18129.0	0.784951	0.392476	−	0.919762i	$-0.371619\pi$
$811$	18129.0	0.784951	0.392476	+	0.919762i	$0.371619\pi$
$812$	60015.3	2.59375
$813$	−33169.4	−1.43088
$814$	5886.63	0.253472
$815$	−8385.46	−0.360405
$816$	30968.0	1.32855
$817$	−4723.25	−0.202259
$818$	6462.91	0.276247
$819$	8927.63	0.380900
$820$	−2326.71	−0.0990882
$821$	24012.4	1.02075	0.510376	−	0.859951i	$-0.329506\pi$
$821$	24012.4	1.02075	0.510376	+	0.859951i	$0.329506\pi$
$822$	14240.0	0.604231
$823$	231.768	0.00981642	0.00490821	−	0.999988i	$-0.498438\pi$
$823$	231.768	0.00981642	0.00490821	+	0.999988i	$0.498438\pi$
$824$	73418.8	3.10396
$825$	−5821.32	−0.245664
$826$	−40704.0	−1.71462
$827$	41497.0	1.74485	0.872425	−	0.488748i	$-0.162546\pi$
$827$	41497.0	1.74485	0.872425	+	0.488748i	$0.162546\pi$
$828$	−49139.7	−2.06247
$829$	−40514.8	−1.69739	−0.848696	−	0.528882i	$-0.822612\pi$
$829$	−40514.8	−1.69739	−0.848696	+	0.528882i	$0.822612\pi$
$830$	−14990.6	−0.626905
$831$	12402.3	0.517725
$832$	−14860.6	−0.619231
$833$	−2736.03	−0.113803
$834$	55794.2	2.31654
$835$	−9325.27	−0.386484
$836$	−23047.5	−0.953485
$837$	−1068.94	−0.0441435
$838$	−72563.6	−2.99125
$839$	−5605.63	−0.230665	−0.115333	−	0.993327i	$-0.536793\pi$
$839$	−5605.63	−0.230665	−0.115333	+	0.993327i	$0.536793\pi$
$840$	56144.8	2.30617
$841$	−6514.28	−0.267099
$842$	43066.6	1.76268
$843$	21674.3	0.885529
$844$	61518.3	2.50894
$845$	−845.000	−0.0344010
$846$	−17445.9	−0.708985
$847$	8811.62	0.357463
$848$	−8595.85	−0.348093
$849$	22763.3	0.920180
$850$	2769.83	0.111770
$851$	2738.33	0.110304
$852$	−109969.	−4.42190
$853$	626.565	0.0251503	0.0125751	−	0.999921i	$-0.495997\pi$
$853$	626.565	0.0251503	0.0125751	+	0.999921i	$0.495997\pi$
$854$	−36540.7	−1.46416
$855$	5791.22	0.231644
$856$	6983.75	0.278855
$857$	464.028	0.0184958	0.00924789	−	0.999957i	$-0.497056\pi$
$857$	464.028	0.0184958	0.00924789	+	0.999957i	$0.497056\pi$
$858$	−16187.2	−0.644083
$859$	−35027.6	−1.39130	−0.695650	−	0.718381i	$-0.744883\pi$
$859$	−35027.6	−1.39130	−0.695650	+	0.718381i	$0.744883\pi$
$860$	−13231.3	−0.524632
$861$	3766.88	0.149100
$862$	25392.0	1.00331
$863$	15129.1	0.596756	0.298378	−	0.954448i	$-0.403554\pi$
$863$	15129.1	0.596756	0.298378	+	0.954448i	$0.403554\pi$
$864$	17451.6	0.687170
$865$	−16562.6	−0.651037
$866$	22332.6	0.876318
$867$	34296.3	1.34344
$868$	−13915.7	−0.544157
$869$	−36523.9	−1.42577
$870$	27342.9	1.06553
$871$	3477.43	0.135279
$872$	−38502.0	−1.49523
$873$	28505.9	1.10513
$874$	−14885.7	−0.576105
$875$	2724.47	0.105262
$876$	58871.4	2.27064
$877$	−43349.5	−1.66911	−0.834554	−	0.550926i	$-0.814275\pi$
$877$	−43349.5	−1.66911	−0.834554	+	0.550926i	$0.814275\pi$
$878$	−39241.9	−1.50837
$879$	9707.06	0.372481
$880$	−29743.0	−1.13936
$881$	−16901.2	−0.646327	−0.323164	−	0.946343i	$-0.604746\pi$
$881$	−16901.2	−0.646327	−0.323164	+	0.946343i	$0.604746\pi$
$882$	−22249.7	−0.849418
$883$	−29564.7	−1.12676	−0.563380	−	0.826198i	$-0.690499\pi$
$883$	−29564.7	−1.12676	−0.563380	+	0.826198i	$0.690499\pi$
$884$	5547.26	0.211057
$885$	−13356.6	−0.507318
$886$	42601.9	1.61539
$887$	−4484.72	−0.169766	−0.0848828	−	0.996391i	$-0.527052\pi$
$887$	−4484.72	−0.169766	−0.0848828	+	0.996391i	$0.527052\pi$
$888$	−18630.0	−0.704032
$889$	−34282.3	−1.29335
$890$	11862.7	0.446786
$891$	−17868.3	−0.671842
$892$	8140.61	0.305569
$893$	−3806.30	−0.142635
$894$	55926.4	2.09224
$895$	7531.55	0.281287
$896$	44986.1	1.67732
$897$	−7529.96	−0.280288
$898$	−77299.1	−2.87250
$899$	−4144.59	−0.153759
$900$	16223.0	0.600852
$901$	911.409	0.0336997
$902$	−3678.11	−0.135773
$903$	21421.1	0.789423
$904$	−52268.8	−1.92305
$905$	10565.3	0.388068
$906$	23935.5	0.877708
$907$	34321.9	1.25649	0.628247	−	0.778014i	$-0.283773\pi$
$907$	34321.9	1.25649	0.628247	+	0.778014i	$0.283773\pi$
$908$	47448.6	1.73418
$909$	33493.3	1.22211
$910$	7575.89	0.275976
$911$	−38826.5	−1.41205	−0.706026	−	0.708186i	$-0.749514\pi$
$911$	−38826.5	−1.41205	−0.706026	+	0.708186i	$0.749514\pi$
$912$	54944.9	1.99496
$913$	−17067.7	−0.618683
$914$	70477.7	2.55054
$915$	−11990.4	−0.433214
$916$	87852.2	3.16891
$917$	−33910.6	−1.22118
$918$	−3820.38	−0.137354
$919$	4482.85	0.160909	0.0804546	−	0.996758i	$-0.474363\pi$
$919$	4482.85	0.160909	0.0804546	+	0.996758i	$0.474363\pi$
$920$	−25501.8	−0.913881
$921$	5398.64	0.193150
$922$	−75468.2	−2.69568
$923$	−9074.74	−0.323617
$924$	104526.	3.72148
$925$	−904.033	−0.0321345
$926$	−16524.4	−0.586419
$927$	−34345.4	−1.21688
$928$	67664.5	2.39353
$929$	6272.95	0.221538	0.110769	−	0.993846i	$-0.464669\pi$
$929$	6272.95	0.221538	0.110769	+	0.993846i	$0.464669\pi$
$930$	−6339.97	−0.223544
$931$	−4854.39	−0.170887
$932$	51809.5	1.82090
$933$	53524.4	1.87815
$934$	−51733.0	−1.81237
$935$	3153.62	0.110304
$936$	27588.3	0.963409
$937$	4547.33	0.158543	0.0792716	−	0.996853i	$-0.474741\pi$
$937$	4547.33	0.158543	0.0792716	+	0.996853i	$0.474741\pi$
$938$	−31177.1	−1.08525
$939$	21104.7	0.733467
$940$	−10662.6	−0.369975
$941$	25521.6	0.884144	0.442072	−	0.896980i	$-0.354244\pi$
$941$	25521.6	0.884144	0.442072	+	0.896980i	$0.354244\pi$
$942$	94688.0	3.27506
$943$	−1710.98	−0.0590849
$944$	−68243.0	−2.35288
$945$	−3757.81	−0.129356
$946$	−20916.3	−0.718865
$947$	−20572.6	−0.705936	−0.352968	−	0.935635i	$-0.614827\pi$
$947$	−20572.6	−0.705936	−0.352968	+	0.935635i	$0.614827\pi$
$948$	189009.	6.47544
$949$	4858.14	0.166177
$950$	4914.36	0.167835
$951$	−21498.2	−0.733045
$952$	−30415.7	−1.03548
$953$	−8335.60	−0.283333	−0.141667	−	0.989914i	$-0.545246\pi$
$953$	−8335.60	−0.283333	−0.141667	+	0.989914i	$0.545246\pi$
$954$	7411.69	0.251533
$955$	−2564.96	−0.0869110
$956$	122210.	4.13448
$957$	31131.6	1.05156
$958$	10806.5	0.364451
$959$	−7588.00	−0.255505
$960$	43719.2	1.46982
$961$	961.000	0.0322581
$962$	−2513.83	−0.0842506
$963$	−3267.00	−0.109323
$964$	14261.4	0.476481
$965$	−4927.48	−0.164374
$966$	67510.2	2.24856
$967$	−6623.27	−0.220259	−0.110129	−	0.993917i	$-0.535127\pi$
$967$	−6623.27	−0.220259	−0.110129	+	0.993917i	$0.535127\pi$
$968$	27229.8	0.904130
$969$	−5825.75	−0.193137
$970$	24189.8	0.800708
$971$	39476.4	1.30469	0.652347	−	0.757921i	$-0.273785\pi$
$971$	39476.4	1.30469	0.652347	+	0.757921i	$0.273785\pi$
$972$	111642.	3.68407
$973$	−29730.7	−0.979571
$974$	32747.6	1.07731
$975$	2485.94	0.0816553
$976$	−61262.9	−2.00920
$977$	5886.05	0.192744	0.0963722	−	0.995345i	$-0.469276\pi$
$977$	5886.05	0.192744	0.0963722	+	0.995345i	$0.469276\pi$
$978$	68598.2	2.24287
$979$	13506.4	0.440927
$980$	−13598.6	−0.443258
$981$	18011.3	0.586193
$982$	−57819.8	−1.87892
$983$	−40253.9	−1.30610	−0.653051	−	0.757314i	$-0.726511\pi$
$983$	−40253.9	−1.30610	−0.653051	+	0.757314i	$0.726511\pi$
$984$	11640.5	0.377118
$985$	8850.55	0.286296
$986$	−14812.7	−0.478429
$987$	17262.5	0.556708
$988$	9842.21	0.316926
$989$	−9729.79	−0.312830
$990$	25645.6	0.823304
$991$	48429.2	1.55238	0.776188	−	0.630501i	$-0.217151\pi$
$991$	48429.2	1.55238	0.776188	+	0.630501i	$0.217151\pi$
$992$	−15689.3	−0.502153
$993$	−11094.5	−0.354557
$994$	81360.0	2.59616
$995$	9314.54	0.296775
$996$	88324.0	2.80989
$997$	48321.0	1.53495	0.767474	−	0.641081i	$-0.221514\pi$
$997$	48321.0	1.53495	0.767474	+	0.641081i	$0.221514\pi$
$998$	66339.8	2.10416
$999$	1246.92	0.0394902

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2015.4.a.d.1.1	✓	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)

\(f(q)\)	\(=\)	\(q-5.34747 q^{2} -7.64905 q^{3} +20.5954 q^{4} -5.00000 q^{5} +40.9031 q^{6} -21.7958 q^{7} -67.3535 q^{8} +31.5080 q^{9} +O(q^{10})\)	\(q-5.34747 q^{2} -7.64905 q^{3} +20.5954 q^{4} -5.00000 q^{5} +40.9031 q^{6} -21.7958 q^{7} -67.3535 q^{8} +31.5080 q^{9} +26.7373 q^{10} +30.4421 q^{11} -157.535 q^{12} -13.0000 q^{13} +116.552 q^{14} +38.2453 q^{15} +195.407 q^{16} -20.7188 q^{17} -168.488 q^{18} -36.7603 q^{19} -102.977 q^{20} +166.717 q^{21} -162.788 q^{22} -75.7254 q^{23} +515.190 q^{24} +25.0000 q^{25} +69.5171 q^{26} -34.4820 q^{27} -448.892 q^{28} -133.696 q^{29} -204.515 q^{30} +31.0000 q^{31} -506.106 q^{32} -232.853 q^{33} +110.793 q^{34} +108.979 q^{35} +648.920 q^{36} -36.1613 q^{37} +196.575 q^{38} +99.4377 q^{39} +336.767 q^{40} +22.5945 q^{41} -891.513 q^{42} +128.488 q^{43} +626.966 q^{44} -157.540 q^{45} +404.939 q^{46} +103.544 q^{47} -1494.68 q^{48} +132.055 q^{49} -133.687 q^{50} +158.479 q^{51} -267.740 q^{52} -43.9894 q^{53} +184.392 q^{54} -152.210 q^{55} +1468.02 q^{56} +281.182 q^{57} +714.937 q^{58} -349.234 q^{59} +787.677 q^{60} -313.514 q^{61} -165.771 q^{62} -686.741 q^{63} +1143.13 q^{64} +65.0000 q^{65} +1245.17 q^{66} -267.495 q^{67} -426.713 q^{68} +579.227 q^{69} -582.760 q^{70} +698.057 q^{71} -2122.17 q^{72} -373.703 q^{73} +193.372 q^{74} -191.226 q^{75} -757.093 q^{76} -663.508 q^{77} -531.740 q^{78} -1199.79 q^{79} -977.036 q^{80} -586.961 q^{81} -120.823 q^{82} -560.661 q^{83} +3433.60 q^{84} +103.594 q^{85} -687.084 q^{86} +1022.65 q^{87} -2050.38 q^{88} +443.677 q^{89} +842.440 q^{90} +283.345 q^{91} -1559.59 q^{92} -237.121 q^{93} -553.697 q^{94} +183.802 q^{95} +3871.23 q^{96} +904.719 q^{97} -706.160 q^{98} +959.169 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 5 q^{2} - 17 q^{3} + 149 q^{4} - 200 q^{5} - 35 q^{6} - 20 q^{7} - 39 q^{8} + 247 q^{9}+O(q^{10}) \) 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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