LMFDB - Embedded newform 2015.4.a.d.1.3

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			1.3
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)

$f(q)$	$=$	$q-5.15631 q^{2} +4.91805 q^{3} +18.5876 q^{4} -5.00000 q^{5} -25.3590 q^{6} +12.2185 q^{7} -54.5927 q^{8} -2.81278 q^{9} +O(q^{10})$	\(q-5.15631 q^{2} +4.91805 q^{3} +18.5876 q^{4} -5.00000 q^{5} -25.3590 q^{6} +12.2185 q^{7} -54.5927 q^{8} -2.81278 q^{9} +25.7816 q^{10} +0.204412 q^{11} +91.4145 q^{12} -13.0000 q^{13} -63.0027 q^{14} -24.5903 q^{15} +132.797 q^{16} +116.248 q^{17} +14.5036 q^{18} -19.1042 q^{19} -92.9378 q^{20} +60.0914 q^{21} -1.05401 q^{22} -162.478 q^{23} -268.490 q^{24} +25.0000 q^{25} +67.0321 q^{26} -146.621 q^{27} +227.113 q^{28} +40.9893 q^{29} +126.795 q^{30} +31.0000 q^{31} -248.000 q^{32} +1.00531 q^{33} -599.409 q^{34} -61.0927 q^{35} -52.2827 q^{36} +6.38224 q^{37} +98.5070 q^{38} -63.9347 q^{39} +272.964 q^{40} +47.2831 q^{41} -309.850 q^{42} -221.328 q^{43} +3.79953 q^{44} +14.0639 q^{45} +837.788 q^{46} +393.370 q^{47} +653.101 q^{48} -193.707 q^{49} -128.908 q^{50} +571.712 q^{51} -241.638 q^{52} +321.421 q^{53} +756.022 q^{54} -1.02206 q^{55} -667.044 q^{56} -93.9553 q^{57} -211.353 q^{58} +173.952 q^{59} -457.073 q^{60} -691.729 q^{61} -159.846 q^{62} -34.3681 q^{63} +216.389 q^{64} +65.0000 q^{65} -5.18370 q^{66} -415.895 q^{67} +2160.76 q^{68} -799.076 q^{69} +315.013 q^{70} +608.218 q^{71} +153.557 q^{72} +1192.68 q^{73} -32.9088 q^{74} +122.951 q^{75} -355.100 q^{76} +2.49762 q^{77} +329.667 q^{78} -682.284 q^{79} -663.984 q^{80} -645.143 q^{81} -243.806 q^{82} -650.672 q^{83} +1116.95 q^{84} -581.238 q^{85} +1141.24 q^{86} +201.587 q^{87} -11.1594 q^{88} +651.566 q^{89} -72.5178 q^{90} -158.841 q^{91} -3020.07 q^{92} +152.460 q^{93} -2028.34 q^{94} +95.5208 q^{95} -1219.67 q^{96} -1241.58 q^{97} +998.814 q^{98} -0.574967 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−5.15631	−1.82303	−0.911516	−	0.411265i	$-0.865087\pi$
$2$	−5.15631	−1.82303	−0.911516	+	0.411265i	$0.865087\pi$
$3$	4.91805	0.946479	0.473240	−	0.880934i	$-0.343084\pi$
$3$	4.91805	0.946479	0.473240	+	0.880934i	$0.343084\pi$
$4$	18.5876	2.32344
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	−25.3590	−1.72546
$7$	12.2185	0.659740	0.329870	−	0.944026i	$-0.392995\pi$
$7$	12.2185	0.659740	0.329870	+	0.944026i	$0.392995\pi$
$8$	−54.5927	−2.41268
$9$	−2.81278	−0.104177
$10$	25.7816	0.815285
$11$	0.204412	0.00560297	0.00280149	−	0.999996i	$-0.499108\pi$
$11$	0.204412	0.00560297	0.00280149	+	0.999996i	$0.499108\pi$
$12$	91.4145	2.19909
$13$	−13.0000	−0.277350
$13$	−13.0000	−0.277350
$14$	−63.0027	−1.20273
$15$	−24.5903	−0.423278
$16$	132.797	2.07495
$17$	116.248	1.65848	0.829241	−	0.558891i	$-0.188773\pi$
$17$	116.248	1.65848	0.829241	+	0.558891i	$0.188773\pi$
$18$	14.5036	0.189918
$19$	−19.1042	−0.230673	−0.115337	−	0.993326i	$-0.536795\pi$
$19$	−19.1042	−0.230673	−0.115337	+	0.993326i	$0.536795\pi$
$20$	−92.9378	−1.03908
$21$	60.0914	0.624430
$22$	−1.05401	−0.0102144
$23$	−162.478	−1.47300	−0.736501	−	0.676436i	$-0.763523\pi$
$23$	−162.478	−1.47300	−0.736501	+	0.676436i	$0.763523\pi$
$24$	−268.490	−2.28355
$25$	25.0000	0.200000
$26$	67.0321	0.505618
$27$	−146.621	−1.04508
$28$	227.113	1.53287
$29$	40.9893	0.262466	0.131233	−	0.991352i	$-0.458106\pi$
$29$	40.9893	0.262466	0.131233	+	0.991352i	$0.458106\pi$
$30$	126.795	0.771650
$31$	31.0000	0.179605
$31$	31.0000	0.179605
$32$	−248.000	−1.37002
$33$	1.00531	0.00530310
$34$	−599.409	−3.02346
$35$	−61.0927	−0.295045
$36$	−52.2827	−0.242049
$37$	6.38224	0.0283577	0.0141788	−	0.999899i	$-0.495487\pi$
$37$	6.38224	0.0283577	0.0141788	+	0.999899i	$0.495487\pi$
$38$	98.5070	0.420525
$39$	−63.9347	−0.262506
$40$	272.964	1.07898
$41$	47.2831	0.180107	0.0900534	−	0.995937i	$-0.471296\pi$
$41$	47.2831	0.180107	0.0900534	+	0.995937i	$0.471296\pi$
$42$	−309.850	−1.13836
$43$	−221.328	−0.784934	−0.392467	−	0.919766i	$-0.628378\pi$
$43$	−221.328	−0.784934	−0.392467	+	0.919766i	$0.628378\pi$
$44$	3.79953	0.0130182
$45$	14.0639	0.0465894
$46$	837.788	2.68533
$47$	393.370	1.22083	0.610414	−	0.792082i	$-0.291003\pi$
$47$	393.370	1.22083	0.610414	+	0.792082i	$0.291003\pi$
$48$	653.101	1.96390
$49$	−193.707	−0.564744
$50$	−128.908	−0.364606
$51$	571.712	1.56972
$52$	−241.638	−0.644407
$53$	321.421	0.833031	0.416515	−	0.909129i	$-0.363251\pi$
$53$	321.421	0.833031	0.416515	+	0.909129i	$0.363251\pi$
$54$	756.022	1.90522
$55$	−1.02206	−0.00250572
$56$	−667.044	−1.59174
$57$	−93.9553	−0.218328
$58$	−211.353	−0.478484
$59$	173.952	0.383840	0.191920	−	0.981411i	$-0.438529\pi$
$59$	173.952	0.383840	0.191920	+	0.981411i	$0.438529\pi$
$60$	−457.073	−0.983464
$61$	−691.729	−1.45191	−0.725957	−	0.687740i	$-0.758603\pi$
$61$	−691.729	−1.45191	−0.725957	+	0.687740i	$0.758603\pi$
$62$	−159.846	−0.327426
$63$	−34.3681	−0.0687297
$64$	216.389	0.422635
$65$	65.0000	0.124035
$66$	−5.18370	−0.00966771
$67$	−415.895	−0.758354	−0.379177	−	0.925324i	$-0.623793\pi$
$67$	−415.895	−0.758354	−0.379177	+	0.925324i	$0.623793\pi$
$68$	2160.76	3.85339
$69$	−799.076	−1.39417
$70$	315.013	0.537876
$71$	608.218	1.01665	0.508325	−	0.861165i	$-0.330265\pi$
$71$	608.218	1.01665	0.508325	+	0.861165i	$0.330265\pi$
$72$	153.557	0.251346
$73$	1192.68	1.91223	0.956117	−	0.292985i	$-0.0946488\pi$
$73$	1192.68	1.91223	0.956117	+	0.292985i	$0.0946488\pi$
$74$	−32.9088	−0.0516969
$75$	122.951	0.189296
$76$	−355.100	−0.535957
$77$	2.49762	0.00369650
$78$	329.667	0.478557
$79$	−682.284	−0.971683	−0.485841	−	0.874047i	$-0.661487\pi$
$79$	−682.284	−0.971683	−0.485841	+	0.874047i	$0.661487\pi$
$80$	−663.984	−0.927945
$81$	−645.143	−0.884970
$82$	−243.806	−0.328340
$83$	−650.672	−0.860489	−0.430244	−	0.902712i	$-0.641573\pi$
$83$	−650.672	−0.860489	−0.430244	+	0.902712i	$0.641573\pi$
$84$	1116.95	1.45083
$85$	−581.238	−0.741696
$86$	1141.24	1.43096
$87$	201.587	0.248419
$88$	−11.1594	−0.0135182
$89$	651.566	0.776021	0.388011	−	0.921655i	$-0.373162\pi$
$89$	651.566	0.776021	0.388011	+	0.921655i	$0.373162\pi$
$90$	−72.5178	−0.0849339
$91$	−158.841	−0.182979
$92$	−3020.07	−3.42244
$93$	152.460	0.169993
$94$	−2028.34	−2.22561
$95$	95.5208	0.103160
$96$	−1219.67	−1.29669
$97$	−1241.58	−1.29962	−0.649810	−	0.760096i	$-0.725152\pi$
$97$	−1241.58	−1.29962	−0.649810	+	0.760096i	$0.725152\pi$
$98$	998.814	1.02955
$99$	−0.574967	−0.000583701 0
$100$	464.689	0.464689
$101$	1720.13	1.69465	0.847326	−	0.531073i	$-0.178211\pi$
$101$	1720.13	1.69465	0.847326	+	0.531073i	$0.178211\pi$
$102$	−2947.92	−2.86165
$103$	139.030	0.133000	0.0665002	−	0.997786i	$-0.478817\pi$
$103$	139.030	0.133000	0.0665002	+	0.997786i	$0.478817\pi$
$104$	709.706	0.669157
$105$	−300.457	−0.279254
$106$	−1657.35	−1.51864
$107$	−1138.87	−1.02896	−0.514482	−	0.857501i	$-0.672016\pi$
$107$	−1138.87	−1.02896	−0.514482	+	0.857501i	$0.672016\pi$
$108$	−2725.32	−2.42819
$109$	−1418.98	−1.24692	−0.623458	−	0.781857i	$-0.714273\pi$
$109$	−1418.98	−1.24692	−0.623458	+	0.781857i	$0.714273\pi$
$110$	5.27007	0.00456802
$111$	31.3882	0.0268399
$112$	1622.58	1.36893
$113$	−1031.82	−0.858988	−0.429494	−	0.903070i	$-0.641308\pi$
$113$	−1031.82	−0.858988	−0.429494	+	0.903070i	$0.641308\pi$
$114$	484.463	0.398018
$115$	812.391	0.658747
$116$	761.890	0.609825
$117$	36.5661	0.0288935
$118$	−896.949	−0.699753
$119$	1420.38	1.09417
$120$	1342.45	1.02124
$121$	−1330.96	−0.999969
$122$	3566.77	2.64689
$123$	232.541	0.170467
$124$	576.214	0.417303
$125$	−125.000	−0.0894427
$126$	177.213	0.125296
$127$	−160.242	−0.111962	−0.0559808	−	0.998432i	$-0.517829\pi$
$127$	−160.242	−0.111962	−0.0559808	+	0.998432i	$0.517829\pi$
$128$	868.226	0.599540
$129$	−1088.50	−0.742924
$130$	−335.160	−0.226119
$131$	−2156.18	−1.43806	−0.719030	−	0.694979i	$-0.755414\pi$
$131$	−2156.18	−1.43806	−0.719030	+	0.694979i	$0.755414\pi$
$132$	18.6863	0.0123214
$133$	−233.425	−0.152184
$134$	2144.49	1.38250
$135$	733.104	0.467374
$136$	−6346.28	−4.00139
$137$	1171.03	0.730274	0.365137	−	0.930954i	$-0.381022\pi$
$137$	1171.03	0.730274	0.365137	+	0.930954i	$0.381022\pi$
$138$	4120.29	2.54161
$139$	1909.44	1.16515	0.582577	−	0.812775i	$-0.302044\pi$
$139$	1909.44	1.16515	0.582577	+	0.812775i	$0.302044\pi$
$140$	−1135.56	−0.685520
$141$	1934.62	1.15549
$142$	−3136.16	−1.85339
$143$	−2.65736	−0.00155398
$144$	−373.528	−0.216162
$145$	−204.946	−0.117378
$146$	−6149.85	−3.48606
$147$	−952.661	−0.534518
$148$	118.630	0.0658874
$149$	−2585.00	−1.42128	−0.710642	−	0.703554i	$-0.751595\pi$
$149$	−2585.00	−1.42128	−0.710642	+	0.703554i	$0.751595\pi$
$150$	−633.975	−0.345092
$151$	−3212.68	−1.73142	−0.865710	−	0.500546i	$-0.833133\pi$
$151$	−3212.68	−1.73142	−0.865710	+	0.500546i	$0.833133\pi$
$152$	1042.95	0.556542
$153$	−326.979	−0.172776
$154$	−12.8785	−0.00673884
$155$	−155.000	−0.0803219
$156$	−1188.39	−0.609918
$157$	−3442.58	−1.74998	−0.874992	−	0.484137i	$-0.839134\pi$
$157$	−3442.58	−1.74998	−0.874992	+	0.484137i	$0.839134\pi$
$158$	3518.07	1.77141
$159$	1580.77	0.788446
$160$	1240.00	0.612690
$161$	−1985.25	−0.971798
$162$	3326.56	1.61333
$163$	2980.68	1.43230	0.716150	−	0.697946i	$-0.245903\pi$
$163$	2980.68	1.43230	0.716150	+	0.697946i	$0.245903\pi$
$164$	878.877	0.418468
$165$	−5.02655	−0.00237162
$166$	3355.07	1.56870
$167$	−915.284	−0.424113	−0.212056	−	0.977257i	$-0.568016\pi$
$167$	−915.284	−0.424113	−0.212056	+	0.977257i	$0.568016\pi$
$168$	−3280.56	−1.50655
$169$	169.000	0.0769231
$170$	2997.05	1.35213
$171$	53.7358	0.0240309
$172$	−4113.94	−1.82375
$173$	−3611.72	−1.58725	−0.793623	−	0.608409i	$-0.791808\pi$
$173$	−3611.72	−1.58725	−0.793623	+	0.608409i	$0.791808\pi$
$174$	−1039.45	−0.452875
$175$	305.464	0.131948
$176$	27.1453	0.0116259
$177$	855.503	0.363297
$178$	−3359.68	−1.41471
$179$	1127.37	0.470747	0.235374	−	0.971905i	$-0.424369\pi$
$179$	1127.37	0.470747	0.235374	+	0.971905i	$0.424369\pi$
$180$	261.413	0.108248
$181$	4791.85	1.96782	0.983911	−	0.178660i	$-0.0571763\pi$
$181$	4791.85	1.96782	0.983911	+	0.178660i	$0.0571763\pi$
$182$	819.035	0.333576
$183$	−3401.96	−1.37421
$184$	8870.13	3.55388
$185$	−31.9112	−0.0126819
$186$	−786.129	−0.309902
$187$	23.7625	0.00929243
$188$	7311.79	2.83653
$189$	−1791.49	−0.689481
$190$	−492.535	−0.188065
$191$	551.391	0.208886	0.104443	−	0.994531i	$-0.466694\pi$
$191$	551.391	0.208886	0.104443	+	0.994531i	$0.466694\pi$
$192$	1064.21	0.400015
$193$	−1481.20	−0.552430	−0.276215	−	0.961096i	$-0.589080\pi$
$193$	−1481.20	−0.552430	−0.276215	+	0.961096i	$0.589080\pi$
$194$	6401.97	2.36925
$195$	319.673	0.117396
$196$	−3600.54	−1.31215
$197$	3633.76	1.31419	0.657093	−	0.753810i	$-0.271786\pi$
$197$	3633.76	1.31419	0.657093	+	0.753810i	$0.271786\pi$
$198$	2.96471	0.00106410
$199$	1744.54	0.621444	0.310722	−	0.950501i	$-0.399429\pi$
$199$	1744.54	0.621444	0.310722	+	0.950501i	$0.399429\pi$
$200$	−1364.82	−0.482536
$201$	−2045.39	−0.717766
$202$	−8869.55	−3.08940
$203$	500.829	0.173159
$204$	10626.7	3.64715
$205$	−236.415	−0.0805462
$206$	−716.882	−0.242464
$207$	457.015	0.153453
$208$	−1726.36	−0.575487
$209$	−3.90513	−0.00129246
$210$	1549.25	0.509088
$211$	3629.18	1.18409	0.592044	−	0.805905i	$-0.298321\pi$
$211$	3629.18	1.18409	0.592044	+	0.805905i	$0.298321\pi$
$212$	5974.44	1.93550
$213$	2991.25	0.962239
$214$	5872.39	1.87583
$215$	1106.64	0.351033
$216$	8004.43	2.52145
$217$	378.775	0.118493
$218$	7316.72	2.27317
$219$	5865.68	1.80989
$220$	−18.9976	−0.00582191
$221$	−1511.22	−0.459980
$222$	−161.847	−0.0489301
$223$	−2834.88	−0.851291	−0.425645	−	0.904890i	$-0.639953\pi$
$223$	−2834.88	−0.851291	−0.425645	+	0.904890i	$0.639953\pi$
$224$	−3030.19	−0.903854
$225$	−70.3195	−0.0208354
$226$	5320.39	1.56596
$227$	2835.21	0.828985	0.414492	−	0.910053i	$-0.363959\pi$
$227$	2835.21	0.828985	0.414492	+	0.910053i	$0.363959\pi$
$228$	−1746.40	−0.507272
$229$	−595.675	−0.171892	−0.0859462	−	0.996300i	$-0.527391\pi$
$229$	−595.675	−0.171892	−0.0859462	+	0.996300i	$0.527391\pi$
$230$	−4188.94	−1.20092
$231$	12.2834	0.00349866
$232$	−2237.72	−0.633247
$233$	−849.581	−0.238875	−0.119438	−	0.992842i	$-0.538109\pi$
$233$	−849.581	−0.238875	−0.119438	+	0.992842i	$0.538109\pi$
$234$	−188.546	−0.0526738
$235$	−1966.85	−0.545971
$236$	3233.34	0.891831
$237$	−3355.51	−0.919677
$238$	−7323.91	−1.99470
$239$	2833.54	0.766889	0.383445	−	0.923564i	$-0.374738\pi$
$239$	2833.54	0.766889	0.383445	+	0.923564i	$0.374738\pi$
$240$	−3265.51	−0.878281
$241$	1663.05	0.444509	0.222255	−	0.974989i	$-0.428658\pi$
$241$	1663.05	0.444509	0.222255	+	0.974989i	$0.428658\pi$
$242$	6862.84	1.82297
$243$	785.913	0.207475
$244$	−12857.5	−3.37344
$245$	968.535	0.252561
$246$	−1199.05	−0.310767
$247$	248.354	0.0639773
$248$	−1692.37	−0.433330
$249$	−3200.04	−0.814435
$250$	644.539	0.163057
$251$	4010.77	1.00860	0.504298	−	0.863530i	$-0.331751\pi$
$251$	4010.77	1.00860	0.504298	+	0.863530i	$0.331751\pi$
$252$	−638.818	−0.159690
$253$	−33.2126	−0.00825319
$254$	826.255	0.204110
$255$	−2858.56	−0.702000
$256$	−6207.96	−1.51562
$257$	−2043.43	−0.495976	−0.247988	−	0.968763i	$-0.579769\pi$
$257$	−2043.43	−0.495976	−0.247988	+	0.968763i	$0.579769\pi$
$258$	5612.65	1.35437
$259$	77.9817	0.0187087
$260$	1208.19	0.288188
$261$	−115.294	−0.0273429
$262$	11117.9	2.62163
$263$	−7032.19	−1.64876	−0.824379	−	0.566038i	$-0.808476\pi$
$263$	−7032.19	−1.64876	−0.824379	+	0.566038i	$0.808476\pi$
$264$	−54.8827	−0.0127947
$265$	−1607.11	−0.372543
$266$	1203.61	0.277437
$267$	3204.44	0.734488
$268$	−7730.48	−1.76199
$269$	−518.063	−0.117423	−0.0587117	−	0.998275i	$-0.518699\pi$
$269$	−518.063	−0.117423	−0.0587117	+	0.998275i	$0.518699\pi$
$270$	−3780.11	−0.852038
$271$	8088.32	1.81303	0.906513	−	0.422177i	$-0.138734\pi$
$271$	8088.32	1.81303	0.906513	+	0.422177i	$0.138734\pi$
$272$	15437.3	3.44127
$273$	−781.189	−0.173186
$274$	−6038.18	−1.33131
$275$	5.11031	0.00112059
$276$	−14852.9	−3.23927
$277$	−3134.22	−0.679844	−0.339922	−	0.940454i	$-0.610401\pi$
$277$	−3134.22	−0.679844	−0.339922	+	0.940454i	$0.610401\pi$
$278$	−9845.66	−2.12411
$279$	−87.1961	−0.0187107
$280$	3335.22	0.711848
$281$	−5105.18	−1.08381	−0.541903	−	0.840441i	$-0.682296\pi$
$281$	−5105.18	−1.08381	−0.541903	+	0.840441i	$0.682296\pi$
$282$	−9975.48	−2.10649
$283$	−5263.17	−1.10552	−0.552761	−	0.833340i	$-0.686426\pi$
$283$	−5263.17	−1.10552	−0.552761	+	0.833340i	$0.686426\pi$
$284$	11305.3	2.36213
$285$	469.776	0.0976391
$286$	13.7022	0.00283296
$287$	577.731	0.118824
$288$	697.568	0.142724
$289$	8600.51	1.75056
$290$	1056.77	0.213985
$291$	−6106.15	−1.23006
$292$	22169.1	4.44297
$293$	−4900.18	−0.977035	−0.488518	−	0.872554i	$-0.662462\pi$
$293$	−4900.18	−0.977035	−0.488518	+	0.872554i	$0.662462\pi$
$294$	4912.22	0.974443
$295$	−869.758	−0.171659
$296$	−348.424	−0.0684180
$297$	−29.9711	−0.00585556
$298$	13329.1	2.59104
$299$	2112.22	0.408537
$300$	2285.36	0.439818
$301$	−2704.30	−0.517852
$302$	16565.6	3.15643
$303$	8459.71	1.60395
$304$	−2536.97	−0.478636
$305$	3458.64	0.649316
$306$	1686.00	0.314975
$307$	−7311.22	−1.35920	−0.679599	−	0.733584i	$-0.737846\pi$
$307$	−7311.22	−1.35920	−0.679599	+	0.733584i	$0.737846\pi$
$308$	46.4247	0.00858862
$309$	683.757	0.125882
$310$	799.228	0.146429
$311$	2387.42	0.435299	0.217649	−	0.976027i	$-0.430161\pi$
$311$	2387.42	0.435299	0.217649	+	0.976027i	$0.430161\pi$
$312$	3490.37	0.633343
$313$	−7627.16	−1.37736	−0.688678	−	0.725067i	$-0.741809\pi$
$313$	−7627.16	−1.37736	−0.688678	+	0.725067i	$0.741809\pi$
$314$	17751.0	3.19028
$315$	171.840	0.0307369
$316$	−12682.0	−2.25765
$317$	607.179	0.107579	0.0537895	−	0.998552i	$-0.482870\pi$
$317$	607.179	0.107579	0.0537895	+	0.998552i	$0.482870\pi$
$318$	−8150.93	−1.43736
$319$	8.37872	0.00147059
$320$	−1081.95	−0.189008
$321$	−5601.04	−0.973894
$322$	10236.6	1.77162
$323$	−2220.81	−0.382568
$324$	−11991.6	−2.05618
$325$	−325.000	−0.0554700
$326$	−15369.3	−2.61113
$327$	−6978.63	−1.18018
$328$	−2581.31	−0.434540
$329$	4806.41	0.805429
$330$	25.9185	0.00432353
$331$	8567.85	1.42275	0.711377	−	0.702810i	$-0.248072\pi$
$331$	8567.85	1.42275	0.711377	+	0.702810i	$0.248072\pi$
$332$	−12094.4	−1.99930
$333$	−17.9518	−0.00295422
$334$	4719.49	0.773171
$335$	2079.48	0.339146
$336$	7979.95	1.29566
$337$	−5542.89	−0.895967	−0.447983	−	0.894042i	$-0.647858\pi$
$337$	−5542.89	−0.895967	−0.447983	+	0.894042i	$0.647858\pi$
$338$	−871.417	−0.140233
$339$	−5074.55	−0.813014
$340$	−10803.8	−1.72329
$341$	6.33679	0.00100632
$342$	−277.079	−0.0438090
$343$	−6557.78	−1.03232
$344$	12082.9	1.89380
$345$	3995.38	0.623490
$346$	18623.1	2.89360
$347$	11040.1	1.70796	0.853980	−	0.520305i	$-0.174182\pi$
$347$	11040.1	1.70796	0.853980	+	0.520305i	$0.174182\pi$
$348$	3747.01	0.577187
$349$	−3494.58	−0.535991	−0.267995	−	0.963420i	$-0.586361\pi$
$349$	−3494.58	−0.535991	−0.267995	+	0.963420i	$0.586361\pi$
$350$	−1575.07	−0.240545
$351$	1906.07	0.289853
$352$	−50.6942	−0.00767616
$353$	−9217.39	−1.38978	−0.694889	−	0.719117i	$-0.744547\pi$
$353$	−9217.39	−1.38978	−0.694889	+	0.719117i	$0.744547\pi$
$354$	−4411.24	−0.662302
$355$	−3041.09	−0.454660
$356$	12111.0	1.80304
$357$	6985.49	1.03561
$358$	−5813.08	−0.858187
$359$	2550.45	0.374952	0.187476	−	0.982269i	$-0.439969\pi$
$359$	2550.45	0.374952	0.187476	+	0.982269i	$0.439969\pi$
$360$	−767.786	−0.112405
$361$	−6494.03	−0.946790
$362$	−24708.3	−3.58740
$363$	−6545.72	−0.946450
$364$	−2952.47	−0.425141
$365$	−5963.42	−0.855177
$366$	17541.6	2.50522
$367$	−12470.4	−1.77370	−0.886852	−	0.462054i	$-0.847113\pi$
$367$	−12470.4	−1.77370	−0.886852	+	0.462054i	$0.847113\pi$
$368$	−21576.6	−3.05640
$369$	−132.997	−0.0187630
$370$	164.544	0.0231196
$371$	3927.30	0.549583
$372$	2833.85	0.394969
$373$	1363.92	0.189332	0.0946660	−	0.995509i	$-0.469822\pi$
$373$	1363.92	0.189332	0.0946660	+	0.995509i	$0.469822\pi$
$374$	−122.527	−0.0169404
$375$	−614.756	−0.0846557
$376$	−21475.2	−2.94547
$377$	−532.860	−0.0727950
$378$	9237.50	1.25695
$379$	−5452.24	−0.738952	−0.369476	−	0.929240i	$-0.620463\pi$
$379$	−5452.24	−0.738952	−0.369476	+	0.929240i	$0.620463\pi$
$380$	1775.50	0.239687
$381$	−788.076	−0.105969
$382$	−2843.15	−0.380806
$383$	1033.34	0.137862	0.0689309	−	0.997621i	$-0.478041\pi$
$383$	1033.34	0.137862	0.0689309	+	0.997621i	$0.478041\pi$
$384$	4269.98	0.567452
$385$	−12.4881	−0.00165313
$386$	7637.52	1.00710
$387$	622.546	0.0817721
$388$	−23077.9	−3.01960
$389$	−8982.70	−1.17080	−0.585400	−	0.810745i	$-0.699062\pi$
$389$	−8982.70	−1.17080	−0.585400	+	0.810745i	$0.699062\pi$
$390$	−1648.34	−0.214017
$391$	−18887.7	−2.44295
$392$	10575.0	1.36255
$393$	−10604.2	−1.36109
$394$	−18736.8	−2.39580
$395$	3411.42	0.434550
$396$	−10.6872	−0.00135620
$397$	10408.0	1.31578	0.657889	−	0.753115i	$-0.271450\pi$
$397$	10408.0	1.31578	0.657889	+	0.753115i	$0.271450\pi$
$398$	−8995.41	−1.13291
$399$	−1148.00	−0.144039
$400$	3319.92	0.414990
$401$	−6567.90	−0.817918	−0.408959	−	0.912553i	$-0.634108\pi$
$401$	−6567.90	−0.817918	−0.408959	+	0.912553i	$0.634108\pi$
$402$	10546.7	1.30851
$403$	−403.000	−0.0498135
$404$	31973.1	3.93743
$405$	3225.72	0.395771
$406$	−2582.43	−0.315675
$407$	1.30461	0.000158887 0
$408$	−31211.3	−3.78723
$409$	−6400.38	−0.773785	−0.386893	−	0.922125i	$-0.626452\pi$
$409$	−6400.38	−0.773785	−0.386893	+	0.922125i	$0.626452\pi$
$410$	1219.03	0.146838
$411$	5759.17	0.691189
$412$	2584.23	0.309019
$413$	2125.44	0.253235
$414$	−2356.51	−0.279749
$415$	3253.36	0.384822
$416$	3223.99	0.379974
$417$	9390.72	1.10279
$418$	20.1361	0.00235619
$419$	8971.74	1.04606	0.523029	−	0.852315i	$-0.324802\pi$
$419$	8971.74	1.04606	0.523029	+	0.852315i	$0.324802\pi$
$420$	−5584.77	−0.648830
$421$	8990.10	1.04074	0.520369	−	0.853942i	$-0.325794\pi$
$421$	8990.10	1.04074	0.520369	+	0.853942i	$0.325794\pi$
$422$	−18713.2	−2.15863
$423$	−1106.46	−0.127182
$424$	−17547.3	−2.00984
$425$	2906.19	0.331696
$426$	−15423.8	−1.75419
$427$	−8451.92	−0.957886
$428$	−21168.9	−2.39074
$429$	−13.0690	−0.00147081
$430$	−5706.18	−0.639945
$431$	−4830.53	−0.539857	−0.269928	−	0.962880i	$-0.587000\pi$
$431$	−4830.53	−0.539857	−0.269928	+	0.962880i	$0.587000\pi$
$432$	−19470.8	−2.16849
$433$	−7593.43	−0.842764	−0.421382	−	0.906883i	$-0.638455\pi$
$433$	−7593.43	−0.842764	−0.421382	+	0.906883i	$0.638455\pi$
$434$	−1953.08	−0.216016
$435$	−1007.94	−0.111096
$436$	−26375.4	−2.89714
$437$	3104.01	0.339783
$438$	−30245.3	−3.29949
$439$	8694.10	0.945209	0.472604	−	0.881275i	$-0.343314\pi$
$439$	8694.10	0.945209	0.472604	+	0.881275i	$0.343314\pi$
$440$	55.7972	0.00604551
$441$	544.855	0.0588333
$442$	7792.32	0.838558
$443$	−5454.62	−0.585004	−0.292502	−	0.956265i	$-0.594488\pi$
$443$	−5454.62	−0.585004	−0.292502	+	0.956265i	$0.594488\pi$
$444$	583.429	0.0623611
$445$	−3257.83	−0.347047
$446$	14617.5	1.55193
$447$	−12713.1	−1.34522
$448$	2643.96	0.278829
$449$	−17399.3	−1.82879	−0.914394	−	0.404825i	$-0.867333\pi$
$449$	−17399.3	−1.82879	−0.914394	+	0.404825i	$0.867333\pi$
$450$	362.589	0.0379836
$451$	9.66526	0.00100913
$452$	−19179.0	−1.99581
$453$	−15800.1	−1.63875
$454$	−14619.2	−1.51126
$455$	794.206	0.0818306
$456$	5129.27	0.526755
$457$	13497.6	1.38160	0.690801	−	0.723045i	$-0.257258\pi$
$457$	13497.6	1.38160	0.690801	+	0.723045i	$0.257258\pi$
$458$	3071.49	0.313365
$459$	−17044.3	−1.73325
$460$	15100.4	1.53056
$461$	−17635.6	−1.78172	−0.890858	−	0.454281i	$-0.849896\pi$
$461$	−17635.6	−1.78172	−0.890858	+	0.454281i	$0.849896\pi$
$462$	−63.3373	−0.00637817
$463$	−12651.3	−1.26989	−0.634944	−	0.772558i	$-0.718977\pi$
$463$	−12651.3	−1.26989	−0.634944	+	0.772558i	$0.718977\pi$
$464$	5443.24	0.544604
$465$	−762.298	−0.0760230
$466$	4380.70	0.435477
$467$	−19490.8	−1.93132	−0.965661	−	0.259806i	$-0.916341\pi$
$467$	−19490.8	−1.93132	−0.965661	+	0.259806i	$0.916341\pi$
$468$	679.675	0.0671324
$469$	−5081.64	−0.500316
$470$	10141.7	0.995323
$471$	−16930.8	−1.65632
$472$	−9496.49	−0.926084
$473$	−45.2422	−0.00439796
$474$	17302.0	1.67660
$475$	−477.604	−0.0461347
$476$	26401.3	2.54223
$477$	−904.087	−0.0867826
$478$	−14610.6	−1.39806
$479$	−5855.12	−0.558512	−0.279256	−	0.960217i	$-0.590088\pi$
$479$	−5855.12	−0.558512	−0.279256	+	0.960217i	$0.590088\pi$
$480$	6098.37	0.579899
$481$	−82.9691	−0.00786500
$482$	−8575.22	−0.810354
$483$	−9763.55	−0.919787
$484$	−24739.3	−2.32337
$485$	6207.89	0.581208
$486$	−4052.41	−0.378233
$487$	−10625.1	−0.988647	−0.494323	−	0.869278i	$-0.664584\pi$
$487$	−10625.1	−0.988647	−0.494323	+	0.869278i	$0.664584\pi$
$488$	37763.4	3.50301
$489$	14659.1	1.35564
$490$	−4994.07	−0.460427
$491$	3662.10	0.336595	0.168298	−	0.985736i	$-0.446173\pi$
$491$	3662.10	0.336595	0.168298	+	0.985736i	$0.446173\pi$
$492$	4322.36	0.396071
$493$	4764.91	0.435295
$494$	−1280.59	−0.116633
$495$	2.87483	0.000261039 0
$496$	4116.70	0.372672
$497$	7431.54	0.670725
$498$	16500.4	1.48474
$499$	−10020.5	−0.898957	−0.449478	−	0.893291i	$-0.648390\pi$
$499$	−10020.5	−0.898957	−0.449478	+	0.893291i	$0.648390\pi$
$500$	−2323.44	−0.207815
$501$	−4501.42	−0.401414
$502$	−20680.8	−1.83870
$503$	−5396.53	−0.478368	−0.239184	−	0.970974i	$-0.576880\pi$
$503$	−5396.53	−0.478368	−0.239184	+	0.970974i	$0.576880\pi$
$504$	1876.25	0.165823
$505$	−8600.67	−0.757871
$506$	171.254	0.0150458
$507$	831.151	0.0728061
$508$	−2978.50	−0.260137
$509$	17741.2	1.54492	0.772459	−	0.635065i	$-0.219027\pi$
$509$	17741.2	1.54492	0.772459	+	0.635065i	$0.219027\pi$
$510$	14739.6	1.27977
$511$	14572.9	1.26158
$512$	25064.4	2.16347
$513$	2801.07	0.241072
$514$	10536.6	0.904181
$515$	−695.150	−0.0594796
$516$	−20232.6	−1.72614
$517$	80.4098	0.00684027
$518$	−402.098	−0.0341065
$519$	−17762.6	−1.50230
$520$	−3548.53	−0.299256
$521$	−14350.2	−1.20670	−0.603351	−	0.797476i	$-0.706168\pi$
$521$	−14350.2	−1.20670	−0.603351	+	0.797476i	$0.706168\pi$
$522$	594.490	0.0498470
$523$	−6110.33	−0.510872	−0.255436	−	0.966826i	$-0.582219\pi$
$523$	−6110.33	−0.510872	−0.255436	+	0.966826i	$0.582219\pi$
$524$	−40078.0	−3.34125
$525$	1502.29	0.124886
$526$	36260.2	3.00574
$527$	3603.68	0.297872
$528$	133.502	0.0110037
$529$	14232.2	1.16973
$530$	8286.74	0.679157
$531$	−489.287	−0.0399873
$532$	−4338.80	−0.353592
$533$	−614.680	−0.0499526
$534$	−16523.1	−1.33899
$535$	5694.37	0.460167
$536$	22704.9	1.82967
$537$	5544.47	0.445553
$538$	2671.30	0.214067
$539$	−39.5961	−0.00316424
$540$	13626.6	1.08592
$541$	12576.8	0.999482	0.499741	−	0.866175i	$-0.333429\pi$
$541$	12576.8	0.999482	0.499741	+	0.866175i	$0.333429\pi$
$542$	−41705.9	−3.30521
$543$	23566.6	1.86250
$544$	−28829.4	−2.27215
$545$	7094.91	0.557638
$546$	4028.05	0.315723
$547$	−18248.8	−1.42644	−0.713220	−	0.700941i	$-0.752764\pi$
$547$	−18248.8	−1.42644	−0.713220	+	0.700941i	$0.752764\pi$
$548$	21766.5	1.69675
$549$	1945.68	0.151256
$550$	−26.3504	−0.00204288
$551$	−783.066	−0.0605440
$552$	43623.7	3.36368
$553$	−8336.52	−0.641058
$554$	16161.0	1.23938
$555$	−156.941	−0.0120032
$556$	35491.8	2.70717
$557$	17065.1	1.29815	0.649077	−	0.760723i	$-0.275155\pi$
$557$	17065.1	1.29815	0.649077	+	0.760723i	$0.275155\pi$
$558$	449.610	0.0341103
$559$	2877.26	0.217702
$560$	−8112.92	−0.612202
$561$	116.865	0.00879509
$562$	26323.9	1.97581
$563$	3215.97	0.240741	0.120370	−	0.992729i	$-0.461592\pi$
$563$	3215.97	0.240741	0.120370	+	0.992729i	$0.461592\pi$
$564$	35959.8	2.68471
$565$	5159.11	0.384151
$566$	27138.5	2.01540
$567$	−7882.72	−0.583850
$568$	−33204.3	−2.45285
$569$	22512.9	1.65868	0.829341	−	0.558742i	$-0.188716\pi$
$569$	22512.9	1.65868	0.829341	+	0.558742i	$0.188716\pi$
$570$	−2422.31	−0.177999
$571$	−7094.70	−0.519972	−0.259986	−	0.965612i	$-0.583718\pi$
$571$	−7094.70	−0.519972	−0.259986	+	0.965612i	$0.583718\pi$
$572$	−49.3939	−0.00361060
$573$	2711.77	0.197706
$574$	−2978.96	−0.216619
$575$	−4061.95	−0.294600
$576$	−608.655	−0.0440288
$577$	6436.91	0.464423	0.232212	−	0.972665i	$-0.425404\pi$
$577$	6436.91	0.464423	0.232212	+	0.972665i	$0.425404\pi$
$578$	−44346.9	−3.19133
$579$	−7284.61	−0.522864
$580$	−3809.45	−0.272722
$581$	−7950.27	−0.567698
$582$	31485.2	2.24245
$583$	65.7025	0.00466745
$584$	−65111.9	−4.61361
$585$	−182.831	−0.0129216
$586$	25266.8	1.78117
$587$	−13881.1	−0.976038	−0.488019	−	0.872833i	$-0.662280\pi$
$587$	−13881.1	−0.976038	−0.488019	+	0.872833i	$0.662280\pi$
$588$	−17707.6	−1.24192
$589$	−592.229	−0.0414302
$590$	4484.74	0.312939
$591$	17871.0	1.24385
$592$	847.540	0.0588407
$593$	−10776.8	−0.746287	−0.373143	−	0.927774i	$-0.621720\pi$
$593$	−10776.8	−0.746287	−0.373143	+	0.927774i	$0.621720\pi$
$594$	154.540	0.0106749
$595$	−7101.89	−0.489326
$596$	−48048.8	−3.30227
$597$	8579.75	0.588184
$598$	−10891.2	−0.744776
$599$	−2480.27	−0.169184	−0.0845919	−	0.996416i	$-0.526959\pi$
$599$	−2480.27	−0.169184	−0.0845919	+	0.996416i	$0.526959\pi$
$600$	−6712.25	−0.456710
$601$	−24284.9	−1.64826	−0.824130	−	0.566401i	$-0.808335\pi$
$601$	−24284.9	−1.64826	−0.824130	+	0.566401i	$0.808335\pi$
$602$	13944.2	0.944061
$603$	1169.82	0.0790030
$604$	−59715.9	−4.02286
$605$	6654.79	0.447200
$606$	−43620.9	−2.92406
$607$	117.596	0.00786336	0.00393168	−	0.999992i	$-0.498749\pi$
$607$	117.596	0.00786336	0.00393168	+	0.999992i	$0.498749\pi$
$608$	4737.82	0.316027
$609$	2463.10	0.163892
$610$	−17833.8	−1.18372
$611$	−5113.81	−0.338597
$612$	−6077.74	−0.401435
$613$	400.765	0.0264058	0.0132029	−	0.999913i	$-0.495797\pi$
$613$	400.765	0.0264058	0.0132029	+	0.999913i	$0.495797\pi$
$614$	37699.0	2.47786
$615$	−1162.70	−0.0762353
$616$	−136.352	−0.00891848
$617$	19180.2	1.25149	0.625744	−	0.780029i	$-0.284796\pi$
$617$	19180.2	1.25149	0.625744	+	0.780029i	$0.284796\pi$
$618$	−3525.66	−0.229487
$619$	9511.42	0.617603	0.308802	−	0.951126i	$-0.400072\pi$
$619$	9511.42	0.617603	0.308802	+	0.951126i	$0.400072\pi$
$620$	−2881.07	−0.186624
$621$	23822.7	1.53941
$622$	−12310.3	−0.793564
$623$	7961.19	0.511972
$624$	−8490.31	−0.544687
$625$	625.000	0.0400000
$626$	39328.0	2.51096
$627$	−19.2056	−0.00122328
$628$	−63989.1	−4.06599
$629$	741.920	0.0470307
$630$	−886.063	−0.0560343
$631$	−12079.1	−0.762063	−0.381031	−	0.924562i	$-0.624431\pi$
$631$	−12079.1	−0.762063	−0.381031	+	0.924562i	$0.624431\pi$
$632$	37247.7	2.34436
$633$	17848.5	1.12072
$634$	−3130.80	−0.196120
$635$	801.208	0.0500708
$636$	29382.6	1.83191
$637$	2518.19	0.156632
$638$	−43.2033	−0.00268093
$639$	−1710.78	−0.105912
$640$	−4341.13	−0.268122
$641$	−8925.94	−0.550005	−0.275003	−	0.961443i	$-0.588679\pi$
$641$	−8925.94	−0.550005	−0.275003	+	0.961443i	$0.588679\pi$
$642$	28880.7	1.77544
$643$	−18968.7	−1.16338	−0.581689	−	0.813411i	$-0.697608\pi$
$643$	−18968.7	−1.16338	−0.581689	+	0.813411i	$0.697608\pi$
$644$	−36900.9	−2.25792
$645$	5442.51	0.332246
$646$	11451.2	0.697433
$647$	14885.3	0.904486	0.452243	−	0.891895i	$-0.350624\pi$
$647$	14885.3	0.904486	0.452243	+	0.891895i	$0.350624\pi$
$648$	35220.1	2.13515
$649$	35.5579	0.00215065
$650$	1675.80	0.101124
$651$	1862.83	0.112151
$652$	55403.6	3.32787
$653$	7848.77	0.470362	0.235181	−	0.971952i	$-0.424432\pi$
$653$	7848.77	0.470362	0.235181	+	0.971952i	$0.424432\pi$
$654$	35984.0	2.15151
$655$	10780.9	0.643120
$656$	6279.04	0.373712
$657$	−3354.76	−0.199211
$658$	−24783.4	−1.46832
$659$	458.609	0.0271091	0.0135545	−	0.999908i	$-0.495685\pi$
$659$	458.609	0.0271091	0.0135545	+	0.999908i	$0.495685\pi$
$660$	−93.4314	−0.00551032
$661$	−11010.0	−0.647866	−0.323933	−	0.946080i	$-0.605005\pi$
$661$	−11010.0	−0.647866	−0.323933	+	0.946080i	$0.605005\pi$
$662$	−44178.5	−2.59373
$663$	−7432.25	−0.435362
$664$	35522.0	2.07608
$665$	1167.13	0.0680590
$666$	92.5652	0.00538563
$667$	−6659.86	−0.386613
$668$	−17012.9	−0.985402
$669$	−13942.1	−0.805729
$670$	−10722.4	−0.618274
$671$	−141.398	−0.00813504
$672$	−14902.7	−0.855480
$673$	−13691.0	−0.784173	−0.392086	−	0.919928i	$-0.628247\pi$
$673$	−13691.0	−0.784173	−0.392086	+	0.919928i	$0.628247\pi$
$674$	28580.9	1.63338
$675$	−3665.52	−0.209016
$676$	3141.30	0.178726
$677$	28914.0	1.64144	0.820720	−	0.571331i	$-0.193573\pi$
$677$	28914.0	1.64144	0.820720	+	0.571331i	$0.193573\pi$
$678$	26166.0	1.48215
$679$	−15170.3	−0.857411
$680$	31731.4	1.78947
$681$	13943.7	0.784617
$682$	−32.6744	−0.00183456
$683$	−31012.7	−1.73743	−0.868716	−	0.495310i	$-0.835055\pi$
$683$	−31012.7	−1.73743	−0.868716	+	0.495310i	$0.835055\pi$
$684$	998.817	0.0558344
$685$	−5855.13	−0.326588
$686$	33814.0	1.88196
$687$	−2929.56	−0.162693
$688$	−29391.6	−1.62870
$689$	−4178.48	−0.231041
$690$	−20601.4	−1.13664
$691$	−12284.7	−0.676313	−0.338157	−	0.941090i	$-0.609803\pi$
$691$	−12284.7	−0.676313	−0.338157	+	0.941090i	$0.609803\pi$
$692$	−67133.0	−3.68788
$693$	−7.02526	−0.000385090 0
$694$	−56926.1	−3.11367
$695$	−9547.20	−0.521073
$696$	−11005.2	−0.599355
$697$	5496.55	0.298704
$698$	18019.2	0.977128
$699$	−4178.28	−0.226090
$700$	5677.82	0.306574
$701$	−11146.6	−0.600571	−0.300286	−	0.953849i	$-0.597082\pi$
$701$	−11146.6	−0.600571	−0.300286	+	0.953849i	$0.597082\pi$
$702$	−9828.29	−0.528412
$703$	−121.927	−0.00654136
$704$	44.2326	0.00236801
$705$	−9673.08	−0.516750
$706$	47527.7	2.53361
$707$	21017.6	1.11803
$708$	15901.7	0.844100
$709$	−27322.2	−1.44726	−0.723629	−	0.690189i	$-0.757527\pi$
$709$	−27322.2	−1.44726	−0.723629	+	0.690189i	$0.757527\pi$
$710$	15680.8	0.828860
$711$	1919.11	0.101227
$712$	−35570.8	−1.87229
$713$	−5036.82	−0.264559
$714$	−36019.4	−1.88794
$715$	13.2868	0.000694963 0
$716$	20955.1	1.09376
$717$	13935.5	0.725845
$718$	−13150.9	−0.683550
$719$	−16987.4	−0.881119	−0.440560	−	0.897723i	$-0.645220\pi$
$719$	−16987.4	−0.881119	−0.440560	+	0.897723i	$0.645220\pi$
$720$	1867.64	0.0966705
$721$	1698.75	0.0877456
$722$	33485.2	1.72603
$723$	8178.98	0.420719
$724$	89068.9	4.57212
$725$	1024.73	0.0524932
$726$	33751.8	1.72541
$727$	1298.47	0.0662413	0.0331207	−	0.999451i	$-0.489455\pi$
$727$	1298.47	0.0662413	0.0331207	+	0.999451i	$0.489455\pi$
$728$	8671.57	0.441470
$729$	21284.0	1.08134
$730$	30749.2	1.55901
$731$	−25728.8	−1.30180
$732$	−63234.1	−3.19289
$733$	14335.1	0.722346	0.361173	−	0.932499i	$-0.382376\pi$
$733$	14335.1	0.722346	0.361173	+	0.932499i	$0.382376\pi$
$734$	64301.2	3.23352
$735$	4763.31	0.239044
$736$	40294.5	2.01804
$737$	−85.0142	−0.00424904
$738$	685.773	0.0342055
$739$	32758.7	1.63065	0.815323	−	0.579006i	$-0.196559\pi$
$739$	32758.7	1.63065	0.815323	+	0.579006i	$0.196559\pi$
$740$	−593.151	−0.0294658
$741$	1221.42	0.0605532
$742$	−20250.4	−1.00191
$743$	6640.56	0.327885	0.163943	−	0.986470i	$-0.447579\pi$
$743$	6640.56	0.327885	0.163943	+	0.986470i	$0.447579\pi$
$744$	−8323.18	−0.410138
$745$	12925.0	0.635617
$746$	−7032.77	−0.345158
$747$	1830.20	0.0896431
$748$	441.686	0.0215904
$749$	−13915.4	−0.678849
$750$	3169.88	0.154330
$751$	28778.2	1.39831	0.699155	−	0.714970i	$-0.253560\pi$
$751$	28778.2	1.39831	0.699155	+	0.714970i	$0.253560\pi$
$752$	52238.3	2.53316
$753$	19725.2	0.954614
$754$	2747.60	0.132708
$755$	16063.4	0.774314
$756$	−33299.5	−1.60197
$757$	−14023.9	−0.673323	−0.336662	−	0.941626i	$-0.609298\pi$
$757$	−14023.9	−0.673323	−0.336662	+	0.941626i	$0.609298\pi$
$758$	28113.5	1.34713
$759$	−163.341	−0.00781147
$760$	−5214.74	−0.248893
$761$	6739.74	0.321045	0.160523	−	0.987032i	$-0.448682\pi$
$761$	6739.74	0.321045	0.160523	+	0.987032i	$0.448682\pi$
$762$	4063.56	0.193186
$763$	−17337.9	−0.822640
$764$	10249.0	0.485335
$765$	1634.89	0.0772676
$766$	−5328.21	−0.251326
$767$	−2261.37	−0.106458
$768$	−30531.1	−1.43450
$769$	23226.3	1.08916	0.544580	−	0.838709i	$-0.316689\pi$
$769$	23226.3	1.08916	0.544580	+	0.838709i	$0.316689\pi$
$770$	64.3926	0.00301370
$771$	−10049.7	−0.469431
$772$	−27531.9	−1.28354
$773$	6530.75	0.303874	0.151937	−	0.988390i	$-0.451449\pi$
$773$	6530.75	0.303874	0.151937	+	0.988390i	$0.451449\pi$
$774$	−3210.04	−0.149073
$775$	775.000	0.0359211
$776$	67781.2	3.13557
$777$	383.518	0.0177074
$778$	46317.6	2.13440
$779$	−903.304	−0.0415459
$780$	5941.94	0.272764
$781$	124.327	0.00569627
$782$	97390.9	4.45357
$783$	−6009.88	−0.274298
$784$	−25723.7	−1.17181
$785$	17212.9	0.782617
$786$	54678.5	2.48132
$787$	23091.7	1.04591	0.522955	−	0.852360i	$-0.324830\pi$
$787$	23091.7	1.04591	0.522955	+	0.852360i	$0.324830\pi$
$788$	67542.7	3.05344
$789$	−34584.7	−1.56052
$790$	−17590.3	−0.792198
$791$	−12607.4	−0.566708
$792$	31.3890	0.00140828
$793$	8992.47	0.402689
$794$	−53667.0	−2.39870
$795$	−7903.83	−0.352604
$796$	32426.8	1.44389
$797$	−17395.6	−0.773131	−0.386565	−	0.922262i	$-0.626339\pi$
$797$	−17395.6	−0.773131	−0.386565	+	0.922262i	$0.626339\pi$
$798$	5919.43	0.262588
$799$	45728.4	2.02472
$800$	−6199.99	−0.274003
$801$	−1832.71	−0.0808435
$802$	33866.1	1.49109
$803$	243.799	0.0107142
$804$	−38018.9	−1.66769
$805$	9926.24	0.434601
$806$	2077.99	0.0908117
$807$	−2547.86	−0.111139
$808$	−93906.9	−4.08865
$809$	−4541.39	−0.197363	−0.0986816	−	0.995119i	$-0.531463\pi$
$809$	−4541.39	−0.197363	−0.0986816	+	0.995119i	$0.531463\pi$
$810$	−16632.8	−0.721502
$811$	−33634.3	−1.45630	−0.728150	−	0.685418i	$-0.759620\pi$
$811$	−33634.3	−1.45630	−0.728150	+	0.685418i	$0.759620\pi$
$812$	9309.19	0.402326
$813$	39778.8	1.71599
$814$	−6.72697	−0.000289656 0
$815$	−14903.4	−0.640544
$816$	75921.5	3.25709
$817$	4228.28	0.181064
$818$	33002.3	1.41064
$819$	446.785	0.0190622
$820$	−4394.39	−0.187145
$821$	18488.6	0.785941	0.392970	−	0.919551i	$-0.371447\pi$
$821$	18488.6	0.785941	0.392970	+	0.919551i	$0.371447\pi$
$822$	−29696.1	−1.26006
$823$	−17673.2	−0.748542	−0.374271	−	0.927319i	$-0.622107\pi$
$823$	−17673.2	−0.748542	−0.374271	+	0.927319i	$0.622107\pi$
$824$	−7590.03	−0.320887
$825$	25.1328	0.00106062
$826$	−10959.4	−0.461655
$827$	17617.8	0.740786	0.370393	−	0.928875i	$-0.379223\pi$
$827$	17617.8	0.740786	0.370393	+	0.928875i	$0.379223\pi$
$828$	8494.79	0.356539
$829$	−17033.1	−0.713612	−0.356806	−	0.934178i	$-0.616134\pi$
$829$	−17033.1	−0.713612	−0.356806	+	0.934178i	$0.616134\pi$
$830$	−16775.3	−0.701543
$831$	−15414.2	−0.643458
$832$	−2813.06	−0.117218
$833$	−22518.0	−0.936617
$834$	−48421.5	−2.01043
$835$	4576.42	0.189669
$836$	−72.5868	−0.00300295
$837$	−4545.24	−0.187702
$838$	−46261.1	−1.90700
$839$	8504.10	0.349933	0.174967	−	0.984574i	$-0.444018\pi$
$839$	8504.10	0.349933	0.174967	+	0.984574i	$0.444018\pi$
$840$	16402.8	0.673750
$841$	−22708.9	−0.931112
$842$	−46355.7	−1.89730
$843$	−25107.5	−1.02580
$844$	67457.5	2.75116
$845$	−845.000	−0.0344010
$846$	5705.27	0.231857
$847$	−16262.4	−0.659719
$848$	42683.7	1.72850
$849$	−25884.5	−1.04635
$850$	−14985.2	−0.604693
$851$	−1036.97	−0.0417709
$852$	55600.0	2.23571
$853$	3590.09	0.144106	0.0720530	−	0.997401i	$-0.477045\pi$
$853$	3590.09	0.144106	0.0720530	+	0.997401i	$0.477045\pi$
$854$	43580.7	1.74626
$855$	−268.679	−0.0107469
$856$	62174.3	2.48256
$857$	−32760.9	−1.30582	−0.652912	−	0.757434i	$-0.726453\pi$
$857$	−32760.9	−1.30582	−0.652912	+	0.757434i	$0.726453\pi$
$858$	67.3881	0.00268134
$859$	−26506.4	−1.05284	−0.526418	−	0.850226i	$-0.676465\pi$
$859$	−26506.4	−1.05284	−0.526418	+	0.850226i	$0.676465\pi$
$860$	20569.7	0.815606
$861$	2841.31	0.112464
$862$	24907.7	0.984176
$863$	−3888.73	−0.153388	−0.0766941	−	0.997055i	$-0.524436\pi$
$863$	−3888.73	−0.153388	−0.0766941	+	0.997055i	$0.524436\pi$
$864$	36361.9	1.43178
$865$	18058.6	0.709838
$866$	39154.1	1.53639
$867$	42297.8	1.65687
$868$	7040.50	0.275311
$869$	−139.467	−0.00544431
$870$	5197.24	0.202532
$871$	5406.64	0.210330
$872$	77466.1	3.00841
$873$	3492.29	0.135391
$874$	−16005.2	−0.619434
$875$	−1527.32	−0.0590089
$876$	109029.	4.20518
$877$	−43660.9	−1.68110	−0.840549	−	0.541736i	$-0.817767\pi$
$877$	−43660.9	−1.68110	−0.840549	+	0.541736i	$0.817767\pi$
$878$	−44829.5	−1.72315
$879$	−24099.3	−0.924744
$880$	−135.727	−0.00519925
$881$	26087.2	0.997616	0.498808	−	0.866713i	$-0.333771\pi$
$881$	26087.2	0.997616	0.498808	+	0.866713i	$0.333771\pi$
$882$	−2809.44	−0.107255
$883$	−15871.7	−0.604900	−0.302450	−	0.953165i	$-0.597805\pi$
$883$	−15871.7	−0.604900	−0.302450	+	0.953165i	$0.597805\pi$
$884$	−28089.9	−1.06874
$885$	−4277.51	−0.162471
$886$	28125.7	1.06648
$887$	−33935.1	−1.28459	−0.642293	−	0.766459i	$-0.722017\pi$
$887$	−33935.1	−1.28459	−0.642293	+	0.766459i	$0.722017\pi$
$888$	−1713.57	−0.0647562
$889$	−1957.92	−0.0738656
$890$	16798.4	0.632678
$891$	−131.875	−0.00495846
$892$	−52693.5	−1.97793
$893$	−7515.01	−0.281613
$894$	65553.0	2.45237
$895$	−5636.86	−0.210525
$896$	10608.5	0.395540
$897$	10388.0	0.386672
$898$	89716.5	3.33394
$899$	1270.67	0.0471403
$900$	−1307.07	−0.0484099
$901$	37364.5	1.38157
$902$	−49.8371	−0.00183968
$903$	−13299.9	−0.490136
$904$	56329.9	2.07246
$905$	−23959.3	−0.880037
$906$	81470.4	2.98750
$907$	20119.0	0.736537	0.368269	−	0.929719i	$-0.379951\pi$
$907$	20119.0	0.736537	0.368269	+	0.929719i	$0.379951\pi$
$908$	52699.6	1.92610
$909$	−4838.36	−0.176544
$910$	−4095.17	−0.149180
$911$	−7562.44	−0.275033	−0.137516	−	0.990500i	$-0.543912\pi$
$911$	−7562.44	−0.275033	−0.137516	+	0.990500i	$0.543912\pi$
$912$	−12477.0	−0.453019
$913$	−133.006	−0.00482129
$914$	−69598.0	−2.51871
$915$	17009.8	0.614564
$916$	−11072.1	−0.399382
$917$	−26345.3	−0.948746
$918$	87885.8	3.15976
$919$	−27653.7	−0.992613	−0.496306	−	0.868147i	$-0.665311\pi$
$919$	−27653.7	−0.992613	−0.496306	+	0.868147i	$0.665311\pi$
$920$	−44350.6	−1.58935
$921$	−35957.0	−1.28645
$922$	90934.6	3.24813
$923$	−7906.84	−0.281968
$924$	228.319	0.00812895
$925$	159.556	0.00567153
$926$	65234.3	2.31504
$927$	−391.061	−0.0138556
$928$	−10165.3	−0.359583
$929$	165.859	0.00585753	0.00292877	−	0.999996i	$-0.499068\pi$
$929$	165.859	0.00585753	0.00292877	+	0.999996i	$0.499068\pi$
$930$	3930.65	0.138592
$931$	3700.61	0.130271
$932$	−15791.6	−0.555013
$933$	11741.4	0.412001
$934$	100501.	3.52086
$935$	−118.812	−0.00415570
$936$	−1996.24	−0.0697108
$937$	43941.1	1.53201	0.766006	−	0.642834i	$-0.222241\pi$
$937$	43941.1	1.53201	0.766006	+	0.642834i	$0.222241\pi$
$938$	26202.5	0.912092
$939$	−37510.7	−1.30364
$940$	−36559.0	−1.26853
$941$	4193.67	0.145281	0.0726407	−	0.997358i	$-0.476857\pi$
$941$	4193.67	0.145281	0.0726407	+	0.997358i	$0.476857\pi$
$942$	87300.3	3.01953
$943$	−7682.47	−0.265298
$944$	23100.2	0.796449
$945$	8957.46	0.308345
$946$	233.283	0.00801763
$947$	39886.1	1.36866	0.684331	−	0.729172i	$-0.260094\pi$
$947$	39886.1	1.36866	0.684331	+	0.729172i	$0.260094\pi$
$948$	−62370.7	−2.13682
$949$	−15504.9	−0.530358
$950$	2462.68	0.0841050
$951$	2986.14	0.101821
$952$	−77542.3	−2.63987
$953$	−14261.1	−0.484746	−0.242373	−	0.970183i	$-0.577926\pi$
$953$	−14261.1	−0.484746	−0.242373	+	0.970183i	$0.577926\pi$
$954$	4661.76	0.158207
$955$	−2756.96	−0.0934168
$956$	52668.6	1.78182
$957$	41.2070	0.00139188
$958$	30190.8	1.01819
$959$	14308.2	0.481791
$960$	−5321.06	−0.178892
$961$	961.000	0.0322581
$962$	427.815	0.0143381
$963$	3203.40	0.107194
$964$	30912.1	1.03279
$965$	7405.99	0.247054
$966$	50343.9	1.67680
$967$	−47322.6	−1.57372	−0.786862	−	0.617129i	$-0.788296\pi$
$967$	−47322.6	−1.57372	−0.786862	+	0.617129i	$0.788296\pi$
$968$	72660.6	2.41260
$969$	−10922.1	−0.362093
$970$	−32009.8	−1.05956
$971$	16596.8	0.548524	0.274262	−	0.961655i	$-0.411567\pi$
$971$	16596.8	0.548524	0.274262	+	0.961655i	$0.411567\pi$
$972$	14608.2	0.482056
$973$	23330.6	0.768699
$974$	54786.5	1.80233
$975$	−1598.37	−0.0525012
$976$	−91859.3	−3.01265
$977$	−58151.8	−1.90424	−0.952119	−	0.305728i	$-0.901100\pi$
$977$	−58151.8	−1.90424	−0.952119	+	0.305728i	$0.901100\pi$
$978$	−75587.1	−2.47138
$979$	133.188	0.00434802
$980$	18002.7	0.586811
$981$	3991.28	0.129900
$982$	−18882.9	−0.613624
$983$	−44789.6	−1.45327	−0.726636	−	0.687023i	$-0.758917\pi$
$983$	−44789.6	−1.45327	−0.726636	+	0.687023i	$0.758917\pi$
$984$	−12695.0	−0.411283
$985$	−18168.8	−0.587722
$986$	−24569.3	−0.793557
$987$	23638.2	0.762322
$988$	4616.30	0.148648
$989$	35960.9	1.15621
$990$	−14.8235	−0.000475882 0
$991$	22270.0	0.713853	0.356927	−	0.934132i	$-0.383825\pi$
$991$	22270.0	0.713853	0.356927	+	0.934132i	$0.383825\pi$
$992$	−7687.99	−0.246062
$993$	42137.1	1.34661
$994$	−38319.4	−1.22275
$995$	−8722.71	−0.277918
$996$	−59480.9	−1.89229
$997$	−49983.6	−1.58776	−0.793880	−	0.608075i	$-0.791942\pi$
$997$	−49983.6	−1.58776	−0.793880	+	0.608075i	$0.791942\pi$
$998$	51668.8	1.63883
$999$	−935.769	−0.0296360

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2015.4.a.d.1.3	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2015.4.a.d.1.3	✓	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)

\(f(q)\)	\(=\)	\(q-5.15631 q^{2} +4.91805 q^{3} +18.5876 q^{4} -5.00000 q^{5} -25.3590 q^{6} +12.2185 q^{7} -54.5927 q^{8} -2.81278 q^{9} +O(q^{10})\)	\(q-5.15631 q^{2} +4.91805 q^{3} +18.5876 q^{4} -5.00000 q^{5} -25.3590 q^{6} +12.2185 q^{7} -54.5927 q^{8} -2.81278 q^{9} +25.7816 q^{10} +0.204412 q^{11} +91.4145 q^{12} -13.0000 q^{13} -63.0027 q^{14} -24.5903 q^{15} +132.797 q^{16} +116.248 q^{17} +14.5036 q^{18} -19.1042 q^{19} -92.9378 q^{20} +60.0914 q^{21} -1.05401 q^{22} -162.478 q^{23} -268.490 q^{24} +25.0000 q^{25} +67.0321 q^{26} -146.621 q^{27} +227.113 q^{28} +40.9893 q^{29} +126.795 q^{30} +31.0000 q^{31} -248.000 q^{32} +1.00531 q^{33} -599.409 q^{34} -61.0927 q^{35} -52.2827 q^{36} +6.38224 q^{37} +98.5070 q^{38} -63.9347 q^{39} +272.964 q^{40} +47.2831 q^{41} -309.850 q^{42} -221.328 q^{43} +3.79953 q^{44} +14.0639 q^{45} +837.788 q^{46} +393.370 q^{47} +653.101 q^{48} -193.707 q^{49} -128.908 q^{50} +571.712 q^{51} -241.638 q^{52} +321.421 q^{53} +756.022 q^{54} -1.02206 q^{55} -667.044 q^{56} -93.9553 q^{57} -211.353 q^{58} +173.952 q^{59} -457.073 q^{60} -691.729 q^{61} -159.846 q^{62} -34.3681 q^{63} +216.389 q^{64} +65.0000 q^{65} -5.18370 q^{66} -415.895 q^{67} +2160.76 q^{68} -799.076 q^{69} +315.013 q^{70} +608.218 q^{71} +153.557 q^{72} +1192.68 q^{73} -32.9088 q^{74} +122.951 q^{75} -355.100 q^{76} +2.49762 q^{77} +329.667 q^{78} -682.284 q^{79} -663.984 q^{80} -645.143 q^{81} -243.806 q^{82} -650.672 q^{83} +1116.95 q^{84} -581.238 q^{85} +1141.24 q^{86} +201.587 q^{87} -11.1594 q^{88} +651.566 q^{89} -72.5178 q^{90} -158.841 q^{91} -3020.07 q^{92} +152.460 q^{93} -2028.34 q^{94} +95.5208 q^{95} -1219.67 q^{96} -1241.58 q^{97} +998.814 q^{98} -0.574967 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 5 q^{2} - 17 q^{3} + 149 q^{4} - 200 q^{5} - 35 q^{6} - 20 q^{7} - 39 q^{8} + 247 q^{9}+O(q^{10}) \) 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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