LMFDB - Embedded newform 2015.4.a.d.1.2

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			1.2
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)

$f(q)$	$=$	$q-5.25776 q^{2} +3.13707 q^{3} +19.6441 q^{4} -5.00000 q^{5} -16.4940 q^{6} -24.7609 q^{7} -61.2219 q^{8} -17.1588 q^{9} +O(q^{10})$	\(q-5.25776 q^{2} +3.13707 q^{3} +19.6441 q^{4} -5.00000 q^{5} -16.4940 q^{6} -24.7609 q^{7} -61.2219 q^{8} -17.1588 q^{9} +26.2888 q^{10} +17.6389 q^{11} +61.6249 q^{12} -13.0000 q^{13} +130.187 q^{14} -15.6854 q^{15} +164.737 q^{16} -95.7248 q^{17} +90.2168 q^{18} +115.115 q^{19} -98.2204 q^{20} -77.6768 q^{21} -92.7410 q^{22} +20.0669 q^{23} -192.057 q^{24} +25.0000 q^{25} +68.3509 q^{26} -138.529 q^{27} -486.406 q^{28} +88.6046 q^{29} +82.4699 q^{30} +31.0000 q^{31} -376.376 q^{32} +55.3344 q^{33} +503.299 q^{34} +123.805 q^{35} -337.069 q^{36} -266.342 q^{37} -605.247 q^{38} -40.7819 q^{39} +306.109 q^{40} +446.914 q^{41} +408.407 q^{42} -151.893 q^{43} +346.500 q^{44} +85.7939 q^{45} -105.507 q^{46} +273.231 q^{47} +516.793 q^{48} +270.104 q^{49} -131.444 q^{50} -300.296 q^{51} -255.373 q^{52} +470.930 q^{53} +728.354 q^{54} -88.1944 q^{55} +1515.91 q^{56} +361.124 q^{57} -465.862 q^{58} +227.273 q^{59} -308.125 q^{60} +77.6487 q^{61} -162.991 q^{62} +424.868 q^{63} +660.996 q^{64} +65.0000 q^{65} -290.935 q^{66} +656.030 q^{67} -1880.43 q^{68} +62.9512 q^{69} -650.936 q^{70} -335.473 q^{71} +1050.49 q^{72} +789.209 q^{73} +1400.36 q^{74} +78.4268 q^{75} +2261.33 q^{76} -436.755 q^{77} +214.422 q^{78} +763.462 q^{79} -823.687 q^{80} +28.7109 q^{81} -2349.77 q^{82} +778.019 q^{83} -1525.89 q^{84} +478.624 q^{85} +798.620 q^{86} +277.959 q^{87} -1079.88 q^{88} -1411.89 q^{89} -451.084 q^{90} +321.892 q^{91} +394.195 q^{92} +97.2492 q^{93} -1436.58 q^{94} -575.574 q^{95} -1180.72 q^{96} -1186.45 q^{97} -1420.14 q^{98} -302.662 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−5.25776	−1.85890	−0.929450	−	0.368948i	$-0.879718\pi$
$2$	−5.25776	−1.85890	−0.929450	+	0.368948i	$0.879718\pi$
$3$	3.13707	0.603730	0.301865	−	0.953351i	$-0.402391\pi$
$3$	3.13707	0.603730	0.301865	+	0.953351i	$0.402391\pi$
$4$	19.6441	2.45551
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	−16.4940	−1.12227
$7$	−24.7609	−1.33697	−0.668483	−	0.743728i	$-0.733056\pi$
$7$	−24.7609	−1.33697	−0.668483	+	0.743728i	$0.733056\pi$
$8$	−61.2219	−2.70565
$9$	−17.1588	−0.635510
$10$	26.2888	0.831326
$11$	17.6389	0.483484	0.241742	−	0.970341i	$-0.422281\pi$
$11$	17.6389	0.483484	0.241742	+	0.970341i	$0.422281\pi$
$12$	61.6249	1.48246
$13$	−13.0000	−0.277350
$13$	−13.0000	−0.277350
$14$	130.187	2.48528
$15$	−15.6854	−0.269996
$16$	164.737	2.57402
$17$	−95.7248	−1.36569	−0.682843	−	0.730565i	$-0.739257\pi$
$17$	−95.7248	−1.36569	−0.682843	+	0.730565i	$0.739257\pi$
$18$	90.2168	1.18135
$19$	115.115	1.38996	0.694978	−	0.719031i	$-0.255414\pi$
$19$	115.115	1.38996	0.694978	+	0.719031i	$0.255414\pi$
$20$	−98.2204	−1.09814
$21$	−77.6768	−0.807166
$22$	−92.7410	−0.898748
$23$	20.0669	0.181923	0.0909616	−	0.995854i	$-0.471006\pi$
$23$	20.0669	0.181923	0.0909616	+	0.995854i	$0.471006\pi$
$24$	−192.057	−1.63348
$25$	25.0000	0.200000
$26$	68.3509	0.515566
$27$	−138.529	−0.987406
$28$	−486.406	−3.28293
$29$	88.6046	0.567361	0.283680	−	0.958919i	$-0.408445\pi$
$29$	88.6046	0.567361	0.283680	+	0.958919i	$0.408445\pi$
$30$	82.4699	0.501896
$31$	31.0000	0.179605
$31$	31.0000	0.179605
$32$	−376.376	−2.07920
$33$	55.3344	0.291893
$34$	503.299	2.53868
$35$	123.805	0.597909
$36$	−337.069	−1.56050
$37$	−266.342	−1.18341	−0.591707	−	0.806153i	$-0.701546\pi$
$37$	−266.342	−1.18341	−0.591707	+	0.806153i	$0.701546\pi$
$38$	−605.247	−2.58379
$39$	−40.7819	−0.167444
$40$	306.109	1.21000
$41$	446.914	1.70235	0.851174	−	0.524884i	$-0.175891\pi$
$41$	446.914	1.70235	0.851174	+	0.524884i	$0.175891\pi$
$42$	408.407	1.50044
$43$	−151.893	−0.538687	−0.269343	−	0.963044i	$-0.586807\pi$
$43$	−151.893	−0.538687	−0.269343	+	0.963044i	$0.586807\pi$
$44$	346.500	1.18720
$45$	85.7939	0.284209
$46$	−105.507	−0.338177
$47$	273.231	0.847975	0.423988	−	0.905668i	$-0.360630\pi$
$47$	273.231	0.847975	0.423988	+	0.905668i	$0.360630\pi$
$48$	516.793	1.55401
$49$	270.104	0.787476
$50$	−131.444	−0.371780
$51$	−300.296	−0.824506
$52$	−255.373	−0.681036
$53$	470.930	1.22051	0.610256	−	0.792204i	$-0.291066\pi$
$53$	470.930	1.22051	0.610256	+	0.792204i	$0.291066\pi$
$54$	728.354	1.83549
$55$	−88.1944	−0.216220
$56$	1515.91	3.61736
$57$	361.124	0.839158
$58$	−465.862	−1.05467
$59$	227.273	0.501499	0.250750	−	0.968052i	$-0.419323\pi$
$59$	227.273	0.501499	0.250750	+	0.968052i	$0.419323\pi$
$60$	−308.125	−0.662978
$61$	77.6487	0.162982	0.0814910	−	0.996674i	$-0.474032\pi$
$61$	77.6487	0.162982	0.0814910	+	0.996674i	$0.474032\pi$
$62$	−162.991	−0.333868
$63$	424.868	0.849655
$64$	660.996	1.29101
$65$	65.0000	0.124035
$66$	−290.935	−0.542601
$67$	656.030	1.19622	0.598111	−	0.801414i	$-0.295918\pi$
$67$	656.030	1.19622	0.598111	+	0.801414i	$0.295918\pi$
$68$	−1880.43	−3.35346
$69$	62.9512	0.109832
$70$	−650.936	−1.11145
$71$	−335.473	−0.560750	−0.280375	−	0.959890i	$-0.590459\pi$
$71$	−335.473	−0.560750	−0.280375	+	0.959890i	$0.590459\pi$
$72$	1050.49	1.71947
$73$	789.209	1.26534	0.632670	−	0.774421i	$-0.281959\pi$
$73$	789.209	1.26534	0.632670	+	0.774421i	$0.281959\pi$
$74$	1400.36	2.19985
$75$	78.4268	0.120746
$76$	2261.33	3.41305
$77$	−436.755	−0.646401
$78$	214.422	0.311263
$79$	763.462	1.08729	0.543646	−	0.839314i	$-0.317043\pi$
$79$	763.462	1.08729	0.543646	+	0.839314i	$0.317043\pi$
$80$	−823.687	−1.15114
$81$	28.7109	0.0393840
$82$	−2349.77	−3.16449
$83$	778.019	1.02890	0.514450	−	0.857520i	$-0.327996\pi$
$83$	778.019	1.02890	0.514450	+	0.857520i	$0.327996\pi$
$84$	−1525.89	−1.98200
$85$	478.624	0.610754
$86$	798.620	1.00136
$87$	277.959	0.342533
$88$	−1079.88	−1.30814
$89$	−1411.89	−1.68157	−0.840787	−	0.541366i	$-0.817907\pi$
$89$	−1411.89	−1.68157	−0.840787	+	0.541366i	$0.817907\pi$
$90$	−451.084	−0.528316
$91$	321.892	0.370807
$92$	394.195	0.446714
$93$	97.2492	0.108433
$94$	−1436.58	−1.57630
$95$	−575.574	−0.621607
$96$	−1180.72	−1.25528
$97$	−1186.45	−1.24192	−0.620960	−	0.783842i	$-0.713257\pi$
$97$	−1186.45	−1.24192	−0.620960	+	0.783842i	$0.713257\pi$
$98$	−1420.14	−1.46384
$99$	−302.662	−0.307259
$100$	491.102	0.491102
$101$	−1167.77	−1.15047	−0.575236	−	0.817988i	$-0.695090\pi$
$101$	−1167.77	−1.15047	−0.575236	+	0.817988i	$0.695090\pi$
$102$	1578.88	1.53267
$103$	−974.285	−0.932031	−0.466016	−	0.884777i	$-0.654311\pi$
$103$	−974.285	−0.932031	−0.466016	+	0.884777i	$0.654311\pi$
$104$	795.884	0.750412
$105$	388.384	0.360975
$106$	−2476.04	−2.26881
$107$	−1188.38	−1.07369	−0.536846	−	0.843680i	$-0.680384\pi$
$107$	−1188.38	−1.07369	−0.536846	+	0.843680i	$0.680384\pi$
$108$	−2721.28	−2.42459
$109$	659.303	0.579356	0.289678	−	0.957124i	$-0.406452\pi$
$109$	659.303	0.579356	0.289678	+	0.957124i	$0.406452\pi$
$110$	463.705	0.401932
$111$	−835.533	−0.714462
$112$	−4079.05	−3.44138
$113$	1844.13	1.53523	0.767614	−	0.640912i	$-0.221444\pi$
$113$	1844.13	1.53523	0.767614	+	0.640912i	$0.221444\pi$
$114$	−1898.70	−1.55991
$115$	−100.334	−0.0813585
$116$	1740.56	1.39316
$117$	223.064	0.176259
$118$	−1194.95	−0.932237
$119$	2370.24	1.82588
$120$	960.287	0.730515
$121$	−1019.87	−0.766244
$122$	−408.259	−0.302967
$123$	1402.00	1.02776
$124$	608.967	0.441023
$125$	−125.000	−0.0894427
$126$	−2233.85	−1.57942
$127$	−1659.03	−1.15917	−0.579586	−	0.814911i	$-0.696786\pi$
$127$	−1659.03	−1.15917	−0.579586	+	0.814911i	$0.696786\pi$
$128$	−464.353	−0.320652
$129$	−476.500	−0.325221
$130$	−341.755	−0.230568
$131$	−126.611	−0.0844429	−0.0422214	−	0.999108i	$-0.513443\pi$
$131$	−126.611	−0.0844429	−0.0422214	+	0.999108i	$0.513443\pi$
$132$	1086.99	0.716748
$133$	−2850.35	−1.85832
$134$	−3449.25	−2.22366
$135$	692.646	0.441581
$136$	5860.45	3.69507
$137$	−1696.72	−1.05811	−0.529054	−	0.848588i	$-0.677453\pi$
$137$	−1696.72	−1.05811	−0.529054	+	0.848588i	$0.677453\pi$
$138$	−330.983	−0.204168
$139$	−2332.21	−1.42313	−0.711567	−	0.702618i	$-0.752014\pi$
$139$	−2332.21	−1.42313	−0.711567	+	0.702618i	$0.752014\pi$
$140$	2432.03	1.46817
$141$	857.145	0.511948
$142$	1763.84	1.04238
$143$	−229.305	−0.134094
$144$	−2826.69	−1.63582
$145$	−443.023	−0.253731
$146$	−4149.47	−2.35214
$147$	847.336	0.475422
$148$	−5232.04	−2.90589
$149$	2481.70	1.36449	0.682244	−	0.731124i	$-0.261004\pi$
$149$	2481.70	1.36449	0.682244	+	0.731124i	$0.261004\pi$
$150$	−412.350	−0.224455
$151$	−226.146	−0.121877	−0.0609386	−	0.998142i	$-0.519409\pi$
$151$	−226.146	−0.121877	−0.0609386	+	0.998142i	$0.519409\pi$
$152$	−7047.55	−3.76073
$153$	1642.52	0.867908
$154$	2296.36	1.20159
$155$	−155.000	−0.0803219
$156$	−801.124	−0.411162
$157$	3325.60	1.69052	0.845260	−	0.534355i	$-0.179445\pi$
$157$	3325.60	1.69052	0.845260	+	0.534355i	$0.179445\pi$
$158$	−4014.10	−2.02117
$159$	1477.34	0.736860
$160$	1881.88	0.929847
$161$	−496.875	−0.243225
$162$	−150.955	−0.0732109
$163$	1741.42	0.836799	0.418400	−	0.908263i	$-0.362591\pi$
$163$	1741.42	0.836799	0.418400	+	0.908263i	$0.362591\pi$
$164$	8779.22	4.18013
$165$	−276.672	−0.130539
$166$	−4090.64	−1.91262
$167$	2149.87	0.996177	0.498089	−	0.867126i	$-0.334035\pi$
$167$	2149.87	0.996177	0.498089	+	0.867126i	$0.334035\pi$
$168$	4755.52	2.18391
$169$	169.000	0.0769231
$170$	−2516.49	−1.13533
$171$	−1975.23	−0.883332
$172$	−2983.81	−1.32275
$173$	335.646	0.147507	0.0737535	−	0.997277i	$-0.476502\pi$
$173$	335.646	0.147507	0.0737535	+	0.997277i	$0.476502\pi$
$174$	−1461.44	−0.636734
$175$	−619.023	−0.267393
$176$	2905.78	1.24450
$177$	712.972	0.302770
$178$	7423.39	3.12588
$179$	2502.54	1.04497	0.522483	−	0.852650i	$-0.325006\pi$
$179$	2502.54	1.04497	0.522483	+	0.852650i	$0.325006\pi$
$180$	1685.34	0.697878
$181$	−1747.11	−0.717467	−0.358733	−	0.933440i	$-0.616791\pi$
$181$	−1747.11	−0.717467	−0.358733	+	0.933440i	$0.616791\pi$
$182$	−1692.43	−0.689294
$183$	243.590	0.0983971
$184$	−1228.53	−0.492220
$185$	1331.71	0.529239
$186$	−511.313	−0.201566
$187$	−1688.48	−0.660287
$188$	5367.37	2.08221
$189$	3430.11	1.32013
$190$	3026.23	1.15551
$191$	121.309	0.0459562	0.0229781	−	0.999736i	$-0.492685\pi$
$191$	121.309	0.0459562	0.0229781	+	0.999736i	$0.492685\pi$
$192$	2073.59	0.779419
$193$	−3280.94	−1.22366	−0.611832	−	0.790987i	$-0.709567\pi$
$193$	−3280.94	−1.22366	−0.611832	+	0.790987i	$0.709567\pi$
$194$	6238.10	2.30861
$195$	203.910	0.0748835
$196$	5305.95	1.93365
$197$	−154.507	−0.0558791	−0.0279395	−	0.999610i	$-0.508895\pi$
$197$	−154.507	−0.0558791	−0.0279395	+	0.999610i	$0.508895\pi$
$198$	1591.32	0.571164
$199$	−209.411	−0.0745967	−0.0372983	−	0.999304i	$-0.511875\pi$
$199$	−209.411	−0.0745967	−0.0372983	+	0.999304i	$0.511875\pi$
$200$	−1530.55	−0.541130
$201$	2058.01	0.722194
$202$	6139.87	2.13861
$203$	−2193.93	−0.758541
$204$	−5899.03	−2.02458
$205$	−2234.57	−0.761313
$206$	5122.56	1.73255
$207$	−344.323	−0.115614
$208$	−2141.59	−0.713905
$209$	2030.50	0.672021
$210$	−2042.03	−0.671017
$211$	−4715.38	−1.53848	−0.769242	−	0.638958i	$-0.779366\pi$
$211$	−4715.38	−1.53848	−0.769242	+	0.638958i	$0.779366\pi$
$212$	9250.98	2.99698
$213$	−1052.40	−0.338542
$214$	6248.22	1.99589
$215$	759.467	0.240908
$216$	8481.02	2.67158
$217$	−767.589	−0.240126
$218$	−3466.46	−1.07697
$219$	2475.80	0.763924
$220$	−1732.50	−0.530932
$221$	1244.42	0.378773
$222$	4393.04	1.32811
$223$	774.431	0.232555	0.116277	−	0.993217i	$-0.462904\pi$
$223$	774.431	0.232555	0.116277	+	0.993217i	$0.462904\pi$
$224$	9319.42	2.77982
$225$	−428.970	−0.127102
$226$	−9695.98	−2.85384
$227$	1280.51	0.374408	0.187204	−	0.982321i	$-0.440057\pi$
$227$	1280.51	0.374408	0.187204	+	0.982321i	$0.440057\pi$
$228$	7093.94	2.06056
$229$	1076.47	0.310632	0.155316	−	0.987865i	$-0.450360\pi$
$229$	1076.47	0.310632	0.155316	+	0.987865i	$0.450360\pi$
$230$	527.535	0.151237
$231$	−1370.13	−0.390251
$232$	−5424.54	−1.53508
$233$	42.4576	0.0119377	0.00596886	−	0.999982i	$-0.498100\pi$
$233$	42.4576	0.0119377	0.00596886	+	0.999982i	$0.498100\pi$
$234$	−1172.82	−0.327648
$235$	−1366.16	−0.379226
$236$	4464.58	1.23144
$237$	2395.03	0.656431
$238$	−12462.1	−3.39412
$239$	−4190.59	−1.13417	−0.567086	−	0.823659i	$-0.691929\pi$
$239$	−4190.59	−1.13417	−0.567086	+	0.823659i	$0.691929\pi$
$240$	−2583.97	−0.694976
$241$	1776.49	0.474828	0.237414	−	0.971409i	$-0.423700\pi$
$241$	1776.49	0.474828	0.237414	+	0.971409i	$0.423700\pi$
$242$	5362.24	1.42437
$243$	3830.36	1.01118
$244$	1525.34	0.400204
$245$	−1350.52	−0.352170
$246$	−7371.39	−1.91050
$247$	−1496.49	−0.385504
$248$	−1897.88	−0.485949
$249$	2440.70	0.621177
$250$	657.221	0.166265
$251$	1274.51	0.320502	0.160251	−	0.987076i	$-0.448770\pi$
$251$	1274.51	0.320502	0.160251	+	0.987076i	$0.448770\pi$
$252$	8346.14	2.08634
$253$	353.957	0.0879569
$254$	8722.78	2.15479
$255$	1501.48	0.368730
$256$	−2846.51	−0.694948
$257$	−221.916	−0.0538627	−0.0269314	−	0.999637i	$-0.508574\pi$
$257$	−221.916	−0.0538627	−0.0269314	+	0.999637i	$0.508574\pi$
$258$	2505.33	0.604554
$259$	6594.87	1.58218
$260$	1276.87	0.304569
$261$	−1520.35	−0.360564
$262$	665.689	0.156971
$263$	−4832.74	−1.13308	−0.566539	−	0.824035i	$-0.691718\pi$
$263$	−4832.74	−1.13308	−0.566539	+	0.824035i	$0.691718\pi$
$264$	−3387.68	−0.789762
$265$	−2354.65	−0.545830
$266$	14986.5	3.45444
$267$	−4429.20	−1.01522
$268$	12887.1	2.93733
$269$	3907.62	0.885694	0.442847	−	0.896597i	$-0.353968\pi$
$269$	3907.62	0.885694	0.442847	+	0.896597i	$0.353968\pi$
$270$	−3641.77	−0.820856
$271$	−5833.41	−1.30758	−0.653790	−	0.756676i	$-0.726822\pi$
$271$	−5833.41	−1.30758	−0.653790	+	0.756676i	$0.726822\pi$
$272$	−15769.5	−3.51531
$273$	1009.80	0.223867
$274$	8920.97	1.96692
$275$	440.972	0.0966967
$276$	1236.62	0.269695
$277$	−5186.42	−1.12499	−0.562494	−	0.826801i	$-0.690158\pi$
$277$	−5186.42	−1.12499	−0.562494	+	0.826801i	$0.690158\pi$
$278$	12262.2	2.64547
$279$	−531.922	−0.114141
$280$	−7579.55	−1.61773
$281$	4470.43	0.949053	0.474526	−	0.880241i	$-0.342619\pi$
$281$	4470.43	0.949053	0.474526	+	0.880241i	$0.342619\pi$
$282$	−4506.67	−0.951660
$283$	−4722.48	−0.991951	−0.495976	−	0.868336i	$-0.665189\pi$
$283$	−4722.48	−0.991951	−0.495976	+	0.868336i	$0.665189\pi$
$284$	−6590.05	−1.37693
$285$	−1805.62	−0.375283
$286$	1205.63	0.249268
$287$	−11066.0	−2.27598
$288$	6458.15	1.32135
$289$	4250.24	0.865101
$290$	2329.31	0.471661
$291$	−3721.99	−0.749784
$292$	15503.3	3.10706
$293$	326.194	0.0650391	0.0325196	−	0.999471i	$-0.489647\pi$
$293$	326.194	0.0650391	0.0325196	+	0.999471i	$0.489647\pi$
$294$	−4455.09	−0.883763
$295$	−1136.37	−0.224277
$296$	16305.9	3.20190
$297$	−2443.50	−0.477395
$298$	−13048.2	−2.53645
$299$	−260.869	−0.0504564
$300$	1540.62	0.296493
$301$	3761.02	0.720205
$302$	1189.02	0.226558
$303$	−3663.38	−0.694574
$304$	18963.7	3.57778
$305$	−388.244	−0.0728878
$306$	−8635.99	−1.61336
$307$	−7094.34	−1.31888	−0.659438	−	0.751759i	$-0.729206\pi$
$307$	−7094.34	−1.31888	−0.659438	+	0.751759i	$0.729206\pi$
$308$	−8579.66	−1.58724
$309$	−3056.40	−0.562695
$310$	814.953	0.149310
$311$	2208.40	0.402658	0.201329	−	0.979524i	$-0.435474\pi$
$311$	2208.40	0.402658	0.201329	+	0.979524i	$0.435474\pi$
$312$	2496.75	0.453046
$313$	−4406.35	−0.795724	−0.397862	−	0.917445i	$-0.630248\pi$
$313$	−4406.35	−0.795724	−0.397862	+	0.917445i	$0.630248\pi$
$314$	−17485.2	−3.14251
$315$	−2124.34	−0.379977
$316$	14997.5	2.66986
$317$	−573.929	−0.101688	−0.0508439	−	0.998707i	$-0.516191\pi$
$317$	−573.929	−0.101688	−0.0508439	+	0.998707i	$0.516191\pi$
$318$	−7767.51	−1.36975
$319$	1562.89	0.274310
$320$	−3304.98	−0.577356
$321$	−3728.03	−0.648219
$322$	2612.45	0.452131
$323$	−11019.4	−1.89824
$324$	564.000	0.0967078
$325$	−325.000	−0.0554700
$326$	−9155.96	−1.55553
$327$	2068.28	0.349774
$328$	−27360.9	−4.60595
$329$	−6765.46	−1.13371
$330$	1454.68	0.242659
$331$	625.759	0.103912	0.0519560	−	0.998649i	$-0.483454\pi$
$331$	625.759	0.103912	0.0519560	+	0.998649i	$0.483454\pi$
$332$	15283.5	2.52647
$333$	4570.10	0.752072
$334$	−11303.5	−1.85179
$335$	−3280.15	−0.534966
$336$	−12796.3	−2.07766
$337$	2969.52	0.480001	0.240000	−	0.970773i	$-0.422852\pi$
$337$	2969.52	0.480001	0.240000	+	0.970773i	$0.422852\pi$
$338$	−888.562	−0.142992
$339$	5785.16	0.926863
$340$	9402.13	1.49971
$341$	546.805	0.0868362
$342$	10385.3	1.64203
$343$	1804.97	0.284138
$344$	9299.20	1.45750
$345$	−314.756	−0.0491186
$346$	−1764.75	−0.274201
$347$	−7985.19	−1.23535	−0.617677	−	0.786432i	$-0.711926\pi$
$347$	−7985.19	−1.23535	−0.617677	+	0.786432i	$0.711926\pi$
$348$	5460.25	0.841092
$349$	11043.0	1.69375	0.846877	−	0.531789i	$-0.178480\pi$
$349$	11043.0	1.69375	0.846877	+	0.531789i	$0.178480\pi$
$350$	3254.68	0.497057
$351$	1800.88	0.273857
$352$	−6638.85	−1.00526
$353$	−3368.16	−0.507844	−0.253922	−	0.967225i	$-0.581721\pi$
$353$	−3368.16	−0.507844	−0.253922	+	0.967225i	$0.581721\pi$
$354$	−3748.64	−0.562819
$355$	1677.36	0.250775
$356$	−27735.3	−4.12912
$357$	7435.60	1.10234
$358$	−13157.8	−1.94249
$359$	7542.33	1.10883	0.554413	−	0.832241i	$-0.312943\pi$
$359$	7542.33	1.10883	0.554413	+	0.832241i	$0.312943\pi$
$360$	−5252.46	−0.768970
$361$	6392.43	0.931978
$362$	9185.88	1.33370
$363$	−3199.41	−0.462604
$364$	6323.28	0.910522
$365$	−3946.04	−0.565878
$366$	−1280.74	−0.182910
$367$	680.889	0.0968449	0.0484225	−	0.998827i	$-0.484581\pi$
$367$	680.889	0.0968449	0.0484225	+	0.998827i	$0.484581\pi$
$368$	3305.77	0.468274
$369$	−7668.50	−1.08186
$370$	−7001.81	−0.983802
$371$	−11660.7	−1.63178
$372$	1910.37	0.266259
$373$	6260.36	0.869032	0.434516	−	0.900664i	$-0.356919\pi$
$373$	6260.36	0.869032	0.434516	+	0.900664i	$0.356919\pi$
$374$	8877.62	1.22741
$375$	−392.134	−0.0539992
$376$	−16727.7	−2.29432
$377$	−1151.86	−0.157358
$378$	−18034.7	−2.45399
$379$	−3309.07	−0.448484	−0.224242	−	0.974534i	$-0.571991\pi$
$379$	−3309.07	−0.448484	−0.224242	+	0.974534i	$0.571991\pi$
$380$	−11306.6	−1.52636
$381$	−5204.49	−0.699827
$382$	−637.816	−0.0854280
$383$	2233.79	0.298019	0.149009	−	0.988836i	$-0.452392\pi$
$383$	2233.79	0.298019	0.149009	+	0.988836i	$0.452392\pi$
$384$	−1456.71	−0.193587
$385$	2183.78	0.289079
$386$	17250.4	2.27467
$387$	2606.31	0.342341
$388$	−23306.8	−3.04955
$389$	−2375.67	−0.309644	−0.154822	−	0.987942i	$-0.549480\pi$
$389$	−2375.67	−0.309644	−0.154822	+	0.987942i	$0.549480\pi$
$390$	−1072.11	−0.139201
$391$	−1920.90	−0.248450
$392$	−16536.3	−2.13063
$393$	−397.186	−0.0509807
$394$	812.362	0.103874
$395$	−3817.31	−0.486252
$396$	−5945.51	−0.754478
$397$	8938.16	1.12996	0.564979	−	0.825105i	$-0.308884\pi$
$397$	8938.16	1.12996	0.564979	+	0.825105i	$0.308884\pi$
$398$	1101.03	0.138668
$399$	−8941.76	−1.12192
$400$	4118.44	0.514805
$401$	11168.6	1.39086	0.695430	−	0.718594i	$-0.255214\pi$
$401$	11168.6	1.39086	0.695430	+	0.718594i	$0.255214\pi$
$402$	−10820.5	−1.34249
$403$	−403.000	−0.0498135
$404$	−22939.8	−2.82500
$405$	−143.555	−0.0176131
$406$	11535.2	1.41005
$407$	−4697.97	−0.572161
$408$	18384.7	2.23082
$409$	−16132.4	−1.95036	−0.975178	−	0.221423i	$-0.928930\pi$
$409$	−16132.4	−1.95036	−0.975178	+	0.221423i	$0.928930\pi$
$410$	11748.8	1.41520
$411$	−5322.74	−0.638811
$412$	−19138.9	−2.28861
$413$	−5627.50	−0.670487
$414$	1810.37	0.214915
$415$	−3890.10	−0.460138
$416$	4892.89	0.576667
$417$	−7316.32	−0.859189
$418$	−10675.9	−1.24922
$419$	−10470.2	−1.22077	−0.610385	−	0.792105i	$-0.708985\pi$
$419$	−10470.2	−1.22077	−0.610385	+	0.792105i	$0.708985\pi$
$420$	7629.45	0.886379
$421$	−12383.2	−1.43353	−0.716767	−	0.697313i	$-0.754379\pi$
$421$	−12383.2	−1.43353	−0.716767	+	0.697313i	$0.754379\pi$
$422$	24792.3	2.85989
$423$	−4688.31	−0.538897
$424$	−28831.2	−3.30228
$425$	−2393.12	−0.273137
$426$	5533.28	0.629315
$427$	−1922.66	−0.217901
$428$	−23344.6	−2.63646
$429$	−719.347	−0.0809567
$430$	−3993.10	−0.447824
$431$	−16436.2	−1.83690	−0.918450	−	0.395537i	$-0.870559\pi$
$431$	−16436.2	−1.83690	−0.918450	+	0.395537i	$0.870559\pi$
$432$	−22821.0	−2.54161
$433$	−15059.4	−1.67138	−0.835691	−	0.549200i	$-0.814932\pi$
$433$	−15059.4	−1.67138	−0.835691	+	0.549200i	$0.814932\pi$
$434$	4035.80	0.446370
$435$	−1389.79	−0.153185
$436$	12951.4	1.42261
$437$	2310.00	0.252865
$438$	−13017.2	−1.42006
$439$	−2958.41	−0.321633	−0.160817	−	0.986984i	$-0.551413\pi$
$439$	−2958.41	−0.321633	−0.160817	+	0.986984i	$0.551413\pi$
$440$	5399.42	0.585017
$441$	−4634.66	−0.500449
$442$	−6542.88	−0.704102
$443$	−4624.28	−0.495951	−0.247975	−	0.968766i	$-0.579765\pi$
$443$	−4624.28	−0.495951	−0.247975	+	0.968766i	$0.579765\pi$
$444$	−16413.3	−1.75437
$445$	7059.45	0.752023
$446$	−4071.78	−0.432296
$447$	7785.27	0.823782
$448$	−16366.9	−1.72603
$449$	−12005.4	−1.26185	−0.630925	−	0.775844i	$-0.717324\pi$
$449$	−12005.4	−1.26185	−0.630925	+	0.775844i	$0.717324\pi$
$450$	2255.42	0.236270
$451$	7883.06	0.823057
$452$	36226.2	3.76977
$453$	−709.435	−0.0735809
$454$	−6732.64	−0.695988
$455$	−1609.46	−0.165830
$456$	−22108.7	−2.27047
$457$	15203.2	1.55618	0.778092	−	0.628151i	$-0.216188\pi$
$457$	15203.2	1.55618	0.778092	+	0.628151i	$0.216188\pi$
$458$	−5659.80	−0.577435
$459$	13260.7	1.34849
$460$	−1970.98	−0.199777
$461$	16328.3	1.64965	0.824823	−	0.565391i	$-0.191275\pi$
$461$	16328.3	1.64965	0.824823	+	0.565391i	$0.191275\pi$
$462$	7203.83	0.725438
$463$	6754.08	0.677946	0.338973	−	0.940796i	$-0.389921\pi$
$463$	6754.08	0.677946	0.338973	+	0.940796i	$0.389921\pi$
$464$	14596.5	1.46040
$465$	−486.246	−0.0484927
$466$	−223.232	−0.0221910
$467$	8299.31	0.822369	0.411184	−	0.911552i	$-0.365115\pi$
$467$	8299.31	0.822369	0.411184	+	0.911552i	$0.365115\pi$
$468$	4381.89	0.432806
$469$	−16243.9	−1.59931
$470$	7182.92	0.704944
$471$	10432.6	1.02062
$472$	−13914.1	−1.35688
$473$	−2679.23	−0.260446
$474$	−12592.5	−1.22024
$475$	2877.87	0.277991
$476$	46561.1	4.48346
$477$	−8080.58	−0.775648
$478$	22033.2	2.10831
$479$	5807.27	0.553948	0.276974	−	0.960877i	$-0.410668\pi$
$479$	5807.27	0.553948	0.276974	+	0.960877i	$0.410668\pi$
$480$	5903.59	0.561377
$481$	3462.44	0.328220
$482$	−9340.35	−0.882658
$483$	−1558.73	−0.146842
$484$	−20034.4	−1.88152
$485$	5932.27	0.555403
$486$	−20139.1	−1.87969
$487$	−7961.13	−0.740767	−0.370383	−	0.928879i	$-0.620774\pi$
$487$	−7961.13	−0.740767	−0.370383	+	0.928879i	$0.620774\pi$
$488$	−4753.80	−0.440972
$489$	5462.95	0.505201
$490$	7100.72	0.654649
$491$	−82.6449	−0.00759616	−0.00379808	−	0.999993i	$-0.501209\pi$
$491$	−82.6449	−0.00759616	−0.00379808	+	0.999993i	$0.501209\pi$
$492$	27541.0	2.52367
$493$	−8481.66	−0.774837
$494$	7868.21	0.716614
$495$	1513.31	0.137410
$496$	5106.86	0.462308
$497$	8306.62	0.749704
$498$	−12832.6	−1.15471
$499$	−7299.90	−0.654887	−0.327444	−	0.944871i	$-0.606187\pi$
$499$	−7299.90	−0.654887	−0.327444	+	0.944871i	$0.606187\pi$
$500$	−2455.51	−0.219628
$501$	6744.28	0.601422
$502$	−6701.05	−0.595782
$503$	1997.07	0.177028	0.0885139	−	0.996075i	$-0.471788\pi$
$503$	1997.07	0.177028	0.0885139	+	0.996075i	$0.471788\pi$
$504$	−26011.2	−2.29887
$505$	5838.86	0.514507
$506$	−1861.02	−0.163503
$507$	530.165	0.0464407
$508$	−32590.1	−2.84636
$509$	14065.2	1.22481	0.612405	−	0.790544i	$-0.290202\pi$
$509$	14065.2	1.22481	0.612405	+	0.790544i	$0.290202\pi$
$510$	−7894.42	−0.685433
$511$	−19541.5	−1.69172
$512$	18681.1	1.61249
$513$	−15946.8	−1.37245
$514$	1166.78	0.100125
$515$	4871.43	0.416817
$516$	−9360.42	−0.798584
$517$	4819.49	0.409982
$518$	−34674.3	−2.94112
$519$	1052.95	0.0890543
$520$	−3979.42	−0.335595
$521$	−5640.74	−0.474329	−0.237165	−	0.971469i	$-0.576218\pi$
$521$	−5640.74	−0.474329	−0.237165	+	0.971469i	$0.576218\pi$
$522$	7993.63	0.670252
$523$	−16888.7	−1.41203	−0.706013	−	0.708198i	$-0.749508\pi$
$523$	−16888.7	−1.41203	−0.706013	+	0.708198i	$0.749508\pi$
$524$	−2487.15	−0.207350
$525$	−1941.92	−0.161433
$526$	25409.4	2.10628
$527$	−2967.47	−0.245285
$528$	9115.65	0.751340
$529$	−11764.3	−0.966904
$530$	12380.2	1.01464
$531$	−3899.73	−0.318708
$532$	−55992.6	−4.56313
$533$	−5809.88	−0.472146
$534$	23287.7	1.88719
$535$	5941.90	0.480169
$536$	−40163.4	−3.23656
$537$	7850.66	0.630877
$538$	−20545.3	−1.64642
$539$	4764.33	0.380732
$540$	13606.4	1.08431
$541$	−3224.19	−0.256227	−0.128113	−	0.991760i	$-0.540892\pi$
$541$	−3224.19	−0.256227	−0.128113	+	0.991760i	$0.540892\pi$
$542$	30670.7	2.43066
$543$	−5480.80	−0.433156
$544$	36028.5	2.83954
$545$	−3296.52	−0.259096
$546$	−5309.28	−0.416147
$547$	23113.2	1.80667	0.903337	−	0.428932i	$-0.141110\pi$
$547$	23113.2	1.80667	0.903337	+	0.428932i	$0.141110\pi$
$548$	−33330.6	−2.59820
$549$	−1332.36	−0.103577
$550$	−2318.53	−0.179750
$551$	10199.7	0.788606
$552$	−3853.99	−0.297168
$553$	−18904.0	−1.45367
$554$	27269.0	2.09124
$555$	4177.67	0.319517
$556$	−45814.2	−3.49452
$557$	−1025.89	−0.0780400	−0.0390200	−	0.999238i	$-0.512424\pi$
$557$	−1025.89	−0.0780400	−0.0390200	+	0.999238i	$0.512424\pi$
$558$	2796.72	0.212177
$559$	1974.61	0.149405
$560$	20395.3	1.53903
$561$	−5296.88	−0.398635
$562$	−23504.5	−1.76419
$563$	2494.76	0.186752	0.0933761	−	0.995631i	$-0.470234\pi$
$563$	2494.76	0.186752	0.0933761	+	0.995631i	$0.470234\pi$
$564$	16837.8	1.25709
$565$	−9220.63	−0.686575
$566$	24829.7	1.84394
$567$	−710.909	−0.0526550
$568$	20538.3	1.51719
$569$	7231.75	0.532813	0.266407	−	0.963861i	$-0.414164\pi$
$569$	7231.75	0.532813	0.266407	+	0.963861i	$0.414164\pi$
$570$	9493.51	0.697613
$571$	5263.37	0.385753	0.192877	−	0.981223i	$-0.438218\pi$
$571$	5263.37	0.385753	0.192877	+	0.981223i	$0.438218\pi$
$572$	−4504.49	−0.329270
$573$	380.556	0.0277451
$574$	58182.5	4.23082
$575$	501.672	0.0363846
$576$	−11341.9	−0.820449
$577$	−3032.76	−0.218814	−0.109407	−	0.993997i	$-0.534895\pi$
$577$	−3032.76	−0.218814	−0.109407	+	0.993997i	$0.534895\pi$
$578$	−22346.8	−1.60814
$579$	−10292.5	−0.738763
$580$	−8702.78	−0.623040
$581$	−19264.5	−1.37560
$582$	19569.4	1.39377
$583$	8306.67	0.590098
$584$	−48316.8	−3.42357
$585$	−1115.32	−0.0788254
$586$	−1715.05	−0.120901
$587$	−5252.74	−0.369342	−0.184671	−	0.982800i	$-0.559122\pi$
$587$	−5252.74	−0.369342	−0.184671	+	0.982800i	$0.559122\pi$
$588$	16645.1	1.16740
$589$	3568.56	0.249643
$590$	5974.75	0.416909
$591$	−484.700	−0.0337358
$592$	−43876.5	−3.04613
$593$	−2590.06	−0.179361	−0.0896806	−	0.995971i	$-0.528585\pi$
$593$	−2590.06	−0.179361	−0.0896806	+	0.995971i	$0.528585\pi$
$594$	12847.3	0.887429
$595$	−11851.2	−0.816556
$596$	48750.7	3.35052
$597$	−656.937	−0.0450362
$598$	1371.59	0.0937934
$599$	18537.3	1.26447	0.632233	−	0.774779i	$-0.282139\pi$
$599$	18537.3	1.26447	0.632233	+	0.774779i	$0.282139\pi$
$600$	−4801.43	−0.326696
$601$	6849.21	0.464867	0.232433	−	0.972612i	$-0.425331\pi$
$601$	6849.21	0.464867	0.232433	+	0.972612i	$0.425331\pi$
$602$	−19774.6	−1.33879
$603$	−11256.7	−0.760211
$604$	−4442.42	−0.299271
$605$	5099.35	0.342675
$606$	19261.2	1.29114
$607$	25422.1	1.69992	0.849960	−	0.526847i	$-0.176626\pi$
$607$	25422.1	1.69992	0.849960	+	0.526847i	$0.176626\pi$
$608$	−43326.5	−2.89000
$609$	−6882.53	−0.457954
$610$	2041.29	0.135491
$611$	−3552.00	−0.235186
$612$	32265.8	2.13116
$613$	18020.9	1.18737	0.593685	−	0.804698i	$-0.297673\pi$
$613$	18020.9	1.18737	0.593685	+	0.804698i	$0.297673\pi$
$614$	37300.4	2.45166
$615$	−7010.00	−0.459627
$616$	26739.0	1.74893
$617$	−2206.61	−0.143979	−0.0719893	−	0.997405i	$-0.522935\pi$
$617$	−2206.61	−0.143979	−0.0719893	+	0.997405i	$0.522935\pi$
$618$	16069.8	1.04599
$619$	−24782.4	−1.60919	−0.804596	−	0.593822i	$-0.797618\pi$
$619$	−24782.4	−1.60919	−0.804596	+	0.593822i	$0.797618\pi$
$620$	−3044.83	−0.197231
$621$	−2779.85	−0.179632
$622$	−11611.2	−0.748501
$623$	34959.7	2.24821
$624$	−6718.31	−0.431006
$625$	625.000	0.0400000
$626$	23167.6	1.47917
$627$	6369.81	0.405719
$628$	65328.4	4.15109
$629$	25495.5	1.61617
$630$	11169.3	0.706340
$631$	−30967.3	−1.95371	−0.976853	−	0.213911i	$-0.931380\pi$
$631$	−30967.3	−1.95371	−0.976853	+	0.213911i	$0.931380\pi$
$632$	−46740.5	−2.94183
$633$	−14792.5	−0.928828
$634$	3017.58	0.189028
$635$	8295.14	0.518398
$636$	29021.0	1.80937
$637$	−3511.35	−0.218406
$638$	−8217.28	−0.509914
$639$	5756.30	0.356363
$640$	2321.77	0.143400
$641$	−15035.0	−0.926438	−0.463219	−	0.886244i	$-0.653306\pi$
$641$	−15035.0	−0.926438	−0.463219	+	0.886244i	$0.653306\pi$
$642$	19601.1	1.20498
$643$	−11791.2	−0.723173	−0.361587	−	0.932339i	$-0.617765\pi$
$643$	−11791.2	−0.723173	−0.361587	+	0.932339i	$0.617765\pi$
$644$	−9760.65	−0.597241
$645$	2382.50	0.145443
$646$	57937.1	3.52865
$647$	−28573.3	−1.73621	−0.868107	−	0.496376i	$-0.834664\pi$
$647$	−28573.3	−1.73621	−0.868107	+	0.496376i	$0.834664\pi$
$648$	−1757.74	−0.106559
$649$	4008.84	0.242467
$650$	1708.77	0.103113
$651$	−2407.98	−0.144971
$652$	34208.5	2.05477
$653$	−28620.6	−1.71518	−0.857588	−	0.514338i	$-0.828038\pi$
$653$	−28620.6	−1.71518	−0.857588	+	0.514338i	$0.828038\pi$
$654$	−10874.5	−0.650196
$655$	633.053	0.0377640
$656$	73623.5	4.38188
$657$	−13541.9	−0.804137
$658$	35571.2	2.10746
$659$	24377.8	1.44101	0.720504	−	0.693451i	$-0.243910\pi$
$659$	24377.8	1.44101	0.720504	+	0.693451i	$0.243910\pi$
$660$	−5434.97	−0.320539
$661$	−28604.5	−1.68319	−0.841594	−	0.540111i	$-0.818382\pi$
$661$	−28604.5	−1.68319	−0.841594	+	0.540111i	$0.818382\pi$
$662$	−3290.10	−0.193162
$663$	3903.84	0.228677
$664$	−47631.8	−2.78384
$665$	14251.8	0.831067
$666$	−24028.5	−1.39803
$667$	1778.02	0.103216
$668$	42232.2	2.44612
$669$	2429.45	0.140400
$670$	17246.3	0.994449
$671$	1369.64	0.0787992
$672$	29235.7	1.67826
$673$	−6925.30	−0.396658	−0.198329	−	0.980135i	$-0.563551\pi$
$673$	−6925.30	−0.396658	−0.198329	+	0.980135i	$0.563551\pi$
$674$	−15613.1	−0.892274
$675$	−3463.23	−0.197481
$676$	3319.85	0.188885
$677$	−3998.41	−0.226989	−0.113494	−	0.993539i	$-0.536204\pi$
$677$	−3998.41	−0.226989	−0.113494	+	0.993539i	$0.536204\pi$
$678$	−30417.0	−1.72295
$679$	29377.7	1.66040
$680$	−29302.3	−1.65249
$681$	4017.06	0.226042
$682$	−2874.97	−0.161420
$683$	6286.98	0.352218	0.176109	−	0.984371i	$-0.443649\pi$
$683$	6286.98	0.352218	0.176109	+	0.984371i	$0.443649\pi$
$684$	−38801.6	−2.16903
$685$	8483.62	0.473200
$686$	−9490.11	−0.528184
$687$	3376.95	0.187538
$688$	−25022.5	−1.38659
$689$	−6122.09	−0.338509
$690$	1654.91	0.0913065
$691$	10334.4	0.568941	0.284470	−	0.958685i	$-0.408182\pi$
$691$	10334.4	0.568941	0.284470	+	0.958685i	$0.408182\pi$
$692$	6593.46	0.362205
$693$	7494.19	0.410794
$694$	41984.3	2.29640
$695$	11661.1	0.636445
$696$	−17017.2	−0.926773
$697$	−42780.8	−2.32487
$698$	−58061.7	−3.14852
$699$	133.192	0.00720715
$700$	−12160.2	−0.656586
$701$	10353.1	0.557821	0.278910	−	0.960317i	$-0.410027\pi$
$701$	10353.1	0.557821	0.278910	+	0.960317i	$0.410027\pi$
$702$	−9468.60	−0.509073
$703$	−30659.9	−1.64489
$704$	11659.2	0.624181
$705$	−4285.73	−0.228950
$706$	17709.0	0.944032
$707$	28915.1	1.53814
$708$	14005.7	0.743455
$709$	−24175.4	−1.28057	−0.640287	−	0.768136i	$-0.721185\pi$
$709$	−24175.4	−1.28057	−0.640287	+	0.768136i	$0.721185\pi$
$710$	−8819.18	−0.466166
$711$	−13100.1	−0.690986
$712$	86438.6	4.54975
$713$	622.073	0.0326744
$714$	−39094.6	−2.04913
$715$	1146.53	0.0599688
$716$	49160.2	2.56592
$717$	−13146.2	−0.684733
$718$	−39655.8	−2.06120
$719$	−32926.1	−1.70784	−0.853920	−	0.520405i	$-0.825781\pi$
$719$	−32926.1	−1.70784	−0.853920	+	0.520405i	$0.825781\pi$
$720$	14133.5	0.731560
$721$	24124.2	1.24609
$722$	−33609.9	−1.73245
$723$	5572.97	0.286668
$724$	−34320.3	−1.76175
$725$	2215.11	0.113472
$726$	16821.7	0.859935
$727$	−18524.5	−0.945030	−0.472515	−	0.881323i	$-0.656654\pi$
$727$	−18524.5	−0.945030	−0.472515	+	0.881323i	$0.656654\pi$
$728$	−19706.8	−1.00327
$729$	11240.9	0.571098
$730$	20747.4	1.05191
$731$	14540.0	0.735677
$732$	4785.10	0.241615
$733$	−25887.4	−1.30447	−0.652233	−	0.758019i	$-0.726167\pi$
$733$	−25887.4	−1.30447	−0.652233	+	0.758019i	$0.726167\pi$
$734$	−3579.95	−0.180025
$735$	−4236.68	−0.212615
$736$	−7552.69	−0.378255
$737$	11571.6	0.578353
$738$	40319.2	2.01107
$739$	−8577.29	−0.426956	−0.213478	−	0.976948i	$-0.568479\pi$
$739$	−8577.29	−0.426956	−0.213478	+	0.976948i	$0.568479\pi$
$740$	26160.2	1.29955
$741$	−4694.61	−0.232740
$742$	61309.0	3.03332
$743$	5729.02	0.282877	0.141438	−	0.989947i	$-0.454827\pi$
$743$	5729.02	0.282877	0.141438	+	0.989947i	$0.454827\pi$
$744$	−5953.78	−0.293382
$745$	−12408.5	−0.610218
$746$	−32915.5	−1.61544
$747$	−13349.9	−0.653877
$748$	−33168.6	−1.62134
$749$	29425.4	1.43549
$750$	2061.75	0.100379
$751$	22369.7	1.08692	0.543462	−	0.839434i	$-0.317113\pi$
$751$	22369.7	1.08692	0.543462	+	0.839434i	$0.317113\pi$
$752$	45011.4	2.18271
$753$	3998.21	0.193497
$754$	6056.21	0.292512
$755$	1130.73	0.0545052
$756$	67381.5	3.24159
$757$	−30784.4	−1.47804	−0.739022	−	0.673682i	$-0.764712\pi$
$757$	−30784.4	−1.47804	−0.739022	+	0.673682i	$0.764712\pi$
$758$	17398.3	0.833687
$759$	1110.39	0.0531022
$760$	35237.7	1.68185
$761$	3228.51	0.153789	0.0768946	−	0.997039i	$-0.475500\pi$
$761$	3228.51	0.153789	0.0768946	+	0.997039i	$0.475500\pi$
$762$	27364.0	1.30091
$763$	−16325.0	−0.774579
$764$	2383.01	0.112846
$765$	−8212.61	−0.388140
$766$	−11744.7	−0.553987
$767$	−2954.55	−0.139091
$768$	−8929.69	−0.419561
$769$	−5079.09	−0.238175	−0.119088	−	0.992884i	$-0.537997\pi$
$769$	−5079.09	−0.238175	−0.119088	+	0.992884i	$0.537997\pi$
$770$	−11481.8	−0.537370
$771$	−696.166	−0.0325185
$772$	−64451.1	−3.00472
$773$	−7012.09	−0.326271	−0.163135	−	0.986604i	$-0.552161\pi$
$773$	−7012.09	−0.326271	−0.163135	+	0.986604i	$0.552161\pi$
$774$	−13703.3	−0.636378
$775$	775.000	0.0359211
$776$	72637.0	3.36020
$777$	20688.6	0.955211
$778$	12490.7	0.575597
$779$	51446.4	2.36619
$780$	4005.62	0.183877
$781$	−5917.36	−0.271114
$782$	10099.6	0.461844
$783$	−12274.3	−0.560216
$784$	44496.3	2.02698
$785$	−16628.0	−0.756024
$786$	2088.31	0.0947680
$787$	−24045.8	−1.08913	−0.544563	−	0.838720i	$-0.683304\pi$
$787$	−24045.8	−1.08913	−0.544563	+	0.838720i	$0.683304\pi$
$788$	−3035.15	−0.137212
$789$	−15160.6	−0.684072
$790$	20070.5	0.903894
$791$	−45662.3	−2.05255
$792$	18529.5	0.831335
$793$	−1009.43	−0.0452031
$794$	−46994.7	−2.10048
$795$	−7386.70	−0.329534
$796$	−4113.68	−0.183173
$797$	−40671.0	−1.80758	−0.903789	−	0.427977i	$-0.859226\pi$
$797$	−40671.0	−1.80758	−0.903789	+	0.427977i	$0.859226\pi$
$798$	47013.7	2.08555
$799$	−26155.0	−1.15807
$800$	−9409.39	−0.415840
$801$	24226.3	1.06866
$802$	−58722.1	−2.58547
$803$	13920.8	0.611772
$804$	40427.8	1.77336
$805$	2484.37	0.108773
$806$	2118.88	0.0925984
$807$	12258.5	0.534720
$808$	71493.2	3.11277
$809$	22111.3	0.960931	0.480465	−	0.877014i	$-0.340468\pi$
$809$	22111.3	0.960931	0.480465	+	0.877014i	$0.340468\pi$
$810$	754.776	0.0327409
$811$	691.260	0.0299303	0.0149651	−	0.999888i	$-0.495236\pi$
$811$	691.260	0.0299303	0.0149651	+	0.999888i	$0.495236\pi$
$812$	−43097.8	−1.86261
$813$	−18299.8	−0.789425
$814$	24700.8	1.06359
$815$	−8707.08	−0.374228
$816$	−49469.9	−2.12230
$817$	−17485.2	−0.748751
$818$	84820.3	3.62552
$819$	−5523.28	−0.235652
$820$	−43896.1	−1.86941
$821$	2212.21	0.0940399	0.0470200	−	0.998894i	$-0.485028\pi$
$821$	2212.21	0.0940399	0.0470200	+	0.998894i	$0.485028\pi$
$822$	27985.7	1.18749
$823$	−34010.4	−1.44050	−0.720248	−	0.693717i	$-0.755972\pi$
$823$	−34010.4	−1.44050	−0.720248	+	0.693717i	$0.755972\pi$
$824$	59647.6	2.52175
$825$	1383.36	0.0583787
$826$	29588.1	1.24637
$827$	−17409.3	−0.732018	−0.366009	−	0.930611i	$-0.619276\pi$
$827$	−17409.3	−0.732018	−0.366009	+	0.930611i	$0.619276\pi$
$828$	−6763.91	−0.283892
$829$	−12732.2	−0.533425	−0.266712	−	0.963776i	$-0.585937\pi$
$829$	−12732.2	−0.533425	−0.266712	+	0.963776i	$0.585937\pi$
$830$	20453.2	0.855351
$831$	−16270.2	−0.679189
$832$	−8592.94	−0.358061
$833$	−25855.7	−1.07545
$834$	38467.5	1.59715
$835$	−10749.3	−0.445504
$836$	39887.3	1.65016
$837$	−4294.41	−0.177343
$838$	55049.8	2.26929
$839$	−9737.03	−0.400667	−0.200334	−	0.979728i	$-0.564203\pi$
$839$	−9737.03	−0.400667	−0.200334	+	0.979728i	$0.564203\pi$
$840$	−23777.6	−0.976673
$841$	−16538.2	−0.678102
$842$	65107.7	2.66480
$843$	14024.1	0.572971
$844$	−92629.3	−3.77776
$845$	−845.000	−0.0344010
$846$	24650.0	1.00176
$847$	25252.9	1.02444
$848$	77579.7	3.14163
$849$	−14814.8	−0.598870
$850$	12582.5	0.507735
$851$	−5344.65	−0.215290
$852$	−20673.5	−0.831293
$853$	37511.5	1.50571	0.752855	−	0.658187i	$-0.228676\pi$
$853$	37511.5	1.50571	0.752855	+	0.658187i	$0.228676\pi$
$854$	10108.9	0.405057
$855$	9876.16	0.395038
$856$	72754.8	2.90503
$857$	30998.6	1.23558	0.617790	−	0.786343i	$-0.288028\pi$
$857$	30998.6	1.23558	0.617790	+	0.786343i	$0.288028\pi$
$858$	3782.16	0.150490
$859$	−29194.1	−1.15959	−0.579797	−	0.814761i	$-0.696868\pi$
$859$	−29194.1	−1.15959	−0.579797	+	0.814761i	$0.696868\pi$
$860$	14919.0	0.591552
$861$	−34714.9	−1.37408
$862$	86417.7	3.41461
$863$	24574.9	0.969339	0.484669	−	0.874697i	$-0.338940\pi$
$863$	24574.9	0.969339	0.484669	+	0.874697i	$0.338940\pi$
$864$	52139.1	2.05302
$865$	−1678.23	−0.0659671
$866$	79178.7	3.10693
$867$	13333.3	0.522287
$868$	−15078.6	−0.589632
$869$	13466.6	0.525688
$870$	7307.21	0.284756
$871$	−8528.39	−0.331772
$872$	−40363.8	−1.56753
$873$	20358.1	0.789253
$874$	−12145.4	−0.470051
$875$	3095.12	0.119582
$876$	48634.9	1.87582
$877$	26637.1	1.02562	0.512811	−	0.858501i	$-0.328604\pi$
$877$	26637.1	1.02562	0.512811	+	0.858501i	$0.328604\pi$
$878$	15554.6	0.597884
$879$	1023.29	0.0392661
$880$	−14528.9	−0.556556
$881$	−3393.51	−0.129773	−0.0648866	−	0.997893i	$-0.520669\pi$
$881$	−3393.51	−0.129773	−0.0648866	+	0.997893i	$0.520669\pi$
$882$	24367.9	0.930285
$883$	−3387.06	−0.129087	−0.0645434	−	0.997915i	$-0.520559\pi$
$883$	−3387.06	−0.129087	−0.0645434	+	0.997915i	$0.520559\pi$
$884$	24445.5	0.930082
$885$	−3564.86	−0.135403
$886$	24313.4	0.921924
$887$	18874.3	0.714472	0.357236	−	0.934014i	$-0.383719\pi$
$887$	18874.3	0.714472	0.357236	+	0.934014i	$0.383719\pi$
$888$	51152.9	1.93308
$889$	41079.1	1.54977
$890$	−37116.9	−1.39794
$891$	506.428	0.0190415
$892$	15213.0	0.571041
$893$	31453.0	1.17865
$894$	−40933.1	−1.53133
$895$	−12512.7	−0.467323
$896$	11497.8	0.428700
$897$	−818.366	−0.0304620
$898$	63121.7	2.34565
$899$	2746.74	0.101901
$900$	−8426.72	−0.312101
$901$	−45079.7	−1.66684
$902$	−41447.3	−1.52998
$903$	11798.6	0.434809
$904$	−112901.	−4.15379
$905$	8735.54	0.320861
$906$	3730.04	0.136780
$907$	−1943.68	−0.0711565	−0.0355783	−	0.999367i	$-0.511327\pi$
$907$	−1943.68	−0.0711565	−0.0355783	+	0.999367i	$0.511327\pi$
$908$	25154.5	0.919364
$909$	20037.5	0.731137
$910$	8462.17	0.308262
$911$	−26988.2	−0.981512	−0.490756	−	0.871297i	$-0.663279\pi$
$911$	−26988.2	−0.981512	−0.490756	+	0.871297i	$0.663279\pi$
$912$	59490.6	2.16001
$913$	13723.4	0.497456
$914$	−79934.9	−2.89279
$915$	−1217.95	−0.0440045
$916$	21146.2	0.762761
$917$	3135.00	0.112897
$918$	−69721.6	−2.50670
$919$	11152.0	0.400294	0.200147	−	0.979766i	$-0.435858\pi$
$919$	11152.0	0.400294	0.200147	+	0.979766i	$0.435858\pi$
$920$	6142.66	0.220128
$921$	−22255.4	−0.796245
$922$	−85850.6	−3.06653
$923$	4361.14	0.155524
$924$	−26915.0	−0.958267
$925$	−6658.54	−0.236683
$926$	−35511.4	−1.26023
$927$	16717.6	0.592315
$928$	−33348.6	−1.17966
$929$	7512.76	0.265324	0.132662	−	0.991161i	$-0.457648\pi$
$929$	7512.76	0.265324	0.132662	+	0.991161i	$0.457648\pi$
$930$	2556.57	0.0901432
$931$	31093.0	1.09456
$932$	834.040	0.0293132
$933$	6927.90	0.243097
$934$	−43635.8	−1.52870
$935$	8442.39	0.295289
$936$	−13656.4	−0.476895
$937$	6230.57	0.217229	0.108615	−	0.994084i	$-0.465359\pi$
$937$	6230.57	0.217229	0.108615	+	0.994084i	$0.465359\pi$
$938$	85406.7	2.97295
$939$	−13823.0	−0.480402
$940$	−26836.9	−0.931194
$941$	23863.8	0.826713	0.413356	−	0.910569i	$-0.364356\pi$
$941$	23863.8	0.826713	0.413356	+	0.910569i	$0.364356\pi$
$942$	−54852.4	−1.89723
$943$	8968.17	0.309696
$944$	37440.4	1.29087
$945$	−17150.6	−0.590379
$946$	14086.8	0.484144
$947$	−41758.7	−1.43292	−0.716460	−	0.697628i	$-0.754239\pi$
$947$	−41758.7	−1.43292	−0.716460	+	0.697628i	$0.754239\pi$
$948$	47048.2	1.61187
$949$	−10259.7	−0.350942
$950$	−15131.2	−0.516758
$951$	−1800.46	−0.0613920
$952$	−145110.	−4.94018
$953$	−6676.52	−0.226940	−0.113470	−	0.993541i	$-0.536197\pi$
$953$	−6676.52	−0.226940	−0.113470	+	0.993541i	$0.536197\pi$
$954$	42485.8	1.44185
$955$	−606.547	−0.0205522
$956$	−82320.4	−2.78497
$957$	4902.88	0.165609
$958$	−30533.3	−1.02973
$959$	42012.5	1.41465
$960$	−10368.0	−0.348567
$961$	961.000	0.0322581
$962$	−18204.7	−0.610128
$963$	20391.1	0.682342
$964$	34897.5	1.16595
$965$	16404.7	0.547240
$966$	8195.44	0.272965
$967$	−6289.84	−0.209170	−0.104585	−	0.994516i	$-0.533351\pi$
$967$	−6289.84	−0.209170	−0.104585	+	0.994516i	$0.533351\pi$
$968$	62438.4	2.07319
$969$	−34568.5	−1.14603
$970$	−31190.5	−1.03244
$971$	−57140.5	−1.88849	−0.944246	−	0.329241i	$-0.893207\pi$
$971$	−57140.5	−1.88849	−0.944246	+	0.329241i	$0.893207\pi$
$972$	75243.9	2.48297
$973$	57747.8	1.90268
$974$	41857.8	1.37701
$975$	−1019.55	−0.0334889
$976$	12791.7	0.419519
$977$	−12411.4	−0.406423	−0.203212	−	0.979135i	$-0.565138\pi$
$977$	−12411.4	−0.406423	−0.203212	+	0.979135i	$0.565138\pi$
$978$	−28722.9	−0.939118
$979$	−24904.2	−0.813014
$980$	−26529.7	−0.864757
$981$	−11312.8	−0.368187
$982$	434.527	0.0141205
$983$	4476.91	0.145261	0.0726303	−	0.997359i	$-0.476861\pi$
$983$	4476.91	0.145261	0.0726303	+	0.997359i	$0.476861\pi$
$984$	−85833.1	−2.78075
$985$	772.535	0.0249899
$986$	44594.6	1.44035
$987$	−21223.7	−0.684456
$988$	−29397.2	−0.946610
$989$	−3048.03	−0.0979996
$990$	−7956.62	−0.255432
$991$	44021.2	1.41108	0.705540	−	0.708670i	$-0.250704\pi$
$991$	44021.2	1.41108	0.705540	+	0.708670i	$0.250704\pi$
$992$	−11667.6	−0.373436
$993$	1963.05	0.0627347
$994$	−43674.2	−1.39362
$995$	1047.05	0.0333606
$996$	47945.3	1.52531
$997$	46877.3	1.48908	0.744542	−	0.667575i	$-0.232668\pi$
$997$	46877.3	1.48908	0.744542	+	0.667575i	$0.232668\pi$
$998$	38381.2	1.21737
$999$	36896.1	1.16851

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2015.4.a.d.1.2	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2015.4.a.d.1.2	✓	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)

\(f(q)\)	\(=\)	\(q-5.25776 q^{2} +3.13707 q^{3} +19.6441 q^{4} -5.00000 q^{5} -16.4940 q^{6} -24.7609 q^{7} -61.2219 q^{8} -17.1588 q^{9} +O(q^{10})\)	\(q-5.25776 q^{2} +3.13707 q^{3} +19.6441 q^{4} -5.00000 q^{5} -16.4940 q^{6} -24.7609 q^{7} -61.2219 q^{8} -17.1588 q^{9} +26.2888 q^{10} +17.6389 q^{11} +61.6249 q^{12} -13.0000 q^{13} +130.187 q^{14} -15.6854 q^{15} +164.737 q^{16} -95.7248 q^{17} +90.2168 q^{18} +115.115 q^{19} -98.2204 q^{20} -77.6768 q^{21} -92.7410 q^{22} +20.0669 q^{23} -192.057 q^{24} +25.0000 q^{25} +68.3509 q^{26} -138.529 q^{27} -486.406 q^{28} +88.6046 q^{29} +82.4699 q^{30} +31.0000 q^{31} -376.376 q^{32} +55.3344 q^{33} +503.299 q^{34} +123.805 q^{35} -337.069 q^{36} -266.342 q^{37} -605.247 q^{38} -40.7819 q^{39} +306.109 q^{40} +446.914 q^{41} +408.407 q^{42} -151.893 q^{43} +346.500 q^{44} +85.7939 q^{45} -105.507 q^{46} +273.231 q^{47} +516.793 q^{48} +270.104 q^{49} -131.444 q^{50} -300.296 q^{51} -255.373 q^{52} +470.930 q^{53} +728.354 q^{54} -88.1944 q^{55} +1515.91 q^{56} +361.124 q^{57} -465.862 q^{58} +227.273 q^{59} -308.125 q^{60} +77.6487 q^{61} -162.991 q^{62} +424.868 q^{63} +660.996 q^{64} +65.0000 q^{65} -290.935 q^{66} +656.030 q^{67} -1880.43 q^{68} +62.9512 q^{69} -650.936 q^{70} -335.473 q^{71} +1050.49 q^{72} +789.209 q^{73} +1400.36 q^{74} +78.4268 q^{75} +2261.33 q^{76} -436.755 q^{77} +214.422 q^{78} +763.462 q^{79} -823.687 q^{80} +28.7109 q^{81} -2349.77 q^{82} +778.019 q^{83} -1525.89 q^{84} +478.624 q^{85} +798.620 q^{86} +277.959 q^{87} -1079.88 q^{88} -1411.89 q^{89} -451.084 q^{90} +321.892 q^{91} +394.195 q^{92} +97.2492 q^{93} -1436.58 q^{94} -575.574 q^{95} -1180.72 q^{96} -1186.45 q^{97} -1420.14 q^{98} -302.662 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 5 q^{2} - 17 q^{3} + 149 q^{4} - 200 q^{5} - 35 q^{6} - 20 q^{7} - 39 q^{8} + 247 q^{9}+O(q^{10}) \) 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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