LMFDB - Embedded newform 1997.4.a.a.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1997,4,Mod(1,1997)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1997, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1997.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1997 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1997.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:	$117.826814281$
Analytic rank:	$1$
Dimension:	$239$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	1997.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.12919 q^{2} -8.38676 q^{3} +18.3086 q^{4} -1.93936 q^{5} +43.0173 q^{6} -30.3660 q^{7} -52.8747 q^{8} +43.3378 q^{9} +O(q^{10})$	\(q-5.12919 q^{2} -8.38676 q^{3} +18.3086 q^{4} -1.93936 q^{5} +43.0173 q^{6} -30.3660 q^{7} -52.8747 q^{8} +43.3378 q^{9} +9.94735 q^{10} +49.2603 q^{11} -153.550 q^{12} +18.4387 q^{13} +155.753 q^{14} +16.2650 q^{15} +124.736 q^{16} +53.6669 q^{17} -222.288 q^{18} -17.9547 q^{19} -35.5070 q^{20} +254.673 q^{21} -252.666 q^{22} -161.082 q^{23} +443.448 q^{24} -121.239 q^{25} -94.5758 q^{26} -137.021 q^{27} -555.959 q^{28} -68.8603 q^{29} -83.4260 q^{30} +313.247 q^{31} -216.796 q^{32} -413.134 q^{33} -275.268 q^{34} +58.8907 q^{35} +793.453 q^{36} -27.8007 q^{37} +92.0929 q^{38} -154.641 q^{39} +102.543 q^{40} -166.096 q^{41} -1306.26 q^{42} +227.594 q^{43} +901.887 q^{44} -84.0475 q^{45} +826.219 q^{46} -258.445 q^{47} -1046.13 q^{48} +579.095 q^{49} +621.857 q^{50} -450.092 q^{51} +337.587 q^{52} -503.063 q^{53} +702.806 q^{54} -95.5335 q^{55} +1605.60 q^{56} +150.582 q^{57} +353.198 q^{58} -208.109 q^{59} +297.788 q^{60} +696.393 q^{61} -1606.70 q^{62} -1316.00 q^{63} +114.101 q^{64} -35.7594 q^{65} +2119.05 q^{66} -870.951 q^{67} +982.566 q^{68} +1350.95 q^{69} -302.061 q^{70} +131.478 q^{71} -2291.47 q^{72} -729.284 q^{73} +142.595 q^{74} +1016.80 q^{75} -328.725 q^{76} -1495.84 q^{77} +793.185 q^{78} -1230.78 q^{79} -241.908 q^{80} -20.9586 q^{81} +851.938 q^{82} +345.703 q^{83} +4662.70 q^{84} -104.080 q^{85} -1167.37 q^{86} +577.515 q^{87} -2604.63 q^{88} +549.818 q^{89} +431.096 q^{90} -559.911 q^{91} -2949.18 q^{92} -2627.13 q^{93} +1325.61 q^{94} +34.8206 q^{95} +1818.21 q^{96} +8.50889 q^{97} -2970.29 q^{98} +2134.83 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 239 q - 16 q^{2} - 106 q^{3} + 872 q^{4} - 85 q^{5} - 111 q^{6} - 352 q^{7} - 210 q^{8} + 1961 q^{9}+O(q^{10}) $ 239 * q - 16 * q^2 - 106 * q^3 + 872 * q^4 - 85 * q^5 - 111 * q^6 - 352 * q^7 - 210 * q^8 + 1961 * q^9	\( 239 q - 16 q^{2} - 106 q^{3} + 872 q^{4} - 85 q^{5} - 111 q^{6} - 352 q^{7} - 210 q^{8} + 1961 q^{9} - 273 q^{10} - 294 q^{11} - 864 q^{12} - 797 q^{13} - 220 q^{14} - 580 q^{15} + 2816 q^{16} - 439 q^{17} - 536 q^{18} - 1704 q^{19} - 933 q^{20} - 596 q^{21} - 1046 q^{22} - 829 q^{23} - 1237 q^{24} + 4364 q^{25} - 818 q^{26} - 3670 q^{27} - 3690 q^{28} - 316 q^{29} - 888 q^{30} - 2595 q^{31} - 1881 q^{32} - 2066 q^{33} - 2605 q^{34} - 2450 q^{35} + 5863 q^{36} - 1912 q^{37} - 1709 q^{38} - 914 q^{39} - 3582 q^{40} - 1064 q^{41} - 3228 q^{42} - 5184 q^{43} - 2656 q^{44} - 3967 q^{45} - 2521 q^{46} - 4909 q^{47} - 7461 q^{48} + 7193 q^{49} - 1906 q^{50} - 3240 q^{51} - 9614 q^{52} - 2722 q^{53} - 3754 q^{54} - 6018 q^{55} - 2347 q^{56} - 2032 q^{57} - 6709 q^{58} - 6318 q^{59} - 5821 q^{60} - 2990 q^{61} - 2117 q^{62} - 8738 q^{63} + 6866 q^{64} - 1738 q^{65} - 3080 q^{66} - 14729 q^{67} - 3897 q^{68} - 2080 q^{69} - 7445 q^{70} - 3240 q^{71} - 8263 q^{72} - 8828 q^{73} - 3103 q^{74} - 12716 q^{75} - 14843 q^{76} - 3818 q^{77} - 8029 q^{78} - 4794 q^{79} - 10336 q^{80} + 11899 q^{81} - 13447 q^{82} - 11434 q^{83} - 7957 q^{84} - 8188 q^{85} - 5196 q^{86} - 11266 q^{87} - 11861 q^{88} - 4845 q^{89} - 7759 q^{90} - 12734 q^{91} - 8644 q^{92} - 10130 q^{93} - 6909 q^{94} - 3686 q^{95} - 11958 q^{96} - 16108 q^{97} - 6845 q^{98} - 12372 q^{99}+O(q^{100}) \) 239 * q - 16 * q^2 - 106 * q^3 + 872 * q^4 - 85 * q^5 - 111 * q^6 - 352 * q^7 - 210 * q^8 + 1961 * q^9 - 273 * q^10 - 294 * q^11 - 864 * q^12 - 797 * q^13 - 220 * q^14 - 580 * q^15 + 2816 * q^16 - 439 * q^17 - 536 * q^18 - 1704 * q^19 - 933 * q^20 - 596 * q^21 - 1046 * q^22 - 829 * q^23 - 1237 * q^24 + 4364 * q^25 - 818 * q^26 - 3670 * q^27 - 3690 * q^28 - 316 * q^29 - 888 * q^30 - 2595 * q^31 - 1881 * q^32 - 2066 * q^33 - 2605 * q^34 - 2450 * q^35 + 5863 * q^36 - 1912 * q^37 - 1709 * q^38 - 914 * q^39 - 3582 * q^40 - 1064 * q^41 - 3228 * q^42 - 5184 * q^43 - 2656 * q^44 - 3967 * q^45 - 2521 * q^46 - 4909 * q^47 - 7461 * q^48 + 7193 * q^49 - 1906 * q^50 - 3240 * q^51 - 9614 * q^52 - 2722 * q^53 - 3754 * q^54 - 6018 * q^55 - 2347 * q^56 - 2032 * q^57 - 6709 * q^58 - 6318 * q^59 - 5821 * q^60 - 2990 * q^61 - 2117 * q^62 - 8738 * q^63 + 6866 * q^64 - 1738 * q^65 - 3080 * q^66 - 14729 * q^67 - 3897 * q^68 - 2080 * q^69 - 7445 * q^70 - 3240 * q^71 - 8263 * q^72 - 8828 * q^73 - 3103 * q^74 - 12716 * q^75 - 14843 * q^76 - 3818 * q^77 - 8029 * q^78 - 4794 * q^79 - 10336 * q^80 + 11899 * q^81 - 13447 * q^82 - 11434 * q^83 - 7957 * q^84 - 8188 * q^85 - 5196 * q^86 - 11266 * q^87 - 11861 * q^88 - 4845 * q^89 - 7759 * q^90 - 12734 * q^91 - 8644 * q^92 - 10130 * q^93 - 6909 * q^94 - 3686 * q^95 - 11958 * q^96 - 16108 * q^97 - 6845 * q^98 - 12372 * 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 $

$2$	−5.12919	−1.81344	−0.906721	−	0.421730i	$-0.861423\pi$
$2$	−5.12919	−1.81344	−0.906721	+	0.421730i	$0.861423\pi$
$3$	−8.38676	−1.61403	−0.807016	−	0.590529i	$-0.798919\pi$
$3$	−8.38676	−1.61403	−0.807016	+	0.590529i	$0.798919\pi$
$4$	18.3086	2.28857
$5$	−1.93936	−0.173462	−0.0867308	−	0.996232i	$-0.527642\pi$
$5$	−1.93936	−0.173462	−0.0867308	+	0.996232i	$0.527642\pi$
$6$	43.0173	2.92696
$7$	−30.3660	−1.63961	−0.819806	−	0.572642i	$-0.805919\pi$
$7$	−30.3660	−1.63961	−0.819806	+	0.572642i	$0.805919\pi$
$8$	−52.8747	−2.33676
$9$	43.3378	1.60510
$10$	9.94735	0.314563
$11$	49.2603	1.35023	0.675116	−	0.737712i	$-0.264094\pi$
$11$	49.2603	1.35023	0.675116	+	0.737712i	$0.264094\pi$
$12$	−153.550	−3.69383
$13$	18.4387	0.393384	0.196692	−	0.980465i	$-0.436980\pi$
$13$	18.4387	0.393384	0.196692	+	0.980465i	$0.436980\pi$
$14$	155.753	2.97334
$15$	16.2650	0.279973
$16$	124.736	1.94900
$17$	53.6669	0.765655	0.382828	−	0.923820i	$-0.374950\pi$
$17$	53.6669	0.765655	0.382828	+	0.923820i	$0.374950\pi$
$18$	−222.288	−2.91076
$19$	−17.9547	−0.216794	−0.108397	−	0.994108i	$-0.534572\pi$
$19$	−17.9547	−0.216794	−0.108397	+	0.994108i	$0.534572\pi$
$20$	−35.5070	−0.396980
$21$	254.673	2.64639
$22$	−252.666	−2.44857
$23$	−161.082	−1.46034	−0.730171	−	0.683265i	$-0.760560\pi$
$23$	−161.082	−1.46034	−0.730171	+	0.683265i	$0.760560\pi$
$24$	443.448	3.77160
$25$	−121.239	−0.969911
$26$	−94.5758	−0.713379
$27$	−137.021	−0.976654
$28$	−555.959	−3.75237
$29$	−68.8603	−0.440932	−0.220466	−	0.975395i	$-0.570758\pi$
$29$	−68.8603	−0.440932	−0.220466	+	0.975395i	$0.570758\pi$
$30$	−83.4260	−0.507715
$31$	313.247	1.81486	0.907432	−	0.420199i	$-0.138040\pi$
$31$	313.247	1.81486	0.907432	+	0.420199i	$0.138040\pi$
$32$	−216.796	−1.19764
$33$	−413.134	−2.17932
$34$	−275.268	−1.38847
$35$	58.8907	0.284410
$36$	793.453	3.67339
$37$	−27.8007	−0.123524	−0.0617622	−	0.998091i	$-0.519672\pi$
$37$	−27.8007	−0.123524	−0.0617622	+	0.998091i	$0.519672\pi$
$38$	92.0929	0.393143
$39$	−154.641	−0.634934
$40$	102.543	0.405337
$41$	−166.096	−0.632679	−0.316340	−	0.948646i	$-0.602454\pi$
$41$	−166.096	−0.632679	−0.316340	+	0.948646i	$0.602454\pi$
$42$	−1306.26	−4.79907
$43$	227.594	0.807158	0.403579	−	0.914945i	$-0.367766\pi$
$43$	227.594	0.807158	0.403579	+	0.914945i	$0.367766\pi$
$44$	901.887	3.09010
$45$	−84.0475	−0.278424
$46$	826.219	2.64825
$47$	−258.445	−0.802086	−0.401043	−	0.916059i	$-0.631352\pi$
$47$	−258.445	−0.802086	−0.401043	+	0.916059i	$0.631352\pi$
$48$	−1046.13	−3.14575
$49$	579.095	1.68832
$50$	621.857	1.75888
$51$	−450.092	−1.23579
$52$	337.587	0.900288
$53$	−503.063	−1.30379	−0.651896	−	0.758308i	$-0.726026\pi$
$53$	−503.063	−1.30379	−0.651896	+	0.758308i	$0.726026\pi$
$54$	702.806	1.77111
$55$	−95.5335	−0.234213
$56$	1605.60	3.83137
$57$	150.582	0.349912
$58$	353.198	0.799606
$59$	−208.109	−0.459211	−0.229605	−	0.973284i	$-0.573744\pi$
$59$	−208.109	−0.459211	−0.229605	+	0.973284i	$0.573744\pi$
$60$	297.788	0.640739
$61$	696.393	1.46170	0.730852	−	0.682536i	$-0.239123\pi$
$61$	696.393	1.46170	0.730852	+	0.682536i	$0.239123\pi$
$62$	−1606.70	−3.29115
$63$	−1316.00	−2.63174
$64$	114.101	0.222853
$65$	−35.7594	−0.0682370
$66$	2119.05	3.95207
$67$	−870.951	−1.58811	−0.794057	−	0.607843i	$-0.792035\pi$
$67$	−870.951	−1.58811	−0.794057	+	0.607843i	$0.792035\pi$
$68$	982.566	1.75226
$69$	1350.95	2.35704
$70$	−302.061	−0.515761
$71$	131.478	0.219769	0.109885	−	0.993944i	$-0.464952\pi$
$71$	131.478	0.219769	0.109885	+	0.993944i	$0.464952\pi$
$72$	−2291.47	−3.75073
$73$	−729.284	−1.16926	−0.584632	−	0.811299i	$-0.698761\pi$
$73$	−729.284	−1.16926	−0.584632	+	0.811299i	$0.698761\pi$
$74$	142.595	0.224004
$75$	1016.80	1.56547
$76$	−328.725	−0.496149
$77$	−1495.84	−2.21385
$78$	793.185	1.15142
$79$	−1230.78	−1.75283	−0.876413	−	0.481560i	$-0.840070\pi$
$79$	−1230.78	−1.75283	−0.876413	+	0.481560i	$0.840070\pi$
$80$	−241.908	−0.338076
$81$	−20.9586	−0.0287498
$82$	851.938	1.14733
$83$	345.703	0.457179	0.228589	−	0.973523i	$-0.426589\pi$
$83$	345.703	0.457179	0.228589	+	0.973523i	$0.426589\pi$
$84$	4662.70	6.05645
$85$	−104.080	−0.132812
$86$	−1167.37	−1.46374
$87$	577.515	0.711679
$88$	−2604.63	−3.15516
$89$	549.818	0.654838	0.327419	−	0.944879i	$-0.393821\pi$
$89$	549.818	0.654838	0.327419	+	0.944879i	$0.393821\pi$
$90$	431.096	0.504905
$91$	−559.911	−0.644996
$92$	−2949.18	−3.34210
$93$	−2627.13	−2.92925
$94$	1325.61	1.45454
$95$	34.8206	0.0376054
$96$	1818.21	1.93303
$97$	8.50889	0.00890667	0.00445333	−	0.999990i	$-0.498582\pi$
$97$	8.50889	0.00890667	0.00445333	+	0.999990i	$0.498582\pi$
$98$	−2970.29	−3.06168
$99$	2134.83	2.16726
$100$	−2219.71	−2.21971
$101$	−168.246	−0.165753	−0.0828766	−	0.996560i	$-0.526411\pi$
$101$	−168.246	−0.165753	−0.0828766	+	0.996560i	$0.526411\pi$
$102$	2308.61	2.24104
$103$	1864.72	1.78385	0.891924	−	0.452186i	$-0.149356\pi$
$103$	1864.72	1.78385	0.891924	+	0.452186i	$0.149356\pi$
$104$	−974.944	−0.919241
$105$	−493.902	−0.459047
$106$	2580.30	2.36435
$107$	687.234	0.620910	0.310455	−	0.950588i	$-0.399519\pi$
$107$	687.234	0.620910	0.310455	+	0.950588i	$0.399519\pi$
$108$	−2508.66	−2.23515
$109$	840.108	0.738237	0.369118	−	0.929382i	$-0.379660\pi$
$109$	840.108	0.738237	0.369118	+	0.929382i	$0.379660\pi$
$110$	490.010	0.424733
$111$	233.158	0.199373
$112$	−3787.73	−3.19560
$113$	646.659	0.538341	0.269171	−	0.963093i	$-0.413250\pi$
$113$	646.659	0.538341	0.269171	+	0.963093i	$0.413250\pi$
$114$	−772.361	−0.634546
$115$	312.396	0.253313
$116$	−1260.74	−1.00911
$117$	799.094	0.631421
$118$	1067.43	0.832752
$119$	−1629.65	−1.25538
$120$	−860.005	−0.654228
$121$	1095.58	0.823125
$122$	−3571.93	−2.65072
$123$	1393.01	1.02117
$124$	5735.11	4.15345
$125$	477.546	0.341704
$126$	6749.99	4.77251
$127$	350.980	0.245232	0.122616	−	0.992454i	$-0.460872\pi$
$127$	350.980	0.245232	0.122616	+	0.992454i	$0.460872\pi$
$128$	1149.12	0.793508
$129$	−1908.78	−1.30278
$130$	183.417	0.123744
$131$	−1754.39	−1.17009	−0.585044	−	0.811001i	$-0.698923\pi$
$131$	−1754.39	−1.17009	−0.585044	+	0.811001i	$0.698923\pi$
$132$	−7563.91	−4.98753
$133$	545.212	0.355458
$134$	4467.28	2.87995
$135$	265.733	0.169412
$136$	−2837.62	−1.78915
$137$	2189.77	1.36558	0.682792	−	0.730613i	$-0.260765\pi$
$137$	2189.77	1.36558	0.682792	+	0.730613i	$0.260765\pi$
$138$	−6929.30	−4.27436
$139$	−121.549	−0.0741703	−0.0370852	−	0.999312i	$-0.511807\pi$
$139$	−121.549	−0.0741703	−0.0370852	+	0.999312i	$0.511807\pi$
$140$	1078.21	0.650893
$141$	2167.52	1.29459
$142$	−674.378	−0.398539
$143$	908.298	0.531159
$144$	5405.77	3.12834
$145$	133.545	0.0764849
$146$	3740.64	2.12039
$147$	−4856.73	−2.72501
$148$	−508.991	−0.282695
$149$	2981.73	1.63942	0.819709	−	0.572781i	$-0.194135\pi$
$149$	2981.73	1.63942	0.819709	+	0.572781i	$0.194135\pi$
$150$	−5215.37	−2.83889
$151$	−2280.03	−1.22878	−0.614391	−	0.789002i	$-0.710598\pi$
$151$	−2280.03	−1.22878	−0.614391	+	0.789002i	$0.710598\pi$
$152$	949.348	0.506594
$153$	2325.80	1.22895
$154$	7672.45	4.01470
$155$	−607.499	−0.314809
$156$	−2831.27	−1.45309
$157$	2657.83	1.35107	0.675535	−	0.737328i	$-0.263913\pi$
$157$	2657.83	1.35107	0.675535	+	0.737328i	$0.263913\pi$
$158$	6312.89	3.17865
$159$	4219.07	2.10436
$160$	420.445	0.207744
$161$	4891.41	2.39439
$162$	107.501	0.0521361
$163$	701.339	0.337013	0.168507	−	0.985701i	$-0.446106\pi$
$163$	701.339	0.337013	0.168507	+	0.985701i	$0.446106\pi$
$164$	−3040.99	−1.44793
$165$	801.217	0.378028
$166$	−1773.18	−0.829067
$167$	236.738	0.109697	0.0548483	−	0.998495i	$-0.482532\pi$
$167$	236.738	0.109697	0.0548483	+	0.998495i	$0.482532\pi$
$168$	−13465.7	−6.18396
$169$	−1857.01	−0.845249
$170$	533.844	0.240847
$171$	−778.115	−0.347976
$172$	4166.93	1.84724
$173$	3091.97	1.35883	0.679416	−	0.733753i	$-0.262233\pi$
$173$	3091.97	1.35883	0.679416	+	0.733753i	$0.262233\pi$
$174$	−2962.18	−1.29059
$175$	3681.54	1.59028
$176$	6144.53	2.63160
$177$	1745.36	0.741181
$178$	−2820.12	−1.18751
$179$	4002.49	1.67128	0.835642	−	0.549274i	$-0.185096\pi$
$179$	4002.49	1.67128	0.835642	+	0.549274i	$0.185096\pi$
$180$	−1538.79	−0.637193
$181$	−2124.92	−0.872618	−0.436309	−	0.899797i	$-0.643715\pi$
$181$	−2124.92	−0.872618	−0.436309	+	0.899797i	$0.643715\pi$
$182$	2871.89	1.16966
$183$	−5840.48	−2.35924
$184$	8517.15	3.41246
$185$	53.9156	0.0214268
$186$	13475.0	5.31203
$187$	2643.65	1.03381
$188$	−4731.76	−1.83563
$189$	4160.78	1.60133
$190$	−178.601	−0.0681953
$191$	−1941.63	−0.735555	−0.367778	−	0.929914i	$-0.619881\pi$
$191$	−1941.63	−0.735555	−0.367778	+	0.929914i	$0.619881\pi$
$192$	−956.935	−0.359692
$193$	−3459.84	−1.29039	−0.645194	−	0.764019i	$-0.723223\pi$
$193$	−3459.84	−1.29039	−0.645194	+	0.764019i	$0.723223\pi$
$194$	−43.6437	−0.0161517
$195$	299.905	0.110137
$196$	10602.4	3.86386
$197$	1864.84	0.674437	0.337218	−	0.941426i	$-0.390514\pi$
$197$	1864.84	0.674437	0.337218	+	0.941426i	$0.390514\pi$
$198$	−10950.0	−3.93020
$199$	−252.721	−0.0900247	−0.0450123	−	0.998986i	$-0.514333\pi$
$199$	−252.721	−0.0900247	−0.0450123	+	0.998986i	$0.514333\pi$
$200$	6410.47	2.26644
$201$	7304.46	2.56327
$202$	862.964	0.300584
$203$	2091.01	0.722958
$204$	−8240.54	−2.82820
$205$	322.120	0.109746
$206$	−9564.50	−3.23491
$207$	−6980.92	−2.34400
$208$	2299.97	0.766704
$209$	−884.453	−0.292722
$210$	2533.32	0.832455
$211$	−2130.22	−0.695027	−0.347513	−	0.937675i	$-0.612974\pi$
$211$	−2130.22	−0.695027	−0.347513	+	0.937675i	$0.612974\pi$
$212$	−9210.37	−2.98383
$213$	−1102.68	−0.354715
$214$	−3524.95	−1.12599
$215$	−441.387	−0.140011
$216$	7244.94	2.28220
$217$	−9512.06	−2.97567
$218$	−4309.08	−1.33875
$219$	6116.33	1.88723
$220$	−1749.08	−0.536015
$221$	989.551	0.301196
$222$	−1195.91	−0.361551
$223$	1744.22	0.523774	0.261887	−	0.965099i	$-0.415655\pi$
$223$	1744.22	0.523774	0.261887	+	0.965099i	$0.415655\pi$
$224$	6583.23	1.96366
$225$	−5254.22	−1.55681
$226$	−3316.84	−0.976251
$227$	1663.88	0.486500	0.243250	−	0.969964i	$-0.421786\pi$
$227$	1663.88	0.486500	0.243250	+	0.969964i	$0.421786\pi$
$228$	2756.94	0.800801
$229$	3668.44	1.05859	0.529295	−	0.848438i	$-0.322456\pi$
$229$	3668.44	1.05859	0.529295	+	0.848438i	$0.322456\pi$
$230$	−1602.34	−0.459369
$231$	12545.3	3.57323
$232$	3640.97	1.03035
$233$	3558.94	1.00066	0.500330	−	0.865835i	$-0.333212\pi$
$233$	3558.94	1.00066	0.500330	+	0.865835i	$0.333212\pi$
$234$	−4098.70	−1.14505
$235$	501.218	0.139131
$236$	−3810.18	−1.05094
$237$	10322.2	2.82912
$238$	8358.79	2.27655
$239$	4420.59	1.19642	0.598209	−	0.801340i	$-0.295879\pi$
$239$	4420.59	1.19642	0.598209	+	0.801340i	$0.295879\pi$
$240$	2028.82	0.545666
$241$	5429.91	1.45133	0.725666	−	0.688047i	$-0.241532\pi$
$241$	5429.91	1.45133	0.725666	+	0.688047i	$0.241532\pi$
$242$	−5619.43	−1.49269
$243$	3875.34	1.02306
$244$	12750.0	3.34522
$245$	−1123.07	−0.292860
$246$	−7145.00	−1.85182
$247$	−331.062	−0.0852832
$248$	−16562.8	−4.24089
$249$	−2899.33	−0.737901
$250$	−2449.42	−0.619661
$251$	−3729.34	−0.937823	−0.468912	−	0.883245i	$-0.655354\pi$
$251$	−3729.34	−0.937823	−0.468912	+	0.883245i	$0.655354\pi$
$252$	−24094.0	−6.02294
$253$	−7934.94	−1.97180
$254$	−1800.24	−0.444714
$255$	872.890	0.214363
$256$	−6806.87	−1.66183
$257$	751.802	0.182475	0.0912376	−	0.995829i	$-0.470918\pi$
$257$	751.802	0.182475	0.0912376	+	0.995829i	$0.470918\pi$
$258$	9790.49	2.36252
$259$	844.196	0.202532
$260$	−654.704	−0.156165
$261$	−2984.25	−0.707741
$262$	8998.59	2.12189
$263$	118.799	0.0278536	0.0139268	−	0.999903i	$-0.495567\pi$
$263$	118.799	0.0278536	0.0139268	+	0.999903i	$0.495567\pi$
$264$	21844.4	5.09253
$265$	975.620	0.226158
$266$	−2796.50	−0.644602
$267$	−4611.19	−1.05693
$268$	−15945.9	−3.63452
$269$	7422.26	1.68232	0.841159	−	0.540788i	$-0.181874\pi$
$269$	7422.26	1.68232	0.841159	+	0.540788i	$0.181874\pi$
$270$	−1362.99	−0.307219
$271$	−7441.78	−1.66810	−0.834051	−	0.551687i	$-0.813984\pi$
$271$	−7441.78	−1.66810	−0.834051	+	0.551687i	$0.813984\pi$
$272$	6694.19	1.49226
$273$	4695.84	1.04105
$274$	−11231.8	−2.47641
$275$	−5972.27	−1.30960
$276$	24734.1	5.39426
$277$	5729.19	1.24272	0.621360	−	0.783525i	$-0.286580\pi$
$277$	5729.19	1.24272	0.621360	+	0.783525i	$0.286580\pi$
$278$	623.449	0.134504
$279$	13575.4	2.91304
$280$	−3113.83	−0.664596
$281$	−3753.58	−0.796868	−0.398434	−	0.917197i	$-0.630446\pi$
$281$	−3753.58	−0.796868	−0.398434	+	0.917197i	$0.630446\pi$
$282$	−11117.6	−2.34767
$283$	−4919.97	−1.03343	−0.516717	−	0.856156i	$-0.672846\pi$
$283$	−4919.97	−1.03343	−0.516717	+	0.856156i	$0.672846\pi$
$284$	2407.18	0.502958
$285$	−292.032	−0.0606964
$286$	−4658.84	−0.963226
$287$	5043.68	1.03735
$288$	−9395.44	−1.92233
$289$	−2032.86	−0.413772
$290$	−684.978	−0.138701
$291$	−71.3620	−0.0143757
$292$	−13352.2	−2.67595
$293$	−9161.52	−1.82670	−0.913348	−	0.407180i	$-0.866512\pi$
$293$	−9161.52	−1.82670	−0.913348	+	0.407180i	$0.866512\pi$
$294$	24911.1	4.94165
$295$	403.598	0.0796555
$296$	1469.95	0.288646
$297$	−6749.69	−1.31871
$298$	−15293.9	−2.97299
$299$	−2970.14	−0.574475
$300$	18616.2	3.58269
$301$	−6911.14	−1.32343
$302$	11694.7	2.22832
$303$	1411.04	0.267531
$304$	−2239.59	−0.422531
$305$	−1350.56	−0.253550
$306$	−11929.5	−2.22864
$307$	−140.007	−0.0260281	−0.0130141	−	0.999915i	$-0.504143\pi$
$307$	−140.007	−0.0260281	−0.0130141	+	0.999915i	$0.504143\pi$
$308$	−27386.7	−5.06657
$309$	−15639.0	−2.87919
$310$	3115.98	0.570889
$311$	1267.60	0.231122	0.115561	−	0.993300i	$-0.463133\pi$
$311$	1267.60	0.231122	0.115561	+	0.993300i	$0.463133\pi$
$312$	8176.62	1.48369
$313$	4311.58	0.778610	0.389305	−	0.921109i	$-0.372715\pi$
$313$	4311.58	0.778610	0.389305	+	0.921109i	$0.372715\pi$
$314$	−13632.5	−2.45009
$315$	2552.19	0.456507
$316$	−22533.8	−4.01147
$317$	3840.07	0.680379	0.340189	−	0.940357i	$-0.389509\pi$
$317$	3840.07	0.680379	0.340189	+	0.940357i	$0.389509\pi$
$318$	−21640.4	−3.81614
$319$	−3392.08	−0.595361
$320$	−221.282	−0.0386564
$321$	−5763.66	−1.00217
$322$	−25089.0	−4.34209
$323$	−963.572	−0.165989
$324$	−383.723	−0.0657960
$325$	−2235.49	−0.381547
$326$	−3597.30	−0.611154
$327$	−7045.79	−1.19154
$328$	8782.29	1.47842
$329$	7847.94	1.31511
$330$	−4109.59	−0.685532
$331$	3525.32	0.585406	0.292703	−	0.956203i	$-0.405445\pi$
$331$	3525.32	0.585406	0.292703	+	0.956203i	$0.405445\pi$
$332$	6329.33	1.04629
$333$	−1204.82	−0.198269
$334$	−1214.27	−0.198929
$335$	1689.09	0.275477
$336$	31766.8	5.15780
$337$	−4302.15	−0.695410	−0.347705	−	0.937604i	$-0.613039\pi$
$337$	−4302.15	−0.695410	−0.347705	+	0.937604i	$0.613039\pi$
$338$	9524.97	1.53281
$339$	−5423.37	−0.868900
$340$	−1905.55	−0.303950
$341$	15430.6	2.45049
$342$	3991.10	0.631035
$343$	−7169.27	−1.12858
$344$	−12034.0	−1.88613
$345$	−2619.99	−0.408856
$346$	−15859.3	−2.46417
$347$	−2132.28	−0.329875	−0.164938	−	0.986304i	$-0.552742\pi$
$347$	−2132.28	−0.329875	−0.164938	+	0.986304i	$0.552742\pi$
$348$	10573.5	1.62873
$349$	5038.38	0.772774	0.386387	−	0.922337i	$-0.373723\pi$
$349$	5038.38	0.772774	0.386387	+	0.922337i	$0.373723\pi$
$350$	−18883.3	−2.88388
$351$	−2526.49	−0.384200
$352$	−10679.4	−1.61709
$353$	5339.79	0.805123	0.402561	−	0.915393i	$-0.368120\pi$
$353$	5339.79	0.805123	0.402561	+	0.915393i	$0.368120\pi$
$354$	−8952.27	−1.34409
$355$	−254.984	−0.0381215
$356$	10066.4	1.49865
$357$	13667.5	2.02622
$358$	−20529.5	−3.03078
$359$	−2624.10	−0.385779	−0.192889	−	0.981220i	$-0.561786\pi$
$359$	−2624.10	−0.385779	−0.192889	+	0.981220i	$0.561786\pi$
$360$	4443.99	0.650608
$361$	−6536.63	−0.953000
$362$	10899.1	1.58244
$363$	−9188.36	−1.32855
$364$	−10251.2	−1.47612
$365$	1414.35	0.202823
$366$	29956.9	4.27834
$367$	−3812.34	−0.542242	−0.271121	−	0.962545i	$-0.587394\pi$
$367$	−3812.34	−0.542242	−0.271121	+	0.962545i	$0.587394\pi$
$368$	−20092.7	−2.84620
$369$	−7198.23	−1.01551
$370$	−276.543	−0.0388562
$371$	15276.0	2.13771
$372$	−48099.0	−6.70381
$373$	7348.32	1.02006	0.510029	−	0.860157i	$-0.329635\pi$
$373$	7348.32	1.02006	0.510029	+	0.860157i	$0.329635\pi$
$374$	−13559.8	−1.87476
$375$	−4005.06	−0.551522
$376$	13665.2	1.87428
$377$	−1269.70	−0.173456
$378$	−21341.4	−2.90393
$379$	−3654.56	−0.495310	−0.247655	−	0.968848i	$-0.579660\pi$
$379$	−3654.56	−0.495310	−0.247655	+	0.968848i	$0.579660\pi$
$380$	637.516	0.0860628
$381$	−2943.59	−0.395812
$382$	9958.97	1.33389
$383$	4245.99	0.566475	0.283238	−	0.959050i	$-0.408591\pi$
$383$	4245.99	0.566475	0.283238	+	0.959050i	$0.408591\pi$
$384$	−9637.42	−1.28075
$385$	2900.97	0.384019
$386$	17746.2	2.34004
$387$	9863.43	1.29557
$388$	155.786	0.0203836
$389$	−2866.12	−0.373568	−0.186784	−	0.982401i	$-0.559806\pi$
$389$	−2866.12	−0.373568	−0.186784	+	0.982401i	$0.559806\pi$
$390$	−1538.27	−0.199727
$391$	−8644.76	−1.11812
$392$	−30619.5	−3.94520
$393$	14713.6	1.88856
$394$	−9565.10	−1.22305
$395$	2386.92	0.304048
$396$	39085.8	4.95993
$397$	−3136.16	−0.396472	−0.198236	−	0.980154i	$-0.563521\pi$
$397$	−3136.16	−0.396472	−0.198236	+	0.980154i	$0.563521\pi$
$398$	1296.25	0.163255
$399$	−4572.56	−0.573720
$400$	−15122.8	−1.89035
$401$	8375.48	1.04302	0.521511	−	0.853245i	$-0.325369\pi$
$401$	8375.48	1.04302	0.521511	+	0.853245i	$0.325369\pi$
$402$	−37466.0	−4.64834
$403$	5775.88	0.713938
$404$	−3080.34	−0.379338
$405$	40.6463	0.00498699
$406$	−10725.2	−1.31104
$407$	−1369.47	−0.166787
$408$	23798.5	2.88774
$409$	−2177.36	−0.263236	−0.131618	−	0.991300i	$-0.542017\pi$
$409$	−2177.36	−0.263236	−0.131618	+	0.991300i	$0.542017\pi$
$410$	−1652.22	−0.199017
$411$	−18365.1	−2.20410
$412$	34140.4	4.08247
$413$	6319.43	0.752927
$414$	35806.5	4.25070
$415$	−670.443	−0.0793030
$416$	−3997.44	−0.471132
$417$	1019.40	0.119713
$418$	4536.53	0.530834
$419$	−9691.40	−1.12997	−0.564983	−	0.825103i	$-0.691117\pi$
$419$	−9691.40	−1.12997	−0.564983	+	0.825103i	$0.691117\pi$
$420$	−9042.65	−1.05056
$421$	−4873.78	−0.564213	−0.282106	−	0.959383i	$-0.591033\pi$
$421$	−4873.78	−0.564213	−0.282106	+	0.959383i	$0.591033\pi$
$422$	10926.3	1.26039
$423$	−11200.4	−1.28743
$424$	26599.3	3.04664
$425$	−6506.52	−0.742618
$426$	5655.84	0.643255
$427$	−21146.7	−2.39663
$428$	12582.3	1.42100
$429$	−7617.68	−0.857308
$430$	2263.96	0.253902
$431$	−13222.3	−1.47771	−0.738856	−	0.673863i	$-0.764634\pi$
$431$	−13222.3	−1.47771	−0.738856	+	0.673863i	$0.764634\pi$
$432$	−17091.4	−1.90350
$433$	−2328.01	−0.258377	−0.129188	−	0.991620i	$-0.541237\pi$
$433$	−2328.01	−0.258377	−0.129188	+	0.991620i	$0.541237\pi$
$434$	48789.2	5.39621
$435$	−1120.01	−0.123449
$436$	15381.2	1.68951
$437$	2892.17	0.316593
$438$	−31371.8	−3.42238
$439$	−8492.43	−0.923283	−0.461642	−	0.887066i	$-0.652739\pi$
$439$	−8492.43	−0.923283	−0.461642	+	0.887066i	$0.652739\pi$
$440$	5051.31	0.547299
$441$	25096.7	2.70993
$442$	−5075.59	−0.546202
$443$	8930.79	0.957821	0.478911	−	0.877864i	$-0.341032\pi$
$443$	8930.79	0.957821	0.478911	+	0.877864i	$0.341032\pi$
$444$	4268.79	0.456279
$445$	−1066.30	−0.113589
$446$	−8946.43	−0.949834
$447$	−25007.1	−2.64607
$448$	−3464.78	−0.365392
$449$	16036.7	1.68556	0.842782	−	0.538255i	$-0.180916\pi$
$449$	16036.7	1.68556	0.842782	+	0.538255i	$0.180916\pi$
$450$	26949.9	2.82318
$451$	−8181.95	−0.854263
$452$	11839.4	1.23203
$453$	19122.0	1.98329
$454$	−8534.35	−0.882240
$455$	1085.87	0.111882
$456$	−7961.96	−0.817660
$457$	−5226.85	−0.535015	−0.267508	−	0.963556i	$-0.586200\pi$
$457$	−5226.85	−0.535015	−0.267508	+	0.963556i	$0.586200\pi$
$458$	−18816.1	−1.91969
$459$	−7353.48	−0.747781
$460$	5719.52	0.579726
$461$	9304.11	0.939991	0.469995	−	0.882669i	$-0.344256\pi$
$461$	9304.11	0.939991	0.469995	+	0.882669i	$0.344256\pi$
$462$	−64347.0	−6.47985
$463$	−14435.9	−1.44901	−0.724505	−	0.689269i	$-0.757932\pi$
$463$	−14435.9	−1.44901	−0.724505	+	0.689269i	$0.757932\pi$
$464$	−8589.35	−0.859376
$465$	5094.94	0.508113
$466$	−18254.5	−1.81464
$467$	16341.7	1.61928	0.809639	−	0.586928i	$-0.199663\pi$
$467$	16341.7	1.61928	0.809639	+	0.586928i	$0.199663\pi$
$468$	14630.3	1.44505
$469$	26447.3	2.60389
$470$	−2570.84	−0.252307
$471$	−22290.6	−2.18067
$472$	11003.7	1.07306
$473$	11211.4	1.08985
$474$	−52944.7	−5.13044
$475$	2176.80	0.210271
$476$	−29836.6	−2.87302
$477$	−21801.6	−2.09272
$478$	−22674.0	−2.16964
$479$	−20844.6	−1.98834	−0.994168	−	0.107840i	$-0.965606\pi$
$479$	−20844.6	−1.98834	−0.994168	+	0.107840i	$0.965606\pi$
$480$	−3526.17	−0.335306
$481$	−512.610	−0.0485925
$482$	−27851.0	−2.63191
$483$	−41023.1	−3.86463
$484$	20058.5	1.88378
$485$	−16.5018	−0.00154497
$486$	−19877.3	−1.85526
$487$	−16527.2	−1.53783	−0.768913	−	0.639354i	$-0.779202\pi$
$487$	−16527.2	−1.53783	−0.768913	+	0.639354i	$0.779202\pi$
$488$	−36821.6	−3.41565
$489$	−5881.97	−0.543950
$490$	5760.46	0.531084
$491$	−10579.0	−0.972351	−0.486176	−	0.873861i	$-0.661608\pi$
$491$	−10579.0	−0.972351	−0.486176	+	0.873861i	$0.661608\pi$
$492$	25504.0	2.33701
$493$	−3695.52	−0.337602
$494$	1698.08	0.154656
$495$	−4140.21	−0.375936
$496$	39073.1	3.53717
$497$	−3992.47	−0.360336
$498$	14871.2	1.33814
$499$	−5007.41	−0.449223	−0.224612	−	0.974448i	$-0.572111\pi$
$499$	−5007.41	−0.449223	−0.224612	+	0.974448i	$0.572111\pi$
$500$	8743.19	0.782015
$501$	−1985.47	−0.177054
$502$	19128.5	1.70069
$503$	10246.4	0.908278	0.454139	−	0.890931i	$-0.349947\pi$
$503$	10246.4	0.908278	0.454139	+	0.890931i	$0.349947\pi$
$504$	69582.9	6.14974
$505$	326.289	0.0287518
$506$	40699.8	3.57574
$507$	15574.3	1.36426
$508$	6425.95	0.561231
$509$	4287.29	0.373342	0.186671	−	0.982423i	$-0.440230\pi$
$509$	4287.29	0.373342	0.186671	+	0.982423i	$0.440230\pi$
$510$	−4477.22	−0.388734
$511$	22145.5	1.91714
$512$	25720.8	2.22013
$513$	2460.16	0.211733
$514$	−3856.14	−0.330908
$515$	−3616.36	−0.309429
$516$	−34947.1	−2.98151
$517$	−12731.1	−1.08300
$518$	−4330.04	−0.367280
$519$	−25931.6	−2.19320
$520$	1890.77	0.159453
$521$	−1995.17	−0.167773	−0.0838867	−	0.996475i	$-0.526733\pi$
$521$	−1995.17	−0.167773	−0.0838867	+	0.996475i	$0.526733\pi$
$522$	15306.8	1.28345
$523$	−11493.6	−0.960956	−0.480478	−	0.877007i	$-0.659537\pi$
$523$	−11493.6	−0.960956	−0.480478	+	0.877007i	$0.659537\pi$
$524$	−32120.4	−2.67784
$525$	−30876.2	−2.56676
$526$	−609.345	−0.0505108
$527$	16811.0	1.38956
$528$	−51532.7	−4.24748
$529$	13780.3	1.13260
$530$	−5004.14	−0.410125
$531$	−9018.96	−0.737080
$532$	9982.06	0.813491
$533$	−3062.60	−0.248886
$534$	23651.7	1.91668
$535$	−1332.79	−0.107704
$536$	46051.3	3.71103
$537$	−33567.9	−2.69751
$538$	−38070.2	−3.05079
$539$	28526.4	2.27963
$540$	4865.19	0.387712
$541$	19987.8	1.58843	0.794215	−	0.607636i	$-0.207882\pi$
$541$	19987.8	1.58843	0.794215	+	0.607636i	$0.207882\pi$
$542$	38170.3	3.02501
$543$	17821.2	1.40843
$544$	−11634.8	−0.916979
$545$	−1629.27	−0.128056
$546$	−24085.9	−1.88788
$547$	15685.6	1.22608	0.613040	−	0.790052i	$-0.289946\pi$
$547$	15685.6	1.22608	0.613040	+	0.790052i	$0.289946\pi$
$548$	40091.7	3.12524
$549$	30180.1	2.34618
$550$	30632.9	2.37489
$551$	1236.36	0.0955914
$552$	−71431.3	−5.50782
$553$	37373.8	2.87395
$554$	−29386.1	−2.25360
$555$	−452.177	−0.0345835
$556$	−2225.40	−0.169744
$557$	−13704.4	−1.04250	−0.521251	−	0.853404i	$-0.674534\pi$
$557$	−13704.4	−1.04250	−0.521251	+	0.853404i	$0.674534\pi$
$558$	−69630.9	−5.28263
$559$	4196.55	0.317523
$560$	7345.77	0.554314
$561$	−22171.7	−1.66861
$562$	19252.8	1.44507
$563$	2862.79	0.214302	0.107151	−	0.994243i	$-0.465827\pi$
$563$	2862.79	0.214302	0.107151	+	0.994243i	$0.465827\pi$
$564$	39684.2	2.96277
$565$	−1254.10	−0.0933816
$566$	25235.5	1.87407
$567$	636.429	0.0471385
$568$	−6951.88	−0.513547
$569$	10087.3	0.743205	0.371602	−	0.928392i	$-0.378808\pi$
$569$	10087.3	0.743205	0.371602	+	0.928392i	$0.378808\pi$
$570$	1497.89	0.110069
$571$	−19985.8	−1.46476	−0.732381	−	0.680895i	$-0.761591\pi$
$571$	−19985.8	−1.46476	−0.732381	+	0.680895i	$0.761591\pi$
$572$	16629.7	1.21560
$573$	16283.9	1.18721
$574$	−25870.0	−1.88117
$575$	19529.4	1.41640
$576$	4944.87	0.357702
$577$	−12283.5	−0.886252	−0.443126	−	0.896459i	$-0.646131\pi$
$577$	−12283.5	−0.886252	−0.443126	+	0.896459i	$0.646131\pi$
$578$	10426.9	0.750352
$579$	29016.9	2.08273
$580$	2445.02	0.175041
$581$	−10497.6	−0.749595
$582$	366.029	0.0260694
$583$	−24781.0	−1.76042
$584$	38560.7	2.73228
$585$	−1549.73	−0.109527
$586$	46991.2	3.31261
$587$	−7779.53	−0.547011	−0.273505	−	0.961870i	$-0.588183\pi$
$587$	−7779.53	−0.547011	−0.273505	+	0.961870i	$0.588183\pi$
$588$	−88919.9	−6.23639
$589$	−5624.24	−0.393451
$590$	−2070.13	−0.144451
$591$	−15639.9	−1.08856
$592$	−3467.74	−0.240749
$593$	11584.9	0.802252	0.401126	−	0.916023i	$-0.368619\pi$
$593$	11584.9	0.802252	0.401126	+	0.916023i	$0.368619\pi$
$594$	34620.4	2.39140
$595$	3160.48	0.217760
$596$	54591.4	3.75193
$597$	2119.51	0.145303
$598$	15234.4	1.04178
$599$	28409.3	1.93785	0.968927	−	0.247347i	$-0.0795588\pi$
$599$	28409.3	1.93785	0.968927	+	0.247347i	$0.0795588\pi$
$600$	−53763.1	−3.65812
$601$	12385.1	0.840595	0.420298	−	0.907386i	$-0.361926\pi$
$601$	12385.1	0.840595	0.420298	+	0.907386i	$0.361926\pi$
$602$	35448.5	2.39996
$603$	−37745.1	−2.54908
$604$	−41744.1	−2.81216
$605$	−2124.72	−0.142781
$606$	−7237.47	−0.485152
$607$	−22669.5	−1.51586	−0.757928	−	0.652338i	$-0.773788\pi$
$607$	−22669.5	−1.51586	−0.757928	+	0.652338i	$0.773788\pi$
$608$	3892.50	0.259641
$609$	−17536.8	−1.16688
$610$	6927.26	0.459798
$611$	−4765.40	−0.315528
$612$	42582.2	2.81255
$613$	19466.4	1.28261	0.641305	−	0.767286i	$-0.278393\pi$
$613$	19466.4	1.28261	0.641305	+	0.767286i	$0.278393\pi$
$614$	718.124	0.0472005
$615$	−2701.54	−0.177133
$616$	79092.1	5.17324
$617$	−20507.3	−1.33807	−0.669037	−	0.743229i	$-0.733293\pi$
$617$	−20507.3	−1.33807	−0.669037	+	0.743229i	$0.733293\pi$
$618$	80215.2	5.22124
$619$	−1997.52	−0.129705	−0.0648523	−	0.997895i	$-0.520658\pi$
$619$	−1997.52	−0.129705	−0.0648523	+	0.997895i	$0.520658\pi$
$620$	−11122.4	−0.720465
$621$	22071.5	1.42625
$622$	−6501.74	−0.419126
$623$	−16695.8	−1.07368
$624$	−19289.3	−1.23748
$625$	14228.7	0.910638
$626$	−22114.9	−1.41196
$627$	7417.69	0.472463
$628$	48661.1	3.09202
$629$	−1491.98	−0.0945771
$630$	−13090.7	−0.827848
$631$	625.302	0.0394499	0.0197250	−	0.999805i	$-0.493721\pi$
$631$	625.302	0.0394499	0.0197250	+	0.999805i	$0.493721\pi$
$632$	65077.0	4.09592
$633$	17865.7	1.12180
$634$	−19696.5	−1.23383
$635$	−680.677	−0.0425383
$636$	77245.2	4.81599
$637$	10677.8	0.664159
$638$	17398.6	1.07965
$639$	5697.98	0.352752
$640$	−2228.56	−0.137643
$641$	−6974.99	−0.429790	−0.214895	−	0.976637i	$-0.568941\pi$
$641$	−6974.99	−0.429790	−0.214895	+	0.976637i	$0.568941\pi$
$642$	29562.9	1.81738
$643$	24757.6	1.51842	0.759209	−	0.650846i	$-0.225586\pi$
$643$	24757.6	1.51842	0.759209	+	0.650846i	$0.225586\pi$
$644$	89554.9	5.47974
$645$	3701.81	0.225982
$646$	4942.34	0.301012
$647$	−6707.60	−0.407578	−0.203789	−	0.979015i	$-0.565326\pi$
$647$	−6707.60	−0.407578	−0.203789	+	0.979015i	$0.565326\pi$
$648$	1108.18	0.0671812
$649$	−10251.5	−0.620041
$650$	11466.3	0.691914
$651$	79775.4	4.80283
$652$	12840.5	0.771279
$653$	17608.4	1.05524	0.527619	−	0.849481i	$-0.323085\pi$
$653$	17608.4	1.05524	0.527619	+	0.849481i	$0.323085\pi$
$654$	36139.2	2.16079
$655$	3402.39	0.202966
$656$	−20718.1	−1.23309
$657$	−31605.5	−1.87679
$658$	−40253.6	−2.38488
$659$	−19536.3	−1.15482	−0.577410	−	0.816454i	$-0.695937\pi$
$659$	−19536.3	−1.15482	−0.577410	+	0.816454i	$0.695937\pi$
$660$	14669.1	0.865145
$661$	−10140.7	−0.596712	−0.298356	−	0.954455i	$-0.596438\pi$
$661$	−10140.7	−0.596712	−0.298356	+	0.954455i	$0.596438\pi$
$662$	−18082.0	−1.06160
$663$	−8299.12	−0.486141
$664$	−18278.9	−1.06831
$665$	−1057.36	−0.0616583
$666$	6179.75	0.359550
$667$	11092.1	0.643912
$668$	4334.34	0.251049
$669$	−14628.4	−0.845388
$670$	−8663.66	−0.499562
$671$	34304.5	1.97364
$672$	−55212.0	−3.16942
$673$	7289.71	0.417530	0.208765	−	0.977966i	$-0.433056\pi$
$673$	7289.71	0.417530	0.208765	+	0.977966i	$0.433056\pi$
$674$	22066.5	1.26109
$675$	16612.2	0.947268
$676$	−33999.3	−1.93442
$677$	−25984.5	−1.47513	−0.737566	−	0.675275i	$-0.764025\pi$
$677$	−25984.5	−1.47513	−0.737566	+	0.675275i	$0.764025\pi$
$678$	27817.5	1.57570
$679$	−258.381	−0.0146035
$680$	5503.18	0.310349
$681$	−13954.6	−0.785227
$682$	−79146.7	−4.44382
$683$	−10346.0	−0.579619	−0.289809	−	0.957084i	$-0.593592\pi$
$683$	−10346.0	−0.579619	−0.289809	+	0.957084i	$0.593592\pi$
$684$	−14246.2	−0.796369
$685$	−4246.76	−0.236877
$686$	36772.6	2.04662
$687$	−30766.3	−1.70860
$688$	28389.2	1.57315
$689$	−9275.85	−0.512891
$690$	13438.4	0.741437
$691$	32668.3	1.79850	0.899248	−	0.437439i	$-0.144114\pi$
$691$	32668.3	1.79850	0.899248	+	0.437439i	$0.144114\pi$
$692$	56609.6	3.10979
$693$	−64826.3	−3.55346
$694$	10936.9	0.598210
$695$	235.728	0.0128657
$696$	−30535.9	−1.66302
$697$	−8913.87	−0.484414
$698$	−25842.8	−1.40138
$699$	−29848.0	−1.61510
$700$	67403.9	3.63947
$701$	13892.5	0.748518	0.374259	−	0.927324i	$-0.377897\pi$
$701$	13892.5	0.748518	0.374259	+	0.927324i	$0.377897\pi$
$702$	12958.9	0.696724
$703$	499.152	0.0267793
$704$	5620.64	0.300903
$705$	−4203.59	−0.224562
$706$	−27388.8	−1.46004
$707$	5108.95	0.271771
$708$	31955.0	1.69625
$709$	5872.11	0.311046	0.155523	−	0.987832i	$-0.450294\pi$
$709$	5872.11	0.311046	0.155523	+	0.987832i	$0.450294\pi$
$710$	1307.86	0.0691312
$711$	−53339.1	−2.81346
$712$	−29071.5	−1.53020
$713$	−50458.3	−2.65032
$714$	−70103.2	−3.67443
$715$	−1761.52	−0.0921357
$716$	73279.9	3.82486
$717$	−37074.4	−1.93106
$718$	13459.5	0.699588
$719$	−16199.5	−0.840248	−0.420124	−	0.907467i	$-0.638013\pi$
$719$	−16199.5	−0.840248	−0.420124	+	0.907467i	$0.638013\pi$
$720$	−10483.7	−0.542647
$721$	−56624.1	−2.92482
$722$	33527.6	1.72821
$723$	−45539.3	−2.34250
$724$	−38904.3	−1.99705
$725$	8348.55	0.427665
$726$	47128.8	2.40925
$727$	219.630	0.0112044	0.00560221	−	0.999984i	$-0.498217\pi$
$727$	219.630	0.0112044	0.00560221	+	0.999984i	$0.498217\pi$
$728$	29605.2	1.50720
$729$	−31935.6	−1.62250
$730$	−7254.45	−0.367807
$731$	12214.3	0.618005
$732$	−106931.	−5.39929
$733$	3407.33	0.171695	0.0858477	−	0.996308i	$-0.472640\pi$
$733$	3407.33	0.171695	0.0858477	+	0.996308i	$0.472640\pi$
$734$	19554.2	0.983324
$735$	9418.96	0.472685
$736$	34921.9	1.74896
$737$	−42903.3	−2.14432
$738$	36921.1	1.84158
$739$	38733.4	1.92805	0.964026	−	0.265809i	$-0.0856389\pi$
$739$	38733.4	1.92805	0.964026	+	0.265809i	$0.0856389\pi$
$740$	987.118	0.0490367
$741$	2776.53	0.137650
$742$	−78353.6	−3.87662
$743$	−25280.2	−1.24824	−0.624118	−	0.781330i	$-0.714542\pi$
$743$	−25280.2	−1.24824	−0.624118	+	0.781330i	$0.714542\pi$
$744$	138909.	6.84494
$745$	−5782.66	−0.284376
$746$	−37690.9	−1.84982
$747$	14982.0	0.733818
$748$	48401.5	2.36595
$749$	−20868.6	−1.01805
$750$	20542.7	1.00015
$751$	9891.83	0.480637	0.240318	−	0.970694i	$-0.422748\pi$
$751$	9891.83	0.480637	0.240318	+	0.970694i	$0.422748\pi$
$752$	−32237.3	−1.56326
$753$	31277.1	1.51368
$754$	6512.52	0.314552
$755$	4421.79	0.213146
$756$	76178.0	3.66477
$757$	−36638.5	−1.75911	−0.879556	−	0.475796i	$-0.842160\pi$
$757$	−36638.5	−1.75911	−0.879556	+	0.475796i	$0.842160\pi$
$758$	18745.0	0.898216
$759$	66548.4	3.18255
$760$	−1841.13	−0.0878747
$761$	−13528.4	−0.644421	−0.322210	−	0.946668i	$-0.604426\pi$
$761$	−13528.4	−0.644421	−0.322210	+	0.946668i	$0.604426\pi$
$762$	15098.2	0.717783
$763$	−25510.7	−1.21042
$764$	−35548.4	−1.68337
$765$	−4510.57	−0.213177
$766$	−21778.5	−1.02727
$767$	−3837.26	−0.180646
$768$	57087.6	2.68226
$769$	36233.3	1.69910	0.849548	−	0.527511i	$-0.176875\pi$
$769$	36233.3	1.69910	0.849548	+	0.527511i	$0.176875\pi$
$770$	−14879.6	−0.696396
$771$	−6305.18	−0.294521
$772$	−63344.8	−2.95315
$773$	−33605.4	−1.56365	−0.781825	−	0.623499i	$-0.785711\pi$
$773$	−33605.4	−1.56365	−0.781825	+	0.623499i	$0.785711\pi$
$774$	−50591.4	−2.34944
$775$	−37977.7	−1.76026
$776$	−449.905	−0.0208127
$777$	−7080.07	−0.326893
$778$	14700.9	0.677444
$779$	2982.20	0.137161
$780$	5490.84	0.252056
$781$	6476.67	0.296739
$782$	44340.6	2.02764
$783$	9435.30	0.430639
$784$	72233.9	3.29054
$785$	−5154.49	−0.234359
$786$	−75469.0	−3.42480
$787$	20448.9	0.926207	0.463103	−	0.886304i	$-0.346736\pi$
$787$	20448.9	0.926207	0.463103	+	0.886304i	$0.346736\pi$
$788$	34142.5	1.54350
$789$	−996.342	−0.0449566
$790$	−12243.0	−0.551374
$791$	−19636.5	−0.882670
$792$	−112879.	−5.06435
$793$	12840.6	0.575011
$794$	16086.0	0.718979
$795$	−8182.29	−0.365026
$796$	−4626.96	−0.206028
$797$	16406.8	0.729182	0.364591	−	0.931168i	$-0.381209\pi$
$797$	16406.8	0.729182	0.364591	+	0.931168i	$0.381209\pi$
$798$	23453.5	1.04041
$799$	−13869.9	−0.614122
$800$	26284.1	1.16160
$801$	23827.9	1.05108
$802$	−42959.4	−1.89146
$803$	−35924.8	−1.57878
$804$	133734.	5.86623
$805$	−9486.21	−0.415335
$806$	−29625.6	−1.29469
$807$	−62248.7	−2.71532
$808$	8895.94	0.387324
$809$	−5322.91	−0.231327	−0.115664	−	0.993288i	$-0.536899\pi$
$809$	−5322.91	−0.231327	−0.115664	+	0.993288i	$0.536899\pi$
$810$	−208.483	−0.00904362
$811$	20286.9	0.878385	0.439193	−	0.898393i	$-0.355265\pi$
$811$	20286.9	0.878385	0.439193	+	0.898393i	$0.355265\pi$
$812$	38283.5	1.65454
$813$	62412.4	2.69237
$814$	7024.28	0.302458
$815$	−1360.15	−0.0584589
$816$	−56142.5	−2.40856
$817$	−4086.38	−0.174987
$818$	11168.1	0.477364
$819$	−24265.3	−1.03528
$820$	5897.57	0.251161
$821$	−22573.4	−0.959581	−0.479791	−	0.877383i	$-0.659287\pi$
$821$	−22573.4	−0.959581	−0.479791	+	0.877383i	$0.659287\pi$
$822$	94198.2	3.99700
$823$	−21515.3	−0.911271	−0.455635	−	0.890167i	$-0.650588\pi$
$823$	−21515.3	−0.911271	−0.455635	+	0.890167i	$0.650588\pi$
$824$	−98596.6	−4.16841
$825$	50088.0	2.11374
$826$	−32413.6	−1.36539
$827$	−19800.6	−0.832568	−0.416284	−	0.909235i	$-0.636668\pi$
$827$	−19800.6	−0.832568	−0.416284	+	0.909235i	$0.636668\pi$
$828$	−127811.	−5.36441
$829$	20920.3	0.876468	0.438234	−	0.898861i	$-0.355604\pi$
$829$	20920.3	0.876468	0.438234	+	0.898861i	$0.355604\pi$
$830$	3438.83	0.143811
$831$	−48049.3	−2.00579
$832$	2103.87	0.0876667
$833$	31078.3	1.29267
$834$	−5228.72	−0.217093
$835$	−459.121	−0.0190282
$836$	−16193.1	−0.669916
$837$	−42921.3	−1.77250
$838$	49709.0	2.04913
$839$	43556.9	1.79231	0.896156	−	0.443739i	$-0.146348\pi$
$839$	43556.9	1.79231	0.896156	+	0.443739i	$0.146348\pi$
$840$	26114.9	1.07268
$841$	−19647.3	−0.805579
$842$	24998.5	1.02317
$843$	31480.4	1.28617
$844$	−39001.4	−1.59062
$845$	3601.42	0.146618
$846$	57449.1	2.33468
$847$	−33268.4	−1.34960
$848$	−62749.9	−2.54109
$849$	41262.6	1.66800
$850$	33373.2	1.34669
$851$	4478.18	0.180388
$852$	−20188.5	−0.811791
$853$	−26425.5	−1.06072	−0.530359	−	0.847773i	$-0.677943\pi$
$853$	−26425.5	−1.06072	−0.530359	+	0.847773i	$0.677943\pi$
$854$	108465.	4.34615
$855$	1509.05	0.0603605
$856$	−36337.3	−1.45092
$857$	−10849.7	−0.432462	−0.216231	−	0.976342i	$-0.569376\pi$
$857$	−10849.7	−0.432462	−0.216231	+	0.976342i	$0.569376\pi$
$858$	39072.5	1.55468
$859$	−15990.6	−0.635148	−0.317574	−	0.948234i	$-0.602868\pi$
$859$	−15990.6	−0.635148	−0.317574	+	0.948234i	$0.602868\pi$
$860$	−8081.18	−0.320426
$861$	−42300.1	−1.67431
$862$	67819.5	2.67975
$863$	−31374.3	−1.23754	−0.618768	−	0.785573i	$-0.712368\pi$
$863$	−31374.3	−1.23754	−0.618768	+	0.785573i	$0.712368\pi$
$864$	29705.5	1.16968
$865$	−5996.44	−0.235705
$866$	11940.8	0.468552
$867$	17049.1	0.667842
$868$	−174152.	−6.81004
$869$	−60628.5	−2.36672
$870$	5744.74	0.223868
$871$	−16059.3	−0.624738
$872$	−44420.5	−1.72508
$873$	368.756	0.0142961
$874$	−14834.5	−0.574124
$875$	−14501.2	−0.560262
$876$	111981.	4.31907
$877$	−25637.7	−0.987140	−0.493570	−	0.869706i	$-0.664308\pi$
$877$	−25637.7	−0.987140	−0.493570	+	0.869706i	$0.664308\pi$
$878$	43559.3	1.67432
$879$	76835.5	2.94835
$880$	−11916.5	−0.456481
$881$	−32476.6	−1.24196	−0.620978	−	0.783828i	$-0.713264\pi$
$881$	−32476.6	−1.24196	−0.620978	+	0.783828i	$0.713264\pi$
$882$	−128726.	−4.91431
$883$	−17108.6	−0.652040	−0.326020	−	0.945363i	$-0.605708\pi$
$883$	−17108.6	−0.652040	−0.326020	+	0.945363i	$0.605708\pi$
$884$	18117.3	0.689310
$885$	−3384.88	−0.128567
$886$	−45807.7	−1.73695
$887$	−2921.47	−0.110590	−0.0552950	−	0.998470i	$-0.517610\pi$
$887$	−2921.47	−0.110590	−0.0552950	+	0.998470i	$0.517610\pi$
$888$	−12328.1	−0.465885
$889$	−10657.9	−0.402085
$890$	5469.23	0.205988
$891$	−1032.43	−0.0388189
$892$	31934.2	1.19870
$893$	4640.29	0.173887
$894$	128266.	4.79850
$895$	−7762.26	−0.289904
$896$	−34894.3	−1.30104
$897$	24909.9	0.927221
$898$	−82255.2	−3.05667
$899$	−21570.3	−0.800232
$900$	−96197.4	−3.56287
$901$	−26997.8	−0.998255
$902$	41966.8	1.54916
$903$	57962.0	2.13605
$904$	−34191.9	−1.25797
$905$	4120.98	0.151366
$906$	−98080.6	−3.59659
$907$	−24617.8	−0.901237	−0.450619	−	0.892717i	$-0.648797\pi$
$907$	−24617.8	−0.901237	−0.450619	+	0.892717i	$0.648797\pi$
$908$	30463.3	1.11339
$909$	−7291.39	−0.266051
$910$	−5569.63	−0.202892
$911$	50192.2	1.82540	0.912701	−	0.408628i	$-0.133992\pi$
$911$	50192.2	1.82540	0.912701	+	0.408628i	$0.133992\pi$
$912$	18782.9	0.681978
$913$	17029.4	0.617297
$914$	26809.5	0.970219
$915$	11326.8	0.409238
$916$	67163.9	2.42266
$917$	53273.8	1.91849
$918$	37717.4	1.35606
$919$	−21851.3	−0.784340	−0.392170	−	0.919893i	$-0.628275\pi$
$919$	−21851.3	−0.784340	−0.392170	+	0.919893i	$0.628275\pi$
$920$	−16517.8	−0.591931
$921$	1174.21	0.0420102
$922$	−47722.6	−1.70462
$923$	2424.30	0.0864536
$924$	229686.	8.17761
$925$	3370.52	0.119808
$926$	74044.3	2.62770
$927$	80812.8	2.86326
$928$	14928.6	0.528078
$929$	36903.8	1.30331	0.651655	−	0.758516i	$-0.274075\pi$
$929$	36903.8	1.30331	0.651655	+	0.758516i	$0.274075\pi$
$930$	−26132.9	−0.921433
$931$	−10397.5	−0.366018
$932$	65159.1	2.29008
$933$	−10631.0	−0.373038
$934$	−83819.6	−2.93647
$935$	−5126.99	−0.179327
$936$	−42251.9	−1.47548
$937$	−12314.8	−0.429357	−0.214678	−	0.976685i	$-0.568870\pi$
$937$	−12314.8	−0.429357	−0.214678	+	0.976685i	$0.568870\pi$
$938$	−135653.	−4.72200
$939$	−36160.2	−1.25670
$940$	9176.59	0.318412
$941$	24093.2	0.834660	0.417330	−	0.908755i	$-0.362966\pi$
$941$	24093.2	0.834660	0.417330	+	0.908755i	$0.362966\pi$
$942$	114333.	3.95452
$943$	26755.0	0.923928
$944$	−25958.6	−0.895000
$945$	−8069.25	−0.277770
$946$	−57505.3	−1.97638
$947$	22835.4	0.783582	0.391791	−	0.920054i	$-0.371856\pi$
$947$	22835.4	0.783582	0.391791	+	0.920054i	$0.371856\pi$
$948$	188986.	6.47465
$949$	−13447.1	−0.459969
$950$	−11165.2	−0.381314
$951$	−32205.8	−1.09815
$952$	86167.3	2.93351
$953$	21437.9	0.728691	0.364346	−	0.931264i	$-0.381293\pi$
$953$	21437.9	0.728691	0.364346	+	0.931264i	$0.381293\pi$
$954$	111825.	3.79503
$955$	3765.51	0.127591
$956$	80934.7	2.73809
$957$	28448.6	0.960932
$958$	106916.	3.60573
$959$	−66494.7	−2.23903
$960$	1855.84	0.0623928
$961$	68332.6	2.29373
$962$	2629.27	0.0881197
$963$	29783.2	0.996624
$964$	99414.0	3.32148
$965$	6709.88	0.223833
$966$	210415.	7.00828
$967$	34871.1	1.15965	0.579824	−	0.814742i	$-0.303121\pi$
$967$	34871.1	1.15965	0.579824	+	0.814742i	$0.303121\pi$
$968$	−57928.4	−1.92344
$969$	8081.25	0.267912
$970$	84.6409	0.00280171
$971$	3457.35	0.114265	0.0571327	−	0.998367i	$-0.481804\pi$
$971$	3457.35	0.114265	0.0571327	+	0.998367i	$0.481804\pi$
$972$	70952.0	2.34134
$973$	3690.97	0.121610
$974$	84771.4	2.78876
$975$	18748.5	0.615830
$976$	86865.1	2.84886
$977$	6402.96	0.209671	0.104836	−	0.994490i	$-0.466568\pi$
$977$	6402.96	0.209671	0.104836	+	0.994490i	$0.466568\pi$
$978$	30169.7	0.986422
$979$	27084.2	0.884183
$980$	−20561.9	−0.670231
$981$	36408.4	1.18494
$982$	54261.8	1.76330
$983$	36760.1	1.19274	0.596370	−	0.802710i	$-0.296609\pi$
$983$	36760.1	1.19274	0.596370	+	0.802710i	$0.296609\pi$
$984$	−73654.9	−2.38621
$985$	−3616.59	−0.116989
$986$	18955.0	0.612222
$987$	−65818.8	−2.12263
$988$	−6061.27	−0.195177
$989$	−36661.3	−1.17873
$990$	21235.9	0.681739
$991$	−25928.1	−0.831114	−0.415557	−	0.909567i	$-0.636413\pi$
$991$	−25928.1	−0.831114	−0.415557	+	0.909567i	$0.636413\pi$
$992$	−67910.6	−2.17355
$993$	−29566.0	−0.944864
$994$	20478.2	0.653449
$995$	490.117	0.0156158
$996$	−53082.6	−1.68874
$997$	−20101.8	−0.638547	−0.319273	−	0.947663i	$-0.603439\pi$
$997$	−20101.8	−0.638547	−0.319273	+	0.947663i	$0.603439\pi$
$998$	25684.0	0.814641
$999$	3809.27	0.120641

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1997.4.a.a.1.13	✓	239

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1997.4.a.a.1.13	✓	239	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:	\( N \)	\(=\)	\( 1997 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1997.a (trivial)

\(f(q)\)	\(=\)	\(q-5.12919 q^{2} -8.38676 q^{3} +18.3086 q^{4} -1.93936 q^{5} +43.0173 q^{6} -30.3660 q^{7} -52.8747 q^{8} +43.3378 q^{9} +O(q^{10})\)	\(q-5.12919 q^{2} -8.38676 q^{3} +18.3086 q^{4} -1.93936 q^{5} +43.0173 q^{6} -30.3660 q^{7} -52.8747 q^{8} +43.3378 q^{9} +9.94735 q^{10} +49.2603 q^{11} -153.550 q^{12} +18.4387 q^{13} +155.753 q^{14} +16.2650 q^{15} +124.736 q^{16} +53.6669 q^{17} -222.288 q^{18} -17.9547 q^{19} -35.5070 q^{20} +254.673 q^{21} -252.666 q^{22} -161.082 q^{23} +443.448 q^{24} -121.239 q^{25} -94.5758 q^{26} -137.021 q^{27} -555.959 q^{28} -68.8603 q^{29} -83.4260 q^{30} +313.247 q^{31} -216.796 q^{32} -413.134 q^{33} -275.268 q^{34} +58.8907 q^{35} +793.453 q^{36} -27.8007 q^{37} +92.0929 q^{38} -154.641 q^{39} +102.543 q^{40} -166.096 q^{41} -1306.26 q^{42} +227.594 q^{43} +901.887 q^{44} -84.0475 q^{45} +826.219 q^{46} -258.445 q^{47} -1046.13 q^{48} +579.095 q^{49} +621.857 q^{50} -450.092 q^{51} +337.587 q^{52} -503.063 q^{53} +702.806 q^{54} -95.5335 q^{55} +1605.60 q^{56} +150.582 q^{57} +353.198 q^{58} -208.109 q^{59} +297.788 q^{60} +696.393 q^{61} -1606.70 q^{62} -1316.00 q^{63} +114.101 q^{64} -35.7594 q^{65} +2119.05 q^{66} -870.951 q^{67} +982.566 q^{68} +1350.95 q^{69} -302.061 q^{70} +131.478 q^{71} -2291.47 q^{72} -729.284 q^{73} +142.595 q^{74} +1016.80 q^{75} -328.725 q^{76} -1495.84 q^{77} +793.185 q^{78} -1230.78 q^{79} -241.908 q^{80} -20.9586 q^{81} +851.938 q^{82} +345.703 q^{83} +4662.70 q^{84} -104.080 q^{85} -1167.37 q^{86} +577.515 q^{87} -2604.63 q^{88} +549.818 q^{89} +431.096 q^{90} -559.911 q^{91} -2949.18 q^{92} -2627.13 q^{93} +1325.61 q^{94} +34.8206 q^{95} +1818.21 q^{96} +8.50889 q^{97} -2970.29 q^{98} +2134.83 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 239 q - 16 q^{2} - 106 q^{3} + 872 q^{4} - 85 q^{5} - 111 q^{6} - 352 q^{7} - 210 q^{8} + 1961 q^{9}+O(q^{10}) \) 239 * q - 16 * q^2 - 106 * q^3 + 872 * q^4 - 85 * q^5 - 111 * q^6 - 352 * q^7 - 210 * q^8 + 1961 * q^9	\( 239 q - 16 q^{2} - 106 q^{3} + 872 q^{4} - 85 q^{5} - 111 q^{6} - 352 q^{7} - 210 q^{8} + 1961 q^{9} - 273 q^{10} - 294 q^{11} - 864 q^{12} - 797 q^{13} - 220 q^{14} - 580 q^{15} + 2816 q^{16} - 439 q^{17} - 536 q^{18} - 1704 q^{19} - 933 q^{20} - 596 q^{21} - 1046 q^{22} - 829 q^{23} - 1237 q^{24} + 4364 q^{25} - 818 q^{26} - 3670 q^{27} - 3690 q^{28} - 316 q^{29} - 888 q^{30} - 2595 q^{31} - 1881 q^{32} - 2066 q^{33} - 2605 q^{34} - 2450 q^{35} + 5863 q^{36} - 1912 q^{37} - 1709 q^{38} - 914 q^{39} - 3582 q^{40} - 1064 q^{41} - 3228 q^{42} - 5184 q^{43} - 2656 q^{44} - 3967 q^{45} - 2521 q^{46} - 4909 q^{47} - 7461 q^{48} + 7193 q^{49} - 1906 q^{50} - 3240 q^{51} - 9614 q^{52} - 2722 q^{53} - 3754 q^{54} - 6018 q^{55} - 2347 q^{56} - 2032 q^{57} - 6709 q^{58} - 6318 q^{59} - 5821 q^{60} - 2990 q^{61} - 2117 q^{62} - 8738 q^{63} + 6866 q^{64} - 1738 q^{65} - 3080 q^{66} - 14729 q^{67} - 3897 q^{68} - 2080 q^{69} - 7445 q^{70} - 3240 q^{71} - 8263 q^{72} - 8828 q^{73} - 3103 q^{74} - 12716 q^{75} - 14843 q^{76} - 3818 q^{77} - 8029 q^{78} - 4794 q^{79} - 10336 q^{80} + 11899 q^{81} - 13447 q^{82} - 11434 q^{83} - 7957 q^{84} - 8188 q^{85} - 5196 q^{86} - 11266 q^{87} - 11861 q^{88} - 4845 q^{89} - 7759 q^{90} - 12734 q^{91} - 8644 q^{92} - 10130 q^{93} - 6909 q^{94} - 3686 q^{95} - 11958 q^{96} - 16108 q^{97} - 6845 q^{98} - 12372 q^{99}+O(q^{100}) \) 239 * q - 16 * q^2 - 106 * q^3 + 872 * q^4 - 85 * q^5 - 111 * q^6 - 352 * q^7 - 210 * q^8 + 1961 * q^9 - 273 * q^10 - 294 * q^11 - 864 * q^12 - 797 * q^13 - 220 * q^14 - 580 * q^15 + 2816 * q^16 - 439 * q^17 - 536 * q^18 - 1704 * q^19 - 933 * q^20 - 596 * q^21 - 1046 * q^22 - 829 * q^23 - 1237 * q^24 + 4364 * q^25 - 818 * q^26 - 3670 * q^27 - 3690 * q^28 - 316 * q^29 - 888 * q^30 - 2595 * q^31 - 1881 * q^32 - 2066 * q^33 - 2605 * q^34 - 2450 * q^35 + 5863 * q^36 - 1912 * q^37 - 1709 * q^38 - 914 * q^39 - 3582 * q^40 - 1064 * q^41 - 3228 * q^42 - 5184 * q^43 - 2656 * q^44 - 3967 * q^45 - 2521 * q^46 - 4909 * q^47 - 7461 * q^48 + 7193 * q^49 - 1906 * q^50 - 3240 * q^51 - 9614 * q^52 - 2722 * q^53 - 3754 * q^54 - 6018 * q^55 - 2347 * q^56 - 2032 * q^57 - 6709 * q^58 - 6318 * q^59 - 5821 * q^60 - 2990 * q^61 - 2117 * q^62 - 8738 * q^63 + 6866 * q^64 - 1738 * q^65 - 3080 * q^66 - 14729 * q^67 - 3897 * q^68 - 2080 * q^69 - 7445 * q^70 - 3240 * q^71 - 8263 * q^72 - 8828 * q^73 - 3103 * q^74 - 12716 * q^75 - 14843 * q^76 - 3818 * q^77 - 8029 * q^78 - 4794 * q^79 - 10336 * q^80 + 11899 * q^81 - 13447 * q^82 - 11434 * q^83 - 7957 * q^84 - 8188 * q^85 - 5196 * q^86 - 11266 * q^87 - 11861 * q^88 - 4845 * q^89 - 7759 * q^90 - 12734 * q^91 - 8644 * q^92 - 10130 * q^93 - 6909 * q^94 - 3686 * q^95 - 11958 * q^96 - 16108 * q^97 - 6845 * q^98 - 12372 * q^99

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