LMFDB - Embedded newform 4009.2.a.c.1.27

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4009,2,Mod(1,4009)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4009, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("4009.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4009 = 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4009.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:	$32.0120261703$
Analytic rank:	$1$
Dimension:	$71$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.27
Character	$\chi$	$=$	4009.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.07838 q^{2} -2.13566 q^{3} -0.837104 q^{4} +2.78695 q^{5} +2.30305 q^{6} -4.27141 q^{7} +3.05947 q^{8} +1.56105 q^{9} +O(q^{10})$	\(q-1.07838 q^{2} -2.13566 q^{3} -0.837104 q^{4} +2.78695 q^{5} +2.30305 q^{6} -4.27141 q^{7} +3.05947 q^{8} +1.56105 q^{9} -3.00538 q^{10} -4.47166 q^{11} +1.78777 q^{12} -1.15286 q^{13} +4.60619 q^{14} -5.95197 q^{15} -1.62505 q^{16} +0.787588 q^{17} -1.68340 q^{18} +1.00000 q^{19} -2.33296 q^{20} +9.12229 q^{21} +4.82214 q^{22} +3.81302 q^{23} -6.53398 q^{24} +2.76707 q^{25} +1.24322 q^{26} +3.07312 q^{27} +3.57562 q^{28} -6.26705 q^{29} +6.41846 q^{30} +8.84576 q^{31} -4.36652 q^{32} +9.54996 q^{33} -0.849316 q^{34} -11.9042 q^{35} -1.30676 q^{36} +4.70964 q^{37} -1.07838 q^{38} +2.46213 q^{39} +8.52657 q^{40} +3.65660 q^{41} -9.83726 q^{42} -4.71302 q^{43} +3.74325 q^{44} +4.35055 q^{45} -4.11187 q^{46} -6.92243 q^{47} +3.47055 q^{48} +11.2450 q^{49} -2.98394 q^{50} -1.68202 q^{51} +0.965068 q^{52} +12.8637 q^{53} -3.31397 q^{54} -12.4623 q^{55} -13.0682 q^{56} -2.13566 q^{57} +6.75824 q^{58} -5.96865 q^{59} +4.98242 q^{60} -6.37582 q^{61} -9.53905 q^{62} -6.66788 q^{63} +7.95885 q^{64} -3.21297 q^{65} -10.2984 q^{66} -1.59307 q^{67} -0.659293 q^{68} -8.14332 q^{69} +12.8372 q^{70} +8.02668 q^{71} +4.77597 q^{72} +5.06085 q^{73} -5.07876 q^{74} -5.90952 q^{75} -0.837104 q^{76} +19.1003 q^{77} -2.65510 q^{78} -4.60528 q^{79} -4.52892 q^{80} -11.2463 q^{81} -3.94319 q^{82} +4.34006 q^{83} -7.63631 q^{84} +2.19496 q^{85} +5.08241 q^{86} +13.3843 q^{87} -13.6809 q^{88} +12.7724 q^{89} -4.69153 q^{90} +4.92436 q^{91} -3.19190 q^{92} -18.8915 q^{93} +7.46499 q^{94} +2.78695 q^{95} +9.32541 q^{96} -14.3043 q^{97} -12.1263 q^{98} -6.98048 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 71 q - 15 q^{2} - 8 q^{3} + 69 q^{4} - 18 q^{5} - 9 q^{6} - 19 q^{7} - 39 q^{8} + 63 q^{9}+O(q^{10}) $ 71 * q - 15 * q^2 - 8 * q^3 + 69 * q^4 - 18 * q^5 - 9 * q^6 - 19 * q^7 - 39 * q^8 + 63 * q^9	\( 71 q - 15 q^{2} - 8 q^{3} + 69 q^{4} - 18 q^{5} - 9 q^{6} - 19 q^{7} - 39 q^{8} + 63 q^{9} - 10 q^{10} - 52 q^{11} - 9 q^{12} - 15 q^{13} - 53 q^{14} - 33 q^{15} + 53 q^{16} - 10 q^{17} - 35 q^{18} + 71 q^{19} - 33 q^{20} - 38 q^{21} - 6 q^{22} - 65 q^{23} - 30 q^{24} + 51 q^{25} - 4 q^{26} - 23 q^{27} - 29 q^{28} - 97 q^{29} - 27 q^{30} - 53 q^{31} - 78 q^{32} - 17 q^{33} - 24 q^{34} - 38 q^{35} + 24 q^{36} - 33 q^{37} - 15 q^{38} - 86 q^{39} + 25 q^{40} - 69 q^{41} + 64 q^{42} - 10 q^{43} - 94 q^{44} - 34 q^{45} - 6 q^{46} - 37 q^{47} - q^{48} + 74 q^{49} - 41 q^{50} - 46 q^{51} - 30 q^{52} - 50 q^{53} - 17 q^{54} - 30 q^{55} - 116 q^{56} - 8 q^{57} + 11 q^{58} - 93 q^{59} - 56 q^{60} - 18 q^{61} - q^{62} - 84 q^{63} + 93 q^{64} - 78 q^{65} - 53 q^{66} - 5 q^{67} - 9 q^{68} - 69 q^{69} - 10 q^{70} - 221 q^{71} - 73 q^{72} - 34 q^{73} - 58 q^{74} - 70 q^{75} + 69 q^{76} - 2 q^{77} + 7 q^{78} - 68 q^{79} - 71 q^{80} + 39 q^{81} + 26 q^{82} - 45 q^{83} - 10 q^{84} - 44 q^{85} - 80 q^{86} - 7 q^{87} - 46 q^{88} - 143 q^{89} + 41 q^{90} - 30 q^{91} - 46 q^{92} + 32 q^{93} + 41 q^{94} - 18 q^{95} - 140 q^{96} - 18 q^{97} - 97 q^{98} - 142 q^{99}+O(q^{100}) \) 71 * q - 15 * q^2 - 8 * q^3 + 69 * q^4 - 18 * q^5 - 9 * q^6 - 19 * q^7 - 39 * q^8 + 63 * q^9 - 10 * q^10 - 52 * q^11 - 9 * q^12 - 15 * q^13 - 53 * q^14 - 33 * q^15 + 53 * q^16 - 10 * q^17 - 35 * q^18 + 71 * q^19 - 33 * q^20 - 38 * q^21 - 6 * q^22 - 65 * q^23 - 30 * q^24 + 51 * q^25 - 4 * q^26 - 23 * q^27 - 29 * q^28 - 97 * q^29 - 27 * q^30 - 53 * q^31 - 78 * q^32 - 17 * q^33 - 24 * q^34 - 38 * q^35 + 24 * q^36 - 33 * q^37 - 15 * q^38 - 86 * q^39 + 25 * q^40 - 69 * q^41 + 64 * q^42 - 10 * q^43 - 94 * q^44 - 34 * q^45 - 6 * q^46 - 37 * q^47 - q^48 + 74 * q^49 - 41 * q^50 - 46 * q^51 - 30 * q^52 - 50 * q^53 - 17 * q^54 - 30 * q^55 - 116 * q^56 - 8 * q^57 + 11 * q^58 - 93 * q^59 - 56 * q^60 - 18 * q^61 - q^62 - 84 * q^63 + 93 * q^64 - 78 * q^65 - 53 * q^66 - 5 * q^67 - 9 * q^68 - 69 * q^69 - 10 * q^70 - 221 * q^71 - 73 * q^72 - 34 * q^73 - 58 * q^74 - 70 * q^75 + 69 * q^76 - 2 * q^77 + 7 * q^78 - 68 * q^79 - 71 * q^80 + 39 * q^81 + 26 * q^82 - 45 * q^83 - 10 * q^84 - 44 * q^85 - 80 * q^86 - 7 * q^87 - 46 * q^88 - 143 * q^89 + 41 * q^90 - 30 * q^91 - 46 * q^92 + 32 * q^93 + 41 * q^94 - 18 * q^95 - 140 * q^96 - 18 * q^97 - 97 * q^98 - 142 * 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 $

$2$	−1.07838	−0.762527	−0.381264	−	0.924466i	$-0.624511\pi$
$2$	−1.07838	−0.762527	−0.381264	+	0.924466i	$0.624511\pi$
$3$	−2.13566	−1.23302	−0.616512	−	0.787345i	$-0.711455\pi$
$3$	−2.13566	−1.23302	−0.616512	+	0.787345i	$0.711455\pi$
$4$	−0.837104	−0.418552
$5$	2.78695	1.24636	0.623180	−	0.782078i	$-0.285840\pi$
$5$	2.78695	1.24636	0.623180	+	0.782078i	$0.285840\pi$
$6$	2.30305	0.940215
$7$	−4.27141	−1.61444	−0.807221	−	0.590249i	$-0.799030\pi$
$7$	−4.27141	−1.61444	−0.807221	+	0.590249i	$0.799030\pi$
$8$	3.05947	1.08168
$9$	1.56105	0.520349
$10$	−3.00538	−0.950383
$11$	−4.47166	−1.34826	−0.674129	−	0.738614i	$-0.735481\pi$
$11$	−4.47166	−1.34826	−0.674129	+	0.738614i	$0.735481\pi$
$12$	1.78777	0.516085
$13$	−1.15286	−0.319747	−0.159874	−	0.987137i	$-0.551109\pi$
$13$	−1.15286	−0.319747	−0.159874	+	0.987137i	$0.551109\pi$
$14$	4.60619	1.23106
$15$	−5.95197	−1.53679
$16$	−1.62505	−0.406262
$17$	0.787588	0.191018	0.0955090	−	0.995429i	$-0.469552\pi$
$17$	0.787588	0.191018	0.0955090	+	0.995429i	$0.469552\pi$
$18$	−1.68340	−0.396780
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−2.33296	−0.521667
$21$	9.12229	1.99065
$22$	4.82214	1.02808
$23$	3.81302	0.795070	0.397535	−	0.917587i	$-0.369866\pi$
$23$	3.81302	0.795070	0.397535	+	0.917587i	$0.369866\pi$
$24$	−6.53398	−1.33374
$25$	2.76707	0.553413
$26$	1.24322	0.243816
$27$	3.07312	0.591421
$28$	3.57562	0.675729
$29$	−6.26705	−1.16376	−0.581881	−	0.813274i	$-0.697683\pi$
$29$	−6.26705	−1.16376	−0.581881	+	0.813274i	$0.697683\pi$
$30$	6.41846	1.17185
$31$	8.84576	1.58874	0.794372	−	0.607431i	$-0.207800\pi$
$31$	8.84576	1.58874	0.794372	+	0.607431i	$0.207800\pi$
$32$	−4.36652	−0.771899
$33$	9.54996	1.66243
$34$	−0.849316	−0.145656
$35$	−11.9042	−2.01218
$36$	−1.30676	−0.217793
$37$	4.70964	0.774260	0.387130	−	0.922025i	$-0.373466\pi$
$37$	4.70964	0.774260	0.387130	+	0.922025i	$0.373466\pi$
$38$	−1.07838	−0.174936
$39$	2.46213	0.394256
$40$	8.52657	1.34817
$41$	3.65660	0.571065	0.285533	−	0.958369i	$-0.407829\pi$
$41$	3.65660	0.571065	0.285533	+	0.958369i	$0.407829\pi$
$42$	−9.83726	−1.51792
$43$	−4.71302	−0.718729	−0.359365	−	0.933197i	$-0.617007\pi$
$43$	−4.71302	−0.718729	−0.359365	+	0.933197i	$0.617007\pi$
$44$	3.74325	0.564316
$45$	4.35055	0.648542
$46$	−4.11187	−0.606262
$47$	−6.92243	−1.00974	−0.504870	−	0.863195i	$-0.668460\pi$
$47$	−6.92243	−1.00974	−0.504870	+	0.863195i	$0.668460\pi$
$48$	3.47055	0.500931
$49$	11.2450	1.60642
$50$	−2.98394	−0.421993
$51$	−1.68202	−0.235530
$52$	0.965068	0.133831
$53$	12.8637	1.76696	0.883480	−	0.468469i	$-0.155194\pi$
$53$	12.8637	1.76696	0.883480	+	0.468469i	$0.155194\pi$
$54$	−3.31397	−0.450975
$55$	−12.4623	−1.68041
$56$	−13.0682	−1.74632
$57$	−2.13566	−0.282875
$58$	6.75824	0.887400
$59$	−5.96865	−0.777053	−0.388526	−	0.921438i	$-0.627016\pi$
$59$	−5.96865	−0.777053	−0.388526	+	0.921438i	$0.627016\pi$
$60$	4.98242	0.643228
$61$	−6.37582	−0.816340	−0.408170	−	0.912906i	$-0.633833\pi$
$61$	−6.37582	−0.816340	−0.408170	+	0.912906i	$0.633833\pi$
$62$	−9.53905	−1.21146
$63$	−6.66788	−0.840074
$64$	7.95885	0.994856
$65$	−3.21297	−0.398520
$66$	−10.2984	−1.26765
$67$	−1.59307	−0.194624	−0.0973122	−	0.995254i	$-0.531025\pi$
$67$	−1.59307	−0.194624	−0.0973122	+	0.995254i	$0.531025\pi$
$68$	−0.659293	−0.0799510
$69$	−8.14332	−0.980340
$70$	12.8372	1.53434
$71$	8.02668	0.952591	0.476296	−	0.879285i	$-0.341979\pi$
$71$	8.02668	0.952591	0.476296	+	0.879285i	$0.341979\pi$
$72$	4.77597	0.562854
$73$	5.06085	0.592328	0.296164	−	0.955137i	$-0.404293\pi$
$73$	5.06085	0.592328	0.296164	+	0.955137i	$0.404293\pi$
$74$	−5.07876	−0.590394
$75$	−5.90952	−0.682372
$76$	−0.837104	−0.0960225
$77$	19.1003	2.17668
$78$	−2.65510	−0.300631
$79$	−4.60528	−0.518134	−0.259067	−	0.965859i	$-0.583415\pi$
$79$	−4.60528	−0.518134	−0.259067	+	0.965859i	$0.583415\pi$
$80$	−4.52892	−0.506348
$81$	−11.2463	−1.24959
$82$	−3.94319	−0.435453
$83$	4.34006	0.476383	0.238192	−	0.971218i	$-0.423445\pi$
$83$	4.34006	0.476383	0.238192	+	0.971218i	$0.423445\pi$
$84$	−7.63631	−0.833190
$85$	2.19496	0.238077
$86$	5.08241	0.548051
$87$	13.3843	1.43495
$88$	−13.6809	−1.45839
$89$	12.7724	1.35387	0.676935	−	0.736043i	$-0.263308\pi$
$89$	12.7724	1.35387	0.676935	+	0.736043i	$0.263308\pi$
$90$	−4.69153	−0.494531
$91$	4.92436	0.516213
$92$	−3.19190	−0.332778
$93$	−18.8915	−1.95896
$94$	7.46499	0.769955
$95$	2.78695	0.285935
$96$	9.32541	0.951770
$97$	−14.3043	−1.45238	−0.726190	−	0.687494i	$-0.758711\pi$
$97$	−14.3043	−1.45238	−0.726190	+	0.687494i	$0.758711\pi$
$98$	−12.1263	−1.22494
$99$	−6.98048	−0.701564
$100$	−2.31632	−0.231632
$101$	16.6859	1.66031	0.830155	−	0.557533i	$-0.188252\pi$
$101$	16.6859	1.66031	0.830155	+	0.557533i	$0.188252\pi$
$102$	1.81385	0.179598
$103$	−12.3140	−1.21333	−0.606665	−	0.794958i	$-0.707493\pi$
$103$	−12.3140	−1.21333	−0.606665	+	0.794958i	$0.707493\pi$
$104$	−3.52715	−0.345866
$105$	25.4233	2.48106
$106$	−13.8719	−1.34736
$107$	−2.85555	−0.276057	−0.138028	−	0.990428i	$-0.544077\pi$
$107$	−2.85555	−0.276057	−0.138028	+	0.990428i	$0.544077\pi$
$108$	−2.57252	−0.247541
$109$	4.23503	0.405642	0.202821	−	0.979216i	$-0.434989\pi$
$109$	4.23503	0.405642	0.202821	+	0.979216i	$0.434989\pi$
$110$	13.4390	1.28136
$111$	−10.0582	−0.954681
$112$	6.94125	0.655886
$113$	15.5785	1.46550	0.732752	−	0.680495i	$-0.238235\pi$
$113$	15.5785	1.46550	0.732752	+	0.680495i	$0.238235\pi$
$114$	2.30305	0.215700
$115$	10.6267	0.990943
$116$	5.24618	0.487095
$117$	−1.79968	−0.166380
$118$	6.43646	0.592524
$119$	−3.36411	−0.308388
$120$	−18.2099	−1.66232
$121$	8.99577	0.817797
$122$	6.87553	0.622481
$123$	−7.80926	−0.704138
$124$	−7.40482	−0.664973
$125$	−6.22306	−0.556608
$126$	7.19048	0.640579
$127$	−9.82171	−0.871536	−0.435768	−	0.900059i	$-0.643523\pi$
$127$	−9.82171	−0.871536	−0.435768	+	0.900059i	$0.643523\pi$
$128$	0.150409	0.0132944
$129$	10.0654	0.886211
$130$	3.46479	0.303882
$131$	7.27061	0.635236	0.317618	−	0.948219i	$-0.397117\pi$
$131$	7.27061	0.635236	0.317618	+	0.948219i	$0.397117\pi$
$132$	−7.99431	−0.695815
$133$	−4.27141	−0.370379
$134$	1.71793	0.148406
$135$	8.56461	0.737124
$136$	2.40960	0.206621
$137$	8.01751	0.684983	0.342491	−	0.939521i	$-0.388729\pi$
$137$	8.01751	0.684983	0.342491	+	0.939521i	$0.388729\pi$
$138$	8.78156	0.747536
$139$	18.7182	1.58765	0.793827	−	0.608143i	$-0.208085\pi$
$139$	18.7182	1.58765	0.793827	+	0.608143i	$0.208085\pi$
$140$	9.96506	0.842201
$141$	14.7840	1.24504
$142$	−8.65578	−0.726377
$143$	5.15522	0.431101
$144$	−2.53678	−0.211398
$145$	−17.4659	−1.45047
$146$	−5.45750	−0.451666
$147$	−24.0155	−1.98076
$148$	−3.94246	−0.324068
$149$	−5.02968	−0.412047	−0.206024	−	0.978547i	$-0.566052\pi$
$149$	−5.02968	−0.412047	−0.206024	+	0.978547i	$0.566052\pi$
$150$	6.37268	0.520327
$151$	−3.40259	−0.276899	−0.138449	−	0.990370i	$-0.544212\pi$
$151$	−3.40259	−0.276899	−0.138449	+	0.990370i	$0.544212\pi$
$152$	3.05947	0.248155
$153$	1.22946	0.0993961
$154$	−20.5973	−1.65978
$155$	24.6526	1.98015
$156$	−2.06106	−0.165017
$157$	20.9239	1.66991	0.834954	−	0.550320i	$-0.185494\pi$
$157$	20.9239	1.66991	0.834954	+	0.550320i	$0.185494\pi$
$158$	4.96622	0.395091
$159$	−27.4724	−2.17870
$160$	−12.1693	−0.962064
$161$	−16.2870	−1.28359
$162$	12.1277	0.952843
$163$	−21.1410	−1.65589	−0.827944	−	0.560810i	$-0.810490\pi$
$163$	−21.1410	−1.65589	−0.827944	+	0.560810i	$0.810490\pi$
$164$	−3.06096	−0.239021
$165$	26.6152	2.07199
$166$	−4.68022	−0.363255
$167$	4.22698	0.327094	0.163547	−	0.986536i	$-0.447707\pi$
$167$	4.22698	0.327094	0.163547	+	0.986536i	$0.447707\pi$
$168$	27.9093	2.15325
$169$	−11.6709	−0.897762
$170$	−2.36700	−0.181540
$171$	1.56105	0.119376
$172$	3.94529	0.300826
$173$	−11.5197	−0.875823	−0.437912	−	0.899018i	$-0.644282\pi$
$173$	−11.5197	−0.875823	−0.437912	+	0.899018i	$0.644282\pi$
$174$	−14.4333	−1.09419
$175$	−11.8193	−0.893454
$176$	7.26666	0.547745
$177$	12.7470	0.958125
$178$	−13.7734	−1.03236
$179$	−9.15809	−0.684508	−0.342254	−	0.939607i	$-0.611190\pi$
$179$	−9.15809	−0.684508	−0.342254	+	0.939607i	$0.611190\pi$
$180$	−3.64187	−0.271449
$181$	18.7773	1.39571	0.697853	−	0.716241i	$-0.254139\pi$
$181$	18.7773	1.39571	0.697853	+	0.716241i	$0.254139\pi$
$182$	−5.31032	−0.393627
$183$	13.6166	1.00657
$184$	11.6658	0.860015
$185$	13.1255	0.965007
$186$	20.3722	1.49376
$187$	−3.52183	−0.257541
$188$	5.79480	0.422629
$189$	−13.1265	−0.954816
$190$	−3.00538	−0.218033
$191$	−3.30960	−0.239474	−0.119737	−	0.992806i	$-0.538205\pi$
$191$	−3.30960	−0.239474	−0.119737	+	0.992806i	$0.538205\pi$
$192$	−16.9974	−1.22668
$193$	2.13307	0.153542	0.0767709	−	0.997049i	$-0.475539\pi$
$193$	2.13307	0.153542	0.0767709	+	0.997049i	$0.475539\pi$
$194$	15.4254	1.10748
$195$	6.86182	0.491385
$196$	−9.41322	−0.672373
$197$	7.18011	0.511561	0.255781	−	0.966735i	$-0.417667\pi$
$197$	7.18011	0.511561	0.255781	+	0.966735i	$0.417667\pi$
$198$	7.52758	0.534962
$199$	−8.85155	−0.627470	−0.313735	−	0.949511i	$-0.601580\pi$
$199$	−8.85155	−0.627470	−0.313735	+	0.949511i	$0.601580\pi$
$200$	8.46575	0.598619
$201$	3.40226	0.239977
$202$	−17.9937	−1.26603
$203$	26.7692	1.87883
$204$	1.40803	0.0985816
$205$	10.1908	0.711753
$206$	13.2791	0.925197
$207$	5.95231	0.413714
$208$	1.87346	0.129901
$209$	−4.47166	−0.309311
$210$	−27.4159	−1.89188
$211$	1.00000	0.0688428
$211$	1.00000	0.0688428
$212$	−10.7682	−0.739565
$213$	−17.1423	−1.17457
$214$	3.07936	0.210501
$215$	−13.1349	−0.895796
$216$	9.40209	0.639731
$217$	−37.7839	−2.56494
$218$	−4.56696	−0.309313
$219$	−10.8083	−0.730355
$220$	10.4322	0.703341
$221$	−0.907982	−0.0610775
$222$	10.8465	0.727970
$223$	8.30018	0.555821	0.277911	−	0.960607i	$-0.410358\pi$
$223$	8.30018	0.555821	0.277911	+	0.960607i	$0.410358\pi$
$224$	18.6512	1.24619
$225$	4.31952	0.287968
$226$	−16.7995	−1.11749
$227$	6.85357	0.454887	0.227444	−	0.973791i	$-0.426963\pi$
$227$	6.85357	0.454887	0.227444	+	0.973791i	$0.426963\pi$
$228$	1.78777	0.118398
$229$	−23.8674	−1.57720	−0.788600	−	0.614906i	$-0.789194\pi$
$229$	−23.8674	−1.57720	−0.788600	+	0.614906i	$0.789194\pi$
$230$	−11.4596	−0.755621
$231$	−40.7918	−2.68390
$232$	−19.1738	−1.25882
$233$	0.487447	0.0319337	0.0159669	−	0.999873i	$-0.494917\pi$
$233$	0.487447	0.0319337	0.0159669	+	0.999873i	$0.494917\pi$
$234$	1.94073	0.126869
$235$	−19.2925	−1.25850
$236$	4.99639	0.325237
$237$	9.83531	0.638872
$238$	3.62778	0.235154
$239$	−23.3431	−1.50994	−0.754970	−	0.655760i	$-0.772348\pi$
$239$	−23.3431	−1.50994	−0.754970	+	0.655760i	$0.772348\pi$
$240$	9.67223	0.624340
$241$	−10.5153	−0.677352	−0.338676	−	0.940903i	$-0.609979\pi$
$241$	−10.5153	−0.677352	−0.338676	+	0.940903i	$0.609979\pi$
$242$	−9.70083	−0.623593
$243$	14.7989	0.949349
$244$	5.33723	0.341681
$245$	31.3391	2.00218
$246$	8.42133	0.536924
$247$	−1.15286	−0.0733550
$248$	27.0633	1.71852
$249$	−9.26889	−0.587392
$250$	6.71080	0.424428
$251$	−30.1466	−1.90283	−0.951417	−	0.307905i	$-0.900372\pi$
$251$	−30.1466	−1.90283	−0.951417	+	0.307905i	$0.900372\pi$
$252$	5.58171	0.351615
$253$	−17.0505	−1.07196
$254$	10.5915	0.664570
$255$	−4.68770	−0.293555
$256$	−16.0799	−1.00499
$257$	−23.7597	−1.48209	−0.741044	−	0.671456i	$-0.765669\pi$
$257$	−23.7597	−1.48209	−0.741044	+	0.671456i	$0.765669\pi$
$258$	−10.8543	−0.675760
$259$	−20.1168	−1.25000
$260$	2.68959	0.166801
$261$	−9.78316	−0.605562
$262$	−7.84046	−0.484385
$263$	28.8051	1.77620	0.888101	−	0.459649i	$-0.152025\pi$
$263$	28.8051	1.77620	0.888101	+	0.459649i	$0.152025\pi$
$264$	29.2178	1.79823
$265$	35.8503	2.20227
$266$	4.60619	0.282424
$267$	−27.2775	−1.66936
$268$	1.33357	0.0814605
$269$	−25.5733	−1.55923	−0.779617	−	0.626257i	$-0.784586\pi$
$269$	−25.5733	−1.55923	−0.779617	+	0.626257i	$0.784586\pi$
$270$	−9.23587	−0.562077
$271$	−25.6620	−1.55886	−0.779428	−	0.626492i	$-0.784490\pi$
$271$	−25.6620	−1.55886	−0.779428	+	0.626492i	$0.784490\pi$
$272$	−1.27987	−0.0776033
$273$	−10.5168	−0.636504
$274$	−8.64590	−0.522318
$275$	−12.3734	−0.746144
$276$	6.81681	0.410324
$277$	29.3406	1.76291	0.881453	−	0.472271i	$-0.156566\pi$
$277$	29.3406	1.76291	0.881453	+	0.472271i	$0.156566\pi$
$278$	−20.1852	−1.21063
$279$	13.8086	0.826702
$280$	−36.4205	−2.17654
$281$	−9.64538	−0.575395	−0.287697	−	0.957721i	$-0.592890\pi$
$281$	−9.64538	−0.575395	−0.287697	+	0.957721i	$0.592890\pi$
$282$	−15.9427	−0.949373
$283$	−14.6022	−0.868008	−0.434004	−	0.900911i	$-0.642900\pi$
$283$	−14.6022	−0.868008	−0.434004	+	0.900911i	$0.642900\pi$
$284$	−6.71917	−0.398709
$285$	−5.95197	−0.352564
$286$	−5.55927	−0.328727
$287$	−15.6189	−0.921952
$288$	−6.81634	−0.401657
$289$	−16.3797	−0.963512
$290$	18.8348	1.10602
$291$	30.5491	1.79082
$292$	−4.23646	−0.247920
$293$	−12.1269	−0.708463	−0.354232	−	0.935158i	$-0.615258\pi$
$293$	−12.1269	−0.708463	−0.354232	+	0.935158i	$0.615258\pi$
$294$	25.8977	1.51038
$295$	−16.6343	−0.968487
$296$	14.4090	0.837505
$297$	−13.7419	−0.797388
$298$	5.42388	0.314197
$299$	−4.39590	−0.254221
$300$	4.94688	0.285608
$301$	20.1313	1.16035
$302$	3.66927	0.211143
$303$	−35.6354	−2.04720
$304$	−1.62505	−0.0932028
$305$	−17.7691	−1.01745
$306$	−1.32582	−0.0757922
$307$	−11.7405	−0.670066	−0.335033	−	0.942206i	$-0.608747\pi$
$307$	−11.7405	−0.670066	−0.335033	+	0.942206i	$0.608747\pi$
$308$	−15.9890	−0.911056
$309$	26.2984	1.49607
$310$	−26.5848	−1.50992
$311$	6.32415	0.358610	0.179305	−	0.983794i	$-0.442615\pi$
$311$	6.32415	0.358610	0.179305	+	0.983794i	$0.442615\pi$
$312$	7.53280	0.426461
$313$	9.27552	0.524283	0.262142	−	0.965029i	$-0.415571\pi$
$313$	9.27552	0.524283	0.262142	+	0.965029i	$0.415571\pi$
$314$	−22.5638	−1.27335
$315$	−18.5830	−1.04703
$316$	3.85510	0.216866
$317$	−0.0355267	−0.00199538	−0.000997688	−	1.00000i	$-0.500318\pi$
$317$	−0.0355267	−0.00199538	−0.000997688		1.00000i	$0.500318\pi$
$318$	29.6256	1.66132
$319$	28.0241	1.56905
$320$	22.1809	1.23995
$321$	6.09849	0.340385
$322$	17.5635	0.978776
$323$	0.787588	0.0438225
$324$	9.41431	0.523017
$325$	−3.19005	−0.176952
$326$	22.7979	1.26266
$327$	−9.04459	−0.500167
$328$	11.1873	0.617713
$329$	29.5686	1.63017
$330$	−28.7012	−1.57995
$331$	34.2542	1.88278	0.941390	−	0.337320i	$-0.109521\pi$
$331$	34.2542	1.88278	0.941390	+	0.337320i	$0.109521\pi$
$332$	−3.63308	−0.199391
$333$	7.35197	0.402885
$334$	−4.55828	−0.249418
$335$	−4.43980	−0.242572
$336$	−14.8242	−0.808724
$337$	−30.4856	−1.66066	−0.830329	−	0.557273i	$-0.811848\pi$
$337$	−30.4856	−1.66066	−0.830329	+	0.557273i	$0.811848\pi$
$338$	12.5856	0.684568
$339$	−33.2705	−1.80700
$340$	−1.83741	−0.0996478
$341$	−39.5552	−2.14204
$342$	−1.68340	−0.0910276
$343$	−18.1320	−0.979038
$344$	−14.4193	−0.777439
$345$	−22.6950	−1.22186
$346$	12.4225	0.667839
$347$	15.9552	0.856519	0.428259	−	0.903656i	$-0.359127\pi$
$347$	15.9552	0.856519	0.428259	+	0.903656i	$0.359127\pi$
$348$	−11.2041	−0.600600
$349$	29.7514	1.59255	0.796277	−	0.604933i	$-0.206800\pi$
$349$	29.7514	1.59255	0.796277	+	0.604933i	$0.206800\pi$
$350$	12.7456	0.681283
$351$	−3.54289	−0.189105
$352$	19.5256	1.04072
$353$	6.52234	0.347149	0.173575	−	0.984821i	$-0.444468\pi$
$353$	6.52234	0.347149	0.173575	+	0.984821i	$0.444468\pi$
$354$	−13.7461	−0.730596
$355$	22.3699	1.18727
$356$	−10.6918	−0.566666
$357$	7.18460	0.380250
$358$	9.87587	0.521956
$359$	−19.3021	−1.01873	−0.509363	−	0.860552i	$-0.670119\pi$
$359$	−19.3021	−1.01873	−0.509363	+	0.860552i	$0.670119\pi$
$360$	13.3104	0.701518
$361$	1.00000	0.0526316
$362$	−20.2490	−1.06426
$363$	−19.2119	−1.00836
$364$	−4.12221	−0.216062
$365$	14.1043	0.738254
$366$	−14.6838	−0.767535
$367$	−26.8532	−1.40172	−0.700862	−	0.713297i	$-0.747201\pi$
$367$	−26.8532	−1.40172	−0.700862	+	0.713297i	$0.747201\pi$
$368$	−6.19634	−0.323006
$369$	5.70813	0.297153
$370$	−14.1542	−0.735844
$371$	−54.9460	−2.85266
$372$	15.8142	0.819927
$373$	−23.1963	−1.20106	−0.600531	−	0.799602i	$-0.705044\pi$
$373$	−23.1963	−1.20106	−0.600531	+	0.799602i	$0.705044\pi$
$374$	3.79785	0.196382
$375$	13.2904	0.686311
$376$	−21.1790	−1.09222
$377$	7.22506	0.372110
$378$	14.1554	0.728073
$379$	−4.99400	−0.256524	−0.128262	−	0.991740i	$-0.540940\pi$
$379$	−4.99400	−0.256524	−0.128262	+	0.991740i	$0.540940\pi$
$380$	−2.33296	−0.119679
$381$	20.9758	1.07462
$382$	3.56900	0.182606
$383$	9.99534	0.510738	0.255369	−	0.966844i	$-0.417803\pi$
$383$	9.99534	0.510738	0.255369	+	0.966844i	$0.417803\pi$
$384$	−0.321222	−0.0163923
$385$	53.2316	2.71293
$386$	−2.30025	−0.117080
$387$	−7.35725	−0.373990
$388$	11.9742	0.607897
$389$	−9.09297	−0.461032	−0.230516	−	0.973069i	$-0.574041\pi$
$389$	−9.09297	−0.461032	−0.230516	+	0.973069i	$0.574041\pi$
$390$	−7.39962	−0.374694
$391$	3.00309	0.151873
$392$	34.4036	1.73765
$393$	−15.5276	−0.783262
$394$	−7.74286	−0.390080
$395$	−12.8347	−0.645782
$396$	5.84339	0.293641
$397$	−14.2902	−0.717206	−0.358603	−	0.933490i	$-0.616747\pi$
$397$	−14.2902	−0.717206	−0.358603	+	0.933490i	$0.616747\pi$
$398$	9.54530	0.478463
$399$	9.12229	0.456686
$400$	−4.49661	−0.224831
$401$	−10.1371	−0.506221	−0.253111	−	0.967437i	$-0.581454\pi$
$401$	−10.1371	−0.506221	−0.253111	+	0.967437i	$0.581454\pi$
$402$	−3.66891	−0.182989
$403$	−10.1980	−0.507997
$404$	−13.9678	−0.694926
$405$	−31.3428	−1.55743
$406$	−28.8672	−1.43266
$407$	−21.0599	−1.04390
$408$	−5.14608	−0.254769
$409$	−25.3245	−1.25222	−0.626109	−	0.779736i	$-0.715353\pi$
$409$	−25.3245	−1.25222	−0.626109	+	0.779736i	$0.715353\pi$
$410$	−10.9895	−0.542731
$411$	−17.1227	−0.844600
$412$	10.3081	0.507842
$413$	25.4946	1.25451
$414$	−6.41883	−0.315468
$415$	12.0955	0.593745
$416$	5.03401	0.246813
$417$	−39.9757	−1.95762
$418$	4.82214	0.235858
$419$	−0.822065	−0.0401605	−0.0200803	−	0.999798i	$-0.506392\pi$
$419$	−0.822065	−0.0401605	−0.0200803	+	0.999798i	$0.506392\pi$
$420$	−21.2820	−1.03845
$421$	−27.2591	−1.32853	−0.664265	−	0.747498i	$-0.731255\pi$
$421$	−27.2591	−1.32853	−0.664265	+	0.747498i	$0.731255\pi$
$422$	−1.07838	−0.0524945
$423$	−10.8062	−0.525418
$424$	39.3559	1.91129
$425$	2.17931	0.105712
$426$	18.4858	0.895640
$427$	27.2338	1.31793
$428$	2.39040	0.115544
$429$	−11.0098	−0.531559
$430$	14.1644	0.683069
$431$	−18.3531	−0.884037	−0.442019	−	0.897006i	$-0.645737\pi$
$431$	−18.3531	−0.884037	−0.442019	+	0.897006i	$0.645737\pi$
$432$	−4.99396	−0.240272
$433$	26.1021	1.25439	0.627193	−	0.778864i	$-0.284204\pi$
$433$	26.1021	1.25439	0.627193	+	0.778864i	$0.284204\pi$
$434$	40.7452	1.95583
$435$	37.3013	1.78846
$436$	−3.54516	−0.169783
$437$	3.81302	0.182402
$438$	11.6554	0.556915
$439$	−26.8670	−1.28229	−0.641146	−	0.767419i	$-0.721541\pi$
$439$	−26.8670	−1.28229	−0.641146	+	0.767419i	$0.721541\pi$
$440$	−38.1279	−1.81768
$441$	17.5539	0.835902
$442$	0.979146	0.0465732
$443$	5.67230	0.269499	0.134750	−	0.990880i	$-0.456977\pi$
$443$	5.67230	0.269499	0.134750	+	0.990880i	$0.456977\pi$
$444$	8.41976	0.399584
$445$	35.5960	1.68741
$446$	−8.95072	−0.423829
$447$	10.7417	0.508064
$448$	−33.9955	−1.60614
$449$	−21.5902	−1.01890	−0.509452	−	0.860499i	$-0.670152\pi$
$449$	−21.5902	−1.01890	−0.509452	+	0.860499i	$0.670152\pi$
$450$	−4.65807	−0.219584
$451$	−16.3511	−0.769943
$452$	−13.0409	−0.613390
$453$	7.26677	0.341423
$454$	−7.39072	−0.346864
$455$	13.7239	0.643388
$456$	−6.53398	−0.305982
$457$	−9.52687	−0.445648	−0.222824	−	0.974859i	$-0.571528\pi$
$457$	−9.52687	−0.445648	−0.222824	+	0.974859i	$0.571528\pi$
$458$	25.7380	1.20266
$459$	2.42035	0.112972
$460$	−8.89564	−0.414762
$461$	−28.2286	−1.31474	−0.657368	−	0.753570i	$-0.728330\pi$
$461$	−28.2286	−1.31474	−0.657368	+	0.753570i	$0.728330\pi$
$462$	43.9889	2.04655
$463$	35.9557	1.67100	0.835502	−	0.549487i	$-0.185177\pi$
$463$	35.9557	1.67100	0.835502	+	0.549487i	$0.185177\pi$
$464$	10.1843	0.472792
$465$	−52.6497	−2.44157
$466$	−0.525651	−0.0243503
$467$	32.2263	1.49125	0.745627	−	0.666364i	$-0.232150\pi$
$467$	32.2263	1.49125	0.745627	+	0.666364i	$0.232150\pi$
$468$	1.50652	0.0696388
$469$	6.80466	0.314210
$470$	20.8045	0.959641
$471$	−44.6863	−2.05904
$472$	−18.2609	−0.840526
$473$	21.0751	0.969032
$474$	−10.6062	−0.487157
$475$	2.76707	0.126962
$476$	2.81611	0.129076
$477$	20.0808	0.919436
$478$	25.1726	1.15137
$479$	−13.7413	−0.627856	−0.313928	−	0.949447i	$-0.601645\pi$
$479$	−13.7413	−0.627856	−0.313928	+	0.949447i	$0.601645\pi$
$480$	25.9894	1.18625
$481$	−5.42958	−0.247567
$482$	11.3395	0.516500
$483$	34.7835	1.58270
$484$	−7.53040	−0.342291
$485$	−39.8653	−1.81019
$486$	−15.9588	−0.723904
$487$	36.9203	1.67302	0.836510	−	0.547952i	$-0.184592\pi$
$487$	36.9203	1.67302	0.836510	+	0.547952i	$0.184592\pi$
$488$	−19.5066	−0.883022
$489$	45.1499	2.04175
$490$	−33.7954	−1.52672
$491$	−24.4651	−1.10409	−0.552047	−	0.833813i	$-0.686153\pi$
$491$	−24.4651	−1.10409	−0.552047	+	0.833813i	$0.686153\pi$
$492$	6.53717	0.294718
$493$	−4.93585	−0.222300
$494$	1.24322	0.0559352
$495$	−19.4542	−0.874402
$496$	−14.3748	−0.645446
$497$	−34.2852	−1.53790
$498$	9.99536	0.447903
$499$	−21.3827	−0.957220	−0.478610	−	0.878028i	$-0.658859\pi$
$499$	−21.3827	−0.957220	−0.478610	+	0.878028i	$0.658859\pi$
$500$	5.20935	0.232969
$501$	−9.02740	−0.403314
$502$	32.5093	1.45096
$503$	6.39532	0.285153	0.142577	−	0.989784i	$-0.454461\pi$
$503$	6.39532	0.285153	0.142577	+	0.989784i	$0.454461\pi$
$504$	−20.4001	−0.908695
$505$	46.5027	2.06934
$506$	18.3869	0.817398
$507$	24.9251	1.10696
$508$	8.22180	0.364783
$509$	−1.21316	−0.0537723	−0.0268862	−	0.999639i	$-0.508559\pi$
$509$	−1.21316	−0.0537723	−0.0268862	+	0.999639i	$0.508559\pi$
$510$	5.05510	0.223844
$511$	−21.6170	−0.956279
$512$	17.0394	0.753040
$513$	3.07312	0.135681
$514$	25.6219	1.13013
$515$	−34.3183	−1.51225
$516$	−8.42581	−0.370926
$517$	30.9548	1.36139
$518$	21.6935	0.953158
$519$	24.6021	1.07991
$520$	−9.82998	−0.431073
$521$	−1.51651	−0.0664394	−0.0332197	−	0.999448i	$-0.510576\pi$
$521$	−1.51651	−0.0664394	−0.0332197	+	0.999448i	$0.510576\pi$
$522$	10.5499	0.461758
$523$	−28.1236	−1.22976	−0.614880	−	0.788621i	$-0.710796\pi$
$523$	−28.1236	−1.22976	−0.614880	+	0.788621i	$0.710796\pi$
$524$	−6.08626	−0.265880
$525$	25.2420	1.10165
$526$	−31.0628	−1.35440
$527$	6.96681	0.303479
$528$	−15.5191	−0.675383
$529$	−8.46087	−0.367864
$530$	−38.6601	−1.67929
$531$	−9.31735	−0.404339
$532$	3.57562	0.155023
$533$	−4.21557	−0.182597
$534$	29.4154	1.27293
$535$	−7.95827	−0.344066
$536$	−4.87394	−0.210522
$537$	19.5586	0.844015
$538$	27.5777	1.18896
$539$	−50.2837	−2.16587
$540$	−7.16947	−0.308525
$541$	32.5975	1.40147	0.700737	−	0.713420i	$-0.252855\pi$
$541$	32.5975	1.40147	0.700737	+	0.713420i	$0.252855\pi$
$542$	27.6733	1.18867
$543$	−40.1019	−1.72094
$544$	−3.43902	−0.147447
$545$	11.8028	0.505577
$546$	11.3410	0.485351
$547$	−21.4560	−0.917391	−0.458695	−	0.888594i	$-0.651683\pi$
$547$	−21.4560	−0.917391	−0.458695	+	0.888594i	$0.651683\pi$
$548$	−6.71150	−0.286701
$549$	−9.95295	−0.424782
$550$	13.3432	0.568955
$551$	−6.26705	−0.266985
$552$	−24.9142	−1.06042
$553$	19.6710	0.836498
$554$	−31.6402	−1.34426
$555$	−28.0316	−1.18988
$556$	−15.6691	−0.664516
$557$	11.6332	0.492914	0.246457	−	0.969154i	$-0.420734\pi$
$557$	11.6332	0.492914	0.246457	+	0.969154i	$0.420734\pi$
$558$	−14.8909	−0.630383
$559$	5.43348	0.229812
$560$	19.3449	0.817471
$561$	7.52143	0.317555
$562$	10.4013	0.438754
$563$	−12.6656	−0.533790	−0.266895	−	0.963726i	$-0.585998\pi$
$563$	−12.6656	−0.533790	−0.266895	+	0.963726i	$0.585998\pi$
$564$	−12.3757	−0.521112
$565$	43.4165	1.82655
$566$	15.7466	0.661880
$567$	48.0375	2.01738
$568$	24.5573	1.03040
$569$	−3.12308	−0.130926	−0.0654631	−	0.997855i	$-0.520852\pi$
$569$	−3.12308	−0.130926	−0.0654631	+	0.997855i	$0.520852\pi$
$570$	6.41846	0.268840
$571$	−4.06047	−0.169925	−0.0849627	−	0.996384i	$-0.527077\pi$
$571$	−4.06047	−0.169925	−0.0849627	+	0.996384i	$0.527077\pi$
$572$	−4.31546	−0.180438
$573$	7.06818	0.295278
$574$	16.8430	0.703014
$575$	10.5509	0.440002
$576$	12.4241	0.517672
$577$	22.8859	0.952754	0.476377	−	0.879241i	$-0.341950\pi$
$577$	22.8859	0.952754	0.476377	+	0.879241i	$0.341950\pi$
$578$	17.6635	0.734704
$579$	−4.55552	−0.189321
$580$	14.6208	0.607096
$581$	−18.5382	−0.769094
$582$	−32.9434	−1.36555
$583$	−57.5220	−2.38232
$584$	15.4835	0.640712
$585$	−5.01560	−0.207370
$586$	13.0774	0.540223
$587$	11.3057	0.466636	0.233318	−	0.972401i	$-0.425042\pi$
$587$	11.3057	0.466636	0.233318	+	0.972401i	$0.425042\pi$
$588$	20.1034	0.829052
$589$	8.84576	0.364483
$590$	17.9381	0.738498
$591$	−15.3343	−0.630768
$592$	−7.65339	−0.314552
$593$	−10.3222	−0.423881	−0.211940	−	0.977283i	$-0.567978\pi$
$593$	−10.3222	−0.423881	−0.211940	+	0.977283i	$0.567978\pi$
$594$	14.8190	0.608030
$595$	−9.37560	−0.384362
$596$	4.21036	0.172463
$597$	18.9039	0.773685
$598$	4.74043	0.193851
$599$	15.0388	0.614468	0.307234	−	0.951634i	$-0.400597\pi$
$599$	15.0388	0.614468	0.307234	+	0.951634i	$0.400597\pi$
$600$	−18.0800	−0.738112
$601$	−6.60911	−0.269591	−0.134796	−	0.990873i	$-0.543038\pi$
$601$	−6.60911	−0.269591	−0.134796	+	0.990873i	$0.543038\pi$
$602$	−21.7091	−0.884797
$603$	−2.48686	−0.101273
$604$	2.84832	0.115897
$605$	25.0707	1.01927
$606$	38.4284	1.56105
$607$	−8.08796	−0.328280	−0.164140	−	0.986437i	$-0.552485\pi$
$607$	−8.08796	−0.328280	−0.164140	+	0.986437i	$0.552485\pi$
$608$	−4.36652	−0.177086
$609$	−57.1699	−2.31664
$610$	19.1617	0.775836
$611$	7.98063	0.322862
$612$	−1.02919	−0.0416024
$613$	31.3376	1.26572	0.632858	−	0.774268i	$-0.281882\pi$
$613$	31.3376	1.26572	0.632858	+	0.774268i	$0.281882\pi$
$614$	12.6607	0.510944
$615$	−21.7640	−0.877609
$616$	58.4368	2.35449
$617$	40.6882	1.63804	0.819022	−	0.573762i	$-0.194517\pi$
$617$	40.6882	1.63804	0.819022	+	0.573762i	$0.194517\pi$
$618$	−28.3596	−1.14079
$619$	19.6814	0.791064	0.395532	−	0.918452i	$-0.370560\pi$
$619$	19.6814	0.791064	0.395532	+	0.918452i	$0.370560\pi$
$620$	−20.6368	−0.828795
$621$	11.7179	0.470221
$622$	−6.81981	−0.273450
$623$	−54.5562	−2.18575
$624$	−4.00107	−0.160171
$625$	−31.1787	−1.24715
$626$	−10.0025	−0.399780
$627$	9.54996	0.381389
$628$	−17.5155	−0.698944
$629$	3.70925	0.147898
$630$	20.0395	0.798392
$631$	−35.7543	−1.42335	−0.711677	−	0.702506i	$-0.752064\pi$
$631$	−35.7543	−1.42335	−0.711677	+	0.702506i	$0.752064\pi$
$632$	−14.0897	−0.560458
$633$	−2.13566	−0.0848849
$634$	0.0383111	0.00152153
$635$	−27.3726	−1.08625
$636$	22.9973	0.911902
$637$	−12.9639	−0.513650
$638$	−30.2206	−1.19644
$639$	12.5300	0.495680
$640$	0.419181	0.0165696
$641$	36.3868	1.43719	0.718596	−	0.695428i	$-0.244785\pi$
$641$	36.3868	1.43719	0.718596	+	0.695428i	$0.244785\pi$
$642$	−6.57647	−0.259553
$643$	−23.7001	−0.934639	−0.467319	−	0.884089i	$-0.654780\pi$
$643$	−23.7001	−0.934639	−0.467319	+	0.884089i	$0.654780\pi$
$644$	13.6339	0.537251
$645$	28.0518	1.10454
$646$	−0.849316	−0.0334159
$647$	7.25700	0.285302	0.142651	−	0.989773i	$-0.454437\pi$
$647$	7.25700	0.285302	0.142651	+	0.989773i	$0.454437\pi$
$648$	−34.4076	−1.35166
$649$	26.6898	1.04767
$650$	3.44008	0.134931
$651$	80.6936	3.16263
$652$	17.6972	0.693076
$653$	36.3473	1.42238	0.711190	−	0.703000i	$-0.248157\pi$
$653$	36.3473	1.42238	0.711190	+	0.703000i	$0.248157\pi$
$654$	9.75347	0.381391
$655$	20.2628	0.791733
$656$	−5.94215	−0.232002
$657$	7.90023	0.308217
$658$	−31.8861	−1.24305
$659$	−12.5293	−0.488070	−0.244035	−	0.969766i	$-0.578471\pi$
$659$	−12.5293	−0.488070	−0.244035	+	0.969766i	$0.578471\pi$
$660$	−22.2797	−0.867237
$661$	8.19654	0.318809	0.159404	−	0.987213i	$-0.449043\pi$
$661$	8.19654	0.318809	0.159404	+	0.987213i	$0.449043\pi$
$662$	−36.9389	−1.43567
$663$	1.93914	0.0753100
$664$	13.2783	0.515297
$665$	−11.9042	−0.461625
$666$	−7.92819	−0.307211
$667$	−23.8964	−0.925272
$668$	−3.53842	−0.136906
$669$	−17.7264	−0.685341
$670$	4.78777	0.184968
$671$	28.5105	1.10064
$672$	−39.8327	−1.53658
$673$	14.9712	0.577096	0.288548	−	0.957465i	$-0.406827\pi$
$673$	14.9712	0.577096	0.288548	+	0.957465i	$0.406827\pi$
$674$	32.8750	1.26630
$675$	8.50352	0.327301
$676$	9.76977	0.375760
$677$	−46.6090	−1.79133	−0.895665	−	0.444729i	$-0.853300\pi$
$677$	−46.6090	−1.79133	−0.895665	+	0.444729i	$0.853300\pi$
$678$	35.8781	1.37789
$679$	61.0996	2.34479
$680$	6.71542	0.257525
$681$	−14.6369	−0.560887
$682$	42.6554	1.63336
$683$	−6.98792	−0.267385	−0.133693	−	0.991023i	$-0.542684\pi$
$683$	−6.98792	−0.267385	−0.133693	+	0.991023i	$0.542684\pi$
$684$	−1.30676	−0.0499652
$685$	22.3444	0.853735
$686$	19.5532	0.746543
$687$	50.9726	1.94473
$688$	7.65889	0.291992
$689$	−14.8301	−0.564980
$690$	24.4737	0.931699
$691$	−5.91545	−0.225034	−0.112517	−	0.993650i	$-0.535891\pi$
$691$	−5.91545	−0.225034	−0.112517	+	0.993650i	$0.535891\pi$
$692$	9.64316	0.366578
$693$	29.8165	1.13264
$694$	−17.2057	−0.653119
$695$	52.1665	1.97879
$696$	40.9488	1.55216
$697$	2.87990	0.109084
$698$	−32.0832	−1.21437
$699$	−1.04102	−0.0393751
$700$	9.89398	0.373957
$701$	−3.19457	−0.120657	−0.0603286	−	0.998179i	$-0.519215\pi$
$701$	−3.19457	−0.120657	−0.0603286	+	0.998179i	$0.519215\pi$
$702$	3.82056	0.144198
$703$	4.70964	0.177627
$704$	−35.5893	−1.34132
$705$	41.2021	1.55176
$706$	−7.03354	−0.264711
$707$	−71.2724	−2.68048
$708$	−10.6706	−0.401025
$709$	−6.82801	−0.256431	−0.128216	−	0.991746i	$-0.540925\pi$
$709$	−6.82801	−0.256431	−0.128216	+	0.991746i	$0.540925\pi$
$710$	−24.1232	−0.905327
$711$	−7.18905	−0.269611
$712$	39.0767	1.46446
$713$	33.7291	1.26316
$714$	−7.74771	−0.289951
$715$	14.3673	0.537308
$716$	7.66628	0.286502
$717$	49.8529	1.86179
$718$	20.8149	0.776806
$719$	25.5592	0.953197	0.476598	−	0.879121i	$-0.341870\pi$
$719$	25.5592	0.953197	0.476598	+	0.879121i	$0.341870\pi$
$720$	−7.06986	−0.263478
$721$	52.5980	1.95885
$722$	−1.07838	−0.0401330
$723$	22.4572	0.835192
$724$	−15.7186	−0.584176
$725$	−17.3414	−0.644042
$726$	20.7177	0.768905
$727$	40.6579	1.50792	0.753960	−	0.656921i	$-0.228141\pi$
$727$	40.6579	1.50792	0.753960	+	0.656921i	$0.228141\pi$
$728$	15.0659	0.558380
$729$	2.13343	0.0790160
$730$	−15.2098	−0.562939
$731$	−3.71192	−0.137290
$732$	−11.3985	−0.421301
$733$	2.26763	0.0837568	0.0418784	−	0.999123i	$-0.486666\pi$
$733$	2.26763	0.0837568	0.0418784	+	0.999123i	$0.486666\pi$
$734$	28.9578	1.06885
$735$	−66.9298	−2.46874
$736$	−16.6496	−0.613714
$737$	7.12367	0.262404
$738$	−6.15551	−0.226588
$739$	10.1648	0.373917	0.186958	−	0.982368i	$-0.440137\pi$
$739$	10.1648	0.373917	0.186958	+	0.982368i	$0.440137\pi$
$740$	−10.9874	−0.403906
$741$	2.46213	0.0904485
$742$	59.2525	2.17523
$743$	1.69671	0.0622462	0.0311231	−	0.999516i	$-0.490092\pi$
$743$	1.69671	0.0622462	0.0311231	+	0.999516i	$0.490092\pi$
$744$	−57.7980	−2.11898
$745$	−14.0174	−0.513559
$746$	25.0144	0.915842
$747$	6.77504	0.247886
$748$	2.94814	0.107795
$749$	12.1972	0.445678
$750$	−14.3320	−0.523331
$751$	−6.70724	−0.244751	−0.122375	−	0.992484i	$-0.539051\pi$
$751$	−6.70724	−0.244751	−0.122375	+	0.992484i	$0.539051\pi$
$752$	11.2493	0.410219
$753$	64.3828	2.34624
$754$	−7.79134	−0.283744
$755$	−9.48282	−0.345115
$756$	10.9883	0.399640
$757$	46.8601	1.70316	0.851580	−	0.524225i	$-0.175645\pi$
$757$	46.8601	1.70316	0.851580	+	0.524225i	$0.175645\pi$
$758$	5.38541	0.195607
$759$	36.4142	1.32175
$760$	8.52657	0.309291
$761$	11.6599	0.422671	0.211336	−	0.977414i	$-0.432219\pi$
$761$	11.6599	0.422671	0.211336	+	0.977414i	$0.432219\pi$
$762$	−22.6198	−0.819431
$763$	−18.0896	−0.654886
$764$	2.77048	0.100233
$765$	3.42644	0.123883
$766$	−10.7787	−0.389451
$767$	6.88105	0.248460
$768$	34.3412	1.23918
$769$	−18.8033	−0.678065	−0.339033	−	0.940775i	$-0.610100\pi$
$769$	−18.8033	−0.678065	−0.339033	+	0.940775i	$0.610100\pi$
$770$	−57.4037	−2.06868
$771$	50.7426	1.82745
$772$	−1.78560	−0.0642653
$773$	16.5657	0.595828	0.297914	−	0.954593i	$-0.403709\pi$
$773$	16.5657	0.595828	0.297914	+	0.954593i	$0.403709\pi$
$774$	7.93389	0.285178
$775$	24.4768	0.879233
$776$	−43.7635	−1.57102
$777$	42.9627	1.54128
$778$	9.80564	0.351549
$779$	3.65660	0.131011
$780$	−5.74406	−0.205670
$781$	−35.8926	−1.28434
$782$	−3.23846	−0.115807
$783$	−19.2594	−0.688274
$784$	−18.2736	−0.652629
$785$	58.3137	2.08131
$786$	16.7446	0.597259
$787$	−35.0497	−1.24939	−0.624693	−	0.780871i	$-0.714776\pi$
$787$	−35.0497	−1.24939	−0.624693	+	0.780871i	$0.714776\pi$
$788$	−6.01050	−0.214115
$789$	−61.5180	−2.19010
$790$	13.8406	0.492426
$791$	−66.5424	−2.36597
$792$	−21.3565	−0.758871
$793$	7.35046	0.261022
$794$	15.4102	0.546889
$795$	−76.5641	−2.71545
$796$	7.40967	0.262629
$797$	−30.0406	−1.06409	−0.532046	−	0.846716i	$-0.678577\pi$
$797$	−30.0406	−1.06409	−0.532046	+	0.846716i	$0.678577\pi$
$798$	−9.83726	−0.348235
$799$	−5.45202	−0.192879
$800$	−12.0825	−0.427179
$801$	19.9383	0.704485
$802$	10.9316	0.386007
$803$	−22.6304	−0.798610
$804$	−2.84804	−0.100443
$805$	−45.3910	−1.59982
$806$	10.9972	0.387361
$807$	54.6160	1.92257
$808$	51.0500	1.79593
$809$	−28.2978	−0.994899	−0.497449	−	0.867493i	$-0.665730\pi$
$809$	−28.2978	−0.994899	−0.497449	+	0.867493i	$0.665730\pi$
$810$	33.7993	1.18759
$811$	12.2869	0.431451	0.215726	−	0.976454i	$-0.430788\pi$
$811$	12.2869	0.431451	0.215726	+	0.976454i	$0.430788\pi$
$812$	−22.4086	−0.786387
$813$	54.8054	1.92211
$814$	22.7105	0.796003
$815$	−58.9187	−2.06383
$816$	2.73336	0.0956868
$817$	−4.71302	−0.164888
$818$	27.3094	0.954850
$819$	7.68716	0.268611
$820$	−8.53073	−0.297906
$821$	−13.8772	−0.484319	−0.242159	−	0.970236i	$-0.577856\pi$
$821$	−13.8772	−0.484319	−0.242159	+	0.970236i	$0.577856\pi$
$822$	18.4647	0.644031
$823$	2.87462	0.100203	0.0501015	−	0.998744i	$-0.484046\pi$
$823$	2.87462	0.100203	0.0501015	+	0.998744i	$0.484046\pi$
$824$	−37.6741	−1.31244
$825$	26.4254	0.920013
$826$	−27.4928	−0.956596
$827$	15.9839	0.555814	0.277907	−	0.960608i	$-0.410359\pi$
$827$	15.9839	0.555814	0.277907	+	0.960608i	$0.410359\pi$
$828$	−4.98270	−0.173161
$829$	8.69494	0.301988	0.150994	−	0.988535i	$-0.451753\pi$
$829$	8.69494	0.301988	0.150994	+	0.988535i	$0.451753\pi$
$830$	−13.0435	−0.452747
$831$	−62.6616	−2.17371
$832$	−9.17547	−0.318102
$833$	8.85640	0.306856
$834$	43.1088	1.49274
$835$	11.7804	0.407676
$836$	3.74325	0.129463
$837$	27.1840	0.939617
$838$	0.886496	0.0306235
$839$	−8.44022	−0.291389	−0.145694	−	0.989330i	$-0.546542\pi$
$839$	−8.44022	−0.291389	−0.145694	+	0.989330i	$0.546542\pi$
$840$	77.7818	2.68373
$841$	10.2759	0.354342
$842$	29.3956	1.01304
$843$	20.5993	0.709476
$844$	−0.837104	−0.0288143
$845$	−32.5262	−1.11893
$846$	11.6532	0.400645
$847$	−38.4247	−1.32029
$848$	−20.9041	−0.717848
$849$	31.1853	1.07028
$850$	−2.35011	−0.0806083
$851$	17.9580	0.615591
$852$	14.3499	0.491618
$853$	−40.4587	−1.38528	−0.692639	−	0.721284i	$-0.743552\pi$
$853$	−40.4587	−1.38528	−0.692639	+	0.721284i	$0.743552\pi$
$854$	−29.3682	−1.00496
$855$	4.35055	0.148786
$856$	−8.73647	−0.298606
$857$	−45.2245	−1.54484	−0.772420	−	0.635113i	$-0.780954\pi$
$857$	−45.2245	−1.54484	−0.772420	+	0.635113i	$0.780954\pi$
$858$	11.8727	0.405328
$859$	−3.50684	−0.119652	−0.0598259	−	0.998209i	$-0.519055\pi$
$859$	−3.50684	−0.119652	−0.0598259	+	0.998209i	$0.519055\pi$
$860$	10.9953	0.374937
$861$	33.3566	1.13679
$862$	19.7915	0.674102
$863$	21.1476	0.719874	0.359937	−	0.932977i	$-0.382798\pi$
$863$	21.1476	0.719874	0.359937	+	0.932977i	$0.382798\pi$
$864$	−13.4188	−0.456518
$865$	−32.1047	−1.09159
$866$	−28.1479	−0.956503
$867$	34.9815	1.18803
$868$	31.6291	1.07356
$869$	20.5932	0.698578
$870$	−40.2248	−1.36375
$871$	1.83659	0.0622306
$872$	12.9569	0.438777
$873$	−22.3297	−0.755745
$874$	−4.11187	−0.139086
$875$	26.5813	0.898611
$876$	9.04764	0.305692
$877$	49.5793	1.67417	0.837087	−	0.547069i	$-0.184257\pi$
$877$	49.5793	1.67417	0.837087	+	0.547069i	$0.184257\pi$
$878$	28.9727	0.977782
$879$	25.8990	0.873553
$880$	20.2518	0.682688
$881$	9.95332	0.335336	0.167668	−	0.985844i	$-0.446376\pi$
$881$	9.95332	0.335336	0.167668	+	0.985844i	$0.446376\pi$
$882$	−18.9297	−0.637398
$883$	29.9754	1.00875	0.504377	−	0.863484i	$-0.331722\pi$
$883$	29.9754	1.00875	0.504377	+	0.863484i	$0.331722\pi$
$884$	0.760076	0.0255641
$885$	35.5253	1.19417
$886$	−6.11687	−0.205500
$887$	−33.2140	−1.11522	−0.557609	−	0.830104i	$-0.688281\pi$
$887$	−33.2140	−1.11522	−0.557609	+	0.830104i	$0.688281\pi$
$888$	−30.7727	−1.03266
$889$	41.9526	1.40704
$890$	−38.3858	−1.28670
$891$	50.2895	1.68476
$892$	−6.94812	−0.232640
$893$	−6.92243	−0.231650
$894$	−11.5836	−0.387413
$895$	−25.5231	−0.853143
$896$	−0.642458	−0.0214630
$897$	9.38815	0.313461
$898$	23.2823	0.776941
$899$	−55.4368	−1.84892
$900$	−3.61589	−0.120530
$901$	10.1313	0.337521
$902$	17.6326	0.587103
$903$	−42.9936	−1.43074
$904$	47.6620	1.58521
$905$	52.3313	1.73955
$906$	−7.83631	−0.260344
$907$	−36.5945	−1.21510	−0.607550	−	0.794281i	$-0.707848\pi$
$907$	−36.5945	−1.21510	−0.607550	+	0.794281i	$0.707848\pi$
$908$	−5.73715	−0.190394
$909$	26.0475	0.863941
$910$	−14.7996	−0.490601
$911$	−14.3638	−0.475895	−0.237948	−	0.971278i	$-0.576475\pi$
$911$	−14.3638	−0.475895	−0.237948	+	0.971278i	$0.576475\pi$
$912$	3.47055	0.114921
$913$	−19.4073	−0.642287
$914$	10.2735	0.339819
$915$	37.9487	1.25454
$916$	19.9795	0.660141
$917$	−31.0558	−1.02555
$918$	−2.61005	−0.0861443
$919$	15.2635	0.503496	0.251748	−	0.967793i	$-0.418995\pi$
$919$	15.2635	0.503496	0.251748	+	0.967793i	$0.418995\pi$
$920$	32.5120	1.07189
$921$	25.0737	0.826208
$922$	30.4410	1.00252
$923$	−9.25367	−0.304588
$924$	34.1470	1.12335
$925$	13.0319	0.428486
$926$	−38.7738	−1.27419
$927$	−19.2227	−0.631355
$928$	27.3652	0.898307
$929$	6.56596	0.215422	0.107711	−	0.994182i	$-0.465648\pi$
$929$	6.56596	0.215422	0.107711	+	0.994182i	$0.465648\pi$
$930$	56.7762	1.86176
$931$	11.2450	0.368539
$932$	−0.408044	−0.0133659
$933$	−13.5062	−0.442174
$934$	−34.7520	−1.13712
$935$	−9.81514	−0.320989
$936$	−5.50605	−0.179971
$937$	−30.5558	−0.998216	−0.499108	−	0.866540i	$-0.666339\pi$
$937$	−30.5558	−0.998216	−0.499108	+	0.866540i	$0.666339\pi$
$938$	−7.33798	−0.239594
$939$	−19.8094	−0.646454
$940$	16.1498	0.526748
$941$	0.332581	0.0108418	0.00542091	−	0.999985i	$-0.498274\pi$
$941$	0.332581	0.0108418	0.00542091	+	0.999985i	$0.498274\pi$
$942$	48.1887	1.57007
$943$	13.9427	0.454037
$944$	9.69934	0.315687
$945$	−36.5830	−1.19004
$946$	−22.7268	−0.738913
$947$	−22.4661	−0.730050	−0.365025	−	0.930998i	$-0.618940\pi$
$947$	−22.4661	−0.730050	−0.365025	+	0.930998i	$0.618940\pi$
$948$	−8.23318	−0.267401
$949$	−5.83448	−0.189395
$950$	−2.98394	−0.0968118
$951$	0.0758729	0.00246035
$952$	−10.2924	−0.333578
$953$	−47.8901	−1.55131	−0.775657	−	0.631155i	$-0.782581\pi$
$953$	−47.8901	−1.55131	−0.775657	+	0.631155i	$0.782581\pi$
$954$	−21.6546	−0.701095
$955$	−9.22368	−0.298471
$956$	19.5406	0.631989
$957$	−59.8501	−1.93468
$958$	14.8183	0.478758
$959$	−34.2461	−1.10586
$960$	−47.3708	−1.52889
$961$	47.2474	1.52411
$962$	5.85513	0.188777
$963$	−4.45765	−0.143646
$964$	8.80244	0.283507
$965$	5.94476	0.191368
$966$	−37.5097	−1.20685
$967$	−40.3551	−1.29773	−0.648867	−	0.760902i	$-0.724757\pi$
$967$	−40.3551	−1.29773	−0.648867	+	0.760902i	$0.724757\pi$
$968$	27.5223	0.884599
$969$	−1.68202	−0.0540343
$970$	42.9898	1.38032
$971$	40.8700	1.31158	0.655790	−	0.754944i	$-0.272336\pi$
$971$	40.8700	1.31158	0.655790	+	0.754944i	$0.272336\pi$
$972$	−12.3882	−0.397352
$973$	−79.9530	−2.56318
$974$	−39.8140	−1.27572
$975$	6.81287	0.218187
$976$	10.3610	0.331648
$977$	30.5769	0.978241	0.489121	−	0.872216i	$-0.337318\pi$
$977$	30.5769	0.978241	0.489121	+	0.872216i	$0.337318\pi$
$978$	−48.6886	−1.55689
$979$	−57.1138	−1.82537
$980$	−26.2341	−0.838019
$981$	6.61108	0.211076
$982$	26.3826	0.841901
$983$	−5.87764	−0.187467	−0.0937337	−	0.995597i	$-0.529880\pi$
$983$	−5.87764	−0.187467	−0.0937337	+	0.995597i	$0.529880\pi$
$984$	−23.8922	−0.761655
$985$	20.0106	0.637590
$986$	5.32271	0.169509
$987$	−63.1485	−2.01004
$988$	0.965068	0.0307029
$989$	−17.9709	−0.571440
$990$	20.9790	0.666755
$991$	41.6381	1.32268	0.661339	−	0.750087i	$-0.269988\pi$
$991$	41.6381	1.32268	0.661339	+	0.750087i	$0.269988\pi$
$992$	−38.6252	−1.22635
$993$	−73.1553	−2.32151
$994$	36.9724	1.17269
$995$	−24.6688	−0.782053
$996$	7.75903	0.245854
$997$	−32.2368	−1.02095	−0.510474	−	0.859893i	$-0.670530\pi$
$997$	−32.2368	−1.02095	−0.510474	+	0.859893i	$0.670530\pi$
$998$	23.0586	0.729906
$999$	14.4733	0.457914

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4009.2.a.c.1.27	✓	71

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4009.2.a.c.1.27	✓	71	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:	\( N \)	\(=\)	\( 4009 = 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4009.a (trivial)

\(f(q)\)	\(=\)	\(q-1.07838 q^{2} -2.13566 q^{3} -0.837104 q^{4} +2.78695 q^{5} +2.30305 q^{6} -4.27141 q^{7} +3.05947 q^{8} +1.56105 q^{9} +O(q^{10})\)	\(q-1.07838 q^{2} -2.13566 q^{3} -0.837104 q^{4} +2.78695 q^{5} +2.30305 q^{6} -4.27141 q^{7} +3.05947 q^{8} +1.56105 q^{9} -3.00538 q^{10} -4.47166 q^{11} +1.78777 q^{12} -1.15286 q^{13} +4.60619 q^{14} -5.95197 q^{15} -1.62505 q^{16} +0.787588 q^{17} -1.68340 q^{18} +1.00000 q^{19} -2.33296 q^{20} +9.12229 q^{21} +4.82214 q^{22} +3.81302 q^{23} -6.53398 q^{24} +2.76707 q^{25} +1.24322 q^{26} +3.07312 q^{27} +3.57562 q^{28} -6.26705 q^{29} +6.41846 q^{30} +8.84576 q^{31} -4.36652 q^{32} +9.54996 q^{33} -0.849316 q^{34} -11.9042 q^{35} -1.30676 q^{36} +4.70964 q^{37} -1.07838 q^{38} +2.46213 q^{39} +8.52657 q^{40} +3.65660 q^{41} -9.83726 q^{42} -4.71302 q^{43} +3.74325 q^{44} +4.35055 q^{45} -4.11187 q^{46} -6.92243 q^{47} +3.47055 q^{48} +11.2450 q^{49} -2.98394 q^{50} -1.68202 q^{51} +0.965068 q^{52} +12.8637 q^{53} -3.31397 q^{54} -12.4623 q^{55} -13.0682 q^{56} -2.13566 q^{57} +6.75824 q^{58} -5.96865 q^{59} +4.98242 q^{60} -6.37582 q^{61} -9.53905 q^{62} -6.66788 q^{63} +7.95885 q^{64} -3.21297 q^{65} -10.2984 q^{66} -1.59307 q^{67} -0.659293 q^{68} -8.14332 q^{69} +12.8372 q^{70} +8.02668 q^{71} +4.77597 q^{72} +5.06085 q^{73} -5.07876 q^{74} -5.90952 q^{75} -0.837104 q^{76} +19.1003 q^{77} -2.65510 q^{78} -4.60528 q^{79} -4.52892 q^{80} -11.2463 q^{81} -3.94319 q^{82} +4.34006 q^{83} -7.63631 q^{84} +2.19496 q^{85} +5.08241 q^{86} +13.3843 q^{87} -13.6809 q^{88} +12.7724 q^{89} -4.69153 q^{90} +4.92436 q^{91} -3.19190 q^{92} -18.8915 q^{93} +7.46499 q^{94} +2.78695 q^{95} +9.32541 q^{96} -14.3043 q^{97} -12.1263 q^{98} -6.98048 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 71 q - 15 q^{2} - 8 q^{3} + 69 q^{4} - 18 q^{5} - 9 q^{6} - 19 q^{7} - 39 q^{8} + 63 q^{9}+O(q^{10}) \) 71 * q - 15 * q^2 - 8 * q^3 + 69 * q^4 - 18 * q^5 - 9 * q^6 - 19 * q^7 - 39 * q^8 + 63 * q^9	\( 71 q - 15 q^{2} - 8 q^{3} + 69 q^{4} - 18 q^{5} - 9 q^{6} - 19 q^{7} - 39 q^{8} + 63 q^{9} - 10 q^{10} - 52 q^{11} - 9 q^{12} - 15 q^{13} - 53 q^{14} - 33 q^{15} + 53 q^{16} - 10 q^{17} - 35 q^{18} + 71 q^{19} - 33 q^{20} - 38 q^{21} - 6 q^{22} - 65 q^{23} - 30 q^{24} + 51 q^{25} - 4 q^{26} - 23 q^{27} - 29 q^{28} - 97 q^{29} - 27 q^{30} - 53 q^{31} - 78 q^{32} - 17 q^{33} - 24 q^{34} - 38 q^{35} + 24 q^{36} - 33 q^{37} - 15 q^{38} - 86 q^{39} + 25 q^{40} - 69 q^{41} + 64 q^{42} - 10 q^{43} - 94 q^{44} - 34 q^{45} - 6 q^{46} - 37 q^{47} - q^{48} + 74 q^{49} - 41 q^{50} - 46 q^{51} - 30 q^{52} - 50 q^{53} - 17 q^{54} - 30 q^{55} - 116 q^{56} - 8 q^{57} + 11 q^{58} - 93 q^{59} - 56 q^{60} - 18 q^{61} - q^{62} - 84 q^{63} + 93 q^{64} - 78 q^{65} - 53 q^{66} - 5 q^{67} - 9 q^{68} - 69 q^{69} - 10 q^{70} - 221 q^{71} - 73 q^{72} - 34 q^{73} - 58 q^{74} - 70 q^{75} + 69 q^{76} - 2 q^{77} + 7 q^{78} - 68 q^{79} - 71 q^{80} + 39 q^{81} + 26 q^{82} - 45 q^{83} - 10 q^{84} - 44 q^{85} - 80 q^{86} - 7 q^{87} - 46 q^{88} - 143 q^{89} + 41 q^{90} - 30 q^{91} - 46 q^{92} + 32 q^{93} + 41 q^{94} - 18 q^{95} - 140 q^{96} - 18 q^{97} - 97 q^{98} - 142 q^{99}+O(q^{100}) \) 71 * q - 15 * q^2 - 8 * q^3 + 69 * q^4 - 18 * q^5 - 9 * q^6 - 19 * q^7 - 39 * q^8 + 63 * q^9 - 10 * q^10 - 52 * q^11 - 9 * q^12 - 15 * q^13 - 53 * q^14 - 33 * q^15 + 53 * q^16 - 10 * q^17 - 35 * q^18 + 71 * q^19 - 33 * q^20 - 38 * q^21 - 6 * q^22 - 65 * q^23 - 30 * q^24 + 51 * q^25 - 4 * q^26 - 23 * q^27 - 29 * q^28 - 97 * q^29 - 27 * q^30 - 53 * q^31 - 78 * q^32 - 17 * q^33 - 24 * q^34 - 38 * q^35 + 24 * q^36 - 33 * q^37 - 15 * q^38 - 86 * q^39 + 25 * q^40 - 69 * q^41 + 64 * q^42 - 10 * q^43 - 94 * q^44 - 34 * q^45 - 6 * q^46 - 37 * q^47 - q^48 + 74 * q^49 - 41 * q^50 - 46 * q^51 - 30 * q^52 - 50 * q^53 - 17 * q^54 - 30 * q^55 - 116 * q^56 - 8 * q^57 + 11 * q^58 - 93 * q^59 - 56 * q^60 - 18 * q^61 - q^62 - 84 * q^63 + 93 * q^64 - 78 * q^65 - 53 * q^66 - 5 * q^67 - 9 * q^68 - 69 * q^69 - 10 * q^70 - 221 * q^71 - 73 * q^72 - 34 * q^73 - 58 * q^74 - 70 * q^75 + 69 * q^76 - 2 * q^77 + 7 * q^78 - 68 * q^79 - 71 * q^80 + 39 * q^81 + 26 * q^82 - 45 * q^83 - 10 * q^84 - 44 * q^85 - 80 * q^86 - 7 * q^87 - 46 * q^88 - 143 * q^89 + 41 * q^90 - 30 * q^91 - 46 * q^92 + 32 * q^93 + 41 * q^94 - 18 * q^95 - 140 * q^96 - 18 * q^97 - 97 * q^98 - 142 * q^99

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