LMFDB - Embedded newform 1339.2.a.e.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1339,2,Mod(1,1339)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1339, 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("1339.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1339 = 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1339.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:	$10.6919688306$
Analytic rank:	$1$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	1339.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.33589 q^{2} +2.00110 q^{3} -0.215389 q^{4} -3.88298 q^{5} +2.67326 q^{6} +2.54624 q^{7} -2.95952 q^{8} +1.00441 q^{9} +O(q^{10})$	\(q+1.33589 q^{2} +2.00110 q^{3} -0.215389 q^{4} -3.88298 q^{5} +2.67326 q^{6} +2.54624 q^{7} -2.95952 q^{8} +1.00441 q^{9} -5.18725 q^{10} -3.83983 q^{11} -0.431016 q^{12} -1.00000 q^{13} +3.40150 q^{14} -7.77025 q^{15} -3.52283 q^{16} -3.24118 q^{17} +1.34178 q^{18} +1.25285 q^{19} +0.836354 q^{20} +5.09528 q^{21} -5.12961 q^{22} -3.59617 q^{23} -5.92231 q^{24} +10.0776 q^{25} -1.33589 q^{26} -3.99338 q^{27} -0.548432 q^{28} -4.68376 q^{29} -10.3802 q^{30} +5.40323 q^{31} +1.21292 q^{32} -7.68390 q^{33} -4.32987 q^{34} -9.88700 q^{35} -0.216339 q^{36} -4.58286 q^{37} +1.67367 q^{38} -2.00110 q^{39} +11.4918 q^{40} -10.5512 q^{41} +6.80675 q^{42} -4.94298 q^{43} +0.827059 q^{44} -3.90010 q^{45} -4.80410 q^{46} +12.8196 q^{47} -7.04954 q^{48} -0.516680 q^{49} +13.4626 q^{50} -6.48593 q^{51} +0.215389 q^{52} -4.12024 q^{53} -5.33473 q^{54} +14.9100 q^{55} -7.53565 q^{56} +2.50708 q^{57} -6.25700 q^{58} +10.4487 q^{59} +1.67363 q^{60} +13.8061 q^{61} +7.21814 q^{62} +2.55746 q^{63} +8.66599 q^{64} +3.88298 q^{65} -10.2649 q^{66} -8.63783 q^{67} +0.698116 q^{68} -7.19631 q^{69} -13.2080 q^{70} -10.1729 q^{71} -2.97257 q^{72} +7.80471 q^{73} -6.12221 q^{74} +20.1662 q^{75} -0.269851 q^{76} -9.77712 q^{77} -2.67326 q^{78} -2.73046 q^{79} +13.6791 q^{80} -11.0044 q^{81} -14.0953 q^{82} +0.267981 q^{83} -1.09747 q^{84} +12.5855 q^{85} -6.60330 q^{86} -9.37268 q^{87} +11.3641 q^{88} +5.09593 q^{89} -5.21012 q^{90} -2.54624 q^{91} +0.774578 q^{92} +10.8124 q^{93} +17.1256 q^{94} -4.86480 q^{95} +2.42719 q^{96} -1.27333 q^{97} -0.690230 q^{98} -3.85676 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q - q^{2} - 6 q^{3} + 15 q^{4} - 18 q^{5} - 8 q^{6} - 2 q^{7} + 6 q^{8} + 11 q^{9}+O(q^{10}) $ 21 * q - q^2 - 6 * q^3 + 15 * q^4 - 18 * q^5 - 8 * q^6 - 2 * q^7 + 6 * q^8 + 11 * q^9	\( 21 q - q^{2} - 6 q^{3} + 15 q^{4} - 18 q^{5} - 8 q^{6} - 2 q^{7} + 6 q^{8} + 11 q^{9} - 10 q^{10} - 5 q^{11} - 22 q^{12} - 21 q^{13} - 24 q^{14} - q^{15} - 5 q^{16} - 18 q^{17} + 10 q^{18} - 6 q^{19} - 30 q^{20} - 17 q^{21} - 8 q^{22} - 14 q^{23} - 13 q^{24} + 11 q^{25} + q^{26} - 33 q^{27} - 2 q^{28} - 36 q^{29} + 2 q^{30} + q^{31} - 9 q^{32} - 11 q^{33} - 25 q^{34} - 37 q^{35} + 3 q^{36} + 5 q^{37} - 13 q^{38} + 6 q^{39} - 2 q^{40} - 32 q^{41} + 7 q^{42} + 2 q^{43} + 4 q^{44} - 32 q^{45} - 5 q^{46} - 12 q^{47} - 18 q^{48} + 5 q^{49} - 2 q^{50} - 27 q^{51} - 15 q^{52} - 49 q^{53} - 31 q^{54} - 9 q^{55} - 53 q^{56} + 14 q^{57} - 2 q^{58} - 34 q^{59} + 25 q^{60} - 27 q^{61} - 12 q^{62} + 41 q^{63} - 70 q^{64} + 18 q^{65} - 15 q^{66} - 12 q^{67} - 20 q^{68} - 70 q^{69} + 70 q^{70} - 26 q^{71} - 14 q^{72} + 23 q^{73} + 20 q^{74} - 9 q^{75} - 36 q^{76} - 62 q^{77} + 8 q^{78} - 7 q^{79} - 41 q^{80} - 3 q^{81} - 33 q^{82} - q^{83} - 48 q^{84} + 10 q^{85} - 23 q^{86} - 7 q^{87} + 9 q^{88} - 16 q^{89} - 30 q^{90} + 2 q^{91} - 27 q^{92} + 2 q^{93} - 37 q^{94} - 35 q^{95} + 55 q^{96} - 30 q^{97} - 43 q^{98} - 42 q^{99}+O(q^{100}) \) 21 * q - q^2 - 6 * q^3 + 15 * q^4 - 18 * q^5 - 8 * q^6 - 2 * q^7 + 6 * q^8 + 11 * q^9 - 10 * q^10 - 5 * q^11 - 22 * q^12 - 21 * q^13 - 24 * q^14 - q^15 - 5 * q^16 - 18 * q^17 + 10 * q^18 - 6 * q^19 - 30 * q^20 - 17 * q^21 - 8 * q^22 - 14 * q^23 - 13 * q^24 + 11 * q^25 + q^26 - 33 * q^27 - 2 * q^28 - 36 * q^29 + 2 * q^30 + q^31 - 9 * q^32 - 11 * q^33 - 25 * q^34 - 37 * q^35 + 3 * q^36 + 5 * q^37 - 13 * q^38 + 6 * q^39 - 2 * q^40 - 32 * q^41 + 7 * q^42 + 2 * q^43 + 4 * q^44 - 32 * q^45 - 5 * q^46 - 12 * q^47 - 18 * q^48 + 5 * q^49 - 2 * q^50 - 27 * q^51 - 15 * q^52 - 49 * q^53 - 31 * q^54 - 9 * q^55 - 53 * q^56 + 14 * q^57 - 2 * q^58 - 34 * q^59 + 25 * q^60 - 27 * q^61 - 12 * q^62 + 41 * q^63 - 70 * q^64 + 18 * q^65 - 15 * q^66 - 12 * q^67 - 20 * q^68 - 70 * q^69 + 70 * q^70 - 26 * q^71 - 14 * q^72 + 23 * q^73 + 20 * q^74 - 9 * q^75 - 36 * q^76 - 62 * q^77 + 8 * q^78 - 7 * q^79 - 41 * q^80 - 3 * q^81 - 33 * q^82 - q^83 - 48 * q^84 + 10 * q^85 - 23 * q^86 - 7 * q^87 + 9 * q^88 - 16 * q^89 - 30 * q^90 + 2 * q^91 - 27 * q^92 + 2 * q^93 - 37 * q^94 - 35 * q^95 + 55 * q^96 - 30 * q^97 - 43 * q^98 - 42 * 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 $

$2$	1.33589	0.944619	0.472310	−	0.881433i	$-0.343420\pi$
$2$	1.33589	0.944619	0.472310	+	0.881433i	$0.343420\pi$
$3$	2.00110	1.15534	0.577668	−	0.816272i	$-0.303963\pi$
$3$	2.00110	1.15534	0.577668	+	0.816272i	$0.303963\pi$
$4$	−0.215389	−0.107695
$5$	−3.88298	−1.73652	−0.868262	−	0.496106i	$-0.834763\pi$
$5$	−3.88298	−1.73652	−0.868262	+	0.496106i	$0.834763\pi$
$6$	2.67326	1.09135
$7$	2.54624	0.962387	0.481193	−	0.876614i	$-0.340203\pi$
$7$	2.54624	0.962387	0.481193	+	0.876614i	$0.340203\pi$
$8$	−2.95952	−1.04635
$9$	1.00441	0.334803
$10$	−5.18725	−1.64035
$11$	−3.83983	−1.15775	−0.578877	−	0.815415i	$-0.696509\pi$
$11$	−3.83983	−1.15775	−0.578877	+	0.815415i	$0.696509\pi$
$12$	−0.431016	−0.124424
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	3.40150	0.909089
$15$	−7.77025	−2.00627
$16$	−3.52283	−0.880707
$17$	−3.24118	−0.786102	−0.393051	−	0.919517i	$-0.628580\pi$
$17$	−3.24118	−0.786102	−0.393051	+	0.919517i	$0.628580\pi$
$18$	1.34178	0.316261
$19$	1.25285	0.287423	0.143712	−	0.989620i	$-0.454096\pi$
$19$	1.25285	0.287423	0.143712	+	0.989620i	$0.454096\pi$
$20$	0.836354	0.187014
$21$	5.09528	1.11188
$22$	−5.12961	−1.09364
$23$	−3.59617	−0.749854	−0.374927	−	0.927054i	$-0.622332\pi$
$23$	−3.59617	−0.749854	−0.374927	+	0.927054i	$0.622332\pi$
$24$	−5.92231	−1.20889
$25$	10.0776	2.01551
$26$	−1.33589	−0.261990
$27$	−3.99338	−0.768527
$28$	−0.548432	−0.103644
$29$	−4.68376	−0.869752	−0.434876	−	0.900490i	$-0.643208\pi$
$29$	−4.68376	−0.869752	−0.434876	+	0.900490i	$0.643208\pi$
$30$	−10.3802	−1.89516
$31$	5.40323	0.970449	0.485225	−	0.874390i	$-0.338738\pi$
$31$	5.40323	0.970449	0.485225	+	0.874390i	$0.338738\pi$
$32$	1.21292	0.214417
$33$	−7.68390	−1.33759
$34$	−4.32987	−0.742567
$35$	−9.88700	−1.67121
$36$	−0.216339	−0.0360565
$37$	−4.58286	−0.753417	−0.376708	−	0.926332i	$-0.622944\pi$
$37$	−4.58286	−0.753417	−0.376708	+	0.926332i	$0.622944\pi$
$38$	1.67367	0.271506
$39$	−2.00110	−0.320433
$40$	11.4918	1.81701
$41$	−10.5512	−1.64783	−0.823913	−	0.566716i	$-0.808214\pi$
$41$	−10.5512	−1.64783	−0.823913	+	0.566716i	$0.808214\pi$
$42$	6.80675	1.05030
$43$	−4.94298	−0.753798	−0.376899	−	0.926254i	$-0.623010\pi$
$43$	−4.94298	−0.753798	−0.376899	+	0.926254i	$0.623010\pi$
$44$	0.827059	0.124684
$45$	−3.90010	−0.581393
$46$	−4.80410	−0.708326
$47$	12.8196	1.86993	0.934963	−	0.354744i	$-0.115432\pi$
$47$	12.8196	1.86993	0.934963	+	0.354744i	$0.115432\pi$
$48$	−7.04954	−1.01751
$49$	−0.516680	−0.0738115
$50$	13.4626	1.90389
$51$	−6.48593	−0.908212
$52$	0.215389	0.0298691
$53$	−4.12024	−0.565958	−0.282979	−	0.959126i	$-0.591323\pi$
$53$	−4.12024	−0.565958	−0.282979	+	0.959126i	$0.591323\pi$
$54$	−5.33473	−0.725965
$55$	14.9100	2.01047
$56$	−7.53565	−1.00699
$57$	2.50708	0.332071
$58$	−6.25700	−0.821585
$59$	10.4487	1.36030	0.680152	−	0.733071i	$-0.261914\pi$
$59$	10.4487	1.36030	0.680152	+	0.733071i	$0.261914\pi$
$60$	1.67363	0.216065
$61$	13.8061	1.76769	0.883846	−	0.467778i	$-0.154945\pi$
$61$	13.8061	1.76769	0.883846	+	0.467778i	$0.154945\pi$
$62$	7.21814	0.916705
$63$	2.55746	0.322210
$64$	8.66599	1.08325
$65$	3.88298	0.481625
$66$	−10.2649	−1.26352
$67$	−8.63783	−1.05528	−0.527639	−	0.849469i	$-0.676923\pi$
$67$	−8.63783	−1.05528	−0.527639	+	0.849469i	$0.676923\pi$
$68$	0.698116	0.0846590
$69$	−7.19631	−0.866334
$70$	−13.2080	−1.57865
$71$	−10.1729	−1.20731	−0.603653	−	0.797247i	$-0.706289\pi$
$71$	−10.1729	−1.20731	−0.603653	+	0.797247i	$0.706289\pi$
$72$	−2.97257	−0.350321
$73$	7.80471	0.913473	0.456736	−	0.889602i	$-0.349018\pi$
$73$	7.80471	0.913473	0.456736	+	0.889602i	$0.349018\pi$
$74$	−6.12221	−0.711692
$75$	20.1662	2.32860
$76$	−0.269851	−0.0309540
$77$	−9.77712	−1.11421
$78$	−2.67326	−0.302687
$79$	−2.73046	−0.307201	−0.153600	−	0.988133i	$-0.549087\pi$
$79$	−2.73046	−0.307201	−0.153600	+	0.988133i	$0.549087\pi$
$80$	13.6791	1.52937
$81$	−11.0044	−1.22271
$82$	−14.0953	−1.55657
$83$	0.267981	0.0294148	0.0147074	−	0.999892i	$-0.495318\pi$
$83$	0.267981	0.0294148	0.0147074	+	0.999892i	$0.495318\pi$
$84$	−1.09747	−0.119744
$85$	12.5855	1.36508
$86$	−6.60330	−0.712052
$87$	−9.37268	−1.00486
$88$	11.3641	1.21141
$89$	5.09593	0.540167	0.270084	−	0.962837i	$-0.412949\pi$
$89$	5.09593	0.540167	0.270084	+	0.962837i	$0.412949\pi$
$90$	−5.21012	−0.549195
$91$	−2.54624	−0.266918
$92$	0.774578	0.0807553
$93$	10.8124	1.12120
$94$	17.1256	1.76637
$95$	−4.86480	−0.499118
$96$	2.42719	0.247724
$97$	−1.27333	−0.129287	−0.0646436	−	0.997908i	$-0.520591\pi$
$97$	−1.27333	−0.129287	−0.0646436	+	0.997908i	$0.520591\pi$
$98$	−0.690230	−0.0697237
$99$	−3.85676	−0.387619
$100$	−2.17060	−0.217060
$101$	−16.1375	−1.60574	−0.802870	−	0.596154i	$-0.796695\pi$
$101$	−16.1375	−1.60574	−0.802870	+	0.596154i	$0.796695\pi$
$102$	−8.66451	−0.857915
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	2.95952	0.290205
$105$	−19.7849	−1.93081
$106$	−5.50420	−0.534615
$107$	7.59643	0.734374	0.367187	−	0.930147i	$-0.380321\pi$
$107$	7.59643	0.734374	0.367187	+	0.930147i	$0.380321\pi$
$108$	0.860132	0.0827663
$109$	−9.42933	−0.903166	−0.451583	−	0.892229i	$-0.649141\pi$
$109$	−9.42933	−0.903166	−0.451583	+	0.892229i	$0.649141\pi$
$110$	19.9182	1.89912
$111$	−9.17076	−0.870450
$112$	−8.96995	−0.847581
$113$	11.2501	1.05832	0.529159	−	0.848523i	$-0.322508\pi$
$113$	11.2501	1.05832	0.529159	+	0.848523i	$0.322508\pi$
$114$	3.34919	0.313680
$115$	13.9639	1.30214
$116$	1.00883	0.0936677
$117$	−1.00441	−0.0928576
$118$	13.9583	1.28497
$119$	−8.25281	−0.756534
$120$	22.9962	2.09926
$121$	3.74432	0.340393
$122$	18.4435	1.66980
$123$	−21.1141	−1.90379
$124$	−1.16380	−0.104512
$125$	−19.7161	−1.76346
$126$	3.41650	0.304366
$127$	4.19682	0.372407	0.186204	−	0.982511i	$-0.440382\pi$
$127$	4.19682	0.372407	0.186204	+	0.982511i	$0.440382\pi$
$128$	9.15099	0.808841
$129$	−9.89141	−0.870890
$130$	5.18725	0.454952
$131$	−11.6486	−1.01774	−0.508872	−	0.860842i	$-0.669937\pi$
$131$	−11.6486	−1.01774	−0.508872	+	0.860842i	$0.669937\pi$
$132$	1.65503	0.144052
$133$	3.19005	0.276613
$134$	−11.5392	−0.996836
$135$	15.5062	1.33456
$136$	9.59235	0.822537
$137$	19.0192	1.62492	0.812461	−	0.583016i	$-0.198127\pi$
$137$	19.0192	1.62492	0.812461	+	0.583016i	$0.198127\pi$
$138$	−9.61350	−0.818355
$139$	8.74299	0.741570	0.370785	−	0.928719i	$-0.379089\pi$
$139$	8.74299	0.741570	0.370785	+	0.928719i	$0.379089\pi$
$140$	2.12955	0.179980
$141$	25.6533	2.16040
$142$	−13.5900	−1.14044
$143$	3.83983	0.321103
$144$	−3.53836	−0.294863
$145$	18.1870	1.51035
$146$	10.4263	0.862884
$147$	−1.03393	−0.0852771
$148$	0.987099	0.0811390
$149$	20.2796	1.66137	0.830685	−	0.556743i	$-0.187949\pi$
$149$	20.2796	1.66137	0.830685	+	0.556743i	$0.187949\pi$
$150$	26.9400	2.19964
$151$	−0.148377	−0.0120748	−0.00603739	−	0.999982i	$-0.501922\pi$
$151$	−0.148377	−0.0120748	−0.00603739	+	0.999982i	$0.501922\pi$
$152$	−3.70784	−0.300745
$153$	−3.25547	−0.263189
$154$	−13.0612	−1.05250
$155$	−20.9807	−1.68521
$156$	0.431016	0.0345089
$157$	−22.3379	−1.78276	−0.891379	−	0.453259i	$-0.850261\pi$
$157$	−22.3379	−1.78276	−0.891379	+	0.453259i	$0.850261\pi$
$158$	−3.64761	−0.290188
$159$	−8.24502	−0.653873
$160$	−4.70977	−0.372340
$161$	−9.15671	−0.721650
$162$	−14.7007	−1.15500
$163$	−8.53278	−0.668339	−0.334170	−	0.942513i	$-0.608456\pi$
$163$	−8.53278	−0.668339	−0.334170	+	0.942513i	$0.608456\pi$
$164$	2.27262	0.177462
$165$	29.8365	2.32276
$166$	0.357994	0.0277858
$167$	−9.56498	−0.740161	−0.370080	−	0.929000i	$-0.620670\pi$
$167$	−9.56498	−0.740161	−0.370080	+	0.929000i	$0.620670\pi$
$168$	−15.0796	−1.16342
$169$	1.00000	0.0769231
$170$	16.8128	1.28948
$171$	1.25837	0.0962302
$172$	1.06467	0.0811800
$173$	−21.7385	−1.65275	−0.826373	−	0.563123i	$-0.809600\pi$
$173$	−21.7385	−1.65275	−0.826373	+	0.563123i	$0.809600\pi$
$174$	−12.5209	−0.949207
$175$	25.6599	1.93970
$176$	13.5271	1.01964
$177$	20.9089	1.57161
$178$	6.80761	0.510252
$179$	−23.3080	−1.74212	−0.871060	−	0.491176i	$-0.836567\pi$
$179$	−23.3080	−1.74212	−0.871060	+	0.491176i	$0.836567\pi$
$180$	0.840041	0.0626130
$181$	14.5441	1.08105	0.540527	−	0.841326i	$-0.318225\pi$
$181$	14.5441	1.08105	0.540527	+	0.841326i	$0.318225\pi$
$182$	−3.40150	−0.252136
$183$	27.6275	2.04228
$184$	10.6430	0.784609
$185$	17.7952	1.30833
$186$	14.4442	1.05910
$187$	12.4456	0.910112
$188$	−2.76120	−0.201381
$189$	−10.1681	−0.739620
$190$	−6.49885	−0.471476
$191$	−2.51192	−0.181756	−0.0908781	−	0.995862i	$-0.528967\pi$
$191$	−2.51192	−0.181756	−0.0908781	+	0.995862i	$0.528967\pi$
$192$	17.3415	1.25152
$193$	26.6131	1.91566	0.957828	−	0.287344i	$-0.0927722\pi$
$193$	26.6131	1.91566	0.957828	+	0.287344i	$0.0927722\pi$
$194$	−1.70103	−0.122127
$195$	7.77025	0.556439
$196$	0.111287	0.00794910
$197$	−0.417994	−0.0297808	−0.0148904	−	0.999889i	$-0.504740\pi$
$197$	−0.417994	−0.0297808	−0.0148904	+	0.999889i	$0.504740\pi$
$198$	−5.15222	−0.366152
$199$	−11.5265	−0.817094	−0.408547	−	0.912737i	$-0.633964\pi$
$199$	−11.5265	−0.817094	−0.408547	+	0.912737i	$0.633964\pi$
$200$	−29.8248	−2.10893
$201$	−17.2852	−1.21920
$202$	−21.5580	−1.51681
$203$	−11.9260	−0.837038
$204$	1.39700	0.0978097
$205$	40.9703	2.86149
$206$	−1.33589	−0.0930761
$207$	−3.61203	−0.251053
$208$	3.52283	0.244264
$209$	−4.81073	−0.332765
$210$	−26.4305	−1.82388
$211$	10.4824	0.721641	0.360821	−	0.932635i	$-0.382497\pi$
$211$	10.4824	0.721641	0.360821	+	0.932635i	$0.382497\pi$
$212$	0.887456	0.0609507
$213$	−20.3571	−1.39485
$214$	10.1480	0.693704
$215$	19.1935	1.30899
$216$	11.8185	0.804148
$217$	13.7579	0.933948
$218$	−12.5966	−0.853148
$219$	15.6180	1.05537
$220$	−3.21146	−0.216517
$221$	3.24118	0.218025
$222$	−12.2512	−0.822244
$223$	−20.7856	−1.39191	−0.695954	−	0.718086i	$-0.745018\pi$
$223$	−20.7856	−1.39191	−0.695954	+	0.718086i	$0.745018\pi$
$224$	3.08839	0.206352
$225$	10.1220	0.674800
$226$	15.0289	0.999707
$227$	14.9523	0.992421	0.496211	−	0.868202i	$-0.334724\pi$
$227$	14.9523	0.992421	0.496211	+	0.868202i	$0.334724\pi$
$228$	−0.539998	−0.0357623
$229$	1.95472	0.129171	0.0645857	−	0.997912i	$-0.479427\pi$
$229$	1.95472	0.129171	0.0645857	+	0.997912i	$0.479427\pi$
$230$	18.6543	1.23003
$231$	−19.5650	−1.28728
$232$	13.8617	0.910065
$233$	15.6526	1.02544	0.512719	−	0.858556i	$-0.328638\pi$
$233$	15.6526	1.02544	0.512719	+	0.858556i	$0.328638\pi$
$234$	−1.34178	−0.0877151
$235$	−49.7782	−3.24717
$236$	−2.25054	−0.146497
$237$	−5.46393	−0.354921
$238$	−11.0249	−0.714637
$239$	−15.6831	−1.01445	−0.507226	−	0.861813i	$-0.669329\pi$
$239$	−15.6831	−1.01445	−0.507226	+	0.861813i	$0.669329\pi$
$240$	27.3733	1.76694
$241$	11.6781	0.752251	0.376126	−	0.926569i	$-0.377256\pi$
$241$	11.6781	0.752251	0.376126	+	0.926569i	$0.377256\pi$
$242$	5.00201	0.321541
$243$	−10.0408	−0.644115
$244$	−2.97369	−0.190371
$245$	2.00626	0.128175
$246$	−28.2062	−1.79836
$247$	−1.25285	−0.0797169
$248$	−15.9910	−1.01543
$249$	0.536258	0.0339840
$250$	−26.3386	−1.66580
$251$	0.195462	0.0123374	0.00616871	−	0.999981i	$-0.498036\pi$
$251$	0.195462	0.0123374	0.00616871	+	0.999981i	$0.498036\pi$
$252$	−0.550850	−0.0347003
$253$	13.8087	0.868146
$254$	5.60650	0.351783
$255$	25.1848	1.57713
$256$	−5.10724	−0.319202
$257$	−11.6389	−0.726016	−0.363008	−	0.931786i	$-0.618250\pi$
$257$	−11.6389	−0.726016	−0.363008	+	0.931786i	$0.618250\pi$
$258$	−13.2139	−0.822659
$259$	−11.6690	−0.725079
$260$	−0.836354	−0.0518685
$261$	−4.70441	−0.291196
$262$	−15.5613	−0.961381
$263$	−14.3288	−0.883554	−0.441777	−	0.897125i	$-0.645652\pi$
$263$	−14.3288	−0.883554	−0.441777	+	0.897125i	$0.645652\pi$
$264$	22.7407	1.39959
$265$	15.9988	0.982800
$266$	4.26157	0.261294
$267$	10.1975	0.624075
$268$	1.86050	0.113648
$269$	−11.7742	−0.717885	−0.358942	−	0.933360i	$-0.616863\pi$
$269$	−11.7742	−0.717885	−0.358942	+	0.933360i	$0.616863\pi$
$270$	20.7147	1.26066
$271$	−20.4986	−1.24520	−0.622601	−	0.782540i	$-0.713924\pi$
$271$	−20.4986	−1.24520	−0.622601	+	0.782540i	$0.713924\pi$
$272$	11.4181	0.692326
$273$	−5.09528	−0.308380
$274$	25.4076	1.53493
$275$	−38.6962	−2.33347
$276$	1.55001	0.0932995
$277$	−26.1895	−1.57357	−0.786787	−	0.617225i	$-0.788257\pi$
$277$	−26.1895	−1.57357	−0.786787	+	0.617225i	$0.788257\pi$
$278$	11.6797	0.700502
$279$	5.42705	0.324909
$280$	29.2608	1.74867
$281$	−18.5939	−1.10922	−0.554609	−	0.832111i	$-0.687132\pi$
$281$	−18.5939	−1.10922	−0.554609	+	0.832111i	$0.687132\pi$
$282$	34.2700	2.04075
$283$	−8.26743	−0.491448	−0.245724	−	0.969340i	$-0.579026\pi$
$283$	−8.26743	−0.491448	−0.245724	+	0.969340i	$0.579026\pi$
$284$	2.19114	0.130021
$285$	−9.73495	−0.576649
$286$	5.12961	0.303320
$287$	−26.8659	−1.58585
$288$	1.21827	0.0717874
$289$	−6.49474	−0.382044
$290$	24.2959	1.42670
$291$	−2.54807	−0.149370
$292$	−1.68105	−0.0983762
$293$	26.8458	1.56835	0.784175	−	0.620539i	$-0.213086\pi$
$293$	26.8458	1.56835	0.784175	+	0.620539i	$0.213086\pi$
$294$	−1.38122	−0.0805544
$295$	−40.5721	−2.36220
$296$	13.5631	0.788338
$297$	15.3339	0.889764
$298$	27.0914	1.56936
$299$	3.59617	0.207972
$300$	−4.34360	−0.250778
$301$	−12.5860	−0.725445
$302$	−0.198216	−0.0114061
$303$	−32.2928	−1.85517
$304$	−4.41357	−0.253136
$305$	−53.6090	−3.06964
$306$	−4.34896	−0.248614
$307$	−26.9090	−1.53578	−0.767890	−	0.640582i	$-0.778693\pi$
$307$	−26.9090	−1.53578	−0.767890	+	0.640582i	$0.778693\pi$
$308$	2.10589	0.119994
$309$	−2.00110	−0.113839
$310$	−28.0279	−1.59188
$311$	9.84348	0.558172	0.279086	−	0.960266i	$-0.409968\pi$
$311$	9.84348	0.558172	0.279086	+	0.960266i	$0.409968\pi$
$312$	5.92231	0.335285
$313$	−3.13291	−0.177082	−0.0885412	−	0.996073i	$-0.528220\pi$
$313$	−3.13291	−0.177082	−0.0885412	+	0.996073i	$0.528220\pi$
$314$	−29.8410	−1.68403
$315$	−9.93059	−0.559525
$316$	0.588113	0.0330839
$317$	10.7317	0.602754	0.301377	−	0.953505i	$-0.402554\pi$
$317$	10.7317	0.602754	0.301377	+	0.953505i	$0.402554\pi$
$318$	−11.0145	−0.617661
$319$	17.9849	1.00696
$320$	−33.6499	−1.88109
$321$	15.2012	0.848450
$322$	−12.2324	−0.681684
$323$	−4.06071	−0.225944
$324$	2.37023	0.131679
$325$	−10.0776	−0.559003
$326$	−11.3989	−0.631326
$327$	−18.8691	−1.04346
$328$	31.2266	1.72420
$329$	32.6417	1.79959
$330$	39.8583	2.19413
$331$	−20.4312	−1.12300	−0.561500	−	0.827477i	$-0.689776\pi$
$331$	−20.4312	−1.12300	−0.561500	+	0.827477i	$0.689776\pi$
$332$	−0.0577203	−0.00316782
$333$	−4.60306	−0.252246
$334$	−12.7778	−0.699170
$335$	33.5406	1.83252
$336$	−17.9498	−0.979241
$337$	3.58735	0.195415	0.0977076	−	0.995215i	$-0.468849\pi$
$337$	3.58735	0.195415	0.0977076	+	0.995215i	$0.468849\pi$
$338$	1.33589	0.0726630
$339$	22.5125	1.22271
$340$	−2.71077	−0.147012
$341$	−20.7475	−1.12354
$342$	1.68105	0.0909009
$343$	−19.1392	−1.03342
$344$	14.6289	0.788736
$345$	27.9432	1.50441
$346$	−29.0403	−1.56122
$347$	6.87209	0.368913	0.184457	−	0.982841i	$-0.440947\pi$
$347$	6.87209	0.368913	0.184457	+	0.982841i	$0.440947\pi$
$348$	2.01878	0.108218
$349$	13.8445	0.741077	0.370538	−	0.928817i	$-0.379173\pi$
$349$	13.8445	0.741077	0.370538	+	0.928817i	$0.379173\pi$
$350$	34.2789	1.83228
$351$	3.99338	0.213151
$352$	−4.65743	−0.248242
$353$	10.6017	0.564272	0.282136	−	0.959374i	$-0.408957\pi$
$353$	10.6017	0.564272	0.282136	+	0.959374i	$0.408957\pi$
$354$	27.9320	1.48457
$355$	39.5014	2.09652
$356$	−1.09761	−0.0581731
$357$	−16.5147	−0.874052
$358$	−31.1370	−1.64564
$359$	−10.1497	−0.535682	−0.267841	−	0.963463i	$-0.586310\pi$
$359$	−10.1497	−0.535682	−0.267841	+	0.963463i	$0.586310\pi$
$360$	11.5424	0.608340
$361$	−17.4304	−0.917388
$362$	19.4294	1.02118
$363$	7.49276	0.393268
$364$	0.548432	0.0287457
$365$	−30.3056	−1.58627
$366$	36.9073	1.92918
$367$	−6.00710	−0.313568	−0.156784	−	0.987633i	$-0.550113\pi$
$367$	−6.00710	−0.313568	−0.156784	+	0.987633i	$0.550113\pi$
$368$	12.6687	0.660402
$369$	−10.5978	−0.551697
$370$	23.7724	1.23587
$371$	−10.4911	−0.544671
$372$	−2.32888	−0.120747
$373$	−23.7751	−1.23103	−0.615514	−	0.788126i	$-0.711052\pi$
$373$	−23.7751	−1.23103	−0.615514	+	0.788126i	$0.711052\pi$
$374$	16.6260	0.859709
$375$	−39.4540	−2.03740
$376$	−37.9398	−1.95660
$377$	4.68376	0.241226
$378$	−13.5835	−0.698659
$379$	18.1574	0.932683	0.466342	−	0.884605i	$-0.345572\pi$
$379$	18.1574	0.932683	0.466342	+	0.884605i	$0.345572\pi$
$380$	1.04783	0.0537523
$381$	8.39826	0.430256
$382$	−3.35566	−0.171690
$383$	−6.12410	−0.312927	−0.156463	−	0.987684i	$-0.550009\pi$
$383$	−6.12410	−0.312927	−0.156463	+	0.987684i	$0.550009\pi$
$384$	18.3121	0.934484
$385$	37.9644	1.93485
$386$	35.5523	1.80956
$387$	−4.96477	−0.252374
$388$	0.274262	0.0139235
$389$	24.0692	1.22036	0.610178	−	0.792264i	$-0.291098\pi$
$389$	24.0692	1.22036	0.610178	+	0.792264i	$0.291098\pi$
$390$	10.3802	0.525623
$391$	11.6558	0.589462
$392$	1.52913	0.0772326
$393$	−23.3101	−1.17584
$394$	−0.558395	−0.0281316
$395$	10.6023	0.533462
$396$	0.830706	0.0417445
$397$	−29.7844	−1.49484	−0.747419	−	0.664353i	$-0.768707\pi$
$397$	−29.7844	−1.49484	−0.747419	+	0.664353i	$0.768707\pi$
$398$	−15.3982	−0.771843
$399$	6.38362	0.319581
$400$	−35.5016	−1.77508
$401$	−6.86406	−0.342775	−0.171387	−	0.985204i	$-0.554825\pi$
$401$	−6.86406	−0.342775	−0.171387	+	0.985204i	$0.554825\pi$
$402$	−23.0911	−1.15168
$403$	−5.40323	−0.269154
$404$	3.47585	0.172930
$405$	42.7299	2.12326
$406$	−15.9318	−0.790682
$407$	17.5974	0.872271
$408$	19.1953	0.950308
$409$	35.7409	1.76727	0.883637	−	0.468172i	$-0.155087\pi$
$409$	35.7409	1.76727	0.883637	+	0.468172i	$0.155087\pi$
$410$	54.7319	2.70302
$411$	38.0594	1.87733
$412$	0.215389	0.0106115
$413$	26.6048	1.30914
$414$	−4.82528	−0.237150
$415$	−1.04057	−0.0510794
$416$	−1.21292	−0.0594685
$417$	17.4956	0.856764
$418$	−6.42663	−0.314337
$419$	32.7880	1.60180	0.800898	−	0.598800i	$-0.204356\pi$
$419$	32.7880	1.60180	0.800898	+	0.598800i	$0.204356\pi$
$420$	4.26146	0.207938
$421$	−23.7667	−1.15832	−0.579158	−	0.815215i	$-0.696619\pi$
$421$	−23.7667	−1.15832	−0.579158	+	0.815215i	$0.696619\pi$
$422$	14.0034	0.681676
$423$	12.8761	0.626057
$424$	12.1939	0.592190
$425$	−32.6632	−1.58440
$426$	−27.1949	−1.31760
$427$	35.1536	1.70120
$428$	−1.63619	−0.0790882
$429$	7.68390	0.370982
$430$	25.6405	1.23649
$431$	18.1279	0.873189	0.436594	−	0.899658i	$-0.356184\pi$
$431$	18.1279	0.873189	0.436594	+	0.899658i	$0.356184\pi$
$432$	14.0680	0.676847
$433$	−2.72216	−0.130819	−0.0654094	−	0.997859i	$-0.520835\pi$
$433$	−2.72216	−0.130819	−0.0654094	+	0.997859i	$0.520835\pi$
$434$	18.3791	0.882225
$435$	36.3940	1.74496
$436$	2.03098	0.0972662
$437$	−4.50546	−0.215526
$438$	20.8640	0.996921
$439$	−15.2952	−0.730001	−0.365001	−	0.931007i	$-0.618931\pi$
$439$	−15.2952	−0.730001	−0.365001	+	0.931007i	$0.618931\pi$
$440$	−44.1265	−2.10365
$441$	−0.518958	−0.0247123
$442$	4.32987	0.205951
$443$	12.6368	0.600395	0.300197	−	0.953877i	$-0.402947\pi$
$443$	12.6368	0.600395	0.300197	+	0.953877i	$0.402947\pi$
$444$	1.97529	0.0937429
$445$	−19.7874	−0.938013
$446$	−27.7674	−1.31482
$447$	40.5816	1.91944
$448$	22.0657	1.04250
$449$	12.4661	0.588311	0.294155	−	0.955758i	$-0.404962\pi$
$449$	12.4661	0.588311	0.294155	+	0.955758i	$0.404962\pi$
$450$	13.5219	0.637429
$451$	40.5150	1.90778
$452$	−2.42315	−0.113975
$453$	−0.296918	−0.0139504
$454$	19.9747	0.937460
$455$	9.88700	0.463510
$456$	−7.41976	−0.347462
$457$	12.0044	0.561544	0.280772	−	0.959775i	$-0.409410\pi$
$457$	12.0044	0.561544	0.280772	+	0.959775i	$0.409410\pi$
$458$	2.61129	0.122018
$459$	12.9433	0.604140
$460$	−3.00767	−0.140233
$461$	−6.78252	−0.315893	−0.157947	−	0.987448i	$-0.550487\pi$
$461$	−6.78252	−0.315893	−0.157947	+	0.987448i	$0.550487\pi$
$462$	−26.1368	−1.21599
$463$	10.3900	0.482864	0.241432	−	0.970418i	$-0.422383\pi$
$463$	10.3900	0.482864	0.241432	+	0.970418i	$0.422383\pi$
$464$	16.5001	0.765997
$465$	−41.9845	−1.94698
$466$	20.9102	0.968648
$467$	−25.0483	−1.15910	−0.579548	−	0.814938i	$-0.696771\pi$
$467$	−25.0483	−1.15910	−0.579548	+	0.814938i	$0.696771\pi$
$468$	0.216339	0.0100003
$469$	−21.9940	−1.01559
$470$	−66.4984	−3.06734
$471$	−44.7004	−2.05969
$472$	−30.9231	−1.42335
$473$	18.9802	0.872712
$474$	−7.29923	−0.335265
$475$	12.6257	0.579306
$476$	1.77757	0.0814747
$477$	−4.13840	−0.189485
$478$	−20.9509	−0.958272
$479$	0.623855	0.0285046	0.0142523	−	0.999898i	$-0.495463\pi$
$479$	0.623855	0.0285046	0.0142523	+	0.999898i	$0.495463\pi$
$480$	−9.42473	−0.430178
$481$	4.58286	0.208960
$482$	15.6007	0.710591
$483$	−18.3235	−0.833748
$484$	−0.806487	−0.0366585
$485$	4.94433	0.224510
$486$	−13.4134	−0.608443
$487$	−41.4598	−1.87872	−0.939362	−	0.342926i	$-0.888582\pi$
$487$	−41.4598	−1.87872	−0.939362	+	0.342926i	$0.888582\pi$
$488$	−40.8595	−1.84962
$489$	−17.0750	−0.772157
$490$	2.68015	0.121077
$491$	20.8808	0.942338	0.471169	−	0.882043i	$-0.343832\pi$
$491$	20.8808	0.942338	0.471169	+	0.882043i	$0.343832\pi$
$492$	4.54775	0.205029
$493$	15.1809	0.683714
$494$	−1.67367	−0.0753021
$495$	14.9757	0.673110
$496$	−19.0347	−0.854682
$497$	−25.9027	−1.16190
$498$	0.716383	0.0321019
$499$	−3.68923	−0.165153	−0.0825764	−	0.996585i	$-0.526315\pi$
$499$	−3.68923	−0.165153	−0.0825764	+	0.996585i	$0.526315\pi$
$500$	4.24665	0.189916
$501$	−19.1405	−0.855135
$502$	0.261116	0.0116542
$503$	19.4452	0.867021	0.433510	−	0.901149i	$-0.357275\pi$
$503$	19.4452	0.867021	0.433510	+	0.901149i	$0.357275\pi$
$504$	−7.56887	−0.337144
$505$	62.6617	2.78841
$506$	18.4470	0.820067
$507$	2.00110	0.0888721
$508$	−0.903950	−0.0401063
$509$	8.32849	0.369154	0.184577	−	0.982818i	$-0.440908\pi$
$509$	8.32849	0.369154	0.184577	+	0.982818i	$0.440908\pi$
$510$	33.6442	1.48979
$511$	19.8726	0.879114
$512$	−25.1247	−1.11037
$513$	−5.00311	−0.220893
$514$	−15.5484	−0.685809
$515$	3.88298	0.171105
$516$	2.13050	0.0937903
$517$	−49.2250	−2.16491
$518$	−15.5886	−0.684923
$519$	−43.5009	−1.90948
$520$	−11.4918	−0.503948
$521$	8.48817	0.371873	0.185937	−	0.982562i	$-0.440468\pi$
$521$	8.48817	0.371873	0.185937	+	0.982562i	$0.440468\pi$
$522$	−6.28459	−0.275069
$523$	−25.5800	−1.11854	−0.559268	−	0.828987i	$-0.688918\pi$
$523$	−25.5800	−1.11854	−0.559268	+	0.828987i	$0.688918\pi$
$524$	2.50899	0.109606
$525$	51.3480	2.24101
$526$	−19.1418	−0.834622
$527$	−17.5129	−0.762872
$528$	27.0691	1.17803
$529$	−10.0675	−0.437719
$530$	21.3727	0.928372
$531$	10.4948	0.455433
$532$	−0.687103	−0.0297897
$533$	10.5512	0.457025
$534$	13.6227	0.589513
$535$	−29.4968	−1.27526
$536$	25.5639	1.10419
$537$	−46.6417	−2.01274
$538$	−15.7291	−0.678128
$539$	1.98397	0.0854555
$540$	−3.33988	−0.143726
$541$	4.86264	0.209061	0.104531	−	0.994522i	$-0.466666\pi$
$541$	4.86264	0.209061	0.104531	+	0.994522i	$0.466666\pi$
$542$	−27.3839	−1.17624
$543$	29.1042	1.24898
$544$	−3.93131	−0.168553
$545$	36.6139	1.56837
$546$	−6.80675	−0.291302
$547$	19.6656	0.840839	0.420419	−	0.907330i	$-0.361883\pi$
$547$	19.6656	0.840839	0.420419	+	0.907330i	$0.361883\pi$
$548$	−4.09654	−0.174995
$549$	13.8670	0.591828
$550$	−51.6940	−2.20424
$551$	−5.86805	−0.249987
$552$	21.2976	0.906488
$553$	−6.95240	−0.295646
$554$	−34.9864	−1.48643
$555$	35.6099	1.51156
$556$	−1.88315	−0.0798632
$557$	−42.6016	−1.80509	−0.902543	−	0.430599i	$-0.858302\pi$
$557$	−42.6016	−1.80509	−0.902543	+	0.430599i	$0.858302\pi$
$558$	7.24996	0.306915
$559$	4.94298	0.209066
$560$	34.8302	1.47184
$561$	24.9049	1.05149
$562$	−24.8395	−1.04779
$563$	−3.22868	−0.136073	−0.0680364	−	0.997683i	$-0.521673\pi$
$563$	−3.22868	−0.136073	−0.0680364	+	0.997683i	$0.521673\pi$
$564$	−5.52544	−0.232663
$565$	−43.6838	−1.83779
$566$	−11.0444	−0.464231
$567$	−28.0198	−1.17672
$568$	30.1071	1.26326
$569$	−31.4540	−1.31862	−0.659311	−	0.751871i	$-0.729152\pi$
$569$	−31.4540	−1.31862	−0.659311	+	0.751871i	$0.729152\pi$
$570$	−13.0049	−0.544714
$571$	−3.09352	−0.129460	−0.0647299	−	0.997903i	$-0.520619\pi$
$571$	−3.09352	−0.129460	−0.0647299	+	0.997903i	$0.520619\pi$
$572$	−0.827059	−0.0345811
$573$	−5.02661	−0.209990
$574$	−35.8900	−1.49802
$575$	−36.2407	−1.51134
$576$	8.70420	0.362675
$577$	5.72858	0.238484	0.119242	−	0.992865i	$-0.461954\pi$
$577$	5.72858	0.238484	0.119242	+	0.992865i	$0.461954\pi$
$578$	−8.67629	−0.360886
$579$	53.2556	2.21323
$580$	−3.91728	−0.162656
$581$	0.682344	0.0283084
$582$	−3.40394	−0.141098
$583$	15.8210	0.655240
$584$	−23.0982	−0.955812
$585$	3.90010	0.161249
$586$	35.8632	1.48149
$587$	0.183700	0.00758212	0.00379106	−	0.999993i	$-0.498793\pi$
$587$	0.183700	0.00758212	0.00379106	+	0.999993i	$0.498793\pi$
$588$	0.222698	0.00918389
$589$	6.76944	0.278930
$590$	−54.2000	−2.23138
$591$	−0.836449	−0.0344069
$592$	16.1446	0.663540
$593$	30.0876	1.23555	0.617776	−	0.786354i	$-0.288034\pi$
$593$	30.0876	1.23555	0.617776	+	0.786354i	$0.288034\pi$
$594$	20.4845	0.840488
$595$	32.0455	1.31374
$596$	−4.36801	−0.178921
$597$	−23.0658	−0.944019
$598$	4.80410	0.196454
$599$	0.468431	0.0191396	0.00956979	−	0.999954i	$-0.496954\pi$
$599$	0.468431	0.0191396	0.00956979	+	0.999954i	$0.496954\pi$
$600$	−59.6825	−2.43653
$601$	−33.8936	−1.38255	−0.691274	−	0.722592i	$-0.742950\pi$
$601$	−33.8936	−1.38255	−0.691274	+	0.722592i	$0.742950\pi$
$602$	−16.8136	−0.685269
$603$	−8.67591	−0.353310
$604$	0.0319589	0.00130039
$605$	−14.5391	−0.591100
$606$	−43.1397	−1.75243
$607$	−19.8595	−0.806071	−0.403036	−	0.915184i	$-0.632045\pi$
$607$	−19.8595	−0.806071	−0.403036	+	0.915184i	$0.632045\pi$
$608$	1.51961	0.0616284
$609$	−23.8651	−0.967061
$610$	−71.6158	−2.89964
$611$	−12.8196	−0.518624
$612$	0.701194	0.0283441
$613$	29.4113	1.18791	0.593955	−	0.804498i	$-0.297566\pi$
$613$	29.4113	1.18791	0.593955	+	0.804498i	$0.297566\pi$
$614$	−35.9476	−1.45073
$615$	81.9857	3.30598
$616$	28.9356	1.16585
$617$	29.9441	1.20550	0.602751	−	0.797929i	$-0.294071\pi$
$617$	29.9441	1.20550	0.602751	+	0.797929i	$0.294071\pi$
$618$	−2.67326	−0.107534
$619$	−4.61298	−0.185411	−0.0927057	−	0.995694i	$-0.529552\pi$
$619$	−4.61298	−0.185411	−0.0927057	+	0.995694i	$0.529552\pi$
$620$	4.51901	0.181488
$621$	14.3609	0.576283
$622$	13.1498	0.527260
$623$	12.9754	0.519850
$624$	7.04954	0.282207
$625$	26.1696	1.04678
$626$	−4.18523	−0.167275
$627$	−9.62677	−0.384456
$628$	4.81135	0.191994
$629$	14.8539	0.592263
$630$	−13.2662	−0.528538
$631$	−6.31019	−0.251205	−0.125602	−	0.992081i	$-0.540086\pi$
$631$	−6.31019	−0.251205	−0.125602	+	0.992081i	$0.540086\pi$
$632$	8.08087	0.321440
$633$	20.9764	0.833739
$634$	14.3365	0.569373
$635$	−16.2962	−0.646694
$636$	1.77589	0.0704186
$637$	0.516680	0.0204716
$638$	24.0258	0.951192
$639$	−10.2178	−0.404210
$640$	−35.5332	−1.40457
$641$	9.92556	0.392036	0.196018	−	0.980600i	$-0.437199\pi$
$641$	9.92556	0.392036	0.196018	+	0.980600i	$0.437199\pi$
$642$	20.3072	0.801462
$643$	45.4735	1.79330	0.896650	−	0.442741i	$-0.145994\pi$
$643$	45.4735	1.79330	0.896650	+	0.442741i	$0.145994\pi$
$644$	1.97226	0.0777178
$645$	38.4082	1.51232
$646$	−5.42468	−0.213431
$647$	−13.3073	−0.523162	−0.261581	−	0.965182i	$-0.584244\pi$
$647$	−13.3073	−0.523162	−0.261581	+	0.965182i	$0.584244\pi$
$648$	32.5677	1.27938
$649$	−40.1212	−1.57490
$650$	−13.4626	−0.528045
$651$	27.5310	1.07902
$652$	1.83787	0.0719766
$653$	−23.6327	−0.924817	−0.462409	−	0.886667i	$-0.653015\pi$
$653$	−23.6327	−0.924817	−0.462409	+	0.886667i	$0.653015\pi$
$654$	−25.2070	−0.985673
$655$	45.2314	1.76734
$656$	37.1702	1.45125
$657$	7.83912	0.305833
$658$	43.6058	1.69993
$659$	−27.6068	−1.07541	−0.537704	−	0.843134i	$-0.680708\pi$
$659$	−27.6068	−1.07541	−0.537704	+	0.843134i	$0.680708\pi$
$660$	−6.42646	−0.250149
$661$	−27.7878	−1.08082	−0.540411	−	0.841401i	$-0.681731\pi$
$661$	−27.7878	−1.08082	−0.540411	+	0.841401i	$0.681731\pi$
$662$	−27.2939	−1.06081
$663$	6.48593	0.251893
$664$	−0.793097	−0.0307781
$665$	−12.3869	−0.480344
$666$	−6.14920	−0.238277
$667$	16.8436	0.652187
$668$	2.06020	0.0797114
$669$	−41.5942	−1.60812
$670$	44.8066	1.73103
$671$	−53.0132	−2.04655
$672$	6.18019	0.238406
$673$	24.1157	0.929590	0.464795	−	0.885418i	$-0.346128\pi$
$673$	24.1157	0.929590	0.464795	+	0.885418i	$0.346128\pi$
$674$	4.79231	0.184593
$675$	−40.2436	−1.54898
$676$	−0.215389	−0.00828421
$677$	−10.4256	−0.400687	−0.200343	−	0.979726i	$-0.564206\pi$
$677$	−10.4256	−0.400687	−0.200343	+	0.979726i	$0.564206\pi$
$678$	30.0743	1.15500
$679$	−3.24220	−0.124424
$680$	−37.2470	−1.42836
$681$	29.9211	1.14658
$682$	−27.7165	−1.06132
$683$	−0.771045	−0.0295032	−0.0147516	−	0.999891i	$-0.504696\pi$
$683$	−0.771045	−0.0295032	−0.0147516	+	0.999891i	$0.504696\pi$
$684$	−0.271040	−0.0103635
$685$	−73.8513	−2.82171
$686$	−25.5680	−0.976190
$687$	3.91159	0.149236
$688$	17.4133	0.663875
$689$	4.12024	0.156969
$690$	37.3291	1.42109
$691$	−44.3328	−1.68650	−0.843249	−	0.537524i	$-0.819360\pi$
$691$	−44.3328	−1.68650	−0.843249	+	0.537524i	$0.819360\pi$
$692$	4.68224	0.177992
$693$	−9.82023	−0.373040
$694$	9.18038	0.348483
$695$	−33.9489	−1.28775
$696$	27.7387	1.05143
$697$	34.1985	1.29536
$698$	18.4947	0.700035
$699$	31.3225	1.18473
$700$	−5.52687	−0.208896
$701$	−20.4429	−0.772118	−0.386059	−	0.922474i	$-0.626164\pi$
$701$	−20.4429	−0.772118	−0.386059	+	0.922474i	$0.626164\pi$
$702$	5.33473	0.201346
$703$	−5.74163	−0.216550
$704$	−33.2760	−1.25414
$705$	−99.6113	−3.75158
$706$	14.1628	0.533022
$707$	−41.0899	−1.54534
$708$	−4.50355	−0.169254
$709$	22.3465	0.839242	0.419621	−	0.907699i	$-0.362163\pi$
$709$	22.3465	0.839242	0.419621	+	0.907699i	$0.362163\pi$
$710$	52.7696	1.98041
$711$	−2.74250	−0.102852
$712$	−15.0815	−0.565204
$713$	−19.4310	−0.727695
$714$	−22.0619	−0.825646
$715$	−14.9100	−0.557603
$716$	5.02029	0.187617
$717$	−31.3834	−1.17203
$718$	−13.5589	−0.506015
$719$	41.8009	1.55891	0.779455	−	0.626458i	$-0.215496\pi$
$719$	41.8009	1.55891	0.779455	+	0.626458i	$0.215496\pi$
$720$	13.7394	0.512037
$721$	−2.54624	−0.0948268
$722$	−23.2851	−0.866582
$723$	23.3690	0.869104
$724$	−3.13265	−0.116424
$725$	−47.2009	−1.75300
$726$	10.0095	0.371488
$727$	40.3623	1.49696	0.748478	−	0.663160i	$-0.230785\pi$
$727$	40.3623	1.49696	0.748478	+	0.663160i	$0.230785\pi$
$728$	7.53565	0.279290
$729$	12.9206	0.478540
$730$	−40.4850	−1.49842
$731$	16.0211	0.592562
$732$	−5.95066	−0.219943
$733$	−19.5235	−0.721116	−0.360558	−	0.932737i	$-0.617414\pi$
$733$	−19.5235	−0.721116	−0.360558	+	0.932737i	$0.617414\pi$
$734$	−8.02485	−0.296203
$735$	4.01473	0.148086
$736$	−4.36189	−0.160781
$737$	33.1678	1.22175
$738$	−14.1575	−0.521143
$739$	34.2846	1.26118	0.630590	−	0.776116i	$-0.282813\pi$
$739$	34.2846	1.26118	0.630590	+	0.776116i	$0.282813\pi$
$740$	−3.83289	−0.140900
$741$	−2.50708	−0.0920999
$742$	−14.0150	−0.514507
$743$	9.36580	0.343598	0.171799	−	0.985132i	$-0.445042\pi$
$743$	9.36580	0.343598	0.171799	+	0.985132i	$0.445042\pi$
$744$	−31.9996	−1.17316
$745$	−78.7454	−2.88501
$746$	−31.7610	−1.16285
$747$	0.269163	0.00984815
$748$	−2.68065	−0.0980142
$749$	19.3423	0.706752
$750$	−52.7063	−1.92456
$751$	15.9871	0.583376	0.291688	−	0.956513i	$-0.405783\pi$
$751$	15.9871	0.583376	0.291688	+	0.956513i	$0.405783\pi$
$752$	−45.1612	−1.64686
$753$	0.391138	0.0142539
$754$	6.25700	0.227867
$755$	0.576147	0.0209681
$756$	2.19010	0.0796532
$757$	−14.7652	−0.536649	−0.268325	−	0.963329i	$-0.586470\pi$
$757$	−14.7652	−0.536649	−0.268325	+	0.963329i	$0.586470\pi$
$758$	24.2564	0.881031
$759$	27.6326	1.00300
$760$	14.3975	0.522252
$761$	−24.5755	−0.890863	−0.445431	−	0.895316i	$-0.646950\pi$
$761$	−24.5755	−0.890863	−0.445431	+	0.895316i	$0.646950\pi$
$762$	11.2192	0.406428
$763$	−24.0093	−0.869195
$764$	0.541041	0.0195742
$765$	12.6409	0.457034
$766$	−8.18114	−0.295597
$767$	−10.4487	−0.377280
$768$	−10.2201	−0.368786
$769$	−0.956052	−0.0344761	−0.0172381	−	0.999851i	$-0.505487\pi$
$769$	−0.956052	−0.0344761	−0.0172381	+	0.999851i	$0.505487\pi$
$770$	50.7164	1.82769
$771$	−23.2907	−0.838793
$772$	−5.73219	−0.206306
$773$	−24.2225	−0.871222	−0.435611	−	0.900135i	$-0.643468\pi$
$773$	−24.2225	−0.871222	−0.435611	+	0.900135i	$0.643468\pi$
$774$	−6.63241	−0.238397
$775$	54.4515	1.95595
$776$	3.76845	0.135280
$777$	−23.3509	−0.837710
$778$	32.1539	1.15277
$779$	−13.2191	−0.473624
$780$	−1.67363	−0.0599255
$781$	39.0624	1.39776
$782$	15.5710	0.556817
$783$	18.7040	0.668428
$784$	1.82018	0.0650063
$785$	86.7377	3.09580
$786$	−31.1398	−1.11072
$787$	−22.7568	−0.811194	−0.405597	−	0.914052i	$-0.632936\pi$
$787$	−22.7568	−0.811194	−0.405597	+	0.914052i	$0.632936\pi$
$788$	0.0900315	0.00320724
$789$	−28.6735	−1.02080
$790$	14.1636	0.503918
$791$	28.6453	1.01851
$792$	11.4142	0.405585
$793$	−13.8061	−0.490270
$794$	−39.7888	−1.41205
$795$	32.0153	1.13547
$796$	2.48269	0.0879967
$797$	−19.0731	−0.675605	−0.337803	−	0.941217i	$-0.609684\pi$
$797$	−19.0731	−0.675605	−0.337803	+	0.941217i	$0.609684\pi$
$798$	8.52783	0.301882
$799$	−41.5506	−1.46995
$800$	12.2233	0.432160
$801$	5.11839	0.180849
$802$	−9.16966	−0.323792
$803$	−29.9688	−1.05758
$804$	3.72304	0.131302
$805$	35.5553	1.25316
$806$	−7.21814	−0.254248
$807$	−23.5613	−0.829399
$808$	47.7593	1.68017
$809$	11.3422	0.398771	0.199386	−	0.979921i	$-0.436105\pi$
$809$	11.3422	0.398771	0.199386	+	0.979921i	$0.436105\pi$
$810$	57.0826	2.00568
$811$	−13.3127	−0.467473	−0.233736	−	0.972300i	$-0.575095\pi$
$811$	−13.3127	−0.467473	−0.233736	+	0.972300i	$0.575095\pi$
$812$	2.56873	0.0901446
$813$	−41.0198	−1.43863
$814$	23.5083	0.823964
$815$	33.1327	1.16059
$816$	22.8488	0.799869
$817$	−6.19281	−0.216659
$818$	47.7461	1.66940
$819$	−2.55746	−0.0893649
$820$	−8.82457	−0.308167
$821$	30.0747	1.04961	0.524806	−	0.851222i	$-0.324138\pi$
$821$	30.0747	1.04961	0.524806	+	0.851222i	$0.324138\pi$
$822$	50.8433	1.77336
$823$	−16.0204	−0.558435	−0.279217	−	0.960228i	$-0.590075\pi$
$823$	−16.0204	−0.558435	−0.279217	+	0.960228i	$0.590075\pi$
$824$	2.95952	0.103100
$825$	−77.4350	−2.69594
$826$	35.5412	1.23664
$827$	−20.0489	−0.697168	−0.348584	−	0.937278i	$-0.613337\pi$
$827$	−20.0489	−0.697168	−0.348584	+	0.937278i	$0.613337\pi$
$828$	0.777992	0.0270371
$829$	40.3768	1.40235	0.701173	−	0.712991i	$-0.252660\pi$
$829$	40.3768	1.40235	0.701173	+	0.712991i	$0.252660\pi$
$830$	−1.39009	−0.0482506
$831$	−52.4078	−1.81801
$832$	−8.66599	−0.300439
$833$	1.67465	0.0580233
$834$	23.3723	0.809315
$835$	37.1407	1.28531
$836$	1.03618	0.0358371
$837$	−21.5772	−0.745816
$838$	43.8012	1.51309
$839$	26.9258	0.929583	0.464791	−	0.885420i	$-0.346129\pi$
$839$	26.9258	0.929583	0.464791	+	0.885420i	$0.346129\pi$
$840$	58.5538	2.02030
$841$	−7.06239	−0.243531
$842$	−31.7497	−1.09417
$843$	−37.2083	−1.28152
$844$	−2.25781	−0.0777169
$845$	−3.88298	−0.133579
$846$	17.2011	0.591385
$847$	9.53392	0.327589
$848$	14.5149	0.498444
$849$	−16.5440	−0.567788
$850$	−43.6346	−1.49665
$851$	16.4807	0.564953
$852$	4.38470	0.150217
$853$	22.6905	0.776907	0.388454	−	0.921468i	$-0.373009\pi$
$853$	22.6905	0.776907	0.388454	+	0.921468i	$0.373009\pi$
$854$	46.9615	1.60699
$855$	−4.88624	−0.167106
$856$	−22.4818	−0.768412
$857$	20.9947	0.717166	0.358583	−	0.933498i	$-0.383260\pi$
$857$	20.9947	0.717166	0.358583	+	0.933498i	$0.383260\pi$
$858$	10.2649	0.350437
$859$	−2.64911	−0.0903863	−0.0451932	−	0.998978i	$-0.514390\pi$
$859$	−2.64911	−0.0903863	−0.0451932	+	0.998978i	$0.514390\pi$
$860$	−4.13408	−0.140971
$861$	−53.7615	−1.83219
$862$	24.2169	0.824831
$863$	−25.4518	−0.866389	−0.433195	−	0.901300i	$-0.642614\pi$
$863$	−25.4518	−0.866389	−0.433195	+	0.901300i	$0.642614\pi$
$864$	−4.84367	−0.164785
$865$	84.4102	2.87003
$866$	−3.63652	−0.123574
$867$	−12.9966	−0.441389
$868$	−2.96331	−0.100581
$869$	10.4845	0.355663
$870$	48.6185	1.64832
$871$	8.63783	0.292682
$872$	27.9063	0.945027
$873$	−1.27894	−0.0432857
$874$	−6.01882	−0.203590
$875$	−50.2019	−1.69714
$876$	−3.36396	−0.113658
$877$	17.2113	0.581185	0.290593	−	0.956847i	$-0.406148\pi$
$877$	17.2113	0.581185	0.290593	+	0.956847i	$0.406148\pi$
$878$	−20.4328	−0.689573
$879$	53.7213	1.81197
$880$	−52.5254	−1.77063
$881$	52.0996	1.75528	0.877640	−	0.479320i	$-0.159117\pi$
$881$	52.0996	1.75528	0.877640	+	0.479320i	$0.159117\pi$
$882$	−0.693273	−0.0233437
$883$	10.1507	0.341597	0.170799	−	0.985306i	$-0.445365\pi$
$883$	10.1507	0.341597	0.170799	+	0.985306i	$0.445365\pi$
$884$	−0.698116	−0.0234802
$885$	−81.1889	−2.72913
$886$	16.8815	0.567144
$887$	7.68887	0.258167	0.129083	−	0.991634i	$-0.458796\pi$
$887$	7.68887	0.258167	0.129083	+	0.991634i	$0.458796\pi$
$888$	27.1411	0.910795
$889$	10.6861	0.358400
$890$	−26.4339	−0.886065
$891$	42.2550	1.41560
$892$	4.47700	0.149901
$893$	16.0610	0.537461
$894$	54.2126	1.81314
$895$	90.5046	3.02523
$896$	23.3006	0.778418
$897$	7.19631	0.240278
$898$	16.6534	0.555730
$899$	−25.3075	−0.844051
$900$	−2.18017	−0.0726724
$901$	13.3544	0.444901
$902$	54.1237	1.80212
$903$	−25.1859	−0.838133
$904$	−33.2948	−1.10737
$905$	−56.4745	−1.87728
$906$	−0.396651	−0.0131778
$907$	27.7770	0.922321	0.461161	−	0.887317i	$-0.347433\pi$
$907$	27.7770	0.922321	0.461161	+	0.887317i	$0.347433\pi$
$908$	−3.22057	−0.106878
$909$	−16.2086	−0.537607
$910$	13.2080	0.437840
$911$	32.9841	1.09281	0.546406	−	0.837521i	$-0.315996\pi$
$911$	32.9841	1.09281	0.546406	+	0.837521i	$0.315996\pi$
$912$	−8.83201	−0.292457
$913$	−1.02900	−0.0340550
$914$	16.0366	0.530445
$915$	−107.277	−3.54647
$916$	−0.421026	−0.0139111
$917$	−29.6601	−0.979464
$918$	17.2908	0.570682
$919$	30.5665	1.00830	0.504149	−	0.863617i	$-0.331806\pi$
$919$	30.5665	1.00830	0.504149	+	0.863617i	$0.331806\pi$
$920$	−41.3264	−1.36249
$921$	−53.8477	−1.77434
$922$	−9.06072	−0.298399
$923$	10.1729	0.334847
$924$	4.21410	0.138634
$925$	−46.1841	−1.51852
$926$	13.8799	0.456123
$927$	−1.00441	−0.0329891
$928$	−5.68105	−0.186490
$929$	−2.83980	−0.0931709	−0.0465855	−	0.998914i	$-0.514834\pi$
$929$	−2.83980	−0.0931709	−0.0465855	+	0.998914i	$0.514834\pi$
$930$	−56.0868	−1.83916
$931$	−0.647323	−0.0212151
$932$	−3.37141	−0.110434
$933$	19.6978	0.644877
$934$	−33.4618	−1.09490
$935$	−48.3261	−1.58043
$936$	2.97257	0.0971615
$937$	−23.1964	−0.757793	−0.378897	−	0.925439i	$-0.623696\pi$
$937$	−23.1964	−0.757793	−0.378897	+	0.925439i	$0.623696\pi$
$938$	−29.3816	−0.959342
$939$	−6.26927	−0.204590
$940$	10.7217	0.349703
$941$	19.1725	0.625004	0.312502	−	0.949917i	$-0.398833\pi$
$941$	19.1725	0.625004	0.312502	+	0.949917i	$0.398833\pi$
$942$	−59.7150	−1.94562
$943$	37.9441	1.23563
$944$	−36.8089	−1.19803
$945$	39.4826	1.28437
$946$	25.3556	0.824380
$947$	−56.6997	−1.84249	−0.921246	−	0.388980i	$-0.872827\pi$
$947$	−56.6997	−1.84249	−0.921246	+	0.388980i	$0.872827\pi$
$948$	1.17687	0.0382231
$949$	−7.80471	−0.253352
$950$	16.8666	0.547224
$951$	21.4753	0.696384
$952$	24.4244	0.791599
$953$	−49.2055	−1.59392	−0.796961	−	0.604031i	$-0.793560\pi$
$953$	−49.2055	−1.59392	−0.796961	+	0.604031i	$0.793560\pi$
$954$	−5.52847	−0.178991
$955$	9.75375	0.315624
$956$	3.37797	0.109251
$957$	35.9895	1.16338
$958$	0.833403	0.0269260
$959$	48.4274	1.56380
$960$	−67.3369	−2.17329
$961$	−1.80507	−0.0582281
$962$	6.12221	0.197388
$963$	7.62992	0.245871
$964$	−2.51534	−0.0810135
$965$	−103.338	−3.32658
$966$	−24.4782	−0.787574
$967$	24.6168	0.791621	0.395811	−	0.918332i	$-0.370464\pi$
$967$	24.6168	0.791621	0.395811	+	0.918332i	$0.370464\pi$
$968$	−11.0814	−0.356170
$969$	−8.12590	−0.261042
$970$	6.60509	0.212077
$971$	−43.5571	−1.39781	−0.698906	−	0.715213i	$-0.746330\pi$
$971$	−43.5571	−1.39781	−0.698906	+	0.715213i	$0.746330\pi$
$972$	2.16267	0.0693678
$973$	22.2617	0.713678
$974$	−55.3859	−1.77468
$975$	−20.1662	−0.645837
$976$	−48.6366	−1.55682
$977$	28.7155	0.918691	0.459346	−	0.888258i	$-0.348084\pi$
$977$	28.7155	0.918691	0.459346	+	0.888258i	$0.348084\pi$
$978$	−22.8103	−0.729394
$979$	−19.5675	−0.625380
$980$	−0.432128	−0.0138038
$981$	−9.47090	−0.302383
$982$	27.8945	0.890151
$983$	−11.7717	−0.375459	−0.187730	−	0.982221i	$-0.560113\pi$
$983$	−11.7717	−0.375459	−0.187730	+	0.982221i	$0.560113\pi$
$984$	62.4877	1.99203
$985$	1.62306	0.0517151
$986$	20.2801	0.645849
$987$	65.3193	2.07914
$988$	0.269851	0.00858509
$989$	17.7758	0.565238
$990$	20.0060	0.635832
$991$	34.6827	1.10173	0.550866	−	0.834594i	$-0.314298\pi$
$991$	34.6827	1.10173	0.550866	+	0.834594i	$0.314298\pi$
$992$	6.55371	0.208081
$993$	−40.8849	−1.29744
$994$	−34.6033	−1.09755
$995$	44.7573	1.41890
$996$	−0.115504	−0.00365989
$997$	0.688779	0.0218138	0.0109069	−	0.999941i	$-0.496528\pi$
$997$	0.688779	0.0218138	0.0109069	+	0.999941i	$0.496528\pi$
$998$	−4.92842	−0.156006
$999$	18.3011	0.579021

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1339.2.a.e.1.15	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1339.2.a.e.1.15	✓	21	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:	\( N \)	\(=\)	\( 1339 = 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1339.a (trivial)

\(f(q)\)	\(=\)	\(q+1.33589 q^{2} +2.00110 q^{3} -0.215389 q^{4} -3.88298 q^{5} +2.67326 q^{6} +2.54624 q^{7} -2.95952 q^{8} +1.00441 q^{9} +O(q^{10})\)	\(q+1.33589 q^{2} +2.00110 q^{3} -0.215389 q^{4} -3.88298 q^{5} +2.67326 q^{6} +2.54624 q^{7} -2.95952 q^{8} +1.00441 q^{9} -5.18725 q^{10} -3.83983 q^{11} -0.431016 q^{12} -1.00000 q^{13} +3.40150 q^{14} -7.77025 q^{15} -3.52283 q^{16} -3.24118 q^{17} +1.34178 q^{18} +1.25285 q^{19} +0.836354 q^{20} +5.09528 q^{21} -5.12961 q^{22} -3.59617 q^{23} -5.92231 q^{24} +10.0776 q^{25} -1.33589 q^{26} -3.99338 q^{27} -0.548432 q^{28} -4.68376 q^{29} -10.3802 q^{30} +5.40323 q^{31} +1.21292 q^{32} -7.68390 q^{33} -4.32987 q^{34} -9.88700 q^{35} -0.216339 q^{36} -4.58286 q^{37} +1.67367 q^{38} -2.00110 q^{39} +11.4918 q^{40} -10.5512 q^{41} +6.80675 q^{42} -4.94298 q^{43} +0.827059 q^{44} -3.90010 q^{45} -4.80410 q^{46} +12.8196 q^{47} -7.04954 q^{48} -0.516680 q^{49} +13.4626 q^{50} -6.48593 q^{51} +0.215389 q^{52} -4.12024 q^{53} -5.33473 q^{54} +14.9100 q^{55} -7.53565 q^{56} +2.50708 q^{57} -6.25700 q^{58} +10.4487 q^{59} +1.67363 q^{60} +13.8061 q^{61} +7.21814 q^{62} +2.55746 q^{63} +8.66599 q^{64} +3.88298 q^{65} -10.2649 q^{66} -8.63783 q^{67} +0.698116 q^{68} -7.19631 q^{69} -13.2080 q^{70} -10.1729 q^{71} -2.97257 q^{72} +7.80471 q^{73} -6.12221 q^{74} +20.1662 q^{75} -0.269851 q^{76} -9.77712 q^{77} -2.67326 q^{78} -2.73046 q^{79} +13.6791 q^{80} -11.0044 q^{81} -14.0953 q^{82} +0.267981 q^{83} -1.09747 q^{84} +12.5855 q^{85} -6.60330 q^{86} -9.37268 q^{87} +11.3641 q^{88} +5.09593 q^{89} -5.21012 q^{90} -2.54624 q^{91} +0.774578 q^{92} +10.8124 q^{93} +17.1256 q^{94} -4.86480 q^{95} +2.42719 q^{96} -1.27333 q^{97} -0.690230 q^{98} -3.85676 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q - q^{2} - 6 q^{3} + 15 q^{4} - 18 q^{5} - 8 q^{6} - 2 q^{7} + 6 q^{8} + 11 q^{9}+O(q^{10}) \) 21 * q - q^2 - 6 * q^3 + 15 * q^4 - 18 * q^5 - 8 * q^6 - 2 * q^7 + 6 * q^8 + 11 * q^9	\( 21 q - q^{2} - 6 q^{3} + 15 q^{4} - 18 q^{5} - 8 q^{6} - 2 q^{7} + 6 q^{8} + 11 q^{9} - 10 q^{10} - 5 q^{11} - 22 q^{12} - 21 q^{13} - 24 q^{14} - q^{15} - 5 q^{16} - 18 q^{17} + 10 q^{18} - 6 q^{19} - 30 q^{20} - 17 q^{21} - 8 q^{22} - 14 q^{23} - 13 q^{24} + 11 q^{25} + q^{26} - 33 q^{27} - 2 q^{28} - 36 q^{29} + 2 q^{30} + q^{31} - 9 q^{32} - 11 q^{33} - 25 q^{34} - 37 q^{35} + 3 q^{36} + 5 q^{37} - 13 q^{38} + 6 q^{39} - 2 q^{40} - 32 q^{41} + 7 q^{42} + 2 q^{43} + 4 q^{44} - 32 q^{45} - 5 q^{46} - 12 q^{47} - 18 q^{48} + 5 q^{49} - 2 q^{50} - 27 q^{51} - 15 q^{52} - 49 q^{53} - 31 q^{54} - 9 q^{55} - 53 q^{56} + 14 q^{57} - 2 q^{58} - 34 q^{59} + 25 q^{60} - 27 q^{61} - 12 q^{62} + 41 q^{63} - 70 q^{64} + 18 q^{65} - 15 q^{66} - 12 q^{67} - 20 q^{68} - 70 q^{69} + 70 q^{70} - 26 q^{71} - 14 q^{72} + 23 q^{73} + 20 q^{74} - 9 q^{75} - 36 q^{76} - 62 q^{77} + 8 q^{78} - 7 q^{79} - 41 q^{80} - 3 q^{81} - 33 q^{82} - q^{83} - 48 q^{84} + 10 q^{85} - 23 q^{86} - 7 q^{87} + 9 q^{88} - 16 q^{89} - 30 q^{90} + 2 q^{91} - 27 q^{92} + 2 q^{93} - 37 q^{94} - 35 q^{95} + 55 q^{96} - 30 q^{97} - 43 q^{98} - 42 q^{99}+O(q^{100}) \) 21 * q - q^2 - 6 * q^3 + 15 * q^4 - 18 * q^5 - 8 * q^6 - 2 * q^7 + 6 * q^8 + 11 * q^9 - 10 * q^10 - 5 * q^11 - 22 * q^12 - 21 * q^13 - 24 * q^14 - q^15 - 5 * q^16 - 18 * q^17 + 10 * q^18 - 6 * q^19 - 30 * q^20 - 17 * q^21 - 8 * q^22 - 14 * q^23 - 13 * q^24 + 11 * q^25 + q^26 - 33 * q^27 - 2 * q^28 - 36 * q^29 + 2 * q^30 + q^31 - 9 * q^32 - 11 * q^33 - 25 * q^34 - 37 * q^35 + 3 * q^36 + 5 * q^37 - 13 * q^38 + 6 * q^39 - 2 * q^40 - 32 * q^41 + 7 * q^42 + 2 * q^43 + 4 * q^44 - 32 * q^45 - 5 * q^46 - 12 * q^47 - 18 * q^48 + 5 * q^49 - 2 * q^50 - 27 * q^51 - 15 * q^52 - 49 * q^53 - 31 * q^54 - 9 * q^55 - 53 * q^56 + 14 * q^57 - 2 * q^58 - 34 * q^59 + 25 * q^60 - 27 * q^61 - 12 * q^62 + 41 * q^63 - 70 * q^64 + 18 * q^65 - 15 * q^66 - 12 * q^67 - 20 * q^68 - 70 * q^69 + 70 * q^70 - 26 * q^71 - 14 * q^72 + 23 * q^73 + 20 * q^74 - 9 * q^75 - 36 * q^76 - 62 * q^77 + 8 * q^78 - 7 * q^79 - 41 * q^80 - 3 * q^81 - 33 * q^82 - q^83 - 48 * q^84 + 10 * q^85 - 23 * q^86 - 7 * q^87 + 9 * q^88 - 16 * q^89 - 30 * q^90 + 2 * q^91 - 27 * q^92 + 2 * q^93 - 37 * q^94 - 35 * q^95 + 55 * q^96 - 30 * q^97 - 43 * q^98 - 42 * q^99

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