LMFDB - Embedded newform 8018.2.a.i.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, 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("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.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:	$64.0240523407$
Analytic rank:	$0$
Dimension:	$43$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.91293 q^{3} +1.00000 q^{4} +2.71400 q^{5} +2.91293 q^{6} +1.04550 q^{7} -1.00000 q^{8} +5.48515 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.91293 q^{3} +1.00000 q^{4} +2.71400 q^{5} +2.91293 q^{6} +1.04550 q^{7} -1.00000 q^{8} +5.48515 q^{9} -2.71400 q^{10} +1.91532 q^{11} -2.91293 q^{12} -0.807158 q^{13} -1.04550 q^{14} -7.90569 q^{15} +1.00000 q^{16} +3.06854 q^{17} -5.48515 q^{18} +1.00000 q^{19} +2.71400 q^{20} -3.04548 q^{21} -1.91532 q^{22} +8.03994 q^{23} +2.91293 q^{24} +2.36580 q^{25} +0.807158 q^{26} -7.23905 q^{27} +1.04550 q^{28} +3.67644 q^{29} +7.90569 q^{30} -5.42951 q^{31} -1.00000 q^{32} -5.57920 q^{33} -3.06854 q^{34} +2.83750 q^{35} +5.48515 q^{36} -11.8395 q^{37} -1.00000 q^{38} +2.35119 q^{39} -2.71400 q^{40} +3.89041 q^{41} +3.04548 q^{42} +5.87343 q^{43} +1.91532 q^{44} +14.8867 q^{45} -8.03994 q^{46} +9.31636 q^{47} -2.91293 q^{48} -5.90692 q^{49} -2.36580 q^{50} -8.93844 q^{51} -0.807158 q^{52} +10.1275 q^{53} +7.23905 q^{54} +5.19819 q^{55} -1.04550 q^{56} -2.91293 q^{57} -3.67644 q^{58} +13.2760 q^{59} -7.90569 q^{60} -3.81249 q^{61} +5.42951 q^{62} +5.73474 q^{63} +1.00000 q^{64} -2.19063 q^{65} +5.57920 q^{66} -14.6917 q^{67} +3.06854 q^{68} -23.4198 q^{69} -2.83750 q^{70} -2.83404 q^{71} -5.48515 q^{72} -1.08964 q^{73} +11.8395 q^{74} -6.89139 q^{75} +1.00000 q^{76} +2.00248 q^{77} -2.35119 q^{78} +12.7905 q^{79} +2.71400 q^{80} +4.63139 q^{81} -3.89041 q^{82} +6.89354 q^{83} -3.04548 q^{84} +8.32803 q^{85} -5.87343 q^{86} -10.7092 q^{87} -1.91532 q^{88} +1.63592 q^{89} -14.8867 q^{90} -0.843886 q^{91} +8.03994 q^{92} +15.8158 q^{93} -9.31636 q^{94} +2.71400 q^{95} +2.91293 q^{96} +9.41240 q^{97} +5.90692 q^{98} +10.5058 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 43 q - 43 q^{2} + 43 q^{4} + 19 q^{7} - 43 q^{8} + 53 q^{9}+O(q^{10}) $ 43 * q - 43 * q^2 + 43 * q^4 + 19 * q^7 - 43 * q^8 + 53 * q^9	$ 43 q - 43 q^{2} + 43 q^{4} + 19 q^{7} - 43 q^{8} + 53 q^{9} + 14 q^{11} + 3 q^{13} - 19 q^{14} + q^{15} + 43 q^{16} + 8 q^{17} - 53 q^{18} + 43 q^{19} - 14 q^{22} + 43 q^{23} + 97 q^{25} - 3 q^{26} + 15 q^{27} + 19 q^{28} - 25 q^{29} - q^{30} + 22 q^{31} - 43 q^{32} + 22 q^{33} - 8 q^{34} - 6 q^{35} + 53 q^{36} + 42 q^{37} - 43 q^{38} + 9 q^{39} - 40 q^{41} + 72 q^{43} + 14 q^{44} - q^{45} - 43 q^{46} + 27 q^{47} + 86 q^{49} - 97 q^{50} - 3 q^{51} + 3 q^{52} - 5 q^{53} - 15 q^{54} + 86 q^{55} - 19 q^{56} + 25 q^{58} - 43 q^{59} + q^{60} + 31 q^{61} - 22 q^{62} + 38 q^{63} + 43 q^{64} - 32 q^{65} - 22 q^{66} + 15 q^{67} + 8 q^{68} - 7 q^{69} + 6 q^{70} + 14 q^{71} - 53 q^{72} + 93 q^{73} - 42 q^{74} - 13 q^{75} + 43 q^{76} + 38 q^{77} - 9 q^{78} + 15 q^{79} + 43 q^{81} + 40 q^{82} + 34 q^{83} + 16 q^{85} - 72 q^{86} + 60 q^{87} - 14 q^{88} - 37 q^{89} + q^{90} - 3 q^{91} + 43 q^{92} + 19 q^{93} - 27 q^{94} + 27 q^{97} - 86 q^{98} - 24 q^{99}+O(q^{100}) $ 43 * q - 43 * q^2 + 43 * q^4 + 19 * q^7 - 43 * q^8 + 53 * q^9 + 14 * q^11 + 3 * q^13 - 19 * q^14 + q^15 + 43 * q^16 + 8 * q^17 - 53 * q^18 + 43 * q^19 - 14 * q^22 + 43 * q^23 + 97 * q^25 - 3 * q^26 + 15 * q^27 + 19 * q^28 - 25 * q^29 - q^30 + 22 * q^31 - 43 * q^32 + 22 * q^33 - 8 * q^34 - 6 * q^35 + 53 * q^36 + 42 * q^37 - 43 * q^38 + 9 * q^39 - 40 * q^41 + 72 * q^43 + 14 * q^44 - q^45 - 43 * q^46 + 27 * q^47 + 86 * q^49 - 97 * q^50 - 3 * q^51 + 3 * q^52 - 5 * q^53 - 15 * q^54 + 86 * q^55 - 19 * q^56 + 25 * q^58 - 43 * q^59 + q^60 + 31 * q^61 - 22 * q^62 + 38 * q^63 + 43 * q^64 - 32 * q^65 - 22 * q^66 + 15 * q^67 + 8 * q^68 - 7 * q^69 + 6 * q^70 + 14 * q^71 - 53 * q^72 + 93 * q^73 - 42 * q^74 - 13 * q^75 + 43 * q^76 + 38 * q^77 - 9 * q^78 + 15 * q^79 + 43 * q^81 + 40 * q^82 + 34 * q^83 + 16 * q^85 - 72 * q^86 + 60 * q^87 - 14 * q^88 - 37 * q^89 + q^90 - 3 * q^91 + 43 * q^92 + 19 * q^93 - 27 * q^94 + 27 * q^97 - 86 * q^98 - 24 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.91293	−1.68178	−0.840890	−	0.541206i	$-0.817968\pi$
$3$	−2.91293	−1.68178	−0.840890	+	0.541206i	$0.817968\pi$
$4$	1.00000	0.500000
$5$	2.71400	1.21374	0.606869	−	0.794802i	$-0.292425\pi$
$5$	2.71400	1.21374	0.606869	+	0.794802i	$0.292425\pi$
$6$	2.91293	1.18920
$7$	1.04550	0.395163	0.197582	−	0.980286i	$-0.436691\pi$
$7$	1.04550	0.395163	0.197582	+	0.980286i	$0.436691\pi$
$8$	−1.00000	−0.353553
$9$	5.48515	1.82838
$10$	−2.71400	−0.858242
$11$	1.91532	0.577492	0.288746	−	0.957406i	$-0.406762\pi$
$11$	1.91532	0.577492	0.288746	+	0.957406i	$0.406762\pi$
$12$	−2.91293	−0.840890
$13$	−0.807158	−0.223865	−0.111933	−	0.993716i	$-0.535704\pi$
$13$	−0.807158	−0.223865	−0.111933	+	0.993716i	$0.535704\pi$
$14$	−1.04550	−0.279423
$15$	−7.90569	−2.04124
$16$	1.00000	0.250000
$17$	3.06854	0.744231	0.372115	−	0.928186i	$-0.378633\pi$
$17$	3.06854	0.744231	0.372115	+	0.928186i	$0.378633\pi$
$18$	−5.48515	−1.29286
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	2.71400	0.606869
$21$	−3.04548	−0.664577
$22$	−1.91532	−0.408348
$23$	8.03994	1.67644	0.838222	−	0.545329i	$-0.183595\pi$
$23$	8.03994	1.67644	0.838222	+	0.545329i	$0.183595\pi$
$24$	2.91293	0.594599
$25$	2.36580	0.473159
$26$	0.807158	0.158297
$27$	−7.23905	−1.39316
$28$	1.04550	0.197582
$29$	3.67644	0.682698	0.341349	−	0.939937i	$-0.389116\pi$
$29$	3.67644	0.682698	0.341349	+	0.939937i	$0.389116\pi$
$30$	7.90569	1.44337
$31$	−5.42951	−0.975168	−0.487584	−	0.873076i	$-0.662122\pi$
$31$	−5.42951	−0.975168	−0.487584	+	0.873076i	$0.662122\pi$
$32$	−1.00000	−0.176777
$33$	−5.57920	−0.971214
$34$	−3.06854	−0.526251
$35$	2.83750	0.479624
$36$	5.48515	0.914191
$37$	−11.8395	−1.94640	−0.973198	−	0.229969i	$-0.926138\pi$
$37$	−11.8395	−1.94640	−0.973198	+	0.229969i	$0.926138\pi$
$38$	−1.00000	−0.162221
$39$	2.35119	0.376492
$40$	−2.71400	−0.429121
$41$	3.89041	0.607580	0.303790	−	0.952739i	$-0.401748\pi$
$41$	3.89041	0.607580	0.303790	+	0.952739i	$0.401748\pi$
$42$	3.04548	0.469927
$43$	5.87343	0.895690	0.447845	−	0.894111i	$-0.352192\pi$
$43$	5.87343	0.895690	0.447845	+	0.894111i	$0.352192\pi$
$44$	1.91532	0.288746
$45$	14.8867	2.21918
$46$	−8.03994	−1.18542
$47$	9.31636	1.35893	0.679466	−	0.733707i	$-0.262212\pi$
$47$	9.31636	1.35893	0.679466	+	0.733707i	$0.262212\pi$
$48$	−2.91293	−0.420445
$49$	−5.90692	−0.843846
$50$	−2.36580	−0.334574
$51$	−8.93844	−1.25163
$52$	−0.807158	−0.111933
$53$	10.1275	1.39112	0.695561	−	0.718468i	$-0.255156\pi$
$53$	10.1275	1.39112	0.695561	+	0.718468i	$0.255156\pi$
$54$	7.23905	0.985110
$55$	5.19819	0.700924
$56$	−1.04550	−0.139711
$57$	−2.91293	−0.385827
$58$	−3.67644	−0.482740
$59$	13.2760	1.72838	0.864192	−	0.503162i	$-0.167830\pi$
$59$	13.2760	1.72838	0.864192	+	0.503162i	$0.167830\pi$
$60$	−7.90569	−1.02062
$61$	−3.81249	−0.488139	−0.244070	−	0.969758i	$-0.578483\pi$
$61$	−3.81249	−0.488139	−0.244070	+	0.969758i	$0.578483\pi$
$62$	5.42951	0.689548
$63$	5.73474	0.722509
$64$	1.00000	0.125000
$65$	−2.19063	−0.271714
$66$	5.57920	0.686752
$67$	−14.6917	−1.79488	−0.897441	−	0.441135i	$-0.854576\pi$
$67$	−14.6917	−1.79488	−0.897441	+	0.441135i	$0.854576\pi$
$68$	3.06854	0.372115
$69$	−23.4198	−2.81941
$70$	−2.83750	−0.339146
$71$	−2.83404	−0.336339	−0.168169	−	0.985758i	$-0.553786\pi$
$71$	−2.83404	−0.336339	−0.168169	+	0.985758i	$0.553786\pi$
$72$	−5.48515	−0.646431
$73$	−1.08964	−0.127533	−0.0637665	−	0.997965i	$-0.520311\pi$
$73$	−1.08964	−0.127533	−0.0637665	+	0.997965i	$0.520311\pi$
$74$	11.8395	1.37631
$75$	−6.89139	−0.795750
$76$	1.00000	0.114708
$77$	2.00248	0.228204
$78$	−2.35119	−0.266220
$79$	12.7905	1.43904	0.719522	−	0.694470i	$-0.244361\pi$
$79$	12.7905	1.43904	0.719522	+	0.694470i	$0.244361\pi$
$80$	2.71400	0.303434
$81$	4.63139	0.514599
$82$	−3.89041	−0.429624
$83$	6.89354	0.756665	0.378332	−	0.925670i	$-0.376498\pi$
$83$	6.89354	0.756665	0.378332	+	0.925670i	$0.376498\pi$
$84$	−3.04548	−0.332289
$85$	8.32803	0.903301
$86$	−5.87343	−0.633349
$87$	−10.7092	−1.14815
$88$	−1.91532	−0.204174
$89$	1.63592	0.173407	0.0867036	−	0.996234i	$-0.472367\pi$
$89$	1.63592	0.173407	0.0867036	+	0.996234i	$0.472367\pi$
$90$	−14.8867	−1.56919
$91$	−0.843886	−0.0884633
$92$	8.03994	0.838222
$93$	15.8158	1.64002
$94$	−9.31636	−0.960909
$95$	2.71400	0.278451
$96$	2.91293	0.297299
$97$	9.41240	0.955685	0.477842	−	0.878446i	$-0.341419\pi$
$97$	9.41240	0.955685	0.477842	+	0.878446i	$0.341419\pi$
$98$	5.90692	0.596689
$99$	10.5058	1.05588
$100$	2.36580	0.236580
$101$	10.8568	1.08030	0.540148	−	0.841570i	$-0.318368\pi$
$101$	10.8568	1.08030	0.540148	+	0.841570i	$0.318368\pi$
$102$	8.93844	0.885038
$103$	7.73903	0.762550	0.381275	−	0.924462i	$-0.375485\pi$
$103$	7.73903	0.762550	0.381275	+	0.924462i	$0.375485\pi$
$104$	0.807158	0.0791483
$105$	−8.26542	−0.806623
$106$	−10.1275	−0.983671
$107$	13.6331	1.31796	0.658981	−	0.752159i	$-0.270988\pi$
$107$	13.6331	1.31796	0.658981	+	0.752159i	$0.270988\pi$
$108$	−7.23905	−0.696578
$109$	−10.6938	−1.02428	−0.512139	−	0.858902i	$-0.671147\pi$
$109$	−10.6938	−1.02428	−0.512139	+	0.858902i	$0.671147\pi$
$110$	−5.19819	−0.495628
$111$	34.4875	3.27341
$112$	1.04550	0.0987908
$113$	4.89338	0.460331	0.230165	−	0.973152i	$-0.426073\pi$
$113$	4.89338	0.460331	0.230165	+	0.973152i	$0.426073\pi$
$114$	2.91293	0.272821
$115$	21.8204	2.03476
$116$	3.67644	0.341349
$117$	−4.42738	−0.409311
$118$	−13.2760	−1.22215
$119$	3.20817	0.294093
$120$	7.90569	0.721687
$121$	−7.33153	−0.666503
$122$	3.81249	0.345167
$123$	−11.3325	−1.02182
$124$	−5.42951	−0.487584
$125$	−7.14923	−0.639446
$126$	−5.73474	−0.510891
$127$	4.85521	0.430830	0.215415	−	0.976523i	$-0.430890\pi$
$127$	4.85521	0.430830	0.215415	+	0.976523i	$0.430890\pi$
$128$	−1.00000	−0.0883883
$129$	−17.1089	−1.50635
$130$	2.19063	0.192131
$131$	−5.42755	−0.474207	−0.237103	−	0.971484i	$-0.576198\pi$
$131$	−5.42755	−0.474207	−0.237103	+	0.971484i	$0.576198\pi$
$132$	−5.57920	−0.485607
$133$	1.04550	0.0906566
$134$	14.6917	1.26917
$135$	−19.6468	−1.69093
$136$	−3.06854	−0.263125
$137$	−0.349324	−0.0298448	−0.0149224	−	0.999889i	$-0.504750\pi$
$137$	−0.349324	−0.0298448	−0.0149224	+	0.999889i	$0.504750\pi$
$138$	23.4198	1.99362
$139$	−3.98902	−0.338344	−0.169172	−	0.985587i	$-0.554109\pi$
$139$	−3.98902	−0.338344	−0.169172	+	0.985587i	$0.554109\pi$
$140$	2.83750	0.239812
$141$	−27.1379	−2.28542
$142$	2.83404	0.237827
$143$	−1.54597	−0.129280
$144$	5.48515	0.457096
$145$	9.97786	0.828616
$146$	1.08964	0.0901794
$147$	17.2064	1.41916
$148$	−11.8395	−0.973198
$149$	−7.93543	−0.650096	−0.325048	−	0.945698i	$-0.605380\pi$
$149$	−7.93543	−0.650096	−0.325048	+	0.945698i	$0.605380\pi$
$150$	6.89139	0.562680
$151$	7.49138	0.609640	0.304820	−	0.952410i	$-0.401404\pi$
$151$	7.49138	0.609640	0.304820	+	0.952410i	$0.401404\pi$
$152$	−1.00000	−0.0811107
$153$	16.8314	1.36074
$154$	−2.00248	−0.161364
$155$	−14.7357	−1.18360
$156$	2.35119	0.188246
$157$	12.3973	0.989410	0.494705	−	0.869061i	$-0.335276\pi$
$157$	12.3973	0.989410	0.494705	+	0.869061i	$0.335276\pi$
$158$	−12.7905	−1.01756
$159$	−29.5007	−2.33956
$160$	−2.71400	−0.214561
$161$	8.40579	0.662469
$162$	−4.63139	−0.363877
$163$	20.1155	1.57557	0.787784	−	0.615952i	$-0.211228\pi$
$163$	20.1155	1.57557	0.787784	+	0.615952i	$0.211228\pi$
$164$	3.89041	0.303790
$165$	−15.1420	−1.17880
$166$	−6.89354	−0.535043
$167$	3.75981	0.290942	0.145471	−	0.989362i	$-0.453530\pi$
$167$	3.75981	0.290942	0.145471	+	0.989362i	$0.453530\pi$
$168$	3.04548	0.234964
$169$	−12.3485	−0.949884
$170$	−8.32803	−0.638730
$171$	5.48515	0.419460
$172$	5.87343	0.447845
$173$	−21.6307	−1.64456	−0.822278	−	0.569086i	$-0.807297\pi$
$173$	−21.6307	−1.64456	−0.822278	+	0.569086i	$0.807297\pi$
$174$	10.7092	0.811862
$175$	2.47345	0.186975
$176$	1.91532	0.144373
$177$	−38.6719	−2.90676
$178$	−1.63592	−0.122617
$179$	−2.94563	−0.220167	−0.110084	−	0.993922i	$-0.535112\pi$
$179$	−2.94563	−0.220167	−0.110084	+	0.993922i	$0.535112\pi$
$180$	14.8867	1.10959
$181$	1.09237	0.0811953	0.0405976	−	0.999176i	$-0.487074\pi$
$181$	1.09237	0.0811953	0.0405976	+	0.999176i	$0.487074\pi$
$182$	0.843886	0.0625530
$183$	11.1055	0.820943
$184$	−8.03994	−0.592712
$185$	−32.1323	−2.36241
$186$	−15.8158	−1.15967
$187$	5.87725	0.429787
$188$	9.31636	0.679466
$189$	−7.56845	−0.550524
$190$	−2.71400	−0.196894
$191$	−16.2655	−1.17693	−0.588465	−	0.808523i	$-0.700267\pi$
$191$	−16.2655	−1.17693	−0.588465	+	0.808523i	$0.700267\pi$
$192$	−2.91293	−0.210222
$193$	12.7920	0.920790	0.460395	−	0.887714i	$-0.347708\pi$
$193$	12.7920	0.920790	0.460395	+	0.887714i	$0.347708\pi$
$194$	−9.41240	−0.675771
$195$	6.38114	0.456963
$196$	−5.90692	−0.421923
$197$	−9.98707	−0.711549	−0.355775	−	0.934572i	$-0.615783\pi$
$197$	−9.98707	−0.711549	−0.355775	+	0.934572i	$0.615783\pi$
$198$	−10.5058	−0.746617
$199$	−9.66190	−0.684914	−0.342457	−	0.939534i	$-0.611259\pi$
$199$	−9.66190	−0.684914	−0.342457	+	0.939534i	$0.611259\pi$
$200$	−2.36580	−0.167287
$201$	42.7960	3.01860
$202$	−10.8568	−0.763884
$203$	3.84373	0.269777
$204$	−8.93844	−0.625816
$205$	10.5586	0.737443
$206$	−7.73903	−0.539204
$207$	44.1003	3.06518
$208$	−0.807158	−0.0559663
$209$	1.91532	0.132486
$210$	8.26542	0.570368
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	10.1275	0.695561
$213$	8.25535	0.565647
$214$	−13.6331	−0.931940
$215$	15.9405	1.08713
$216$	7.23905	0.492555
$217$	−5.67657	−0.385350
$218$	10.6938	0.724274
$219$	3.17405	0.214482
$220$	5.19819	0.350462
$221$	−2.47680	−0.166607
$222$	−34.4875	−2.31465
$223$	−8.77064	−0.587326	−0.293663	−	0.955909i	$-0.594874\pi$
$223$	−8.77064	−0.587326	−0.293663	+	0.955909i	$0.594874\pi$
$224$	−1.04550	−0.0698556
$225$	12.9767	0.865116
$226$	−4.89338	−0.325503
$227$	−6.98855	−0.463846	−0.231923	−	0.972734i	$-0.574502\pi$
$227$	−6.98855	−0.463846	−0.231923	+	0.972734i	$0.574502\pi$
$228$	−2.91293	−0.192913
$229$	4.73353	0.312800	0.156400	−	0.987694i	$-0.450011\pi$
$229$	4.73353	0.312800	0.156400	+	0.987694i	$0.450011\pi$
$230$	−21.8204	−1.43879
$231$	−5.83307	−0.383788
$232$	−3.67644	−0.241370
$233$	13.4203	0.879196	0.439598	−	0.898195i	$-0.355121\pi$
$233$	13.4203	0.879196	0.439598	+	0.898195i	$0.355121\pi$
$234$	4.42738	0.289427
$235$	25.2846	1.64939
$236$	13.2760	0.864192
$237$	−37.2578	−2.42015
$238$	−3.20817	−0.207955
$239$	−9.27553	−0.599984	−0.299992	−	0.953942i	$-0.596984\pi$
$239$	−9.27553	−0.599984	−0.299992	+	0.953942i	$0.596984\pi$
$240$	−7.90569	−0.510310
$241$	−7.87195	−0.507077	−0.253538	−	0.967325i	$-0.581594\pi$
$241$	−7.87195	−0.507077	−0.253538	+	0.967325i	$0.581594\pi$
$242$	7.33153	0.471289
$243$	8.22624	0.527714
$244$	−3.81249	−0.244070
$245$	−16.0314	−1.02421
$246$	11.3325	0.722533
$247$	−0.807158	−0.0513582
$248$	5.42951	0.344774
$249$	−20.0804	−1.27254
$250$	7.14923	0.452157
$251$	−21.6775	−1.36827	−0.684135	−	0.729355i	$-0.739820\pi$
$251$	−21.6775	−1.36827	−0.684135	+	0.729355i	$0.739820\pi$
$252$	5.73474	0.361255
$253$	15.3991	0.968133
$254$	−4.85521	−0.304643
$255$	−24.2589	−1.51915
$256$	1.00000	0.0625000
$257$	2.64026	0.164695	0.0823474	−	0.996604i	$-0.473758\pi$
$257$	2.64026	0.164695	0.0823474	+	0.996604i	$0.473758\pi$
$258$	17.1089	1.06515
$259$	−12.3782	−0.769144
$260$	−2.19063	−0.135857
$261$	20.1658	1.24823
$262$	5.42755	0.335315
$263$	8.46435	0.521934	0.260967	−	0.965348i	$-0.415959\pi$
$263$	8.46435	0.521934	0.260967	+	0.965348i	$0.415959\pi$
$264$	5.57920	0.343376
$265$	27.4861	1.68846
$266$	−1.04550	−0.0641039
$267$	−4.76532	−0.291633
$268$	−14.6917	−0.897441
$269$	−18.7958	−1.14600	−0.573001	−	0.819555i	$-0.694221\pi$
$269$	−18.7958	−1.14600	−0.573001	+	0.819555i	$0.694221\pi$
$270$	19.6468	1.19567
$271$	12.8272	0.779195	0.389598	−	0.920985i	$-0.372614\pi$
$271$	12.8272	0.779195	0.389598	+	0.920985i	$0.372614\pi$
$272$	3.06854	0.186058
$273$	2.45818	0.148776
$274$	0.349324	0.0211034
$275$	4.53127	0.273246
$276$	−23.4198	−1.40970
$277$	−14.2561	−0.856564	−0.428282	−	0.903645i	$-0.640881\pi$
$277$	−14.2561	−0.856564	−0.428282	+	0.903645i	$0.640881\pi$
$278$	3.98902	0.239245
$279$	−29.7816	−1.78298
$280$	−2.83750	−0.169573
$281$	0.855700	0.0510468	0.0255234	−	0.999674i	$-0.491875\pi$
$281$	0.855700	0.0510468	0.0255234	+	0.999674i	$0.491875\pi$
$282$	27.1379	1.61604
$283$	−11.0969	−0.659642	−0.329821	−	0.944044i	$-0.606988\pi$
$283$	−11.0969	−0.659642	−0.329821	+	0.944044i	$0.606988\pi$
$284$	−2.83404	−0.168169
$285$	−7.90569	−0.468292
$286$	1.54597	0.0914151
$287$	4.06744	0.240093
$288$	−5.48515	−0.323215
$289$	−7.58405	−0.446120
$290$	−9.97786	−0.585920
$291$	−27.4176	−1.60725
$292$	−1.08964	−0.0637665
$293$	24.2495	1.41667	0.708336	−	0.705875i	$-0.249446\pi$
$293$	24.2495	1.41667	0.708336	+	0.705875i	$0.249446\pi$
$294$	−17.2064	−1.00350
$295$	36.0310	2.09780
$296$	11.8395	0.688155
$297$	−13.8651	−0.804537
$298$	7.93543	0.459687
$299$	−6.48950	−0.375298
$300$	−6.89139	−0.397875
$301$	6.14069	0.353944
$302$	−7.49138	−0.431080
$303$	−31.6252	−1.81682
$304$	1.00000	0.0573539
$305$	−10.3471	−0.592473
$306$	−16.8314	−0.962187
$307$	−8.66246	−0.494393	−0.247196	−	0.968965i	$-0.579509\pi$
$307$	−8.66246	−0.494393	−0.247196	+	0.968965i	$0.579509\pi$
$308$	2.00248	0.114102
$309$	−22.5432	−1.28244
$310$	14.7357	0.836930
$311$	−10.5945	−0.600759	−0.300380	−	0.953820i	$-0.597113\pi$
$311$	−10.5945	−0.600759	−0.300380	+	0.953820i	$0.597113\pi$
$312$	−2.35119	−0.133110
$313$	−7.50496	−0.424205	−0.212103	−	0.977247i	$-0.568031\pi$
$313$	−7.50496	−0.424205	−0.212103	+	0.977247i	$0.568031\pi$
$314$	−12.3973	−0.699618
$315$	15.5641	0.876937
$316$	12.7905	0.719522
$317$	−10.4072	−0.584525	−0.292263	−	0.956338i	$-0.594408\pi$
$317$	−10.4072	−0.584525	−0.292263	+	0.956338i	$0.594408\pi$
$318$	29.5007	1.65432
$319$	7.04157	0.394252
$320$	2.71400	0.151717
$321$	−39.7123	−2.21652
$322$	−8.40579	−0.468436
$323$	3.06854	0.170738
$324$	4.63139	0.257300
$325$	−1.90957	−0.105924
$326$	−20.1155	−1.11409
$327$	31.1502	1.72261
$328$	−3.89041	−0.214812
$329$	9.74029	0.537000
$330$	15.1420	0.833537
$331$	−4.44099	−0.244099	−0.122049	−	0.992524i	$-0.538947\pi$
$331$	−4.44099	−0.244099	−0.122049	+	0.992524i	$0.538947\pi$
$332$	6.89354	0.378332
$333$	−64.9412	−3.55876
$334$	−3.75981	−0.205727
$335$	−39.8734	−2.17852
$336$	−3.04548	−0.166144
$337$	−25.0304	−1.36349	−0.681746	−	0.731589i	$-0.738779\pi$
$337$	−25.0304	−1.36349	−0.681746	+	0.731589i	$0.738779\pi$
$338$	12.3485	0.671670
$339$	−14.2541	−0.774174
$340$	8.32803	0.451651
$341$	−10.3993	−0.563152
$342$	−5.48515	−0.296603
$343$	−13.4942	−0.728620
$344$	−5.87343	−0.316674
$345$	−63.5613	−3.42202
$346$	21.6307	1.16288
$347$	7.41359	0.397983	0.198991	−	0.980001i	$-0.436233\pi$
$347$	7.41359	0.397983	0.198991	+	0.980001i	$0.436233\pi$
$348$	−10.7092	−0.574073
$349$	4.20232	0.224945	0.112473	−	0.993655i	$-0.464123\pi$
$349$	4.20232	0.224945	0.112473	+	0.993655i	$0.464123\pi$
$350$	−2.47345	−0.132211
$351$	5.84306	0.311879
$352$	−1.91532	−0.102087
$353$	−9.33220	−0.496703	−0.248351	−	0.968670i	$-0.579889\pi$
$353$	−9.33220	−0.496703	−0.248351	+	0.968670i	$0.579889\pi$
$354$	38.6719	2.05539
$355$	−7.69158	−0.408227
$356$	1.63592	0.0867036
$357$	−9.34517	−0.494599
$358$	2.94563	0.155682
$359$	3.20438	0.169120	0.0845602	−	0.996418i	$-0.473051\pi$
$359$	3.20438	0.169120	0.0845602	+	0.996418i	$0.473051\pi$
$360$	−14.8867	−0.784597
$361$	1.00000	0.0526316
$362$	−1.09237	−0.0574137
$363$	21.3562	1.12091
$364$	−0.843886	−0.0442317
$365$	−2.95729	−0.154792
$366$	−11.1055	−0.580494
$367$	−10.9140	−0.569708	−0.284854	−	0.958571i	$-0.591945\pi$
$367$	−10.9140	−0.569708	−0.284854	+	0.958571i	$0.591945\pi$
$368$	8.03994	0.419111
$369$	21.3395	1.11089
$370$	32.1323	1.67048
$371$	10.5884	0.549720
$372$	15.8158	0.820009
$373$	−17.0225	−0.881392	−0.440696	−	0.897656i	$-0.645268\pi$
$373$	−17.0225	−0.881392	−0.440696	+	0.897656i	$0.645268\pi$
$374$	−5.87725	−0.303906
$375$	20.8252	1.07541
$376$	−9.31636	−0.480455
$377$	−2.96747	−0.152832
$378$	7.56845	0.389279
$379$	24.6026	1.26375	0.631874	−	0.775071i	$-0.282286\pi$
$379$	24.6026	1.26375	0.631874	+	0.775071i	$0.282286\pi$
$380$	2.71400	0.139225
$381$	−14.1429	−0.724562
$382$	16.2655	0.832215
$383$	12.2802	0.627489	0.313744	−	0.949507i	$-0.398416\pi$
$383$	12.2802	0.627489	0.313744	+	0.949507i	$0.398416\pi$
$384$	2.91293	0.148650
$385$	5.43473	0.276979
$386$	−12.7920	−0.651097
$387$	32.2166	1.63766
$388$	9.41240	0.477842
$389$	−27.5770	−1.39821	−0.699104	−	0.715020i	$-0.746417\pi$
$389$	−27.5770	−1.39821	−0.699104	+	0.715020i	$0.746417\pi$
$390$	−6.38114	−0.323121
$391$	24.6709	1.24766
$392$	5.90692	0.298345
$393$	15.8100	0.797511
$394$	9.98707	0.503141
$395$	34.7134	1.74662
$396$	10.5058	0.527938
$397$	27.8213	1.39631	0.698155	−	0.715947i	$-0.254005\pi$
$397$	27.8213	1.39631	0.698155	+	0.715947i	$0.254005\pi$
$398$	9.66190	0.484307
$399$	−3.04548	−0.152464
$400$	2.36580	0.118290
$401$	18.2204	0.909882	0.454941	−	0.890522i	$-0.349660\pi$
$401$	18.2204	0.909882	0.454941	+	0.890522i	$0.349660\pi$
$402$	−42.7960	−2.13447
$403$	4.38247	0.218306
$404$	10.8568	0.540148
$405$	12.5696	0.624589
$406$	−3.84373	−0.190761
$407$	−22.6764	−1.12403
$408$	8.93844	0.442519
$409$	−22.2303	−1.09922	−0.549609	−	0.835422i	$-0.685223\pi$
$409$	−22.2303	−1.09922	−0.549609	+	0.835422i	$0.685223\pi$
$410$	−10.5586	−0.521451
$411$	1.01756	0.0501923
$412$	7.73903	0.381275
$413$	13.8801	0.682994
$414$	−44.1003	−2.16741
$415$	18.7091	0.918393
$416$	0.807158	0.0395742
$417$	11.6197	0.569020
$418$	−1.91532	−0.0936816
$419$	15.2647	0.745727	0.372864	−	0.927886i	$-0.378376\pi$
$419$	15.2647	0.745727	0.372864	+	0.927886i	$0.378376\pi$
$420$	−8.26542	−0.403311
$421$	−25.8064	−1.25773	−0.628864	−	0.777515i	$-0.716480\pi$
$421$	−25.8064	−1.25773	−0.628864	+	0.777515i	$0.716480\pi$
$422$	1.00000	0.0486792
$423$	51.1016	2.48465
$424$	−10.1275	−0.491836
$425$	7.25955	0.352140
$426$	−8.25535	−0.399973
$427$	−3.98597	−0.192895
$428$	13.6331	0.658981
$429$	4.50330	0.217421
$430$	−15.9405	−0.768719
$431$	36.2604	1.74660	0.873301	−	0.487182i	$-0.161975\pi$
$431$	36.2604	1.74660	0.873301	+	0.487182i	$0.161975\pi$
$432$	−7.23905	−0.348289
$433$	18.0964	0.869656	0.434828	−	0.900513i	$-0.356809\pi$
$433$	18.0964	0.869656	0.434828	+	0.900513i	$0.356809\pi$
$434$	5.67657	0.272484
$435$	−29.0648	−1.39355
$436$	−10.6938	−0.512139
$437$	8.03994	0.384603
$438$	−3.17405	−0.151662
$439$	3.80676	0.181687	0.0908433	−	0.995865i	$-0.471044\pi$
$439$	3.80676	0.181687	0.0908433	+	0.995865i	$0.471044\pi$
$440$	−5.19819	−0.247814
$441$	−32.4003	−1.54287
$442$	2.47680	0.117809
$443$	−18.8706	−0.896570	−0.448285	−	0.893891i	$-0.647965\pi$
$443$	−18.8706	−0.896570	−0.448285	+	0.893891i	$0.647965\pi$
$444$	34.4875	1.63670
$445$	4.43989	0.210471
$446$	8.77064	0.415302
$447$	23.1153	1.09332
$448$	1.04550	0.0493954
$449$	14.4551	0.682176	0.341088	−	0.940031i	$-0.389205\pi$
$449$	14.4551	0.682176	0.341088	+	0.940031i	$0.389205\pi$
$450$	−12.9767	−0.611729
$451$	7.45140	0.350873
$452$	4.89338	0.230165
$453$	−21.8218	−1.02528
$454$	6.98855	0.327989
$455$	−2.29031	−0.107371
$456$	2.91293	0.136410
$457$	15.1590	0.709108	0.354554	−	0.935036i	$-0.384633\pi$
$457$	15.1590	0.709108	0.354554	+	0.935036i	$0.384633\pi$
$458$	−4.73353	−0.221183
$459$	−22.2133	−1.03683
$460$	21.8204	1.01738
$461$	−14.1974	−0.661239	−0.330620	−	0.943764i	$-0.607258\pi$
$461$	−14.1974	−0.661239	−0.330620	+	0.943764i	$0.607258\pi$
$462$	5.83307	0.271379
$463$	28.5735	1.32792	0.663961	−	0.747767i	$-0.268874\pi$
$463$	28.5735	1.32792	0.663961	+	0.747767i	$0.268874\pi$
$464$	3.67644	0.170674
$465$	42.9240	1.99055
$466$	−13.4203	−0.621685
$467$	34.8486	1.61260	0.806300	−	0.591507i	$-0.201467\pi$
$467$	34.8486	1.61260	0.806300	+	0.591507i	$0.201467\pi$
$468$	−4.42738	−0.204656
$469$	−15.3603	−0.709271
$470$	−25.2846	−1.16629
$471$	−36.1123	−1.66397
$472$	−13.2760	−0.611076
$473$	11.2495	0.517254
$474$	37.2578	1.71131
$475$	2.36580	0.108550
$476$	3.20817	0.147046
$477$	55.5509	2.54350
$478$	9.27553	0.424253
$479$	29.9247	1.36730	0.683648	−	0.729812i	$-0.260392\pi$
$479$	29.9247	1.36730	0.683648	+	0.729812i	$0.260392\pi$
$480$	7.90569	0.360844
$481$	9.55632	0.435731
$482$	7.87195	0.358557
$483$	−24.4854	−1.11413
$484$	−7.33153	−0.333252
$485$	25.5453	1.15995
$486$	−8.22624	−0.373150
$487$	−15.1429	−0.686192	−0.343096	−	0.939300i	$-0.611476\pi$
$487$	−15.1429	−0.686192	−0.343096	+	0.939300i	$0.611476\pi$
$488$	3.81249	0.172583
$489$	−58.5950	−2.64976
$490$	16.0314	0.724224
$491$	−22.6136	−1.02054	−0.510268	−	0.860015i	$-0.670454\pi$
$491$	−22.6136	−1.02054	−0.510268	+	0.860015i	$0.670454\pi$
$492$	−11.3325	−0.510908
$493$	11.2813	0.508085
$494$	0.807158	0.0363157
$495$	28.5128	1.28156
$496$	−5.42951	−0.243792
$497$	−2.96300	−0.132909
$498$	20.0804	0.899824
$499$	−15.5567	−0.696412	−0.348206	−	0.937418i	$-0.613209\pi$
$499$	−15.5567	−0.696412	−0.348206	+	0.937418i	$0.613209\pi$
$500$	−7.14923	−0.319723
$501$	−10.9520	−0.489301
$502$	21.6775	0.967513
$503$	−25.4643	−1.13540	−0.567699	−	0.823236i	$-0.692166\pi$
$503$	−25.4643	−1.13540	−0.567699	+	0.823236i	$0.692166\pi$
$504$	−5.73474	−0.255446
$505$	29.4655	1.31120
$506$	−15.3991	−0.684573
$507$	35.9703	1.59750
$508$	4.85521	0.215415
$509$	36.0825	1.59933	0.799665	−	0.600446i	$-0.205010\pi$
$509$	36.0825	1.59933	0.799665	+	0.600446i	$0.205010\pi$
$510$	24.2589	1.07420
$511$	−1.13922	−0.0503963
$512$	−1.00000	−0.0441942
$513$	−7.23905	−0.319612
$514$	−2.64026	−0.116457
$515$	21.0037	0.925535
$516$	−17.1089	−0.753177
$517$	17.8439	0.784772
$518$	12.3782	0.543867
$519$	63.0088	2.76578
$520$	2.19063	0.0960653
$521$	34.7028	1.52036	0.760178	−	0.649715i	$-0.225112\pi$
$521$	34.7028	1.52036	0.760178	+	0.649715i	$0.225112\pi$
$522$	−20.1658	−0.882633
$523$	−18.2068	−0.796126	−0.398063	−	0.917358i	$-0.630317\pi$
$523$	−18.2068	−0.796126	−0.398063	+	0.917358i	$0.630317\pi$
$524$	−5.42755	−0.237103
$525$	−7.20498	−0.314451
$526$	−8.46435	−0.369063
$527$	−16.6607	−0.725750
$528$	−5.57920	−0.242804
$529$	41.6407	1.81046
$530$	−27.4861	−1.19392
$531$	72.8206	3.16015
$532$	1.04550	0.0453283
$533$	−3.14018	−0.136016
$534$	4.76532	0.206215
$535$	37.0003	1.59966
$536$	14.6917	0.634586
$537$	8.58042	0.370272
$538$	18.7958	0.810345
$539$	−11.3137	−0.487314
$540$	−19.6468	−0.845463
$541$	20.1527	0.866434	0.433217	−	0.901290i	$-0.357378\pi$
$541$	20.1527	0.866434	0.433217	+	0.901290i	$0.357378\pi$
$542$	−12.8272	−0.550974
$543$	−3.18200	−0.136553
$544$	−3.06854	−0.131563
$545$	−29.0229	−1.24321
$546$	−2.45818	−0.105200
$547$	32.4207	1.38621	0.693105	−	0.720837i	$-0.256242\pi$
$547$	32.4207	1.38621	0.693105	+	0.720837i	$0.256242\pi$
$548$	−0.349324	−0.0149224
$549$	−20.9121	−0.892505
$550$	−4.53127	−0.193214
$551$	3.67644	0.156622
$552$	23.4198	0.996812
$553$	13.3725	0.568657
$554$	14.2561	0.605683
$555$	93.5991	3.97306
$556$	−3.98902	−0.169172
$557$	36.4455	1.54425	0.772124	−	0.635472i	$-0.219195\pi$
$557$	36.4455	1.54425	0.772124	+	0.635472i	$0.219195\pi$
$558$	29.7816	1.26076
$559$	−4.74079	−0.200514
$560$	2.83750	0.119906
$561$	−17.1200	−0.722808
$562$	−0.855700	−0.0360955
$563$	−15.9781	−0.673398	−0.336699	−	0.941612i	$-0.609310\pi$
$563$	−15.9781	−0.673398	−0.336699	+	0.941612i	$0.609310\pi$
$564$	−27.1379	−1.14271
$565$	13.2806	0.558721
$566$	11.0969	0.466437
$567$	4.84214	0.203351
$568$	2.83404	0.118914
$569$	36.9401	1.54861	0.774306	−	0.632812i	$-0.218099\pi$
$569$	36.9401	1.54861	0.774306	+	0.632812i	$0.218099\pi$
$570$	7.90569	0.331133
$571$	8.56438	0.358408	0.179204	−	0.983812i	$-0.442648\pi$
$571$	8.56438	0.358408	0.179204	+	0.983812i	$0.442648\pi$
$572$	−1.54597	−0.0646402
$573$	47.3802	1.97934
$574$	−4.06744	−0.169772
$575$	19.0209	0.793225
$576$	5.48515	0.228548
$577$	−39.5768	−1.64761	−0.823803	−	0.566876i	$-0.808152\pi$
$577$	−39.5768	−1.64761	−0.823803	+	0.566876i	$0.808152\pi$
$578$	7.58405	0.315455
$579$	−37.2622	−1.54857
$580$	9.97786	0.414308
$581$	7.20722	0.299006
$582$	27.4176	1.13650
$583$	19.3975	0.803361
$584$	1.08964	0.0450897
$585$	−12.0159	−0.496797
$586$	−24.2495	−1.00174
$587$	−15.0877	−0.622736	−0.311368	−	0.950289i	$-0.600787\pi$
$587$	−15.0877	−0.622736	−0.311368	+	0.950289i	$0.600787\pi$
$588$	17.2064	0.709582
$589$	−5.42951	−0.223719
$590$	−36.0310	−1.48337
$591$	29.0916	1.19667
$592$	−11.8395	−0.486599
$593$	14.8139	0.608334	0.304167	−	0.952619i	$-0.401622\pi$
$593$	14.8139	0.608334	0.304167	+	0.952619i	$0.401622\pi$
$594$	13.8651	0.568893
$595$	8.70698	0.356951
$596$	−7.93543	−0.325048
$597$	28.1444	1.15187
$598$	6.48950	0.265375
$599$	18.8276	0.769276	0.384638	−	0.923068i	$-0.374326\pi$
$599$	18.8276	0.769276	0.384638	+	0.923068i	$0.374326\pi$
$600$	6.89139	0.281340
$601$	−26.6665	−1.08775	−0.543874	−	0.839167i	$-0.683043\pi$
$601$	−26.6665	−1.08775	−0.543874	+	0.839167i	$0.683043\pi$
$602$	−6.14069	−0.250276
$603$	−80.5863	−3.28173
$604$	7.49138	0.304820
$605$	−19.8978	−0.808960
$606$	31.6252	1.28469
$607$	−2.06850	−0.0839579	−0.0419790	−	0.999118i	$-0.513366\pi$
$607$	−2.06850	−0.0839579	−0.0419790	+	0.999118i	$0.513366\pi$
$608$	−1.00000	−0.0405554
$609$	−11.1965	−0.453705
$610$	10.3471	0.418942
$611$	−7.51978	−0.304218
$612$	16.8314	0.680369
$613$	23.4376	0.946634	0.473317	−	0.880892i	$-0.343056\pi$
$613$	23.4376	0.946634	0.473317	+	0.880892i	$0.343056\pi$
$614$	8.66246	0.349588
$615$	−30.7564	−1.24022
$616$	−2.00248	−0.0806821
$617$	−0.367420	−0.0147918	−0.00739589	−	0.999973i	$-0.502354\pi$
$617$	−0.367420	−0.0147918	−0.00739589	+	0.999973i	$0.502354\pi$
$618$	22.5432	0.906822
$619$	31.6786	1.27327	0.636636	−	0.771165i	$-0.280326\pi$
$619$	31.6786	1.27327	0.636636	+	0.771165i	$0.280326\pi$
$620$	−14.7357	−0.591799
$621$	−58.2016	−2.33555
$622$	10.5945	0.424801
$623$	1.71036	0.0685241
$624$	2.35119	0.0941230
$625$	−31.2320	−1.24928
$626$	7.50496	0.299958
$627$	−5.57920	−0.222812
$628$	12.3973	0.494705
$629$	−36.3299	−1.44857
$630$	−15.5641	−0.620088
$631$	4.56729	0.181821	0.0909104	−	0.995859i	$-0.471022\pi$
$631$	4.56729	0.181821	0.0909104	+	0.995859i	$0.471022\pi$
$632$	−12.7905	−0.508779
$633$	2.91293	0.115778
$634$	10.4072	0.413322
$635$	13.1770	0.522915
$636$	−29.5007	−1.16978
$637$	4.76782	0.188908
$638$	−7.04157	−0.278779
$639$	−15.5451	−0.614955
$640$	−2.71400	−0.107280
$641$	15.0650	0.595030	0.297515	−	0.954717i	$-0.403842\pi$
$641$	15.0650	0.595030	0.297515	+	0.954717i	$0.403842\pi$
$642$	39.7123	1.56732
$643$	−38.5647	−1.52084	−0.760422	−	0.649429i	$-0.775008\pi$
$643$	−38.5647	−1.52084	−0.760422	+	0.649429i	$0.775008\pi$
$644$	8.40579	0.331234
$645$	−46.4335	−1.82832
$646$	−3.06854	−0.120730
$647$	6.94107	0.272882	0.136441	−	0.990648i	$-0.456434\pi$
$647$	6.94107	0.272882	0.136441	+	0.990648i	$0.456434\pi$
$648$	−4.63139	−0.181938
$649$	25.4278	0.998128
$650$	1.90957	0.0748996
$651$	16.5354	0.648075
$652$	20.1155	0.787784
$653$	−10.4388	−0.408501	−0.204250	−	0.978919i	$-0.565476\pi$
$653$	−10.4388	−0.408501	−0.204250	+	0.978919i	$0.565476\pi$
$654$	−31.1502	−1.21807
$655$	−14.7304	−0.575563
$656$	3.89041	0.151895
$657$	−5.97684	−0.233179
$658$	−9.74029	−0.379716
$659$	−32.5868	−1.26940	−0.634701	−	0.772758i	$-0.718877\pi$
$659$	−32.5868	−1.26940	−0.634701	+	0.772758i	$0.718877\pi$
$660$	−15.1420	−0.589400
$661$	3.64918	0.141937	0.0709684	−	0.997479i	$-0.477391\pi$
$661$	3.64918	0.141937	0.0709684	+	0.997479i	$0.477391\pi$
$662$	4.44099	0.172604
$663$	7.21473	0.280197
$664$	−6.89354	−0.267521
$665$	2.83750	0.110033
$666$	64.9412	2.51642
$667$	29.5584	1.14450
$668$	3.75981	0.145471
$669$	25.5482	0.987752
$670$	39.8734	1.54044
$671$	−7.30215	−0.281897
$672$	3.04548	0.117482
$673$	42.3897	1.63400	0.817002	−	0.576635i	$-0.195634\pi$
$673$	42.3897	1.63400	0.817002	+	0.576635i	$0.195634\pi$
$674$	25.0304	0.964135
$675$	−17.1261	−0.659185
$676$	−12.3485	−0.474942
$677$	−23.5502	−0.905106	−0.452553	−	0.891738i	$-0.649487\pi$
$677$	−23.5502	−0.905106	−0.452553	+	0.891738i	$0.649487\pi$
$678$	14.2541	0.547424
$679$	9.84070	0.377651
$680$	−8.32803	−0.319365
$681$	20.3571	0.780087
$682$	10.3993	0.398208
$683$	23.5248	0.900152	0.450076	−	0.892990i	$-0.351397\pi$
$683$	23.5248	0.900152	0.450076	+	0.892990i	$0.351397\pi$
$684$	5.48515	0.209730
$685$	−0.948065	−0.0362237
$686$	13.4942	0.515212
$687$	−13.7884	−0.526061
$688$	5.87343	0.223923
$689$	−8.17450	−0.311424
$690$	63.5613	2.41974
$691$	9.29670	0.353663	0.176831	−	0.984241i	$-0.443415\pi$
$691$	9.29670	0.353663	0.176831	+	0.984241i	$0.443415\pi$
$692$	−21.6307	−0.822278
$693$	10.9839	0.417243
$694$	−7.41359	−0.281416
$695$	−10.8262	−0.410661
$696$	10.7092	0.405931
$697$	11.9379	0.452180
$698$	−4.20232	−0.159060
$699$	−39.0925	−1.47861
$700$	2.47345	0.0934876
$701$	16.3585	0.617853	0.308927	−	0.951086i	$-0.400030\pi$
$701$	16.3585	0.617853	0.308927	+	0.951086i	$0.400030\pi$
$702$	−5.84306	−0.220532
$703$	−11.8395	−0.446534
$704$	1.91532	0.0721865
$705$	−73.6522	−2.77390
$706$	9.33220	0.351222
$707$	11.3509	0.426893
$708$	−38.6719	−1.45338
$709$	−23.7095	−0.890430	−0.445215	−	0.895424i	$-0.646873\pi$
$709$	−23.7095	−0.890430	−0.445215	+	0.895424i	$0.646873\pi$
$710$	7.69158	0.288660
$711$	70.1578	2.63112
$712$	−1.63592	−0.0613087
$713$	−43.6529	−1.63481
$714$	9.34517	0.349734
$715$	−4.19576	−0.156913
$716$	−2.94563	−0.110084
$717$	27.0189	1.00904
$718$	−3.20438	−0.119586
$719$	41.1896	1.53611	0.768056	−	0.640383i	$-0.221224\pi$
$719$	41.1896	1.53611	0.768056	+	0.640383i	$0.221224\pi$
$720$	14.8867	0.554794
$721$	8.09118	0.301331
$722$	−1.00000	−0.0372161
$723$	22.9304	0.852791
$724$	1.09237	0.0405976
$725$	8.69771	0.323025
$726$	−21.3562	−0.792604
$727$	17.9195	0.664598	0.332299	−	0.943174i	$-0.392176\pi$
$727$	17.9195	0.664598	0.332299	+	0.943174i	$0.392176\pi$
$728$	0.843886	0.0312765
$729$	−37.8566	−1.40210
$730$	2.95729	0.109454
$731$	18.0229	0.666600
$732$	11.1055	0.410471
$733$	−17.0730	−0.630606	−0.315303	−	0.948991i	$-0.602106\pi$
$733$	−17.0730	−0.630606	−0.315303	+	0.948991i	$0.602106\pi$
$734$	10.9140	0.402845
$735$	46.6983	1.72249
$736$	−8.03994	−0.296356
$737$	−28.1394	−1.03653
$738$	−21.3395	−0.785517
$739$	14.6540	0.539055	0.269528	−	0.962993i	$-0.413132\pi$
$739$	14.6540	0.539055	0.269528	+	0.962993i	$0.413132\pi$
$740$	−32.1323	−1.18121
$741$	2.35119	0.0863732
$742$	−10.5884	−0.388711
$743$	−16.5949	−0.608809	−0.304405	−	0.952543i	$-0.598458\pi$
$743$	−16.5949	−0.608809	−0.304405	+	0.952543i	$0.598458\pi$
$744$	−15.8158	−0.579834
$745$	−21.5368	−0.789046
$746$	17.0225	0.623238
$747$	37.8121	1.38347
$748$	5.87725	0.214894
$749$	14.2535	0.520810
$750$	−20.8252	−0.760428
$751$	53.5990	1.95586	0.977928	−	0.208940i	$-0.0670015\pi$
$751$	53.5990	1.95586	0.977928	+	0.208940i	$0.0670015\pi$
$752$	9.31636	0.339733
$753$	63.1449	2.30113
$754$	2.96747	0.108069
$755$	20.3316	0.739943
$756$	−7.56845	−0.275262
$757$	−10.2731	−0.373383	−0.186692	−	0.982419i	$-0.559777\pi$
$757$	−10.2731	−0.373383	−0.186692	+	0.982419i	$0.559777\pi$
$758$	−24.6026	−0.893605
$759$	−44.8564	−1.62819
$760$	−2.71400	−0.0984471
$761$	−43.8690	−1.59025	−0.795125	−	0.606445i	$-0.792595\pi$
$761$	−43.8690	−1.59025	−0.795125	+	0.606445i	$0.792595\pi$
$762$	14.1429	0.512342
$763$	−11.1804	−0.404757
$764$	−16.2655	−0.588465
$765$	45.6804	1.65158
$766$	−12.2802	−0.443702
$767$	−10.7158	−0.386925
$768$	−2.91293	−0.105111
$769$	−44.9736	−1.62179	−0.810895	−	0.585192i	$-0.801019\pi$
$769$	−44.9736	−1.62179	−0.810895	+	0.585192i	$0.801019\pi$
$770$	−5.43473	−0.195854
$771$	−7.69088	−0.276980
$772$	12.7920	0.460395
$773$	−4.49899	−0.161817	−0.0809087	−	0.996722i	$-0.525782\pi$
$773$	−4.49899	−0.161817	−0.0809087	+	0.996722i	$0.525782\pi$
$774$	−32.2166	−1.15800
$775$	−12.8451	−0.461410
$776$	−9.41240	−0.337886
$777$	36.0568	1.29353
$778$	27.5770	0.988682
$779$	3.89041	0.139388
$780$	6.38114	0.228481
$781$	−5.42810	−0.194233
$782$	−24.6709	−0.882230
$783$	−26.6139	−0.951104
$784$	−5.90692	−0.210962
$785$	33.6462	1.20088
$786$	−15.8100	−0.563926
$787$	44.2455	1.57718	0.788591	−	0.614919i	$-0.210811\pi$
$787$	44.2455	1.57718	0.788591	+	0.614919i	$0.210811\pi$
$788$	−9.98707	−0.355775
$789$	−24.6560	−0.877778
$790$	−34.7134	−1.23505
$791$	5.11605	0.181906
$792$	−10.5058	−0.373309
$793$	3.07728	0.109277
$794$	−27.8213	−0.987340
$795$	−80.0649	−2.83961
$796$	−9.66190	−0.342457
$797$	32.1688	1.13948	0.569738	−	0.821826i	$-0.307045\pi$
$797$	32.1688	1.13948	0.569738	+	0.821826i	$0.307045\pi$
$798$	3.04548	0.107809
$799$	28.5877	1.01136
$800$	−2.36580	−0.0836435
$801$	8.97326	0.317055
$802$	−18.2204	−0.643383
$803$	−2.08702	−0.0736492
$804$	42.7960	1.50930
$805$	22.8133	0.804063
$806$	−4.38247	−0.154366
$807$	54.7509	1.92732
$808$	−10.8568	−0.381942
$809$	51.7237	1.81851	0.909254	−	0.416242i	$-0.136653\pi$
$809$	51.7237	1.81851	0.909254	+	0.416242i	$0.136653\pi$
$810$	−12.5696	−0.441651
$811$	−34.6043	−1.21512	−0.607560	−	0.794274i	$-0.707852\pi$
$811$	−34.6043	−1.21512	−0.607560	+	0.794274i	$0.707852\pi$
$812$	3.84373	0.134888
$813$	−37.3646	−1.31043
$814$	22.6764	0.794808
$815$	54.5935	1.91233
$816$	−8.93844	−0.312908
$817$	5.87343	0.205485
$818$	22.2303	0.777264
$819$	−4.62884	−0.161745
$820$	10.5586	0.368721
$821$	54.1266	1.88903	0.944516	−	0.328466i	$-0.106531\pi$
$821$	54.1266	1.88903	0.944516	+	0.328466i	$0.106531\pi$
$822$	−1.01756	−0.0354913
$823$	−10.9317	−0.381057	−0.190528	−	0.981682i	$-0.561020\pi$
$823$	−10.9317	−0.381057	−0.190528	+	0.981682i	$0.561020\pi$
$824$	−7.73903	−0.269602
$825$	−13.1993	−0.459539
$826$	−13.8801	−0.482949
$827$	44.7518	1.55617	0.778087	−	0.628156i	$-0.216190\pi$
$827$	44.7518	1.55617	0.778087	+	0.628156i	$0.216190\pi$
$828$	44.1003	1.53259
$829$	35.6891	1.23954	0.619768	−	0.784785i	$-0.287227\pi$
$829$	35.6891	1.23954	0.619768	+	0.784785i	$0.287227\pi$
$830$	−18.7091	−0.649402
$831$	41.5269	1.44055
$832$	−0.807158	−0.0279832
$833$	−18.1256	−0.628016
$834$	−11.6197	−0.402358
$835$	10.2041	0.353128
$836$	1.91532	0.0662429
$837$	39.3045	1.35856
$838$	−15.2647	−0.527309
$839$	−6.52818	−0.225378	−0.112689	−	0.993630i	$-0.535946\pi$
$839$	−6.52818	−0.225378	−0.112689	+	0.993630i	$0.535946\pi$
$840$	8.26542	0.285184
$841$	−15.4838	−0.533924
$842$	25.8064	0.889348
$843$	−2.49259	−0.0858495
$844$	−1.00000	−0.0344214
$845$	−33.5138	−1.15291
$846$	−51.1016	−1.75691
$847$	−7.66514	−0.263377
$848$	10.1275	0.347780
$849$	32.3244	1.10937
$850$	−7.25955	−0.249000
$851$	−95.1886	−3.26302
$852$	8.25535	0.282824
$853$	8.43031	0.288648	0.144324	−	0.989530i	$-0.453899\pi$
$853$	8.43031	0.288648	0.144324	+	0.989530i	$0.453899\pi$
$854$	3.98597	0.136397
$855$	14.8867	0.509114
$856$	−13.6331	−0.465970
$857$	−1.19404	−0.0407875	−0.0203937	−	0.999792i	$-0.506492\pi$
$857$	−1.19404	−0.0407875	−0.0203937	+	0.999792i	$0.506492\pi$
$858$	−4.50330	−0.153740
$859$	−3.24234	−0.110627	−0.0553136	−	0.998469i	$-0.517616\pi$
$859$	−3.24234	−0.110627	−0.0553136	+	0.998469i	$0.517616\pi$
$860$	15.9405	0.543566
$861$	−11.8482	−0.403784
$862$	−36.2604	−1.23503
$863$	−41.2472	−1.40407	−0.702036	−	0.712141i	$-0.747725\pi$
$863$	−41.2472	−1.40407	−0.702036	+	0.712141i	$0.747725\pi$
$864$	7.23905	0.246278
$865$	−58.7059	−1.99606
$866$	−18.0964	−0.614940
$867$	22.0918	0.750276
$868$	−5.67657	−0.192675
$869$	24.4980	0.831036
$870$	29.0648	0.985388
$871$	11.8586	0.401812
$872$	10.6938	0.362137
$873$	51.6284	1.74736
$874$	−8.03994	−0.271955
$875$	−7.47454	−0.252686
$876$	3.17405	0.107241
$877$	30.9878	1.04639	0.523193	−	0.852215i	$-0.324741\pi$
$877$	30.9878	1.04639	0.523193	+	0.852215i	$0.324741\pi$
$878$	−3.80676	−0.128472
$879$	−70.6371	−2.38253
$880$	5.19819	0.175231
$881$	−6.68498	−0.225223	−0.112611	−	0.993639i	$-0.535922\pi$
$881$	−6.68498	−0.225223	−0.112611	+	0.993639i	$0.535922\pi$
$882$	32.4003	1.09098
$883$	−26.4231	−0.889208	−0.444604	−	0.895727i	$-0.646656\pi$
$883$	−26.4231	−0.889208	−0.444604	+	0.895727i	$0.646656\pi$
$884$	−2.47680	−0.0833037
$885$	−104.956	−3.52804
$886$	18.8706	0.633971
$887$	50.2495	1.68721	0.843606	−	0.536963i	$-0.180428\pi$
$887$	50.2495	1.68721	0.843606	+	0.536963i	$0.180428\pi$
$888$	−34.4875	−1.15732
$889$	5.07614	0.170248
$890$	−4.43989	−0.148825
$891$	8.87062	0.297177
$892$	−8.77064	−0.293663
$893$	9.31636	0.311760
$894$	−23.1153	−0.773092
$895$	−7.99445	−0.267225
$896$	−1.04550	−0.0349278
$897$	18.9035	0.631168
$898$	−14.4551	−0.482372
$899$	−19.9612	−0.665745
$900$	12.9767	0.432558
$901$	31.0767	1.03532
$902$	−7.45140	−0.248104
$903$	−17.8874	−0.595255
$904$	−4.89338	−0.162751
$905$	2.96469	0.0985498
$906$	21.8218	0.724982
$907$	−12.2095	−0.405410	−0.202705	−	0.979240i	$-0.564973\pi$
$907$	−12.2095	−0.405410	−0.202705	+	0.979240i	$0.564973\pi$
$908$	−6.98855	−0.231923
$909$	59.5513	1.97519
$910$	2.29031	0.0759230
$911$	−6.16492	−0.204253	−0.102126	−	0.994771i	$-0.532565\pi$
$911$	−6.16492	−0.204253	−0.102126	+	0.994771i	$0.532565\pi$
$912$	−2.91293	−0.0964567
$913$	13.2034	0.436968
$914$	−15.1590	−0.501415
$915$	30.1403	0.996409
$916$	4.73353	0.156400
$917$	−5.67452	−0.187389
$918$	22.2133	0.733149
$919$	−51.1872	−1.68851	−0.844255	−	0.535941i	$-0.819957\pi$
$919$	−51.1872	−1.68851	−0.844255	+	0.535941i	$0.819957\pi$
$920$	−21.8204	−0.719397
$921$	25.2331	0.831460
$922$	14.1974	0.467567
$923$	2.28752	0.0752945
$924$	−5.83307	−0.191894
$925$	−28.0098	−0.920955
$926$	−28.5735	−0.938983
$927$	42.4497	1.39423
$928$	−3.67644	−0.120685
$929$	0.900308	0.0295381	0.0147691	−	0.999891i	$-0.495299\pi$
$929$	0.900308	0.0295381	0.0147691	+	0.999891i	$0.495299\pi$
$930$	−42.9240	−1.40753
$931$	−5.90692	−0.193592
$932$	13.4203	0.439598
$933$	30.8610	1.01034
$934$	−34.8486	−1.14028
$935$	15.9509	0.521649
$936$	4.42738	0.144713
$937$	57.8114	1.88861	0.944307	−	0.329065i	$-0.106733\pi$
$937$	57.8114	1.88861	0.944307	+	0.329065i	$0.106733\pi$
$938$	15.3603	0.501530
$939$	21.8614	0.713420
$940$	25.2846	0.824693
$941$	−47.3129	−1.54236	−0.771179	−	0.636619i	$-0.780333\pi$
$941$	−47.3129	−1.54236	−0.771179	+	0.636619i	$0.780333\pi$
$942$	36.1123	1.17660
$943$	31.2787	1.01857
$944$	13.2760	0.432096
$945$	−20.5408	−0.668192
$946$	−11.2495	−0.365754
$947$	−13.5857	−0.441477	−0.220738	−	0.975333i	$-0.570847\pi$
$947$	−13.5857	−0.441477	−0.220738	+	0.975333i	$0.570847\pi$
$948$	−37.2578	−1.21008
$949$	0.879513	0.0285502
$950$	−2.36580	−0.0767566
$951$	30.3153	0.983042
$952$	−3.20817	−0.103977
$953$	18.3927	0.595798	0.297899	−	0.954597i	$-0.403714\pi$
$953$	18.3927	0.595798	0.297899	+	0.954597i	$0.403714\pi$
$954$	−55.5509	−1.79853
$955$	−44.1445	−1.42848
$956$	−9.27553	−0.299992
$957$	−20.5116	−0.663046
$958$	−29.9247	−0.966824
$959$	−0.365219	−0.0117936
$960$	−7.90569	−0.255155
$961$	−1.52046	−0.0490472
$962$	−9.55632	−0.308108
$963$	74.7796	2.40974
$964$	−7.87195	−0.253538
$965$	34.7176	1.11760
$966$	24.4854	0.787806
$967$	−4.34796	−0.139821	−0.0699105	−	0.997553i	$-0.522271\pi$
$967$	−4.34796	−0.139821	−0.0699105	+	0.997553i	$0.522271\pi$
$968$	7.33153	0.235644
$969$	−8.93844	−0.287144
$970$	−25.5453	−0.820209
$971$	−54.2533	−1.74107	−0.870535	−	0.492106i	$-0.836227\pi$
$971$	−54.2533	−1.74107	−0.870535	+	0.492106i	$0.836227\pi$
$972$	8.22624	0.263857
$973$	−4.17053	−0.133701
$974$	15.1429	0.485211
$975$	5.56244	0.178141
$976$	−3.81249	−0.122035
$977$	−24.2978	−0.777356	−0.388678	−	0.921374i	$-0.627068\pi$
$977$	−24.2978	−0.777356	−0.388678	+	0.921374i	$0.627068\pi$
$978$	58.5950	1.87366
$979$	3.13332	0.100141
$980$	−16.0314	−0.512104
$981$	−58.6569	−1.87277
$982$	22.6136	0.721628
$983$	41.2528	1.31576	0.657880	−	0.753123i	$-0.271453\pi$
$983$	41.2528	1.31576	0.657880	+	0.753123i	$0.271453\pi$
$984$	11.3325	0.361266
$985$	−27.1049	−0.863634
$986$	−11.2813	−0.359270
$987$	−28.3728	−0.903115
$988$	−0.807158	−0.0256791
$989$	47.2221	1.50157
$990$	−28.5128	−0.906197
$991$	7.73665	0.245763	0.122881	−	0.992421i	$-0.460787\pi$
$991$	7.73665	0.245763	0.122881	+	0.992421i	$0.460787\pi$
$992$	5.42951	0.172387
$993$	12.9363	0.410520
$994$	2.96300	0.0939806
$995$	−26.2224	−0.831306
$996$	−20.0804	−0.636272
$997$	−5.75421	−0.182238	−0.0911188	−	0.995840i	$-0.529044\pi$
$997$	−5.75421	−0.182238	−0.0911188	+	0.995840i	$0.529044\pi$
$998$	15.5567	0.492438
$999$	85.7065	2.71163

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.i.1.3	✓	43

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.i.1.3	✓	43	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:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.91293 q^{3} +1.00000 q^{4} +2.71400 q^{5} +2.91293 q^{6} +1.04550 q^{7} -1.00000 q^{8} +5.48515 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.91293 q^{3} +1.00000 q^{4} +2.71400 q^{5} +2.91293 q^{6} +1.04550 q^{7} -1.00000 q^{8} +5.48515 q^{9} -2.71400 q^{10} +1.91532 q^{11} -2.91293 q^{12} -0.807158 q^{13} -1.04550 q^{14} -7.90569 q^{15} +1.00000 q^{16} +3.06854 q^{17} -5.48515 q^{18} +1.00000 q^{19} +2.71400 q^{20} -3.04548 q^{21} -1.91532 q^{22} +8.03994 q^{23} +2.91293 q^{24} +2.36580 q^{25} +0.807158 q^{26} -7.23905 q^{27} +1.04550 q^{28} +3.67644 q^{29} +7.90569 q^{30} -5.42951 q^{31} -1.00000 q^{32} -5.57920 q^{33} -3.06854 q^{34} +2.83750 q^{35} +5.48515 q^{36} -11.8395 q^{37} -1.00000 q^{38} +2.35119 q^{39} -2.71400 q^{40} +3.89041 q^{41} +3.04548 q^{42} +5.87343 q^{43} +1.91532 q^{44} +14.8867 q^{45} -8.03994 q^{46} +9.31636 q^{47} -2.91293 q^{48} -5.90692 q^{49} -2.36580 q^{50} -8.93844 q^{51} -0.807158 q^{52} +10.1275 q^{53} +7.23905 q^{54} +5.19819 q^{55} -1.04550 q^{56} -2.91293 q^{57} -3.67644 q^{58} +13.2760 q^{59} -7.90569 q^{60} -3.81249 q^{61} +5.42951 q^{62} +5.73474 q^{63} +1.00000 q^{64} -2.19063 q^{65} +5.57920 q^{66} -14.6917 q^{67} +3.06854 q^{68} -23.4198 q^{69} -2.83750 q^{70} -2.83404 q^{71} -5.48515 q^{72} -1.08964 q^{73} +11.8395 q^{74} -6.89139 q^{75} +1.00000 q^{76} +2.00248 q^{77} -2.35119 q^{78} +12.7905 q^{79} +2.71400 q^{80} +4.63139 q^{81} -3.89041 q^{82} +6.89354 q^{83} -3.04548 q^{84} +8.32803 q^{85} -5.87343 q^{86} -10.7092 q^{87} -1.91532 q^{88} +1.63592 q^{89} -14.8867 q^{90} -0.843886 q^{91} +8.03994 q^{92} +15.8158 q^{93} -9.31636 q^{94} +2.71400 q^{95} +2.91293 q^{96} +9.41240 q^{97} +5.90692 q^{98} +10.5058 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 43 q - 43 q^{2} + 43 q^{4} + 19 q^{7} - 43 q^{8} + 53 q^{9}+O(q^{10}) \) 43 * q - 43 * q^2 + 43 * q^4 + 19 * q^7 - 43 * q^8 + 53 * q^9	\( 43 q - 43 q^{2} + 43 q^{4} + 19 q^{7} - 43 q^{8} + 53 q^{9} + 14 q^{11} + 3 q^{13} - 19 q^{14} + q^{15} + 43 q^{16} + 8 q^{17} - 53 q^{18} + 43 q^{19} - 14 q^{22} + 43 q^{23} + 97 q^{25} - 3 q^{26} + 15 q^{27} + 19 q^{28} - 25 q^{29} - q^{30} + 22 q^{31} - 43 q^{32} + 22 q^{33} - 8 q^{34} - 6 q^{35} + 53 q^{36} + 42 q^{37} - 43 q^{38} + 9 q^{39} - 40 q^{41} + 72 q^{43} + 14 q^{44} - q^{45} - 43 q^{46} + 27 q^{47} + 86 q^{49} - 97 q^{50} - 3 q^{51} + 3 q^{52} - 5 q^{53} - 15 q^{54} + 86 q^{55} - 19 q^{56} + 25 q^{58} - 43 q^{59} + q^{60} + 31 q^{61} - 22 q^{62} + 38 q^{63} + 43 q^{64} - 32 q^{65} - 22 q^{66} + 15 q^{67} + 8 q^{68} - 7 q^{69} + 6 q^{70} + 14 q^{71} - 53 q^{72} + 93 q^{73} - 42 q^{74} - 13 q^{75} + 43 q^{76} + 38 q^{77} - 9 q^{78} + 15 q^{79} + 43 q^{81} + 40 q^{82} + 34 q^{83} + 16 q^{85} - 72 q^{86} + 60 q^{87} - 14 q^{88} - 37 q^{89} + q^{90} - 3 q^{91} + 43 q^{92} + 19 q^{93} - 27 q^{94} + 27 q^{97} - 86 q^{98} - 24 q^{99}+O(q^{100}) \) 43 * q - 43 * q^2 + 43 * q^4 + 19 * q^7 - 43 * q^8 + 53 * q^9 + 14 * q^11 + 3 * q^13 - 19 * q^14 + q^15 + 43 * q^16 + 8 * q^17 - 53 * q^18 + 43 * q^19 - 14 * q^22 + 43 * q^23 + 97 * q^25 - 3 * q^26 + 15 * q^27 + 19 * q^28 - 25 * q^29 - q^30 + 22 * q^31 - 43 * q^32 + 22 * q^33 - 8 * q^34 - 6 * q^35 + 53 * q^36 + 42 * q^37 - 43 * q^38 + 9 * q^39 - 40 * q^41 + 72 * q^43 + 14 * q^44 - q^45 - 43 * q^46 + 27 * q^47 + 86 * q^49 - 97 * q^50 - 3 * q^51 + 3 * q^52 - 5 * q^53 - 15 * q^54 + 86 * q^55 - 19 * q^56 + 25 * q^58 - 43 * q^59 + q^60 + 31 * q^61 - 22 * q^62 + 38 * q^63 + 43 * q^64 - 32 * q^65 - 22 * q^66 + 15 * q^67 + 8 * q^68 - 7 * q^69 + 6 * q^70 + 14 * q^71 - 53 * q^72 + 93 * q^73 - 42 * q^74 - 13 * q^75 + 43 * q^76 + 38 * q^77 - 9 * q^78 + 15 * q^79 + 43 * q^81 + 40 * q^82 + 34 * q^83 + 16 * q^85 - 72 * q^86 + 60 * q^87 - 14 * q^88 - 37 * q^89 + q^90 - 3 * q^91 + 43 * q^92 + 19 * q^93 - 27 * q^94 + 27 * q^97 - 86 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

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Database

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