LMFDB - Embedded newform 6017.2.a.e.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6017,2,Mod(1,6017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6017, 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("6017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6017 = 11 \cdot 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6017.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:	$48.0459868962$
Analytic rank:	$0$
Dimension:	$119$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	6017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.33754 q^{2} +1.15439 q^{3} +3.46412 q^{4} -4.35932 q^{5} -2.69844 q^{6} +3.66625 q^{7} -3.42244 q^{8} -1.66738 q^{9} +O(q^{10})$	\(q-2.33754 q^{2} +1.15439 q^{3} +3.46412 q^{4} -4.35932 q^{5} -2.69844 q^{6} +3.66625 q^{7} -3.42244 q^{8} -1.66738 q^{9} +10.1901 q^{10} +1.00000 q^{11} +3.99894 q^{12} +1.86776 q^{13} -8.57002 q^{14} -5.03236 q^{15} +1.07186 q^{16} -4.71132 q^{17} +3.89759 q^{18} -1.90392 q^{19} -15.1012 q^{20} +4.23228 q^{21} -2.33754 q^{22} -4.80721 q^{23} -3.95082 q^{24} +14.0037 q^{25} -4.36598 q^{26} -5.38798 q^{27} +12.7003 q^{28} -5.41729 q^{29} +11.7634 q^{30} +1.57474 q^{31} +4.33934 q^{32} +1.15439 q^{33} +11.0129 q^{34} -15.9824 q^{35} -5.77601 q^{36} -8.15011 q^{37} +4.45050 q^{38} +2.15613 q^{39} +14.9195 q^{40} -6.85770 q^{41} -9.89314 q^{42} -0.602984 q^{43} +3.46412 q^{44} +7.26867 q^{45} +11.2371 q^{46} +7.92371 q^{47} +1.23735 q^{48} +6.44137 q^{49} -32.7343 q^{50} -5.43869 q^{51} +6.47014 q^{52} +5.70152 q^{53} +12.5946 q^{54} -4.35932 q^{55} -12.5475 q^{56} -2.19787 q^{57} +12.6631 q^{58} +12.9919 q^{59} -17.4327 q^{60} +6.33668 q^{61} -3.68103 q^{62} -6.11304 q^{63} -12.2871 q^{64} -8.14218 q^{65} -2.69844 q^{66} +1.90627 q^{67} -16.3205 q^{68} -5.54940 q^{69} +37.3595 q^{70} -14.5542 q^{71} +5.70652 q^{72} -9.17144 q^{73} +19.0512 q^{74} +16.1657 q^{75} -6.59540 q^{76} +3.66625 q^{77} -5.04004 q^{78} +8.52958 q^{79} -4.67260 q^{80} -1.21768 q^{81} +16.0302 q^{82} +1.57642 q^{83} +14.6611 q^{84} +20.5381 q^{85} +1.40950 q^{86} -6.25366 q^{87} -3.42244 q^{88} +17.6157 q^{89} -16.9908 q^{90} +6.84768 q^{91} -16.6527 q^{92} +1.81787 q^{93} -18.5220 q^{94} +8.29980 q^{95} +5.00929 q^{96} -16.3642 q^{97} -15.0570 q^{98} -1.66738 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 119 q + 15 q^{2} + 15 q^{3} + 133 q^{4} + 6 q^{5} + 16 q^{6} + 72 q^{7} + 39 q^{8} + 128 q^{9}+O(q^{10}) $ 119 * q + 15 * q^2 + 15 * q^3 + 133 * q^4 + 6 * q^5 + 16 * q^6 + 72 * q^7 + 39 * q^8 + 128 * q^9	\( 119 q + 15 q^{2} + 15 q^{3} + 133 q^{4} + 6 q^{5} + 16 q^{6} + 72 q^{7} + 39 q^{8} + 128 q^{9} + 22 q^{10} + 119 q^{11} + 40 q^{12} + 67 q^{13} + 3 q^{14} + 22 q^{15} + 145 q^{16} + 57 q^{17} + 53 q^{18} + 68 q^{19} + 25 q^{20} + 21 q^{21} + 15 q^{22} + 21 q^{23} + 34 q^{24} + 137 q^{25} + 10 q^{26} + 54 q^{27} + 149 q^{28} + 46 q^{29} + 10 q^{30} + 87 q^{31} + 58 q^{32} + 15 q^{33} + 16 q^{34} + 40 q^{35} + 137 q^{36} + 39 q^{37} + 27 q^{38} + 72 q^{39} + 46 q^{40} + 50 q^{41} - 4 q^{42} + 122 q^{43} + 133 q^{44} + 12 q^{45} + 22 q^{46} + 92 q^{47} + 9 q^{48} + 161 q^{49} + 2 q^{50} - 12 q^{51} + 177 q^{52} + 12 q^{53} + 19 q^{54} + 6 q^{55} - 16 q^{56} + 43 q^{57} + 56 q^{58} + 39 q^{59} + 27 q^{60} + 114 q^{61} + 66 q^{62} + 196 q^{63} + 161 q^{64} + 7 q^{65} + 16 q^{66} + 59 q^{67} + 139 q^{68} - 24 q^{69} + 9 q^{70} + 11 q^{71} + 92 q^{72} + 123 q^{73} + q^{74} + 19 q^{75} + 92 q^{76} + 72 q^{77} - 101 q^{78} + 78 q^{79} - 34 q^{80} + 139 q^{81} + 73 q^{82} + 108 q^{83} - 31 q^{84} + 30 q^{85} - 18 q^{86} + 164 q^{87} + 39 q^{88} + 15 q^{89} - 41 q^{90} + 60 q^{91} - 26 q^{92} - 2 q^{93} + 45 q^{94} + 75 q^{95} + 42 q^{96} + 73 q^{97} + 32 q^{98} + 128 q^{99}+O(q^{100}) \) 119 * q + 15 * q^2 + 15 * q^3 + 133 * q^4 + 6 * q^5 + 16 * q^6 + 72 * q^7 + 39 * q^8 + 128 * q^9 + 22 * q^10 + 119 * q^11 + 40 * q^12 + 67 * q^13 + 3 * q^14 + 22 * q^15 + 145 * q^16 + 57 * q^17 + 53 * q^18 + 68 * q^19 + 25 * q^20 + 21 * q^21 + 15 * q^22 + 21 * q^23 + 34 * q^24 + 137 * q^25 + 10 * q^26 + 54 * q^27 + 149 * q^28 + 46 * q^29 + 10 * q^30 + 87 * q^31 + 58 * q^32 + 15 * q^33 + 16 * q^34 + 40 * q^35 + 137 * q^36 + 39 * q^37 + 27 * q^38 + 72 * q^39 + 46 * q^40 + 50 * q^41 - 4 * q^42 + 122 * q^43 + 133 * q^44 + 12 * q^45 + 22 * q^46 + 92 * q^47 + 9 * q^48 + 161 * q^49 + 2 * q^50 - 12 * q^51 + 177 * q^52 + 12 * q^53 + 19 * q^54 + 6 * q^55 - 16 * q^56 + 43 * q^57 + 56 * q^58 + 39 * q^59 + 27 * q^60 + 114 * q^61 + 66 * q^62 + 196 * q^63 + 161 * q^64 + 7 * q^65 + 16 * q^66 + 59 * q^67 + 139 * q^68 - 24 * q^69 + 9 * q^70 + 11 * q^71 + 92 * q^72 + 123 * q^73 + q^74 + 19 * q^75 + 92 * q^76 + 72 * q^77 - 101 * q^78 + 78 * q^79 - 34 * q^80 + 139 * q^81 + 73 * q^82 + 108 * q^83 - 31 * q^84 + 30 * q^85 - 18 * q^86 + 164 * q^87 + 39 * q^88 + 15 * q^89 - 41 * q^90 + 60 * q^91 - 26 * q^92 - 2 * q^93 + 45 * q^94 + 75 * q^95 + 42 * q^96 + 73 * q^97 + 32 * q^98 + 128 * 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 $

$2$	−2.33754	−1.65289	−0.826447	−	0.563015i	$-0.809641\pi$
$2$	−2.33754	−1.65289	−0.826447	+	0.563015i	$0.809641\pi$
$3$	1.15439	0.666487	0.333244	−	0.942841i	$-0.391857\pi$
$3$	1.15439	0.666487	0.333244	+	0.942841i	$0.391857\pi$
$4$	3.46412	1.73206
$5$	−4.35932	−1.94955	−0.974774	−	0.223193i	$-0.928352\pi$
$5$	−4.35932	−1.94955	−0.974774	+	0.223193i	$0.928352\pi$
$6$	−2.69844	−1.10163
$7$	3.66625	1.38571	0.692856	−	0.721076i	$-0.256352\pi$
$7$	3.66625	1.38571	0.692856	+	0.721076i	$0.256352\pi$
$8$	−3.42244	−1.21001
$9$	−1.66738	−0.555795
$10$	10.1901	3.22240
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	3.99894	1.15439
$13$	1.86776	0.518024	0.259012	−	0.965874i	$-0.416603\pi$
$13$	1.86776	0.518024	0.259012	+	0.965874i	$0.416603\pi$
$14$	−8.57002	−2.29043
$15$	−5.03236	−1.29935
$16$	1.07186	0.267966
$17$	−4.71132	−1.14266	−0.571331	−	0.820720i	$-0.693573\pi$
$17$	−4.71132	−1.14266	−0.571331	+	0.820720i	$0.693573\pi$
$18$	3.89759	0.918670
$19$	−1.90392	−0.436789	−0.218395	−	0.975861i	$-0.570082\pi$
$19$	−1.90392	−0.436789	−0.218395	+	0.975861i	$0.570082\pi$
$20$	−15.1012	−3.37673
$21$	4.23228	0.923559
$22$	−2.33754	−0.498366
$23$	−4.80721	−1.00237	−0.501187	−	0.865339i	$-0.667103\pi$
$23$	−4.80721	−1.00237	−0.501187	+	0.865339i	$0.667103\pi$
$24$	−3.95082	−0.806459
$25$	14.0037	2.80074
$26$	−4.36598	−0.856239
$27$	−5.38798	−1.03692
$28$	12.7003	2.40013
$29$	−5.41729	−1.00596	−0.502982	−	0.864297i	$-0.667764\pi$
$29$	−5.41729	−1.00596	−0.502982	+	0.864297i	$0.667764\pi$
$30$	11.7634	2.14769
$31$	1.57474	0.282832	0.141416	−	0.989950i	$-0.454834\pi$
$31$	1.57474	0.282832	0.141416	+	0.989950i	$0.454834\pi$
$32$	4.33934	0.767094
$33$	1.15439	0.200953
$34$	11.0129	1.88870
$35$	−15.9824	−2.70151
$36$	−5.77601	−0.962669
$37$	−8.15011	−1.33987	−0.669935	−	0.742420i	$-0.733678\pi$
$37$	−8.15011	−1.33987	−0.669935	+	0.742420i	$0.733678\pi$
$38$	4.45050	0.721966
$39$	2.15613	0.345256
$40$	14.9195	2.35898
$41$	−6.85770	−1.07099	−0.535496	−	0.844538i	$-0.679875\pi$
$41$	−6.85770	−1.07099	−0.535496	+	0.844538i	$0.679875\pi$
$42$	−9.89314	−1.52654
$43$	−0.602984	−0.0919543	−0.0459771	−	0.998942i	$-0.514640\pi$
$43$	−0.602984	−0.0919543	−0.0459771	+	0.998942i	$0.514640\pi$
$44$	3.46412	0.522235
$45$	7.26867	1.08355
$46$	11.2371	1.65682
$47$	7.92371	1.15579	0.577896	−	0.816110i	$-0.303874\pi$
$47$	7.92371	1.15579	0.577896	+	0.816110i	$0.303874\pi$
$48$	1.23735	0.178596
$49$	6.44137	0.920195
$50$	−32.7343	−4.62932
$51$	−5.43869	−0.761569
$52$	6.47014	0.897248
$53$	5.70152	0.783164	0.391582	−	0.920143i	$-0.371928\pi$
$53$	5.70152	0.783164	0.391582	+	0.920143i	$0.371928\pi$
$54$	12.5946	1.71391
$55$	−4.35932	−0.587811
$56$	−12.5475	−1.67673
$57$	−2.19787	−0.291114
$58$	12.6631	1.66275
$59$	12.9919	1.69140	0.845699	−	0.533660i	$-0.179184\pi$
$59$	12.9919	1.69140	0.845699	+	0.533660i	$0.179184\pi$
$60$	−17.4327	−2.25055
$61$	6.33668	0.811328	0.405664	−	0.914022i	$-0.367040\pi$
$61$	6.33668	0.811328	0.405664	+	0.914022i	$0.367040\pi$
$62$	−3.68103	−0.467492
$63$	−6.11304	−0.770171
$64$	−12.2871	−1.53589
$65$	−8.14218	−1.00991
$66$	−2.69844	−0.332155
$67$	1.90627	0.232888	0.116444	−	0.993197i	$-0.462850\pi$
$67$	1.90627	0.232888	0.116444	+	0.993197i	$0.462850\pi$
$68$	−16.3205	−1.97916
$69$	−5.54940	−0.668069
$70$	37.3595	4.46531
$71$	−14.5542	−1.72726	−0.863631	−	0.504124i	$-0.831816\pi$
$71$	−14.5542	−1.72726	−0.863631	+	0.504124i	$0.831816\pi$
$72$	5.70652	0.672519
$73$	−9.17144	−1.07344	−0.536718	−	0.843762i	$-0.680336\pi$
$73$	−9.17144	−1.07344	−0.536718	+	0.843762i	$0.680336\pi$
$74$	19.0512	2.21466
$75$	16.1657	1.86666
$76$	−6.59540	−0.756544
$77$	3.66625	0.417808
$78$	−5.04004	−0.570672
$79$	8.52958	0.959653	0.479827	−	0.877363i	$-0.340700\pi$
$79$	8.52958	0.959653	0.479827	+	0.877363i	$0.340700\pi$
$80$	−4.67260	−0.522413
$81$	−1.21768	−0.135297
$82$	16.0302	1.77024
$83$	1.57642	0.173034	0.0865172	−	0.996250i	$-0.472426\pi$
$83$	1.57642	0.173034	0.0865172	+	0.996250i	$0.472426\pi$
$84$	14.6611	1.59966
$85$	20.5381	2.22767
$86$	1.40950	0.151991
$87$	−6.25366	−0.670463
$88$	−3.42244	−0.364833
$89$	17.6157	1.86726	0.933630	−	0.358239i	$-0.116623\pi$
$89$	17.6157	1.86726	0.933630	+	0.358239i	$0.116623\pi$
$90$	−16.9908	−1.79099
$91$	6.84768	0.717832
$92$	−16.6527	−1.73617
$93$	1.81787	0.188504
$94$	−18.5220	−1.91040
$95$	8.29980	0.851542
$96$	5.00929	0.511258
$97$	−16.3642	−1.66153	−0.830766	−	0.556621i	$-0.812098\pi$
$97$	−16.3642	−1.66153	−0.830766	+	0.556621i	$0.812098\pi$
$98$	−15.0570	−1.52099
$99$	−1.66738	−0.167578
$100$	48.5104	4.85104
$101$	−7.99603	−0.795635	−0.397817	−	0.917465i	$-0.630232\pi$
$101$	−7.99603	−0.795635	−0.397817	+	0.917465i	$0.630232\pi$
$102$	12.7132	1.25879
$103$	14.2444	1.40355	0.701774	−	0.712400i	$-0.252392\pi$
$103$	14.2444	1.40355	0.701774	+	0.712400i	$0.252392\pi$
$104$	−6.39230	−0.626816
$105$	−18.4499	−1.80052
$106$	−13.3276	−1.29449
$107$	5.47160	0.528959	0.264480	−	0.964391i	$-0.414800\pi$
$107$	5.47160	0.528959	0.264480	+	0.964391i	$0.414800\pi$
$108$	−18.6646	−1.79600
$109$	−4.29572	−0.411455	−0.205728	−	0.978609i	$-0.565956\pi$
$109$	−4.29572	−0.411455	−0.205728	+	0.978609i	$0.565956\pi$
$110$	10.1901	0.971589
$111$	−9.40840	−0.893006
$112$	3.92972	0.371324
$113$	20.5106	1.92947	0.964737	−	0.263217i	$-0.0847835\pi$
$113$	20.5106	1.92947	0.964737	+	0.263217i	$0.0847835\pi$
$114$	5.13761	0.481181
$115$	20.9562	1.95417
$116$	−18.7661	−1.74239
$117$	−3.11428	−0.287915
$118$	−30.3691	−2.79570
$119$	−17.2728	−1.58340
$120$	17.2229	1.57223
$121$	1.00000	0.0909091
$122$	−14.8123	−1.34104
$123$	−7.91645	−0.713802
$124$	5.45510	0.489882
$125$	−39.2500	−3.51063
$126$	14.2895	1.27301
$127$	17.3912	1.54322	0.771610	−	0.636096i	$-0.219452\pi$
$127$	17.3912	1.54322	0.771610	+	0.636096i	$0.219452\pi$
$128$	20.0430	1.77157
$129$	−0.696079	−0.0612863
$130$	19.0327	1.66928
$131$	−7.38761	−0.645459	−0.322729	−	0.946491i	$-0.604600\pi$
$131$	−7.38761	−0.645459	−0.322729	+	0.946491i	$0.604600\pi$
$132$	3.99894	0.348063
$133$	−6.98024	−0.605264
$134$	−4.45600	−0.384940
$135$	23.4879	2.02152
$136$	16.1242	1.38264
$137$	−10.5812	−0.904015	−0.452007	−	0.892014i	$-0.649292\pi$
$137$	−10.5812	−0.904015	−0.452007	+	0.892014i	$0.649292\pi$
$138$	12.9720	1.10425
$139$	−10.3195	−0.875290	−0.437645	−	0.899148i	$-0.644187\pi$
$139$	−10.3195	−0.875290	−0.437645	+	0.899148i	$0.644187\pi$
$140$	−55.3647	−4.67917
$141$	9.14705	0.770321
$142$	34.0210	2.85498
$143$	1.86776	0.156190
$144$	−1.78721	−0.148934
$145$	23.6157	1.96118
$146$	21.4387	1.77428
$147$	7.43585	0.613298
$148$	−28.2329	−2.32073
$149$	−13.6643	−1.11943	−0.559713	−	0.828687i	$-0.689089\pi$
$149$	−13.6643	−1.11943	−0.559713	+	0.828687i	$0.689089\pi$
$150$	−37.7881	−3.08538
$151$	−5.86091	−0.476954	−0.238477	−	0.971148i	$-0.576648\pi$
$151$	−5.86091	−0.476954	−0.238477	+	0.971148i	$0.576648\pi$
$152$	6.51604	0.528521
$153$	7.85557	0.635085
$154$	−8.57002	−0.690592
$155$	−6.86482	−0.551395
$156$	7.46907	0.598004
$157$	−16.9171	−1.35013	−0.675065	−	0.737758i	$-0.735885\pi$
$157$	−16.9171	−1.35013	−0.675065	+	0.737758i	$0.735885\pi$
$158$	−19.9383	−1.58620
$159$	6.58177	0.521969
$160$	−18.9166	−1.49549
$161$	−17.6244	−1.38900
$162$	2.84637	0.223632
$163$	−13.1119	−1.02701	−0.513503	−	0.858088i	$-0.671653\pi$
$163$	−13.1119	−1.02701	−0.513503	+	0.858088i	$0.671653\pi$
$164$	−23.7558	−1.85502
$165$	−5.03236	−0.391768
$166$	−3.68495	−0.286008
$167$	7.19365	0.556661	0.278330	−	0.960485i	$-0.410219\pi$
$167$	7.19365	0.556661	0.278330	+	0.960485i	$0.410219\pi$
$168$	−14.4847	−1.11752
$169$	−9.51146	−0.731651
$170$	−48.0088	−3.68211
$171$	3.17457	0.242765
$172$	−2.08881	−0.159270
$173$	−23.7090	−1.80256	−0.901282	−	0.433233i	$-0.857373\pi$
$173$	−23.7090	−1.80256	−0.901282	+	0.433233i	$0.857373\pi$
$174$	14.6182	1.10820
$175$	51.3410	3.88101
$176$	1.07186	0.0807948
$177$	14.9977	1.12730
$178$	−41.1775	−3.08638
$179$	5.60300	0.418788	0.209394	−	0.977831i	$-0.432851\pi$
$179$	5.60300	0.418788	0.209394	+	0.977831i	$0.432851\pi$
$180$	25.1795	1.87677
$181$	1.27009	0.0944048	0.0472024	−	0.998885i	$-0.484969\pi$
$181$	1.27009	0.0944048	0.0472024	+	0.998885i	$0.484969\pi$
$182$	−16.0068	−1.18650
$183$	7.31499	0.540740
$184$	16.4524	1.21288
$185$	35.5290	2.61214
$186$	−4.24935	−0.311577
$187$	−4.71132	−0.344525
$188$	27.4487	2.00190
$189$	−19.7537	−1.43687
$190$	−19.4012	−1.40751
$191$	−2.80250	−0.202782	−0.101391	−	0.994847i	$-0.532329\pi$
$191$	−2.80250	−0.202782	−0.101391	+	0.994847i	$0.532329\pi$
$192$	−14.1841	−1.02365
$193$	−6.89524	−0.496330	−0.248165	−	0.968718i	$-0.579828\pi$
$193$	−6.89524	−0.496330	−0.248165	+	0.968718i	$0.579828\pi$
$194$	38.2521	2.74634
$195$	−9.39925	−0.673094
$196$	22.3136	1.59383
$197$	−0.298101	−0.0212388	−0.0106194	−	0.999944i	$-0.503380\pi$
$197$	−0.298101	−0.0212388	−0.0106194	+	0.999944i	$0.503380\pi$
$198$	3.89759	0.276989
$199$	11.5386	0.817948	0.408974	−	0.912546i	$-0.365887\pi$
$199$	11.5386	0.817948	0.408974	+	0.912546i	$0.365887\pi$
$200$	−47.9267	−3.38893
$201$	2.20058	0.155217
$202$	18.6911	1.31510
$203$	−19.8611	−1.39398
$204$	−18.8403	−1.31908
$205$	29.8949	2.08795
$206$	−33.2970	−2.31991
$207$	8.01547	0.557114
$208$	2.00199	0.138813
$209$	−1.90392	−0.131697
$210$	43.1274	2.97607
$211$	12.9027	0.888258	0.444129	−	0.895963i	$-0.353513\pi$
$211$	12.9027	0.888258	0.444129	+	0.895963i	$0.353513\pi$
$212$	19.7507	1.35648
$213$	−16.8012	−1.15120
$214$	−12.7901	−0.874314
$215$	2.62860	0.179269
$216$	18.4400	1.25468
$217$	5.77340	0.391924
$218$	10.0414	0.680092
$219$	−10.5874	−0.715431
$220$	−15.1012	−1.01812
$221$	−8.79962	−0.591926
$222$	21.9926	1.47604
$223$	−1.98033	−0.132613	−0.0663063	−	0.997799i	$-0.521121\pi$
$223$	−1.98033	−0.132613	−0.0663063	+	0.997799i	$0.521121\pi$
$224$	15.9091	1.06297
$225$	−23.3495	−1.55664
$226$	−47.9444	−3.18921
$227$	26.6974	1.77197	0.885983	−	0.463718i	$-0.153485\pi$
$227$	26.6974	1.77197	0.885983	+	0.463718i	$0.153485\pi$
$228$	−7.61366	−0.504227
$229$	24.9509	1.64880	0.824402	−	0.566005i	$-0.191512\pi$
$229$	24.9509	1.64880	0.824402	+	0.566005i	$0.191512\pi$
$230$	−48.9860	−3.23004
$231$	4.23228	0.278463
$232$	18.5403	1.21723
$233$	15.4753	1.01382	0.506909	−	0.862000i	$-0.330788\pi$
$233$	15.4753	1.01382	0.506909	+	0.862000i	$0.330788\pi$
$234$	7.27976	0.475893
$235$	−34.5420	−2.25327
$236$	45.0054	2.92960
$237$	9.84646	0.639597
$238$	40.3760	2.61719
$239$	21.8138	1.41102	0.705510	−	0.708700i	$-0.250718\pi$
$239$	21.8138	1.41102	0.705510	+	0.708700i	$0.250718\pi$
$240$	−5.39401	−0.348182
$241$	26.5320	1.70908	0.854539	−	0.519387i	$-0.173840\pi$
$241$	26.5320	1.70908	0.854539	+	0.519387i	$0.173840\pi$
$242$	−2.33754	−0.150263
$243$	14.7583	0.946743
$244$	21.9510	1.40527
$245$	−28.0800	−1.79397
$246$	18.5051	1.17984
$247$	−3.55607	−0.226267
$248$	−5.38946	−0.342231
$249$	1.81980	0.115325
$250$	91.7486	5.80269
$251$	3.31111	0.208995	0.104498	−	0.994525i	$-0.466677\pi$
$251$	3.31111	0.208995	0.104498	+	0.994525i	$0.466677\pi$
$252$	−21.1763	−1.33398
$253$	−4.80721	−0.302227
$254$	−40.6527	−2.55078
$255$	23.7090	1.48472
$256$	−22.2772	−1.39233
$257$	6.08481	0.379560	0.189780	−	0.981827i	$-0.439222\pi$
$257$	6.08481	0.379560	0.189780	+	0.981827i	$0.439222\pi$
$258$	1.62712	0.101300
$259$	−29.8803	−1.85667
$260$	−28.2054	−1.74923
$261$	9.03270	0.559110
$262$	17.2689	1.06687
$263$	−4.39557	−0.271042	−0.135521	−	0.990774i	$-0.543271\pi$
$263$	−4.39557	−0.271042	−0.135521	+	0.990774i	$0.543271\pi$
$264$	−3.95082	−0.243156
$265$	−24.8548	−1.52682
$266$	16.3166	1.00044
$267$	20.3354	1.24450
$268$	6.60355	0.403376
$269$	7.17255	0.437318	0.218659	−	0.975801i	$-0.429832\pi$
$269$	7.17255	0.437318	0.218659	+	0.975801i	$0.429832\pi$
$270$	−54.9041	−3.34136
$271$	24.2436	1.47269	0.736346	−	0.676606i	$-0.236550\pi$
$271$	24.2436	1.47269	0.736346	+	0.676606i	$0.236550\pi$
$272$	−5.04989	−0.306195
$273$	7.90489	0.478426
$274$	24.7341	1.49424
$275$	14.0037	0.844455
$276$	−19.2237	−1.15713
$277$	17.0847	1.02652	0.513259	−	0.858234i	$-0.328438\pi$
$277$	17.0847	1.02652	0.513259	+	0.858234i	$0.328438\pi$
$278$	24.1223	1.44676
$279$	−2.62570	−0.157197
$280$	54.6986	3.26886
$281$	22.6576	1.35164	0.675819	−	0.737068i	$-0.263790\pi$
$281$	22.6576	1.35164	0.675819	+	0.737068i	$0.263790\pi$
$282$	−21.3816	−1.27326
$283$	−20.6403	−1.22694	−0.613471	−	0.789718i	$-0.710227\pi$
$283$	−20.6403	−1.22694	−0.613471	+	0.789718i	$0.710227\pi$
$284$	−50.4173	−2.99172
$285$	9.58121	0.567542
$286$	−4.36598	−0.258166
$287$	−25.1420	−1.48409
$288$	−7.23535	−0.426347
$289$	5.19649	0.305676
$290$	−55.2027	−3.24162
$291$	−18.8907	−1.10739
$292$	−31.7709	−1.85925
$293$	1.63878	0.0957388	0.0478694	−	0.998854i	$-0.484757\pi$
$293$	1.63878	0.0957388	0.0478694	+	0.998854i	$0.484757\pi$
$294$	−17.3816	−1.01372
$295$	−56.6358	−3.29746
$296$	27.8932	1.62126
$297$	−5.38798	−0.312642
$298$	31.9410	1.85029
$299$	−8.97873	−0.519253
$300$	55.9999	3.23316
$301$	−2.21069	−0.127422
$302$	13.7001	0.788354
$303$	−9.23053	−0.530280
$304$	−2.04075	−0.117045
$305$	−27.6236	−1.58172
$306$	−18.3628	−1.04973
$307$	−12.7785	−0.729306	−0.364653	−	0.931143i	$-0.618812\pi$
$307$	−12.7785	−0.729306	−0.364653	+	0.931143i	$0.618812\pi$
$308$	12.7003	0.723667
$309$	16.4436	0.935446
$310$	16.0468	0.911398
$311$	3.46632	0.196557	0.0982784	−	0.995159i	$-0.468666\pi$
$311$	3.46632	0.196557	0.0982784	+	0.995159i	$0.468666\pi$
$312$	−7.37920	−0.417765
$313$	−30.4293	−1.71997	−0.859983	−	0.510322i	$-0.829526\pi$
$313$	−30.4293	−1.71997	−0.859983	+	0.510322i	$0.829526\pi$
$314$	39.5445	2.23162
$315$	26.6487	1.50149
$316$	29.5475	1.66217
$317$	34.3571	1.92969	0.964843	−	0.262826i	$-0.0846545\pi$
$317$	34.3571	1.92969	0.964843	+	0.262826i	$0.0846545\pi$
$318$	−15.3852	−0.862759
$319$	−5.41729	−0.303310
$320$	53.5636	2.99429
$321$	6.31636	0.352545
$322$	41.1979	2.29587
$323$	8.96997	0.499102
$324$	−4.21817	−0.234343
$325$	26.1556	1.45085
$326$	30.6498	1.69753
$327$	−4.95893	−0.274230
$328$	23.4700	1.29591
$329$	29.0503	1.60159
$330$	11.7634	0.647552
$331$	−5.39070	−0.296300	−0.148150	−	0.988965i	$-0.547332\pi$
$331$	−5.39070	−0.296300	−0.148150	+	0.988965i	$0.547332\pi$
$332$	5.46090	0.299706
$333$	13.5894	0.744693
$334$	−16.8155	−0.920101
$335$	−8.31006	−0.454027
$336$	4.53643	0.247483
$337$	19.7156	1.07398	0.536988	−	0.843590i	$-0.319562\pi$
$337$	19.7156	1.07398	0.536988	+	0.843590i	$0.319562\pi$
$338$	22.2335	1.20934
$339$	23.6772	1.28597
$340$	71.1465	3.85846
$341$	1.57474	0.0852772
$342$	−7.42069	−0.401265
$343$	−2.04809	−0.110586
$344$	2.06368	0.111266
$345$	24.1916	1.30243
$346$	55.4209	2.97945
$347$	−21.7610	−1.16819	−0.584095	−	0.811685i	$-0.698550\pi$
$347$	−21.7610	−1.16819	−0.584095	+	0.811685i	$0.698550\pi$
$348$	−21.6634	−1.16128
$349$	−7.12003	−0.381127	−0.190563	−	0.981675i	$-0.561031\pi$
$349$	−7.12003	−0.381127	−0.190563	+	0.981675i	$0.561031\pi$
$350$	−120.012	−6.41491
$351$	−10.0635	−0.537148
$352$	4.33934	0.231288
$353$	4.36646	0.232403	0.116202	−	0.993226i	$-0.462928\pi$
$353$	4.36646	0.232403	0.116202	+	0.993226i	$0.462928\pi$
$354$	−35.0578	−1.86330
$355$	63.4463	3.36738
$356$	61.0228	3.23420
$357$	−19.9396	−1.05532
$358$	−13.0973	−0.692211
$359$	−15.6390	−0.825396	−0.412698	−	0.910868i	$-0.635414\pi$
$359$	−15.6390	−0.825396	−0.412698	+	0.910868i	$0.635414\pi$
$360$	−24.8765	−1.31111
$361$	−15.3751	−0.809215
$362$	−2.96888	−0.156041
$363$	1.15439	0.0605897
$364$	23.7211	1.24333
$365$	39.9813	2.09272
$366$	−17.0991	−0.893785
$367$	−19.7315	−1.02997	−0.514987	−	0.857198i	$-0.672203\pi$
$367$	−19.7315	−1.02997	−0.514987	+	0.857198i	$0.672203\pi$
$368$	−5.15268	−0.268602
$369$	11.4344	0.595252
$370$	−83.0505	−4.31759
$371$	20.9032	1.08524
$372$	6.29731	0.326500
$373$	5.31810	0.275361	0.137680	−	0.990477i	$-0.456035\pi$
$373$	5.31810	0.275361	0.137680	+	0.990477i	$0.456035\pi$
$374$	11.0129	0.569464
$375$	−45.3098	−2.33979
$376$	−27.1184	−1.39852
$377$	−10.1182	−0.521114
$378$	46.1751	2.37499
$379$	−8.62122	−0.442843	−0.221421	−	0.975178i	$-0.571070\pi$
$379$	−8.62122	−0.442843	−0.221421	+	0.975178i	$0.571070\pi$
$380$	28.7515	1.47492
$381$	20.0762	1.02854
$382$	6.55097	0.335177
$383$	−3.79534	−0.193933	−0.0969663	−	0.995288i	$-0.530914\pi$
$383$	−3.79534	−0.193933	−0.0969663	+	0.995288i	$0.530914\pi$
$384$	23.1375	1.18073
$385$	−15.9824	−0.814536
$386$	16.1179	0.820381
$387$	1.00541	0.0511077
$388$	−56.6875	−2.87787
$389$	26.9479	1.36631	0.683157	−	0.730272i	$-0.260606\pi$
$389$	26.9479	1.36631	0.683157	+	0.730272i	$0.260606\pi$
$390$	21.9712	1.11255
$391$	22.6483	1.14537
$392$	−22.0452	−1.11345
$393$	−8.52818	−0.430190
$394$	0.696824	0.0351055
$395$	−37.1832	−1.87089
$396$	−5.77601	−0.290256
$397$	−10.9183	−0.547971	−0.273986	−	0.961734i	$-0.588342\pi$
$397$	−10.9183	−0.547971	−0.273986	+	0.961734i	$0.588342\pi$
$398$	−26.9719	−1.35198
$399$	−8.05792	−0.403401
$400$	15.0101	0.750503
$401$	−9.58137	−0.478471	−0.239235	−	0.970962i	$-0.576897\pi$
$401$	−9.58137	−0.478471	−0.239235	+	0.970962i	$0.576897\pi$
$402$	−5.14396	−0.256557
$403$	2.94125	0.146514
$404$	−27.6992	−1.37808
$405$	5.30824	0.263769
$406$	46.4262	2.30409
$407$	−8.15011	−0.403986
$408$	18.6136	0.921509
$409$	34.1314	1.68769	0.843845	−	0.536587i	$-0.180287\pi$
$409$	34.1314	1.68769	0.843845	+	0.536587i	$0.180287\pi$
$410$	−69.8807	−3.45116
$411$	−12.2149	−0.602514
$412$	49.3444	2.43102
$413$	47.6314	2.34379
$414$	−18.7365	−0.920850
$415$	−6.87212	−0.337339
$416$	8.10485	0.397373
$417$	−11.9127	−0.583370
$418$	4.45050	0.217681
$419$	22.4669	1.09758	0.548789	−	0.835961i	$-0.315089\pi$
$419$	22.4669	1.09758	0.548789	+	0.835961i	$0.315089\pi$
$420$	−63.9125	−3.11861
$421$	−18.1634	−0.885232	−0.442616	−	0.896711i	$-0.645949\pi$
$421$	−18.1634	−0.885232	−0.442616	+	0.896711i	$0.645949\pi$
$422$	−30.1606	−1.46820
$423$	−13.2119	−0.642383
$424$	−19.5131	−0.947639
$425$	−65.9758	−3.20030
$426$	39.2735	1.90281
$427$	23.2318	1.12427
$428$	18.9543	0.916188
$429$	2.15613	0.104099
$430$	−6.14448	−0.296313
$431$	25.2502	1.21626	0.608131	−	0.793837i	$-0.291920\pi$
$431$	25.2502	1.21626	0.608131	+	0.793837i	$0.291920\pi$
$432$	−5.77519	−0.277859
$433$	2.38608	0.114668	0.0573338	−	0.998355i	$-0.481740\pi$
$433$	2.38608	0.114668	0.0573338	+	0.998355i	$0.481740\pi$
$434$	−13.4956	−0.647809
$435$	27.2617	1.30710
$436$	−14.8809	−0.712664
$437$	9.15255	0.437826
$438$	24.7486	1.18253
$439$	26.6729	1.27303	0.636515	−	0.771264i	$-0.280375\pi$
$439$	26.6729	1.27303	0.636515	+	0.771264i	$0.280375\pi$
$440$	14.9195	0.711259
$441$	−10.7402	−0.511440
$442$	20.5695	0.978391
$443$	−5.93105	−0.281793	−0.140896	−	0.990024i	$-0.544998\pi$
$443$	−5.93105	−0.281793	−0.140896	+	0.990024i	$0.544998\pi$
$444$	−32.5918	−1.54674
$445$	−76.7925	−3.64031
$446$	4.62911	0.219195
$447$	−15.7740	−0.746083
$448$	−45.0476	−2.12830
$449$	23.9214	1.12892	0.564460	−	0.825460i	$-0.309084\pi$
$449$	23.9214	1.12892	0.564460	+	0.825460i	$0.309084\pi$
$450$	54.5806	2.57295
$451$	−6.85770	−0.322916
$452$	71.0510	3.34196
$453$	−6.76577	−0.317884
$454$	−62.4063	−2.92887
$455$	−29.8512	−1.39945
$456$	7.52205	0.352252
$457$	−21.8767	−1.02335	−0.511675	−	0.859179i	$-0.670975\pi$
$457$	−21.8767	−1.02335	−0.511675	+	0.859179i	$0.670975\pi$
$458$	−58.3239	−2.72530
$459$	25.3845	1.18485
$460$	72.5947	3.38474
$461$	21.8037	1.01550	0.507749	−	0.861505i	$-0.330478\pi$
$461$	21.8037	1.01550	0.507749	+	0.861505i	$0.330478\pi$
$462$	−9.89314	−0.460270
$463$	22.0834	1.02630	0.513151	−	0.858298i	$-0.328478\pi$
$463$	22.0834	1.02630	0.513151	+	0.858298i	$0.328478\pi$
$464$	−5.80660	−0.269565
$465$	−7.92467	−0.367498
$466$	−36.1741	−1.67573
$467$	−6.67512	−0.308888	−0.154444	−	0.988002i	$-0.549359\pi$
$467$	−6.67512	−0.308888	−0.154444	+	0.988002i	$0.549359\pi$
$468$	−10.7882	−0.498686
$469$	6.98887	0.322716
$470$	80.7435	3.72442
$471$	−19.5289	−0.899845
$472$	−44.4639	−2.04661
$473$	−0.602984	−0.0277253
$474$	−23.0165	−1.05719
$475$	−26.6619	−1.22333
$476$	−59.8351	−2.74254
$477$	−9.50662	−0.435278
$478$	−50.9908	−2.33227
$479$	−31.7651	−1.45138	−0.725691	−	0.688020i	$-0.758480\pi$
$479$	−31.7651	−1.45138	−0.725691	+	0.688020i	$0.758480\pi$
$480$	−21.8371	−0.996723
$481$	−15.2225	−0.694085
$482$	−62.0198	−2.82492
$483$	−20.3455	−0.925750
$484$	3.46412	0.157460
$485$	71.3368	3.23924
$486$	−34.4981	−1.56487
$487$	9.70651	0.439844	0.219922	−	0.975517i	$-0.429420\pi$
$487$	9.70651	0.439844	0.219922	+	0.975517i	$0.429420\pi$
$488$	−21.6869	−0.981718
$489$	−15.1363	−0.684487
$490$	65.6383	2.96523
$491$	31.3703	1.41572	0.707861	−	0.706352i	$-0.249660\pi$
$491$	31.3703	1.41572	0.707861	+	0.706352i	$0.249660\pi$
$492$	−27.4235	−1.23635
$493$	25.5225	1.14948
$494$	8.31247	0.373996
$495$	7.26867	0.326702
$496$	1.68791	0.0757895
$497$	−53.3592	−2.39349
$498$	−4.25387	−0.190620
$499$	12.3182	0.551436	0.275718	−	0.961239i	$-0.411084\pi$
$499$	12.3182	0.551436	0.275718	+	0.961239i	$0.411084\pi$
$500$	−135.967	−6.08061
$501$	8.30427	0.371007
$502$	−7.73986	−0.345447
$503$	12.8519	0.573037	0.286519	−	0.958075i	$-0.407502\pi$
$503$	12.8519	0.573037	0.286519	+	0.958075i	$0.407502\pi$
$504$	20.9215	0.931917
$505$	34.8573	1.55113
$506$	11.2371	0.499549
$507$	−10.9799	−0.487636
$508$	60.2452	2.67295
$509$	−13.4229	−0.594960	−0.297480	−	0.954728i	$-0.596146\pi$
$509$	−13.4229	−0.594960	−0.297480	+	0.954728i	$0.596146\pi$
$510$	−55.4209	−2.45408
$511$	−33.6248	−1.48747
$512$	11.9880	0.529798
$513$	10.2583	0.452914
$514$	−14.2235	−0.627373
$515$	−62.0962	−2.73628
$516$	−2.41130	−0.106151
$517$	7.92371	0.348485
$518$	69.8466	3.06888
$519$	−27.3695	−1.20139
$520$	27.8661	1.22201
$521$	1.79867	0.0788010	0.0394005	−	0.999223i	$-0.487455\pi$
$521$	1.79867	0.0788010	0.0394005	+	0.999223i	$0.487455\pi$
$522$	−21.1143	−0.924149
$523$	22.6215	0.989168	0.494584	−	0.869130i	$-0.335320\pi$
$523$	22.6215	0.989168	0.494584	+	0.869130i	$0.335320\pi$
$524$	−25.5915	−1.11797
$525$	59.2675	2.58665
$526$	10.2748	0.448004
$527$	−7.41912	−0.323182
$528$	1.23735	0.0538487
$529$	0.109289	0.00475168
$530$	58.0991	2.52366
$531$	−21.6625	−0.940070
$532$	−24.1804	−1.04835
$533$	−12.8085	−0.554800
$534$	−47.5349	−2.05703
$535$	−23.8525	−1.03123
$536$	−6.52410	−0.281798
$537$	6.46804	0.279117
$538$	−16.7661	−0.722840
$539$	6.44137	0.277449
$540$	81.3650	3.50139
$541$	0.195026	0.00838480	0.00419240	−	0.999991i	$-0.498666\pi$
$541$	0.195026	0.00838480	0.00419240	+	0.999991i	$0.498666\pi$
$542$	−56.6704	−2.43420
$543$	1.46617	0.0629196
$544$	−20.4440	−0.876529
$545$	18.7264	0.802152
$546$	−18.4780	−0.790787
$547$	−1.00000	−0.0427569
$547$	−1.00000	−0.0427569
$548$	−36.6546	−1.56581
$549$	−10.5657	−0.450932
$550$	−32.7343	−1.39579
$551$	10.3141	0.439395
$552$	18.9924	0.808372
$553$	31.2716	1.32980
$554$	−39.9361	−1.69672
$555$	41.0143	1.74096
$556$	−35.7480	−1.51605
$557$	2.49901	0.105886	0.0529432	−	0.998598i	$-0.483140\pi$
$557$	2.49901	0.105886	0.0529432	+	0.998598i	$0.483140\pi$
$558$	6.13770	0.259830
$559$	−1.12623	−0.0476345
$560$	−17.1309	−0.723914
$561$	−5.43869	−0.229622
$562$	−52.9631	−2.23411
$563$	−22.8368	−0.962458	−0.481229	−	0.876595i	$-0.659810\pi$
$563$	−22.8368	−0.962458	−0.481229	+	0.876595i	$0.659810\pi$
$564$	31.6864	1.33424
$565$	−89.4123	−3.76160
$566$	48.2477	2.02800
$567$	−4.46430	−0.187483
$568$	49.8107	2.09001
$569$	−20.1273	−0.843778	−0.421889	−	0.906647i	$-0.638633\pi$
$569$	−20.1273	−0.843778	−0.421889	+	0.906647i	$0.638633\pi$
$570$	−22.3965	−0.938086
$571$	32.3847	1.35526	0.677629	−	0.735404i	$-0.263008\pi$
$571$	32.3847	1.35526	0.677629	+	0.735404i	$0.263008\pi$
$572$	6.47014	0.270530
$573$	−3.23518	−0.135152
$574$	58.7706	2.45304
$575$	−67.3187	−2.80738
$576$	20.4874	0.853640
$577$	38.9969	1.62346	0.811731	−	0.584032i	$-0.198526\pi$
$577$	38.9969	1.62346	0.811731	+	0.584032i	$0.198526\pi$
$578$	−12.1470	−0.505250
$579$	−7.95979	−0.330798
$580$	81.8075	3.39687
$581$	5.77954	0.239776
$582$	44.1578	1.83040
$583$	5.70152	0.236133
$584$	31.3887	1.29887
$585$	13.5761	0.561304
$586$	−3.83073	−0.158246
$587$	−5.19145	−0.214274	−0.107137	−	0.994244i	$-0.534168\pi$
$587$	−5.19145	−0.214274	−0.107137	+	0.994244i	$0.534168\pi$
$588$	25.7586	1.06227
$589$	−2.99819	−0.123538
$590$	132.389	5.45036
$591$	−0.344125	−0.0141554
$592$	−8.73582	−0.359040
$593$	−17.9746	−0.738128	−0.369064	−	0.929404i	$-0.620322\pi$
$593$	−17.9746	−0.738128	−0.369064	+	0.929404i	$0.620322\pi$
$594$	12.5946	0.516765
$595$	75.2979	3.08691
$596$	−47.3348	−1.93891
$597$	13.3200	0.545152
$598$	20.9882	0.858271
$599$	−25.7102	−1.05049	−0.525244	−	0.850952i	$-0.676026\pi$
$599$	−25.7102	−1.05049	−0.525244	+	0.850952i	$0.676026\pi$
$600$	−55.3261	−2.25868
$601$	6.22089	0.253755	0.126878	−	0.991918i	$-0.459504\pi$
$601$	6.22089	0.253755	0.126878	+	0.991918i	$0.459504\pi$
$602$	5.16759	0.210615
$603$	−3.17849	−0.129438
$604$	−20.3029	−0.826112
$605$	−4.35932	−0.177232
$606$	21.5768	0.876497
$607$	−7.38613	−0.299794	−0.149897	−	0.988702i	$-0.547894\pi$
$607$	−7.38613	−0.299794	−0.149897	+	0.988702i	$0.547894\pi$
$608$	−8.26176	−0.335058
$609$	−22.9275	−0.929067
$610$	64.5714	2.61442
$611$	14.7996	0.598728
$612$	27.2126	1.10000
$613$	38.1004	1.53886	0.769431	−	0.638730i	$-0.220540\pi$
$613$	38.1004	1.53886	0.769431	+	0.638730i	$0.220540\pi$
$614$	29.8703	1.20547
$615$	34.5104	1.39159
$616$	−12.5475	−0.505553
$617$	−10.0976	−0.406512	−0.203256	−	0.979126i	$-0.565152\pi$
$617$	−10.0976	−0.406512	−0.203256	+	0.979126i	$0.565152\pi$
$618$	−38.4378	−1.54619
$619$	3.80442	0.152913	0.0764564	−	0.997073i	$-0.475639\pi$
$619$	3.80442	0.152913	0.0764564	+	0.997073i	$0.475639\pi$
$620$	−23.7805	−0.955049
$621$	25.9012	1.03938
$622$	−8.10267	−0.324887
$623$	64.5835	2.58748
$624$	2.31108	0.0925170
$625$	101.085	4.04340
$626$	71.1299	2.84292
$627$	−2.19787	−0.0877743
$628$	−58.6028	−2.33850
$629$	38.3977	1.53102
$630$	−62.2926	−2.48180
$631$	12.8480	0.511469	0.255734	−	0.966747i	$-0.417683\pi$
$631$	12.8480	0.511469	0.255734	+	0.966747i	$0.417683\pi$
$632$	−29.1919	−1.16119
$633$	14.8947	0.592013
$634$	−80.3112	−3.18957
$635$	−75.8139	−3.00858
$636$	22.8000	0.904080
$637$	12.0309	0.476683
$638$	12.6631	0.501339
$639$	24.2674	0.960004
$640$	−87.3741	−3.45376
$641$	18.5891	0.734223	0.367112	−	0.930177i	$-0.380347\pi$
$641$	18.5891	0.734223	0.367112	+	0.930177i	$0.380347\pi$
$642$	−14.7648	−0.582719
$643$	15.3840	0.606685	0.303342	−	0.952882i	$-0.401897\pi$
$643$	15.3840	0.606685	0.303342	+	0.952882i	$0.401897\pi$
$644$	−61.0531	−2.40583
$645$	3.03443	0.119481
$646$	−20.9677	−0.824963
$647$	7.27543	0.286027	0.143013	−	0.989721i	$-0.454321\pi$
$647$	7.27543	0.286027	0.143013	+	0.989721i	$0.454321\pi$
$648$	4.16742	0.163712
$649$	12.9919	0.509976
$650$	−61.1398	−2.39810
$651$	6.66475	0.261212
$652$	−45.4213	−1.77884
$653$	24.4232	0.955753	0.477877	−	0.878427i	$-0.341407\pi$
$653$	24.4232	0.955753	0.477877	+	0.878427i	$0.341407\pi$
$654$	11.5917	0.453273
$655$	32.2050	1.25835
$656$	−7.35052	−0.286990
$657$	15.2923	0.596610
$658$	−67.9064	−2.64727
$659$	−16.6152	−0.647237	−0.323618	−	0.946188i	$-0.604899\pi$
$659$	−16.6152	−0.647237	−0.323618	+	0.946188i	$0.604899\pi$
$660$	−17.4327	−0.678566
$661$	32.6837	1.27125	0.635624	−	0.771998i	$-0.280743\pi$
$661$	32.6837	1.27125	0.635624	+	0.771998i	$0.280743\pi$
$662$	12.6010	0.489752
$663$	−10.1582	−0.394511
$664$	−5.39519	−0.209374
$665$	30.4291	1.17999
$666$	−31.7658	−1.23090
$667$	26.0420	1.00835
$668$	24.9196	0.964169
$669$	−2.28607	−0.0883846
$670$	19.4251	0.750458
$671$	6.33668	0.244625
$672$	18.3653	0.708456
$673$	6.59157	0.254087	0.127043	−	0.991897i	$-0.459451\pi$
$673$	6.59157	0.254087	0.127043	+	0.991897i	$0.459451\pi$
$674$	−46.0861	−1.77517
$675$	−75.4516	−2.90413
$676$	−32.9488	−1.26726
$677$	51.1724	1.96671	0.983357	−	0.181684i	$-0.0581547\pi$
$677$	51.1724	1.96671	0.983357	+	0.181684i	$0.0581547\pi$
$678$	−55.3465	−2.12557
$679$	−59.9952	−2.30240
$680$	−70.2905	−2.69552
$681$	30.8191	1.18099
$682$	−3.68103	−0.140954
$683$	41.8848	1.60268	0.801338	−	0.598211i	$-0.204122\pi$
$683$	41.8848	1.60268	0.801338	+	0.598211i	$0.204122\pi$
$684$	10.9971	0.420483
$685$	46.1270	1.76242
$686$	4.78749	0.182787
$687$	28.8031	1.09891
$688$	−0.646318	−0.0246406
$689$	10.6491	0.405698
$690$	−56.5490	−2.15278
$691$	20.6787	0.786655	0.393327	−	0.919398i	$-0.371324\pi$
$691$	20.6787	0.786655	0.393327	+	0.919398i	$0.371324\pi$
$692$	−82.1308	−3.12214
$693$	−6.11304	−0.232215
$694$	50.8672	1.93089
$695$	44.9861	1.70642
$696$	21.4027	0.811269
$697$	32.3088	1.22378
$698$	16.6434	0.629962
$699$	17.8645	0.675696
$700$	177.851	6.72214
$701$	13.0695	0.493627	0.246813	−	0.969063i	$-0.420617\pi$
$701$	13.0695	0.493627	0.246813	+	0.969063i	$0.420617\pi$
$702$	23.5238	0.887849
$703$	15.5172	0.585241
$704$	−12.2871	−0.463089
$705$	−39.8750	−1.50178
$706$	−10.2068	−0.384138
$707$	−29.3154	−1.10252
$708$	51.9537	1.95254
$709$	14.3435	0.538683	0.269341	−	0.963045i	$-0.413194\pi$
$709$	14.3435	0.538683	0.269341	+	0.963045i	$0.413194\pi$
$710$	−148.309	−5.56593
$711$	−14.2221	−0.533370
$712$	−60.2886	−2.25941
$713$	−7.57013	−0.283504
$714$	46.6097	1.74432
$715$	−8.14218	−0.304500
$716$	19.4094	0.725364
$717$	25.1817	0.940427
$718$	36.5569	1.36429
$719$	−28.0515	−1.04614	−0.523072	−	0.852289i	$-0.675214\pi$
$719$	−28.0515	−1.04614	−0.523072	+	0.852289i	$0.675214\pi$
$720$	7.79103	0.290354
$721$	52.2237	1.94491
$722$	35.9400	1.33755
$723$	30.6283	1.13908
$724$	4.39973	0.163514
$725$	−75.8620	−2.81744
$726$	−2.69844	−0.100148
$727$	37.3416	1.38492	0.692461	−	0.721455i	$-0.256527\pi$
$727$	37.3416	1.38492	0.692461	+	0.721455i	$0.256527\pi$
$728$	−23.4357	−0.868586
$729$	20.6898	0.766290
$730$	−93.4580	−3.45904
$731$	2.84085	0.105073
$732$	25.3400	0.936593
$733$	39.7594	1.46855	0.734274	−	0.678854i	$-0.237523\pi$
$733$	39.7594	1.46855	0.734274	+	0.678854i	$0.237523\pi$
$734$	46.1232	1.70244
$735$	−32.4153	−1.19565
$736$	−20.8601	−0.768914
$737$	1.90627	0.0702185
$738$	−26.7285	−0.983888
$739$	21.2900	0.783164	0.391582	−	0.920143i	$-0.371928\pi$
$739$	21.2900	0.783164	0.391582	+	0.920143i	$0.371928\pi$
$740$	123.076	4.52438
$741$	−4.10509	−0.150804
$742$	−48.8621	−1.79378
$743$	14.7452	0.540948	0.270474	−	0.962727i	$-0.412820\pi$
$743$	14.7452	0.540948	0.270474	+	0.962727i	$0.412820\pi$
$744$	−6.22154	−0.228093
$745$	59.5672	2.18237
$746$	−12.4313	−0.455142
$747$	−2.62850	−0.0961716
$748$	−16.3205	−0.596738
$749$	20.0602	0.732985
$750$	105.914	3.86742
$751$	−54.5489	−1.99052	−0.995259	−	0.0972571i	$-0.968993\pi$
$751$	−54.5489	−1.99052	−0.995259	+	0.0972571i	$0.968993\pi$
$752$	8.49315	0.309713
$753$	3.82231	0.139293
$754$	23.6517	0.861346
$755$	25.5496	0.929845
$756$	−68.4290	−2.48874
$757$	23.1288	0.840632	0.420316	−	0.907378i	$-0.361919\pi$
$757$	23.1288	0.840632	0.420316	+	0.907378i	$0.361919\pi$
$758$	20.1525	0.731972
$759$	−5.54940	−0.201430
$760$	−28.4055	−1.03038
$761$	7.64864	0.277263	0.138632	−	0.990344i	$-0.455730\pi$
$761$	7.64864	0.277263	0.138632	+	0.990344i	$0.455730\pi$
$762$	−46.9291	−1.70006
$763$	−15.7492	−0.570158
$764$	−9.70819	−0.351230
$765$	−34.2450	−1.23813
$766$	8.87177	0.320550
$767$	24.2657	0.876185
$768$	−25.7166	−0.927968
$769$	−44.6248	−1.60921	−0.804605	−	0.593811i	$-0.797623\pi$
$769$	−44.6248	−1.60921	−0.804605	+	0.593811i	$0.797623\pi$
$770$	37.3595	1.34634
$771$	7.02424	0.252972
$772$	−23.8859	−0.859673
$773$	−12.6713	−0.455754	−0.227877	−	0.973690i	$-0.573178\pi$
$773$	−12.6713	−0.455754	−0.227877	+	0.973690i	$0.573178\pi$
$774$	−2.35018	−0.0844756
$775$	22.0522	0.792140
$776$	56.0054	2.01048
$777$	−34.4935	−1.23745
$778$	−62.9920	−2.25837
$779$	13.0565	0.467798
$780$	−32.5601	−1.16584
$781$	−14.5542	−0.520789
$782$	−52.9414	−1.89318
$783$	29.1882	1.04310
$784$	6.90427	0.246581
$785$	73.7471	2.63215
$786$	19.9350	0.711058
$787$	24.8373	0.885354	0.442677	−	0.896681i	$-0.354029\pi$
$787$	24.8373	0.885354	0.442677	+	0.896681i	$0.354029\pi$
$788$	−1.03266	−0.0367869
$789$	−5.07420	−0.180646
$790$	86.9174	3.09238
$791$	75.1969	2.67369
$792$	5.70652	0.202772
$793$	11.8354	0.420287
$794$	25.5219	0.905739
$795$	−28.6921	−1.01760
$796$	39.9710	1.41673
$797$	−39.9069	−1.41358	−0.706788	−	0.707426i	$-0.749856\pi$
$797$	−39.9069	−1.41358	−0.706788	+	0.707426i	$0.749856\pi$
$798$	18.8357	0.666778
$799$	−37.3311	−1.32068
$800$	60.7668	2.14843
$801$	−29.3721	−1.03781
$802$	22.3969	0.790862
$803$	−9.17144	−0.323653
$804$	7.62307	0.268845
$805$	76.8306	2.70792
$806$	−6.87530	−0.242172
$807$	8.27991	0.291467
$808$	27.3659	0.962729
$809$	46.6981	1.64182	0.820910	−	0.571058i	$-0.193467\pi$
$809$	46.6981	1.64182	0.820910	+	0.571058i	$0.193467\pi$
$810$	−12.4083	−0.435982
$811$	−29.4148	−1.03289	−0.516447	−	0.856319i	$-0.672746\pi$
$811$	−29.4148	−1.03289	−0.516447	+	0.856319i	$0.672746\pi$
$812$	−68.8012	−2.41445
$813$	27.9865	0.981530
$814$	19.0512	0.667746
$815$	57.1592	2.00220
$816$	−5.82954	−0.204075
$817$	1.14803	0.0401646
$818$	−79.7837	−2.78957
$819$	−11.4177	−0.398967
$820$	103.559	3.61645
$821$	−19.8063	−0.691244	−0.345622	−	0.938374i	$-0.612332\pi$
$821$	−19.8063	−0.691244	−0.345622	+	0.938374i	$0.612332\pi$
$822$	28.5528	0.995892
$823$	−50.4086	−1.75713	−0.878566	−	0.477620i	$-0.841500\pi$
$823$	−50.4086	−1.75713	−0.878566	+	0.477620i	$0.841500\pi$
$824$	−48.7507	−1.69831
$825$	16.1657	0.562818
$826$	−111.341	−3.87403
$827$	−2.47817	−0.0861746	−0.0430873	−	0.999071i	$-0.513719\pi$
$827$	−2.47817	−0.0861746	−0.0430873	+	0.999071i	$0.513719\pi$
$828$	27.7665	0.964953
$829$	−44.7403	−1.55390	−0.776948	−	0.629565i	$-0.783233\pi$
$829$	−44.7403	−1.55390	−0.776948	+	0.629565i	$0.783233\pi$
$830$	16.0639	0.557586
$831$	19.7224	0.684161
$832$	−22.9494	−0.795629
$833$	−30.3473	−1.05147
$834$	27.8466	0.964248
$835$	−31.3594	−1.08524
$836$	−6.59540	−0.228107
$837$	−8.48469	−0.293274
$838$	−52.5173	−1.81418
$839$	−16.0051	−0.552557	−0.276278	−	0.961078i	$-0.589101\pi$
$839$	−16.0051	−0.552557	−0.276278	+	0.961078i	$0.589101\pi$
$840$	63.1435	2.17866
$841$	0.346980	0.0119648
$842$	42.4579	1.46319
$843$	26.1557	0.900849
$844$	44.6964	1.53851
$845$	41.4635	1.42639
$846$	30.8834	1.06179
$847$	3.66625	0.125974
$848$	6.11126	0.209861
$849$	−23.8270	−0.817741
$850$	154.221	5.28975
$851$	39.1793	1.34305
$852$	−58.2013	−1.99394
$853$	−5.22320	−0.178839	−0.0894195	−	0.995994i	$-0.528501\pi$
$853$	−5.22320	−0.178839	−0.0894195	+	0.995994i	$0.528501\pi$
$854$	−54.3054	−1.85829
$855$	−13.8390	−0.473283
$856$	−18.7262	−0.640048
$857$	31.1053	1.06254	0.531268	−	0.847204i	$-0.321716\pi$
$857$	31.1053	1.06254	0.531268	+	0.847204i	$0.321716\pi$
$858$	−5.04004	−0.172064
$859$	4.65935	0.158975	0.0794874	−	0.996836i	$-0.474672\pi$
$859$	4.65935	0.158975	0.0794874	+	0.996836i	$0.474672\pi$
$860$	9.10579	0.310505
$861$	−29.0237	−0.989124
$862$	−59.0236	−2.01035
$863$	36.3729	1.23815	0.619074	−	0.785333i	$-0.287508\pi$
$863$	36.3729	1.23815	0.619074	+	0.785333i	$0.287508\pi$
$864$	−23.3803	−0.795413
$865$	103.355	3.51418
$866$	−5.57756	−0.189533
$867$	5.99877	0.203729
$868$	19.9997	0.678835
$869$	8.52958	0.289346
$870$	−63.7255	−2.16050
$871$	3.56046	0.120642
$872$	14.7018	0.497866
$873$	27.2854	0.923471
$874$	−21.3945	−0.723680
$875$	−143.900	−4.86472
$876$	−36.6760	−1.23917
$877$	25.5707	0.863463	0.431731	−	0.902002i	$-0.357903\pi$
$877$	25.5707	0.863463	0.431731	+	0.902002i	$0.357903\pi$
$878$	−62.3492	−2.10418
$879$	1.89180	0.0638087
$880$	−4.67260	−0.157513
$881$	−35.5465	−1.19759	−0.598797	−	0.800901i	$-0.704354\pi$
$881$	−35.5465	−1.19759	−0.598797	+	0.800901i	$0.704354\pi$
$882$	25.1058	0.845356
$883$	−22.7792	−0.766580	−0.383290	−	0.923628i	$-0.625209\pi$
$883$	−22.7792	−0.766580	−0.383290	+	0.923628i	$0.625209\pi$
$884$	−30.4829	−1.02525
$885$	−65.3798	−2.19772
$886$	13.8641	0.465773
$887$	0.998063	0.0335117	0.0167558	−	0.999860i	$-0.494666\pi$
$887$	0.998063	0.0335117	0.0167558	+	0.999860i	$0.494666\pi$
$888$	32.1996	1.08055
$889$	63.7605	2.13846
$890$	179.506	6.01705
$891$	−1.21768	−0.0407937
$892$	−6.86009	−0.229693
$893$	−15.0861	−0.504838
$894$	36.8723	1.23320
$895$	−24.4253	−0.816447
$896$	73.4827	2.45489
$897$	−10.3650	−0.346076
$898$	−55.9174	−1.86599
$899$	−8.53084	−0.284519
$900$	−80.8855	−2.69618
$901$	−26.8617	−0.894891
$902$	16.0302	0.533746
$903$	−2.55200	−0.0849252
$904$	−70.1961	−2.33469
$905$	−5.53672	−0.184047
$906$	15.8153	0.525428
$907$	50.8159	1.68731	0.843657	−	0.536882i	$-0.180398\pi$
$907$	50.8159	1.68731	0.843657	+	0.536882i	$0.180398\pi$
$908$	92.4827	3.06915
$909$	13.3325	0.442210
$910$	69.7786	2.31314
$911$	−0.461605	−0.0152936	−0.00764682	−	0.999971i	$-0.502434\pi$
$911$	−0.461605	−0.0152936	−0.00764682	+	0.999971i	$0.502434\pi$
$912$	−2.35582	−0.0780088
$913$	1.57642	0.0521718
$914$	51.1378	1.69149
$915$	−31.8884	−1.05420
$916$	86.4329	2.85582
$917$	−27.0848	−0.894419
$918$	−59.3373	−1.95842
$919$	−36.5189	−1.20465	−0.602323	−	0.798252i	$-0.705758\pi$
$919$	−36.5189	−1.20465	−0.602323	+	0.798252i	$0.705758\pi$
$920$	−71.7212	−2.36458
$921$	−14.7513	−0.486073
$922$	−50.9670	−1.67851
$923$	−27.1837	−0.894764
$924$	14.6611	0.482315
$925$	−114.132	−3.75263
$926$	−51.6209	−1.69637
$927$	−23.7510	−0.780084
$928$	−23.5074	−0.771669
$929$	51.0512	1.67494	0.837468	−	0.546487i	$-0.184035\pi$
$929$	51.0512	1.67494	0.837468	+	0.546487i	$0.184035\pi$
$930$	18.5243	0.607435
$931$	−12.2639	−0.401931
$932$	53.6081	1.75599
$933$	4.00148	0.131003
$934$	15.6034	0.510558
$935$	20.5381	0.671669
$936$	10.6584	0.348381
$937$	−9.51799	−0.310939	−0.155470	−	0.987841i	$-0.549689\pi$
$937$	−9.51799	−0.310939	−0.155470	+	0.987841i	$0.549689\pi$
$938$	−16.3368	−0.533415
$939$	−35.1273	−1.14634
$940$	−119.658	−3.90280
$941$	10.5965	0.345436	0.172718	−	0.984971i	$-0.444745\pi$
$941$	10.5965	0.345436	0.172718	+	0.984971i	$0.444745\pi$
$942$	45.6497	1.48735
$943$	32.9664	1.07353
$944$	13.9255	0.453238
$945$	86.1126	2.80124
$946$	1.40950	0.0458269
$947$	10.1189	0.328821	0.164410	−	0.986392i	$-0.447428\pi$
$947$	10.1189	0.328821	0.164410	+	0.986392i	$0.447428\pi$
$948$	34.1093	1.10782
$949$	−17.1301	−0.556066
$950$	62.3234	2.02204
$951$	39.6615	1.28611
$952$	59.1152	1.91593
$953$	1.59356	0.0516204	0.0258102	−	0.999667i	$-0.491783\pi$
$953$	1.59356	0.0516204	0.0258102	+	0.999667i	$0.491783\pi$
$954$	22.2222	0.719469
$955$	12.2170	0.395333
$956$	75.5656	2.44397
$957$	−6.25366	−0.202152
$958$	74.2522	2.39898
$959$	−38.7934	−1.25270
$960$	61.8332	1.99566
$961$	−28.5202	−0.920006
$962$	35.5832	1.14725
$963$	−9.12326	−0.293993
$964$	91.9100	2.96022
$965$	30.0586	0.967620
$966$	47.5584	1.53017
$967$	22.5632	0.725584	0.362792	−	0.931870i	$-0.381824\pi$
$967$	22.5632	0.725584	0.362792	+	0.931870i	$0.381824\pi$
$968$	−3.42244	−0.110001
$969$	10.3548	0.332645
$970$	−166.753	−5.35412
$971$	−59.5378	−1.91066	−0.955330	−	0.295541i	$-0.904500\pi$
$971$	−59.5378	−1.91066	−0.955330	+	0.295541i	$0.904500\pi$
$972$	51.1243	1.63981
$973$	−37.8339	−1.21290
$974$	−22.6894	−0.727015
$975$	30.1937	0.966973
$976$	6.79206	0.217409
$977$	25.8915	0.828341	0.414171	−	0.910199i	$-0.364072\pi$
$977$	25.8915	0.828341	0.414171	+	0.910199i	$0.364072\pi$
$978$	35.3818	1.13138
$979$	17.6157	0.563000
$980$	−97.2724	−3.10725
$981$	7.16262	0.228685
$982$	−73.3295	−2.34004
$983$	14.8542	0.473777	0.236888	−	0.971537i	$-0.423872\pi$
$983$	14.8542	0.473777	0.236888	+	0.971537i	$0.423872\pi$
$984$	27.0935	0.863711
$985$	1.29952	0.0414061
$986$	−59.6601	−1.89996
$987$	33.5354	1.06744
$988$	−12.3186	−0.391908
$989$	2.89867	0.0921725
$990$	−16.9908	−0.540004
$991$	−50.7336	−1.61161	−0.805803	−	0.592183i	$-0.798266\pi$
$991$	−50.7336	−1.61161	−0.805803	+	0.592183i	$0.798266\pi$
$992$	6.83335	0.216959
$993$	−6.22297	−0.197480
$994$	124.730	3.95618
$995$	−50.3004	−1.59463
$996$	6.30400	0.199750
$997$	13.8757	0.439448	0.219724	−	0.975562i	$-0.429484\pi$
$997$	13.8757	0.439448	0.219724	+	0.975562i	$0.429484\pi$
$998$	−28.7942	−0.911466
$999$	43.9126	1.38933

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6017.2.a.e.1.14	✓	119

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6017.2.a.e.1.14	✓	119	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:	\( N \)	\(=\)	\( 6017 = 11 \cdot 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6017.a (trivial)

\(f(q)\)	\(=\)	\(q-2.33754 q^{2} +1.15439 q^{3} +3.46412 q^{4} -4.35932 q^{5} -2.69844 q^{6} +3.66625 q^{7} -3.42244 q^{8} -1.66738 q^{9} +O(q^{10})\)	\(q-2.33754 q^{2} +1.15439 q^{3} +3.46412 q^{4} -4.35932 q^{5} -2.69844 q^{6} +3.66625 q^{7} -3.42244 q^{8} -1.66738 q^{9} +10.1901 q^{10} +1.00000 q^{11} +3.99894 q^{12} +1.86776 q^{13} -8.57002 q^{14} -5.03236 q^{15} +1.07186 q^{16} -4.71132 q^{17} +3.89759 q^{18} -1.90392 q^{19} -15.1012 q^{20} +4.23228 q^{21} -2.33754 q^{22} -4.80721 q^{23} -3.95082 q^{24} +14.0037 q^{25} -4.36598 q^{26} -5.38798 q^{27} +12.7003 q^{28} -5.41729 q^{29} +11.7634 q^{30} +1.57474 q^{31} +4.33934 q^{32} +1.15439 q^{33} +11.0129 q^{34} -15.9824 q^{35} -5.77601 q^{36} -8.15011 q^{37} +4.45050 q^{38} +2.15613 q^{39} +14.9195 q^{40} -6.85770 q^{41} -9.89314 q^{42} -0.602984 q^{43} +3.46412 q^{44} +7.26867 q^{45} +11.2371 q^{46} +7.92371 q^{47} +1.23735 q^{48} +6.44137 q^{49} -32.7343 q^{50} -5.43869 q^{51} +6.47014 q^{52} +5.70152 q^{53} +12.5946 q^{54} -4.35932 q^{55} -12.5475 q^{56} -2.19787 q^{57} +12.6631 q^{58} +12.9919 q^{59} -17.4327 q^{60} +6.33668 q^{61} -3.68103 q^{62} -6.11304 q^{63} -12.2871 q^{64} -8.14218 q^{65} -2.69844 q^{66} +1.90627 q^{67} -16.3205 q^{68} -5.54940 q^{69} +37.3595 q^{70} -14.5542 q^{71} +5.70652 q^{72} -9.17144 q^{73} +19.0512 q^{74} +16.1657 q^{75} -6.59540 q^{76} +3.66625 q^{77} -5.04004 q^{78} +8.52958 q^{79} -4.67260 q^{80} -1.21768 q^{81} +16.0302 q^{82} +1.57642 q^{83} +14.6611 q^{84} +20.5381 q^{85} +1.40950 q^{86} -6.25366 q^{87} -3.42244 q^{88} +17.6157 q^{89} -16.9908 q^{90} +6.84768 q^{91} -16.6527 q^{92} +1.81787 q^{93} -18.5220 q^{94} +8.29980 q^{95} +5.00929 q^{96} -16.3642 q^{97} -15.0570 q^{98} -1.66738 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 119 q + 15 q^{2} + 15 q^{3} + 133 q^{4} + 6 q^{5} + 16 q^{6} + 72 q^{7} + 39 q^{8} + 128 q^{9}+O(q^{10}) \) 119 * q + 15 * q^2 + 15 * q^3 + 133 * q^4 + 6 * q^5 + 16 * q^6 + 72 * q^7 + 39 * q^8 + 128 * q^9	\( 119 q + 15 q^{2} + 15 q^{3} + 133 q^{4} + 6 q^{5} + 16 q^{6} + 72 q^{7} + 39 q^{8} + 128 q^{9} + 22 q^{10} + 119 q^{11} + 40 q^{12} + 67 q^{13} + 3 q^{14} + 22 q^{15} + 145 q^{16} + 57 q^{17} + 53 q^{18} + 68 q^{19} + 25 q^{20} + 21 q^{21} + 15 q^{22} + 21 q^{23} + 34 q^{24} + 137 q^{25} + 10 q^{26} + 54 q^{27} + 149 q^{28} + 46 q^{29} + 10 q^{30} + 87 q^{31} + 58 q^{32} + 15 q^{33} + 16 q^{34} + 40 q^{35} + 137 q^{36} + 39 q^{37} + 27 q^{38} + 72 q^{39} + 46 q^{40} + 50 q^{41} - 4 q^{42} + 122 q^{43} + 133 q^{44} + 12 q^{45} + 22 q^{46} + 92 q^{47} + 9 q^{48} + 161 q^{49} + 2 q^{50} - 12 q^{51} + 177 q^{52} + 12 q^{53} + 19 q^{54} + 6 q^{55} - 16 q^{56} + 43 q^{57} + 56 q^{58} + 39 q^{59} + 27 q^{60} + 114 q^{61} + 66 q^{62} + 196 q^{63} + 161 q^{64} + 7 q^{65} + 16 q^{66} + 59 q^{67} + 139 q^{68} - 24 q^{69} + 9 q^{70} + 11 q^{71} + 92 q^{72} + 123 q^{73} + q^{74} + 19 q^{75} + 92 q^{76} + 72 q^{77} - 101 q^{78} + 78 q^{79} - 34 q^{80} + 139 q^{81} + 73 q^{82} + 108 q^{83} - 31 q^{84} + 30 q^{85} - 18 q^{86} + 164 q^{87} + 39 q^{88} + 15 q^{89} - 41 q^{90} + 60 q^{91} - 26 q^{92} - 2 q^{93} + 45 q^{94} + 75 q^{95} + 42 q^{96} + 73 q^{97} + 32 q^{98} + 128 q^{99}+O(q^{100}) \) 119 * q + 15 * q^2 + 15 * q^3 + 133 * q^4 + 6 * q^5 + 16 * q^6 + 72 * q^7 + 39 * q^8 + 128 * q^9 + 22 * q^10 + 119 * q^11 + 40 * q^12 + 67 * q^13 + 3 * q^14 + 22 * q^15 + 145 * q^16 + 57 * q^17 + 53 * q^18 + 68 * q^19 + 25 * q^20 + 21 * q^21 + 15 * q^22 + 21 * q^23 + 34 * q^24 + 137 * q^25 + 10 * q^26 + 54 * q^27 + 149 * q^28 + 46 * q^29 + 10 * q^30 + 87 * q^31 + 58 * q^32 + 15 * q^33 + 16 * q^34 + 40 * q^35 + 137 * q^36 + 39 * q^37 + 27 * q^38 + 72 * q^39 + 46 * q^40 + 50 * q^41 - 4 * q^42 + 122 * q^43 + 133 * q^44 + 12 * q^45 + 22 * q^46 + 92 * q^47 + 9 * q^48 + 161 * q^49 + 2 * q^50 - 12 * q^51 + 177 * q^52 + 12 * q^53 + 19 * q^54 + 6 * q^55 - 16 * q^56 + 43 * q^57 + 56 * q^58 + 39 * q^59 + 27 * q^60 + 114 * q^61 + 66 * q^62 + 196 * q^63 + 161 * q^64 + 7 * q^65 + 16 * q^66 + 59 * q^67 + 139 * q^68 - 24 * q^69 + 9 * q^70 + 11 * q^71 + 92 * q^72 + 123 * q^73 + q^74 + 19 * q^75 + 92 * q^76 + 72 * q^77 - 101 * q^78 + 78 * q^79 - 34 * q^80 + 139 * q^81 + 73 * q^82 + 108 * q^83 - 31 * q^84 + 30 * q^85 - 18 * q^86 + 164 * q^87 + 39 * q^88 + 15 * q^89 - 41 * q^90 + 60 * q^91 - 26 * q^92 - 2 * q^93 + 45 * q^94 + 75 * q^95 + 42 * q^96 + 73 * q^97 + 32 * q^98 + 128 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more