LMFDB - Embedded newform 6017.2.a.f.1.10

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:	$121$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
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)

$f(q)$	$=$	$q-2.54623 q^{2} -1.76925 q^{3} +4.48328 q^{4} -0.663879 q^{5} +4.50492 q^{6} -3.59601 q^{7} -6.32301 q^{8} +0.130248 q^{9} +O(q^{10})$	\(q-2.54623 q^{2} -1.76925 q^{3} +4.48328 q^{4} -0.663879 q^{5} +4.50492 q^{6} -3.59601 q^{7} -6.32301 q^{8} +0.130248 q^{9} +1.69039 q^{10} -1.00000 q^{11} -7.93205 q^{12} +2.37087 q^{13} +9.15627 q^{14} +1.17457 q^{15} +7.13326 q^{16} +0.864490 q^{17} -0.331642 q^{18} -0.433464 q^{19} -2.97636 q^{20} +6.36225 q^{21} +2.54623 q^{22} +7.71083 q^{23} +11.1870 q^{24} -4.55926 q^{25} -6.03679 q^{26} +5.07731 q^{27} -16.1219 q^{28} +3.04739 q^{29} -2.99072 q^{30} +6.27472 q^{31} -5.51689 q^{32} +1.76925 q^{33} -2.20119 q^{34} +2.38732 q^{35} +0.583939 q^{36} +5.25374 q^{37} +1.10370 q^{38} -4.19467 q^{39} +4.19771 q^{40} -0.827912 q^{41} -16.1997 q^{42} +3.20055 q^{43} -4.48328 q^{44} -0.0864690 q^{45} -19.6335 q^{46} -2.66970 q^{47} -12.6205 q^{48} +5.93131 q^{49} +11.6089 q^{50} -1.52950 q^{51} +10.6293 q^{52} +0.411986 q^{53} -12.9280 q^{54} +0.663879 q^{55} +22.7376 q^{56} +0.766906 q^{57} -7.75936 q^{58} -11.0557 q^{59} +5.26592 q^{60} -3.37352 q^{61} -15.9769 q^{62} -0.468374 q^{63} -0.219240 q^{64} -1.57397 q^{65} -4.50492 q^{66} +10.4408 q^{67} +3.87575 q^{68} -13.6424 q^{69} -6.07866 q^{70} -7.58971 q^{71} -0.823560 q^{72} -11.1191 q^{73} -13.3772 q^{74} +8.06648 q^{75} -1.94334 q^{76} +3.59601 q^{77} +10.6806 q^{78} -7.43624 q^{79} -4.73562 q^{80} -9.37378 q^{81} +2.10805 q^{82} +8.56768 q^{83} +28.5238 q^{84} -0.573917 q^{85} -8.14934 q^{86} -5.39160 q^{87} +6.32301 q^{88} -2.14094 q^{89} +0.220170 q^{90} -8.52569 q^{91} +34.5698 q^{92} -11.1015 q^{93} +6.79766 q^{94} +0.287768 q^{95} +9.76077 q^{96} +15.9031 q^{97} -15.1025 q^{98} -0.130248 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 121 q + 2 q^{2} + 18 q^{3} + 138 q^{4} + 13 q^{5} + 10 q^{6} + 56 q^{7} + 12 q^{8} + 143 q^{9}+O(q^{10}) $ 121 * q + 2 * q^2 + 18 * q^3 + 138 * q^4 + 13 * q^5 + 10 * q^6 + 56 * q^7 + 12 * q^8 + 143 * q^9	\( 121 q + 2 q^{2} + 18 q^{3} + 138 q^{4} + 13 q^{5} + 10 q^{6} + 56 q^{7} + 12 q^{8} + 143 q^{9} + 20 q^{10} - 121 q^{11} + 40 q^{12} + 31 q^{13} + 7 q^{14} + 53 q^{15} + 164 q^{16} - 23 q^{17} + 14 q^{18} + 62 q^{19} + 53 q^{20} + 19 q^{21} - 2 q^{22} + 34 q^{23} + 34 q^{24} + 172 q^{25} + 34 q^{26} + 87 q^{27} + 91 q^{28} - 30 q^{29} + 2 q^{30} + 102 q^{31} + 31 q^{32} - 18 q^{33} + 30 q^{34} + 20 q^{35} + 164 q^{36} + 58 q^{37} + 35 q^{38} + 42 q^{39} + 52 q^{40} - 12 q^{41} + 56 q^{42} + 96 q^{43} - 138 q^{44} + 72 q^{45} + 48 q^{46} + 136 q^{47} + 99 q^{48} + 199 q^{49} - 7 q^{50} + 22 q^{51} + 81 q^{52} + 24 q^{53} + 37 q^{54} - 13 q^{55} + 28 q^{56} + 25 q^{57} + 76 q^{58} + 58 q^{59} + 81 q^{60} + 14 q^{61} - 2 q^{62} + 152 q^{63} + 236 q^{64} - 29 q^{65} - 10 q^{66} + 112 q^{67} - 61 q^{68} + 41 q^{69} + 105 q^{70} + 56 q^{71} + 71 q^{72} + 113 q^{73} - 23 q^{74} + 111 q^{75} + 144 q^{76} - 56 q^{77} + 59 q^{78} + 80 q^{79} + 100 q^{80} + 177 q^{81} + 123 q^{82} + 6 q^{83} + 79 q^{84} + 26 q^{85} + 14 q^{86} + 180 q^{87} - 12 q^{88} + 26 q^{89} + 75 q^{90} + 72 q^{91} + 58 q^{92} + 139 q^{93} + 37 q^{94} + 39 q^{95} + 66 q^{96} + 136 q^{97} + 7 q^{98} - 143 q^{99}+O(q^{100}) \) 121 * q + 2 * q^2 + 18 * q^3 + 138 * q^4 + 13 * q^5 + 10 * q^6 + 56 * q^7 + 12 * q^8 + 143 * q^9 + 20 * q^10 - 121 * q^11 + 40 * q^12 + 31 * q^13 + 7 * q^14 + 53 * q^15 + 164 * q^16 - 23 * q^17 + 14 * q^18 + 62 * q^19 + 53 * q^20 + 19 * q^21 - 2 * q^22 + 34 * q^23 + 34 * q^24 + 172 * q^25 + 34 * q^26 + 87 * q^27 + 91 * q^28 - 30 * q^29 + 2 * q^30 + 102 * q^31 + 31 * q^32 - 18 * q^33 + 30 * q^34 + 20 * q^35 + 164 * q^36 + 58 * q^37 + 35 * q^38 + 42 * q^39 + 52 * q^40 - 12 * q^41 + 56 * q^42 + 96 * q^43 - 138 * q^44 + 72 * q^45 + 48 * q^46 + 136 * q^47 + 99 * q^48 + 199 * q^49 - 7 * q^50 + 22 * q^51 + 81 * q^52 + 24 * q^53 + 37 * q^54 - 13 * q^55 + 28 * q^56 + 25 * q^57 + 76 * q^58 + 58 * q^59 + 81 * q^60 + 14 * q^61 - 2 * q^62 + 152 * q^63 + 236 * q^64 - 29 * q^65 - 10 * q^66 + 112 * q^67 - 61 * q^68 + 41 * q^69 + 105 * q^70 + 56 * q^71 + 71 * q^72 + 113 * q^73 - 23 * q^74 + 111 * q^75 + 144 * q^76 - 56 * q^77 + 59 * q^78 + 80 * q^79 + 100 * q^80 + 177 * q^81 + 123 * q^82 + 6 * q^83 + 79 * q^84 + 26 * q^85 + 14 * q^86 + 180 * q^87 - 12 * q^88 + 26 * q^89 + 75 * q^90 + 72 * q^91 + 58 * q^92 + 139 * q^93 + 37 * q^94 + 39 * q^95 + 66 * q^96 + 136 * q^97 + 7 * q^98 - 143 * 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 $

$2$	−2.54623	−1.80046	−0.900228	−	0.435419i	$-0.856600\pi$
$2$	−2.54623	−1.80046	−0.900228	+	0.435419i	$0.856600\pi$
$3$	−1.76925	−1.02148	−0.510739	−	0.859736i	$-0.670628\pi$
$3$	−1.76925	−1.02148	−0.510739	+	0.859736i	$0.670628\pi$
$4$	4.48328	2.24164
$5$	−0.663879	−0.296896	−0.148448	−	0.988920i	$-0.547428\pi$
$5$	−0.663879	−0.296896	−0.148448	+	0.988920i	$0.547428\pi$
$6$	4.50492	1.83912
$7$	−3.59601	−1.35917	−0.679583	−	0.733599i	$-0.737839\pi$
$7$	−3.59601	−1.35917	−0.679583	+	0.733599i	$0.737839\pi$
$8$	−6.32301	−2.23552
$9$	0.130248	0.0434160
$10$	1.69039	0.534548
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−7.93205	−2.28979
$13$	2.37087	0.657562	0.328781	−	0.944406i	$-0.393362\pi$
$13$	2.37087	0.657562	0.328781	+	0.944406i	$0.393362\pi$
$14$	9.15627	2.44712
$15$	1.17457	0.303272
$16$	7.13326	1.78331
$17$	0.864490	0.209670	0.104835	−	0.994490i	$-0.466569\pi$
$17$	0.864490	0.209670	0.104835	+	0.994490i	$0.466569\pi$
$18$	−0.331642	−0.0781687
$19$	−0.433464	−0.0994435	−0.0497217	−	0.998763i	$-0.515833\pi$
$19$	−0.433464	−0.0994435	−0.0497217	+	0.998763i	$0.515833\pi$
$20$	−2.97636	−0.665534
$21$	6.36225	1.38836
$22$	2.54623	0.542858
$23$	7.71083	1.60782	0.803910	−	0.594751i	$-0.202749\pi$
$23$	7.71083	1.60782	0.803910	+	0.594751i	$0.202749\pi$
$24$	11.1870	2.28353
$25$	−4.55926	−0.911853
$26$	−6.03679	−1.18391
$27$	5.07731	0.977129
$28$	−16.1219	−3.04676
$29$	3.04739	0.565887	0.282943	−	0.959137i	$-0.408689\pi$
$29$	3.04739	0.565887	0.282943	+	0.959137i	$0.408689\pi$
$30$	−2.99072	−0.546028
$31$	6.27472	1.12697	0.563486	−	0.826125i	$-0.309460\pi$
$31$	6.27472	1.12697	0.563486	+	0.826125i	$0.309460\pi$
$32$	−5.51689	−0.975258
$33$	1.76925	0.307987
$34$	−2.20119	−0.377501
$35$	2.38732	0.403530
$36$	0.583939	0.0973232
$37$	5.25374	0.863710	0.431855	−	0.901943i	$-0.357859\pi$
$37$	5.25374	0.863710	0.431855	+	0.901943i	$0.357859\pi$
$38$	1.10370	0.179044
$39$	−4.19467	−0.671685
$40$	4.19771	0.663716
$41$	−0.827912	−0.129298	−0.0646490	−	0.997908i	$-0.520593\pi$
$41$	−0.827912	−0.129298	−0.0646490	+	0.997908i	$0.520593\pi$
$42$	−16.1997	−2.49967
$43$	3.20055	0.488080	0.244040	−	0.969765i	$-0.421527\pi$
$43$	3.20055	0.488080	0.244040	+	0.969765i	$0.421527\pi$
$44$	−4.48328	−0.675880
$45$	−0.0864690	−0.0128900
$46$	−19.6335	−2.89481
$47$	−2.66970	−0.389415	−0.194708	−	0.980861i	$-0.562376\pi$
$47$	−2.66970	−0.389415	−0.194708	+	0.980861i	$0.562376\pi$
$48$	−12.6205	−1.82161
$49$	5.93131	0.847330
$50$	11.6089	1.64175
$51$	−1.52950	−0.214173
$52$	10.6293	1.47402
$53$	0.411986	0.0565906	0.0282953	−	0.999600i	$-0.490992\pi$
$53$	0.411986	0.0565906	0.0282953	+	0.999600i	$0.490992\pi$
$54$	−12.9280	−1.75928
$55$	0.663879	0.0895174
$56$	22.7376	3.03844
$57$	0.766906	0.101579
$58$	−7.75936	−1.01885
$59$	−11.0557	−1.43933	−0.719663	−	0.694324i	$-0.755704\pi$
$59$	−11.0557	−1.43933	−0.719663	+	0.694324i	$0.755704\pi$
$60$	5.26592	0.679828
$61$	−3.37352	−0.431935	−0.215968	−	0.976401i	$-0.569291\pi$
$61$	−3.37352	−0.431935	−0.215968	+	0.976401i	$0.569291\pi$
$62$	−15.9769	−2.02906
$63$	−0.468374	−0.0590096
$64$	−0.219240	−0.0274050
$65$	−1.57397	−0.195227
$66$	−4.50492	−0.554517
$67$	10.4408	1.27555	0.637773	−	0.770224i	$-0.279856\pi$
$67$	10.4408	1.27555	0.637773	+	0.770224i	$0.279856\pi$
$68$	3.87575	0.470004
$69$	−13.6424	−1.64235
$70$	−6.07866	−0.726539
$71$	−7.58971	−0.900733	−0.450366	−	0.892844i	$-0.648707\pi$
$71$	−7.58971	−0.900733	−0.450366	+	0.892844i	$0.648707\pi$
$72$	−0.823560	−0.0970574
$73$	−11.1191	−1.30139	−0.650695	−	0.759339i	$-0.725522\pi$
$73$	−11.1191	−1.30139	−0.650695	+	0.759339i	$0.725522\pi$
$74$	−13.3772	−1.55507
$75$	8.06648	0.931437
$76$	−1.94334	−0.222917
$77$	3.59601	0.409804
$78$	10.6806	1.20934
$79$	−7.43624	−0.836642	−0.418321	−	0.908299i	$-0.637381\pi$
$79$	−7.43624	−0.836642	−0.418321	+	0.908299i	$0.637381\pi$
$80$	−4.73562	−0.529458
$81$	−9.37378	−1.04153
$82$	2.10805	0.232795
$83$	8.56768	0.940425	0.470212	−	0.882553i	$-0.344177\pi$
$83$	8.56768	0.940425	0.470212	+	0.882553i	$0.344177\pi$
$84$	28.5238	3.11220
$85$	−0.573917	−0.0622501
$86$	−8.14934	−0.878766
$87$	−5.39160	−0.578040
$88$	6.32301	0.674035
$89$	−2.14094	−0.226939	−0.113470	−	0.993541i	$-0.536196\pi$
$89$	−2.14094	−0.226939	−0.113470	+	0.993541i	$0.536196\pi$
$90$	0.220170	0.0232079
$91$	−8.52569	−0.893735
$92$	34.5698	3.60416
$93$	−11.1015	−1.15118
$94$	6.79766	0.701125
$95$	0.287768	0.0295243
$96$	9.76077	0.996204
$97$	15.9031	1.61471	0.807356	−	0.590065i	$-0.200898\pi$
$97$	15.9031	1.61471	0.807356	+	0.590065i	$0.200898\pi$
$98$	−15.1025	−1.52558
$99$	−0.130248	−0.0130904
$100$	−20.4405	−2.04405
$101$	−18.5255	−1.84336	−0.921680	−	0.387950i	$-0.873183\pi$
$101$	−18.5255	−1.84336	−0.921680	+	0.387950i	$0.873183\pi$
$102$	3.89446	0.385609
$103$	−4.56476	−0.449779	−0.224890	−	0.974384i	$-0.572202\pi$
$103$	−4.56476	−0.449779	−0.224890	+	0.974384i	$0.572202\pi$
$104$	−14.9910	−1.46999
$105$	−4.22376	−0.412197
$106$	−1.04901	−0.101889
$107$	−11.8468	−1.14528	−0.572638	−	0.819808i	$-0.694080\pi$
$107$	−11.8468	−1.14528	−0.572638	+	0.819808i	$0.694080\pi$
$108$	22.7630	2.19037
$109$	8.58578	0.822369	0.411184	−	0.911552i	$-0.365115\pi$
$109$	8.58578	0.822369	0.411184	+	0.911552i	$0.365115\pi$
$110$	−1.69039	−0.161172
$111$	−9.29519	−0.882261
$112$	−25.6513	−2.42382
$113$	2.69394	0.253425	0.126712	−	0.991940i	$-0.459557\pi$
$113$	2.69394	0.253425	0.126712	+	0.991940i	$0.459557\pi$
$114$	−1.95272	−0.182889
$115$	−5.11906	−0.477355
$116$	13.6623	1.26851
$117$	0.308802	0.0285487
$118$	28.1503	2.59144
$119$	−3.10872	−0.284976
$120$	−7.42680	−0.677971
$121$	1.00000	0.0909091
$122$	8.58976	0.777681
$123$	1.46478	0.132075
$124$	28.1313	2.52627
$125$	6.34620	0.567621
$126$	1.19259	0.106244
$127$	−7.28935	−0.646825	−0.323413	−	0.946258i	$-0.604830\pi$
$127$	−7.28935	−0.646825	−0.323413	+	0.946258i	$0.604830\pi$
$128$	11.5920	1.02460
$129$	−5.66258	−0.498562
$130$	4.00770	0.351498
$131$	9.39709	0.821028	0.410514	−	0.911854i	$-0.365349\pi$
$131$	9.39709	0.821028	0.410514	+	0.911854i	$0.365349\pi$
$132$	7.93205	0.690396
$133$	1.55874	0.135160
$134$	−26.5847	−2.29656
$135$	−3.37072	−0.290105
$136$	−5.46618	−0.468721
$137$	−14.9699	−1.27896	−0.639480	−	0.768807i	$-0.720850\pi$
$137$	−14.9699	−1.27896	−0.639480	+	0.768807i	$0.720850\pi$
$138$	34.7367	2.95698
$139$	10.5242	0.892651	0.446325	−	0.894871i	$-0.352732\pi$
$139$	10.5242	0.892651	0.446325	+	0.894871i	$0.352732\pi$
$140$	10.7030	0.904570
$141$	4.72336	0.397779
$142$	19.3251	1.62173
$143$	−2.37087	−0.198262
$144$	0.929093	0.0774244
$145$	−2.02310	−0.168009
$146$	28.3117	2.34309
$147$	−10.4940	−0.865529
$148$	23.5540	1.93613
$149$	2.16860	0.177658	0.0888292	−	0.996047i	$-0.471687\pi$
$149$	2.16860	0.177658	0.0888292	+	0.996047i	$0.471687\pi$
$150$	−20.5391	−1.67701
$151$	10.6063	0.863129	0.431565	−	0.902082i	$-0.357962\pi$
$151$	10.6063	0.863129	0.431565	+	0.902082i	$0.357962\pi$
$152$	2.74080	0.222308
$153$	0.112598	0.00910303
$154$	−9.15627	−0.737834
$155$	−4.16565	−0.334593
$156$	−18.8059	−1.50568
$157$	2.43305	0.194179	0.0970893	−	0.995276i	$-0.469047\pi$
$157$	2.43305	0.194179	0.0970893	+	0.995276i	$0.469047\pi$
$158$	18.9344	1.50634
$159$	−0.728906	−0.0578060
$160$	3.66255	0.289550
$161$	−27.7283	−2.18529
$162$	23.8678	1.87523
$163$	6.30007	0.493459	0.246730	−	0.969084i	$-0.420644\pi$
$163$	6.30007	0.493459	0.246730	+	0.969084i	$0.420644\pi$
$164$	−3.71176	−0.289840
$165$	−1.17457	−0.0914400
$166$	−21.8153	−1.69319
$167$	−8.23261	−0.637059	−0.318529	−	0.947913i	$-0.603189\pi$
$167$	−8.23261	−0.637059	−0.318529	+	0.947913i	$0.603189\pi$
$168$	−40.2285	−3.10370
$169$	−7.37896	−0.567612
$170$	1.46132	0.112078
$171$	−0.0564579	−0.00431744
$172$	14.3490	1.09410
$173$	−10.5745	−0.803962	−0.401981	−	0.915648i	$-0.631678\pi$
$173$	−10.5745	−0.803962	−0.401981	+	0.915648i	$0.631678\pi$
$174$	13.7283	1.04074
$175$	16.3952	1.23936
$176$	−7.13326	−0.537689
$177$	19.5602	1.47024
$178$	5.45133	0.408594
$179$	−0.395686	−0.0295749	−0.0147875	−	0.999891i	$-0.504707\pi$
$179$	−0.395686	−0.0295749	−0.0147875	+	0.999891i	$0.504707\pi$
$180$	−0.387665	−0.0288948
$181$	8.98573	0.667904	0.333952	−	0.942590i	$-0.391618\pi$
$181$	8.98573	0.667904	0.333952	+	0.942590i	$0.391618\pi$
$182$	21.7084	1.60913
$183$	5.96861	0.441212
$184$	−48.7556	−3.59431
$185$	−3.48785	−0.256432
$186$	28.2671	2.07264
$187$	−0.864490	−0.0632178
$188$	−11.9690	−0.872929
$189$	−18.2581	−1.32808
$190$	−0.732722	−0.0531573
$191$	10.7584	0.778449	0.389225	−	0.921143i	$-0.372743\pi$
$191$	10.7584	0.778449	0.389225	+	0.921143i	$0.372743\pi$
$192$	0.387891	0.0279936
$193$	19.4827	1.40239	0.701197	−	0.712967i	$-0.252649\pi$
$193$	19.4827	1.40239	0.701197	+	0.712967i	$0.252649\pi$
$194$	−40.4929	−2.90722
$195$	2.78475	0.199420
$196$	26.5918	1.89941
$197$	−16.4192	−1.16982	−0.584910	−	0.811098i	$-0.698870\pi$
$197$	−16.4192	−1.16982	−0.584910	+	0.811098i	$0.698870\pi$
$198$	0.331642	0.0235687
$199$	6.44984	0.457217	0.228609	−	0.973518i	$-0.426582\pi$
$199$	6.44984	0.457217	0.228609	+	0.973518i	$0.426582\pi$
$200$	28.8283	2.03847
$201$	−18.4724	−1.30294
$202$	47.1703	3.31889
$203$	−10.9585	−0.769134
$204$	−6.85718	−0.480099
$205$	0.549633	0.0383880
$206$	11.6229	0.809807
$207$	1.00432	0.0698052
$208$	16.9120	1.17264
$209$	0.433464	0.0299833
$210$	10.7547	0.742143
$211$	−19.0062	−1.30844	−0.654222	−	0.756303i	$-0.727004\pi$
$211$	−19.0062	−1.30844	−0.654222	+	0.756303i	$0.727004\pi$
$212$	1.84705	0.126856
$213$	13.4281	0.920078
$214$	30.1647	2.06202
$215$	−2.12478	−0.144909
$216$	−32.1039	−2.18439
$217$	−22.5640	−1.53174
$218$	−21.8614	−1.48064
$219$	19.6724	1.32934
$220$	2.97636	0.200666
$221$	2.04960	0.137871
$222$	23.6677	1.58847
$223$	21.3514	1.42979	0.714896	−	0.699231i	$-0.246474\pi$
$223$	21.3514	1.42979	0.714896	+	0.699231i	$0.246474\pi$
$224$	19.8388	1.32554
$225$	−0.593836	−0.0395890
$226$	−6.85939	−0.456280
$227$	16.9954	1.12802	0.564011	−	0.825767i	$-0.309258\pi$
$227$	16.9954	1.12802	0.564011	+	0.825767i	$0.309258\pi$
$228$	3.43826	0.227704
$229$	−10.5687	−0.698398	−0.349199	−	0.937049i	$-0.613546\pi$
$229$	−10.5687	−0.698398	−0.349199	+	0.937049i	$0.613546\pi$
$230$	13.0343	0.859456
$231$	−6.36225	−0.418605
$232$	−19.2687	−1.26505
$233$	−6.02817	−0.394919	−0.197459	−	0.980311i	$-0.563269\pi$
$233$	−6.02817	−0.394919	−0.197459	+	0.980311i	$0.563269\pi$
$234$	−0.786280	−0.0514007
$235$	1.77236	0.115616
$236$	−49.5657	−3.22645
$237$	13.1566	0.854611
$238$	7.91551	0.513086
$239$	−24.6934	−1.59728	−0.798642	−	0.601807i	$-0.794448\pi$
$239$	−24.6934	−1.59728	−0.798642	+	0.601807i	$0.794448\pi$
$240$	8.37850	0.540830
$241$	7.96234	0.512899	0.256450	−	0.966558i	$-0.417447\pi$
$241$	7.96234	0.512899	0.256450	+	0.966558i	$0.417447\pi$
$242$	−2.54623	−0.163678
$243$	1.35263	0.0867716
$244$	−15.1245	−0.968244
$245$	−3.93767	−0.251569
$246$	−3.72967	−0.237795
$247$	−1.02769	−0.0653902
$248$	−39.6751	−2.51937
$249$	−15.1584	−0.960623
$250$	−16.1589	−1.02198
$251$	−4.45640	−0.281285	−0.140643	−	0.990060i	$-0.544917\pi$
$251$	−4.45640	−0.281285	−0.140643	+	0.990060i	$0.544917\pi$
$252$	−2.09985	−0.132278
$253$	−7.71083	−0.484776
$254$	18.5604	1.16458
$255$	1.01540	0.0635870
$256$	−29.0775	−1.81734
$257$	19.1814	1.19650	0.598250	−	0.801310i	$-0.295863\pi$
$257$	19.1814	1.19650	0.598250	+	0.801310i	$0.295863\pi$
$258$	14.4182	0.897639
$259$	−18.8925	−1.17393
$260$	−7.05657	−0.437630
$261$	0.396917	0.0245686
$262$	−23.9271	−1.47822
$263$	−18.8486	−1.16225	−0.581127	−	0.813813i	$-0.697388\pi$
$263$	−18.8486	−1.16225	−0.581127	+	0.813813i	$0.697388\pi$
$264$	−11.1870	−0.688511
$265$	−0.273509	−0.0168015
$266$	−3.96891	−0.243350
$267$	3.78786	0.231813
$268$	46.8090	2.85932
$269$	1.81484	0.110653	0.0553265	−	0.998468i	$-0.482380\pi$
$269$	1.81484	0.110653	0.0553265	+	0.998468i	$0.482380\pi$
$270$	8.58263	0.522322
$271$	−5.58690	−0.339380	−0.169690	−	0.985498i	$-0.554277\pi$
$271$	−5.58690	−0.339380	−0.169690	+	0.985498i	$0.554277\pi$
$272$	6.16663	0.373907
$273$	15.0841	0.912931
$274$	38.1167	2.30271
$275$	4.55926	0.274934
$276$	−61.1627	−3.68156
$277$	17.6667	1.06149	0.530745	−	0.847531i	$-0.321912\pi$
$277$	17.6667	1.06149	0.530745	+	0.847531i	$0.321912\pi$
$278$	−26.7970	−1.60718
$279$	0.817270	0.0489287
$280$	−15.0950	−0.902100
$281$	−7.69962	−0.459321	−0.229660	−	0.973271i	$-0.573762\pi$
$281$	−7.69962	−0.459321	−0.229660	+	0.973271i	$0.573762\pi$
$282$	−12.0268	−0.716183
$283$	−9.64049	−0.573068	−0.286534	−	0.958070i	$-0.592503\pi$
$283$	−9.64049	−0.573068	−0.286534	+	0.958070i	$0.592503\pi$
$284$	−34.0268	−2.01912
$285$	−0.509133	−0.0301584
$286$	6.03679	0.356963
$287$	2.97718	0.175737
$288$	−0.718565	−0.0423418
$289$	−16.2527	−0.956039
$290$	5.15128	0.302493
$291$	−28.1365	−1.64939
$292$	−49.8500	−2.91725
$293$	−16.8094	−0.982013	−0.491007	−	0.871156i	$-0.663371\pi$
$293$	−16.8094	−0.982013	−0.491007	+	0.871156i	$0.663371\pi$
$294$	26.7201	1.55835
$295$	7.33963	0.427330
$296$	−33.2195	−1.93084
$297$	−5.07731	−0.294615
$298$	−5.52175	−0.319866
$299$	18.2814	1.05724
$300$	36.1643	2.08795
$301$	−11.5092	−0.663381
$302$	−27.0061	−1.55403
$303$	32.7763	1.88295
$304$	−3.09201	−0.177339
$305$	2.23961	0.128240
$306$	−0.286701	−0.0163896
$307$	7.08964	0.404627	0.202314	−	0.979321i	$-0.435154\pi$
$307$	7.08964	0.404627	0.202314	+	0.979321i	$0.435154\pi$
$308$	16.1219	0.918633
$309$	8.07620	0.459439
$310$	10.6067	0.602421
$311$	−11.5590	−0.655451	−0.327725	−	0.944773i	$-0.606282\pi$
$311$	−11.5590	−0.655451	−0.327725	+	0.944773i	$0.606282\pi$
$312$	26.5229	1.50156
$313$	−26.1214	−1.47647	−0.738234	−	0.674545i	$-0.764340\pi$
$313$	−26.1214	−1.47647	−0.738234	+	0.674545i	$0.764340\pi$
$314$	−6.19511	−0.349610
$315$	0.310944	0.0175197
$316$	−33.3387	−1.87545
$317$	24.0659	1.35168	0.675839	−	0.737049i	$-0.263782\pi$
$317$	24.0659	1.35168	0.675839	+	0.737049i	$0.263782\pi$
$318$	1.85596	0.104077
$319$	−3.04739	−0.170621
$320$	0.145549	0.00813644
$321$	20.9600	1.16987
$322$	70.6025	3.93452
$323$	−0.374725	−0.0208503
$324$	−42.0253	−2.33474
$325$	−10.8094	−0.599600
$326$	−16.0414	−0.888451
$327$	−15.1904	−0.840031
$328$	5.23489	0.289048
$329$	9.60026	0.529280
$330$	2.99072	0.164634
$331$	6.32706	0.347767	0.173883	−	0.984766i	$-0.444368\pi$
$331$	6.32706	0.347767	0.173883	+	0.984766i	$0.444368\pi$
$332$	38.4113	2.10809
$333$	0.684290	0.0374989
$334$	20.9621	1.14700
$335$	−6.93143	−0.378704
$336$	45.3836	2.47588
$337$	33.6648	1.83384	0.916919	−	0.399073i	$-0.130668\pi$
$337$	33.6648	1.83384	0.916919	+	0.399073i	$0.130668\pi$
$338$	18.7885	1.02196
$339$	−4.76626	−0.258868
$340$	−2.57303	−0.139542
$341$	−6.27472	−0.339795
$342$	0.143755	0.00777336
$343$	3.84301	0.207503
$344$	−20.2371	−1.09111
$345$	9.05690	0.487607
$346$	26.9250	1.44750
$347$	−17.9486	−0.963531	−0.481766	−	0.876300i	$-0.660004\pi$
$347$	−17.9486	−0.963531	−0.481766	+	0.876300i	$0.660004\pi$
$348$	−24.1721	−1.29576
$349$	−10.2951	−0.551082	−0.275541	−	0.961289i	$-0.588857\pi$
$349$	−10.2951	−0.551082	−0.275541	+	0.961289i	$0.588857\pi$
$350$	−41.7459	−2.23141
$351$	12.0377	0.642523
$352$	5.51689	0.294051
$353$	−19.6296	−1.04478	−0.522389	−	0.852707i	$-0.674959\pi$
$353$	−19.6296	−1.04478	−0.522389	+	0.852707i	$0.674959\pi$
$354$	−49.8049	−2.64710
$355$	5.03865	0.267424
$356$	−9.59844	−0.508717
$357$	5.50010	0.291096
$358$	1.00751	0.0532484
$359$	18.6737	0.985561	0.492780	−	0.870154i	$-0.335981\pi$
$359$	18.6737	0.985561	0.492780	+	0.870154i	$0.335981\pi$
$360$	0.546744	0.0288159
$361$	−18.8121	−0.990111
$362$	−22.8797	−1.20253
$363$	−1.76925	−0.0928616
$364$	−38.2231	−2.00343
$365$	7.38172	0.386377
$366$	−15.1974	−0.794383
$367$	−4.28026	−0.223428	−0.111714	−	0.993740i	$-0.535634\pi$
$367$	−4.28026	−0.223428	−0.111714	+	0.993740i	$0.535634\pi$
$368$	55.0033	2.86725
$369$	−0.107834	−0.00561361
$370$	8.88087	0.461694
$371$	−1.48151	−0.0769160
$372$	−49.7714	−2.58053
$373$	−2.33403	−0.120851	−0.0604257	−	0.998173i	$-0.519246\pi$
$373$	−2.33403	−0.120851	−0.0604257	+	0.998173i	$0.519246\pi$
$374$	2.20119	0.113821
$375$	−11.2280	−0.579812
$376$	16.8805	0.870545
$377$	7.22498	0.372106
$378$	46.4892	2.39115
$379$	8.57064	0.440244	0.220122	−	0.975472i	$-0.429354\pi$
$379$	8.57064	0.440244	0.220122	+	0.975472i	$0.429354\pi$
$380$	1.29014	0.0661830
$381$	12.8967	0.660717
$382$	−27.3933	−1.40156
$383$	19.0896	0.975431	0.487715	−	0.873003i	$-0.337830\pi$
$383$	19.0896	0.975431	0.487715	+	0.873003i	$0.337830\pi$
$384$	−20.5092	−1.04661
$385$	−2.38732	−0.121669
$386$	−49.6074	−2.52495
$387$	0.416866	0.0211905
$388$	71.2979	3.61960
$389$	−7.91748	−0.401432	−0.200716	−	0.979649i	$-0.564327\pi$
$389$	−7.91748	−0.401432	−0.200716	+	0.979649i	$0.564327\pi$
$390$	−7.09062	−0.359048
$391$	6.66594	0.337111
$392$	−37.5037	−1.89422
$393$	−16.6258	−0.838661
$394$	41.8071	2.10621
$395$	4.93676	0.248395
$396$	−0.583939	−0.0293440
$397$	−4.53224	−0.227466	−0.113733	−	0.993511i	$-0.536281\pi$
$397$	−4.53224	−0.227466	−0.113733	+	0.993511i	$0.536281\pi$
$398$	−16.4228	−0.823200
$399$	−2.75781	−0.138063
$400$	−32.5224	−1.62612
$401$	−24.4009	−1.21852	−0.609260	−	0.792970i	$-0.708533\pi$
$401$	−24.4009	−1.21852	−0.609260	+	0.792970i	$0.708533\pi$
$402$	47.0349	2.34589
$403$	14.8766	0.741054
$404$	−83.0553	−4.13215
$405$	6.22306	0.309226
$406$	27.9028	1.38479
$407$	−5.25374	−0.260418
$408$	9.67104	0.478788
$409$	−31.2051	−1.54299	−0.771497	−	0.636233i	$-0.780492\pi$
$409$	−31.2051	−1.54299	−0.771497	+	0.636233i	$0.780492\pi$
$410$	−1.39949	−0.0691160
$411$	26.4854	1.30643
$412$	−20.4651	−1.00824
$413$	39.7563	1.95628
$414$	−2.55723	−0.125681
$415$	−5.68790	−0.279208
$416$	−13.0799	−0.641293
$417$	−18.6199	−0.911823
$418$	−1.10370	−0.0539837
$419$	25.7468	1.25781	0.628907	−	0.777481i	$-0.283503\pi$
$419$	25.7468	1.25781	0.628907	+	0.777481i	$0.283503\pi$
$420$	−18.9363	−0.923998
$421$	2.01752	0.0983277	0.0491639	−	0.998791i	$-0.484344\pi$
$421$	2.01752	0.0983277	0.0491639	+	0.998791i	$0.484344\pi$
$422$	48.3942	2.35579
$423$	−0.347723	−0.0169069
$424$	−2.60499	−0.126509
$425$	−3.94144	−0.191188
$426$	−34.1910	−1.65656
$427$	12.1312	0.587072
$428$	−53.1127	−2.56730
$429$	4.19467	0.202521
$430$	5.41017	0.260902
$431$	−24.4643	−1.17840	−0.589201	−	0.807987i	$-0.700557\pi$
$431$	−24.4643	−1.17840	−0.589201	+	0.807987i	$0.700557\pi$
$432$	36.2178	1.74253
$433$	4.98047	0.239346	0.119673	−	0.992813i	$-0.461815\pi$
$433$	4.98047	0.239346	0.119673	+	0.992813i	$0.461815\pi$
$434$	57.4530	2.75783
$435$	3.57937	0.171618
$436$	38.4925	1.84346
$437$	−3.34237	−0.159887
$438$	−50.0905	−2.39342
$439$	32.4820	1.55028	0.775141	−	0.631788i	$-0.217679\pi$
$439$	32.4820	1.55028	0.775141	+	0.631788i	$0.217679\pi$
$440$	−4.19771	−0.200118
$441$	0.772542	0.0367877
$442$	−5.21874	−0.248230
$443$	−2.52365	−0.119902	−0.0599510	−	0.998201i	$-0.519094\pi$
$443$	−2.52365	−0.119902	−0.0599510	+	0.998201i	$0.519094\pi$
$444$	−41.6730	−1.97771
$445$	1.42133	0.0673773
$446$	−54.3654	−2.57428
$447$	−3.83679	−0.181474
$448$	0.788391	0.0372480
$449$	−18.2746	−0.862431	−0.431216	−	0.902249i	$-0.641915\pi$
$449$	−18.2746	−0.862431	−0.431216	+	0.902249i	$0.641915\pi$
$450$	1.51204	0.0712783
$451$	0.827912	0.0389848
$452$	12.0777	0.568087
$453$	−18.7652	−0.881667
$454$	−43.2741	−2.03095
$455$	5.66003	0.265346
$456$	−4.84915	−0.227082
$457$	12.6503	0.591756	0.295878	−	0.955226i	$-0.404388\pi$
$457$	12.6503	0.591756	0.295878	+	0.955226i	$0.404388\pi$
$458$	26.9103	1.25744
$459$	4.38929	0.204874
$460$	−22.9502	−1.07006
$461$	4.80598	0.223837	0.111918	−	0.993717i	$-0.464300\pi$
$461$	4.80598	0.223837	0.111918	+	0.993717i	$0.464300\pi$
$462$	16.1997	0.753680
$463$	36.7310	1.70704	0.853518	−	0.521064i	$-0.174465\pi$
$463$	36.7310	1.70704	0.853518	+	0.521064i	$0.174465\pi$
$464$	21.7378	1.00915
$465$	7.37009	0.341780
$466$	15.3491	0.711034
$467$	32.3530	1.49712	0.748559	−	0.663068i	$-0.230746\pi$
$467$	32.3530	1.49712	0.748559	+	0.663068i	$0.230746\pi$
$468$	1.38445	0.0639960
$469$	−37.5452	−1.73368
$470$	−4.51282	−0.208161
$471$	−4.30468	−0.198349
$472$	69.9051	3.21764
$473$	−3.20055	−0.147162
$474$	−33.4996	−1.53869
$475$	1.97628	0.0906778
$476$	−13.9373	−0.638814
$477$	0.0536604	0.00245694
$478$	62.8751	2.87584
$479$	17.6184	0.805004	0.402502	−	0.915419i	$-0.368141\pi$
$479$	17.6184	0.805004	0.402502	+	0.915419i	$0.368141\pi$
$480$	−6.47997	−0.295769
$481$	12.4560	0.567943
$482$	−20.2739	−0.923453
$483$	49.0582	2.23223
$484$	4.48328	0.203786
$485$	−10.5577	−0.479401
$486$	−3.44412	−0.156228
$487$	−14.9484	−0.677377	−0.338688	−	0.940899i	$-0.609983\pi$
$487$	−14.9484	−0.677377	−0.338688	+	0.940899i	$0.609983\pi$
$488$	21.3308	0.965600
$489$	−11.1464	−0.504057
$490$	10.0262	0.452939
$491$	−14.7603	−0.666123	−0.333061	−	0.942905i	$-0.608082\pi$
$491$	−14.7603	−0.666123	−0.333061	+	0.942905i	$0.608082\pi$
$492$	6.56704	0.296065
$493$	2.63444	0.118649
$494$	2.61673	0.117732
$495$	0.0864690	0.00388649
$496$	44.7592	2.00975
$497$	27.2927	1.22424
$498$	38.5967	1.72956
$499$	40.6004	1.81752	0.908762	−	0.417315i	$-0.137029\pi$
$499$	40.6004	1.81752	0.908762	+	0.417315i	$0.137029\pi$
$500$	28.4518	1.27240
$501$	14.5656	0.650741
$502$	11.3470	0.506442
$503$	−22.6138	−1.00830	−0.504149	−	0.863616i	$-0.668194\pi$
$503$	−22.6138	−1.00830	−0.504149	+	0.863616i	$0.668194\pi$
$504$	2.96153	0.131917
$505$	12.2987	0.547286
$506$	19.6335	0.872818
$507$	13.0552	0.579803
$508$	−32.6802	−1.44995
$509$	31.3724	1.39056	0.695279	−	0.718740i	$-0.255281\pi$
$509$	31.3724	1.39056	0.695279	+	0.718740i	$0.255281\pi$
$510$	−2.58545	−0.114486
$511$	39.9844	1.76880
$512$	50.8538	2.24744
$513$	−2.20083	−0.0971691
$514$	−48.8401	−2.15425
$515$	3.03045	0.133538
$516$	−25.3869	−1.11760
$517$	2.66970	0.117413
$518$	48.1047	2.11360
$519$	18.7089	0.821229
$520$	9.95224	0.436435
$521$	31.1167	1.36325	0.681623	−	0.731704i	$-0.261274\pi$
$521$	31.1167	1.36325	0.681623	+	0.731704i	$0.261274\pi$
$522$	−1.01064	−0.0442346
$523$	17.9552	0.785126	0.392563	−	0.919725i	$-0.371589\pi$
$523$	17.9552	0.785126	0.392563	+	0.919725i	$0.371589\pi$
$524$	42.1298	1.84045
$525$	−29.0072	−1.26598
$526$	47.9928	2.09259
$527$	5.42443	0.236292
$528$	12.6205	0.549238
$529$	36.4570	1.58508
$530$	0.696416	0.0302504
$531$	−1.43998	−0.0624898
$532$	6.98828	0.302980
$533$	−1.96287	−0.0850215
$534$	−9.64476	−0.417370
$535$	7.86486	0.340028
$536$	−66.0172	−2.85151
$537$	0.700067	0.0302101
$538$	−4.62101	−0.199226
$539$	−5.93131	−0.255480
$540$	−15.1119	−0.650312
$541$	3.39609	0.146009	0.0730046	−	0.997332i	$-0.476741\pi$
$541$	3.39609	0.146009	0.0730046	+	0.997332i	$0.476741\pi$
$542$	14.2255	0.611038
$543$	−15.8980	−0.682249
$544$	−4.76930	−0.204482
$545$	−5.69992	−0.244158
$546$	−38.4075	−1.64369
$547$	1.00000	0.0427569
$547$	1.00000	0.0427569
$548$	−67.1141	−2.86697
$549$	−0.439395	−0.0187529
$550$	−11.6089	−0.495007
$551$	−1.32094	−0.0562737
$552$	86.2610	3.67151
$553$	26.7408	1.13713
$554$	−44.9835	−1.91117
$555$	6.17088	0.261939
$556$	47.1830	2.00100
$557$	37.3688	1.58336	0.791682	−	0.610933i	$-0.209205\pi$
$557$	37.3688	1.58336	0.791682	+	0.610933i	$0.209205\pi$
$558$	−2.08096	−0.0880939
$559$	7.58810	0.320943
$560$	17.0294	0.719621
$561$	1.52950	0.0645756
$562$	19.6050	0.826987
$563$	2.81180	0.118503	0.0592516	−	0.998243i	$-0.481129\pi$
$563$	2.81180	0.118503	0.0592516	+	0.998243i	$0.481129\pi$
$564$	21.1762	0.891677
$565$	−1.78845	−0.0752407
$566$	24.5469	1.03178
$567$	33.7082	1.41561
$568$	47.9898	2.01361
$569$	−18.8624	−0.790752	−0.395376	−	0.918519i	$-0.629386\pi$
$569$	−18.8624	−0.790752	−0.395376	+	0.918519i	$0.629386\pi$
$570$	1.29637	0.0542989
$571$	−25.5974	−1.07122	−0.535610	−	0.844466i	$-0.679918\pi$
$571$	−25.5974	−1.07122	−0.535610	+	0.844466i	$0.679918\pi$
$572$	−10.6293	−0.444433
$573$	−19.0343	−0.795168
$574$	−7.58059	−0.316408
$575$	−35.1557	−1.46610
$576$	−0.0285556	−0.00118982
$577$	−26.4065	−1.09932	−0.549658	−	0.835389i	$-0.685242\pi$
$577$	−26.4065	−1.09932	−0.549658	+	0.835389i	$0.685242\pi$
$578$	41.3830	1.72131
$579$	−34.4698	−1.43251
$580$	−9.07013	−0.376617
$581$	−30.8095	−1.27819
$582$	71.6420	2.96966
$583$	−0.411986	−0.0170627
$584$	70.3060	2.90928
$585$	−0.205007	−0.00847600
$586$	42.8005	1.76807
$587$	9.99745	0.412639	0.206320	−	0.978485i	$-0.433851\pi$
$587$	9.99745	0.412639	0.206320	+	0.978485i	$0.433851\pi$
$588$	−47.0475	−1.94021
$589$	−2.71986	−0.112070
$590$	−18.6884	−0.769388
$591$	29.0497	1.19495
$592$	37.4763	1.54027
$593$	−34.2421	−1.40616	−0.703078	−	0.711113i	$-0.748192\pi$
$593$	−34.2421	−1.40616	−0.703078	+	0.711113i	$0.748192\pi$
$594$	12.9280	0.530442
$595$	2.06381	0.0846081
$596$	9.72244	0.398246
$597$	−11.4114	−0.467037
$598$	−46.5487	−1.90352
$599$	26.3043	1.07477	0.537383	−	0.843338i	$-0.319413\pi$
$599$	26.3043	1.07477	0.537383	+	0.843338i	$0.319413\pi$
$600$	−51.0044	−2.08225
$601$	−20.6853	−0.843771	−0.421885	−	0.906649i	$-0.638632\pi$
$601$	−20.6853	−0.843771	−0.421885	+	0.906649i	$0.638632\pi$
$602$	29.3051	1.19439
$603$	1.35989	0.0553792
$604$	47.5511	1.93483
$605$	−0.663879	−0.0269905
$606$	−83.4561	−3.39017
$607$	9.78395	0.397118	0.198559	−	0.980089i	$-0.436374\pi$
$607$	9.78395	0.397118	0.198559	+	0.980089i	$0.436374\pi$
$608$	2.39137	0.0969830
$609$	19.3883	0.785653
$610$	−5.70256	−0.230890
$611$	−6.32951	−0.256065
$612$	0.504810	0.0204057
$613$	−28.8933	−1.16699	−0.583495	−	0.812116i	$-0.698315\pi$
$613$	−28.8933	−1.16699	−0.583495	+	0.812116i	$0.698315\pi$
$614$	−18.0519	−0.728514
$615$	−0.972439	−0.0392125
$616$	−22.7376	−0.916125
$617$	22.4455	0.903621	0.451811	−	0.892114i	$-0.350778\pi$
$617$	22.4455	0.903621	0.451811	+	0.892114i	$0.350778\pi$
$618$	−20.5639	−0.827200
$619$	15.8897	0.638661	0.319331	−	0.947643i	$-0.396542\pi$
$619$	15.8897	0.638661	0.319331	+	0.947643i	$0.396542\pi$
$620$	−18.6758	−0.750038
$621$	39.1503	1.57105
$622$	29.4319	1.18011
$623$	7.69885	0.308448
$624$	−29.9217	−1.19782
$625$	18.5832	0.743329
$626$	66.5110	2.65831
$627$	−0.766906	−0.0306273
$628$	10.9081	0.435279
$629$	4.54181	0.181094
$630$	−0.791734	−0.0315434
$631$	46.2269	1.84026	0.920131	−	0.391610i	$-0.128082\pi$
$631$	46.2269	1.84026	0.920131	+	0.391610i	$0.128082\pi$
$632$	47.0194	1.87033
$633$	33.6268	1.33655
$634$	−61.2774	−2.43364
$635$	4.83925	0.192040
$636$	−3.26789	−0.129580
$637$	14.0624	0.557172
$638$	7.75936	0.307196
$639$	−0.988545	−0.0391062
$640$	−7.69570	−0.304199
$641$	18.9648	0.749063	0.374532	−	0.927214i	$-0.377804\pi$
$641$	18.9648	0.749063	0.374532	+	0.927214i	$0.377804\pi$
$642$	−53.3690	−2.10631
$643$	35.0808	1.38345	0.691726	−	0.722160i	$-0.256851\pi$
$643$	35.0808	1.38345	0.691726	+	0.722160i	$0.256851\pi$
$644$	−124.314	−4.89864
$645$	3.75927	0.148021
$646$	0.954137	0.0375400
$647$	−20.0508	−0.788276	−0.394138	−	0.919051i	$-0.628957\pi$
$647$	−20.0508	−0.788276	−0.394138	+	0.919051i	$0.628957\pi$
$648$	59.2705	2.32836
$649$	11.0557	0.433973
$650$	27.5233	1.07955
$651$	39.9213	1.56464
$652$	28.2450	1.10616
$653$	−6.78128	−0.265372	−0.132686	−	0.991158i	$-0.542360\pi$
$653$	−6.78128	−0.265372	−0.132686	+	0.991158i	$0.542360\pi$
$654$	38.6782	1.51244
$655$	−6.23853	−0.243760
$656$	−5.90571	−0.230579
$657$	−1.44824	−0.0565012
$658$	−24.4445	−0.952945
$659$	−37.0129	−1.44182	−0.720908	−	0.693030i	$-0.756275\pi$
$659$	−37.0129	−1.44182	−0.720908	+	0.693030i	$0.756275\pi$
$660$	−5.26592	−0.204976
$661$	5.62057	0.218615	0.109307	−	0.994008i	$-0.465137\pi$
$661$	5.62057	0.218615	0.109307	+	0.994008i	$0.465137\pi$
$662$	−16.1101	−0.626138
$663$	−3.62625	−0.140832
$664$	−54.1735	−2.10234
$665$	−1.03482	−0.0401285
$666$	−1.74236	−0.0675151
$667$	23.4979	0.909844
$668$	−36.9091	−1.42806
$669$	−37.7759	−1.46050
$670$	17.6490	0.681840
$671$	3.37352	0.130233
$672$	−35.0998	−1.35401
$673$	20.5314	0.791429	0.395714	−	0.918374i	$-0.370497\pi$
$673$	20.5314	0.791429	0.395714	+	0.918374i	$0.370497\pi$
$674$	−85.7183	−3.30174
$675$	−23.1488	−0.890998
$676$	−33.0820	−1.27238
$677$	18.4013	0.707219	0.353610	−	0.935393i	$-0.384954\pi$
$677$	18.4013	0.707219	0.353610	+	0.935393i	$0.384954\pi$
$678$	12.1360	0.466080
$679$	−57.1876	−2.19466
$680$	3.62888	0.139161
$681$	−30.0690	−1.15225
$682$	15.9769	0.611786
$683$	5.41507	0.207202	0.103601	−	0.994619i	$-0.466964\pi$
$683$	5.41507	0.207202	0.103601	+	0.994619i	$0.466964\pi$
$684$	−0.253117	−0.00967815
$685$	9.93817	0.379718
$686$	−9.78519	−0.373600
$687$	18.6987	0.713398
$688$	22.8304	0.870399
$689$	0.976766	0.0372118
$690$	−23.0609	−0.877915
$691$	37.1200	1.41211	0.706055	−	0.708157i	$-0.250473\pi$
$691$	37.1200	1.41211	0.706055	+	0.708157i	$0.250473\pi$
$692$	−47.4083	−1.80219
$693$	0.468374	0.0177921
$694$	45.7012	1.73480
$695$	−6.98680	−0.265024
$696$	34.0911	1.29222
$697$	−0.715722	−0.0271099
$698$	26.2136	0.992200
$699$	10.6653	0.403400
$700$	73.5042	2.77820
$701$	−7.93806	−0.299817	−0.149908	−	0.988700i	$-0.547898\pi$
$701$	−7.93806	−0.299817	−0.149908	+	0.988700i	$0.547898\pi$
$702$	−30.6506	−1.15683
$703$	−2.27731	−0.0858903
$704$	0.219240	0.00826293
$705$	−3.13574	−0.118099
$706$	49.9814	1.88108
$707$	66.6181	2.50543
$708$	87.6941	3.29575
$709$	9.62710	0.361553	0.180777	−	0.983524i	$-0.442139\pi$
$709$	9.62710	0.361553	0.180777	+	0.983524i	$0.442139\pi$
$710$	−12.8296	−0.481484
$711$	−0.968556	−0.0363237
$712$	13.5372	0.507327
$713$	48.3833	1.81197
$714$	−14.0045	−0.524106
$715$	1.57397	0.0588633
$716$	−1.77397	−0.0662964
$717$	43.6888	1.63159
$718$	−47.5476	−1.77446
$719$	17.1560	0.639811	0.319905	−	0.947449i	$-0.396349\pi$
$719$	17.1560	0.639811	0.319905	+	0.947449i	$0.396349\pi$
$720$	−0.616805	−0.0229870
$721$	16.4149	0.611324
$722$	47.8999	1.78265
$723$	−14.0874	−0.523915
$724$	40.2856	1.49720
$725$	−13.8939	−0.516005
$726$	4.50492	0.167193
$727$	3.74979	0.139072	0.0695360	−	0.997579i	$-0.477848\pi$
$727$	3.74979	0.139072	0.0695360	+	0.997579i	$0.477848\pi$
$728$	53.9080	1.99796
$729$	25.7282	0.952896
$730$	−18.7956	−0.695655
$731$	2.76685	0.102336
$732$	26.7590	0.989039
$733$	−34.0730	−1.25851	−0.629257	−	0.777197i	$-0.716641\pi$
$733$	−34.0730	−1.25851	−0.629257	+	0.777197i	$0.716641\pi$
$734$	10.8985	0.402272
$735$	6.96673	0.256972
$736$	−42.5398	−1.56804
$737$	−10.4408	−0.384592
$738$	0.274570	0.0101071
$739$	18.1980	0.669426	0.334713	−	0.942320i	$-0.391361\pi$
$739$	18.1980	0.669426	0.334713	+	0.942320i	$0.391361\pi$
$740$	−15.6370	−0.574828
$741$	1.81824	0.0667946
$742$	3.77226	0.138484
$743$	44.6648	1.63859	0.819297	−	0.573370i	$-0.194364\pi$
$743$	44.6648	1.63859	0.819297	+	0.573370i	$0.194364\pi$
$744$	70.1951	2.57348
$745$	−1.43969	−0.0527460
$746$	5.94298	0.217588
$747$	1.11592	0.0408295
$748$	−3.87575	−0.141712
$749$	42.6014	1.55662
$750$	28.5891	1.04393
$751$	−15.9881	−0.583416	−0.291708	−	0.956507i	$-0.594224\pi$
$751$	−15.9881	−0.583416	−0.291708	+	0.956507i	$0.594224\pi$
$752$	−19.0436	−0.694450
$753$	7.88448	0.287327
$754$	−18.3965	−0.669960
$755$	−7.04131	−0.256259
$756$	−81.8561	−2.97708
$757$	49.3497	1.79365	0.896823	−	0.442389i	$-0.145869\pi$
$757$	49.3497	1.79365	0.896823	+	0.442389i	$0.145869\pi$
$758$	−21.8228	−0.792640
$759$	13.6424	0.495188
$760$	−1.81956	−0.0660023
$761$	−28.9266	−1.04859	−0.524294	−	0.851537i	$-0.675671\pi$
$761$	−28.9266	−1.04859	−0.524294	+	0.851537i	$0.675671\pi$
$762$	−32.8379	−1.18959
$763$	−30.8746	−1.11774
$764$	48.2329	1.74500
$765$	−0.0747516	−0.00270265
$766$	−48.6064	−1.75622
$767$	−26.2116	−0.946446
$768$	51.4453	1.85637
$769$	21.4805	0.774607	0.387303	−	0.921952i	$-0.373407\pi$
$769$	21.4805	0.774607	0.387303	+	0.921952i	$0.373407\pi$
$770$	6.07866	0.219060
$771$	−33.9366	−1.22220
$772$	87.3464	3.14367
$773$	−39.5584	−1.42282	−0.711408	−	0.702780i	$-0.751942\pi$
$773$	−39.5584	−1.42282	−0.711408	+	0.702780i	$0.751942\pi$
$774$	−1.06144	−0.0381525
$775$	−28.6081	−1.02763
$776$	−100.555	−3.60972
$777$	33.4256	1.19914
$778$	20.1597	0.722761
$779$	0.358870	0.0128578
$780$	12.4848	0.447029
$781$	7.58971	0.271581
$782$	−16.9730	−0.606954
$783$	15.4726	0.552944
$784$	42.3096	1.51106
$785$	−1.61525	−0.0576508
$786$	42.3331	1.50997
$787$	26.9185	0.959540	0.479770	−	0.877394i	$-0.340720\pi$
$787$	26.9185	0.959540	0.479770	+	0.877394i	$0.340720\pi$
$788$	−73.6120	−2.62232
$789$	33.3479	1.18722
$790$	−12.5701	−0.447225
$791$	−9.68745	−0.344446
$792$	0.823560	0.0292639
$793$	−7.99820	−0.284024
$794$	11.5401	0.409543
$795$	0.483906	0.0171624
$796$	28.9165	1.02492
$797$	−12.0097	−0.425405	−0.212703	−	0.977117i	$-0.568227\pi$
$797$	−12.0097	−0.425405	−0.212703	+	0.977117i	$0.568227\pi$
$798$	7.02201	0.248576
$799$	−2.30793	−0.0816486
$800$	25.1530	0.889292
$801$	−0.278854	−0.00985281
$802$	62.1302	2.19389
$803$	11.1191	0.392384
$804$	−82.8169	−2.92073
$805$	18.4082	0.648804
$806$	−37.8791	−1.33424
$807$	−3.21091	−0.113030
$808$	117.137	4.12087
$809$	8.61994	0.303061	0.151530	−	0.988453i	$-0.451580\pi$
$809$	8.61994	0.303061	0.151530	+	0.988453i	$0.451580\pi$
$810$	−15.8453	−0.556748
$811$	−0.230276	−0.00808608	−0.00404304	−	0.999992i	$-0.501287\pi$
$811$	−0.230276	−0.00808608	−0.00404304	+	0.999992i	$0.501287\pi$
$812$	−49.1299	−1.72412
$813$	9.88462	0.346669
$814$	13.3772	0.468872
$815$	−4.18248	−0.146506
$816$	−10.9103	−0.381938
$817$	−1.38732	−0.0485363
$818$	79.4554	2.77809
$819$	−1.11046	−0.0388025
$820$	2.46416	0.0860522
$821$	−31.5401	−1.10076	−0.550378	−	0.834915i	$-0.685516\pi$
$821$	−31.5401	−1.10076	−0.550378	+	0.834915i	$0.685516\pi$
$822$	−67.4380	−2.35217
$823$	−51.3808	−1.79102	−0.895511	−	0.445040i	$-0.853189\pi$
$823$	−51.3808	−1.79102	−0.895511	+	0.445040i	$0.853189\pi$
$824$	28.8630	1.00549
$825$	−8.06648	−0.280839
$826$	−101.229	−3.52220
$827$	45.2084	1.57205	0.786025	−	0.618195i	$-0.212136\pi$
$827$	45.2084	1.57205	0.786025	+	0.618195i	$0.212136\pi$
$828$	4.50266	0.156478
$829$	−34.5407	−1.19965	−0.599824	−	0.800132i	$-0.704763\pi$
$829$	−34.5407	−1.19965	−0.599824	+	0.800132i	$0.704763\pi$
$830$	14.4827	0.502702
$831$	−31.2569	−1.08429
$832$	−0.519791	−0.0180205
$833$	5.12756	0.177660
$834$	47.4106	1.64170
$835$	5.46546	0.189140
$836$	1.94334	0.0672119
$837$	31.8587	1.10120
$838$	−65.5573	−2.26464
$839$	43.2213	1.49217	0.746083	−	0.665853i	$-0.231932\pi$
$839$	43.2213	1.49217	0.746083	+	0.665853i	$0.231932\pi$
$840$	26.7069	0.921475
$841$	−19.7134	−0.679772
$842$	−5.13706	−0.177035
$843$	13.6226	0.469186
$844$	−85.2103	−2.93306
$845$	4.89874	0.168522
$846$	0.885382	0.0304401
$847$	−3.59601	−0.123560
$848$	2.93880	0.100919
$849$	17.0564	0.585376
$850$	10.0358	0.344225
$851$	40.5108	1.38869
$852$	60.2019	2.06248
$853$	−33.0952	−1.13316	−0.566580	−	0.824007i	$-0.691734\pi$
$853$	−33.0952	−1.13316	−0.566580	+	0.824007i	$0.691734\pi$
$854$	−30.8889	−1.05700
$855$	0.0374812	0.00128183
$856$	74.9076	2.56029
$857$	3.76327	0.128551	0.0642754	−	0.997932i	$-0.479526\pi$
$857$	3.76327	0.128551	0.0642754	+	0.997932i	$0.479526\pi$
$858$	−10.6806	−0.364629
$859$	12.6305	0.430945	0.215473	−	0.976510i	$-0.430871\pi$
$859$	12.6305	0.430945	0.215473	+	0.976510i	$0.430871\pi$
$860$	−9.52598	−0.324833
$861$	−5.26738	−0.179512
$862$	62.2916	2.12166
$863$	−1.22511	−0.0417032	−0.0208516	−	0.999783i	$-0.506638\pi$
$863$	−1.22511	−0.0417032	−0.0208516	+	0.999783i	$0.506638\pi$
$864$	−28.0110	−0.952953
$865$	7.02017	0.238693
$866$	−12.6814	−0.430932
$867$	28.7550	0.976572
$868$	−101.161	−3.43362
$869$	7.43624	0.252257
$870$	−9.11390	−0.308990
$871$	24.7538	0.838751
$872$	−54.2879	−1.83842
$873$	2.07134	0.0701044
$874$	8.51044	0.287870
$875$	−22.8210	−0.771491
$876$	88.1971	2.97990
$877$	−39.9594	−1.34933	−0.674667	−	0.738122i	$-0.735713\pi$
$877$	−39.9594	−1.34933	−0.674667	+	0.738122i	$0.735713\pi$
$878$	−82.7067	−2.79122
$879$	29.7400	1.00310
$880$	4.73562	0.159638
$881$	11.7891	0.397187	0.198593	−	0.980082i	$-0.436363\pi$
$881$	11.7891	0.397187	0.198593	+	0.980082i	$0.436363\pi$
$882$	−1.96707	−0.0662347
$883$	−20.0506	−0.674755	−0.337377	−	0.941369i	$-0.609540\pi$
$883$	−20.0506	−0.674755	−0.337377	+	0.941369i	$0.609540\pi$
$884$	9.18892	0.309057
$885$	−12.9856	−0.436508
$886$	6.42578	0.215878
$887$	4.17582	0.140210	0.0701052	−	0.997540i	$-0.477666\pi$
$887$	4.17582	0.140210	0.0701052	+	0.997540i	$0.477666\pi$
$888$	58.7736	1.97231
$889$	26.2126	0.879142
$890$	−3.61902	−0.121310
$891$	9.37378	0.314033
$892$	95.7242	3.20508
$893$	1.15722	0.0387248
$894$	9.76935	0.326736
$895$	0.262687	0.00878067
$896$	−41.6851	−1.39260
$897$	−32.3444	−1.07995
$898$	46.5313	1.55277
$899$	19.1215	0.637739
$900$	−2.66233	−0.0887444
$901$	0.356158	0.0118653
$902$	−2.10805	−0.0701905
$903$	20.3627	0.677628
$904$	−17.0338	−0.566536
$905$	−5.96544	−0.198298
$906$	47.7805	1.58740
$907$	−2.93935	−0.0975994	−0.0487997	−	0.998809i	$-0.515540\pi$
$907$	−2.93935	−0.0975994	−0.0487997	+	0.998809i	$0.515540\pi$
$908$	76.1950	2.52862
$909$	−2.41292	−0.0800314
$910$	−14.4117	−0.477744
$911$	5.02116	0.166358	0.0831792	−	0.996535i	$-0.473493\pi$
$911$	5.02116	0.166358	0.0831792	+	0.996535i	$0.473493\pi$
$912$	5.47054	0.181148
$913$	−8.56768	−0.283549
$914$	−32.2105	−1.06543
$915$	−3.96243	−0.130994
$916$	−47.3824	−1.56556
$917$	−33.7921	−1.11591
$918$	−11.1761	−0.368867
$919$	16.5767	0.546816	0.273408	−	0.961898i	$-0.411849\pi$
$919$	16.5767	0.546816	0.273408	+	0.961898i	$0.411849\pi$
$920$	32.3679	1.06714
$921$	−12.5434	−0.413318
$922$	−12.2371	−0.403008
$923$	−17.9942	−0.592287
$924$	−28.5238	−0.938363
$925$	−23.9532	−0.787577
$926$	−93.5256	−3.07344
$927$	−0.594551	−0.0195276
$928$	−16.8121	−0.551886
$929$	−28.3954	−0.931621	−0.465811	−	0.884884i	$-0.654237\pi$
$929$	−28.3954	−0.931621	−0.465811	+	0.884884i	$0.654237\pi$
$930$	−18.7659	−0.615359
$931$	−2.57101	−0.0842615
$932$	−27.0260	−0.885266
$933$	20.4508	0.669528
$934$	−82.3781	−2.69549
$935$	0.573917	0.0187691
$936$	−1.95256	−0.0638213
$937$	19.1184	0.624570	0.312285	−	0.949988i	$-0.398906\pi$
$937$	19.1184	0.624570	0.312285	+	0.949988i	$0.398906\pi$
$938$	95.5988	3.12141
$939$	46.2153	1.50818
$940$	7.94597	0.259169
$941$	−11.5339	−0.375995	−0.187998	−	0.982169i	$-0.560200\pi$
$941$	−11.5339	−0.375995	−0.187998	+	0.982169i	$0.560200\pi$
$942$	10.9607	0.357119
$943$	−6.38389	−0.207888
$944$	−78.8629	−2.56677
$945$	12.1212	0.394301
$946$	8.14934	0.264958
$947$	−13.3167	−0.432735	−0.216367	−	0.976312i	$-0.569421\pi$
$947$	−13.3167	−0.432735	−0.216367	+	0.976312i	$0.569421\pi$
$948$	58.9846	1.91573
$949$	−26.3619	−0.855744
$950$	−5.03205	−0.163261
$951$	−42.5787	−1.38071
$952$	19.6565	0.637069
$953$	−33.3553	−1.08048	−0.540242	−	0.841510i	$-0.681667\pi$
$953$	−33.3553	−1.08048	−0.540242	+	0.841510i	$0.681667\pi$
$954$	−0.136632	−0.00442361
$955$	−7.14227	−0.231118
$956$	−110.707	−3.58054
$957$	5.39160	0.174286
$958$	−44.8604	−1.44937
$959$	53.8318	1.73832
$960$	−0.257513	−0.00831119
$961$	8.37207	0.270067
$962$	−31.7157	−1.02256
$963$	−1.54303	−0.0497234
$964$	35.6974	1.14974
$965$	−12.9342	−0.416365
$966$	−124.914	−4.01903
$967$	−11.9491	−0.384259	−0.192129	−	0.981370i	$-0.561539\pi$
$967$	−11.9491	−0.384259	−0.192129	+	0.981370i	$0.561539\pi$
$968$	−6.32301	−0.203229
$969$	0.662983	0.0212981
$970$	26.8824	0.863141
$971$	32.5444	1.04440	0.522200	−	0.852823i	$-0.325112\pi$
$971$	32.5444	1.04440	0.522200	+	0.852823i	$0.325112\pi$
$972$	6.06424	0.194511
$973$	−37.8452	−1.21326
$974$	38.0621	1.21959
$975$	19.1246	0.612478
$976$	−24.0642	−0.770276
$977$	−13.9280	−0.445597	−0.222798	−	0.974865i	$-0.571519\pi$
$977$	−13.9280	−0.445597	−0.222798	+	0.974865i	$0.571519\pi$
$978$	28.3813	0.907533
$979$	2.14094	0.0684248
$980$	−17.6537	−0.563927
$981$	1.11828	0.0357040
$982$	37.5831	1.19932
$983$	28.5968	0.912096	0.456048	−	0.889955i	$-0.349265\pi$
$983$	28.5968	0.912096	0.456048	+	0.889955i	$0.349265\pi$
$984$	−9.26183	−0.295256
$985$	10.9004	0.347315
$986$	−6.70789	−0.213623
$987$	−16.9853	−0.540647
$988$	−4.60742	−0.146581
$989$	24.6789	0.784744
$990$	−0.220170	−0.00699746
$991$	−46.2655	−1.46967	−0.734836	−	0.678245i	$-0.762741\pi$
$991$	−46.2655	−1.46967	−0.734836	+	0.678245i	$0.762741\pi$
$992$	−34.6169	−1.09909
$993$	−11.1942	−0.355236
$994$	−69.4934	−2.20420
$995$	−4.28192	−0.135746
$996$	−67.9593	−2.15337
$997$	14.5092	0.459512	0.229756	−	0.973248i	$-0.426207\pi$
$997$	14.5092	0.459512	0.229756	+	0.973248i	$0.426207\pi$
$998$	−103.378	−3.27237
$999$	26.6749	0.843956

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6017.2.a.f.1.10	✓	121

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6017.2.a.f.1.10	✓	121	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)

\(f(q)\)	\(=\)	\(q-2.54623 q^{2} -1.76925 q^{3} +4.48328 q^{4} -0.663879 q^{5} +4.50492 q^{6} -3.59601 q^{7} -6.32301 q^{8} +0.130248 q^{9} +O(q^{10})\)	\(q-2.54623 q^{2} -1.76925 q^{3} +4.48328 q^{4} -0.663879 q^{5} +4.50492 q^{6} -3.59601 q^{7} -6.32301 q^{8} +0.130248 q^{9} +1.69039 q^{10} -1.00000 q^{11} -7.93205 q^{12} +2.37087 q^{13} +9.15627 q^{14} +1.17457 q^{15} +7.13326 q^{16} +0.864490 q^{17} -0.331642 q^{18} -0.433464 q^{19} -2.97636 q^{20} +6.36225 q^{21} +2.54623 q^{22} +7.71083 q^{23} +11.1870 q^{24} -4.55926 q^{25} -6.03679 q^{26} +5.07731 q^{27} -16.1219 q^{28} +3.04739 q^{29} -2.99072 q^{30} +6.27472 q^{31} -5.51689 q^{32} +1.76925 q^{33} -2.20119 q^{34} +2.38732 q^{35} +0.583939 q^{36} +5.25374 q^{37} +1.10370 q^{38} -4.19467 q^{39} +4.19771 q^{40} -0.827912 q^{41} -16.1997 q^{42} +3.20055 q^{43} -4.48328 q^{44} -0.0864690 q^{45} -19.6335 q^{46} -2.66970 q^{47} -12.6205 q^{48} +5.93131 q^{49} +11.6089 q^{50} -1.52950 q^{51} +10.6293 q^{52} +0.411986 q^{53} -12.9280 q^{54} +0.663879 q^{55} +22.7376 q^{56} +0.766906 q^{57} -7.75936 q^{58} -11.0557 q^{59} +5.26592 q^{60} -3.37352 q^{61} -15.9769 q^{62} -0.468374 q^{63} -0.219240 q^{64} -1.57397 q^{65} -4.50492 q^{66} +10.4408 q^{67} +3.87575 q^{68} -13.6424 q^{69} -6.07866 q^{70} -7.58971 q^{71} -0.823560 q^{72} -11.1191 q^{73} -13.3772 q^{74} +8.06648 q^{75} -1.94334 q^{76} +3.59601 q^{77} +10.6806 q^{78} -7.43624 q^{79} -4.73562 q^{80} -9.37378 q^{81} +2.10805 q^{82} +8.56768 q^{83} +28.5238 q^{84} -0.573917 q^{85} -8.14934 q^{86} -5.39160 q^{87} +6.32301 q^{88} -2.14094 q^{89} +0.220170 q^{90} -8.52569 q^{91} +34.5698 q^{92} -11.1015 q^{93} +6.79766 q^{94} +0.287768 q^{95} +9.76077 q^{96} +15.9031 q^{97} -15.1025 q^{98} -0.130248 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 121 q + 2 q^{2} + 18 q^{3} + 138 q^{4} + 13 q^{5} + 10 q^{6} + 56 q^{7} + 12 q^{8} + 143 q^{9}+O(q^{10}) \) 121 * q + 2 * q^2 + 18 * q^3 + 138 * q^4 + 13 * q^5 + 10 * q^6 + 56 * q^7 + 12 * q^8 + 143 * q^9	\( 121 q + 2 q^{2} + 18 q^{3} + 138 q^{4} + 13 q^{5} + 10 q^{6} + 56 q^{7} + 12 q^{8} + 143 q^{9} + 20 q^{10} - 121 q^{11} + 40 q^{12} + 31 q^{13} + 7 q^{14} + 53 q^{15} + 164 q^{16} - 23 q^{17} + 14 q^{18} + 62 q^{19} + 53 q^{20} + 19 q^{21} - 2 q^{22} + 34 q^{23} + 34 q^{24} + 172 q^{25} + 34 q^{26} + 87 q^{27} + 91 q^{28} - 30 q^{29} + 2 q^{30} + 102 q^{31} + 31 q^{32} - 18 q^{33} + 30 q^{34} + 20 q^{35} + 164 q^{36} + 58 q^{37} + 35 q^{38} + 42 q^{39} + 52 q^{40} - 12 q^{41} + 56 q^{42} + 96 q^{43} - 138 q^{44} + 72 q^{45} + 48 q^{46} + 136 q^{47} + 99 q^{48} + 199 q^{49} - 7 q^{50} + 22 q^{51} + 81 q^{52} + 24 q^{53} + 37 q^{54} - 13 q^{55} + 28 q^{56} + 25 q^{57} + 76 q^{58} + 58 q^{59} + 81 q^{60} + 14 q^{61} - 2 q^{62} + 152 q^{63} + 236 q^{64} - 29 q^{65} - 10 q^{66} + 112 q^{67} - 61 q^{68} + 41 q^{69} + 105 q^{70} + 56 q^{71} + 71 q^{72} + 113 q^{73} - 23 q^{74} + 111 q^{75} + 144 q^{76} - 56 q^{77} + 59 q^{78} + 80 q^{79} + 100 q^{80} + 177 q^{81} + 123 q^{82} + 6 q^{83} + 79 q^{84} + 26 q^{85} + 14 q^{86} + 180 q^{87} - 12 q^{88} + 26 q^{89} + 75 q^{90} + 72 q^{91} + 58 q^{92} + 139 q^{93} + 37 q^{94} + 39 q^{95} + 66 q^{96} + 136 q^{97} + 7 q^{98} - 143 q^{99}+O(q^{100}) \) 121 * q + 2 * q^2 + 18 * q^3 + 138 * q^4 + 13 * q^5 + 10 * q^6 + 56 * q^7 + 12 * q^8 + 143 * q^9 + 20 * q^10 - 121 * q^11 + 40 * q^12 + 31 * q^13 + 7 * q^14 + 53 * q^15 + 164 * q^16 - 23 * q^17 + 14 * q^18 + 62 * q^19 + 53 * q^20 + 19 * q^21 - 2 * q^22 + 34 * q^23 + 34 * q^24 + 172 * q^25 + 34 * q^26 + 87 * q^27 + 91 * q^28 - 30 * q^29 + 2 * q^30 + 102 * q^31 + 31 * q^32 - 18 * q^33 + 30 * q^34 + 20 * q^35 + 164 * q^36 + 58 * q^37 + 35 * q^38 + 42 * q^39 + 52 * q^40 - 12 * q^41 + 56 * q^42 + 96 * q^43 - 138 * q^44 + 72 * q^45 + 48 * q^46 + 136 * q^47 + 99 * q^48 + 199 * q^49 - 7 * q^50 + 22 * q^51 + 81 * q^52 + 24 * q^53 + 37 * q^54 - 13 * q^55 + 28 * q^56 + 25 * q^57 + 76 * q^58 + 58 * q^59 + 81 * q^60 + 14 * q^61 - 2 * q^62 + 152 * q^63 + 236 * q^64 - 29 * q^65 - 10 * q^66 + 112 * q^67 - 61 * q^68 + 41 * q^69 + 105 * q^70 + 56 * q^71 + 71 * q^72 + 113 * q^73 - 23 * q^74 + 111 * q^75 + 144 * q^76 - 56 * q^77 + 59 * q^78 + 80 * q^79 + 100 * q^80 + 177 * q^81 + 123 * q^82 + 6 * q^83 + 79 * q^84 + 26 * q^85 + 14 * q^86 + 180 * q^87 - 12 * q^88 + 26 * q^89 + 75 * q^90 + 72 * q^91 + 58 * q^92 + 139 * q^93 + 37 * q^94 + 39 * q^95 + 66 * q^96 + 136 * q^97 + 7 * q^98 - 143 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more