LMFDB - Embedded newform 6017.2.a.f.1.17

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			1.17
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)

$f(q)$	$=$	$q-2.26471 q^{2} +2.40007 q^{3} +3.12892 q^{4} +2.90605 q^{5} -5.43547 q^{6} +2.22739 q^{7} -2.55669 q^{8} +2.76034 q^{9} +O(q^{10})$	\(q-2.26471 q^{2} +2.40007 q^{3} +3.12892 q^{4} +2.90605 q^{5} -5.43547 q^{6} +2.22739 q^{7} -2.55669 q^{8} +2.76034 q^{9} -6.58136 q^{10} -1.00000 q^{11} +7.50964 q^{12} +6.30048 q^{13} -5.04439 q^{14} +6.97472 q^{15} -0.467685 q^{16} -0.896955 q^{17} -6.25138 q^{18} -2.22648 q^{19} +9.09280 q^{20} +5.34589 q^{21} +2.26471 q^{22} +4.47739 q^{23} -6.13623 q^{24} +3.44511 q^{25} -14.2688 q^{26} -0.575194 q^{27} +6.96932 q^{28} -6.63826 q^{29} -15.7957 q^{30} +9.11413 q^{31} +6.17255 q^{32} -2.40007 q^{33} +2.03134 q^{34} +6.47289 q^{35} +8.63690 q^{36} +4.21519 q^{37} +5.04233 q^{38} +15.1216 q^{39} -7.42985 q^{40} -1.64037 q^{41} -12.1069 q^{42} -2.13008 q^{43} -3.12892 q^{44} +8.02169 q^{45} -10.1400 q^{46} -11.0526 q^{47} -1.12248 q^{48} -2.03875 q^{49} -7.80218 q^{50} -2.15276 q^{51} +19.7137 q^{52} +9.03466 q^{53} +1.30265 q^{54} -2.90605 q^{55} -5.69473 q^{56} -5.34370 q^{57} +15.0338 q^{58} +9.56003 q^{59} +21.8234 q^{60} -1.71805 q^{61} -20.6409 q^{62} +6.14835 q^{63} -13.0437 q^{64} +18.3095 q^{65} +5.43547 q^{66} +14.6108 q^{67} -2.80650 q^{68} +10.7461 q^{69} -14.6592 q^{70} -6.31978 q^{71} -7.05733 q^{72} -2.07545 q^{73} -9.54620 q^{74} +8.26851 q^{75} -6.96647 q^{76} -2.22739 q^{77} -34.2461 q^{78} +3.22444 q^{79} -1.35911 q^{80} -9.66154 q^{81} +3.71497 q^{82} -15.4616 q^{83} +16.7269 q^{84} -2.60659 q^{85} +4.82402 q^{86} -15.9323 q^{87} +2.55669 q^{88} +8.24373 q^{89} -18.1668 q^{90} +14.0336 q^{91} +14.0094 q^{92} +21.8746 q^{93} +25.0311 q^{94} -6.47024 q^{95} +14.8146 q^{96} -2.52172 q^{97} +4.61717 q^{98} -2.76034 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.26471	−1.60139	−0.800697	−	0.599070i	$-0.795537\pi$
$2$	−2.26471	−1.60139	−0.800697	+	0.599070i	$0.795537\pi$
$3$	2.40007	1.38568	0.692841	−	0.721090i	$-0.256359\pi$
$3$	2.40007	1.38568	0.692841	+	0.721090i	$0.256359\pi$
$4$	3.12892	1.56446
$5$	2.90605	1.29962	0.649812	−	0.760095i	$-0.274848\pi$
$5$	2.90605	1.29962	0.649812	+	0.760095i	$0.274848\pi$
$6$	−5.43547	−2.21902
$7$	2.22739	0.841873	0.420937	−	0.907090i	$-0.361701\pi$
$7$	2.22739	0.841873	0.420937	+	0.907090i	$0.361701\pi$
$8$	−2.55669	−0.903925
$9$	2.76034	0.920114
$10$	−6.58136	−2.08121
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	7.50964	2.16785
$13$	6.30048	1.74744	0.873720	−	0.486430i	$-0.161701\pi$
$13$	6.30048	1.74744	0.873720	+	0.486430i	$0.161701\pi$
$14$	−5.04439	−1.34817
$15$	6.97472	1.80087
$16$	−0.467685	−0.116921
$17$	−0.896955	−0.217543	−0.108772	−	0.994067i	$-0.534692\pi$
$17$	−0.896955	−0.217543	−0.108772	+	0.994067i	$0.534692\pi$
$18$	−6.25138	−1.47347
$19$	−2.22648	−0.510789	−0.255394	−	0.966837i	$-0.582205\pi$
$19$	−2.22648	−0.510789	−0.255394	+	0.966837i	$0.582205\pi$
$20$	9.09280	2.03321
$21$	5.34589	1.16657
$22$	2.26471	0.482838
$23$	4.47739	0.933601	0.466800	−	0.884363i	$-0.345407\pi$
$23$	4.47739	0.933601	0.466800	+	0.884363i	$0.345407\pi$
$24$	−6.13623	−1.25255
$25$	3.44511	0.689022
$26$	−14.2688	−2.79834
$27$	−0.575194	−0.110696
$28$	6.96932	1.31708
$29$	−6.63826	−1.23269	−0.616347	−	0.787475i	$-0.711388\pi$
$29$	−6.63826	−1.23269	−0.616347	+	0.787475i	$0.711388\pi$
$30$	−15.7957	−2.88389
$31$	9.11413	1.63695	0.818473	−	0.574545i	$-0.194821\pi$
$31$	9.11413	1.63695	0.818473	+	0.574545i	$0.194821\pi$
$32$	6.17255	1.09116
$33$	−2.40007	−0.417799
$34$	2.03134	0.348373
$35$	6.47289	1.09412
$36$	8.63690	1.43948
$37$	4.21519	0.692974	0.346487	−	0.938055i	$-0.387375\pi$
$37$	4.21519	0.692974	0.346487	+	0.938055i	$0.387375\pi$
$38$	5.04233	0.817974
$39$	15.1216	2.42139
$40$	−7.42985	−1.17476
$41$	−1.64037	−0.256183	−0.128092	−	0.991762i	$-0.540885\pi$
$41$	−1.64037	−0.256183	−0.128092	+	0.991762i	$0.540885\pi$
$42$	−12.1069	−1.86814
$43$	−2.13008	−0.324834	−0.162417	−	0.986722i	$-0.551929\pi$
$43$	−2.13008	−0.324834	−0.162417	+	0.986722i	$0.551929\pi$
$44$	−3.12892	−0.471703
$45$	8.02169	1.19580
$46$	−10.1400	−1.49506
$47$	−11.0526	−1.61219	−0.806097	−	0.591784i	$-0.798424\pi$
$47$	−11.0526	−1.61219	−0.806097	+	0.591784i	$0.798424\pi$
$48$	−1.12248	−0.162016
$49$	−2.03875	−0.291249
$50$	−7.80218	−1.10340
$51$	−2.15276	−0.301446
$52$	19.7137	2.73380
$53$	9.03466	1.24101	0.620503	−	0.784204i	$-0.286928\pi$
$53$	9.03466	1.24101	0.620503	+	0.784204i	$0.286928\pi$
$54$	1.30265	0.177268
$55$	−2.90605	−0.391851
$56$	−5.69473	−0.760991
$57$	−5.34370	−0.707791
$58$	15.0338	1.97403
$59$	9.56003	1.24461	0.622305	−	0.782775i	$-0.286196\pi$
$59$	9.56003	1.24461	0.622305	+	0.782775i	$0.286196\pi$
$60$	21.8234	2.81738
$61$	−1.71805	−0.219973	−0.109987	−	0.993933i	$-0.535081\pi$
$61$	−1.71805	−0.219973	−0.109987	+	0.993933i	$0.535081\pi$
$62$	−20.6409	−2.62140
$63$	6.14835	0.774620
$64$	−13.0437	−1.63046
$65$	18.3095	2.27101
$66$	5.43547	0.669060
$67$	14.6108	1.78499	0.892494	−	0.451058i	$-0.148953\pi$
$67$	14.6108	1.78499	0.892494	+	0.451058i	$0.148953\pi$
$68$	−2.80650	−0.340338
$69$	10.7461	1.29367
$70$	−14.6592	−1.75211
$71$	−6.31978	−0.750020	−0.375010	−	0.927021i	$-0.622361\pi$
$71$	−6.31978	−0.750020	−0.375010	+	0.927021i	$0.622361\pi$
$72$	−7.05733	−0.831715
$73$	−2.07545	−0.242913	−0.121456	−	0.992597i	$-0.538756\pi$
$73$	−2.07545	−0.242913	−0.121456	+	0.992597i	$0.538756\pi$
$74$	−9.54620	−1.10972
$75$	8.26851	0.954765
$76$	−6.96647	−0.799109
$77$	−2.22739	−0.253834
$78$	−34.2461	−3.87761
$79$	3.22444	0.362778	0.181389	−	0.983411i	$-0.441941\pi$
$79$	3.22444	0.362778	0.181389	+	0.983411i	$0.441941\pi$
$80$	−1.35911	−0.151954
$81$	−9.66154	−1.07350
$82$	3.71497	0.410250
$83$	−15.4616	−1.69713	−0.848566	−	0.529090i	$-0.822533\pi$
$83$	−15.4616	−1.69713	−0.848566	+	0.529090i	$0.822533\pi$
$84$	16.7269	1.82505
$85$	−2.60659	−0.282725
$86$	4.82402	0.520188
$87$	−15.9323	−1.70812
$88$	2.55669	0.272544
$89$	8.24373	0.873834	0.436917	−	0.899502i	$-0.356070\pi$
$89$	8.24373	0.873834	0.436917	+	0.899502i	$0.356070\pi$
$90$	−18.1668	−1.91495
$91$	14.0336	1.47112
$92$	14.0094	1.46058
$93$	21.8746	2.26829
$94$	25.0311	2.58176
$95$	−6.47024	−0.663833
$96$	14.8146	1.51200
$97$	−2.52172	−0.256042	−0.128021	−	0.991771i	$-0.540863\pi$
$97$	−2.52172	−0.256042	−0.128021	+	0.991771i	$0.540863\pi$
$98$	4.61717	0.466405
$99$	−2.76034	−0.277425
$100$	10.7795	1.07795
$101$	16.3208	1.62398	0.811992	−	0.583668i	$-0.198383\pi$
$101$	16.3208	1.62398	0.811992	+	0.583668i	$0.198383\pi$
$102$	4.87537	0.482734
$103$	12.2066	1.20275	0.601377	−	0.798966i	$-0.294619\pi$
$103$	12.2066	1.20275	0.601377	+	0.798966i	$0.294619\pi$
$104$	−16.1084	−1.57955
$105$	15.5354	1.51610
$106$	−20.4609	−1.98734
$107$	−7.56420	−0.731259	−0.365630	−	0.930760i	$-0.619146\pi$
$107$	−7.56420	−0.731259	−0.365630	+	0.930760i	$0.619146\pi$
$108$	−1.79974	−0.173180
$109$	−9.82156	−0.940735	−0.470367	−	0.882471i	$-0.655879\pi$
$109$	−9.82156	−0.940735	−0.470367	+	0.882471i	$0.655879\pi$
$110$	6.58136	0.627508
$111$	10.1168	0.960241
$112$	−1.04172	−0.0984328
$113$	−13.2286	−1.24444	−0.622221	−	0.782842i	$-0.713769\pi$
$113$	−13.2286	−1.24444	−0.622221	+	0.782842i	$0.713769\pi$
$114$	12.1019	1.13345
$115$	13.0115	1.21333
$116$	−20.7706	−1.92850
$117$	17.3915	1.60784
$118$	−21.6507	−1.99311
$119$	−1.99787	−0.183144
$120$	−17.8322	−1.62785
$121$	1.00000	0.0909091
$122$	3.89088	0.352264
$123$	−3.93701	−0.354989
$124$	28.5174	2.56094
$125$	−4.51858	−0.404154
$126$	−13.9243	−1.24047
$127$	8.52040	0.756063	0.378032	−	0.925793i	$-0.376601\pi$
$127$	8.52040	0.756063	0.378032	+	0.925793i	$0.376601\pi$
$128$	17.1951	1.51984
$129$	−5.11235	−0.450117
$130$	−41.4657	−3.63679
$131$	15.4050	1.34594	0.672970	−	0.739670i	$-0.265018\pi$
$131$	15.4050	1.34594	0.672970	+	0.739670i	$0.265018\pi$
$132$	−7.50964	−0.653630
$133$	−4.95922	−0.430019
$134$	−33.0892	−2.85847
$135$	−1.67154	−0.143863
$136$	2.29323	0.196643
$137$	6.97281	0.595727	0.297864	−	0.954608i	$-0.403726\pi$
$137$	6.97281	0.595727	0.297864	+	0.954608i	$0.403726\pi$
$138$	−24.3367	−2.07168
$139$	−10.2487	−0.869284	−0.434642	−	0.900603i	$-0.643125\pi$
$139$	−10.2487	−0.869284	−0.434642	+	0.900603i	$0.643125\pi$
$140$	20.2532	1.71171
$141$	−26.5271	−2.23399
$142$	14.3125	1.20108
$143$	−6.30048	−0.526873
$144$	−1.29097	−0.107581
$145$	−19.2911	−1.60204
$146$	4.70029	0.388999
$147$	−4.89313	−0.403579
$148$	13.1890	1.08413
$149$	7.88191	0.645712	0.322856	−	0.946448i	$-0.395357\pi$
$149$	7.88191	0.645712	0.322856	+	0.946448i	$0.395357\pi$
$150$	−18.7258	−1.52896
$151$	−9.04358	−0.735956	−0.367978	−	0.929834i	$-0.619950\pi$
$151$	−9.04358	−0.735956	−0.367978	+	0.929834i	$0.619950\pi$
$152$	5.69240	0.461715
$153$	−2.47590	−0.200165
$154$	5.04439	0.406489
$155$	26.4861	2.12741
$156$	47.3143	3.78818
$157$	−0.826975	−0.0659998	−0.0329999	−	0.999455i	$-0.510506\pi$
$157$	−0.826975	−0.0659998	−0.0329999	+	0.999455i	$0.510506\pi$
$158$	−7.30244	−0.580951
$159$	21.6838	1.71964
$160$	17.9377	1.41810
$161$	9.97288	0.785973
$162$	21.8806	1.71910
$163$	−3.68896	−0.288941	−0.144471	−	0.989509i	$-0.546148\pi$
$163$	−3.68896	−0.288941	−0.144471	+	0.989509i	$0.546148\pi$
$164$	−5.13260	−0.400789
$165$	−6.97472	−0.542981
$166$	35.0161	2.71778
$167$	−12.3115	−0.952693	−0.476346	−	0.879258i	$-0.658039\pi$
$167$	−12.3115	−0.952693	−0.476346	+	0.879258i	$0.658039\pi$
$168$	−13.6678	−1.05449
$169$	26.6961	2.05354
$170$	5.90318	0.452754
$171$	−6.14584	−0.469984
$172$	−6.66486	−0.508191
$173$	−7.30289	−0.555229	−0.277614	−	0.960693i	$-0.589544\pi$
$173$	−7.30289	−0.555229	−0.277614	+	0.960693i	$0.589544\pi$
$174$	36.0821	2.73538
$175$	7.67359	0.580069
$176$	0.467685	0.0352531
$177$	22.9448	1.72463
$178$	−18.6697	−1.39935
$179$	24.5936	1.83821	0.919107	−	0.394007i	$-0.128911\pi$
$179$	24.5936	1.83821	0.919107	+	0.394007i	$0.128911\pi$
$180$	25.0992	1.87079
$181$	22.4081	1.66558	0.832791	−	0.553588i	$-0.186742\pi$
$181$	22.4081	1.66558	0.832791	+	0.553588i	$0.186742\pi$
$182$	−31.7821	−2.35585
$183$	−4.12343	−0.304813
$184$	−11.4473	−0.843905
$185$	12.2496	0.900605
$186$	−49.5396	−3.63242
$187$	0.896955	0.0655918
$188$	−34.5829	−2.52222
$189$	−1.28118	−0.0931921
$190$	14.6532	1.06306
$191$	5.97476	0.432318	0.216159	−	0.976358i	$-0.430647\pi$
$191$	5.97476	0.432318	0.216159	+	0.976358i	$0.430647\pi$
$192$	−31.3058	−2.25930
$193$	24.9862	1.79854	0.899272	−	0.437390i	$-0.144097\pi$
$193$	24.9862	1.79854	0.899272	+	0.437390i	$0.144097\pi$
$194$	5.71098	0.410024
$195$	43.9441	3.14690
$196$	−6.37908	−0.455648
$197$	−4.63803	−0.330446	−0.165223	−	0.986256i	$-0.552834\pi$
$197$	−4.63803	−0.330446	−0.165223	+	0.986256i	$0.552834\pi$
$198$	6.25138	0.444267
$199$	−1.33297	−0.0944919	−0.0472459	−	0.998883i	$-0.515044\pi$
$199$	−1.33297	−0.0944919	−0.0472459	+	0.998883i	$0.515044\pi$
$200$	−8.80807	−0.622825
$201$	35.0669	2.47343
$202$	−36.9620	−2.60064
$203$	−14.7860	−1.03777
$204$	−6.73581	−0.471601
$205$	−4.76700	−0.332942
$206$	−27.6445	−1.92608
$207$	12.3591	0.859019
$208$	−2.94664	−0.204313
$209$	2.22648	0.154009
$210$	−35.1832	−2.42787
$211$	17.6717	1.21657	0.608284	−	0.793719i	$-0.291858\pi$
$211$	17.6717	1.21657	0.608284	+	0.793719i	$0.291858\pi$
$212$	28.2688	1.94151
$213$	−15.1679	−1.03929
$214$	17.1307	1.17103
$215$	−6.19012	−0.422162
$216$	1.47059	0.100061
$217$	20.3007	1.37810
$218$	22.2430	1.50649
$219$	−4.98123	−0.336600
$220$	−9.09280	−0.613036
$221$	−5.65125	−0.380144
$222$	−22.9116	−1.53772
$223$	1.37143	0.0918378	0.0459189	−	0.998945i	$-0.485378\pi$
$223$	1.37143	0.0918378	0.0459189	+	0.998945i	$0.485378\pi$
$224$	13.7487	0.918620
$225$	9.50969	0.633979
$226$	29.9590	1.99284
$227$	2.98940	0.198414	0.0992068	−	0.995067i	$-0.468369\pi$
$227$	2.98940	0.198414	0.0992068	+	0.995067i	$0.468369\pi$
$228$	−16.7200	−1.10731
$229$	−16.0462	−1.06036	−0.530180	−	0.847885i	$-0.677876\pi$
$229$	−16.0462	−1.06036	−0.530180	+	0.847885i	$0.677876\pi$
$230$	−29.4673	−1.94302
$231$	−5.34589	−0.351734
$232$	16.9720	1.11426
$233$	−6.02108	−0.394454	−0.197227	−	0.980358i	$-0.563194\pi$
$233$	−6.02108	−0.394454	−0.197227	+	0.980358i	$0.563194\pi$
$234$	−39.3867	−2.57479
$235$	−32.1195	−2.09525
$236$	29.9126	1.94714
$237$	7.73889	0.502695
$238$	4.52459	0.293286
$239$	−15.4681	−1.00055	−0.500274	−	0.865867i	$-0.666767\pi$
$239$	−15.4681	−1.00055	−0.500274	+	0.865867i	$0.666767\pi$
$240$	−3.26197	−0.210559
$241$	−12.8412	−0.827177	−0.413589	−	0.910464i	$-0.635725\pi$
$241$	−12.8412	−0.827177	−0.413589	+	0.910464i	$0.635725\pi$
$242$	−2.26471	−0.145581
$243$	−21.4628	−1.37684
$244$	−5.37564	−0.344140
$245$	−5.92469	−0.378515
$246$	8.91620	0.568476
$247$	−14.0279	−0.892572
$248$	−23.3020	−1.47968
$249$	−37.1090	−2.35168
$250$	10.2333	0.647210
$251$	4.64066	0.292916	0.146458	−	0.989217i	$-0.453213\pi$
$251$	4.64066	0.292916	0.146458	+	0.989217i	$0.453213\pi$
$252$	19.2377	1.21186
$253$	−4.47739	−0.281491
$254$	−19.2963	−1.21075
$255$	−6.25601	−0.391766
$256$	−12.8546	−0.803411
$257$	−16.8543	−1.05134	−0.525671	−	0.850688i	$-0.676186\pi$
$257$	−16.8543	−1.05134	−0.525671	+	0.850688i	$0.676186\pi$
$258$	11.5780	0.720815
$259$	9.38887	0.583396
$260$	57.2890	3.55291
$261$	−18.3239	−1.13422
$262$	−34.8879	−2.15538
$263$	−11.0794	−0.683187	−0.341594	−	0.939848i	$-0.610967\pi$
$263$	−11.0794	−0.683187	−0.341594	+	0.939848i	$0.610967\pi$
$264$	6.13623	0.377659
$265$	26.2552	1.61284
$266$	11.2312	0.688630
$267$	19.7855	1.21086
$268$	45.7160	2.79255
$269$	14.9880	0.913837	0.456919	−	0.889508i	$-0.348953\pi$
$269$	14.9880	0.913837	0.456919	+	0.889508i	$0.348953\pi$
$270$	3.78556	0.230382
$271$	−13.6067	−0.826546	−0.413273	−	0.910607i	$-0.635614\pi$
$271$	−13.6067	−0.826546	−0.413273	+	0.910607i	$0.635614\pi$
$272$	0.419492	0.0254354
$273$	33.6817	2.03851
$274$	−15.7914	−0.953993
$275$	−3.44511	−0.207748
$276$	33.6236	2.02390
$277$	14.7494	0.886205	0.443102	−	0.896471i	$-0.353878\pi$
$277$	14.7494	0.886205	0.443102	+	0.896471i	$0.353878\pi$
$278$	23.2104	1.39207
$279$	25.1581	1.50618
$280$	−16.5492	−0.989002
$281$	−29.4341	−1.75589	−0.877944	−	0.478763i	$-0.841085\pi$
$281$	−29.4341	−1.75589	−0.877944	+	0.478763i	$0.841085\pi$
$282$	60.0763	3.57749
$283$	−21.7256	−1.29145	−0.645726	−	0.763569i	$-0.723445\pi$
$283$	−21.7256	−1.29145	−0.645726	+	0.763569i	$0.723445\pi$
$284$	−19.7741	−1.17338
$285$	−15.5290	−0.919861
$286$	14.2688	0.843731
$287$	−3.65375	−0.215674
$288$	17.0383	1.00399
$289$	−16.1955	−0.952675
$290$	43.6888	2.56549
$291$	−6.05232	−0.354793
$292$	−6.49392	−0.380028
$293$	14.5636	0.850813	0.425406	−	0.905002i	$-0.360131\pi$
$293$	14.5636	0.850813	0.425406	+	0.905002i	$0.360131\pi$
$294$	11.0815	0.646289
$295$	27.7819	1.61752
$296$	−10.7769	−0.626396
$297$	0.575194	0.0333761
$298$	−17.8503	−1.03404
$299$	28.2097	1.63141
$300$	25.8715	1.49369
$301$	−4.74452	−0.273469
$302$	20.4811	1.17856
$303$	39.1712	2.25033
$304$	1.04129	0.0597220
$305$	−4.99272	−0.285883
$306$	5.60721	0.320543
$307$	−31.3585	−1.78972	−0.894861	−	0.446345i	$-0.852725\pi$
$307$	−31.3585	−1.78972	−0.894861	+	0.446345i	$0.852725\pi$
$308$	−6.96932	−0.397114
$309$	29.2967	1.66663
$310$	−59.9834	−3.40683
$311$	−21.7027	−1.23065	−0.615323	−	0.788275i	$-0.710974\pi$
$311$	−21.7027	−1.23065	−0.615323	+	0.788275i	$0.710974\pi$
$312$	−38.6612	−2.18876
$313$	13.6646	0.772366	0.386183	−	0.922422i	$-0.373793\pi$
$313$	13.6646	0.772366	0.386183	+	0.922422i	$0.373793\pi$
$314$	1.87286	0.105692
$315$	17.8674	1.00671
$316$	10.0890	0.567553
$317$	14.8044	0.831496	0.415748	−	0.909480i	$-0.363520\pi$
$317$	14.8044	0.831496	0.415748	+	0.909480i	$0.363520\pi$
$318$	−49.1076	−2.75382
$319$	6.63826	0.371671
$320$	−37.9055	−2.11898
$321$	−18.1546	−1.01329
$322$	−22.5857	−1.25865
$323$	1.99705	0.111119
$324$	−30.2302	−1.67946
$325$	21.7059	1.20402
$326$	8.35443	0.462709
$327$	−23.5724	−1.30356
$328$	4.19392	0.231571
$329$	−24.6185	−1.35726
$330$	15.7957	0.869527
$331$	11.8365	0.650592	0.325296	−	0.945612i	$-0.394536\pi$
$331$	11.8365	0.650592	0.325296	+	0.945612i	$0.394536\pi$
$332$	−48.3782	−2.65510
$333$	11.6354	0.637615
$334$	27.8820	1.52564
$335$	42.4596	2.31981
$336$	−2.50019	−0.136397
$337$	7.30611	0.397989	0.198995	−	0.980001i	$-0.436232\pi$
$337$	7.30611	0.397989	0.198995	+	0.980001i	$0.436232\pi$
$338$	−60.4589	−3.28853
$339$	−31.7496	−1.72440
$340$	−8.15583	−0.442312
$341$	−9.11413	−0.493558
$342$	13.9186	0.752629
$343$	−20.1328	−1.08707
$344$	5.44595	0.293626
$345$	31.2286	1.68129
$346$	16.5390	0.889140
$347$	−0.414264	−0.0222389	−0.0111194	−	0.999938i	$-0.503539\pi$
$347$	−0.414264	−0.0222389	−0.0111194	+	0.999938i	$0.503539\pi$
$348$	−49.8510	−2.67229
$349$	3.23929	0.173395	0.0866976	−	0.996235i	$-0.472369\pi$
$349$	3.23929	0.173395	0.0866976	+	0.996235i	$0.472369\pi$
$350$	−17.3785	−0.928919
$351$	−3.62400	−0.193435
$352$	−6.17255	−0.328998
$353$	−28.3935	−1.51124	−0.755618	−	0.655013i	$-0.772663\pi$
$353$	−28.3935	−1.51124	−0.755618	+	0.655013i	$0.772663\pi$
$354$	−51.9633	−2.76182
$355$	−18.3656	−0.974744
$356$	25.7940	1.36708
$357$	−4.79502	−0.253779
$358$	−55.6975	−2.94371
$359$	13.3128	0.702622	0.351311	−	0.936259i	$-0.385736\pi$
$359$	13.3128	0.702622	0.351311	+	0.936259i	$0.385736\pi$
$360$	−20.5089	−1.08092
$361$	−14.0428	−0.739095
$362$	−50.7479	−2.66725
$363$	2.40007	0.125971
$364$	43.9101	2.30151
$365$	−6.03135	−0.315695
$366$	9.33840	0.488126
$367$	−11.5594	−0.603394	−0.301697	−	0.953404i	$-0.597553\pi$
$367$	−11.5594	−0.603394	−0.301697	+	0.953404i	$0.597553\pi$
$368$	−2.09401	−0.109158
$369$	−4.52799	−0.235718
$370$	−27.7417	−1.44222
$371$	20.1237	1.04477
$372$	68.4439	3.54865
$373$	−5.23621	−0.271121	−0.135560	−	0.990769i	$-0.543283\pi$
$373$	−5.23621	−0.271121	−0.135560	+	0.990769i	$0.543283\pi$
$374$	−2.03134	−0.105038
$375$	−10.8449	−0.560029
$376$	28.2582	1.45730
$377$	−41.8242	−2.15406
$378$	2.90150	0.149237
$379$	19.4471	0.998933	0.499466	−	0.866333i	$-0.333529\pi$
$379$	19.4471	0.998933	0.499466	+	0.866333i	$0.333529\pi$
$380$	−20.2449	−1.03854
$381$	20.4496	1.04766
$382$	−13.5311	−0.692312
$383$	−16.0024	−0.817682	−0.408841	−	0.912606i	$-0.634067\pi$
$383$	−16.0024	−0.817682	−0.408841	+	0.912606i	$0.634067\pi$
$384$	41.2694	2.10602
$385$	−6.47289	−0.329889
$386$	−56.5865	−2.88018
$387$	−5.87975	−0.298885
$388$	−7.89028	−0.400568
$389$	−29.8579	−1.51386	−0.756929	−	0.653497i	$-0.773301\pi$
$389$	−29.8579	−1.51386	−0.756929	+	0.653497i	$0.773301\pi$
$390$	−99.5208	−5.03943
$391$	−4.01602	−0.203099
$392$	5.21243	0.263268
$393$	36.9730	1.86504
$394$	10.5038	0.529174
$395$	9.37038	0.471475
$396$	−8.63690	−0.434021
$397$	26.2568	1.31779	0.658896	−	0.752234i	$-0.271024\pi$
$397$	26.2568	1.31779	0.658896	+	0.752234i	$0.271024\pi$
$398$	3.01880	0.151319
$399$	−11.9025	−0.595870
$400$	−1.61123	−0.0805613
$401$	−27.4785	−1.37221	−0.686107	−	0.727501i	$-0.740682\pi$
$401$	−27.4785	−1.37221	−0.686107	+	0.727501i	$0.740682\pi$
$402$	−79.4164	−3.96093
$403$	57.4234	2.86046
$404$	51.0667	2.54066
$405$	−28.0769	−1.39515
$406$	33.4860	1.66188
$407$	−4.21519	−0.208939
$408$	5.50392	0.272485
$409$	26.8563	1.32796	0.663978	−	0.747752i	$-0.268867\pi$
$409$	26.8563	1.32796	0.663978	+	0.747752i	$0.268867\pi$
$410$	10.7959	0.533171
$411$	16.7352	0.825488
$412$	38.1936	1.88166
$413$	21.2939	1.04780
$414$	−27.9899	−1.37563
$415$	−44.9322	−2.20563
$416$	38.8900	1.90674
$417$	−24.5976	−1.20455
$418$	−5.04233	−0.246628
$419$	−0.383344	−0.0187276	−0.00936378	−	0.999956i	$-0.502981\pi$
$419$	−0.383344	−0.0187276	−0.00936378	+	0.999956i	$0.502981\pi$
$420$	48.6091	2.37188
$421$	−6.13651	−0.299075	−0.149538	−	0.988756i	$-0.547778\pi$
$421$	−6.13651	−0.299075	−0.149538	+	0.988756i	$0.547778\pi$
$422$	−40.0213	−1.94821
$423$	−30.5091	−1.48340
$424$	−23.0988	−1.12178
$425$	−3.09011	−0.149892
$426$	34.3510	1.66431
$427$	−3.82676	−0.185190
$428$	−23.6678	−1.14403
$429$	−15.1216	−0.730078
$430$	14.0188	0.676048
$431$	−13.5160	−0.651042	−0.325521	−	0.945535i	$-0.605540\pi$
$431$	−13.5160	−0.651042	−0.325521	+	0.945535i	$0.605540\pi$
$432$	0.269009	0.0129427
$433$	−31.2874	−1.50358	−0.751788	−	0.659405i	$-0.770808\pi$
$433$	−31.2874	−1.50358	−0.751788	+	0.659405i	$0.770808\pi$
$434$	−45.9753	−2.20688
$435$	−46.3000	−2.21992
$436$	−30.7309	−1.47174
$437$	−9.96880	−0.476873
$438$	11.2810	0.539029
$439$	14.3302	0.683944	0.341972	−	0.939710i	$-0.388905\pi$
$439$	14.3302	0.683944	0.341972	+	0.939710i	$0.388905\pi$
$440$	7.42985	0.354204
$441$	−5.62764	−0.267983
$442$	12.7984	0.608760
$443$	−15.3750	−0.730490	−0.365245	−	0.930911i	$-0.619015\pi$
$443$	−15.3750	−0.730490	−0.365245	+	0.930911i	$0.619015\pi$
$444$	31.6546	1.50226
$445$	23.9567	1.13566
$446$	−3.10590	−0.147068
$447$	18.9172	0.894751
$448$	−29.0533	−1.37264
$449$	26.4079	1.24627	0.623133	−	0.782116i	$-0.285860\pi$
$449$	26.4079	1.24627	0.623133	+	0.782116i	$0.285860\pi$
$450$	−21.5367	−1.01525
$451$	1.64037	0.0772422
$452$	−41.3913	−1.94688
$453$	−21.7052	−1.01980
$454$	−6.77014	−0.317738
$455$	40.7823	1.91191
$456$	13.6622	0.639790
$457$	−32.2906	−1.51049	−0.755246	−	0.655441i	$-0.772483\pi$
$457$	−32.2906	−1.51049	−0.755246	+	0.655441i	$0.772483\pi$
$458$	36.3400	1.69805
$459$	0.515923	0.0240812
$460$	40.7120	1.89821
$461$	−41.2060	−1.91915	−0.959576	−	0.281448i	$-0.909185\pi$
$461$	−41.2060	−1.91915	−0.959576	+	0.281448i	$0.909185\pi$
$462$	12.1069	0.563264
$463$	−24.3427	−1.13130	−0.565652	−	0.824644i	$-0.691375\pi$
$463$	−24.3427	−1.13130	−0.565652	+	0.824644i	$0.691375\pi$
$464$	3.10461	0.144128
$465$	63.5685	2.94792
$466$	13.6360	0.631677
$467$	19.4190	0.898603	0.449302	−	0.893380i	$-0.351673\pi$
$467$	19.4190	0.898603	0.449302	+	0.893380i	$0.351673\pi$
$468$	54.4166	2.51541
$469$	32.5438	1.50273
$470$	72.7414	3.35531
$471$	−1.98480	−0.0914547
$472$	−24.4420	−1.12503
$473$	2.13008	0.0979412
$474$	−17.5264	−0.805013
$475$	−7.67045	−0.351945
$476$	−6.25117	−0.286522
$477$	24.9388	1.14187
$478$	35.0308	1.60227
$479$	−5.25923	−0.240300	−0.120150	−	0.992756i	$-0.538338\pi$
$479$	−5.25923	−0.240300	−0.120150	+	0.992756i	$0.538338\pi$
$480$	43.0518	1.96504
$481$	26.5577	1.21093
$482$	29.0817	1.32464
$483$	23.9356	1.08911
$484$	3.12892	0.142224
$485$	−7.32825	−0.332759
$486$	48.6071	2.20486
$487$	−25.9349	−1.17522	−0.587610	−	0.809144i	$-0.699931\pi$
$487$	−25.9349	−1.17522	−0.587610	+	0.809144i	$0.699931\pi$
$488$	4.39251	0.198840
$489$	−8.85376	−0.400381
$490$	13.4177	0.606151
$491$	−33.9538	−1.53231	−0.766157	−	0.642654i	$-0.777833\pi$
$491$	−33.9538	−1.53231	−0.766157	+	0.642654i	$0.777833\pi$
$492$	−12.3186	−0.555366
$493$	5.95422	0.268165
$494$	31.7691	1.42936
$495$	−8.02169	−0.360548
$496$	−4.26254	−0.191394
$497$	−14.0766	−0.631422
$498$	84.0411	3.76597
$499$	27.8017	1.24457	0.622287	−	0.782789i	$-0.286204\pi$
$499$	27.8017	1.24457	0.622287	+	0.782789i	$0.286204\pi$
$500$	−14.1383	−0.632284
$501$	−29.5485	−1.32013
$502$	−10.5098	−0.469074
$503$	9.76960	0.435605	0.217802	−	0.975993i	$-0.430111\pi$
$503$	9.76960	0.435605	0.217802	+	0.975993i	$0.430111\pi$
$504$	−15.7194	−0.700198
$505$	47.4291	2.11057
$506$	10.1400	0.450778
$507$	64.0725	2.84556
$508$	26.6597	1.18283
$509$	12.8454	0.569364	0.284682	−	0.958622i	$-0.408112\pi$
$509$	12.8454	0.569364	0.284682	+	0.958622i	$0.408112\pi$
$510$	14.1681	0.627372
$511$	−4.62283	−0.204502
$512$	−5.27825	−0.233268
$513$	1.28065	0.0565423
$514$	38.1701	1.68361
$515$	35.4730	1.56313
$516$	−15.9961	−0.704191
$517$	11.0526	0.486095
$518$	−21.2631	−0.934247
$519$	−17.5275	−0.769370
$520$	−46.8117	−2.05283
$521$	−8.90370	−0.390078	−0.195039	−	0.980795i	$-0.562483\pi$
$521$	−8.90370	−0.390078	−0.195039	+	0.980795i	$0.562483\pi$
$522$	41.4983	1.81633
$523$	−8.33103	−0.364290	−0.182145	−	0.983272i	$-0.558304\pi$
$523$	−8.33103	−0.364290	−0.182145	+	0.983272i	$0.558304\pi$
$524$	48.2010	2.10567
$525$	18.4172	0.803791
$526$	25.0917	1.09405
$527$	−8.17497	−0.356107
$528$	1.12248	0.0488495
$529$	−2.95297	−0.128390
$530$	−59.4604	−2.58279
$531$	26.3890	1.14518
$532$	−15.5170	−0.672749
$533$	−10.3351	−0.447665
$534$	−44.8086	−1.93906
$535$	−21.9819	−0.950362
$536$	−37.3552	−1.61350
$537$	59.0265	2.54718
$538$	−33.9436	−1.46341
$539$	2.03875	0.0878150
$540$	−5.23012	−0.225069
$541$	−33.1038	−1.42324	−0.711621	−	0.702563i	$-0.752039\pi$
$541$	−33.1038	−1.42324	−0.711621	+	0.702563i	$0.752039\pi$
$542$	30.8152	1.32363
$543$	53.7811	2.30797
$544$	−5.53649	−0.237375
$545$	−28.5419	−1.22260
$546$	−76.2793	−3.26445
$547$	1.00000	0.0427569
$547$	1.00000	0.0427569
$548$	21.8174	0.931992
$549$	−4.74240	−0.202401
$550$	7.80218	0.332686
$551$	14.7799	0.629646
$552$	−27.4743	−1.16938
$553$	7.18208	0.305413
$554$	−33.4031	−1.41916
$555$	29.3998	1.24795
$556$	−32.0674	−1.35996
$557$	−28.0960	−1.19047	−0.595233	−	0.803553i	$-0.702940\pi$
$557$	−28.0960	−1.19047	−0.595233	+	0.803553i	$0.702940\pi$
$558$	−56.9759	−2.41198
$559$	−13.4205	−0.567628
$560$	−3.02727	−0.127926
$561$	2.15276	0.0908894
$562$	66.6597	2.81187
$563$	44.8284	1.88929	0.944646	−	0.328091i	$-0.106405\pi$
$563$	44.8284	1.88929	0.944646	+	0.328091i	$0.106405\pi$
$564$	−83.0014	−3.49499
$565$	−38.4429	−1.61731
$566$	49.2022	2.06812
$567$	−21.5200	−0.903754
$568$	16.1577	0.677963
$569$	−3.73399	−0.156537	−0.0782684	−	0.996932i	$-0.524939\pi$
$569$	−3.73399	−0.156537	−0.0782684	+	0.996932i	$0.524939\pi$
$570$	35.1688	1.47306
$571$	43.8805	1.83634	0.918171	−	0.396185i	$-0.129666\pi$
$571$	43.8805	1.83634	0.918171	+	0.396185i	$0.129666\pi$
$572$	−19.7137	−0.824272
$573$	14.3398	0.599056
$574$	8.27469	0.345379
$575$	15.4251	0.643271
$576$	−36.0050	−1.50021
$577$	−4.34050	−0.180697	−0.0903486	−	0.995910i	$-0.528798\pi$
$577$	−4.34050	−0.180697	−0.0903486	+	0.995910i	$0.528798\pi$
$578$	36.6781	1.52561
$579$	59.9686	2.49221
$580$	−60.3604	−2.50633
$581$	−34.4390	−1.42877
$582$	13.7068	0.568163
$583$	−9.03466	−0.374177
$584$	5.30627	0.219575
$585$	50.5405	2.08959
$586$	−32.9823	−1.36249
$587$	−14.8076	−0.611174	−0.305587	−	0.952164i	$-0.598853\pi$
$587$	−14.8076	−0.611174	−0.305587	+	0.952164i	$0.598853\pi$
$588$	−15.3102	−0.631384
$589$	−20.2924	−0.836134
$590$	−62.9180	−2.59029
$591$	−11.1316	−0.457893
$592$	−1.97138	−0.0810233
$593$	−3.58712	−0.147305	−0.0736526	−	0.997284i	$-0.523466\pi$
$593$	−3.58712	−0.147305	−0.0736526	+	0.997284i	$0.523466\pi$
$594$	−1.30265	−0.0534483
$595$	−5.80589	−0.238018
$596$	24.6619	1.01019
$597$	−3.19923	−0.130936
$598$	−63.8869	−2.61253
$599$	26.3718	1.07752	0.538762	−	0.842458i	$-0.318892\pi$
$599$	26.3718	1.07752	0.538762	+	0.842458i	$0.318892\pi$
$600$	−21.1400	−0.863037
$601$	40.6923	1.65987	0.829936	−	0.557858i	$-0.188377\pi$
$601$	40.6923	1.65987	0.829936	+	0.557858i	$0.188377\pi$
$602$	10.7450	0.437932
$603$	40.3307	1.64239
$604$	−28.2967	−1.15138
$605$	2.90605	0.118148
$606$	−88.7115	−3.60366
$607$	10.2238	0.414971	0.207486	−	0.978238i	$-0.433472\pi$
$607$	10.2238	0.414971	0.207486	+	0.978238i	$0.433472\pi$
$608$	−13.7430	−0.557353
$609$	−35.4874	−1.43802
$610$	11.3071	0.457811
$611$	−69.6370	−2.81721
$612$	−7.74691	−0.313150
$613$	−13.5400	−0.546876	−0.273438	−	0.961890i	$-0.588161\pi$
$613$	−13.5400	−0.546876	−0.273438	+	0.961890i	$0.588161\pi$
$614$	71.0179	2.86605
$615$	−11.4411	−0.461352
$616$	5.69473	0.229447
$617$	33.2214	1.33744	0.668722	−	0.743513i	$-0.266842\pi$
$617$	33.2214	1.33744	0.668722	+	0.743513i	$0.266842\pi$
$618$	−66.3487	−2.66894
$619$	9.04033	0.363362	0.181681	−	0.983358i	$-0.441846\pi$
$619$	9.04033	0.363362	0.181681	+	0.983358i	$0.441846\pi$
$620$	82.8730	3.32826
$621$	−2.57537	−0.103346
$622$	49.1503	1.97075
$623$	18.3620	0.735657
$624$	−7.07215	−0.283112
$625$	−30.3568	−1.21427
$626$	−30.9463	−1.23686
$627$	5.34370	0.213407
$628$	−2.58754	−0.103254
$629$	−3.78084	−0.150752
$630$	−40.4645	−1.61215
$631$	−17.5309	−0.697893	−0.348946	−	0.937143i	$-0.613460\pi$
$631$	−17.5309	−0.697893	−0.348946	+	0.937143i	$0.613460\pi$
$632$	−8.24389	−0.327924
$633$	42.4133	1.68578
$634$	−33.5276	−1.33155
$635$	24.7607	0.982598
$636$	67.8471	2.69031
$637$	−12.8451	−0.508941
$638$	−15.0338	−0.595192
$639$	−17.4448	−0.690105
$640$	49.9697	1.97523
$641$	−14.0223	−0.553846	−0.276923	−	0.960892i	$-0.589315\pi$
$641$	−14.0223	−0.553846	−0.276923	+	0.960892i	$0.589315\pi$
$642$	41.1150	1.62268
$643$	26.3216	1.03802	0.519011	−	0.854767i	$-0.326300\pi$
$643$	26.3216	1.03802	0.519011	+	0.854767i	$0.326300\pi$
$644$	31.2044	1.22963
$645$	−14.8567	−0.584983
$646$	−4.52274	−0.177945
$647$	−1.17257	−0.0460984	−0.0230492	−	0.999734i	$-0.507337\pi$
$647$	−1.17257	−0.0460984	−0.0230492	+	0.999734i	$0.507337\pi$
$648$	24.7015	0.970368
$649$	−9.56003	−0.375264
$650$	−49.1575	−1.92812
$651$	48.7231	1.90961
$652$	−11.5425	−0.452038
$653$	−27.8465	−1.08972	−0.544860	−	0.838527i	$-0.683417\pi$
$653$	−27.8465	−1.08972	−0.544860	+	0.838527i	$0.683417\pi$
$654$	53.3848	2.08751
$655$	44.7676	1.74921
$656$	0.767178	0.0299533
$657$	−5.72895	−0.223508
$658$	55.7539	2.17351
$659$	31.4448	1.22492	0.612458	−	0.790503i	$-0.290181\pi$
$659$	31.4448	1.22492	0.612458	+	0.790503i	$0.290181\pi$
$660$	−21.8234	−0.849473
$661$	−10.3826	−0.403838	−0.201919	−	0.979402i	$-0.564718\pi$
$661$	−10.3826	−0.403838	−0.201919	+	0.979402i	$0.564718\pi$
$662$	−26.8062	−1.04185
$663$	−13.5634	−0.526759
$664$	39.5305	1.53408
$665$	−14.4117	−0.558863
$666$	−26.3508	−1.02107
$667$	−29.7221	−1.15084
$668$	−38.5217	−1.49045
$669$	3.29153	0.127258
$670$	−96.1587	−3.71494
$671$	1.71805	0.0663245
$672$	32.9977	1.27292
$673$	24.5829	0.947599	0.473800	−	0.880633i	$-0.342882\pi$
$673$	24.5829	0.947599	0.473800	+	0.880633i	$0.342882\pi$
$674$	−16.5462	−0.637337
$675$	−1.98161	−0.0762720
$676$	83.5299	3.21269
$677$	−18.7401	−0.720241	−0.360121	−	0.932906i	$-0.617264\pi$
$677$	−18.7401	−0.720241	−0.360121	+	0.932906i	$0.617264\pi$
$678$	71.9037	2.76144
$679$	−5.61685	−0.215555
$680$	6.66424	0.255562
$681$	7.17478	0.274938
$682$	20.6409	0.790381
$683$	28.4579	1.08891	0.544456	−	0.838790i	$-0.316736\pi$
$683$	28.4579	1.08891	0.544456	+	0.838790i	$0.316736\pi$
$684$	−19.2299	−0.735272
$685$	20.2633	0.774221
$686$	45.5950	1.74082
$687$	−38.5119	−1.46932
$688$	0.996206	0.0379800
$689$	56.9227	2.16858
$690$	−70.7237	−2.69241
$691$	35.1906	1.33871	0.669356	−	0.742942i	$-0.266570\pi$
$691$	35.1906	1.33871	0.669356	+	0.742942i	$0.266570\pi$
$692$	−22.8502	−0.868634
$693$	−6.14835	−0.233557
$694$	0.938189	0.0356132
$695$	−29.7832	−1.12974
$696$	40.7339	1.54402
$697$	1.47134	0.0557310
$698$	−7.33606	−0.277674
$699$	−14.4510	−0.546588
$700$	24.0101	0.907496
$701$	−44.1461	−1.66738	−0.833688	−	0.552235i	$-0.813775\pi$
$701$	−44.1461	−1.66738	−0.833688	+	0.552235i	$0.813775\pi$
$702$	8.20731	0.309765
$703$	−9.38503	−0.353963
$704$	13.0437	0.491602
$705$	−77.0891	−2.90334
$706$	64.3032	2.42008
$707$	36.3528	1.36719
$708$	71.7924	2.69812
$709$	−1.70949	−0.0642014	−0.0321007	−	0.999485i	$-0.510220\pi$
$709$	−1.70949	−0.0642014	−0.0321007	+	0.999485i	$0.510220\pi$
$710$	41.5928	1.56095
$711$	8.90057	0.333797
$712$	−21.0766	−0.789881
$713$	40.8075	1.52825
$714$	10.8593	0.406401
$715$	−18.3095	−0.684736
$716$	76.9516	2.87582
$717$	−37.1245	−1.38644
$718$	−30.1496	−1.12517
$719$	−7.86550	−0.293334	−0.146667	−	0.989186i	$-0.546855\pi$
$719$	−7.86550	−0.293334	−0.146667	+	0.989186i	$0.546855\pi$
$720$	−3.75162	−0.139815
$721$	27.1889	1.01257
$722$	31.8029	1.18358
$723$	−30.8199	−1.14620
$724$	70.1133	2.60574
$725$	−22.8695	−0.849354
$726$	−5.43547	−0.201729
$727$	9.50640	0.352573	0.176286	−	0.984339i	$-0.443591\pi$
$727$	9.50640	0.352573	0.176286	+	0.984339i	$0.443591\pi$
$728$	−35.8796	−1.32978
$729$	−22.5276	−0.834357
$730$	13.6593	0.505553
$731$	1.91059	0.0706656
$732$	−12.9019	−0.476868
$733$	42.4248	1.56699	0.783497	−	0.621395i	$-0.213434\pi$
$733$	42.4248	1.56699	0.783497	+	0.621395i	$0.213434\pi$
$734$	26.1786	0.966271
$735$	−14.2197	−0.524501
$736$	27.6369	1.01871
$737$	−14.6108	−0.538194
$738$	10.2546	0.377477
$739$	31.0873	1.14357	0.571783	−	0.820405i	$-0.306252\pi$
$739$	31.0873	1.14357	0.571783	+	0.820405i	$0.306252\pi$
$740$	38.3279	1.40896
$741$	−33.6679	−1.23682
$742$	−45.5744	−1.67309
$743$	11.8372	0.434265	0.217133	−	0.976142i	$-0.430330\pi$
$743$	11.8372	0.434265	0.217133	+	0.976142i	$0.430330\pi$
$744$	−55.9264	−2.05036
$745$	22.9052	0.839182
$746$	11.8585	0.434171
$747$	−42.6793	−1.56156
$748$	2.80650	0.102616
$749$	−16.8484	−0.615627
$750$	24.5606	0.896828
$751$	−35.0759	−1.27994	−0.639969	−	0.768400i	$-0.721053\pi$
$751$	−35.0759	−1.27994	−0.639969	+	0.768400i	$0.721053\pi$
$752$	5.16915	0.188500
$753$	11.1379	0.405888
$754$	94.7199	3.44950
$755$	−26.2811	−0.956466
$756$	−4.00871	−0.145795
$757$	−36.0009	−1.30847	−0.654237	−	0.756289i	$-0.727010\pi$
$757$	−36.0009	−1.30847	−0.654237	+	0.756289i	$0.727010\pi$
$758$	−44.0422	−1.59968
$759$	−10.7461	−0.390057
$760$	16.5424	0.600056
$761$	−3.27360	−0.118668	−0.0593340	−	0.998238i	$-0.518898\pi$
$761$	−3.27360	−0.118668	−0.0593340	+	0.998238i	$0.518898\pi$
$762$	−46.3124	−1.67772
$763$	−21.8764	−0.791979
$764$	18.6946	0.676345
$765$	−7.19509	−0.260139
$766$	36.2407	1.30943
$767$	60.2328	2.17488
$768$	−30.8519	−1.11327
$769$	43.8610	1.58167	0.790835	−	0.612030i	$-0.209647\pi$
$769$	43.8610	1.58167	0.790835	+	0.612030i	$0.209647\pi$
$770$	14.6592	0.528282
$771$	−40.4515	−1.45683
$772$	78.1798	2.81375
$773$	−55.1511	−1.98365	−0.991823	−	0.127619i	$-0.959267\pi$
$773$	−55.1511	−1.98365	−0.991823	+	0.127619i	$0.959267\pi$
$774$	13.3160	0.478632
$775$	31.3992	1.12789
$776$	6.44726	0.231443
$777$	22.5340	0.808401
$778$	67.6197	2.42428
$779$	3.65225	0.130856
$780$	137.498	4.92321
$781$	6.31978	0.226140
$782$	9.09513	0.325241
$783$	3.81829	0.136454
$784$	0.953490	0.0340532
$785$	−2.40323	−0.0857749
$786$	−83.7333	−2.98667
$787$	−15.2864	−0.544900	−0.272450	−	0.962170i	$-0.587834\pi$
$787$	−15.2864	−0.544900	−0.272450	+	0.962170i	$0.587834\pi$
$788$	−14.5120	−0.516970
$789$	−26.5914	−0.946680
$790$	−21.2212	−0.755017
$791$	−29.4652	−1.04766
$792$	7.05733	0.250771
$793$	−10.8245	−0.384390
$794$	−59.4642	−2.11030
$795$	63.0142	2.23488
$796$	−4.17077	−0.147829
$797$	9.23811	0.327231	0.163615	−	0.986524i	$-0.447684\pi$
$797$	9.23811	0.327231	0.163615	+	0.986524i	$0.447684\pi$
$798$	26.9557	0.954222
$799$	9.91372	0.350722
$800$	21.2651	0.751835
$801$	22.7555	0.804027
$802$	62.2310	2.19745
$803$	2.07545	0.0732410
$804$	109.722	3.86958
$805$	28.9817	1.02147
$806$	−130.048	−4.58073
$807$	35.9724	1.26629
$808$	−41.7273	−1.46796
$809$	38.7649	1.36290	0.681450	−	0.731865i	$-0.261350\pi$
$809$	38.7649	1.36290	0.681450	+	0.731865i	$0.261350\pi$
$810$	63.5861	2.23419
$811$	20.3474	0.714493	0.357247	−	0.934010i	$-0.383716\pi$
$811$	20.3474	0.714493	0.357247	+	0.934010i	$0.383716\pi$
$812$	−46.2642	−1.62356
$813$	−32.6570	−1.14533
$814$	9.54620	0.334594
$815$	−10.7203	−0.375515
$816$	1.00681	0.0352454
$817$	4.74257	0.165922
$818$	−60.8217	−2.12658
$819$	38.7376	1.35360
$820$	−14.9156	−0.520875
$821$	33.9620	1.18528	0.592641	−	0.805466i	$-0.298085\pi$
$821$	33.9620	1.18528	0.592641	+	0.805466i	$0.298085\pi$
$822$	−37.9005	−1.32193
$823$	46.6641	1.62661	0.813304	−	0.581840i	$-0.197667\pi$
$823$	46.6641	1.62661	0.813304	+	0.581840i	$0.197667\pi$
$824$	−31.2085	−1.08720
$825$	−8.26851	−0.287873
$826$	−48.2245	−1.67795
$827$	30.8221	1.07179	0.535895	−	0.844285i	$-0.319974\pi$
$827$	30.8221	1.07179	0.535895	+	0.844285i	$0.319974\pi$
$828$	38.6708	1.34390
$829$	−14.4517	−0.501927	−0.250963	−	0.967997i	$-0.580747\pi$
$829$	−14.4517	−0.501927	−0.250963	+	0.967997i	$0.580747\pi$
$830$	101.758	3.53209
$831$	35.3996	1.22800
$832$	−82.1814	−2.84913
$833$	1.82866	0.0633594
$834$	55.7065	1.92896
$835$	−35.7778	−1.23814
$836$	6.96647	0.240941
$837$	−5.24239	−0.181204
$838$	0.868164	0.0299902
$839$	19.3792	0.669045	0.334522	−	0.942388i	$-0.391425\pi$
$839$	19.3792	0.669045	0.334522	+	0.942388i	$0.391425\pi$
$840$	−39.7192	−1.37044
$841$	15.0665	0.519535
$842$	13.8974	0.478937
$843$	−70.6438	−2.43310
$844$	55.2933	1.90328
$845$	77.5800	2.66883
$846$	69.0943	2.37551
$847$	2.22739	0.0765339
$848$	−4.22537	−0.145100
$849$	−52.1430	−1.78954
$850$	6.99821	0.240036
$851$	18.8731	0.646960
$852$	−47.4593	−1.62593
$853$	13.7587	0.471090	0.235545	−	0.971863i	$-0.424313\pi$
$853$	13.7587	0.471090	0.235545	+	0.971863i	$0.424313\pi$
$854$	8.66650	0.296562
$855$	−17.8601	−0.610802
$856$	19.3393	0.661004
$857$	9.26259	0.316404	0.158202	−	0.987407i	$-0.449430\pi$
$857$	9.26259	0.316404	0.158202	+	0.987407i	$0.449430\pi$
$858$	34.2461	1.16914
$859$	−33.7390	−1.15116	−0.575580	−	0.817746i	$-0.695224\pi$
$859$	−33.7390	−1.15116	−0.575580	+	0.817746i	$0.695224\pi$
$860$	−19.3684	−0.660457
$861$	−8.76925	−0.298855
$862$	30.6098	1.04257
$863$	30.2815	1.03079	0.515397	−	0.856952i	$-0.327645\pi$
$863$	30.2815	1.03079	0.515397	+	0.856952i	$0.327645\pi$
$864$	−3.55041	−0.120787
$865$	−21.2225	−0.721588
$866$	70.8569	2.40782
$867$	−38.8703	−1.32010
$868$	63.5194	2.15599
$869$	−3.22444	−0.109382
$870$	104.856	3.55496
$871$	92.0548	3.11916
$872$	25.1107	0.850354
$873$	−6.96082	−0.235588
$874$	22.5765	0.763661
$875$	−10.0646	−0.340247
$876$	−15.5859	−0.526598
$877$	7.39214	0.249615	0.124807	−	0.992181i	$-0.460169\pi$
$877$	7.39214	0.249615	0.124807	+	0.992181i	$0.460169\pi$
$878$	−32.4538	−1.09526
$879$	34.9536	1.17896
$880$	1.35911	0.0458157
$881$	−50.0138	−1.68501	−0.842504	−	0.538691i	$-0.818919\pi$
$881$	−50.0138	−1.68501	−0.842504	+	0.538691i	$0.818919\pi$
$882$	12.7450	0.429146
$883$	28.2190	0.949645	0.474823	−	0.880082i	$-0.342512\pi$
$883$	28.2190	0.949645	0.474823	+	0.880082i	$0.342512\pi$
$884$	−17.6823	−0.594721
$885$	66.6785	2.24137
$886$	34.8200	1.16980
$887$	−28.8518	−0.968748	−0.484374	−	0.874861i	$-0.660953\pi$
$887$	−28.8518	−0.968748	−0.484374	+	0.874861i	$0.660953\pi$
$888$	−25.8654	−0.867986
$889$	18.9782	0.636509
$890$	−54.2550	−1.81863
$891$	9.66154	0.323674
$892$	4.29110	0.143677
$893$	24.6084	0.823490
$894$	−42.8419	−1.43285
$895$	71.4703	2.38899
$896$	38.3001	1.27952
$897$	67.7053	2.26062
$898$	−59.8063	−1.99576
$899$	−60.5020	−2.01785
$900$	29.7551	0.991836
$901$	−8.10368	−0.269973
$902$	−3.71497	−0.123695
$903$	−11.3872	−0.378941
$904$	33.8214	1.12488
$905$	65.1190	2.16463
$906$	49.1561	1.63310
$907$	−28.4396	−0.944320	−0.472160	−	0.881513i	$-0.656526\pi$
$907$	−28.4396	−0.944320	−0.472160	+	0.881513i	$0.656526\pi$
$908$	9.35361	0.310411
$909$	45.0511	1.49425
$910$	−92.3603	−3.06171
$911$	−53.4627	−1.77130	−0.885649	−	0.464356i	$-0.846286\pi$
$911$	−53.4627	−1.77130	−0.885649	+	0.464356i	$0.846286\pi$
$912$	2.49917	0.0827557
$913$	15.4616	0.511704
$914$	73.1290	2.41889
$915$	−11.9829	−0.396142
$916$	−50.2072	−1.65889
$917$	34.3129	1.13311
$918$	−1.16842	−0.0385635
$919$	16.4426	0.542392	0.271196	−	0.962524i	$-0.412581\pi$
$919$	16.4426	0.542392	0.271196	+	0.962524i	$0.412581\pi$
$920$	−33.2664	−1.09676
$921$	−75.2626	−2.47999
$922$	93.3197	3.07332
$923$	−39.8177	−1.31061
$924$	−16.7269	−0.550274
$925$	14.5218	0.477474
$926$	55.1293	1.81166
$927$	33.6944	1.10667
$928$	−40.9750	−1.34507
$929$	25.9956	0.852888	0.426444	−	0.904514i	$-0.359766\pi$
$929$	25.9956	0.852888	0.426444	+	0.904514i	$0.359766\pi$
$930$	−143.964	−4.72078
$931$	4.53922	0.148767
$932$	−18.8395	−0.617109
$933$	−52.0880	−1.70528
$934$	−43.9784	−1.43902
$935$	2.60659	0.0852447
$936$	−44.4646	−1.45337
$937$	7.09486	0.231779	0.115889	−	0.993262i	$-0.463028\pi$
$937$	7.09486	0.231779	0.115889	+	0.993262i	$0.463028\pi$
$938$	−73.7024	−2.40647
$939$	32.7959	1.07025
$940$	−100.499	−3.27793
$941$	14.7845	0.481960	0.240980	−	0.970530i	$-0.422531\pi$
$941$	14.7845	0.481960	0.240980	+	0.970530i	$0.422531\pi$
$942$	4.49500	0.146455
$943$	−7.34459	−0.239173
$944$	−4.47108	−0.145521
$945$	−3.72317	−0.121115
$946$	−4.82402	−0.156842
$947$	−21.9232	−0.712408	−0.356204	−	0.934408i	$-0.615929\pi$
$947$	−21.9232	−0.712408	−0.356204	+	0.934408i	$0.615929\pi$
$948$	24.2144	0.786447
$949$	−13.0763	−0.424475
$950$	17.3714	0.563602
$951$	35.5315	1.15219
$952$	5.10792	0.165549
$953$	−21.2598	−0.688671	−0.344336	−	0.938847i	$-0.611896\pi$
$953$	−21.2598	−0.688671	−0.344336	+	0.938847i	$0.611896\pi$
$954$	−56.4791	−1.82858
$955$	17.3629	0.561851
$956$	−48.3985	−1.56532
$957$	15.9323	0.515018
$958$	11.9106	0.384815
$959$	15.5311	0.501527
$960$	−90.9760	−2.93624
$961$	52.0674	1.67959
$962$	−60.1457	−1.93917
$963$	−20.8798	−0.672842
$964$	−40.1793	−1.29409
$965$	72.6110	2.33743
$966$	−54.2073	−1.74409
$967$	−5.99138	−0.192670	−0.0963349	−	0.995349i	$-0.530712\pi$
$967$	−5.99138	−0.192670	−0.0963349	+	0.995349i	$0.530712\pi$
$968$	−2.55669	−0.0821750
$969$	4.79306	0.153975
$970$	16.5964	0.532877
$971$	−28.8081	−0.924495	−0.462248	−	0.886751i	$-0.652957\pi$
$971$	−28.8081	−0.924495	−0.462248	+	0.886751i	$0.652957\pi$
$972$	−67.1554	−2.15401
$973$	−22.8278	−0.731827
$974$	58.7350	1.88199
$975$	52.0956	1.66839
$976$	0.803504	0.0257195
$977$	−39.6943	−1.26993	−0.634967	−	0.772539i	$-0.718986\pi$
$977$	−39.6943	−1.26993	−0.634967	+	0.772539i	$0.718986\pi$
$978$	20.0512	0.641168
$979$	−8.24373	−0.263471
$980$	−18.5379	−0.592172
$981$	−27.1109	−0.865583
$982$	76.8956	2.45384
$983$	46.8682	1.49486	0.747431	−	0.664339i	$-0.231287\pi$
$983$	46.8682	1.49486	0.747431	+	0.664339i	$0.231287\pi$
$984$	10.0657	0.320883
$985$	−13.4783	−0.429455
$986$	−13.4846	−0.429437
$987$	−59.0862	−1.88073
$988$	−43.8921	−1.39639
$989$	−9.53721	−0.303265
$990$	18.1668	0.577379
$991$	35.6494	1.13244	0.566220	−	0.824254i	$-0.308405\pi$
$991$	35.6494	1.13244	0.566220	+	0.824254i	$0.308405\pi$
$992$	56.2574	1.78617
$993$	28.4084	0.901513
$994$	31.8795	1.01116
$995$	−3.87368	−0.122804
$996$	−116.111	−3.67912
$997$	−38.4897	−1.21898	−0.609490	−	0.792794i	$-0.708626\pi$
$997$	−38.4897	−1.21898	−0.609490	+	0.792794i	$0.708626\pi$
$998$	−62.9629	−1.99305
$999$	−2.42455	−0.0767094

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6017.2.a.f.1.17	✓	121

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6017.2.a.f.1.17	✓	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)

\(f(q)\)	\(=\)	\(q-2.26471 q^{2} +2.40007 q^{3} +3.12892 q^{4} +2.90605 q^{5} -5.43547 q^{6} +2.22739 q^{7} -2.55669 q^{8} +2.76034 q^{9} +O(q^{10})\)	\(q-2.26471 q^{2} +2.40007 q^{3} +3.12892 q^{4} +2.90605 q^{5} -5.43547 q^{6} +2.22739 q^{7} -2.55669 q^{8} +2.76034 q^{9} -6.58136 q^{10} -1.00000 q^{11} +7.50964 q^{12} +6.30048 q^{13} -5.04439 q^{14} +6.97472 q^{15} -0.467685 q^{16} -0.896955 q^{17} -6.25138 q^{18} -2.22648 q^{19} +9.09280 q^{20} +5.34589 q^{21} +2.26471 q^{22} +4.47739 q^{23} -6.13623 q^{24} +3.44511 q^{25} -14.2688 q^{26} -0.575194 q^{27} +6.96932 q^{28} -6.63826 q^{29} -15.7957 q^{30} +9.11413 q^{31} +6.17255 q^{32} -2.40007 q^{33} +2.03134 q^{34} +6.47289 q^{35} +8.63690 q^{36} +4.21519 q^{37} +5.04233 q^{38} +15.1216 q^{39} -7.42985 q^{40} -1.64037 q^{41} -12.1069 q^{42} -2.13008 q^{43} -3.12892 q^{44} +8.02169 q^{45} -10.1400 q^{46} -11.0526 q^{47} -1.12248 q^{48} -2.03875 q^{49} -7.80218 q^{50} -2.15276 q^{51} +19.7137 q^{52} +9.03466 q^{53} +1.30265 q^{54} -2.90605 q^{55} -5.69473 q^{56} -5.34370 q^{57} +15.0338 q^{58} +9.56003 q^{59} +21.8234 q^{60} -1.71805 q^{61} -20.6409 q^{62} +6.14835 q^{63} -13.0437 q^{64} +18.3095 q^{65} +5.43547 q^{66} +14.6108 q^{67} -2.80650 q^{68} +10.7461 q^{69} -14.6592 q^{70} -6.31978 q^{71} -7.05733 q^{72} -2.07545 q^{73} -9.54620 q^{74} +8.26851 q^{75} -6.96647 q^{76} -2.22739 q^{77} -34.2461 q^{78} +3.22444 q^{79} -1.35911 q^{80} -9.66154 q^{81} +3.71497 q^{82} -15.4616 q^{83} +16.7269 q^{84} -2.60659 q^{85} +4.82402 q^{86} -15.9323 q^{87} +2.55669 q^{88} +8.24373 q^{89} -18.1668 q^{90} +14.0336 q^{91} +14.0094 q^{92} +21.8746 q^{93} +25.0311 q^{94} -6.47024 q^{95} +14.8146 q^{96} -2.52172 q^{97} +4.61717 q^{98} -2.76034 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 121 q + 2 q^{2} + 18 q^{3} + 138 q^{4} + 13 q^{5} + 10 q^{6} + 56 q^{7} + 12 q^{8} + 143 q^{9}+O(q^{10}) \) 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