Properties

Label 6018.2.a.y.1.6
Level $6018$
Weight $2$
Character 6018.1
Self dual yes
Analytic conductor $48.054$
Analytic rank $1$
Dimension $10$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [6018,2,Mod(1,6018)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6018, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("6018.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6018.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: \(48.0539719364\)
Analytic rank: \(1\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - 2x^{9} - 33x^{8} + 53x^{7} + 356x^{6} - 433x^{5} - 1296x^{4} + 1135x^{3} + 930x^{2} - 186x - 104 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(-0.313984\) of defining polynomial
Character \(\chi\) \(=\) 6018.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.313984 q^{5} -1.00000 q^{6} +2.10092 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.313984 q^{5} -1.00000 q^{6} +2.10092 q^{7} -1.00000 q^{8} +1.00000 q^{9} -0.313984 q^{10} -0.847786 q^{11} +1.00000 q^{12} -6.84610 q^{13} -2.10092 q^{14} +0.313984 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} +7.75129 q^{19} +0.313984 q^{20} +2.10092 q^{21} +0.847786 q^{22} -5.38960 q^{23} -1.00000 q^{24} -4.90141 q^{25} +6.84610 q^{26} +1.00000 q^{27} +2.10092 q^{28} -3.96402 q^{29} -0.313984 q^{30} +1.75978 q^{31} -1.00000 q^{32} -0.847786 q^{33} +1.00000 q^{34} +0.659654 q^{35} +1.00000 q^{36} +3.06470 q^{37} -7.75129 q^{38} -6.84610 q^{39} -0.313984 q^{40} +4.08035 q^{41} -2.10092 q^{42} +0.863891 q^{43} -0.847786 q^{44} +0.313984 q^{45} +5.38960 q^{46} -8.06572 q^{47} +1.00000 q^{48} -2.58614 q^{49} +4.90141 q^{50} -1.00000 q^{51} -6.84610 q^{52} -10.2118 q^{53} -1.00000 q^{54} -0.266191 q^{55} -2.10092 q^{56} +7.75129 q^{57} +3.96402 q^{58} +1.00000 q^{59} +0.313984 q^{60} +7.82924 q^{61} -1.75978 q^{62} +2.10092 q^{63} +1.00000 q^{64} -2.14956 q^{65} +0.847786 q^{66} -6.38895 q^{67} -1.00000 q^{68} -5.38960 q^{69} -0.659654 q^{70} +11.4183 q^{71} -1.00000 q^{72} -9.05018 q^{73} -3.06470 q^{74} -4.90141 q^{75} +7.75129 q^{76} -1.78113 q^{77} +6.84610 q^{78} +7.33532 q^{79} +0.313984 q^{80} +1.00000 q^{81} -4.08035 q^{82} -0.416311 q^{83} +2.10092 q^{84} -0.313984 q^{85} -0.863891 q^{86} -3.96402 q^{87} +0.847786 q^{88} -13.6489 q^{89} -0.313984 q^{90} -14.3831 q^{91} -5.38960 q^{92} +1.75978 q^{93} +8.06572 q^{94} +2.43378 q^{95} -1.00000 q^{96} -2.22173 q^{97} +2.58614 q^{98} -0.847786 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 10 q^{2} + 10 q^{3} + 10 q^{4} - 2 q^{5} - 10 q^{6} - 6 q^{7} - 10 q^{8} + 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q - 10 q^{2} + 10 q^{3} + 10 q^{4} - 2 q^{5} - 10 q^{6} - 6 q^{7} - 10 q^{8} + 10 q^{9} + 2 q^{10} - 3 q^{11} + 10 q^{12} - 10 q^{13} + 6 q^{14} - 2 q^{15} + 10 q^{16} - 10 q^{17} - 10 q^{18} + 8 q^{19} - 2 q^{20} - 6 q^{21} + 3 q^{22} - 9 q^{23} - 10 q^{24} + 20 q^{25} + 10 q^{26} + 10 q^{27} - 6 q^{28} - 24 q^{29} + 2 q^{30} - 7 q^{31} - 10 q^{32} - 3 q^{33} + 10 q^{34} - 22 q^{35} + 10 q^{36} - 4 q^{37} - 8 q^{38} - 10 q^{39} + 2 q^{40} - 9 q^{41} + 6 q^{42} - 11 q^{43} - 3 q^{44} - 2 q^{45} + 9 q^{46} - 18 q^{47} + 10 q^{48} + 6 q^{49} - 20 q^{50} - 10 q^{51} - 10 q^{52} - 9 q^{53} - 10 q^{54} + q^{55} + 6 q^{56} + 8 q^{57} + 24 q^{58} + 10 q^{59} - 2 q^{60} - 25 q^{61} + 7 q^{62} - 6 q^{63} + 10 q^{64} - 28 q^{65} + 3 q^{66} + 2 q^{67} - 10 q^{68} - 9 q^{69} + 22 q^{70} - 30 q^{71} - 10 q^{72} - 11 q^{73} + 4 q^{74} + 20 q^{75} + 8 q^{76} + 4 q^{77} + 10 q^{78} + 3 q^{79} - 2 q^{80} + 10 q^{81} + 9 q^{82} - q^{83} - 6 q^{84} + 2 q^{85} + 11 q^{86} - 24 q^{87} + 3 q^{88} - 14 q^{89} + 2 q^{90} - 13 q^{91} - 9 q^{92} - 7 q^{93} + 18 q^{94} - 35 q^{95} - 10 q^{96} - 10 q^{97} - 6 q^{98} - 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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 \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 1.00000 0.577350
\(4\) 1.00000 0.500000
\(5\) 0.313984 0.140418 0.0702089 0.997532i \(-0.477633\pi\)
0.0702089 + 0.997532i \(0.477633\pi\)
\(6\) −1.00000 −0.408248
\(7\) 2.10092 0.794073 0.397036 0.917803i \(-0.370039\pi\)
0.397036 + 0.917803i \(0.370039\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) −0.313984 −0.0992903
\(11\) −0.847786 −0.255617 −0.127809 0.991799i \(-0.540794\pi\)
−0.127809 + 0.991799i \(0.540794\pi\)
\(12\) 1.00000 0.288675
\(13\) −6.84610 −1.89877 −0.949384 0.314119i \(-0.898291\pi\)
−0.949384 + 0.314119i \(0.898291\pi\)
\(14\) −2.10092 −0.561494
\(15\) 0.313984 0.0810702
\(16\) 1.00000 0.250000
\(17\) −1.00000 −0.242536
\(18\) −1.00000 −0.235702
\(19\) 7.75129 1.77827 0.889134 0.457646i \(-0.151307\pi\)
0.889134 + 0.457646i \(0.151307\pi\)
\(20\) 0.313984 0.0702089
\(21\) 2.10092 0.458458
\(22\) 0.847786 0.180749
\(23\) −5.38960 −1.12381 −0.561904 0.827202i \(-0.689931\pi\)
−0.561904 + 0.827202i \(0.689931\pi\)
\(24\) −1.00000 −0.204124
\(25\) −4.90141 −0.980283
\(26\) 6.84610 1.34263
\(27\) 1.00000 0.192450
\(28\) 2.10092 0.397036
\(29\) −3.96402 −0.736099 −0.368050 0.929806i \(-0.619974\pi\)
−0.368050 + 0.929806i \(0.619974\pi\)
\(30\) −0.313984 −0.0573253
\(31\) 1.75978 0.316066 0.158033 0.987434i \(-0.449485\pi\)
0.158033 + 0.987434i \(0.449485\pi\)
\(32\) −1.00000 −0.176777
\(33\) −0.847786 −0.147581
\(34\) 1.00000 0.171499
\(35\) 0.659654 0.111502
\(36\) 1.00000 0.166667
\(37\) 3.06470 0.503833 0.251916 0.967749i \(-0.418939\pi\)
0.251916 + 0.967749i \(0.418939\pi\)
\(38\) −7.75129 −1.25743
\(39\) −6.84610 −1.09625
\(40\) −0.313984 −0.0496452
\(41\) 4.08035 0.637244 0.318622 0.947882i \(-0.396780\pi\)
0.318622 + 0.947882i \(0.396780\pi\)
\(42\) −2.10092 −0.324179
\(43\) 0.863891 0.131742 0.0658711 0.997828i \(-0.479017\pi\)
0.0658711 + 0.997828i \(0.479017\pi\)
\(44\) −0.847786 −0.127809
\(45\) 0.313984 0.0468059
\(46\) 5.38960 0.794653
\(47\) −8.06572 −1.17651 −0.588253 0.808677i \(-0.700184\pi\)
−0.588253 + 0.808677i \(0.700184\pi\)
\(48\) 1.00000 0.144338
\(49\) −2.58614 −0.369448
\(50\) 4.90141 0.693165
\(51\) −1.00000 −0.140028
\(52\) −6.84610 −0.949384
\(53\) −10.2118 −1.40269 −0.701347 0.712820i \(-0.747418\pi\)
−0.701347 + 0.712820i \(0.747418\pi\)
\(54\) −1.00000 −0.136083
\(55\) −0.266191 −0.0358932
\(56\) −2.10092 −0.280747
\(57\) 7.75129 1.02668
\(58\) 3.96402 0.520501
\(59\) 1.00000 0.130189
\(60\) 0.313984 0.0405351
\(61\) 7.82924 1.00243 0.501216 0.865322i \(-0.332886\pi\)
0.501216 + 0.865322i \(0.332886\pi\)
\(62\) −1.75978 −0.223492
\(63\) 2.10092 0.264691
\(64\) 1.00000 0.125000
\(65\) −2.14956 −0.266621
\(66\) 0.847786 0.104355
\(67\) −6.38895 −0.780535 −0.390268 0.920702i \(-0.627617\pi\)
−0.390268 + 0.920702i \(0.627617\pi\)
\(68\) −1.00000 −0.121268
\(69\) −5.38960 −0.648831
\(70\) −0.659654 −0.0788437
\(71\) 11.4183 1.35510 0.677550 0.735477i \(-0.263042\pi\)
0.677550 + 0.735477i \(0.263042\pi\)
\(72\) −1.00000 −0.117851
\(73\) −9.05018 −1.05924 −0.529622 0.848234i \(-0.677666\pi\)
−0.529622 + 0.848234i \(0.677666\pi\)
\(74\) −3.06470 −0.356264
\(75\) −4.90141 −0.565967
\(76\) 7.75129 0.889134
\(77\) −1.78113 −0.202979
\(78\) 6.84610 0.775168
\(79\) 7.33532 0.825288 0.412644 0.910892i \(-0.364605\pi\)
0.412644 + 0.910892i \(0.364605\pi\)
\(80\) 0.313984 0.0351044
\(81\) 1.00000 0.111111
\(82\) −4.08035 −0.450599
\(83\) −0.416311 −0.0456960 −0.0228480 0.999739i \(-0.507273\pi\)
−0.0228480 + 0.999739i \(0.507273\pi\)
\(84\) 2.10092 0.229229
\(85\) −0.313984 −0.0340563
\(86\) −0.863891 −0.0931558
\(87\) −3.96402 −0.424987
\(88\) 0.847786 0.0903743
\(89\) −13.6489 −1.44678 −0.723391 0.690438i \(-0.757418\pi\)
−0.723391 + 0.690438i \(0.757418\pi\)
\(90\) −0.313984 −0.0330968
\(91\) −14.3831 −1.50776
\(92\) −5.38960 −0.561904
\(93\) 1.75978 0.182481
\(94\) 8.06572 0.831915
\(95\) 2.43378 0.249700
\(96\) −1.00000 −0.102062
\(97\) −2.22173 −0.225583 −0.112791 0.993619i \(-0.535979\pi\)
−0.112791 + 0.993619i \(0.535979\pi\)
\(98\) 2.58614 0.261239
\(99\) −0.847786 −0.0852057
\(100\) −4.90141 −0.490141
\(101\) −4.27600 −0.425478 −0.212739 0.977109i \(-0.568238\pi\)
−0.212739 + 0.977109i \(0.568238\pi\)
\(102\) 1.00000 0.0990148
\(103\) −15.1099 −1.48883 −0.744413 0.667720i \(-0.767270\pi\)
−0.744413 + 0.667720i \(0.767270\pi\)
\(104\) 6.84610 0.671316
\(105\) 0.659654 0.0643757
\(106\) 10.2118 0.991854
\(107\) 14.9644 1.44666 0.723332 0.690500i \(-0.242609\pi\)
0.723332 + 0.690500i \(0.242609\pi\)
\(108\) 1.00000 0.0962250
\(109\) −12.5270 −1.19987 −0.599936 0.800048i \(-0.704807\pi\)
−0.599936 + 0.800048i \(0.704807\pi\)
\(110\) 0.266191 0.0253803
\(111\) 3.06470 0.290888
\(112\) 2.10092 0.198518
\(113\) 6.13747 0.577365 0.288682 0.957425i \(-0.406783\pi\)
0.288682 + 0.957425i \(0.406783\pi\)
\(114\) −7.75129 −0.725975
\(115\) −1.69225 −0.157803
\(116\) −3.96402 −0.368050
\(117\) −6.84610 −0.632922
\(118\) −1.00000 −0.0920575
\(119\) −2.10092 −0.192591
\(120\) −0.313984 −0.0286626
\(121\) −10.2813 −0.934660
\(122\) −7.82924 −0.708826
\(123\) 4.08035 0.367913
\(124\) 1.75978 0.158033
\(125\) −3.10888 −0.278067
\(126\) −2.10092 −0.187165
\(127\) −17.4017 −1.54415 −0.772075 0.635532i \(-0.780781\pi\)
−0.772075 + 0.635532i \(0.780781\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0.863891 0.0760614
\(130\) 2.14956 0.188529
\(131\) −19.2845 −1.68490 −0.842448 0.538778i \(-0.818886\pi\)
−0.842448 + 0.538778i \(0.818886\pi\)
\(132\) −0.847786 −0.0737903
\(133\) 16.2848 1.41207
\(134\) 6.38895 0.551922
\(135\) 0.313984 0.0270234
\(136\) 1.00000 0.0857493
\(137\) −12.4313 −1.06208 −0.531039 0.847347i \(-0.678198\pi\)
−0.531039 + 0.847347i \(0.678198\pi\)
\(138\) 5.38960 0.458793
\(139\) 20.6438 1.75098 0.875492 0.483232i \(-0.160537\pi\)
0.875492 + 0.483232i \(0.160537\pi\)
\(140\) 0.659654 0.0557509
\(141\) −8.06572 −0.679256
\(142\) −11.4183 −0.958200
\(143\) 5.80403 0.485357
\(144\) 1.00000 0.0833333
\(145\) −1.24464 −0.103361
\(146\) 9.05018 0.748998
\(147\) −2.58614 −0.213301
\(148\) 3.06470 0.251916
\(149\) −21.1802 −1.73515 −0.867574 0.497308i \(-0.834322\pi\)
−0.867574 + 0.497308i \(0.834322\pi\)
\(150\) 4.90141 0.400199
\(151\) 19.1223 1.55615 0.778076 0.628170i \(-0.216196\pi\)
0.778076 + 0.628170i \(0.216196\pi\)
\(152\) −7.75129 −0.628713
\(153\) −1.00000 −0.0808452
\(154\) 1.78113 0.143527
\(155\) 0.552542 0.0443812
\(156\) −6.84610 −0.548127
\(157\) −16.5189 −1.31835 −0.659176 0.751989i \(-0.729095\pi\)
−0.659176 + 0.751989i \(0.729095\pi\)
\(158\) −7.33532 −0.583567
\(159\) −10.2118 −0.809846
\(160\) −0.313984 −0.0248226
\(161\) −11.3231 −0.892386
\(162\) −1.00000 −0.0785674
\(163\) −3.73417 −0.292482 −0.146241 0.989249i \(-0.546718\pi\)
−0.146241 + 0.989249i \(0.546718\pi\)
\(164\) 4.08035 0.318622
\(165\) −0.266191 −0.0207229
\(166\) 0.416311 0.0323120
\(167\) −6.56448 −0.507974 −0.253987 0.967208i \(-0.581742\pi\)
−0.253987 + 0.967208i \(0.581742\pi\)
\(168\) −2.10092 −0.162089
\(169\) 33.8691 2.60532
\(170\) 0.313984 0.0240814
\(171\) 7.75129 0.592756
\(172\) 0.863891 0.0658711
\(173\) 0.502200 0.0381815 0.0190908 0.999818i \(-0.493923\pi\)
0.0190908 + 0.999818i \(0.493923\pi\)
\(174\) 3.96402 0.300511
\(175\) −10.2975 −0.778416
\(176\) −0.847786 −0.0639043
\(177\) 1.00000 0.0751646
\(178\) 13.6489 1.02303
\(179\) −9.83124 −0.734822 −0.367411 0.930059i \(-0.619756\pi\)
−0.367411 + 0.930059i \(0.619756\pi\)
\(180\) 0.313984 0.0234030
\(181\) −5.83704 −0.433864 −0.216932 0.976187i \(-0.569605\pi\)
−0.216932 + 0.976187i \(0.569605\pi\)
\(182\) 14.3831 1.06615
\(183\) 7.82924 0.578754
\(184\) 5.38960 0.397326
\(185\) 0.962264 0.0707471
\(186\) −1.75978 −0.129033
\(187\) 0.847786 0.0619962
\(188\) −8.06572 −0.588253
\(189\) 2.10092 0.152819
\(190\) −2.43378 −0.176565
\(191\) 15.5630 1.12610 0.563050 0.826423i \(-0.309628\pi\)
0.563050 + 0.826423i \(0.309628\pi\)
\(192\) 1.00000 0.0721688
\(193\) −1.10959 −0.0798701 −0.0399350 0.999202i \(-0.512715\pi\)
−0.0399350 + 0.999202i \(0.512715\pi\)
\(194\) 2.22173 0.159511
\(195\) −2.14956 −0.153933
\(196\) −2.58614 −0.184724
\(197\) −21.1479 −1.50672 −0.753361 0.657607i \(-0.771569\pi\)
−0.753361 + 0.657607i \(0.771569\pi\)
\(198\) 0.847786 0.0602495
\(199\) 7.69680 0.545612 0.272806 0.962069i \(-0.412048\pi\)
0.272806 + 0.962069i \(0.412048\pi\)
\(200\) 4.90141 0.346582
\(201\) −6.38895 −0.450642
\(202\) 4.27600 0.300858
\(203\) −8.32808 −0.584516
\(204\) −1.00000 −0.0700140
\(205\) 1.28116 0.0894803
\(206\) 15.1099 1.05276
\(207\) −5.38960 −0.374603
\(208\) −6.84610 −0.474692
\(209\) −6.57144 −0.454556
\(210\) −0.659654 −0.0455205
\(211\) 26.6228 1.83279 0.916394 0.400278i \(-0.131087\pi\)
0.916394 + 0.400278i \(0.131087\pi\)
\(212\) −10.2118 −0.701347
\(213\) 11.4183 0.782367
\(214\) −14.9644 −1.02295
\(215\) 0.271248 0.0184989
\(216\) −1.00000 −0.0680414
\(217\) 3.69715 0.250979
\(218\) 12.5270 0.848438
\(219\) −9.05018 −0.611555
\(220\) −0.266191 −0.0179466
\(221\) 6.84610 0.460519
\(222\) −3.06470 −0.205689
\(223\) 20.4920 1.37225 0.686124 0.727485i \(-0.259311\pi\)
0.686124 + 0.727485i \(0.259311\pi\)
\(224\) −2.10092 −0.140374
\(225\) −4.90141 −0.326761
\(226\) −6.13747 −0.408259
\(227\) 8.46757 0.562012 0.281006 0.959706i \(-0.409332\pi\)
0.281006 + 0.959706i \(0.409332\pi\)
\(228\) 7.75129 0.513342
\(229\) 11.5494 0.763205 0.381603 0.924326i \(-0.375372\pi\)
0.381603 + 0.924326i \(0.375372\pi\)
\(230\) 1.69225 0.111583
\(231\) −1.78113 −0.117190
\(232\) 3.96402 0.260250
\(233\) 0.514865 0.0337300 0.0168650 0.999858i \(-0.494631\pi\)
0.0168650 + 0.999858i \(0.494631\pi\)
\(234\) 6.84610 0.447544
\(235\) −2.53250 −0.165202
\(236\) 1.00000 0.0650945
\(237\) 7.33532 0.476480
\(238\) 2.10092 0.136182
\(239\) −28.4503 −1.84030 −0.920149 0.391569i \(-0.871933\pi\)
−0.920149 + 0.391569i \(0.871933\pi\)
\(240\) 0.313984 0.0202676
\(241\) 7.96535 0.513093 0.256547 0.966532i \(-0.417415\pi\)
0.256547 + 0.966532i \(0.417415\pi\)
\(242\) 10.2813 0.660904
\(243\) 1.00000 0.0641500
\(244\) 7.82924 0.501216
\(245\) −0.812005 −0.0518771
\(246\) −4.08035 −0.260154
\(247\) −53.0662 −3.37652
\(248\) −1.75978 −0.111746
\(249\) −0.416311 −0.0263826
\(250\) 3.10888 0.196623
\(251\) 23.3659 1.47484 0.737422 0.675432i \(-0.236043\pi\)
0.737422 + 0.675432i \(0.236043\pi\)
\(252\) 2.10092 0.132345
\(253\) 4.56922 0.287265
\(254\) 17.4017 1.09188
\(255\) −0.313984 −0.0196624
\(256\) 1.00000 0.0625000
\(257\) −17.2084 −1.07343 −0.536716 0.843763i \(-0.680335\pi\)
−0.536716 + 0.843763i \(0.680335\pi\)
\(258\) −0.863891 −0.0537835
\(259\) 6.43868 0.400080
\(260\) −2.14956 −0.133310
\(261\) −3.96402 −0.245366
\(262\) 19.2845 1.19140
\(263\) 22.8845 1.41112 0.705561 0.708649i \(-0.250695\pi\)
0.705561 + 0.708649i \(0.250695\pi\)
\(264\) 0.847786 0.0521776
\(265\) −3.20633 −0.196963
\(266\) −16.2848 −0.998488
\(267\) −13.6489 −0.835300
\(268\) −6.38895 −0.390268
\(269\) −14.5179 −0.885171 −0.442586 0.896726i \(-0.645939\pi\)
−0.442586 + 0.896726i \(0.645939\pi\)
\(270\) −0.313984 −0.0191084
\(271\) 20.9878 1.27492 0.637458 0.770485i \(-0.279986\pi\)
0.637458 + 0.770485i \(0.279986\pi\)
\(272\) −1.00000 −0.0606339
\(273\) −14.3831 −0.870505
\(274\) 12.4313 0.751003
\(275\) 4.15535 0.250577
\(276\) −5.38960 −0.324416
\(277\) −21.6987 −1.30375 −0.651873 0.758328i \(-0.726017\pi\)
−0.651873 + 0.758328i \(0.726017\pi\)
\(278\) −20.6438 −1.23813
\(279\) 1.75978 0.105355
\(280\) −0.659654 −0.0394219
\(281\) −7.10977 −0.424133 −0.212067 0.977255i \(-0.568019\pi\)
−0.212067 + 0.977255i \(0.568019\pi\)
\(282\) 8.06572 0.480306
\(283\) 16.3119 0.969640 0.484820 0.874614i \(-0.338885\pi\)
0.484820 + 0.874614i \(0.338885\pi\)
\(284\) 11.4183 0.677550
\(285\) 2.43378 0.144165
\(286\) −5.80403 −0.343199
\(287\) 8.57249 0.506018
\(288\) −1.00000 −0.0589256
\(289\) 1.00000 0.0588235
\(290\) 1.24464 0.0730875
\(291\) −2.22173 −0.130240
\(292\) −9.05018 −0.529622
\(293\) −9.86065 −0.576065 −0.288033 0.957621i \(-0.593001\pi\)
−0.288033 + 0.957621i \(0.593001\pi\)
\(294\) 2.58614 0.150827
\(295\) 0.313984 0.0182808
\(296\) −3.06470 −0.178132
\(297\) −0.847786 −0.0491935
\(298\) 21.1802 1.22693
\(299\) 36.8977 2.13385
\(300\) −4.90141 −0.282983
\(301\) 1.81497 0.104613
\(302\) −19.1223 −1.10037
\(303\) −4.27600 −0.245650
\(304\) 7.75129 0.444567
\(305\) 2.45825 0.140759
\(306\) 1.00000 0.0571662
\(307\) −26.5184 −1.51349 −0.756744 0.653711i \(-0.773211\pi\)
−0.756744 + 0.653711i \(0.773211\pi\)
\(308\) −1.78113 −0.101489
\(309\) −15.1099 −0.859574
\(310\) −0.552542 −0.0313823
\(311\) 13.4756 0.764130 0.382065 0.924136i \(-0.375213\pi\)
0.382065 + 0.924136i \(0.375213\pi\)
\(312\) 6.84610 0.387584
\(313\) −9.63155 −0.544408 −0.272204 0.962240i \(-0.587752\pi\)
−0.272204 + 0.962240i \(0.587752\pi\)
\(314\) 16.5189 0.932216
\(315\) 0.659654 0.0371673
\(316\) 7.33532 0.412644
\(317\) −19.5266 −1.09672 −0.548361 0.836242i \(-0.684748\pi\)
−0.548361 + 0.836242i \(0.684748\pi\)
\(318\) 10.2118 0.572647
\(319\) 3.36064 0.188160
\(320\) 0.313984 0.0175522
\(321\) 14.9644 0.835232
\(322\) 11.3231 0.631012
\(323\) −7.75129 −0.431294
\(324\) 1.00000 0.0555556
\(325\) 33.5556 1.86133
\(326\) 3.73417 0.206816
\(327\) −12.5270 −0.692747
\(328\) −4.08035 −0.225300
\(329\) −16.9454 −0.934231
\(330\) 0.266191 0.0146533
\(331\) −18.6116 −1.02299 −0.511494 0.859287i \(-0.670908\pi\)
−0.511494 + 0.859287i \(0.670908\pi\)
\(332\) −0.416311 −0.0228480
\(333\) 3.06470 0.167944
\(334\) 6.56448 0.359192
\(335\) −2.00603 −0.109601
\(336\) 2.10092 0.114615
\(337\) 12.8151 0.698084 0.349042 0.937107i \(-0.386507\pi\)
0.349042 + 0.937107i \(0.386507\pi\)
\(338\) −33.8691 −1.84224
\(339\) 6.13747 0.333342
\(340\) −0.313984 −0.0170282
\(341\) −1.49192 −0.0807918
\(342\) −7.75129 −0.419142
\(343\) −20.1397 −1.08744
\(344\) −0.863891 −0.0465779
\(345\) −1.69225 −0.0911074
\(346\) −0.502200 −0.0269984
\(347\) −13.0323 −0.699610 −0.349805 0.936823i \(-0.613752\pi\)
−0.349805 + 0.936823i \(0.613752\pi\)
\(348\) −3.96402 −0.212494
\(349\) −3.18606 −0.170546 −0.0852729 0.996358i \(-0.527176\pi\)
−0.0852729 + 0.996358i \(0.527176\pi\)
\(350\) 10.2975 0.550423
\(351\) −6.84610 −0.365418
\(352\) 0.847786 0.0451871
\(353\) 12.9841 0.691075 0.345538 0.938405i \(-0.387697\pi\)
0.345538 + 0.938405i \(0.387697\pi\)
\(354\) −1.00000 −0.0531494
\(355\) 3.58515 0.190280
\(356\) −13.6489 −0.723391
\(357\) −2.10092 −0.111192
\(358\) 9.83124 0.519597
\(359\) 10.0009 0.527827 0.263913 0.964546i \(-0.414987\pi\)
0.263913 + 0.964546i \(0.414987\pi\)
\(360\) −0.313984 −0.0165484
\(361\) 41.0826 2.16224
\(362\) 5.83704 0.306788
\(363\) −10.2813 −0.539626
\(364\) −14.3831 −0.753880
\(365\) −2.84161 −0.148737
\(366\) −7.82924 −0.409241
\(367\) 19.6011 1.02317 0.511583 0.859234i \(-0.329059\pi\)
0.511583 + 0.859234i \(0.329059\pi\)
\(368\) −5.38960 −0.280952
\(369\) 4.08035 0.212415
\(370\) −0.962264 −0.0500257
\(371\) −21.4541 −1.11384
\(372\) 1.75978 0.0912403
\(373\) 38.5365 1.99534 0.997671 0.0682033i \(-0.0217266\pi\)
0.997671 + 0.0682033i \(0.0217266\pi\)
\(374\) −0.847786 −0.0438380
\(375\) −3.10888 −0.160542
\(376\) 8.06572 0.415958
\(377\) 27.1381 1.39768
\(378\) −2.10092 −0.108060
\(379\) −20.4575 −1.05083 −0.525415 0.850846i \(-0.676090\pi\)
−0.525415 + 0.850846i \(0.676090\pi\)
\(380\) 2.43378 0.124850
\(381\) −17.4017 −0.891515
\(382\) −15.5630 −0.796274
\(383\) −30.2752 −1.54699 −0.773494 0.633804i \(-0.781493\pi\)
−0.773494 + 0.633804i \(0.781493\pi\)
\(384\) −1.00000 −0.0510310
\(385\) −0.559245 −0.0285018
\(386\) 1.10959 0.0564767
\(387\) 0.863891 0.0439141
\(388\) −2.22173 −0.112791
\(389\) −22.4006 −1.13575 −0.567877 0.823113i \(-0.692235\pi\)
−0.567877 + 0.823113i \(0.692235\pi\)
\(390\) 2.14956 0.108847
\(391\) 5.38960 0.272564
\(392\) 2.58614 0.130620
\(393\) −19.2845 −0.972775
\(394\) 21.1479 1.06541
\(395\) 2.30317 0.115885
\(396\) −0.847786 −0.0426028
\(397\) −19.3679 −0.972047 −0.486024 0.873946i \(-0.661553\pi\)
−0.486024 + 0.873946i \(0.661553\pi\)
\(398\) −7.69680 −0.385806
\(399\) 16.2848 0.815262
\(400\) −4.90141 −0.245071
\(401\) 14.5880 0.728490 0.364245 0.931303i \(-0.381327\pi\)
0.364245 + 0.931303i \(0.381327\pi\)
\(402\) 6.38895 0.318652
\(403\) −12.0476 −0.600135
\(404\) −4.27600 −0.212739
\(405\) 0.313984 0.0156020
\(406\) 8.32808 0.413316
\(407\) −2.59821 −0.128788
\(408\) 1.00000 0.0495074
\(409\) −15.7198 −0.777292 −0.388646 0.921387i \(-0.627057\pi\)
−0.388646 + 0.921387i \(0.627057\pi\)
\(410\) −1.28116 −0.0632721
\(411\) −12.4313 −0.613191
\(412\) −15.1099 −0.744413
\(413\) 2.10092 0.103379
\(414\) 5.38960 0.264884
\(415\) −0.130715 −0.00641654
\(416\) 6.84610 0.335658
\(417\) 20.6438 1.01093
\(418\) 6.57144 0.321419
\(419\) 10.3992 0.508033 0.254016 0.967200i \(-0.418248\pi\)
0.254016 + 0.967200i \(0.418248\pi\)
\(420\) 0.659654 0.0321878
\(421\) 1.46278 0.0712914 0.0356457 0.999364i \(-0.488651\pi\)
0.0356457 + 0.999364i \(0.488651\pi\)
\(422\) −26.6228 −1.29598
\(423\) −8.06572 −0.392169
\(424\) 10.2118 0.495927
\(425\) 4.90141 0.237754
\(426\) −11.4183 −0.553217
\(427\) 16.4486 0.796004
\(428\) 14.9644 0.723332
\(429\) 5.80403 0.280221
\(430\) −0.271248 −0.0130807
\(431\) −8.94044 −0.430646 −0.215323 0.976543i \(-0.569080\pi\)
−0.215323 + 0.976543i \(0.569080\pi\)
\(432\) 1.00000 0.0481125
\(433\) −1.52494 −0.0732839 −0.0366419 0.999328i \(-0.511666\pi\)
−0.0366419 + 0.999328i \(0.511666\pi\)
\(434\) −3.69715 −0.177469
\(435\) −1.24464 −0.0596757
\(436\) −12.5270 −0.599936
\(437\) −41.7764 −1.99843
\(438\) 9.05018 0.432434
\(439\) −33.9597 −1.62081 −0.810403 0.585873i \(-0.800752\pi\)
−0.810403 + 0.585873i \(0.800752\pi\)
\(440\) 0.266191 0.0126901
\(441\) −2.58614 −0.123149
\(442\) −6.84610 −0.325636
\(443\) 28.1430 1.33712 0.668558 0.743660i \(-0.266912\pi\)
0.668558 + 0.743660i \(0.266912\pi\)
\(444\) 3.06470 0.145444
\(445\) −4.28554 −0.203154
\(446\) −20.4920 −0.970326
\(447\) −21.1802 −1.00179
\(448\) 2.10092 0.0992591
\(449\) −23.7418 −1.12045 −0.560223 0.828342i \(-0.689285\pi\)
−0.560223 + 0.828342i \(0.689285\pi\)
\(450\) 4.90141 0.231055
\(451\) −3.45926 −0.162890
\(452\) 6.13747 0.288682
\(453\) 19.1223 0.898445
\(454\) −8.46757 −0.397403
\(455\) −4.51606 −0.211716
\(456\) −7.75129 −0.362988
\(457\) 28.6991 1.34249 0.671244 0.741236i \(-0.265760\pi\)
0.671244 + 0.741236i \(0.265760\pi\)
\(458\) −11.5494 −0.539668
\(459\) −1.00000 −0.0466760
\(460\) −1.69225 −0.0789013
\(461\) −17.6993 −0.824338 −0.412169 0.911107i \(-0.635229\pi\)
−0.412169 + 0.911107i \(0.635229\pi\)
\(462\) 1.78113 0.0828656
\(463\) −11.4644 −0.532794 −0.266397 0.963863i \(-0.585833\pi\)
−0.266397 + 0.963863i \(0.585833\pi\)
\(464\) −3.96402 −0.184025
\(465\) 0.552542 0.0256235
\(466\) −0.514865 −0.0238507
\(467\) −9.50755 −0.439957 −0.219978 0.975505i \(-0.570599\pi\)
−0.219978 + 0.975505i \(0.570599\pi\)
\(468\) −6.84610 −0.316461
\(469\) −13.4227 −0.619802
\(470\) 2.53250 0.116816
\(471\) −16.5189 −0.761151
\(472\) −1.00000 −0.0460287
\(473\) −0.732395 −0.0336755
\(474\) −7.33532 −0.336922
\(475\) −37.9923 −1.74321
\(476\) −2.10092 −0.0962955
\(477\) −10.2118 −0.467565
\(478\) 28.4503 1.30129
\(479\) 7.89050 0.360526 0.180263 0.983618i \(-0.442305\pi\)
0.180263 + 0.983618i \(0.442305\pi\)
\(480\) −0.313984 −0.0143313
\(481\) −20.9812 −0.956661
\(482\) −7.96535 −0.362812
\(483\) −11.3231 −0.515219
\(484\) −10.2813 −0.467330
\(485\) −0.697588 −0.0316758
\(486\) −1.00000 −0.0453609
\(487\) 29.3249 1.32884 0.664419 0.747360i \(-0.268679\pi\)
0.664419 + 0.747360i \(0.268679\pi\)
\(488\) −7.82924 −0.354413
\(489\) −3.73417 −0.168865
\(490\) 0.812005 0.0366827
\(491\) 0.731272 0.0330018 0.0165009 0.999864i \(-0.494747\pi\)
0.0165009 + 0.999864i \(0.494747\pi\)
\(492\) 4.08035 0.183956
\(493\) 3.96402 0.178530
\(494\) 53.0662 2.38756
\(495\) −0.266191 −0.0119644
\(496\) 1.75978 0.0790164
\(497\) 23.9889 1.07605
\(498\) 0.416311 0.0186553
\(499\) 39.9939 1.79037 0.895186 0.445693i \(-0.147043\pi\)
0.895186 + 0.445693i \(0.147043\pi\)
\(500\) −3.10888 −0.139033
\(501\) −6.56448 −0.293279
\(502\) −23.3659 −1.04287
\(503\) 32.2843 1.43948 0.719742 0.694242i \(-0.244260\pi\)
0.719742 + 0.694242i \(0.244260\pi\)
\(504\) −2.10092 −0.0935824
\(505\) −1.34259 −0.0597446
\(506\) −4.56922 −0.203127
\(507\) 33.8691 1.50418
\(508\) −17.4017 −0.772075
\(509\) −2.70844 −0.120050 −0.0600248 0.998197i \(-0.519118\pi\)
−0.0600248 + 0.998197i \(0.519118\pi\)
\(510\) 0.313984 0.0139034
\(511\) −19.0137 −0.841116
\(512\) −1.00000 −0.0441942
\(513\) 7.75129 0.342228
\(514\) 17.2084 0.759031
\(515\) −4.74427 −0.209057
\(516\) 0.863891 0.0380307
\(517\) 6.83800 0.300735
\(518\) −6.43868 −0.282899
\(519\) 0.502200 0.0220441
\(520\) 2.14956 0.0942646
\(521\) −9.80592 −0.429605 −0.214802 0.976658i \(-0.568911\pi\)
−0.214802 + 0.976658i \(0.568911\pi\)
\(522\) 3.96402 0.173500
\(523\) −19.8161 −0.866499 −0.433249 0.901274i \(-0.642633\pi\)
−0.433249 + 0.901274i \(0.642633\pi\)
\(524\) −19.2845 −0.842448
\(525\) −10.2975 −0.449419
\(526\) −22.8845 −0.997814
\(527\) −1.75978 −0.0766572
\(528\) −0.847786 −0.0368951
\(529\) 6.04777 0.262946
\(530\) 3.20633 0.139274
\(531\) 1.00000 0.0433963
\(532\) 16.2848 0.706037
\(533\) −27.9345 −1.20998
\(534\) 13.6489 0.590646
\(535\) 4.69858 0.203137
\(536\) 6.38895 0.275961
\(537\) −9.83124 −0.424250
\(538\) 14.5179 0.625911
\(539\) 2.19249 0.0944373
\(540\) 0.313984 0.0135117
\(541\) 4.12466 0.177333 0.0886664 0.996061i \(-0.471739\pi\)
0.0886664 + 0.996061i \(0.471739\pi\)
\(542\) −20.9878 −0.901502
\(543\) −5.83704 −0.250492
\(544\) 1.00000 0.0428746
\(545\) −3.93329 −0.168483
\(546\) 14.3831 0.615540
\(547\) −2.56799 −0.109799 −0.0548997 0.998492i \(-0.517484\pi\)
−0.0548997 + 0.998492i \(0.517484\pi\)
\(548\) −12.4313 −0.531039
\(549\) 7.82924 0.334144
\(550\) −4.15535 −0.177185
\(551\) −30.7263 −1.30898
\(552\) 5.38960 0.229397
\(553\) 15.4109 0.655339
\(554\) 21.6987 0.921888
\(555\) 0.962264 0.0408458
\(556\) 20.6438 0.875492
\(557\) 3.15332 0.133610 0.0668052 0.997766i \(-0.478719\pi\)
0.0668052 + 0.997766i \(0.478719\pi\)
\(558\) −1.75978 −0.0744974
\(559\) −5.91429 −0.250148
\(560\) 0.659654 0.0278755
\(561\) 0.847786 0.0357935
\(562\) 7.10977 0.299907
\(563\) −15.6236 −0.658457 −0.329229 0.944250i \(-0.606789\pi\)
−0.329229 + 0.944250i \(0.606789\pi\)
\(564\) −8.06572 −0.339628
\(565\) 1.92707 0.0810722
\(566\) −16.3119 −0.685639
\(567\) 2.10092 0.0882303
\(568\) −11.4183 −0.479100
\(569\) −6.69051 −0.280481 −0.140240 0.990117i \(-0.544788\pi\)
−0.140240 + 0.990117i \(0.544788\pi\)
\(570\) −2.43378 −0.101940
\(571\) −44.1225 −1.84647 −0.923234 0.384237i \(-0.874465\pi\)
−0.923234 + 0.384237i \(0.874465\pi\)
\(572\) 5.80403 0.242679
\(573\) 15.5630 0.650155
\(574\) −8.57249 −0.357809
\(575\) 26.4167 1.10165
\(576\) 1.00000 0.0416667
\(577\) 20.4682 0.852103 0.426052 0.904699i \(-0.359904\pi\)
0.426052 + 0.904699i \(0.359904\pi\)
\(578\) −1.00000 −0.0415945
\(579\) −1.10959 −0.0461130
\(580\) −1.24464 −0.0516807
\(581\) −0.874635 −0.0362860
\(582\) 2.22173 0.0920938
\(583\) 8.65739 0.358552
\(584\) 9.05018 0.374499
\(585\) −2.14956 −0.0888735
\(586\) 9.86065 0.407340
\(587\) −29.1919 −1.20488 −0.602440 0.798164i \(-0.705805\pi\)
−0.602440 + 0.798164i \(0.705805\pi\)
\(588\) −2.58614 −0.106651
\(589\) 13.6406 0.562050
\(590\) −0.313984 −0.0129265
\(591\) −21.1479 −0.869907
\(592\) 3.06470 0.125958
\(593\) −23.0992 −0.948568 −0.474284 0.880372i \(-0.657293\pi\)
−0.474284 + 0.880372i \(0.657293\pi\)
\(594\) 0.847786 0.0347851
\(595\) −0.659654 −0.0270432
\(596\) −21.1802 −0.867574
\(597\) 7.69680 0.315009
\(598\) −36.8977 −1.50886
\(599\) −38.8922 −1.58909 −0.794545 0.607205i \(-0.792291\pi\)
−0.794545 + 0.607205i \(0.792291\pi\)
\(600\) 4.90141 0.200099
\(601\) 25.1438 1.02564 0.512818 0.858498i \(-0.328602\pi\)
0.512818 + 0.858498i \(0.328602\pi\)
\(602\) −1.81497 −0.0739725
\(603\) −6.38895 −0.260178
\(604\) 19.1223 0.778076
\(605\) −3.22815 −0.131243
\(606\) 4.27600 0.173701
\(607\) −27.7869 −1.12784 −0.563918 0.825831i \(-0.690707\pi\)
−0.563918 + 0.825831i \(0.690707\pi\)
\(608\) −7.75129 −0.314356
\(609\) −8.32808 −0.337471
\(610\) −2.45825 −0.0995318
\(611\) 55.2187 2.23391
\(612\) −1.00000 −0.0404226
\(613\) 6.59027 0.266178 0.133089 0.991104i \(-0.457510\pi\)
0.133089 + 0.991104i \(0.457510\pi\)
\(614\) 26.5184 1.07020
\(615\) 1.28116 0.0516615
\(616\) 1.78113 0.0717637
\(617\) 37.1523 1.49570 0.747848 0.663870i \(-0.231087\pi\)
0.747848 + 0.663870i \(0.231087\pi\)
\(618\) 15.1099 0.607810
\(619\) −7.71680 −0.310164 −0.155082 0.987902i \(-0.549564\pi\)
−0.155082 + 0.987902i \(0.549564\pi\)
\(620\) 0.552542 0.0221906
\(621\) −5.38960 −0.216277
\(622\) −13.4756 −0.540321
\(623\) −28.6753 −1.14885
\(624\) −6.84610 −0.274063
\(625\) 23.5309 0.941237
\(626\) 9.63155 0.384954
\(627\) −6.57144 −0.262438
\(628\) −16.5189 −0.659176
\(629\) −3.06470 −0.122197
\(630\) −0.659654 −0.0262812
\(631\) −30.5736 −1.21712 −0.608559 0.793509i \(-0.708252\pi\)
−0.608559 + 0.793509i \(0.708252\pi\)
\(632\) −7.33532 −0.291783
\(633\) 26.6228 1.05816
\(634\) 19.5266 0.775500
\(635\) −5.46384 −0.216826
\(636\) −10.2118 −0.404923
\(637\) 17.7050 0.701497
\(638\) −3.36064 −0.133049
\(639\) 11.4183 0.451700
\(640\) −0.313984 −0.0124113
\(641\) −15.0331 −0.593773 −0.296887 0.954913i \(-0.595948\pi\)
−0.296887 + 0.954913i \(0.595948\pi\)
\(642\) −14.9644 −0.590598
\(643\) 36.2393 1.42914 0.714569 0.699565i \(-0.246623\pi\)
0.714569 + 0.699565i \(0.246623\pi\)
\(644\) −11.3231 −0.446193
\(645\) 0.271248 0.0106804
\(646\) 7.75129 0.304971
\(647\) −27.5268 −1.08219 −0.541096 0.840961i \(-0.681990\pi\)
−0.541096 + 0.840961i \(0.681990\pi\)
\(648\) −1.00000 −0.0392837
\(649\) −0.847786 −0.0332785
\(650\) −33.5556 −1.31616
\(651\) 3.69715 0.144903
\(652\) −3.73417 −0.146241
\(653\) 2.88900 0.113055 0.0565277 0.998401i \(-0.481997\pi\)
0.0565277 + 0.998401i \(0.481997\pi\)
\(654\) 12.5270 0.489846
\(655\) −6.05502 −0.236589
\(656\) 4.08035 0.159311
\(657\) −9.05018 −0.353081
\(658\) 16.9454 0.660601
\(659\) 12.2383 0.476737 0.238368 0.971175i \(-0.423387\pi\)
0.238368 + 0.971175i \(0.423387\pi\)
\(660\) −0.266191 −0.0103615
\(661\) 36.3610 1.41428 0.707140 0.707074i \(-0.249985\pi\)
0.707140 + 0.707074i \(0.249985\pi\)
\(662\) 18.6116 0.723362
\(663\) 6.84610 0.265881
\(664\) 0.416311 0.0161560
\(665\) 5.11317 0.198280
\(666\) −3.06470 −0.118755
\(667\) 21.3645 0.827235
\(668\) −6.56448 −0.253987
\(669\) 20.4920 0.792268
\(670\) 2.00603 0.0774996
\(671\) −6.63752 −0.256239
\(672\) −2.10092 −0.0810447
\(673\) 9.15795 0.353013 0.176506 0.984299i \(-0.443520\pi\)
0.176506 + 0.984299i \(0.443520\pi\)
\(674\) −12.8151 −0.493620
\(675\) −4.90141 −0.188656
\(676\) 33.8691 1.30266
\(677\) 45.3330 1.74229 0.871145 0.491025i \(-0.163378\pi\)
0.871145 + 0.491025i \(0.163378\pi\)
\(678\) −6.13747 −0.235708
\(679\) −4.66768 −0.179129
\(680\) 0.313984 0.0120407
\(681\) 8.46757 0.324478
\(682\) 1.49192 0.0571284
\(683\) 33.9416 1.29874 0.649369 0.760474i \(-0.275033\pi\)
0.649369 + 0.760474i \(0.275033\pi\)
\(684\) 7.75129 0.296378
\(685\) −3.90323 −0.149135
\(686\) 20.1397 0.768937
\(687\) 11.5494 0.440637
\(688\) 0.863891 0.0329355
\(689\) 69.9108 2.66339
\(690\) 1.69225 0.0644227
\(691\) −12.8355 −0.488285 −0.244142 0.969739i \(-0.578506\pi\)
−0.244142 + 0.969739i \(0.578506\pi\)
\(692\) 0.502200 0.0190908
\(693\) −1.78113 −0.0676595
\(694\) 13.0323 0.494699
\(695\) 6.48182 0.245869
\(696\) 3.96402 0.150256
\(697\) −4.08035 −0.154554
\(698\) 3.18606 0.120594
\(699\) 0.514865 0.0194740
\(700\) −10.2975 −0.389208
\(701\) 18.9973 0.717520 0.358760 0.933430i \(-0.383200\pi\)
0.358760 + 0.933430i \(0.383200\pi\)
\(702\) 6.84610 0.258389
\(703\) 23.7554 0.895950
\(704\) −0.847786 −0.0319521
\(705\) −2.53250 −0.0953796
\(706\) −12.9841 −0.488664
\(707\) −8.98353 −0.337860
\(708\) 1.00000 0.0375823
\(709\) 24.6962 0.927484 0.463742 0.885970i \(-0.346507\pi\)
0.463742 + 0.885970i \(0.346507\pi\)
\(710\) −3.58515 −0.134548
\(711\) 7.33532 0.275096
\(712\) 13.6489 0.511515
\(713\) −9.48450 −0.355197
\(714\) 2.10092 0.0786249
\(715\) 1.82237 0.0681528
\(716\) −9.83124 −0.367411
\(717\) −28.4503 −1.06250
\(718\) −10.0009 −0.373230
\(719\) −52.8158 −1.96970 −0.984849 0.173416i \(-0.944519\pi\)
−0.984849 + 0.173416i \(0.944519\pi\)
\(720\) 0.313984 0.0117015
\(721\) −31.7447 −1.18224
\(722\) −41.0826 −1.52893
\(723\) 7.96535 0.296235
\(724\) −5.83704 −0.216932
\(725\) 19.4293 0.721586
\(726\) 10.2813 0.381573
\(727\) 38.9838 1.44583 0.722914 0.690938i \(-0.242802\pi\)
0.722914 + 0.690938i \(0.242802\pi\)
\(728\) 14.3831 0.533073
\(729\) 1.00000 0.0370370
\(730\) 2.84161 0.105173
\(731\) −0.863891 −0.0319522
\(732\) 7.82924 0.289377
\(733\) −35.5586 −1.31339 −0.656693 0.754158i \(-0.728045\pi\)
−0.656693 + 0.754158i \(0.728045\pi\)
\(734\) −19.6011 −0.723488
\(735\) −0.812005 −0.0299513
\(736\) 5.38960 0.198663
\(737\) 5.41646 0.199518
\(738\) −4.08035 −0.150200
\(739\) 14.3912 0.529389 0.264694 0.964332i \(-0.414729\pi\)
0.264694 + 0.964332i \(0.414729\pi\)
\(740\) 0.962264 0.0353735
\(741\) −53.0662 −1.94943
\(742\) 21.4541 0.787605
\(743\) −36.1816 −1.32737 −0.663687 0.748010i \(-0.731009\pi\)
−0.663687 + 0.748010i \(0.731009\pi\)
\(744\) −1.75978 −0.0645166
\(745\) −6.65023 −0.243645
\(746\) −38.5365 −1.41092
\(747\) −0.416311 −0.0152320
\(748\) 0.847786 0.0309981
\(749\) 31.4390 1.14876
\(750\) 3.10888 0.113520
\(751\) −45.3318 −1.65418 −0.827090 0.562070i \(-0.810005\pi\)
−0.827090 + 0.562070i \(0.810005\pi\)
\(752\) −8.06572 −0.294126
\(753\) 23.3659 0.851502
\(754\) −27.1381 −0.988310
\(755\) 6.00409 0.218511
\(756\) 2.10092 0.0764097
\(757\) −33.2244 −1.20756 −0.603781 0.797150i \(-0.706340\pi\)
−0.603781 + 0.797150i \(0.706340\pi\)
\(758\) 20.4575 0.743049
\(759\) 4.56922 0.165852
\(760\) −2.43378 −0.0882825
\(761\) −2.29216 −0.0830906 −0.0415453 0.999137i \(-0.513228\pi\)
−0.0415453 + 0.999137i \(0.513228\pi\)
\(762\) 17.4017 0.630396
\(763\) −26.3183 −0.952786
\(764\) 15.5630 0.563050
\(765\) −0.313984 −0.0113521
\(766\) 30.2752 1.09389
\(767\) −6.84610 −0.247198
\(768\) 1.00000 0.0360844
\(769\) −29.0977 −1.04929 −0.524644 0.851322i \(-0.675802\pi\)
−0.524644 + 0.851322i \(0.675802\pi\)
\(770\) 0.559245 0.0201538
\(771\) −17.2084 −0.619746
\(772\) −1.10959 −0.0399350
\(773\) −20.9442 −0.753310 −0.376655 0.926354i \(-0.622926\pi\)
−0.376655 + 0.926354i \(0.622926\pi\)
\(774\) −0.863891 −0.0310519
\(775\) −8.62541 −0.309834
\(776\) 2.22173 0.0797556
\(777\) 6.43868 0.230986
\(778\) 22.4006 0.803100
\(779\) 31.6280 1.13319
\(780\) −2.14956 −0.0769667
\(781\) −9.68025 −0.346387
\(782\) −5.38960 −0.192732
\(783\) −3.96402 −0.141662
\(784\) −2.58614 −0.0923621
\(785\) −5.18667 −0.185120
\(786\) 19.2845 0.687856
\(787\) −13.6835 −0.487763 −0.243881 0.969805i \(-0.578421\pi\)
−0.243881 + 0.969805i \(0.578421\pi\)
\(788\) −21.1479 −0.753361
\(789\) 22.8845 0.814712
\(790\) −2.30317 −0.0819431
\(791\) 12.8943 0.458470
\(792\) 0.847786 0.0301248
\(793\) −53.5998 −1.90338
\(794\) 19.3679 0.687341
\(795\) −3.20633 −0.113717
\(796\) 7.69680 0.272806
\(797\) 5.80094 0.205480 0.102740 0.994708i \(-0.467239\pi\)
0.102740 + 0.994708i \(0.467239\pi\)
\(798\) −16.2848 −0.576477
\(799\) 8.06572 0.285345
\(800\) 4.90141 0.173291
\(801\) −13.6489 −0.482261
\(802\) −14.5880 −0.515120
\(803\) 7.67261 0.270761
\(804\) −6.38895 −0.225321
\(805\) −3.55527 −0.125307
\(806\) 12.0476 0.424360
\(807\) −14.5179 −0.511054
\(808\) 4.27600 0.150429
\(809\) 17.3000 0.608237 0.304119 0.952634i \(-0.401638\pi\)
0.304119 + 0.952634i \(0.401638\pi\)
\(810\) −0.313984 −0.0110323
\(811\) −7.82370 −0.274727 −0.137364 0.990521i \(-0.543863\pi\)
−0.137364 + 0.990521i \(0.543863\pi\)
\(812\) −8.32808 −0.292258
\(813\) 20.9878 0.736073
\(814\) 2.59821 0.0910670
\(815\) −1.17247 −0.0410697
\(816\) −1.00000 −0.0350070
\(817\) 6.69628 0.234273
\(818\) 15.7198 0.549628
\(819\) −14.3831 −0.502586
\(820\) 1.28116 0.0447402
\(821\) 19.9952 0.697838 0.348919 0.937153i \(-0.386549\pi\)
0.348919 + 0.937153i \(0.386549\pi\)
\(822\) 12.4313 0.433592
\(823\) 41.1031 1.43276 0.716382 0.697709i \(-0.245797\pi\)
0.716382 + 0.697709i \(0.245797\pi\)
\(824\) 15.1099 0.526379
\(825\) 4.15535 0.144671
\(826\) −2.10092 −0.0731003
\(827\) 37.8778 1.31714 0.658570 0.752519i \(-0.271162\pi\)
0.658570 + 0.752519i \(0.271162\pi\)
\(828\) −5.38960 −0.187301
\(829\) −7.40449 −0.257168 −0.128584 0.991699i \(-0.541043\pi\)
−0.128584 + 0.991699i \(0.541043\pi\)
\(830\) 0.130715 0.00453718
\(831\) −21.6987 −0.752718
\(832\) −6.84610 −0.237346
\(833\) 2.58614 0.0896044
\(834\) −20.6438 −0.714836
\(835\) −2.06114 −0.0713286
\(836\) −6.57144 −0.227278
\(837\) 1.75978 0.0608269
\(838\) −10.3992 −0.359233
\(839\) 11.1425 0.384680 0.192340 0.981328i \(-0.438392\pi\)
0.192340 + 0.981328i \(0.438392\pi\)
\(840\) −0.659654 −0.0227602
\(841\) −13.2866 −0.458158
\(842\) −1.46278 −0.0504107
\(843\) −7.10977 −0.244873
\(844\) 26.6228 0.916394
\(845\) 10.6343 0.365833
\(846\) 8.06572 0.277305
\(847\) −21.6001 −0.742188
\(848\) −10.2118 −0.350673
\(849\) 16.3119 0.559822
\(850\) −4.90141 −0.168117
\(851\) −16.5175 −0.566212
\(852\) 11.4183 0.391184
\(853\) 8.32368 0.284997 0.142499 0.989795i \(-0.454486\pi\)
0.142499 + 0.989795i \(0.454486\pi\)
\(854\) −16.4486 −0.562860
\(855\) 2.43378 0.0832335
\(856\) −14.9644 −0.511473
\(857\) −42.4814 −1.45114 −0.725568 0.688150i \(-0.758423\pi\)
−0.725568 + 0.688150i \(0.758423\pi\)
\(858\) −5.80403 −0.198146
\(859\) 9.00887 0.307379 0.153689 0.988119i \(-0.450885\pi\)
0.153689 + 0.988119i \(0.450885\pi\)
\(860\) 0.271248 0.00924947
\(861\) 8.57249 0.292150
\(862\) 8.94044 0.304513
\(863\) −2.81180 −0.0957149 −0.0478574 0.998854i \(-0.515239\pi\)
−0.0478574 + 0.998854i \(0.515239\pi\)
\(864\) −1.00000 −0.0340207
\(865\) 0.157682 0.00536136
\(866\) 1.52494 0.0518195
\(867\) 1.00000 0.0339618
\(868\) 3.69715 0.125490
\(869\) −6.21878 −0.210958
\(870\) 1.24464 0.0421971
\(871\) 43.7394 1.48205
\(872\) 12.5270 0.424219
\(873\) −2.22173 −0.0751943
\(874\) 41.7764 1.41311
\(875\) −6.53151 −0.220805
\(876\) −9.05018 −0.305777
\(877\) −17.9219 −0.605180 −0.302590 0.953121i \(-0.597851\pi\)
−0.302590 + 0.953121i \(0.597851\pi\)
\(878\) 33.9597 1.14608
\(879\) −9.86065 −0.332591
\(880\) −0.266191 −0.00897329
\(881\) 53.5071 1.80270 0.901350 0.433091i \(-0.142577\pi\)
0.901350 + 0.433091i \(0.142577\pi\)
\(882\) 2.58614 0.0870798
\(883\) −0.645428 −0.0217204 −0.0108602 0.999941i \(-0.503457\pi\)
−0.0108602 + 0.999941i \(0.503457\pi\)
\(884\) 6.84610 0.230259
\(885\) 0.313984 0.0105544
\(886\) −28.1430 −0.945483
\(887\) 55.3586 1.85876 0.929379 0.369126i \(-0.120343\pi\)
0.929379 + 0.369126i \(0.120343\pi\)
\(888\) −3.06470 −0.102844
\(889\) −36.5595 −1.22617
\(890\) 4.28554 0.143652
\(891\) −0.847786 −0.0284019
\(892\) 20.4920 0.686124
\(893\) −62.5197 −2.09214
\(894\) 21.1802 0.708371
\(895\) −3.08685 −0.103182
\(896\) −2.10092 −0.0701868
\(897\) 36.8977 1.23198
\(898\) 23.7418 0.792275
\(899\) −6.97579 −0.232656
\(900\) −4.90141 −0.163380
\(901\) 10.2118 0.340203
\(902\) 3.45926 0.115181
\(903\) 1.81497 0.0603983
\(904\) −6.13747 −0.204129
\(905\) −1.83274 −0.0609222
\(906\) −19.1223 −0.635296
\(907\) 46.6071 1.54756 0.773782 0.633452i \(-0.218362\pi\)
0.773782 + 0.633452i \(0.218362\pi\)
\(908\) 8.46757 0.281006
\(909\) −4.27600 −0.141826
\(910\) 4.51606 0.149706
\(911\) 2.80799 0.0930328 0.0465164 0.998918i \(-0.485188\pi\)
0.0465164 + 0.998918i \(0.485188\pi\)
\(912\) 7.75129 0.256671
\(913\) 0.352942 0.0116807
\(914\) −28.6991 −0.949283
\(915\) 2.45825 0.0812674
\(916\) 11.5494 0.381603
\(917\) −40.5152 −1.33793
\(918\) 1.00000 0.0330049
\(919\) −56.7154 −1.87087 −0.935435 0.353500i \(-0.884992\pi\)
−0.935435 + 0.353500i \(0.884992\pi\)
\(920\) 1.69225 0.0557917
\(921\) −26.5184 −0.873813
\(922\) 17.6993 0.582895
\(923\) −78.1707 −2.57302
\(924\) −1.78113 −0.0585948
\(925\) −15.0213 −0.493899
\(926\) 11.4644 0.376742
\(927\) −15.1099 −0.496275
\(928\) 3.96402 0.130125
\(929\) −55.5629 −1.82296 −0.911480 0.411344i \(-0.865059\pi\)
−0.911480 + 0.411344i \(0.865059\pi\)
\(930\) −0.552542 −0.0181186
\(931\) −20.0459 −0.656979
\(932\) 0.514865 0.0168650
\(933\) 13.4756 0.441170
\(934\) 9.50755 0.311096
\(935\) 0.266191 0.00870537
\(936\) 6.84610 0.223772
\(937\) −29.2649 −0.956044 −0.478022 0.878348i \(-0.658646\pi\)
−0.478022 + 0.878348i \(0.658646\pi\)
\(938\) 13.4227 0.438266
\(939\) −9.63155 −0.314314
\(940\) −2.53250 −0.0826011
\(941\) −52.3904 −1.70788 −0.853939 0.520373i \(-0.825793\pi\)
−0.853939 + 0.520373i \(0.825793\pi\)
\(942\) 16.5189 0.538215
\(943\) −21.9914 −0.716140
\(944\) 1.00000 0.0325472
\(945\) 0.659654 0.0214586
\(946\) 0.732395 0.0238122
\(947\) 49.6228 1.61252 0.806262 0.591558i \(-0.201487\pi\)
0.806262 + 0.591558i \(0.201487\pi\)
\(948\) 7.33532 0.238240
\(949\) 61.9585 2.01126
\(950\) 37.9923 1.23263
\(951\) −19.5266 −0.633193
\(952\) 2.10092 0.0680912
\(953\) 31.3574 1.01577 0.507883 0.861426i \(-0.330428\pi\)
0.507883 + 0.861426i \(0.330428\pi\)
\(954\) 10.2118 0.330618
\(955\) 4.88653 0.158125
\(956\) −28.4503 −0.920149
\(957\) 3.36064 0.108634
\(958\) −7.89050 −0.254931
\(959\) −26.1172 −0.843368
\(960\) 0.313984 0.0101338
\(961\) −27.9032 −0.900103
\(962\) 20.9812 0.676462
\(963\) 14.9644 0.482222
\(964\) 7.96535 0.256547
\(965\) −0.348393 −0.0112152
\(966\) 11.3231 0.364315
\(967\) −58.7412 −1.88899 −0.944495 0.328525i \(-0.893449\pi\)
−0.944495 + 0.328525i \(0.893449\pi\)
\(968\) 10.2813 0.330452
\(969\) −7.75129 −0.249007
\(970\) 0.697588 0.0223982
\(971\) −43.7603 −1.40433 −0.702167 0.712012i \(-0.747784\pi\)
−0.702167 + 0.712012i \(0.747784\pi\)
\(972\) 1.00000 0.0320750
\(973\) 43.3710 1.39041
\(974\) −29.3249 −0.939630
\(975\) 33.5556 1.07464
\(976\) 7.82924 0.250608
\(977\) −26.2814 −0.840818 −0.420409 0.907335i \(-0.638113\pi\)
−0.420409 + 0.907335i \(0.638113\pi\)
\(978\) 3.73417 0.119405
\(979\) 11.5714 0.369822
\(980\) −0.812005 −0.0259386
\(981\) −12.5270 −0.399958
\(982\) −0.731272 −0.0233358
\(983\) 33.6563 1.07347 0.536734 0.843751i \(-0.319658\pi\)
0.536734 + 0.843751i \(0.319658\pi\)
\(984\) −4.08035 −0.130077
\(985\) −6.64008 −0.211571
\(986\) −3.96402 −0.126240
\(987\) −16.9454 −0.539379
\(988\) −53.0662 −1.68826
\(989\) −4.65603 −0.148053
\(990\) 0.266191 0.00846010
\(991\) 10.9954 0.349281 0.174640 0.984632i \(-0.444124\pi\)
0.174640 + 0.984632i \(0.444124\pi\)
\(992\) −1.75978 −0.0558730
\(993\) −18.6116 −0.590623
\(994\) −23.9889 −0.760881
\(995\) 2.41667 0.0766136
\(996\) −0.416311 −0.0131913
\(997\) −38.9527 −1.23365 −0.616823 0.787102i \(-0.711581\pi\)
−0.616823 + 0.787102i \(0.711581\pi\)
\(998\) −39.9939 −1.26598
\(999\) 3.06470 0.0969627
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 6018.2.a.y.1.6 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6018.2.a.y.1.6 10 1.1 even 1 trivial