Properties

Label 6002.2.a.d.1.3
Level $6002$
Weight $2$
Character 6002.1
Self dual yes
Analytic conductor $47.926$
Analytic rank $0$
Dimension $79$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [6002,2,Mod(1,6002)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6002, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("6002.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6002 = 2 \cdot 3001 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6002.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: \(47.9262112932\)
Analytic rank: \(0\)
Dimension: \(79\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Character \(\chi\) \(=\) 6002.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -3.27666 q^{3} +1.00000 q^{4} +3.56247 q^{5} -3.27666 q^{6} +2.04525 q^{7} +1.00000 q^{8} +7.73650 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -3.27666 q^{3} +1.00000 q^{4} +3.56247 q^{5} -3.27666 q^{6} +2.04525 q^{7} +1.00000 q^{8} +7.73650 q^{9} +3.56247 q^{10} +0.471336 q^{11} -3.27666 q^{12} -2.29668 q^{13} +2.04525 q^{14} -11.6730 q^{15} +1.00000 q^{16} -0.845777 q^{17} +7.73650 q^{18} -6.71359 q^{19} +3.56247 q^{20} -6.70159 q^{21} +0.471336 q^{22} -0.936843 q^{23} -3.27666 q^{24} +7.69116 q^{25} -2.29668 q^{26} -15.5199 q^{27} +2.04525 q^{28} +5.58919 q^{29} -11.6730 q^{30} +7.95563 q^{31} +1.00000 q^{32} -1.54441 q^{33} -0.845777 q^{34} +7.28613 q^{35} +7.73650 q^{36} -1.11578 q^{37} -6.71359 q^{38} +7.52545 q^{39} +3.56247 q^{40} +1.90954 q^{41} -6.70159 q^{42} +11.3011 q^{43} +0.471336 q^{44} +27.5610 q^{45} -0.936843 q^{46} -4.71665 q^{47} -3.27666 q^{48} -2.81695 q^{49} +7.69116 q^{50} +2.77132 q^{51} -2.29668 q^{52} +11.6804 q^{53} -15.5199 q^{54} +1.67912 q^{55} +2.04525 q^{56} +21.9982 q^{57} +5.58919 q^{58} -9.77373 q^{59} -11.6730 q^{60} -2.54567 q^{61} +7.95563 q^{62} +15.8231 q^{63} +1.00000 q^{64} -8.18186 q^{65} -1.54441 q^{66} +13.5921 q^{67} -0.845777 q^{68} +3.06972 q^{69} +7.28613 q^{70} -8.96504 q^{71} +7.73650 q^{72} +12.8974 q^{73} -1.11578 q^{74} -25.2013 q^{75} -6.71359 q^{76} +0.964000 q^{77} +7.52545 q^{78} +16.9174 q^{79} +3.56247 q^{80} +27.6439 q^{81} +1.90954 q^{82} -13.8011 q^{83} -6.70159 q^{84} -3.01305 q^{85} +11.3011 q^{86} -18.3139 q^{87} +0.471336 q^{88} -7.63995 q^{89} +27.5610 q^{90} -4.69729 q^{91} -0.936843 q^{92} -26.0679 q^{93} -4.71665 q^{94} -23.9169 q^{95} -3.27666 q^{96} +1.68621 q^{97} -2.81695 q^{98} +3.64649 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 79 q + 79 q^{2} + 17 q^{3} + 79 q^{4} + 18 q^{5} + 17 q^{6} + 19 q^{7} + 79 q^{8} + 118 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 79 q + 79 q^{2} + 17 q^{3} + 79 q^{4} + 18 q^{5} + 17 q^{6} + 19 q^{7} + 79 q^{8} + 118 q^{9} + 18 q^{10} + 28 q^{11} + 17 q^{12} + 47 q^{13} + 19 q^{14} + 14 q^{15} + 79 q^{16} + 36 q^{17} + 118 q^{18} + 29 q^{19} + 18 q^{20} + 45 q^{21} + 28 q^{22} + 23 q^{23} + 17 q^{24} + 161 q^{25} + 47 q^{26} + 50 q^{27} + 19 q^{28} + 53 q^{29} + 14 q^{30} + 29 q^{31} + 79 q^{32} + 34 q^{33} + 36 q^{34} + 33 q^{35} + 118 q^{36} + 89 q^{37} + 29 q^{38} - 7 q^{39} + 18 q^{40} + 58 q^{41} + 45 q^{42} + 88 q^{43} + 28 q^{44} + 45 q^{45} + 23 q^{46} + 3 q^{47} + 17 q^{48} + 162 q^{49} + 161 q^{50} + 29 q^{51} + 47 q^{52} + 88 q^{53} + 50 q^{54} + 37 q^{55} + 19 q^{56} + 54 q^{57} + 53 q^{58} + 37 q^{59} + 14 q^{60} + 55 q^{61} + 29 q^{62} + 21 q^{63} + 79 q^{64} + 55 q^{65} + 34 q^{66} + 107 q^{67} + 36 q^{68} + 39 q^{69} + 33 q^{70} - 5 q^{71} + 118 q^{72} + 71 q^{73} + 89 q^{74} + 37 q^{75} + 29 q^{76} + 61 q^{77} - 7 q^{78} + 29 q^{79} + 18 q^{80} + 215 q^{81} + 58 q^{82} + 42 q^{83} + 45 q^{84} + 84 q^{85} + 88 q^{86} + 15 q^{87} + 28 q^{88} + 72 q^{89} + 45 q^{90} + 70 q^{91} + 23 q^{92} + 97 q^{93} + 3 q^{94} - 18 q^{95} + 17 q^{96} + 93 q^{97} + 162 q^{98} + 49 q^{99}+O(q^{100}) \) 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
\(3\) −3.27666 −1.89178 −0.945890 0.324487i \(-0.894808\pi\)
−0.945890 + 0.324487i \(0.894808\pi\)
\(4\) 1.00000 0.500000
\(5\) 3.56247 1.59318 0.796592 0.604518i \(-0.206634\pi\)
0.796592 + 0.604518i \(0.206634\pi\)
\(6\) −3.27666 −1.33769
\(7\) 2.04525 0.773032 0.386516 0.922283i \(-0.373678\pi\)
0.386516 + 0.922283i \(0.373678\pi\)
\(8\) 1.00000 0.353553
\(9\) 7.73650 2.57883
\(10\) 3.56247 1.12655
\(11\) 0.471336 0.142113 0.0710566 0.997472i \(-0.477363\pi\)
0.0710566 + 0.997472i \(0.477363\pi\)
\(12\) −3.27666 −0.945890
\(13\) −2.29668 −0.636986 −0.318493 0.947925i \(-0.603177\pi\)
−0.318493 + 0.947925i \(0.603177\pi\)
\(14\) 2.04525 0.546616
\(15\) −11.6730 −3.01395
\(16\) 1.00000 0.250000
\(17\) −0.845777 −0.205131 −0.102565 0.994726i \(-0.532705\pi\)
−0.102565 + 0.994726i \(0.532705\pi\)
\(18\) 7.73650 1.82351
\(19\) −6.71359 −1.54020 −0.770102 0.637921i \(-0.779795\pi\)
−0.770102 + 0.637921i \(0.779795\pi\)
\(20\) 3.56247 0.796592
\(21\) −6.70159 −1.46241
\(22\) 0.471336 0.100489
\(23\) −0.936843 −0.195345 −0.0976726 0.995219i \(-0.531140\pi\)
−0.0976726 + 0.995219i \(0.531140\pi\)
\(24\) −3.27666 −0.668845
\(25\) 7.69116 1.53823
\(26\) −2.29668 −0.450417
\(27\) −15.5199 −2.98681
\(28\) 2.04525 0.386516
\(29\) 5.58919 1.03789 0.518943 0.854809i \(-0.326326\pi\)
0.518943 + 0.854809i \(0.326326\pi\)
\(30\) −11.6730 −2.13119
\(31\) 7.95563 1.42887 0.714437 0.699700i \(-0.246683\pi\)
0.714437 + 0.699700i \(0.246683\pi\)
\(32\) 1.00000 0.176777
\(33\) −1.54441 −0.268847
\(34\) −0.845777 −0.145049
\(35\) 7.28613 1.23158
\(36\) 7.73650 1.28942
\(37\) −1.11578 −0.183433 −0.0917163 0.995785i \(-0.529235\pi\)
−0.0917163 + 0.995785i \(0.529235\pi\)
\(38\) −6.71359 −1.08909
\(39\) 7.52545 1.20504
\(40\) 3.56247 0.563275
\(41\) 1.90954 0.298220 0.149110 0.988821i \(-0.452359\pi\)
0.149110 + 0.988821i \(0.452359\pi\)
\(42\) −6.70159 −1.03408
\(43\) 11.3011 1.72340 0.861700 0.507418i \(-0.169400\pi\)
0.861700 + 0.507418i \(0.169400\pi\)
\(44\) 0.471336 0.0710566
\(45\) 27.5610 4.10855
\(46\) −0.936843 −0.138130
\(47\) −4.71665 −0.687995 −0.343997 0.938971i \(-0.611781\pi\)
−0.343997 + 0.938971i \(0.611781\pi\)
\(48\) −3.27666 −0.472945
\(49\) −2.81695 −0.402422
\(50\) 7.69116 1.08769
\(51\) 2.77132 0.388063
\(52\) −2.29668 −0.318493
\(53\) 11.6804 1.60443 0.802216 0.597034i \(-0.203654\pi\)
0.802216 + 0.597034i \(0.203654\pi\)
\(54\) −15.5199 −2.11199
\(55\) 1.67912 0.226412
\(56\) 2.04525 0.273308
\(57\) 21.9982 2.91373
\(58\) 5.58919 0.733897
\(59\) −9.77373 −1.27243 −0.636216 0.771511i \(-0.719501\pi\)
−0.636216 + 0.771511i \(0.719501\pi\)
\(60\) −11.6730 −1.50698
\(61\) −2.54567 −0.325939 −0.162970 0.986631i \(-0.552107\pi\)
−0.162970 + 0.986631i \(0.552107\pi\)
\(62\) 7.95563 1.01037
\(63\) 15.8231 1.99352
\(64\) 1.00000 0.125000
\(65\) −8.18186 −1.01483
\(66\) −1.54441 −0.190103
\(67\) 13.5921 1.66054 0.830271 0.557360i \(-0.188186\pi\)
0.830271 + 0.557360i \(0.188186\pi\)
\(68\) −0.845777 −0.102565
\(69\) 3.06972 0.369550
\(70\) 7.28613 0.870859
\(71\) −8.96504 −1.06395 −0.531977 0.846759i \(-0.678551\pi\)
−0.531977 + 0.846759i \(0.678551\pi\)
\(72\) 7.73650 0.911755
\(73\) 12.8974 1.50953 0.754764 0.655996i \(-0.227751\pi\)
0.754764 + 0.655996i \(0.227751\pi\)
\(74\) −1.11578 −0.129706
\(75\) −25.2013 −2.91000
\(76\) −6.71359 −0.770102
\(77\) 0.964000 0.109858
\(78\) 7.52545 0.852090
\(79\) 16.9174 1.90335 0.951676 0.307103i \(-0.0993597\pi\)
0.951676 + 0.307103i \(0.0993597\pi\)
\(80\) 3.56247 0.398296
\(81\) 27.6439 3.07155
\(82\) 1.90954 0.210874
\(83\) −13.8011 −1.51487 −0.757435 0.652910i \(-0.773548\pi\)
−0.757435 + 0.652910i \(0.773548\pi\)
\(84\) −6.70159 −0.731203
\(85\) −3.01305 −0.326811
\(86\) 11.3011 1.21863
\(87\) −18.3139 −1.96345
\(88\) 0.471336 0.0502446
\(89\) −7.63995 −0.809833 −0.404916 0.914354i \(-0.632699\pi\)
−0.404916 + 0.914354i \(0.632699\pi\)
\(90\) 27.5610 2.90519
\(91\) −4.69729 −0.492410
\(92\) −0.936843 −0.0976726
\(93\) −26.0679 −2.70312
\(94\) −4.71665 −0.486486
\(95\) −23.9169 −2.45383
\(96\) −3.27666 −0.334423
\(97\) 1.68621 0.171209 0.0856045 0.996329i \(-0.472718\pi\)
0.0856045 + 0.996329i \(0.472718\pi\)
\(98\) −2.81695 −0.284555
\(99\) 3.64649 0.366486
\(100\) 7.69116 0.769116
\(101\) 14.0715 1.40017 0.700084 0.714061i \(-0.253146\pi\)
0.700084 + 0.714061i \(0.253146\pi\)
\(102\) 2.77132 0.274402
\(103\) −13.3315 −1.31359 −0.656797 0.754068i \(-0.728089\pi\)
−0.656797 + 0.754068i \(0.728089\pi\)
\(104\) −2.29668 −0.225208
\(105\) −23.8742 −2.32988
\(106\) 11.6804 1.13450
\(107\) 16.5427 1.59925 0.799623 0.600502i \(-0.205033\pi\)
0.799623 + 0.600502i \(0.205033\pi\)
\(108\) −15.5199 −1.49340
\(109\) 17.2086 1.64828 0.824142 0.566383i \(-0.191658\pi\)
0.824142 + 0.566383i \(0.191658\pi\)
\(110\) 1.67912 0.160098
\(111\) 3.65602 0.347014
\(112\) 2.04525 0.193258
\(113\) 12.6791 1.19275 0.596374 0.802706i \(-0.296607\pi\)
0.596374 + 0.802706i \(0.296607\pi\)
\(114\) 21.9982 2.06032
\(115\) −3.33747 −0.311221
\(116\) 5.58919 0.518943
\(117\) −17.7683 −1.64268
\(118\) −9.77373 −0.899745
\(119\) −1.72982 −0.158573
\(120\) −11.6730 −1.06559
\(121\) −10.7778 −0.979804
\(122\) −2.54567 −0.230474
\(123\) −6.25692 −0.564167
\(124\) 7.95563 0.714437
\(125\) 9.58717 0.857502
\(126\) 15.8231 1.40963
\(127\) −5.09659 −0.452249 −0.226124 0.974098i \(-0.572606\pi\)
−0.226124 + 0.974098i \(0.572606\pi\)
\(128\) 1.00000 0.0883883
\(129\) −37.0298 −3.26029
\(130\) −8.18186 −0.717596
\(131\) −1.53453 −0.134072 −0.0670360 0.997751i \(-0.521354\pi\)
−0.0670360 + 0.997751i \(0.521354\pi\)
\(132\) −1.54441 −0.134423
\(133\) −13.7310 −1.19063
\(134\) 13.5921 1.17418
\(135\) −55.2891 −4.75853
\(136\) −0.845777 −0.0725247
\(137\) −17.6053 −1.50412 −0.752061 0.659094i \(-0.770940\pi\)
−0.752061 + 0.659094i \(0.770940\pi\)
\(138\) 3.06972 0.261312
\(139\) −8.48784 −0.719929 −0.359965 0.932966i \(-0.617211\pi\)
−0.359965 + 0.932966i \(0.617211\pi\)
\(140\) 7.28613 0.615791
\(141\) 15.4549 1.30153
\(142\) −8.96504 −0.752330
\(143\) −1.08251 −0.0905240
\(144\) 7.73650 0.644708
\(145\) 19.9113 1.65354
\(146\) 12.8974 1.06740
\(147\) 9.23020 0.761294
\(148\) −1.11578 −0.0917163
\(149\) −0.583085 −0.0477682 −0.0238841 0.999715i \(-0.507603\pi\)
−0.0238841 + 0.999715i \(0.507603\pi\)
\(150\) −25.2013 −2.05768
\(151\) −11.5921 −0.943355 −0.471677 0.881771i \(-0.656351\pi\)
−0.471677 + 0.881771i \(0.656351\pi\)
\(152\) −6.71359 −0.544544
\(153\) −6.54335 −0.528998
\(154\) 0.964000 0.0776813
\(155\) 28.3417 2.27646
\(156\) 7.52545 0.602518
\(157\) 1.81603 0.144935 0.0724676 0.997371i \(-0.476913\pi\)
0.0724676 + 0.997371i \(0.476913\pi\)
\(158\) 16.9174 1.34587
\(159\) −38.2728 −3.03523
\(160\) 3.56247 0.281638
\(161\) −1.91608 −0.151008
\(162\) 27.6439 2.17191
\(163\) −3.62185 −0.283686 −0.141843 0.989889i \(-0.545303\pi\)
−0.141843 + 0.989889i \(0.545303\pi\)
\(164\) 1.90954 0.149110
\(165\) −5.50190 −0.428322
\(166\) −13.8011 −1.07118
\(167\) 8.99378 0.695960 0.347980 0.937502i \(-0.386868\pi\)
0.347980 + 0.937502i \(0.386868\pi\)
\(168\) −6.70159 −0.517039
\(169\) −7.72524 −0.594249
\(170\) −3.01305 −0.231090
\(171\) −51.9397 −3.97193
\(172\) 11.3011 0.861700
\(173\) 17.6342 1.34071 0.670353 0.742043i \(-0.266143\pi\)
0.670353 + 0.742043i \(0.266143\pi\)
\(174\) −18.3139 −1.38837
\(175\) 15.7303 1.18910
\(176\) 0.471336 0.0355283
\(177\) 32.0252 2.40716
\(178\) −7.63995 −0.572638
\(179\) 26.3068 1.96627 0.983133 0.182894i \(-0.0585464\pi\)
0.983133 + 0.182894i \(0.0585464\pi\)
\(180\) 27.5610 2.05428
\(181\) 11.3135 0.840928 0.420464 0.907309i \(-0.361867\pi\)
0.420464 + 0.907309i \(0.361867\pi\)
\(182\) −4.69729 −0.348187
\(183\) 8.34128 0.616605
\(184\) −0.936843 −0.0690650
\(185\) −3.97492 −0.292242
\(186\) −26.0679 −1.91139
\(187\) −0.398645 −0.0291518
\(188\) −4.71665 −0.343997
\(189\) −31.7421 −2.30890
\(190\) −23.9169 −1.73512
\(191\) 5.66197 0.409686 0.204843 0.978795i \(-0.434332\pi\)
0.204843 + 0.978795i \(0.434332\pi\)
\(192\) −3.27666 −0.236473
\(193\) −23.8043 −1.71347 −0.856735 0.515757i \(-0.827511\pi\)
−0.856735 + 0.515757i \(0.827511\pi\)
\(194\) 1.68621 0.121063
\(195\) 26.8092 1.91984
\(196\) −2.81695 −0.201211
\(197\) 23.7215 1.69008 0.845042 0.534700i \(-0.179575\pi\)
0.845042 + 0.534700i \(0.179575\pi\)
\(198\) 3.64649 0.259145
\(199\) −15.8567 −1.12405 −0.562026 0.827119i \(-0.689978\pi\)
−0.562026 + 0.827119i \(0.689978\pi\)
\(200\) 7.69116 0.543847
\(201\) −44.5368 −3.14138
\(202\) 14.0715 0.990068
\(203\) 11.4313 0.802319
\(204\) 2.77132 0.194031
\(205\) 6.80267 0.475119
\(206\) −13.3315 −0.928851
\(207\) −7.24788 −0.503763
\(208\) −2.29668 −0.159246
\(209\) −3.16436 −0.218883
\(210\) −23.8742 −1.64747
\(211\) −19.5749 −1.34759 −0.673797 0.738916i \(-0.735338\pi\)
−0.673797 + 0.738916i \(0.735338\pi\)
\(212\) 11.6804 0.802216
\(213\) 29.3754 2.01277
\(214\) 16.5427 1.13084
\(215\) 40.2597 2.74569
\(216\) −15.5199 −1.05600
\(217\) 16.2713 1.10457
\(218\) 17.2086 1.16551
\(219\) −42.2605 −2.85570
\(220\) 1.67912 0.113206
\(221\) 1.94248 0.130665
\(222\) 3.65602 0.245376
\(223\) 10.8650 0.727576 0.363788 0.931482i \(-0.381483\pi\)
0.363788 + 0.931482i \(0.381483\pi\)
\(224\) 2.04525 0.136654
\(225\) 59.5027 3.96684
\(226\) 12.6791 0.843401
\(227\) 2.55851 0.169814 0.0849071 0.996389i \(-0.472941\pi\)
0.0849071 + 0.996389i \(0.472941\pi\)
\(228\) 21.9982 1.45686
\(229\) −1.11411 −0.0736227 −0.0368114 0.999322i \(-0.511720\pi\)
−0.0368114 + 0.999322i \(0.511720\pi\)
\(230\) −3.33747 −0.220066
\(231\) −3.15870 −0.207827
\(232\) 5.58919 0.366948
\(233\) 17.6860 1.15865 0.579323 0.815098i \(-0.303317\pi\)
0.579323 + 0.815098i \(0.303317\pi\)
\(234\) −17.7683 −1.16155
\(235\) −16.8029 −1.09610
\(236\) −9.77373 −0.636216
\(237\) −55.4325 −3.60072
\(238\) −1.72982 −0.112128
\(239\) −9.39637 −0.607801 −0.303900 0.952704i \(-0.598289\pi\)
−0.303900 + 0.952704i \(0.598289\pi\)
\(240\) −11.6730 −0.753488
\(241\) 17.6099 1.13435 0.567176 0.823597i \(-0.308036\pi\)
0.567176 + 0.823597i \(0.308036\pi\)
\(242\) −10.7778 −0.692826
\(243\) −44.0200 −2.82389
\(244\) −2.54567 −0.162970
\(245\) −10.0353 −0.641132
\(246\) −6.25692 −0.398926
\(247\) 15.4190 0.981087
\(248\) 7.95563 0.505183
\(249\) 45.2216 2.86580
\(250\) 9.58717 0.606346
\(251\) 25.6215 1.61721 0.808607 0.588349i \(-0.200222\pi\)
0.808607 + 0.588349i \(0.200222\pi\)
\(252\) 15.8231 0.996760
\(253\) −0.441568 −0.0277611
\(254\) −5.09659 −0.319788
\(255\) 9.87274 0.618255
\(256\) 1.00000 0.0625000
\(257\) 2.63639 0.164454 0.0822269 0.996614i \(-0.473797\pi\)
0.0822269 + 0.996614i \(0.473797\pi\)
\(258\) −37.0298 −2.30538
\(259\) −2.28204 −0.141799
\(260\) −8.18186 −0.507417
\(261\) 43.2408 2.67654
\(262\) −1.53453 −0.0948033
\(263\) −18.4191 −1.13577 −0.567884 0.823108i \(-0.692238\pi\)
−0.567884 + 0.823108i \(0.692238\pi\)
\(264\) −1.54441 −0.0950517
\(265\) 41.6112 2.55615
\(266\) −13.7310 −0.841900
\(267\) 25.0335 1.53203
\(268\) 13.5921 0.830271
\(269\) 1.06313 0.0648201 0.0324100 0.999475i \(-0.489682\pi\)
0.0324100 + 0.999475i \(0.489682\pi\)
\(270\) −55.2891 −3.36479
\(271\) 20.5714 1.24963 0.624813 0.780775i \(-0.285175\pi\)
0.624813 + 0.780775i \(0.285175\pi\)
\(272\) −0.845777 −0.0512827
\(273\) 15.3914 0.931532
\(274\) −17.6053 −1.06357
\(275\) 3.62512 0.218603
\(276\) 3.06972 0.184775
\(277\) 22.3471 1.34271 0.671354 0.741137i \(-0.265713\pi\)
0.671354 + 0.741137i \(0.265713\pi\)
\(278\) −8.48784 −0.509067
\(279\) 61.5488 3.68483
\(280\) 7.28613 0.435430
\(281\) −30.5708 −1.82370 −0.911851 0.410521i \(-0.865347\pi\)
−0.911851 + 0.410521i \(0.865347\pi\)
\(282\) 15.4549 0.920324
\(283\) −3.21210 −0.190940 −0.0954699 0.995432i \(-0.530435\pi\)
−0.0954699 + 0.995432i \(0.530435\pi\)
\(284\) −8.96504 −0.531977
\(285\) 78.3677 4.64210
\(286\) −1.08251 −0.0640102
\(287\) 3.90549 0.230534
\(288\) 7.73650 0.455878
\(289\) −16.2847 −0.957921
\(290\) 19.9113 1.16923
\(291\) −5.52515 −0.323890
\(292\) 12.8974 0.754764
\(293\) −10.9476 −0.639564 −0.319782 0.947491i \(-0.603610\pi\)
−0.319782 + 0.947491i \(0.603610\pi\)
\(294\) 9.23020 0.538316
\(295\) −34.8186 −2.02722
\(296\) −1.11578 −0.0648532
\(297\) −7.31509 −0.424464
\(298\) −0.583085 −0.0337772
\(299\) 2.15163 0.124432
\(300\) −25.2013 −1.45500
\(301\) 23.1136 1.33224
\(302\) −11.5921 −0.667052
\(303\) −46.1076 −2.64881
\(304\) −6.71359 −0.385051
\(305\) −9.06885 −0.519281
\(306\) −6.54335 −0.374058
\(307\) −11.9302 −0.680894 −0.340447 0.940264i \(-0.610578\pi\)
−0.340447 + 0.940264i \(0.610578\pi\)
\(308\) 0.964000 0.0549290
\(309\) 43.6828 2.48503
\(310\) 28.3417 1.60970
\(311\) −22.0615 −1.25099 −0.625495 0.780228i \(-0.715103\pi\)
−0.625495 + 0.780228i \(0.715103\pi\)
\(312\) 7.52545 0.426045
\(313\) 19.8960 1.12459 0.562295 0.826937i \(-0.309918\pi\)
0.562295 + 0.826937i \(0.309918\pi\)
\(314\) 1.81603 0.102485
\(315\) 56.3692 3.17604
\(316\) 16.9174 0.951676
\(317\) 8.61942 0.484115 0.242057 0.970262i \(-0.422178\pi\)
0.242057 + 0.970262i \(0.422178\pi\)
\(318\) −38.2728 −2.14623
\(319\) 2.63439 0.147497
\(320\) 3.56247 0.199148
\(321\) −54.2049 −3.02542
\(322\) −1.91608 −0.106779
\(323\) 5.67820 0.315943
\(324\) 27.6439 1.53577
\(325\) −17.6642 −0.979832
\(326\) −3.62185 −0.200596
\(327\) −56.3867 −3.11819
\(328\) 1.90954 0.105437
\(329\) −9.64673 −0.531842
\(330\) −5.50190 −0.302870
\(331\) −24.9534 −1.37156 −0.685782 0.727807i \(-0.740540\pi\)
−0.685782 + 0.727807i \(0.740540\pi\)
\(332\) −13.8011 −0.757435
\(333\) −8.63221 −0.473042
\(334\) 8.99378 0.492118
\(335\) 48.4215 2.64555
\(336\) −6.70159 −0.365602
\(337\) 27.0511 1.47357 0.736785 0.676127i \(-0.236343\pi\)
0.736785 + 0.676127i \(0.236343\pi\)
\(338\) −7.72524 −0.420198
\(339\) −41.5451 −2.25642
\(340\) −3.01305 −0.163406
\(341\) 3.74978 0.203062
\(342\) −51.9397 −2.80858
\(343\) −20.0781 −1.08412
\(344\) 11.3011 0.609314
\(345\) 10.9358 0.588761
\(346\) 17.6342 0.948022
\(347\) −0.206449 −0.0110828 −0.00554139 0.999985i \(-0.501764\pi\)
−0.00554139 + 0.999985i \(0.501764\pi\)
\(348\) −18.3139 −0.981727
\(349\) 29.5719 1.58295 0.791474 0.611202i \(-0.209314\pi\)
0.791474 + 0.611202i \(0.209314\pi\)
\(350\) 15.7303 0.840822
\(351\) 35.6443 1.90255
\(352\) 0.471336 0.0251223
\(353\) −28.6723 −1.52607 −0.763035 0.646357i \(-0.776292\pi\)
−0.763035 + 0.646357i \(0.776292\pi\)
\(354\) 32.0252 1.70212
\(355\) −31.9377 −1.69507
\(356\) −7.63995 −0.404916
\(357\) 5.66805 0.299985
\(358\) 26.3068 1.39036
\(359\) −17.4411 −0.920508 −0.460254 0.887787i \(-0.652242\pi\)
−0.460254 + 0.887787i \(0.652242\pi\)
\(360\) 27.5610 1.45259
\(361\) 26.0723 1.37223
\(362\) 11.3135 0.594626
\(363\) 35.3153 1.85357
\(364\) −4.69729 −0.246205
\(365\) 45.9466 2.40496
\(366\) 8.34128 0.436006
\(367\) 30.2560 1.57935 0.789676 0.613524i \(-0.210249\pi\)
0.789676 + 0.613524i \(0.210249\pi\)
\(368\) −0.936843 −0.0488363
\(369\) 14.7732 0.769060
\(370\) −3.97492 −0.206646
\(371\) 23.8894 1.24028
\(372\) −26.0679 −1.35156
\(373\) −16.2820 −0.843052 −0.421526 0.906816i \(-0.638505\pi\)
−0.421526 + 0.906816i \(0.638505\pi\)
\(374\) −0.398645 −0.0206134
\(375\) −31.4139 −1.62221
\(376\) −4.71665 −0.243243
\(377\) −12.8366 −0.661119
\(378\) −31.7421 −1.63264
\(379\) 21.0865 1.08314 0.541570 0.840655i \(-0.317830\pi\)
0.541570 + 0.840655i \(0.317830\pi\)
\(380\) −23.9169 −1.22691
\(381\) 16.6998 0.855556
\(382\) 5.66197 0.289691
\(383\) 22.5117 1.15029 0.575146 0.818051i \(-0.304945\pi\)
0.575146 + 0.818051i \(0.304945\pi\)
\(384\) −3.27666 −0.167211
\(385\) 3.43422 0.175024
\(386\) −23.8043 −1.21161
\(387\) 87.4309 4.44436
\(388\) 1.68621 0.0856045
\(389\) 10.3804 0.526308 0.263154 0.964754i \(-0.415237\pi\)
0.263154 + 0.964754i \(0.415237\pi\)
\(390\) 26.8092 1.35753
\(391\) 0.792360 0.0400714
\(392\) −2.81695 −0.142278
\(393\) 5.02812 0.253635
\(394\) 23.7215 1.19507
\(395\) 60.2675 3.03239
\(396\) 3.64649 0.183243
\(397\) 2.44123 0.122522 0.0612609 0.998122i \(-0.480488\pi\)
0.0612609 + 0.998122i \(0.480488\pi\)
\(398\) −15.8567 −0.794825
\(399\) 44.9917 2.25240
\(400\) 7.69116 0.384558
\(401\) 1.44526 0.0721729 0.0360864 0.999349i \(-0.488511\pi\)
0.0360864 + 0.999349i \(0.488511\pi\)
\(402\) −44.5368 −2.22129
\(403\) −18.2716 −0.910172
\(404\) 14.0715 0.700084
\(405\) 98.4805 4.89354
\(406\) 11.4313 0.567325
\(407\) −0.525906 −0.0260682
\(408\) 2.77132 0.137201
\(409\) −1.28590 −0.0635837 −0.0317918 0.999495i \(-0.510121\pi\)
−0.0317918 + 0.999495i \(0.510121\pi\)
\(410\) 6.80267 0.335960
\(411\) 57.6865 2.84547
\(412\) −13.3315 −0.656797
\(413\) −19.9897 −0.983630
\(414\) −7.24788 −0.356214
\(415\) −49.1661 −2.41347
\(416\) −2.29668 −0.112604
\(417\) 27.8118 1.36195
\(418\) −3.16436 −0.154774
\(419\) 9.90362 0.483824 0.241912 0.970298i \(-0.422226\pi\)
0.241912 + 0.970298i \(0.422226\pi\)
\(420\) −23.8742 −1.16494
\(421\) −5.87673 −0.286414 −0.143207 0.989693i \(-0.545741\pi\)
−0.143207 + 0.989693i \(0.545741\pi\)
\(422\) −19.5749 −0.952893
\(423\) −36.4904 −1.77422
\(424\) 11.6804 0.567252
\(425\) −6.50500 −0.315539
\(426\) 29.3754 1.42324
\(427\) −5.20652 −0.251961
\(428\) 16.5427 0.799623
\(429\) 3.54702 0.171252
\(430\) 40.2597 1.94150
\(431\) 6.53342 0.314704 0.157352 0.987543i \(-0.449704\pi\)
0.157352 + 0.987543i \(0.449704\pi\)
\(432\) −15.5199 −0.746701
\(433\) −16.7479 −0.804854 −0.402427 0.915452i \(-0.631833\pi\)
−0.402427 + 0.915452i \(0.631833\pi\)
\(434\) 16.2713 0.781045
\(435\) −65.2426 −3.12814
\(436\) 17.2086 0.824142
\(437\) 6.28958 0.300871
\(438\) −42.2605 −2.01928
\(439\) 8.76042 0.418112 0.209056 0.977904i \(-0.432961\pi\)
0.209056 + 0.977904i \(0.432961\pi\)
\(440\) 1.67912 0.0800488
\(441\) −21.7934 −1.03778
\(442\) 1.94248 0.0923944
\(443\) 16.4273 0.780483 0.390241 0.920713i \(-0.372392\pi\)
0.390241 + 0.920713i \(0.372392\pi\)
\(444\) 3.65602 0.173507
\(445\) −27.2171 −1.29021
\(446\) 10.8650 0.514474
\(447\) 1.91057 0.0903669
\(448\) 2.04525 0.0966290
\(449\) −0.923403 −0.0435781 −0.0217890 0.999763i \(-0.506936\pi\)
−0.0217890 + 0.999763i \(0.506936\pi\)
\(450\) 59.5027 2.80498
\(451\) 0.900035 0.0423810
\(452\) 12.6791 0.596374
\(453\) 37.9835 1.78462
\(454\) 2.55851 0.120077
\(455\) −16.7339 −0.784499
\(456\) 21.9982 1.03016
\(457\) 4.48696 0.209891 0.104945 0.994478i \(-0.466533\pi\)
0.104945 + 0.994478i \(0.466533\pi\)
\(458\) −1.11411 −0.0520591
\(459\) 13.1264 0.612686
\(460\) −3.33747 −0.155610
\(461\) 18.3102 0.852791 0.426395 0.904537i \(-0.359783\pi\)
0.426395 + 0.904537i \(0.359783\pi\)
\(462\) −3.15870 −0.146956
\(463\) 0.366767 0.0170451 0.00852255 0.999964i \(-0.497287\pi\)
0.00852255 + 0.999964i \(0.497287\pi\)
\(464\) 5.58919 0.259472
\(465\) −92.8660 −4.30656
\(466\) 17.6860 0.819286
\(467\) 19.9240 0.921974 0.460987 0.887407i \(-0.347496\pi\)
0.460987 + 0.887407i \(0.347496\pi\)
\(468\) −17.7683 −0.821340
\(469\) 27.7993 1.28365
\(470\) −16.8029 −0.775061
\(471\) −5.95052 −0.274185
\(472\) −9.77373 −0.449873
\(473\) 5.32661 0.244918
\(474\) −55.4325 −2.54610
\(475\) −51.6353 −2.36919
\(476\) −1.72982 −0.0792864
\(477\) 90.3657 4.13756
\(478\) −9.39637 −0.429780
\(479\) −19.0667 −0.871182 −0.435591 0.900145i \(-0.643461\pi\)
−0.435591 + 0.900145i \(0.643461\pi\)
\(480\) −11.6730 −0.532797
\(481\) 2.56259 0.116844
\(482\) 17.6099 0.802108
\(483\) 6.27834 0.285674
\(484\) −10.7778 −0.489902
\(485\) 6.00708 0.272767
\(486\) −44.0200 −1.99679
\(487\) −17.6870 −0.801473 −0.400737 0.916193i \(-0.631246\pi\)
−0.400737 + 0.916193i \(0.631246\pi\)
\(488\) −2.54567 −0.115237
\(489\) 11.8676 0.536671
\(490\) −10.0353 −0.453349
\(491\) −23.0384 −1.03971 −0.519854 0.854255i \(-0.674014\pi\)
−0.519854 + 0.854255i \(0.674014\pi\)
\(492\) −6.25692 −0.282084
\(493\) −4.72721 −0.212903
\(494\) 15.4190 0.693734
\(495\) 12.9905 0.583879
\(496\) 7.95563 0.357219
\(497\) −18.3358 −0.822471
\(498\) 45.2216 2.02643
\(499\) −14.1952 −0.635466 −0.317733 0.948180i \(-0.602922\pi\)
−0.317733 + 0.948180i \(0.602922\pi\)
\(500\) 9.58717 0.428751
\(501\) −29.4696 −1.31660
\(502\) 25.6215 1.14354
\(503\) −3.71122 −0.165475 −0.0827375 0.996571i \(-0.526366\pi\)
−0.0827375 + 0.996571i \(0.526366\pi\)
\(504\) 15.8231 0.704816
\(505\) 50.1293 2.23072
\(506\) −0.441568 −0.0196301
\(507\) 25.3130 1.12419
\(508\) −5.09659 −0.226124
\(509\) 5.24058 0.232285 0.116142 0.993233i \(-0.462947\pi\)
0.116142 + 0.993233i \(0.462947\pi\)
\(510\) 9.87274 0.437172
\(511\) 26.3784 1.16691
\(512\) 1.00000 0.0441942
\(513\) 104.194 4.60029
\(514\) 2.63639 0.116286
\(515\) −47.4931 −2.09279
\(516\) −37.0298 −1.63015
\(517\) −2.22313 −0.0977731
\(518\) −2.28204 −0.100267
\(519\) −57.7814 −2.53632
\(520\) −8.18186 −0.358798
\(521\) −24.2581 −1.06277 −0.531383 0.847132i \(-0.678328\pi\)
−0.531383 + 0.847132i \(0.678328\pi\)
\(522\) 43.2408 1.89260
\(523\) 37.8312 1.65424 0.827121 0.562024i \(-0.189977\pi\)
0.827121 + 0.562024i \(0.189977\pi\)
\(524\) −1.53453 −0.0670360
\(525\) −51.5430 −2.24952
\(526\) −18.4191 −0.803110
\(527\) −6.72869 −0.293106
\(528\) −1.54441 −0.0672117
\(529\) −22.1223 −0.961840
\(530\) 41.6112 1.80747
\(531\) −75.6145 −3.28139
\(532\) −13.7310 −0.595313
\(533\) −4.38561 −0.189962
\(534\) 25.0335 1.08331
\(535\) 58.9329 2.54789
\(536\) 13.5921 0.587090
\(537\) −86.1986 −3.71974
\(538\) 1.06313 0.0458347
\(539\) −1.32773 −0.0571894
\(540\) −55.2891 −2.37926
\(541\) −39.2704 −1.68836 −0.844182 0.536056i \(-0.819914\pi\)
−0.844182 + 0.536056i \(0.819914\pi\)
\(542\) 20.5714 0.883618
\(543\) −37.0706 −1.59085
\(544\) −0.845777 −0.0362624
\(545\) 61.3050 2.62602
\(546\) 15.3914 0.658692
\(547\) −1.52187 −0.0650703 −0.0325351 0.999471i \(-0.510358\pi\)
−0.0325351 + 0.999471i \(0.510358\pi\)
\(548\) −17.6053 −0.752061
\(549\) −19.6945 −0.840543
\(550\) 3.62512 0.154576
\(551\) −37.5235 −1.59856
\(552\) 3.06972 0.130656
\(553\) 34.6002 1.47135
\(554\) 22.3471 0.949438
\(555\) 13.0245 0.552857
\(556\) −8.48784 −0.359965
\(557\) −45.2088 −1.91556 −0.957780 0.287502i \(-0.907175\pi\)
−0.957780 + 0.287502i \(0.907175\pi\)
\(558\) 61.5488 2.60557
\(559\) −25.9550 −1.09778
\(560\) 7.28613 0.307895
\(561\) 1.30622 0.0551488
\(562\) −30.5708 −1.28955
\(563\) −14.6315 −0.616646 −0.308323 0.951282i \(-0.599768\pi\)
−0.308323 + 0.951282i \(0.599768\pi\)
\(564\) 15.4549 0.650767
\(565\) 45.1688 1.90027
\(566\) −3.21210 −0.135015
\(567\) 56.5387 2.37440
\(568\) −8.96504 −0.376165
\(569\) 24.0122 1.00664 0.503322 0.864099i \(-0.332111\pi\)
0.503322 + 0.864099i \(0.332111\pi\)
\(570\) 78.3677 3.28246
\(571\) −5.63877 −0.235975 −0.117988 0.993015i \(-0.537644\pi\)
−0.117988 + 0.993015i \(0.537644\pi\)
\(572\) −1.08251 −0.0452620
\(573\) −18.5523 −0.775035
\(574\) 3.90549 0.163012
\(575\) −7.20541 −0.300486
\(576\) 7.73650 0.322354
\(577\) −14.4960 −0.603478 −0.301739 0.953391i \(-0.597567\pi\)
−0.301739 + 0.953391i \(0.597567\pi\)
\(578\) −16.2847 −0.677353
\(579\) 77.9985 3.24151
\(580\) 19.9113 0.826772
\(581\) −28.2268 −1.17104
\(582\) −5.52515 −0.229025
\(583\) 5.50541 0.228011
\(584\) 12.8974 0.533699
\(585\) −63.2989 −2.61709
\(586\) −10.9476 −0.452240
\(587\) −1.74785 −0.0721415 −0.0360708 0.999349i \(-0.511484\pi\)
−0.0360708 + 0.999349i \(0.511484\pi\)
\(588\) 9.23020 0.380647
\(589\) −53.4109 −2.20076
\(590\) −34.8186 −1.43346
\(591\) −77.7272 −3.19727
\(592\) −1.11578 −0.0458582
\(593\) 10.2000 0.418864 0.209432 0.977823i \(-0.432839\pi\)
0.209432 + 0.977823i \(0.432839\pi\)
\(594\) −7.31509 −0.300142
\(595\) −6.16244 −0.252635
\(596\) −0.583085 −0.0238841
\(597\) 51.9571 2.12646
\(598\) 2.15163 0.0879868
\(599\) −7.36660 −0.300991 −0.150496 0.988611i \(-0.548087\pi\)
−0.150496 + 0.988611i \(0.548087\pi\)
\(600\) −25.2013 −1.02884
\(601\) −44.8588 −1.82983 −0.914914 0.403649i \(-0.867742\pi\)
−0.914914 + 0.403649i \(0.867742\pi\)
\(602\) 23.1136 0.942038
\(603\) 105.155 4.28226
\(604\) −11.5921 −0.471677
\(605\) −38.3957 −1.56101
\(606\) −46.1076 −1.87299
\(607\) 10.7337 0.435668 0.217834 0.975986i \(-0.430101\pi\)
0.217834 + 0.975986i \(0.430101\pi\)
\(608\) −6.71359 −0.272272
\(609\) −37.4565 −1.51781
\(610\) −9.06885 −0.367187
\(611\) 10.8327 0.438243
\(612\) −6.54335 −0.264499
\(613\) −4.27600 −0.172706 −0.0863530 0.996265i \(-0.527521\pi\)
−0.0863530 + 0.996265i \(0.527521\pi\)
\(614\) −11.9302 −0.481465
\(615\) −22.2900 −0.898821
\(616\) 0.964000 0.0388407
\(617\) 1.39353 0.0561014 0.0280507 0.999607i \(-0.491070\pi\)
0.0280507 + 0.999607i \(0.491070\pi\)
\(618\) 43.6828 1.75718
\(619\) −33.9034 −1.36269 −0.681347 0.731961i \(-0.738605\pi\)
−0.681347 + 0.731961i \(0.738605\pi\)
\(620\) 28.3417 1.13823
\(621\) 14.5397 0.583458
\(622\) −22.0615 −0.884584
\(623\) −15.6256 −0.626027
\(624\) 7.52545 0.301259
\(625\) −4.30185 −0.172074
\(626\) 19.8960 0.795206
\(627\) 10.3685 0.414079
\(628\) 1.81603 0.0724676
\(629\) 0.943698 0.0376277
\(630\) 56.3692 2.24580
\(631\) 4.31000 0.171578 0.0857892 0.996313i \(-0.472659\pi\)
0.0857892 + 0.996313i \(0.472659\pi\)
\(632\) 16.9174 0.672937
\(633\) 64.1404 2.54935
\(634\) 8.61942 0.342321
\(635\) −18.1564 −0.720515
\(636\) −38.2728 −1.51762
\(637\) 6.46965 0.256337
\(638\) 2.63439 0.104296
\(639\) −69.3580 −2.74376
\(640\) 3.56247 0.140819
\(641\) −32.6126 −1.28812 −0.644060 0.764975i \(-0.722751\pi\)
−0.644060 + 0.764975i \(0.722751\pi\)
\(642\) −54.2049 −2.13930
\(643\) 21.3863 0.843393 0.421697 0.906737i \(-0.361435\pi\)
0.421697 + 0.906737i \(0.361435\pi\)
\(644\) −1.91608 −0.0755040
\(645\) −131.917 −5.19425
\(646\) 5.67820 0.223406
\(647\) 21.0434 0.827302 0.413651 0.910436i \(-0.364253\pi\)
0.413651 + 0.910436i \(0.364253\pi\)
\(648\) 27.6439 1.08596
\(649\) −4.60671 −0.180829
\(650\) −17.6642 −0.692846
\(651\) −53.3154 −2.08959
\(652\) −3.62185 −0.141843
\(653\) −7.46964 −0.292310 −0.146155 0.989262i \(-0.546690\pi\)
−0.146155 + 0.989262i \(0.546690\pi\)
\(654\) −56.3867 −2.20489
\(655\) −5.46669 −0.213601
\(656\) 1.90954 0.0745550
\(657\) 99.7809 3.89282
\(658\) −9.64673 −0.376069
\(659\) 19.3845 0.755114 0.377557 0.925986i \(-0.376764\pi\)
0.377557 + 0.925986i \(0.376764\pi\)
\(660\) −5.50190 −0.214161
\(661\) −15.9933 −0.622068 −0.311034 0.950399i \(-0.600675\pi\)
−0.311034 + 0.950399i \(0.600675\pi\)
\(662\) −24.9534 −0.969843
\(663\) −6.36485 −0.247190
\(664\) −13.8011 −0.535588
\(665\) −48.9161 −1.89689
\(666\) −8.63221 −0.334491
\(667\) −5.23619 −0.202746
\(668\) 8.99378 0.347980
\(669\) −35.6010 −1.37641
\(670\) 48.4215 1.87068
\(671\) −1.19986 −0.0463202
\(672\) −6.70159 −0.258519
\(673\) 12.4468 0.479790 0.239895 0.970799i \(-0.422887\pi\)
0.239895 + 0.970799i \(0.422887\pi\)
\(674\) 27.0511 1.04197
\(675\) −119.366 −4.59440
\(676\) −7.72524 −0.297125
\(677\) −26.2182 −1.00765 −0.503823 0.863807i \(-0.668074\pi\)
−0.503823 + 0.863807i \(0.668074\pi\)
\(678\) −41.5451 −1.59553
\(679\) 3.44873 0.132350
\(680\) −3.01305 −0.115545
\(681\) −8.38336 −0.321251
\(682\) 3.74978 0.143586
\(683\) 40.5984 1.55345 0.776727 0.629838i \(-0.216879\pi\)
0.776727 + 0.629838i \(0.216879\pi\)
\(684\) −51.9397 −1.98596
\(685\) −62.7182 −2.39634
\(686\) −20.0781 −0.766586
\(687\) 3.65057 0.139278
\(688\) 11.3011 0.430850
\(689\) −26.8263 −1.02200
\(690\) 10.9358 0.416317
\(691\) −23.9742 −0.912020 −0.456010 0.889975i \(-0.650722\pi\)
−0.456010 + 0.889975i \(0.650722\pi\)
\(692\) 17.6342 0.670353
\(693\) 7.45798 0.283305
\(694\) −0.206449 −0.00783670
\(695\) −30.2376 −1.14698
\(696\) −18.3139 −0.694186
\(697\) −1.61504 −0.0611742
\(698\) 29.5719 1.11931
\(699\) −57.9508 −2.19190
\(700\) 15.7303 0.594551
\(701\) −20.7561 −0.783948 −0.391974 0.919976i \(-0.628208\pi\)
−0.391974 + 0.919976i \(0.628208\pi\)
\(702\) 35.6443 1.34531
\(703\) 7.49087 0.282524
\(704\) 0.471336 0.0177641
\(705\) 55.0574 2.07358
\(706\) −28.6723 −1.07909
\(707\) 28.7798 1.08237
\(708\) 32.0252 1.20358
\(709\) 49.9311 1.87520 0.937601 0.347712i \(-0.113041\pi\)
0.937601 + 0.347712i \(0.113041\pi\)
\(710\) −31.9377 −1.19860
\(711\) 130.881 4.90843
\(712\) −7.63995 −0.286319
\(713\) −7.45318 −0.279124
\(714\) 5.66805 0.212121
\(715\) −3.85640 −0.144221
\(716\) 26.3068 0.983133
\(717\) 30.7887 1.14983
\(718\) −17.4411 −0.650898
\(719\) −4.80534 −0.179209 −0.0896045 0.995977i \(-0.528560\pi\)
−0.0896045 + 0.995977i \(0.528560\pi\)
\(720\) 27.5610 1.02714
\(721\) −27.2663 −1.01545
\(722\) 26.0723 0.970311
\(723\) −57.7016 −2.14594
\(724\) 11.3135 0.420464
\(725\) 42.9874 1.59651
\(726\) 35.3153 1.31067
\(727\) −32.5873 −1.20859 −0.604297 0.796759i \(-0.706546\pi\)
−0.604297 + 0.796759i \(0.706546\pi\)
\(728\) −4.69729 −0.174093
\(729\) 61.3069 2.27063
\(730\) 45.9466 1.70056
\(731\) −9.55820 −0.353523
\(732\) 8.34128 0.308303
\(733\) −35.4866 −1.31073 −0.655364 0.755313i \(-0.727485\pi\)
−0.655364 + 0.755313i \(0.727485\pi\)
\(734\) 30.2560 1.11677
\(735\) 32.8823 1.21288
\(736\) −0.936843 −0.0345325
\(737\) 6.40646 0.235985
\(738\) 14.7732 0.543808
\(739\) 3.93090 0.144600 0.0723002 0.997383i \(-0.476966\pi\)
0.0723002 + 0.997383i \(0.476966\pi\)
\(740\) −3.97492 −0.146121
\(741\) −50.5228 −1.85600
\(742\) 23.8894 0.877008
\(743\) 40.9247 1.50138 0.750690 0.660654i \(-0.229721\pi\)
0.750690 + 0.660654i \(0.229721\pi\)
\(744\) −26.0679 −0.955696
\(745\) −2.07722 −0.0761034
\(746\) −16.2820 −0.596128
\(747\) −106.772 −3.90660
\(748\) −0.398645 −0.0145759
\(749\) 33.8340 1.23627
\(750\) −31.4139 −1.14707
\(751\) 27.4971 1.00338 0.501691 0.865047i \(-0.332711\pi\)
0.501691 + 0.865047i \(0.332711\pi\)
\(752\) −4.71665 −0.171999
\(753\) −83.9529 −3.05941
\(754\) −12.8366 −0.467482
\(755\) −41.2966 −1.50294
\(756\) −31.7421 −1.15445
\(757\) 16.4204 0.596811 0.298406 0.954439i \(-0.403545\pi\)
0.298406 + 0.954439i \(0.403545\pi\)
\(758\) 21.0865 0.765896
\(759\) 1.44687 0.0525180
\(760\) −23.9169 −0.867559
\(761\) 24.2726 0.879882 0.439941 0.898027i \(-0.354999\pi\)
0.439941 + 0.898027i \(0.354999\pi\)
\(762\) 16.6998 0.604969
\(763\) 35.1959 1.27418
\(764\) 5.66197 0.204843
\(765\) −23.3105 −0.842791
\(766\) 22.5117 0.813379
\(767\) 22.4472 0.810521
\(768\) −3.27666 −0.118236
\(769\) 30.3008 1.09267 0.546337 0.837566i \(-0.316022\pi\)
0.546337 + 0.837566i \(0.316022\pi\)
\(770\) 3.43422 0.123761
\(771\) −8.63857 −0.311110
\(772\) −23.8043 −0.856735
\(773\) −2.83667 −0.102028 −0.0510139 0.998698i \(-0.516245\pi\)
−0.0510139 + 0.998698i \(0.516245\pi\)
\(774\) 87.4309 3.14264
\(775\) 61.1881 2.19794
\(776\) 1.68621 0.0605315
\(777\) 7.47748 0.268253
\(778\) 10.3804 0.372156
\(779\) −12.8199 −0.459320
\(780\) 26.8092 0.959922
\(781\) −4.22555 −0.151202
\(782\) 0.792360 0.0283347
\(783\) −86.7437 −3.09997
\(784\) −2.81695 −0.100605
\(785\) 6.46955 0.230908
\(786\) 5.02812 0.179347
\(787\) 9.80178 0.349396 0.174698 0.984622i \(-0.444105\pi\)
0.174698 + 0.984622i \(0.444105\pi\)
\(788\) 23.7215 0.845042
\(789\) 60.3530 2.14862
\(790\) 60.2675 2.14422
\(791\) 25.9319 0.922033
\(792\) 3.64649 0.129572
\(793\) 5.84659 0.207619
\(794\) 2.44123 0.0866359
\(795\) −136.346 −4.83568
\(796\) −15.8567 −0.562026
\(797\) 6.13117 0.217177 0.108589 0.994087i \(-0.465367\pi\)
0.108589 + 0.994087i \(0.465367\pi\)
\(798\) 44.9917 1.59269
\(799\) 3.98923 0.141129
\(800\) 7.69116 0.271924
\(801\) −59.1065 −2.08842
\(802\) 1.44526 0.0510339
\(803\) 6.07902 0.214524
\(804\) −44.5368 −1.57069
\(805\) −6.82596 −0.240584
\(806\) −18.2716 −0.643589
\(807\) −3.48351 −0.122625
\(808\) 14.0715 0.495034
\(809\) −19.0418 −0.669476 −0.334738 0.942311i \(-0.608648\pi\)
−0.334738 + 0.942311i \(0.608648\pi\)
\(810\) 98.4805 3.46025
\(811\) 11.9108 0.418244 0.209122 0.977890i \(-0.432939\pi\)
0.209122 + 0.977890i \(0.432939\pi\)
\(812\) 11.4313 0.401160
\(813\) −67.4056 −2.36402
\(814\) −0.525906 −0.0184330
\(815\) −12.9027 −0.451963
\(816\) 2.77132 0.0970157
\(817\) −75.8709 −2.65439
\(818\) −1.28590 −0.0449604
\(819\) −36.3406 −1.26984
\(820\) 6.80267 0.237560
\(821\) −11.8408 −0.413247 −0.206624 0.978421i \(-0.566248\pi\)
−0.206624 + 0.978421i \(0.566248\pi\)
\(822\) 57.6865 2.01205
\(823\) 8.96652 0.312553 0.156277 0.987713i \(-0.450051\pi\)
0.156277 + 0.987713i \(0.450051\pi\)
\(824\) −13.3315 −0.464425
\(825\) −11.8783 −0.413549
\(826\) −19.9897 −0.695532
\(827\) −37.4133 −1.30099 −0.650494 0.759511i \(-0.725438\pi\)
−0.650494 + 0.759511i \(0.725438\pi\)
\(828\) −7.24788 −0.251881
\(829\) 3.31799 0.115239 0.0576193 0.998339i \(-0.481649\pi\)
0.0576193 + 0.998339i \(0.481649\pi\)
\(830\) −49.1661 −1.70658
\(831\) −73.2239 −2.54011
\(832\) −2.29668 −0.0796232
\(833\) 2.38251 0.0825492
\(834\) 27.8118 0.963043
\(835\) 32.0400 1.10879
\(836\) −3.16436 −0.109442
\(837\) −123.471 −4.26777
\(838\) 9.90362 0.342115
\(839\) 29.5697 1.02086 0.510429 0.859920i \(-0.329487\pi\)
0.510429 + 0.859920i \(0.329487\pi\)
\(840\) −23.8742 −0.823737
\(841\) 2.23905 0.0772087
\(842\) −5.87673 −0.202525
\(843\) 100.170 3.45004
\(844\) −19.5749 −0.673797
\(845\) −27.5209 −0.946748
\(846\) −36.4904 −1.25457
\(847\) −22.0434 −0.757420
\(848\) 11.6804 0.401108
\(849\) 10.5250 0.361216
\(850\) −6.50500 −0.223120
\(851\) 1.04531 0.0358327
\(852\) 29.3754 1.00638
\(853\) −35.4884 −1.21510 −0.607550 0.794282i \(-0.707847\pi\)
−0.607550 + 0.794282i \(0.707847\pi\)
\(854\) −5.20652 −0.178164
\(855\) −185.033 −6.32801
\(856\) 16.5427 0.565419
\(857\) 40.7442 1.39180 0.695898 0.718141i \(-0.255007\pi\)
0.695898 + 0.718141i \(0.255007\pi\)
\(858\) 3.54702 0.121093
\(859\) 1.87841 0.0640905 0.0320453 0.999486i \(-0.489798\pi\)
0.0320453 + 0.999486i \(0.489798\pi\)
\(860\) 40.2597 1.37285
\(861\) −12.7970 −0.436119
\(862\) 6.53342 0.222529
\(863\) 10.8542 0.369481 0.184741 0.982787i \(-0.440855\pi\)
0.184741 + 0.982787i \(0.440855\pi\)
\(864\) −15.5199 −0.527998
\(865\) 62.8213 2.13599
\(866\) −16.7479 −0.569118
\(867\) 53.3593 1.81218
\(868\) 16.2713 0.552283
\(869\) 7.97376 0.270491
\(870\) −65.2426 −2.21193
\(871\) −31.2168 −1.05774
\(872\) 17.2086 0.582757
\(873\) 13.0454 0.441519
\(874\) 6.28958 0.212748
\(875\) 19.6081 0.662876
\(876\) −42.2605 −1.42785
\(877\) 5.12005 0.172892 0.0864459 0.996257i \(-0.472449\pi\)
0.0864459 + 0.996257i \(0.472449\pi\)
\(878\) 8.76042 0.295650
\(879\) 35.8715 1.20991
\(880\) 1.67912 0.0566031
\(881\) 5.25485 0.177040 0.0885202 0.996074i \(-0.471786\pi\)
0.0885202 + 0.996074i \(0.471786\pi\)
\(882\) −21.7934 −0.733820
\(883\) −9.72610 −0.327309 −0.163655 0.986518i \(-0.552328\pi\)
−0.163655 + 0.986518i \(0.552328\pi\)
\(884\) 1.94248 0.0653327
\(885\) 114.089 3.83505
\(886\) 16.4273 0.551885
\(887\) 36.5362 1.22677 0.613383 0.789785i \(-0.289808\pi\)
0.613383 + 0.789785i \(0.289808\pi\)
\(888\) 3.65602 0.122688
\(889\) −10.4238 −0.349603
\(890\) −27.2171 −0.912318
\(891\) 13.0296 0.436507
\(892\) 10.8650 0.363788
\(893\) 31.6657 1.05965
\(894\) 1.91057 0.0638990
\(895\) 93.7172 3.13262
\(896\) 2.04525 0.0683270
\(897\) −7.05017 −0.235398
\(898\) −0.923403 −0.0308144
\(899\) 44.4656 1.48301
\(900\) 59.5027 1.98342
\(901\) −9.87904 −0.329119
\(902\) 0.900035 0.0299679
\(903\) −75.7352 −2.52031
\(904\) 12.6791 0.421700
\(905\) 40.3041 1.33975
\(906\) 37.9835 1.26192
\(907\) 39.2322 1.30268 0.651341 0.758785i \(-0.274207\pi\)
0.651341 + 0.758785i \(0.274207\pi\)
\(908\) 2.55851 0.0849071
\(909\) 108.864 3.61080
\(910\) −16.7339 −0.554725
\(911\) −42.6189 −1.41203 −0.706014 0.708198i \(-0.749508\pi\)
−0.706014 + 0.708198i \(0.749508\pi\)
\(912\) 21.9982 0.728432
\(913\) −6.50497 −0.215283
\(914\) 4.48696 0.148415
\(915\) 29.7155 0.982365
\(916\) −1.11411 −0.0368114
\(917\) −3.13849 −0.103642
\(918\) 13.1264 0.433235
\(919\) −50.2593 −1.65790 −0.828951 0.559322i \(-0.811062\pi\)
−0.828951 + 0.559322i \(0.811062\pi\)
\(920\) −3.33747 −0.110033
\(921\) 39.0913 1.28810
\(922\) 18.3102 0.603014
\(923\) 20.5899 0.677724
\(924\) −3.15870 −0.103914
\(925\) −8.58162 −0.282162
\(926\) 0.366767 0.0120527
\(927\) −103.139 −3.38754
\(928\) 5.58919 0.183474
\(929\) −11.0745 −0.363342 −0.181671 0.983359i \(-0.558151\pi\)
−0.181671 + 0.983359i \(0.558151\pi\)
\(930\) −92.8660 −3.04520
\(931\) 18.9119 0.619812
\(932\) 17.6860 0.579323
\(933\) 72.2879 2.36660
\(934\) 19.9240 0.651934
\(935\) −1.42016 −0.0464442
\(936\) −17.7683 −0.580775
\(937\) 8.24204 0.269256 0.134628 0.990896i \(-0.457016\pi\)
0.134628 + 0.990896i \(0.457016\pi\)
\(938\) 27.7993 0.907679
\(939\) −65.1925 −2.12748
\(940\) −16.8029 −0.548051
\(941\) 4.99278 0.162760 0.0813799 0.996683i \(-0.474067\pi\)
0.0813799 + 0.996683i \(0.474067\pi\)
\(942\) −5.95052 −0.193878
\(943\) −1.78894 −0.0582559
\(944\) −9.77373 −0.318108
\(945\) −113.080 −3.67849
\(946\) 5.32661 0.173183
\(947\) 14.1834 0.460897 0.230449 0.973085i \(-0.425981\pi\)
0.230449 + 0.973085i \(0.425981\pi\)
\(948\) −55.4325 −1.80036
\(949\) −29.6213 −0.961548
\(950\) −51.6353 −1.67527
\(951\) −28.2429 −0.915839
\(952\) −1.72982 −0.0560639
\(953\) 1.74320 0.0564679 0.0282340 0.999601i \(-0.491012\pi\)
0.0282340 + 0.999601i \(0.491012\pi\)
\(954\) 90.3657 2.92570
\(955\) 20.1706 0.652704
\(956\) −9.39637 −0.303900
\(957\) −8.63199 −0.279033
\(958\) −19.0667 −0.616018
\(959\) −36.0072 −1.16273
\(960\) −11.6730 −0.376744
\(961\) 32.2921 1.04168
\(962\) 2.56259 0.0826212
\(963\) 127.983 4.12419
\(964\) 17.6099 0.567176
\(965\) −84.8019 −2.72987
\(966\) 6.27834 0.202002
\(967\) −33.1406 −1.06573 −0.532865 0.846200i \(-0.678885\pi\)
−0.532865 + 0.846200i \(0.678885\pi\)
\(968\) −10.7778 −0.346413
\(969\) −18.6055 −0.597696
\(970\) 6.00708 0.192876
\(971\) −51.1828 −1.64253 −0.821266 0.570545i \(-0.806732\pi\)
−0.821266 + 0.570545i \(0.806732\pi\)
\(972\) −44.0200 −1.41194
\(973\) −17.3598 −0.556528
\(974\) −17.6870 −0.566727
\(975\) 57.8795 1.85363
\(976\) −2.54567 −0.0814848
\(977\) −11.5368 −0.369094 −0.184547 0.982824i \(-0.559082\pi\)
−0.184547 + 0.982824i \(0.559082\pi\)
\(978\) 11.8676 0.379484
\(979\) −3.60098 −0.115088
\(980\) −10.0353 −0.320566
\(981\) 133.134 4.25065
\(982\) −23.0384 −0.735185
\(983\) −3.33851 −0.106482 −0.0532409 0.998582i \(-0.516955\pi\)
−0.0532409 + 0.998582i \(0.516955\pi\)
\(984\) −6.25692 −0.199463
\(985\) 84.5069 2.69261
\(986\) −4.72721 −0.150545
\(987\) 31.6091 1.00613
\(988\) 15.4190 0.490544
\(989\) −10.5873 −0.336658
\(990\) 12.9905 0.412865
\(991\) 46.2203 1.46824 0.734118 0.679022i \(-0.237596\pi\)
0.734118 + 0.679022i \(0.237596\pi\)
\(992\) 7.95563 0.252592
\(993\) 81.7639 2.59470
\(994\) −18.3358 −0.581575
\(995\) −56.4890 −1.79082
\(996\) 45.2216 1.43290
\(997\) 33.2994 1.05460 0.527301 0.849678i \(-0.323204\pi\)
0.527301 + 0.849678i \(0.323204\pi\)
\(998\) −14.1952 −0.449342
\(999\) 17.3167 0.547878
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 6002.2.a.d.1.3 79
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6002.2.a.d.1.3 79 1.1 even 1 trivial