Properties

Label 8042.2.a.c.1.10
Level 8042
Weight 2
Character 8042.1
Self dual Yes
Analytic conductor 64.216
Analytic rank 0
Dimension 86
CM No

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Newspace parameters

Level: \( N \) = \( 8042 = 2 \cdot 4021 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8042.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2156933055\)
Analytic rank: \(0\)
Dimension: \(86\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) = 8042.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-2.53308 q^{3}\) \(+1.00000 q^{4}\) \(-2.12930 q^{5}\) \(+2.53308 q^{6}\) \(-1.20392 q^{7}\) \(-1.00000 q^{8}\) \(+3.41648 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-2.53308 q^{3}\) \(+1.00000 q^{4}\) \(-2.12930 q^{5}\) \(+2.53308 q^{6}\) \(-1.20392 q^{7}\) \(-1.00000 q^{8}\) \(+3.41648 q^{9}\) \(+2.12930 q^{10}\) \(-3.06628 q^{11}\) \(-2.53308 q^{12}\) \(+2.94048 q^{13}\) \(+1.20392 q^{14}\) \(+5.39369 q^{15}\) \(+1.00000 q^{16}\) \(-0.513898 q^{17}\) \(-3.41648 q^{18}\) \(+4.03318 q^{19}\) \(-2.12930 q^{20}\) \(+3.04963 q^{21}\) \(+3.06628 q^{22}\) \(+6.16231 q^{23}\) \(+2.53308 q^{24}\) \(-0.466073 q^{25}\) \(-2.94048 q^{26}\) \(-1.05499 q^{27}\) \(-1.20392 q^{28}\) \(+0.113495 q^{29}\) \(-5.39369 q^{30}\) \(+6.64630 q^{31}\) \(-1.00000 q^{32}\) \(+7.76713 q^{33}\) \(+0.513898 q^{34}\) \(+2.56351 q^{35}\) \(+3.41648 q^{36}\) \(+1.12473 q^{37}\) \(-4.03318 q^{38}\) \(-7.44846 q^{39}\) \(+2.12930 q^{40}\) \(+7.47821 q^{41}\) \(-3.04963 q^{42}\) \(+10.9649 q^{43}\) \(-3.06628 q^{44}\) \(-7.27473 q^{45}\) \(-6.16231 q^{46}\) \(-9.30504 q^{47}\) \(-2.53308 q^{48}\) \(-5.55057 q^{49}\) \(+0.466073 q^{50}\) \(+1.30174 q^{51}\) \(+2.94048 q^{52}\) \(-0.632478 q^{53}\) \(+1.05499 q^{54}\) \(+6.52904 q^{55}\) \(+1.20392 q^{56}\) \(-10.2163 q^{57}\) \(-0.113495 q^{58}\) \(-12.6898 q^{59}\) \(+5.39369 q^{60}\) \(+8.24791 q^{61}\) \(-6.64630 q^{62}\) \(-4.11318 q^{63}\) \(+1.00000 q^{64}\) \(-6.26117 q^{65}\) \(-7.76713 q^{66}\) \(+3.19595 q^{67}\) \(-0.513898 q^{68}\) \(-15.6096 q^{69}\) \(-2.56351 q^{70}\) \(-5.15906 q^{71}\) \(-3.41648 q^{72}\) \(-12.7258 q^{73}\) \(-1.12473 q^{74}\) \(+1.18060 q^{75}\) \(+4.03318 q^{76}\) \(+3.69156 q^{77}\) \(+7.44846 q^{78}\) \(+6.64324 q^{79}\) \(-2.12930 q^{80}\) \(-7.57709 q^{81}\) \(-7.47821 q^{82}\) \(+3.76008 q^{83}\) \(+3.04963 q^{84}\) \(+1.09424 q^{85}\) \(-10.9649 q^{86}\) \(-0.287492 q^{87}\) \(+3.06628 q^{88}\) \(-5.64721 q^{89}\) \(+7.27473 q^{90}\) \(-3.54011 q^{91}\) \(+6.16231 q^{92}\) \(-16.8356 q^{93}\) \(+9.30504 q^{94}\) \(-8.58785 q^{95}\) \(+2.53308 q^{96}\) \(+18.1952 q^{97}\) \(+5.55057 q^{98}\) \(-10.4759 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(86q \) \(\mathstrut -\mathstrut 86q^{2} \) \(\mathstrut +\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 86q^{4} \) \(\mathstrut -\mathstrut 4q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut +\mathstrut 35q^{7} \) \(\mathstrut -\mathstrut 86q^{8} \) \(\mathstrut +\mathstrut 72q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(86q \) \(\mathstrut -\mathstrut 86q^{2} \) \(\mathstrut +\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 86q^{4} \) \(\mathstrut -\mathstrut 4q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut +\mathstrut 35q^{7} \) \(\mathstrut -\mathstrut 86q^{8} \) \(\mathstrut +\mathstrut 72q^{9} \) \(\mathstrut +\mathstrut 4q^{10} \) \(\mathstrut +\mathstrut 13q^{11} \) \(\mathstrut +\mathstrut 12q^{12} \) \(\mathstrut +\mathstrut 45q^{13} \) \(\mathstrut -\mathstrut 35q^{14} \) \(\mathstrut +\mathstrut 17q^{15} \) \(\mathstrut +\mathstrut 86q^{16} \) \(\mathstrut +\mathstrut 5q^{17} \) \(\mathstrut -\mathstrut 72q^{18} \) \(\mathstrut +\mathstrut 47q^{19} \) \(\mathstrut -\mathstrut 4q^{20} \) \(\mathstrut +\mathstrut 15q^{21} \) \(\mathstrut -\mathstrut 13q^{22} \) \(\mathstrut +\mathstrut 6q^{23} \) \(\mathstrut -\mathstrut 12q^{24} \) \(\mathstrut +\mathstrut 112q^{25} \) \(\mathstrut -\mathstrut 45q^{26} \) \(\mathstrut +\mathstrut 51q^{27} \) \(\mathstrut +\mathstrut 35q^{28} \) \(\mathstrut -\mathstrut 14q^{29} \) \(\mathstrut -\mathstrut 17q^{30} \) \(\mathstrut +\mathstrut 24q^{31} \) \(\mathstrut -\mathstrut 86q^{32} \) \(\mathstrut +\mathstrut 43q^{33} \) \(\mathstrut -\mathstrut 5q^{34} \) \(\mathstrut +\mathstrut 42q^{35} \) \(\mathstrut +\mathstrut 72q^{36} \) \(\mathstrut +\mathstrut 61q^{37} \) \(\mathstrut -\mathstrut 47q^{38} \) \(\mathstrut +\mathstrut 20q^{39} \) \(\mathstrut +\mathstrut 4q^{40} \) \(\mathstrut -\mathstrut 16q^{41} \) \(\mathstrut -\mathstrut 15q^{42} \) \(\mathstrut +\mathstrut 72q^{43} \) \(\mathstrut +\mathstrut 13q^{44} \) \(\mathstrut +\mathstrut 6q^{45} \) \(\mathstrut -\mathstrut 6q^{46} \) \(\mathstrut +\mathstrut 11q^{47} \) \(\mathstrut +\mathstrut 12q^{48} \) \(\mathstrut +\mathstrut 89q^{49} \) \(\mathstrut -\mathstrut 112q^{50} \) \(\mathstrut +\mathstrut 56q^{51} \) \(\mathstrut +\mathstrut 45q^{52} \) \(\mathstrut -\mathstrut 7q^{53} \) \(\mathstrut -\mathstrut 51q^{54} \) \(\mathstrut +\mathstrut 48q^{55} \) \(\mathstrut -\mathstrut 35q^{56} \) \(\mathstrut +\mathstrut 65q^{57} \) \(\mathstrut +\mathstrut 14q^{58} \) \(\mathstrut +\mathstrut 24q^{59} \) \(\mathstrut +\mathstrut 17q^{60} \) \(\mathstrut +\mathstrut 31q^{61} \) \(\mathstrut -\mathstrut 24q^{62} \) \(\mathstrut +\mathstrut 98q^{63} \) \(\mathstrut +\mathstrut 86q^{64} \) \(\mathstrut -\mathstrut 9q^{65} \) \(\mathstrut -\mathstrut 43q^{66} \) \(\mathstrut +\mathstrut 157q^{67} \) \(\mathstrut +\mathstrut 5q^{68} \) \(\mathstrut +\mathstrut q^{69} \) \(\mathstrut -\mathstrut 42q^{70} \) \(\mathstrut -\mathstrut 11q^{71} \) \(\mathstrut -\mathstrut 72q^{72} \) \(\mathstrut +\mathstrut 74q^{73} \) \(\mathstrut -\mathstrut 61q^{74} \) \(\mathstrut +\mathstrut 76q^{75} \) \(\mathstrut +\mathstrut 47q^{76} \) \(\mathstrut -\mathstrut 13q^{77} \) \(\mathstrut -\mathstrut 20q^{78} \) \(\mathstrut +\mathstrut 57q^{79} \) \(\mathstrut -\mathstrut 4q^{80} \) \(\mathstrut +\mathstrut 34q^{81} \) \(\mathstrut +\mathstrut 16q^{82} \) \(\mathstrut +\mathstrut 65q^{83} \) \(\mathstrut +\mathstrut 15q^{84} \) \(\mathstrut +\mathstrut 102q^{85} \) \(\mathstrut -\mathstrut 72q^{86} \) \(\mathstrut +\mathstrut 49q^{87} \) \(\mathstrut -\mathstrut 13q^{88} \) \(\mathstrut -\mathstrut 34q^{89} \) \(\mathstrut -\mathstrut 6q^{90} \) \(\mathstrut +\mathstrut 91q^{91} \) \(\mathstrut +\mathstrut 6q^{92} \) \(\mathstrut +\mathstrut 57q^{93} \) \(\mathstrut -\mathstrut 11q^{94} \) \(\mathstrut -\mathstrut 13q^{95} \) \(\mathstrut -\mathstrut 12q^{96} \) \(\mathstrut +\mathstrut 64q^{97} \) \(\mathstrut -\mathstrut 89q^{98} \) \(\mathstrut +\mathstrut 56q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −2.53308 −1.46247 −0.731237 0.682124i \(-0.761056\pi\)
−0.731237 + 0.682124i \(0.761056\pi\)
\(4\) 1.00000 0.500000
\(5\) −2.12930 −0.952253 −0.476126 0.879377i \(-0.657960\pi\)
−0.476126 + 0.879377i \(0.657960\pi\)
\(6\) 2.53308 1.03412
\(7\) −1.20392 −0.455040 −0.227520 0.973773i \(-0.573062\pi\)
−0.227520 + 0.973773i \(0.573062\pi\)
\(8\) −1.00000 −0.353553
\(9\) 3.41648 1.13883
\(10\) 2.12930 0.673344
\(11\) −3.06628 −0.924519 −0.462260 0.886745i \(-0.652961\pi\)
−0.462260 + 0.886745i \(0.652961\pi\)
\(12\) −2.53308 −0.731237
\(13\) 2.94048 0.815542 0.407771 0.913084i \(-0.366306\pi\)
0.407771 + 0.913084i \(0.366306\pi\)
\(14\) 1.20392 0.321762
\(15\) 5.39369 1.39264
\(16\) 1.00000 0.250000
\(17\) −0.513898 −0.124639 −0.0623193 0.998056i \(-0.519850\pi\)
−0.0623193 + 0.998056i \(0.519850\pi\)
\(18\) −3.41648 −0.805273
\(19\) 4.03318 0.925274 0.462637 0.886548i \(-0.346903\pi\)
0.462637 + 0.886548i \(0.346903\pi\)
\(20\) −2.12930 −0.476126
\(21\) 3.04963 0.665483
\(22\) 3.06628 0.653734
\(23\) 6.16231 1.28493 0.642466 0.766315i \(-0.277912\pi\)
0.642466 + 0.766315i \(0.277912\pi\)
\(24\) 2.53308 0.517062
\(25\) −0.466073 −0.0932146
\(26\) −2.94048 −0.576675
\(27\) −1.05499 −0.203032
\(28\) −1.20392 −0.227520
\(29\) 0.113495 0.0210755 0.0105378 0.999944i \(-0.496646\pi\)
0.0105378 + 0.999944i \(0.496646\pi\)
\(30\) −5.39369 −0.984748
\(31\) 6.64630 1.19371 0.596855 0.802349i \(-0.296417\pi\)
0.596855 + 0.802349i \(0.296417\pi\)
\(32\) −1.00000 −0.176777
\(33\) 7.76713 1.35208
\(34\) 0.513898 0.0881328
\(35\) 2.56351 0.433313
\(36\) 3.41648 0.569414
\(37\) 1.12473 0.184904 0.0924522 0.995717i \(-0.470529\pi\)
0.0924522 + 0.995717i \(0.470529\pi\)
\(38\) −4.03318 −0.654268
\(39\) −7.44846 −1.19271
\(40\) 2.12930 0.336672
\(41\) 7.47821 1.16790 0.583950 0.811790i \(-0.301506\pi\)
0.583950 + 0.811790i \(0.301506\pi\)
\(42\) −3.04963 −0.470568
\(43\) 10.9649 1.67212 0.836062 0.548634i \(-0.184852\pi\)
0.836062 + 0.548634i \(0.184852\pi\)
\(44\) −3.06628 −0.462260
\(45\) −7.27473 −1.08445
\(46\) −6.16231 −0.908584
\(47\) −9.30504 −1.35728 −0.678640 0.734471i \(-0.737430\pi\)
−0.678640 + 0.734471i \(0.737430\pi\)
\(48\) −2.53308 −0.365618
\(49\) −5.55057 −0.792939
\(50\) 0.466073 0.0659127
\(51\) 1.30174 0.182281
\(52\) 2.94048 0.407771
\(53\) −0.632478 −0.0868775 −0.0434388 0.999056i \(-0.513831\pi\)
−0.0434388 + 0.999056i \(0.513831\pi\)
\(54\) 1.05499 0.143566
\(55\) 6.52904 0.880376
\(56\) 1.20392 0.160881
\(57\) −10.2163 −1.35319
\(58\) −0.113495 −0.0149027
\(59\) −12.6898 −1.65208 −0.826038 0.563615i \(-0.809410\pi\)
−0.826038 + 0.563615i \(0.809410\pi\)
\(60\) 5.39369 0.696322
\(61\) 8.24791 1.05604 0.528018 0.849233i \(-0.322935\pi\)
0.528018 + 0.849233i \(0.322935\pi\)
\(62\) −6.64630 −0.844080
\(63\) −4.11318 −0.518212
\(64\) 1.00000 0.125000
\(65\) −6.26117 −0.776602
\(66\) −7.76713 −0.956068
\(67\) 3.19595 0.390448 0.195224 0.980759i \(-0.437457\pi\)
0.195224 + 0.980759i \(0.437457\pi\)
\(68\) −0.513898 −0.0623193
\(69\) −15.6096 −1.87918
\(70\) −2.56351 −0.306398
\(71\) −5.15906 −0.612267 −0.306134 0.951989i \(-0.599035\pi\)
−0.306134 + 0.951989i \(0.599035\pi\)
\(72\) −3.41648 −0.402637
\(73\) −12.7258 −1.48945 −0.744723 0.667373i \(-0.767419\pi\)
−0.744723 + 0.667373i \(0.767419\pi\)
\(74\) −1.12473 −0.130747
\(75\) 1.18060 0.136324
\(76\) 4.03318 0.462637
\(77\) 3.69156 0.420693
\(78\) 7.44846 0.843372
\(79\) 6.64324 0.747423 0.373712 0.927545i \(-0.378085\pi\)
0.373712 + 0.927545i \(0.378085\pi\)
\(80\) −2.12930 −0.238063
\(81\) −7.57709 −0.841899
\(82\) −7.47821 −0.825830
\(83\) 3.76008 0.412723 0.206361 0.978476i \(-0.433838\pi\)
0.206361 + 0.978476i \(0.433838\pi\)
\(84\) 3.04963 0.332742
\(85\) 1.09424 0.118687
\(86\) −10.9649 −1.18237
\(87\) −0.287492 −0.0308224
\(88\) 3.06628 0.326867
\(89\) −5.64721 −0.598603 −0.299301 0.954159i \(-0.596754\pi\)
−0.299301 + 0.954159i \(0.596754\pi\)
\(90\) 7.27473 0.766824
\(91\) −3.54011 −0.371104
\(92\) 6.16231 0.642466
\(93\) −16.8356 −1.74577
\(94\) 9.30504 0.959742
\(95\) −8.58785 −0.881095
\(96\) 2.53308 0.258531
\(97\) 18.1952 1.84745 0.923723 0.383060i \(-0.125130\pi\)
0.923723 + 0.383060i \(0.125130\pi\)
\(98\) 5.55057 0.560693
\(99\) −10.4759 −1.05287
\(100\) −0.466073 −0.0466073
\(101\) 12.5521 1.24898 0.624492 0.781031i \(-0.285306\pi\)
0.624492 + 0.781031i \(0.285306\pi\)
\(102\) −1.30174 −0.128892
\(103\) −4.42601 −0.436107 −0.218054 0.975937i \(-0.569971\pi\)
−0.218054 + 0.975937i \(0.569971\pi\)
\(104\) −2.94048 −0.288338
\(105\) −6.49358 −0.633708
\(106\) 0.632478 0.0614317
\(107\) −10.7491 −1.03916 −0.519579 0.854423i \(-0.673911\pi\)
−0.519579 + 0.854423i \(0.673911\pi\)
\(108\) −1.05499 −0.101516
\(109\) 0.866909 0.0830348 0.0415174 0.999138i \(-0.486781\pi\)
0.0415174 + 0.999138i \(0.486781\pi\)
\(110\) −6.52904 −0.622520
\(111\) −2.84903 −0.270418
\(112\) −1.20392 −0.113760
\(113\) 18.6280 1.75238 0.876188 0.481969i \(-0.160078\pi\)
0.876188 + 0.481969i \(0.160078\pi\)
\(114\) 10.2163 0.956849
\(115\) −13.1214 −1.22358
\(116\) 0.113495 0.0105378
\(117\) 10.0461 0.928762
\(118\) 12.6898 1.16819
\(119\) 0.618693 0.0567155
\(120\) −5.39369 −0.492374
\(121\) −1.59791 −0.145264
\(122\) −8.24791 −0.746731
\(123\) −18.9429 −1.70802
\(124\) 6.64630 0.596855
\(125\) 11.6389 1.04102
\(126\) 4.11318 0.366431
\(127\) 13.2106 1.17225 0.586124 0.810221i \(-0.300653\pi\)
0.586124 + 0.810221i \(0.300653\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −27.7748 −2.44544
\(130\) 6.26117 0.549141
\(131\) 1.78277 0.155762 0.0778808 0.996963i \(-0.475185\pi\)
0.0778808 + 0.996963i \(0.475185\pi\)
\(132\) 7.76713 0.676042
\(133\) −4.85563 −0.421036
\(134\) −3.19595 −0.276088
\(135\) 2.24639 0.193338
\(136\) 0.513898 0.0440664
\(137\) −17.1499 −1.46521 −0.732607 0.680652i \(-0.761697\pi\)
−0.732607 + 0.680652i \(0.761697\pi\)
\(138\) 15.6096 1.32878
\(139\) −22.9002 −1.94237 −0.971185 0.238326i \(-0.923401\pi\)
−0.971185 + 0.238326i \(0.923401\pi\)
\(140\) 2.56351 0.216656
\(141\) 23.5704 1.98499
\(142\) 5.15906 0.432938
\(143\) −9.01634 −0.753984
\(144\) 3.41648 0.284707
\(145\) −0.241666 −0.0200692
\(146\) 12.7258 1.05320
\(147\) 14.0600 1.15965
\(148\) 1.12473 0.0924522
\(149\) 3.81534 0.312565 0.156282 0.987712i \(-0.450049\pi\)
0.156282 + 0.987712i \(0.450049\pi\)
\(150\) −1.18060 −0.0963956
\(151\) 2.63594 0.214510 0.107255 0.994232i \(-0.465794\pi\)
0.107255 + 0.994232i \(0.465794\pi\)
\(152\) −4.03318 −0.327134
\(153\) −1.75572 −0.141942
\(154\) −3.69156 −0.297475
\(155\) −14.1520 −1.13671
\(156\) −7.44846 −0.596354
\(157\) −12.1405 −0.968915 −0.484458 0.874815i \(-0.660983\pi\)
−0.484458 + 0.874815i \(0.660983\pi\)
\(158\) −6.64324 −0.528508
\(159\) 1.60212 0.127056
\(160\) 2.12930 0.168336
\(161\) −7.41894 −0.584694
\(162\) 7.57709 0.595312
\(163\) 3.78720 0.296636 0.148318 0.988940i \(-0.452614\pi\)
0.148318 + 0.988940i \(0.452614\pi\)
\(164\) 7.47821 0.583950
\(165\) −16.5386 −1.28753
\(166\) −3.76008 −0.291839
\(167\) 0.835722 0.0646701 0.0323350 0.999477i \(-0.489706\pi\)
0.0323350 + 0.999477i \(0.489706\pi\)
\(168\) −3.04963 −0.235284
\(169\) −4.35359 −0.334891
\(170\) −1.09424 −0.0839247
\(171\) 13.7793 1.05373
\(172\) 10.9649 0.836062
\(173\) −17.9559 −1.36516 −0.682580 0.730811i \(-0.739142\pi\)
−0.682580 + 0.730811i \(0.739142\pi\)
\(174\) 0.287492 0.0217947
\(175\) 0.561116 0.0424163
\(176\) −3.06628 −0.231130
\(177\) 32.1443 2.41612
\(178\) 5.64721 0.423276
\(179\) −15.0728 −1.12659 −0.563297 0.826254i \(-0.690467\pi\)
−0.563297 + 0.826254i \(0.690467\pi\)
\(180\) −7.27473 −0.542226
\(181\) −0.830708 −0.0617460 −0.0308730 0.999523i \(-0.509829\pi\)
−0.0308730 + 0.999523i \(0.509829\pi\)
\(182\) 3.54011 0.262410
\(183\) −20.8926 −1.54443
\(184\) −6.16231 −0.454292
\(185\) −2.39489 −0.176076
\(186\) 16.8356 1.23445
\(187\) 1.57576 0.115231
\(188\) −9.30504 −0.678640
\(189\) 1.27012 0.0923878
\(190\) 8.58785 0.623028
\(191\) 1.57893 0.114247 0.0571237 0.998367i \(-0.481807\pi\)
0.0571237 + 0.998367i \(0.481807\pi\)
\(192\) −2.53308 −0.182809
\(193\) 2.09273 0.150638 0.0753190 0.997159i \(-0.476003\pi\)
0.0753190 + 0.997159i \(0.476003\pi\)
\(194\) −18.1952 −1.30634
\(195\) 15.8600 1.13576
\(196\) −5.55057 −0.396470
\(197\) 13.2338 0.942868 0.471434 0.881901i \(-0.343737\pi\)
0.471434 + 0.881901i \(0.343737\pi\)
\(198\) 10.4759 0.744490
\(199\) 12.5057 0.886502 0.443251 0.896397i \(-0.353825\pi\)
0.443251 + 0.896397i \(0.353825\pi\)
\(200\) 0.466073 0.0329564
\(201\) −8.09560 −0.571019
\(202\) −12.5521 −0.883165
\(203\) −0.136639 −0.00959020
\(204\) 1.30174 0.0911403
\(205\) −15.9234 −1.11214
\(206\) 4.42601 0.308375
\(207\) 21.0534 1.46332
\(208\) 2.94048 0.203885
\(209\) −12.3669 −0.855433
\(210\) 6.49358 0.448099
\(211\) −21.2655 −1.46397 −0.731987 0.681319i \(-0.761407\pi\)
−0.731987 + 0.681319i \(0.761407\pi\)
\(212\) −0.632478 −0.0434388
\(213\) 13.0683 0.895425
\(214\) 10.7491 0.734795
\(215\) −23.3475 −1.59229
\(216\) 1.05499 0.0717828
\(217\) −8.00162 −0.543185
\(218\) −0.866909 −0.0587145
\(219\) 32.2355 2.17828
\(220\) 6.52904 0.440188
\(221\) −1.51111 −0.101648
\(222\) 2.84903 0.191214
\(223\) −10.1800 −0.681705 −0.340853 0.940117i \(-0.610716\pi\)
−0.340853 + 0.940117i \(0.610716\pi\)
\(224\) 1.20392 0.0804404
\(225\) −1.59233 −0.106155
\(226\) −18.6280 −1.23912
\(227\) 9.15917 0.607916 0.303958 0.952686i \(-0.401692\pi\)
0.303958 + 0.952686i \(0.401692\pi\)
\(228\) −10.2163 −0.676594
\(229\) −7.22664 −0.477549 −0.238775 0.971075i \(-0.576746\pi\)
−0.238775 + 0.971075i \(0.576746\pi\)
\(230\) 13.1214 0.865201
\(231\) −9.35102 −0.615252
\(232\) −0.113495 −0.00745133
\(233\) −11.1930 −0.733277 −0.366639 0.930363i \(-0.619491\pi\)
−0.366639 + 0.930363i \(0.619491\pi\)
\(234\) −10.0461 −0.656734
\(235\) 19.8132 1.29247
\(236\) −12.6898 −0.826038
\(237\) −16.8278 −1.09309
\(238\) −0.618693 −0.0401039
\(239\) 13.4255 0.868423 0.434212 0.900811i \(-0.357027\pi\)
0.434212 + 0.900811i \(0.357027\pi\)
\(240\) 5.39369 0.348161
\(241\) −12.9413 −0.833621 −0.416810 0.908993i \(-0.636852\pi\)
−0.416810 + 0.908993i \(0.636852\pi\)
\(242\) 1.59791 0.102717
\(243\) 22.3583 1.43429
\(244\) 8.24791 0.528018
\(245\) 11.8188 0.755078
\(246\) 18.9429 1.20775
\(247\) 11.8595 0.754600
\(248\) −6.64630 −0.422040
\(249\) −9.52458 −0.603596
\(250\) −11.6389 −0.736110
\(251\) 29.1185 1.83795 0.918973 0.394321i \(-0.129020\pi\)
0.918973 + 0.394321i \(0.129020\pi\)
\(252\) −4.11318 −0.259106
\(253\) −18.8954 −1.18794
\(254\) −13.2106 −0.828904
\(255\) −2.77181 −0.173577
\(256\) 1.00000 0.0625000
\(257\) −1.53352 −0.0956582 −0.0478291 0.998856i \(-0.515230\pi\)
−0.0478291 + 0.998856i \(0.515230\pi\)
\(258\) 27.7748 1.72919
\(259\) −1.35409 −0.0841388
\(260\) −6.26117 −0.388301
\(261\) 0.387755 0.0240014
\(262\) −1.78277 −0.110140
\(263\) 10.5843 0.652659 0.326329 0.945256i \(-0.394188\pi\)
0.326329 + 0.945256i \(0.394188\pi\)
\(264\) −7.76713 −0.478034
\(265\) 1.34674 0.0827294
\(266\) 4.85563 0.297718
\(267\) 14.3048 0.875440
\(268\) 3.19595 0.195224
\(269\) −16.9355 −1.03257 −0.516287 0.856415i \(-0.672686\pi\)
−0.516287 + 0.856415i \(0.672686\pi\)
\(270\) −2.24639 −0.136711
\(271\) 28.2892 1.71845 0.859223 0.511602i \(-0.170948\pi\)
0.859223 + 0.511602i \(0.170948\pi\)
\(272\) −0.513898 −0.0311596
\(273\) 8.96736 0.542729
\(274\) 17.1499 1.03606
\(275\) 1.42911 0.0861787
\(276\) −15.6096 −0.939589
\(277\) 1.00398 0.0603234 0.0301617 0.999545i \(-0.490398\pi\)
0.0301617 + 0.999545i \(0.490398\pi\)
\(278\) 22.9002 1.37346
\(279\) 22.7070 1.35943
\(280\) −2.56351 −0.153199
\(281\) −22.4590 −1.33979 −0.669896 0.742455i \(-0.733662\pi\)
−0.669896 + 0.742455i \(0.733662\pi\)
\(282\) −23.5704 −1.40360
\(283\) 10.6085 0.630609 0.315305 0.948991i \(-0.397893\pi\)
0.315305 + 0.948991i \(0.397893\pi\)
\(284\) −5.15906 −0.306134
\(285\) 21.7537 1.28858
\(286\) 9.01634 0.533147
\(287\) −9.00318 −0.531441
\(288\) −3.41648 −0.201318
\(289\) −16.7359 −0.984465
\(290\) 0.241666 0.0141911
\(291\) −46.0900 −2.70184
\(292\) −12.7258 −0.744723
\(293\) −2.18696 −0.127763 −0.0638817 0.997957i \(-0.520348\pi\)
−0.0638817 + 0.997957i \(0.520348\pi\)
\(294\) −14.0600 −0.819998
\(295\) 27.0205 1.57319
\(296\) −1.12473 −0.0653736
\(297\) 3.23489 0.187707
\(298\) −3.81534 −0.221016
\(299\) 18.1201 1.04792
\(300\) 1.18060 0.0681620
\(301\) −13.2008 −0.760883
\(302\) −2.63594 −0.151681
\(303\) −31.7955 −1.82661
\(304\) 4.03318 0.231318
\(305\) −17.5623 −1.00561
\(306\) 1.75572 0.100368
\(307\) 24.8860 1.42032 0.710160 0.704040i \(-0.248622\pi\)
0.710160 + 0.704040i \(0.248622\pi\)
\(308\) 3.69156 0.210346
\(309\) 11.2114 0.637795
\(310\) 14.1520 0.803778
\(311\) −2.33950 −0.132661 −0.0663303 0.997798i \(-0.521129\pi\)
−0.0663303 + 0.997798i \(0.521129\pi\)
\(312\) 7.44846 0.421686
\(313\) −9.59628 −0.542414 −0.271207 0.962521i \(-0.587423\pi\)
−0.271207 + 0.962521i \(0.587423\pi\)
\(314\) 12.1405 0.685126
\(315\) 8.75820 0.493469
\(316\) 6.64324 0.373712
\(317\) 32.5612 1.82882 0.914411 0.404788i \(-0.132655\pi\)
0.914411 + 0.404788i \(0.132655\pi\)
\(318\) −1.60212 −0.0898422
\(319\) −0.348008 −0.0194847
\(320\) −2.12930 −0.119032
\(321\) 27.2284 1.51974
\(322\) 7.41894 0.413441
\(323\) −2.07264 −0.115325
\(324\) −7.57709 −0.420949
\(325\) −1.37048 −0.0760205
\(326\) −3.78720 −0.209754
\(327\) −2.19595 −0.121436
\(328\) −7.47821 −0.412915
\(329\) 11.2025 0.617616
\(330\) 16.5386 0.910419
\(331\) 29.2281 1.60652 0.803260 0.595629i \(-0.203097\pi\)
0.803260 + 0.595629i \(0.203097\pi\)
\(332\) 3.76008 0.206361
\(333\) 3.84262 0.210574
\(334\) −0.835722 −0.0457287
\(335\) −6.80515 −0.371805
\(336\) 3.04963 0.166371
\(337\) −4.99392 −0.272036 −0.136018 0.990706i \(-0.543431\pi\)
−0.136018 + 0.990706i \(0.543431\pi\)
\(338\) 4.35359 0.236804
\(339\) −47.1862 −2.56280
\(340\) 1.09424 0.0593437
\(341\) −20.3794 −1.10361
\(342\) −13.7793 −0.745098
\(343\) 15.1099 0.815858
\(344\) −10.9649 −0.591185
\(345\) 33.2376 1.78945
\(346\) 17.9559 0.965314
\(347\) 1.46788 0.0787997 0.0393999 0.999224i \(-0.487455\pi\)
0.0393999 + 0.999224i \(0.487455\pi\)
\(348\) −0.287492 −0.0154112
\(349\) −6.77065 −0.362425 −0.181212 0.983444i \(-0.558002\pi\)
−0.181212 + 0.983444i \(0.558002\pi\)
\(350\) −0.561116 −0.0299929
\(351\) −3.10217 −0.165582
\(352\) 3.06628 0.163433
\(353\) −29.8279 −1.58758 −0.793790 0.608192i \(-0.791895\pi\)
−0.793790 + 0.608192i \(0.791895\pi\)
\(354\) −32.1443 −1.70845
\(355\) 10.9852 0.583033
\(356\) −5.64721 −0.299301
\(357\) −1.56720 −0.0829449
\(358\) 15.0728 0.796623
\(359\) 2.57061 0.135672 0.0678358 0.997696i \(-0.478391\pi\)
0.0678358 + 0.997696i \(0.478391\pi\)
\(360\) 7.27473 0.383412
\(361\) −2.73349 −0.143868
\(362\) 0.830708 0.0436610
\(363\) 4.04763 0.212445
\(364\) −3.54011 −0.185552
\(365\) 27.0972 1.41833
\(366\) 20.8926 1.09207
\(367\) 24.4069 1.27403 0.637014 0.770852i \(-0.280169\pi\)
0.637014 + 0.770852i \(0.280169\pi\)
\(368\) 6.16231 0.321233
\(369\) 25.5492 1.33004
\(370\) 2.39489 0.124504
\(371\) 0.761454 0.0395327
\(372\) −16.8356 −0.872884
\(373\) −15.3279 −0.793650 −0.396825 0.917894i \(-0.629888\pi\)
−0.396825 + 0.917894i \(0.629888\pi\)
\(374\) −1.57576 −0.0814804
\(375\) −29.4823 −1.52246
\(376\) 9.30504 0.479871
\(377\) 0.333730 0.0171880
\(378\) −1.27012 −0.0653280
\(379\) −22.1185 −1.13615 −0.568075 0.822976i \(-0.692312\pi\)
−0.568075 + 0.822976i \(0.692312\pi\)
\(380\) −8.58785 −0.440547
\(381\) −33.4634 −1.71438
\(382\) −1.57893 −0.0807851
\(383\) −20.8364 −1.06469 −0.532345 0.846528i \(-0.678689\pi\)
−0.532345 + 0.846528i \(0.678689\pi\)
\(384\) 2.53308 0.129266
\(385\) −7.86045 −0.400606
\(386\) −2.09273 −0.106517
\(387\) 37.4613 1.90426
\(388\) 18.1952 0.923723
\(389\) −5.44060 −0.275849 −0.137925 0.990443i \(-0.544043\pi\)
−0.137925 + 0.990443i \(0.544043\pi\)
\(390\) −15.8600 −0.803104
\(391\) −3.16680 −0.160152
\(392\) 5.55057 0.280346
\(393\) −4.51591 −0.227797
\(394\) −13.2338 −0.666708
\(395\) −14.1455 −0.711736
\(396\) −10.4759 −0.526434
\(397\) −23.7638 −1.19267 −0.596337 0.802735i \(-0.703378\pi\)
−0.596337 + 0.802735i \(0.703378\pi\)
\(398\) −12.5057 −0.626852
\(399\) 12.2997 0.615754
\(400\) −0.466073 −0.0233037
\(401\) 3.18365 0.158984 0.0794918 0.996836i \(-0.474670\pi\)
0.0794918 + 0.996836i \(0.474670\pi\)
\(402\) 8.09560 0.403772
\(403\) 19.5433 0.973521
\(404\) 12.5521 0.624492
\(405\) 16.1339 0.801700
\(406\) 0.136639 0.00678130
\(407\) −3.44874 −0.170948
\(408\) −1.30174 −0.0644459
\(409\) 28.8154 1.42483 0.712414 0.701760i \(-0.247602\pi\)
0.712414 + 0.701760i \(0.247602\pi\)
\(410\) 15.9234 0.786399
\(411\) 43.4420 2.14284
\(412\) −4.42601 −0.218054
\(413\) 15.2776 0.751759
\(414\) −21.0534 −1.03472
\(415\) −8.00635 −0.393016
\(416\) −2.94048 −0.144169
\(417\) 58.0080 2.84066
\(418\) 12.3669 0.604883
\(419\) 25.0695 1.22473 0.612363 0.790577i \(-0.290219\pi\)
0.612363 + 0.790577i \(0.290219\pi\)
\(420\) −6.49358 −0.316854
\(421\) 21.7468 1.05987 0.529936 0.848038i \(-0.322216\pi\)
0.529936 + 0.848038i \(0.322216\pi\)
\(422\) 21.2655 1.03519
\(423\) −31.7905 −1.54571
\(424\) 0.632478 0.0307159
\(425\) 0.239514 0.0116181
\(426\) −13.0683 −0.633161
\(427\) −9.92984 −0.480539
\(428\) −10.7491 −0.519579
\(429\) 22.8391 1.10268
\(430\) 23.3475 1.12592
\(431\) −10.2615 −0.494279 −0.247139 0.968980i \(-0.579491\pi\)
−0.247139 + 0.968980i \(0.579491\pi\)
\(432\) −1.05499 −0.0507581
\(433\) 17.4472 0.838458 0.419229 0.907881i \(-0.362300\pi\)
0.419229 + 0.907881i \(0.362300\pi\)
\(434\) 8.00162 0.384090
\(435\) 0.612158 0.0293507
\(436\) 0.866909 0.0415174
\(437\) 24.8537 1.18891
\(438\) −32.2355 −1.54027
\(439\) −38.6564 −1.84497 −0.922484 0.386036i \(-0.873844\pi\)
−0.922484 + 0.386036i \(0.873844\pi\)
\(440\) −6.52904 −0.311260
\(441\) −18.9634 −0.903021
\(442\) 1.51111 0.0718760
\(443\) 28.1368 1.33682 0.668411 0.743793i \(-0.266975\pi\)
0.668411 + 0.743793i \(0.266975\pi\)
\(444\) −2.84903 −0.135209
\(445\) 12.0246 0.570021
\(446\) 10.1800 0.482038
\(447\) −9.66454 −0.457117
\(448\) −1.20392 −0.0568799
\(449\) −21.8623 −1.03174 −0.515872 0.856666i \(-0.672532\pi\)
−0.515872 + 0.856666i \(0.672532\pi\)
\(450\) 1.59233 0.0750632
\(451\) −22.9303 −1.07975
\(452\) 18.6280 0.876188
\(453\) −6.67704 −0.313715
\(454\) −9.15917 −0.429861
\(455\) 7.53795 0.353385
\(456\) 10.2163 0.478424
\(457\) 12.9541 0.605966 0.302983 0.952996i \(-0.402017\pi\)
0.302983 + 0.952996i \(0.402017\pi\)
\(458\) 7.22664 0.337678
\(459\) 0.542156 0.0253057
\(460\) −13.1214 −0.611790
\(461\) −15.9404 −0.742417 −0.371209 0.928549i \(-0.621057\pi\)
−0.371209 + 0.928549i \(0.621057\pi\)
\(462\) 9.35102 0.435049
\(463\) 39.4991 1.83568 0.917840 0.396951i \(-0.129932\pi\)
0.917840 + 0.396951i \(0.129932\pi\)
\(464\) 0.113495 0.00526888
\(465\) 35.8480 1.66241
\(466\) 11.1930 0.518505
\(467\) 32.1352 1.48704 0.743519 0.668715i \(-0.233155\pi\)
0.743519 + 0.668715i \(0.233155\pi\)
\(468\) 10.0461 0.464381
\(469\) −3.84768 −0.177669
\(470\) −19.8132 −0.913917
\(471\) 30.7528 1.41701
\(472\) 12.6898 0.584097
\(473\) −33.6214 −1.54591
\(474\) 16.8278 0.772929
\(475\) −1.87976 −0.0862491
\(476\) 0.618693 0.0283577
\(477\) −2.16085 −0.0989386
\(478\) −13.4255 −0.614068
\(479\) 11.1418 0.509081 0.254541 0.967062i \(-0.418076\pi\)
0.254541 + 0.967062i \(0.418076\pi\)
\(480\) −5.39369 −0.246187
\(481\) 3.30724 0.150797
\(482\) 12.9413 0.589459
\(483\) 18.7928 0.855100
\(484\) −1.59791 −0.0726322
\(485\) −38.7432 −1.75924
\(486\) −22.3583 −1.01419
\(487\) −17.9409 −0.812978 −0.406489 0.913656i \(-0.633247\pi\)
−0.406489 + 0.913656i \(0.633247\pi\)
\(488\) −8.24791 −0.373365
\(489\) −9.59327 −0.433823
\(490\) −11.8188 −0.533921
\(491\) −40.9212 −1.84675 −0.923375 0.383900i \(-0.874581\pi\)
−0.923375 + 0.383900i \(0.874581\pi\)
\(492\) −18.9429 −0.854011
\(493\) −0.0583250 −0.00262682
\(494\) −11.8595 −0.533583
\(495\) 22.3064 1.00260
\(496\) 6.64630 0.298427
\(497\) 6.21110 0.278606
\(498\) 9.52458 0.426807
\(499\) −23.3987 −1.04747 −0.523734 0.851882i \(-0.675462\pi\)
−0.523734 + 0.851882i \(0.675462\pi\)
\(500\) 11.6389 0.520508
\(501\) −2.11695 −0.0945783
\(502\) −29.1185 −1.29962
\(503\) 3.38932 0.151122 0.0755612 0.997141i \(-0.475925\pi\)
0.0755612 + 0.997141i \(0.475925\pi\)
\(504\) 4.11318 0.183216
\(505\) −26.7273 −1.18935
\(506\) 18.8954 0.840003
\(507\) 11.0280 0.489770
\(508\) 13.2106 0.586124
\(509\) −14.7430 −0.653470 −0.326735 0.945116i \(-0.605948\pi\)
−0.326735 + 0.945116i \(0.605948\pi\)
\(510\) 2.77181 0.122738
\(511\) 15.3209 0.677757
\(512\) −1.00000 −0.0441942
\(513\) −4.25495 −0.187861
\(514\) 1.53352 0.0676406
\(515\) 9.42431 0.415285
\(516\) −27.7748 −1.22272
\(517\) 28.5319 1.25483
\(518\) 1.35409 0.0594951
\(519\) 45.4837 1.99651
\(520\) 6.26117 0.274570
\(521\) −14.9116 −0.653290 −0.326645 0.945147i \(-0.605918\pi\)
−0.326645 + 0.945147i \(0.605918\pi\)
\(522\) −0.387755 −0.0169716
\(523\) 27.1952 1.18916 0.594582 0.804035i \(-0.297318\pi\)
0.594582 + 0.804035i \(0.297318\pi\)
\(524\) 1.78277 0.0778808
\(525\) −1.42135 −0.0620328
\(526\) −10.5843 −0.461499
\(527\) −3.41552 −0.148782
\(528\) 7.76713 0.338021
\(529\) 14.9741 0.651048
\(530\) −1.34674 −0.0584985
\(531\) −43.3546 −1.88143
\(532\) −4.85563 −0.210518
\(533\) 21.9895 0.952472
\(534\) −14.3048 −0.619030
\(535\) 22.8881 0.989540
\(536\) −3.19595 −0.138044
\(537\) 38.1806 1.64762
\(538\) 16.9355 0.730141
\(539\) 17.0196 0.733087
\(540\) 2.24639 0.0966691
\(541\) −12.4078 −0.533452 −0.266726 0.963772i \(-0.585942\pi\)
−0.266726 + 0.963772i \(0.585942\pi\)
\(542\) −28.2892 −1.21512
\(543\) 2.10425 0.0903019
\(544\) 0.513898 0.0220332
\(545\) −1.84591 −0.0790701
\(546\) −8.96736 −0.383768
\(547\) 11.2214 0.479793 0.239896 0.970798i \(-0.422887\pi\)
0.239896 + 0.970798i \(0.422887\pi\)
\(548\) −17.1499 −0.732607
\(549\) 28.1789 1.20264
\(550\) −1.42911 −0.0609376
\(551\) 0.457746 0.0195006
\(552\) 15.6096 0.664390
\(553\) −7.99794 −0.340107
\(554\) −1.00398 −0.0426551
\(555\) 6.06644 0.257506
\(556\) −22.9002 −0.971185
\(557\) −10.8678 −0.460483 −0.230242 0.973133i \(-0.573952\pi\)
−0.230242 + 0.973133i \(0.573952\pi\)
\(558\) −22.7070 −0.961262
\(559\) 32.2419 1.36369
\(560\) 2.56351 0.108328
\(561\) −3.99151 −0.168522
\(562\) 22.4590 0.947377
\(563\) 0.670584 0.0282618 0.0141309 0.999900i \(-0.495502\pi\)
0.0141309 + 0.999900i \(0.495502\pi\)
\(564\) 23.5704 0.992493
\(565\) −39.6647 −1.66871
\(566\) −10.6085 −0.445908
\(567\) 9.12222 0.383097
\(568\) 5.15906 0.216469
\(569\) 21.5616 0.903910 0.451955 0.892041i \(-0.350727\pi\)
0.451955 + 0.892041i \(0.350727\pi\)
\(570\) −21.7537 −0.911162
\(571\) 14.8583 0.621799 0.310899 0.950443i \(-0.399370\pi\)
0.310899 + 0.950443i \(0.399370\pi\)
\(572\) −9.01634 −0.376992
\(573\) −3.99956 −0.167084
\(574\) 9.00318 0.375785
\(575\) −2.87209 −0.119774
\(576\) 3.41648 0.142354
\(577\) 40.0292 1.66644 0.833219 0.552943i \(-0.186495\pi\)
0.833219 + 0.552943i \(0.186495\pi\)
\(578\) 16.7359 0.696122
\(579\) −5.30105 −0.220304
\(580\) −0.241666 −0.0100346
\(581\) −4.52684 −0.187805
\(582\) 46.0900 1.91049
\(583\) 1.93936 0.0803200
\(584\) 12.7258 0.526599
\(585\) −21.3912 −0.884416
\(586\) 2.18696 0.0903423
\(587\) −4.78535 −0.197512 −0.0987562 0.995112i \(-0.531486\pi\)
−0.0987562 + 0.995112i \(0.531486\pi\)
\(588\) 14.0600 0.579826
\(589\) 26.8057 1.10451
\(590\) −27.0205 −1.11242
\(591\) −33.5222 −1.37892
\(592\) 1.12473 0.0462261
\(593\) −4.00197 −0.164341 −0.0821707 0.996618i \(-0.526185\pi\)
−0.0821707 + 0.996618i \(0.526185\pi\)
\(594\) −3.23489 −0.132729
\(595\) −1.31738 −0.0540075
\(596\) 3.81534 0.156282
\(597\) −31.6778 −1.29649
\(598\) −18.1201 −0.740988
\(599\) −5.02840 −0.205455 −0.102727 0.994710i \(-0.532757\pi\)
−0.102727 + 0.994710i \(0.532757\pi\)
\(600\) −1.18060 −0.0481978
\(601\) 4.88081 0.199093 0.0995463 0.995033i \(-0.468261\pi\)
0.0995463 + 0.995033i \(0.468261\pi\)
\(602\) 13.2008 0.538026
\(603\) 10.9189 0.444653
\(604\) 2.63594 0.107255
\(605\) 3.40243 0.138328
\(606\) 31.7955 1.29161
\(607\) −28.6821 −1.16417 −0.582086 0.813127i \(-0.697763\pi\)
−0.582086 + 0.813127i \(0.697763\pi\)
\(608\) −4.03318 −0.163567
\(609\) 0.346118 0.0140254
\(610\) 17.5623 0.711077
\(611\) −27.3613 −1.10692
\(612\) −1.75572 −0.0709710
\(613\) 27.9728 1.12981 0.564906 0.825156i \(-0.308913\pi\)
0.564906 + 0.825156i \(0.308913\pi\)
\(614\) −24.8860 −1.00432
\(615\) 40.3351 1.62647
\(616\) −3.69156 −0.148737
\(617\) 7.45984 0.300322 0.150161 0.988662i \(-0.452021\pi\)
0.150161 + 0.988662i \(0.452021\pi\)
\(618\) −11.2114 −0.450990
\(619\) 40.5111 1.62828 0.814140 0.580669i \(-0.197209\pi\)
0.814140 + 0.580669i \(0.197209\pi\)
\(620\) −14.1520 −0.568357
\(621\) −6.50116 −0.260883
\(622\) 2.33950 0.0938052
\(623\) 6.79879 0.272388
\(624\) −7.44846 −0.298177
\(625\) −22.4524 −0.898096
\(626\) 9.59628 0.383545
\(627\) 31.3262 1.25105
\(628\) −12.1405 −0.484458
\(629\) −0.577996 −0.0230462
\(630\) −8.75820 −0.348935
\(631\) 37.8225 1.50569 0.752844 0.658199i \(-0.228681\pi\)
0.752844 + 0.658199i \(0.228681\pi\)
\(632\) −6.64324 −0.264254
\(633\) 53.8670 2.14102
\(634\) −32.5612 −1.29317
\(635\) −28.1293 −1.11628
\(636\) 1.60212 0.0635280
\(637\) −16.3213 −0.646675
\(638\) 0.348008 0.0137778
\(639\) −17.6258 −0.697267
\(640\) 2.12930 0.0841680
\(641\) 16.3878 0.647278 0.323639 0.946181i \(-0.395094\pi\)
0.323639 + 0.946181i \(0.395094\pi\)
\(642\) −27.2284 −1.07462
\(643\) 21.6475 0.853692 0.426846 0.904324i \(-0.359625\pi\)
0.426846 + 0.904324i \(0.359625\pi\)
\(644\) −7.41894 −0.292347
\(645\) 59.1410 2.32868
\(646\) 2.07264 0.0815470
\(647\) −11.1367 −0.437830 −0.218915 0.975744i \(-0.570252\pi\)
−0.218915 + 0.975744i \(0.570252\pi\)
\(648\) 7.57709 0.297656
\(649\) 38.9106 1.52737
\(650\) 1.37048 0.0537546
\(651\) 20.2687 0.794394
\(652\) 3.78720 0.148318
\(653\) −13.0889 −0.512207 −0.256104 0.966649i \(-0.582439\pi\)
−0.256104 + 0.966649i \(0.582439\pi\)
\(654\) 2.19595 0.0858684
\(655\) −3.79606 −0.148325
\(656\) 7.47821 0.291975
\(657\) −43.4776 −1.69622
\(658\) −11.2025 −0.436721
\(659\) 2.78635 0.108541 0.0542704 0.998526i \(-0.482717\pi\)
0.0542704 + 0.998526i \(0.482717\pi\)
\(660\) −16.5386 −0.643763
\(661\) 45.7348 1.77888 0.889438 0.457056i \(-0.151096\pi\)
0.889438 + 0.457056i \(0.151096\pi\)
\(662\) −29.2281 −1.13598
\(663\) 3.82775 0.148657
\(664\) −3.76008 −0.145920
\(665\) 10.3391 0.400933
\(666\) −3.84262 −0.148899
\(667\) 0.699393 0.0270806
\(668\) 0.835722 0.0323350
\(669\) 25.7868 0.996976
\(670\) 6.80515 0.262906
\(671\) −25.2904 −0.976326
\(672\) −3.04963 −0.117642
\(673\) −25.1312 −0.968736 −0.484368 0.874864i \(-0.660950\pi\)
−0.484368 + 0.874864i \(0.660950\pi\)
\(674\) 4.99392 0.192359
\(675\) 0.491702 0.0189256
\(676\) −4.35359 −0.167446
\(677\) 19.2415 0.739512 0.369756 0.929129i \(-0.379441\pi\)
0.369756 + 0.929129i \(0.379441\pi\)
\(678\) 47.1862 1.81218
\(679\) −21.9056 −0.840661
\(680\) −1.09424 −0.0419623
\(681\) −23.2009 −0.889060
\(682\) 20.3794 0.780368
\(683\) 42.2614 1.61709 0.808544 0.588435i \(-0.200256\pi\)
0.808544 + 0.588435i \(0.200256\pi\)
\(684\) 13.7793 0.526864
\(685\) 36.5173 1.39525
\(686\) −15.1099 −0.576899
\(687\) 18.3056 0.698403
\(688\) 10.9649 0.418031
\(689\) −1.85979 −0.0708523
\(690\) −33.2376 −1.26533
\(691\) 33.6529 1.28022 0.640109 0.768284i \(-0.278889\pi\)
0.640109 + 0.768284i \(0.278889\pi\)
\(692\) −17.9559 −0.682580
\(693\) 12.6122 0.479097
\(694\) −1.46788 −0.0557198
\(695\) 48.7615 1.84963
\(696\) 0.287492 0.0108974
\(697\) −3.84304 −0.145565
\(698\) 6.77065 0.256273
\(699\) 28.3527 1.07240
\(700\) 0.561116 0.0212082
\(701\) 12.2484 0.462614 0.231307 0.972881i \(-0.425700\pi\)
0.231307 + 0.972881i \(0.425700\pi\)
\(702\) 3.10217 0.117084
\(703\) 4.53623 0.171087
\(704\) −3.06628 −0.115565
\(705\) −50.1885 −1.89021
\(706\) 29.8279 1.12259
\(707\) −15.1118 −0.568337
\(708\) 32.1443 1.20806
\(709\) 9.34150 0.350827 0.175414 0.984495i \(-0.443874\pi\)
0.175414 + 0.984495i \(0.443874\pi\)
\(710\) −10.9852 −0.412267
\(711\) 22.6965 0.851186
\(712\) 5.64721 0.211638
\(713\) 40.9566 1.53384
\(714\) 1.56720 0.0586509
\(715\) 19.1985 0.717983
\(716\) −15.0728 −0.563297
\(717\) −34.0078 −1.27005
\(718\) −2.57061 −0.0959343
\(719\) −14.8460 −0.553663 −0.276832 0.960918i \(-0.589284\pi\)
−0.276832 + 0.960918i \(0.589284\pi\)
\(720\) −7.27473 −0.271113
\(721\) 5.32856 0.198446
\(722\) 2.73349 0.101730
\(723\) 32.7813 1.21915
\(724\) −0.830708 −0.0308730
\(725\) −0.0528971 −0.00196455
\(726\) −4.04763 −0.150222
\(727\) 19.9246 0.738963 0.369482 0.929238i \(-0.379535\pi\)
0.369482 + 0.929238i \(0.379535\pi\)
\(728\) 3.54011 0.131205
\(729\) −33.9041 −1.25571
\(730\) −27.0972 −1.00291
\(731\) −5.63482 −0.208411
\(732\) −20.8926 −0.772213
\(733\) 14.8687 0.549189 0.274594 0.961560i \(-0.411456\pi\)
0.274594 + 0.961560i \(0.411456\pi\)
\(734\) −24.4069 −0.900874
\(735\) −29.9381 −1.10428
\(736\) −6.16231 −0.227146
\(737\) −9.79969 −0.360976
\(738\) −25.5492 −0.940479
\(739\) 39.0133 1.43513 0.717565 0.696492i \(-0.245257\pi\)
0.717565 + 0.696492i \(0.245257\pi\)
\(740\) −2.39489 −0.0880378
\(741\) −30.0410 −1.10358
\(742\) −0.761454 −0.0279539
\(743\) 30.8331 1.13116 0.565578 0.824695i \(-0.308653\pi\)
0.565578 + 0.824695i \(0.308653\pi\)
\(744\) 16.8356 0.617223
\(745\) −8.12400 −0.297640
\(746\) 15.3279 0.561195
\(747\) 12.8463 0.470020
\(748\) 1.57576 0.0576154
\(749\) 12.9411 0.472858
\(750\) 29.4823 1.07654
\(751\) −34.8453 −1.27152 −0.635762 0.771885i \(-0.719314\pi\)
−0.635762 + 0.771885i \(0.719314\pi\)
\(752\) −9.30504 −0.339320
\(753\) −73.7595 −2.68795
\(754\) −0.333730 −0.0121537
\(755\) −5.61271 −0.204267
\(756\) 1.27012 0.0461939
\(757\) 41.4239 1.50558 0.752789 0.658261i \(-0.228708\pi\)
0.752789 + 0.658261i \(0.228708\pi\)
\(758\) 22.1185 0.803380
\(759\) 47.8635 1.73734
\(760\) 8.58785 0.311514
\(761\) −6.14816 −0.222871 −0.111435 0.993772i \(-0.535545\pi\)
−0.111435 + 0.993772i \(0.535545\pi\)
\(762\) 33.4634 1.21225
\(763\) −1.04369 −0.0377841
\(764\) 1.57893 0.0571237
\(765\) 3.73847 0.135165
\(766\) 20.8364 0.752849
\(767\) −37.3142 −1.34734
\(768\) −2.53308 −0.0914046
\(769\) −49.1402 −1.77204 −0.886020 0.463647i \(-0.846541\pi\)
−0.886020 + 0.463647i \(0.846541\pi\)
\(770\) 7.86045 0.283271
\(771\) 3.88452 0.139898
\(772\) 2.09273 0.0753190
\(773\) 40.0773 1.44148 0.720741 0.693205i \(-0.243802\pi\)
0.720741 + 0.693205i \(0.243802\pi\)
\(774\) −37.4613 −1.34652
\(775\) −3.09766 −0.111271
\(776\) −18.1952 −0.653171
\(777\) 3.43000 0.123051
\(778\) 5.44060 0.195055
\(779\) 30.1609 1.08063
\(780\) 15.8600 0.567880
\(781\) 15.8191 0.566053
\(782\) 3.16680 0.113245
\(783\) −0.119736 −0.00427902
\(784\) −5.55057 −0.198235
\(785\) 25.8507 0.922652
\(786\) 4.51591 0.161077
\(787\) −53.7358 −1.91547 −0.957737 0.287645i \(-0.907128\pi\)
−0.957737 + 0.287645i \(0.907128\pi\)
\(788\) 13.2338 0.471434
\(789\) −26.8110 −0.954496
\(790\) 14.1455 0.503273
\(791\) −22.4267 −0.797401
\(792\) 10.4759 0.372245
\(793\) 24.2528 0.861242
\(794\) 23.7638 0.843347
\(795\) −3.41139 −0.120990
\(796\) 12.5057 0.443251
\(797\) 23.6070 0.836204 0.418102 0.908400i \(-0.362695\pi\)
0.418102 + 0.908400i \(0.362695\pi\)
\(798\) −12.2997 −0.435404
\(799\) 4.78184 0.169169
\(800\) 0.466073 0.0164782
\(801\) −19.2936 −0.681706
\(802\) −3.18365 −0.112418
\(803\) 39.0210 1.37702
\(804\) −8.09560 −0.285510
\(805\) 15.7972 0.556777
\(806\) −19.5433 −0.688383
\(807\) 42.8989 1.51011
\(808\) −12.5521 −0.441583
\(809\) −53.7426 −1.88949 −0.944745 0.327806i \(-0.893691\pi\)
−0.944745 + 0.327806i \(0.893691\pi\)
\(810\) −16.1339 −0.566888
\(811\) 7.63651 0.268154 0.134077 0.990971i \(-0.457193\pi\)
0.134077 + 0.990971i \(0.457193\pi\)
\(812\) −0.136639 −0.00479510
\(813\) −71.6587 −2.51318
\(814\) 3.44874 0.120878
\(815\) −8.06409 −0.282473
\(816\) 1.30174 0.0455701
\(817\) 44.2232 1.54717
\(818\) −28.8154 −1.00751
\(819\) −12.0947 −0.422624
\(820\) −15.9234 −0.556068
\(821\) 12.1277 0.423261 0.211630 0.977350i \(-0.432123\pi\)
0.211630 + 0.977350i \(0.432123\pi\)
\(822\) −43.4420 −1.51521
\(823\) −20.9603 −0.730630 −0.365315 0.930884i \(-0.619039\pi\)
−0.365315 + 0.930884i \(0.619039\pi\)
\(824\) 4.42601 0.154187
\(825\) −3.62005 −0.126034
\(826\) −15.2776 −0.531574
\(827\) 14.3923 0.500469 0.250235 0.968185i \(-0.419492\pi\)
0.250235 + 0.968185i \(0.419492\pi\)
\(828\) 21.0534 0.731658
\(829\) 15.1220 0.525210 0.262605 0.964903i \(-0.415418\pi\)
0.262605 + 0.964903i \(0.415418\pi\)
\(830\) 8.00635 0.277905
\(831\) −2.54316 −0.0882213
\(832\) 2.94048 0.101943
\(833\) 2.85243 0.0988308
\(834\) −58.0080 −2.00865
\(835\) −1.77950 −0.0615823
\(836\) −12.3669 −0.427717
\(837\) −7.01176 −0.242362
\(838\) −25.0695 −0.866012
\(839\) 20.6046 0.711349 0.355675 0.934610i \(-0.384251\pi\)
0.355675 + 0.934610i \(0.384251\pi\)
\(840\) 6.49358 0.224050
\(841\) −28.9871 −0.999556
\(842\) −21.7468 −0.749443
\(843\) 56.8905 1.95941
\(844\) −21.2655 −0.731987
\(845\) 9.27010 0.318901
\(846\) 31.7905 1.09298
\(847\) 1.92376 0.0661011
\(848\) −0.632478 −0.0217194
\(849\) −26.8721 −0.922249
\(850\) −0.239514 −0.00821527
\(851\) 6.93093 0.237589
\(852\) 13.0683 0.447712
\(853\) −38.1574 −1.30648 −0.653242 0.757150i \(-0.726591\pi\)
−0.653242 + 0.757150i \(0.726591\pi\)
\(854\) 9.92984 0.339792
\(855\) −29.3403 −1.00342
\(856\) 10.7491 0.367398
\(857\) 14.0341 0.479396 0.239698 0.970848i \(-0.422952\pi\)
0.239698 + 0.970848i \(0.422952\pi\)
\(858\) −22.8391 −0.779714
\(859\) −23.4889 −0.801432 −0.400716 0.916202i \(-0.631239\pi\)
−0.400716 + 0.916202i \(0.631239\pi\)
\(860\) −23.3475 −0.796143
\(861\) 22.8058 0.777218
\(862\) 10.2615 0.349508
\(863\) 7.95156 0.270674 0.135337 0.990800i \(-0.456788\pi\)
0.135337 + 0.990800i \(0.456788\pi\)
\(864\) 1.05499 0.0358914
\(865\) 38.2335 1.29998
\(866\) −17.4472 −0.592879
\(867\) 42.3934 1.43975
\(868\) −8.00162 −0.271593
\(869\) −20.3701 −0.691007
\(870\) −0.612158 −0.0207541
\(871\) 9.39763 0.318427
\(872\) −0.866909 −0.0293572
\(873\) 62.1638 2.10392
\(874\) −24.8537 −0.840689
\(875\) −14.0123 −0.473704
\(876\) 32.2355 1.08914
\(877\) −15.2971 −0.516546 −0.258273 0.966072i \(-0.583153\pi\)
−0.258273 + 0.966072i \(0.583153\pi\)
\(878\) 38.6564 1.30459
\(879\) 5.53973 0.186851
\(880\) 6.52904 0.220094
\(881\) −53.1095 −1.78931 −0.894653 0.446762i \(-0.852577\pi\)
−0.894653 + 0.446762i \(0.852577\pi\)
\(882\) 18.9634 0.638532
\(883\) −33.1576 −1.11584 −0.557920 0.829894i \(-0.688401\pi\)
−0.557920 + 0.829894i \(0.688401\pi\)
\(884\) −1.51111 −0.0508240
\(885\) −68.4450 −2.30075
\(886\) −28.1368 −0.945275
\(887\) −30.1350 −1.01184 −0.505918 0.862582i \(-0.668846\pi\)
−0.505918 + 0.862582i \(0.668846\pi\)
\(888\) 2.84903 0.0956071
\(889\) −15.9045 −0.533419
\(890\) −12.0246 −0.403066
\(891\) 23.2335 0.778351
\(892\) −10.1800 −0.340853
\(893\) −37.5289 −1.25586
\(894\) 9.66454 0.323231
\(895\) 32.0946 1.07280
\(896\) 1.20392 0.0402202
\(897\) −45.8998 −1.53255
\(898\) 21.8623 0.729553
\(899\) 0.754323 0.0251581
\(900\) −1.59233 −0.0530777
\(901\) 0.325029 0.0108283
\(902\) 22.9303 0.763496
\(903\) 33.4387 1.11277
\(904\) −18.6280 −0.619559
\(905\) 1.76883 0.0587978
\(906\) 6.67704 0.221830
\(907\) 28.3830 0.942441 0.471220 0.882016i \(-0.343814\pi\)
0.471220 + 0.882016i \(0.343814\pi\)
\(908\) 9.15917 0.303958
\(909\) 42.8842 1.42238
\(910\) −7.53795 −0.249881
\(911\) −31.4396 −1.04164 −0.520820 0.853667i \(-0.674374\pi\)
−0.520820 + 0.853667i \(0.674374\pi\)
\(912\) −10.2163 −0.338297
\(913\) −11.5295 −0.381570
\(914\) −12.9541 −0.428483
\(915\) 44.4867 1.47068
\(916\) −7.22664 −0.238775
\(917\) −2.14632 −0.0708777
\(918\) −0.542156 −0.0178938
\(919\) −27.8992 −0.920309 −0.460155 0.887839i \(-0.652206\pi\)
−0.460155 + 0.887839i \(0.652206\pi\)
\(920\) 13.1214 0.432601
\(921\) −63.0382 −2.07718
\(922\) 15.9404 0.524968
\(923\) −15.1701 −0.499330
\(924\) −9.35102 −0.307626
\(925\) −0.524206 −0.0172358
\(926\) −39.4991 −1.29802
\(927\) −15.1214 −0.496651
\(928\) −0.113495 −0.00372566
\(929\) −1.36636 −0.0448289 −0.0224144 0.999749i \(-0.507135\pi\)
−0.0224144 + 0.999749i \(0.507135\pi\)
\(930\) −35.8480 −1.17550
\(931\) −22.3864 −0.733686
\(932\) −11.1930 −0.366639
\(933\) 5.92613 0.194013
\(934\) −32.1352 −1.05149
\(935\) −3.35526 −0.109729
\(936\) −10.0461 −0.328367
\(937\) −7.59756 −0.248201 −0.124101 0.992270i \(-0.539605\pi\)
−0.124101 + 0.992270i \(0.539605\pi\)
\(938\) 3.84768 0.125631
\(939\) 24.3081 0.793266
\(940\) 19.8132 0.646237
\(941\) 9.74433 0.317656 0.158828 0.987306i \(-0.449228\pi\)
0.158828 + 0.987306i \(0.449228\pi\)
\(942\) −30.7528 −1.00198
\(943\) 46.0831 1.50067
\(944\) −12.6898 −0.413019
\(945\) −2.70447 −0.0879765
\(946\) 33.6214 1.09312
\(947\) 43.7432 1.42146 0.710732 0.703463i \(-0.248364\pi\)
0.710732 + 0.703463i \(0.248364\pi\)
\(948\) −16.8278 −0.546543
\(949\) −37.4201 −1.21471
\(950\) 1.87976 0.0609873
\(951\) −82.4801 −2.67460
\(952\) −0.618693 −0.0200519
\(953\) 1.73391 0.0561670 0.0280835 0.999606i \(-0.491060\pi\)
0.0280835 + 0.999606i \(0.491060\pi\)
\(954\) 2.16085 0.0699602
\(955\) −3.36202 −0.108792
\(956\) 13.4255 0.434212
\(957\) 0.881533 0.0284959
\(958\) −11.1418 −0.359975
\(959\) 20.6471 0.666730
\(960\) 5.39369 0.174081
\(961\) 13.1732 0.424943
\(962\) −3.30724 −0.106630
\(963\) −36.7242 −1.18342
\(964\) −12.9413 −0.416810
\(965\) −4.45605 −0.143445
\(966\) −18.7928 −0.604647
\(967\) 45.9708 1.47832 0.739161 0.673529i \(-0.235222\pi\)
0.739161 + 0.673529i \(0.235222\pi\)
\(968\) 1.59791 0.0513587
\(969\) 5.25016 0.168659
\(970\) 38.7432 1.24397
\(971\) −14.1606 −0.454437 −0.227218 0.973844i \(-0.572963\pi\)
−0.227218 + 0.973844i \(0.572963\pi\)
\(972\) 22.3583 0.717143
\(973\) 27.5701 0.883855
\(974\) 17.9409 0.574862
\(975\) 3.47153 0.111178
\(976\) 8.24791 0.264009
\(977\) 43.6485 1.39644 0.698220 0.715883i \(-0.253976\pi\)
0.698220 + 0.715883i \(0.253976\pi\)
\(978\) 9.59327 0.306759
\(979\) 17.3159 0.553420
\(980\) 11.8188 0.377539
\(981\) 2.96178 0.0945624
\(982\) 40.9212 1.30585
\(983\) 33.2087 1.05919 0.529597 0.848250i \(-0.322343\pi\)
0.529597 + 0.848250i \(0.322343\pi\)
\(984\) 18.9429 0.603877
\(985\) −28.1787 −0.897849
\(986\) 0.0583250 0.00185745
\(987\) −28.3769 −0.903247
\(988\) 11.8595 0.377300
\(989\) 67.5689 2.14857
\(990\) −22.3064 −0.708943
\(991\) −3.34825 −0.106361 −0.0531803 0.998585i \(-0.516936\pi\)
−0.0531803 + 0.998585i \(0.516936\pi\)
\(992\) −6.64630 −0.211020
\(993\) −74.0370 −2.34949
\(994\) −6.21110 −0.197004
\(995\) −26.6283 −0.844174
\(996\) −9.52458 −0.301798
\(997\) −56.1298 −1.77765 −0.888825 0.458247i \(-0.848477\pi\)
−0.888825 + 0.458247i \(0.848477\pi\)
\(998\) 23.3987 0.740672
\(999\) −1.18658 −0.0375416
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 \(a_p\))