Properties

Label 8007.2.a.j.1.19
Level 8007
Weight 2
Character 8007.1
Self dual Yes
Analytic conductor 63.936
Analytic rank 0
Dimension 64
CM No

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Newspace parameters

Level: \( N \) = \( 8007 = 3 \cdot 17 \cdot 157 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8007.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9362168984\)
Analytic rank: \(0\)
Dimension: \(64\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.43835 q^{2}\) \(-1.00000 q^{3}\) \(+0.0688642 q^{4}\) \(-3.82222 q^{5}\) \(+1.43835 q^{6}\) \(+1.52533 q^{7}\) \(+2.77766 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.43835 q^{2}\) \(-1.00000 q^{3}\) \(+0.0688642 q^{4}\) \(-3.82222 q^{5}\) \(+1.43835 q^{6}\) \(+1.52533 q^{7}\) \(+2.77766 q^{8}\) \(+1.00000 q^{9}\) \(+5.49771 q^{10}\) \(-6.21763 q^{11}\) \(-0.0688642 q^{12}\) \(+0.752284 q^{13}\) \(-2.19396 q^{14}\) \(+3.82222 q^{15}\) \(-4.13299 q^{16}\) \(+1.00000 q^{17}\) \(-1.43835 q^{18}\) \(-0.430910 q^{19}\) \(-0.263214 q^{20}\) \(-1.52533 q^{21}\) \(+8.94315 q^{22}\) \(+2.71393 q^{23}\) \(-2.77766 q^{24}\) \(+9.60936 q^{25}\) \(-1.08205 q^{26}\) \(-1.00000 q^{27}\) \(+0.105040 q^{28}\) \(-6.66763 q^{29}\) \(-5.49771 q^{30}\) \(+2.38194 q^{31}\) \(+0.389384 q^{32}\) \(+6.21763 q^{33}\) \(-1.43835 q^{34}\) \(-5.83013 q^{35}\) \(+0.0688642 q^{36}\) \(-5.35717 q^{37}\) \(+0.619801 q^{38}\) \(-0.752284 q^{39}\) \(-10.6168 q^{40}\) \(-3.02822 q^{41}\) \(+2.19396 q^{42}\) \(+5.74718 q^{43}\) \(-0.428172 q^{44}\) \(-3.82222 q^{45}\) \(-3.90359 q^{46}\) \(+5.51028 q^{47}\) \(+4.13299 q^{48}\) \(-4.67338 q^{49}\) \(-13.8217 q^{50}\) \(-1.00000 q^{51}\) \(+0.0518055 q^{52}\) \(+2.44838 q^{53}\) \(+1.43835 q^{54}\) \(+23.7651 q^{55}\) \(+4.23683 q^{56}\) \(+0.430910 q^{57}\) \(+9.59042 q^{58}\) \(-0.432944 q^{59}\) \(+0.263214 q^{60}\) \(-0.540135 q^{61}\) \(-3.42608 q^{62}\) \(+1.52533 q^{63}\) \(+7.70590 q^{64}\) \(-2.87540 q^{65}\) \(-8.94315 q^{66}\) \(-1.20411 q^{67}\) \(+0.0688642 q^{68}\) \(-2.71393 q^{69}\) \(+8.38579 q^{70}\) \(+7.20238 q^{71}\) \(+2.77766 q^{72}\) \(-8.32312 q^{73}\) \(+7.70550 q^{74}\) \(-9.60936 q^{75}\) \(-0.0296743 q^{76}\) \(-9.48390 q^{77}\) \(+1.08205 q^{78}\) \(+13.1773 q^{79}\) \(+15.7972 q^{80}\) \(+1.00000 q^{81}\) \(+4.35566 q^{82}\) \(-12.0488 q^{83}\) \(-0.105040 q^{84}\) \(-3.82222 q^{85}\) \(-8.26649 q^{86}\) \(+6.66763 q^{87}\) \(-17.2704 q^{88}\) \(-13.6432 q^{89}\) \(+5.49771 q^{90}\) \(+1.14748 q^{91}\) \(+0.186893 q^{92}\) \(-2.38194 q^{93}\) \(-7.92574 q^{94}\) \(+1.64703 q^{95}\) \(-0.389384 q^{96}\) \(-13.3215 q^{97}\) \(+6.72198 q^{98}\) \(-6.21763 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(64q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut -\mathstrut 64q^{3} \) \(\mathstrut +\mathstrut 77q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 64q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(64q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut -\mathstrut 64q^{3} \) \(\mathstrut +\mathstrut 77q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 64q^{9} \) \(\mathstrut +\mathstrut 12q^{10} \) \(\mathstrut -\mathstrut 7q^{11} \) \(\mathstrut -\mathstrut 77q^{12} \) \(\mathstrut +\mathstrut 24q^{13} \) \(\mathstrut -\mathstrut 14q^{14} \) \(\mathstrut +\mathstrut 3q^{15} \) \(\mathstrut +\mathstrut 103q^{16} \) \(\mathstrut +\mathstrut 64q^{17} \) \(\mathstrut +\mathstrut 5q^{18} \) \(\mathstrut +\mathstrut 26q^{19} \) \(\mathstrut -\mathstrut 24q^{20} \) \(\mathstrut -\mathstrut 5q^{21} \) \(\mathstrut +\mathstrut 25q^{22} \) \(\mathstrut +\mathstrut 20q^{23} \) \(\mathstrut -\mathstrut 18q^{24} \) \(\mathstrut +\mathstrut 141q^{25} \) \(\mathstrut +\mathstrut 9q^{26} \) \(\mathstrut -\mathstrut 64q^{27} \) \(\mathstrut +\mathstrut 14q^{28} \) \(\mathstrut +\mathstrut 5q^{29} \) \(\mathstrut -\mathstrut 12q^{30} \) \(\mathstrut +\mathstrut 11q^{31} \) \(\mathstrut +\mathstrut 31q^{32} \) \(\mathstrut +\mathstrut 7q^{33} \) \(\mathstrut +\mathstrut 5q^{34} \) \(\mathstrut -\mathstrut 3q^{35} \) \(\mathstrut +\mathstrut 77q^{36} \) \(\mathstrut +\mathstrut 50q^{37} \) \(\mathstrut +\mathstrut 8q^{38} \) \(\mathstrut -\mathstrut 24q^{39} \) \(\mathstrut +\mathstrut 28q^{40} \) \(\mathstrut -\mathstrut 9q^{41} \) \(\mathstrut +\mathstrut 14q^{42} \) \(\mathstrut +\mathstrut 59q^{43} \) \(\mathstrut -\mathstrut 6q^{44} \) \(\mathstrut -\mathstrut 3q^{45} \) \(\mathstrut +\mathstrut 11q^{47} \) \(\mathstrut -\mathstrut 103q^{48} \) \(\mathstrut +\mathstrut 163q^{49} \) \(\mathstrut +\mathstrut 20q^{50} \) \(\mathstrut -\mathstrut 64q^{51} \) \(\mathstrut +\mathstrut 65q^{52} \) \(\mathstrut +\mathstrut 39q^{53} \) \(\mathstrut -\mathstrut 5q^{54} \) \(\mathstrut +\mathstrut 35q^{55} \) \(\mathstrut -\mathstrut 34q^{56} \) \(\mathstrut -\mathstrut 26q^{57} \) \(\mathstrut -\mathstrut 27q^{58} \) \(\mathstrut -\mathstrut 65q^{59} \) \(\mathstrut +\mathstrut 24q^{60} \) \(\mathstrut +\mathstrut 15q^{61} \) \(\mathstrut +\mathstrut 18q^{62} \) \(\mathstrut +\mathstrut 5q^{63} \) \(\mathstrut +\mathstrut 152q^{64} \) \(\mathstrut +\mathstrut 49q^{65} \) \(\mathstrut -\mathstrut 25q^{66} \) \(\mathstrut +\mathstrut 56q^{67} \) \(\mathstrut +\mathstrut 77q^{68} \) \(\mathstrut -\mathstrut 20q^{69} \) \(\mathstrut +\mathstrut 28q^{70} \) \(\mathstrut -\mathstrut 18q^{71} \) \(\mathstrut +\mathstrut 18q^{72} \) \(\mathstrut +\mathstrut 37q^{73} \) \(\mathstrut -\mathstrut 76q^{74} \) \(\mathstrut -\mathstrut 141q^{75} \) \(\mathstrut +\mathstrut 30q^{76} \) \(\mathstrut +\mathstrut 80q^{77} \) \(\mathstrut -\mathstrut 9q^{78} \) \(\mathstrut +\mathstrut 20q^{79} \) \(\mathstrut -\mathstrut 144q^{80} \) \(\mathstrut +\mathstrut 64q^{81} \) \(\mathstrut +\mathstrut 27q^{82} \) \(\mathstrut +\mathstrut 3q^{83} \) \(\mathstrut -\mathstrut 14q^{84} \) \(\mathstrut -\mathstrut 3q^{85} \) \(\mathstrut +\mathstrut 12q^{86} \) \(\mathstrut -\mathstrut 5q^{87} \) \(\mathstrut +\mathstrut 108q^{88} \) \(\mathstrut +\mathstrut 42q^{89} \) \(\mathstrut +\mathstrut 12q^{90} \) \(\mathstrut +\mathstrut 25q^{91} \) \(\mathstrut +\mathstrut 18q^{92} \) \(\mathstrut -\mathstrut 11q^{93} \) \(\mathstrut +\mathstrut 60q^{94} \) \(\mathstrut +\mathstrut 42q^{95} \) \(\mathstrut -\mathstrut 31q^{96} \) \(\mathstrut +\mathstrut 72q^{97} \) \(\mathstrut +\mathstrut 18q^{98} \) \(\mathstrut -\mathstrut 7q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.43835 −1.01707 −0.508535 0.861041i \(-0.669813\pi\)
−0.508535 + 0.861041i \(0.669813\pi\)
\(3\) −1.00000 −0.577350
\(4\) 0.0688642 0.0344321
\(5\) −3.82222 −1.70935 −0.854674 0.519165i \(-0.826243\pi\)
−0.854674 + 0.519165i \(0.826243\pi\)
\(6\) 1.43835 0.587206
\(7\) 1.52533 0.576519 0.288259 0.957552i \(-0.406923\pi\)
0.288259 + 0.957552i \(0.406923\pi\)
\(8\) 2.77766 0.982050
\(9\) 1.00000 0.333333
\(10\) 5.49771 1.73853
\(11\) −6.21763 −1.87468 −0.937342 0.348410i \(-0.886722\pi\)
−0.937342 + 0.348410i \(0.886722\pi\)
\(12\) −0.0688642 −0.0198794
\(13\) 0.752284 0.208646 0.104323 0.994543i \(-0.466732\pi\)
0.104323 + 0.994543i \(0.466732\pi\)
\(14\) −2.19396 −0.586360
\(15\) 3.82222 0.986893
\(16\) −4.13299 −1.03325
\(17\) 1.00000 0.242536
\(18\) −1.43835 −0.339023
\(19\) −0.430910 −0.0988575 −0.0494287 0.998778i \(-0.515740\pi\)
−0.0494287 + 0.998778i \(0.515740\pi\)
\(20\) −0.263214 −0.0588565
\(21\) −1.52533 −0.332853
\(22\) 8.94315 1.90669
\(23\) 2.71393 0.565893 0.282947 0.959136i \(-0.408688\pi\)
0.282947 + 0.959136i \(0.408688\pi\)
\(24\) −2.77766 −0.566987
\(25\) 9.60936 1.92187
\(26\) −1.08205 −0.212208
\(27\) −1.00000 −0.192450
\(28\) 0.105040 0.0198508
\(29\) −6.66763 −1.23815 −0.619074 0.785333i \(-0.712492\pi\)
−0.619074 + 0.785333i \(0.712492\pi\)
\(30\) −5.49771 −1.00374
\(31\) 2.38194 0.427810 0.213905 0.976854i \(-0.431382\pi\)
0.213905 + 0.976854i \(0.431382\pi\)
\(32\) 0.389384 0.0688340
\(33\) 6.21763 1.08235
\(34\) −1.43835 −0.246676
\(35\) −5.83013 −0.985471
\(36\) 0.0688642 0.0114774
\(37\) −5.35717 −0.880713 −0.440356 0.897823i \(-0.645148\pi\)
−0.440356 + 0.897823i \(0.645148\pi\)
\(38\) 0.619801 0.100545
\(39\) −0.752284 −0.120462
\(40\) −10.6168 −1.67867
\(41\) −3.02822 −0.472929 −0.236465 0.971640i \(-0.575989\pi\)
−0.236465 + 0.971640i \(0.575989\pi\)
\(42\) 2.19396 0.338535
\(43\) 5.74718 0.876437 0.438219 0.898868i \(-0.355610\pi\)
0.438219 + 0.898868i \(0.355610\pi\)
\(44\) −0.428172 −0.0645494
\(45\) −3.82222 −0.569783
\(46\) −3.90359 −0.575553
\(47\) 5.51028 0.803757 0.401879 0.915693i \(-0.368357\pi\)
0.401879 + 0.915693i \(0.368357\pi\)
\(48\) 4.13299 0.596545
\(49\) −4.67338 −0.667626
\(50\) −13.8217 −1.95468
\(51\) −1.00000 −0.140028
\(52\) 0.0518055 0.00718413
\(53\) 2.44838 0.336311 0.168155 0.985761i \(-0.446219\pi\)
0.168155 + 0.985761i \(0.446219\pi\)
\(54\) 1.43835 0.195735
\(55\) 23.7651 3.20449
\(56\) 4.23683 0.566170
\(57\) 0.430910 0.0570754
\(58\) 9.59042 1.25928
\(59\) −0.432944 −0.0563645 −0.0281822 0.999603i \(-0.508972\pi\)
−0.0281822 + 0.999603i \(0.508972\pi\)
\(60\) 0.263214 0.0339808
\(61\) −0.540135 −0.0691573 −0.0345786 0.999402i \(-0.511009\pi\)
−0.0345786 + 0.999402i \(0.511009\pi\)
\(62\) −3.42608 −0.435113
\(63\) 1.52533 0.192173
\(64\) 7.70590 0.963238
\(65\) −2.87540 −0.356649
\(66\) −8.94315 −1.10083
\(67\) −1.20411 −0.147105 −0.0735527 0.997291i \(-0.523434\pi\)
−0.0735527 + 0.997291i \(0.523434\pi\)
\(68\) 0.0688642 0.00835102
\(69\) −2.71393 −0.326719
\(70\) 8.38579 1.00229
\(71\) 7.20238 0.854765 0.427383 0.904071i \(-0.359436\pi\)
0.427383 + 0.904071i \(0.359436\pi\)
\(72\) 2.77766 0.327350
\(73\) −8.32312 −0.974148 −0.487074 0.873361i \(-0.661936\pi\)
−0.487074 + 0.873361i \(0.661936\pi\)
\(74\) 7.70550 0.895747
\(75\) −9.60936 −1.10959
\(76\) −0.0296743 −0.00340387
\(77\) −9.48390 −1.08079
\(78\) 1.08205 0.122518
\(79\) 13.1773 1.48256 0.741281 0.671195i \(-0.234219\pi\)
0.741281 + 0.671195i \(0.234219\pi\)
\(80\) 15.7972 1.76618
\(81\) 1.00000 0.111111
\(82\) 4.35566 0.481002
\(83\) −12.0488 −1.32253 −0.661266 0.750151i \(-0.729981\pi\)
−0.661266 + 0.750151i \(0.729981\pi\)
\(84\) −0.105040 −0.0114608
\(85\) −3.82222 −0.414578
\(86\) −8.26649 −0.891398
\(87\) 6.66763 0.714845
\(88\) −17.2704 −1.84103
\(89\) −13.6432 −1.44617 −0.723087 0.690757i \(-0.757277\pi\)
−0.723087 + 0.690757i \(0.757277\pi\)
\(90\) 5.49771 0.579509
\(91\) 1.14748 0.120288
\(92\) 0.186893 0.0194849
\(93\) −2.38194 −0.246996
\(94\) −7.92574 −0.817478
\(95\) 1.64703 0.168982
\(96\) −0.389384 −0.0397413
\(97\) −13.3215 −1.35259 −0.676295 0.736631i \(-0.736416\pi\)
−0.676295 + 0.736631i \(0.736416\pi\)
\(98\) 6.72198 0.679023
\(99\) −6.21763 −0.624895
\(100\) 0.661742 0.0661742
\(101\) −10.4000 −1.03484 −0.517418 0.855733i \(-0.673107\pi\)
−0.517418 + 0.855733i \(0.673107\pi\)
\(102\) 1.43835 0.142418
\(103\) 2.07038 0.204000 0.102000 0.994784i \(-0.467476\pi\)
0.102000 + 0.994784i \(0.467476\pi\)
\(104\) 2.08959 0.204901
\(105\) 5.83013 0.568962
\(106\) −3.52164 −0.342051
\(107\) −7.33432 −0.709036 −0.354518 0.935049i \(-0.615355\pi\)
−0.354518 + 0.935049i \(0.615355\pi\)
\(108\) −0.0688642 −0.00662646
\(109\) 16.4064 1.57145 0.785724 0.618577i \(-0.212291\pi\)
0.785724 + 0.618577i \(0.212291\pi\)
\(110\) −34.1827 −3.25919
\(111\) 5.35717 0.508480
\(112\) −6.30415 −0.595686
\(113\) −17.5365 −1.64969 −0.824847 0.565356i \(-0.808739\pi\)
−0.824847 + 0.565356i \(0.808739\pi\)
\(114\) −0.619801 −0.0580497
\(115\) −10.3732 −0.967309
\(116\) −0.459161 −0.0426321
\(117\) 0.752284 0.0695487
\(118\) 0.622727 0.0573266
\(119\) 1.52533 0.139826
\(120\) 10.6168 0.969179
\(121\) 27.6589 2.51444
\(122\) 0.776906 0.0703378
\(123\) 3.02822 0.273046
\(124\) 0.164031 0.0147304
\(125\) −17.6180 −1.57580
\(126\) −2.19396 −0.195453
\(127\) 2.03917 0.180947 0.0904735 0.995899i \(-0.471162\pi\)
0.0904735 + 0.995899i \(0.471162\pi\)
\(128\) −11.8626 −1.04851
\(129\) −5.74718 −0.506011
\(130\) 4.13584 0.362737
\(131\) 3.84201 0.335678 0.167839 0.985814i \(-0.446321\pi\)
0.167839 + 0.985814i \(0.446321\pi\)
\(132\) 0.428172 0.0372676
\(133\) −0.657277 −0.0569932
\(134\) 1.73194 0.149617
\(135\) 3.82222 0.328964
\(136\) 2.77766 0.238182
\(137\) −17.9908 −1.53706 −0.768529 0.639815i \(-0.779011\pi\)
−0.768529 + 0.639815i \(0.779011\pi\)
\(138\) 3.90359 0.332296
\(139\) −13.9294 −1.18148 −0.590739 0.806863i \(-0.701164\pi\)
−0.590739 + 0.806863i \(0.701164\pi\)
\(140\) −0.401487 −0.0339319
\(141\) −5.51028 −0.464049
\(142\) −10.3596 −0.869356
\(143\) −4.67742 −0.391146
\(144\) −4.13299 −0.344416
\(145\) 25.4852 2.11643
\(146\) 11.9716 0.990777
\(147\) 4.67338 0.385454
\(148\) −0.368917 −0.0303248
\(149\) −0.887102 −0.0726742 −0.0363371 0.999340i \(-0.511569\pi\)
−0.0363371 + 0.999340i \(0.511569\pi\)
\(150\) 13.8217 1.12853
\(151\) −10.6702 −0.868327 −0.434163 0.900834i \(-0.642956\pi\)
−0.434163 + 0.900834i \(0.642956\pi\)
\(152\) −1.19692 −0.0970830
\(153\) 1.00000 0.0808452
\(154\) 13.6412 1.09924
\(155\) −9.10431 −0.731276
\(156\) −0.0518055 −0.00414776
\(157\) −1.00000 −0.0798087
\(158\) −18.9536 −1.50787
\(159\) −2.44838 −0.194169
\(160\) −1.48831 −0.117661
\(161\) 4.13962 0.326248
\(162\) −1.43835 −0.113008
\(163\) −23.5485 −1.84446 −0.922230 0.386643i \(-0.873635\pi\)
−0.922230 + 0.386643i \(0.873635\pi\)
\(164\) −0.208536 −0.0162840
\(165\) −23.7651 −1.85011
\(166\) 17.3305 1.34511
\(167\) 11.6666 0.902787 0.451394 0.892325i \(-0.350927\pi\)
0.451394 + 0.892325i \(0.350927\pi\)
\(168\) −4.23683 −0.326879
\(169\) −12.4341 −0.956467
\(170\) 5.49771 0.421655
\(171\) −0.430910 −0.0329525
\(172\) 0.395775 0.0301776
\(173\) 1.44556 0.109904 0.0549521 0.998489i \(-0.482499\pi\)
0.0549521 + 0.998489i \(0.482499\pi\)
\(174\) −9.59042 −0.727048
\(175\) 14.6574 1.10800
\(176\) 25.6974 1.93701
\(177\) 0.432944 0.0325420
\(178\) 19.6237 1.47086
\(179\) 16.9096 1.26388 0.631941 0.775017i \(-0.282259\pi\)
0.631941 + 0.775017i \(0.282259\pi\)
\(180\) −0.263214 −0.0196188
\(181\) −4.83726 −0.359551 −0.179775 0.983708i \(-0.557537\pi\)
−0.179775 + 0.983708i \(0.557537\pi\)
\(182\) −1.65048 −0.122342
\(183\) 0.540135 0.0399280
\(184\) 7.53837 0.555736
\(185\) 20.4763 1.50544
\(186\) 3.42608 0.251212
\(187\) −6.21763 −0.454678
\(188\) 0.379461 0.0276751
\(189\) −1.52533 −0.110951
\(190\) −2.36902 −0.171866
\(191\) −8.80081 −0.636804 −0.318402 0.947956i \(-0.603146\pi\)
−0.318402 + 0.947956i \(0.603146\pi\)
\(192\) −7.70590 −0.556125
\(193\) −27.0924 −1.95015 −0.975075 0.221875i \(-0.928782\pi\)
−0.975075 + 0.221875i \(0.928782\pi\)
\(194\) 19.1610 1.37568
\(195\) 2.87540 0.205911
\(196\) −0.321829 −0.0229878
\(197\) 3.57134 0.254447 0.127224 0.991874i \(-0.459393\pi\)
0.127224 + 0.991874i \(0.459393\pi\)
\(198\) 8.94315 0.635562
\(199\) 22.2088 1.57434 0.787170 0.616736i \(-0.211545\pi\)
0.787170 + 0.616736i \(0.211545\pi\)
\(200\) 26.6915 1.88738
\(201\) 1.20411 0.0849314
\(202\) 14.9589 1.05250
\(203\) −10.1703 −0.713816
\(204\) −0.0688642 −0.00482146
\(205\) 11.5745 0.808401
\(206\) −2.97793 −0.207483
\(207\) 2.71393 0.188631
\(208\) −3.10918 −0.215583
\(209\) 2.67924 0.185327
\(210\) −8.38579 −0.578675
\(211\) 5.44530 0.374870 0.187435 0.982277i \(-0.439983\pi\)
0.187435 + 0.982277i \(0.439983\pi\)
\(212\) 0.168606 0.0115799
\(213\) −7.20238 −0.493499
\(214\) 10.5494 0.721139
\(215\) −21.9670 −1.49814
\(216\) −2.77766 −0.188996
\(217\) 3.63324 0.246640
\(218\) −23.5982 −1.59827
\(219\) 8.32312 0.562424
\(220\) 1.63657 0.110337
\(221\) 0.752284 0.0506041
\(222\) −7.70550 −0.517160
\(223\) −12.4484 −0.833609 −0.416804 0.908996i \(-0.636850\pi\)
−0.416804 + 0.908996i \(0.636850\pi\)
\(224\) 0.593937 0.0396841
\(225\) 9.60936 0.640624
\(226\) 25.2237 1.67785
\(227\) −16.5389 −1.09772 −0.548862 0.835913i \(-0.684939\pi\)
−0.548862 + 0.835913i \(0.684939\pi\)
\(228\) 0.0296743 0.00196523
\(229\) 13.5732 0.896941 0.448470 0.893798i \(-0.351969\pi\)
0.448470 + 0.893798i \(0.351969\pi\)
\(230\) 14.9204 0.983821
\(231\) 9.48390 0.623995
\(232\) −18.5204 −1.21592
\(233\) 21.9632 1.43886 0.719430 0.694565i \(-0.244403\pi\)
0.719430 + 0.694565i \(0.244403\pi\)
\(234\) −1.08205 −0.0707359
\(235\) −21.0615 −1.37390
\(236\) −0.0298143 −0.00194075
\(237\) −13.1773 −0.855958
\(238\) −2.19396 −0.142213
\(239\) −16.2697 −1.05240 −0.526199 0.850361i \(-0.676383\pi\)
−0.526199 + 0.850361i \(0.676383\pi\)
\(240\) −15.7972 −1.01970
\(241\) −14.2950 −0.920820 −0.460410 0.887707i \(-0.652298\pi\)
−0.460410 + 0.887707i \(0.652298\pi\)
\(242\) −39.7833 −2.55736
\(243\) −1.00000 −0.0641500
\(244\) −0.0371960 −0.00238123
\(245\) 17.8627 1.14121
\(246\) −4.35566 −0.277707
\(247\) −0.324167 −0.0206262
\(248\) 6.61623 0.420131
\(249\) 12.0488 0.763564
\(250\) 25.3409 1.60270
\(251\) −9.95840 −0.628568 −0.314284 0.949329i \(-0.601764\pi\)
−0.314284 + 0.949329i \(0.601764\pi\)
\(252\) 0.105040 0.00661692
\(253\) −16.8742 −1.06087
\(254\) −2.93305 −0.184036
\(255\) 3.82222 0.239357
\(256\) 1.65080 0.103175
\(257\) 22.4003 1.39729 0.698647 0.715467i \(-0.253786\pi\)
0.698647 + 0.715467i \(0.253786\pi\)
\(258\) 8.26649 0.514649
\(259\) −8.17142 −0.507747
\(260\) −0.198012 −0.0122802
\(261\) −6.66763 −0.412716
\(262\) −5.52617 −0.341408
\(263\) −19.9317 −1.22904 −0.614521 0.788901i \(-0.710651\pi\)
−0.614521 + 0.788901i \(0.710651\pi\)
\(264\) 17.2704 1.06292
\(265\) −9.35824 −0.574872
\(266\) 0.945398 0.0579661
\(267\) 13.6432 0.834948
\(268\) −0.0829201 −0.00506515
\(269\) −28.6672 −1.74787 −0.873935 0.486042i \(-0.838440\pi\)
−0.873935 + 0.486042i \(0.838440\pi\)
\(270\) −5.49771 −0.334580
\(271\) 25.0172 1.51969 0.759844 0.650105i \(-0.225275\pi\)
0.759844 + 0.650105i \(0.225275\pi\)
\(272\) −4.13299 −0.250599
\(273\) −1.14748 −0.0694485
\(274\) 25.8772 1.56330
\(275\) −59.7474 −3.60291
\(276\) −0.186893 −0.0112496
\(277\) −5.46635 −0.328441 −0.164221 0.986424i \(-0.552511\pi\)
−0.164221 + 0.986424i \(0.552511\pi\)
\(278\) 20.0354 1.20165
\(279\) 2.38194 0.142603
\(280\) −16.1941 −0.967783
\(281\) −3.24236 −0.193423 −0.0967114 0.995312i \(-0.530832\pi\)
−0.0967114 + 0.995312i \(0.530832\pi\)
\(282\) 7.92574 0.471971
\(283\) −4.98257 −0.296183 −0.148091 0.988974i \(-0.547313\pi\)
−0.148091 + 0.988974i \(0.547313\pi\)
\(284\) 0.495986 0.0294314
\(285\) −1.64703 −0.0975617
\(286\) 6.72779 0.397823
\(287\) −4.61903 −0.272653
\(288\) 0.389384 0.0229447
\(289\) 1.00000 0.0588235
\(290\) −36.6567 −2.15256
\(291\) 13.3215 0.780918
\(292\) −0.573165 −0.0335420
\(293\) −20.5351 −1.19967 −0.599837 0.800122i \(-0.704768\pi\)
−0.599837 + 0.800122i \(0.704768\pi\)
\(294\) −6.72198 −0.392034
\(295\) 1.65481 0.0963465
\(296\) −14.8804 −0.864904
\(297\) 6.21763 0.360783
\(298\) 1.27597 0.0739148
\(299\) 2.04165 0.118071
\(300\) −0.661742 −0.0382057
\(301\) 8.76632 0.505282
\(302\) 15.3475 0.883149
\(303\) 10.4000 0.597463
\(304\) 1.78094 0.102144
\(305\) 2.06452 0.118214
\(306\) −1.43835 −0.0822253
\(307\) 1.02037 0.0582354 0.0291177 0.999576i \(-0.490730\pi\)
0.0291177 + 0.999576i \(0.490730\pi\)
\(308\) −0.653101 −0.0372139
\(309\) −2.07038 −0.117780
\(310\) 13.0952 0.743759
\(311\) −8.34372 −0.473129 −0.236564 0.971616i \(-0.576021\pi\)
−0.236564 + 0.971616i \(0.576021\pi\)
\(312\) −2.08959 −0.118300
\(313\) −15.1766 −0.857833 −0.428917 0.903344i \(-0.641105\pi\)
−0.428917 + 0.903344i \(0.641105\pi\)
\(314\) 1.43835 0.0811711
\(315\) −5.83013 −0.328490
\(316\) 0.907445 0.0510478
\(317\) 6.18538 0.347405 0.173703 0.984798i \(-0.444427\pi\)
0.173703 + 0.984798i \(0.444427\pi\)
\(318\) 3.52164 0.197484
\(319\) 41.4568 2.32114
\(320\) −29.4536 −1.64651
\(321\) 7.33432 0.409362
\(322\) −5.95425 −0.331817
\(323\) −0.430910 −0.0239765
\(324\) 0.0688642 0.00382579
\(325\) 7.22897 0.400991
\(326\) 33.8711 1.87594
\(327\) −16.4064 −0.907276
\(328\) −8.41137 −0.464440
\(329\) 8.40497 0.463381
\(330\) 34.1827 1.88170
\(331\) −4.63627 −0.254832 −0.127416 0.991849i \(-0.540668\pi\)
−0.127416 + 0.991849i \(0.540668\pi\)
\(332\) −0.829734 −0.0455376
\(333\) −5.35717 −0.293571
\(334\) −16.7807 −0.918198
\(335\) 4.60237 0.251454
\(336\) 6.30415 0.343919
\(337\) 9.56869 0.521240 0.260620 0.965441i \(-0.416073\pi\)
0.260620 + 0.965441i \(0.416073\pi\)
\(338\) 17.8846 0.972794
\(339\) 17.5365 0.952451
\(340\) −0.263214 −0.0142748
\(341\) −14.8100 −0.802008
\(342\) 0.619801 0.0335150
\(343\) −17.8057 −0.961418
\(344\) 15.9637 0.860706
\(345\) 10.3732 0.558476
\(346\) −2.07923 −0.111780
\(347\) −17.9573 −0.963999 −0.482000 0.876171i \(-0.660089\pi\)
−0.482000 + 0.876171i \(0.660089\pi\)
\(348\) 0.459161 0.0246136
\(349\) 1.40644 0.0752850 0.0376425 0.999291i \(-0.488015\pi\)
0.0376425 + 0.999291i \(0.488015\pi\)
\(350\) −21.0825 −1.12691
\(351\) −0.752284 −0.0401540
\(352\) −2.42104 −0.129042
\(353\) 25.1640 1.33934 0.669671 0.742657i \(-0.266435\pi\)
0.669671 + 0.742657i \(0.266435\pi\)
\(354\) −0.622727 −0.0330975
\(355\) −27.5291 −1.46109
\(356\) −0.939526 −0.0497948
\(357\) −1.52533 −0.0807288
\(358\) −24.3220 −1.28546
\(359\) 10.9395 0.577364 0.288682 0.957425i \(-0.406783\pi\)
0.288682 + 0.957425i \(0.406783\pi\)
\(360\) −10.6168 −0.559556
\(361\) −18.8143 −0.990227
\(362\) 6.95770 0.365688
\(363\) −27.6589 −1.45171
\(364\) 0.0790202 0.00414178
\(365\) 31.8128 1.66516
\(366\) −0.776906 −0.0406095
\(367\) 11.8429 0.618193 0.309096 0.951031i \(-0.399973\pi\)
0.309096 + 0.951031i \(0.399973\pi\)
\(368\) −11.2166 −0.584707
\(369\) −3.02822 −0.157643
\(370\) −29.4521 −1.53114
\(371\) 3.73457 0.193889
\(372\) −0.164031 −0.00850460
\(373\) 13.1676 0.681792 0.340896 0.940101i \(-0.389270\pi\)
0.340896 + 0.940101i \(0.389270\pi\)
\(374\) 8.94315 0.462439
\(375\) 17.6180 0.909790
\(376\) 15.3057 0.789330
\(377\) −5.01596 −0.258335
\(378\) 2.19396 0.112845
\(379\) −7.35145 −0.377619 −0.188809 0.982014i \(-0.560463\pi\)
−0.188809 + 0.982014i \(0.560463\pi\)
\(380\) 0.113422 0.00581840
\(381\) −2.03917 −0.104470
\(382\) 12.6587 0.647675
\(383\) 27.5449 1.40748 0.703740 0.710457i \(-0.251512\pi\)
0.703740 + 0.710457i \(0.251512\pi\)
\(384\) 11.8626 0.605360
\(385\) 36.2495 1.84745
\(386\) 38.9684 1.98344
\(387\) 5.74718 0.292146
\(388\) −0.917373 −0.0465725
\(389\) 22.1334 1.12221 0.561105 0.827745i \(-0.310376\pi\)
0.561105 + 0.827745i \(0.310376\pi\)
\(390\) −4.13584 −0.209426
\(391\) 2.71393 0.137249
\(392\) −12.9811 −0.655643
\(393\) −3.84201 −0.193804
\(394\) −5.13685 −0.258791
\(395\) −50.3665 −2.53422
\(396\) −0.428172 −0.0215165
\(397\) −1.32029 −0.0662636 −0.0331318 0.999451i \(-0.510548\pi\)
−0.0331318 + 0.999451i \(0.510548\pi\)
\(398\) −31.9441 −1.60121
\(399\) 0.657277 0.0329050
\(400\) −39.7154 −1.98577
\(401\) 13.4317 0.670747 0.335374 0.942085i \(-0.391137\pi\)
0.335374 + 0.942085i \(0.391137\pi\)
\(402\) −1.73194 −0.0863812
\(403\) 1.79190 0.0892608
\(404\) −0.716187 −0.0356316
\(405\) −3.82222 −0.189928
\(406\) 14.6285 0.726001
\(407\) 33.3088 1.65106
\(408\) −2.77766 −0.137515
\(409\) 4.94784 0.244655 0.122327 0.992490i \(-0.460964\pi\)
0.122327 + 0.992490i \(0.460964\pi\)
\(410\) −16.6483 −0.822201
\(411\) 17.9908 0.887421
\(412\) 0.142575 0.00702416
\(413\) −0.660380 −0.0324952
\(414\) −3.90359 −0.191851
\(415\) 46.0533 2.26067
\(416\) 0.292927 0.0143619
\(417\) 13.9294 0.682127
\(418\) −3.85369 −0.188490
\(419\) 21.6961 1.05992 0.529961 0.848022i \(-0.322206\pi\)
0.529961 + 0.848022i \(0.322206\pi\)
\(420\) 0.401487 0.0195906
\(421\) 22.6335 1.10309 0.551544 0.834146i \(-0.314039\pi\)
0.551544 + 0.834146i \(0.314039\pi\)
\(422\) −7.83227 −0.381269
\(423\) 5.51028 0.267919
\(424\) 6.80076 0.330274
\(425\) 9.60936 0.466123
\(426\) 10.3596 0.501923
\(427\) −0.823882 −0.0398705
\(428\) −0.505073 −0.0244136
\(429\) 4.67742 0.225828
\(430\) 31.5963 1.52371
\(431\) −38.5731 −1.85800 −0.929001 0.370076i \(-0.879332\pi\)
−0.929001 + 0.370076i \(0.879332\pi\)
\(432\) 4.13299 0.198848
\(433\) 30.2645 1.45442 0.727210 0.686416i \(-0.240817\pi\)
0.727210 + 0.686416i \(0.240817\pi\)
\(434\) −5.22589 −0.250851
\(435\) −25.4852 −1.22192
\(436\) 1.12981 0.0541083
\(437\) −1.16946 −0.0559428
\(438\) −11.9716 −0.572025
\(439\) −22.9509 −1.09538 −0.547692 0.836680i \(-0.684494\pi\)
−0.547692 + 0.836680i \(0.684494\pi\)
\(440\) 66.0114 3.14697
\(441\) −4.67338 −0.222542
\(442\) −1.08205 −0.0514680
\(443\) 24.5386 1.16586 0.582931 0.812522i \(-0.301906\pi\)
0.582931 + 0.812522i \(0.301906\pi\)
\(444\) 0.368917 0.0175080
\(445\) 52.1472 2.47201
\(446\) 17.9053 0.847839
\(447\) 0.887102 0.0419585
\(448\) 11.7540 0.555324
\(449\) −5.93024 −0.279865 −0.139933 0.990161i \(-0.544689\pi\)
−0.139933 + 0.990161i \(0.544689\pi\)
\(450\) −13.8217 −0.651560
\(451\) 18.8284 0.886593
\(452\) −1.20764 −0.0568024
\(453\) 10.6702 0.501329
\(454\) 23.7888 1.11646
\(455\) −4.38591 −0.205615
\(456\) 1.19692 0.0560509
\(457\) 24.6957 1.15522 0.577609 0.816314i \(-0.303986\pi\)
0.577609 + 0.816314i \(0.303986\pi\)
\(458\) −19.5230 −0.912252
\(459\) −1.00000 −0.0466760
\(460\) −0.714345 −0.0333065
\(461\) 23.8315 1.10994 0.554972 0.831869i \(-0.312729\pi\)
0.554972 + 0.831869i \(0.312729\pi\)
\(462\) −13.6412 −0.634647
\(463\) −4.56006 −0.211924 −0.105962 0.994370i \(-0.533792\pi\)
−0.105962 + 0.994370i \(0.533792\pi\)
\(464\) 27.5572 1.27931
\(465\) 9.10431 0.422202
\(466\) −31.5909 −1.46342
\(467\) 4.46006 0.206387 0.103194 0.994661i \(-0.467094\pi\)
0.103194 + 0.994661i \(0.467094\pi\)
\(468\) 0.0518055 0.00239471
\(469\) −1.83666 −0.0848090
\(470\) 30.2939 1.39735
\(471\) 1.00000 0.0460776
\(472\) −1.20257 −0.0553527
\(473\) −35.7338 −1.64304
\(474\) 18.9536 0.870569
\(475\) −4.14077 −0.189992
\(476\) 0.105040 0.00481452
\(477\) 2.44838 0.112104
\(478\) 23.4016 1.07036
\(479\) −22.3970 −1.02334 −0.511672 0.859181i \(-0.670974\pi\)
−0.511672 + 0.859181i \(0.670974\pi\)
\(480\) 1.48831 0.0679318
\(481\) −4.03011 −0.183757
\(482\) 20.5612 0.936538
\(483\) −4.13962 −0.188359
\(484\) 1.90471 0.0865776
\(485\) 50.9176 2.31205
\(486\) 1.43835 0.0652451
\(487\) 15.0572 0.682305 0.341152 0.940008i \(-0.389183\pi\)
0.341152 + 0.940008i \(0.389183\pi\)
\(488\) −1.50031 −0.0679159
\(489\) 23.5485 1.06490
\(490\) −25.6929 −1.16069
\(491\) −18.0724 −0.815595 −0.407797 0.913072i \(-0.633703\pi\)
−0.407797 + 0.913072i \(0.633703\pi\)
\(492\) 0.208536 0.00940155
\(493\) −6.66763 −0.300295
\(494\) 0.466267 0.0209783
\(495\) 23.7651 1.06816
\(496\) −9.84454 −0.442033
\(497\) 10.9860 0.492788
\(498\) −17.3305 −0.776599
\(499\) −17.9654 −0.804240 −0.402120 0.915587i \(-0.631726\pi\)
−0.402120 + 0.915587i \(0.631726\pi\)
\(500\) −1.21325 −0.0542582
\(501\) −11.6666 −0.521225
\(502\) 14.3237 0.639298
\(503\) 32.6699 1.45668 0.728339 0.685217i \(-0.240292\pi\)
0.728339 + 0.685217i \(0.240292\pi\)
\(504\) 4.23683 0.188723
\(505\) 39.7510 1.76890
\(506\) 24.2711 1.07898
\(507\) 12.4341 0.552216
\(508\) 0.140426 0.00623039
\(509\) −3.30044 −0.146289 −0.0731447 0.997321i \(-0.523303\pi\)
−0.0731447 + 0.997321i \(0.523303\pi\)
\(510\) −5.49771 −0.243443
\(511\) −12.6955 −0.561614
\(512\) 21.3507 0.943578
\(513\) 0.430910 0.0190251
\(514\) −32.2196 −1.42115
\(515\) −7.91343 −0.348707
\(516\) −0.395775 −0.0174230
\(517\) −34.2609 −1.50679
\(518\) 11.7534 0.516415
\(519\) −1.44556 −0.0634532
\(520\) −7.98687 −0.350247
\(521\) −16.3043 −0.714305 −0.357152 0.934046i \(-0.616252\pi\)
−0.357152 + 0.934046i \(0.616252\pi\)
\(522\) 9.59042 0.419761
\(523\) 20.3052 0.887885 0.443943 0.896055i \(-0.353579\pi\)
0.443943 + 0.896055i \(0.353579\pi\)
\(524\) 0.264577 0.0115581
\(525\) −14.6574 −0.639702
\(526\) 28.6689 1.25002
\(527\) 2.38194 0.103759
\(528\) −25.6974 −1.11833
\(529\) −15.6346 −0.679765
\(530\) 13.4605 0.584685
\(531\) −0.432944 −0.0187882
\(532\) −0.0452629 −0.00196240
\(533\) −2.27809 −0.0986749
\(534\) −19.6237 −0.849201
\(535\) 28.0334 1.21199
\(536\) −3.34461 −0.144465
\(537\) −16.9096 −0.729702
\(538\) 41.2336 1.77771
\(539\) 29.0573 1.25159
\(540\) 0.263214 0.0113269
\(541\) 22.4265 0.964190 0.482095 0.876119i \(-0.339876\pi\)
0.482095 + 0.876119i \(0.339876\pi\)
\(542\) −35.9837 −1.54563
\(543\) 4.83726 0.207587
\(544\) 0.389384 0.0166947
\(545\) −62.7089 −2.68615
\(546\) 1.65048 0.0706341
\(547\) 4.64730 0.198704 0.0993521 0.995052i \(-0.468323\pi\)
0.0993521 + 0.995052i \(0.468323\pi\)
\(548\) −1.23892 −0.0529242
\(549\) −0.540135 −0.0230524
\(550\) 85.9380 3.66441
\(551\) 2.87315 0.122400
\(552\) −7.53837 −0.320854
\(553\) 20.0997 0.854725
\(554\) 7.86255 0.334048
\(555\) −20.4763 −0.869169
\(556\) −0.959239 −0.0406808
\(557\) −26.6556 −1.12943 −0.564717 0.825284i \(-0.691015\pi\)
−0.564717 + 0.825284i \(0.691015\pi\)
\(558\) −3.42608 −0.145038
\(559\) 4.32352 0.182865
\(560\) 24.0958 1.01823
\(561\) 6.21763 0.262508
\(562\) 4.66366 0.196725
\(563\) −1.29370 −0.0545230 −0.0272615 0.999628i \(-0.508679\pi\)
−0.0272615 + 0.999628i \(0.508679\pi\)
\(564\) −0.379461 −0.0159782
\(565\) 67.0283 2.81990
\(566\) 7.16670 0.301239
\(567\) 1.52533 0.0640576
\(568\) 20.0057 0.839423
\(569\) 27.8421 1.16720 0.583600 0.812041i \(-0.301644\pi\)
0.583600 + 0.812041i \(0.301644\pi\)
\(570\) 2.36902 0.0992272
\(571\) 1.12877 0.0472376 0.0236188 0.999721i \(-0.492481\pi\)
0.0236188 + 0.999721i \(0.492481\pi\)
\(572\) −0.322107 −0.0134680
\(573\) 8.80081 0.367659
\(574\) 6.64380 0.277307
\(575\) 26.0791 1.08757
\(576\) 7.70590 0.321079
\(577\) 12.6322 0.525887 0.262944 0.964811i \(-0.415307\pi\)
0.262944 + 0.964811i \(0.415307\pi\)
\(578\) −1.43835 −0.0598277
\(579\) 27.0924 1.12592
\(580\) 1.75502 0.0728731
\(581\) −18.3784 −0.762465
\(582\) −19.1610 −0.794249
\(583\) −15.2231 −0.630476
\(584\) −23.1188 −0.956662
\(585\) −2.87540 −0.118883
\(586\) 29.5368 1.22015
\(587\) −39.4026 −1.62632 −0.813159 0.582042i \(-0.802254\pi\)
−0.813159 + 0.582042i \(0.802254\pi\)
\(588\) 0.321829 0.0132720
\(589\) −1.02640 −0.0422922
\(590\) −2.38020 −0.0979912
\(591\) −3.57134 −0.146905
\(592\) 22.1411 0.909993
\(593\) −0.206735 −0.00848960 −0.00424480 0.999991i \(-0.501351\pi\)
−0.00424480 + 0.999991i \(0.501351\pi\)
\(594\) −8.94315 −0.366942
\(595\) −5.83013 −0.239012
\(596\) −0.0610896 −0.00250233
\(597\) −22.2088 −0.908946
\(598\) −2.93661 −0.120087
\(599\) 11.7651 0.480711 0.240355 0.970685i \(-0.422736\pi\)
0.240355 + 0.970685i \(0.422736\pi\)
\(600\) −26.6915 −1.08968
\(601\) 33.4307 1.36367 0.681833 0.731507i \(-0.261183\pi\)
0.681833 + 0.731507i \(0.261183\pi\)
\(602\) −12.6091 −0.513908
\(603\) −1.20411 −0.0490351
\(604\) −0.734794 −0.0298983
\(605\) −105.718 −4.29806
\(606\) −14.9589 −0.607662
\(607\) −10.8257 −0.439402 −0.219701 0.975567i \(-0.570508\pi\)
−0.219701 + 0.975567i \(0.570508\pi\)
\(608\) −0.167789 −0.00680475
\(609\) 10.1703 0.412122
\(610\) −2.96951 −0.120232
\(611\) 4.14530 0.167701
\(612\) 0.0688642 0.00278367
\(613\) 28.6449 1.15696 0.578479 0.815697i \(-0.303646\pi\)
0.578479 + 0.815697i \(0.303646\pi\)
\(614\) −1.46765 −0.0592295
\(615\) −11.5745 −0.466731
\(616\) −26.3430 −1.06139
\(617\) 36.4882 1.46896 0.734480 0.678630i \(-0.237426\pi\)
0.734480 + 0.678630i \(0.237426\pi\)
\(618\) 2.97793 0.119790
\(619\) 3.28412 0.132000 0.0659999 0.997820i \(-0.478976\pi\)
0.0659999 + 0.997820i \(0.478976\pi\)
\(620\) −0.626961 −0.0251794
\(621\) −2.71393 −0.108906
\(622\) 12.0012 0.481205
\(623\) −20.8103 −0.833746
\(624\) 3.10918 0.124467
\(625\) 19.2931 0.771722
\(626\) 21.8294 0.872477
\(627\) −2.67924 −0.106998
\(628\) −0.0688642 −0.00274798
\(629\) −5.35717 −0.213604
\(630\) 8.38579 0.334098
\(631\) −38.7077 −1.54093 −0.770465 0.637482i \(-0.779976\pi\)
−0.770465 + 0.637482i \(0.779976\pi\)
\(632\) 36.6020 1.45595
\(633\) −5.44530 −0.216431
\(634\) −8.89677 −0.353336
\(635\) −7.79415 −0.309302
\(636\) −0.168606 −0.00668565
\(637\) −3.51571 −0.139298
\(638\) −59.6296 −2.36076
\(639\) 7.20238 0.284922
\(640\) 45.3414 1.79228
\(641\) 17.4010 0.687297 0.343649 0.939098i \(-0.388337\pi\)
0.343649 + 0.939098i \(0.388337\pi\)
\(642\) −10.5494 −0.416350
\(643\) 39.6465 1.56350 0.781752 0.623589i \(-0.214326\pi\)
0.781752 + 0.623589i \(0.214326\pi\)
\(644\) 0.285072 0.0112334
\(645\) 21.9670 0.864950
\(646\) 0.619801 0.0243857
\(647\) 38.8783 1.52846 0.764232 0.644941i \(-0.223118\pi\)
0.764232 + 0.644941i \(0.223118\pi\)
\(648\) 2.77766 0.109117
\(649\) 2.69188 0.105666
\(650\) −10.3978 −0.407836
\(651\) −3.63324 −0.142398
\(652\) −1.62165 −0.0635086
\(653\) 44.5681 1.74409 0.872043 0.489430i \(-0.162795\pi\)
0.872043 + 0.489430i \(0.162795\pi\)
\(654\) 23.5982 0.922763
\(655\) −14.6850 −0.573790
\(656\) 12.5156 0.488653
\(657\) −8.32312 −0.324716
\(658\) −12.0893 −0.471291
\(659\) 10.9948 0.428298 0.214149 0.976801i \(-0.431302\pi\)
0.214149 + 0.976801i \(0.431302\pi\)
\(660\) −1.63657 −0.0637033
\(661\) −21.5533 −0.838325 −0.419162 0.907911i \(-0.637676\pi\)
−0.419162 + 0.907911i \(0.637676\pi\)
\(662\) 6.66860 0.259183
\(663\) −0.752284 −0.0292163
\(664\) −33.4676 −1.29879
\(665\) 2.51226 0.0974212
\(666\) 7.70550 0.298582
\(667\) −18.0955 −0.700660
\(668\) 0.803410 0.0310849
\(669\) 12.4484 0.481284
\(670\) −6.61984 −0.255747
\(671\) 3.35836 0.129648
\(672\) −0.593937 −0.0229116
\(673\) −45.3412 −1.74778 −0.873888 0.486127i \(-0.838409\pi\)
−0.873888 + 0.486127i \(0.838409\pi\)
\(674\) −13.7632 −0.530138
\(675\) −9.60936 −0.369865
\(676\) −0.856263 −0.0329332
\(677\) −34.9181 −1.34201 −0.671005 0.741453i \(-0.734137\pi\)
−0.671005 + 0.741453i \(0.734137\pi\)
\(678\) −25.2237 −0.968710
\(679\) −20.3196 −0.779794
\(680\) −10.6168 −0.407136
\(681\) 16.5389 0.633772
\(682\) 21.3021 0.815699
\(683\) 24.2071 0.926259 0.463129 0.886291i \(-0.346727\pi\)
0.463129 + 0.886291i \(0.346727\pi\)
\(684\) −0.0296743 −0.00113462
\(685\) 68.7648 2.62737
\(686\) 25.6109 0.977829
\(687\) −13.5732 −0.517849
\(688\) −23.7530 −0.905576
\(689\) 1.84188 0.0701699
\(690\) −14.9204 −0.568009
\(691\) −30.5579 −1.16248 −0.581239 0.813733i \(-0.697432\pi\)
−0.581239 + 0.813733i \(0.697432\pi\)
\(692\) 0.0995477 0.00378423
\(693\) −9.48390 −0.360264
\(694\) 25.8290 0.980455
\(695\) 53.2413 2.01956
\(696\) 18.5204 0.702014
\(697\) −3.02822 −0.114702
\(698\) −2.02296 −0.0765702
\(699\) −21.9632 −0.830726
\(700\) 1.00937 0.0381506
\(701\) 30.6330 1.15699 0.578497 0.815685i \(-0.303640\pi\)
0.578497 + 0.815685i \(0.303640\pi\)
\(702\) 1.08205 0.0408394
\(703\) 2.30845 0.0870650
\(704\) −47.9124 −1.80577
\(705\) 21.0615 0.793222
\(706\) −36.1947 −1.36221
\(707\) −15.8634 −0.596603
\(708\) 0.0298143 0.00112049
\(709\) 17.2995 0.649697 0.324849 0.945766i \(-0.394687\pi\)
0.324849 + 0.945766i \(0.394687\pi\)
\(710\) 39.5966 1.48603
\(711\) 13.1773 0.494187
\(712\) −37.8961 −1.42021
\(713\) 6.46443 0.242095
\(714\) 2.19396 0.0821068
\(715\) 17.8781 0.668604
\(716\) 1.16447 0.0435181
\(717\) 16.2697 0.607602
\(718\) −15.7349 −0.587220
\(719\) 24.7255 0.922104 0.461052 0.887373i \(-0.347472\pi\)
0.461052 + 0.887373i \(0.347472\pi\)
\(720\) 15.7972 0.588726
\(721\) 3.15800 0.117610
\(722\) 27.0617 1.00713
\(723\) 14.2950 0.531635
\(724\) −0.333114 −0.0123801
\(725\) −64.0717 −2.37956
\(726\) 39.7833 1.47650
\(727\) −31.4252 −1.16550 −0.582749 0.812652i \(-0.698023\pi\)
−0.582749 + 0.812652i \(0.698023\pi\)
\(728\) 3.18730 0.118129
\(729\) 1.00000 0.0370370
\(730\) −45.7581 −1.69358
\(731\) 5.74718 0.212567
\(732\) 0.0371960 0.00137480
\(733\) 1.65325 0.0610643 0.0305321 0.999534i \(-0.490280\pi\)
0.0305321 + 0.999534i \(0.490280\pi\)
\(734\) −17.0342 −0.628745
\(735\) −17.8627 −0.658876
\(736\) 1.05676 0.0389527
\(737\) 7.48670 0.275776
\(738\) 4.35566 0.160334
\(739\) 13.4396 0.494382 0.247191 0.968967i \(-0.420492\pi\)
0.247191 + 0.968967i \(0.420492\pi\)
\(740\) 1.41008 0.0518357
\(741\) 0.324167 0.0119086
\(742\) −5.37164 −0.197199
\(743\) 14.0910 0.516949 0.258474 0.966018i \(-0.416780\pi\)
0.258474 + 0.966018i \(0.416780\pi\)
\(744\) −6.61623 −0.242563
\(745\) 3.39070 0.124226
\(746\) −18.9397 −0.693430
\(747\) −12.0488 −0.440844
\(748\) −0.428172 −0.0156555
\(749\) −11.1872 −0.408772
\(750\) −25.3409 −0.925320
\(751\) 37.1478 1.35554 0.677770 0.735274i \(-0.262946\pi\)
0.677770 + 0.735274i \(0.262946\pi\)
\(752\) −22.7739 −0.830479
\(753\) 9.95840 0.362904
\(754\) 7.21472 0.262745
\(755\) 40.7838 1.48427
\(756\) −0.105040 −0.00382028
\(757\) −3.17696 −0.115469 −0.0577343 0.998332i \(-0.518388\pi\)
−0.0577343 + 0.998332i \(0.518388\pi\)
\(758\) 10.5740 0.384065
\(759\) 16.8742 0.612494
\(760\) 4.57489 0.165949
\(761\) 1.30286 0.0472287 0.0236144 0.999721i \(-0.492483\pi\)
0.0236144 + 0.999721i \(0.492483\pi\)
\(762\) 2.93305 0.106253
\(763\) 25.0251 0.905969
\(764\) −0.606061 −0.0219265
\(765\) −3.82222 −0.138193
\(766\) −39.6194 −1.43151
\(767\) −0.325697 −0.0117602
\(768\) −1.65080 −0.0595683
\(769\) −10.5979 −0.382170 −0.191085 0.981574i \(-0.561201\pi\)
−0.191085 + 0.981574i \(0.561201\pi\)
\(770\) −52.1397 −1.87898
\(771\) −22.4003 −0.806728
\(772\) −1.86569 −0.0671478
\(773\) 0.433004 0.0155741 0.00778703 0.999970i \(-0.497521\pi\)
0.00778703 + 0.999970i \(0.497521\pi\)
\(774\) −8.26649 −0.297133
\(775\) 22.8890 0.822196
\(776\) −37.0025 −1.32831
\(777\) 8.17142 0.293148
\(778\) −31.8357 −1.14137
\(779\) 1.30489 0.0467526
\(780\) 0.198012 0.00708997
\(781\) −44.7817 −1.60242
\(782\) −3.90359 −0.139592
\(783\) 6.66763 0.238282
\(784\) 19.3150 0.689822
\(785\) 3.82222 0.136421
\(786\) 5.52617 0.197112
\(787\) −38.2522 −1.36354 −0.681772 0.731565i \(-0.738790\pi\)
−0.681772 + 0.731565i \(0.738790\pi\)
\(788\) 0.245937 0.00876116
\(789\) 19.9317 0.709587
\(790\) 72.4450 2.57748
\(791\) −26.7488 −0.951079
\(792\) −17.2704 −0.613678
\(793\) −0.406336 −0.0144294
\(794\) 1.89905 0.0673947
\(795\) 9.35824 0.331903
\(796\) 1.52939 0.0542079
\(797\) 19.2828 0.683032 0.341516 0.939876i \(-0.389060\pi\)
0.341516 + 0.939876i \(0.389060\pi\)
\(798\) −0.945398 −0.0334667
\(799\) 5.51028 0.194940
\(800\) 3.74173 0.132290
\(801\) −13.6432 −0.482058
\(802\) −19.3196 −0.682197
\(803\) 51.7500 1.82622
\(804\) 0.0829201 0.00292437
\(805\) −15.8226 −0.557672
\(806\) −2.57739 −0.0907846
\(807\) 28.6672 1.00913
\(808\) −28.8876 −1.01626
\(809\) −52.6404 −1.85074 −0.925368 0.379069i \(-0.876244\pi\)
−0.925368 + 0.379069i \(0.876244\pi\)
\(810\) 5.49771 0.193170
\(811\) −17.7049 −0.621705 −0.310852 0.950458i \(-0.600614\pi\)
−0.310852 + 0.950458i \(0.600614\pi\)
\(812\) −0.700370 −0.0245782
\(813\) −25.0172 −0.877393
\(814\) −47.9099 −1.67924
\(815\) 90.0075 3.15282
\(816\) 4.13299 0.144683
\(817\) −2.47652 −0.0866424
\(818\) −7.11674 −0.248831
\(819\) 1.14748 0.0400961
\(820\) 0.797072 0.0278350
\(821\) 6.77416 0.236420 0.118210 0.992989i \(-0.462284\pi\)
0.118210 + 0.992989i \(0.462284\pi\)
\(822\) −25.8772 −0.902570
\(823\) 51.2795 1.78749 0.893745 0.448576i \(-0.148069\pi\)
0.893745 + 0.448576i \(0.148069\pi\)
\(824\) 5.75080 0.200338
\(825\) 59.7474 2.08014
\(826\) 0.949860 0.0330499
\(827\) −36.6917 −1.27590 −0.637948 0.770079i \(-0.720217\pi\)
−0.637948 + 0.770079i \(0.720217\pi\)
\(828\) 0.186893 0.00649497
\(829\) −6.20366 −0.215462 −0.107731 0.994180i \(-0.534359\pi\)
−0.107731 + 0.994180i \(0.534359\pi\)
\(830\) −66.2410 −2.29926
\(831\) 5.46635 0.189626
\(832\) 5.79703 0.200976
\(833\) −4.67338 −0.161923
\(834\) −20.0354 −0.693771
\(835\) −44.5923 −1.54318
\(836\) 0.184504 0.00638119
\(837\) −2.38194 −0.0823320
\(838\) −31.2067 −1.07802
\(839\) 5.91264 0.204127 0.102063 0.994778i \(-0.467456\pi\)
0.102063 + 0.994778i \(0.467456\pi\)
\(840\) 16.1941 0.558750
\(841\) 15.4573 0.533011
\(842\) −32.5550 −1.12192
\(843\) 3.24236 0.111673
\(844\) 0.374986 0.0129076
\(845\) 47.5257 1.63494
\(846\) −7.92574 −0.272493
\(847\) 42.1888 1.44962
\(848\) −10.1191 −0.347492
\(849\) 4.98257 0.171001
\(850\) −13.8217 −0.474080
\(851\) −14.5390 −0.498389
\(852\) −0.495986 −0.0169922
\(853\) 8.11731 0.277931 0.138966 0.990297i \(-0.455622\pi\)
0.138966 + 0.990297i \(0.455622\pi\)
\(854\) 1.18503 0.0405511
\(855\) 1.64703 0.0563273
\(856\) −20.3722 −0.696309
\(857\) 28.1373 0.961152 0.480576 0.876953i \(-0.340428\pi\)
0.480576 + 0.876953i \(0.340428\pi\)
\(858\) −6.72779 −0.229683
\(859\) 3.70191 0.126308 0.0631538 0.998004i \(-0.479884\pi\)
0.0631538 + 0.998004i \(0.479884\pi\)
\(860\) −1.51274 −0.0515840
\(861\) 4.61903 0.157416
\(862\) 55.4819 1.88972
\(863\) 21.3274 0.725994 0.362997 0.931790i \(-0.381753\pi\)
0.362997 + 0.931790i \(0.381753\pi\)
\(864\) −0.389384 −0.0132471
\(865\) −5.52526 −0.187865
\(866\) −43.5311 −1.47925
\(867\) −1.00000 −0.0339618
\(868\) 0.250200 0.00849235
\(869\) −81.9315 −2.77934
\(870\) 36.6567 1.24278
\(871\) −0.905833 −0.0306930
\(872\) 45.5714 1.54324
\(873\) −13.3215 −0.450863
\(874\) 1.68210 0.0568977
\(875\) −26.8732 −0.908479
\(876\) 0.573165 0.0193655
\(877\) −45.0430 −1.52099 −0.760497 0.649342i \(-0.775045\pi\)
−0.760497 + 0.649342i \(0.775045\pi\)
\(878\) 33.0115 1.11408
\(879\) 20.5351 0.692632
\(880\) −98.2210 −3.31103
\(881\) 48.7808 1.64347 0.821733 0.569873i \(-0.193008\pi\)
0.821733 + 0.569873i \(0.193008\pi\)
\(882\) 6.72198 0.226341
\(883\) −38.6289 −1.29997 −0.649983 0.759949i \(-0.725224\pi\)
−0.649983 + 0.759949i \(0.725224\pi\)
\(884\) 0.0518055 0.00174241
\(885\) −1.65481 −0.0556257
\(886\) −35.2951 −1.18576
\(887\) −32.8324 −1.10240 −0.551202 0.834372i \(-0.685831\pi\)
−0.551202 + 0.834372i \(0.685831\pi\)
\(888\) 14.8804 0.499353
\(889\) 3.11040 0.104319
\(890\) −75.0062 −2.51421
\(891\) −6.21763 −0.208298
\(892\) −0.857252 −0.0287029
\(893\) −2.37443 −0.0794574
\(894\) −1.27597 −0.0426747
\(895\) −64.6321 −2.16041
\(896\) −18.0943 −0.604488
\(897\) −2.04165 −0.0681686
\(898\) 8.52979 0.284643
\(899\) −15.8819 −0.529692
\(900\) 0.661742 0.0220581
\(901\) 2.44838 0.0815673
\(902\) −27.0819 −0.901728
\(903\) −8.76632 −0.291725
\(904\) −48.7104 −1.62008
\(905\) 18.4891 0.614598
\(906\) −15.3475 −0.509887
\(907\) −33.9394 −1.12694 −0.563469 0.826137i \(-0.690534\pi\)
−0.563469 + 0.826137i \(0.690534\pi\)
\(908\) −1.13894 −0.0377970
\(909\) −10.4000 −0.344946
\(910\) 6.30850 0.209125
\(911\) 18.1495 0.601320 0.300660 0.953731i \(-0.402793\pi\)
0.300660 + 0.953731i \(0.402793\pi\)
\(912\) −1.78094 −0.0589730
\(913\) 74.9152 2.47933
\(914\) −35.5212 −1.17494
\(915\) −2.06452 −0.0682508
\(916\) 0.934707 0.0308836
\(917\) 5.86031 0.193524
\(918\) 1.43835 0.0474728
\(919\) 42.6785 1.40783 0.703917 0.710282i \(-0.251433\pi\)
0.703917 + 0.710282i \(0.251433\pi\)
\(920\) −28.8133 −0.949946
\(921\) −1.02037 −0.0336222
\(922\) −34.2781 −1.12889
\(923\) 5.41824 0.178343
\(924\) 0.653101 0.0214855
\(925\) −51.4790 −1.69262
\(926\) 6.55898 0.215542
\(927\) 2.07038 0.0680001
\(928\) −2.59627 −0.0852267
\(929\) 35.1992 1.15485 0.577423 0.816445i \(-0.304058\pi\)
0.577423 + 0.816445i \(0.304058\pi\)
\(930\) −13.0952 −0.429410
\(931\) 2.01381 0.0659998
\(932\) 1.51248 0.0495430
\(933\) 8.34372 0.273161
\(934\) −6.41516 −0.209910
\(935\) 23.7651 0.777203
\(936\) 2.08959 0.0683003
\(937\) 41.2389 1.34721 0.673607 0.739089i \(-0.264744\pi\)
0.673607 + 0.739089i \(0.264744\pi\)
\(938\) 2.64177 0.0862568
\(939\) 15.1766 0.495270
\(940\) −1.45038 −0.0473063
\(941\) −41.2104 −1.34342 −0.671711 0.740813i \(-0.734440\pi\)
−0.671711 + 0.740813i \(0.734440\pi\)
\(942\) −1.43835 −0.0468641
\(943\) −8.21839 −0.267627
\(944\) 1.78935 0.0582384
\(945\) 5.83013 0.189654
\(946\) 51.3979 1.67109
\(947\) 19.3450 0.628628 0.314314 0.949319i \(-0.398225\pi\)
0.314314 + 0.949319i \(0.398225\pi\)
\(948\) −0.907445 −0.0294724
\(949\) −6.26135 −0.203252
\(950\) 5.95589 0.193235
\(951\) −6.18538 −0.200575
\(952\) 4.23683 0.137317
\(953\) −14.8511 −0.481075 −0.240537 0.970640i \(-0.577324\pi\)
−0.240537 + 0.970640i \(0.577324\pi\)
\(954\) −3.52164 −0.114017
\(955\) 33.6386 1.08852
\(956\) −1.12040 −0.0362363
\(957\) −41.4568 −1.34011
\(958\) 32.2148 1.04081
\(959\) −27.4418 −0.886143
\(960\) 29.4536 0.950612
\(961\) −25.3263 −0.816979
\(962\) 5.79673 0.186894
\(963\) −7.33432 −0.236345
\(964\) −0.984412 −0.0317058
\(965\) 103.553 3.33349
\(966\) 5.95425 0.191575
\(967\) 17.2977 0.556258 0.278129 0.960544i \(-0.410286\pi\)
0.278129 + 0.960544i \(0.410286\pi\)
\(968\) 76.8269 2.46931
\(969\) 0.430910 0.0138428
\(970\) −73.2375 −2.35152
\(971\) 1.61175 0.0517236 0.0258618 0.999666i \(-0.491767\pi\)
0.0258618 + 0.999666i \(0.491767\pi\)
\(972\) −0.0688642 −0.00220882
\(973\) −21.2469 −0.681144
\(974\) −21.6575 −0.693952
\(975\) −7.22897 −0.231512
\(976\) 2.23237 0.0714565
\(977\) 55.4200 1.77304 0.886521 0.462688i \(-0.153115\pi\)
0.886521 + 0.462688i \(0.153115\pi\)
\(978\) −33.8711 −1.08308
\(979\) 84.8281 2.71112
\(980\) 1.23010 0.0392941
\(981\) 16.4064 0.523816
\(982\) 25.9945 0.829517
\(983\) 18.4063 0.587070 0.293535 0.955948i \(-0.405168\pi\)
0.293535 + 0.955948i \(0.405168\pi\)
\(984\) 8.41137 0.268145
\(985\) −13.6504 −0.434939
\(986\) 9.59042 0.305421
\(987\) −8.40497 −0.267533
\(988\) −0.0223235 −0.000710205 0
\(989\) 15.5974 0.495970
\(990\) −34.1827 −1.08640
\(991\) −1.33640 −0.0424523 −0.0212261 0.999775i \(-0.506757\pi\)
−0.0212261 + 0.999775i \(0.506757\pi\)
\(992\) 0.927490 0.0294478
\(993\) 4.63627 0.147128
\(994\) −15.8017 −0.501200
\(995\) −84.8869 −2.69110
\(996\) 0.829734 0.0262911
\(997\) 12.4321 0.393728 0.196864 0.980431i \(-0.436924\pi\)
0.196864 + 0.980431i \(0.436924\pi\)
\(998\) 25.8405 0.817968
\(999\) 5.35717 0.169493
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 \(a_p\))