Properties

Label 8007.2.a.j.1.10
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 1.10
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.16822 q^{2}\) \(-1.00000 q^{3}\) \(+2.70116 q^{4}\) \(-4.31017 q^{5}\) \(+2.16822 q^{6}\) \(-1.36362 q^{7}\) \(-1.52027 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.16822 q^{2}\) \(-1.00000 q^{3}\) \(+2.70116 q^{4}\) \(-4.31017 q^{5}\) \(+2.16822 q^{6}\) \(-1.36362 q^{7}\) \(-1.52027 q^{8}\) \(+1.00000 q^{9}\) \(+9.34539 q^{10}\) \(+0.114623 q^{11}\) \(-2.70116 q^{12}\) \(+0.931925 q^{13}\) \(+2.95662 q^{14}\) \(+4.31017 q^{15}\) \(-2.10606 q^{16}\) \(+1.00000 q^{17}\) \(-2.16822 q^{18}\) \(+6.13855 q^{19}\) \(-11.6425 q^{20}\) \(+1.36362 q^{21}\) \(-0.248527 q^{22}\) \(-4.88123 q^{23}\) \(+1.52027 q^{24}\) \(+13.5776 q^{25}\) \(-2.02061 q^{26}\) \(-1.00000 q^{27}\) \(-3.68336 q^{28}\) \(-7.21659 q^{29}\) \(-9.34539 q^{30}\) \(-5.66271 q^{31}\) \(+7.60691 q^{32}\) \(-0.114623 q^{33}\) \(-2.16822 q^{34}\) \(+5.87744 q^{35}\) \(+2.70116 q^{36}\) \(+7.77973 q^{37}\) \(-13.3097 q^{38}\) \(-0.931925 q^{39}\) \(+6.55261 q^{40}\) \(+11.3656 q^{41}\) \(-2.95662 q^{42}\) \(+2.77017 q^{43}\) \(+0.309614 q^{44}\) \(-4.31017 q^{45}\) \(+10.5836 q^{46}\) \(-7.97282 q^{47}\) \(+2.10606 q^{48}\) \(-5.14054 q^{49}\) \(-29.4391 q^{50}\) \(-1.00000 q^{51}\) \(+2.51728 q^{52}\) \(+12.4294 q^{53}\) \(+2.16822 q^{54}\) \(-0.494044 q^{55}\) \(+2.07307 q^{56}\) \(-6.13855 q^{57}\) \(+15.6471 q^{58}\) \(+5.18445 q^{59}\) \(+11.6425 q^{60}\) \(+14.4443 q^{61}\) \(+12.2780 q^{62}\) \(-1.36362 q^{63}\) \(-12.2813 q^{64}\) \(-4.01676 q^{65}\) \(+0.248527 q^{66}\) \(+7.29253 q^{67}\) \(+2.70116 q^{68}\) \(+4.88123 q^{69}\) \(-12.7436 q^{70}\) \(-4.93808 q^{71}\) \(-1.52027 q^{72}\) \(+7.06100 q^{73}\) \(-16.8681 q^{74}\) \(-13.5776 q^{75}\) \(+16.5812 q^{76}\) \(-0.156302 q^{77}\) \(+2.02061 q^{78}\) \(-12.1982 q^{79}\) \(+9.07746 q^{80}\) \(+1.00000 q^{81}\) \(-24.6431 q^{82}\) \(-7.31701 q^{83}\) \(+3.68336 q^{84}\) \(-4.31017 q^{85}\) \(-6.00633 q^{86}\) \(+7.21659 q^{87}\) \(-0.174257 q^{88}\) \(+8.87217 q^{89}\) \(+9.34539 q^{90}\) \(-1.27079 q^{91}\) \(-13.1850 q^{92}\) \(+5.66271 q^{93}\) \(+17.2868 q^{94}\) \(-26.4582 q^{95}\) \(-7.60691 q^{96}\) \(+15.8368 q^{97}\) \(+11.1458 q^{98}\) \(+0.114623 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(64q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut -\mathstrut 64q^{3} \) \(\mathstrut +\mathstrut 77q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 64q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(64q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut -\mathstrut 64q^{3} \) \(\mathstrut +\mathstrut 77q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 64q^{9} \) \(\mathstrut +\mathstrut 12q^{10} \) \(\mathstrut -\mathstrut 7q^{11} \) \(\mathstrut -\mathstrut 77q^{12} \) \(\mathstrut +\mathstrut 24q^{13} \) \(\mathstrut -\mathstrut 14q^{14} \) \(\mathstrut +\mathstrut 3q^{15} \) \(\mathstrut +\mathstrut 103q^{16} \) \(\mathstrut +\mathstrut 64q^{17} \) \(\mathstrut +\mathstrut 5q^{18} \) \(\mathstrut +\mathstrut 26q^{19} \) \(\mathstrut -\mathstrut 24q^{20} \) \(\mathstrut -\mathstrut 5q^{21} \) \(\mathstrut +\mathstrut 25q^{22} \) \(\mathstrut +\mathstrut 20q^{23} \) \(\mathstrut -\mathstrut 18q^{24} \) \(\mathstrut +\mathstrut 141q^{25} \) \(\mathstrut +\mathstrut 9q^{26} \) \(\mathstrut -\mathstrut 64q^{27} \) \(\mathstrut +\mathstrut 14q^{28} \) \(\mathstrut +\mathstrut 5q^{29} \) \(\mathstrut -\mathstrut 12q^{30} \) \(\mathstrut +\mathstrut 11q^{31} \) \(\mathstrut +\mathstrut 31q^{32} \) \(\mathstrut +\mathstrut 7q^{33} \) \(\mathstrut +\mathstrut 5q^{34} \) \(\mathstrut -\mathstrut 3q^{35} \) \(\mathstrut +\mathstrut 77q^{36} \) \(\mathstrut +\mathstrut 50q^{37} \) \(\mathstrut +\mathstrut 8q^{38} \) \(\mathstrut -\mathstrut 24q^{39} \) \(\mathstrut +\mathstrut 28q^{40} \) \(\mathstrut -\mathstrut 9q^{41} \) \(\mathstrut +\mathstrut 14q^{42} \) \(\mathstrut +\mathstrut 59q^{43} \) \(\mathstrut -\mathstrut 6q^{44} \) \(\mathstrut -\mathstrut 3q^{45} \) \(\mathstrut +\mathstrut 11q^{47} \) \(\mathstrut -\mathstrut 103q^{48} \) \(\mathstrut +\mathstrut 163q^{49} \) \(\mathstrut +\mathstrut 20q^{50} \) \(\mathstrut -\mathstrut 64q^{51} \) \(\mathstrut +\mathstrut 65q^{52} \) \(\mathstrut +\mathstrut 39q^{53} \) \(\mathstrut -\mathstrut 5q^{54} \) \(\mathstrut +\mathstrut 35q^{55} \) \(\mathstrut -\mathstrut 34q^{56} \) \(\mathstrut -\mathstrut 26q^{57} \) \(\mathstrut -\mathstrut 27q^{58} \) \(\mathstrut -\mathstrut 65q^{59} \) \(\mathstrut +\mathstrut 24q^{60} \) \(\mathstrut +\mathstrut 15q^{61} \) \(\mathstrut +\mathstrut 18q^{62} \) \(\mathstrut +\mathstrut 5q^{63} \) \(\mathstrut +\mathstrut 152q^{64} \) \(\mathstrut +\mathstrut 49q^{65} \) \(\mathstrut -\mathstrut 25q^{66} \) \(\mathstrut +\mathstrut 56q^{67} \) \(\mathstrut +\mathstrut 77q^{68} \) \(\mathstrut -\mathstrut 20q^{69} \) \(\mathstrut +\mathstrut 28q^{70} \) \(\mathstrut -\mathstrut 18q^{71} \) \(\mathstrut +\mathstrut 18q^{72} \) \(\mathstrut +\mathstrut 37q^{73} \) \(\mathstrut -\mathstrut 76q^{74} \) \(\mathstrut -\mathstrut 141q^{75} \) \(\mathstrut +\mathstrut 30q^{76} \) \(\mathstrut +\mathstrut 80q^{77} \) \(\mathstrut -\mathstrut 9q^{78} \) \(\mathstrut +\mathstrut 20q^{79} \) \(\mathstrut -\mathstrut 144q^{80} \) \(\mathstrut +\mathstrut 64q^{81} \) \(\mathstrut +\mathstrut 27q^{82} \) \(\mathstrut +\mathstrut 3q^{83} \) \(\mathstrut -\mathstrut 14q^{84} \) \(\mathstrut -\mathstrut 3q^{85} \) \(\mathstrut +\mathstrut 12q^{86} \) \(\mathstrut -\mathstrut 5q^{87} \) \(\mathstrut +\mathstrut 108q^{88} \) \(\mathstrut +\mathstrut 42q^{89} \) \(\mathstrut +\mathstrut 12q^{90} \) \(\mathstrut +\mathstrut 25q^{91} \) \(\mathstrut +\mathstrut 18q^{92} \) \(\mathstrut -\mathstrut 11q^{93} \) \(\mathstrut +\mathstrut 60q^{94} \) \(\mathstrut +\mathstrut 42q^{95} \) \(\mathstrut -\mathstrut 31q^{96} \) \(\mathstrut +\mathstrut 72q^{97} \) \(\mathstrut +\mathstrut 18q^{98} \) \(\mathstrut -\mathstrut 7q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.16822 −1.53316 −0.766580 0.642149i \(-0.778043\pi\)
−0.766580 + 0.642149i \(0.778043\pi\)
\(3\) −1.00000 −0.577350
\(4\) 2.70116 1.35058
\(5\) −4.31017 −1.92757 −0.963784 0.266684i \(-0.914072\pi\)
−0.963784 + 0.266684i \(0.914072\pi\)
\(6\) 2.16822 0.885170
\(7\) −1.36362 −0.515400 −0.257700 0.966225i \(-0.582965\pi\)
−0.257700 + 0.966225i \(0.582965\pi\)
\(8\) −1.52027 −0.537495
\(9\) 1.00000 0.333333
\(10\) 9.34539 2.95527
\(11\) 0.114623 0.0345600 0.0172800 0.999851i \(-0.494499\pi\)
0.0172800 + 0.999851i \(0.494499\pi\)
\(12\) −2.70116 −0.779758
\(13\) 0.931925 0.258469 0.129235 0.991614i \(-0.458748\pi\)
0.129235 + 0.991614i \(0.458748\pi\)
\(14\) 2.95662 0.790191
\(15\) 4.31017 1.11288
\(16\) −2.10606 −0.526514
\(17\) 1.00000 0.242536
\(18\) −2.16822 −0.511053
\(19\) 6.13855 1.40828 0.704140 0.710062i \(-0.251333\pi\)
0.704140 + 0.710062i \(0.251333\pi\)
\(20\) −11.6425 −2.60333
\(21\) 1.36362 0.297566
\(22\) −0.248527 −0.0529861
\(23\) −4.88123 −1.01781 −0.508904 0.860823i \(-0.669949\pi\)
−0.508904 + 0.860823i \(0.669949\pi\)
\(24\) 1.52027 0.310323
\(25\) 13.5776 2.71552
\(26\) −2.02061 −0.396275
\(27\) −1.00000 −0.192450
\(28\) −3.68336 −0.696089
\(29\) −7.21659 −1.34009 −0.670044 0.742322i \(-0.733725\pi\)
−0.670044 + 0.742322i \(0.733725\pi\)
\(30\) −9.34539 −1.70623
\(31\) −5.66271 −1.01705 −0.508526 0.861046i \(-0.669810\pi\)
−0.508526 + 0.861046i \(0.669810\pi\)
\(32\) 7.60691 1.34473
\(33\) −0.114623 −0.0199533
\(34\) −2.16822 −0.371846
\(35\) 5.87744 0.993468
\(36\) 2.70116 0.450193
\(37\) 7.77973 1.27898 0.639490 0.768800i \(-0.279146\pi\)
0.639490 + 0.768800i \(0.279146\pi\)
\(38\) −13.3097 −2.15912
\(39\) −0.931925 −0.149227
\(40\) 6.55261 1.03606
\(41\) 11.3656 1.77501 0.887505 0.460798i \(-0.152437\pi\)
0.887505 + 0.460798i \(0.152437\pi\)
\(42\) −2.95662 −0.456217
\(43\) 2.77017 0.422447 0.211224 0.977438i \(-0.432255\pi\)
0.211224 + 0.977438i \(0.432255\pi\)
\(44\) 0.309614 0.0466761
\(45\) −4.31017 −0.642523
\(46\) 10.5836 1.56046
\(47\) −7.97282 −1.16296 −0.581478 0.813562i \(-0.697525\pi\)
−0.581478 + 0.813562i \(0.697525\pi\)
\(48\) 2.10606 0.303983
\(49\) −5.14054 −0.734363
\(50\) −29.4391 −4.16332
\(51\) −1.00000 −0.140028
\(52\) 2.51728 0.349084
\(53\) 12.4294 1.70731 0.853653 0.520841i \(-0.174382\pi\)
0.853653 + 0.520841i \(0.174382\pi\)
\(54\) 2.16822 0.295057
\(55\) −0.494044 −0.0666168
\(56\) 2.07307 0.277025
\(57\) −6.13855 −0.813070
\(58\) 15.6471 2.05457
\(59\) 5.18445 0.674958 0.337479 0.941333i \(-0.390426\pi\)
0.337479 + 0.941333i \(0.390426\pi\)
\(60\) 11.6425 1.50304
\(61\) 14.4443 1.84940 0.924701 0.380694i \(-0.124315\pi\)
0.924701 + 0.380694i \(0.124315\pi\)
\(62\) 12.2780 1.55930
\(63\) −1.36362 −0.171800
\(64\) −12.2813 −1.53517
\(65\) −4.01676 −0.498217
\(66\) 0.248527 0.0305915
\(67\) 7.29253 0.890925 0.445462 0.895301i \(-0.353039\pi\)
0.445462 + 0.895301i \(0.353039\pi\)
\(68\) 2.70116 0.327564
\(69\) 4.88123 0.587632
\(70\) −12.7436 −1.52315
\(71\) −4.93808 −0.586042 −0.293021 0.956106i \(-0.594661\pi\)
−0.293021 + 0.956106i \(0.594661\pi\)
\(72\) −1.52027 −0.179165
\(73\) 7.06100 0.826427 0.413214 0.910634i \(-0.364406\pi\)
0.413214 + 0.910634i \(0.364406\pi\)
\(74\) −16.8681 −1.96088
\(75\) −13.5776 −1.56781
\(76\) 16.5812 1.90199
\(77\) −0.156302 −0.0178122
\(78\) 2.02061 0.228790
\(79\) −12.1982 −1.37240 −0.686201 0.727412i \(-0.740723\pi\)
−0.686201 + 0.727412i \(0.740723\pi\)
\(80\) 9.07746 1.01489
\(81\) 1.00000 0.111111
\(82\) −24.6431 −2.72137
\(83\) −7.31701 −0.803147 −0.401573 0.915827i \(-0.631537\pi\)
−0.401573 + 0.915827i \(0.631537\pi\)
\(84\) 3.68336 0.401887
\(85\) −4.31017 −0.467504
\(86\) −6.00633 −0.647679
\(87\) 7.21659 0.773700
\(88\) −0.174257 −0.0185759
\(89\) 8.87217 0.940448 0.470224 0.882547i \(-0.344173\pi\)
0.470224 + 0.882547i \(0.344173\pi\)
\(90\) 9.34539 0.985090
\(91\) −1.27079 −0.133215
\(92\) −13.1850 −1.37463
\(93\) 5.66271 0.587196
\(94\) 17.2868 1.78300
\(95\) −26.4582 −2.71455
\(96\) −7.60691 −0.776377
\(97\) 15.8368 1.60798 0.803992 0.594640i \(-0.202705\pi\)
0.803992 + 0.594640i \(0.202705\pi\)
\(98\) 11.1458 1.12590
\(99\) 0.114623 0.0115200
\(100\) 36.6752 3.66752
\(101\) 16.8733 1.67895 0.839476 0.543397i \(-0.182862\pi\)
0.839476 + 0.543397i \(0.182862\pi\)
\(102\) 2.16822 0.214685
\(103\) −12.1412 −1.19631 −0.598155 0.801380i \(-0.704099\pi\)
−0.598155 + 0.801380i \(0.704099\pi\)
\(104\) −1.41677 −0.138926
\(105\) −5.87744 −0.573579
\(106\) −26.9496 −2.61757
\(107\) −9.69737 −0.937480 −0.468740 0.883336i \(-0.655292\pi\)
−0.468740 + 0.883336i \(0.655292\pi\)
\(108\) −2.70116 −0.259919
\(109\) −1.05377 −0.100933 −0.0504666 0.998726i \(-0.516071\pi\)
−0.0504666 + 0.998726i \(0.516071\pi\)
\(110\) 1.07119 0.102134
\(111\) −7.77973 −0.738419
\(112\) 2.87186 0.271365
\(113\) −4.35515 −0.409698 −0.204849 0.978794i \(-0.565670\pi\)
−0.204849 + 0.978794i \(0.565670\pi\)
\(114\) 13.3097 1.24657
\(115\) 21.0390 1.96189
\(116\) −19.4932 −1.80990
\(117\) 0.931925 0.0861565
\(118\) −11.2410 −1.03482
\(119\) −1.36362 −0.125003
\(120\) −6.55261 −0.598169
\(121\) −10.9869 −0.998806
\(122\) −31.3183 −2.83543
\(123\) −11.3656 −1.02480
\(124\) −15.2959 −1.37361
\(125\) −36.9709 −3.30678
\(126\) 2.95662 0.263397
\(127\) 17.7905 1.57865 0.789325 0.613976i \(-0.210431\pi\)
0.789325 + 0.613976i \(0.210431\pi\)
\(128\) 11.4147 1.00893
\(129\) −2.77017 −0.243900
\(130\) 8.70920 0.763847
\(131\) −17.0617 −1.49069 −0.745344 0.666680i \(-0.767715\pi\)
−0.745344 + 0.666680i \(0.767715\pi\)
\(132\) −0.309614 −0.0269485
\(133\) −8.37065 −0.725827
\(134\) −15.8118 −1.36593
\(135\) 4.31017 0.370961
\(136\) −1.52027 −0.130362
\(137\) −13.9010 −1.18764 −0.593820 0.804598i \(-0.702381\pi\)
−0.593820 + 0.804598i \(0.702381\pi\)
\(138\) −10.5836 −0.900933
\(139\) −13.7253 −1.16417 −0.582083 0.813130i \(-0.697762\pi\)
−0.582083 + 0.813130i \(0.697762\pi\)
\(140\) 15.8759 1.34176
\(141\) 7.97282 0.671433
\(142\) 10.7068 0.898496
\(143\) 0.106820 0.00893272
\(144\) −2.10606 −0.175505
\(145\) 31.1048 2.58311
\(146\) −15.3098 −1.26705
\(147\) 5.14054 0.423985
\(148\) 21.0143 1.72736
\(149\) −11.4677 −0.939475 −0.469737 0.882806i \(-0.655651\pi\)
−0.469737 + 0.882806i \(0.655651\pi\)
\(150\) 29.4391 2.40370
\(151\) −3.57720 −0.291108 −0.145554 0.989350i \(-0.546496\pi\)
−0.145554 + 0.989350i \(0.546496\pi\)
\(152\) −9.33222 −0.756943
\(153\) 1.00000 0.0808452
\(154\) 0.338896 0.0273090
\(155\) 24.4073 1.96044
\(156\) −2.51728 −0.201544
\(157\) −1.00000 −0.0798087
\(158\) 26.4483 2.10411
\(159\) −12.4294 −0.985714
\(160\) −32.7871 −2.59205
\(161\) 6.65615 0.524578
\(162\) −2.16822 −0.170351
\(163\) −3.71098 −0.290666 −0.145333 0.989383i \(-0.546425\pi\)
−0.145333 + 0.989383i \(0.546425\pi\)
\(164\) 30.7003 2.39729
\(165\) 0.494044 0.0384612
\(166\) 15.8649 1.23135
\(167\) −14.1416 −1.09431 −0.547154 0.837032i \(-0.684289\pi\)
−0.547154 + 0.837032i \(0.684289\pi\)
\(168\) −2.07307 −0.159940
\(169\) −12.1315 −0.933194
\(170\) 9.34539 0.716758
\(171\) 6.13855 0.469426
\(172\) 7.48268 0.570549
\(173\) 19.7602 1.50234 0.751170 0.660109i \(-0.229490\pi\)
0.751170 + 0.660109i \(0.229490\pi\)
\(174\) −15.6471 −1.18621
\(175\) −18.5147 −1.39958
\(176\) −0.241402 −0.0181963
\(177\) −5.18445 −0.389687
\(178\) −19.2368 −1.44186
\(179\) −6.93544 −0.518379 −0.259189 0.965827i \(-0.583455\pi\)
−0.259189 + 0.965827i \(0.583455\pi\)
\(180\) −11.6425 −0.867778
\(181\) −10.8175 −0.804059 −0.402029 0.915627i \(-0.631695\pi\)
−0.402029 + 0.915627i \(0.631695\pi\)
\(182\) 2.75535 0.204240
\(183\) −14.4443 −1.06775
\(184\) 7.42077 0.547067
\(185\) −33.5320 −2.46532
\(186\) −12.2780 −0.900265
\(187\) 0.114623 0.00838204
\(188\) −21.5359 −1.57066
\(189\) 1.36362 0.0991888
\(190\) 57.3671 4.16185
\(191\) 13.3118 0.963205 0.481603 0.876390i \(-0.340055\pi\)
0.481603 + 0.876390i \(0.340055\pi\)
\(192\) 12.2813 0.886328
\(193\) −3.51300 −0.252871 −0.126436 0.991975i \(-0.540354\pi\)
−0.126436 + 0.991975i \(0.540354\pi\)
\(194\) −34.3376 −2.46530
\(195\) 4.01676 0.287646
\(196\) −13.8854 −0.991816
\(197\) −5.48140 −0.390533 −0.195267 0.980750i \(-0.562557\pi\)
−0.195267 + 0.980750i \(0.562557\pi\)
\(198\) −0.248527 −0.0176620
\(199\) −12.7640 −0.904814 −0.452407 0.891812i \(-0.649434\pi\)
−0.452407 + 0.891812i \(0.649434\pi\)
\(200\) −20.6415 −1.45958
\(201\) −7.29253 −0.514376
\(202\) −36.5849 −2.57410
\(203\) 9.84069 0.690681
\(204\) −2.70116 −0.189119
\(205\) −48.9877 −3.42145
\(206\) 26.3248 1.83414
\(207\) −4.88123 −0.339269
\(208\) −1.96269 −0.136088
\(209\) 0.703617 0.0486702
\(210\) 12.7436 0.879389
\(211\) −12.0394 −0.828824 −0.414412 0.910089i \(-0.636013\pi\)
−0.414412 + 0.910089i \(0.636013\pi\)
\(212\) 33.5737 2.30585
\(213\) 4.93808 0.338351
\(214\) 21.0260 1.43731
\(215\) −11.9399 −0.814296
\(216\) 1.52027 0.103441
\(217\) 7.72179 0.524189
\(218\) 2.28481 0.154747
\(219\) −7.06100 −0.477138
\(220\) −1.33449 −0.0899714
\(221\) 0.931925 0.0626881
\(222\) 16.8681 1.13211
\(223\) 5.99300 0.401321 0.200660 0.979661i \(-0.435691\pi\)
0.200660 + 0.979661i \(0.435691\pi\)
\(224\) −10.3729 −0.693071
\(225\) 13.5776 0.905173
\(226\) 9.44291 0.628133
\(227\) 1.09079 0.0723981 0.0361991 0.999345i \(-0.488475\pi\)
0.0361991 + 0.999345i \(0.488475\pi\)
\(228\) −16.5812 −1.09812
\(229\) −3.35295 −0.221569 −0.110785 0.993844i \(-0.535336\pi\)
−0.110785 + 0.993844i \(0.535336\pi\)
\(230\) −45.6170 −3.00790
\(231\) 0.156302 0.0102839
\(232\) 10.9711 0.720291
\(233\) 6.21743 0.407317 0.203659 0.979042i \(-0.434717\pi\)
0.203659 + 0.979042i \(0.434717\pi\)
\(234\) −2.02061 −0.132092
\(235\) 34.3642 2.24168
\(236\) 14.0040 0.911585
\(237\) 12.1982 0.792357
\(238\) 2.95662 0.191649
\(239\) 20.5409 1.32868 0.664341 0.747430i \(-0.268712\pi\)
0.664341 + 0.747430i \(0.268712\pi\)
\(240\) −9.07746 −0.585948
\(241\) −15.7471 −1.01436 −0.507180 0.861840i \(-0.669312\pi\)
−0.507180 + 0.861840i \(0.669312\pi\)
\(242\) 23.8219 1.53133
\(243\) −1.00000 −0.0641500
\(244\) 39.0164 2.49777
\(245\) 22.1566 1.41553
\(246\) 24.6431 1.57119
\(247\) 5.72066 0.363997
\(248\) 8.60883 0.546661
\(249\) 7.31701 0.463697
\(250\) 80.1609 5.06982
\(251\) −29.1549 −1.84024 −0.920121 0.391633i \(-0.871910\pi\)
−0.920121 + 0.391633i \(0.871910\pi\)
\(252\) −3.68336 −0.232030
\(253\) −0.559500 −0.0351755
\(254\) −38.5736 −2.42032
\(255\) 4.31017 0.269914
\(256\) −0.186947 −0.0116842
\(257\) 23.1484 1.44396 0.721979 0.691915i \(-0.243233\pi\)
0.721979 + 0.691915i \(0.243233\pi\)
\(258\) 6.00633 0.373938
\(259\) −10.6086 −0.659186
\(260\) −10.8499 −0.672882
\(261\) −7.21659 −0.446696
\(262\) 36.9934 2.28546
\(263\) −7.46636 −0.460396 −0.230198 0.973144i \(-0.573937\pi\)
−0.230198 + 0.973144i \(0.573937\pi\)
\(264\) 0.174257 0.0107248
\(265\) −53.5728 −3.29095
\(266\) 18.1494 1.11281
\(267\) −8.87217 −0.542968
\(268\) 19.6983 1.20326
\(269\) −11.5724 −0.705581 −0.352791 0.935702i \(-0.614767\pi\)
−0.352791 + 0.935702i \(0.614767\pi\)
\(270\) −9.34539 −0.568742
\(271\) 4.86324 0.295421 0.147711 0.989031i \(-0.452810\pi\)
0.147711 + 0.989031i \(0.452810\pi\)
\(272\) −2.10606 −0.127698
\(273\) 1.27079 0.0769118
\(274\) 30.1403 1.82084
\(275\) 1.55630 0.0938484
\(276\) 13.1850 0.793643
\(277\) 12.5877 0.756320 0.378160 0.925740i \(-0.376557\pi\)
0.378160 + 0.925740i \(0.376557\pi\)
\(278\) 29.7594 1.78485
\(279\) −5.66271 −0.339018
\(280\) −8.93527 −0.533984
\(281\) 3.85751 0.230120 0.115060 0.993359i \(-0.463294\pi\)
0.115060 + 0.993359i \(0.463294\pi\)
\(282\) −17.2868 −1.02941
\(283\) 19.5546 1.16240 0.581202 0.813760i \(-0.302583\pi\)
0.581202 + 0.813760i \(0.302583\pi\)
\(284\) −13.3385 −0.791496
\(285\) 26.4582 1.56725
\(286\) −0.231608 −0.0136953
\(287\) −15.4984 −0.914840
\(288\) 7.60691 0.448242
\(289\) 1.00000 0.0588235
\(290\) −67.4418 −3.96032
\(291\) −15.8368 −0.928370
\(292\) 19.0729 1.11616
\(293\) −30.0136 −1.75341 −0.876706 0.481026i \(-0.840264\pi\)
−0.876706 + 0.481026i \(0.840264\pi\)
\(294\) −11.1458 −0.650036
\(295\) −22.3459 −1.30103
\(296\) −11.8273 −0.687445
\(297\) −0.114623 −0.00665108
\(298\) 24.8646 1.44037
\(299\) −4.54894 −0.263072
\(300\) −36.6752 −2.11745
\(301\) −3.77746 −0.217729
\(302\) 7.75614 0.446315
\(303\) −16.8733 −0.969343
\(304\) −12.9281 −0.741478
\(305\) −62.2574 −3.56485
\(306\) −2.16822 −0.123949
\(307\) 28.1322 1.60559 0.802794 0.596257i \(-0.203346\pi\)
0.802794 + 0.596257i \(0.203346\pi\)
\(308\) −0.422196 −0.0240569
\(309\) 12.1412 0.690690
\(310\) −52.9202 −3.00567
\(311\) 9.81225 0.556402 0.278201 0.960523i \(-0.410262\pi\)
0.278201 + 0.960523i \(0.410262\pi\)
\(312\) 1.41677 0.0802090
\(313\) 27.1723 1.53587 0.767935 0.640528i \(-0.221285\pi\)
0.767935 + 0.640528i \(0.221285\pi\)
\(314\) 2.16822 0.122359
\(315\) 5.87744 0.331156
\(316\) −32.9492 −1.85354
\(317\) −1.67557 −0.0941093 −0.0470547 0.998892i \(-0.514983\pi\)
−0.0470547 + 0.998892i \(0.514983\pi\)
\(318\) 26.9496 1.51126
\(319\) −0.827185 −0.0463135
\(320\) 52.9346 2.95913
\(321\) 9.69737 0.541255
\(322\) −14.4320 −0.804262
\(323\) 6.13855 0.341558
\(324\) 2.70116 0.150064
\(325\) 12.6533 0.701879
\(326\) 8.04620 0.445638
\(327\) 1.05377 0.0582738
\(328\) −17.2787 −0.954059
\(329\) 10.8719 0.599387
\(330\) −1.07119 −0.0589672
\(331\) 7.75589 0.426302 0.213151 0.977019i \(-0.431627\pi\)
0.213151 + 0.977019i \(0.431627\pi\)
\(332\) −19.7644 −1.08471
\(333\) 7.77973 0.426327
\(334\) 30.6620 1.67775
\(335\) −31.4321 −1.71732
\(336\) −2.87186 −0.156673
\(337\) 26.1123 1.42243 0.711213 0.702977i \(-0.248146\pi\)
0.711213 + 0.702977i \(0.248146\pi\)
\(338\) 26.3037 1.43074
\(339\) 4.35515 0.236539
\(340\) −11.6425 −0.631401
\(341\) −0.649075 −0.0351494
\(342\) −13.3097 −0.719706
\(343\) 16.5551 0.893891
\(344\) −4.21140 −0.227063
\(345\) −21.0390 −1.13270
\(346\) −42.8444 −2.30333
\(347\) 10.3882 0.557665 0.278833 0.960340i \(-0.410053\pi\)
0.278833 + 0.960340i \(0.410053\pi\)
\(348\) 19.4932 1.04494
\(349\) −12.6661 −0.677999 −0.339000 0.940787i \(-0.610089\pi\)
−0.339000 + 0.940787i \(0.610089\pi\)
\(350\) 40.1438 2.14578
\(351\) −0.931925 −0.0497425
\(352\) 0.871925 0.0464738
\(353\) −20.0624 −1.06781 −0.533906 0.845544i \(-0.679276\pi\)
−0.533906 + 0.845544i \(0.679276\pi\)
\(354\) 11.2410 0.597453
\(355\) 21.2840 1.12964
\(356\) 23.9651 1.27015
\(357\) 1.36362 0.0721704
\(358\) 15.0375 0.794758
\(359\) 12.7533 0.673091 0.336546 0.941667i \(-0.390741\pi\)
0.336546 + 0.941667i \(0.390741\pi\)
\(360\) 6.55261 0.345353
\(361\) 18.6817 0.983250
\(362\) 23.4547 1.23275
\(363\) 10.9869 0.576661
\(364\) −3.43261 −0.179918
\(365\) −30.4341 −1.59299
\(366\) 31.3183 1.63704
\(367\) −23.1275 −1.20725 −0.603624 0.797269i \(-0.706277\pi\)
−0.603624 + 0.797269i \(0.706277\pi\)
\(368\) 10.2802 0.535890
\(369\) 11.3656 0.591670
\(370\) 72.7046 3.77973
\(371\) −16.9490 −0.879946
\(372\) 15.2959 0.793055
\(373\) −13.0302 −0.674680 −0.337340 0.941383i \(-0.609527\pi\)
−0.337340 + 0.941383i \(0.609527\pi\)
\(374\) −0.248527 −0.0128510
\(375\) 36.9709 1.90917
\(376\) 12.1208 0.625083
\(377\) −6.72532 −0.346372
\(378\) −2.95662 −0.152072
\(379\) 26.5772 1.36518 0.682589 0.730802i \(-0.260854\pi\)
0.682589 + 0.730802i \(0.260854\pi\)
\(380\) −71.4678 −3.66622
\(381\) −17.7905 −0.911434
\(382\) −28.8628 −1.47675
\(383\) −12.0316 −0.614785 −0.307393 0.951583i \(-0.599456\pi\)
−0.307393 + 0.951583i \(0.599456\pi\)
\(384\) −11.4147 −0.582505
\(385\) 0.673688 0.0343343
\(386\) 7.61695 0.387692
\(387\) 2.77017 0.140816
\(388\) 42.7777 2.17171
\(389\) −3.72378 −0.188803 −0.0944016 0.995534i \(-0.530094\pi\)
−0.0944016 + 0.995534i \(0.530094\pi\)
\(390\) −8.70920 −0.441007
\(391\) −4.88123 −0.246855
\(392\) 7.81499 0.394716
\(393\) 17.0617 0.860649
\(394\) 11.8849 0.598750
\(395\) 52.5762 2.64540
\(396\) 0.309614 0.0155587
\(397\) 2.15881 0.108348 0.0541739 0.998532i \(-0.482747\pi\)
0.0541739 + 0.998532i \(0.482747\pi\)
\(398\) 27.6750 1.38722
\(399\) 8.37065 0.419056
\(400\) −28.5952 −1.42976
\(401\) −19.9592 −0.996714 −0.498357 0.866972i \(-0.666063\pi\)
−0.498357 + 0.866972i \(0.666063\pi\)
\(402\) 15.8118 0.788620
\(403\) −5.27722 −0.262877
\(404\) 45.5774 2.26756
\(405\) −4.31017 −0.214174
\(406\) −21.3367 −1.05892
\(407\) 0.891734 0.0442016
\(408\) 1.52027 0.0752644
\(409\) 26.8393 1.32712 0.663559 0.748124i \(-0.269045\pi\)
0.663559 + 0.748124i \(0.269045\pi\)
\(410\) 106.216 5.24563
\(411\) 13.9010 0.685684
\(412\) −32.7954 −1.61571
\(413\) −7.06963 −0.347874
\(414\) 10.5836 0.520154
\(415\) 31.5376 1.54812
\(416\) 7.08907 0.347570
\(417\) 13.7253 0.672131
\(418\) −1.52559 −0.0746192
\(419\) −4.58517 −0.224000 −0.112000 0.993708i \(-0.535726\pi\)
−0.112000 + 0.993708i \(0.535726\pi\)
\(420\) −15.8759 −0.774665
\(421\) 17.4572 0.850813 0.425407 0.905002i \(-0.360131\pi\)
0.425407 + 0.905002i \(0.360131\pi\)
\(422\) 26.1040 1.27072
\(423\) −7.97282 −0.387652
\(424\) −18.8960 −0.917669
\(425\) 13.5776 0.658610
\(426\) −10.7068 −0.518747
\(427\) −19.6965 −0.953182
\(428\) −26.1942 −1.26614
\(429\) −0.106820 −0.00515731
\(430\) 25.8883 1.24845
\(431\) 20.4666 0.985841 0.492921 0.870074i \(-0.335929\pi\)
0.492921 + 0.870074i \(0.335929\pi\)
\(432\) 2.10606 0.101328
\(433\) 21.4035 1.02859 0.514294 0.857614i \(-0.328054\pi\)
0.514294 + 0.857614i \(0.328054\pi\)
\(434\) −16.7425 −0.803666
\(435\) −31.1048 −1.49136
\(436\) −2.84641 −0.136318
\(437\) −29.9637 −1.43336
\(438\) 15.3098 0.731529
\(439\) 11.6463 0.555847 0.277924 0.960603i \(-0.410354\pi\)
0.277924 + 0.960603i \(0.410354\pi\)
\(440\) 0.751078 0.0358062
\(441\) −5.14054 −0.244788
\(442\) −2.02061 −0.0961108
\(443\) −9.18461 −0.436374 −0.218187 0.975907i \(-0.570014\pi\)
−0.218187 + 0.975907i \(0.570014\pi\)
\(444\) −21.0143 −0.997294
\(445\) −38.2406 −1.81278
\(446\) −12.9941 −0.615289
\(447\) 11.4677 0.542406
\(448\) 16.7471 0.791224
\(449\) 3.77833 0.178310 0.0891551 0.996018i \(-0.471583\pi\)
0.0891551 + 0.996018i \(0.471583\pi\)
\(450\) −29.4391 −1.38777
\(451\) 1.30276 0.0613444
\(452\) −11.7640 −0.553330
\(453\) 3.57720 0.168071
\(454\) −2.36506 −0.110998
\(455\) 5.47733 0.256781
\(456\) 9.33222 0.437021
\(457\) −20.2882 −0.949043 −0.474521 0.880244i \(-0.657379\pi\)
−0.474521 + 0.880244i \(0.657379\pi\)
\(458\) 7.26992 0.339701
\(459\) −1.00000 −0.0466760
\(460\) 56.8296 2.64969
\(461\) −7.78141 −0.362417 −0.181208 0.983445i \(-0.558001\pi\)
−0.181208 + 0.983445i \(0.558001\pi\)
\(462\) −0.338896 −0.0157669
\(463\) 12.3304 0.573040 0.286520 0.958074i \(-0.407501\pi\)
0.286520 + 0.958074i \(0.407501\pi\)
\(464\) 15.1985 0.705575
\(465\) −24.4073 −1.13186
\(466\) −13.4807 −0.624483
\(467\) −34.3145 −1.58789 −0.793943 0.607992i \(-0.791975\pi\)
−0.793943 + 0.607992i \(0.791975\pi\)
\(468\) 2.51728 0.116361
\(469\) −9.94424 −0.459183
\(470\) −74.5091 −3.43685
\(471\) 1.00000 0.0460776
\(472\) −7.88175 −0.362787
\(473\) 0.317525 0.0145998
\(474\) −26.4483 −1.21481
\(475\) 83.3467 3.82421
\(476\) −3.68336 −0.168826
\(477\) 12.4294 0.569102
\(478\) −44.5371 −2.03708
\(479\) 38.2688 1.74855 0.874274 0.485433i \(-0.161338\pi\)
0.874274 + 0.485433i \(0.161338\pi\)
\(480\) 32.7871 1.49652
\(481\) 7.25012 0.330577
\(482\) 34.1431 1.55518
\(483\) −6.65615 −0.302865
\(484\) −29.6773 −1.34897
\(485\) −68.2594 −3.09950
\(486\) 2.16822 0.0983523
\(487\) −36.9846 −1.67593 −0.837967 0.545721i \(-0.816256\pi\)
−0.837967 + 0.545721i \(0.816256\pi\)
\(488\) −21.9592 −0.994045
\(489\) 3.71098 0.167816
\(490\) −48.0403 −2.17024
\(491\) −18.1402 −0.818655 −0.409328 0.912387i \(-0.634237\pi\)
−0.409328 + 0.912387i \(0.634237\pi\)
\(492\) −30.7003 −1.38408
\(493\) −7.21659 −0.325019
\(494\) −12.4036 −0.558066
\(495\) −0.494044 −0.0222056
\(496\) 11.9260 0.535492
\(497\) 6.73366 0.302046
\(498\) −15.8649 −0.710922
\(499\) −8.71037 −0.389930 −0.194965 0.980810i \(-0.562459\pi\)
−0.194965 + 0.980810i \(0.562459\pi\)
\(500\) −99.8643 −4.46607
\(501\) 14.1416 0.631799
\(502\) 63.2142 2.82139
\(503\) −3.40185 −0.151681 −0.0758404 0.997120i \(-0.524164\pi\)
−0.0758404 + 0.997120i \(0.524164\pi\)
\(504\) 2.07307 0.0923417
\(505\) −72.7267 −3.23629
\(506\) 1.21312 0.0539296
\(507\) 12.1315 0.538780
\(508\) 48.0549 2.13209
\(509\) 31.4767 1.39518 0.697591 0.716496i \(-0.254255\pi\)
0.697591 + 0.716496i \(0.254255\pi\)
\(510\) −9.34539 −0.413821
\(511\) −9.62852 −0.425941
\(512\) −22.4241 −0.991015
\(513\) −6.13855 −0.271023
\(514\) −50.1907 −2.21382
\(515\) 52.3308 2.30597
\(516\) −7.48268 −0.329406
\(517\) −0.913866 −0.0401918
\(518\) 23.0017 1.01064
\(519\) −19.7602 −0.867376
\(520\) 6.10654 0.267789
\(521\) 21.5342 0.943432 0.471716 0.881750i \(-0.343635\pi\)
0.471716 + 0.881750i \(0.343635\pi\)
\(522\) 15.6471 0.684856
\(523\) 19.7500 0.863608 0.431804 0.901968i \(-0.357877\pi\)
0.431804 + 0.901968i \(0.357877\pi\)
\(524\) −46.0864 −2.01329
\(525\) 18.5147 0.808047
\(526\) 16.1887 0.705860
\(527\) −5.66271 −0.246672
\(528\) 0.241402 0.0105057
\(529\) 0.826450 0.0359326
\(530\) 116.157 5.04555
\(531\) 5.18445 0.224986
\(532\) −22.6104 −0.980287
\(533\) 10.5919 0.458786
\(534\) 19.2368 0.832457
\(535\) 41.7974 1.80706
\(536\) −11.0866 −0.478868
\(537\) 6.93544 0.299286
\(538\) 25.0914 1.08177
\(539\) −0.589223 −0.0253796
\(540\) 11.6425 0.501012
\(541\) −14.1009 −0.606244 −0.303122 0.952952i \(-0.598029\pi\)
−0.303122 + 0.952952i \(0.598029\pi\)
\(542\) −10.5446 −0.452928
\(543\) 10.8175 0.464224
\(544\) 7.60691 0.326144
\(545\) 4.54194 0.194555
\(546\) −2.75535 −0.117918
\(547\) −25.1485 −1.07527 −0.537636 0.843177i \(-0.680682\pi\)
−0.537636 + 0.843177i \(0.680682\pi\)
\(548\) −37.5487 −1.60400
\(549\) 14.4443 0.616468
\(550\) −3.37439 −0.143885
\(551\) −44.2994 −1.88722
\(552\) −7.42077 −0.315849
\(553\) 16.6337 0.707336
\(554\) −27.2928 −1.15956
\(555\) 33.5320 1.42335
\(556\) −37.0743 −1.57230
\(557\) 37.9372 1.60745 0.803725 0.595000i \(-0.202848\pi\)
0.803725 + 0.595000i \(0.202848\pi\)
\(558\) 12.2780 0.519768
\(559\) 2.58159 0.109190
\(560\) −12.3782 −0.523075
\(561\) −0.114623 −0.00483937
\(562\) −8.36391 −0.352810
\(563\) −8.73288 −0.368047 −0.184024 0.982922i \(-0.558912\pi\)
−0.184024 + 0.982922i \(0.558912\pi\)
\(564\) 21.5359 0.906823
\(565\) 18.7715 0.789721
\(566\) −42.3987 −1.78215
\(567\) −1.36362 −0.0572667
\(568\) 7.50719 0.314995
\(569\) 35.0367 1.46882 0.734408 0.678709i \(-0.237460\pi\)
0.734408 + 0.678709i \(0.237460\pi\)
\(570\) −57.3671 −2.40284
\(571\) 16.3557 0.684467 0.342233 0.939615i \(-0.388817\pi\)
0.342233 + 0.939615i \(0.388817\pi\)
\(572\) 0.288537 0.0120643
\(573\) −13.3118 −0.556107
\(574\) 33.6038 1.40260
\(575\) −66.2754 −2.76388
\(576\) −12.2813 −0.511722
\(577\) −20.7701 −0.864670 −0.432335 0.901713i \(-0.642310\pi\)
−0.432335 + 0.901713i \(0.642310\pi\)
\(578\) −2.16822 −0.0901859
\(579\) 3.51300 0.145995
\(580\) 84.0189 3.48870
\(581\) 9.97763 0.413942
\(582\) 34.3376 1.42334
\(583\) 1.42469 0.0590046
\(584\) −10.7346 −0.444201
\(585\) −4.01676 −0.166072
\(586\) 65.0759 2.68826
\(587\) −1.75785 −0.0725544 −0.0362772 0.999342i \(-0.511550\pi\)
−0.0362772 + 0.999342i \(0.511550\pi\)
\(588\) 13.8854 0.572625
\(589\) −34.7608 −1.43229
\(590\) 48.4507 1.99468
\(591\) 5.48140 0.225475
\(592\) −16.3845 −0.673401
\(593\) −6.73374 −0.276522 −0.138261 0.990396i \(-0.544151\pi\)
−0.138261 + 0.990396i \(0.544151\pi\)
\(594\) 0.248527 0.0101972
\(595\) 5.87744 0.240952
\(596\) −30.9762 −1.26884
\(597\) 12.7640 0.522394
\(598\) 9.86309 0.403332
\(599\) −3.29737 −0.134727 −0.0673635 0.997729i \(-0.521459\pi\)
−0.0673635 + 0.997729i \(0.521459\pi\)
\(600\) 20.6415 0.842688
\(601\) −39.3597 −1.60552 −0.802759 0.596304i \(-0.796635\pi\)
−0.802759 + 0.596304i \(0.796635\pi\)
\(602\) 8.19035 0.333814
\(603\) 7.29253 0.296975
\(604\) −9.66258 −0.393165
\(605\) 47.3553 1.92527
\(606\) 36.5849 1.48616
\(607\) 17.4571 0.708563 0.354281 0.935139i \(-0.384725\pi\)
0.354281 + 0.935139i \(0.384725\pi\)
\(608\) 46.6954 1.89375
\(609\) −9.84069 −0.398765
\(610\) 134.988 5.46548
\(611\) −7.43007 −0.300588
\(612\) 2.70116 0.109188
\(613\) −30.7059 −1.24020 −0.620101 0.784522i \(-0.712908\pi\)
−0.620101 + 0.784522i \(0.712908\pi\)
\(614\) −60.9966 −2.46162
\(615\) 48.9877 1.97538
\(616\) 0.237620 0.00957400
\(617\) 11.8349 0.476455 0.238228 0.971209i \(-0.423434\pi\)
0.238228 + 0.971209i \(0.423434\pi\)
\(618\) −26.3248 −1.05894
\(619\) −14.6966 −0.590706 −0.295353 0.955388i \(-0.595437\pi\)
−0.295353 + 0.955388i \(0.595437\pi\)
\(620\) 65.9279 2.64773
\(621\) 4.88123 0.195877
\(622\) −21.2751 −0.853053
\(623\) −12.0983 −0.484707
\(624\) 1.96269 0.0785703
\(625\) 91.4630 3.65852
\(626\) −58.9154 −2.35473
\(627\) −0.703617 −0.0280997
\(628\) −2.70116 −0.107788
\(629\) 7.77973 0.310198
\(630\) −12.7436 −0.507715
\(631\) −43.4787 −1.73086 −0.865430 0.501030i \(-0.832955\pi\)
−0.865430 + 0.501030i \(0.832955\pi\)
\(632\) 18.5445 0.737659
\(633\) 12.0394 0.478522
\(634\) 3.63299 0.144285
\(635\) −76.6800 −3.04295
\(636\) −33.5737 −1.33129
\(637\) −4.79060 −0.189810
\(638\) 1.79352 0.0710060
\(639\) −4.93808 −0.195347
\(640\) −49.1994 −1.94478
\(641\) 14.3617 0.567253 0.283627 0.958935i \(-0.408462\pi\)
0.283627 + 0.958935i \(0.408462\pi\)
\(642\) −21.0260 −0.829830
\(643\) −28.6351 −1.12926 −0.564630 0.825344i \(-0.690981\pi\)
−0.564630 + 0.825344i \(0.690981\pi\)
\(644\) 17.9793 0.708485
\(645\) 11.9399 0.470134
\(646\) −13.3097 −0.523663
\(647\) 44.3215 1.74246 0.871230 0.490875i \(-0.163323\pi\)
0.871230 + 0.490875i \(0.163323\pi\)
\(648\) −1.52027 −0.0597217
\(649\) 0.594256 0.0233266
\(650\) −27.4351 −1.07609
\(651\) −7.72179 −0.302641
\(652\) −10.0239 −0.392568
\(653\) 17.6276 0.689820 0.344910 0.938636i \(-0.387909\pi\)
0.344910 + 0.938636i \(0.387909\pi\)
\(654\) −2.28481 −0.0893430
\(655\) 73.5389 2.87340
\(656\) −23.9366 −0.934567
\(657\) 7.06100 0.275476
\(658\) −23.5726 −0.918956
\(659\) 47.6082 1.85455 0.927277 0.374377i \(-0.122143\pi\)
0.927277 + 0.374377i \(0.122143\pi\)
\(660\) 1.33449 0.0519450
\(661\) −12.7871 −0.497361 −0.248680 0.968586i \(-0.579997\pi\)
−0.248680 + 0.968586i \(0.579997\pi\)
\(662\) −16.8164 −0.653590
\(663\) −0.931925 −0.0361930
\(664\) 11.1238 0.431687
\(665\) 36.0789 1.39908
\(666\) −16.8681 −0.653627
\(667\) 35.2259 1.36395
\(668\) −38.1987 −1.47795
\(669\) −5.99300 −0.231703
\(670\) 68.1515 2.63292
\(671\) 1.65564 0.0639154
\(672\) 10.3729 0.400145
\(673\) 41.7639 1.60988 0.804939 0.593357i \(-0.202198\pi\)
0.804939 + 0.593357i \(0.202198\pi\)
\(674\) −56.6170 −2.18081
\(675\) −13.5776 −0.522602
\(676\) −32.7692 −1.26035
\(677\) 21.6080 0.830462 0.415231 0.909716i \(-0.363701\pi\)
0.415231 + 0.909716i \(0.363701\pi\)
\(678\) −9.44291 −0.362653
\(679\) −21.5954 −0.828755
\(680\) 6.55261 0.251281
\(681\) −1.09079 −0.0417991
\(682\) 1.40734 0.0538897
\(683\) 7.47905 0.286178 0.143089 0.989710i \(-0.454296\pi\)
0.143089 + 0.989710i \(0.454296\pi\)
\(684\) 16.5812 0.633998
\(685\) 59.9156 2.28926
\(686\) −35.8950 −1.37048
\(687\) 3.35295 0.127923
\(688\) −5.83413 −0.222424
\(689\) 11.5832 0.441287
\(690\) 45.6170 1.73661
\(691\) −40.8112 −1.55253 −0.776265 0.630406i \(-0.782888\pi\)
−0.776265 + 0.630406i \(0.782888\pi\)
\(692\) 53.3754 2.02903
\(693\) −0.156302 −0.00593742
\(694\) −22.5238 −0.854990
\(695\) 59.1585 2.24401
\(696\) −10.9711 −0.415860
\(697\) 11.3656 0.430503
\(698\) 27.4628 1.03948
\(699\) −6.21743 −0.235165
\(700\) −50.0111 −1.89024
\(701\) 16.3422 0.617237 0.308619 0.951186i \(-0.400133\pi\)
0.308619 + 0.951186i \(0.400133\pi\)
\(702\) 2.02061 0.0762632
\(703\) 47.7562 1.80116
\(704\) −1.40772 −0.0530554
\(705\) −34.3642 −1.29423
\(706\) 43.4995 1.63713
\(707\) −23.0087 −0.865332
\(708\) −14.0040 −0.526304
\(709\) 3.37434 0.126726 0.0633630 0.997991i \(-0.479817\pi\)
0.0633630 + 0.997991i \(0.479817\pi\)
\(710\) −46.1482 −1.73191
\(711\) −12.1982 −0.457467
\(712\) −13.4881 −0.505486
\(713\) 27.6410 1.03516
\(714\) −2.95662 −0.110649
\(715\) −0.460412 −0.0172184
\(716\) −18.7337 −0.700112
\(717\) −20.5409 −0.767114
\(718\) −27.6518 −1.03196
\(719\) −40.6353 −1.51544 −0.757720 0.652580i \(-0.773687\pi\)
−0.757720 + 0.652580i \(0.773687\pi\)
\(720\) 9.07746 0.338297
\(721\) 16.5560 0.616579
\(722\) −40.5061 −1.50748
\(723\) 15.7471 0.585641
\(724\) −29.2198 −1.08595
\(725\) −97.9839 −3.63903
\(726\) −23.8219 −0.884113
\(727\) 30.3830 1.12684 0.563422 0.826169i \(-0.309485\pi\)
0.563422 + 0.826169i \(0.309485\pi\)
\(728\) 1.93194 0.0716025
\(729\) 1.00000 0.0370370
\(730\) 65.9877 2.44232
\(731\) 2.77017 0.102458
\(732\) −39.0164 −1.44209
\(733\) −30.4662 −1.12529 −0.562647 0.826697i \(-0.690217\pi\)
−0.562647 + 0.826697i \(0.690217\pi\)
\(734\) 50.1455 1.85090
\(735\) −22.1566 −0.817259
\(736\) −37.1311 −1.36867
\(737\) 0.835890 0.0307904
\(738\) −24.6431 −0.907125
\(739\) −9.36228 −0.344397 −0.172199 0.985062i \(-0.555087\pi\)
−0.172199 + 0.985062i \(0.555087\pi\)
\(740\) −90.5752 −3.32961
\(741\) −5.72066 −0.210154
\(742\) 36.7490 1.34910
\(743\) −15.4249 −0.565883 −0.282942 0.959137i \(-0.591310\pi\)
−0.282942 + 0.959137i \(0.591310\pi\)
\(744\) −8.60883 −0.315615
\(745\) 49.4280 1.81090
\(746\) 28.2523 1.03439
\(747\) −7.31701 −0.267716
\(748\) 0.309614 0.0113206
\(749\) 13.2235 0.483177
\(750\) −80.1609 −2.92706
\(751\) −7.67308 −0.279995 −0.139997 0.990152i \(-0.544709\pi\)
−0.139997 + 0.990152i \(0.544709\pi\)
\(752\) 16.7912 0.612312
\(753\) 29.1549 1.06246
\(754\) 14.5820 0.531043
\(755\) 15.4183 0.561131
\(756\) 3.68336 0.133962
\(757\) −22.8009 −0.828711 −0.414356 0.910115i \(-0.635993\pi\)
−0.414356 + 0.910115i \(0.635993\pi\)
\(758\) −57.6251 −2.09304
\(759\) 0.559500 0.0203086
\(760\) 40.2235 1.45906
\(761\) 23.4702 0.850796 0.425398 0.905006i \(-0.360134\pi\)
0.425398 + 0.905006i \(0.360134\pi\)
\(762\) 38.5736 1.39737
\(763\) 1.43695 0.0520209
\(764\) 35.9572 1.30089
\(765\) −4.31017 −0.155835
\(766\) 26.0871 0.942564
\(767\) 4.83152 0.174456
\(768\) 0.186947 0.00674585
\(769\) −54.1620 −1.95313 −0.976567 0.215215i \(-0.930955\pi\)
−0.976567 + 0.215215i \(0.930955\pi\)
\(770\) −1.46070 −0.0526400
\(771\) −23.1484 −0.833669
\(772\) −9.48918 −0.341523
\(773\) 14.4316 0.519067 0.259533 0.965734i \(-0.416431\pi\)
0.259533 + 0.965734i \(0.416431\pi\)
\(774\) −6.00633 −0.215893
\(775\) −76.8860 −2.76183
\(776\) −24.0762 −0.864283
\(777\) 10.6086 0.380581
\(778\) 8.07396 0.289466
\(779\) 69.7683 2.49971
\(780\) 10.8499 0.388489
\(781\) −0.566016 −0.0202536
\(782\) 10.5836 0.378468
\(783\) 7.21659 0.257900
\(784\) 10.8263 0.386652
\(785\) 4.31017 0.153837
\(786\) −36.9934 −1.31951
\(787\) 22.9611 0.818476 0.409238 0.912428i \(-0.365795\pi\)
0.409238 + 0.912428i \(0.365795\pi\)
\(788\) −14.8061 −0.527447
\(789\) 7.46636 0.265810
\(790\) −113.997 −4.05582
\(791\) 5.93877 0.211159
\(792\) −0.174257 −0.00619195
\(793\) 13.4610 0.478014
\(794\) −4.68078 −0.166115
\(795\) 53.5728 1.90003
\(796\) −34.4775 −1.22202
\(797\) 26.7933 0.949068 0.474534 0.880237i \(-0.342617\pi\)
0.474534 + 0.880237i \(0.342617\pi\)
\(798\) −18.1494 −0.642481
\(799\) −7.97282 −0.282058
\(800\) 103.284 3.65163
\(801\) 8.87217 0.313483
\(802\) 43.2758 1.52812
\(803\) 0.809351 0.0285614
\(804\) −19.6983 −0.694705
\(805\) −28.6892 −1.01116
\(806\) 11.4422 0.403033
\(807\) 11.5724 0.407367
\(808\) −25.6518 −0.902429
\(809\) 14.8429 0.521849 0.260924 0.965359i \(-0.415973\pi\)
0.260924 + 0.965359i \(0.415973\pi\)
\(810\) 9.34539 0.328363
\(811\) 27.9323 0.980835 0.490418 0.871487i \(-0.336844\pi\)
0.490418 + 0.871487i \(0.336844\pi\)
\(812\) 26.5813 0.932820
\(813\) −4.86324 −0.170561
\(814\) −1.93347 −0.0677681
\(815\) 15.9949 0.560279
\(816\) 2.10606 0.0737267
\(817\) 17.0048 0.594923
\(818\) −58.1934 −2.03469
\(819\) −1.27079 −0.0444051
\(820\) −132.324 −4.62094
\(821\) −51.4090 −1.79419 −0.897093 0.441841i \(-0.854325\pi\)
−0.897093 + 0.441841i \(0.854325\pi\)
\(822\) −30.1403 −1.05126
\(823\) −7.13857 −0.248835 −0.124418 0.992230i \(-0.539706\pi\)
−0.124418 + 0.992230i \(0.539706\pi\)
\(824\) 18.4579 0.643011
\(825\) −1.55630 −0.0541834
\(826\) 15.3285 0.533346
\(827\) 26.9416 0.936850 0.468425 0.883503i \(-0.344822\pi\)
0.468425 + 0.883503i \(0.344822\pi\)
\(828\) −13.1850 −0.458210
\(829\) −5.74092 −0.199390 −0.0996951 0.995018i \(-0.531787\pi\)
−0.0996951 + 0.995018i \(0.531787\pi\)
\(830\) −68.3803 −2.37352
\(831\) −12.5877 −0.436662
\(832\) −11.4453 −0.396793
\(833\) −5.14054 −0.178109
\(834\) −29.7594 −1.03048
\(835\) 60.9526 2.10935
\(836\) 1.90058 0.0657330
\(837\) 5.66271 0.195732
\(838\) 9.94163 0.343428
\(839\) −49.2262 −1.69948 −0.849739 0.527203i \(-0.823241\pi\)
−0.849739 + 0.527203i \(0.823241\pi\)
\(840\) 8.93527 0.308296
\(841\) 23.0792 0.795835
\(842\) −37.8510 −1.30443
\(843\) −3.85751 −0.132860
\(844\) −32.5203 −1.11939
\(845\) 52.2889 1.79879
\(846\) 17.2868 0.594332
\(847\) 14.9819 0.514784
\(848\) −26.1770 −0.898921
\(849\) −19.5546 −0.671114
\(850\) −29.4391 −1.00975
\(851\) −37.9747 −1.30176
\(852\) 13.3385 0.456971
\(853\) 24.7578 0.847690 0.423845 0.905735i \(-0.360680\pi\)
0.423845 + 0.905735i \(0.360680\pi\)
\(854\) 42.7063 1.46138
\(855\) −26.4582 −0.904851
\(856\) 14.7426 0.503891
\(857\) −24.9219 −0.851316 −0.425658 0.904884i \(-0.639957\pi\)
−0.425658 + 0.904884i \(0.639957\pi\)
\(858\) 0.231608 0.00790698
\(859\) −4.11256 −0.140319 −0.0701594 0.997536i \(-0.522351\pi\)
−0.0701594 + 0.997536i \(0.522351\pi\)
\(860\) −32.2516 −1.09977
\(861\) 15.4984 0.528183
\(862\) −44.3760 −1.51145
\(863\) 14.6865 0.499934 0.249967 0.968254i \(-0.419580\pi\)
0.249967 + 0.968254i \(0.419580\pi\)
\(864\) −7.60691 −0.258792
\(865\) −85.1699 −2.89586
\(866\) −46.4075 −1.57699
\(867\) −1.00000 −0.0339618
\(868\) 20.8578 0.707959
\(869\) −1.39819 −0.0474303
\(870\) 67.4418 2.28649
\(871\) 6.79609 0.230277
\(872\) 1.60201 0.0542511
\(873\) 15.8368 0.535995
\(874\) 64.9677 2.19757
\(875\) 50.4143 1.70431
\(876\) −19.0729 −0.644413
\(877\) 31.6026 1.06714 0.533571 0.845755i \(-0.320850\pi\)
0.533571 + 0.845755i \(0.320850\pi\)
\(878\) −25.2517 −0.852203
\(879\) 30.0136 1.01233
\(880\) 1.04048 0.0350747
\(881\) −51.6522 −1.74021 −0.870103 0.492870i \(-0.835948\pi\)
−0.870103 + 0.492870i \(0.835948\pi\)
\(882\) 11.1458 0.375299
\(883\) 33.7952 1.13730 0.568650 0.822580i \(-0.307466\pi\)
0.568650 + 0.822580i \(0.307466\pi\)
\(884\) 2.51728 0.0846652
\(885\) 22.3459 0.751149
\(886\) 19.9142 0.669031
\(887\) 1.25186 0.0420333 0.0210166 0.999779i \(-0.493310\pi\)
0.0210166 + 0.999779i \(0.493310\pi\)
\(888\) 11.8273 0.396897
\(889\) −24.2595 −0.813636
\(890\) 82.9138 2.77928
\(891\) 0.114623 0.00384000
\(892\) 16.1880 0.542016
\(893\) −48.9415 −1.63777
\(894\) −24.8646 −0.831595
\(895\) 29.8929 0.999210
\(896\) −15.5653 −0.520002
\(897\) 4.54894 0.151885
\(898\) −8.19223 −0.273378
\(899\) 40.8655 1.36294
\(900\) 36.6752 1.22251
\(901\) 12.4294 0.414083
\(902\) −2.82466 −0.0940508
\(903\) 3.77746 0.125706
\(904\) 6.62099 0.220211
\(905\) 46.6253 1.54988
\(906\) −7.75614 −0.257680
\(907\) 42.7089 1.41812 0.709062 0.705146i \(-0.249118\pi\)
0.709062 + 0.705146i \(0.249118\pi\)
\(908\) 2.94639 0.0977794
\(909\) 16.8733 0.559651
\(910\) −11.8760 −0.393687
\(911\) −53.6336 −1.77696 −0.888480 0.458916i \(-0.848238\pi\)
−0.888480 + 0.458916i \(0.848238\pi\)
\(912\) 12.9281 0.428093
\(913\) −0.838696 −0.0277568
\(914\) 43.9892 1.45503
\(915\) 62.2574 2.05817
\(916\) −9.05685 −0.299247
\(917\) 23.2657 0.768300
\(918\) 2.16822 0.0715618
\(919\) −53.2090 −1.75520 −0.877602 0.479390i \(-0.840858\pi\)
−0.877602 + 0.479390i \(0.840858\pi\)
\(920\) −31.9848 −1.05451
\(921\) −28.1322 −0.926986
\(922\) 16.8718 0.555643
\(923\) −4.60192 −0.151474
\(924\) 0.422196 0.0138892
\(925\) 105.630 3.47309
\(926\) −26.7349 −0.878562
\(927\) −12.1412 −0.398770
\(928\) −54.8960 −1.80205
\(929\) 41.8503 1.37307 0.686533 0.727099i \(-0.259132\pi\)
0.686533 + 0.727099i \(0.259132\pi\)
\(930\) 52.9202 1.73532
\(931\) −31.5554 −1.03419
\(932\) 16.7943 0.550115
\(933\) −9.81225 −0.321239
\(934\) 74.4013 2.43448
\(935\) −0.494044 −0.0161570
\(936\) −1.41677 −0.0463087
\(937\) 12.7481 0.416464 0.208232 0.978080i \(-0.433229\pi\)
0.208232 + 0.978080i \(0.433229\pi\)
\(938\) 21.5613 0.704000
\(939\) −27.1723 −0.886735
\(940\) 92.8233 3.02756
\(941\) −9.99812 −0.325930 −0.162965 0.986632i \(-0.552106\pi\)
−0.162965 + 0.986632i \(0.552106\pi\)
\(942\) −2.16822 −0.0706443
\(943\) −55.4782 −1.80662
\(944\) −10.9187 −0.355375
\(945\) −5.87744 −0.191193
\(946\) −0.688462 −0.0223838
\(947\) 34.4391 1.11912 0.559561 0.828789i \(-0.310970\pi\)
0.559561 + 0.828789i \(0.310970\pi\)
\(948\) 32.9492 1.07014
\(949\) 6.58032 0.213606
\(950\) −180.714 −5.86312
\(951\) 1.67557 0.0543340
\(952\) 2.07307 0.0671884
\(953\) 26.0267 0.843088 0.421544 0.906808i \(-0.361488\pi\)
0.421544 + 0.906808i \(0.361488\pi\)
\(954\) −26.9496 −0.872525
\(955\) −57.3760 −1.85664
\(956\) 55.4843 1.79449
\(957\) 0.827185 0.0267391
\(958\) −82.9751 −2.68080
\(959\) 18.9556 0.612110
\(960\) −52.9346 −1.70846
\(961\) 1.06630 0.0343967
\(962\) −15.7198 −0.506828
\(963\) −9.69737 −0.312493
\(964\) −42.5355 −1.36997
\(965\) 15.1416 0.487427
\(966\) 14.4320 0.464341
\(967\) 54.6788 1.75835 0.879175 0.476498i \(-0.158094\pi\)
0.879175 + 0.476498i \(0.158094\pi\)
\(968\) 16.7029 0.536853
\(969\) −6.13855 −0.197199
\(970\) 148.001 4.75203
\(971\) 11.0593 0.354910 0.177455 0.984129i \(-0.443214\pi\)
0.177455 + 0.984129i \(0.443214\pi\)
\(972\) −2.70116 −0.0866397
\(973\) 18.7161 0.600011
\(974\) 80.1907 2.56948
\(975\) −12.6533 −0.405230
\(976\) −30.4205 −0.973736
\(977\) 27.3457 0.874868 0.437434 0.899251i \(-0.355887\pi\)
0.437434 + 0.899251i \(0.355887\pi\)
\(978\) −8.04620 −0.257289
\(979\) 1.01695 0.0325019
\(980\) 59.8486 1.91179
\(981\) −1.05377 −0.0336444
\(982\) 39.3318 1.25513
\(983\) −41.7507 −1.33164 −0.665820 0.746112i \(-0.731918\pi\)
−0.665820 + 0.746112i \(0.731918\pi\)
\(984\) 17.2787 0.550826
\(985\) 23.6258 0.752780
\(986\) 15.6471 0.498306
\(987\) −10.8719 −0.346056
\(988\) 15.4524 0.491607
\(989\) −13.5219 −0.429970
\(990\) 1.07119 0.0340448
\(991\) −11.4470 −0.363627 −0.181814 0.983333i \(-0.558197\pi\)
−0.181814 + 0.983333i \(0.558197\pi\)
\(992\) −43.0758 −1.36766
\(993\) −7.75589 −0.246126
\(994\) −14.6000 −0.463085
\(995\) 55.0149 1.74409
\(996\) 19.7644 0.626260
\(997\) −28.7757 −0.911337 −0.455668 0.890150i \(-0.650600\pi\)
−0.455668 + 0.890150i \(0.650600\pi\)
\(998\) 18.8860 0.597825
\(999\) −7.77973 −0.246140
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 \(a_p\))