Properties

Label 8021.2.a.a.1.11
Level 8021
Weight 2
Character 8021.1
Self dual Yes
Analytic conductor 64.048
Analytic rank 1
Dimension 134
CM No

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Newspace parameters

Level: \( N \) = \( 8021 = 13 \cdot 617 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8021.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0480074613\)
Analytic rank: \(1\)
Dimension: \(134\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) = 8021.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.38388 q^{2} +0.0725376 q^{3} +3.68286 q^{4} -3.05924 q^{5} -0.172921 q^{6} -4.27004 q^{7} -4.01173 q^{8} -2.99474 q^{9} +O(q^{10})\) \(q-2.38388 q^{2} +0.0725376 q^{3} +3.68286 q^{4} -3.05924 q^{5} -0.172921 q^{6} -4.27004 q^{7} -4.01173 q^{8} -2.99474 q^{9} +7.29285 q^{10} +2.46731 q^{11} +0.267146 q^{12} +1.00000 q^{13} +10.1792 q^{14} -0.221910 q^{15} +2.19774 q^{16} -1.27222 q^{17} +7.13908 q^{18} +0.997990 q^{19} -11.2668 q^{20} -0.309739 q^{21} -5.88175 q^{22} -0.383553 q^{23} -0.291001 q^{24} +4.35895 q^{25} -2.38388 q^{26} -0.434844 q^{27} -15.7260 q^{28} -4.72422 q^{29} +0.529005 q^{30} -3.53003 q^{31} +2.78431 q^{32} +0.178972 q^{33} +3.03282 q^{34} +13.0631 q^{35} -11.0292 q^{36} +6.07208 q^{37} -2.37908 q^{38} +0.0725376 q^{39} +12.2728 q^{40} -1.30094 q^{41} +0.738378 q^{42} -9.71207 q^{43} +9.08674 q^{44} +9.16162 q^{45} +0.914343 q^{46} +9.52442 q^{47} +0.159419 q^{48} +11.2333 q^{49} -10.3912 q^{50} -0.0922840 q^{51} +3.68286 q^{52} -11.0135 q^{53} +1.03661 q^{54} -7.54808 q^{55} +17.1303 q^{56} +0.0723917 q^{57} +11.2619 q^{58} -1.91373 q^{59} -0.817263 q^{60} -6.27105 q^{61} +8.41516 q^{62} +12.7877 q^{63} -11.0329 q^{64} -3.05924 q^{65} -0.426648 q^{66} -1.81943 q^{67} -4.68542 q^{68} -0.0278220 q^{69} -31.1408 q^{70} -0.711972 q^{71} +12.0141 q^{72} +0.825468 q^{73} -14.4751 q^{74} +0.316188 q^{75} +3.67546 q^{76} -10.5355 q^{77} -0.172921 q^{78} +4.55458 q^{79} -6.72343 q^{80} +8.95267 q^{81} +3.10129 q^{82} +10.8981 q^{83} -1.14072 q^{84} +3.89204 q^{85} +23.1524 q^{86} -0.342683 q^{87} -9.89817 q^{88} +0.955601 q^{89} -21.8402 q^{90} -4.27004 q^{91} -1.41257 q^{92} -0.256060 q^{93} -22.7050 q^{94} -3.05309 q^{95} +0.201967 q^{96} -1.49314 q^{97} -26.7787 q^{98} -7.38893 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 134q - 6q^{2} - 33q^{3} + 98q^{4} - 8q^{5} - 16q^{6} - 32q^{7} - 15q^{8} + 101q^{9} + O(q^{10}) \) \( 134q - 6q^{2} - 33q^{3} + 98q^{4} - 8q^{5} - 16q^{6} - 32q^{7} - 15q^{8} + 101q^{9} - 33q^{10} - 47q^{11} - 53q^{12} + 134q^{13} - 28q^{14} - 30q^{15} + 30q^{16} - 17q^{17} - 14q^{18} - 87q^{19} - 12q^{20} - 24q^{21} - 52q^{22} - 44q^{23} - 36q^{24} + 58q^{25} - 6q^{26} - 117q^{27} - 71q^{28} - 42q^{29} - 21q^{30} - 82q^{31} - 31q^{32} + 12q^{33} - 30q^{34} - 54q^{35} + 32q^{36} - 55q^{37} - 12q^{38} - 33q^{39} - 86q^{40} - 16q^{41} + 6q^{42} - 148q^{43} - 54q^{44} - 24q^{45} - 57q^{46} - 21q^{47} - 82q^{48} + 12q^{49} - 17q^{50} - 123q^{51} + 98q^{52} - 17q^{53} - 10q^{54} - 148q^{55} - 47q^{56} - q^{57} - 58q^{58} - 64q^{59} - 16q^{60} - 112q^{61} - 15q^{62} - 58q^{63} - 65q^{64} - 8q^{65} - 20q^{66} - 110q^{67} - 8q^{68} - 57q^{69} - 40q^{70} - 78q^{71} - 28q^{72} - 43q^{73} - 52q^{74} - 150q^{75} - 96q^{76} - 24q^{77} - 16q^{78} - 228q^{79} + 20q^{80} + 54q^{81} - 89q^{82} - 12q^{83} + 6q^{84} - 77q^{85} + 29q^{86} - 77q^{87} - 95q^{88} - 32q^{89} - 46q^{90} - 32q^{91} - 62q^{92} - 9q^{93} - 87q^{94} - 61q^{95} - 54q^{96} - 38q^{97} + 6q^{98} - 193q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.38388 −1.68565 −0.842827 0.538184i \(-0.819110\pi\)
−0.842827 + 0.538184i \(0.819110\pi\)
\(3\) 0.0725376 0.0418796 0.0209398 0.999781i \(-0.493334\pi\)
0.0209398 + 0.999781i \(0.493334\pi\)
\(4\) 3.68286 1.84143
\(5\) −3.05924 −1.36813 −0.684067 0.729419i \(-0.739790\pi\)
−0.684067 + 0.729419i \(0.739790\pi\)
\(6\) −0.172921 −0.0705945
\(7\) −4.27004 −1.61392 −0.806962 0.590603i \(-0.798890\pi\)
−0.806962 + 0.590603i \(0.798890\pi\)
\(8\) −4.01173 −1.41836
\(9\) −2.99474 −0.998246
\(10\) 7.29285 2.30620
\(11\) 2.46731 0.743921 0.371960 0.928249i \(-0.378686\pi\)
0.371960 + 0.928249i \(0.378686\pi\)
\(12\) 0.267146 0.0771183
\(13\) 1.00000 0.277350
\(14\) 10.1792 2.72052
\(15\) −0.221910 −0.0572969
\(16\) 2.19774 0.549436
\(17\) −1.27222 −0.308560 −0.154280 0.988027i \(-0.549306\pi\)
−0.154280 + 0.988027i \(0.549306\pi\)
\(18\) 7.13908 1.68270
\(19\) 0.997990 0.228954 0.114477 0.993426i \(-0.463481\pi\)
0.114477 + 0.993426i \(0.463481\pi\)
\(20\) −11.2668 −2.51932
\(21\) −0.309739 −0.0675905
\(22\) −5.88175 −1.25399
\(23\) −0.383553 −0.0799764 −0.0399882 0.999200i \(-0.512732\pi\)
−0.0399882 + 0.999200i \(0.512732\pi\)
\(24\) −0.291001 −0.0594004
\(25\) 4.35895 0.871790
\(26\) −2.38388 −0.467516
\(27\) −0.434844 −0.0836857
\(28\) −15.7260 −2.97193
\(29\) −4.72422 −0.877265 −0.438633 0.898666i \(-0.644537\pi\)
−0.438633 + 0.898666i \(0.644537\pi\)
\(30\) 0.529005 0.0965827
\(31\) −3.53003 −0.634013 −0.317006 0.948423i \(-0.602678\pi\)
−0.317006 + 0.948423i \(0.602678\pi\)
\(32\) 2.78431 0.492202
\(33\) 0.178972 0.0311551
\(34\) 3.03282 0.520125
\(35\) 13.0631 2.20806
\(36\) −11.0292 −1.83820
\(37\) 6.07208 0.998244 0.499122 0.866532i \(-0.333656\pi\)
0.499122 + 0.866532i \(0.333656\pi\)
\(38\) −2.37908 −0.385938
\(39\) 0.0725376 0.0116153
\(40\) 12.2728 1.94051
\(41\) −1.30094 −0.203173 −0.101587 0.994827i \(-0.532392\pi\)
−0.101587 + 0.994827i \(0.532392\pi\)
\(42\) 0.738378 0.113934
\(43\) −9.71207 −1.48108 −0.740538 0.672014i \(-0.765429\pi\)
−0.740538 + 0.672014i \(0.765429\pi\)
\(44\) 9.08674 1.36988
\(45\) 9.16162 1.36573
\(46\) 0.914343 0.134813
\(47\) 9.52442 1.38928 0.694640 0.719357i \(-0.255564\pi\)
0.694640 + 0.719357i \(0.255564\pi\)
\(48\) 0.159419 0.0230102
\(49\) 11.2333 1.60475
\(50\) −10.3912 −1.46954
\(51\) −0.0922840 −0.0129223
\(52\) 3.68286 0.510721
\(53\) −11.0135 −1.51283 −0.756413 0.654095i \(-0.773050\pi\)
−0.756413 + 0.654095i \(0.773050\pi\)
\(54\) 1.03661 0.141065
\(55\) −7.54808 −1.01778
\(56\) 17.1303 2.28913
\(57\) 0.0723917 0.00958852
\(58\) 11.2619 1.47877
\(59\) −1.91373 −0.249147 −0.124574 0.992210i \(-0.539756\pi\)
−0.124574 + 0.992210i \(0.539756\pi\)
\(60\) −0.817263 −0.105508
\(61\) −6.27105 −0.802925 −0.401463 0.915875i \(-0.631498\pi\)
−0.401463 + 0.915875i \(0.631498\pi\)
\(62\) 8.41516 1.06873
\(63\) 12.7877 1.61109
\(64\) −11.0329 −1.37912
\(65\) −3.05924 −0.379452
\(66\) −0.426648 −0.0525167
\(67\) −1.81943 −0.222279 −0.111139 0.993805i \(-0.535450\pi\)
−0.111139 + 0.993805i \(0.535450\pi\)
\(68\) −4.68542 −0.568191
\(69\) −0.0278220 −0.00334938
\(70\) −31.1408 −3.72203
\(71\) −0.711972 −0.0844955 −0.0422478 0.999107i \(-0.513452\pi\)
−0.0422478 + 0.999107i \(0.513452\pi\)
\(72\) 12.0141 1.41587
\(73\) 0.825468 0.0966137 0.0483069 0.998833i \(-0.484617\pi\)
0.0483069 + 0.998833i \(0.484617\pi\)
\(74\) −14.4751 −1.68269
\(75\) 0.316188 0.0365102
\(76\) 3.67546 0.421604
\(77\) −10.5355 −1.20063
\(78\) −0.172921 −0.0195794
\(79\) 4.55458 0.512430 0.256215 0.966620i \(-0.417524\pi\)
0.256215 + 0.966620i \(0.417524\pi\)
\(80\) −6.72343 −0.751702
\(81\) 8.95267 0.994741
\(82\) 3.10129 0.342480
\(83\) 10.8981 1.19622 0.598112 0.801413i \(-0.295918\pi\)
0.598112 + 0.801413i \(0.295918\pi\)
\(84\) −1.14072 −0.124463
\(85\) 3.89204 0.422151
\(86\) 23.1524 2.49658
\(87\) −0.342683 −0.0367395
\(88\) −9.89817 −1.05515
\(89\) 0.955601 0.101294 0.0506468 0.998717i \(-0.483872\pi\)
0.0506468 + 0.998717i \(0.483872\pi\)
\(90\) −21.8402 −2.30216
\(91\) −4.27004 −0.447622
\(92\) −1.41257 −0.147271
\(93\) −0.256060 −0.0265522
\(94\) −22.7050 −2.34185
\(95\) −3.05309 −0.313240
\(96\) 0.201967 0.0206132
\(97\) −1.49314 −0.151605 −0.0758025 0.997123i \(-0.524152\pi\)
−0.0758025 + 0.997123i \(0.524152\pi\)
\(98\) −26.7787 −2.70506
\(99\) −7.38893 −0.742616
\(100\) 16.0534 1.60534
\(101\) 6.85917 0.682513 0.341256 0.939970i \(-0.389148\pi\)
0.341256 + 0.939970i \(0.389148\pi\)
\(102\) 0.219994 0.0217826
\(103\) 12.3642 1.21828 0.609138 0.793064i \(-0.291515\pi\)
0.609138 + 0.793064i \(0.291515\pi\)
\(104\) −4.01173 −0.393383
\(105\) 0.947564 0.0924728
\(106\) 26.2549 2.55010
\(107\) 3.30425 0.319434 0.159717 0.987163i \(-0.448942\pi\)
0.159717 + 0.987163i \(0.448942\pi\)
\(108\) −1.60147 −0.154101
\(109\) 1.91827 0.183737 0.0918684 0.995771i \(-0.470716\pi\)
0.0918684 + 0.995771i \(0.470716\pi\)
\(110\) 17.9937 1.71563
\(111\) 0.440454 0.0418060
\(112\) −9.38446 −0.886748
\(113\) 12.0944 1.13775 0.568875 0.822424i \(-0.307379\pi\)
0.568875 + 0.822424i \(0.307379\pi\)
\(114\) −0.172573 −0.0161629
\(115\) 1.17338 0.109418
\(116\) −17.3986 −1.61542
\(117\) −2.99474 −0.276864
\(118\) 4.56210 0.419976
\(119\) 5.43245 0.497992
\(120\) 0.890243 0.0812677
\(121\) −4.91240 −0.446582
\(122\) 14.9494 1.35345
\(123\) −0.0943672 −0.00850880
\(124\) −13.0006 −1.16749
\(125\) 1.96113 0.175409
\(126\) −30.4842 −2.71575
\(127\) 10.6555 0.945526 0.472763 0.881190i \(-0.343257\pi\)
0.472763 + 0.881190i \(0.343257\pi\)
\(128\) 20.7325 1.83251
\(129\) −0.704490 −0.0620269
\(130\) 7.29285 0.639625
\(131\) 12.3178 1.07621 0.538107 0.842877i \(-0.319140\pi\)
0.538107 + 0.842877i \(0.319140\pi\)
\(132\) 0.659130 0.0573699
\(133\) −4.26146 −0.369515
\(134\) 4.33729 0.374685
\(135\) 1.33029 0.114493
\(136\) 5.10382 0.437649
\(137\) 15.6891 1.34041 0.670204 0.742177i \(-0.266206\pi\)
0.670204 + 0.742177i \(0.266206\pi\)
\(138\) 0.0663242 0.00564589
\(139\) 7.26944 0.616586 0.308293 0.951291i \(-0.400242\pi\)
0.308293 + 0.951291i \(0.400242\pi\)
\(140\) 48.1095 4.06600
\(141\) 0.690879 0.0581825
\(142\) 1.69725 0.142430
\(143\) 2.46731 0.206326
\(144\) −6.58167 −0.548472
\(145\) 14.4525 1.20022
\(146\) −1.96781 −0.162857
\(147\) 0.814834 0.0672064
\(148\) 22.3626 1.83820
\(149\) −8.85272 −0.725243 −0.362621 0.931937i \(-0.618118\pi\)
−0.362621 + 0.931937i \(0.618118\pi\)
\(150\) −0.753752 −0.0615436
\(151\) 17.7747 1.44648 0.723242 0.690595i \(-0.242651\pi\)
0.723242 + 0.690595i \(0.242651\pi\)
\(152\) −4.00367 −0.324740
\(153\) 3.80998 0.308018
\(154\) 25.1153 2.02385
\(155\) 10.7992 0.867414
\(156\) 0.267146 0.0213888
\(157\) 18.0511 1.44063 0.720316 0.693646i \(-0.243997\pi\)
0.720316 + 0.693646i \(0.243997\pi\)
\(158\) −10.8575 −0.863780
\(159\) −0.798895 −0.0633565
\(160\) −8.51789 −0.673398
\(161\) 1.63779 0.129076
\(162\) −21.3421 −1.67679
\(163\) −8.17059 −0.639970 −0.319985 0.947423i \(-0.603678\pi\)
−0.319985 + 0.947423i \(0.603678\pi\)
\(164\) −4.79119 −0.374129
\(165\) −0.547519 −0.0426243
\(166\) −25.9798 −2.01642
\(167\) 12.8700 0.995908 0.497954 0.867203i \(-0.334085\pi\)
0.497954 + 0.867203i \(0.334085\pi\)
\(168\) 1.24259 0.0958677
\(169\) 1.00000 0.0769231
\(170\) −9.27813 −0.711600
\(171\) −2.98872 −0.228553
\(172\) −35.7682 −2.72730
\(173\) 6.51353 0.495214 0.247607 0.968861i \(-0.420356\pi\)
0.247607 + 0.968861i \(0.420356\pi\)
\(174\) 0.816914 0.0619301
\(175\) −18.6129 −1.40700
\(176\) 5.42251 0.408737
\(177\) −0.138818 −0.0104342
\(178\) −2.27803 −0.170746
\(179\) −2.87992 −0.215255 −0.107628 0.994191i \(-0.534325\pi\)
−0.107628 + 0.994191i \(0.534325\pi\)
\(180\) 33.7410 2.51490
\(181\) −8.19581 −0.609190 −0.304595 0.952482i \(-0.598521\pi\)
−0.304595 + 0.952482i \(0.598521\pi\)
\(182\) 10.1792 0.754536
\(183\) −0.454886 −0.0336262
\(184\) 1.53871 0.113435
\(185\) −18.5760 −1.36573
\(186\) 0.610415 0.0447578
\(187\) −3.13896 −0.229544
\(188\) 35.0771 2.55826
\(189\) 1.85680 0.135062
\(190\) 7.27818 0.528015
\(191\) 8.70060 0.629554 0.314777 0.949166i \(-0.398070\pi\)
0.314777 + 0.949166i \(0.398070\pi\)
\(192\) −0.800303 −0.0577569
\(193\) 5.83949 0.420336 0.210168 0.977665i \(-0.432599\pi\)
0.210168 + 0.977665i \(0.432599\pi\)
\(194\) 3.55945 0.255554
\(195\) −0.221910 −0.0158913
\(196\) 41.3706 2.95504
\(197\) −3.31836 −0.236423 −0.118212 0.992988i \(-0.537716\pi\)
−0.118212 + 0.992988i \(0.537716\pi\)
\(198\) 17.6143 1.25179
\(199\) −27.2437 −1.93125 −0.965627 0.259931i \(-0.916300\pi\)
−0.965627 + 0.259931i \(0.916300\pi\)
\(200\) −17.4869 −1.23651
\(201\) −0.131977 −0.00930894
\(202\) −16.3514 −1.15048
\(203\) 20.1726 1.41584
\(204\) −0.339869 −0.0237956
\(205\) 3.97990 0.277968
\(206\) −29.4746 −2.05359
\(207\) 1.14864 0.0798361
\(208\) 2.19774 0.152386
\(209\) 2.46234 0.170324
\(210\) −2.25888 −0.155877
\(211\) −11.8659 −0.816884 −0.408442 0.912784i \(-0.633928\pi\)
−0.408442 + 0.912784i \(0.633928\pi\)
\(212\) −40.5613 −2.78576
\(213\) −0.0516447 −0.00353864
\(214\) −7.87692 −0.538455
\(215\) 29.7116 2.02631
\(216\) 1.74448 0.118697
\(217\) 15.0734 1.02325
\(218\) −4.57291 −0.309717
\(219\) 0.0598774 0.00404614
\(220\) −27.7985 −1.87418
\(221\) −1.27222 −0.0855790
\(222\) −1.04999 −0.0704705
\(223\) 15.5717 1.04276 0.521378 0.853326i \(-0.325418\pi\)
0.521378 + 0.853326i \(0.325418\pi\)
\(224\) −11.8891 −0.794377
\(225\) −13.0539 −0.870261
\(226\) −28.8317 −1.91785
\(227\) −17.2347 −1.14391 −0.571954 0.820286i \(-0.693814\pi\)
−0.571954 + 0.820286i \(0.693814\pi\)
\(228\) 0.266609 0.0176566
\(229\) 3.08595 0.203925 0.101963 0.994788i \(-0.467488\pi\)
0.101963 + 0.994788i \(0.467488\pi\)
\(230\) −2.79719 −0.184442
\(231\) −0.764219 −0.0502819
\(232\) 18.9523 1.24428
\(233\) 29.0422 1.90261 0.951307 0.308244i \(-0.0997412\pi\)
0.951307 + 0.308244i \(0.0997412\pi\)
\(234\) 7.13908 0.466696
\(235\) −29.1375 −1.90072
\(236\) −7.04802 −0.458787
\(237\) 0.330378 0.0214604
\(238\) −12.9503 −0.839442
\(239\) 6.12984 0.396507 0.198253 0.980151i \(-0.436473\pi\)
0.198253 + 0.980151i \(0.436473\pi\)
\(240\) −0.487701 −0.0314810
\(241\) −12.0507 −0.776253 −0.388126 0.921606i \(-0.626878\pi\)
−0.388126 + 0.921606i \(0.626878\pi\)
\(242\) 11.7106 0.752783
\(243\) 1.95394 0.125345
\(244\) −23.0954 −1.47853
\(245\) −34.3653 −2.19552
\(246\) 0.224960 0.0143429
\(247\) 0.997990 0.0635006
\(248\) 14.1615 0.899259
\(249\) 0.790523 0.0500974
\(250\) −4.67508 −0.295678
\(251\) −10.2379 −0.646211 −0.323105 0.946363i \(-0.604727\pi\)
−0.323105 + 0.946363i \(0.604727\pi\)
\(252\) 47.0952 2.96672
\(253\) −0.946343 −0.0594961
\(254\) −25.4015 −1.59383
\(255\) 0.282319 0.0176795
\(256\) −27.3579 −1.70987
\(257\) −31.7414 −1.97997 −0.989986 0.141167i \(-0.954915\pi\)
−0.989986 + 0.141167i \(0.954915\pi\)
\(258\) 1.67942 0.104556
\(259\) −25.9280 −1.61109
\(260\) −11.2668 −0.698735
\(261\) 14.1478 0.875727
\(262\) −29.3642 −1.81412
\(263\) 15.7889 0.973584 0.486792 0.873518i \(-0.338167\pi\)
0.486792 + 0.873518i \(0.338167\pi\)
\(264\) −0.717989 −0.0441892
\(265\) 33.6930 2.06975
\(266\) 10.1588 0.622875
\(267\) 0.0693170 0.00424213
\(268\) −6.70071 −0.409311
\(269\) 8.45013 0.515213 0.257607 0.966250i \(-0.417066\pi\)
0.257607 + 0.966250i \(0.417066\pi\)
\(270\) −3.17125 −0.192996
\(271\) −5.72517 −0.347779 −0.173890 0.984765i \(-0.555634\pi\)
−0.173890 + 0.984765i \(0.555634\pi\)
\(272\) −2.79602 −0.169534
\(273\) −0.309739 −0.0187462
\(274\) −37.4008 −2.25947
\(275\) 10.7549 0.648542
\(276\) −0.102465 −0.00616765
\(277\) −22.3451 −1.34259 −0.671293 0.741192i \(-0.734261\pi\)
−0.671293 + 0.741192i \(0.734261\pi\)
\(278\) −17.3294 −1.03935
\(279\) 10.5715 0.632901
\(280\) −52.4056 −3.13183
\(281\) 6.08074 0.362747 0.181373 0.983414i \(-0.441946\pi\)
0.181373 + 0.983414i \(0.441946\pi\)
\(282\) −1.64697 −0.0980755
\(283\) −11.4280 −0.679327 −0.339663 0.940547i \(-0.610313\pi\)
−0.339663 + 0.940547i \(0.610313\pi\)
\(284\) −2.62209 −0.155593
\(285\) −0.221464 −0.0131184
\(286\) −5.88175 −0.347795
\(287\) 5.55508 0.327906
\(288\) −8.33829 −0.491339
\(289\) −15.3814 −0.904791
\(290\) −34.4530 −2.02315
\(291\) −0.108308 −0.00634915
\(292\) 3.04008 0.177907
\(293\) 10.6980 0.624983 0.312491 0.949921i \(-0.398836\pi\)
0.312491 + 0.949921i \(0.398836\pi\)
\(294\) −1.94246 −0.113287
\(295\) 5.85457 0.340866
\(296\) −24.3596 −1.41587
\(297\) −1.07289 −0.0622555
\(298\) 21.1038 1.22251
\(299\) −0.383553 −0.0221815
\(300\) 1.16448 0.0672310
\(301\) 41.4710 2.39035
\(302\) −42.3726 −2.43827
\(303\) 0.497547 0.0285834
\(304\) 2.19333 0.125796
\(305\) 19.1846 1.09851
\(306\) −9.08251 −0.519213
\(307\) −28.0803 −1.60263 −0.801314 0.598243i \(-0.795866\pi\)
−0.801314 + 0.598243i \(0.795866\pi\)
\(308\) −38.8008 −2.21088
\(309\) 0.896866 0.0510209
\(310\) −25.7440 −1.46216
\(311\) −16.3006 −0.924325 −0.462162 0.886795i \(-0.652926\pi\)
−0.462162 + 0.886795i \(0.652926\pi\)
\(312\) −0.291001 −0.0164747
\(313\) −24.1431 −1.36465 −0.682326 0.731048i \(-0.739031\pi\)
−0.682326 + 0.731048i \(0.739031\pi\)
\(314\) −43.0315 −2.42841
\(315\) −39.1205 −2.20419
\(316\) 16.7739 0.943605
\(317\) 9.14823 0.513816 0.256908 0.966436i \(-0.417296\pi\)
0.256908 + 0.966436i \(0.417296\pi\)
\(318\) 1.90447 0.106797
\(319\) −11.6561 −0.652616
\(320\) 33.7524 1.88682
\(321\) 0.239682 0.0133778
\(322\) −3.90428 −0.217577
\(323\) −1.26967 −0.0706461
\(324\) 32.9715 1.83175
\(325\) 4.35895 0.241791
\(326\) 19.4777 1.07877
\(327\) 0.139147 0.00769482
\(328\) 5.21903 0.288173
\(329\) −40.6697 −2.24219
\(330\) 1.30522 0.0718499
\(331\) 11.9367 0.656102 0.328051 0.944660i \(-0.393608\pi\)
0.328051 + 0.944660i \(0.393608\pi\)
\(332\) 40.1363 2.20276
\(333\) −18.1843 −0.996493
\(334\) −30.6804 −1.67876
\(335\) 5.56607 0.304107
\(336\) −0.680726 −0.0371367
\(337\) −18.4406 −1.00453 −0.502263 0.864715i \(-0.667499\pi\)
−0.502263 + 0.864715i \(0.667499\pi\)
\(338\) −2.38388 −0.129666
\(339\) 0.877302 0.0476485
\(340\) 14.3338 0.777361
\(341\) −8.70967 −0.471655
\(342\) 7.12473 0.385261
\(343\) −18.0762 −0.976025
\(344\) 38.9622 2.10070
\(345\) 0.0851142 0.00458240
\(346\) −15.5274 −0.834760
\(347\) −17.0338 −0.914425 −0.457212 0.889358i \(-0.651152\pi\)
−0.457212 + 0.889358i \(0.651152\pi\)
\(348\) −1.26206 −0.0676533
\(349\) 34.5070 1.84712 0.923559 0.383456i \(-0.125266\pi\)
0.923559 + 0.383456i \(0.125266\pi\)
\(350\) 44.3708 2.37172
\(351\) −0.434844 −0.0232102
\(352\) 6.86975 0.366159
\(353\) −11.9159 −0.634218 −0.317109 0.948389i \(-0.602712\pi\)
−0.317109 + 0.948389i \(0.602712\pi\)
\(354\) 0.330924 0.0175884
\(355\) 2.17809 0.115601
\(356\) 3.51935 0.186525
\(357\) 0.394057 0.0208557
\(358\) 6.86537 0.362846
\(359\) 26.4579 1.39640 0.698198 0.715905i \(-0.253985\pi\)
0.698198 + 0.715905i \(0.253985\pi\)
\(360\) −36.7540 −1.93710
\(361\) −18.0040 −0.947580
\(362\) 19.5378 1.02688
\(363\) −0.356334 −0.0187027
\(364\) −15.7260 −0.824265
\(365\) −2.52531 −0.132181
\(366\) 1.08439 0.0566821
\(367\) −12.1968 −0.636668 −0.318334 0.947979i \(-0.603123\pi\)
−0.318334 + 0.947979i \(0.603123\pi\)
\(368\) −0.842952 −0.0439419
\(369\) 3.89598 0.202817
\(370\) 44.2828 2.30215
\(371\) 47.0283 2.44159
\(372\) −0.943034 −0.0488940
\(373\) 13.3334 0.690379 0.345190 0.938533i \(-0.387815\pi\)
0.345190 + 0.938533i \(0.387815\pi\)
\(374\) 7.48290 0.386932
\(375\) 0.142255 0.00734603
\(376\) −38.2094 −1.97050
\(377\) −4.72422 −0.243310
\(378\) −4.42638 −0.227669
\(379\) −12.2663 −0.630079 −0.315040 0.949079i \(-0.602018\pi\)
−0.315040 + 0.949079i \(0.602018\pi\)
\(380\) −11.2441 −0.576810
\(381\) 0.772927 0.0395982
\(382\) −20.7412 −1.06121
\(383\) 38.0672 1.94514 0.972571 0.232605i \(-0.0747250\pi\)
0.972571 + 0.232605i \(0.0747250\pi\)
\(384\) 1.50389 0.0767450
\(385\) 32.2306 1.64262
\(386\) −13.9206 −0.708540
\(387\) 29.0851 1.47848
\(388\) −5.49901 −0.279170
\(389\) −16.7141 −0.847439 −0.423719 0.905794i \(-0.639276\pi\)
−0.423719 + 0.905794i \(0.639276\pi\)
\(390\) 0.529005 0.0267872
\(391\) 0.487966 0.0246775
\(392\) −45.0648 −2.27612
\(393\) 0.893505 0.0450714
\(394\) 7.91055 0.398528
\(395\) −13.9335 −0.701073
\(396\) −27.2124 −1.36748
\(397\) −15.3935 −0.772579 −0.386290 0.922378i \(-0.626243\pi\)
−0.386290 + 0.922378i \(0.626243\pi\)
\(398\) 64.9456 3.25543
\(399\) −0.309116 −0.0154751
\(400\) 9.57986 0.478993
\(401\) 21.8936 1.09332 0.546658 0.837356i \(-0.315900\pi\)
0.546658 + 0.837356i \(0.315900\pi\)
\(402\) 0.314617 0.0156917
\(403\) −3.53003 −0.175843
\(404\) 25.2614 1.25680
\(405\) −27.3884 −1.36094
\(406\) −48.0890 −2.38662
\(407\) 14.9817 0.742614
\(408\) 0.370219 0.0183286
\(409\) −25.2287 −1.24748 −0.623739 0.781633i \(-0.714387\pi\)
−0.623739 + 0.781633i \(0.714387\pi\)
\(410\) −9.48758 −0.468558
\(411\) 1.13805 0.0561358
\(412\) 45.5355 2.24337
\(413\) 8.17173 0.402104
\(414\) −2.73822 −0.134576
\(415\) −33.3400 −1.63659
\(416\) 2.78431 0.136512
\(417\) 0.527307 0.0258224
\(418\) −5.86992 −0.287107
\(419\) −18.4756 −0.902594 −0.451297 0.892374i \(-0.649039\pi\)
−0.451297 + 0.892374i \(0.649039\pi\)
\(420\) 3.48975 0.170282
\(421\) −2.85206 −0.139001 −0.0695004 0.997582i \(-0.522141\pi\)
−0.0695004 + 0.997582i \(0.522141\pi\)
\(422\) 28.2869 1.37698
\(423\) −28.5232 −1.38684
\(424\) 44.1833 2.14573
\(425\) −5.54556 −0.268999
\(426\) 0.123115 0.00596492
\(427\) 26.7776 1.29586
\(428\) 12.1691 0.588215
\(429\) 0.178972 0.00864086
\(430\) −70.8286 −3.41566
\(431\) −33.4160 −1.60959 −0.804795 0.593552i \(-0.797725\pi\)
−0.804795 + 0.593552i \(0.797725\pi\)
\(432\) −0.955675 −0.0459799
\(433\) 28.3945 1.36455 0.682276 0.731095i \(-0.260990\pi\)
0.682276 + 0.731095i \(0.260990\pi\)
\(434\) −35.9331 −1.72484
\(435\) 1.04835 0.0502646
\(436\) 7.06472 0.338339
\(437\) −0.382782 −0.0183110
\(438\) −0.142740 −0.00682040
\(439\) −8.88657 −0.424133 −0.212066 0.977255i \(-0.568019\pi\)
−0.212066 + 0.977255i \(0.568019\pi\)
\(440\) 30.2809 1.44358
\(441\) −33.6407 −1.60194
\(442\) 3.03282 0.144257
\(443\) 34.8510 1.65582 0.827911 0.560859i \(-0.189529\pi\)
0.827911 + 0.560859i \(0.189529\pi\)
\(444\) 1.62213 0.0769829
\(445\) −2.92341 −0.138583
\(446\) −37.1209 −1.75773
\(447\) −0.642154 −0.0303729
\(448\) 47.1112 2.22579
\(449\) 6.71237 0.316776 0.158388 0.987377i \(-0.449370\pi\)
0.158388 + 0.987377i \(0.449370\pi\)
\(450\) 31.1189 1.46696
\(451\) −3.20982 −0.151145
\(452\) 44.5422 2.09509
\(453\) 1.28933 0.0605781
\(454\) 41.0854 1.92823
\(455\) 13.0631 0.612407
\(456\) −0.290416 −0.0136000
\(457\) −12.9944 −0.607853 −0.303926 0.952696i \(-0.598298\pi\)
−0.303926 + 0.952696i \(0.598298\pi\)
\(458\) −7.35653 −0.343748
\(459\) 0.553219 0.0258220
\(460\) 4.32140 0.201486
\(461\) −28.0745 −1.30756 −0.653779 0.756686i \(-0.726817\pi\)
−0.653779 + 0.756686i \(0.726817\pi\)
\(462\) 1.82180 0.0847580
\(463\) 16.3439 0.759566 0.379783 0.925076i \(-0.375999\pi\)
0.379783 + 0.925076i \(0.375999\pi\)
\(464\) −10.3826 −0.482001
\(465\) 0.783349 0.0363269
\(466\) −69.2329 −3.20715
\(467\) 7.07365 0.327330 0.163665 0.986516i \(-0.447668\pi\)
0.163665 + 0.986516i \(0.447668\pi\)
\(468\) −11.0292 −0.509825
\(469\) 7.76904 0.358741
\(470\) 69.4602 3.20396
\(471\) 1.30938 0.0603330
\(472\) 7.67739 0.353380
\(473\) −23.9626 −1.10180
\(474\) −0.787580 −0.0361747
\(475\) 4.35019 0.199600
\(476\) 20.0070 0.917018
\(477\) 32.9826 1.51017
\(478\) −14.6128 −0.668373
\(479\) 30.3242 1.38555 0.692774 0.721154i \(-0.256388\pi\)
0.692774 + 0.721154i \(0.256388\pi\)
\(480\) −0.617867 −0.0282016
\(481\) 6.07208 0.276863
\(482\) 28.7273 1.30849
\(483\) 0.118801 0.00540564
\(484\) −18.0917 −0.822350
\(485\) 4.56786 0.207416
\(486\) −4.65794 −0.211288
\(487\) −9.57286 −0.433788 −0.216894 0.976195i \(-0.569593\pi\)
−0.216894 + 0.976195i \(0.569593\pi\)
\(488\) 25.1578 1.13884
\(489\) −0.592675 −0.0268017
\(490\) 81.9225 3.70088
\(491\) −21.2584 −0.959378 −0.479689 0.877439i \(-0.659250\pi\)
−0.479689 + 0.877439i \(0.659250\pi\)
\(492\) −0.347541 −0.0156684
\(493\) 6.01026 0.270689
\(494\) −2.37908 −0.107040
\(495\) 22.6045 1.01600
\(496\) −7.75811 −0.348349
\(497\) 3.04015 0.136369
\(498\) −1.88451 −0.0844468
\(499\) −0.956576 −0.0428222 −0.0214111 0.999771i \(-0.506816\pi\)
−0.0214111 + 0.999771i \(0.506816\pi\)
\(500\) 7.22256 0.323003
\(501\) 0.933556 0.0417082
\(502\) 24.4059 1.08929
\(503\) 8.33514 0.371645 0.185823 0.982583i \(-0.440505\pi\)
0.185823 + 0.982583i \(0.440505\pi\)
\(504\) −51.3007 −2.28511
\(505\) −20.9838 −0.933769
\(506\) 2.25596 0.100290
\(507\) 0.0725376 0.00322151
\(508\) 39.2429 1.74112
\(509\) 28.7913 1.27615 0.638075 0.769974i \(-0.279731\pi\)
0.638075 + 0.769974i \(0.279731\pi\)
\(510\) −0.673013 −0.0298015
\(511\) −3.52478 −0.155927
\(512\) 23.7527 1.04973
\(513\) −0.433969 −0.0191602
\(514\) 75.6674 3.33755
\(515\) −37.8249 −1.66677
\(516\) −2.59454 −0.114218
\(517\) 23.4997 1.03351
\(518\) 61.8092 2.71574
\(519\) 0.472475 0.0207394
\(520\) 12.2728 0.538200
\(521\) −20.7726 −0.910066 −0.455033 0.890475i \(-0.650373\pi\)
−0.455033 + 0.890475i \(0.650373\pi\)
\(522\) −33.7266 −1.47617
\(523\) 2.94231 0.128658 0.0643292 0.997929i \(-0.479509\pi\)
0.0643292 + 0.997929i \(0.479509\pi\)
\(524\) 45.3649 1.98177
\(525\) −1.35013 −0.0589247
\(526\) −37.6387 −1.64113
\(527\) 4.49099 0.195631
\(528\) 0.393335 0.0171177
\(529\) −22.8529 −0.993604
\(530\) −80.3200 −3.48888
\(531\) 5.73113 0.248710
\(532\) −15.6944 −0.680437
\(533\) −1.30094 −0.0563501
\(534\) −0.165243 −0.00715077
\(535\) −10.1085 −0.437028
\(536\) 7.29906 0.315272
\(537\) −0.208902 −0.00901480
\(538\) −20.1440 −0.868472
\(539\) 27.7159 1.19381
\(540\) 4.89928 0.210831
\(541\) 2.54836 0.109562 0.0547812 0.998498i \(-0.482554\pi\)
0.0547812 + 0.998498i \(0.482554\pi\)
\(542\) 13.6481 0.586236
\(543\) −0.594504 −0.0255126
\(544\) −3.54227 −0.151874
\(545\) −5.86845 −0.251377
\(546\) 0.738378 0.0315997
\(547\) 29.7942 1.27391 0.636954 0.770902i \(-0.280194\pi\)
0.636954 + 0.770902i \(0.280194\pi\)
\(548\) 57.7807 2.46827
\(549\) 18.7801 0.801517
\(550\) −25.6382 −1.09322
\(551\) −4.71472 −0.200854
\(552\) 0.111614 0.00475063
\(553\) −19.4482 −0.827024
\(554\) 53.2679 2.26314
\(555\) −1.34745 −0.0571962
\(556\) 26.7723 1.13540
\(557\) 6.02751 0.255394 0.127697 0.991813i \(-0.459242\pi\)
0.127697 + 0.991813i \(0.459242\pi\)
\(558\) −25.2012 −1.06685
\(559\) −9.71207 −0.410777
\(560\) 28.7093 1.21319
\(561\) −0.227693 −0.00961320
\(562\) −14.4957 −0.611466
\(563\) −35.0784 −1.47838 −0.739188 0.673499i \(-0.764791\pi\)
−0.739188 + 0.673499i \(0.764791\pi\)
\(564\) 2.54441 0.107139
\(565\) −36.9998 −1.55659
\(566\) 27.2430 1.14511
\(567\) −38.2283 −1.60544
\(568\) 2.85624 0.119845
\(569\) 2.47185 0.103625 0.0518127 0.998657i \(-0.483500\pi\)
0.0518127 + 0.998657i \(0.483500\pi\)
\(570\) 0.527942 0.0221130
\(571\) −6.18518 −0.258842 −0.129421 0.991590i \(-0.541312\pi\)
−0.129421 + 0.991590i \(0.541312\pi\)
\(572\) 9.08674 0.379936
\(573\) 0.631121 0.0263654
\(574\) −13.2426 −0.552736
\(575\) −1.67189 −0.0697226
\(576\) 33.0408 1.37670
\(577\) −22.5398 −0.938345 −0.469173 0.883106i \(-0.655448\pi\)
−0.469173 + 0.883106i \(0.655448\pi\)
\(578\) 36.6674 1.52516
\(579\) 0.423582 0.0176035
\(580\) 53.2266 2.21012
\(581\) −46.5354 −1.93061
\(582\) 0.258194 0.0107025
\(583\) −27.1737 −1.12542
\(584\) −3.31156 −0.137033
\(585\) 9.16162 0.378787
\(586\) −25.5027 −1.05350
\(587\) −12.5970 −0.519935 −0.259968 0.965617i \(-0.583712\pi\)
−0.259968 + 0.965617i \(0.583712\pi\)
\(588\) 3.00092 0.123756
\(589\) −3.52294 −0.145160
\(590\) −13.9566 −0.574583
\(591\) −0.240706 −0.00990130
\(592\) 13.3449 0.548471
\(593\) −37.3313 −1.53301 −0.766507 0.642236i \(-0.778007\pi\)
−0.766507 + 0.642236i \(0.778007\pi\)
\(594\) 2.55764 0.104941
\(595\) −16.6192 −0.681320
\(596\) −32.6033 −1.33548
\(597\) −1.97619 −0.0808801
\(598\) 0.914343 0.0373903
\(599\) 9.83716 0.401935 0.200968 0.979598i \(-0.435591\pi\)
0.200968 + 0.979598i \(0.435591\pi\)
\(600\) −1.26846 −0.0517846
\(601\) −20.3438 −0.829842 −0.414921 0.909857i \(-0.636191\pi\)
−0.414921 + 0.909857i \(0.636191\pi\)
\(602\) −98.8616 −4.02930
\(603\) 5.44872 0.221889
\(604\) 65.4617 2.66360
\(605\) 15.0282 0.610984
\(606\) −1.18609 −0.0481817
\(607\) −12.8597 −0.521960 −0.260980 0.965344i \(-0.584046\pi\)
−0.260980 + 0.965344i \(0.584046\pi\)
\(608\) 2.77872 0.112692
\(609\) 1.46327 0.0592948
\(610\) −45.7338 −1.85171
\(611\) 9.52442 0.385317
\(612\) 14.0316 0.567195
\(613\) 31.9646 1.29104 0.645518 0.763745i \(-0.276641\pi\)
0.645518 + 0.763745i \(0.276641\pi\)
\(614\) 66.9400 2.70148
\(615\) 0.288692 0.0116412
\(616\) 42.2656 1.70293
\(617\) 1.00000 0.0402585
\(618\) −2.13802 −0.0860036
\(619\) −13.9613 −0.561153 −0.280576 0.959832i \(-0.590526\pi\)
−0.280576 + 0.959832i \(0.590526\pi\)
\(620\) 39.7720 1.59728
\(621\) 0.166786 0.00669288
\(622\) 38.8587 1.55809
\(623\) −4.08046 −0.163480
\(624\) 0.159419 0.00638187
\(625\) −27.7943 −1.11177
\(626\) 57.5542 2.30033
\(627\) 0.178612 0.00713310
\(628\) 66.4795 2.65282
\(629\) −7.72505 −0.308018
\(630\) 93.2585 3.71551
\(631\) −6.64143 −0.264391 −0.132196 0.991224i \(-0.542203\pi\)
−0.132196 + 0.991224i \(0.542203\pi\)
\(632\) −18.2717 −0.726811
\(633\) −0.860725 −0.0342107
\(634\) −21.8082 −0.866116
\(635\) −32.5979 −1.29361
\(636\) −2.94222 −0.116667
\(637\) 11.2333 0.445078
\(638\) 27.7867 1.10008
\(639\) 2.13217 0.0843473
\(640\) −63.4258 −2.50713
\(641\) 10.9178 0.431228 0.215614 0.976479i \(-0.430825\pi\)
0.215614 + 0.976479i \(0.430825\pi\)
\(642\) −0.571372 −0.0225503
\(643\) −18.3957 −0.725454 −0.362727 0.931895i \(-0.618154\pi\)
−0.362727 + 0.931895i \(0.618154\pi\)
\(644\) 6.03175 0.237684
\(645\) 2.15520 0.0848611
\(646\) 3.02673 0.119085
\(647\) 9.93421 0.390554 0.195277 0.980748i \(-0.437439\pi\)
0.195277 + 0.980748i \(0.437439\pi\)
\(648\) −35.9157 −1.41090
\(649\) −4.72177 −0.185346
\(650\) −10.3912 −0.407576
\(651\) 1.09339 0.0428532
\(652\) −30.0912 −1.17846
\(653\) −19.6078 −0.767312 −0.383656 0.923476i \(-0.625335\pi\)
−0.383656 + 0.923476i \(0.625335\pi\)
\(654\) −0.331708 −0.0129708
\(655\) −37.6832 −1.47240
\(656\) −2.85914 −0.111631
\(657\) −2.47206 −0.0964443
\(658\) 96.9515 3.77956
\(659\) 20.1274 0.784052 0.392026 0.919954i \(-0.371774\pi\)
0.392026 + 0.919954i \(0.371774\pi\)
\(660\) −2.01644 −0.0784897
\(661\) −4.93888 −0.192100 −0.0960502 0.995376i \(-0.530621\pi\)
−0.0960502 + 0.995376i \(0.530621\pi\)
\(662\) −28.4557 −1.10596
\(663\) −0.0922840 −0.00358401
\(664\) −43.7203 −1.69668
\(665\) 13.0368 0.505546
\(666\) 43.3491 1.67974
\(667\) 1.81199 0.0701605
\(668\) 47.3983 1.83390
\(669\) 1.12953 0.0436702
\(670\) −13.2688 −0.512619
\(671\) −15.4726 −0.597313
\(672\) −0.862409 −0.0332682
\(673\) 45.9981 1.77310 0.886548 0.462636i \(-0.153096\pi\)
0.886548 + 0.462636i \(0.153096\pi\)
\(674\) 43.9602 1.69328
\(675\) −1.89546 −0.0729564
\(676\) 3.68286 0.141649
\(677\) 19.3094 0.742119 0.371060 0.928609i \(-0.378995\pi\)
0.371060 + 0.928609i \(0.378995\pi\)
\(678\) −2.09138 −0.0803189
\(679\) 6.37575 0.244679
\(680\) −15.6138 −0.598762
\(681\) −1.25016 −0.0479064
\(682\) 20.7628 0.795047
\(683\) 37.1164 1.42022 0.710110 0.704091i \(-0.248645\pi\)
0.710110 + 0.704091i \(0.248645\pi\)
\(684\) −11.0070 −0.420864
\(685\) −47.9967 −1.83386
\(686\) 43.0915 1.64524
\(687\) 0.223847 0.00854031
\(688\) −21.3446 −0.813757
\(689\) −11.0135 −0.419582
\(690\) −0.202902 −0.00772434
\(691\) 2.20217 0.0837745 0.0418872 0.999122i \(-0.486663\pi\)
0.0418872 + 0.999122i \(0.486663\pi\)
\(692\) 23.9884 0.911903
\(693\) 31.5511 1.19853
\(694\) 40.6066 1.54140
\(695\) −22.2390 −0.843572
\(696\) 1.37475 0.0521099
\(697\) 1.65509 0.0626910
\(698\) −82.2604 −3.11360
\(699\) 2.10665 0.0796807
\(700\) −68.5487 −2.59090
\(701\) 3.88779 0.146840 0.0734199 0.997301i \(-0.476609\pi\)
0.0734199 + 0.997301i \(0.476609\pi\)
\(702\) 1.03661 0.0391244
\(703\) 6.05987 0.228552
\(704\) −27.2216 −1.02595
\(705\) −2.11356 −0.0796014
\(706\) 28.4060 1.06907
\(707\) −29.2889 −1.10152
\(708\) −0.511246 −0.0192138
\(709\) 13.5534 0.509009 0.254504 0.967072i \(-0.418088\pi\)
0.254504 + 0.967072i \(0.418088\pi\)
\(710\) −5.19230 −0.194864
\(711\) −13.6398 −0.511531
\(712\) −3.83362 −0.143671
\(713\) 1.35396 0.0507060
\(714\) −0.939382 −0.0351555
\(715\) −7.54808 −0.282282
\(716\) −10.6063 −0.396378
\(717\) 0.444644 0.0166055
\(718\) −63.0724 −2.35384
\(719\) 48.4984 1.80869 0.904343 0.426807i \(-0.140362\pi\)
0.904343 + 0.426807i \(0.140362\pi\)
\(720\) 20.1349 0.750384
\(721\) −52.7955 −1.96621
\(722\) 42.9193 1.59729
\(723\) −0.874127 −0.0325091
\(724\) −30.1840 −1.12178
\(725\) −20.5926 −0.764791
\(726\) 0.849455 0.0315262
\(727\) 38.6817 1.43462 0.717312 0.696752i \(-0.245372\pi\)
0.717312 + 0.696752i \(0.245372\pi\)
\(728\) 17.1303 0.634890
\(729\) −26.7163 −0.989492
\(730\) 6.02001 0.222811
\(731\) 12.3559 0.457000
\(732\) −1.67528 −0.0619203
\(733\) −32.9949 −1.21869 −0.609347 0.792904i \(-0.708568\pi\)
−0.609347 + 0.792904i \(0.708568\pi\)
\(734\) 29.0757 1.07320
\(735\) −2.49277 −0.0919473
\(736\) −1.06793 −0.0393645
\(737\) −4.48909 −0.165358
\(738\) −9.28754 −0.341879
\(739\) 19.5545 0.719322 0.359661 0.933083i \(-0.382892\pi\)
0.359661 + 0.933083i \(0.382892\pi\)
\(740\) −68.4126 −2.51490
\(741\) 0.0723917 0.00265938
\(742\) −112.110 −4.11567
\(743\) −26.5914 −0.975542 −0.487771 0.872972i \(-0.662190\pi\)
−0.487771 + 0.872972i \(0.662190\pi\)
\(744\) 1.02724 0.0376606
\(745\) 27.0826 0.992229
\(746\) −31.7853 −1.16374
\(747\) −32.6370 −1.19413
\(748\) −11.5604 −0.422689
\(749\) −14.1093 −0.515542
\(750\) −0.339119 −0.0123829
\(751\) −14.7040 −0.536556 −0.268278 0.963342i \(-0.586455\pi\)
−0.268278 + 0.963342i \(0.586455\pi\)
\(752\) 20.9323 0.763321
\(753\) −0.742632 −0.0270630
\(754\) 11.2619 0.410136
\(755\) −54.3770 −1.97898
\(756\) 6.83834 0.248708
\(757\) −12.1814 −0.442740 −0.221370 0.975190i \(-0.571053\pi\)
−0.221370 + 0.975190i \(0.571053\pi\)
\(758\) 29.2414 1.06210
\(759\) −0.0686454 −0.00249167
\(760\) 12.2482 0.444288
\(761\) −19.8061 −0.717970 −0.358985 0.933343i \(-0.616877\pi\)
−0.358985 + 0.933343i \(0.616877\pi\)
\(762\) −1.84256 −0.0667489
\(763\) −8.19109 −0.296537
\(764\) 32.0431 1.15928
\(765\) −11.6556 −0.421410
\(766\) −90.7474 −3.27884
\(767\) −1.91373 −0.0691009
\(768\) −1.98447 −0.0716086
\(769\) 46.1661 1.66479 0.832397 0.554181i \(-0.186968\pi\)
0.832397 + 0.554181i \(0.186968\pi\)
\(770\) −76.8338 −2.76890
\(771\) −2.30244 −0.0829204
\(772\) 21.5060 0.774019
\(773\) −29.4075 −1.05771 −0.528857 0.848711i \(-0.677379\pi\)
−0.528857 + 0.848711i \(0.677379\pi\)
\(774\) −69.3353 −2.49220
\(775\) −15.3872 −0.552726
\(776\) 5.99006 0.215031
\(777\) −1.88076 −0.0674718
\(778\) 39.8443 1.42849
\(779\) −1.29833 −0.0465174
\(780\) −0.817263 −0.0292627
\(781\) −1.75665 −0.0628580
\(782\) −1.16325 −0.0415977
\(783\) 2.05430 0.0734146
\(784\) 24.6878 0.881709
\(785\) −55.2225 −1.97098
\(786\) −2.13001 −0.0759748
\(787\) −15.1455 −0.539880 −0.269940 0.962877i \(-0.587004\pi\)
−0.269940 + 0.962877i \(0.587004\pi\)
\(788\) −12.2210 −0.435357
\(789\) 1.14529 0.0407733
\(790\) 33.2158 1.18177
\(791\) −51.6438 −1.83624
\(792\) 29.6424 1.05330
\(793\) −6.27105 −0.222691
\(794\) 36.6963 1.30230
\(795\) 2.44401 0.0866801
\(796\) −100.335 −3.55627
\(797\) 11.5353 0.408601 0.204301 0.978908i \(-0.434508\pi\)
0.204301 + 0.978908i \(0.434508\pi\)
\(798\) 0.736893 0.0260857
\(799\) −12.1172 −0.428676
\(800\) 12.1367 0.429097
\(801\) −2.86178 −0.101116
\(802\) −52.1917 −1.84295
\(803\) 2.03668 0.0718729
\(804\) −0.486053 −0.0171418
\(805\) −5.01039 −0.176593
\(806\) 8.41516 0.296411
\(807\) 0.612952 0.0215769
\(808\) −27.5171 −0.968050
\(809\) 13.6513 0.479954 0.239977 0.970779i \(-0.422860\pi\)
0.239977 + 0.970779i \(0.422860\pi\)
\(810\) 65.2905 2.29407
\(811\) 11.8884 0.417459 0.208730 0.977973i \(-0.433067\pi\)
0.208730 + 0.977973i \(0.433067\pi\)
\(812\) 74.2929 2.60717
\(813\) −0.415290 −0.0145649
\(814\) −35.7144 −1.25179
\(815\) 24.9958 0.875565
\(816\) −0.202817 −0.00710000
\(817\) −9.69254 −0.339099
\(818\) 60.1420 2.10282
\(819\) 12.7877 0.446837
\(820\) 14.6574 0.511859
\(821\) 47.8997 1.67171 0.835855 0.548950i \(-0.184972\pi\)
0.835855 + 0.548950i \(0.184972\pi\)
\(822\) −2.71296 −0.0946255
\(823\) 3.92822 0.136929 0.0684646 0.997654i \(-0.478190\pi\)
0.0684646 + 0.997654i \(0.478190\pi\)
\(824\) −49.6017 −1.72796
\(825\) 0.780131 0.0271607
\(826\) −19.4804 −0.677809
\(827\) −7.76641 −0.270065 −0.135032 0.990841i \(-0.543114\pi\)
−0.135032 + 0.990841i \(0.543114\pi\)
\(828\) 4.23029 0.147013
\(829\) −9.22162 −0.320280 −0.160140 0.987094i \(-0.551195\pi\)
−0.160140 + 0.987094i \(0.551195\pi\)
\(830\) 79.4783 2.75873
\(831\) −1.62086 −0.0562269
\(832\) −11.0329 −0.382499
\(833\) −14.2912 −0.495162
\(834\) −1.25703 −0.0435276
\(835\) −39.3723 −1.36254
\(836\) 9.06847 0.313640
\(837\) 1.53501 0.0530578
\(838\) 44.0436 1.52146
\(839\) 19.2824 0.665704 0.332852 0.942979i \(-0.391989\pi\)
0.332852 + 0.942979i \(0.391989\pi\)
\(840\) −3.80137 −0.131160
\(841\) −6.68176 −0.230405
\(842\) 6.79895 0.234307
\(843\) 0.441082 0.0151917
\(844\) −43.7005 −1.50423
\(845\) −3.05924 −0.105241
\(846\) 67.9957 2.33774
\(847\) 20.9762 0.720750
\(848\) −24.2049 −0.831201
\(849\) −0.828963 −0.0284499
\(850\) 13.2199 0.453440
\(851\) −2.32897 −0.0798359
\(852\) −0.190200 −0.00651616
\(853\) −36.6757 −1.25575 −0.627877 0.778313i \(-0.716076\pi\)
−0.627877 + 0.778313i \(0.716076\pi\)
\(854\) −63.8346 −2.18437
\(855\) 9.14320 0.312691
\(856\) −13.2558 −0.453072
\(857\) −9.77484 −0.333902 −0.166951 0.985965i \(-0.553392\pi\)
−0.166951 + 0.985965i \(0.553392\pi\)
\(858\) −0.426648 −0.0145655
\(859\) −27.9366 −0.953183 −0.476592 0.879125i \(-0.658128\pi\)
−0.476592 + 0.879125i \(0.658128\pi\)
\(860\) 109.424 3.73131
\(861\) 0.402952 0.0137326
\(862\) 79.6595 2.71321
\(863\) −16.3864 −0.557801 −0.278900 0.960320i \(-0.589970\pi\)
−0.278900 + 0.960320i \(0.589970\pi\)
\(864\) −1.21074 −0.0411903
\(865\) −19.9264 −0.677519
\(866\) −67.6889 −2.30016
\(867\) −1.11573 −0.0378923
\(868\) 55.5132 1.88424
\(869\) 11.2375 0.381207
\(870\) −2.49914 −0.0847287
\(871\) −1.81943 −0.0616490
\(872\) −7.69558 −0.260605
\(873\) 4.47155 0.151339
\(874\) 0.912505 0.0308659
\(875\) −8.37410 −0.283096
\(876\) 0.220520 0.00745069
\(877\) 47.1694 1.59280 0.796399 0.604772i \(-0.206736\pi\)
0.796399 + 0.604772i \(0.206736\pi\)
\(878\) 21.1845 0.714941
\(879\) 0.776006 0.0261740
\(880\) −16.5887 −0.559207
\(881\) −36.2487 −1.22125 −0.610625 0.791920i \(-0.709082\pi\)
−0.610625 + 0.791920i \(0.709082\pi\)
\(882\) 80.1952 2.70031
\(883\) 57.9434 1.94995 0.974975 0.222315i \(-0.0713612\pi\)
0.974975 + 0.222315i \(0.0713612\pi\)
\(884\) −4.68542 −0.157588
\(885\) 0.424676 0.0142753
\(886\) −83.0805 −2.79114
\(887\) 53.9569 1.81170 0.905848 0.423603i \(-0.139235\pi\)
0.905848 + 0.423603i \(0.139235\pi\)
\(888\) −1.76698 −0.0592961
\(889\) −45.4996 −1.52601
\(890\) 6.96905 0.233603
\(891\) 22.0890 0.740009
\(892\) 57.3483 1.92016
\(893\) 9.50528 0.318082
\(894\) 1.53082 0.0511981
\(895\) 8.81037 0.294498
\(896\) −88.5288 −2.95754
\(897\) −0.0278220 −0.000928950 0
\(898\) −16.0015 −0.533976
\(899\) 16.6767 0.556197
\(900\) −48.0758 −1.60253
\(901\) 14.0117 0.466797
\(902\) 7.65182 0.254778
\(903\) 3.00820 0.100107
\(904\) −48.5197 −1.61374
\(905\) 25.0730 0.833453
\(906\) −3.07361 −0.102114
\(907\) 7.32727 0.243298 0.121649 0.992573i \(-0.461182\pi\)
0.121649 + 0.992573i \(0.461182\pi\)
\(908\) −63.4730 −2.10643
\(909\) −20.5414 −0.681316
\(910\) −31.1408 −1.03231
\(911\) 5.48479 0.181719 0.0908596 0.995864i \(-0.471039\pi\)
0.0908596 + 0.995864i \(0.471039\pi\)
\(912\) 0.159099 0.00526828
\(913\) 26.8890 0.889895
\(914\) 30.9770 1.02463
\(915\) 1.39161 0.0460051
\(916\) 11.3651 0.375515
\(917\) −52.5977 −1.73693
\(918\) −1.31880 −0.0435270
\(919\) −42.3124 −1.39576 −0.697879 0.716215i \(-0.745873\pi\)
−0.697879 + 0.716215i \(0.745873\pi\)
\(920\) −4.70729 −0.155195
\(921\) −2.03688 −0.0671174
\(922\) 66.9260 2.20409
\(923\) −0.711972 −0.0234348
\(924\) −2.81451 −0.0925907
\(925\) 26.4679 0.870259
\(926\) −38.9618 −1.28037
\(927\) −37.0274 −1.21614
\(928\) −13.1537 −0.431792
\(929\) −36.9977 −1.21386 −0.606928 0.794757i \(-0.707598\pi\)
−0.606928 + 0.794757i \(0.707598\pi\)
\(930\) −1.86741 −0.0612347
\(931\) 11.2107 0.367415
\(932\) 106.958 3.50353
\(933\) −1.18241 −0.0387103
\(934\) −16.8627 −0.551765
\(935\) 9.60285 0.314047
\(936\) 12.0141 0.392693
\(937\) 8.92499 0.291567 0.145783 0.989317i \(-0.453430\pi\)
0.145783 + 0.989317i \(0.453430\pi\)
\(938\) −18.5204 −0.604714
\(939\) −1.75128 −0.0571510
\(940\) −107.309 −3.50005
\(941\) −17.2917 −0.563693 −0.281846 0.959460i \(-0.590947\pi\)
−0.281846 + 0.959460i \(0.590947\pi\)
\(942\) −3.12140 −0.101701
\(943\) 0.498981 0.0162490
\(944\) −4.20590 −0.136890
\(945\) −5.68040 −0.184783
\(946\) 57.1239 1.85726
\(947\) 13.5805 0.441308 0.220654 0.975352i \(-0.429181\pi\)
0.220654 + 0.975352i \(0.429181\pi\)
\(948\) 1.21674 0.0395178
\(949\) 0.825468 0.0267958
\(950\) −10.3703 −0.336457
\(951\) 0.663591 0.0215184
\(952\) −21.7935 −0.706332
\(953\) 3.84702 0.124617 0.0623086 0.998057i \(-0.480154\pi\)
0.0623086 + 0.998057i \(0.480154\pi\)
\(954\) −78.6265 −2.54563
\(955\) −26.6172 −0.861314
\(956\) 22.5754 0.730139
\(957\) −0.845504 −0.0273313
\(958\) −72.2891 −2.33556
\(959\) −66.9931 −2.16332
\(960\) 2.44832 0.0790192
\(961\) −18.5389 −0.598028
\(962\) −14.4751 −0.466695
\(963\) −9.89536 −0.318874
\(964\) −44.3810 −1.42942
\(965\) −17.8644 −0.575075
\(966\) −0.283207 −0.00911204
\(967\) −37.8233 −1.21632 −0.608158 0.793816i \(-0.708091\pi\)
−0.608158 + 0.793816i \(0.708091\pi\)
\(968\) 19.7072 0.633415
\(969\) −0.0920985 −0.00295863
\(970\) −10.8892 −0.349632
\(971\) −59.3493 −1.90461 −0.952305 0.305148i \(-0.901294\pi\)
−0.952305 + 0.305148i \(0.901294\pi\)
\(972\) 7.19608 0.230814
\(973\) −31.0408 −0.995123
\(974\) 22.8205 0.731216
\(975\) 0.316188 0.0101261
\(976\) −13.7822 −0.441156
\(977\) 7.75157 0.247995 0.123997 0.992283i \(-0.460429\pi\)
0.123997 + 0.992283i \(0.460429\pi\)
\(978\) 1.41286 0.0451784
\(979\) 2.35776 0.0753544
\(980\) −126.562 −4.04289
\(981\) −5.74471 −0.183415
\(982\) 50.6774 1.61718
\(983\) 2.70192 0.0861779 0.0430889 0.999071i \(-0.486280\pi\)
0.0430889 + 0.999071i \(0.486280\pi\)
\(984\) 0.378576 0.0120686
\(985\) 10.1516 0.323458
\(986\) −14.3277 −0.456288
\(987\) −2.95008 −0.0939021
\(988\) 3.67546 0.116932
\(989\) 3.72510 0.118451
\(990\) −53.8864 −1.71262
\(991\) −45.6185 −1.44912 −0.724560 0.689212i \(-0.757957\pi\)
−0.724560 + 0.689212i \(0.757957\pi\)
\(992\) −9.82872 −0.312062
\(993\) 0.865862 0.0274773
\(994\) −7.24734 −0.229872
\(995\) 83.3450 2.64221
\(996\) 2.91139 0.0922508
\(997\) 12.9654 0.410619 0.205310 0.978697i \(-0.434180\pi\)
0.205310 + 0.978697i \(0.434180\pi\)
\(998\) 2.28036 0.0721835
\(999\) −2.64041 −0.0835387
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 \(a_p\))