Properties

Label 5077.2.a.c.1.17
Level 5077
Weight 2
Character 5077.1
Self dual Yes
Analytic conductor 40.540
Analytic rank 0
Dimension 216
CM No

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Newspace parameters

Level: \( N \) = \( 5077 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 5077.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(40.5400491062\)
Analytic rank: \(0\)
Dimension: \(216\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Character \(\chi\) = 5077.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.43559 q^{2} +3.36410 q^{3} +3.93211 q^{4} +0.698081 q^{5} -8.19357 q^{6} +2.30447 q^{7} -4.70583 q^{8} +8.31717 q^{9} +O(q^{10})\) \(q-2.43559 q^{2} +3.36410 q^{3} +3.93211 q^{4} +0.698081 q^{5} -8.19357 q^{6} +2.30447 q^{7} -4.70583 q^{8} +8.31717 q^{9} -1.70024 q^{10} -5.80455 q^{11} +13.2280 q^{12} -5.40632 q^{13} -5.61274 q^{14} +2.34841 q^{15} +3.59726 q^{16} +0.263357 q^{17} -20.2572 q^{18} +1.83023 q^{19} +2.74493 q^{20} +7.75246 q^{21} +14.1375 q^{22} +8.68402 q^{23} -15.8309 q^{24} -4.51268 q^{25} +13.1676 q^{26} +17.8875 q^{27} +9.06141 q^{28} +4.98208 q^{29} -5.71978 q^{30} +8.70493 q^{31} +0.650197 q^{32} -19.5271 q^{33} -0.641430 q^{34} +1.60870 q^{35} +32.7040 q^{36} +4.86589 q^{37} -4.45770 q^{38} -18.1874 q^{39} -3.28505 q^{40} -2.49494 q^{41} -18.8818 q^{42} -8.28345 q^{43} -22.8241 q^{44} +5.80606 q^{45} -21.1507 q^{46} +12.0630 q^{47} +12.1015 q^{48} -1.68943 q^{49} +10.9911 q^{50} +0.885958 q^{51} -21.2583 q^{52} -3.11653 q^{53} -43.5666 q^{54} -4.05205 q^{55} -10.8444 q^{56} +6.15709 q^{57} -12.1343 q^{58} +8.14615 q^{59} +9.23422 q^{60} -9.99852 q^{61} -21.2017 q^{62} +19.1666 q^{63} -8.77814 q^{64} -3.77405 q^{65} +47.5600 q^{66} +9.95834 q^{67} +1.03555 q^{68} +29.2139 q^{69} -3.91815 q^{70} +3.63439 q^{71} -39.1392 q^{72} +6.71168 q^{73} -11.8513 q^{74} -15.1811 q^{75} +7.19668 q^{76} -13.3764 q^{77} +44.2971 q^{78} -4.60439 q^{79} +2.51118 q^{80} +35.2238 q^{81} +6.07665 q^{82} -3.46577 q^{83} +30.4835 q^{84} +0.183844 q^{85} +20.1751 q^{86} +16.7602 q^{87} +27.3152 q^{88} +6.50532 q^{89} -14.1412 q^{90} -12.4587 q^{91} +34.1465 q^{92} +29.2843 q^{93} -29.3805 q^{94} +1.27765 q^{95} +2.18733 q^{96} -16.3692 q^{97} +4.11477 q^{98} -48.2774 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 216q + 25q^{2} + 62q^{3} + 223q^{4} + 46q^{5} + 26q^{6} + 30q^{7} + 75q^{8} + 234q^{9} + O(q^{10}) \) \( 216q + 25q^{2} + 62q^{3} + 223q^{4} + 46q^{5} + 26q^{6} + 30q^{7} + 75q^{8} + 234q^{9} + 24q^{10} + 89q^{11} + 114q^{12} + 34q^{13} + 53q^{14} + 61q^{15} + 229q^{16} + 76q^{17} + 57q^{18} + 54q^{19} + 118q^{20} + 25q^{21} + 26q^{22} + 109q^{23} + 65q^{24} + 232q^{25} + 58q^{26} + 236q^{27} + 57q^{28} + 54q^{29} + 6q^{30} + 77q^{31} + 155q^{32} + 80q^{33} + 28q^{34} + 137q^{35} + 257q^{36} + 42q^{37} + 104q^{38} + 46q^{39} + 47q^{40} + 109q^{41} + 27q^{42} + 68q^{43} + 145q^{44} + 109q^{45} - 7q^{46} + 264q^{47} + 198q^{48} + 222q^{49} + 86q^{50} + 57q^{51} + 68q^{52} + 95q^{53} + 79q^{54} + 50q^{55} + 108q^{56} + 55q^{57} + 38q^{58} + 292q^{59} + 91q^{60} + 16q^{61} + 91q^{62} + 113q^{63} + 231q^{64} + 68q^{65} - 15q^{66} + 152q^{67} + 199q^{68} + 83q^{69} + 24q^{70} + 131q^{71} + 162q^{72} + 71q^{73} + 10q^{74} + 232q^{75} + 60q^{76} + 131q^{77} + 102q^{78} + 10q^{79} + 236q^{80} + 268q^{81} + 54q^{82} + 299q^{83} - 9q^{85} + 35q^{86} + 103q^{87} + 45q^{88} + 134q^{89} + 8q^{90} + 79q^{91} + 206q^{92} + 95q^{93} + 18q^{94} + 119q^{95} + 77q^{96} + 129q^{97} + 150q^{98} + 221q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.43559 −1.72222 −0.861112 0.508416i \(-0.830231\pi\)
−0.861112 + 0.508416i \(0.830231\pi\)
\(3\) 3.36410 1.94226 0.971132 0.238543i \(-0.0766698\pi\)
0.971132 + 0.238543i \(0.0766698\pi\)
\(4\) 3.93211 1.96605
\(5\) 0.698081 0.312191 0.156096 0.987742i \(-0.450109\pi\)
0.156096 + 0.987742i \(0.450109\pi\)
\(6\) −8.19357 −3.34501
\(7\) 2.30447 0.871007 0.435503 0.900187i \(-0.356570\pi\)
0.435503 + 0.900187i \(0.356570\pi\)
\(8\) −4.70583 −1.66376
\(9\) 8.31717 2.77239
\(10\) −1.70024 −0.537663
\(11\) −5.80455 −1.75014 −0.875069 0.483999i \(-0.839184\pi\)
−0.875069 + 0.483999i \(0.839184\pi\)
\(12\) 13.2280 3.81860
\(13\) −5.40632 −1.49944 −0.749722 0.661753i \(-0.769813\pi\)
−0.749722 + 0.661753i \(0.769813\pi\)
\(14\) −5.61274 −1.50007
\(15\) 2.34841 0.606358
\(16\) 3.59726 0.899315
\(17\) 0.263357 0.0638734 0.0319367 0.999490i \(-0.489833\pi\)
0.0319367 + 0.999490i \(0.489833\pi\)
\(18\) −20.2572 −4.77467
\(19\) 1.83023 0.419884 0.209942 0.977714i \(-0.432672\pi\)
0.209942 + 0.977714i \(0.432672\pi\)
\(20\) 2.74493 0.613785
\(21\) 7.75246 1.69172
\(22\) 14.1375 3.01413
\(23\) 8.68402 1.81074 0.905372 0.424620i \(-0.139592\pi\)
0.905372 + 0.424620i \(0.139592\pi\)
\(24\) −15.8309 −3.23146
\(25\) −4.51268 −0.902537
\(26\) 13.1676 2.58238
\(27\) 17.8875 3.44245
\(28\) 9.06141 1.71245
\(29\) 4.98208 0.925150 0.462575 0.886580i \(-0.346926\pi\)
0.462575 + 0.886580i \(0.346926\pi\)
\(30\) −5.71978 −1.04428
\(31\) 8.70493 1.56345 0.781726 0.623622i \(-0.214340\pi\)
0.781726 + 0.623622i \(0.214340\pi\)
\(32\) 0.650197 0.114940
\(33\) −19.5271 −3.39923
\(34\) −0.641430 −0.110004
\(35\) 1.60870 0.271921
\(36\) 32.7040 5.45067
\(37\) 4.86589 0.799947 0.399973 0.916527i \(-0.369019\pi\)
0.399973 + 0.916527i \(0.369019\pi\)
\(38\) −4.45770 −0.723135
\(39\) −18.1874 −2.91232
\(40\) −3.28505 −0.519412
\(41\) −2.49494 −0.389644 −0.194822 0.980839i \(-0.562413\pi\)
−0.194822 + 0.980839i \(0.562413\pi\)
\(42\) −18.8818 −2.91353
\(43\) −8.28345 −1.26321 −0.631607 0.775289i \(-0.717604\pi\)
−0.631607 + 0.775289i \(0.717604\pi\)
\(44\) −22.8241 −3.44087
\(45\) 5.80606 0.865516
\(46\) −21.1507 −3.11851
\(47\) 12.0630 1.75957 0.879785 0.475373i \(-0.157687\pi\)
0.879785 + 0.475373i \(0.157687\pi\)
\(48\) 12.1015 1.74671
\(49\) −1.68943 −0.241347
\(50\) 10.9911 1.55437
\(51\) 0.885958 0.124059
\(52\) −21.2583 −2.94799
\(53\) −3.11653 −0.428088 −0.214044 0.976824i \(-0.568664\pi\)
−0.214044 + 0.976824i \(0.568664\pi\)
\(54\) −43.5666 −5.92866
\(55\) −4.05205 −0.546378
\(56\) −10.8444 −1.44915
\(57\) 6.15709 0.815526
\(58\) −12.1343 −1.59331
\(59\) 8.14615 1.06054 0.530269 0.847829i \(-0.322091\pi\)
0.530269 + 0.847829i \(0.322091\pi\)
\(60\) 9.23422 1.19213
\(61\) −9.99852 −1.28018 −0.640090 0.768300i \(-0.721103\pi\)
−0.640090 + 0.768300i \(0.721103\pi\)
\(62\) −21.2017 −2.69261
\(63\) 19.1666 2.41477
\(64\) −8.77814 −1.09727
\(65\) −3.77405 −0.468114
\(66\) 47.5600 5.85423
\(67\) 9.95834 1.21661 0.608303 0.793705i \(-0.291851\pi\)
0.608303 + 0.793705i \(0.291851\pi\)
\(68\) 1.03555 0.125579
\(69\) 29.2139 3.51694
\(70\) −3.91815 −0.468308
\(71\) 3.63439 0.431322 0.215661 0.976468i \(-0.430809\pi\)
0.215661 + 0.976468i \(0.430809\pi\)
\(72\) −39.1392 −4.61259
\(73\) 6.71168 0.785542 0.392771 0.919636i \(-0.371516\pi\)
0.392771 + 0.919636i \(0.371516\pi\)
\(74\) −11.8513 −1.37769
\(75\) −15.1811 −1.75296
\(76\) 7.19668 0.825515
\(77\) −13.3764 −1.52438
\(78\) 44.2971 5.01566
\(79\) −4.60439 −0.518034 −0.259017 0.965873i \(-0.583399\pi\)
−0.259017 + 0.965873i \(0.583399\pi\)
\(80\) 2.51118 0.280758
\(81\) 35.2238 3.91375
\(82\) 6.07665 0.671054
\(83\) −3.46577 −0.380417 −0.190209 0.981744i \(-0.560916\pi\)
−0.190209 + 0.981744i \(0.560916\pi\)
\(84\) 30.4835 3.32602
\(85\) 0.183844 0.0199407
\(86\) 20.1751 2.17554
\(87\) 16.7602 1.79689
\(88\) 27.3152 2.91181
\(89\) 6.50532 0.689563 0.344781 0.938683i \(-0.387953\pi\)
0.344781 + 0.938683i \(0.387953\pi\)
\(90\) −14.1412 −1.49061
\(91\) −12.4587 −1.30603
\(92\) 34.1465 3.56002
\(93\) 29.2843 3.03664
\(94\) −29.3805 −3.03037
\(95\) 1.27765 0.131084
\(96\) 2.18733 0.223243
\(97\) −16.3692 −1.66204 −0.831018 0.556246i \(-0.812241\pi\)
−0.831018 + 0.556246i \(0.812241\pi\)
\(98\) 4.11477 0.415654
\(99\) −48.2774 −4.85206
\(100\) −17.7444 −1.77444
\(101\) 8.82414 0.878034 0.439017 0.898479i \(-0.355327\pi\)
0.439017 + 0.898479i \(0.355327\pi\)
\(102\) −2.15783 −0.213657
\(103\) −13.3868 −1.31904 −0.659521 0.751686i \(-0.729241\pi\)
−0.659521 + 0.751686i \(0.729241\pi\)
\(104\) 25.4412 2.49472
\(105\) 5.41184 0.528142
\(106\) 7.59060 0.737264
\(107\) 4.52122 0.437083 0.218541 0.975828i \(-0.429870\pi\)
0.218541 + 0.975828i \(0.429870\pi\)
\(108\) 70.3355 6.76804
\(109\) 19.3166 1.85019 0.925097 0.379732i \(-0.123984\pi\)
0.925097 + 0.379732i \(0.123984\pi\)
\(110\) 9.86913 0.940985
\(111\) 16.3693 1.55371
\(112\) 8.28977 0.783309
\(113\) 6.27471 0.590275 0.295138 0.955455i \(-0.404634\pi\)
0.295138 + 0.955455i \(0.404634\pi\)
\(114\) −14.9962 −1.40452
\(115\) 6.06215 0.565298
\(116\) 19.5901 1.81889
\(117\) −44.9653 −4.15704
\(118\) −19.8407 −1.82649
\(119\) 0.606897 0.0556341
\(120\) −11.0512 −1.00884
\(121\) 22.6928 2.06298
\(122\) 24.3523 2.20476
\(123\) −8.39322 −0.756791
\(124\) 34.2287 3.07383
\(125\) −6.64062 −0.593955
\(126\) −46.6821 −4.15877
\(127\) −13.6066 −1.20739 −0.603697 0.797214i \(-0.706306\pi\)
−0.603697 + 0.797214i \(0.706306\pi\)
\(128\) 20.0796 1.77480
\(129\) −27.8664 −2.45350
\(130\) 9.19205 0.806196
\(131\) 19.1988 1.67741 0.838705 0.544586i \(-0.183313\pi\)
0.838705 + 0.544586i \(0.183313\pi\)
\(132\) −76.7826 −6.68307
\(133\) 4.21771 0.365722
\(134\) −24.2545 −2.09527
\(135\) 12.4869 1.07470
\(136\) −1.23931 −0.106270
\(137\) −10.0487 −0.858516 −0.429258 0.903182i \(-0.641225\pi\)
−0.429258 + 0.903182i \(0.641225\pi\)
\(138\) −71.1532 −6.05696
\(139\) −10.0157 −0.849517 −0.424759 0.905307i \(-0.639641\pi\)
−0.424759 + 0.905307i \(0.639641\pi\)
\(140\) 6.32560 0.534611
\(141\) 40.5811 3.41755
\(142\) −8.85188 −0.742833
\(143\) 31.3813 2.62423
\(144\) 29.9190 2.49325
\(145\) 3.47790 0.288824
\(146\) −16.3469 −1.35288
\(147\) −5.68342 −0.468760
\(148\) 19.1332 1.57274
\(149\) −1.24166 −0.101721 −0.0508604 0.998706i \(-0.516196\pi\)
−0.0508604 + 0.998706i \(0.516196\pi\)
\(150\) 36.9750 3.01900
\(151\) −9.50459 −0.773473 −0.386736 0.922190i \(-0.626398\pi\)
−0.386736 + 0.922190i \(0.626398\pi\)
\(152\) −8.61276 −0.698587
\(153\) 2.19038 0.177082
\(154\) 32.5794 2.62533
\(155\) 6.07675 0.488096
\(156\) −71.5149 −5.72577
\(157\) 23.3148 1.86073 0.930364 0.366638i \(-0.119491\pi\)
0.930364 + 0.366638i \(0.119491\pi\)
\(158\) 11.2144 0.892170
\(159\) −10.4843 −0.831461
\(160\) 0.453890 0.0358832
\(161\) 20.0120 1.57717
\(162\) −85.7907 −6.74035
\(163\) −2.88148 −0.225695 −0.112848 0.993612i \(-0.535997\pi\)
−0.112848 + 0.993612i \(0.535997\pi\)
\(164\) −9.81037 −0.766061
\(165\) −13.6315 −1.06121
\(166\) 8.44120 0.655164
\(167\) −8.18008 −0.632994 −0.316497 0.948594i \(-0.602507\pi\)
−0.316497 + 0.948594i \(0.602507\pi\)
\(168\) −36.4817 −2.81463
\(169\) 16.2283 1.24833
\(170\) −0.447770 −0.0343424
\(171\) 15.2224 1.16408
\(172\) −32.5714 −2.48355
\(173\) 1.01895 0.0774690 0.0387345 0.999250i \(-0.487667\pi\)
0.0387345 + 0.999250i \(0.487667\pi\)
\(174\) −40.8211 −3.09464
\(175\) −10.3993 −0.786115
\(176\) −20.8805 −1.57393
\(177\) 27.4045 2.05985
\(178\) −15.8443 −1.18758
\(179\) −14.7788 −1.10462 −0.552309 0.833639i \(-0.686253\pi\)
−0.552309 + 0.833639i \(0.686253\pi\)
\(180\) 22.8300 1.70165
\(181\) 24.4088 1.81429 0.907145 0.420819i \(-0.138257\pi\)
0.907145 + 0.420819i \(0.138257\pi\)
\(182\) 30.3443 2.24927
\(183\) −33.6360 −2.48645
\(184\) −40.8655 −3.01265
\(185\) 3.39678 0.249736
\(186\) −71.3245 −5.22977
\(187\) −1.52867 −0.111787
\(188\) 47.4330 3.45941
\(189\) 41.2211 2.99839
\(190\) −3.11184 −0.225756
\(191\) 5.46866 0.395698 0.197849 0.980232i \(-0.436604\pi\)
0.197849 + 0.980232i \(0.436604\pi\)
\(192\) −29.5305 −2.13118
\(193\) 5.50851 0.396511 0.198256 0.980150i \(-0.436472\pi\)
0.198256 + 0.980150i \(0.436472\pi\)
\(194\) 39.8686 2.86240
\(195\) −12.6963 −0.909200
\(196\) −6.64303 −0.474502
\(197\) 8.80728 0.627493 0.313746 0.949507i \(-0.398416\pi\)
0.313746 + 0.949507i \(0.398416\pi\)
\(198\) 117.584 8.35634
\(199\) −4.57280 −0.324157 −0.162079 0.986778i \(-0.551820\pi\)
−0.162079 + 0.986778i \(0.551820\pi\)
\(200\) 21.2359 1.50161
\(201\) 33.5009 2.36297
\(202\) −21.4920 −1.51217
\(203\) 11.4810 0.805812
\(204\) 3.48368 0.243907
\(205\) −1.74167 −0.121643
\(206\) 32.6048 2.27169
\(207\) 72.2264 5.02009
\(208\) −19.4480 −1.34847
\(209\) −10.6237 −0.734855
\(210\) −13.1810 −0.909578
\(211\) −0.768490 −0.0529050 −0.0264525 0.999650i \(-0.508421\pi\)
−0.0264525 + 0.999650i \(0.508421\pi\)
\(212\) −12.2545 −0.841645
\(213\) 12.2264 0.837742
\(214\) −11.0118 −0.752755
\(215\) −5.78252 −0.394365
\(216\) −84.1754 −5.72741
\(217\) 20.0602 1.36178
\(218\) −47.0473 −3.18645
\(219\) 22.5788 1.52573
\(220\) −15.9331 −1.07421
\(221\) −1.42379 −0.0957746
\(222\) −39.8690 −2.67583
\(223\) −24.3337 −1.62950 −0.814752 0.579810i \(-0.803127\pi\)
−0.814752 + 0.579810i \(0.803127\pi\)
\(224\) 1.49836 0.100113
\(225\) −37.5327 −2.50218
\(226\) −15.2826 −1.01659
\(227\) 22.8151 1.51429 0.757147 0.653244i \(-0.226593\pi\)
0.757147 + 0.653244i \(0.226593\pi\)
\(228\) 24.2103 1.60337
\(229\) 27.7522 1.83392 0.916960 0.398980i \(-0.130636\pi\)
0.916960 + 0.398980i \(0.130636\pi\)
\(230\) −14.7649 −0.973570
\(231\) −44.9995 −2.96075
\(232\) −23.4448 −1.53923
\(233\) 12.2766 0.804268 0.402134 0.915581i \(-0.368269\pi\)
0.402134 + 0.915581i \(0.368269\pi\)
\(234\) 109.517 7.15936
\(235\) 8.42095 0.549322
\(236\) 32.0316 2.08508
\(237\) −15.4896 −1.00616
\(238\) −1.47815 −0.0958144
\(239\) −21.3553 −1.38136 −0.690680 0.723160i \(-0.742689\pi\)
−0.690680 + 0.723160i \(0.742689\pi\)
\(240\) 8.44786 0.545307
\(241\) 1.12725 0.0726126 0.0363063 0.999341i \(-0.488441\pi\)
0.0363063 + 0.999341i \(0.488441\pi\)
\(242\) −55.2704 −3.55292
\(243\) 64.8338 4.15909
\(244\) −39.3153 −2.51690
\(245\) −1.17936 −0.0753466
\(246\) 20.4425 1.30336
\(247\) −9.89483 −0.629593
\(248\) −40.9639 −2.60121
\(249\) −11.6592 −0.738871
\(250\) 16.1739 1.02292
\(251\) −12.3755 −0.781136 −0.390568 0.920574i \(-0.627721\pi\)
−0.390568 + 0.920574i \(0.627721\pi\)
\(252\) 75.3653 4.74757
\(253\) −50.4068 −3.16905
\(254\) 33.1402 2.07940
\(255\) 0.618471 0.0387301
\(256\) −31.3494 −1.95933
\(257\) 1.94872 0.121558 0.0607790 0.998151i \(-0.480641\pi\)
0.0607790 + 0.998151i \(0.480641\pi\)
\(258\) 67.8711 4.22547
\(259\) 11.2133 0.696759
\(260\) −14.8400 −0.920337
\(261\) 41.4368 2.56487
\(262\) −46.7605 −2.88888
\(263\) 22.1492 1.36578 0.682890 0.730521i \(-0.260723\pi\)
0.682890 + 0.730521i \(0.260723\pi\)
\(264\) 91.8911 5.65551
\(265\) −2.17559 −0.133646
\(266\) −10.2726 −0.629855
\(267\) 21.8845 1.33931
\(268\) 39.1573 2.39191
\(269\) −17.7632 −1.08304 −0.541520 0.840688i \(-0.682151\pi\)
−0.541520 + 0.840688i \(0.682151\pi\)
\(270\) −30.4130 −1.85088
\(271\) 1.35906 0.0825570 0.0412785 0.999148i \(-0.486857\pi\)
0.0412785 + 0.999148i \(0.486857\pi\)
\(272\) 0.947363 0.0574423
\(273\) −41.9123 −2.53665
\(274\) 24.4745 1.47856
\(275\) 26.1941 1.57956
\(276\) 114.872 6.91450
\(277\) 14.9807 0.900104 0.450052 0.893002i \(-0.351405\pi\)
0.450052 + 0.893002i \(0.351405\pi\)
\(278\) 24.3941 1.46306
\(279\) 72.4004 4.33450
\(280\) −7.57029 −0.452411
\(281\) −15.8865 −0.947707 −0.473853 0.880604i \(-0.657137\pi\)
−0.473853 + 0.880604i \(0.657137\pi\)
\(282\) −98.8391 −5.88578
\(283\) 10.8258 0.643528 0.321764 0.946820i \(-0.395724\pi\)
0.321764 + 0.946820i \(0.395724\pi\)
\(284\) 14.2908 0.848003
\(285\) 4.29815 0.254600
\(286\) −76.4320 −4.51952
\(287\) −5.74950 −0.339382
\(288\) 5.40780 0.318657
\(289\) −16.9306 −0.995920
\(290\) −8.47074 −0.497419
\(291\) −55.0675 −3.22811
\(292\) 26.3910 1.54442
\(293\) 5.35413 0.312792 0.156396 0.987694i \(-0.450012\pi\)
0.156396 + 0.987694i \(0.450012\pi\)
\(294\) 13.8425 0.807310
\(295\) 5.68668 0.331091
\(296\) −22.8980 −1.33092
\(297\) −103.829 −6.02476
\(298\) 3.02418 0.175186
\(299\) −46.9486 −2.71511
\(300\) −59.6938 −3.44642
\(301\) −19.0889 −1.10027
\(302\) 23.1493 1.33209
\(303\) 29.6853 1.70537
\(304\) 6.58383 0.377608
\(305\) −6.97978 −0.399661
\(306\) −5.33488 −0.304975
\(307\) −15.8980 −0.907345 −0.453672 0.891169i \(-0.649886\pi\)
−0.453672 + 0.891169i \(0.649886\pi\)
\(308\) −52.5974 −2.99702
\(309\) −45.0346 −2.56193
\(310\) −14.8005 −0.840611
\(311\) −5.04910 −0.286308 −0.143154 0.989700i \(-0.545724\pi\)
−0.143154 + 0.989700i \(0.545724\pi\)
\(312\) 85.5868 4.84540
\(313\) −6.85572 −0.387508 −0.193754 0.981050i \(-0.562066\pi\)
−0.193754 + 0.981050i \(0.562066\pi\)
\(314\) −56.7855 −3.20459
\(315\) 13.3799 0.753870
\(316\) −18.1049 −1.01848
\(317\) −12.1738 −0.683751 −0.341876 0.939745i \(-0.611062\pi\)
−0.341876 + 0.939745i \(0.611062\pi\)
\(318\) 25.5355 1.43196
\(319\) −28.9188 −1.61914
\(320\) −6.12785 −0.342557
\(321\) 15.2098 0.848930
\(322\) −48.7412 −2.71624
\(323\) 0.482004 0.0268194
\(324\) 138.504 7.69465
\(325\) 24.3970 1.35330
\(326\) 7.01812 0.388698
\(327\) 64.9829 3.59356
\(328\) 11.7408 0.648274
\(329\) 27.7988 1.53260
\(330\) 33.2007 1.82764
\(331\) −13.7816 −0.757503 −0.378751 0.925498i \(-0.623646\pi\)
−0.378751 + 0.925498i \(0.623646\pi\)
\(332\) −13.6278 −0.747921
\(333\) 40.4704 2.21776
\(334\) 19.9233 1.09016
\(335\) 6.95173 0.379814
\(336\) 27.8876 1.52139
\(337\) 1.01125 0.0550861 0.0275431 0.999621i \(-0.491232\pi\)
0.0275431 + 0.999621i \(0.491232\pi\)
\(338\) −39.5256 −2.14991
\(339\) 21.1088 1.14647
\(340\) 0.722896 0.0392045
\(341\) −50.5282 −2.73626
\(342\) −37.0754 −2.00481
\(343\) −20.0245 −1.08122
\(344\) 38.9805 2.10169
\(345\) 20.3937 1.09796
\(346\) −2.48173 −0.133419
\(347\) −7.09913 −0.381101 −0.190551 0.981677i \(-0.561027\pi\)
−0.190551 + 0.981677i \(0.561027\pi\)
\(348\) 65.9030 3.53277
\(349\) 31.0340 1.66121 0.830606 0.556861i \(-0.187995\pi\)
0.830606 + 0.556861i \(0.187995\pi\)
\(350\) 25.3285 1.35387
\(351\) −96.7055 −5.16176
\(352\) −3.77410 −0.201160
\(353\) −13.8451 −0.736902 −0.368451 0.929647i \(-0.620112\pi\)
−0.368451 + 0.929647i \(0.620112\pi\)
\(354\) −66.7461 −3.54752
\(355\) 2.53710 0.134655
\(356\) 25.5796 1.35572
\(357\) 2.04166 0.108056
\(358\) 35.9951 1.90240
\(359\) 9.92910 0.524038 0.262019 0.965063i \(-0.415612\pi\)
0.262019 + 0.965063i \(0.415612\pi\)
\(360\) −27.3223 −1.44001
\(361\) −15.6502 −0.823697
\(362\) −59.4498 −3.12461
\(363\) 76.3408 4.00685
\(364\) −48.9889 −2.56772
\(365\) 4.68529 0.245240
\(366\) 81.9236 4.28222
\(367\) −2.06995 −0.108051 −0.0540254 0.998540i \(-0.517205\pi\)
−0.0540254 + 0.998540i \(0.517205\pi\)
\(368\) 31.2387 1.62843
\(369\) −20.7508 −1.08024
\(370\) −8.27318 −0.430102
\(371\) −7.18194 −0.372868
\(372\) 115.149 5.97019
\(373\) 9.62535 0.498382 0.249191 0.968454i \(-0.419835\pi\)
0.249191 + 0.968454i \(0.419835\pi\)
\(374\) 3.72321 0.192523
\(375\) −22.3397 −1.15362
\(376\) −56.7664 −2.92750
\(377\) −26.9348 −1.38721
\(378\) −100.398 −5.16390
\(379\) 4.97991 0.255801 0.127900 0.991787i \(-0.459176\pi\)
0.127900 + 0.991787i \(0.459176\pi\)
\(380\) 5.02386 0.257719
\(381\) −45.7741 −2.34508
\(382\) −13.3194 −0.681481
\(383\) 27.1364 1.38661 0.693304 0.720646i \(-0.256154\pi\)
0.693304 + 0.720646i \(0.256154\pi\)
\(384\) 67.5497 3.44713
\(385\) −9.33781 −0.475899
\(386\) −13.4165 −0.682881
\(387\) −68.8948 −3.50212
\(388\) −64.3653 −3.26765
\(389\) −9.41954 −0.477589 −0.238795 0.971070i \(-0.576752\pi\)
−0.238795 + 0.971070i \(0.576752\pi\)
\(390\) 30.9230 1.56585
\(391\) 2.28700 0.115658
\(392\) 7.95018 0.401545
\(393\) 64.5868 3.25797
\(394\) −21.4509 −1.08068
\(395\) −3.21423 −0.161726
\(396\) −189.832 −9.53942
\(397\) −8.01922 −0.402473 −0.201237 0.979543i \(-0.564496\pi\)
−0.201237 + 0.979543i \(0.564496\pi\)
\(398\) 11.1375 0.558271
\(399\) 14.1888 0.710329
\(400\) −16.2333 −0.811665
\(401\) 11.8733 0.592924 0.296462 0.955045i \(-0.404193\pi\)
0.296462 + 0.955045i \(0.404193\pi\)
\(402\) −81.5944 −4.06956
\(403\) −47.0617 −2.34431
\(404\) 34.6975 1.72626
\(405\) 24.5890 1.22184
\(406\) −27.9631 −1.38779
\(407\) −28.2443 −1.40002
\(408\) −4.16917 −0.206405
\(409\) −0.538172 −0.0266109 −0.0133055 0.999911i \(-0.504235\pi\)
−0.0133055 + 0.999911i \(0.504235\pi\)
\(410\) 4.24200 0.209497
\(411\) −33.8047 −1.66746
\(412\) −52.6384 −2.59331
\(413\) 18.7725 0.923736
\(414\) −175.914 −8.64571
\(415\) −2.41939 −0.118763
\(416\) −3.51518 −0.172346
\(417\) −33.6937 −1.64999
\(418\) 25.8749 1.26559
\(419\) −18.5896 −0.908162 −0.454081 0.890960i \(-0.650032\pi\)
−0.454081 + 0.890960i \(0.650032\pi\)
\(420\) 21.2800 1.03836
\(421\) 8.81101 0.429422 0.214711 0.976678i \(-0.431119\pi\)
0.214711 + 0.976678i \(0.431119\pi\)
\(422\) 1.87173 0.0911143
\(423\) 100.330 4.87821
\(424\) 14.6659 0.712237
\(425\) −1.18845 −0.0576481
\(426\) −29.7786 −1.44278
\(427\) −23.0413 −1.11504
\(428\) 17.7779 0.859329
\(429\) 105.570 5.09696
\(430\) 14.0839 0.679184
\(431\) 18.6929 0.900405 0.450202 0.892927i \(-0.351352\pi\)
0.450202 + 0.892927i \(0.351352\pi\)
\(432\) 64.3459 3.09584
\(433\) −32.5207 −1.56285 −0.781423 0.624001i \(-0.785506\pi\)
−0.781423 + 0.624001i \(0.785506\pi\)
\(434\) −48.8585 −2.34528
\(435\) 11.7000 0.560972
\(436\) 75.9549 3.63758
\(437\) 15.8938 0.760303
\(438\) −54.9926 −2.62765
\(439\) −39.3507 −1.87811 −0.939053 0.343772i \(-0.888295\pi\)
−0.939053 + 0.343772i \(0.888295\pi\)
\(440\) 19.0682 0.909042
\(441\) −14.0513 −0.669109
\(442\) 3.46778 0.164945
\(443\) −14.6061 −0.693956 −0.346978 0.937873i \(-0.612792\pi\)
−0.346978 + 0.937873i \(0.612792\pi\)
\(444\) 64.3660 3.05467
\(445\) 4.54124 0.215275
\(446\) 59.2669 2.80637
\(447\) −4.17707 −0.197568
\(448\) −20.2289 −0.955727
\(449\) 39.5940 1.86856 0.934278 0.356544i \(-0.116045\pi\)
0.934278 + 0.356544i \(0.116045\pi\)
\(450\) 91.4144 4.30932
\(451\) 14.4820 0.681930
\(452\) 24.6729 1.16051
\(453\) −31.9744 −1.50229
\(454\) −55.5684 −2.60795
\(455\) −8.69718 −0.407730
\(456\) −28.9742 −1.35684
\(457\) 27.0443 1.26508 0.632539 0.774529i \(-0.282013\pi\)
0.632539 + 0.774529i \(0.282013\pi\)
\(458\) −67.5931 −3.15842
\(459\) 4.71079 0.219881
\(460\) 23.8370 1.11141
\(461\) −8.56537 −0.398929 −0.199464 0.979905i \(-0.563920\pi\)
−0.199464 + 0.979905i \(0.563920\pi\)
\(462\) 109.600 5.09908
\(463\) −29.2393 −1.35887 −0.679434 0.733737i \(-0.737775\pi\)
−0.679434 + 0.733737i \(0.737775\pi\)
\(464\) 17.9219 0.832001
\(465\) 20.4428 0.948011
\(466\) −29.9008 −1.38513
\(467\) 3.21866 0.148942 0.0744710 0.997223i \(-0.476273\pi\)
0.0744710 + 0.997223i \(0.476273\pi\)
\(468\) −176.808 −8.17297
\(469\) 22.9487 1.05967
\(470\) −20.5100 −0.946056
\(471\) 78.4335 3.61402
\(472\) −38.3344 −1.76448
\(473\) 48.0817 2.21080
\(474\) 37.7264 1.73283
\(475\) −8.25926 −0.378961
\(476\) 2.38638 0.109380
\(477\) −25.9207 −1.18683
\(478\) 52.0128 2.37901
\(479\) 0.0110735 0.000505962 0 0.000252981 1.00000i \(-0.499919\pi\)
0.000252981 1.00000i \(0.499919\pi\)
\(480\) 1.52693 0.0696946
\(481\) −26.3066 −1.19948
\(482\) −2.74552 −0.125055
\(483\) 67.3225 3.06328
\(484\) 89.2305 4.05593
\(485\) −11.4270 −0.518873
\(486\) −157.909 −7.16288
\(487\) 15.0702 0.682898 0.341449 0.939900i \(-0.389082\pi\)
0.341449 + 0.939900i \(0.389082\pi\)
\(488\) 47.0513 2.12991
\(489\) −9.69360 −0.438360
\(490\) 2.87244 0.129764
\(491\) 0.103892 0.00468859 0.00234430 0.999997i \(-0.499254\pi\)
0.00234430 + 0.999997i \(0.499254\pi\)
\(492\) −33.0031 −1.48789
\(493\) 1.31207 0.0590925
\(494\) 24.0998 1.08430
\(495\) −33.7015 −1.51477
\(496\) 31.3139 1.40604
\(497\) 8.37532 0.375685
\(498\) 28.3970 1.27250
\(499\) −16.0334 −0.717752 −0.358876 0.933385i \(-0.616840\pi\)
−0.358876 + 0.933385i \(0.616840\pi\)
\(500\) −26.1117 −1.16775
\(501\) −27.5186 −1.22944
\(502\) 30.1417 1.34529
\(503\) −6.32825 −0.282163 −0.141081 0.989998i \(-0.545058\pi\)
−0.141081 + 0.989998i \(0.545058\pi\)
\(504\) −90.1949 −4.01760
\(505\) 6.15996 0.274115
\(506\) 122.770 5.45781
\(507\) 54.5938 2.42459
\(508\) −53.5027 −2.37380
\(509\) 8.06870 0.357639 0.178820 0.983882i \(-0.442772\pi\)
0.178820 + 0.983882i \(0.442772\pi\)
\(510\) −1.50634 −0.0667020
\(511\) 15.4668 0.684213
\(512\) 36.1951 1.59961
\(513\) 32.7383 1.44543
\(514\) −4.74630 −0.209350
\(515\) −9.34509 −0.411794
\(516\) −109.574 −4.82371
\(517\) −70.0203 −3.07949
\(518\) −27.3110 −1.19997
\(519\) 3.42783 0.150465
\(520\) 17.7600 0.778829
\(521\) 1.92215 0.0842108 0.0421054 0.999113i \(-0.486593\pi\)
0.0421054 + 0.999113i \(0.486593\pi\)
\(522\) −100.923 −4.41729
\(523\) −33.6375 −1.47086 −0.735432 0.677599i \(-0.763021\pi\)
−0.735432 + 0.677599i \(0.763021\pi\)
\(524\) 75.4919 3.29788
\(525\) −34.9844 −1.52684
\(526\) −53.9465 −2.35218
\(527\) 2.29250 0.0998630
\(528\) −70.2440 −3.05698
\(529\) 52.4122 2.27879
\(530\) 5.29885 0.230167
\(531\) 67.7529 2.94023
\(532\) 16.5845 0.719029
\(533\) 13.4884 0.584249
\(534\) −53.3018 −2.30660
\(535\) 3.15618 0.136454
\(536\) −46.8623 −2.02414
\(537\) −49.7173 −2.14546
\(538\) 43.2638 1.86524
\(539\) 9.80639 0.422391
\(540\) 49.0999 2.11292
\(541\) 15.7327 0.676402 0.338201 0.941074i \(-0.390182\pi\)
0.338201 + 0.941074i \(0.390182\pi\)
\(542\) −3.31012 −0.142182
\(543\) 82.1135 3.52383
\(544\) 0.171234 0.00734159
\(545\) 13.4845 0.577614
\(546\) 102.081 4.36867
\(547\) 21.0991 0.902134 0.451067 0.892490i \(-0.351044\pi\)
0.451067 + 0.892490i \(0.351044\pi\)
\(548\) −39.5125 −1.68789
\(549\) −83.1594 −3.54915
\(550\) −63.7981 −2.72036
\(551\) 9.11838 0.388456
\(552\) −137.476 −5.85135
\(553\) −10.6107 −0.451211
\(554\) −36.4869 −1.55018
\(555\) 11.4271 0.485054
\(556\) −39.3827 −1.67020
\(557\) −19.6892 −0.834260 −0.417130 0.908847i \(-0.636964\pi\)
−0.417130 + 0.908847i \(0.636964\pi\)
\(558\) −176.338 −7.46497
\(559\) 44.7830 1.89412
\(560\) 5.78693 0.244542
\(561\) −5.14259 −0.217120
\(562\) 38.6929 1.63216
\(563\) −25.8145 −1.08795 −0.543977 0.839100i \(-0.683082\pi\)
−0.543977 + 0.839100i \(0.683082\pi\)
\(564\) 159.569 6.71908
\(565\) 4.38026 0.184279
\(566\) −26.3673 −1.10830
\(567\) 81.1720 3.40890
\(568\) −17.1028 −0.717617
\(569\) −26.4602 −1.10927 −0.554635 0.832094i \(-0.687142\pi\)
−0.554635 + 0.832094i \(0.687142\pi\)
\(570\) −10.4685 −0.438478
\(571\) 2.76419 0.115678 0.0578389 0.998326i \(-0.481579\pi\)
0.0578389 + 0.998326i \(0.481579\pi\)
\(572\) 123.395 5.15939
\(573\) 18.3971 0.768551
\(574\) 14.0034 0.584492
\(575\) −39.1882 −1.63426
\(576\) −73.0092 −3.04205
\(577\) −17.6003 −0.732711 −0.366355 0.930475i \(-0.619395\pi\)
−0.366355 + 0.930475i \(0.619395\pi\)
\(578\) 41.2361 1.71520
\(579\) 18.5312 0.770129
\(580\) 13.6755 0.567843
\(581\) −7.98675 −0.331346
\(582\) 134.122 5.55953
\(583\) 18.0901 0.749214
\(584\) −31.5840 −1.30696
\(585\) −31.3894 −1.29779
\(586\) −13.0405 −0.538697
\(587\) 4.62540 0.190911 0.0954553 0.995434i \(-0.469569\pi\)
0.0954553 + 0.995434i \(0.469569\pi\)
\(588\) −22.3478 −0.921609
\(589\) 15.9321 0.656469
\(590\) −13.8504 −0.570213
\(591\) 29.6286 1.21876
\(592\) 17.5039 0.719404
\(593\) 25.5520 1.04930 0.524648 0.851319i \(-0.324197\pi\)
0.524648 + 0.851319i \(0.324197\pi\)
\(594\) 252.884 10.3760
\(595\) 0.423663 0.0173685
\(596\) −4.88234 −0.199988
\(597\) −15.3834 −0.629599
\(598\) 114.348 4.67603
\(599\) −43.6239 −1.78242 −0.891211 0.453588i \(-0.850144\pi\)
−0.891211 + 0.453588i \(0.850144\pi\)
\(600\) 71.4397 2.91651
\(601\) −15.0550 −0.614105 −0.307053 0.951693i \(-0.599343\pi\)
−0.307053 + 0.951693i \(0.599343\pi\)
\(602\) 46.4929 1.89491
\(603\) 82.8252 3.37290
\(604\) −37.3731 −1.52069
\(605\) 15.8414 0.644045
\(606\) −72.3012 −2.93704
\(607\) 27.2296 1.10522 0.552608 0.833441i \(-0.313633\pi\)
0.552608 + 0.833441i \(0.313633\pi\)
\(608\) 1.19001 0.0482614
\(609\) 38.6234 1.56510
\(610\) 16.9999 0.688305
\(611\) −65.2165 −2.63838
\(612\) 8.61282 0.348153
\(613\) −22.7527 −0.918974 −0.459487 0.888184i \(-0.651967\pi\)
−0.459487 + 0.888184i \(0.651967\pi\)
\(614\) 38.7209 1.56265
\(615\) −5.85915 −0.236264
\(616\) 62.9470 2.53621
\(617\) −37.5318 −1.51098 −0.755488 0.655163i \(-0.772600\pi\)
−0.755488 + 0.655163i \(0.772600\pi\)
\(618\) 109.686 4.41222
\(619\) 17.0447 0.685083 0.342541 0.939503i \(-0.388712\pi\)
0.342541 + 0.939503i \(0.388712\pi\)
\(620\) 23.8944 0.959623
\(621\) 155.335 6.23339
\(622\) 12.2975 0.493086
\(623\) 14.9913 0.600614
\(624\) −65.4249 −2.61909
\(625\) 17.9277 0.717109
\(626\) 16.6977 0.667376
\(627\) −35.7391 −1.42728
\(628\) 91.6765 3.65829
\(629\) 1.28146 0.0510953
\(630\) −32.5879 −1.29833
\(631\) 25.9830 1.03437 0.517184 0.855874i \(-0.326980\pi\)
0.517184 + 0.855874i \(0.326980\pi\)
\(632\) 21.6675 0.861885
\(633\) −2.58528 −0.102756
\(634\) 29.6505 1.17757
\(635\) −9.49853 −0.376938
\(636\) −41.2255 −1.63470
\(637\) 9.13362 0.361887
\(638\) 70.4343 2.78852
\(639\) 30.2278 1.19579
\(640\) 14.0172 0.554077
\(641\) −41.2948 −1.63105 −0.815524 0.578724i \(-0.803551\pi\)
−0.815524 + 0.578724i \(0.803551\pi\)
\(642\) −37.0450 −1.46205
\(643\) −7.98273 −0.314808 −0.157404 0.987534i \(-0.550312\pi\)
−0.157404 + 0.987534i \(0.550312\pi\)
\(644\) 78.6895 3.10080
\(645\) −19.4530 −0.765960
\(646\) −1.17397 −0.0461891
\(647\) 25.0426 0.984527 0.492263 0.870446i \(-0.336170\pi\)
0.492263 + 0.870446i \(0.336170\pi\)
\(648\) −165.757 −6.51155
\(649\) −47.2848 −1.85609
\(650\) −59.4212 −2.33069
\(651\) 67.4846 2.64493
\(652\) −11.3303 −0.443729
\(653\) 11.1259 0.435390 0.217695 0.976017i \(-0.430146\pi\)
0.217695 + 0.976017i \(0.430146\pi\)
\(654\) −158.272 −6.18892
\(655\) 13.4023 0.523673
\(656\) −8.97494 −0.350413
\(657\) 55.8221 2.17783
\(658\) −67.7065 −2.63947
\(659\) −21.4361 −0.835032 −0.417516 0.908670i \(-0.637099\pi\)
−0.417516 + 0.908670i \(0.637099\pi\)
\(660\) −53.6005 −2.08640
\(661\) 15.4402 0.600555 0.300277 0.953852i \(-0.402921\pi\)
0.300277 + 0.953852i \(0.402921\pi\)
\(662\) 33.5662 1.30459
\(663\) −4.78978 −0.186020
\(664\) 16.3093 0.632924
\(665\) 2.94430 0.114175
\(666\) −98.5694 −3.81948
\(667\) 43.2645 1.67521
\(668\) −32.1650 −1.24450
\(669\) −81.8609 −3.16493
\(670\) −16.9316 −0.654124
\(671\) 58.0369 2.24049
\(672\) 5.04062 0.194446
\(673\) −27.6330 −1.06517 −0.532587 0.846375i \(-0.678780\pi\)
−0.532587 + 0.846375i \(0.678780\pi\)
\(674\) −2.46299 −0.0948707
\(675\) −80.7205 −3.10693
\(676\) 63.8116 2.45429
\(677\) −27.5464 −1.05869 −0.529347 0.848405i \(-0.677563\pi\)
−0.529347 + 0.848405i \(0.677563\pi\)
\(678\) −51.4123 −1.97448
\(679\) −37.7222 −1.44764
\(680\) −0.865140 −0.0331766
\(681\) 76.7524 2.94116
\(682\) 123.066 4.71244
\(683\) 23.7929 0.910409 0.455204 0.890387i \(-0.349566\pi\)
0.455204 + 0.890387i \(0.349566\pi\)
\(684\) 59.8559 2.28865
\(685\) −7.01479 −0.268021
\(686\) 48.7715 1.86211
\(687\) 93.3613 3.56196
\(688\) −29.7977 −1.13603
\(689\) 16.8490 0.641895
\(690\) −49.6707 −1.89093
\(691\) 45.9747 1.74896 0.874479 0.485063i \(-0.161203\pi\)
0.874479 + 0.485063i \(0.161203\pi\)
\(692\) 4.00660 0.152308
\(693\) −111.254 −4.22618
\(694\) 17.2906 0.656342
\(695\) −6.99174 −0.265212
\(696\) −78.8708 −2.98959
\(697\) −0.657059 −0.0248879
\(698\) −75.5861 −2.86098
\(699\) 41.2998 1.56210
\(700\) −40.8913 −1.54555
\(701\) 4.66394 0.176154 0.0880772 0.996114i \(-0.471928\pi\)
0.0880772 + 0.996114i \(0.471928\pi\)
\(702\) 235.535 8.88970
\(703\) 8.90571 0.335885
\(704\) 50.9531 1.92037
\(705\) 28.3289 1.06693
\(706\) 33.7211 1.26911
\(707\) 20.3349 0.764774
\(708\) 107.757 4.04977
\(709\) −19.1799 −0.720315 −0.360157 0.932892i \(-0.617277\pi\)
−0.360157 + 0.932892i \(0.617277\pi\)
\(710\) −6.17933 −0.231906
\(711\) −38.2954 −1.43619
\(712\) −30.6129 −1.14727
\(713\) 75.5938 2.83101
\(714\) −4.97265 −0.186097
\(715\) 21.9067 0.819263
\(716\) −58.1118 −2.17174
\(717\) −71.8414 −2.68297
\(718\) −24.1832 −0.902511
\(719\) 5.19867 0.193878 0.0969389 0.995290i \(-0.469095\pi\)
0.0969389 + 0.995290i \(0.469095\pi\)
\(720\) 20.8859 0.778371
\(721\) −30.8495 −1.14890
\(722\) 38.1176 1.41859
\(723\) 3.79218 0.141033
\(724\) 95.9779 3.56699
\(725\) −22.4826 −0.834982
\(726\) −185.935 −6.90070
\(727\) −24.7358 −0.917398 −0.458699 0.888592i \(-0.651684\pi\)
−0.458699 + 0.888592i \(0.651684\pi\)
\(728\) 58.6285 2.17292
\(729\) 112.436 4.16430
\(730\) −11.4115 −0.422357
\(731\) −2.18150 −0.0806858
\(732\) −132.260 −4.88849
\(733\) −5.67125 −0.209473 −0.104736 0.994500i \(-0.533400\pi\)
−0.104736 + 0.994500i \(0.533400\pi\)
\(734\) 5.04157 0.186088
\(735\) −3.96749 −0.146343
\(736\) 5.64632 0.208126
\(737\) −57.8037 −2.12923
\(738\) 50.5405 1.86042
\(739\) 29.6650 1.09125 0.545623 0.838031i \(-0.316293\pi\)
0.545623 + 0.838031i \(0.316293\pi\)
\(740\) 13.3565 0.490995
\(741\) −33.2872 −1.22284
\(742\) 17.4923 0.642162
\(743\) −44.9300 −1.64832 −0.824160 0.566357i \(-0.808352\pi\)
−0.824160 + 0.566357i \(0.808352\pi\)
\(744\) −137.807 −5.05224
\(745\) −0.866779 −0.0317563
\(746\) −23.4434 −0.858324
\(747\) −28.8254 −1.05466
\(748\) −6.01089 −0.219780
\(749\) 10.4190 0.380702
\(750\) 54.4104 1.98679
\(751\) 41.3512 1.50893 0.754463 0.656343i \(-0.227898\pi\)
0.754463 + 0.656343i \(0.227898\pi\)
\(752\) 43.3938 1.58241
\(753\) −41.6325 −1.51717
\(754\) 65.6021 2.38909
\(755\) −6.63497 −0.241471
\(756\) 162.086 5.89500
\(757\) −52.3079 −1.90116 −0.950581 0.310475i \(-0.899512\pi\)
−0.950581 + 0.310475i \(0.899512\pi\)
\(758\) −12.1290 −0.440546
\(759\) −169.574 −6.15513
\(760\) −6.01241 −0.218093
\(761\) 7.44041 0.269715 0.134857 0.990865i \(-0.456942\pi\)
0.134857 + 0.990865i \(0.456942\pi\)
\(762\) 111.487 4.03875
\(763\) 44.5144 1.61153
\(764\) 21.5034 0.777964
\(765\) 1.52906 0.0552834
\(766\) −66.0933 −2.38805
\(767\) −44.0408 −1.59022
\(768\) −105.462 −3.80554
\(769\) −10.4939 −0.378420 −0.189210 0.981937i \(-0.560593\pi\)
−0.189210 + 0.981937i \(0.560593\pi\)
\(770\) 22.7431 0.819604
\(771\) 6.55570 0.236098
\(772\) 21.6601 0.779563
\(773\) −39.6059 −1.42453 −0.712263 0.701913i \(-0.752330\pi\)
−0.712263 + 0.701913i \(0.752330\pi\)
\(774\) 167.800 6.03144
\(775\) −39.2826 −1.41107
\(776\) 77.0304 2.76523
\(777\) 37.7226 1.35329
\(778\) 22.9421 0.822516
\(779\) −4.56632 −0.163605
\(780\) −49.9232 −1.78754
\(781\) −21.0960 −0.754873
\(782\) −5.57019 −0.199190
\(783\) 89.1169 3.18478
\(784\) −6.07733 −0.217047
\(785\) 16.2757 0.580903
\(786\) −157.307 −5.61096
\(787\) −25.3454 −0.903466 −0.451733 0.892153i \(-0.649194\pi\)
−0.451733 + 0.892153i \(0.649194\pi\)
\(788\) 34.6312 1.23368
\(789\) 74.5123 2.65271
\(790\) 7.82856 0.278528
\(791\) 14.4599 0.514134
\(792\) 227.185 8.07267
\(793\) 54.0552 1.91956
\(794\) 19.5315 0.693149
\(795\) −7.31891 −0.259575
\(796\) −17.9808 −0.637311
\(797\) 11.5777 0.410105 0.205052 0.978751i \(-0.434264\pi\)
0.205052 + 0.978751i \(0.434264\pi\)
\(798\) −34.5581 −1.22334
\(799\) 3.17687 0.112390
\(800\) −2.93413 −0.103737
\(801\) 54.1058 1.91174
\(802\) −28.9185 −1.02115
\(803\) −38.9583 −1.37481
\(804\) 131.729 4.64572
\(805\) 13.9700 0.492379
\(806\) 114.623 4.03742
\(807\) −59.7571 −2.10355
\(808\) −41.5249 −1.46084
\(809\) −2.92118 −0.102703 −0.0513516 0.998681i \(-0.516353\pi\)
−0.0513516 + 0.998681i \(0.516353\pi\)
\(810\) −59.8889 −2.10428
\(811\) 14.6169 0.513270 0.256635 0.966508i \(-0.417386\pi\)
0.256635 + 0.966508i \(0.417386\pi\)
\(812\) 45.1447 1.58427
\(813\) 4.57201 0.160348
\(814\) 68.7915 2.41114
\(815\) −2.01151 −0.0704601
\(816\) 3.18702 0.111568
\(817\) −15.1606 −0.530404
\(818\) 1.31077 0.0458299
\(819\) −103.621 −3.62081
\(820\) −6.84843 −0.239158
\(821\) −11.6140 −0.405330 −0.202665 0.979248i \(-0.564960\pi\)
−0.202665 + 0.979248i \(0.564960\pi\)
\(822\) 82.3345 2.87175
\(823\) −27.8542 −0.970935 −0.485468 0.874255i \(-0.661351\pi\)
−0.485468 + 0.874255i \(0.661351\pi\)
\(824\) 62.9961 2.19457
\(825\) 88.1195 3.06793
\(826\) −45.7223 −1.59088
\(827\) 33.9391 1.18018 0.590089 0.807339i \(-0.299093\pi\)
0.590089 + 0.807339i \(0.299093\pi\)
\(828\) 284.002 9.86976
\(829\) 2.11439 0.0734357 0.0367178 0.999326i \(-0.488310\pi\)
0.0367178 + 0.999326i \(0.488310\pi\)
\(830\) 5.89264 0.204536
\(831\) 50.3966 1.74824
\(832\) 47.4574 1.64529
\(833\) −0.444923 −0.0154157
\(834\) 82.0641 2.84165
\(835\) −5.71036 −0.197615
\(836\) −41.7735 −1.44477
\(837\) 155.709 5.38210
\(838\) 45.2767 1.56406
\(839\) −51.5577 −1.77997 −0.889985 0.455990i \(-0.849285\pi\)
−0.889985 + 0.455990i \(0.849285\pi\)
\(840\) −25.4672 −0.878702
\(841\) −4.17884 −0.144098
\(842\) −21.4600 −0.739561
\(843\) −53.4436 −1.84070
\(844\) −3.02179 −0.104014
\(845\) 11.3287 0.389719
\(846\) −244.363 −8.40137
\(847\) 52.2948 1.79687
\(848\) −11.2110 −0.384986
\(849\) 36.4191 1.24990
\(850\) 2.89457 0.0992829
\(851\) 42.2555 1.44850
\(852\) 48.0757 1.64705
\(853\) −55.9086 −1.91427 −0.957136 0.289637i \(-0.906465\pi\)
−0.957136 + 0.289637i \(0.906465\pi\)
\(854\) 56.1191 1.92036
\(855\) 10.6264 0.363416
\(856\) −21.2761 −0.727202
\(857\) 13.6102 0.464916 0.232458 0.972606i \(-0.425323\pi\)
0.232458 + 0.972606i \(0.425323\pi\)
\(858\) −257.125 −8.77810
\(859\) 34.3481 1.17194 0.585971 0.810332i \(-0.300713\pi\)
0.585971 + 0.810332i \(0.300713\pi\)
\(860\) −22.7375 −0.775342
\(861\) −19.3419 −0.659170
\(862\) −45.5282 −1.55070
\(863\) −3.33437 −0.113503 −0.0567517 0.998388i \(-0.518074\pi\)
−0.0567517 + 0.998388i \(0.518074\pi\)
\(864\) 11.6304 0.395674
\(865\) 0.711306 0.0241851
\(866\) 79.2072 2.69157
\(867\) −56.9564 −1.93434
\(868\) 78.8790 2.67733
\(869\) 26.7264 0.906631
\(870\) −28.4964 −0.966119
\(871\) −53.8380 −1.82423
\(872\) −90.9005 −3.07828
\(873\) −136.145 −4.60781
\(874\) −38.7108 −1.30941
\(875\) −15.3031 −0.517339
\(876\) 88.7821 2.99967
\(877\) 2.11186 0.0713126 0.0356563 0.999364i \(-0.488648\pi\)
0.0356563 + 0.999364i \(0.488648\pi\)
\(878\) 95.8422 3.23452
\(879\) 18.0118 0.607524
\(880\) −14.5763 −0.491366
\(881\) −30.0894 −1.01374 −0.506869 0.862023i \(-0.669197\pi\)
−0.506869 + 0.862023i \(0.669197\pi\)
\(882\) 34.2232 1.15236
\(883\) −29.6099 −0.996451 −0.498226 0.867047i \(-0.666015\pi\)
−0.498226 + 0.867047i \(0.666015\pi\)
\(884\) −5.59850 −0.188298
\(885\) 19.1305 0.643066
\(886\) 35.5745 1.19515
\(887\) 0.0254004 0.000852862 0 0.000426431 1.00000i \(-0.499864\pi\)
0.000426431 1.00000i \(0.499864\pi\)
\(888\) −77.0312 −2.58500
\(889\) −31.3560 −1.05165
\(890\) −11.0606 −0.370753
\(891\) −204.458 −6.84960
\(892\) −95.6827 −3.20369
\(893\) 22.0781 0.738815
\(894\) 10.1736 0.340257
\(895\) −10.3168 −0.344852
\(896\) 46.2727 1.54586
\(897\) −157.940 −5.27346
\(898\) −96.4349 −3.21807
\(899\) 43.3687 1.44643
\(900\) −147.583 −4.91943
\(901\) −0.820760 −0.0273435
\(902\) −35.2722 −1.17444
\(903\) −64.2171 −2.13701
\(904\) −29.5277 −0.982077
\(905\) 17.0393 0.566405
\(906\) 77.8766 2.58728
\(907\) 7.77114 0.258036 0.129018 0.991642i \(-0.458817\pi\)
0.129018 + 0.991642i \(0.458817\pi\)
\(908\) 89.7116 2.97719
\(909\) 73.3918 2.43425
\(910\) 21.1828 0.702202
\(911\) −18.2150 −0.603490 −0.301745 0.953389i \(-0.597569\pi\)
−0.301745 + 0.953389i \(0.597569\pi\)
\(912\) 22.1486 0.733415
\(913\) 20.1172 0.665783
\(914\) −65.8688 −2.17875
\(915\) −23.4807 −0.776247
\(916\) 109.125 3.60559
\(917\) 44.2431 1.46104
\(918\) −11.4736 −0.378684
\(919\) −40.2448 −1.32755 −0.663777 0.747930i \(-0.731048\pi\)
−0.663777 + 0.747930i \(0.731048\pi\)
\(920\) −28.5274 −0.940522
\(921\) −53.4823 −1.76230
\(922\) 20.8617 0.687045
\(923\) −19.6487 −0.646744
\(924\) −176.943 −5.82100
\(925\) −21.9582 −0.721981
\(926\) 71.2151 2.34027
\(927\) −111.340 −3.65690
\(928\) 3.23934 0.106336
\(929\) 17.9221 0.588005 0.294003 0.955805i \(-0.405013\pi\)
0.294003 + 0.955805i \(0.405013\pi\)
\(930\) −49.7903 −1.63269
\(931\) −3.09206 −0.101338
\(932\) 48.2730 1.58123
\(933\) −16.9857 −0.556086
\(934\) −7.83935 −0.256512
\(935\) −1.06713 −0.0348990
\(936\) 211.599 6.91633
\(937\) 1.94084 0.0634046 0.0317023 0.999497i \(-0.489907\pi\)
0.0317023 + 0.999497i \(0.489907\pi\)
\(938\) −55.8936 −1.82499
\(939\) −23.0633 −0.752643
\(940\) 33.1121 1.08000
\(941\) −43.9923 −1.43411 −0.717054 0.697017i \(-0.754510\pi\)
−0.717054 + 0.697017i \(0.754510\pi\)
\(942\) −191.032 −6.22416
\(943\) −21.6661 −0.705545
\(944\) 29.3038 0.953759
\(945\) 28.7757 0.936073
\(946\) −117.107 −3.80749
\(947\) 33.3161 1.08263 0.541313 0.840821i \(-0.317927\pi\)
0.541313 + 0.840821i \(0.317927\pi\)
\(948\) −60.9068 −1.97816
\(949\) −36.2855 −1.17788
\(950\) 20.1162 0.652655
\(951\) −40.9540 −1.32803
\(952\) −2.85595 −0.0925620
\(953\) 9.51135 0.308103 0.154051 0.988063i \(-0.450768\pi\)
0.154051 + 0.988063i \(0.450768\pi\)
\(954\) 63.1323 2.04398
\(955\) 3.81757 0.123534
\(956\) −83.9714 −2.71583
\(957\) −97.2856 −3.14480
\(958\) −0.0269706 −0.000871380 0
\(959\) −23.1568 −0.747773
\(960\) −20.6147 −0.665337
\(961\) 44.7758 1.44438
\(962\) 64.0721 2.06577
\(963\) 37.6037 1.21176
\(964\) 4.43247 0.142760
\(965\) 3.84539 0.123787
\(966\) −163.970 −5.27565
\(967\) −17.8383 −0.573642 −0.286821 0.957984i \(-0.592598\pi\)
−0.286821 + 0.957984i \(0.592598\pi\)
\(968\) −106.788 −3.43231
\(969\) 1.62151 0.0520904
\(970\) 27.8315 0.893615
\(971\) −3.32060 −0.106563 −0.0532815 0.998580i \(-0.516968\pi\)
−0.0532815 + 0.998580i \(0.516968\pi\)
\(972\) 254.934 8.17700
\(973\) −23.0808 −0.739935
\(974\) −36.7050 −1.17610
\(975\) 82.0740 2.62847
\(976\) −35.9673 −1.15128
\(977\) −5.05406 −0.161694 −0.0808468 0.996727i \(-0.525762\pi\)
−0.0808468 + 0.996727i \(0.525762\pi\)
\(978\) 23.6097 0.754954
\(979\) −37.7605 −1.20683
\(980\) −4.63737 −0.148135
\(981\) 160.659 5.12945
\(982\) −0.253039 −0.00807480
\(983\) 13.2633 0.423033 0.211517 0.977374i \(-0.432160\pi\)
0.211517 + 0.977374i \(0.432160\pi\)
\(984\) 39.4971 1.25912
\(985\) 6.14819 0.195898
\(986\) −3.19566 −0.101770
\(987\) 93.5179 2.97671
\(988\) −38.9076 −1.23781
\(989\) −71.9337 −2.28736
\(990\) 82.0832 2.60878
\(991\) −24.0399 −0.763654 −0.381827 0.924234i \(-0.624705\pi\)
−0.381827 + 0.924234i \(0.624705\pi\)
\(992\) 5.65992 0.179703
\(993\) −46.3625 −1.47127
\(994\) −20.3989 −0.647013
\(995\) −3.19219 −0.101199
\(996\) −45.8452 −1.45266
\(997\) 34.6612 1.09773 0.548865 0.835911i \(-0.315060\pi\)
0.548865 + 0.835911i \(0.315060\pi\)
\(998\) 39.0508 1.23613
\(999\) 87.0384 2.75377
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 \(a_p\))