Properties

Label 4017.2.a.j.1.20
Level 4017
Weight 2
Character 4017.1
Self dual Yes
Analytic conductor 32.076
Analytic rank 0
Dimension 25
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 4017 = 3 \cdot 13 \cdot 103 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4017.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0759064919\)
Analytic rank: \(0\)
Dimension: \(25\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.20
Character \(\chi\) = 4017.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.02058 q^{2} -1.00000 q^{3} +2.08276 q^{4} +4.24376 q^{5} -2.02058 q^{6} -1.21618 q^{7} +0.167219 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+2.02058 q^{2} -1.00000 q^{3} +2.08276 q^{4} +4.24376 q^{5} -2.02058 q^{6} -1.21618 q^{7} +0.167219 q^{8} +1.00000 q^{9} +8.57486 q^{10} +4.05959 q^{11} -2.08276 q^{12} +1.00000 q^{13} -2.45739 q^{14} -4.24376 q^{15} -3.82764 q^{16} -3.43411 q^{17} +2.02058 q^{18} +1.65923 q^{19} +8.83871 q^{20} +1.21618 q^{21} +8.20275 q^{22} +0.620280 q^{23} -0.167219 q^{24} +13.0095 q^{25} +2.02058 q^{26} -1.00000 q^{27} -2.53300 q^{28} +7.32374 q^{29} -8.57486 q^{30} +3.81277 q^{31} -8.06850 q^{32} -4.05959 q^{33} -6.93892 q^{34} -5.16116 q^{35} +2.08276 q^{36} -10.7807 q^{37} +3.35262 q^{38} -1.00000 q^{39} +0.709635 q^{40} -1.65147 q^{41} +2.45739 q^{42} +9.74803 q^{43} +8.45515 q^{44} +4.24376 q^{45} +1.25333 q^{46} +9.90352 q^{47} +3.82764 q^{48} -5.52091 q^{49} +26.2867 q^{50} +3.43411 q^{51} +2.08276 q^{52} +13.2309 q^{53} -2.02058 q^{54} +17.2279 q^{55} -0.203368 q^{56} -1.65923 q^{57} +14.7982 q^{58} -7.24509 q^{59} -8.83871 q^{60} -5.43492 q^{61} +7.70403 q^{62} -1.21618 q^{63} -8.64780 q^{64} +4.24376 q^{65} -8.20275 q^{66} +0.936251 q^{67} -7.15243 q^{68} -0.620280 q^{69} -10.4286 q^{70} +2.07572 q^{71} +0.167219 q^{72} -4.79664 q^{73} -21.7833 q^{74} -13.0095 q^{75} +3.45578 q^{76} -4.93718 q^{77} -2.02058 q^{78} -5.55775 q^{79} -16.2435 q^{80} +1.00000 q^{81} -3.33693 q^{82} +6.01550 q^{83} +2.53300 q^{84} -14.5735 q^{85} +19.6967 q^{86} -7.32374 q^{87} +0.678840 q^{88} -3.23079 q^{89} +8.57486 q^{90} -1.21618 q^{91} +1.29189 q^{92} -3.81277 q^{93} +20.0109 q^{94} +7.04138 q^{95} +8.06850 q^{96} +17.3203 q^{97} -11.1555 q^{98} +4.05959 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 25q + 6q^{2} - 25q^{3} + 28q^{4} + 7q^{5} - 6q^{6} + 17q^{7} + 21q^{8} + 25q^{9} + O(q^{10}) \) \( 25q + 6q^{2} - 25q^{3} + 28q^{4} + 7q^{5} - 6q^{6} + 17q^{7} + 21q^{8} + 25q^{9} - 6q^{10} + 21q^{11} - 28q^{12} + 25q^{13} + 10q^{14} - 7q^{15} + 30q^{16} + 14q^{17} + 6q^{18} + 12q^{19} + 24q^{20} - 17q^{21} + 3q^{22} + 41q^{23} - 21q^{24} + 30q^{25} + 6q^{26} - 25q^{27} + 14q^{28} + 22q^{29} + 6q^{30} + 14q^{31} + 28q^{32} - 21q^{33} - 11q^{34} + 14q^{35} + 28q^{36} - 6q^{37} + 16q^{38} - 25q^{39} - 34q^{40} + 33q^{41} - 10q^{42} + 35q^{43} + 45q^{44} + 7q^{45} + 3q^{46} + 48q^{47} - 30q^{48} - 4q^{49} + 7q^{50} - 14q^{51} + 28q^{52} + 18q^{53} - 6q^{54} + 10q^{55} + 32q^{56} - 12q^{57} + 33q^{58} + 46q^{59} - 24q^{60} - 19q^{61} + 5q^{62} + 17q^{63} + 29q^{64} + 7q^{65} - 3q^{66} + 16q^{67} + 20q^{68} - 41q^{69} - 43q^{70} + 60q^{71} + 21q^{72} - 14q^{73} - 50q^{74} - 30q^{75} + 59q^{77} - 6q^{78} + 7q^{79} + 32q^{80} + 25q^{81} + 18q^{82} + 23q^{83} - 14q^{84} - 9q^{85} - 9q^{86} - 22q^{87} + 23q^{88} + 10q^{89} - 6q^{90} + 17q^{91} + 69q^{92} - 14q^{93} - 30q^{94} + 81q^{95} - 28q^{96} - 10q^{97} + 55q^{98} + 21q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.02058 1.42877 0.714384 0.699754i \(-0.246707\pi\)
0.714384 + 0.699754i \(0.246707\pi\)
\(3\) −1.00000 −0.577350
\(4\) 2.08276 1.04138
\(5\) 4.24376 1.89787 0.948933 0.315479i \(-0.102165\pi\)
0.948933 + 0.315479i \(0.102165\pi\)
\(6\) −2.02058 −0.824900
\(7\) −1.21618 −0.459672 −0.229836 0.973229i \(-0.573819\pi\)
−0.229836 + 0.973229i \(0.573819\pi\)
\(8\) 0.167219 0.0591208
\(9\) 1.00000 0.333333
\(10\) 8.57486 2.71161
\(11\) 4.05959 1.22401 0.612007 0.790853i \(-0.290363\pi\)
0.612007 + 0.790853i \(0.290363\pi\)
\(12\) −2.08276 −0.601240
\(13\) 1.00000 0.277350
\(14\) −2.45739 −0.656764
\(15\) −4.24376 −1.09573
\(16\) −3.82764 −0.956909
\(17\) −3.43411 −0.832895 −0.416448 0.909160i \(-0.636725\pi\)
−0.416448 + 0.909160i \(0.636725\pi\)
\(18\) 2.02058 0.476256
\(19\) 1.65923 0.380654 0.190327 0.981721i \(-0.439045\pi\)
0.190327 + 0.981721i \(0.439045\pi\)
\(20\) 8.83871 1.97640
\(21\) 1.21618 0.265392
\(22\) 8.20275 1.74883
\(23\) 0.620280 0.129337 0.0646686 0.997907i \(-0.479401\pi\)
0.0646686 + 0.997907i \(0.479401\pi\)
\(24\) −0.167219 −0.0341334
\(25\) 13.0095 2.60189
\(26\) 2.02058 0.396269
\(27\) −1.00000 −0.192450
\(28\) −2.53300 −0.478692
\(29\) 7.32374 1.35998 0.679992 0.733220i \(-0.261983\pi\)
0.679992 + 0.733220i \(0.261983\pi\)
\(30\) −8.57486 −1.56555
\(31\) 3.81277 0.684795 0.342397 0.939555i \(-0.388761\pi\)
0.342397 + 0.939555i \(0.388761\pi\)
\(32\) −8.06850 −1.42632
\(33\) −4.05959 −0.706685
\(34\) −6.93892 −1.19001
\(35\) −5.16116 −0.872395
\(36\) 2.08276 0.347126
\(37\) −10.7807 −1.77233 −0.886166 0.463368i \(-0.846641\pi\)
−0.886166 + 0.463368i \(0.846641\pi\)
\(38\) 3.35262 0.543867
\(39\) −1.00000 −0.160128
\(40\) 0.709635 0.112203
\(41\) −1.65147 −0.257916 −0.128958 0.991650i \(-0.541163\pi\)
−0.128958 + 0.991650i \(0.541163\pi\)
\(42\) 2.45739 0.379183
\(43\) 9.74803 1.48656 0.743280 0.668980i \(-0.233269\pi\)
0.743280 + 0.668980i \(0.233269\pi\)
\(44\) 8.45515 1.27466
\(45\) 4.24376 0.632622
\(46\) 1.25333 0.184793
\(47\) 9.90352 1.44458 0.722289 0.691592i \(-0.243090\pi\)
0.722289 + 0.691592i \(0.243090\pi\)
\(48\) 3.82764 0.552472
\(49\) −5.52091 −0.788702
\(50\) 26.2867 3.71750
\(51\) 3.43411 0.480872
\(52\) 2.08276 0.288827
\(53\) 13.2309 1.81740 0.908699 0.417452i \(-0.137077\pi\)
0.908699 + 0.417452i \(0.137077\pi\)
\(54\) −2.02058 −0.274967
\(55\) 17.2279 2.32301
\(56\) −0.203368 −0.0271761
\(57\) −1.65923 −0.219771
\(58\) 14.7982 1.94310
\(59\) −7.24509 −0.943230 −0.471615 0.881805i \(-0.656329\pi\)
−0.471615 + 0.881805i \(0.656329\pi\)
\(60\) −8.83871 −1.14107
\(61\) −5.43492 −0.695870 −0.347935 0.937519i \(-0.613117\pi\)
−0.347935 + 0.937519i \(0.613117\pi\)
\(62\) 7.70403 0.978413
\(63\) −1.21618 −0.153224
\(64\) −8.64780 −1.08097
\(65\) 4.24376 0.526373
\(66\) −8.20275 −1.00969
\(67\) 0.936251 0.114381 0.0571906 0.998363i \(-0.481786\pi\)
0.0571906 + 0.998363i \(0.481786\pi\)
\(68\) −7.15243 −0.867359
\(69\) −0.620280 −0.0746729
\(70\) −10.4286 −1.24645
\(71\) 2.07572 0.246342 0.123171 0.992385i \(-0.460694\pi\)
0.123171 + 0.992385i \(0.460694\pi\)
\(72\) 0.167219 0.0197069
\(73\) −4.79664 −0.561404 −0.280702 0.959795i \(-0.590567\pi\)
−0.280702 + 0.959795i \(0.590567\pi\)
\(74\) −21.7833 −2.53225
\(75\) −13.0095 −1.50220
\(76\) 3.45578 0.396405
\(77\) −4.93718 −0.562644
\(78\) −2.02058 −0.228786
\(79\) −5.55775 −0.625295 −0.312648 0.949869i \(-0.601216\pi\)
−0.312648 + 0.949869i \(0.601216\pi\)
\(80\) −16.2435 −1.81608
\(81\) 1.00000 0.111111
\(82\) −3.33693 −0.368502
\(83\) 6.01550 0.660287 0.330143 0.943931i \(-0.392903\pi\)
0.330143 + 0.943931i \(0.392903\pi\)
\(84\) 2.53300 0.276373
\(85\) −14.5735 −1.58072
\(86\) 19.6967 2.12395
\(87\) −7.32374 −0.785187
\(88\) 0.678840 0.0723646
\(89\) −3.23079 −0.342463 −0.171232 0.985231i \(-0.554775\pi\)
−0.171232 + 0.985231i \(0.554775\pi\)
\(90\) 8.57486 0.903870
\(91\) −1.21618 −0.127490
\(92\) 1.29189 0.134689
\(93\) −3.81277 −0.395366
\(94\) 20.0109 2.06397
\(95\) 7.04138 0.722430
\(96\) 8.06850 0.823487
\(97\) 17.3203 1.75861 0.879307 0.476255i \(-0.158006\pi\)
0.879307 + 0.476255i \(0.158006\pi\)
\(98\) −11.1555 −1.12687
\(99\) 4.05959 0.408004
\(100\) 27.0956 2.70956
\(101\) −15.8533 −1.57746 −0.788732 0.614738i \(-0.789262\pi\)
−0.788732 + 0.614738i \(0.789262\pi\)
\(102\) 6.93892 0.687055
\(103\) −1.00000 −0.0985329
\(104\) 0.167219 0.0163971
\(105\) 5.16116 0.503677
\(106\) 26.7341 2.59664
\(107\) 0.437524 0.0422971 0.0211485 0.999776i \(-0.493268\pi\)
0.0211485 + 0.999776i \(0.493268\pi\)
\(108\) −2.08276 −0.200413
\(109\) 14.3428 1.37379 0.686895 0.726757i \(-0.258973\pi\)
0.686895 + 0.726757i \(0.258973\pi\)
\(110\) 34.8105 3.31905
\(111\) 10.7807 1.02326
\(112\) 4.65508 0.439864
\(113\) −18.7081 −1.75991 −0.879957 0.475054i \(-0.842429\pi\)
−0.879957 + 0.475054i \(0.842429\pi\)
\(114\) −3.35262 −0.314002
\(115\) 2.63232 0.245465
\(116\) 15.2536 1.41626
\(117\) 1.00000 0.0924500
\(118\) −14.6393 −1.34766
\(119\) 4.17649 0.382858
\(120\) −0.709635 −0.0647806
\(121\) 5.48030 0.498209
\(122\) −10.9817 −0.994238
\(123\) 1.65147 0.148908
\(124\) 7.94109 0.713131
\(125\) 33.9902 3.04017
\(126\) −2.45739 −0.218921
\(127\) 10.8923 0.966531 0.483266 0.875474i \(-0.339451\pi\)
0.483266 + 0.875474i \(0.339451\pi\)
\(128\) −1.33660 −0.118140
\(129\) −9.74803 −0.858266
\(130\) 8.57486 0.752065
\(131\) −6.92135 −0.604721 −0.302360 0.953194i \(-0.597775\pi\)
−0.302360 + 0.953194i \(0.597775\pi\)
\(132\) −8.45515 −0.735926
\(133\) −2.01792 −0.174976
\(134\) 1.89177 0.163424
\(135\) −4.24376 −0.365244
\(136\) −0.574248 −0.0492414
\(137\) −5.63515 −0.481443 −0.240722 0.970594i \(-0.577384\pi\)
−0.240722 + 0.970594i \(0.577384\pi\)
\(138\) −1.25333 −0.106690
\(139\) 3.33341 0.282737 0.141368 0.989957i \(-0.454850\pi\)
0.141368 + 0.989957i \(0.454850\pi\)
\(140\) −10.7494 −0.908494
\(141\) −9.90352 −0.834027
\(142\) 4.19416 0.351966
\(143\) 4.05959 0.339480
\(144\) −3.82764 −0.318970
\(145\) 31.0801 2.58107
\(146\) −9.69201 −0.802116
\(147\) 5.52091 0.455357
\(148\) −22.4535 −1.84567
\(149\) −7.27603 −0.596076 −0.298038 0.954554i \(-0.596332\pi\)
−0.298038 + 0.954554i \(0.596332\pi\)
\(150\) −26.2867 −2.14630
\(151\) −11.2710 −0.917218 −0.458609 0.888638i \(-0.651652\pi\)
−0.458609 + 0.888638i \(0.651652\pi\)
\(152\) 0.277455 0.0225046
\(153\) −3.43411 −0.277632
\(154\) −9.97599 −0.803889
\(155\) 16.1805 1.29965
\(156\) −2.08276 −0.166754
\(157\) −2.36191 −0.188501 −0.0942504 0.995549i \(-0.530045\pi\)
−0.0942504 + 0.995549i \(0.530045\pi\)
\(158\) −11.2299 −0.893402
\(159\) −13.2309 −1.04928
\(160\) −34.2407 −2.70697
\(161\) −0.754370 −0.0594527
\(162\) 2.02058 0.158752
\(163\) −2.23181 −0.174809 −0.0874045 0.996173i \(-0.527857\pi\)
−0.0874045 + 0.996173i \(0.527857\pi\)
\(164\) −3.43961 −0.268588
\(165\) −17.2279 −1.34119
\(166\) 12.1548 0.943397
\(167\) −12.3389 −0.954812 −0.477406 0.878683i \(-0.658423\pi\)
−0.477406 + 0.878683i \(0.658423\pi\)
\(168\) 0.203368 0.0156902
\(169\) 1.00000 0.0769231
\(170\) −29.4471 −2.25849
\(171\) 1.65923 0.126885
\(172\) 20.3028 1.54807
\(173\) −22.2508 −1.69170 −0.845850 0.533421i \(-0.820906\pi\)
−0.845850 + 0.533421i \(0.820906\pi\)
\(174\) −14.7982 −1.12185
\(175\) −15.8218 −1.19602
\(176\) −15.5386 −1.17127
\(177\) 7.24509 0.544574
\(178\) −6.52809 −0.489301
\(179\) −6.44350 −0.481610 −0.240805 0.970574i \(-0.577411\pi\)
−0.240805 + 0.970574i \(0.577411\pi\)
\(180\) 8.83871 0.658799
\(181\) 11.4170 0.848617 0.424308 0.905518i \(-0.360517\pi\)
0.424308 + 0.905518i \(0.360517\pi\)
\(182\) −2.45739 −0.182154
\(183\) 5.43492 0.401761
\(184\) 0.103722 0.00764652
\(185\) −45.7506 −3.36365
\(186\) −7.70403 −0.564887
\(187\) −13.9411 −1.01947
\(188\) 20.6266 1.50435
\(189\) 1.21618 0.0884639
\(190\) 14.2277 1.03219
\(191\) 15.7818 1.14193 0.570967 0.820973i \(-0.306569\pi\)
0.570967 + 0.820973i \(0.306569\pi\)
\(192\) 8.64780 0.624101
\(193\) 7.09373 0.510618 0.255309 0.966860i \(-0.417823\pi\)
0.255309 + 0.966860i \(0.417823\pi\)
\(194\) 34.9972 2.51265
\(195\) −4.24376 −0.303902
\(196\) −11.4987 −0.821337
\(197\) 16.5534 1.17938 0.589690 0.807630i \(-0.299250\pi\)
0.589690 + 0.807630i \(0.299250\pi\)
\(198\) 8.20275 0.582944
\(199\) 15.6146 1.10689 0.553444 0.832886i \(-0.313313\pi\)
0.553444 + 0.832886i \(0.313313\pi\)
\(200\) 2.17543 0.153826
\(201\) −0.936251 −0.0660380
\(202\) −32.0329 −2.25383
\(203\) −8.90696 −0.625146
\(204\) 7.15243 0.500770
\(205\) −7.00842 −0.489489
\(206\) −2.02058 −0.140781
\(207\) 0.620280 0.0431124
\(208\) −3.82764 −0.265399
\(209\) 6.73581 0.465926
\(210\) 10.4286 0.719638
\(211\) 19.5473 1.34569 0.672847 0.739781i \(-0.265071\pi\)
0.672847 + 0.739781i \(0.265071\pi\)
\(212\) 27.5567 1.89260
\(213\) −2.07572 −0.142226
\(214\) 0.884054 0.0604327
\(215\) 41.3682 2.82129
\(216\) −0.167219 −0.0113778
\(217\) −4.63701 −0.314781
\(218\) 28.9808 1.96283
\(219\) 4.79664 0.324127
\(220\) 35.8816 2.41914
\(221\) −3.43411 −0.231004
\(222\) 21.7833 1.46200
\(223\) −6.75149 −0.452113 −0.226057 0.974114i \(-0.572583\pi\)
−0.226057 + 0.974114i \(0.572583\pi\)
\(224\) 9.81272 0.655640
\(225\) 13.0095 0.867297
\(226\) −37.8014 −2.51451
\(227\) 29.9752 1.98952 0.994762 0.102218i \(-0.0325941\pi\)
0.994762 + 0.102218i \(0.0325941\pi\)
\(228\) −3.45578 −0.228865
\(229\) −25.4484 −1.68168 −0.840840 0.541284i \(-0.817938\pi\)
−0.840840 + 0.541284i \(0.817938\pi\)
\(230\) 5.31881 0.350712
\(231\) 4.93718 0.324843
\(232\) 1.22467 0.0804033
\(233\) −9.37422 −0.614125 −0.307063 0.951689i \(-0.599346\pi\)
−0.307063 + 0.951689i \(0.599346\pi\)
\(234\) 2.02058 0.132090
\(235\) 42.0281 2.74161
\(236\) −15.0898 −0.982260
\(237\) 5.55775 0.361014
\(238\) 8.43895 0.547016
\(239\) −12.4151 −0.803063 −0.401532 0.915845i \(-0.631522\pi\)
−0.401532 + 0.915845i \(0.631522\pi\)
\(240\) 16.2435 1.04852
\(241\) 1.93177 0.124436 0.0622181 0.998063i \(-0.480183\pi\)
0.0622181 + 0.998063i \(0.480183\pi\)
\(242\) 11.0734 0.711825
\(243\) −1.00000 −0.0641500
\(244\) −11.3196 −0.724665
\(245\) −23.4294 −1.49685
\(246\) 3.33693 0.212755
\(247\) 1.65923 0.105574
\(248\) 0.637567 0.0404856
\(249\) −6.01550 −0.381217
\(250\) 68.6800 4.34370
\(251\) −1.98886 −0.125536 −0.0627679 0.998028i \(-0.519993\pi\)
−0.0627679 + 0.998028i \(0.519993\pi\)
\(252\) −2.53300 −0.159564
\(253\) 2.51808 0.158311
\(254\) 22.0087 1.38095
\(255\) 14.5735 0.912631
\(256\) 14.5949 0.912179
\(257\) −18.0229 −1.12423 −0.562117 0.827057i \(-0.690013\pi\)
−0.562117 + 0.827057i \(0.690013\pi\)
\(258\) −19.6967 −1.22626
\(259\) 13.1112 0.814691
\(260\) 8.83871 0.548154
\(261\) 7.32374 0.453328
\(262\) −13.9852 −0.864006
\(263\) −19.2621 −1.18775 −0.593876 0.804556i \(-0.702403\pi\)
−0.593876 + 0.804556i \(0.702403\pi\)
\(264\) −0.678840 −0.0417797
\(265\) 56.1485 3.44918
\(266\) −4.07738 −0.250000
\(267\) 3.23079 0.197721
\(268\) 1.94998 0.119114
\(269\) −24.8531 −1.51532 −0.757662 0.652648i \(-0.773658\pi\)
−0.757662 + 0.652648i \(0.773658\pi\)
\(270\) −8.57486 −0.521849
\(271\) −11.1960 −0.680109 −0.340054 0.940406i \(-0.610445\pi\)
−0.340054 + 0.940406i \(0.610445\pi\)
\(272\) 13.1445 0.797005
\(273\) 1.21618 0.0736064
\(274\) −11.3863 −0.687871
\(275\) 52.8131 3.18475
\(276\) −1.29189 −0.0777628
\(277\) −23.7805 −1.42883 −0.714417 0.699720i \(-0.753308\pi\)
−0.714417 + 0.699720i \(0.753308\pi\)
\(278\) 6.73544 0.403965
\(279\) 3.81277 0.228265
\(280\) −0.863042 −0.0515767
\(281\) −9.04387 −0.539512 −0.269756 0.962929i \(-0.586943\pi\)
−0.269756 + 0.962929i \(0.586943\pi\)
\(282\) −20.0109 −1.19163
\(283\) 19.8620 1.18068 0.590338 0.807156i \(-0.298995\pi\)
0.590338 + 0.807156i \(0.298995\pi\)
\(284\) 4.32322 0.256536
\(285\) −7.04138 −0.417095
\(286\) 8.20275 0.485039
\(287\) 2.00848 0.118557
\(288\) −8.06850 −0.475441
\(289\) −5.20686 −0.306286
\(290\) 62.8000 3.68774
\(291\) −17.3203 −1.01534
\(292\) −9.99024 −0.584634
\(293\) 17.2871 1.00992 0.504962 0.863141i \(-0.331506\pi\)
0.504962 + 0.863141i \(0.331506\pi\)
\(294\) 11.1555 0.650600
\(295\) −30.7464 −1.79012
\(296\) −1.80273 −0.104782
\(297\) −4.05959 −0.235562
\(298\) −14.7018 −0.851654
\(299\) 0.620280 0.0358717
\(300\) −27.0956 −1.56436
\(301\) −11.8553 −0.683330
\(302\) −22.7739 −1.31049
\(303\) 15.8533 0.910749
\(304\) −6.35094 −0.364251
\(305\) −23.0645 −1.32067
\(306\) −6.93892 −0.396671
\(307\) −8.49426 −0.484793 −0.242397 0.970177i \(-0.577934\pi\)
−0.242397 + 0.970177i \(0.577934\pi\)
\(308\) −10.2830 −0.585926
\(309\) 1.00000 0.0568880
\(310\) 32.6940 1.85690
\(311\) −8.87599 −0.503311 −0.251655 0.967817i \(-0.580975\pi\)
−0.251655 + 0.967817i \(0.580975\pi\)
\(312\) −0.167219 −0.00946690
\(313\) 18.2376 1.03085 0.515424 0.856935i \(-0.327634\pi\)
0.515424 + 0.856935i \(0.327634\pi\)
\(314\) −4.77243 −0.269324
\(315\) −5.16116 −0.290798
\(316\) −11.5754 −0.651169
\(317\) −5.44512 −0.305828 −0.152914 0.988239i \(-0.548866\pi\)
−0.152914 + 0.988239i \(0.548866\pi\)
\(318\) −26.7341 −1.49917
\(319\) 29.7314 1.66464
\(320\) −36.6991 −2.05154
\(321\) −0.437524 −0.0244202
\(322\) −1.52427 −0.0849441
\(323\) −5.69800 −0.317045
\(324\) 2.08276 0.115709
\(325\) 13.0095 0.721635
\(326\) −4.50956 −0.249761
\(327\) −14.3428 −0.793158
\(328\) −0.276156 −0.0152482
\(329\) −12.0444 −0.664031
\(330\) −34.8105 −1.91625
\(331\) −3.42791 −0.188415 −0.0942074 0.995553i \(-0.530032\pi\)
−0.0942074 + 0.995553i \(0.530032\pi\)
\(332\) 12.5288 0.687609
\(333\) −10.7807 −0.590777
\(334\) −24.9318 −1.36421
\(335\) 3.97322 0.217080
\(336\) −4.65508 −0.253956
\(337\) 28.9670 1.57793 0.788966 0.614436i \(-0.210617\pi\)
0.788966 + 0.614436i \(0.210617\pi\)
\(338\) 2.02058 0.109905
\(339\) 18.7081 1.01609
\(340\) −30.3532 −1.64613
\(341\) 15.4783 0.838198
\(342\) 3.35262 0.181289
\(343\) 15.2276 0.822216
\(344\) 1.63005 0.0878866
\(345\) −2.63232 −0.141719
\(346\) −44.9597 −2.41705
\(347\) −1.48453 −0.0796939 −0.0398469 0.999206i \(-0.512687\pi\)
−0.0398469 + 0.999206i \(0.512687\pi\)
\(348\) −15.2536 −0.817677
\(349\) −22.4737 −1.20299 −0.601494 0.798877i \(-0.705428\pi\)
−0.601494 + 0.798877i \(0.705428\pi\)
\(350\) −31.9693 −1.70883
\(351\) −1.00000 −0.0533761
\(352\) −32.7548 −1.74584
\(353\) 10.3080 0.548637 0.274319 0.961639i \(-0.411548\pi\)
0.274319 + 0.961639i \(0.411548\pi\)
\(354\) 14.6393 0.778070
\(355\) 8.80884 0.467525
\(356\) −6.72896 −0.356634
\(357\) −4.17649 −0.221043
\(358\) −13.0196 −0.688109
\(359\) 11.4076 0.602070 0.301035 0.953613i \(-0.402668\pi\)
0.301035 + 0.953613i \(0.402668\pi\)
\(360\) 0.709635 0.0374011
\(361\) −16.2469 −0.855102
\(362\) 23.0689 1.21248
\(363\) −5.48030 −0.287641
\(364\) −2.53300 −0.132765
\(365\) −20.3558 −1.06547
\(366\) 10.9817 0.574023
\(367\) −6.08507 −0.317638 −0.158819 0.987308i \(-0.550769\pi\)
−0.158819 + 0.987308i \(0.550769\pi\)
\(368\) −2.37420 −0.123764
\(369\) −1.65147 −0.0859719
\(370\) −92.4428 −4.80587
\(371\) −16.0911 −0.835407
\(372\) −7.94109 −0.411726
\(373\) −1.97406 −0.102213 −0.0511065 0.998693i \(-0.516275\pi\)
−0.0511065 + 0.998693i \(0.516275\pi\)
\(374\) −28.1692 −1.45659
\(375\) −33.9902 −1.75525
\(376\) 1.65605 0.0854045
\(377\) 7.32374 0.377192
\(378\) 2.45739 0.126394
\(379\) −15.2851 −0.785142 −0.392571 0.919722i \(-0.628414\pi\)
−0.392571 + 0.919722i \(0.628414\pi\)
\(380\) 14.6655 0.752324
\(381\) −10.8923 −0.558027
\(382\) 31.8885 1.63156
\(383\) 19.3274 0.987584 0.493792 0.869580i \(-0.335610\pi\)
0.493792 + 0.869580i \(0.335610\pi\)
\(384\) 1.33660 0.0682083
\(385\) −20.9522 −1.06782
\(386\) 14.3335 0.729555
\(387\) 9.74803 0.495520
\(388\) 36.0741 1.83138
\(389\) 30.7435 1.55876 0.779379 0.626552i \(-0.215535\pi\)
0.779379 + 0.626552i \(0.215535\pi\)
\(390\) −8.57486 −0.434205
\(391\) −2.13011 −0.107724
\(392\) −0.923200 −0.0466287
\(393\) 6.92135 0.349136
\(394\) 33.4475 1.68506
\(395\) −23.5857 −1.18673
\(396\) 8.45515 0.424887
\(397\) 7.25712 0.364224 0.182112 0.983278i \(-0.441707\pi\)
0.182112 + 0.983278i \(0.441707\pi\)
\(398\) 31.5505 1.58149
\(399\) 2.01792 0.101022
\(400\) −49.7955 −2.48977
\(401\) −29.5473 −1.47552 −0.737761 0.675062i \(-0.764117\pi\)
−0.737761 + 0.675062i \(0.764117\pi\)
\(402\) −1.89177 −0.0943531
\(403\) 3.81277 0.189928
\(404\) −33.0186 −1.64274
\(405\) 4.24376 0.210874
\(406\) −17.9973 −0.893189
\(407\) −43.7652 −2.16936
\(408\) 0.574248 0.0284295
\(409\) −16.2027 −0.801172 −0.400586 0.916259i \(-0.631193\pi\)
−0.400586 + 0.916259i \(0.631193\pi\)
\(410\) −14.1611 −0.699367
\(411\) 5.63515 0.277962
\(412\) −2.08276 −0.102610
\(413\) 8.81131 0.433576
\(414\) 1.25333 0.0615977
\(415\) 25.5283 1.25314
\(416\) −8.06850 −0.395591
\(417\) −3.33341 −0.163238
\(418\) 13.6103 0.665700
\(419\) −32.2123 −1.57367 −0.786837 0.617161i \(-0.788283\pi\)
−0.786837 + 0.617161i \(0.788283\pi\)
\(420\) 10.7494 0.524519
\(421\) 6.11492 0.298023 0.149011 0.988835i \(-0.452391\pi\)
0.149011 + 0.988835i \(0.452391\pi\)
\(422\) 39.4970 1.92269
\(423\) 9.90352 0.481526
\(424\) 2.21245 0.107446
\(425\) −44.6760 −2.16710
\(426\) −4.19416 −0.203208
\(427\) 6.60983 0.319872
\(428\) 0.911257 0.0440473
\(429\) −4.05959 −0.195999
\(430\) 83.5880 4.03097
\(431\) −18.6807 −0.899819 −0.449909 0.893074i \(-0.648544\pi\)
−0.449909 + 0.893074i \(0.648544\pi\)
\(432\) 3.82764 0.184157
\(433\) 14.7179 0.707296 0.353648 0.935379i \(-0.384941\pi\)
0.353648 + 0.935379i \(0.384941\pi\)
\(434\) −9.36946 −0.449749
\(435\) −31.0801 −1.49018
\(436\) 29.8725 1.43063
\(437\) 1.02919 0.0492328
\(438\) 9.69201 0.463102
\(439\) −26.5916 −1.26915 −0.634574 0.772862i \(-0.718824\pi\)
−0.634574 + 0.772862i \(0.718824\pi\)
\(440\) 2.88083 0.137338
\(441\) −5.52091 −0.262901
\(442\) −6.93892 −0.330051
\(443\) 34.8003 1.65341 0.826707 0.562633i \(-0.190212\pi\)
0.826707 + 0.562633i \(0.190212\pi\)
\(444\) 22.4535 1.06560
\(445\) −13.7107 −0.649949
\(446\) −13.6420 −0.645965
\(447\) 7.27603 0.344144
\(448\) 10.5173 0.496893
\(449\) −21.5453 −1.01678 −0.508392 0.861126i \(-0.669760\pi\)
−0.508392 + 0.861126i \(0.669760\pi\)
\(450\) 26.2867 1.23917
\(451\) −6.70428 −0.315692
\(452\) −38.9645 −1.83274
\(453\) 11.2710 0.529556
\(454\) 60.5674 2.84257
\(455\) −5.16116 −0.241959
\(456\) −0.277455 −0.0129930
\(457\) −28.0211 −1.31077 −0.655386 0.755294i \(-0.727494\pi\)
−0.655386 + 0.755294i \(0.727494\pi\)
\(458\) −51.4207 −2.40273
\(459\) 3.43411 0.160291
\(460\) 5.48248 0.255622
\(461\) −16.3892 −0.763320 −0.381660 0.924303i \(-0.624647\pi\)
−0.381660 + 0.924303i \(0.624647\pi\)
\(462\) 9.97599 0.464125
\(463\) −18.0571 −0.839184 −0.419592 0.907713i \(-0.637827\pi\)
−0.419592 + 0.907713i \(0.637827\pi\)
\(464\) −28.0326 −1.30138
\(465\) −16.1805 −0.750352
\(466\) −18.9414 −0.877443
\(467\) −6.48507 −0.300093 −0.150047 0.988679i \(-0.547942\pi\)
−0.150047 + 0.988679i \(0.547942\pi\)
\(468\) 2.08276 0.0962755
\(469\) −1.13865 −0.0525778
\(470\) 84.9213 3.91713
\(471\) 2.36191 0.108831
\(472\) −1.21151 −0.0557645
\(473\) 39.5730 1.81957
\(474\) 11.2299 0.515806
\(475\) 21.5857 0.990421
\(476\) 8.69862 0.398701
\(477\) 13.2309 0.605799
\(478\) −25.0857 −1.14739
\(479\) 20.4016 0.932174 0.466087 0.884739i \(-0.345663\pi\)
0.466087 + 0.884739i \(0.345663\pi\)
\(480\) 34.2407 1.56287
\(481\) −10.7807 −0.491557
\(482\) 3.90330 0.177791
\(483\) 0.754370 0.0343250
\(484\) 11.4141 0.518824
\(485\) 73.5033 3.33761
\(486\) −2.02058 −0.0916555
\(487\) 17.5842 0.796818 0.398409 0.917208i \(-0.369562\pi\)
0.398409 + 0.917208i \(0.369562\pi\)
\(488\) −0.908821 −0.0411404
\(489\) 2.23181 0.100926
\(490\) −47.3411 −2.13865
\(491\) −30.8946 −1.39425 −0.697126 0.716949i \(-0.745538\pi\)
−0.697126 + 0.716949i \(0.745538\pi\)
\(492\) 3.43961 0.155069
\(493\) −25.1505 −1.13272
\(494\) 3.35262 0.150841
\(495\) 17.2279 0.774337
\(496\) −14.5939 −0.655286
\(497\) −2.52444 −0.113237
\(498\) −12.1548 −0.544670
\(499\) −10.6668 −0.477513 −0.238756 0.971079i \(-0.576740\pi\)
−0.238756 + 0.971079i \(0.576740\pi\)
\(500\) 70.7933 3.16597
\(501\) 12.3389 0.551261
\(502\) −4.01866 −0.179362
\(503\) −10.3392 −0.461001 −0.230501 0.973072i \(-0.574036\pi\)
−0.230501 + 0.973072i \(0.574036\pi\)
\(504\) −0.203368 −0.00905871
\(505\) −67.2776 −2.99381
\(506\) 5.08800 0.226189
\(507\) −1.00000 −0.0444116
\(508\) 22.6859 1.00653
\(509\) −24.3375 −1.07874 −0.539370 0.842069i \(-0.681337\pi\)
−0.539370 + 0.842069i \(0.681337\pi\)
\(510\) 29.4471 1.30394
\(511\) 5.83356 0.258062
\(512\) 32.1634 1.42143
\(513\) −1.65923 −0.0732569
\(514\) −36.4167 −1.60627
\(515\) −4.24376 −0.187002
\(516\) −20.3028 −0.893780
\(517\) 40.2043 1.76818
\(518\) 26.4923 1.16400
\(519\) 22.2508 0.976704
\(520\) 0.709635 0.0311196
\(521\) −26.3881 −1.15608 −0.578041 0.816007i \(-0.696183\pi\)
−0.578041 + 0.816007i \(0.696183\pi\)
\(522\) 14.7982 0.647700
\(523\) 18.3475 0.802281 0.401141 0.916016i \(-0.368614\pi\)
0.401141 + 0.916016i \(0.368614\pi\)
\(524\) −14.4155 −0.629743
\(525\) 15.8218 0.690520
\(526\) −38.9207 −1.69702
\(527\) −13.0935 −0.570362
\(528\) 15.5386 0.676233
\(529\) −22.6153 −0.983272
\(530\) 113.453 4.92807
\(531\) −7.24509 −0.314410
\(532\) −4.20284 −0.182216
\(533\) −1.65147 −0.0715330
\(534\) 6.52809 0.282498
\(535\) 1.85675 0.0802741
\(536\) 0.156559 0.00676231
\(537\) 6.44350 0.278057
\(538\) −50.2179 −2.16505
\(539\) −22.4127 −0.965382
\(540\) −8.83871 −0.380358
\(541\) −5.17117 −0.222326 −0.111163 0.993802i \(-0.535458\pi\)
−0.111163 + 0.993802i \(0.535458\pi\)
\(542\) −22.6225 −0.971718
\(543\) −11.4170 −0.489949
\(544\) 27.7081 1.18798
\(545\) 60.8672 2.60727
\(546\) 2.45739 0.105166
\(547\) −26.5534 −1.13534 −0.567670 0.823256i \(-0.692155\pi\)
−0.567670 + 0.823256i \(0.692155\pi\)
\(548\) −11.7367 −0.501365
\(549\) −5.43492 −0.231957
\(550\) 106.713 4.55027
\(551\) 12.1518 0.517684
\(552\) −0.103722 −0.00441472
\(553\) 6.75920 0.287431
\(554\) −48.0506 −2.04147
\(555\) 45.7506 1.94200
\(556\) 6.94269 0.294436
\(557\) −0.441419 −0.0187035 −0.00935175 0.999956i \(-0.502977\pi\)
−0.00935175 + 0.999956i \(0.502977\pi\)
\(558\) 7.70403 0.326138
\(559\) 9.74803 0.412298
\(560\) 19.7550 0.834803
\(561\) 13.9411 0.588594
\(562\) −18.2739 −0.770838
\(563\) 29.8132 1.25648 0.628238 0.778021i \(-0.283776\pi\)
0.628238 + 0.778021i \(0.283776\pi\)
\(564\) −20.6266 −0.868538
\(565\) −79.3928 −3.34008
\(566\) 40.1329 1.68691
\(567\) −1.21618 −0.0510746
\(568\) 0.347099 0.0145639
\(569\) −5.42326 −0.227355 −0.113677 0.993518i \(-0.536263\pi\)
−0.113677 + 0.993518i \(0.536263\pi\)
\(570\) −14.2277 −0.595933
\(571\) −21.4510 −0.897698 −0.448849 0.893608i \(-0.648166\pi\)
−0.448849 + 0.893608i \(0.648166\pi\)
\(572\) 8.45515 0.353528
\(573\) −15.7818 −0.659295
\(574\) 4.05829 0.169390
\(575\) 8.06950 0.336522
\(576\) −8.64780 −0.360325
\(577\) −30.4323 −1.26691 −0.633456 0.773778i \(-0.718364\pi\)
−0.633456 + 0.773778i \(0.718364\pi\)
\(578\) −10.5209 −0.437611
\(579\) −7.09373 −0.294805
\(580\) 64.7324 2.68787
\(581\) −7.31591 −0.303515
\(582\) −34.9972 −1.45068
\(583\) 53.7119 2.22452
\(584\) −0.802088 −0.0331906
\(585\) 4.24376 0.175458
\(586\) 34.9301 1.44295
\(587\) 1.12160 0.0462934 0.0231467 0.999732i \(-0.492632\pi\)
0.0231467 + 0.999732i \(0.492632\pi\)
\(588\) 11.4987 0.474199
\(589\) 6.32628 0.260670
\(590\) −62.1256 −2.55767
\(591\) −16.5534 −0.680915
\(592\) 41.2645 1.69596
\(593\) 12.0433 0.494558 0.247279 0.968944i \(-0.420464\pi\)
0.247279 + 0.968944i \(0.420464\pi\)
\(594\) −8.20275 −0.336563
\(595\) 17.7240 0.726614
\(596\) −15.1542 −0.620741
\(597\) −15.6146 −0.639062
\(598\) 1.25333 0.0512524
\(599\) 32.3003 1.31975 0.659877 0.751373i \(-0.270608\pi\)
0.659877 + 0.751373i \(0.270608\pi\)
\(600\) −2.17543 −0.0888114
\(601\) 21.3067 0.869119 0.434559 0.900643i \(-0.356904\pi\)
0.434559 + 0.900643i \(0.356904\pi\)
\(602\) −23.9547 −0.976320
\(603\) 0.936251 0.0381271
\(604\) −23.4747 −0.955172
\(605\) 23.2570 0.945533
\(606\) 32.0329 1.30125
\(607\) −36.9882 −1.50130 −0.750652 0.660698i \(-0.770260\pi\)
−0.750652 + 0.660698i \(0.770260\pi\)
\(608\) −13.3875 −0.542936
\(609\) 8.90696 0.360928
\(610\) −46.6037 −1.88693
\(611\) 9.90352 0.400654
\(612\) −7.15243 −0.289120
\(613\) 19.1093 0.771816 0.385908 0.922537i \(-0.373888\pi\)
0.385908 + 0.922537i \(0.373888\pi\)
\(614\) −17.1634 −0.692657
\(615\) 7.00842 0.282607
\(616\) −0.825590 −0.0332640
\(617\) −3.65596 −0.147183 −0.0735917 0.997288i \(-0.523446\pi\)
−0.0735917 + 0.997288i \(0.523446\pi\)
\(618\) 2.02058 0.0812798
\(619\) 23.4365 0.941990 0.470995 0.882136i \(-0.343895\pi\)
0.470995 + 0.882136i \(0.343895\pi\)
\(620\) 33.7000 1.35343
\(621\) −0.620280 −0.0248910
\(622\) −17.9347 −0.719115
\(623\) 3.92922 0.157421
\(624\) 3.82764 0.153228
\(625\) 79.1987 3.16795
\(626\) 36.8505 1.47284
\(627\) −6.73581 −0.269002
\(628\) −4.91928 −0.196301
\(629\) 37.0221 1.47617
\(630\) −10.4286 −0.415483
\(631\) −37.5569 −1.49511 −0.747557 0.664197i \(-0.768774\pi\)
−0.747557 + 0.664197i \(0.768774\pi\)
\(632\) −0.929360 −0.0369679
\(633\) −19.5473 −0.776937
\(634\) −11.0023 −0.436958
\(635\) 46.2241 1.83435
\(636\) −27.5567 −1.09269
\(637\) −5.52091 −0.218747
\(638\) 60.0748 2.37838
\(639\) 2.07572 0.0821141
\(640\) −5.67222 −0.224214
\(641\) −36.3157 −1.43438 −0.717192 0.696875i \(-0.754573\pi\)
−0.717192 + 0.696875i \(0.754573\pi\)
\(642\) −0.884054 −0.0348908
\(643\) −38.3686 −1.51311 −0.756554 0.653931i \(-0.773119\pi\)
−0.756554 + 0.653931i \(0.773119\pi\)
\(644\) −1.57117 −0.0619128
\(645\) −41.3682 −1.62887
\(646\) −11.5133 −0.452984
\(647\) 11.2521 0.442365 0.221183 0.975232i \(-0.429008\pi\)
0.221183 + 0.975232i \(0.429008\pi\)
\(648\) 0.167219 0.00656897
\(649\) −29.4121 −1.15453
\(650\) 26.2867 1.03105
\(651\) 4.63701 0.181739
\(652\) −4.64832 −0.182042
\(653\) 29.2608 1.14506 0.572531 0.819883i \(-0.305962\pi\)
0.572531 + 0.819883i \(0.305962\pi\)
\(654\) −28.9808 −1.13324
\(655\) −29.3725 −1.14768
\(656\) 6.32121 0.246802
\(657\) −4.79664 −0.187135
\(658\) −24.3368 −0.948747
\(659\) 3.94572 0.153703 0.0768516 0.997043i \(-0.475513\pi\)
0.0768516 + 0.997043i \(0.475513\pi\)
\(660\) −35.8816 −1.39669
\(661\) 7.62241 0.296477 0.148239 0.988952i \(-0.452640\pi\)
0.148239 + 0.988952i \(0.452640\pi\)
\(662\) −6.92637 −0.269201
\(663\) 3.43411 0.133370
\(664\) 1.00590 0.0390367
\(665\) −8.56357 −0.332081
\(666\) −21.7833 −0.844084
\(667\) 4.54276 0.175897
\(668\) −25.6989 −0.994321
\(669\) 6.75149 0.261028
\(670\) 8.02822 0.310157
\(671\) −22.0636 −0.851755
\(672\) −9.81272 −0.378534
\(673\) −46.1283 −1.77811 −0.889057 0.457797i \(-0.848639\pi\)
−0.889057 + 0.457797i \(0.848639\pi\)
\(674\) 58.5302 2.25450
\(675\) −13.0095 −0.500734
\(676\) 2.08276 0.0801061
\(677\) −28.9183 −1.11142 −0.555710 0.831377i \(-0.687553\pi\)
−0.555710 + 0.831377i \(0.687553\pi\)
\(678\) 37.8014 1.45175
\(679\) −21.0646 −0.808385
\(680\) −2.43697 −0.0934535
\(681\) −29.9752 −1.14865
\(682\) 31.2752 1.19759
\(683\) 20.7401 0.793596 0.396798 0.917906i \(-0.370121\pi\)
0.396798 + 0.917906i \(0.370121\pi\)
\(684\) 3.45578 0.132135
\(685\) −23.9142 −0.913715
\(686\) 30.7687 1.17476
\(687\) 25.4484 0.970918
\(688\) −37.3119 −1.42250
\(689\) 13.2309 0.504056
\(690\) −5.31881 −0.202484
\(691\) 18.4788 0.702966 0.351483 0.936194i \(-0.385678\pi\)
0.351483 + 0.936194i \(0.385678\pi\)
\(692\) −46.3431 −1.76170
\(693\) −4.93718 −0.187548
\(694\) −2.99962 −0.113864
\(695\) 14.1462 0.536596
\(696\) −1.22467 −0.0464208
\(697\) 5.67133 0.214817
\(698\) −45.4100 −1.71879
\(699\) 9.37422 0.354566
\(700\) −32.9530 −1.24551
\(701\) 25.7966 0.974323 0.487162 0.873312i \(-0.338032\pi\)
0.487162 + 0.873312i \(0.338032\pi\)
\(702\) −2.02058 −0.0762620
\(703\) −17.8877 −0.674646
\(704\) −35.1065 −1.32313
\(705\) −42.0281 −1.58287
\(706\) 20.8281 0.783876
\(707\) 19.2804 0.725115
\(708\) 15.0898 0.567108
\(709\) 40.5176 1.52167 0.760836 0.648944i \(-0.224789\pi\)
0.760836 + 0.648944i \(0.224789\pi\)
\(710\) 17.7990 0.667984
\(711\) −5.55775 −0.208432
\(712\) −0.540249 −0.0202467
\(713\) 2.36499 0.0885695
\(714\) −8.43895 −0.315820
\(715\) 17.2279 0.644288
\(716\) −13.4202 −0.501538
\(717\) 12.4151 0.463649
\(718\) 23.0500 0.860219
\(719\) −20.3243 −0.757970 −0.378985 0.925403i \(-0.623727\pi\)
−0.378985 + 0.925403i \(0.623727\pi\)
\(720\) −16.2435 −0.605361
\(721\) 1.21618 0.0452928
\(722\) −32.8283 −1.22174
\(723\) −1.93177 −0.0718433
\(724\) 23.7788 0.883732
\(725\) 95.2778 3.53853
\(726\) −11.0734 −0.410972
\(727\) 27.9800 1.03772 0.518860 0.854859i \(-0.326356\pi\)
0.518860 + 0.854859i \(0.326356\pi\)
\(728\) −0.203368 −0.00753731
\(729\) 1.00000 0.0370370
\(730\) −41.1305 −1.52231
\(731\) −33.4758 −1.23815
\(732\) 11.3196 0.418385
\(733\) −11.9413 −0.441060 −0.220530 0.975380i \(-0.570779\pi\)
−0.220530 + 0.975380i \(0.570779\pi\)
\(734\) −12.2954 −0.453831
\(735\) 23.4294 0.864207
\(736\) −5.00472 −0.184477
\(737\) 3.80080 0.140004
\(738\) −3.33693 −0.122834
\(739\) 20.6859 0.760943 0.380472 0.924793i \(-0.375762\pi\)
0.380472 + 0.924793i \(0.375762\pi\)
\(740\) −95.2873 −3.50283
\(741\) −1.65923 −0.0609535
\(742\) −32.5133 −1.19360
\(743\) −47.2844 −1.73470 −0.867348 0.497702i \(-0.834177\pi\)
−0.867348 + 0.497702i \(0.834177\pi\)
\(744\) −0.637567 −0.0233744
\(745\) −30.8777 −1.13127
\(746\) −3.98875 −0.146039
\(747\) 6.01550 0.220096
\(748\) −29.0360 −1.06166
\(749\) −0.532107 −0.0194428
\(750\) −68.6800 −2.50784
\(751\) −26.3475 −0.961433 −0.480717 0.876876i \(-0.659623\pi\)
−0.480717 + 0.876876i \(0.659623\pi\)
\(752\) −37.9071 −1.38233
\(753\) 1.98886 0.0724782
\(754\) 14.7982 0.538919
\(755\) −47.8312 −1.74076
\(756\) 2.53300 0.0921244
\(757\) −44.7771 −1.62745 −0.813726 0.581249i \(-0.802564\pi\)
−0.813726 + 0.581249i \(0.802564\pi\)
\(758\) −30.8848 −1.12179
\(759\) −2.51808 −0.0914006
\(760\) 1.17745 0.0427106
\(761\) −16.9868 −0.615773 −0.307886 0.951423i \(-0.599622\pi\)
−0.307886 + 0.951423i \(0.599622\pi\)
\(762\) −22.0087 −0.797291
\(763\) −17.4434 −0.631492
\(764\) 32.8697 1.18919
\(765\) −14.5735 −0.526908
\(766\) 39.0526 1.41103
\(767\) −7.24509 −0.261605
\(768\) −14.5949 −0.526647
\(769\) 2.26014 0.0815028 0.0407514 0.999169i \(-0.487025\pi\)
0.0407514 + 0.999169i \(0.487025\pi\)
\(770\) −42.3357 −1.52567
\(771\) 18.0229 0.649077
\(772\) 14.7745 0.531747
\(773\) −41.3043 −1.48561 −0.742807 0.669506i \(-0.766506\pi\)
−0.742807 + 0.669506i \(0.766506\pi\)
\(774\) 19.6967 0.707983
\(775\) 49.6021 1.78176
\(776\) 2.89629 0.103971
\(777\) −13.1112 −0.470362
\(778\) 62.1199 2.22711
\(779\) −2.74017 −0.0981767
\(780\) −8.83871 −0.316477
\(781\) 8.42657 0.301526
\(782\) −4.30407 −0.153913
\(783\) −7.32374 −0.261729
\(784\) 21.1320 0.754716
\(785\) −10.0234 −0.357749
\(786\) 13.9852 0.498834
\(787\) 40.9492 1.45968 0.729841 0.683617i \(-0.239594\pi\)
0.729841 + 0.683617i \(0.239594\pi\)
\(788\) 34.4767 1.22818
\(789\) 19.2621 0.685749
\(790\) −47.6569 −1.69556
\(791\) 22.7524 0.808983
\(792\) 0.678840 0.0241215
\(793\) −5.43492 −0.193000
\(794\) 14.6636 0.520392
\(795\) −56.1485 −1.99138
\(796\) 32.5214 1.15269
\(797\) 1.80291 0.0638624 0.0319312 0.999490i \(-0.489834\pi\)
0.0319312 + 0.999490i \(0.489834\pi\)
\(798\) 4.07738 0.144338
\(799\) −34.0098 −1.20318
\(800\) −104.967 −3.71114
\(801\) −3.23079 −0.114154
\(802\) −59.7028 −2.10818
\(803\) −19.4724 −0.687166
\(804\) −1.94998 −0.0687706
\(805\) −3.20136 −0.112833
\(806\) 7.70403 0.271363
\(807\) 24.8531 0.874872
\(808\) −2.65097 −0.0932608
\(809\) 39.4624 1.38742 0.693712 0.720253i \(-0.255974\pi\)
0.693712 + 0.720253i \(0.255974\pi\)
\(810\) 8.57486 0.301290
\(811\) −37.6751 −1.32295 −0.661476 0.749966i \(-0.730070\pi\)
−0.661476 + 0.749966i \(0.730070\pi\)
\(812\) −18.5510 −0.651014
\(813\) 11.1960 0.392661
\(814\) −88.4312 −3.09951
\(815\) −9.47126 −0.331764
\(816\) −13.1445 −0.460151
\(817\) 16.1743 0.565865
\(818\) −32.7389 −1.14469
\(819\) −1.21618 −0.0424967
\(820\) −14.5968 −0.509744
\(821\) 40.6738 1.41953 0.709763 0.704441i \(-0.248802\pi\)
0.709763 + 0.704441i \(0.248802\pi\)
\(822\) 11.3863 0.397143
\(823\) 43.8682 1.52915 0.764575 0.644534i \(-0.222949\pi\)
0.764575 + 0.644534i \(0.222949\pi\)
\(824\) −0.167219 −0.00582534
\(825\) −52.8131 −1.83872
\(826\) 17.8040 0.619480
\(827\) 19.1748 0.666772 0.333386 0.942790i \(-0.391809\pi\)
0.333386 + 0.942790i \(0.391809\pi\)
\(828\) 1.29189 0.0448964
\(829\) 24.3429 0.845463 0.422732 0.906255i \(-0.361071\pi\)
0.422732 + 0.906255i \(0.361071\pi\)
\(830\) 51.5821 1.79044
\(831\) 23.7805 0.824938
\(832\) −8.64780 −0.299808
\(833\) 18.9594 0.656906
\(834\) −6.73544 −0.233229
\(835\) −52.3632 −1.81210
\(836\) 14.0291 0.485205
\(837\) −3.81277 −0.131789
\(838\) −65.0877 −2.24842
\(839\) −17.5743 −0.606733 −0.303367 0.952874i \(-0.598111\pi\)
−0.303367 + 0.952874i \(0.598111\pi\)
\(840\) 0.863042 0.0297778
\(841\) 24.6371 0.849555
\(842\) 12.3557 0.425805
\(843\) 9.04387 0.311487
\(844\) 40.7124 1.40138
\(845\) 4.24376 0.145990
\(846\) 20.0109 0.687989
\(847\) −6.66501 −0.229013
\(848\) −50.6429 −1.73908
\(849\) −19.8620 −0.681663
\(850\) −90.2715 −3.09629
\(851\) −6.68704 −0.229229
\(852\) −4.32322 −0.148111
\(853\) 6.37049 0.218121 0.109061 0.994035i \(-0.465216\pi\)
0.109061 + 0.994035i \(0.465216\pi\)
\(854\) 13.3557 0.457023
\(855\) 7.04138 0.240810
\(856\) 0.0731622 0.00250063
\(857\) −5.13585 −0.175437 −0.0877187 0.996145i \(-0.527958\pi\)
−0.0877187 + 0.996145i \(0.527958\pi\)
\(858\) −8.20275 −0.280037
\(859\) 44.3382 1.51280 0.756400 0.654109i \(-0.226956\pi\)
0.756400 + 0.654109i \(0.226956\pi\)
\(860\) 86.1600 2.93803
\(861\) −2.00848 −0.0684487
\(862\) −37.7460 −1.28563
\(863\) −52.4564 −1.78564 −0.892818 0.450418i \(-0.851275\pi\)
−0.892818 + 0.450418i \(0.851275\pi\)
\(864\) 8.06850 0.274496
\(865\) −94.4271 −3.21062
\(866\) 29.7387 1.01056
\(867\) 5.20686 0.176834
\(868\) −9.65777 −0.327806
\(869\) −22.5622 −0.765370
\(870\) −62.8000 −2.12912
\(871\) 0.936251 0.0317237
\(872\) 2.39838 0.0812195
\(873\) 17.3203 0.586205
\(874\) 2.07956 0.0703422
\(875\) −41.3381 −1.39748
\(876\) 9.99024 0.337539
\(877\) 9.30250 0.314123 0.157062 0.987589i \(-0.449798\pi\)
0.157062 + 0.987589i \(0.449798\pi\)
\(878\) −53.7305 −1.81332
\(879\) −17.2871 −0.583080
\(880\) −65.9422 −2.22291
\(881\) 15.7383 0.530236 0.265118 0.964216i \(-0.414589\pi\)
0.265118 + 0.964216i \(0.414589\pi\)
\(882\) −11.1555 −0.375624
\(883\) 45.9361 1.54587 0.772937 0.634483i \(-0.218787\pi\)
0.772937 + 0.634483i \(0.218787\pi\)
\(884\) −7.15243 −0.240562
\(885\) 30.7464 1.03353
\(886\) 70.3170 2.36234
\(887\) 2.85477 0.0958539 0.0479269 0.998851i \(-0.484739\pi\)
0.0479269 + 0.998851i \(0.484739\pi\)
\(888\) 1.80273 0.0604957
\(889\) −13.2469 −0.444287
\(890\) −27.7036 −0.928627
\(891\) 4.05959 0.136001
\(892\) −14.0617 −0.470821
\(893\) 16.4323 0.549884
\(894\) 14.7018 0.491703
\(895\) −27.3446 −0.914030
\(896\) 1.62555 0.0543058
\(897\) −0.620280 −0.0207105
\(898\) −43.5340 −1.45275
\(899\) 27.9238 0.931309
\(900\) 27.0956 0.903185
\(901\) −45.4363 −1.51370
\(902\) −13.5466 −0.451051
\(903\) 11.8553 0.394521
\(904\) −3.12835 −0.104047
\(905\) 48.4508 1.61056
\(906\) 22.7739 0.756613
\(907\) 9.72972 0.323070 0.161535 0.986867i \(-0.448355\pi\)
0.161535 + 0.986867i \(0.448355\pi\)
\(908\) 62.4311 2.07185
\(909\) −15.8533 −0.525821
\(910\) −10.4286 −0.345703
\(911\) −11.1063 −0.367969 −0.183985 0.982929i \(-0.558900\pi\)
−0.183985 + 0.982929i \(0.558900\pi\)
\(912\) 6.35094 0.210301
\(913\) 24.4205 0.808200
\(914\) −56.6190 −1.87279
\(915\) 23.0645 0.762488
\(916\) −53.0029 −1.75127
\(917\) 8.41758 0.277973
\(918\) 6.93892 0.229018
\(919\) −37.3887 −1.23334 −0.616669 0.787222i \(-0.711518\pi\)
−0.616669 + 0.787222i \(0.711518\pi\)
\(920\) 0.440173 0.0145121
\(921\) 8.49426 0.279896
\(922\) −33.1157 −1.09061
\(923\) 2.07572 0.0683231
\(924\) 10.2830 0.338285
\(925\) −140.251 −4.61142
\(926\) −36.4859 −1.19900
\(927\) −1.00000 −0.0328443
\(928\) −59.0915 −1.93977
\(929\) −29.5395 −0.969159 −0.484580 0.874747i \(-0.661027\pi\)
−0.484580 + 0.874747i \(0.661027\pi\)
\(930\) −32.6940 −1.07208
\(931\) −9.16048 −0.300223
\(932\) −19.5242 −0.639537
\(933\) 8.87599 0.290587
\(934\) −13.1036 −0.428764
\(935\) −59.1627 −1.93483
\(936\) 0.167219 0.00546572
\(937\) −31.9308 −1.04313 −0.521567 0.853211i \(-0.674652\pi\)
−0.521567 + 0.853211i \(0.674652\pi\)
\(938\) −2.30073 −0.0751215
\(939\) −18.2376 −0.595160
\(940\) 87.5344 2.85506
\(941\) −16.5704 −0.540179 −0.270090 0.962835i \(-0.587053\pi\)
−0.270090 + 0.962835i \(0.587053\pi\)
\(942\) 4.77243 0.155494
\(943\) −1.02437 −0.0333581
\(944\) 27.7316 0.902585
\(945\) 5.16116 0.167892
\(946\) 79.9606 2.59974
\(947\) 30.5313 0.992134 0.496067 0.868284i \(-0.334777\pi\)
0.496067 + 0.868284i \(0.334777\pi\)
\(948\) 11.5754 0.375953
\(949\) −4.79664 −0.155705
\(950\) 43.6158 1.41508
\(951\) 5.44512 0.176570
\(952\) 0.698388 0.0226349
\(953\) 21.5883 0.699314 0.349657 0.936878i \(-0.386298\pi\)
0.349657 + 0.936878i \(0.386298\pi\)
\(954\) 26.7341 0.865547
\(955\) 66.9742 2.16724
\(956\) −25.8576 −0.836293
\(957\) −29.7314 −0.961079
\(958\) 41.2232 1.33186
\(959\) 6.85334 0.221306
\(960\) 36.6991 1.18446
\(961\) −16.4627 −0.531056
\(962\) −21.7833 −0.702320
\(963\) 0.437524 0.0140990
\(964\) 4.02341 0.129585
\(965\) 30.1041 0.969084
\(966\) 1.52427 0.0490425
\(967\) 61.1908 1.96776 0.983882 0.178820i \(-0.0572279\pi\)
0.983882 + 0.178820i \(0.0572279\pi\)
\(968\) 0.916409 0.0294545
\(969\) 5.69800 0.183046
\(970\) 148.520 4.76868
\(971\) −8.70220 −0.279267 −0.139633 0.990203i \(-0.544592\pi\)
−0.139633 + 0.990203i \(0.544592\pi\)
\(972\) −2.08276 −0.0668045
\(973\) −4.05402 −0.129966
\(974\) 35.5304 1.13847
\(975\) −13.0095 −0.416636
\(976\) 20.8029 0.665885
\(977\) 32.4949 1.03961 0.519803 0.854286i \(-0.326006\pi\)
0.519803 + 0.854286i \(0.326006\pi\)
\(978\) 4.50956 0.144200
\(979\) −13.1157 −0.419180
\(980\) −48.7978 −1.55879
\(981\) 14.3428 0.457930
\(982\) −62.4250 −1.99206
\(983\) −32.0897 −1.02350 −0.511751 0.859134i \(-0.671003\pi\)
−0.511751 + 0.859134i \(0.671003\pi\)
\(984\) 0.276156 0.00880354
\(985\) 70.2485 2.23830
\(986\) −50.8188 −1.61840
\(987\) 12.0444 0.383379
\(988\) 3.45578 0.109943
\(989\) 6.04650 0.192268
\(990\) 34.8105 1.10635
\(991\) −43.9747 −1.39690 −0.698451 0.715658i \(-0.746127\pi\)
−0.698451 + 0.715658i \(0.746127\pi\)
\(992\) −30.7634 −0.976737
\(993\) 3.42791 0.108781
\(994\) −5.10084 −0.161789
\(995\) 66.2644 2.10072
\(996\) −12.5288 −0.396991
\(997\) 21.7999 0.690410 0.345205 0.938527i \(-0.387809\pi\)
0.345205 + 0.938527i \(0.387809\pi\)
\(998\) −21.5532 −0.682255
\(999\) 10.7807 0.341086
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 \(a_p\))