Properties

Label 8001.2.a.z.1.5
Level 8001
Weight 2
Character 8001.1
Self dual Yes
Analytic conductor 63.888
Analytic rank 1
Dimension 32
CM No

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Newspace parameters

Level: \( N \) = \( 8001 = 3^{2} \cdot 7 \cdot 127 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8001.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.8883066572\)
Analytic rank: \(1\)
Dimension: \(32\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) = 8001.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.23843 q^{2} +3.01059 q^{4} -0.715002 q^{5} -1.00000 q^{7} -2.26213 q^{8} +O(q^{10})\) \(q-2.23843 q^{2} +3.01059 q^{4} -0.715002 q^{5} -1.00000 q^{7} -2.26213 q^{8} +1.60049 q^{10} -3.48743 q^{11} -3.88025 q^{13} +2.23843 q^{14} -0.957541 q^{16} +2.02085 q^{17} +1.32595 q^{19} -2.15258 q^{20} +7.80638 q^{22} +4.77444 q^{23} -4.48877 q^{25} +8.68568 q^{26} -3.01059 q^{28} +8.26004 q^{29} -4.73204 q^{31} +6.66766 q^{32} -4.52353 q^{34} +0.715002 q^{35} -10.4983 q^{37} -2.96805 q^{38} +1.61743 q^{40} -0.827289 q^{41} +2.69972 q^{43} -10.4992 q^{44} -10.6873 q^{46} +9.44282 q^{47} +1.00000 q^{49} +10.0478 q^{50} -11.6818 q^{52} -7.12745 q^{53} +2.49352 q^{55} +2.26213 q^{56} -18.4895 q^{58} +6.64479 q^{59} +9.79645 q^{61} +10.5924 q^{62} -13.0100 q^{64} +2.77439 q^{65} +10.4839 q^{67} +6.08393 q^{68} -1.60049 q^{70} -8.80029 q^{71} +6.52998 q^{73} +23.4997 q^{74} +3.99189 q^{76} +3.48743 q^{77} -1.16978 q^{79} +0.684644 q^{80} +1.85183 q^{82} +4.68620 q^{83} -1.44491 q^{85} -6.04313 q^{86} +7.88902 q^{88} +3.95955 q^{89} +3.88025 q^{91} +14.3739 q^{92} -21.1371 q^{94} -0.948058 q^{95} +6.83283 q^{97} -2.23843 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 30q^{4} - 32q^{7} + O(q^{10}) \) \( 32q + 30q^{4} - 32q^{7} - 16q^{10} - 14q^{13} + 18q^{16} - 30q^{19} - 10q^{22} + 36q^{25} - 30q^{28} - 58q^{31} - 34q^{34} + 8q^{37} - 34q^{40} + 6q^{43} - 36q^{46} + 32q^{49} - 56q^{52} - 88q^{55} - 22q^{58} - 46q^{61} + 20q^{64} - 8q^{67} + 16q^{70} - 60q^{73} - 128q^{76} - 74q^{79} - 52q^{82} - 16q^{85} - 64q^{88} + 14q^{91} - 58q^{94} - 44q^{97} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.23843 −1.58281 −0.791406 0.611291i \(-0.790651\pi\)
−0.791406 + 0.611291i \(0.790651\pi\)
\(3\) 0 0
\(4\) 3.01059 1.50529
\(5\) −0.715002 −0.319759 −0.159879 0.987137i \(-0.551111\pi\)
−0.159879 + 0.987137i \(0.551111\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) −2.26213 −0.799784
\(9\) 0 0
\(10\) 1.60049 0.506118
\(11\) −3.48743 −1.05150 −0.525750 0.850639i \(-0.676215\pi\)
−0.525750 + 0.850639i \(0.676215\pi\)
\(12\) 0 0
\(13\) −3.88025 −1.07619 −0.538093 0.842885i \(-0.680855\pi\)
−0.538093 + 0.842885i \(0.680855\pi\)
\(14\) 2.23843 0.598247
\(15\) 0 0
\(16\) −0.957541 −0.239385
\(17\) 2.02085 0.490127 0.245064 0.969507i \(-0.421191\pi\)
0.245064 + 0.969507i \(0.421191\pi\)
\(18\) 0 0
\(19\) 1.32595 0.304194 0.152097 0.988366i \(-0.451397\pi\)
0.152097 + 0.988366i \(0.451397\pi\)
\(20\) −2.15258 −0.481331
\(21\) 0 0
\(22\) 7.80638 1.66433
\(23\) 4.77444 0.995540 0.497770 0.867309i \(-0.334152\pi\)
0.497770 + 0.867309i \(0.334152\pi\)
\(24\) 0 0
\(25\) −4.48877 −0.897754
\(26\) 8.68568 1.70340
\(27\) 0 0
\(28\) −3.01059 −0.568947
\(29\) 8.26004 1.53385 0.766925 0.641737i \(-0.221786\pi\)
0.766925 + 0.641737i \(0.221786\pi\)
\(30\) 0 0
\(31\) −4.73204 −0.849900 −0.424950 0.905217i \(-0.639708\pi\)
−0.424950 + 0.905217i \(0.639708\pi\)
\(32\) 6.66766 1.17869
\(33\) 0 0
\(34\) −4.52353 −0.775779
\(35\) 0.715002 0.120857
\(36\) 0 0
\(37\) −10.4983 −1.72591 −0.862954 0.505283i \(-0.831388\pi\)
−0.862954 + 0.505283i \(0.831388\pi\)
\(38\) −2.96805 −0.481482
\(39\) 0 0
\(40\) 1.61743 0.255738
\(41\) −0.827289 −0.129201 −0.0646004 0.997911i \(-0.520577\pi\)
−0.0646004 + 0.997911i \(0.520577\pi\)
\(42\) 0 0
\(43\) 2.69972 0.411703 0.205851 0.978583i \(-0.434004\pi\)
0.205851 + 0.978583i \(0.434004\pi\)
\(44\) −10.4992 −1.58281
\(45\) 0 0
\(46\) −10.6873 −1.57575
\(47\) 9.44282 1.37738 0.688688 0.725058i \(-0.258187\pi\)
0.688688 + 0.725058i \(0.258187\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 10.0478 1.42098
\(51\) 0 0
\(52\) −11.6818 −1.61998
\(53\) −7.12745 −0.979030 −0.489515 0.871995i \(-0.662826\pi\)
−0.489515 + 0.871995i \(0.662826\pi\)
\(54\) 0 0
\(55\) 2.49352 0.336226
\(56\) 2.26213 0.302290
\(57\) 0 0
\(58\) −18.4895 −2.42780
\(59\) 6.64479 0.865078 0.432539 0.901615i \(-0.357618\pi\)
0.432539 + 0.901615i \(0.357618\pi\)
\(60\) 0 0
\(61\) 9.79645 1.25431 0.627153 0.778896i \(-0.284220\pi\)
0.627153 + 0.778896i \(0.284220\pi\)
\(62\) 10.5924 1.34523
\(63\) 0 0
\(64\) −13.0100 −1.62625
\(65\) 2.77439 0.344120
\(66\) 0 0
\(67\) 10.4839 1.28081 0.640407 0.768036i \(-0.278766\pi\)
0.640407 + 0.768036i \(0.278766\pi\)
\(68\) 6.08393 0.737785
\(69\) 0 0
\(70\) −1.60049 −0.191295
\(71\) −8.80029 −1.04440 −0.522201 0.852823i \(-0.674889\pi\)
−0.522201 + 0.852823i \(0.674889\pi\)
\(72\) 0 0
\(73\) 6.52998 0.764276 0.382138 0.924105i \(-0.375188\pi\)
0.382138 + 0.924105i \(0.375188\pi\)
\(74\) 23.4997 2.73179
\(75\) 0 0
\(76\) 3.99189 0.457901
\(77\) 3.48743 0.397429
\(78\) 0 0
\(79\) −1.16978 −0.131611 −0.0658053 0.997832i \(-0.520962\pi\)
−0.0658053 + 0.997832i \(0.520962\pi\)
\(80\) 0.684644 0.0765455
\(81\) 0 0
\(82\) 1.85183 0.204501
\(83\) 4.68620 0.514377 0.257189 0.966361i \(-0.417204\pi\)
0.257189 + 0.966361i \(0.417204\pi\)
\(84\) 0 0
\(85\) −1.44491 −0.156722
\(86\) −6.04313 −0.651648
\(87\) 0 0
\(88\) 7.88902 0.840973
\(89\) 3.95955 0.419712 0.209856 0.977732i \(-0.432701\pi\)
0.209856 + 0.977732i \(0.432701\pi\)
\(90\) 0 0
\(91\) 3.88025 0.406760
\(92\) 14.3739 1.49858
\(93\) 0 0
\(94\) −21.1371 −2.18013
\(95\) −0.948058 −0.0972687
\(96\) 0 0
\(97\) 6.83283 0.693768 0.346884 0.937908i \(-0.387240\pi\)
0.346884 + 0.937908i \(0.387240\pi\)
\(98\) −2.23843 −0.226116
\(99\) 0 0
\(100\) −13.5138 −1.35138
\(101\) 14.4018 1.43303 0.716517 0.697569i \(-0.245735\pi\)
0.716517 + 0.697569i \(0.245735\pi\)
\(102\) 0 0
\(103\) 4.78657 0.471635 0.235817 0.971797i \(-0.424223\pi\)
0.235817 + 0.971797i \(0.424223\pi\)
\(104\) 8.77763 0.860717
\(105\) 0 0
\(106\) 15.9543 1.54962
\(107\) −8.11171 −0.784189 −0.392094 0.919925i \(-0.628249\pi\)
−0.392094 + 0.919925i \(0.628249\pi\)
\(108\) 0 0
\(109\) 0.982270 0.0940844 0.0470422 0.998893i \(-0.485020\pi\)
0.0470422 + 0.998893i \(0.485020\pi\)
\(110\) −5.58158 −0.532183
\(111\) 0 0
\(112\) 0.957541 0.0904791
\(113\) −5.77508 −0.543273 −0.271637 0.962400i \(-0.587565\pi\)
−0.271637 + 0.962400i \(0.587565\pi\)
\(114\) 0 0
\(115\) −3.41374 −0.318333
\(116\) 24.8676 2.30889
\(117\) 0 0
\(118\) −14.8739 −1.36926
\(119\) −2.02085 −0.185251
\(120\) 0 0
\(121\) 1.16215 0.105650
\(122\) −21.9287 −1.98533
\(123\) 0 0
\(124\) −14.2462 −1.27935
\(125\) 6.78450 0.606824
\(126\) 0 0
\(127\) −1.00000 −0.0887357
\(128\) 15.7868 1.39537
\(129\) 0 0
\(130\) −6.21028 −0.544678
\(131\) 1.06804 0.0933152 0.0466576 0.998911i \(-0.485143\pi\)
0.0466576 + 0.998911i \(0.485143\pi\)
\(132\) 0 0
\(133\) −1.32595 −0.114975
\(134\) −23.4675 −2.02729
\(135\) 0 0
\(136\) −4.57142 −0.391996
\(137\) −12.8058 −1.09408 −0.547038 0.837108i \(-0.684245\pi\)
−0.547038 + 0.837108i \(0.684245\pi\)
\(138\) 0 0
\(139\) −4.13929 −0.351090 −0.175545 0.984471i \(-0.556169\pi\)
−0.175545 + 0.984471i \(0.556169\pi\)
\(140\) 2.15258 0.181926
\(141\) 0 0
\(142\) 19.6989 1.65309
\(143\) 13.5321 1.13161
\(144\) 0 0
\(145\) −5.90595 −0.490462
\(146\) −14.6169 −1.20971
\(147\) 0 0
\(148\) −31.6060 −2.59800
\(149\) −13.5650 −1.11129 −0.555646 0.831419i \(-0.687529\pi\)
−0.555646 + 0.831419i \(0.687529\pi\)
\(150\) 0 0
\(151\) 3.40613 0.277187 0.138594 0.990349i \(-0.455742\pi\)
0.138594 + 0.990349i \(0.455742\pi\)
\(152\) −2.99948 −0.243290
\(153\) 0 0
\(154\) −7.80638 −0.629056
\(155\) 3.38342 0.271763
\(156\) 0 0
\(157\) −20.5876 −1.64307 −0.821536 0.570157i \(-0.806882\pi\)
−0.821536 + 0.570157i \(0.806882\pi\)
\(158\) 2.61848 0.208315
\(159\) 0 0
\(160\) −4.76739 −0.376895
\(161\) −4.77444 −0.376279
\(162\) 0 0
\(163\) 14.3948 1.12749 0.563744 0.825950i \(-0.309360\pi\)
0.563744 + 0.825950i \(0.309360\pi\)
\(164\) −2.49063 −0.194485
\(165\) 0 0
\(166\) −10.4898 −0.814163
\(167\) −14.7266 −1.13958 −0.569788 0.821792i \(-0.692975\pi\)
−0.569788 + 0.821792i \(0.692975\pi\)
\(168\) 0 0
\(169\) 2.05631 0.158178
\(170\) 3.23433 0.248062
\(171\) 0 0
\(172\) 8.12773 0.619733
\(173\) 12.1096 0.920678 0.460339 0.887743i \(-0.347728\pi\)
0.460339 + 0.887743i \(0.347728\pi\)
\(174\) 0 0
\(175\) 4.48877 0.339319
\(176\) 3.33935 0.251713
\(177\) 0 0
\(178\) −8.86320 −0.664325
\(179\) −10.2816 −0.768484 −0.384242 0.923232i \(-0.625537\pi\)
−0.384242 + 0.923232i \(0.625537\pi\)
\(180\) 0 0
\(181\) −6.97609 −0.518529 −0.259264 0.965806i \(-0.583480\pi\)
−0.259264 + 0.965806i \(0.583480\pi\)
\(182\) −8.68568 −0.643825
\(183\) 0 0
\(184\) −10.8004 −0.796217
\(185\) 7.50630 0.551874
\(186\) 0 0
\(187\) −7.04755 −0.515368
\(188\) 28.4284 2.07336
\(189\) 0 0
\(190\) 2.12217 0.153958
\(191\) 16.8925 1.22230 0.611150 0.791515i \(-0.290707\pi\)
0.611150 + 0.791515i \(0.290707\pi\)
\(192\) 0 0
\(193\) 5.01576 0.361043 0.180521 0.983571i \(-0.442222\pi\)
0.180521 + 0.983571i \(0.442222\pi\)
\(194\) −15.2948 −1.09810
\(195\) 0 0
\(196\) 3.01059 0.215042
\(197\) −8.79497 −0.626616 −0.313308 0.949652i \(-0.601437\pi\)
−0.313308 + 0.949652i \(0.601437\pi\)
\(198\) 0 0
\(199\) −21.9618 −1.55683 −0.778417 0.627747i \(-0.783977\pi\)
−0.778417 + 0.627747i \(0.783977\pi\)
\(200\) 10.1542 0.718010
\(201\) 0 0
\(202\) −32.2375 −2.26822
\(203\) −8.26004 −0.579741
\(204\) 0 0
\(205\) 0.591514 0.0413131
\(206\) −10.7144 −0.746509
\(207\) 0 0
\(208\) 3.71549 0.257623
\(209\) −4.62416 −0.319860
\(210\) 0 0
\(211\) 10.3601 0.713221 0.356610 0.934253i \(-0.383932\pi\)
0.356610 + 0.934253i \(0.383932\pi\)
\(212\) −21.4578 −1.47373
\(213\) 0 0
\(214\) 18.1575 1.24122
\(215\) −1.93030 −0.131646
\(216\) 0 0
\(217\) 4.73204 0.321232
\(218\) −2.19875 −0.148918
\(219\) 0 0
\(220\) 7.50696 0.506119
\(221\) −7.84138 −0.527468
\(222\) 0 0
\(223\) −6.35678 −0.425681 −0.212841 0.977087i \(-0.568272\pi\)
−0.212841 + 0.977087i \(0.568272\pi\)
\(224\) −6.66766 −0.445501
\(225\) 0 0
\(226\) 12.9271 0.859900
\(227\) 7.68768 0.510249 0.255124 0.966908i \(-0.417884\pi\)
0.255124 + 0.966908i \(0.417884\pi\)
\(228\) 0 0
\(229\) −10.5663 −0.698244 −0.349122 0.937077i \(-0.613520\pi\)
−0.349122 + 0.937077i \(0.613520\pi\)
\(230\) 7.64142 0.503861
\(231\) 0 0
\(232\) −18.6853 −1.22675
\(233\) 25.1211 1.64574 0.822869 0.568231i \(-0.192372\pi\)
0.822869 + 0.568231i \(0.192372\pi\)
\(234\) 0 0
\(235\) −6.75164 −0.440428
\(236\) 20.0047 1.30220
\(237\) 0 0
\(238\) 4.52353 0.293217
\(239\) −10.8412 −0.701257 −0.350629 0.936515i \(-0.614032\pi\)
−0.350629 + 0.936515i \(0.614032\pi\)
\(240\) 0 0
\(241\) −17.8749 −1.15142 −0.575712 0.817652i \(-0.695275\pi\)
−0.575712 + 0.817652i \(0.695275\pi\)
\(242\) −2.60141 −0.167225
\(243\) 0 0
\(244\) 29.4931 1.88810
\(245\) −0.715002 −0.0456798
\(246\) 0 0
\(247\) −5.14502 −0.327369
\(248\) 10.7045 0.679737
\(249\) 0 0
\(250\) −15.1866 −0.960488
\(251\) 4.79178 0.302455 0.151227 0.988499i \(-0.451677\pi\)
0.151227 + 0.988499i \(0.451677\pi\)
\(252\) 0 0
\(253\) −16.6505 −1.04681
\(254\) 2.23843 0.140452
\(255\) 0 0
\(256\) −9.31760 −0.582350
\(257\) 6.08661 0.379672 0.189836 0.981816i \(-0.439204\pi\)
0.189836 + 0.981816i \(0.439204\pi\)
\(258\) 0 0
\(259\) 10.4983 0.652332
\(260\) 8.35253 0.518002
\(261\) 0 0
\(262\) −2.39074 −0.147700
\(263\) 25.1166 1.54876 0.774378 0.632723i \(-0.218063\pi\)
0.774378 + 0.632723i \(0.218063\pi\)
\(264\) 0 0
\(265\) 5.09614 0.313053
\(266\) 2.96805 0.181983
\(267\) 0 0
\(268\) 31.5627 1.92800
\(269\) 12.2844 0.748995 0.374498 0.927228i \(-0.377815\pi\)
0.374498 + 0.927228i \(0.377815\pi\)
\(270\) 0 0
\(271\) −0.354378 −0.0215269 −0.0107635 0.999942i \(-0.503426\pi\)
−0.0107635 + 0.999942i \(0.503426\pi\)
\(272\) −1.93504 −0.117329
\(273\) 0 0
\(274\) 28.6650 1.73172
\(275\) 15.6543 0.943988
\(276\) 0 0
\(277\) −18.8044 −1.12984 −0.564922 0.825144i \(-0.691094\pi\)
−0.564922 + 0.825144i \(0.691094\pi\)
\(278\) 9.26552 0.555709
\(279\) 0 0
\(280\) −1.61743 −0.0966599
\(281\) 22.7302 1.35597 0.677985 0.735076i \(-0.262854\pi\)
0.677985 + 0.735076i \(0.262854\pi\)
\(282\) 0 0
\(283\) −9.78820 −0.581848 −0.290924 0.956746i \(-0.593963\pi\)
−0.290924 + 0.956746i \(0.593963\pi\)
\(284\) −26.4940 −1.57213
\(285\) 0 0
\(286\) −30.2907 −1.79112
\(287\) 0.827289 0.0488333
\(288\) 0 0
\(289\) −12.9162 −0.759775
\(290\) 13.2201 0.776309
\(291\) 0 0
\(292\) 19.6591 1.15046
\(293\) −6.16187 −0.359981 −0.179990 0.983668i \(-0.557607\pi\)
−0.179990 + 0.983668i \(0.557607\pi\)
\(294\) 0 0
\(295\) −4.75104 −0.276616
\(296\) 23.7485 1.38035
\(297\) 0 0
\(298\) 30.3645 1.75897
\(299\) −18.5260 −1.07139
\(300\) 0 0
\(301\) −2.69972 −0.155609
\(302\) −7.62440 −0.438735
\(303\) 0 0
\(304\) −1.26965 −0.0728195
\(305\) −7.00449 −0.401076
\(306\) 0 0
\(307\) −13.7893 −0.786999 −0.393500 0.919325i \(-0.628736\pi\)
−0.393500 + 0.919325i \(0.628736\pi\)
\(308\) 10.4992 0.598248
\(309\) 0 0
\(310\) −7.57357 −0.430150
\(311\) −7.99152 −0.453158 −0.226579 0.973993i \(-0.572754\pi\)
−0.226579 + 0.973993i \(0.572754\pi\)
\(312\) 0 0
\(313\) 8.19550 0.463237 0.231618 0.972807i \(-0.425598\pi\)
0.231618 + 0.972807i \(0.425598\pi\)
\(314\) 46.0840 2.60067
\(315\) 0 0
\(316\) −3.52173 −0.198113
\(317\) 9.71596 0.545703 0.272851 0.962056i \(-0.412033\pi\)
0.272851 + 0.962056i \(0.412033\pi\)
\(318\) 0 0
\(319\) −28.8063 −1.61284
\(320\) 9.30220 0.520009
\(321\) 0 0
\(322\) 10.6873 0.595578
\(323\) 2.67954 0.149094
\(324\) 0 0
\(325\) 17.4175 0.966151
\(326\) −32.2218 −1.78460
\(327\) 0 0
\(328\) 1.87144 0.103333
\(329\) −9.44282 −0.520599
\(330\) 0 0
\(331\) 26.7460 1.47009 0.735047 0.678017i \(-0.237160\pi\)
0.735047 + 0.678017i \(0.237160\pi\)
\(332\) 14.1082 0.774289
\(333\) 0 0
\(334\) 32.9644 1.80373
\(335\) −7.49602 −0.409551
\(336\) 0 0
\(337\) 7.80788 0.425322 0.212661 0.977126i \(-0.431787\pi\)
0.212661 + 0.977126i \(0.431787\pi\)
\(338\) −4.60292 −0.250366
\(339\) 0 0
\(340\) −4.35003 −0.235913
\(341\) 16.5027 0.893669
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) −6.10711 −0.329273
\(345\) 0 0
\(346\) −27.1066 −1.45726
\(347\) −16.8929 −0.906859 −0.453429 0.891292i \(-0.649800\pi\)
−0.453429 + 0.891292i \(0.649800\pi\)
\(348\) 0 0
\(349\) −14.8133 −0.792937 −0.396468 0.918048i \(-0.629764\pi\)
−0.396468 + 0.918048i \(0.629764\pi\)
\(350\) −10.0478 −0.537078
\(351\) 0 0
\(352\) −23.2530 −1.23939
\(353\) −32.0204 −1.70427 −0.852137 0.523319i \(-0.824694\pi\)
−0.852137 + 0.523319i \(0.824694\pi\)
\(354\) 0 0
\(355\) 6.29223 0.333957
\(356\) 11.9206 0.631790
\(357\) 0 0
\(358\) 23.0147 1.21637
\(359\) −7.14129 −0.376903 −0.188451 0.982083i \(-0.560347\pi\)
−0.188451 + 0.982083i \(0.560347\pi\)
\(360\) 0 0
\(361\) −17.2419 −0.907466
\(362\) 15.6155 0.820733
\(363\) 0 0
\(364\) 11.6818 0.612294
\(365\) −4.66895 −0.244384
\(366\) 0 0
\(367\) 19.0108 0.992356 0.496178 0.868221i \(-0.334736\pi\)
0.496178 + 0.868221i \(0.334736\pi\)
\(368\) −4.57172 −0.238317
\(369\) 0 0
\(370\) −16.8024 −0.873513
\(371\) 7.12745 0.370039
\(372\) 0 0
\(373\) 32.6219 1.68910 0.844550 0.535476i \(-0.179868\pi\)
0.844550 + 0.535476i \(0.179868\pi\)
\(374\) 15.7755 0.815731
\(375\) 0 0
\(376\) −21.3609 −1.10160
\(377\) −32.0510 −1.65071
\(378\) 0 0
\(379\) 9.55764 0.490943 0.245471 0.969404i \(-0.421057\pi\)
0.245471 + 0.969404i \(0.421057\pi\)
\(380\) −2.85421 −0.146418
\(381\) 0 0
\(382\) −37.8128 −1.93467
\(383\) −19.9990 −1.02190 −0.510950 0.859610i \(-0.670706\pi\)
−0.510950 + 0.859610i \(0.670706\pi\)
\(384\) 0 0
\(385\) −2.49352 −0.127082
\(386\) −11.2275 −0.571462
\(387\) 0 0
\(388\) 20.5708 1.04432
\(389\) −4.07409 −0.206565 −0.103282 0.994652i \(-0.532934\pi\)
−0.103282 + 0.994652i \(0.532934\pi\)
\(390\) 0 0
\(391\) 9.64841 0.487941
\(392\) −2.26213 −0.114255
\(393\) 0 0
\(394\) 19.6870 0.991814
\(395\) 0.836396 0.0420837
\(396\) 0 0
\(397\) 21.7833 1.09327 0.546636 0.837370i \(-0.315908\pi\)
0.546636 + 0.837370i \(0.315908\pi\)
\(398\) 49.1602 2.46418
\(399\) 0 0
\(400\) 4.29818 0.214909
\(401\) 17.3330 0.865568 0.432784 0.901498i \(-0.357531\pi\)
0.432784 + 0.901498i \(0.357531\pi\)
\(402\) 0 0
\(403\) 18.3615 0.914651
\(404\) 43.3579 2.15714
\(405\) 0 0
\(406\) 18.4895 0.917621
\(407\) 36.6120 1.81479
\(408\) 0 0
\(409\) −12.4744 −0.616821 −0.308410 0.951253i \(-0.599797\pi\)
−0.308410 + 0.951253i \(0.599797\pi\)
\(410\) −1.32406 −0.0653909
\(411\) 0 0
\(412\) 14.4104 0.709948
\(413\) −6.64479 −0.326969
\(414\) 0 0
\(415\) −3.35065 −0.164477
\(416\) −25.8721 −1.26849
\(417\) 0 0
\(418\) 10.3509 0.506278
\(419\) −10.7981 −0.527524 −0.263762 0.964588i \(-0.584963\pi\)
−0.263762 + 0.964588i \(0.584963\pi\)
\(420\) 0 0
\(421\) −7.59997 −0.370400 −0.185200 0.982701i \(-0.559293\pi\)
−0.185200 + 0.982701i \(0.559293\pi\)
\(422\) −23.1905 −1.12889
\(423\) 0 0
\(424\) 16.1232 0.783013
\(425\) −9.07111 −0.440014
\(426\) 0 0
\(427\) −9.79645 −0.474083
\(428\) −24.4210 −1.18043
\(429\) 0 0
\(430\) 4.32086 0.208370
\(431\) −34.8208 −1.67726 −0.838630 0.544701i \(-0.816643\pi\)
−0.838630 + 0.544701i \(0.816643\pi\)
\(432\) 0 0
\(433\) −33.9006 −1.62916 −0.814578 0.580054i \(-0.803032\pi\)
−0.814578 + 0.580054i \(0.803032\pi\)
\(434\) −10.5924 −0.508450
\(435\) 0 0
\(436\) 2.95721 0.141625
\(437\) 6.33067 0.302837
\(438\) 0 0
\(439\) 6.04032 0.288289 0.144144 0.989557i \(-0.453957\pi\)
0.144144 + 0.989557i \(0.453957\pi\)
\(440\) −5.64067 −0.268908
\(441\) 0 0
\(442\) 17.5524 0.834883
\(443\) −32.0832 −1.52432 −0.762159 0.647390i \(-0.775860\pi\)
−0.762159 + 0.647390i \(0.775860\pi\)
\(444\) 0 0
\(445\) −2.83109 −0.134207
\(446\) 14.2292 0.673774
\(447\) 0 0
\(448\) 13.0100 0.614666
\(449\) −7.01644 −0.331126 −0.165563 0.986199i \(-0.552944\pi\)
−0.165563 + 0.986199i \(0.552944\pi\)
\(450\) 0 0
\(451\) 2.88511 0.135855
\(452\) −17.3864 −0.817786
\(453\) 0 0
\(454\) −17.2084 −0.807628
\(455\) −2.77439 −0.130065
\(456\) 0 0
\(457\) 16.8482 0.788126 0.394063 0.919083i \(-0.371069\pi\)
0.394063 + 0.919083i \(0.371069\pi\)
\(458\) 23.6521 1.10519
\(459\) 0 0
\(460\) −10.2774 −0.479184
\(461\) −17.7603 −0.827181 −0.413591 0.910463i \(-0.635726\pi\)
−0.413591 + 0.910463i \(0.635726\pi\)
\(462\) 0 0
\(463\) 10.1828 0.473236 0.236618 0.971603i \(-0.423961\pi\)
0.236618 + 0.971603i \(0.423961\pi\)
\(464\) −7.90932 −0.367181
\(465\) 0 0
\(466\) −56.2319 −2.60489
\(467\) −1.65415 −0.0765449 −0.0382724 0.999267i \(-0.512185\pi\)
−0.0382724 + 0.999267i \(0.512185\pi\)
\(468\) 0 0
\(469\) −10.4839 −0.484102
\(470\) 15.1131 0.697115
\(471\) 0 0
\(472\) −15.0314 −0.691876
\(473\) −9.41506 −0.432905
\(474\) 0 0
\(475\) −5.95189 −0.273091
\(476\) −6.08393 −0.278857
\(477\) 0 0
\(478\) 24.2672 1.10996
\(479\) −12.7961 −0.584670 −0.292335 0.956316i \(-0.594432\pi\)
−0.292335 + 0.956316i \(0.594432\pi\)
\(480\) 0 0
\(481\) 40.7359 1.85740
\(482\) 40.0118 1.82249
\(483\) 0 0
\(484\) 3.49877 0.159035
\(485\) −4.88549 −0.221839
\(486\) 0 0
\(487\) 5.81280 0.263403 0.131702 0.991289i \(-0.457956\pi\)
0.131702 + 0.991289i \(0.457956\pi\)
\(488\) −22.1609 −1.00317
\(489\) 0 0
\(490\) 1.60049 0.0723026
\(491\) 5.28049 0.238305 0.119153 0.992876i \(-0.461982\pi\)
0.119153 + 0.992876i \(0.461982\pi\)
\(492\) 0 0
\(493\) 16.6923 0.751782
\(494\) 11.5168 0.518164
\(495\) 0 0
\(496\) 4.53113 0.203454
\(497\) 8.80029 0.394747
\(498\) 0 0
\(499\) −20.0549 −0.897778 −0.448889 0.893587i \(-0.648180\pi\)
−0.448889 + 0.893587i \(0.648180\pi\)
\(500\) 20.4253 0.913448
\(501\) 0 0
\(502\) −10.7261 −0.478729
\(503\) 14.1949 0.632920 0.316460 0.948606i \(-0.397506\pi\)
0.316460 + 0.948606i \(0.397506\pi\)
\(504\) 0 0
\(505\) −10.2973 −0.458225
\(506\) 37.2711 1.65690
\(507\) 0 0
\(508\) −3.01059 −0.133573
\(509\) 34.0499 1.50923 0.754617 0.656166i \(-0.227823\pi\)
0.754617 + 0.656166i \(0.227823\pi\)
\(510\) 0 0
\(511\) −6.52998 −0.288869
\(512\) −10.7167 −0.473617
\(513\) 0 0
\(514\) −13.6245 −0.600950
\(515\) −3.42241 −0.150809
\(516\) 0 0
\(517\) −32.9311 −1.44831
\(518\) −23.4997 −1.03252
\(519\) 0 0
\(520\) −6.27603 −0.275222
\(521\) 4.82296 0.211298 0.105649 0.994403i \(-0.466308\pi\)
0.105649 + 0.994403i \(0.466308\pi\)
\(522\) 0 0
\(523\) −2.29591 −0.100393 −0.0501965 0.998739i \(-0.515985\pi\)
−0.0501965 + 0.998739i \(0.515985\pi\)
\(524\) 3.21543 0.140467
\(525\) 0 0
\(526\) −56.2219 −2.45139
\(527\) −9.56273 −0.416559
\(528\) 0 0
\(529\) −0.204717 −0.00890074
\(530\) −11.4074 −0.495505
\(531\) 0 0
\(532\) −3.99189 −0.173070
\(533\) 3.21009 0.139044
\(534\) 0 0
\(535\) 5.79989 0.250751
\(536\) −23.7160 −1.02437
\(537\) 0 0
\(538\) −27.4979 −1.18552
\(539\) −3.48743 −0.150214
\(540\) 0 0
\(541\) −13.1848 −0.566857 −0.283429 0.958993i \(-0.591472\pi\)
−0.283429 + 0.958993i \(0.591472\pi\)
\(542\) 0.793252 0.0340731
\(543\) 0 0
\(544\) 13.4743 0.577706
\(545\) −0.702325 −0.0300843
\(546\) 0 0
\(547\) −0.144810 −0.00619164 −0.00309582 0.999995i \(-0.500985\pi\)
−0.00309582 + 0.999995i \(0.500985\pi\)
\(548\) −38.5531 −1.64691
\(549\) 0 0
\(550\) −35.0410 −1.49416
\(551\) 10.9524 0.466588
\(552\) 0 0
\(553\) 1.16978 0.0497441
\(554\) 42.0923 1.78833
\(555\) 0 0
\(556\) −12.4617 −0.528493
\(557\) −6.35824 −0.269407 −0.134704 0.990886i \(-0.543008\pi\)
−0.134704 + 0.990886i \(0.543008\pi\)
\(558\) 0 0
\(559\) −10.4756 −0.443069
\(560\) −0.684644 −0.0289315
\(561\) 0 0
\(562\) −50.8800 −2.14624
\(563\) −27.7532 −1.16966 −0.584829 0.811157i \(-0.698838\pi\)
−0.584829 + 0.811157i \(0.698838\pi\)
\(564\) 0 0
\(565\) 4.12919 0.173716
\(566\) 21.9102 0.920956
\(567\) 0 0
\(568\) 19.9074 0.835296
\(569\) 6.89351 0.288991 0.144495 0.989505i \(-0.453844\pi\)
0.144495 + 0.989505i \(0.453844\pi\)
\(570\) 0 0
\(571\) 15.4924 0.648337 0.324168 0.945999i \(-0.394916\pi\)
0.324168 + 0.945999i \(0.394916\pi\)
\(572\) 40.7395 1.70340
\(573\) 0 0
\(574\) −1.85183 −0.0772940
\(575\) −21.4314 −0.893750
\(576\) 0 0
\(577\) 26.1702 1.08948 0.544741 0.838605i \(-0.316628\pi\)
0.544741 + 0.838605i \(0.316628\pi\)
\(578\) 28.9120 1.20258
\(579\) 0 0
\(580\) −17.7804 −0.738289
\(581\) −4.68620 −0.194416
\(582\) 0 0
\(583\) 24.8565 1.02945
\(584\) −14.7717 −0.611256
\(585\) 0 0
\(586\) 13.7929 0.569781
\(587\) 34.8064 1.43662 0.718308 0.695725i \(-0.244917\pi\)
0.718308 + 0.695725i \(0.244917\pi\)
\(588\) 0 0
\(589\) −6.27446 −0.258534
\(590\) 10.6349 0.437831
\(591\) 0 0
\(592\) 10.0525 0.413157
\(593\) −24.0643 −0.988203 −0.494101 0.869404i \(-0.664503\pi\)
−0.494101 + 0.869404i \(0.664503\pi\)
\(594\) 0 0
\(595\) 1.44491 0.0592355
\(596\) −40.8387 −1.67282
\(597\) 0 0
\(598\) 41.4692 1.69580
\(599\) −0.508407 −0.0207729 −0.0103865 0.999946i \(-0.503306\pi\)
−0.0103865 + 0.999946i \(0.503306\pi\)
\(600\) 0 0
\(601\) 23.1016 0.942333 0.471166 0.882044i \(-0.343833\pi\)
0.471166 + 0.882044i \(0.343833\pi\)
\(602\) 6.04313 0.246300
\(603\) 0 0
\(604\) 10.2545 0.417248
\(605\) −0.830943 −0.0337826
\(606\) 0 0
\(607\) −35.7095 −1.44940 −0.724701 0.689063i \(-0.758022\pi\)
−0.724701 + 0.689063i \(0.758022\pi\)
\(608\) 8.84098 0.358549
\(609\) 0 0
\(610\) 15.6791 0.634827
\(611\) −36.6405 −1.48231
\(612\) 0 0
\(613\) −9.75584 −0.394035 −0.197017 0.980400i \(-0.563126\pi\)
−0.197017 + 0.980400i \(0.563126\pi\)
\(614\) 30.8665 1.24567
\(615\) 0 0
\(616\) −7.88902 −0.317858
\(617\) 4.62163 0.186060 0.0930299 0.995663i \(-0.470345\pi\)
0.0930299 + 0.995663i \(0.470345\pi\)
\(618\) 0 0
\(619\) −46.6480 −1.87494 −0.937471 0.348062i \(-0.886840\pi\)
−0.937471 + 0.348062i \(0.886840\pi\)
\(620\) 10.1861 0.409083
\(621\) 0 0
\(622\) 17.8885 0.717263
\(623\) −3.95955 −0.158636
\(624\) 0 0
\(625\) 17.5929 0.703717
\(626\) −18.3451 −0.733217
\(627\) 0 0
\(628\) −61.9808 −2.47330
\(629\) −21.2154 −0.845914
\(630\) 0 0
\(631\) −40.7101 −1.62064 −0.810322 0.585984i \(-0.800708\pi\)
−0.810322 + 0.585984i \(0.800708\pi\)
\(632\) 2.64620 0.105260
\(633\) 0 0
\(634\) −21.7485 −0.863745
\(635\) 0.715002 0.0283740
\(636\) 0 0
\(637\) −3.88025 −0.153741
\(638\) 64.4810 2.55283
\(639\) 0 0
\(640\) −11.2876 −0.446181
\(641\) 16.0725 0.634826 0.317413 0.948287i \(-0.397186\pi\)
0.317413 + 0.948287i \(0.397186\pi\)
\(642\) 0 0
\(643\) 6.75968 0.266576 0.133288 0.991077i \(-0.457446\pi\)
0.133288 + 0.991077i \(0.457446\pi\)
\(644\) −14.3739 −0.566410
\(645\) 0 0
\(646\) −5.99798 −0.235987
\(647\) 26.3074 1.03425 0.517125 0.855910i \(-0.327002\pi\)
0.517125 + 0.855910i \(0.327002\pi\)
\(648\) 0 0
\(649\) −23.1732 −0.909628
\(650\) −38.9880 −1.52924
\(651\) 0 0
\(652\) 43.3368 1.69720
\(653\) 15.4078 0.602954 0.301477 0.953473i \(-0.402520\pi\)
0.301477 + 0.953473i \(0.402520\pi\)
\(654\) 0 0
\(655\) −0.763652 −0.0298384
\(656\) 0.792163 0.0309288
\(657\) 0 0
\(658\) 21.1371 0.824011
\(659\) −11.1639 −0.434885 −0.217442 0.976073i \(-0.569771\pi\)
−0.217442 + 0.976073i \(0.569771\pi\)
\(660\) 0 0
\(661\) 16.7973 0.653338 0.326669 0.945139i \(-0.394074\pi\)
0.326669 + 0.945139i \(0.394074\pi\)
\(662\) −59.8692 −2.32688
\(663\) 0 0
\(664\) −10.6008 −0.411391
\(665\) 0.948058 0.0367641
\(666\) 0 0
\(667\) 39.4371 1.52701
\(668\) −44.3356 −1.71539
\(669\) 0 0
\(670\) 16.7794 0.648243
\(671\) −34.1644 −1.31890
\(672\) 0 0
\(673\) 36.1418 1.39317 0.696583 0.717476i \(-0.254703\pi\)
0.696583 + 0.717476i \(0.254703\pi\)
\(674\) −17.4774 −0.673205
\(675\) 0 0
\(676\) 6.19071 0.238104
\(677\) 36.2462 1.39306 0.696528 0.717530i \(-0.254727\pi\)
0.696528 + 0.717530i \(0.254727\pi\)
\(678\) 0 0
\(679\) −6.83283 −0.262220
\(680\) 3.26858 0.125344
\(681\) 0 0
\(682\) −36.9401 −1.41451
\(683\) −21.5032 −0.822796 −0.411398 0.911456i \(-0.634959\pi\)
−0.411398 + 0.911456i \(0.634959\pi\)
\(684\) 0 0
\(685\) 9.15620 0.349840
\(686\) 2.23843 0.0854638
\(687\) 0 0
\(688\) −2.58509 −0.0985555
\(689\) 27.6562 1.05362
\(690\) 0 0
\(691\) −16.8476 −0.640913 −0.320456 0.947263i \(-0.603836\pi\)
−0.320456 + 0.947263i \(0.603836\pi\)
\(692\) 36.4571 1.38589
\(693\) 0 0
\(694\) 37.8137 1.43539
\(695\) 2.95960 0.112264
\(696\) 0 0
\(697\) −1.67182 −0.0633248
\(698\) 33.1585 1.25507
\(699\) 0 0
\(700\) 13.5138 0.510775
\(701\) 8.39278 0.316991 0.158495 0.987360i \(-0.449336\pi\)
0.158495 + 0.987360i \(0.449336\pi\)
\(702\) 0 0
\(703\) −13.9202 −0.525011
\(704\) 45.3715 1.71000
\(705\) 0 0
\(706\) 71.6756 2.69755
\(707\) −14.4018 −0.541636
\(708\) 0 0
\(709\) −22.8508 −0.858181 −0.429091 0.903261i \(-0.641166\pi\)
−0.429091 + 0.903261i \(0.641166\pi\)
\(710\) −14.0847 −0.528591
\(711\) 0 0
\(712\) −8.95703 −0.335679
\(713\) −22.5929 −0.846109
\(714\) 0 0
\(715\) −9.67547 −0.361842
\(716\) −30.9537 −1.15679
\(717\) 0 0
\(718\) 15.9853 0.596566
\(719\) −29.0142 −1.08205 −0.541023 0.841008i \(-0.681963\pi\)
−0.541023 + 0.841008i \(0.681963\pi\)
\(720\) 0 0
\(721\) −4.78657 −0.178261
\(722\) 38.5948 1.43635
\(723\) 0 0
\(724\) −21.0021 −0.780538
\(725\) −37.0774 −1.37702
\(726\) 0 0
\(727\) 1.71536 0.0636190 0.0318095 0.999494i \(-0.489873\pi\)
0.0318095 + 0.999494i \(0.489873\pi\)
\(728\) −8.77763 −0.325321
\(729\) 0 0
\(730\) 10.4511 0.386814
\(731\) 5.45571 0.201787
\(732\) 0 0
\(733\) 32.0548 1.18397 0.591986 0.805948i \(-0.298344\pi\)
0.591986 + 0.805948i \(0.298344\pi\)
\(734\) −42.5544 −1.57071
\(735\) 0 0
\(736\) 31.8343 1.17343
\(737\) −36.5619 −1.34677
\(738\) 0 0
\(739\) 15.0497 0.553613 0.276807 0.960926i \(-0.410724\pi\)
0.276807 + 0.960926i \(0.410724\pi\)
\(740\) 22.5984 0.830732
\(741\) 0 0
\(742\) −15.9543 −0.585701
\(743\) 1.95125 0.0715845 0.0357922 0.999359i \(-0.488605\pi\)
0.0357922 + 0.999359i \(0.488605\pi\)
\(744\) 0 0
\(745\) 9.69904 0.355345
\(746\) −73.0221 −2.67353
\(747\) 0 0
\(748\) −21.2173 −0.775780
\(749\) 8.11171 0.296395
\(750\) 0 0
\(751\) −13.9594 −0.509385 −0.254692 0.967022i \(-0.581974\pi\)
−0.254692 + 0.967022i \(0.581974\pi\)
\(752\) −9.04188 −0.329724
\(753\) 0 0
\(754\) 71.7440 2.61276
\(755\) −2.43539 −0.0886330
\(756\) 0 0
\(757\) −23.9434 −0.870238 −0.435119 0.900373i \(-0.643294\pi\)
−0.435119 + 0.900373i \(0.643294\pi\)
\(758\) −21.3941 −0.777070
\(759\) 0 0
\(760\) 2.14463 0.0777940
\(761\) −17.6709 −0.640569 −0.320285 0.947321i \(-0.603779\pi\)
−0.320285 + 0.947321i \(0.603779\pi\)
\(762\) 0 0
\(763\) −0.982270 −0.0355606
\(764\) 50.8564 1.83992
\(765\) 0 0
\(766\) 44.7664 1.61748
\(767\) −25.7834 −0.930985
\(768\) 0 0
\(769\) −3.34345 −0.120568 −0.0602839 0.998181i \(-0.519201\pi\)
−0.0602839 + 0.998181i \(0.519201\pi\)
\(770\) 5.58158 0.201146
\(771\) 0 0
\(772\) 15.1004 0.543475
\(773\) −35.6247 −1.28133 −0.640665 0.767821i \(-0.721341\pi\)
−0.640665 + 0.767821i \(0.721341\pi\)
\(774\) 0 0
\(775\) 21.2411 0.763002
\(776\) −15.4568 −0.554865
\(777\) 0 0
\(778\) 9.11958 0.326953
\(779\) −1.09694 −0.0393021
\(780\) 0 0
\(781\) 30.6904 1.09819
\(782\) −21.5973 −0.772319
\(783\) 0 0
\(784\) −0.957541 −0.0341979
\(785\) 14.7202 0.525386
\(786\) 0 0
\(787\) −49.3147 −1.75788 −0.878939 0.476935i \(-0.841748\pi\)
−0.878939 + 0.476935i \(0.841748\pi\)
\(788\) −26.4780 −0.943240
\(789\) 0 0
\(790\) −1.87222 −0.0666105
\(791\) 5.77508 0.205338
\(792\) 0 0
\(793\) −38.0126 −1.34987
\(794\) −48.7605 −1.73045
\(795\) 0 0
\(796\) −66.1181 −2.34349
\(797\) 18.8764 0.668637 0.334318 0.942460i \(-0.391494\pi\)
0.334318 + 0.942460i \(0.391494\pi\)
\(798\) 0 0
\(799\) 19.0825 0.675089
\(800\) −29.9296 −1.05817
\(801\) 0 0
\(802\) −38.7988 −1.37003
\(803\) −22.7728 −0.803636
\(804\) 0 0
\(805\) 3.41374 0.120318
\(806\) −41.1010 −1.44772
\(807\) 0 0
\(808\) −32.5788 −1.14612
\(809\) 27.6464 0.971994 0.485997 0.873960i \(-0.338457\pi\)
0.485997 + 0.873960i \(0.338457\pi\)
\(810\) 0 0
\(811\) −40.0155 −1.40514 −0.702568 0.711617i \(-0.747963\pi\)
−0.702568 + 0.711617i \(0.747963\pi\)
\(812\) −24.8676 −0.872680
\(813\) 0 0
\(814\) −81.9536 −2.87247
\(815\) −10.2923 −0.360524
\(816\) 0 0
\(817\) 3.57969 0.125237
\(818\) 27.9232 0.976311
\(819\) 0 0
\(820\) 1.78080 0.0621884
\(821\) −7.00349 −0.244423 −0.122212 0.992504i \(-0.538999\pi\)
−0.122212 + 0.992504i \(0.538999\pi\)
\(822\) 0 0
\(823\) 7.48955 0.261069 0.130535 0.991444i \(-0.458331\pi\)
0.130535 + 0.991444i \(0.458331\pi\)
\(824\) −10.8278 −0.377206
\(825\) 0 0
\(826\) 14.8739 0.517530
\(827\) 5.69107 0.197898 0.0989490 0.995093i \(-0.468452\pi\)
0.0989490 + 0.995093i \(0.468452\pi\)
\(828\) 0 0
\(829\) −46.9867 −1.63192 −0.815958 0.578111i \(-0.803790\pi\)
−0.815958 + 0.578111i \(0.803790\pi\)
\(830\) 7.50020 0.260336
\(831\) 0 0
\(832\) 50.4821 1.75015
\(833\) 2.02085 0.0700182
\(834\) 0 0
\(835\) 10.5295 0.364389
\(836\) −13.9214 −0.481483
\(837\) 0 0
\(838\) 24.1709 0.834971
\(839\) −23.2141 −0.801441 −0.400721 0.916200i \(-0.631240\pi\)
−0.400721 + 0.916200i \(0.631240\pi\)
\(840\) 0 0
\(841\) 39.2282 1.35270
\(842\) 17.0120 0.586273
\(843\) 0 0
\(844\) 31.1901 1.07361
\(845\) −1.47027 −0.0505788
\(846\) 0 0
\(847\) −1.16215 −0.0399321
\(848\) 6.82482 0.234365
\(849\) 0 0
\(850\) 20.3051 0.696459
\(851\) −50.1234 −1.71821
\(852\) 0 0
\(853\) −30.3267 −1.03837 −0.519183 0.854663i \(-0.673764\pi\)
−0.519183 + 0.854663i \(0.673764\pi\)
\(854\) 21.9287 0.750385
\(855\) 0 0
\(856\) 18.3498 0.627182
\(857\) −22.4832 −0.768011 −0.384005 0.923331i \(-0.625456\pi\)
−0.384005 + 0.923331i \(0.625456\pi\)
\(858\) 0 0
\(859\) −36.3023 −1.23862 −0.619309 0.785147i \(-0.712587\pi\)
−0.619309 + 0.785147i \(0.712587\pi\)
\(860\) −5.81134 −0.198165
\(861\) 0 0
\(862\) 77.9441 2.65479
\(863\) −32.5087 −1.10661 −0.553305 0.832979i \(-0.686633\pi\)
−0.553305 + 0.832979i \(0.686633\pi\)
\(864\) 0 0
\(865\) −8.65842 −0.294395
\(866\) 75.8841 2.57865
\(867\) 0 0
\(868\) 14.2462 0.483549
\(869\) 4.07953 0.138388
\(870\) 0 0
\(871\) −40.6802 −1.37839
\(872\) −2.22202 −0.0752472
\(873\) 0 0
\(874\) −14.1708 −0.479334
\(875\) −6.78450 −0.229358
\(876\) 0 0
\(877\) −6.43887 −0.217425 −0.108713 0.994073i \(-0.534673\pi\)
−0.108713 + 0.994073i \(0.534673\pi\)
\(878\) −13.5209 −0.456307
\(879\) 0 0
\(880\) −2.38765 −0.0804876
\(881\) −50.9542 −1.71669 −0.858346 0.513072i \(-0.828507\pi\)
−0.858346 + 0.513072i \(0.828507\pi\)
\(882\) 0 0
\(883\) −1.41232 −0.0475284 −0.0237642 0.999718i \(-0.507565\pi\)
−0.0237642 + 0.999718i \(0.507565\pi\)
\(884\) −23.6072 −0.793994
\(885\) 0 0
\(886\) 71.8161 2.41271
\(887\) −9.49697 −0.318877 −0.159438 0.987208i \(-0.550968\pi\)
−0.159438 + 0.987208i \(0.550968\pi\)
\(888\) 0 0
\(889\) 1.00000 0.0335389
\(890\) 6.33721 0.212424
\(891\) 0 0
\(892\) −19.1376 −0.640775
\(893\) 12.5207 0.418990
\(894\) 0 0
\(895\) 7.35138 0.245730
\(896\) −15.7868 −0.527399
\(897\) 0 0
\(898\) 15.7058 0.524110
\(899\) −39.0869 −1.30362
\(900\) 0 0
\(901\) −14.4035 −0.479849
\(902\) −6.45813 −0.215032
\(903\) 0 0
\(904\) 13.0640 0.434502
\(905\) 4.98792 0.165804
\(906\) 0 0
\(907\) −48.9510 −1.62539 −0.812695 0.582689i \(-0.802000\pi\)
−0.812695 + 0.582689i \(0.802000\pi\)
\(908\) 23.1444 0.768074
\(909\) 0 0
\(910\) 6.21028 0.205869
\(911\) −5.99796 −0.198721 −0.0993607 0.995051i \(-0.531680\pi\)
−0.0993607 + 0.995051i \(0.531680\pi\)
\(912\) 0 0
\(913\) −16.3428 −0.540867
\(914\) −37.7136 −1.24746
\(915\) 0 0
\(916\) −31.8109 −1.05106
\(917\) −1.06804 −0.0352698
\(918\) 0 0
\(919\) −0.999658 −0.0329757 −0.0164878 0.999864i \(-0.505248\pi\)
−0.0164878 + 0.999864i \(0.505248\pi\)
\(920\) 7.72232 0.254597
\(921\) 0 0
\(922\) 39.7553 1.30927
\(923\) 34.1473 1.12397
\(924\) 0 0
\(925\) 47.1244 1.54944
\(926\) −22.7936 −0.749044
\(927\) 0 0
\(928\) 55.0751 1.80793
\(929\) −55.3468 −1.81587 −0.907935 0.419110i \(-0.862342\pi\)
−0.907935 + 0.419110i \(0.862342\pi\)
\(930\) 0 0
\(931\) 1.32595 0.0434563
\(932\) 75.6293 2.47732
\(933\) 0 0
\(934\) 3.70270 0.121156
\(935\) 5.03902 0.164794
\(936\) 0 0
\(937\) −1.27880 −0.0417766 −0.0208883 0.999782i \(-0.506649\pi\)
−0.0208883 + 0.999782i \(0.506649\pi\)
\(938\) 23.4675 0.766242
\(939\) 0 0
\(940\) −20.3264 −0.662974
\(941\) −22.7871 −0.742837 −0.371419 0.928466i \(-0.621128\pi\)
−0.371419 + 0.928466i \(0.621128\pi\)
\(942\) 0 0
\(943\) −3.94984 −0.128625
\(944\) −6.36265 −0.207087
\(945\) 0 0
\(946\) 21.0750 0.685207
\(947\) −8.91484 −0.289693 −0.144847 0.989454i \(-0.546269\pi\)
−0.144847 + 0.989454i \(0.546269\pi\)
\(948\) 0 0
\(949\) −25.3379 −0.822504
\(950\) 13.3229 0.432252
\(951\) 0 0
\(952\) 4.57142 0.148161
\(953\) −8.13381 −0.263480 −0.131740 0.991284i \(-0.542056\pi\)
−0.131740 + 0.991284i \(0.542056\pi\)
\(954\) 0 0
\(955\) −12.0782 −0.390841
\(956\) −32.6383 −1.05560
\(957\) 0 0
\(958\) 28.6433 0.925423
\(959\) 12.8058 0.413522
\(960\) 0 0
\(961\) −8.60776 −0.277670
\(962\) −91.1847 −2.93991
\(963\) 0 0
\(964\) −53.8140 −1.73323
\(965\) −3.58628 −0.115447
\(966\) 0 0
\(967\) −15.9426 −0.512679 −0.256339 0.966587i \(-0.582516\pi\)
−0.256339 + 0.966587i \(0.582516\pi\)
\(968\) −2.62895 −0.0844975
\(969\) 0 0
\(970\) 10.9358 0.351129
\(971\) 43.2242 1.38713 0.693566 0.720393i \(-0.256039\pi\)
0.693566 + 0.720393i \(0.256039\pi\)
\(972\) 0 0
\(973\) 4.13929 0.132699
\(974\) −13.0116 −0.416918
\(975\) 0 0
\(976\) −9.38050 −0.300262
\(977\) 11.4772 0.367190 0.183595 0.983002i \(-0.441227\pi\)
0.183595 + 0.983002i \(0.441227\pi\)
\(978\) 0 0
\(979\) −13.8087 −0.441327
\(980\) −2.15258 −0.0687616
\(981\) 0 0
\(982\) −11.8200 −0.377192
\(983\) 32.2991 1.03018 0.515090 0.857136i \(-0.327758\pi\)
0.515090 + 0.857136i \(0.327758\pi\)
\(984\) 0 0
\(985\) 6.28842 0.200366
\(986\) −37.3645 −1.18993
\(987\) 0 0
\(988\) −15.4895 −0.492787
\(989\) 12.8896 0.409866
\(990\) 0 0
\(991\) −46.4069 −1.47416 −0.737081 0.675804i \(-0.763796\pi\)
−0.737081 + 0.675804i \(0.763796\pi\)
\(992\) −31.5516 −1.00177
\(993\) 0 0
\(994\) −19.6989 −0.624810
\(995\) 15.7028 0.497812
\(996\) 0 0
\(997\) 36.8281 1.16636 0.583179 0.812344i \(-0.301809\pi\)
0.583179 + 0.812344i \(0.301809\pi\)
\(998\) 44.8915 1.42101
\(999\) 0 0
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 \(a_p\))