Properties

Label 4028.2.a.d.1.16
Level 4028
Weight 2
Character 4028.1
Self dual Yes
Analytic conductor 32.164
Analytic rank 1
Dimension 19
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4028 = 2^{2} \cdot 19 \cdot 53 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4028.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.1637419342\)
Analytic rank: \(1\)
Dimension: \(19\)
Coefficient field: \(\mathbb{Q}[x]/(x^{19} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Root \(-1.94972\)
Character \(\chi\) = 4028.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.94972 q^{3} +1.42435 q^{5} -4.01869 q^{7} +0.801405 q^{9} +O(q^{10})\) \(q+1.94972 q^{3} +1.42435 q^{5} -4.01869 q^{7} +0.801405 q^{9} -1.76924 q^{11} -0.162788 q^{13} +2.77708 q^{15} +3.69306 q^{17} -1.00000 q^{19} -7.83532 q^{21} +1.52669 q^{23} -2.97122 q^{25} -4.28664 q^{27} +2.66959 q^{29} -10.7471 q^{31} -3.44952 q^{33} -5.72403 q^{35} +1.29232 q^{37} -0.317391 q^{39} -7.80202 q^{41} +4.54569 q^{43} +1.14148 q^{45} -8.83786 q^{47} +9.14987 q^{49} +7.20043 q^{51} +1.00000 q^{53} -2.52002 q^{55} -1.94972 q^{57} -2.95882 q^{59} -7.23691 q^{61} -3.22060 q^{63} -0.231867 q^{65} +14.9269 q^{67} +2.97662 q^{69} -11.1361 q^{71} +0.331709 q^{73} -5.79305 q^{75} +7.11002 q^{77} -4.60353 q^{79} -10.7620 q^{81} -8.46798 q^{83} +5.26021 q^{85} +5.20494 q^{87} +3.52631 q^{89} +0.654194 q^{91} -20.9539 q^{93} -1.42435 q^{95} +14.8111 q^{97} -1.41788 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 19q - 4q^{3} - 2q^{5} - 11q^{7} + 19q^{9} + O(q^{10}) \) \( 19q - 4q^{3} - 2q^{5} - 11q^{7} + 19q^{9} - 11q^{11} + q^{13} - 20q^{15} - q^{17} - 19q^{19} - 10q^{21} - 16q^{23} + 21q^{25} - 4q^{27} - 9q^{31} + 7q^{33} - 25q^{37} - 25q^{39} + q^{41} - 41q^{43} - 27q^{45} - 29q^{47} + 14q^{49} - 24q^{51} + 19q^{53} - 28q^{55} + 4q^{57} - 42q^{59} + q^{61} - 41q^{63} + 2q^{65} - 41q^{67} - 25q^{69} - 20q^{73} + 11q^{75} - 19q^{77} - 38q^{79} + 23q^{81} - 36q^{83} - 58q^{85} - 30q^{87} - 25q^{89} - 55q^{91} - 38q^{93} + 2q^{95} - 13q^{97} + q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.94972 1.12567 0.562835 0.826569i \(-0.309710\pi\)
0.562835 + 0.826569i \(0.309710\pi\)
\(4\) 0 0
\(5\) 1.42435 0.636989 0.318495 0.947925i \(-0.396823\pi\)
0.318495 + 0.947925i \(0.396823\pi\)
\(6\) 0 0
\(7\) −4.01869 −1.51892 −0.759461 0.650553i \(-0.774537\pi\)
−0.759461 + 0.650553i \(0.774537\pi\)
\(8\) 0 0
\(9\) 0.801405 0.267135
\(10\) 0 0
\(11\) −1.76924 −0.533445 −0.266723 0.963773i \(-0.585941\pi\)
−0.266723 + 0.963773i \(0.585941\pi\)
\(12\) 0 0
\(13\) −0.162788 −0.0451492 −0.0225746 0.999745i \(-0.507186\pi\)
−0.0225746 + 0.999745i \(0.507186\pi\)
\(14\) 0 0
\(15\) 2.77708 0.717040
\(16\) 0 0
\(17\) 3.69306 0.895698 0.447849 0.894109i \(-0.352190\pi\)
0.447849 + 0.894109i \(0.352190\pi\)
\(18\) 0 0
\(19\) −1.00000 −0.229416
\(20\) 0 0
\(21\) −7.83532 −1.70981
\(22\) 0 0
\(23\) 1.52669 0.318337 0.159169 0.987251i \(-0.449119\pi\)
0.159169 + 0.987251i \(0.449119\pi\)
\(24\) 0 0
\(25\) −2.97122 −0.594245
\(26\) 0 0
\(27\) −4.28664 −0.824965
\(28\) 0 0
\(29\) 2.66959 0.495730 0.247865 0.968795i \(-0.420271\pi\)
0.247865 + 0.968795i \(0.420271\pi\)
\(30\) 0 0
\(31\) −10.7471 −1.93024 −0.965119 0.261810i \(-0.915681\pi\)
−0.965119 + 0.261810i \(0.915681\pi\)
\(32\) 0 0
\(33\) −3.44952 −0.600484
\(34\) 0 0
\(35\) −5.72403 −0.967537
\(36\) 0 0
\(37\) 1.29232 0.212455 0.106228 0.994342i \(-0.466123\pi\)
0.106228 + 0.994342i \(0.466123\pi\)
\(38\) 0 0
\(39\) −0.317391 −0.0508232
\(40\) 0 0
\(41\) −7.80202 −1.21847 −0.609235 0.792989i \(-0.708524\pi\)
−0.609235 + 0.792989i \(0.708524\pi\)
\(42\) 0 0
\(43\) 4.54569 0.693211 0.346606 0.938011i \(-0.387334\pi\)
0.346606 + 0.938011i \(0.387334\pi\)
\(44\) 0 0
\(45\) 1.14148 0.170162
\(46\) 0 0
\(47\) −8.83786 −1.28913 −0.644567 0.764548i \(-0.722962\pi\)
−0.644567 + 0.764548i \(0.722962\pi\)
\(48\) 0 0
\(49\) 9.14987 1.30712
\(50\) 0 0
\(51\) 7.20043 1.00826
\(52\) 0 0
\(53\) 1.00000 0.137361
\(54\) 0 0
\(55\) −2.52002 −0.339799
\(56\) 0 0
\(57\) −1.94972 −0.258247
\(58\) 0 0
\(59\) −2.95882 −0.385205 −0.192603 0.981277i \(-0.561693\pi\)
−0.192603 + 0.981277i \(0.561693\pi\)
\(60\) 0 0
\(61\) −7.23691 −0.926592 −0.463296 0.886204i \(-0.653333\pi\)
−0.463296 + 0.886204i \(0.653333\pi\)
\(62\) 0 0
\(63\) −3.22060 −0.405757
\(64\) 0 0
\(65\) −0.231867 −0.0287596
\(66\) 0 0
\(67\) 14.9269 1.82361 0.911806 0.410621i \(-0.134688\pi\)
0.911806 + 0.410621i \(0.134688\pi\)
\(68\) 0 0
\(69\) 2.97662 0.358343
\(70\) 0 0
\(71\) −11.1361 −1.32161 −0.660807 0.750556i \(-0.729786\pi\)
−0.660807 + 0.750556i \(0.729786\pi\)
\(72\) 0 0
\(73\) 0.331709 0.0388236 0.0194118 0.999812i \(-0.493821\pi\)
0.0194118 + 0.999812i \(0.493821\pi\)
\(74\) 0 0
\(75\) −5.79305 −0.668924
\(76\) 0 0
\(77\) 7.11002 0.810262
\(78\) 0 0
\(79\) −4.60353 −0.517937 −0.258969 0.965886i \(-0.583383\pi\)
−0.258969 + 0.965886i \(0.583383\pi\)
\(80\) 0 0
\(81\) −10.7620 −1.19577
\(82\) 0 0
\(83\) −8.46798 −0.929482 −0.464741 0.885447i \(-0.653853\pi\)
−0.464741 + 0.885447i \(0.653853\pi\)
\(84\) 0 0
\(85\) 5.26021 0.570550
\(86\) 0 0
\(87\) 5.20494 0.558029
\(88\) 0 0
\(89\) 3.52631 0.373788 0.186894 0.982380i \(-0.440158\pi\)
0.186894 + 0.982380i \(0.440158\pi\)
\(90\) 0 0
\(91\) 0.654194 0.0685782
\(92\) 0 0
\(93\) −20.9539 −2.17281
\(94\) 0 0
\(95\) −1.42435 −0.146135
\(96\) 0 0
\(97\) 14.8111 1.50384 0.751918 0.659257i \(-0.229129\pi\)
0.751918 + 0.659257i \(0.229129\pi\)
\(98\) 0 0
\(99\) −1.41788 −0.142502
\(100\) 0 0
\(101\) −4.70443 −0.468109 −0.234054 0.972224i \(-0.575199\pi\)
−0.234054 + 0.972224i \(0.575199\pi\)
\(102\) 0 0
\(103\) −3.54468 −0.349267 −0.174634 0.984633i \(-0.555874\pi\)
−0.174634 + 0.984633i \(0.555874\pi\)
\(104\) 0 0
\(105\) −11.1602 −1.08913
\(106\) 0 0
\(107\) −4.86249 −0.470074 −0.235037 0.971986i \(-0.575521\pi\)
−0.235037 + 0.971986i \(0.575521\pi\)
\(108\) 0 0
\(109\) −3.01434 −0.288722 −0.144361 0.989525i \(-0.546113\pi\)
−0.144361 + 0.989525i \(0.546113\pi\)
\(110\) 0 0
\(111\) 2.51965 0.239155
\(112\) 0 0
\(113\) −2.73218 −0.257022 −0.128511 0.991708i \(-0.541020\pi\)
−0.128511 + 0.991708i \(0.541020\pi\)
\(114\) 0 0
\(115\) 2.17455 0.202777
\(116\) 0 0
\(117\) −0.130459 −0.0120609
\(118\) 0 0
\(119\) −14.8413 −1.36050
\(120\) 0 0
\(121\) −7.86980 −0.715436
\(122\) 0 0
\(123\) −15.2117 −1.37160
\(124\) 0 0
\(125\) −11.3538 −1.01552
\(126\) 0 0
\(127\) −11.3238 −1.00482 −0.502411 0.864629i \(-0.667554\pi\)
−0.502411 + 0.864629i \(0.667554\pi\)
\(128\) 0 0
\(129\) 8.86282 0.780328
\(130\) 0 0
\(131\) −19.2810 −1.68459 −0.842295 0.539017i \(-0.818796\pi\)
−0.842295 + 0.539017i \(0.818796\pi\)
\(132\) 0 0
\(133\) 4.01869 0.348465
\(134\) 0 0
\(135\) −6.10569 −0.525494
\(136\) 0 0
\(137\) −3.20964 −0.274218 −0.137109 0.990556i \(-0.543781\pi\)
−0.137109 + 0.990556i \(0.543781\pi\)
\(138\) 0 0
\(139\) 2.54096 0.215521 0.107761 0.994177i \(-0.465632\pi\)
0.107761 + 0.994177i \(0.465632\pi\)
\(140\) 0 0
\(141\) −17.2313 −1.45114
\(142\) 0 0
\(143\) 0.288010 0.0240846
\(144\) 0 0
\(145\) 3.80243 0.315774
\(146\) 0 0
\(147\) 17.8397 1.47139
\(148\) 0 0
\(149\) 12.5830 1.03084 0.515422 0.856937i \(-0.327635\pi\)
0.515422 + 0.856937i \(0.327635\pi\)
\(150\) 0 0
\(151\) −0.0949678 −0.00772837 −0.00386419 0.999993i \(-0.501230\pi\)
−0.00386419 + 0.999993i \(0.501230\pi\)
\(152\) 0 0
\(153\) 2.95963 0.239272
\(154\) 0 0
\(155\) −15.3077 −1.22954
\(156\) 0 0
\(157\) 3.06340 0.244486 0.122243 0.992500i \(-0.460991\pi\)
0.122243 + 0.992500i \(0.460991\pi\)
\(158\) 0 0
\(159\) 1.94972 0.154623
\(160\) 0 0
\(161\) −6.13530 −0.483530
\(162\) 0 0
\(163\) 9.09905 0.712693 0.356346 0.934354i \(-0.384022\pi\)
0.356346 + 0.934354i \(0.384022\pi\)
\(164\) 0 0
\(165\) −4.91332 −0.382502
\(166\) 0 0
\(167\) 4.22356 0.326829 0.163415 0.986557i \(-0.447749\pi\)
0.163415 + 0.986557i \(0.447749\pi\)
\(168\) 0 0
\(169\) −12.9735 −0.997962
\(170\) 0 0
\(171\) −0.801405 −0.0612850
\(172\) 0 0
\(173\) 23.7089 1.80256 0.901279 0.433240i \(-0.142630\pi\)
0.901279 + 0.433240i \(0.142630\pi\)
\(174\) 0 0
\(175\) 11.9404 0.902612
\(176\) 0 0
\(177\) −5.76887 −0.433615
\(178\) 0 0
\(179\) −9.81120 −0.733323 −0.366662 0.930354i \(-0.619499\pi\)
−0.366662 + 0.930354i \(0.619499\pi\)
\(180\) 0 0
\(181\) 6.32977 0.470488 0.235244 0.971936i \(-0.424411\pi\)
0.235244 + 0.971936i \(0.424411\pi\)
\(182\) 0 0
\(183\) −14.1099 −1.04304
\(184\) 0 0
\(185\) 1.84071 0.135332
\(186\) 0 0
\(187\) −6.53390 −0.477806
\(188\) 0 0
\(189\) 17.2267 1.25306
\(190\) 0 0
\(191\) 22.6326 1.63764 0.818820 0.574050i \(-0.194628\pi\)
0.818820 + 0.574050i \(0.194628\pi\)
\(192\) 0 0
\(193\) −11.4711 −0.825706 −0.412853 0.910798i \(-0.635468\pi\)
−0.412853 + 0.910798i \(0.635468\pi\)
\(194\) 0 0
\(195\) −0.452076 −0.0323738
\(196\) 0 0
\(197\) −13.9329 −0.992679 −0.496340 0.868128i \(-0.665323\pi\)
−0.496340 + 0.868128i \(0.665323\pi\)
\(198\) 0 0
\(199\) −10.0427 −0.711907 −0.355954 0.934504i \(-0.615844\pi\)
−0.355954 + 0.934504i \(0.615844\pi\)
\(200\) 0 0
\(201\) 29.1033 2.05279
\(202\) 0 0
\(203\) −10.7282 −0.752975
\(204\) 0 0
\(205\) −11.1128 −0.776153
\(206\) 0 0
\(207\) 1.22350 0.0850390
\(208\) 0 0
\(209\) 1.76924 0.122381
\(210\) 0 0
\(211\) −0.736794 −0.0507230 −0.0253615 0.999678i \(-0.508074\pi\)
−0.0253615 + 0.999678i \(0.508074\pi\)
\(212\) 0 0
\(213\) −21.7123 −1.48770
\(214\) 0 0
\(215\) 6.47466 0.441568
\(216\) 0 0
\(217\) 43.1893 2.93188
\(218\) 0 0
\(219\) 0.646740 0.0437026
\(220\) 0 0
\(221\) −0.601185 −0.0404401
\(222\) 0 0
\(223\) −1.32103 −0.0884629 −0.0442315 0.999021i \(-0.514084\pi\)
−0.0442315 + 0.999021i \(0.514084\pi\)
\(224\) 0 0
\(225\) −2.38115 −0.158744
\(226\) 0 0
\(227\) 10.2954 0.683332 0.341666 0.939821i \(-0.389009\pi\)
0.341666 + 0.939821i \(0.389009\pi\)
\(228\) 0 0
\(229\) 14.9132 0.985491 0.492745 0.870174i \(-0.335993\pi\)
0.492745 + 0.870174i \(0.335993\pi\)
\(230\) 0 0
\(231\) 13.8625 0.912088
\(232\) 0 0
\(233\) 2.93685 0.192399 0.0961997 0.995362i \(-0.469331\pi\)
0.0961997 + 0.995362i \(0.469331\pi\)
\(234\) 0 0
\(235\) −12.5882 −0.821165
\(236\) 0 0
\(237\) −8.97559 −0.583027
\(238\) 0 0
\(239\) −2.93200 −0.189655 −0.0948276 0.995494i \(-0.530230\pi\)
−0.0948276 + 0.995494i \(0.530230\pi\)
\(240\) 0 0
\(241\) 22.5700 1.45386 0.726930 0.686711i \(-0.240946\pi\)
0.726930 + 0.686711i \(0.240946\pi\)
\(242\) 0 0
\(243\) −8.12288 −0.521083
\(244\) 0 0
\(245\) 13.0326 0.832624
\(246\) 0 0
\(247\) 0.162788 0.0103579
\(248\) 0 0
\(249\) −16.5102 −1.04629
\(250\) 0 0
\(251\) 15.4083 0.972562 0.486281 0.873802i \(-0.338353\pi\)
0.486281 + 0.873802i \(0.338353\pi\)
\(252\) 0 0
\(253\) −2.70108 −0.169815
\(254\) 0 0
\(255\) 10.2559 0.642252
\(256\) 0 0
\(257\) 0.167907 0.0104737 0.00523686 0.999986i \(-0.498333\pi\)
0.00523686 + 0.999986i \(0.498333\pi\)
\(258\) 0 0
\(259\) −5.19342 −0.322703
\(260\) 0 0
\(261\) 2.13942 0.132427
\(262\) 0 0
\(263\) −8.62095 −0.531590 −0.265795 0.964030i \(-0.585635\pi\)
−0.265795 + 0.964030i \(0.585635\pi\)
\(264\) 0 0
\(265\) 1.42435 0.0874972
\(266\) 0 0
\(267\) 6.87531 0.420762
\(268\) 0 0
\(269\) −20.5238 −1.25136 −0.625678 0.780081i \(-0.715178\pi\)
−0.625678 + 0.780081i \(0.715178\pi\)
\(270\) 0 0
\(271\) −12.1308 −0.736892 −0.368446 0.929649i \(-0.620110\pi\)
−0.368446 + 0.929649i \(0.620110\pi\)
\(272\) 0 0
\(273\) 1.27549 0.0771964
\(274\) 0 0
\(275\) 5.25680 0.316997
\(276\) 0 0
\(277\) 19.2451 1.15633 0.578163 0.815921i \(-0.303770\pi\)
0.578163 + 0.815921i \(0.303770\pi\)
\(278\) 0 0
\(279\) −8.61279 −0.515634
\(280\) 0 0
\(281\) −18.6933 −1.11515 −0.557574 0.830127i \(-0.688268\pi\)
−0.557574 + 0.830127i \(0.688268\pi\)
\(282\) 0 0
\(283\) 7.24216 0.430502 0.215251 0.976559i \(-0.430943\pi\)
0.215251 + 0.976559i \(0.430943\pi\)
\(284\) 0 0
\(285\) −2.77708 −0.164500
\(286\) 0 0
\(287\) 31.3539 1.85076
\(288\) 0 0
\(289\) −3.36132 −0.197725
\(290\) 0 0
\(291\) 28.8774 1.69282
\(292\) 0 0
\(293\) 28.5009 1.66504 0.832521 0.553994i \(-0.186897\pi\)
0.832521 + 0.553994i \(0.186897\pi\)
\(294\) 0 0
\(295\) −4.21440 −0.245372
\(296\) 0 0
\(297\) 7.58409 0.440073
\(298\) 0 0
\(299\) −0.248527 −0.0143727
\(300\) 0 0
\(301\) −18.2677 −1.05293
\(302\) 0 0
\(303\) −9.17232 −0.526936
\(304\) 0 0
\(305\) −10.3079 −0.590229
\(306\) 0 0
\(307\) −4.60309 −0.262712 −0.131356 0.991335i \(-0.541933\pi\)
−0.131356 + 0.991335i \(0.541933\pi\)
\(308\) 0 0
\(309\) −6.91112 −0.393160
\(310\) 0 0
\(311\) 1.69986 0.0963901 0.0481951 0.998838i \(-0.484653\pi\)
0.0481951 + 0.998838i \(0.484653\pi\)
\(312\) 0 0
\(313\) −1.68364 −0.0951649 −0.0475825 0.998867i \(-0.515152\pi\)
−0.0475825 + 0.998867i \(0.515152\pi\)
\(314\) 0 0
\(315\) −4.58726 −0.258463
\(316\) 0 0
\(317\) −19.4273 −1.09115 −0.545573 0.838063i \(-0.683688\pi\)
−0.545573 + 0.838063i \(0.683688\pi\)
\(318\) 0 0
\(319\) −4.72313 −0.264445
\(320\) 0 0
\(321\) −9.48048 −0.529149
\(322\) 0 0
\(323\) −3.69306 −0.205487
\(324\) 0 0
\(325\) 0.483679 0.0268297
\(326\) 0 0
\(327\) −5.87712 −0.325006
\(328\) 0 0
\(329\) 35.5166 1.95809
\(330\) 0 0
\(331\) 12.1416 0.667365 0.333682 0.942686i \(-0.391709\pi\)
0.333682 + 0.942686i \(0.391709\pi\)
\(332\) 0 0
\(333\) 1.03567 0.0567543
\(334\) 0 0
\(335\) 21.2612 1.16162
\(336\) 0 0
\(337\) 11.7602 0.640619 0.320309 0.947313i \(-0.396213\pi\)
0.320309 + 0.947313i \(0.396213\pi\)
\(338\) 0 0
\(339\) −5.32699 −0.289323
\(340\) 0 0
\(341\) 19.0142 1.02968
\(342\) 0 0
\(343\) −8.63967 −0.466498
\(344\) 0 0
\(345\) 4.23975 0.228261
\(346\) 0 0
\(347\) 20.8677 1.12024 0.560118 0.828413i \(-0.310756\pi\)
0.560118 + 0.828413i \(0.310756\pi\)
\(348\) 0 0
\(349\) 33.9337 1.81643 0.908216 0.418502i \(-0.137445\pi\)
0.908216 + 0.418502i \(0.137445\pi\)
\(350\) 0 0
\(351\) 0.697813 0.0372465
\(352\) 0 0
\(353\) 8.87569 0.472405 0.236203 0.971704i \(-0.424097\pi\)
0.236203 + 0.971704i \(0.424097\pi\)
\(354\) 0 0
\(355\) −15.8617 −0.841854
\(356\) 0 0
\(357\) −28.9363 −1.53147
\(358\) 0 0
\(359\) −3.06841 −0.161945 −0.0809723 0.996716i \(-0.525803\pi\)
−0.0809723 + 0.996716i \(0.525803\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) −15.3439 −0.805346
\(364\) 0 0
\(365\) 0.472470 0.0247302
\(366\) 0 0
\(367\) 11.7441 0.613038 0.306519 0.951865i \(-0.400836\pi\)
0.306519 + 0.951865i \(0.400836\pi\)
\(368\) 0 0
\(369\) −6.25258 −0.325496
\(370\) 0 0
\(371\) −4.01869 −0.208640
\(372\) 0 0
\(373\) −19.9768 −1.03436 −0.517179 0.855877i \(-0.673018\pi\)
−0.517179 + 0.855877i \(0.673018\pi\)
\(374\) 0 0
\(375\) −22.1368 −1.14314
\(376\) 0 0
\(377\) −0.434576 −0.0223818
\(378\) 0 0
\(379\) 5.66779 0.291135 0.145567 0.989348i \(-0.453499\pi\)
0.145567 + 0.989348i \(0.453499\pi\)
\(380\) 0 0
\(381\) −22.0782 −1.13110
\(382\) 0 0
\(383\) 6.72159 0.343457 0.171728 0.985144i \(-0.445065\pi\)
0.171728 + 0.985144i \(0.445065\pi\)
\(384\) 0 0
\(385\) 10.1272 0.516128
\(386\) 0 0
\(387\) 3.64294 0.185181
\(388\) 0 0
\(389\) −9.08084 −0.460417 −0.230208 0.973141i \(-0.573941\pi\)
−0.230208 + 0.973141i \(0.573941\pi\)
\(390\) 0 0
\(391\) 5.63816 0.285134
\(392\) 0 0
\(393\) −37.5926 −1.89629
\(394\) 0 0
\(395\) −6.55704 −0.329921
\(396\) 0 0
\(397\) −10.9518 −0.549657 −0.274828 0.961493i \(-0.588621\pi\)
−0.274828 + 0.961493i \(0.588621\pi\)
\(398\) 0 0
\(399\) 7.83532 0.392257
\(400\) 0 0
\(401\) −1.26592 −0.0632169 −0.0316084 0.999500i \(-0.510063\pi\)
−0.0316084 + 0.999500i \(0.510063\pi\)
\(402\) 0 0
\(403\) 1.74950 0.0871488
\(404\) 0 0
\(405\) −15.3288 −0.761695
\(406\) 0 0
\(407\) −2.28641 −0.113333
\(408\) 0 0
\(409\) 17.2219 0.851570 0.425785 0.904824i \(-0.359998\pi\)
0.425785 + 0.904824i \(0.359998\pi\)
\(410\) 0 0
\(411\) −6.25789 −0.308679
\(412\) 0 0
\(413\) 11.8906 0.585097
\(414\) 0 0
\(415\) −12.0614 −0.592070
\(416\) 0 0
\(417\) 4.95415 0.242606
\(418\) 0 0
\(419\) 19.0193 0.929152 0.464576 0.885533i \(-0.346207\pi\)
0.464576 + 0.885533i \(0.346207\pi\)
\(420\) 0 0
\(421\) −27.6185 −1.34604 −0.673021 0.739623i \(-0.735004\pi\)
−0.673021 + 0.739623i \(0.735004\pi\)
\(422\) 0 0
\(423\) −7.08270 −0.344373
\(424\) 0 0
\(425\) −10.9729 −0.532264
\(426\) 0 0
\(427\) 29.0829 1.40742
\(428\) 0 0
\(429\) 0.561539 0.0271114
\(430\) 0 0
\(431\) −15.3626 −0.739990 −0.369995 0.929034i \(-0.620641\pi\)
−0.369995 + 0.929034i \(0.620641\pi\)
\(432\) 0 0
\(433\) −6.98336 −0.335599 −0.167799 0.985821i \(-0.553666\pi\)
−0.167799 + 0.985821i \(0.553666\pi\)
\(434\) 0 0
\(435\) 7.41367 0.355458
\(436\) 0 0
\(437\) −1.52669 −0.0730316
\(438\) 0 0
\(439\) −31.0799 −1.48336 −0.741682 0.670752i \(-0.765971\pi\)
−0.741682 + 0.670752i \(0.765971\pi\)
\(440\) 0 0
\(441\) 7.33275 0.349179
\(442\) 0 0
\(443\) 13.0078 0.618018 0.309009 0.951059i \(-0.400003\pi\)
0.309009 + 0.951059i \(0.400003\pi\)
\(444\) 0 0
\(445\) 5.02270 0.238099
\(446\) 0 0
\(447\) 24.5334 1.16039
\(448\) 0 0
\(449\) 10.7300 0.506381 0.253191 0.967416i \(-0.418520\pi\)
0.253191 + 0.967416i \(0.418520\pi\)
\(450\) 0 0
\(451\) 13.8036 0.649987
\(452\) 0 0
\(453\) −0.185161 −0.00869960
\(454\) 0 0
\(455\) 0.931802 0.0436836
\(456\) 0 0
\(457\) −30.6499 −1.43374 −0.716871 0.697206i \(-0.754426\pi\)
−0.716871 + 0.697206i \(0.754426\pi\)
\(458\) 0 0
\(459\) −15.8308 −0.738919
\(460\) 0 0
\(461\) −1.50835 −0.0702507 −0.0351254 0.999383i \(-0.511183\pi\)
−0.0351254 + 0.999383i \(0.511183\pi\)
\(462\) 0 0
\(463\) −13.4523 −0.625181 −0.312591 0.949888i \(-0.601197\pi\)
−0.312591 + 0.949888i \(0.601197\pi\)
\(464\) 0 0
\(465\) −29.8457 −1.38406
\(466\) 0 0
\(467\) 33.4845 1.54948 0.774738 0.632282i \(-0.217882\pi\)
0.774738 + 0.632282i \(0.217882\pi\)
\(468\) 0 0
\(469\) −59.9866 −2.76993
\(470\) 0 0
\(471\) 5.97278 0.275211
\(472\) 0 0
\(473\) −8.04241 −0.369790
\(474\) 0 0
\(475\) 2.97122 0.136329
\(476\) 0 0
\(477\) 0.801405 0.0366938
\(478\) 0 0
\(479\) −3.80274 −0.173752 −0.0868758 0.996219i \(-0.527688\pi\)
−0.0868758 + 0.996219i \(0.527688\pi\)
\(480\) 0 0
\(481\) −0.210373 −0.00959220
\(482\) 0 0
\(483\) −11.9621 −0.544295
\(484\) 0 0
\(485\) 21.0962 0.957927
\(486\) 0 0
\(487\) −41.6493 −1.88731 −0.943655 0.330932i \(-0.892637\pi\)
−0.943655 + 0.330932i \(0.892637\pi\)
\(488\) 0 0
\(489\) 17.7406 0.802258
\(490\) 0 0
\(491\) 23.7177 1.07036 0.535182 0.844737i \(-0.320243\pi\)
0.535182 + 0.844737i \(0.320243\pi\)
\(492\) 0 0
\(493\) 9.85894 0.444024
\(494\) 0 0
\(495\) −2.01955 −0.0907721
\(496\) 0 0
\(497\) 44.7526 2.00743
\(498\) 0 0
\(499\) 16.2505 0.727472 0.363736 0.931502i \(-0.381501\pi\)
0.363736 + 0.931502i \(0.381501\pi\)
\(500\) 0 0
\(501\) 8.23476 0.367902
\(502\) 0 0
\(503\) 24.0712 1.07328 0.536641 0.843811i \(-0.319693\pi\)
0.536641 + 0.843811i \(0.319693\pi\)
\(504\) 0 0
\(505\) −6.70076 −0.298180
\(506\) 0 0
\(507\) −25.2947 −1.12338
\(508\) 0 0
\(509\) −32.1638 −1.42564 −0.712819 0.701348i \(-0.752582\pi\)
−0.712819 + 0.701348i \(0.752582\pi\)
\(510\) 0 0
\(511\) −1.33304 −0.0589701
\(512\) 0 0
\(513\) 4.28664 0.189260
\(514\) 0 0
\(515\) −5.04886 −0.222479
\(516\) 0 0
\(517\) 15.6363 0.687682
\(518\) 0 0
\(519\) 46.2258 2.02909
\(520\) 0 0
\(521\) −24.6898 −1.08168 −0.540840 0.841125i \(-0.681894\pi\)
−0.540840 + 0.841125i \(0.681894\pi\)
\(522\) 0 0
\(523\) 32.2724 1.41117 0.705587 0.708623i \(-0.250683\pi\)
0.705587 + 0.708623i \(0.250683\pi\)
\(524\) 0 0
\(525\) 23.2805 1.01604
\(526\) 0 0
\(527\) −39.6897 −1.72891
\(528\) 0 0
\(529\) −20.6692 −0.898661
\(530\) 0 0
\(531\) −2.37121 −0.102902
\(532\) 0 0
\(533\) 1.27007 0.0550130
\(534\) 0 0
\(535\) −6.92589 −0.299432
\(536\) 0 0
\(537\) −19.1291 −0.825481
\(538\) 0 0
\(539\) −16.1883 −0.697279
\(540\) 0 0
\(541\) 15.4223 0.663055 0.331528 0.943445i \(-0.392436\pi\)
0.331528 + 0.943445i \(0.392436\pi\)
\(542\) 0 0
\(543\) 12.3413 0.529614
\(544\) 0 0
\(545\) −4.29348 −0.183913
\(546\) 0 0
\(547\) 27.9367 1.19449 0.597245 0.802059i \(-0.296262\pi\)
0.597245 + 0.802059i \(0.296262\pi\)
\(548\) 0 0
\(549\) −5.79970 −0.247525
\(550\) 0 0
\(551\) −2.66959 −0.113728
\(552\) 0 0
\(553\) 18.5002 0.786707
\(554\) 0 0
\(555\) 3.58887 0.152339
\(556\) 0 0
\(557\) −29.4559 −1.24809 −0.624044 0.781389i \(-0.714511\pi\)
−0.624044 + 0.781389i \(0.714511\pi\)
\(558\) 0 0
\(559\) −0.739983 −0.0312980
\(560\) 0 0
\(561\) −12.7393 −0.537852
\(562\) 0 0
\(563\) −28.3290 −1.19392 −0.596962 0.802269i \(-0.703626\pi\)
−0.596962 + 0.802269i \(0.703626\pi\)
\(564\) 0 0
\(565\) −3.89159 −0.163720
\(566\) 0 0
\(567\) 43.2490 1.81629
\(568\) 0 0
\(569\) 33.5542 1.40666 0.703332 0.710862i \(-0.251695\pi\)
0.703332 + 0.710862i \(0.251695\pi\)
\(570\) 0 0
\(571\) 43.1494 1.80574 0.902872 0.429909i \(-0.141454\pi\)
0.902872 + 0.429909i \(0.141454\pi\)
\(572\) 0 0
\(573\) 44.1273 1.84344
\(574\) 0 0
\(575\) −4.53614 −0.189170
\(576\) 0 0
\(577\) 3.79949 0.158175 0.0790873 0.996868i \(-0.474799\pi\)
0.0790873 + 0.996868i \(0.474799\pi\)
\(578\) 0 0
\(579\) −22.3654 −0.929473
\(580\) 0 0
\(581\) 34.0302 1.41181
\(582\) 0 0
\(583\) −1.76924 −0.0732743
\(584\) 0 0
\(585\) −0.185819 −0.00768269
\(586\) 0 0
\(587\) −6.94946 −0.286835 −0.143417 0.989662i \(-0.545809\pi\)
−0.143417 + 0.989662i \(0.545809\pi\)
\(588\) 0 0
\(589\) 10.7471 0.442827
\(590\) 0 0
\(591\) −27.1653 −1.11743
\(592\) 0 0
\(593\) −17.2668 −0.709063 −0.354532 0.935044i \(-0.615360\pi\)
−0.354532 + 0.935044i \(0.615360\pi\)
\(594\) 0 0
\(595\) −21.1392 −0.866621
\(596\) 0 0
\(597\) −19.5804 −0.801373
\(598\) 0 0
\(599\) −9.97441 −0.407543 −0.203772 0.979018i \(-0.565320\pi\)
−0.203772 + 0.979018i \(0.565320\pi\)
\(600\) 0 0
\(601\) −1.42390 −0.0580821 −0.0290410 0.999578i \(-0.509245\pi\)
−0.0290410 + 0.999578i \(0.509245\pi\)
\(602\) 0 0
\(603\) 11.9625 0.487151
\(604\) 0 0
\(605\) −11.2094 −0.455725
\(606\) 0 0
\(607\) −30.0325 −1.21898 −0.609490 0.792794i \(-0.708626\pi\)
−0.609490 + 0.792794i \(0.708626\pi\)
\(608\) 0 0
\(609\) −20.9171 −0.847602
\(610\) 0 0
\(611\) 1.43870 0.0582034
\(612\) 0 0
\(613\) 43.3035 1.74901 0.874505 0.485016i \(-0.161186\pi\)
0.874505 + 0.485016i \(0.161186\pi\)
\(614\) 0 0
\(615\) −21.6669 −0.873693
\(616\) 0 0
\(617\) −34.5602 −1.39134 −0.695670 0.718362i \(-0.744892\pi\)
−0.695670 + 0.718362i \(0.744892\pi\)
\(618\) 0 0
\(619\) 13.9032 0.558816 0.279408 0.960172i \(-0.409862\pi\)
0.279408 + 0.960172i \(0.409862\pi\)
\(620\) 0 0
\(621\) −6.54438 −0.262617
\(622\) 0 0
\(623\) −14.1711 −0.567755
\(624\) 0 0
\(625\) −1.31571 −0.0526285
\(626\) 0 0
\(627\) 3.44952 0.137760
\(628\) 0 0
\(629\) 4.77260 0.190296
\(630\) 0 0
\(631\) −29.8687 −1.18906 −0.594528 0.804075i \(-0.702661\pi\)
−0.594528 + 0.804075i \(0.702661\pi\)
\(632\) 0 0
\(633\) −1.43654 −0.0570974
\(634\) 0 0
\(635\) −16.1290 −0.640061
\(636\) 0 0
\(637\) −1.48949 −0.0590157
\(638\) 0 0
\(639\) −8.92454 −0.353049
\(640\) 0 0
\(641\) 23.0211 0.909280 0.454640 0.890675i \(-0.349768\pi\)
0.454640 + 0.890675i \(0.349768\pi\)
\(642\) 0 0
\(643\) −13.5428 −0.534076 −0.267038 0.963686i \(-0.586045\pi\)
−0.267038 + 0.963686i \(0.586045\pi\)
\(644\) 0 0
\(645\) 12.6238 0.497060
\(646\) 0 0
\(647\) −30.7319 −1.20819 −0.604097 0.796911i \(-0.706466\pi\)
−0.604097 + 0.796911i \(0.706466\pi\)
\(648\) 0 0
\(649\) 5.23485 0.205486
\(650\) 0 0
\(651\) 84.2071 3.30034
\(652\) 0 0
\(653\) 17.3399 0.678564 0.339282 0.940685i \(-0.389816\pi\)
0.339282 + 0.940685i \(0.389816\pi\)
\(654\) 0 0
\(655\) −27.4629 −1.07307
\(656\) 0 0
\(657\) 0.265833 0.0103711
\(658\) 0 0
\(659\) 13.4149 0.522571 0.261286 0.965262i \(-0.415854\pi\)
0.261286 + 0.965262i \(0.415854\pi\)
\(660\) 0 0
\(661\) 5.94449 0.231214 0.115607 0.993295i \(-0.463119\pi\)
0.115607 + 0.993295i \(0.463119\pi\)
\(662\) 0 0
\(663\) −1.17214 −0.0455222
\(664\) 0 0
\(665\) 5.72403 0.221968
\(666\) 0 0
\(667\) 4.07564 0.157809
\(668\) 0 0
\(669\) −2.57564 −0.0995801
\(670\) 0 0
\(671\) 12.8038 0.494286
\(672\) 0 0
\(673\) 33.1464 1.27770 0.638849 0.769332i \(-0.279411\pi\)
0.638849 + 0.769332i \(0.279411\pi\)
\(674\) 0 0
\(675\) 12.7366 0.490231
\(676\) 0 0
\(677\) 34.0632 1.30915 0.654577 0.755996i \(-0.272847\pi\)
0.654577 + 0.755996i \(0.272847\pi\)
\(678\) 0 0
\(679\) −59.5211 −2.28421
\(680\) 0 0
\(681\) 20.0732 0.769207
\(682\) 0 0
\(683\) −15.3969 −0.589146 −0.294573 0.955629i \(-0.595177\pi\)
−0.294573 + 0.955629i \(0.595177\pi\)
\(684\) 0 0
\(685\) −4.57165 −0.174674
\(686\) 0 0
\(687\) 29.0765 1.10934
\(688\) 0 0
\(689\) −0.162788 −0.00620172
\(690\) 0 0
\(691\) −23.1007 −0.878793 −0.439396 0.898293i \(-0.644808\pi\)
−0.439396 + 0.898293i \(0.644808\pi\)
\(692\) 0 0
\(693\) 5.69800 0.216449
\(694\) 0 0
\(695\) 3.61921 0.137285
\(696\) 0 0
\(697\) −28.8133 −1.09138
\(698\) 0 0
\(699\) 5.72603 0.216579
\(700\) 0 0
\(701\) 31.9502 1.20674 0.603371 0.797461i \(-0.293824\pi\)
0.603371 + 0.797461i \(0.293824\pi\)
\(702\) 0 0
\(703\) −1.29232 −0.0487406
\(704\) 0 0
\(705\) −24.5435 −0.924361
\(706\) 0 0
\(707\) 18.9057 0.711020
\(708\) 0 0
\(709\) 27.7244 1.04121 0.520605 0.853797i \(-0.325706\pi\)
0.520605 + 0.853797i \(0.325706\pi\)
\(710\) 0 0
\(711\) −3.68929 −0.138359
\(712\) 0 0
\(713\) −16.4075 −0.614467
\(714\) 0 0
\(715\) 0.410228 0.0153417
\(716\) 0 0
\(717\) −5.71657 −0.213489
\(718\) 0 0
\(719\) −41.8691 −1.56146 −0.780728 0.624871i \(-0.785151\pi\)
−0.780728 + 0.624871i \(0.785151\pi\)
\(720\) 0 0
\(721\) 14.2450 0.530510
\(722\) 0 0
\(723\) 44.0051 1.63657
\(724\) 0 0
\(725\) −7.93194 −0.294585
\(726\) 0 0
\(727\) −35.9844 −1.33459 −0.667293 0.744795i \(-0.732547\pi\)
−0.667293 + 0.744795i \(0.732547\pi\)
\(728\) 0 0
\(729\) 16.4486 0.609206
\(730\) 0 0
\(731\) 16.7875 0.620908
\(732\) 0 0
\(733\) −17.0063 −0.628144 −0.314072 0.949399i \(-0.601693\pi\)
−0.314072 + 0.949399i \(0.601693\pi\)
\(734\) 0 0
\(735\) 25.4100 0.937261
\(736\) 0 0
\(737\) −26.4092 −0.972797
\(738\) 0 0
\(739\) 11.8096 0.434422 0.217211 0.976125i \(-0.430304\pi\)
0.217211 + 0.976125i \(0.430304\pi\)
\(740\) 0 0
\(741\) 0.317391 0.0116596
\(742\) 0 0
\(743\) −40.6894 −1.49275 −0.746375 0.665525i \(-0.768208\pi\)
−0.746375 + 0.665525i \(0.768208\pi\)
\(744\) 0 0
\(745\) 17.9227 0.656636
\(746\) 0 0
\(747\) −6.78628 −0.248297
\(748\) 0 0
\(749\) 19.5408 0.714006
\(750\) 0 0
\(751\) −2.94419 −0.107435 −0.0537175 0.998556i \(-0.517107\pi\)
−0.0537175 + 0.998556i \(0.517107\pi\)
\(752\) 0 0
\(753\) 30.0418 1.09479
\(754\) 0 0
\(755\) −0.135268 −0.00492289
\(756\) 0 0
\(757\) −10.8143 −0.393052 −0.196526 0.980499i \(-0.562966\pi\)
−0.196526 + 0.980499i \(0.562966\pi\)
\(758\) 0 0
\(759\) −5.26635 −0.191156
\(760\) 0 0
\(761\) −23.6050 −0.855679 −0.427839 0.903855i \(-0.640725\pi\)
−0.427839 + 0.903855i \(0.640725\pi\)
\(762\) 0 0
\(763\) 12.1137 0.438546
\(764\) 0 0
\(765\) 4.21556 0.152414
\(766\) 0 0
\(767\) 0.481660 0.0173917
\(768\) 0 0
\(769\) 26.5819 0.958568 0.479284 0.877660i \(-0.340896\pi\)
0.479284 + 0.877660i \(0.340896\pi\)
\(770\) 0 0
\(771\) 0.327371 0.0117900
\(772\) 0 0
\(773\) −41.0455 −1.47630 −0.738151 0.674635i \(-0.764301\pi\)
−0.738151 + 0.674635i \(0.764301\pi\)
\(774\) 0 0
\(775\) 31.9321 1.14703
\(776\) 0 0
\(777\) −10.1257 −0.363258
\(778\) 0 0
\(779\) 7.80202 0.279536
\(780\) 0 0
\(781\) 19.7024 0.705008
\(782\) 0 0
\(783\) −11.4436 −0.408960
\(784\) 0 0
\(785\) 4.36336 0.155735
\(786\) 0 0
\(787\) −14.3395 −0.511147 −0.255573 0.966790i \(-0.582264\pi\)
−0.255573 + 0.966790i \(0.582264\pi\)
\(788\) 0 0
\(789\) −16.8084 −0.598396
\(790\) 0 0
\(791\) 10.9798 0.390397
\(792\) 0 0
\(793\) 1.17808 0.0418349
\(794\) 0 0
\(795\) 2.77708 0.0984931
\(796\) 0 0
\(797\) −6.29350 −0.222927 −0.111464 0.993769i \(-0.535554\pi\)
−0.111464 + 0.993769i \(0.535554\pi\)
\(798\) 0 0
\(799\) −32.6387 −1.15467
\(800\) 0 0
\(801\) 2.82600 0.0998518
\(802\) 0 0
\(803\) −0.586872 −0.0207103
\(804\) 0 0
\(805\) −8.73883 −0.308003
\(806\) 0 0
\(807\) −40.0156 −1.40862
\(808\) 0 0
\(809\) 6.44386 0.226554 0.113277 0.993563i \(-0.463865\pi\)
0.113277 + 0.993563i \(0.463865\pi\)
\(810\) 0 0
\(811\) −3.73893 −0.131291 −0.0656457 0.997843i \(-0.520911\pi\)
−0.0656457 + 0.997843i \(0.520911\pi\)
\(812\) 0 0
\(813\) −23.6516 −0.829498
\(814\) 0 0
\(815\) 12.9602 0.453978
\(816\) 0 0
\(817\) −4.54569 −0.159034
\(818\) 0 0
\(819\) 0.524274 0.0183196
\(820\) 0 0
\(821\) −2.42599 −0.0846677 −0.0423339 0.999104i \(-0.513479\pi\)
−0.0423339 + 0.999104i \(0.513479\pi\)
\(822\) 0 0
\(823\) −7.88782 −0.274952 −0.137476 0.990505i \(-0.543899\pi\)
−0.137476 + 0.990505i \(0.543899\pi\)
\(824\) 0 0
\(825\) 10.2493 0.356834
\(826\) 0 0
\(827\) −19.4720 −0.677109 −0.338554 0.940947i \(-0.609938\pi\)
−0.338554 + 0.940947i \(0.609938\pi\)
\(828\) 0 0
\(829\) 1.52092 0.0528239 0.0264119 0.999651i \(-0.491592\pi\)
0.0264119 + 0.999651i \(0.491592\pi\)
\(830\) 0 0
\(831\) 37.5225 1.30164
\(832\) 0 0
\(833\) 33.7910 1.17079
\(834\) 0 0
\(835\) 6.01584 0.208187
\(836\) 0 0
\(837\) 46.0690 1.59238
\(838\) 0 0
\(839\) −32.8160 −1.13293 −0.566467 0.824084i \(-0.691690\pi\)
−0.566467 + 0.824084i \(0.691690\pi\)
\(840\) 0 0
\(841\) −21.8733 −0.754252
\(842\) 0 0
\(843\) −36.4467 −1.25529
\(844\) 0 0
\(845\) −18.4788 −0.635691
\(846\) 0 0
\(847\) 31.6263 1.08669
\(848\) 0 0
\(849\) 14.1202 0.484603
\(850\) 0 0
\(851\) 1.97297 0.0676325
\(852\) 0 0
\(853\) −37.4185 −1.28119 −0.640593 0.767881i \(-0.721311\pi\)
−0.640593 + 0.767881i \(0.721311\pi\)
\(854\) 0 0
\(855\) −1.14148 −0.0390379
\(856\) 0 0
\(857\) 23.2022 0.792571 0.396285 0.918127i \(-0.370299\pi\)
0.396285 + 0.918127i \(0.370299\pi\)
\(858\) 0 0
\(859\) −20.1674 −0.688103 −0.344051 0.938951i \(-0.611799\pi\)
−0.344051 + 0.938951i \(0.611799\pi\)
\(860\) 0 0
\(861\) 61.1313 2.08335
\(862\) 0 0
\(863\) −33.0397 −1.12468 −0.562342 0.826905i \(-0.690099\pi\)
−0.562342 + 0.826905i \(0.690099\pi\)
\(864\) 0 0
\(865\) 33.7699 1.14821
\(866\) 0 0
\(867\) −6.55364 −0.222573
\(868\) 0 0
\(869\) 8.14473 0.276291
\(870\) 0 0
\(871\) −2.42992 −0.0823347
\(872\) 0 0
\(873\) 11.8697 0.401727
\(874\) 0 0
\(875\) 45.6275 1.54249
\(876\) 0 0
\(877\) 36.0491 1.21729 0.608645 0.793443i \(-0.291713\pi\)
0.608645 + 0.793443i \(0.291713\pi\)
\(878\) 0 0
\(879\) 55.5688 1.87429
\(880\) 0 0
\(881\) 30.4686 1.02651 0.513257 0.858235i \(-0.328439\pi\)
0.513257 + 0.858235i \(0.328439\pi\)
\(882\) 0 0
\(883\) −28.5425 −0.960530 −0.480265 0.877123i \(-0.659460\pi\)
−0.480265 + 0.877123i \(0.659460\pi\)
\(884\) 0 0
\(885\) −8.21689 −0.276208
\(886\) 0 0
\(887\) 43.9704 1.47638 0.738191 0.674591i \(-0.235680\pi\)
0.738191 + 0.674591i \(0.235680\pi\)
\(888\) 0 0
\(889\) 45.5068 1.52625
\(890\) 0 0
\(891\) 19.0405 0.637880
\(892\) 0 0
\(893\) 8.83786 0.295748
\(894\) 0 0
\(895\) −13.9746 −0.467119
\(896\) 0 0
\(897\) −0.484558 −0.0161789
\(898\) 0 0
\(899\) −28.6904 −0.956877
\(900\) 0 0
\(901\) 3.69306 0.123034
\(902\) 0 0
\(903\) −35.6169 −1.18526
\(904\) 0 0
\(905\) 9.01581 0.299696
\(906\) 0 0
\(907\) −3.54621 −0.117750 −0.0588750 0.998265i \(-0.518751\pi\)
−0.0588750 + 0.998265i \(0.518751\pi\)
\(908\) 0 0
\(909\) −3.77016 −0.125048
\(910\) 0 0
\(911\) 45.2186 1.49816 0.749080 0.662480i \(-0.230496\pi\)
0.749080 + 0.662480i \(0.230496\pi\)
\(912\) 0 0
\(913\) 14.9819 0.495827
\(914\) 0 0
\(915\) −20.0975 −0.664404
\(916\) 0 0
\(917\) 77.4844 2.55876
\(918\) 0 0
\(919\) 35.3502 1.16610 0.583048 0.812438i \(-0.301860\pi\)
0.583048 + 0.812438i \(0.301860\pi\)
\(920\) 0 0
\(921\) −8.97473 −0.295727
\(922\) 0 0
\(923\) 1.81282 0.0596698
\(924\) 0 0
\(925\) −3.83976 −0.126251
\(926\) 0 0
\(927\) −2.84072 −0.0933015
\(928\) 0 0
\(929\) −3.67818 −0.120677 −0.0603385 0.998178i \(-0.519218\pi\)
−0.0603385 + 0.998178i \(0.519218\pi\)
\(930\) 0 0
\(931\) −9.14987 −0.299875
\(932\) 0 0
\(933\) 3.31425 0.108504
\(934\) 0 0
\(935\) −9.30656 −0.304357
\(936\) 0 0
\(937\) 3.59956 0.117592 0.0587962 0.998270i \(-0.481274\pi\)
0.0587962 + 0.998270i \(0.481274\pi\)
\(938\) 0 0
\(939\) −3.28262 −0.107124
\(940\) 0 0
\(941\) 12.4926 0.407246 0.203623 0.979049i \(-0.434728\pi\)
0.203623 + 0.979049i \(0.434728\pi\)
\(942\) 0 0
\(943\) −11.9113 −0.387885
\(944\) 0 0
\(945\) 24.5369 0.798184
\(946\) 0 0
\(947\) 49.8307 1.61928 0.809640 0.586926i \(-0.199662\pi\)
0.809640 + 0.586926i \(0.199662\pi\)
\(948\) 0 0
\(949\) −0.0539982 −0.00175286
\(950\) 0 0
\(951\) −37.8778 −1.22827
\(952\) 0 0
\(953\) 9.62384 0.311747 0.155873 0.987777i \(-0.450181\pi\)
0.155873 + 0.987777i \(0.450181\pi\)
\(954\) 0 0
\(955\) 32.2368 1.04316
\(956\) 0 0
\(957\) −9.20878 −0.297678
\(958\) 0 0
\(959\) 12.8985 0.416515
\(960\) 0 0
\(961\) 84.5005 2.72582
\(962\) 0 0
\(963\) −3.89682 −0.125573
\(964\) 0 0
\(965\) −16.3388 −0.525966
\(966\) 0 0
\(967\) 12.6937 0.408203 0.204102 0.978950i \(-0.434573\pi\)
0.204102 + 0.978950i \(0.434573\pi\)
\(968\) 0 0
\(969\) −7.20043 −0.231311
\(970\) 0 0
\(971\) 4.07752 0.130854 0.0654269 0.997857i \(-0.479159\pi\)
0.0654269 + 0.997857i \(0.479159\pi\)
\(972\) 0 0
\(973\) −10.2113 −0.327360
\(974\) 0 0
\(975\) 0.943038 0.0302014
\(976\) 0 0
\(977\) 43.4477 1.39001 0.695007 0.719003i \(-0.255401\pi\)
0.695007 + 0.719003i \(0.255401\pi\)
\(978\) 0 0
\(979\) −6.23888 −0.199395
\(980\) 0 0
\(981\) −2.41571 −0.0771277
\(982\) 0 0
\(983\) 5.09640 0.162550 0.0812749 0.996692i \(-0.474101\pi\)
0.0812749 + 0.996692i \(0.474101\pi\)
\(984\) 0 0
\(985\) −19.8454 −0.632326
\(986\) 0 0
\(987\) 69.2474 2.20417
\(988\) 0 0
\(989\) 6.93987 0.220675
\(990\) 0 0
\(991\) −0.598040 −0.0189974 −0.00949868 0.999955i \(-0.503024\pi\)
−0.00949868 + 0.999955i \(0.503024\pi\)
\(992\) 0 0
\(993\) 23.6728 0.751233
\(994\) 0 0
\(995\) −14.3043 −0.453477
\(996\) 0 0
\(997\) 41.6843 1.32016 0.660078 0.751197i \(-0.270523\pi\)
0.660078 + 0.751197i \(0.270523\pi\)
\(998\) 0 0
\(999\) −5.53970 −0.175268
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 \(a_p\))