Properties

Label 6026.2.a.i.1.18
Level 6026
Weight 2
Character 6026.1
Self dual Yes
Analytic conductor 48.118
Analytic rank 1
Dimension 25
CM No

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Newspace parameters

Level: \( N \) = \( 6026 = 2 \cdot 23 \cdot 131 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6026.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.117852258\)
Analytic rank: \(1\)
Dimension: \(25\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) = 6026.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.11977 q^{3} +1.00000 q^{4} +0.636447 q^{5} -1.11977 q^{6} +1.86618 q^{7} -1.00000 q^{8} -1.74612 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.11977 q^{3} +1.00000 q^{4} +0.636447 q^{5} -1.11977 q^{6} +1.86618 q^{7} -1.00000 q^{8} -1.74612 q^{9} -0.636447 q^{10} -3.79485 q^{11} +1.11977 q^{12} +4.96673 q^{13} -1.86618 q^{14} +0.712674 q^{15} +1.00000 q^{16} +5.06752 q^{17} +1.74612 q^{18} -4.24394 q^{19} +0.636447 q^{20} +2.08969 q^{21} +3.79485 q^{22} +1.00000 q^{23} -1.11977 q^{24} -4.59493 q^{25} -4.96673 q^{26} -5.31455 q^{27} +1.86618 q^{28} -4.06138 q^{29} -0.712674 q^{30} -0.357056 q^{31} -1.00000 q^{32} -4.24935 q^{33} -5.06752 q^{34} +1.18772 q^{35} -1.74612 q^{36} -7.63738 q^{37} +4.24394 q^{38} +5.56159 q^{39} -0.636447 q^{40} -10.6418 q^{41} -2.08969 q^{42} -4.52005 q^{43} -3.79485 q^{44} -1.11131 q^{45} -1.00000 q^{46} +5.70178 q^{47} +1.11977 q^{48} -3.51737 q^{49} +4.59493 q^{50} +5.67445 q^{51} +4.96673 q^{52} -2.51477 q^{53} +5.31455 q^{54} -2.41522 q^{55} -1.86618 q^{56} -4.75223 q^{57} +4.06138 q^{58} +2.98882 q^{59} +0.712674 q^{60} +0.0976123 q^{61} +0.357056 q^{62} -3.25857 q^{63} +1.00000 q^{64} +3.16106 q^{65} +4.24935 q^{66} -10.2862 q^{67} +5.06752 q^{68} +1.11977 q^{69} -1.18772 q^{70} -10.1578 q^{71} +1.74612 q^{72} +2.78214 q^{73} +7.63738 q^{74} -5.14526 q^{75} -4.24394 q^{76} -7.08187 q^{77} -5.56159 q^{78} -7.67664 q^{79} +0.636447 q^{80} -0.712717 q^{81} +10.6418 q^{82} +8.91829 q^{83} +2.08969 q^{84} +3.22521 q^{85} +4.52005 q^{86} -4.54780 q^{87} +3.79485 q^{88} +17.4191 q^{89} +1.11131 q^{90} +9.26882 q^{91} +1.00000 q^{92} -0.399820 q^{93} -5.70178 q^{94} -2.70104 q^{95} -1.11977 q^{96} -4.30272 q^{97} +3.51737 q^{98} +6.62625 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 25q - 25q^{2} - 4q^{3} + 25q^{4} - 3q^{5} + 4q^{6} - 11q^{7} - 25q^{8} + 19q^{9} + O(q^{10}) \) \( 25q - 25q^{2} - 4q^{3} + 25q^{4} - 3q^{5} + 4q^{6} - 11q^{7} - 25q^{8} + 19q^{9} + 3q^{10} - 12q^{11} - 4q^{12} - 6q^{13} + 11q^{14} + 25q^{16} + 8q^{17} - 19q^{18} - 23q^{19} - 3q^{20} - 16q^{21} + 12q^{22} + 25q^{23} + 4q^{24} + 4q^{25} + 6q^{26} - 13q^{27} - 11q^{28} - 7q^{29} - 7q^{31} - 25q^{32} + 3q^{33} - 8q^{34} - 18q^{35} + 19q^{36} - 7q^{37} + 23q^{38} - 2q^{39} + 3q^{40} - 10q^{41} + 16q^{42} - 26q^{43} - 12q^{44} + 20q^{45} - 25q^{46} - 2q^{47} - 4q^{48} + 2q^{49} - 4q^{50} - 28q^{51} - 6q^{52} + 47q^{53} + 13q^{54} - 38q^{55} + 11q^{56} - 4q^{57} + 7q^{58} - 19q^{59} - 26q^{61} + 7q^{62} - 15q^{63} + 25q^{64} + 13q^{65} - 3q^{66} - 34q^{67} + 8q^{68} - 4q^{69} + 18q^{70} - 10q^{71} - 19q^{72} - 22q^{73} + 7q^{74} - 8q^{75} - 23q^{76} + 28q^{77} + 2q^{78} - 21q^{79} - 3q^{80} - 27q^{81} + 10q^{82} - 16q^{83} - 16q^{84} - 42q^{85} + 26q^{86} - 17q^{87} + 12q^{88} + 27q^{89} - 20q^{90} - 26q^{91} + 25q^{92} - 27q^{93} + 2q^{94} + 4q^{96} + 4q^{97} - 2q^{98} - 2q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 1.11977 0.646499 0.323249 0.946314i \(-0.395225\pi\)
0.323249 + 0.946314i \(0.395225\pi\)
\(4\) 1.00000 0.500000
\(5\) 0.636447 0.284628 0.142314 0.989822i \(-0.454546\pi\)
0.142314 + 0.989822i \(0.454546\pi\)
\(6\) −1.11977 −0.457144
\(7\) 1.86618 0.705350 0.352675 0.935746i \(-0.385272\pi\)
0.352675 + 0.935746i \(0.385272\pi\)
\(8\) −1.00000 −0.353553
\(9\) −1.74612 −0.582039
\(10\) −0.636447 −0.201262
\(11\) −3.79485 −1.14419 −0.572095 0.820187i \(-0.693869\pi\)
−0.572095 + 0.820187i \(0.693869\pi\)
\(12\) 1.11977 0.323249
\(13\) 4.96673 1.37752 0.688762 0.724988i \(-0.258155\pi\)
0.688762 + 0.724988i \(0.258155\pi\)
\(14\) −1.86618 −0.498758
\(15\) 0.712674 0.184012
\(16\) 1.00000 0.250000
\(17\) 5.06752 1.22905 0.614527 0.788896i \(-0.289347\pi\)
0.614527 + 0.788896i \(0.289347\pi\)
\(18\) 1.74612 0.411564
\(19\) −4.24394 −0.973626 −0.486813 0.873506i \(-0.661841\pi\)
−0.486813 + 0.873506i \(0.661841\pi\)
\(20\) 0.636447 0.142314
\(21\) 2.08969 0.456008
\(22\) 3.79485 0.809064
\(23\) 1.00000 0.208514
\(24\) −1.11977 −0.228572
\(25\) −4.59493 −0.918987
\(26\) −4.96673 −0.974057
\(27\) −5.31455 −1.02279
\(28\) 1.86618 0.352675
\(29\) −4.06138 −0.754179 −0.377089 0.926177i \(-0.623075\pi\)
−0.377089 + 0.926177i \(0.623075\pi\)
\(30\) −0.712674 −0.130116
\(31\) −0.357056 −0.0641292 −0.0320646 0.999486i \(-0.510208\pi\)
−0.0320646 + 0.999486i \(0.510208\pi\)
\(32\) −1.00000 −0.176777
\(33\) −4.24935 −0.739717
\(34\) −5.06752 −0.869073
\(35\) 1.18772 0.200762
\(36\) −1.74612 −0.291020
\(37\) −7.63738 −1.25558 −0.627789 0.778384i \(-0.716040\pi\)
−0.627789 + 0.778384i \(0.716040\pi\)
\(38\) 4.24394 0.688458
\(39\) 5.56159 0.890568
\(40\) −0.636447 −0.100631
\(41\) −10.6418 −1.66197 −0.830984 0.556296i \(-0.812222\pi\)
−0.830984 + 0.556296i \(0.812222\pi\)
\(42\) −2.08969 −0.322446
\(43\) −4.52005 −0.689301 −0.344651 0.938731i \(-0.612003\pi\)
−0.344651 + 0.938731i \(0.612003\pi\)
\(44\) −3.79485 −0.572095
\(45\) −1.11131 −0.165665
\(46\) −1.00000 −0.147442
\(47\) 5.70178 0.831690 0.415845 0.909435i \(-0.363486\pi\)
0.415845 + 0.909435i \(0.363486\pi\)
\(48\) 1.11977 0.161625
\(49\) −3.51737 −0.502482
\(50\) 4.59493 0.649822
\(51\) 5.67445 0.794582
\(52\) 4.96673 0.688762
\(53\) −2.51477 −0.345430 −0.172715 0.984972i \(-0.555254\pi\)
−0.172715 + 0.984972i \(0.555254\pi\)
\(54\) 5.31455 0.723219
\(55\) −2.41522 −0.325668
\(56\) −1.86618 −0.249379
\(57\) −4.75223 −0.629448
\(58\) 4.06138 0.533285
\(59\) 2.98882 0.389111 0.194556 0.980891i \(-0.437674\pi\)
0.194556 + 0.980891i \(0.437674\pi\)
\(60\) 0.712674 0.0920058
\(61\) 0.0976123 0.0124980 0.00624898 0.999980i \(-0.498011\pi\)
0.00624898 + 0.999980i \(0.498011\pi\)
\(62\) 0.357056 0.0453462
\(63\) −3.25857 −0.410541
\(64\) 1.00000 0.125000
\(65\) 3.16106 0.392082
\(66\) 4.24935 0.523059
\(67\) −10.2862 −1.25665 −0.628327 0.777949i \(-0.716260\pi\)
−0.628327 + 0.777949i \(0.716260\pi\)
\(68\) 5.06752 0.614527
\(69\) 1.11977 0.134804
\(70\) −1.18772 −0.141960
\(71\) −10.1578 −1.20550 −0.602752 0.797928i \(-0.705929\pi\)
−0.602752 + 0.797928i \(0.705929\pi\)
\(72\) 1.74612 0.205782
\(73\) 2.78214 0.325625 0.162812 0.986657i \(-0.447943\pi\)
0.162812 + 0.986657i \(0.447943\pi\)
\(74\) 7.63738 0.887827
\(75\) −5.14526 −0.594124
\(76\) −4.24394 −0.486813
\(77\) −7.08187 −0.807054
\(78\) −5.56159 −0.629726
\(79\) −7.67664 −0.863689 −0.431845 0.901948i \(-0.642137\pi\)
−0.431845 + 0.901948i \(0.642137\pi\)
\(80\) 0.636447 0.0711570
\(81\) −0.712717 −0.0791908
\(82\) 10.6418 1.17519
\(83\) 8.91829 0.978909 0.489455 0.872029i \(-0.337196\pi\)
0.489455 + 0.872029i \(0.337196\pi\)
\(84\) 2.08969 0.228004
\(85\) 3.22521 0.349823
\(86\) 4.52005 0.487410
\(87\) −4.54780 −0.487576
\(88\) 3.79485 0.404532
\(89\) 17.4191 1.84642 0.923210 0.384297i \(-0.125556\pi\)
0.923210 + 0.384297i \(0.125556\pi\)
\(90\) 1.11131 0.117143
\(91\) 9.26882 0.971636
\(92\) 1.00000 0.104257
\(93\) −0.399820 −0.0414594
\(94\) −5.70178 −0.588094
\(95\) −2.70104 −0.277121
\(96\) −1.11977 −0.114286
\(97\) −4.30272 −0.436875 −0.218437 0.975851i \(-0.570096\pi\)
−0.218437 + 0.975851i \(0.570096\pi\)
\(98\) 3.51737 0.355308
\(99\) 6.62625 0.665964
\(100\) −4.59493 −0.459493
\(101\) 4.49228 0.446998 0.223499 0.974704i \(-0.428252\pi\)
0.223499 + 0.974704i \(0.428252\pi\)
\(102\) −5.67445 −0.561854
\(103\) −3.08692 −0.304163 −0.152082 0.988368i \(-0.548598\pi\)
−0.152082 + 0.988368i \(0.548598\pi\)
\(104\) −4.96673 −0.487028
\(105\) 1.32998 0.129792
\(106\) 2.51477 0.244256
\(107\) 1.69383 0.163748 0.0818742 0.996643i \(-0.473909\pi\)
0.0818742 + 0.996643i \(0.473909\pi\)
\(108\) −5.31455 −0.511393
\(109\) 7.93509 0.760044 0.380022 0.924977i \(-0.375916\pi\)
0.380022 + 0.924977i \(0.375916\pi\)
\(110\) 2.41522 0.230282
\(111\) −8.55210 −0.811729
\(112\) 1.86618 0.176337
\(113\) −5.65699 −0.532165 −0.266082 0.963950i \(-0.585729\pi\)
−0.266082 + 0.963950i \(0.585729\pi\)
\(114\) 4.75223 0.445087
\(115\) 0.636447 0.0593490
\(116\) −4.06138 −0.377089
\(117\) −8.67250 −0.801773
\(118\) −2.98882 −0.275143
\(119\) 9.45691 0.866913
\(120\) −0.712674 −0.0650579
\(121\) 3.40088 0.309171
\(122\) −0.0976123 −0.00883740
\(123\) −11.9163 −1.07446
\(124\) −0.357056 −0.0320646
\(125\) −6.10667 −0.546197
\(126\) 3.25857 0.290297
\(127\) 1.03933 0.0922255 0.0461128 0.998936i \(-0.485317\pi\)
0.0461128 + 0.998936i \(0.485317\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −5.06141 −0.445633
\(130\) −3.16106 −0.277244
\(131\) 1.00000 0.0873704
\(132\) −4.24935 −0.369859
\(133\) −7.91995 −0.686747
\(134\) 10.2862 0.888589
\(135\) −3.38243 −0.291114
\(136\) −5.06752 −0.434536
\(137\) 6.72726 0.574749 0.287374 0.957818i \(-0.407218\pi\)
0.287374 + 0.957818i \(0.407218\pi\)
\(138\) −1.11977 −0.0953210
\(139\) 7.58352 0.643226 0.321613 0.946871i \(-0.395775\pi\)
0.321613 + 0.946871i \(0.395775\pi\)
\(140\) 1.18772 0.100381
\(141\) 6.38468 0.537687
\(142\) 10.1578 0.852420
\(143\) −18.8480 −1.57615
\(144\) −1.74612 −0.145510
\(145\) −2.58485 −0.214660
\(146\) −2.78214 −0.230252
\(147\) −3.93864 −0.324854
\(148\) −7.63738 −0.627789
\(149\) −5.10361 −0.418104 −0.209052 0.977905i \(-0.567038\pi\)
−0.209052 + 0.977905i \(0.567038\pi\)
\(150\) 5.14526 0.420109
\(151\) −0.328452 −0.0267290 −0.0133645 0.999911i \(-0.504254\pi\)
−0.0133645 + 0.999911i \(0.504254\pi\)
\(152\) 4.24394 0.344229
\(153\) −8.84849 −0.715358
\(154\) 7.08187 0.570673
\(155\) −0.227247 −0.0182529
\(156\) 5.56159 0.445284
\(157\) −22.3938 −1.78722 −0.893611 0.448843i \(-0.851836\pi\)
−0.893611 + 0.448843i \(0.851836\pi\)
\(158\) 7.67664 0.610720
\(159\) −2.81596 −0.223320
\(160\) −0.636447 −0.0503156
\(161\) 1.86618 0.147076
\(162\) 0.712717 0.0559963
\(163\) −12.2746 −0.961421 −0.480710 0.876879i \(-0.659621\pi\)
−0.480710 + 0.876879i \(0.659621\pi\)
\(164\) −10.6418 −0.830984
\(165\) −2.70449 −0.210544
\(166\) −8.91829 −0.692194
\(167\) −8.24844 −0.638283 −0.319142 0.947707i \(-0.603395\pi\)
−0.319142 + 0.947707i \(0.603395\pi\)
\(168\) −2.08969 −0.161223
\(169\) 11.6684 0.897572
\(170\) −3.22521 −0.247362
\(171\) 7.41042 0.566689
\(172\) −4.52005 −0.344651
\(173\) 23.2506 1.76771 0.883856 0.467759i \(-0.154939\pi\)
0.883856 + 0.467759i \(0.154939\pi\)
\(174\) 4.54780 0.344768
\(175\) −8.57498 −0.648207
\(176\) −3.79485 −0.286047
\(177\) 3.34679 0.251560
\(178\) −17.4191 −1.30562
\(179\) −17.8986 −1.33781 −0.668904 0.743349i \(-0.733236\pi\)
−0.668904 + 0.743349i \(0.733236\pi\)
\(180\) −1.11131 −0.0828323
\(181\) −2.94330 −0.218774 −0.109387 0.993999i \(-0.534889\pi\)
−0.109387 + 0.993999i \(0.534889\pi\)
\(182\) −9.26882 −0.687050
\(183\) 0.109303 0.00807992
\(184\) −1.00000 −0.0737210
\(185\) −4.86079 −0.357372
\(186\) 0.399820 0.0293162
\(187\) −19.2305 −1.40627
\(188\) 5.70178 0.415845
\(189\) −9.91791 −0.721422
\(190\) 2.70104 0.195954
\(191\) −2.04805 −0.148192 −0.0740960 0.997251i \(-0.523607\pi\)
−0.0740960 + 0.997251i \(0.523607\pi\)
\(192\) 1.11977 0.0808123
\(193\) −14.1280 −1.01696 −0.508479 0.861074i \(-0.669792\pi\)
−0.508479 + 0.861074i \(0.669792\pi\)
\(194\) 4.30272 0.308917
\(195\) 3.53966 0.253480
\(196\) −3.51737 −0.251241
\(197\) 1.94453 0.138542 0.0692712 0.997598i \(-0.477933\pi\)
0.0692712 + 0.997598i \(0.477933\pi\)
\(198\) −6.62625 −0.470907
\(199\) −8.14793 −0.577592 −0.288796 0.957391i \(-0.593255\pi\)
−0.288796 + 0.957391i \(0.593255\pi\)
\(200\) 4.59493 0.324911
\(201\) −11.5181 −0.812426
\(202\) −4.49228 −0.316075
\(203\) −7.57926 −0.531960
\(204\) 5.67445 0.397291
\(205\) −6.77294 −0.473043
\(206\) 3.08692 0.215076
\(207\) −1.74612 −0.121364
\(208\) 4.96673 0.344381
\(209\) 16.1051 1.11401
\(210\) −1.32998 −0.0917771
\(211\) −14.4008 −0.991393 −0.495697 0.868496i \(-0.665087\pi\)
−0.495697 + 0.868496i \(0.665087\pi\)
\(212\) −2.51477 −0.172715
\(213\) −11.3743 −0.779357
\(214\) −1.69383 −0.115788
\(215\) −2.87677 −0.196194
\(216\) 5.31455 0.361610
\(217\) −0.666331 −0.0452335
\(218\) −7.93509 −0.537432
\(219\) 3.11535 0.210516
\(220\) −2.41522 −0.162834
\(221\) 25.1690 1.69305
\(222\) 8.55210 0.573979
\(223\) 3.88305 0.260028 0.130014 0.991512i \(-0.458498\pi\)
0.130014 + 0.991512i \(0.458498\pi\)
\(224\) −1.86618 −0.124689
\(225\) 8.02330 0.534887
\(226\) 5.65699 0.376297
\(227\) −17.4252 −1.15655 −0.578277 0.815840i \(-0.696275\pi\)
−0.578277 + 0.815840i \(0.696275\pi\)
\(228\) −4.75223 −0.314724
\(229\) 10.4745 0.692176 0.346088 0.938202i \(-0.387510\pi\)
0.346088 + 0.938202i \(0.387510\pi\)
\(230\) −0.636447 −0.0419661
\(231\) −7.93006 −0.521759
\(232\) 4.06138 0.266642
\(233\) 17.3090 1.13395 0.566974 0.823736i \(-0.308114\pi\)
0.566974 + 0.823736i \(0.308114\pi\)
\(234\) 8.67250 0.566939
\(235\) 3.62888 0.236722
\(236\) 2.98882 0.194556
\(237\) −8.59606 −0.558374
\(238\) −9.45691 −0.613000
\(239\) 15.6341 1.01129 0.505644 0.862742i \(-0.331255\pi\)
0.505644 + 0.862742i \(0.331255\pi\)
\(240\) 0.712674 0.0460029
\(241\) 1.84963 0.119145 0.0595726 0.998224i \(-0.481026\pi\)
0.0595726 + 0.998224i \(0.481026\pi\)
\(242\) −3.40088 −0.218617
\(243\) 15.1456 0.971590
\(244\) 0.0976123 0.00624898
\(245\) −2.23862 −0.143020
\(246\) 11.9163 0.759759
\(247\) −21.0785 −1.34119
\(248\) 0.357056 0.0226731
\(249\) 9.98642 0.632864
\(250\) 6.10667 0.386220
\(251\) 28.0505 1.77053 0.885266 0.465086i \(-0.153977\pi\)
0.885266 + 0.465086i \(0.153977\pi\)
\(252\) −3.25857 −0.205271
\(253\) −3.79485 −0.238580
\(254\) −1.03933 −0.0652133
\(255\) 3.61149 0.226160
\(256\) 1.00000 0.0625000
\(257\) 4.53644 0.282975 0.141488 0.989940i \(-0.454811\pi\)
0.141488 + 0.989940i \(0.454811\pi\)
\(258\) 5.06141 0.315110
\(259\) −14.2527 −0.885621
\(260\) 3.16106 0.196041
\(261\) 7.09164 0.438962
\(262\) −1.00000 −0.0617802
\(263\) −5.84276 −0.360280 −0.180140 0.983641i \(-0.557655\pi\)
−0.180140 + 0.983641i \(0.557655\pi\)
\(264\) 4.24935 0.261530
\(265\) −1.60052 −0.0983191
\(266\) 7.91995 0.485603
\(267\) 19.5053 1.19371
\(268\) −10.2862 −0.628327
\(269\) −10.6290 −0.648064 −0.324032 0.946046i \(-0.605039\pi\)
−0.324032 + 0.946046i \(0.605039\pi\)
\(270\) 3.38243 0.205848
\(271\) 0.362476 0.0220188 0.0110094 0.999939i \(-0.496496\pi\)
0.0110094 + 0.999939i \(0.496496\pi\)
\(272\) 5.06752 0.307264
\(273\) 10.3789 0.628162
\(274\) −6.72726 −0.406409
\(275\) 17.4371 1.05150
\(276\) 1.11977 0.0674022
\(277\) 15.6917 0.942825 0.471412 0.881913i \(-0.343744\pi\)
0.471412 + 0.881913i \(0.343744\pi\)
\(278\) −7.58352 −0.454829
\(279\) 0.623462 0.0373257
\(280\) −1.18772 −0.0709801
\(281\) 13.8686 0.827332 0.413666 0.910429i \(-0.364248\pi\)
0.413666 + 0.910429i \(0.364248\pi\)
\(282\) −6.38468 −0.380202
\(283\) −28.8464 −1.71474 −0.857370 0.514701i \(-0.827903\pi\)
−0.857370 + 0.514701i \(0.827903\pi\)
\(284\) −10.1578 −0.602752
\(285\) −3.02454 −0.179158
\(286\) 18.8480 1.11451
\(287\) −19.8595 −1.17227
\(288\) 1.74612 0.102891
\(289\) 8.67977 0.510575
\(290\) 2.58485 0.151788
\(291\) −4.81805 −0.282439
\(292\) 2.78214 0.162812
\(293\) 3.02902 0.176957 0.0884786 0.996078i \(-0.471800\pi\)
0.0884786 + 0.996078i \(0.471800\pi\)
\(294\) 3.93864 0.229706
\(295\) 1.90223 0.110752
\(296\) 7.63738 0.443914
\(297\) 20.1679 1.17026
\(298\) 5.10361 0.295644
\(299\) 4.96673 0.287234
\(300\) −5.14526 −0.297062
\(301\) −8.43523 −0.486199
\(302\) 0.328452 0.0189003
\(303\) 5.03031 0.288984
\(304\) −4.24394 −0.243407
\(305\) 0.0621250 0.00355727
\(306\) 8.84849 0.505835
\(307\) 14.4215 0.823077 0.411538 0.911392i \(-0.364992\pi\)
0.411538 + 0.911392i \(0.364992\pi\)
\(308\) −7.08187 −0.403527
\(309\) −3.45664 −0.196641
\(310\) 0.227247 0.0129068
\(311\) 2.25211 0.127705 0.0638526 0.997959i \(-0.479661\pi\)
0.0638526 + 0.997959i \(0.479661\pi\)
\(312\) −5.56159 −0.314863
\(313\) −14.9317 −0.843989 −0.421995 0.906598i \(-0.638670\pi\)
−0.421995 + 0.906598i \(0.638670\pi\)
\(314\) 22.3938 1.26376
\(315\) −2.07391 −0.116851
\(316\) −7.67664 −0.431845
\(317\) −24.3581 −1.36809 −0.684043 0.729441i \(-0.739780\pi\)
−0.684043 + 0.729441i \(0.739780\pi\)
\(318\) 2.81596 0.157911
\(319\) 15.4123 0.862924
\(320\) 0.636447 0.0355785
\(321\) 1.89669 0.105863
\(322\) −1.86618 −0.103998
\(323\) −21.5062 −1.19664
\(324\) −0.712717 −0.0395954
\(325\) −22.8218 −1.26593
\(326\) 12.2746 0.679827
\(327\) 8.88547 0.491368
\(328\) 10.6418 0.587595
\(329\) 10.6405 0.586632
\(330\) 2.70449 0.148877
\(331\) −22.2301 −1.22188 −0.610939 0.791677i \(-0.709208\pi\)
−0.610939 + 0.791677i \(0.709208\pi\)
\(332\) 8.91829 0.489455
\(333\) 13.3358 0.730795
\(334\) 8.24844 0.451335
\(335\) −6.54660 −0.357679
\(336\) 2.08969 0.114002
\(337\) 24.5990 1.33999 0.669997 0.742363i \(-0.266295\pi\)
0.669997 + 0.742363i \(0.266295\pi\)
\(338\) −11.6684 −0.634679
\(339\) −6.33452 −0.344044
\(340\) 3.22521 0.174912
\(341\) 1.35497 0.0733759
\(342\) −7.41042 −0.400709
\(343\) −19.6273 −1.05978
\(344\) 4.52005 0.243705
\(345\) 0.712674 0.0383691
\(346\) −23.2506 −1.24996
\(347\) 4.27958 0.229740 0.114870 0.993381i \(-0.463355\pi\)
0.114870 + 0.993381i \(0.463355\pi\)
\(348\) −4.54780 −0.243788
\(349\) −0.0773620 −0.00414109 −0.00207055 0.999998i \(-0.500659\pi\)
−0.00207055 + 0.999998i \(0.500659\pi\)
\(350\) 8.57498 0.458352
\(351\) −26.3960 −1.40891
\(352\) 3.79485 0.202266
\(353\) −4.78491 −0.254675 −0.127338 0.991859i \(-0.540643\pi\)
−0.127338 + 0.991859i \(0.540643\pi\)
\(354\) −3.34679 −0.177880
\(355\) −6.46488 −0.343120
\(356\) 17.4191 0.923210
\(357\) 10.5895 0.560458
\(358\) 17.8986 0.945972
\(359\) −17.0838 −0.901648 −0.450824 0.892613i \(-0.648870\pi\)
−0.450824 + 0.892613i \(0.648870\pi\)
\(360\) 1.11131 0.0585713
\(361\) −0.988994 −0.0520523
\(362\) 2.94330 0.154697
\(363\) 3.80820 0.199878
\(364\) 9.26882 0.485818
\(365\) 1.77069 0.0926819
\(366\) −0.109303 −0.00571337
\(367\) −7.19668 −0.375663 −0.187832 0.982201i \(-0.560146\pi\)
−0.187832 + 0.982201i \(0.560146\pi\)
\(368\) 1.00000 0.0521286
\(369\) 18.5818 0.967331
\(370\) 4.86079 0.252700
\(371\) −4.69301 −0.243649
\(372\) −0.399820 −0.0207297
\(373\) −20.4239 −1.05751 −0.528755 0.848775i \(-0.677341\pi\)
−0.528755 + 0.848775i \(0.677341\pi\)
\(374\) 19.2305 0.994384
\(375\) −6.83806 −0.353116
\(376\) −5.70178 −0.294047
\(377\) −20.1718 −1.03890
\(378\) 9.91791 0.510122
\(379\) 29.3881 1.50956 0.754781 0.655976i \(-0.227743\pi\)
0.754781 + 0.655976i \(0.227743\pi\)
\(380\) −2.70104 −0.138561
\(381\) 1.16381 0.0596237
\(382\) 2.04805 0.104788
\(383\) −21.8277 −1.11534 −0.557671 0.830062i \(-0.688305\pi\)
−0.557671 + 0.830062i \(0.688305\pi\)
\(384\) −1.11977 −0.0571430
\(385\) −4.50724 −0.229710
\(386\) 14.1280 0.719098
\(387\) 7.89255 0.401201
\(388\) −4.30272 −0.218437
\(389\) 0.257522 0.0130569 0.00652845 0.999979i \(-0.497922\pi\)
0.00652845 + 0.999979i \(0.497922\pi\)
\(390\) −3.53966 −0.179238
\(391\) 5.06752 0.256276
\(392\) 3.51737 0.177654
\(393\) 1.11977 0.0564849
\(394\) −1.94453 −0.0979642
\(395\) −4.88577 −0.245830
\(396\) 6.62625 0.332982
\(397\) −13.5209 −0.678597 −0.339298 0.940679i \(-0.610190\pi\)
−0.339298 + 0.940679i \(0.610190\pi\)
\(398\) 8.14793 0.408419
\(399\) −8.86851 −0.443981
\(400\) −4.59493 −0.229747
\(401\) 20.4160 1.01953 0.509763 0.860315i \(-0.329733\pi\)
0.509763 + 0.860315i \(0.329733\pi\)
\(402\) 11.5181 0.574472
\(403\) −1.77340 −0.0883395
\(404\) 4.49228 0.223499
\(405\) −0.453607 −0.0225399
\(406\) 7.57926 0.376152
\(407\) 28.9827 1.43662
\(408\) −5.67445 −0.280927
\(409\) 10.0601 0.497439 0.248720 0.968575i \(-0.419990\pi\)
0.248720 + 0.968575i \(0.419990\pi\)
\(410\) 6.77294 0.334492
\(411\) 7.53298 0.371574
\(412\) −3.08692 −0.152082
\(413\) 5.57768 0.274460
\(414\) 1.74612 0.0858170
\(415\) 5.67602 0.278625
\(416\) −4.96673 −0.243514
\(417\) 8.49179 0.415845
\(418\) −16.1051 −0.787726
\(419\) −21.1423 −1.03287 −0.516435 0.856326i \(-0.672741\pi\)
−0.516435 + 0.856326i \(0.672741\pi\)
\(420\) 1.32998 0.0648962
\(421\) −6.57213 −0.320306 −0.160153 0.987092i \(-0.551199\pi\)
−0.160153 + 0.987092i \(0.551199\pi\)
\(422\) 14.4008 0.701021
\(423\) −9.95598 −0.484076
\(424\) 2.51477 0.122128
\(425\) −23.2849 −1.12949
\(426\) 11.3743 0.551089
\(427\) 0.182162 0.00881544
\(428\) 1.69383 0.0818742
\(429\) −21.1054 −1.01898
\(430\) 2.87677 0.138730
\(431\) 41.2475 1.98682 0.993410 0.114612i \(-0.0365623\pi\)
0.993410 + 0.114612i \(0.0365623\pi\)
\(432\) −5.31455 −0.255697
\(433\) 17.6747 0.849393 0.424697 0.905336i \(-0.360381\pi\)
0.424697 + 0.905336i \(0.360381\pi\)
\(434\) 0.666331 0.0319849
\(435\) −2.89444 −0.138778
\(436\) 7.93509 0.380022
\(437\) −4.24394 −0.203015
\(438\) −3.11535 −0.148857
\(439\) −17.5884 −0.839448 −0.419724 0.907652i \(-0.637873\pi\)
−0.419724 + 0.907652i \(0.637873\pi\)
\(440\) 2.41522 0.115141
\(441\) 6.14175 0.292464
\(442\) −25.1690 −1.19717
\(443\) −15.1036 −0.717596 −0.358798 0.933415i \(-0.616813\pi\)
−0.358798 + 0.933415i \(0.616813\pi\)
\(444\) −8.55210 −0.405864
\(445\) 11.0863 0.525542
\(446\) −3.88305 −0.183868
\(447\) −5.71486 −0.270304
\(448\) 1.86618 0.0881687
\(449\) 3.66694 0.173054 0.0865268 0.996250i \(-0.472423\pi\)
0.0865268 + 0.996250i \(0.472423\pi\)
\(450\) −8.02330 −0.378222
\(451\) 40.3840 1.90161
\(452\) −5.65699 −0.266082
\(453\) −0.367790 −0.0172803
\(454\) 17.4252 0.817807
\(455\) 5.89911 0.276555
\(456\) 4.75223 0.222543
\(457\) −5.65616 −0.264584 −0.132292 0.991211i \(-0.542234\pi\)
−0.132292 + 0.991211i \(0.542234\pi\)
\(458\) −10.4745 −0.489442
\(459\) −26.9316 −1.25706
\(460\) 0.636447 0.0296745
\(461\) −26.6194 −1.23979 −0.619895 0.784685i \(-0.712825\pi\)
−0.619895 + 0.784685i \(0.712825\pi\)
\(462\) 7.93006 0.368940
\(463\) 17.6648 0.820954 0.410477 0.911871i \(-0.365362\pi\)
0.410477 + 0.911871i \(0.365362\pi\)
\(464\) −4.06138 −0.188545
\(465\) −0.254464 −0.0118005
\(466\) −17.3090 −0.801822
\(467\) 5.99679 0.277498 0.138749 0.990328i \(-0.455692\pi\)
0.138749 + 0.990328i \(0.455692\pi\)
\(468\) −8.67250 −0.400887
\(469\) −19.1958 −0.886381
\(470\) −3.62888 −0.167388
\(471\) −25.0759 −1.15544
\(472\) −2.98882 −0.137572
\(473\) 17.1529 0.788692
\(474\) 8.59606 0.394830
\(475\) 19.5006 0.894750
\(476\) 9.45691 0.433457
\(477\) 4.39109 0.201054
\(478\) −15.6341 −0.715089
\(479\) 8.62140 0.393922 0.196961 0.980411i \(-0.436893\pi\)
0.196961 + 0.980411i \(0.436893\pi\)
\(480\) −0.712674 −0.0325290
\(481\) −37.9328 −1.72959
\(482\) −1.84963 −0.0842484
\(483\) 2.08969 0.0950842
\(484\) 3.40088 0.154585
\(485\) −2.73845 −0.124347
\(486\) −15.1456 −0.687018
\(487\) 0.190368 0.00862639 0.00431320 0.999991i \(-0.498627\pi\)
0.00431320 + 0.999991i \(0.498627\pi\)
\(488\) −0.0976123 −0.00441870
\(489\) −13.7447 −0.621557
\(490\) 2.23862 0.101131
\(491\) 17.7254 0.799935 0.399968 0.916529i \(-0.369021\pi\)
0.399968 + 0.916529i \(0.369021\pi\)
\(492\) −11.9163 −0.537230
\(493\) −20.5811 −0.926927
\(494\) 21.0785 0.948367
\(495\) 4.21726 0.189552
\(496\) −0.357056 −0.0160323
\(497\) −18.9562 −0.850302
\(498\) −9.98642 −0.447502
\(499\) −2.47226 −0.110674 −0.0553368 0.998468i \(-0.517623\pi\)
−0.0553368 + 0.998468i \(0.517623\pi\)
\(500\) −6.10667 −0.273099
\(501\) −9.23635 −0.412649
\(502\) −28.0505 −1.25195
\(503\) −35.9236 −1.60176 −0.800878 0.598827i \(-0.795634\pi\)
−0.800878 + 0.598827i \(0.795634\pi\)
\(504\) 3.25857 0.145148
\(505\) 2.85910 0.127228
\(506\) 3.79485 0.168702
\(507\) 13.0660 0.580279
\(508\) 1.03933 0.0461128
\(509\) −19.3103 −0.855914 −0.427957 0.903799i \(-0.640767\pi\)
−0.427957 + 0.903799i \(0.640767\pi\)
\(510\) −3.61149 −0.159919
\(511\) 5.19198 0.229679
\(512\) −1.00000 −0.0441942
\(513\) 22.5546 0.995812
\(514\) −4.53644 −0.200094
\(515\) −1.96466 −0.0865734
\(516\) −5.06141 −0.222816
\(517\) −21.6374 −0.951612
\(518\) 14.2527 0.626229
\(519\) 26.0353 1.14282
\(520\) −3.16106 −0.138622
\(521\) −9.35252 −0.409741 −0.204871 0.978789i \(-0.565677\pi\)
−0.204871 + 0.978789i \(0.565677\pi\)
\(522\) −7.09164 −0.310393
\(523\) 17.1841 0.751406 0.375703 0.926740i \(-0.377401\pi\)
0.375703 + 0.926740i \(0.377401\pi\)
\(524\) 1.00000 0.0436852
\(525\) −9.60199 −0.419065
\(526\) 5.84276 0.254757
\(527\) −1.80939 −0.0788182
\(528\) −4.24935 −0.184929
\(529\) 1.00000 0.0434783
\(530\) 1.60052 0.0695221
\(531\) −5.21883 −0.226478
\(532\) −7.91995 −0.343373
\(533\) −52.8550 −2.28940
\(534\) −19.5053 −0.844079
\(535\) 1.07803 0.0466074
\(536\) 10.2862 0.444295
\(537\) −20.0423 −0.864891
\(538\) 10.6290 0.458250
\(539\) 13.3479 0.574935
\(540\) −3.38243 −0.145557
\(541\) −21.8086 −0.937626 −0.468813 0.883297i \(-0.655318\pi\)
−0.468813 + 0.883297i \(0.655318\pi\)
\(542\) −0.362476 −0.0155697
\(543\) −3.29582 −0.141437
\(544\) −5.06752 −0.217268
\(545\) 5.05027 0.216330
\(546\) −10.3789 −0.444177
\(547\) 29.3277 1.25396 0.626980 0.779035i \(-0.284291\pi\)
0.626980 + 0.779035i \(0.284291\pi\)
\(548\) 6.72726 0.287374
\(549\) −0.170443 −0.00727431
\(550\) −17.4371 −0.743520
\(551\) 17.2362 0.734288
\(552\) −1.11977 −0.0476605
\(553\) −14.3260 −0.609203
\(554\) −15.6917 −0.666678
\(555\) −5.44296 −0.231041
\(556\) 7.58352 0.321613
\(557\) 6.74873 0.285953 0.142976 0.989726i \(-0.454333\pi\)
0.142976 + 0.989726i \(0.454333\pi\)
\(558\) −0.623462 −0.0263933
\(559\) −22.4499 −0.949529
\(560\) 1.18772 0.0501905
\(561\) −21.5337 −0.909153
\(562\) −13.8686 −0.585012
\(563\) 44.8127 1.88863 0.944315 0.329042i \(-0.106726\pi\)
0.944315 + 0.329042i \(0.106726\pi\)
\(564\) 6.38468 0.268843
\(565\) −3.60037 −0.151469
\(566\) 28.8464 1.21250
\(567\) −1.33006 −0.0558572
\(568\) 10.1578 0.426210
\(569\) 29.2721 1.22715 0.613576 0.789636i \(-0.289731\pi\)
0.613576 + 0.789636i \(0.289731\pi\)
\(570\) 3.02454 0.126684
\(571\) −34.1229 −1.42800 −0.714000 0.700146i \(-0.753118\pi\)
−0.714000 + 0.700146i \(0.753118\pi\)
\(572\) −18.8480 −0.788075
\(573\) −2.29335 −0.0958060
\(574\) 19.8595 0.828920
\(575\) −4.59493 −0.191622
\(576\) −1.74612 −0.0727549
\(577\) −13.5302 −0.563270 −0.281635 0.959522i \(-0.590877\pi\)
−0.281635 + 0.959522i \(0.590877\pi\)
\(578\) −8.67977 −0.361031
\(579\) −15.8201 −0.657462
\(580\) −2.58485 −0.107330
\(581\) 16.6431 0.690473
\(582\) 4.81805 0.199715
\(583\) 9.54317 0.395238
\(584\) −2.78214 −0.115126
\(585\) −5.51959 −0.228207
\(586\) −3.02902 −0.125128
\(587\) −37.5719 −1.55076 −0.775379 0.631496i \(-0.782441\pi\)
−0.775379 + 0.631496i \(0.782441\pi\)
\(588\) −3.93864 −0.162427
\(589\) 1.51532 0.0624378
\(590\) −1.90223 −0.0783134
\(591\) 2.17743 0.0895674
\(592\) −7.63738 −0.313894
\(593\) −16.0194 −0.657838 −0.328919 0.944358i \(-0.606684\pi\)
−0.328919 + 0.944358i \(0.606684\pi\)
\(594\) −20.1679 −0.827500
\(595\) 6.01882 0.246748
\(596\) −5.10361 −0.209052
\(597\) −9.12380 −0.373412
\(598\) −4.96673 −0.203105
\(599\) 24.1352 0.986139 0.493070 0.869990i \(-0.335875\pi\)
0.493070 + 0.869990i \(0.335875\pi\)
\(600\) 5.14526 0.210055
\(601\) 24.6134 1.00400 0.502002 0.864867i \(-0.332597\pi\)
0.502002 + 0.864867i \(0.332597\pi\)
\(602\) 8.43523 0.343794
\(603\) 17.9609 0.731423
\(604\) −0.328452 −0.0133645
\(605\) 2.16448 0.0879986
\(606\) −5.03031 −0.204342
\(607\) 21.9840 0.892302 0.446151 0.894958i \(-0.352794\pi\)
0.446151 + 0.894958i \(0.352794\pi\)
\(608\) 4.24394 0.172114
\(609\) −8.48702 −0.343911
\(610\) −0.0621250 −0.00251537
\(611\) 28.3192 1.14567
\(612\) −8.84849 −0.357679
\(613\) −47.2030 −1.90651 −0.953255 0.302167i \(-0.902290\pi\)
−0.953255 + 0.302167i \(0.902290\pi\)
\(614\) −14.4215 −0.582003
\(615\) −7.58413 −0.305821
\(616\) 7.08187 0.285337
\(617\) 30.8530 1.24210 0.621048 0.783773i \(-0.286707\pi\)
0.621048 + 0.783773i \(0.286707\pi\)
\(618\) 3.45664 0.139046
\(619\) −25.5199 −1.02573 −0.512865 0.858469i \(-0.671416\pi\)
−0.512865 + 0.858469i \(0.671416\pi\)
\(620\) −0.227247 −0.00912647
\(621\) −5.31455 −0.213266
\(622\) −2.25211 −0.0903012
\(623\) 32.5071 1.30237
\(624\) 5.56159 0.222642
\(625\) 19.0881 0.763524
\(626\) 14.9317 0.596790
\(627\) 18.0340 0.720208
\(628\) −22.3938 −0.893611
\(629\) −38.7026 −1.54317
\(630\) 2.07391 0.0826265
\(631\) −28.7896 −1.14610 −0.573048 0.819522i \(-0.694239\pi\)
−0.573048 + 0.819522i \(0.694239\pi\)
\(632\) 7.67664 0.305360
\(633\) −16.1256 −0.640935
\(634\) 24.3581 0.967383
\(635\) 0.661478 0.0262500
\(636\) −2.81596 −0.111660
\(637\) −17.4699 −0.692181
\(638\) −15.4123 −0.610179
\(639\) 17.7366 0.701651
\(640\) −0.636447 −0.0251578
\(641\) 20.1189 0.794651 0.397325 0.917678i \(-0.369938\pi\)
0.397325 + 0.917678i \(0.369938\pi\)
\(642\) −1.89669 −0.0748566
\(643\) 36.6960 1.44715 0.723575 0.690245i \(-0.242497\pi\)
0.723575 + 0.690245i \(0.242497\pi\)
\(644\) 1.86618 0.0735378
\(645\) −3.22132 −0.126839
\(646\) 21.5062 0.846152
\(647\) −46.3283 −1.82135 −0.910676 0.413120i \(-0.864439\pi\)
−0.910676 + 0.413120i \(0.864439\pi\)
\(648\) 0.712717 0.0279982
\(649\) −11.3421 −0.445217
\(650\) 22.8218 0.895145
\(651\) −0.746136 −0.0292434
\(652\) −12.2746 −0.480710
\(653\) 11.1225 0.435259 0.217629 0.976031i \(-0.430168\pi\)
0.217629 + 0.976031i \(0.430168\pi\)
\(654\) −8.88547 −0.347449
\(655\) 0.636447 0.0248681
\(656\) −10.6418 −0.415492
\(657\) −4.85795 −0.189527
\(658\) −10.6405 −0.414812
\(659\) −16.5408 −0.644339 −0.322170 0.946682i \(-0.604412\pi\)
−0.322170 + 0.946682i \(0.604412\pi\)
\(660\) −2.70449 −0.105272
\(661\) 34.5485 1.34378 0.671890 0.740651i \(-0.265483\pi\)
0.671890 + 0.740651i \(0.265483\pi\)
\(662\) 22.2301 0.863999
\(663\) 28.1835 1.09456
\(664\) −8.91829 −0.346097
\(665\) −5.04063 −0.195467
\(666\) −13.3358 −0.516750
\(667\) −4.06138 −0.157257
\(668\) −8.24844 −0.319142
\(669\) 4.34812 0.168108
\(670\) 6.54660 0.252917
\(671\) −0.370424 −0.0143001
\(672\) −2.08969 −0.0806115
\(673\) −23.6270 −0.910753 −0.455377 0.890299i \(-0.650495\pi\)
−0.455377 + 0.890299i \(0.650495\pi\)
\(674\) −24.5990 −0.947519
\(675\) 24.4200 0.939927
\(676\) 11.6684 0.448786
\(677\) −16.7073 −0.642113 −0.321057 0.947060i \(-0.604038\pi\)
−0.321057 + 0.947060i \(0.604038\pi\)
\(678\) 6.33452 0.243276
\(679\) −8.02965 −0.308150
\(680\) −3.22521 −0.123681
\(681\) −19.5122 −0.747711
\(682\) −1.35497 −0.0518846
\(683\) −26.3686 −1.00897 −0.504483 0.863422i \(-0.668317\pi\)
−0.504483 + 0.863422i \(0.668317\pi\)
\(684\) 7.41042 0.283344
\(685\) 4.28155 0.163590
\(686\) 19.6273 0.749374
\(687\) 11.7290 0.447491
\(688\) −4.52005 −0.172325
\(689\) −12.4902 −0.475838
\(690\) −0.712674 −0.0271310
\(691\) 43.9699 1.67270 0.836348 0.548199i \(-0.184687\pi\)
0.836348 + 0.548199i \(0.184687\pi\)
\(692\) 23.2506 0.883856
\(693\) 12.3658 0.469737
\(694\) −4.27958 −0.162451
\(695\) 4.82651 0.183080
\(696\) 4.54780 0.172384
\(697\) −53.9275 −2.04265
\(698\) 0.0773620 0.00292820
\(699\) 19.3820 0.733096
\(700\) −8.57498 −0.324104
\(701\) −38.2779 −1.44574 −0.722869 0.690985i \(-0.757177\pi\)
−0.722869 + 0.690985i \(0.757177\pi\)
\(702\) 26.3960 0.996252
\(703\) 32.4126 1.22246
\(704\) −3.79485 −0.143024
\(705\) 4.06351 0.153041
\(706\) 4.78491 0.180083
\(707\) 8.38340 0.315290
\(708\) 3.34679 0.125780
\(709\) −9.51077 −0.357185 −0.178592 0.983923i \(-0.557154\pi\)
−0.178592 + 0.983923i \(0.557154\pi\)
\(710\) 6.46488 0.242623
\(711\) 13.4043 0.502701
\(712\) −17.4191 −0.652808
\(713\) −0.357056 −0.0133719
\(714\) −10.5895 −0.396304
\(715\) −11.9958 −0.448616
\(716\) −17.8986 −0.668904
\(717\) 17.5066 0.653796
\(718\) 17.0838 0.637561
\(719\) −9.52897 −0.355371 −0.177685 0.984087i \(-0.556861\pi\)
−0.177685 + 0.984087i \(0.556861\pi\)
\(720\) −1.11131 −0.0414162
\(721\) −5.76075 −0.214542
\(722\) 0.988994 0.0368065
\(723\) 2.07116 0.0770273
\(724\) −2.94330 −0.109387
\(725\) 18.6618 0.693081
\(726\) −3.80820 −0.141335
\(727\) −14.0949 −0.522752 −0.261376 0.965237i \(-0.584176\pi\)
−0.261376 + 0.965237i \(0.584176\pi\)
\(728\) −9.26882 −0.343525
\(729\) 19.0977 0.707322
\(730\) −1.77069 −0.0655360
\(731\) −22.9055 −0.847189
\(732\) 0.109303 0.00403996
\(733\) 20.5946 0.760680 0.380340 0.924847i \(-0.375807\pi\)
0.380340 + 0.924847i \(0.375807\pi\)
\(734\) 7.19668 0.265634
\(735\) −2.50674 −0.0924625
\(736\) −1.00000 −0.0368605
\(737\) 39.0344 1.43785
\(738\) −18.5818 −0.684007
\(739\) −19.6340 −0.722248 −0.361124 0.932518i \(-0.617607\pi\)
−0.361124 + 0.932518i \(0.617607\pi\)
\(740\) −4.86079 −0.178686
\(741\) −23.6031 −0.867080
\(742\) 4.69301 0.172286
\(743\) −43.2166 −1.58546 −0.792731 0.609571i \(-0.791342\pi\)
−0.792731 + 0.609571i \(0.791342\pi\)
\(744\) 0.399820 0.0146581
\(745\) −3.24818 −0.119004
\(746\) 20.4239 0.747772
\(747\) −15.5724 −0.569764
\(748\) −19.2305 −0.703136
\(749\) 3.16099 0.115500
\(750\) 6.83806 0.249691
\(751\) −16.3060 −0.595016 −0.297508 0.954719i \(-0.596155\pi\)
−0.297508 + 0.954719i \(0.596155\pi\)
\(752\) 5.70178 0.207923
\(753\) 31.4101 1.14465
\(754\) 20.1718 0.734613
\(755\) −0.209042 −0.00760783
\(756\) −9.91791 −0.360711
\(757\) −21.1207 −0.767644 −0.383822 0.923407i \(-0.625392\pi\)
−0.383822 + 0.923407i \(0.625392\pi\)
\(758\) −29.3881 −1.06742
\(759\) −4.24935 −0.154242
\(760\) 2.70104 0.0979771
\(761\) 13.5092 0.489708 0.244854 0.969560i \(-0.421260\pi\)
0.244854 + 0.969560i \(0.421260\pi\)
\(762\) −1.16381 −0.0421603
\(763\) 14.8083 0.536097
\(764\) −2.04805 −0.0740960
\(765\) −5.63160 −0.203611
\(766\) 21.8277 0.788666
\(767\) 14.8447 0.536010
\(768\) 1.11977 0.0404062
\(769\) −22.5850 −0.814435 −0.407218 0.913331i \(-0.633501\pi\)
−0.407218 + 0.913331i \(0.633501\pi\)
\(770\) 4.50724 0.162430
\(771\) 5.07976 0.182943
\(772\) −14.1280 −0.508479
\(773\) −27.6284 −0.993725 −0.496863 0.867829i \(-0.665515\pi\)
−0.496863 + 0.867829i \(0.665515\pi\)
\(774\) −7.89255 −0.283692
\(775\) 1.64065 0.0589339
\(776\) 4.30272 0.154459
\(777\) −15.9597 −0.572553
\(778\) −0.257522 −0.00923263
\(779\) 45.1631 1.61814
\(780\) 3.53966 0.126740
\(781\) 38.5472 1.37933
\(782\) −5.06752 −0.181214
\(783\) 21.5844 0.771364
\(784\) −3.51737 −0.125620
\(785\) −14.2525 −0.508693
\(786\) −1.11977 −0.0399408
\(787\) 1.80927 0.0644936 0.0322468 0.999480i \(-0.489734\pi\)
0.0322468 + 0.999480i \(0.489734\pi\)
\(788\) 1.94453 0.0692712
\(789\) −6.54254 −0.232921
\(790\) 4.88577 0.173828
\(791\) −10.5570 −0.375362
\(792\) −6.62625 −0.235454
\(793\) 0.484814 0.0172163
\(794\) 13.5209 0.479841
\(795\) −1.79221 −0.0635631
\(796\) −8.14793 −0.288796
\(797\) 39.8795 1.41261 0.706303 0.707910i \(-0.250362\pi\)
0.706303 + 0.707910i \(0.250362\pi\)
\(798\) 8.86851 0.313942
\(799\) 28.8939 1.02219
\(800\) 4.59493 0.162455
\(801\) −30.4158 −1.07469
\(802\) −20.4160 −0.720914
\(803\) −10.5578 −0.372577
\(804\) −11.5181 −0.406213
\(805\) 1.18772 0.0418618
\(806\) 1.77340 0.0624654
\(807\) −11.9021 −0.418972
\(808\) −4.49228 −0.158038
\(809\) 32.2869 1.13515 0.567574 0.823323i \(-0.307882\pi\)
0.567574 + 0.823323i \(0.307882\pi\)
\(810\) 0.453607 0.0159381
\(811\) −33.2312 −1.16691 −0.583453 0.812147i \(-0.698299\pi\)
−0.583453 + 0.812147i \(0.698299\pi\)
\(812\) −7.57926 −0.265980
\(813\) 0.405889 0.0142352
\(814\) −28.9827 −1.01584
\(815\) −7.81213 −0.273647
\(816\) 5.67445 0.198646
\(817\) 19.1828 0.671122
\(818\) −10.0601 −0.351743
\(819\) −16.1845 −0.565530
\(820\) −6.77294 −0.236521
\(821\) −50.7865 −1.77246 −0.886230 0.463246i \(-0.846685\pi\)
−0.886230 + 0.463246i \(0.846685\pi\)
\(822\) −7.53298 −0.262743
\(823\) 35.0105 1.22039 0.610195 0.792251i \(-0.291091\pi\)
0.610195 + 0.792251i \(0.291091\pi\)
\(824\) 3.08692 0.107538
\(825\) 19.5255 0.679791
\(826\) −5.57768 −0.194072
\(827\) 42.7745 1.48741 0.743707 0.668506i \(-0.233066\pi\)
0.743707 + 0.668506i \(0.233066\pi\)
\(828\) −1.74612 −0.0606818
\(829\) 19.1655 0.665644 0.332822 0.942990i \(-0.391999\pi\)
0.332822 + 0.942990i \(0.391999\pi\)
\(830\) −5.67602 −0.197018
\(831\) 17.5711 0.609535
\(832\) 4.96673 0.172190
\(833\) −17.8244 −0.617578
\(834\) −8.49179 −0.294046
\(835\) −5.24970 −0.181673
\(836\) 16.1051 0.557007
\(837\) 1.89759 0.0655904
\(838\) 21.1423 0.730350
\(839\) 29.2132 1.00855 0.504275 0.863543i \(-0.331760\pi\)
0.504275 + 0.863543i \(0.331760\pi\)
\(840\) −1.32998 −0.0458886
\(841\) −12.5052 −0.431214
\(842\) 6.57213 0.226491
\(843\) 15.5296 0.534869
\(844\) −14.4008 −0.495697
\(845\) 7.42635 0.255474
\(846\) 9.95598 0.342294
\(847\) 6.34665 0.218073
\(848\) −2.51477 −0.0863576
\(849\) −32.3013 −1.10858
\(850\) 23.2849 0.798667
\(851\) −7.63738 −0.261806
\(852\) −11.3743 −0.389679
\(853\) 48.4203 1.65788 0.828939 0.559339i \(-0.188945\pi\)
0.828939 + 0.559339i \(0.188945\pi\)
\(854\) −0.182162 −0.00623346
\(855\) 4.71634 0.161295
\(856\) −1.69383 −0.0578938
\(857\) 58.0286 1.98222 0.991109 0.133050i \(-0.0424771\pi\)
0.991109 + 0.133050i \(0.0424771\pi\)
\(858\) 21.1054 0.720527
\(859\) 5.26179 0.179530 0.0897650 0.995963i \(-0.471388\pi\)
0.0897650 + 0.995963i \(0.471388\pi\)
\(860\) −2.87677 −0.0980972
\(861\) −22.2380 −0.757871
\(862\) −41.2475 −1.40489
\(863\) −23.8187 −0.810799 −0.405400 0.914140i \(-0.632868\pi\)
−0.405400 + 0.914140i \(0.632868\pi\)
\(864\) 5.31455 0.180805
\(865\) 14.7978 0.503140
\(866\) −17.6747 −0.600612
\(867\) 9.71934 0.330086
\(868\) −0.666331 −0.0226167
\(869\) 29.1317 0.988224
\(870\) 2.89444 0.0981306
\(871\) −51.0886 −1.73107
\(872\) −7.93509 −0.268716
\(873\) 7.51305 0.254278
\(874\) 4.24394 0.143553
\(875\) −11.3961 −0.385260
\(876\) 3.11535 0.105258
\(877\) −12.7179 −0.429453 −0.214727 0.976674i \(-0.568886\pi\)
−0.214727 + 0.976674i \(0.568886\pi\)
\(878\) 17.5884 0.593579
\(879\) 3.39180 0.114403
\(880\) −2.41522 −0.0814171
\(881\) 3.33847 0.112476 0.0562380 0.998417i \(-0.482089\pi\)
0.0562380 + 0.998417i \(0.482089\pi\)
\(882\) −6.14175 −0.206803
\(883\) −13.8193 −0.465058 −0.232529 0.972590i \(-0.574700\pi\)
−0.232529 + 0.972590i \(0.574700\pi\)
\(884\) 25.1690 0.846526
\(885\) 2.13005 0.0716010
\(886\) 15.1036 0.507417
\(887\) −16.3300 −0.548307 −0.274154 0.961686i \(-0.588398\pi\)
−0.274154 + 0.961686i \(0.588398\pi\)
\(888\) 8.55210 0.286990
\(889\) 1.93958 0.0650513
\(890\) −11.0863 −0.371615
\(891\) 2.70465 0.0906093
\(892\) 3.88305 0.130014
\(893\) −24.1980 −0.809755
\(894\) 5.71486 0.191134
\(895\) −11.3915 −0.380777
\(896\) −1.86618 −0.0623447
\(897\) 5.56159 0.185696
\(898\) −3.66694 −0.122367
\(899\) 1.45014 0.0483649
\(900\) 8.02330 0.267443
\(901\) −12.7437 −0.424553
\(902\) −40.3840 −1.34464
\(903\) −9.44551 −0.314327
\(904\) 5.65699 0.188149
\(905\) −1.87326 −0.0622692
\(906\) 0.367790 0.0122190
\(907\) −18.2833 −0.607086 −0.303543 0.952818i \(-0.598170\pi\)
−0.303543 + 0.952818i \(0.598170\pi\)
\(908\) −17.4252 −0.578277
\(909\) −7.84405 −0.260171
\(910\) −5.89911 −0.195554
\(911\) 10.4423 0.345969 0.172984 0.984925i \(-0.444659\pi\)
0.172984 + 0.984925i \(0.444659\pi\)
\(912\) −4.75223 −0.157362
\(913\) −33.8436 −1.12006
\(914\) 5.65616 0.187089
\(915\) 0.0695657 0.00229977
\(916\) 10.4745 0.346088
\(917\) 1.86618 0.0616267
\(918\) 26.9316 0.888876
\(919\) 10.3863 0.342611 0.171306 0.985218i \(-0.445201\pi\)
0.171306 + 0.985218i \(0.445201\pi\)
\(920\) −0.636447 −0.0209830
\(921\) 16.1487 0.532118
\(922\) 26.6194 0.876664
\(923\) −50.4509 −1.66061
\(924\) −7.93006 −0.260880
\(925\) 35.0933 1.15386
\(926\) −17.6648 −0.580502
\(927\) 5.39013 0.177035
\(928\) 4.06138 0.133321
\(929\) −20.4370 −0.670515 −0.335257 0.942127i \(-0.608823\pi\)
−0.335257 + 0.942127i \(0.608823\pi\)
\(930\) 0.254464 0.00834422
\(931\) 14.9275 0.489229
\(932\) 17.3090 0.566974
\(933\) 2.52184 0.0825613
\(934\) −5.99679 −0.196221
\(935\) −12.2392 −0.400264
\(936\) 8.67250 0.283470
\(937\) 33.4937 1.09419 0.547096 0.837070i \(-0.315733\pi\)
0.547096 + 0.837070i \(0.315733\pi\)
\(938\) 19.1958 0.626766
\(939\) −16.7200 −0.545638
\(940\) 3.62888 0.118361
\(941\) 40.2658 1.31263 0.656313 0.754488i \(-0.272115\pi\)
0.656313 + 0.754488i \(0.272115\pi\)
\(942\) 25.0759 0.817017
\(943\) −10.6418 −0.346544
\(944\) 2.98882 0.0972778
\(945\) −6.31223 −0.205337
\(946\) −17.1529 −0.557689
\(947\) −41.7682 −1.35728 −0.678642 0.734469i \(-0.737431\pi\)
−0.678642 + 0.734469i \(0.737431\pi\)
\(948\) −8.59606 −0.279187
\(949\) 13.8182 0.448556
\(950\) −19.5006 −0.632684
\(951\) −27.2754 −0.884466
\(952\) −9.45691 −0.306500
\(953\) −0.268038 −0.00868260 −0.00434130 0.999991i \(-0.501382\pi\)
−0.00434130 + 0.999991i \(0.501382\pi\)
\(954\) −4.39109 −0.142167
\(955\) −1.30348 −0.0421796
\(956\) 15.6341 0.505644
\(957\) 17.2582 0.557879
\(958\) −8.62140 −0.278545
\(959\) 12.5543 0.405399
\(960\) 0.712674 0.0230014
\(961\) −30.8725 −0.995887
\(962\) 37.9328 1.22300
\(963\) −2.95762 −0.0953080
\(964\) 1.84963 0.0595726
\(965\) −8.99175 −0.289455
\(966\) −2.08969 −0.0672347
\(967\) 25.1797 0.809726 0.404863 0.914377i \(-0.367319\pi\)
0.404863 + 0.914377i \(0.367319\pi\)
\(968\) −3.40088 −0.109308
\(969\) −24.0820 −0.773626
\(970\) 2.73845 0.0879264
\(971\) 27.6194 0.886350 0.443175 0.896435i \(-0.353852\pi\)
0.443175 + 0.896435i \(0.353852\pi\)
\(972\) 15.1456 0.485795
\(973\) 14.1522 0.453699
\(974\) −0.190368 −0.00609978
\(975\) −25.5552 −0.818420
\(976\) 0.0976123 0.00312449
\(977\) −52.0943 −1.66664 −0.833321 0.552789i \(-0.813564\pi\)
−0.833321 + 0.552789i \(0.813564\pi\)
\(978\) 13.7447 0.439507
\(979\) −66.1028 −2.11265
\(980\) −2.23862 −0.0715102
\(981\) −13.8556 −0.442376
\(982\) −17.7254 −0.565640
\(983\) −25.2099 −0.804070 −0.402035 0.915624i \(-0.631697\pi\)
−0.402035 + 0.915624i \(0.631697\pi\)
\(984\) 11.9163 0.379879
\(985\) 1.23759 0.0394330
\(986\) 20.5811 0.655436
\(987\) 11.9150 0.379257
\(988\) −21.0785 −0.670597
\(989\) −4.52005 −0.143729
\(990\) −4.21726 −0.134033
\(991\) −10.0698 −0.319879 −0.159939 0.987127i \(-0.551130\pi\)
−0.159939 + 0.987127i \(0.551130\pi\)
\(992\) 0.357056 0.0113365
\(993\) −24.8926 −0.789943
\(994\) 18.9562 0.601254
\(995\) −5.18573 −0.164399
\(996\) 9.98642 0.316432
\(997\) 22.0122 0.697134 0.348567 0.937284i \(-0.386668\pi\)
0.348567 + 0.937284i \(0.386668\pi\)
\(998\) 2.47226 0.0782581
\(999\) 40.5893 1.28419
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 \(a_p\))