Properties

Label 4017.2.a.j.1.10
Level 4017
Weight 2
Character 4017.1
Self dual Yes
Analytic conductor 32.076
Analytic rank 0
Dimension 25
CM No

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 1.10
Character \(\chi\) = 4017.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.491539 q^{2} -1.00000 q^{3} -1.75839 q^{4} -1.95668 q^{5} +0.491539 q^{6} -2.76715 q^{7} +1.84740 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-0.491539 q^{2} -1.00000 q^{3} -1.75839 q^{4} -1.95668 q^{5} +0.491539 q^{6} -2.76715 q^{7} +1.84740 q^{8} +1.00000 q^{9} +0.961784 q^{10} +0.480495 q^{11} +1.75839 q^{12} +1.00000 q^{13} +1.36017 q^{14} +1.95668 q^{15} +2.60871 q^{16} -2.47905 q^{17} -0.491539 q^{18} -0.387464 q^{19} +3.44060 q^{20} +2.76715 q^{21} -0.236182 q^{22} -2.25159 q^{23} -1.84740 q^{24} -1.17141 q^{25} -0.491539 q^{26} -1.00000 q^{27} +4.86573 q^{28} -10.3692 q^{29} -0.961784 q^{30} -4.61906 q^{31} -4.97708 q^{32} -0.480495 q^{33} +1.21855 q^{34} +5.41443 q^{35} -1.75839 q^{36} -8.05406 q^{37} +0.190454 q^{38} -1.00000 q^{39} -3.61476 q^{40} +11.4803 q^{41} -1.36017 q^{42} +0.735128 q^{43} -0.844897 q^{44} -1.95668 q^{45} +1.10675 q^{46} +6.95910 q^{47} -2.60871 q^{48} +0.657144 q^{49} +0.575796 q^{50} +2.47905 q^{51} -1.75839 q^{52} -4.35675 q^{53} +0.491539 q^{54} -0.940173 q^{55} -5.11203 q^{56} +0.387464 q^{57} +5.09687 q^{58} -13.8126 q^{59} -3.44060 q^{60} -5.00479 q^{61} +2.27045 q^{62} -2.76715 q^{63} -2.77099 q^{64} -1.95668 q^{65} +0.236182 q^{66} -6.94438 q^{67} +4.35913 q^{68} +2.25159 q^{69} -2.66140 q^{70} -6.52869 q^{71} +1.84740 q^{72} -4.41024 q^{73} +3.95888 q^{74} +1.17141 q^{75} +0.681313 q^{76} -1.32960 q^{77} +0.491539 q^{78} +1.22535 q^{79} -5.10440 q^{80} +1.00000 q^{81} -5.64303 q^{82} -14.8793 q^{83} -4.86573 q^{84} +4.85070 q^{85} -0.361344 q^{86} +10.3692 q^{87} +0.887664 q^{88} -9.52671 q^{89} +0.961784 q^{90} -2.76715 q^{91} +3.95918 q^{92} +4.61906 q^{93} -3.42067 q^{94} +0.758143 q^{95} +4.97708 q^{96} +8.28494 q^{97} -0.323012 q^{98} +0.480495 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 25q + 6q^{2} - 25q^{3} + 28q^{4} + 7q^{5} - 6q^{6} + 17q^{7} + 21q^{8} + 25q^{9} + O(q^{10}) \) \( 25q + 6q^{2} - 25q^{3} + 28q^{4} + 7q^{5} - 6q^{6} + 17q^{7} + 21q^{8} + 25q^{9} - 6q^{10} + 21q^{11} - 28q^{12} + 25q^{13} + 10q^{14} - 7q^{15} + 30q^{16} + 14q^{17} + 6q^{18} + 12q^{19} + 24q^{20} - 17q^{21} + 3q^{22} + 41q^{23} - 21q^{24} + 30q^{25} + 6q^{26} - 25q^{27} + 14q^{28} + 22q^{29} + 6q^{30} + 14q^{31} + 28q^{32} - 21q^{33} - 11q^{34} + 14q^{35} + 28q^{36} - 6q^{37} + 16q^{38} - 25q^{39} - 34q^{40} + 33q^{41} - 10q^{42} + 35q^{43} + 45q^{44} + 7q^{45} + 3q^{46} + 48q^{47} - 30q^{48} - 4q^{49} + 7q^{50} - 14q^{51} + 28q^{52} + 18q^{53} - 6q^{54} + 10q^{55} + 32q^{56} - 12q^{57} + 33q^{58} + 46q^{59} - 24q^{60} - 19q^{61} + 5q^{62} + 17q^{63} + 29q^{64} + 7q^{65} - 3q^{66} + 16q^{67} + 20q^{68} - 41q^{69} - 43q^{70} + 60q^{71} + 21q^{72} - 14q^{73} - 50q^{74} - 30q^{75} + 59q^{77} - 6q^{78} + 7q^{79} + 32q^{80} + 25q^{81} + 18q^{82} + 23q^{83} - 14q^{84} - 9q^{85} - 9q^{86} - 22q^{87} + 23q^{88} + 10q^{89} - 6q^{90} + 17q^{91} + 69q^{92} - 14q^{93} - 30q^{94} + 81q^{95} - 28q^{96} - 10q^{97} + 55q^{98} + 21q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.491539 −0.347571 −0.173785 0.984784i \(-0.555600\pi\)
−0.173785 + 0.984784i \(0.555600\pi\)
\(3\) −1.00000 −0.577350
\(4\) −1.75839 −0.879195
\(5\) −1.95668 −0.875053 −0.437526 0.899206i \(-0.644145\pi\)
−0.437526 + 0.899206i \(0.644145\pi\)
\(6\) 0.491539 0.200670
\(7\) −2.76715 −1.04589 −0.522943 0.852368i \(-0.675166\pi\)
−0.522943 + 0.852368i \(0.675166\pi\)
\(8\) 1.84740 0.653153
\(9\) 1.00000 0.333333
\(10\) 0.961784 0.304143
\(11\) 0.480495 0.144875 0.0724373 0.997373i \(-0.476922\pi\)
0.0724373 + 0.997373i \(0.476922\pi\)
\(12\) 1.75839 0.507603
\(13\) 1.00000 0.277350
\(14\) 1.36017 0.363519
\(15\) 1.95668 0.505212
\(16\) 2.60871 0.652178
\(17\) −2.47905 −0.601258 −0.300629 0.953741i \(-0.597197\pi\)
−0.300629 + 0.953741i \(0.597197\pi\)
\(18\) −0.491539 −0.115857
\(19\) −0.387464 −0.0888904 −0.0444452 0.999012i \(-0.514152\pi\)
−0.0444452 + 0.999012i \(0.514152\pi\)
\(20\) 3.44060 0.769342
\(21\) 2.76715 0.603843
\(22\) −0.236182 −0.0503542
\(23\) −2.25159 −0.469490 −0.234745 0.972057i \(-0.575425\pi\)
−0.234745 + 0.972057i \(0.575425\pi\)
\(24\) −1.84740 −0.377098
\(25\) −1.17141 −0.234283
\(26\) −0.491539 −0.0963988
\(27\) −1.00000 −0.192450
\(28\) 4.86573 0.919537
\(29\) −10.3692 −1.92551 −0.962757 0.270369i \(-0.912854\pi\)
−0.962757 + 0.270369i \(0.912854\pi\)
\(30\) −0.961784 −0.175597
\(31\) −4.61906 −0.829607 −0.414804 0.909911i \(-0.636150\pi\)
−0.414804 + 0.909911i \(0.636150\pi\)
\(32\) −4.97708 −0.879831
\(33\) −0.480495 −0.0836434
\(34\) 1.21855 0.208980
\(35\) 5.41443 0.915205
\(36\) −1.75839 −0.293065
\(37\) −8.05406 −1.32408 −0.662039 0.749469i \(-0.730309\pi\)
−0.662039 + 0.749469i \(0.730309\pi\)
\(38\) 0.190454 0.0308957
\(39\) −1.00000 −0.160128
\(40\) −3.61476 −0.571543
\(41\) 11.4803 1.79293 0.896463 0.443118i \(-0.146128\pi\)
0.896463 + 0.443118i \(0.146128\pi\)
\(42\) −1.36017 −0.209878
\(43\) 0.735128 0.112106 0.0560530 0.998428i \(-0.482148\pi\)
0.0560530 + 0.998428i \(0.482148\pi\)
\(44\) −0.844897 −0.127373
\(45\) −1.95668 −0.291684
\(46\) 1.10675 0.163181
\(47\) 6.95910 1.01509 0.507544 0.861626i \(-0.330553\pi\)
0.507544 + 0.861626i \(0.330553\pi\)
\(48\) −2.60871 −0.376535
\(49\) 0.657144 0.0938777
\(50\) 0.575796 0.0814299
\(51\) 2.47905 0.347136
\(52\) −1.75839 −0.243845
\(53\) −4.35675 −0.598446 −0.299223 0.954183i \(-0.596727\pi\)
−0.299223 + 0.954183i \(0.596727\pi\)
\(54\) 0.491539 0.0668900
\(55\) −0.940173 −0.126773
\(56\) −5.11203 −0.683124
\(57\) 0.387464 0.0513209
\(58\) 5.09687 0.669252
\(59\) −13.8126 −1.79824 −0.899122 0.437697i \(-0.855794\pi\)
−0.899122 + 0.437697i \(0.855794\pi\)
\(60\) −3.44060 −0.444180
\(61\) −5.00479 −0.640797 −0.320399 0.947283i \(-0.603817\pi\)
−0.320399 + 0.947283i \(0.603817\pi\)
\(62\) 2.27045 0.288347
\(63\) −2.76715 −0.348629
\(64\) −2.77099 −0.346374
\(65\) −1.95668 −0.242696
\(66\) 0.236182 0.0290720
\(67\) −6.94438 −0.848391 −0.424196 0.905571i \(-0.639443\pi\)
−0.424196 + 0.905571i \(0.639443\pi\)
\(68\) 4.35913 0.528623
\(69\) 2.25159 0.271060
\(70\) −2.66140 −0.318099
\(71\) −6.52869 −0.774813 −0.387406 0.921909i \(-0.626629\pi\)
−0.387406 + 0.921909i \(0.626629\pi\)
\(72\) 1.84740 0.217718
\(73\) −4.41024 −0.516180 −0.258090 0.966121i \(-0.583093\pi\)
−0.258090 + 0.966121i \(0.583093\pi\)
\(74\) 3.95888 0.460211
\(75\) 1.17141 0.135263
\(76\) 0.681313 0.0781520
\(77\) −1.32960 −0.151522
\(78\) 0.491539 0.0556559
\(79\) 1.22535 0.137862 0.0689311 0.997621i \(-0.478041\pi\)
0.0689311 + 0.997621i \(0.478041\pi\)
\(80\) −5.10440 −0.570690
\(81\) 1.00000 0.111111
\(82\) −5.64303 −0.623169
\(83\) −14.8793 −1.63321 −0.816605 0.577197i \(-0.804146\pi\)
−0.816605 + 0.577197i \(0.804146\pi\)
\(84\) −4.86573 −0.530895
\(85\) 4.85070 0.526132
\(86\) −0.361344 −0.0389647
\(87\) 10.3692 1.11170
\(88\) 0.887664 0.0946253
\(89\) −9.52671 −1.00983 −0.504915 0.863169i \(-0.668476\pi\)
−0.504915 + 0.863169i \(0.668476\pi\)
\(90\) 0.961784 0.101381
\(91\) −2.76715 −0.290077
\(92\) 3.95918 0.412773
\(93\) 4.61906 0.478974
\(94\) −3.42067 −0.352815
\(95\) 0.758143 0.0777838
\(96\) 4.97708 0.507971
\(97\) 8.28494 0.841208 0.420604 0.907244i \(-0.361818\pi\)
0.420604 + 0.907244i \(0.361818\pi\)
\(98\) −0.323012 −0.0326291
\(99\) 0.480495 0.0482915
\(100\) 2.05980 0.205980
\(101\) 10.1155 1.00653 0.503265 0.864132i \(-0.332132\pi\)
0.503265 + 0.864132i \(0.332132\pi\)
\(102\) −1.21855 −0.120654
\(103\) −1.00000 −0.0985329
\(104\) 1.84740 0.181152
\(105\) −5.41443 −0.528394
\(106\) 2.14152 0.208002
\(107\) −6.81812 −0.659132 −0.329566 0.944133i \(-0.606902\pi\)
−0.329566 + 0.944133i \(0.606902\pi\)
\(108\) 1.75839 0.169201
\(109\) −5.37639 −0.514965 −0.257482 0.966283i \(-0.582893\pi\)
−0.257482 + 0.966283i \(0.582893\pi\)
\(110\) 0.462132 0.0440626
\(111\) 8.05406 0.764457
\(112\) −7.21871 −0.682104
\(113\) 3.35708 0.315807 0.157904 0.987455i \(-0.449526\pi\)
0.157904 + 0.987455i \(0.449526\pi\)
\(114\) −0.190454 −0.0178376
\(115\) 4.40564 0.410828
\(116\) 18.2331 1.69290
\(117\) 1.00000 0.0924500
\(118\) 6.78943 0.625017
\(119\) 6.85991 0.628847
\(120\) 3.61476 0.329981
\(121\) −10.7691 −0.979011
\(122\) 2.46005 0.222722
\(123\) −11.4803 −1.03515
\(124\) 8.12210 0.729386
\(125\) 12.0755 1.08006
\(126\) 1.36017 0.121173
\(127\) 16.7237 1.48399 0.741995 0.670405i \(-0.233880\pi\)
0.741995 + 0.670405i \(0.233880\pi\)
\(128\) 11.3162 1.00022
\(129\) −0.735128 −0.0647244
\(130\) 0.961784 0.0843540
\(131\) 10.0919 0.881736 0.440868 0.897572i \(-0.354671\pi\)
0.440868 + 0.897572i \(0.354671\pi\)
\(132\) 0.844897 0.0735388
\(133\) 1.07217 0.0929692
\(134\) 3.41344 0.294876
\(135\) 1.95668 0.168404
\(136\) −4.57979 −0.392713
\(137\) 3.29098 0.281168 0.140584 0.990069i \(-0.455102\pi\)
0.140584 + 0.990069i \(0.455102\pi\)
\(138\) −1.10675 −0.0942125
\(139\) 10.0889 0.855726 0.427863 0.903844i \(-0.359267\pi\)
0.427863 + 0.903844i \(0.359267\pi\)
\(140\) −9.52067 −0.804644
\(141\) −6.95910 −0.586062
\(142\) 3.20911 0.269302
\(143\) 0.480495 0.0401810
\(144\) 2.60871 0.217393
\(145\) 20.2892 1.68493
\(146\) 2.16781 0.179409
\(147\) −0.657144 −0.0542003
\(148\) 14.1622 1.16412
\(149\) −15.3939 −1.26112 −0.630558 0.776142i \(-0.717174\pi\)
−0.630558 + 0.776142i \(0.717174\pi\)
\(150\) −0.575796 −0.0470136
\(151\) 16.5159 1.34405 0.672023 0.740530i \(-0.265426\pi\)
0.672023 + 0.740530i \(0.265426\pi\)
\(152\) −0.715800 −0.0580590
\(153\) −2.47905 −0.200419
\(154\) 0.653552 0.0526647
\(155\) 9.03801 0.725950
\(156\) 1.75839 0.140784
\(157\) 20.8104 1.66085 0.830425 0.557130i \(-0.188098\pi\)
0.830425 + 0.557130i \(0.188098\pi\)
\(158\) −0.602306 −0.0479169
\(159\) 4.35675 0.345513
\(160\) 9.73853 0.769898
\(161\) 6.23051 0.491033
\(162\) −0.491539 −0.0386190
\(163\) −17.6077 −1.37914 −0.689572 0.724217i \(-0.742201\pi\)
−0.689572 + 0.724217i \(0.742201\pi\)
\(164\) −20.1869 −1.57633
\(165\) 0.940173 0.0731924
\(166\) 7.31374 0.567656
\(167\) 12.4143 0.960647 0.480324 0.877091i \(-0.340519\pi\)
0.480324 + 0.877091i \(0.340519\pi\)
\(168\) 5.11203 0.394402
\(169\) 1.00000 0.0769231
\(170\) −2.38431 −0.182868
\(171\) −0.387464 −0.0296301
\(172\) −1.29264 −0.0985629
\(173\) −0.962096 −0.0731468 −0.0365734 0.999331i \(-0.511644\pi\)
−0.0365734 + 0.999331i \(0.511644\pi\)
\(174\) −5.09687 −0.386393
\(175\) 3.24148 0.245033
\(176\) 1.25347 0.0944840
\(177\) 13.8126 1.03822
\(178\) 4.68275 0.350987
\(179\) −16.7816 −1.25431 −0.627157 0.778893i \(-0.715782\pi\)
−0.627157 + 0.778893i \(0.715782\pi\)
\(180\) 3.44060 0.256447
\(181\) −16.9505 −1.25992 −0.629960 0.776627i \(-0.716929\pi\)
−0.629960 + 0.776627i \(0.716929\pi\)
\(182\) 1.36017 0.100822
\(183\) 5.00479 0.369965
\(184\) −4.15958 −0.306649
\(185\) 15.7592 1.15864
\(186\) −2.27045 −0.166477
\(187\) −1.19117 −0.0871070
\(188\) −12.2368 −0.892460
\(189\) 2.76715 0.201281
\(190\) −0.372657 −0.0270354
\(191\) −7.04770 −0.509953 −0.254977 0.966947i \(-0.582068\pi\)
−0.254977 + 0.966947i \(0.582068\pi\)
\(192\) 2.77099 0.199979
\(193\) 6.44544 0.463953 0.231977 0.972721i \(-0.425481\pi\)
0.231977 + 0.972721i \(0.425481\pi\)
\(194\) −4.07237 −0.292379
\(195\) 1.95668 0.140121
\(196\) −1.15551 −0.0825368
\(197\) 25.7287 1.83309 0.916547 0.399927i \(-0.130965\pi\)
0.916547 + 0.399927i \(0.130965\pi\)
\(198\) −0.236182 −0.0167847
\(199\) −19.2453 −1.36427 −0.682133 0.731228i \(-0.738947\pi\)
−0.682133 + 0.731228i \(0.738947\pi\)
\(200\) −2.16407 −0.153023
\(201\) 6.94438 0.489819
\(202\) −4.97216 −0.349840
\(203\) 28.6932 2.01387
\(204\) −4.35913 −0.305200
\(205\) −22.4633 −1.56891
\(206\) 0.491539 0.0342472
\(207\) −2.25159 −0.156497
\(208\) 2.60871 0.180882
\(209\) −0.186175 −0.0128780
\(210\) 2.66140 0.183654
\(211\) 16.2268 1.11710 0.558548 0.829472i \(-0.311359\pi\)
0.558548 + 0.829472i \(0.311359\pi\)
\(212\) 7.66087 0.526151
\(213\) 6.52869 0.447338
\(214\) 3.35137 0.229095
\(215\) −1.43841 −0.0980986
\(216\) −1.84740 −0.125699
\(217\) 12.7816 0.867675
\(218\) 2.64271 0.178987
\(219\) 4.41024 0.298016
\(220\) 1.65319 0.111458
\(221\) −2.47905 −0.166759
\(222\) −3.95888 −0.265703
\(223\) −21.9279 −1.46840 −0.734201 0.678932i \(-0.762443\pi\)
−0.734201 + 0.678932i \(0.762443\pi\)
\(224\) 13.7723 0.920203
\(225\) −1.17141 −0.0780943
\(226\) −1.65013 −0.109765
\(227\) 15.2201 1.01019 0.505096 0.863063i \(-0.331457\pi\)
0.505096 + 0.863063i \(0.331457\pi\)
\(228\) −0.681313 −0.0451211
\(229\) −10.1190 −0.668683 −0.334342 0.942452i \(-0.608514\pi\)
−0.334342 + 0.942452i \(0.608514\pi\)
\(230\) −2.16555 −0.142792
\(231\) 1.32960 0.0874815
\(232\) −19.1560 −1.25765
\(233\) −9.06953 −0.594165 −0.297082 0.954852i \(-0.596014\pi\)
−0.297082 + 0.954852i \(0.596014\pi\)
\(234\) −0.491539 −0.0321329
\(235\) −13.6167 −0.888256
\(236\) 24.2879 1.58101
\(237\) −1.22535 −0.0795948
\(238\) −3.37192 −0.218569
\(239\) 25.2699 1.63458 0.817288 0.576229i \(-0.195476\pi\)
0.817288 + 0.576229i \(0.195476\pi\)
\(240\) 5.10440 0.329488
\(241\) −18.6914 −1.20402 −0.602009 0.798490i \(-0.705633\pi\)
−0.602009 + 0.798490i \(0.705633\pi\)
\(242\) 5.29345 0.340276
\(243\) −1.00000 −0.0641500
\(244\) 8.80036 0.563386
\(245\) −1.28582 −0.0821479
\(246\) 5.64303 0.359787
\(247\) −0.387464 −0.0246538
\(248\) −8.53323 −0.541861
\(249\) 14.8793 0.942934
\(250\) −5.93557 −0.375398
\(251\) 17.3227 1.09340 0.546698 0.837330i \(-0.315884\pi\)
0.546698 + 0.837330i \(0.315884\pi\)
\(252\) 4.86573 0.306512
\(253\) −1.08188 −0.0680171
\(254\) −8.22037 −0.515792
\(255\) −4.85070 −0.303763
\(256\) −0.0203706 −0.00127316
\(257\) 2.03321 0.126828 0.0634141 0.997987i \(-0.479801\pi\)
0.0634141 + 0.997987i \(0.479801\pi\)
\(258\) 0.361344 0.0224963
\(259\) 22.2868 1.38484
\(260\) 3.44060 0.213377
\(261\) −10.3692 −0.641838
\(262\) −4.96058 −0.306466
\(263\) 13.7493 0.847819 0.423909 0.905705i \(-0.360657\pi\)
0.423909 + 0.905705i \(0.360657\pi\)
\(264\) −0.887664 −0.0546319
\(265\) 8.52476 0.523672
\(266\) −0.527015 −0.0323134
\(267\) 9.52671 0.583025
\(268\) 12.2109 0.745901
\(269\) 24.6331 1.50191 0.750954 0.660355i \(-0.229594\pi\)
0.750954 + 0.660355i \(0.229594\pi\)
\(270\) −0.961784 −0.0585323
\(271\) 15.7442 0.956393 0.478196 0.878253i \(-0.341291\pi\)
0.478196 + 0.878253i \(0.341291\pi\)
\(272\) −6.46712 −0.392127
\(273\) 2.76715 0.167476
\(274\) −1.61765 −0.0977256
\(275\) −0.562858 −0.0339416
\(276\) −3.95918 −0.238315
\(277\) −4.02082 −0.241587 −0.120794 0.992678i \(-0.538544\pi\)
−0.120794 + 0.992678i \(0.538544\pi\)
\(278\) −4.95907 −0.297425
\(279\) −4.61906 −0.276536
\(280\) 10.0026 0.597769
\(281\) 18.1106 1.08039 0.540194 0.841541i \(-0.318351\pi\)
0.540194 + 0.841541i \(0.318351\pi\)
\(282\) 3.42067 0.203698
\(283\) −0.376343 −0.0223713 −0.0111856 0.999937i \(-0.503561\pi\)
−0.0111856 + 0.999937i \(0.503561\pi\)
\(284\) 11.4800 0.681211
\(285\) −0.758143 −0.0449085
\(286\) −0.236182 −0.0139657
\(287\) −31.7678 −1.87520
\(288\) −4.97708 −0.293277
\(289\) −10.8543 −0.638489
\(290\) −9.97293 −0.585631
\(291\) −8.28494 −0.485672
\(292\) 7.75492 0.453822
\(293\) 21.4651 1.25400 0.627001 0.779018i \(-0.284282\pi\)
0.627001 + 0.779018i \(0.284282\pi\)
\(294\) 0.323012 0.0188384
\(295\) 27.0268 1.57356
\(296\) −14.8790 −0.864826
\(297\) −0.480495 −0.0278811
\(298\) 7.56669 0.438327
\(299\) −2.25159 −0.130213
\(300\) −2.05980 −0.118923
\(301\) −2.03421 −0.117250
\(302\) −8.11822 −0.467151
\(303\) −10.1155 −0.581120
\(304\) −1.01078 −0.0579723
\(305\) 9.79275 0.560731
\(306\) 1.21855 0.0696599
\(307\) −26.7164 −1.52479 −0.762394 0.647114i \(-0.775976\pi\)
−0.762394 + 0.647114i \(0.775976\pi\)
\(308\) 2.33796 0.133218
\(309\) 1.00000 0.0568880
\(310\) −4.44253 −0.252319
\(311\) 10.4602 0.593142 0.296571 0.955011i \(-0.404157\pi\)
0.296571 + 0.955011i \(0.404157\pi\)
\(312\) −1.84740 −0.104588
\(313\) −11.1601 −0.630806 −0.315403 0.948958i \(-0.602140\pi\)
−0.315403 + 0.948958i \(0.602140\pi\)
\(314\) −10.2291 −0.577263
\(315\) 5.41443 0.305068
\(316\) −2.15464 −0.121208
\(317\) 27.1428 1.52449 0.762247 0.647287i \(-0.224096\pi\)
0.762247 + 0.647287i \(0.224096\pi\)
\(318\) −2.14152 −0.120090
\(319\) −4.98235 −0.278958
\(320\) 5.42194 0.303096
\(321\) 6.81812 0.380550
\(322\) −3.06254 −0.170669
\(323\) 0.960543 0.0534460
\(324\) −1.75839 −0.0976883
\(325\) −1.17141 −0.0649784
\(326\) 8.65490 0.479350
\(327\) 5.37639 0.297315
\(328\) 21.2087 1.17106
\(329\) −19.2569 −1.06167
\(330\) −0.462132 −0.0254395
\(331\) −17.7149 −0.973700 −0.486850 0.873485i \(-0.661854\pi\)
−0.486850 + 0.873485i \(0.661854\pi\)
\(332\) 26.1635 1.43591
\(333\) −8.05406 −0.441360
\(334\) −6.10211 −0.333893
\(335\) 13.5879 0.742387
\(336\) 7.21871 0.393813
\(337\) −30.4798 −1.66034 −0.830171 0.557509i \(-0.811757\pi\)
−0.830171 + 0.557509i \(0.811757\pi\)
\(338\) −0.491539 −0.0267362
\(339\) −3.35708 −0.182331
\(340\) −8.52942 −0.462573
\(341\) −2.21943 −0.120189
\(342\) 0.190454 0.0102986
\(343\) 17.5517 0.947701
\(344\) 1.35807 0.0732223
\(345\) −4.40564 −0.237192
\(346\) 0.472908 0.0254237
\(347\) −15.9376 −0.855575 −0.427788 0.903879i \(-0.640707\pi\)
−0.427788 + 0.903879i \(0.640707\pi\)
\(348\) −18.2331 −0.977397
\(349\) −16.5775 −0.887373 −0.443687 0.896182i \(-0.646330\pi\)
−0.443687 + 0.896182i \(0.646330\pi\)
\(350\) −1.59332 −0.0851664
\(351\) −1.00000 −0.0533761
\(352\) −2.39146 −0.127465
\(353\) −12.3502 −0.657333 −0.328667 0.944446i \(-0.606599\pi\)
−0.328667 + 0.944446i \(0.606599\pi\)
\(354\) −6.78943 −0.360854
\(355\) 12.7745 0.678002
\(356\) 16.7517 0.887837
\(357\) −6.85991 −0.363065
\(358\) 8.24881 0.435963
\(359\) 8.07523 0.426195 0.213097 0.977031i \(-0.431645\pi\)
0.213097 + 0.977031i \(0.431645\pi\)
\(360\) −3.61476 −0.190514
\(361\) −18.8499 −0.992098
\(362\) 8.33184 0.437912
\(363\) 10.7691 0.565232
\(364\) 4.86573 0.255034
\(365\) 8.62942 0.451684
\(366\) −2.46005 −0.128589
\(367\) 18.9159 0.987401 0.493701 0.869632i \(-0.335644\pi\)
0.493701 + 0.869632i \(0.335644\pi\)
\(368\) −5.87376 −0.306191
\(369\) 11.4803 0.597642
\(370\) −7.74626 −0.402709
\(371\) 12.0558 0.625906
\(372\) −8.12210 −0.421111
\(373\) −10.8347 −0.561001 −0.280500 0.959854i \(-0.590500\pi\)
−0.280500 + 0.959854i \(0.590500\pi\)
\(374\) 0.585507 0.0302758
\(375\) −12.0755 −0.623574
\(376\) 12.8562 0.663008
\(377\) −10.3692 −0.534041
\(378\) −1.36017 −0.0699593
\(379\) −17.4704 −0.897396 −0.448698 0.893683i \(-0.648112\pi\)
−0.448698 + 0.893683i \(0.648112\pi\)
\(380\) −1.33311 −0.0683871
\(381\) −16.7237 −0.856782
\(382\) 3.46422 0.177245
\(383\) −14.4202 −0.736836 −0.368418 0.929660i \(-0.620100\pi\)
−0.368418 + 0.929660i \(0.620100\pi\)
\(384\) −11.3162 −0.577478
\(385\) 2.60160 0.132590
\(386\) −3.16819 −0.161257
\(387\) 0.735128 0.0373686
\(388\) −14.5681 −0.739586
\(389\) −29.3126 −1.48621 −0.743105 0.669175i \(-0.766647\pi\)
−0.743105 + 0.669175i \(0.766647\pi\)
\(390\) −0.961784 −0.0487018
\(391\) 5.58181 0.282284
\(392\) 1.21400 0.0613165
\(393\) −10.0919 −0.509070
\(394\) −12.6467 −0.637130
\(395\) −2.39761 −0.120637
\(396\) −0.844897 −0.0424577
\(397\) 10.8183 0.542954 0.271477 0.962445i \(-0.412488\pi\)
0.271477 + 0.962445i \(0.412488\pi\)
\(398\) 9.45984 0.474179
\(399\) −1.07217 −0.0536758
\(400\) −3.05588 −0.152794
\(401\) 19.1319 0.955400 0.477700 0.878523i \(-0.341471\pi\)
0.477700 + 0.878523i \(0.341471\pi\)
\(402\) −3.41344 −0.170247
\(403\) −4.61906 −0.230092
\(404\) −17.7870 −0.884935
\(405\) −1.95668 −0.0972281
\(406\) −14.1038 −0.699961
\(407\) −3.86993 −0.191825
\(408\) 4.57979 0.226733
\(409\) −29.1543 −1.44159 −0.720793 0.693150i \(-0.756222\pi\)
−0.720793 + 0.693150i \(0.756222\pi\)
\(410\) 11.0416 0.545305
\(411\) −3.29098 −0.162332
\(412\) 1.75839 0.0866296
\(413\) 38.2215 1.88076
\(414\) 1.10675 0.0543936
\(415\) 29.1139 1.42914
\(416\) −4.97708 −0.244021
\(417\) −10.0889 −0.494053
\(418\) 0.0915121 0.00447600
\(419\) 21.5025 1.05047 0.525233 0.850958i \(-0.323978\pi\)
0.525233 + 0.850958i \(0.323978\pi\)
\(420\) 9.52067 0.464561
\(421\) 22.1443 1.07925 0.539623 0.841907i \(-0.318567\pi\)
0.539623 + 0.841907i \(0.318567\pi\)
\(422\) −7.97609 −0.388270
\(423\) 6.95910 0.338363
\(424\) −8.04865 −0.390877
\(425\) 2.90399 0.140864
\(426\) −3.20911 −0.155482
\(427\) 13.8490 0.670201
\(428\) 11.9889 0.579505
\(429\) −0.480495 −0.0231985
\(430\) 0.707034 0.0340962
\(431\) 28.9147 1.39277 0.696386 0.717667i \(-0.254790\pi\)
0.696386 + 0.717667i \(0.254790\pi\)
\(432\) −2.60871 −0.125512
\(433\) −14.9288 −0.717432 −0.358716 0.933447i \(-0.616785\pi\)
−0.358716 + 0.933447i \(0.616785\pi\)
\(434\) −6.28268 −0.301578
\(435\) −20.2892 −0.972792
\(436\) 9.45378 0.452754
\(437\) 0.872412 0.0417331
\(438\) −2.16781 −0.103582
\(439\) −21.3339 −1.01821 −0.509106 0.860704i \(-0.670024\pi\)
−0.509106 + 0.860704i \(0.670024\pi\)
\(440\) −1.73687 −0.0828021
\(441\) 0.657144 0.0312926
\(442\) 1.21855 0.0579605
\(443\) 9.47183 0.450020 0.225010 0.974356i \(-0.427759\pi\)
0.225010 + 0.974356i \(0.427759\pi\)
\(444\) −14.1622 −0.672107
\(445\) 18.6407 0.883654
\(446\) 10.7784 0.510374
\(447\) 15.3939 0.728105
\(448\) 7.66777 0.362268
\(449\) −12.4659 −0.588300 −0.294150 0.955759i \(-0.595037\pi\)
−0.294150 + 0.955759i \(0.595037\pi\)
\(450\) 0.575796 0.0271433
\(451\) 5.51624 0.259749
\(452\) −5.90305 −0.277656
\(453\) −16.5159 −0.775985
\(454\) −7.48127 −0.351113
\(455\) 5.41443 0.253832
\(456\) 0.715800 0.0335204
\(457\) 19.7556 0.924126 0.462063 0.886847i \(-0.347109\pi\)
0.462063 + 0.886847i \(0.347109\pi\)
\(458\) 4.97389 0.232415
\(459\) 2.47905 0.115712
\(460\) −7.74683 −0.361198
\(461\) −3.14897 −0.146662 −0.0733310 0.997308i \(-0.523363\pi\)
−0.0733310 + 0.997308i \(0.523363\pi\)
\(462\) −0.653552 −0.0304060
\(463\) −3.25643 −0.151339 −0.0756695 0.997133i \(-0.524109\pi\)
−0.0756695 + 0.997133i \(0.524109\pi\)
\(464\) −27.0503 −1.25578
\(465\) −9.03801 −0.419127
\(466\) 4.45803 0.206514
\(467\) −26.9886 −1.24888 −0.624442 0.781071i \(-0.714674\pi\)
−0.624442 + 0.781071i \(0.714674\pi\)
\(468\) −1.75839 −0.0812816
\(469\) 19.2162 0.887320
\(470\) 6.69314 0.308732
\(471\) −20.8104 −0.958893
\(472\) −25.5173 −1.17453
\(473\) 0.353225 0.0162413
\(474\) 0.602306 0.0276648
\(475\) 0.453881 0.0208255
\(476\) −12.0624 −0.552879
\(477\) −4.35675 −0.199482
\(478\) −12.4212 −0.568131
\(479\) 39.1301 1.78790 0.893949 0.448168i \(-0.147923\pi\)
0.893949 + 0.448168i \(0.147923\pi\)
\(480\) −9.73853 −0.444501
\(481\) −8.05406 −0.367233
\(482\) 9.18754 0.418481
\(483\) −6.23051 −0.283498
\(484\) 18.9363 0.860741
\(485\) −16.2110 −0.736101
\(486\) 0.491539 0.0222967
\(487\) 18.5749 0.841709 0.420855 0.907128i \(-0.361730\pi\)
0.420855 + 0.907128i \(0.361730\pi\)
\(488\) −9.24582 −0.418539
\(489\) 17.6077 0.796249
\(490\) 0.632030 0.0285522
\(491\) −28.4496 −1.28391 −0.641956 0.766742i \(-0.721877\pi\)
−0.641956 + 0.766742i \(0.721877\pi\)
\(492\) 20.1869 0.910095
\(493\) 25.7058 1.15773
\(494\) 0.190454 0.00856893
\(495\) −0.940173 −0.0422576
\(496\) −12.0498 −0.541051
\(497\) 18.0659 0.810366
\(498\) −7.31374 −0.327736
\(499\) 44.1140 1.97482 0.987408 0.158197i \(-0.0505682\pi\)
0.987408 + 0.158197i \(0.0505682\pi\)
\(500\) −21.2334 −0.949585
\(501\) −12.4143 −0.554630
\(502\) −8.51477 −0.380033
\(503\) 28.3813 1.26546 0.632730 0.774372i \(-0.281934\pi\)
0.632730 + 0.774372i \(0.281934\pi\)
\(504\) −5.11203 −0.227708
\(505\) −19.7928 −0.880766
\(506\) 0.531786 0.0236408
\(507\) −1.00000 −0.0444116
\(508\) −29.4068 −1.30472
\(509\) −19.8630 −0.880411 −0.440205 0.897897i \(-0.645094\pi\)
−0.440205 + 0.897897i \(0.645094\pi\)
\(510\) 2.38431 0.105579
\(511\) 12.2038 0.539865
\(512\) −22.6224 −0.999778
\(513\) 0.387464 0.0171070
\(514\) −0.999402 −0.0440818
\(515\) 1.95668 0.0862215
\(516\) 1.29264 0.0569053
\(517\) 3.34381 0.147061
\(518\) −10.9548 −0.481328
\(519\) 0.962096 0.0422313
\(520\) −3.61476 −0.158518
\(521\) −40.0692 −1.75547 −0.877733 0.479151i \(-0.840945\pi\)
−0.877733 + 0.479151i \(0.840945\pi\)
\(522\) 5.09687 0.223084
\(523\) −8.18749 −0.358014 −0.179007 0.983848i \(-0.557288\pi\)
−0.179007 + 0.983848i \(0.557288\pi\)
\(524\) −17.7455 −0.775217
\(525\) −3.24148 −0.141470
\(526\) −6.75833 −0.294677
\(527\) 11.4509 0.498808
\(528\) −1.25347 −0.0545504
\(529\) −17.9303 −0.779579
\(530\) −4.19025 −0.182013
\(531\) −13.8126 −0.599415
\(532\) −1.88530 −0.0817381
\(533\) 11.4803 0.497268
\(534\) −4.68275 −0.202643
\(535\) 13.3409 0.576775
\(536\) −12.8290 −0.554129
\(537\) 16.7816 0.724179
\(538\) −12.1081 −0.522019
\(539\) 0.315754 0.0136005
\(540\) −3.44060 −0.148060
\(541\) −20.8714 −0.897330 −0.448665 0.893700i \(-0.648100\pi\)
−0.448665 + 0.893700i \(0.648100\pi\)
\(542\) −7.73890 −0.332414
\(543\) 16.9505 0.727416
\(544\) 12.3384 0.529005
\(545\) 10.5199 0.450621
\(546\) −1.36017 −0.0582097
\(547\) 42.6030 1.82157 0.910786 0.412878i \(-0.135477\pi\)
0.910786 + 0.412878i \(0.135477\pi\)
\(548\) −5.78683 −0.247201
\(549\) −5.00479 −0.213599
\(550\) 0.276667 0.0117971
\(551\) 4.01770 0.171160
\(552\) 4.15958 0.177044
\(553\) −3.39072 −0.144188
\(554\) 1.97639 0.0839687
\(555\) −15.7592 −0.668940
\(556\) −17.7401 −0.752349
\(557\) 18.9148 0.801446 0.400723 0.916199i \(-0.368759\pi\)
0.400723 + 0.916199i \(0.368759\pi\)
\(558\) 2.27045 0.0961157
\(559\) 0.735128 0.0310926
\(560\) 14.1247 0.596877
\(561\) 1.19117 0.0502912
\(562\) −8.90207 −0.375511
\(563\) 5.08678 0.214382 0.107191 0.994238i \(-0.465814\pi\)
0.107191 + 0.994238i \(0.465814\pi\)
\(564\) 12.2368 0.515262
\(565\) −6.56872 −0.276348
\(566\) 0.184987 0.00777560
\(567\) −2.76715 −0.116210
\(568\) −12.0611 −0.506071
\(569\) 40.8836 1.71393 0.856965 0.515374i \(-0.172347\pi\)
0.856965 + 0.515374i \(0.172347\pi\)
\(570\) 0.372657 0.0156089
\(571\) 44.4352 1.85956 0.929778 0.368120i \(-0.119998\pi\)
0.929778 + 0.368120i \(0.119998\pi\)
\(572\) −0.844897 −0.0353269
\(573\) 7.04770 0.294422
\(574\) 15.6151 0.651764
\(575\) 2.63755 0.109993
\(576\) −2.77099 −0.115458
\(577\) −34.5205 −1.43711 −0.718553 0.695473i \(-0.755195\pi\)
−0.718553 + 0.695473i \(0.755195\pi\)
\(578\) 5.33532 0.221920
\(579\) −6.44544 −0.267863
\(580\) −35.6763 −1.48138
\(581\) 41.1732 1.70815
\(582\) 4.07237 0.168805
\(583\) −2.09340 −0.0866996
\(584\) −8.14746 −0.337144
\(585\) −1.95668 −0.0808986
\(586\) −10.5509 −0.435855
\(587\) 22.8267 0.942159 0.471080 0.882091i \(-0.343864\pi\)
0.471080 + 0.882091i \(0.343864\pi\)
\(588\) 1.15551 0.0476526
\(589\) 1.78972 0.0737441
\(590\) −13.2847 −0.546923
\(591\) −25.7287 −1.05834
\(592\) −21.0107 −0.863535
\(593\) 43.7769 1.79770 0.898850 0.438256i \(-0.144404\pi\)
0.898850 + 0.438256i \(0.144404\pi\)
\(594\) 0.236182 0.00969066
\(595\) −13.4226 −0.550274
\(596\) 27.0684 1.10877
\(597\) 19.2453 0.787659
\(598\) 1.10675 0.0452582
\(599\) −29.2432 −1.19484 −0.597422 0.801927i \(-0.703808\pi\)
−0.597422 + 0.801927i \(0.703808\pi\)
\(600\) 2.16407 0.0883476
\(601\) −39.3488 −1.60507 −0.802536 0.596603i \(-0.796517\pi\)
−0.802536 + 0.596603i \(0.796517\pi\)
\(602\) 0.999895 0.0407527
\(603\) −6.94438 −0.282797
\(604\) −29.0414 −1.18168
\(605\) 21.0717 0.856686
\(606\) 4.97216 0.201980
\(607\) 28.7010 1.16494 0.582470 0.812852i \(-0.302087\pi\)
0.582470 + 0.812852i \(0.302087\pi\)
\(608\) 1.92844 0.0782085
\(609\) −28.6932 −1.16271
\(610\) −4.81352 −0.194894
\(611\) 6.95910 0.281535
\(612\) 4.35913 0.176208
\(613\) 24.7941 1.00143 0.500713 0.865613i \(-0.333071\pi\)
0.500713 + 0.865613i \(0.333071\pi\)
\(614\) 13.1322 0.529971
\(615\) 22.4633 0.905808
\(616\) −2.45630 −0.0989673
\(617\) −18.3698 −0.739539 −0.369770 0.929123i \(-0.620563\pi\)
−0.369770 + 0.929123i \(0.620563\pi\)
\(618\) −0.491539 −0.0197726
\(619\) 19.7081 0.792137 0.396069 0.918221i \(-0.370374\pi\)
0.396069 + 0.918221i \(0.370374\pi\)
\(620\) −15.8923 −0.638251
\(621\) 2.25159 0.0903533
\(622\) −5.14159 −0.206159
\(623\) 26.3619 1.05617
\(624\) −2.60871 −0.104432
\(625\) −17.7707 −0.710829
\(626\) 5.48563 0.219250
\(627\) 0.186175 0.00743509
\(628\) −36.5928 −1.46021
\(629\) 19.9664 0.796113
\(630\) −2.66140 −0.106033
\(631\) −20.0553 −0.798387 −0.399194 0.916867i \(-0.630710\pi\)
−0.399194 + 0.916867i \(0.630710\pi\)
\(632\) 2.26370 0.0900451
\(633\) −16.2268 −0.644956
\(634\) −13.3418 −0.529869
\(635\) −32.7229 −1.29857
\(636\) −7.66087 −0.303773
\(637\) 0.657144 0.0260370
\(638\) 2.44902 0.0969576
\(639\) −6.52869 −0.258271
\(640\) −22.1422 −0.875246
\(641\) −28.3837 −1.12109 −0.560544 0.828125i \(-0.689408\pi\)
−0.560544 + 0.828125i \(0.689408\pi\)
\(642\) −3.35137 −0.132268
\(643\) 22.4343 0.884722 0.442361 0.896837i \(-0.354141\pi\)
0.442361 + 0.896837i \(0.354141\pi\)
\(644\) −10.9557 −0.431713
\(645\) 1.43841 0.0566373
\(646\) −0.472145 −0.0185763
\(647\) 37.1338 1.45988 0.729940 0.683511i \(-0.239548\pi\)
0.729940 + 0.683511i \(0.239548\pi\)
\(648\) 1.84740 0.0725726
\(649\) −6.63687 −0.260520
\(650\) 0.575796 0.0225846
\(651\) −12.7816 −0.500952
\(652\) 30.9613 1.21254
\(653\) 21.2042 0.829786 0.414893 0.909870i \(-0.363819\pi\)
0.414893 + 0.909870i \(0.363819\pi\)
\(654\) −2.64271 −0.103338
\(655\) −19.7466 −0.771565
\(656\) 29.9489 1.16931
\(657\) −4.41024 −0.172060
\(658\) 9.46552 0.369004
\(659\) −36.1974 −1.41005 −0.705026 0.709181i \(-0.749065\pi\)
−0.705026 + 0.709181i \(0.749065\pi\)
\(660\) −1.65319 −0.0643503
\(661\) −39.3570 −1.53081 −0.765405 0.643548i \(-0.777462\pi\)
−0.765405 + 0.643548i \(0.777462\pi\)
\(662\) 8.70758 0.338430
\(663\) 2.47905 0.0962783
\(664\) −27.4879 −1.06674
\(665\) −2.09790 −0.0813530
\(666\) 3.95888 0.153404
\(667\) 23.3472 0.904009
\(668\) −21.8292 −0.844596
\(669\) 21.9279 0.847782
\(670\) −6.67899 −0.258032
\(671\) −2.40477 −0.0928353
\(672\) −13.7723 −0.531279
\(673\) −16.1827 −0.623799 −0.311899 0.950115i \(-0.600965\pi\)
−0.311899 + 0.950115i \(0.600965\pi\)
\(674\) 14.9820 0.577086
\(675\) 1.17141 0.0450878
\(676\) −1.75839 −0.0676304
\(677\) −7.72257 −0.296802 −0.148401 0.988927i \(-0.547413\pi\)
−0.148401 + 0.988927i \(0.547413\pi\)
\(678\) 1.65013 0.0633730
\(679\) −22.9257 −0.879808
\(680\) 8.96116 0.343645
\(681\) −15.2201 −0.583235
\(682\) 1.09094 0.0417742
\(683\) −47.3126 −1.81037 −0.905184 0.425020i \(-0.860267\pi\)
−0.905184 + 0.425020i \(0.860267\pi\)
\(684\) 0.681313 0.0260507
\(685\) −6.43939 −0.246036
\(686\) −8.62733 −0.329393
\(687\) 10.1190 0.386065
\(688\) 1.91774 0.0731130
\(689\) −4.35675 −0.165979
\(690\) 2.16555 0.0824409
\(691\) 13.3320 0.507172 0.253586 0.967313i \(-0.418390\pi\)
0.253586 + 0.967313i \(0.418390\pi\)
\(692\) 1.69174 0.0643103
\(693\) −1.32960 −0.0505074
\(694\) 7.83396 0.297373
\(695\) −19.7406 −0.748805
\(696\) 19.1560 0.726107
\(697\) −28.4603 −1.07801
\(698\) 8.14849 0.308425
\(699\) 9.06953 0.343041
\(700\) −5.69979 −0.215432
\(701\) −5.88540 −0.222289 −0.111144 0.993804i \(-0.535452\pi\)
−0.111144 + 0.993804i \(0.535452\pi\)
\(702\) 0.491539 0.0185520
\(703\) 3.12066 0.117698
\(704\) −1.33145 −0.0501808
\(705\) 13.6167 0.512835
\(706\) 6.07059 0.228470
\(707\) −27.9911 −1.05271
\(708\) −24.2879 −0.912795
\(709\) 22.1855 0.833195 0.416598 0.909091i \(-0.363222\pi\)
0.416598 + 0.909091i \(0.363222\pi\)
\(710\) −6.27918 −0.235654
\(711\) 1.22535 0.0459541
\(712\) −17.5996 −0.659573
\(713\) 10.4002 0.389492
\(714\) 3.37192 0.126191
\(715\) −0.940173 −0.0351605
\(716\) 29.5086 1.10279
\(717\) −25.2699 −0.943723
\(718\) −3.96929 −0.148133
\(719\) 13.4460 0.501451 0.250726 0.968058i \(-0.419331\pi\)
0.250726 + 0.968058i \(0.419331\pi\)
\(720\) −5.10440 −0.190230
\(721\) 2.76715 0.103054
\(722\) 9.26545 0.344824
\(723\) 18.6914 0.695140
\(724\) 29.8056 1.10772
\(725\) 12.1466 0.451115
\(726\) −5.29345 −0.196458
\(727\) −17.2018 −0.637980 −0.318990 0.947758i \(-0.603344\pi\)
−0.318990 + 0.947758i \(0.603344\pi\)
\(728\) −5.11203 −0.189464
\(729\) 1.00000 0.0370370
\(730\) −4.24170 −0.156992
\(731\) −1.82242 −0.0674046
\(732\) −8.80036 −0.325271
\(733\) 8.65637 0.319730 0.159865 0.987139i \(-0.448894\pi\)
0.159865 + 0.987139i \(0.448894\pi\)
\(734\) −9.29790 −0.343192
\(735\) 1.28582 0.0474281
\(736\) 11.2064 0.413072
\(737\) −3.33674 −0.122910
\(738\) −5.64303 −0.207723
\(739\) −32.7796 −1.20582 −0.602909 0.797810i \(-0.705992\pi\)
−0.602909 + 0.797810i \(0.705992\pi\)
\(740\) −27.7108 −1.01867
\(741\) 0.387464 0.0142339
\(742\) −5.92590 −0.217547
\(743\) 30.7713 1.12889 0.564444 0.825471i \(-0.309091\pi\)
0.564444 + 0.825471i \(0.309091\pi\)
\(744\) 8.53323 0.312843
\(745\) 30.1208 1.10354
\(746\) 5.32569 0.194988
\(747\) −14.8793 −0.544403
\(748\) 2.09454 0.0765840
\(749\) 18.8668 0.689377
\(750\) 5.93557 0.216736
\(751\) −1.52787 −0.0557529 −0.0278764 0.999611i \(-0.508874\pi\)
−0.0278764 + 0.999611i \(0.508874\pi\)
\(752\) 18.1543 0.662018
\(753\) −17.3227 −0.631273
\(754\) 5.09687 0.185617
\(755\) −32.3163 −1.17611
\(756\) −4.86573 −0.176965
\(757\) 8.97197 0.326092 0.163046 0.986618i \(-0.447868\pi\)
0.163046 + 0.986618i \(0.447868\pi\)
\(758\) 8.58741 0.311909
\(759\) 1.08188 0.0392697
\(760\) 1.40059 0.0508047
\(761\) 21.9966 0.797376 0.398688 0.917087i \(-0.369466\pi\)
0.398688 + 0.917087i \(0.369466\pi\)
\(762\) 8.22037 0.297793
\(763\) 14.8773 0.538594
\(764\) 12.3926 0.448348
\(765\) 4.85070 0.175377
\(766\) 7.08807 0.256103
\(767\) −13.8126 −0.498743
\(768\) 0.0203706 0.000735062 0
\(769\) 6.77796 0.244420 0.122210 0.992504i \(-0.461002\pi\)
0.122210 + 0.992504i \(0.461002\pi\)
\(770\) −1.27879 −0.0460844
\(771\) −2.03321 −0.0732243
\(772\) −11.3336 −0.407905
\(773\) 3.43558 0.123569 0.0617847 0.998090i \(-0.480321\pi\)
0.0617847 + 0.998090i \(0.480321\pi\)
\(774\) −0.361344 −0.0129882
\(775\) 5.41083 0.194363
\(776\) 15.3056 0.549438
\(777\) −22.2868 −0.799535
\(778\) 14.4083 0.516563
\(779\) −4.44822 −0.159374
\(780\) −3.44060 −0.123193
\(781\) −3.13700 −0.112251
\(782\) −2.74368 −0.0981138
\(783\) 10.3692 0.370565
\(784\) 1.71430 0.0612249
\(785\) −40.7192 −1.45333
\(786\) 4.96058 0.176938
\(787\) −28.2237 −1.00607 −0.503033 0.864267i \(-0.667782\pi\)
−0.503033 + 0.864267i \(0.667782\pi\)
\(788\) −45.2411 −1.61165
\(789\) −13.7493 −0.489489
\(790\) 1.17852 0.0419298
\(791\) −9.28955 −0.330298
\(792\) 0.887664 0.0315418
\(793\) −5.00479 −0.177725
\(794\) −5.31761 −0.188715
\(795\) −8.52476 −0.302342
\(796\) 33.8408 1.19946
\(797\) −25.0026 −0.885636 −0.442818 0.896611i \(-0.646021\pi\)
−0.442818 + 0.896611i \(0.646021\pi\)
\(798\) 0.527015 0.0186561
\(799\) −17.2519 −0.610330
\(800\) 5.83022 0.206129
\(801\) −9.52671 −0.336610
\(802\) −9.40407 −0.332069
\(803\) −2.11910 −0.0747813
\(804\) −12.2109 −0.430646
\(805\) −12.1911 −0.429680
\(806\) 2.27045 0.0799731
\(807\) −24.6331 −0.867127
\(808\) 18.6873 0.657418
\(809\) 35.9696 1.26462 0.632312 0.774714i \(-0.282106\pi\)
0.632312 + 0.774714i \(0.282106\pi\)
\(810\) 0.961784 0.0337936
\(811\) 5.62271 0.197440 0.0987201 0.995115i \(-0.468525\pi\)
0.0987201 + 0.995115i \(0.468525\pi\)
\(812\) −50.4538 −1.77058
\(813\) −15.7442 −0.552174
\(814\) 1.90222 0.0666729
\(815\) 34.4527 1.20682
\(816\) 6.46712 0.226395
\(817\) −0.284836 −0.00996514
\(818\) 14.3305 0.501053
\(819\) −2.76715 −0.0966922
\(820\) 39.4992 1.37937
\(821\) −4.03037 −0.140661 −0.0703304 0.997524i \(-0.522405\pi\)
−0.0703304 + 0.997524i \(0.522405\pi\)
\(822\) 1.61765 0.0564219
\(823\) 43.3982 1.51276 0.756382 0.654130i \(-0.226965\pi\)
0.756382 + 0.654130i \(0.226965\pi\)
\(824\) −1.84740 −0.0643571
\(825\) 0.562858 0.0195962
\(826\) −18.7874 −0.653697
\(827\) −44.5844 −1.55035 −0.775176 0.631746i \(-0.782339\pi\)
−0.775176 + 0.631746i \(0.782339\pi\)
\(828\) 3.95918 0.137591
\(829\) −4.66154 −0.161902 −0.0809510 0.996718i \(-0.525796\pi\)
−0.0809510 + 0.996718i \(0.525796\pi\)
\(830\) −14.3106 −0.496729
\(831\) 4.02082 0.139481
\(832\) −2.77099 −0.0960669
\(833\) −1.62909 −0.0564447
\(834\) 4.95907 0.171719
\(835\) −24.2908 −0.840617
\(836\) 0.327367 0.0113222
\(837\) 4.61906 0.159658
\(838\) −10.5693 −0.365111
\(839\) 41.3981 1.42922 0.714610 0.699523i \(-0.246604\pi\)
0.714610 + 0.699523i \(0.246604\pi\)
\(840\) −10.0026 −0.345122
\(841\) 78.5204 2.70760
\(842\) −10.8848 −0.375114
\(843\) −18.1106 −0.623762
\(844\) −28.5330 −0.982145
\(845\) −1.95668 −0.0673117
\(846\) −3.42067 −0.117605
\(847\) 29.7998 1.02393
\(848\) −11.3655 −0.390293
\(849\) 0.376343 0.0129161
\(850\) −1.42743 −0.0489603
\(851\) 18.1345 0.621641
\(852\) −11.4800 −0.393297
\(853\) 47.5696 1.62875 0.814376 0.580338i \(-0.197079\pi\)
0.814376 + 0.580338i \(0.197079\pi\)
\(854\) −6.80734 −0.232942
\(855\) 0.758143 0.0259279
\(856\) −12.5958 −0.430514
\(857\) 6.16085 0.210451 0.105225 0.994448i \(-0.466444\pi\)
0.105225 + 0.994448i \(0.466444\pi\)
\(858\) 0.236182 0.00806312
\(859\) −3.59898 −0.122796 −0.0613979 0.998113i \(-0.519556\pi\)
−0.0613979 + 0.998113i \(0.519556\pi\)
\(860\) 2.52928 0.0862478
\(861\) 31.7678 1.08265
\(862\) −14.2127 −0.484087
\(863\) −24.7634 −0.842955 −0.421477 0.906839i \(-0.638488\pi\)
−0.421477 + 0.906839i \(0.638488\pi\)
\(864\) 4.97708 0.169324
\(865\) 1.88251 0.0640073
\(866\) 7.33808 0.249358
\(867\) 10.8543 0.368632
\(868\) −22.4751 −0.762855
\(869\) 0.588772 0.0199727
\(870\) 9.97293 0.338114
\(871\) −6.94438 −0.235301
\(872\) −9.93232 −0.336351
\(873\) 8.28494 0.280403
\(874\) −0.428825 −0.0145052
\(875\) −33.4147 −1.12962
\(876\) −7.75492 −0.262014
\(877\) 40.8347 1.37889 0.689444 0.724339i \(-0.257855\pi\)
0.689444 + 0.724339i \(0.257855\pi\)
\(878\) 10.4865 0.353901
\(879\) −21.4651 −0.723999
\(880\) −2.45264 −0.0826785
\(881\) −29.0234 −0.977825 −0.488912 0.872333i \(-0.662606\pi\)
−0.488912 + 0.872333i \(0.662606\pi\)
\(882\) −0.323012 −0.0108764
\(883\) −29.5256 −0.993616 −0.496808 0.867860i \(-0.665495\pi\)
−0.496808 + 0.867860i \(0.665495\pi\)
\(884\) 4.35913 0.146614
\(885\) −27.0268 −0.908495
\(886\) −4.65577 −0.156414
\(887\) −39.9619 −1.34179 −0.670895 0.741553i \(-0.734090\pi\)
−0.670895 + 0.741553i \(0.734090\pi\)
\(888\) 14.8790 0.499308
\(889\) −46.2771 −1.55209
\(890\) −9.16264 −0.307132
\(891\) 0.480495 0.0160972
\(892\) 38.5578 1.29101
\(893\) −2.69640 −0.0902316
\(894\) −7.56669 −0.253068
\(895\) 32.8361 1.09759
\(896\) −31.3137 −1.04612
\(897\) 2.25159 0.0751785
\(898\) 6.12746 0.204476
\(899\) 47.8960 1.59742
\(900\) 2.05980 0.0686601
\(901\) 10.8006 0.359820
\(902\) −2.71145 −0.0902813
\(903\) 2.03421 0.0676943
\(904\) 6.20185 0.206270
\(905\) 33.1667 1.10250
\(906\) 8.11822 0.269710
\(907\) −34.6869 −1.15176 −0.575881 0.817534i \(-0.695341\pi\)
−0.575881 + 0.817534i \(0.695341\pi\)
\(908\) −26.7628 −0.888155
\(909\) 10.1155 0.335510
\(910\) −2.66140 −0.0882247
\(911\) 2.80043 0.0927825 0.0463912 0.998923i \(-0.485228\pi\)
0.0463912 + 0.998923i \(0.485228\pi\)
\(912\) 1.01078 0.0334703
\(913\) −7.14940 −0.236611
\(914\) −9.71064 −0.321199
\(915\) −9.79275 −0.323738
\(916\) 17.7932 0.587903
\(917\) −27.9259 −0.922195
\(918\) −1.21855 −0.0402181
\(919\) −27.9650 −0.922481 −0.461241 0.887275i \(-0.652595\pi\)
−0.461241 + 0.887275i \(0.652595\pi\)
\(920\) 8.13896 0.268334
\(921\) 26.7164 0.880336
\(922\) 1.54784 0.0509754
\(923\) −6.52869 −0.214894
\(924\) −2.33796 −0.0769132
\(925\) 9.43464 0.310209
\(926\) 1.60066 0.0526010
\(927\) −1.00000 −0.0328443
\(928\) 51.6083 1.69413
\(929\) 17.5222 0.574884 0.287442 0.957798i \(-0.407195\pi\)
0.287442 + 0.957798i \(0.407195\pi\)
\(930\) 4.44253 0.145676
\(931\) −0.254620 −0.00834483
\(932\) 15.9478 0.522386
\(933\) −10.4602 −0.342451
\(934\) 13.2660 0.434076
\(935\) 2.33074 0.0762232
\(936\) 1.84740 0.0603840
\(937\) 10.5990 0.346254 0.173127 0.984899i \(-0.444613\pi\)
0.173127 + 0.984899i \(0.444613\pi\)
\(938\) −9.44550 −0.308407
\(939\) 11.1601 0.364196
\(940\) 23.9435 0.780950
\(941\) −58.8341 −1.91794 −0.958968 0.283515i \(-0.908500\pi\)
−0.958968 + 0.283515i \(0.908500\pi\)
\(942\) 10.2291 0.333283
\(943\) −25.8490 −0.841761
\(944\) −36.0330 −1.17278
\(945\) −5.41443 −0.176131
\(946\) −0.173624 −0.00564500
\(947\) 41.2002 1.33883 0.669413 0.742891i \(-0.266546\pi\)
0.669413 + 0.742891i \(0.266546\pi\)
\(948\) 2.15464 0.0699793
\(949\) −4.41024 −0.143162
\(950\) −0.223100 −0.00723833
\(951\) −27.1428 −0.880167
\(952\) 12.6730 0.410733
\(953\) 2.86744 0.0928854 0.0464427 0.998921i \(-0.485212\pi\)
0.0464427 + 0.998921i \(0.485212\pi\)
\(954\) 2.14152 0.0693341
\(955\) 13.7901 0.446236
\(956\) −44.4344 −1.43711
\(957\) 4.98235 0.161056
\(958\) −19.2340 −0.621421
\(959\) −9.10665 −0.294069
\(960\) −5.42194 −0.174992
\(961\) −9.66430 −0.311752
\(962\) 3.95888 0.127640
\(963\) −6.81812 −0.219711
\(964\) 32.8667 1.05857
\(965\) −12.6117 −0.405983
\(966\) 3.06254 0.0985356
\(967\) −6.63065 −0.213227 −0.106614 0.994301i \(-0.534001\pi\)
−0.106614 + 0.994301i \(0.534001\pi\)
\(968\) −19.8948 −0.639444
\(969\) −0.960543 −0.0308571
\(970\) 7.96832 0.255847
\(971\) 24.9652 0.801171 0.400585 0.916259i \(-0.368807\pi\)
0.400585 + 0.916259i \(0.368807\pi\)
\(972\) 1.75839 0.0564004
\(973\) −27.9174 −0.894992
\(974\) −9.13029 −0.292554
\(975\) 1.17141 0.0375153
\(976\) −13.0560 −0.417914
\(977\) 54.4994 1.74359 0.871795 0.489871i \(-0.162956\pi\)
0.871795 + 0.489871i \(0.162956\pi\)
\(978\) −8.65490 −0.276753
\(979\) −4.57753 −0.146299
\(980\) 2.26097 0.0722240
\(981\) −5.37639 −0.171655
\(982\) 13.9841 0.446250
\(983\) −26.3143 −0.839296 −0.419648 0.907687i \(-0.637846\pi\)
−0.419648 + 0.907687i \(0.637846\pi\)
\(984\) −21.2087 −0.676109
\(985\) −50.3428 −1.60405
\(986\) −12.6354 −0.402393
\(987\) 19.2569 0.612954
\(988\) 0.681313 0.0216755
\(989\) −1.65521 −0.0526326
\(990\) 0.462132 0.0146875
\(991\) 49.7884 1.58158 0.790791 0.612086i \(-0.209670\pi\)
0.790791 + 0.612086i \(0.209670\pi\)
\(992\) 22.9894 0.729914
\(993\) 17.7149 0.562166
\(994\) −8.88009 −0.281659
\(995\) 37.6569 1.19380
\(996\) −26.1635 −0.829023
\(997\) −46.8119 −1.48255 −0.741275 0.671202i \(-0.765778\pi\)
−0.741275 + 0.671202i \(0.765778\pi\)
\(998\) −21.6838 −0.686388
\(999\) 8.05406 0.254819
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 \(a_p\))