Properties

Label 8015.2.a.l.1.41
Level 8015
Weight 2
Character 8015.1
Self dual Yes
Analytic conductor 64.000
Analytic rank 0
Dimension 62
CM No

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Newspace parameters

Level: \( N \) = \( 8015 = 5 \cdot 7 \cdot 229 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8015.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0000972201\)
Analytic rank: \(0\)
Dimension: \(62\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.41
Character \(\chi\) = 8015.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.20011 q^{2} +1.31150 q^{3} -0.559734 q^{4} -1.00000 q^{5} +1.57395 q^{6} -1.00000 q^{7} -3.07196 q^{8} -1.27997 q^{9} +O(q^{10})\) \(q+1.20011 q^{2} +1.31150 q^{3} -0.559734 q^{4} -1.00000 q^{5} +1.57395 q^{6} -1.00000 q^{7} -3.07196 q^{8} -1.27997 q^{9} -1.20011 q^{10} -6.01033 q^{11} -0.734091 q^{12} -1.57966 q^{13} -1.20011 q^{14} -1.31150 q^{15} -2.56723 q^{16} +7.68825 q^{17} -1.53610 q^{18} -8.21627 q^{19} +0.559734 q^{20} -1.31150 q^{21} -7.21306 q^{22} -7.09156 q^{23} -4.02888 q^{24} +1.00000 q^{25} -1.89577 q^{26} -5.61318 q^{27} +0.559734 q^{28} +8.87843 q^{29} -1.57395 q^{30} +0.724462 q^{31} +3.06297 q^{32} -7.88255 q^{33} +9.22675 q^{34} +1.00000 q^{35} +0.716441 q^{36} -5.74441 q^{37} -9.86044 q^{38} -2.07172 q^{39} +3.07196 q^{40} +5.70352 q^{41} -1.57395 q^{42} +5.83274 q^{43} +3.36419 q^{44} +1.27997 q^{45} -8.51066 q^{46} +11.1598 q^{47} -3.36692 q^{48} +1.00000 q^{49} +1.20011 q^{50} +10.0831 q^{51} +0.884190 q^{52} +3.05962 q^{53} -6.73644 q^{54} +6.01033 q^{55} +3.07196 q^{56} -10.7756 q^{57} +10.6551 q^{58} +2.42744 q^{59} +0.734091 q^{60} -5.37117 q^{61} +0.869435 q^{62} +1.27997 q^{63} +8.81036 q^{64} +1.57966 q^{65} -9.45993 q^{66} +4.83054 q^{67} -4.30338 q^{68} -9.30058 q^{69} +1.20011 q^{70} +14.6182 q^{71} +3.93201 q^{72} +5.27870 q^{73} -6.89393 q^{74} +1.31150 q^{75} +4.59893 q^{76} +6.01033 q^{77} -2.48630 q^{78} -16.6733 q^{79} +2.56723 q^{80} -3.52178 q^{81} +6.84486 q^{82} +0.146721 q^{83} +0.734091 q^{84} -7.68825 q^{85} +6.99993 q^{86} +11.6441 q^{87} +18.4635 q^{88} -10.5229 q^{89} +1.53610 q^{90} +1.57966 q^{91} +3.96939 q^{92} +0.950132 q^{93} +13.3930 q^{94} +8.21627 q^{95} +4.01708 q^{96} +5.46564 q^{97} +1.20011 q^{98} +7.69302 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} + O(q^{10}) \) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} - 2q^{10} - 13q^{11} + 37q^{12} + 31q^{13} - 2q^{14} - 11q^{15} + 64q^{16} + 30q^{17} + 18q^{18} + 20q^{19} - 64q^{20} - 11q^{21} + 7q^{22} + 29q^{24} + 62q^{25} + 59q^{27} - 64q^{28} - 29q^{29} - 3q^{30} + 20q^{31} + 22q^{32} + 72q^{33} + 13q^{34} + 62q^{35} + 53q^{36} + 35q^{37} + 34q^{38} - 6q^{39} - 15q^{40} + 13q^{41} - 3q^{42} - 4q^{43} - 44q^{44} - 69q^{45} - 19q^{46} + 58q^{47} + 64q^{48} + 62q^{49} + 2q^{50} - 30q^{51} + 82q^{52} + 18q^{53} + 22q^{54} + 13q^{55} - 15q^{56} + 21q^{57} + 18q^{58} - 11q^{59} - 37q^{60} + 24q^{61} + 48q^{62} - 69q^{63} + 65q^{64} - 31q^{65} + 25q^{66} - 6q^{67} + 65q^{68} + 27q^{69} + 2q^{70} - 35q^{71} + 53q^{72} + 116q^{73} - 69q^{74} + 11q^{75} + 65q^{76} + 13q^{77} + 102q^{78} - 83q^{79} - 64q^{80} + 126q^{81} + 71q^{82} + 84q^{83} - 37q^{84} - 30q^{85} + 24q^{86} + 49q^{87} + 20q^{88} - 16q^{89} - 18q^{90} - 31q^{91} + 19q^{92} + 65q^{93} + 54q^{94} - 20q^{95} + 17q^{96} + 155q^{97} + 2q^{98} + 6q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.20011 0.848606 0.424303 0.905520i \(-0.360519\pi\)
0.424303 + 0.905520i \(0.360519\pi\)
\(3\) 1.31150 0.757195 0.378597 0.925561i \(-0.376406\pi\)
0.378597 + 0.925561i \(0.376406\pi\)
\(4\) −0.559734 −0.279867
\(5\) −1.00000 −0.447214
\(6\) 1.57395 0.642561
\(7\) −1.00000 −0.377964
\(8\) −3.07196 −1.08610
\(9\) −1.27997 −0.426656
\(10\) −1.20011 −0.379508
\(11\) −6.01033 −1.81218 −0.906091 0.423083i \(-0.860948\pi\)
−0.906091 + 0.423083i \(0.860948\pi\)
\(12\) −0.734091 −0.211914
\(13\) −1.57966 −0.438119 −0.219059 0.975712i \(-0.570299\pi\)
−0.219059 + 0.975712i \(0.570299\pi\)
\(14\) −1.20011 −0.320743
\(15\) −1.31150 −0.338628
\(16\) −2.56723 −0.641807
\(17\) 7.68825 1.86467 0.932337 0.361590i \(-0.117766\pi\)
0.932337 + 0.361590i \(0.117766\pi\)
\(18\) −1.53610 −0.362063
\(19\) −8.21627 −1.88494 −0.942471 0.334287i \(-0.891504\pi\)
−0.942471 + 0.334287i \(0.891504\pi\)
\(20\) 0.559734 0.125160
\(21\) −1.31150 −0.286193
\(22\) −7.21306 −1.53783
\(23\) −7.09156 −1.47869 −0.739346 0.673325i \(-0.764865\pi\)
−0.739346 + 0.673325i \(0.764865\pi\)
\(24\) −4.02888 −0.822392
\(25\) 1.00000 0.200000
\(26\) −1.89577 −0.371790
\(27\) −5.61318 −1.08026
\(28\) 0.559734 0.105780
\(29\) 8.87843 1.64868 0.824341 0.566093i \(-0.191546\pi\)
0.824341 + 0.566093i \(0.191546\pi\)
\(30\) −1.57395 −0.287362
\(31\) 0.724462 0.130117 0.0650586 0.997881i \(-0.479277\pi\)
0.0650586 + 0.997881i \(0.479277\pi\)
\(32\) 3.06297 0.541462
\(33\) −7.88255 −1.37217
\(34\) 9.22675 1.58237
\(35\) 1.00000 0.169031
\(36\) 0.716441 0.119407
\(37\) −5.74441 −0.944376 −0.472188 0.881498i \(-0.656536\pi\)
−0.472188 + 0.881498i \(0.656536\pi\)
\(38\) −9.86044 −1.59957
\(39\) −2.07172 −0.331741
\(40\) 3.07196 0.485720
\(41\) 5.70352 0.890741 0.445370 0.895346i \(-0.353072\pi\)
0.445370 + 0.895346i \(0.353072\pi\)
\(42\) −1.57395 −0.242865
\(43\) 5.83274 0.889484 0.444742 0.895659i \(-0.353295\pi\)
0.444742 + 0.895659i \(0.353295\pi\)
\(44\) 3.36419 0.507170
\(45\) 1.27997 0.190806
\(46\) −8.51066 −1.25483
\(47\) 11.1598 1.62782 0.813911 0.580990i \(-0.197335\pi\)
0.813911 + 0.580990i \(0.197335\pi\)
\(48\) −3.36692 −0.485973
\(49\) 1.00000 0.142857
\(50\) 1.20011 0.169721
\(51\) 10.0831 1.41192
\(52\) 0.884190 0.122615
\(53\) 3.05962 0.420271 0.210136 0.977672i \(-0.432609\pi\)
0.210136 + 0.977672i \(0.432609\pi\)
\(54\) −6.73644 −0.916713
\(55\) 6.01033 0.810432
\(56\) 3.07196 0.410509
\(57\) −10.7756 −1.42727
\(58\) 10.6551 1.39908
\(59\) 2.42744 0.316026 0.158013 0.987437i \(-0.449491\pi\)
0.158013 + 0.987437i \(0.449491\pi\)
\(60\) 0.734091 0.0947708
\(61\) −5.37117 −0.687708 −0.343854 0.939023i \(-0.611732\pi\)
−0.343854 + 0.939023i \(0.611732\pi\)
\(62\) 0.869435 0.110418
\(63\) 1.27997 0.161261
\(64\) 8.81036 1.10130
\(65\) 1.57966 0.195933
\(66\) −9.45993 −1.16444
\(67\) 4.83054 0.590144 0.295072 0.955475i \(-0.404656\pi\)
0.295072 + 0.955475i \(0.404656\pi\)
\(68\) −4.30338 −0.521861
\(69\) −9.30058 −1.11966
\(70\) 1.20011 0.143441
\(71\) 14.6182 1.73486 0.867432 0.497556i \(-0.165769\pi\)
0.867432 + 0.497556i \(0.165769\pi\)
\(72\) 3.93201 0.463392
\(73\) 5.27870 0.617826 0.308913 0.951090i \(-0.400035\pi\)
0.308913 + 0.951090i \(0.400035\pi\)
\(74\) −6.89393 −0.801403
\(75\) 1.31150 0.151439
\(76\) 4.59893 0.527533
\(77\) 6.01033 0.684940
\(78\) −2.48630 −0.281518
\(79\) −16.6733 −1.87589 −0.937944 0.346788i \(-0.887272\pi\)
−0.937944 + 0.346788i \(0.887272\pi\)
\(80\) 2.56723 0.287025
\(81\) −3.52178 −0.391309
\(82\) 6.84486 0.755888
\(83\) 0.146721 0.0161047 0.00805235 0.999968i \(-0.497437\pi\)
0.00805235 + 0.999968i \(0.497437\pi\)
\(84\) 0.734091 0.0800959
\(85\) −7.68825 −0.833908
\(86\) 6.99993 0.754822
\(87\) 11.6441 1.24837
\(88\) 18.4635 1.96822
\(89\) −10.5229 −1.11543 −0.557715 0.830033i \(-0.688322\pi\)
−0.557715 + 0.830033i \(0.688322\pi\)
\(90\) 1.53610 0.161919
\(91\) 1.57966 0.165593
\(92\) 3.96939 0.413837
\(93\) 0.950132 0.0985241
\(94\) 13.3930 1.38138
\(95\) 8.21627 0.842972
\(96\) 4.01708 0.409992
\(97\) 5.46564 0.554951 0.277476 0.960733i \(-0.410502\pi\)
0.277476 + 0.960733i \(0.410502\pi\)
\(98\) 1.20011 0.121229
\(99\) 7.69302 0.773178
\(100\) −0.559734 −0.0559734
\(101\) 3.54321 0.352563 0.176281 0.984340i \(-0.443593\pi\)
0.176281 + 0.984340i \(0.443593\pi\)
\(102\) 12.1009 1.19817
\(103\) −2.68011 −0.264079 −0.132040 0.991244i \(-0.542153\pi\)
−0.132040 + 0.991244i \(0.542153\pi\)
\(104\) 4.85266 0.475842
\(105\) 1.31150 0.127989
\(106\) 3.67188 0.356645
\(107\) 0.323319 0.0312564 0.0156282 0.999878i \(-0.495025\pi\)
0.0156282 + 0.999878i \(0.495025\pi\)
\(108\) 3.14189 0.302328
\(109\) −3.88346 −0.371968 −0.185984 0.982553i \(-0.559547\pi\)
−0.185984 + 0.982553i \(0.559547\pi\)
\(110\) 7.21306 0.687738
\(111\) −7.53380 −0.715076
\(112\) 2.56723 0.242580
\(113\) 14.5009 1.36413 0.682067 0.731290i \(-0.261081\pi\)
0.682067 + 0.731290i \(0.261081\pi\)
\(114\) −12.9320 −1.21119
\(115\) 7.09156 0.661291
\(116\) −4.96956 −0.461412
\(117\) 2.02191 0.186926
\(118\) 2.91320 0.268182
\(119\) −7.68825 −0.704781
\(120\) 4.02888 0.367785
\(121\) 25.1240 2.28400
\(122\) −6.44600 −0.583593
\(123\) 7.48017 0.674464
\(124\) −0.405506 −0.0364155
\(125\) −1.00000 −0.0894427
\(126\) 1.53610 0.136847
\(127\) −4.88296 −0.433293 −0.216647 0.976250i \(-0.569512\pi\)
−0.216647 + 0.976250i \(0.569512\pi\)
\(128\) 4.44747 0.393105
\(129\) 7.64964 0.673513
\(130\) 1.89577 0.166270
\(131\) −5.57113 −0.486752 −0.243376 0.969932i \(-0.578255\pi\)
−0.243376 + 0.969932i \(0.578255\pi\)
\(132\) 4.41213 0.384027
\(133\) 8.21627 0.712441
\(134\) 5.79718 0.500800
\(135\) 5.61318 0.483105
\(136\) −23.6180 −2.02523
\(137\) −0.631405 −0.0539446 −0.0269723 0.999636i \(-0.508587\pi\)
−0.0269723 + 0.999636i \(0.508587\pi\)
\(138\) −11.1617 −0.950149
\(139\) −0.170401 −0.0144532 −0.00722661 0.999974i \(-0.502300\pi\)
−0.00722661 + 0.999974i \(0.502300\pi\)
\(140\) −0.559734 −0.0473062
\(141\) 14.6361 1.23258
\(142\) 17.5435 1.47222
\(143\) 9.49427 0.793951
\(144\) 3.28597 0.273831
\(145\) −8.87843 −0.737313
\(146\) 6.33503 0.524291
\(147\) 1.31150 0.108171
\(148\) 3.21534 0.264300
\(149\) 1.38289 0.113291 0.0566453 0.998394i \(-0.481960\pi\)
0.0566453 + 0.998394i \(0.481960\pi\)
\(150\) 1.57395 0.128512
\(151\) −6.64230 −0.540543 −0.270271 0.962784i \(-0.587113\pi\)
−0.270271 + 0.962784i \(0.587113\pi\)
\(152\) 25.2401 2.04724
\(153\) −9.84071 −0.795574
\(154\) 7.21306 0.581245
\(155\) −0.724462 −0.0581902
\(156\) 1.15961 0.0928435
\(157\) −5.92159 −0.472594 −0.236297 0.971681i \(-0.575934\pi\)
−0.236297 + 0.971681i \(0.575934\pi\)
\(158\) −20.0097 −1.59189
\(159\) 4.01269 0.318227
\(160\) −3.06297 −0.242149
\(161\) 7.09156 0.558893
\(162\) −4.22653 −0.332067
\(163\) −22.4781 −1.76062 −0.880309 0.474401i \(-0.842665\pi\)
−0.880309 + 0.474401i \(0.842665\pi\)
\(164\) −3.19246 −0.249289
\(165\) 7.88255 0.613655
\(166\) 0.176081 0.0136666
\(167\) −6.31892 −0.488973 −0.244486 0.969653i \(-0.578619\pi\)
−0.244486 + 0.969653i \(0.578619\pi\)
\(168\) 4.02888 0.310835
\(169\) −10.5047 −0.808052
\(170\) −9.22675 −0.707660
\(171\) 10.5166 0.804222
\(172\) −3.26478 −0.248937
\(173\) −23.5114 −1.78754 −0.893769 0.448527i \(-0.851949\pi\)
−0.893769 + 0.448527i \(0.851949\pi\)
\(174\) 13.9742 1.05938
\(175\) −1.00000 −0.0755929
\(176\) 15.4299 1.16307
\(177\) 3.18359 0.239293
\(178\) −12.6287 −0.946561
\(179\) 8.28592 0.619319 0.309659 0.950848i \(-0.399785\pi\)
0.309659 + 0.950848i \(0.399785\pi\)
\(180\) −0.716441 −0.0534004
\(181\) −4.61235 −0.342833 −0.171416 0.985199i \(-0.554834\pi\)
−0.171416 + 0.985199i \(0.554834\pi\)
\(182\) 1.89577 0.140524
\(183\) −7.04429 −0.520729
\(184\) 21.7850 1.60601
\(185\) 5.74441 0.422338
\(186\) 1.14026 0.0836082
\(187\) −46.2089 −3.37913
\(188\) −6.24651 −0.455574
\(189\) 5.61318 0.408299
\(190\) 9.86044 0.715351
\(191\) 23.9389 1.73216 0.866078 0.499910i \(-0.166633\pi\)
0.866078 + 0.499910i \(0.166633\pi\)
\(192\) 11.5548 0.833895
\(193\) −4.64407 −0.334288 −0.167144 0.985933i \(-0.553454\pi\)
−0.167144 + 0.985933i \(0.553454\pi\)
\(194\) 6.55937 0.470935
\(195\) 2.07172 0.148359
\(196\) −0.559734 −0.0399810
\(197\) 19.2151 1.36902 0.684508 0.729005i \(-0.260017\pi\)
0.684508 + 0.729005i \(0.260017\pi\)
\(198\) 9.23248 0.656124
\(199\) 13.7167 0.972349 0.486175 0.873862i \(-0.338392\pi\)
0.486175 + 0.873862i \(0.338392\pi\)
\(200\) −3.07196 −0.217221
\(201\) 6.33525 0.446854
\(202\) 4.25224 0.299187
\(203\) −8.87843 −0.623144
\(204\) −5.64388 −0.395151
\(205\) −5.70352 −0.398351
\(206\) −3.21643 −0.224099
\(207\) 9.07697 0.630893
\(208\) 4.05535 0.281188
\(209\) 49.3825 3.41586
\(210\) 1.57395 0.108613
\(211\) −11.1184 −0.765422 −0.382711 0.923868i \(-0.625009\pi\)
−0.382711 + 0.923868i \(0.625009\pi\)
\(212\) −1.71257 −0.117620
\(213\) 19.1718 1.31363
\(214\) 0.388019 0.0265244
\(215\) −5.83274 −0.397789
\(216\) 17.2435 1.17327
\(217\) −0.724462 −0.0491797
\(218\) −4.66059 −0.315655
\(219\) 6.92302 0.467814
\(220\) −3.36419 −0.226813
\(221\) −12.1448 −0.816949
\(222\) −9.04139 −0.606818
\(223\) 3.97111 0.265925 0.132963 0.991121i \(-0.457551\pi\)
0.132963 + 0.991121i \(0.457551\pi\)
\(224\) −3.06297 −0.204653
\(225\) −1.27997 −0.0853312
\(226\) 17.4027 1.15761
\(227\) −16.0838 −1.06752 −0.533759 0.845637i \(-0.679221\pi\)
−0.533759 + 0.845637i \(0.679221\pi\)
\(228\) 6.03150 0.399446
\(229\) 1.00000 0.0660819
\(230\) 8.51066 0.561176
\(231\) 7.88255 0.518633
\(232\) −27.2742 −1.79064
\(233\) −24.8740 −1.62955 −0.814775 0.579778i \(-0.803139\pi\)
−0.814775 + 0.579778i \(0.803139\pi\)
\(234\) 2.42652 0.158627
\(235\) −11.1598 −0.727984
\(236\) −1.35872 −0.0884453
\(237\) −21.8670 −1.42041
\(238\) −9.22675 −0.598081
\(239\) 26.6971 1.72689 0.863446 0.504441i \(-0.168302\pi\)
0.863446 + 0.504441i \(0.168302\pi\)
\(240\) 3.36692 0.217334
\(241\) −16.9909 −1.09448 −0.547239 0.836977i \(-0.684321\pi\)
−0.547239 + 0.836977i \(0.684321\pi\)
\(242\) 30.1516 1.93822
\(243\) 12.2207 0.783959
\(244\) 3.00643 0.192467
\(245\) −1.00000 −0.0638877
\(246\) 8.97704 0.572355
\(247\) 12.9789 0.825829
\(248\) −2.22552 −0.141321
\(249\) 0.192424 0.0121944
\(250\) −1.20011 −0.0759017
\(251\) −27.9439 −1.76380 −0.881901 0.471435i \(-0.843736\pi\)
−0.881901 + 0.471435i \(0.843736\pi\)
\(252\) −0.716441 −0.0451316
\(253\) 42.6226 2.67966
\(254\) −5.86010 −0.367695
\(255\) −10.0831 −0.631431
\(256\) −12.2833 −0.767704
\(257\) 21.0485 1.31297 0.656484 0.754340i \(-0.272043\pi\)
0.656484 + 0.754340i \(0.272043\pi\)
\(258\) 9.18041 0.571547
\(259\) 5.74441 0.356940
\(260\) −0.884190 −0.0548351
\(261\) −11.3641 −0.703420
\(262\) −6.68597 −0.413060
\(263\) 7.63221 0.470622 0.235311 0.971920i \(-0.424389\pi\)
0.235311 + 0.971920i \(0.424389\pi\)
\(264\) 24.2149 1.49032
\(265\) −3.05962 −0.187951
\(266\) 9.86044 0.604582
\(267\) −13.8008 −0.844598
\(268\) −2.70382 −0.165162
\(269\) −2.76921 −0.168842 −0.0844208 0.996430i \(-0.526904\pi\)
−0.0844208 + 0.996430i \(0.526904\pi\)
\(270\) 6.73644 0.409966
\(271\) 5.90054 0.358432 0.179216 0.983810i \(-0.442644\pi\)
0.179216 + 0.983810i \(0.442644\pi\)
\(272\) −19.7375 −1.19676
\(273\) 2.07172 0.125386
\(274\) −0.757756 −0.0457777
\(275\) −6.01033 −0.362436
\(276\) 5.20585 0.313356
\(277\) −7.23379 −0.434636 −0.217318 0.976101i \(-0.569731\pi\)
−0.217318 + 0.976101i \(0.569731\pi\)
\(278\) −0.204500 −0.0122651
\(279\) −0.927288 −0.0555153
\(280\) −3.07196 −0.183585
\(281\) 30.6794 1.83018 0.915089 0.403253i \(-0.132121\pi\)
0.915089 + 0.403253i \(0.132121\pi\)
\(282\) 17.5649 1.04597
\(283\) −9.24595 −0.549614 −0.274807 0.961499i \(-0.588614\pi\)
−0.274807 + 0.961499i \(0.588614\pi\)
\(284\) −8.18232 −0.485531
\(285\) 10.7756 0.638294
\(286\) 11.3942 0.673752
\(287\) −5.70352 −0.336668
\(288\) −3.92050 −0.231018
\(289\) 42.1092 2.47701
\(290\) −10.6551 −0.625689
\(291\) 7.16818 0.420206
\(292\) −2.95467 −0.172909
\(293\) 0.712517 0.0416257 0.0208128 0.999783i \(-0.493375\pi\)
0.0208128 + 0.999783i \(0.493375\pi\)
\(294\) 1.57395 0.0917944
\(295\) −2.42744 −0.141331
\(296\) 17.6466 1.02569
\(297\) 33.7370 1.95762
\(298\) 1.65962 0.0961391
\(299\) 11.2023 0.647843
\(300\) −0.734091 −0.0423828
\(301\) −5.83274 −0.336193
\(302\) −7.97149 −0.458708
\(303\) 4.64692 0.266959
\(304\) 21.0931 1.20977
\(305\) 5.37117 0.307552
\(306\) −11.8099 −0.675129
\(307\) 33.6200 1.91879 0.959396 0.282062i \(-0.0910185\pi\)
0.959396 + 0.282062i \(0.0910185\pi\)
\(308\) −3.36419 −0.191692
\(309\) −3.51496 −0.199959
\(310\) −0.869435 −0.0493806
\(311\) −25.3852 −1.43946 −0.719732 0.694252i \(-0.755735\pi\)
−0.719732 + 0.694252i \(0.755735\pi\)
\(312\) 6.36426 0.360305
\(313\) 0.0100920 0.000570436 0 0.000285218 1.00000i \(-0.499909\pi\)
0.000285218 1.00000i \(0.499909\pi\)
\(314\) −7.10656 −0.401047
\(315\) −1.27997 −0.0721180
\(316\) 9.33259 0.524999
\(317\) 23.0455 1.29437 0.647183 0.762335i \(-0.275947\pi\)
0.647183 + 0.762335i \(0.275947\pi\)
\(318\) 4.81568 0.270050
\(319\) −53.3623 −2.98771
\(320\) −8.81036 −0.492514
\(321\) 0.424033 0.0236672
\(322\) 8.51066 0.474280
\(323\) −63.1688 −3.51480
\(324\) 1.97126 0.109515
\(325\) −1.57966 −0.0876238
\(326\) −26.9762 −1.49407
\(327\) −5.09316 −0.281653
\(328\) −17.5210 −0.967437
\(329\) −11.1598 −0.615259
\(330\) 9.45993 0.520752
\(331\) 34.9124 1.91896 0.959481 0.281774i \(-0.0909229\pi\)
0.959481 + 0.281774i \(0.0909229\pi\)
\(332\) −0.0821247 −0.00450718
\(333\) 7.35266 0.402923
\(334\) −7.58341 −0.414945
\(335\) −4.83054 −0.263920
\(336\) 3.36692 0.183681
\(337\) −13.7632 −0.749729 −0.374865 0.927080i \(-0.622311\pi\)
−0.374865 + 0.927080i \(0.622311\pi\)
\(338\) −12.6068 −0.685718
\(339\) 19.0180 1.03291
\(340\) 4.30338 0.233383
\(341\) −4.35426 −0.235796
\(342\) 12.6210 0.682468
\(343\) −1.00000 −0.0539949
\(344\) −17.9180 −0.966072
\(345\) 9.30058 0.500727
\(346\) −28.2163 −1.51692
\(347\) −11.7815 −0.632463 −0.316232 0.948682i \(-0.602418\pi\)
−0.316232 + 0.948682i \(0.602418\pi\)
\(348\) −6.51758 −0.349379
\(349\) −7.57492 −0.405476 −0.202738 0.979233i \(-0.564984\pi\)
−0.202738 + 0.979233i \(0.564984\pi\)
\(350\) −1.20011 −0.0641486
\(351\) 8.86691 0.473281
\(352\) −18.4094 −0.981227
\(353\) 23.8905 1.27156 0.635782 0.771869i \(-0.280678\pi\)
0.635782 + 0.771869i \(0.280678\pi\)
\(354\) 3.82066 0.203066
\(355\) −14.6182 −0.775855
\(356\) 5.89005 0.312172
\(357\) −10.0831 −0.533656
\(358\) 9.94402 0.525558
\(359\) 12.3626 0.652474 0.326237 0.945288i \(-0.394219\pi\)
0.326237 + 0.945288i \(0.394219\pi\)
\(360\) −3.93201 −0.207235
\(361\) 48.5072 2.55301
\(362\) −5.53533 −0.290930
\(363\) 32.9502 1.72944
\(364\) −0.884190 −0.0463441
\(365\) −5.27870 −0.276300
\(366\) −8.45393 −0.441894
\(367\) 0.319530 0.0166793 0.00833967 0.999965i \(-0.497345\pi\)
0.00833967 + 0.999965i \(0.497345\pi\)
\(368\) 18.2057 0.949036
\(369\) −7.30032 −0.380040
\(370\) 6.89393 0.358398
\(371\) −3.05962 −0.158848
\(372\) −0.531822 −0.0275737
\(373\) 20.8406 1.07909 0.539543 0.841958i \(-0.318597\pi\)
0.539543 + 0.841958i \(0.318597\pi\)
\(374\) −55.4558 −2.86755
\(375\) −1.31150 −0.0677256
\(376\) −34.2824 −1.76798
\(377\) −14.0249 −0.722319
\(378\) 6.73644 0.346485
\(379\) 31.7082 1.62874 0.814369 0.580347i \(-0.197083\pi\)
0.814369 + 0.580347i \(0.197083\pi\)
\(380\) −4.59893 −0.235920
\(381\) −6.40401 −0.328087
\(382\) 28.7293 1.46992
\(383\) −20.0015 −1.02203 −0.511015 0.859572i \(-0.670730\pi\)
−0.511015 + 0.859572i \(0.670730\pi\)
\(384\) 5.83286 0.297657
\(385\) −6.01033 −0.306315
\(386\) −5.57340 −0.283679
\(387\) −7.46571 −0.379504
\(388\) −3.05930 −0.155313
\(389\) 18.2900 0.927340 0.463670 0.886008i \(-0.346532\pi\)
0.463670 + 0.886008i \(0.346532\pi\)
\(390\) 2.48630 0.125899
\(391\) −54.5217 −2.75728
\(392\) −3.07196 −0.155158
\(393\) −7.30653 −0.368566
\(394\) 23.0602 1.16176
\(395\) 16.6733 0.838922
\(396\) −4.30605 −0.216387
\(397\) 19.5640 0.981888 0.490944 0.871191i \(-0.336652\pi\)
0.490944 + 0.871191i \(0.336652\pi\)
\(398\) 16.4615 0.825142
\(399\) 10.7756 0.539457
\(400\) −2.56723 −0.128361
\(401\) −18.5176 −0.924727 −0.462364 0.886690i \(-0.652999\pi\)
−0.462364 + 0.886690i \(0.652999\pi\)
\(402\) 7.60300 0.379203
\(403\) −1.14440 −0.0570068
\(404\) −1.98326 −0.0986707
\(405\) 3.52178 0.174999
\(406\) −10.6551 −0.528804
\(407\) 34.5258 1.71138
\(408\) −30.9751 −1.53349
\(409\) 31.4871 1.55694 0.778469 0.627684i \(-0.215997\pi\)
0.778469 + 0.627684i \(0.215997\pi\)
\(410\) −6.84486 −0.338044
\(411\) −0.828088 −0.0408466
\(412\) 1.50015 0.0739070
\(413\) −2.42744 −0.119447
\(414\) 10.8934 0.535380
\(415\) −0.146721 −0.00720224
\(416\) −4.83845 −0.237225
\(417\) −0.223481 −0.0109439
\(418\) 59.2645 2.89872
\(419\) 18.7630 0.916634 0.458317 0.888789i \(-0.348453\pi\)
0.458317 + 0.888789i \(0.348453\pi\)
\(420\) −0.734091 −0.0358200
\(421\) 25.9601 1.26522 0.632610 0.774471i \(-0.281984\pi\)
0.632610 + 0.774471i \(0.281984\pi\)
\(422\) −13.3433 −0.649542
\(423\) −14.2842 −0.694519
\(424\) −9.39905 −0.456458
\(425\) 7.68825 0.372935
\(426\) 23.0083 1.11475
\(427\) 5.37117 0.259929
\(428\) −0.180973 −0.00874765
\(429\) 12.4517 0.601176
\(430\) −6.99993 −0.337567
\(431\) −21.4336 −1.03242 −0.516210 0.856462i \(-0.672658\pi\)
−0.516210 + 0.856462i \(0.672658\pi\)
\(432\) 14.4103 0.693317
\(433\) −25.3379 −1.21766 −0.608832 0.793299i \(-0.708362\pi\)
−0.608832 + 0.793299i \(0.708362\pi\)
\(434\) −0.869435 −0.0417342
\(435\) −11.6441 −0.558290
\(436\) 2.17371 0.104102
\(437\) 58.2662 2.78725
\(438\) 8.30839 0.396990
\(439\) −0.475831 −0.0227102 −0.0113551 0.999936i \(-0.503615\pi\)
−0.0113551 + 0.999936i \(0.503615\pi\)
\(440\) −18.4635 −0.880213
\(441\) −1.27997 −0.0609508
\(442\) −14.5751 −0.693268
\(443\) −1.44494 −0.0686510 −0.0343255 0.999411i \(-0.510928\pi\)
−0.0343255 + 0.999411i \(0.510928\pi\)
\(444\) 4.21692 0.200126
\(445\) 10.5229 0.498835
\(446\) 4.76577 0.225666
\(447\) 1.81366 0.0857830
\(448\) −8.81036 −0.416250
\(449\) 3.15932 0.149097 0.0745487 0.997217i \(-0.476248\pi\)
0.0745487 + 0.997217i \(0.476248\pi\)
\(450\) −1.53610 −0.0724126
\(451\) −34.2800 −1.61418
\(452\) −8.11667 −0.381776
\(453\) −8.71137 −0.409296
\(454\) −19.3023 −0.905903
\(455\) −1.57966 −0.0740556
\(456\) 33.1024 1.55016
\(457\) −1.19667 −0.0559781 −0.0279890 0.999608i \(-0.508910\pi\)
−0.0279890 + 0.999608i \(0.508910\pi\)
\(458\) 1.20011 0.0560775
\(459\) −43.1555 −2.01433
\(460\) −3.96939 −0.185074
\(461\) 42.2308 1.96689 0.983443 0.181217i \(-0.0580035\pi\)
0.983443 + 0.181217i \(0.0580035\pi\)
\(462\) 9.45993 0.440116
\(463\) −32.6690 −1.51826 −0.759128 0.650941i \(-0.774374\pi\)
−0.759128 + 0.650941i \(0.774374\pi\)
\(464\) −22.7930 −1.05814
\(465\) −0.950132 −0.0440613
\(466\) −29.8515 −1.38285
\(467\) −25.7555 −1.19182 −0.595911 0.803050i \(-0.703209\pi\)
−0.595911 + 0.803050i \(0.703209\pi\)
\(468\) −1.13173 −0.0523144
\(469\) −4.83054 −0.223053
\(470\) −13.3930 −0.617772
\(471\) −7.76616 −0.357846
\(472\) −7.45701 −0.343237
\(473\) −35.0567 −1.61191
\(474\) −26.2428 −1.20537
\(475\) −8.21627 −0.376989
\(476\) 4.30338 0.197245
\(477\) −3.91621 −0.179311
\(478\) 32.0395 1.46545
\(479\) 16.8432 0.769584 0.384792 0.923003i \(-0.374273\pi\)
0.384792 + 0.923003i \(0.374273\pi\)
\(480\) −4.01708 −0.183354
\(481\) 9.07422 0.413749
\(482\) −20.3909 −0.928780
\(483\) 9.30058 0.423191
\(484\) −14.0628 −0.639217
\(485\) −5.46564 −0.248182
\(486\) 14.6662 0.665273
\(487\) −15.1666 −0.687266 −0.343633 0.939104i \(-0.611658\pi\)
−0.343633 + 0.939104i \(0.611658\pi\)
\(488\) 16.5000 0.746922
\(489\) −29.4800 −1.33313
\(490\) −1.20011 −0.0542155
\(491\) 7.61806 0.343798 0.171899 0.985115i \(-0.445010\pi\)
0.171899 + 0.985115i \(0.445010\pi\)
\(492\) −4.18691 −0.188760
\(493\) 68.2596 3.07426
\(494\) 15.5761 0.700804
\(495\) −7.69302 −0.345776
\(496\) −1.85986 −0.0835102
\(497\) −14.6182 −0.655717
\(498\) 0.230931 0.0103483
\(499\) 4.81338 0.215477 0.107738 0.994179i \(-0.465639\pi\)
0.107738 + 0.994179i \(0.465639\pi\)
\(500\) 0.559734 0.0250321
\(501\) −8.28727 −0.370248
\(502\) −33.5357 −1.49677
\(503\) −12.8581 −0.573313 −0.286656 0.958033i \(-0.592544\pi\)
−0.286656 + 0.958033i \(0.592544\pi\)
\(504\) −3.93201 −0.175146
\(505\) −3.54321 −0.157671
\(506\) 51.1518 2.27398
\(507\) −13.7769 −0.611853
\(508\) 2.73316 0.121264
\(509\) −16.4270 −0.728113 −0.364056 0.931377i \(-0.618608\pi\)
−0.364056 + 0.931377i \(0.618608\pi\)
\(510\) −12.1009 −0.535836
\(511\) −5.27870 −0.233516
\(512\) −23.6362 −1.04458
\(513\) 46.1194 2.03622
\(514\) 25.2605 1.11419
\(515\) 2.68011 0.118100
\(516\) −4.28176 −0.188494
\(517\) −67.0739 −2.94991
\(518\) 6.89393 0.302902
\(519\) −30.8352 −1.35351
\(520\) −4.85266 −0.212803
\(521\) 2.90091 0.127091 0.0635456 0.997979i \(-0.479759\pi\)
0.0635456 + 0.997979i \(0.479759\pi\)
\(522\) −13.6382 −0.596927
\(523\) 5.86604 0.256504 0.128252 0.991742i \(-0.459063\pi\)
0.128252 + 0.991742i \(0.459063\pi\)
\(524\) 3.11835 0.136226
\(525\) −1.31150 −0.0572386
\(526\) 9.15950 0.399373
\(527\) 5.56985 0.242626
\(528\) 20.2363 0.880672
\(529\) 27.2902 1.18653
\(530\) −3.67188 −0.159496
\(531\) −3.10705 −0.134834
\(532\) −4.59893 −0.199389
\(533\) −9.00963 −0.390250
\(534\) −16.5625 −0.716731
\(535\) −0.323319 −0.0139783
\(536\) −14.8392 −0.640957
\(537\) 10.8670 0.468945
\(538\) −3.32336 −0.143280
\(539\) −6.01033 −0.258883
\(540\) −3.14189 −0.135205
\(541\) −20.6586 −0.888181 −0.444090 0.895982i \(-0.646473\pi\)
−0.444090 + 0.895982i \(0.646473\pi\)
\(542\) 7.08131 0.304168
\(543\) −6.04909 −0.259591
\(544\) 23.5489 1.00965
\(545\) 3.88346 0.166349
\(546\) 2.48630 0.106404
\(547\) −15.2735 −0.653048 −0.326524 0.945189i \(-0.605877\pi\)
−0.326524 + 0.945189i \(0.605877\pi\)
\(548\) 0.353419 0.0150973
\(549\) 6.87492 0.293414
\(550\) −7.21306 −0.307566
\(551\) −72.9476 −3.10767
\(552\) 28.5711 1.21607
\(553\) 16.6733 0.709019
\(554\) −8.68135 −0.368835
\(555\) 7.53380 0.319792
\(556\) 0.0953793 0.00404498
\(557\) 14.3284 0.607112 0.303556 0.952814i \(-0.401826\pi\)
0.303556 + 0.952814i \(0.401826\pi\)
\(558\) −1.11285 −0.0471106
\(559\) −9.21374 −0.389700
\(560\) −2.56723 −0.108485
\(561\) −60.6030 −2.55866
\(562\) 36.8186 1.55310
\(563\) −1.97196 −0.0831084 −0.0415542 0.999136i \(-0.513231\pi\)
−0.0415542 + 0.999136i \(0.513231\pi\)
\(564\) −8.19230 −0.344958
\(565\) −14.5009 −0.610059
\(566\) −11.0962 −0.466406
\(567\) 3.52178 0.147901
\(568\) −44.9067 −1.88424
\(569\) −15.7677 −0.661016 −0.330508 0.943803i \(-0.607220\pi\)
−0.330508 + 0.943803i \(0.607220\pi\)
\(570\) 12.9320 0.541660
\(571\) 1.15789 0.0484561 0.0242280 0.999706i \(-0.492287\pi\)
0.0242280 + 0.999706i \(0.492287\pi\)
\(572\) −5.31427 −0.222201
\(573\) 31.3958 1.31158
\(574\) −6.84486 −0.285699
\(575\) −7.09156 −0.295738
\(576\) −11.2770 −0.469874
\(577\) 26.8097 1.11610 0.558052 0.829806i \(-0.311549\pi\)
0.558052 + 0.829806i \(0.311549\pi\)
\(578\) 50.5357 2.10201
\(579\) −6.09070 −0.253121
\(580\) 4.96956 0.206350
\(581\) −0.146721 −0.00608701
\(582\) 8.60261 0.356590
\(583\) −18.3893 −0.761608
\(584\) −16.2160 −0.671023
\(585\) −2.02191 −0.0835958
\(586\) 0.855099 0.0353238
\(587\) −25.2742 −1.04318 −0.521590 0.853197i \(-0.674661\pi\)
−0.521590 + 0.853197i \(0.674661\pi\)
\(588\) −0.734091 −0.0302734
\(589\) −5.95238 −0.245264
\(590\) −2.91320 −0.119934
\(591\) 25.2006 1.03661
\(592\) 14.7472 0.606107
\(593\) 11.3254 0.465080 0.232540 0.972587i \(-0.425296\pi\)
0.232540 + 0.972587i \(0.425296\pi\)
\(594\) 40.4882 1.66125
\(595\) 7.68825 0.315188
\(596\) −0.774049 −0.0317063
\(597\) 17.9894 0.736258
\(598\) 13.4439 0.549764
\(599\) 9.48241 0.387441 0.193720 0.981057i \(-0.437945\pi\)
0.193720 + 0.981057i \(0.437945\pi\)
\(600\) −4.02888 −0.164478
\(601\) −15.1478 −0.617892 −0.308946 0.951080i \(-0.599976\pi\)
−0.308946 + 0.951080i \(0.599976\pi\)
\(602\) −6.99993 −0.285296
\(603\) −6.18293 −0.251788
\(604\) 3.71792 0.151280
\(605\) −25.1240 −1.02144
\(606\) 5.57682 0.226543
\(607\) 20.1310 0.817091 0.408545 0.912738i \(-0.366036\pi\)
0.408545 + 0.912738i \(0.366036\pi\)
\(608\) −25.1662 −1.02062
\(609\) −11.6441 −0.471841
\(610\) 6.44600 0.260991
\(611\) −17.6287 −0.713179
\(612\) 5.50818 0.222655
\(613\) −14.5312 −0.586911 −0.293456 0.955973i \(-0.594805\pi\)
−0.293456 + 0.955973i \(0.594805\pi\)
\(614\) 40.3477 1.62830
\(615\) −7.48017 −0.301630
\(616\) −18.4635 −0.743916
\(617\) 21.2363 0.854941 0.427471 0.904029i \(-0.359405\pi\)
0.427471 + 0.904029i \(0.359405\pi\)
\(618\) −4.21835 −0.169687
\(619\) 45.9627 1.84740 0.923699 0.383118i \(-0.125150\pi\)
0.923699 + 0.383118i \(0.125150\pi\)
\(620\) 0.405506 0.0162855
\(621\) 39.8062 1.59737
\(622\) −30.4651 −1.22154
\(623\) 10.5229 0.421593
\(624\) 5.31859 0.212914
\(625\) 1.00000 0.0400000
\(626\) 0.0121116 0.000484075 0
\(627\) 64.7651 2.58647
\(628\) 3.31452 0.132264
\(629\) −44.1645 −1.76095
\(630\) −1.53610 −0.0611998
\(631\) −30.8632 −1.22864 −0.614322 0.789055i \(-0.710570\pi\)
−0.614322 + 0.789055i \(0.710570\pi\)
\(632\) 51.2196 2.03741
\(633\) −14.5818 −0.579573
\(634\) 27.6572 1.09841
\(635\) 4.88296 0.193775
\(636\) −2.24604 −0.0890613
\(637\) −1.57966 −0.0625884
\(638\) −64.0406 −2.53539
\(639\) −18.7108 −0.740190
\(640\) −4.44747 −0.175802
\(641\) 7.21400 0.284936 0.142468 0.989799i \(-0.454496\pi\)
0.142468 + 0.989799i \(0.454496\pi\)
\(642\) 0.508887 0.0200842
\(643\) 29.3300 1.15666 0.578331 0.815802i \(-0.303704\pi\)
0.578331 + 0.815802i \(0.303704\pi\)
\(644\) −3.96939 −0.156416
\(645\) −7.64964 −0.301204
\(646\) −75.8095 −2.98269
\(647\) −4.78740 −0.188212 −0.0941060 0.995562i \(-0.529999\pi\)
−0.0941060 + 0.995562i \(0.529999\pi\)
\(648\) 10.8188 0.425002
\(649\) −14.5897 −0.572697
\(650\) −1.89577 −0.0743581
\(651\) −0.950132 −0.0372386
\(652\) 12.5817 0.492739
\(653\) 2.57537 0.100782 0.0503910 0.998730i \(-0.483953\pi\)
0.0503910 + 0.998730i \(0.483953\pi\)
\(654\) −6.11236 −0.239012
\(655\) 5.57113 0.217682
\(656\) −14.6423 −0.571684
\(657\) −6.75657 −0.263599
\(658\) −13.3930 −0.522112
\(659\) −33.2515 −1.29529 −0.647647 0.761941i \(-0.724247\pi\)
−0.647647 + 0.761941i \(0.724247\pi\)
\(660\) −4.41213 −0.171742
\(661\) −12.3151 −0.479002 −0.239501 0.970896i \(-0.576984\pi\)
−0.239501 + 0.970896i \(0.576984\pi\)
\(662\) 41.8988 1.62844
\(663\) −15.9279 −0.618590
\(664\) −0.450721 −0.0174914
\(665\) −8.21627 −0.318613
\(666\) 8.82401 0.341923
\(667\) −62.9619 −2.43790
\(668\) 3.53692 0.136847
\(669\) 5.20811 0.201357
\(670\) −5.79718 −0.223965
\(671\) 32.2825 1.24625
\(672\) −4.01708 −0.154962
\(673\) 30.1853 1.16356 0.581779 0.813347i \(-0.302357\pi\)
0.581779 + 0.813347i \(0.302357\pi\)
\(674\) −16.5174 −0.636225
\(675\) −5.61318 −0.216051
\(676\) 5.87983 0.226147
\(677\) 42.4590 1.63183 0.815915 0.578171i \(-0.196234\pi\)
0.815915 + 0.578171i \(0.196234\pi\)
\(678\) 22.8237 0.876538
\(679\) −5.46564 −0.209752
\(680\) 23.6180 0.905710
\(681\) −21.0939 −0.808319
\(682\) −5.22559 −0.200098
\(683\) −19.4029 −0.742430 −0.371215 0.928547i \(-0.621059\pi\)
−0.371215 + 0.928547i \(0.621059\pi\)
\(684\) −5.88648 −0.225075
\(685\) 0.631405 0.0241247
\(686\) −1.20011 −0.0458204
\(687\) 1.31150 0.0500369
\(688\) −14.9740 −0.570877
\(689\) −4.83316 −0.184129
\(690\) 11.1617 0.424920
\(691\) 45.7542 1.74057 0.870285 0.492548i \(-0.163935\pi\)
0.870285 + 0.492548i \(0.163935\pi\)
\(692\) 13.1601 0.500273
\(693\) −7.69302 −0.292234
\(694\) −14.1391 −0.536713
\(695\) 0.170401 0.00646368
\(696\) −35.7701 −1.35586
\(697\) 43.8501 1.66094
\(698\) −9.09074 −0.344090
\(699\) −32.6222 −1.23389
\(700\) 0.559734 0.0211560
\(701\) −21.2959 −0.804337 −0.402168 0.915566i \(-0.631743\pi\)
−0.402168 + 0.915566i \(0.631743\pi\)
\(702\) 10.6413 0.401629
\(703\) 47.1977 1.78009
\(704\) −52.9532 −1.99575
\(705\) −14.6361 −0.551226
\(706\) 28.6713 1.07906
\(707\) −3.54321 −0.133256
\(708\) −1.78196 −0.0669703
\(709\) 34.3167 1.28879 0.644395 0.764693i \(-0.277109\pi\)
0.644395 + 0.764693i \(0.277109\pi\)
\(710\) −17.5435 −0.658395
\(711\) 21.3412 0.800358
\(712\) 32.3261 1.21147
\(713\) −5.13757 −0.192403
\(714\) −12.1009 −0.452864
\(715\) −9.49427 −0.355066
\(716\) −4.63791 −0.173327
\(717\) 35.0133 1.30759
\(718\) 14.8365 0.553693
\(719\) 10.4558 0.389936 0.194968 0.980810i \(-0.437540\pi\)
0.194968 + 0.980810i \(0.437540\pi\)
\(720\) −3.28597 −0.122461
\(721\) 2.68011 0.0998125
\(722\) 58.2140 2.16650
\(723\) −22.2835 −0.828733
\(724\) 2.58169 0.0959477
\(725\) 8.87843 0.329737
\(726\) 39.5439 1.46761
\(727\) 32.5706 1.20798 0.603988 0.796993i \(-0.293577\pi\)
0.603988 + 0.796993i \(0.293577\pi\)
\(728\) −4.85266 −0.179852
\(729\) 26.5928 0.984919
\(730\) −6.33503 −0.234470
\(731\) 44.8435 1.65860
\(732\) 3.94293 0.145735
\(733\) −13.4376 −0.496329 −0.248165 0.968718i \(-0.579827\pi\)
−0.248165 + 0.968718i \(0.579827\pi\)
\(734\) 0.383471 0.0141542
\(735\) −1.31150 −0.0483754
\(736\) −21.7212 −0.800655
\(737\) −29.0331 −1.06945
\(738\) −8.76120 −0.322504
\(739\) 31.0960 1.14388 0.571942 0.820294i \(-0.306190\pi\)
0.571942 + 0.820294i \(0.306190\pi\)
\(740\) −3.21534 −0.118198
\(741\) 17.0219 0.625313
\(742\) −3.67188 −0.134799
\(743\) −12.3886 −0.454495 −0.227248 0.973837i \(-0.572973\pi\)
−0.227248 + 0.973837i \(0.572973\pi\)
\(744\) −2.91877 −0.107007
\(745\) −1.38289 −0.0506651
\(746\) 25.0110 0.915720
\(747\) −0.187798 −0.00687117
\(748\) 25.8647 0.945707
\(749\) −0.323319 −0.0118138
\(750\) −1.57395 −0.0574724
\(751\) 13.5260 0.493569 0.246785 0.969070i \(-0.420626\pi\)
0.246785 + 0.969070i \(0.420626\pi\)
\(752\) −28.6497 −1.04475
\(753\) −36.6484 −1.33554
\(754\) −16.8314 −0.612965
\(755\) 6.64230 0.241738
\(756\) −3.14189 −0.114269
\(757\) 28.3837 1.03162 0.515812 0.856702i \(-0.327490\pi\)
0.515812 + 0.856702i \(0.327490\pi\)
\(758\) 38.0533 1.38216
\(759\) 55.8995 2.02902
\(760\) −25.2401 −0.915555
\(761\) 54.7787 1.98573 0.992863 0.119262i \(-0.0380529\pi\)
0.992863 + 0.119262i \(0.0380529\pi\)
\(762\) −7.68552 −0.278417
\(763\) 3.88346 0.140591
\(764\) −13.3994 −0.484773
\(765\) 9.84071 0.355792
\(766\) −24.0040 −0.867301
\(767\) −3.83453 −0.138457
\(768\) −16.1095 −0.581302
\(769\) 31.5926 1.13926 0.569630 0.821901i \(-0.307087\pi\)
0.569630 + 0.821901i \(0.307087\pi\)
\(770\) −7.21306 −0.259941
\(771\) 27.6051 0.994173
\(772\) 2.59945 0.0935561
\(773\) 50.8082 1.82745 0.913723 0.406339i \(-0.133195\pi\)
0.913723 + 0.406339i \(0.133195\pi\)
\(774\) −8.95968 −0.322049
\(775\) 0.724462 0.0260235
\(776\) −16.7902 −0.602735
\(777\) 7.53380 0.270273
\(778\) 21.9500 0.786946
\(779\) −46.8617 −1.67900
\(780\) −1.15961 −0.0415209
\(781\) −87.8603 −3.14389
\(782\) −65.4321 −2.33985
\(783\) −49.8362 −1.78100
\(784\) −2.56723 −0.0916868
\(785\) 5.92159 0.211351
\(786\) −8.76865 −0.312767
\(787\) 10.0312 0.357573 0.178786 0.983888i \(-0.442783\pi\)
0.178786 + 0.983888i \(0.442783\pi\)
\(788\) −10.7553 −0.383143
\(789\) 10.0096 0.356353
\(790\) 20.0097 0.711915
\(791\) −14.5009 −0.515594
\(792\) −23.6327 −0.839751
\(793\) 8.48462 0.301298
\(794\) 23.4789 0.833237
\(795\) −4.01269 −0.142316
\(796\) −7.67769 −0.272129
\(797\) −8.43287 −0.298707 −0.149354 0.988784i \(-0.547719\pi\)
−0.149354 + 0.988784i \(0.547719\pi\)
\(798\) 12.9320 0.457787
\(799\) 85.7992 3.03536
\(800\) 3.06297 0.108292
\(801\) 13.4690 0.475904
\(802\) −22.2232 −0.784730
\(803\) −31.7267 −1.11961
\(804\) −3.54605 −0.125060
\(805\) −7.09156 −0.249945
\(806\) −1.37341 −0.0483764
\(807\) −3.63182 −0.127846
\(808\) −10.8846 −0.382919
\(809\) 28.2430 0.992970 0.496485 0.868045i \(-0.334624\pi\)
0.496485 + 0.868045i \(0.334624\pi\)
\(810\) 4.22653 0.148505
\(811\) 25.9475 0.911141 0.455570 0.890200i \(-0.349435\pi\)
0.455570 + 0.890200i \(0.349435\pi\)
\(812\) 4.96956 0.174397
\(813\) 7.73856 0.271403
\(814\) 41.4348 1.45229
\(815\) 22.4781 0.787372
\(816\) −25.8857 −0.906182
\(817\) −47.9234 −1.67663
\(818\) 37.7880 1.32123
\(819\) −2.02191 −0.0706514
\(820\) 3.19246 0.111485
\(821\) −26.6090 −0.928661 −0.464331 0.885662i \(-0.653705\pi\)
−0.464331 + 0.885662i \(0.653705\pi\)
\(822\) −0.993797 −0.0346627
\(823\) −28.8724 −1.00643 −0.503214 0.864162i \(-0.667849\pi\)
−0.503214 + 0.864162i \(0.667849\pi\)
\(824\) 8.23320 0.286817
\(825\) −7.88255 −0.274435
\(826\) −2.91320 −0.101363
\(827\) −9.84340 −0.342289 −0.171144 0.985246i \(-0.554746\pi\)
−0.171144 + 0.985246i \(0.554746\pi\)
\(828\) −5.08069 −0.176566
\(829\) −27.3328 −0.949308 −0.474654 0.880173i \(-0.657427\pi\)
−0.474654 + 0.880173i \(0.657427\pi\)
\(830\) −0.176081 −0.00611187
\(831\) −9.48712 −0.329104
\(832\) −13.9174 −0.482498
\(833\) 7.68825 0.266382
\(834\) −0.268202 −0.00928707
\(835\) 6.31892 0.218675
\(836\) −27.6411 −0.955986
\(837\) −4.06654 −0.140560
\(838\) 22.5177 0.777861
\(839\) −24.6751 −0.851881 −0.425940 0.904751i \(-0.640057\pi\)
−0.425940 + 0.904751i \(0.640057\pi\)
\(840\) −4.02888 −0.139010
\(841\) 49.8265 1.71816
\(842\) 31.1550 1.07367
\(843\) 40.2360 1.38580
\(844\) 6.22334 0.214216
\(845\) 10.5047 0.361372
\(846\) −17.1426 −0.589374
\(847\) −25.1240 −0.863272
\(848\) −7.85475 −0.269733
\(849\) −12.1261 −0.416165
\(850\) 9.22675 0.316475
\(851\) 40.7368 1.39644
\(852\) −10.7311 −0.367642
\(853\) 9.87351 0.338063 0.169031 0.985611i \(-0.445936\pi\)
0.169031 + 0.985611i \(0.445936\pi\)
\(854\) 6.44600 0.220577
\(855\) −10.5166 −0.359659
\(856\) −0.993225 −0.0339477
\(857\) 18.4920 0.631674 0.315837 0.948813i \(-0.397715\pi\)
0.315837 + 0.948813i \(0.397715\pi\)
\(858\) 14.9435 0.510162
\(859\) 27.8255 0.949393 0.474697 0.880149i \(-0.342558\pi\)
0.474697 + 0.880149i \(0.342558\pi\)
\(860\) 3.26478 0.111328
\(861\) −7.48017 −0.254924
\(862\) −25.7227 −0.876119
\(863\) 47.6696 1.62269 0.811346 0.584566i \(-0.198735\pi\)
0.811346 + 0.584566i \(0.198735\pi\)
\(864\) −17.1930 −0.584917
\(865\) 23.5114 0.799411
\(866\) −30.4083 −1.03332
\(867\) 55.2262 1.87558
\(868\) 0.405506 0.0137638
\(869\) 100.212 3.39945
\(870\) −13.9742 −0.473769
\(871\) −7.63060 −0.258553
\(872\) 11.9299 0.403996
\(873\) −6.99584 −0.236773
\(874\) 69.9259 2.36528
\(875\) 1.00000 0.0338062
\(876\) −3.87505 −0.130926
\(877\) −53.0784 −1.79233 −0.896165 0.443721i \(-0.853658\pi\)
−0.896165 + 0.443721i \(0.853658\pi\)
\(878\) −0.571050 −0.0192720
\(879\) 0.934466 0.0315188
\(880\) −15.4299 −0.520141
\(881\) −26.9750 −0.908812 −0.454406 0.890795i \(-0.650148\pi\)
−0.454406 + 0.890795i \(0.650148\pi\)
\(882\) −1.53610 −0.0517233
\(883\) 9.09645 0.306120 0.153060 0.988217i \(-0.451087\pi\)
0.153060 + 0.988217i \(0.451087\pi\)
\(884\) 6.79787 0.228637
\(885\) −3.18359 −0.107015
\(886\) −1.73408 −0.0582577
\(887\) 31.8899 1.07076 0.535380 0.844612i \(-0.320169\pi\)
0.535380 + 0.844612i \(0.320169\pi\)
\(888\) 23.1436 0.776647
\(889\) 4.88296 0.163769
\(890\) 12.6287 0.423315
\(891\) 21.1671 0.709123
\(892\) −2.22276 −0.0744237
\(893\) −91.6918 −3.06835
\(894\) 2.17659 0.0727960
\(895\) −8.28592 −0.276968
\(896\) −4.44747 −0.148580
\(897\) 14.6918 0.490543
\(898\) 3.79153 0.126525
\(899\) 6.43209 0.214522
\(900\) 0.716441 0.0238814
\(901\) 23.5231 0.783669
\(902\) −41.1399 −1.36981
\(903\) −7.64964 −0.254564
\(904\) −44.5464 −1.48159
\(905\) 4.61235 0.153320
\(906\) −10.4546 −0.347331
\(907\) −15.6993 −0.521287 −0.260644 0.965435i \(-0.583935\pi\)
−0.260644 + 0.965435i \(0.583935\pi\)
\(908\) 9.00264 0.298763
\(909\) −4.53519 −0.150423
\(910\) −1.89577 −0.0628441
\(911\) −34.0682 −1.12873 −0.564365 0.825525i \(-0.690879\pi\)
−0.564365 + 0.825525i \(0.690879\pi\)
\(912\) 27.6636 0.916032
\(913\) −0.881841 −0.0291847
\(914\) −1.43614 −0.0475033
\(915\) 7.04429 0.232877
\(916\) −0.559734 −0.0184941
\(917\) 5.57113 0.183975
\(918\) −51.7914 −1.70937
\(919\) 57.7799 1.90598 0.952992 0.302995i \(-0.0979864\pi\)
0.952992 + 0.302995i \(0.0979864\pi\)
\(920\) −21.7850 −0.718231
\(921\) 44.0926 1.45290
\(922\) 50.6817 1.66911
\(923\) −23.0918 −0.760076
\(924\) −4.41213 −0.145148
\(925\) −5.74441 −0.188875
\(926\) −39.2064 −1.28840
\(927\) 3.43045 0.112671
\(928\) 27.1944 0.892698
\(929\) −19.6671 −0.645258 −0.322629 0.946525i \(-0.604567\pi\)
−0.322629 + 0.946525i \(0.604567\pi\)
\(930\) −1.14026 −0.0373907
\(931\) −8.21627 −0.269278
\(932\) 13.9228 0.456057
\(933\) −33.2927 −1.08995
\(934\) −30.9095 −1.01139
\(935\) 46.2089 1.51119
\(936\) −6.21125 −0.203021
\(937\) −36.0692 −1.17833 −0.589164 0.808014i \(-0.700543\pi\)
−0.589164 + 0.808014i \(0.700543\pi\)
\(938\) −5.79718 −0.189285
\(939\) 0.0132357 0.000431931 0
\(940\) 6.24651 0.203739
\(941\) −30.4058 −0.991199 −0.495600 0.868551i \(-0.665052\pi\)
−0.495600 + 0.868551i \(0.665052\pi\)
\(942\) −9.32026 −0.303670
\(943\) −40.4469 −1.31713
\(944\) −6.23180 −0.202828
\(945\) −5.61318 −0.182597
\(946\) −42.0719 −1.36787
\(947\) 8.18682 0.266036 0.133018 0.991114i \(-0.457533\pi\)
0.133018 + 0.991114i \(0.457533\pi\)
\(948\) 12.2397 0.397527
\(949\) −8.33856 −0.270681
\(950\) −9.86044 −0.319915
\(951\) 30.2242 0.980088
\(952\) 23.6180 0.765465
\(953\) −16.0845 −0.521027 −0.260514 0.965470i \(-0.583892\pi\)
−0.260514 + 0.965470i \(0.583892\pi\)
\(954\) −4.69989 −0.152165
\(955\) −23.9389 −0.774643
\(956\) −14.9433 −0.483300
\(957\) −69.9846 −2.26228
\(958\) 20.2137 0.653074
\(959\) 0.631405 0.0203891
\(960\) −11.5548 −0.372929
\(961\) −30.4752 −0.983069
\(962\) 10.8901 0.351110
\(963\) −0.413838 −0.0133357
\(964\) 9.51036 0.306308
\(965\) 4.64407 0.149498
\(966\) 11.1617 0.359123
\(967\) 26.3560 0.847553 0.423776 0.905767i \(-0.360704\pi\)
0.423776 + 0.905767i \(0.360704\pi\)
\(968\) −77.1801 −2.48066
\(969\) −82.8458 −2.66139
\(970\) −6.55937 −0.210609
\(971\) −6.27104 −0.201247 −0.100624 0.994925i \(-0.532084\pi\)
−0.100624 + 0.994925i \(0.532084\pi\)
\(972\) −6.84035 −0.219404
\(973\) 0.170401 0.00546281
\(974\) −18.2017 −0.583219
\(975\) −2.07172 −0.0663483
\(976\) 13.7890 0.441376
\(977\) −7.84103 −0.250857 −0.125428 0.992103i \(-0.540031\pi\)
−0.125428 + 0.992103i \(0.540031\pi\)
\(978\) −35.3792 −1.13130
\(979\) 63.2463 2.02136
\(980\) 0.559734 0.0178801
\(981\) 4.97071 0.158702
\(982\) 9.14252 0.291749
\(983\) −30.7804 −0.981743 −0.490872 0.871232i \(-0.663322\pi\)
−0.490872 + 0.871232i \(0.663322\pi\)
\(984\) −22.9788 −0.732538
\(985\) −19.2151 −0.612243
\(986\) 81.9191 2.60883
\(987\) −14.6361 −0.465871
\(988\) −7.26474 −0.231122
\(989\) −41.3632 −1.31527
\(990\) −9.23248 −0.293427
\(991\) −1.28429 −0.0407968 −0.0203984 0.999792i \(-0.506493\pi\)
−0.0203984 + 0.999792i \(0.506493\pi\)
\(992\) 2.21901 0.0704535
\(993\) 45.7877 1.45303
\(994\) −17.5435 −0.556446
\(995\) −13.7167 −0.434848
\(996\) −0.107707 −0.00341281
\(997\) −16.6670 −0.527849 −0.263925 0.964543i \(-0.585017\pi\)
−0.263925 + 0.964543i \(0.585017\pi\)
\(998\) 5.77659 0.182855
\(999\) 32.2444 1.02017
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 \(a_p\))