Properties

Label 4010.2.a.k.1.11
Level 4010
Weight 2
Character 4010.1
Self dual Yes
Analytic conductor 32.020
Analytic rank 1
Dimension 15
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4010 = 2 \cdot 5 \cdot 401 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4010.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0200112105\)
Analytic rank: \(1\)
Dimension: \(15\)
Coefficient field: \(\mathbb{Q}[x]/(x^{15} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Root \(0.698269\)
Character \(\chi\) = 4010.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.23027 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.23027 q^{6} +3.50539 q^{7} -1.00000 q^{8} -1.48643 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.23027 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.23027 q^{6} +3.50539 q^{7} -1.00000 q^{8} -1.48643 q^{9} +1.00000 q^{10} -1.86568 q^{11} +1.23027 q^{12} -6.67672 q^{13} -3.50539 q^{14} -1.23027 q^{15} +1.00000 q^{16} +6.33119 q^{17} +1.48643 q^{18} +4.59396 q^{19} -1.00000 q^{20} +4.31258 q^{21} +1.86568 q^{22} -8.71861 q^{23} -1.23027 q^{24} +1.00000 q^{25} +6.67672 q^{26} -5.51953 q^{27} +3.50539 q^{28} +9.04127 q^{29} +1.23027 q^{30} -8.47326 q^{31} -1.00000 q^{32} -2.29529 q^{33} -6.33119 q^{34} -3.50539 q^{35} -1.48643 q^{36} -3.07987 q^{37} -4.59396 q^{38} -8.21418 q^{39} +1.00000 q^{40} -3.18575 q^{41} -4.31258 q^{42} -2.83884 q^{43} -1.86568 q^{44} +1.48643 q^{45} +8.71861 q^{46} +8.62657 q^{47} +1.23027 q^{48} +5.28775 q^{49} -1.00000 q^{50} +7.78908 q^{51} -6.67672 q^{52} +6.47876 q^{53} +5.51953 q^{54} +1.86568 q^{55} -3.50539 q^{56} +5.65182 q^{57} -9.04127 q^{58} -5.42917 q^{59} -1.23027 q^{60} -4.38698 q^{61} +8.47326 q^{62} -5.21053 q^{63} +1.00000 q^{64} +6.67672 q^{65} +2.29529 q^{66} +2.27426 q^{67} +6.33119 q^{68} -10.7263 q^{69} +3.50539 q^{70} -0.782381 q^{71} +1.48643 q^{72} -1.86149 q^{73} +3.07987 q^{74} +1.23027 q^{75} +4.59396 q^{76} -6.53993 q^{77} +8.21418 q^{78} -8.08705 q^{79} -1.00000 q^{80} -2.33122 q^{81} +3.18575 q^{82} -15.8885 q^{83} +4.31258 q^{84} -6.33119 q^{85} +2.83884 q^{86} +11.1232 q^{87} +1.86568 q^{88} -11.8551 q^{89} -1.48643 q^{90} -23.4045 q^{91} -8.71861 q^{92} -10.4244 q^{93} -8.62657 q^{94} -4.59396 q^{95} -1.23027 q^{96} -15.0823 q^{97} -5.28775 q^{98} +2.77321 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 15q - 15q^{2} - 6q^{3} + 15q^{4} - 15q^{5} + 6q^{6} - 5q^{7} - 15q^{8} + 19q^{9} + O(q^{10}) \) \( 15q - 15q^{2} - 6q^{3} + 15q^{4} - 15q^{5} + 6q^{6} - 5q^{7} - 15q^{8} + 19q^{9} + 15q^{10} - 2q^{11} - 6q^{12} - 13q^{13} + 5q^{14} + 6q^{15} + 15q^{16} + 11q^{17} - 19q^{18} - 15q^{19} - 15q^{20} - 2q^{21} + 2q^{22} - 3q^{23} + 6q^{24} + 15q^{25} + 13q^{26} - 12q^{27} - 5q^{28} + 28q^{29} - 6q^{30} - 12q^{31} - 15q^{32} - 22q^{33} - 11q^{34} + 5q^{35} + 19q^{36} - 23q^{37} + 15q^{38} - 2q^{39} + 15q^{40} + 24q^{41} + 2q^{42} - 24q^{43} - 2q^{44} - 19q^{45} + 3q^{46} - 3q^{47} - 6q^{48} + 20q^{49} - 15q^{50} - 5q^{51} - 13q^{52} + 10q^{53} + 12q^{54} + 2q^{55} + 5q^{56} - 11q^{57} - 28q^{58} + 2q^{59} + 6q^{60} + 15q^{61} + 12q^{62} - 2q^{63} + 15q^{64} + 13q^{65} + 22q^{66} - 48q^{67} + 11q^{68} + 21q^{69} - 5q^{70} + 15q^{71} - 19q^{72} - 47q^{73} + 23q^{74} - 6q^{75} - 15q^{76} + 7q^{77} + 2q^{78} - 34q^{79} - 15q^{80} + 43q^{81} - 24q^{82} - 32q^{83} - 2q^{84} - 11q^{85} + 24q^{86} + 14q^{87} + 2q^{88} + 25q^{89} + 19q^{90} - 32q^{91} - 3q^{92} - 42q^{93} + 3q^{94} + 15q^{95} + 6q^{96} - 34q^{97} - 20q^{98} + 4q^{99} + O(q^{100}) \)

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
\(3\) 1.23027 0.710297 0.355149 0.934810i \(-0.384430\pi\)
0.355149 + 0.934810i \(0.384430\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) −1.23027 −0.502256
\(7\) 3.50539 1.32491 0.662456 0.749101i \(-0.269514\pi\)
0.662456 + 0.749101i \(0.269514\pi\)
\(8\) −1.00000 −0.353553
\(9\) −1.48643 −0.495478
\(10\) 1.00000 0.316228
\(11\) −1.86568 −0.562523 −0.281262 0.959631i \(-0.590753\pi\)
−0.281262 + 0.959631i \(0.590753\pi\)
\(12\) 1.23027 0.355149
\(13\) −6.67672 −1.85179 −0.925895 0.377781i \(-0.876687\pi\)
−0.925895 + 0.377781i \(0.876687\pi\)
\(14\) −3.50539 −0.936855
\(15\) −1.23027 −0.317655
\(16\) 1.00000 0.250000
\(17\) 6.33119 1.53554 0.767770 0.640726i \(-0.221367\pi\)
0.767770 + 0.640726i \(0.221367\pi\)
\(18\) 1.48643 0.350356
\(19\) 4.59396 1.05393 0.526963 0.849888i \(-0.323330\pi\)
0.526963 + 0.849888i \(0.323330\pi\)
\(20\) −1.00000 −0.223607
\(21\) 4.31258 0.941082
\(22\) 1.86568 0.397764
\(23\) −8.71861 −1.81796 −0.908978 0.416843i \(-0.863136\pi\)
−0.908978 + 0.416843i \(0.863136\pi\)
\(24\) −1.23027 −0.251128
\(25\) 1.00000 0.200000
\(26\) 6.67672 1.30941
\(27\) −5.51953 −1.06223
\(28\) 3.50539 0.662456
\(29\) 9.04127 1.67892 0.839461 0.543421i \(-0.182871\pi\)
0.839461 + 0.543421i \(0.182871\pi\)
\(30\) 1.23027 0.224616
\(31\) −8.47326 −1.52184 −0.760921 0.648844i \(-0.775253\pi\)
−0.760921 + 0.648844i \(0.775253\pi\)
\(32\) −1.00000 −0.176777
\(33\) −2.29529 −0.399559
\(34\) −6.33119 −1.08579
\(35\) −3.50539 −0.592519
\(36\) −1.48643 −0.247739
\(37\) −3.07987 −0.506327 −0.253164 0.967424i \(-0.581471\pi\)
−0.253164 + 0.967424i \(0.581471\pi\)
\(38\) −4.59396 −0.745239
\(39\) −8.21418 −1.31532
\(40\) 1.00000 0.158114
\(41\) −3.18575 −0.497531 −0.248765 0.968564i \(-0.580025\pi\)
−0.248765 + 0.968564i \(0.580025\pi\)
\(42\) −4.31258 −0.665445
\(43\) −2.83884 −0.432919 −0.216460 0.976292i \(-0.569451\pi\)
−0.216460 + 0.976292i \(0.569451\pi\)
\(44\) −1.86568 −0.281262
\(45\) 1.48643 0.221584
\(46\) 8.71861 1.28549
\(47\) 8.62657 1.25831 0.629157 0.777278i \(-0.283400\pi\)
0.629157 + 0.777278i \(0.283400\pi\)
\(48\) 1.23027 0.177574
\(49\) 5.28775 0.755393
\(50\) −1.00000 −0.141421
\(51\) 7.78908 1.09069
\(52\) −6.67672 −0.925895
\(53\) 6.47876 0.889926 0.444963 0.895549i \(-0.353217\pi\)
0.444963 + 0.895549i \(0.353217\pi\)
\(54\) 5.51953 0.751113
\(55\) 1.86568 0.251568
\(56\) −3.50539 −0.468427
\(57\) 5.65182 0.748602
\(58\) −9.04127 −1.18718
\(59\) −5.42917 −0.706818 −0.353409 0.935469i \(-0.614978\pi\)
−0.353409 + 0.935469i \(0.614978\pi\)
\(60\) −1.23027 −0.158827
\(61\) −4.38698 −0.561696 −0.280848 0.959752i \(-0.590616\pi\)
−0.280848 + 0.959752i \(0.590616\pi\)
\(62\) 8.47326 1.07611
\(63\) −5.21053 −0.656464
\(64\) 1.00000 0.125000
\(65\) 6.67672 0.828146
\(66\) 2.29529 0.282531
\(67\) 2.27426 0.277845 0.138923 0.990303i \(-0.455636\pi\)
0.138923 + 0.990303i \(0.455636\pi\)
\(68\) 6.33119 0.767770
\(69\) −10.7263 −1.29129
\(70\) 3.50539 0.418974
\(71\) −0.782381 −0.0928515 −0.0464258 0.998922i \(-0.514783\pi\)
−0.0464258 + 0.998922i \(0.514783\pi\)
\(72\) 1.48643 0.175178
\(73\) −1.86149 −0.217871 −0.108936 0.994049i \(-0.534744\pi\)
−0.108936 + 0.994049i \(0.534744\pi\)
\(74\) 3.07987 0.358027
\(75\) 1.23027 0.142059
\(76\) 4.59396 0.526963
\(77\) −6.53993 −0.745294
\(78\) 8.21418 0.930073
\(79\) −8.08705 −0.909864 −0.454932 0.890526i \(-0.650337\pi\)
−0.454932 + 0.890526i \(0.650337\pi\)
\(80\) −1.00000 −0.111803
\(81\) −2.33122 −0.259024
\(82\) 3.18575 0.351808
\(83\) −15.8885 −1.74399 −0.871994 0.489516i \(-0.837173\pi\)
−0.871994 + 0.489516i \(0.837173\pi\)
\(84\) 4.31258 0.470541
\(85\) −6.33119 −0.686714
\(86\) 2.83884 0.306120
\(87\) 11.1232 1.19253
\(88\) 1.86568 0.198882
\(89\) −11.8551 −1.25664 −0.628321 0.777954i \(-0.716257\pi\)
−0.628321 + 0.777954i \(0.716257\pi\)
\(90\) −1.48643 −0.156684
\(91\) −23.4045 −2.45346
\(92\) −8.71861 −0.908978
\(93\) −10.4244 −1.08096
\(94\) −8.62657 −0.889762
\(95\) −4.59396 −0.471330
\(96\) −1.23027 −0.125564
\(97\) −15.0823 −1.53137 −0.765686 0.643215i \(-0.777600\pi\)
−0.765686 + 0.643215i \(0.777600\pi\)
\(98\) −5.28775 −0.534144
\(99\) 2.77321 0.278718
\(100\) 1.00000 0.100000
\(101\) 7.22136 0.718553 0.359276 0.933231i \(-0.383024\pi\)
0.359276 + 0.933231i \(0.383024\pi\)
\(102\) −7.78908 −0.771234
\(103\) −7.70292 −0.758991 −0.379496 0.925194i \(-0.623902\pi\)
−0.379496 + 0.925194i \(0.623902\pi\)
\(104\) 6.67672 0.654707
\(105\) −4.31258 −0.420865
\(106\) −6.47876 −0.629273
\(107\) −0.576866 −0.0557678 −0.0278839 0.999611i \(-0.508877\pi\)
−0.0278839 + 0.999611i \(0.508877\pi\)
\(108\) −5.51953 −0.531117
\(109\) −20.1187 −1.92703 −0.963513 0.267663i \(-0.913749\pi\)
−0.963513 + 0.267663i \(0.913749\pi\)
\(110\) −1.86568 −0.177885
\(111\) −3.78907 −0.359643
\(112\) 3.50539 0.331228
\(113\) 7.13357 0.671070 0.335535 0.942028i \(-0.391083\pi\)
0.335535 + 0.942028i \(0.391083\pi\)
\(114\) −5.65182 −0.529341
\(115\) 8.71861 0.813015
\(116\) 9.04127 0.839461
\(117\) 9.92450 0.917520
\(118\) 5.42917 0.499796
\(119\) 22.1933 2.03445
\(120\) 1.23027 0.112308
\(121\) −7.51924 −0.683568
\(122\) 4.38698 0.397179
\(123\) −3.91934 −0.353395
\(124\) −8.47326 −0.760921
\(125\) −1.00000 −0.0894427
\(126\) 5.21053 0.464190
\(127\) 3.36741 0.298809 0.149405 0.988776i \(-0.452264\pi\)
0.149405 + 0.988776i \(0.452264\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −3.49254 −0.307501
\(130\) −6.67672 −0.585587
\(131\) 2.27447 0.198722 0.0993609 0.995051i \(-0.468320\pi\)
0.0993609 + 0.995051i \(0.468320\pi\)
\(132\) −2.29529 −0.199779
\(133\) 16.1036 1.39636
\(134\) −2.27426 −0.196466
\(135\) 5.51953 0.475045
\(136\) −6.33119 −0.542895
\(137\) −1.03381 −0.0883241 −0.0441621 0.999024i \(-0.514062\pi\)
−0.0441621 + 0.999024i \(0.514062\pi\)
\(138\) 10.7263 0.913080
\(139\) −1.19908 −0.101705 −0.0508524 0.998706i \(-0.516194\pi\)
−0.0508524 + 0.998706i \(0.516194\pi\)
\(140\) −3.50539 −0.296259
\(141\) 10.6130 0.893777
\(142\) 0.782381 0.0656559
\(143\) 12.4566 1.04167
\(144\) −1.48643 −0.123869
\(145\) −9.04127 −0.750836
\(146\) 1.86149 0.154058
\(147\) 6.50537 0.536554
\(148\) −3.07987 −0.253164
\(149\) 3.22469 0.264177 0.132088 0.991238i \(-0.457832\pi\)
0.132088 + 0.991238i \(0.457832\pi\)
\(150\) −1.23027 −0.100451
\(151\) −8.09195 −0.658514 −0.329257 0.944240i \(-0.606798\pi\)
−0.329257 + 0.944240i \(0.606798\pi\)
\(152\) −4.59396 −0.372619
\(153\) −9.41089 −0.760825
\(154\) 6.53993 0.527003
\(155\) 8.47326 0.680589
\(156\) −8.21418 −0.657661
\(157\) 9.24673 0.737970 0.368985 0.929435i \(-0.379705\pi\)
0.368985 + 0.929435i \(0.379705\pi\)
\(158\) 8.08705 0.643371
\(159\) 7.97063 0.632112
\(160\) 1.00000 0.0790569
\(161\) −30.5621 −2.40863
\(162\) 2.33122 0.183158
\(163\) −3.93017 −0.307834 −0.153917 0.988084i \(-0.549189\pi\)
−0.153917 + 0.988084i \(0.549189\pi\)
\(164\) −3.18575 −0.248765
\(165\) 2.29529 0.178688
\(166\) 15.8885 1.23319
\(167\) 17.6116 1.36283 0.681415 0.731898i \(-0.261365\pi\)
0.681415 + 0.731898i \(0.261365\pi\)
\(168\) −4.31258 −0.332723
\(169\) 31.5786 2.42913
\(170\) 6.33119 0.485580
\(171\) −6.82861 −0.522197
\(172\) −2.83884 −0.216460
\(173\) −8.62140 −0.655473 −0.327736 0.944769i \(-0.606286\pi\)
−0.327736 + 0.944769i \(0.606286\pi\)
\(174\) −11.1232 −0.843248
\(175\) 3.50539 0.264983
\(176\) −1.86568 −0.140631
\(177\) −6.67935 −0.502051
\(178\) 11.8551 0.888580
\(179\) −12.5525 −0.938216 −0.469108 0.883141i \(-0.655424\pi\)
−0.469108 + 0.883141i \(0.655424\pi\)
\(180\) 1.48643 0.110792
\(181\) 15.6152 1.16067 0.580334 0.814379i \(-0.302922\pi\)
0.580334 + 0.814379i \(0.302922\pi\)
\(182\) 23.4045 1.73486
\(183\) −5.39718 −0.398971
\(184\) 8.71861 0.642745
\(185\) 3.07987 0.226436
\(186\) 10.4244 0.764355
\(187\) −11.8120 −0.863776
\(188\) 8.62657 0.629157
\(189\) −19.3481 −1.40737
\(190\) 4.59396 0.333281
\(191\) 13.2113 0.955940 0.477970 0.878376i \(-0.341373\pi\)
0.477970 + 0.878376i \(0.341373\pi\)
\(192\) 1.23027 0.0887872
\(193\) −21.5214 −1.54914 −0.774572 0.632485i \(-0.782035\pi\)
−0.774572 + 0.632485i \(0.782035\pi\)
\(194\) 15.0823 1.08284
\(195\) 8.21418 0.588230
\(196\) 5.28775 0.377697
\(197\) −13.5788 −0.967452 −0.483726 0.875219i \(-0.660717\pi\)
−0.483726 + 0.875219i \(0.660717\pi\)
\(198\) −2.77321 −0.197083
\(199\) −9.76276 −0.692064 −0.346032 0.938223i \(-0.612471\pi\)
−0.346032 + 0.938223i \(0.612471\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 2.79796 0.197353
\(202\) −7.22136 −0.508093
\(203\) 31.6932 2.22442
\(204\) 7.78908 0.545345
\(205\) 3.18575 0.222503
\(206\) 7.70292 0.536688
\(207\) 12.9596 0.900757
\(208\) −6.67672 −0.462948
\(209\) −8.57085 −0.592858
\(210\) 4.31258 0.297596
\(211\) 0.164687 0.0113375 0.00566875 0.999984i \(-0.498196\pi\)
0.00566875 + 0.999984i \(0.498196\pi\)
\(212\) 6.47876 0.444963
\(213\) −0.962541 −0.0659522
\(214\) 0.576866 0.0394338
\(215\) 2.83884 0.193607
\(216\) 5.51953 0.375556
\(217\) −29.7021 −2.01631
\(218\) 20.1187 1.36261
\(219\) −2.29014 −0.154753
\(220\) 1.86568 0.125784
\(221\) −42.2716 −2.84350
\(222\) 3.78907 0.254306
\(223\) 22.9746 1.53849 0.769247 0.638952i \(-0.220632\pi\)
0.769247 + 0.638952i \(0.220632\pi\)
\(224\) −3.50539 −0.234214
\(225\) −1.48643 −0.0990955
\(226\) −7.13357 −0.474518
\(227\) −9.13036 −0.606003 −0.303002 0.952990i \(-0.597989\pi\)
−0.303002 + 0.952990i \(0.597989\pi\)
\(228\) 5.65182 0.374301
\(229\) 15.1182 0.999042 0.499521 0.866302i \(-0.333509\pi\)
0.499521 + 0.866302i \(0.333509\pi\)
\(230\) −8.71861 −0.574888
\(231\) −8.04589 −0.529380
\(232\) −9.04127 −0.593588
\(233\) −7.18355 −0.470610 −0.235305 0.971922i \(-0.575609\pi\)
−0.235305 + 0.971922i \(0.575609\pi\)
\(234\) −9.92450 −0.648785
\(235\) −8.62657 −0.562735
\(236\) −5.42917 −0.353409
\(237\) −9.94927 −0.646274
\(238\) −22.1933 −1.43858
\(239\) 9.40800 0.608553 0.304276 0.952584i \(-0.401585\pi\)
0.304276 + 0.952584i \(0.401585\pi\)
\(240\) −1.23027 −0.0794137
\(241\) −18.3916 −1.18471 −0.592355 0.805677i \(-0.701802\pi\)
−0.592355 + 0.805677i \(0.701802\pi\)
\(242\) 7.51924 0.483355
\(243\) 13.6906 0.878249
\(244\) −4.38698 −0.280848
\(245\) −5.28775 −0.337822
\(246\) 3.91934 0.249888
\(247\) −30.6726 −1.95165
\(248\) 8.47326 0.538053
\(249\) −19.5472 −1.23875
\(250\) 1.00000 0.0632456
\(251\) −0.0298497 −0.00188409 −0.000942047 1.00000i \(-0.500300\pi\)
−0.000942047 1.00000i \(0.500300\pi\)
\(252\) −5.21053 −0.328232
\(253\) 16.2661 1.02264
\(254\) −3.36741 −0.211290
\(255\) −7.78908 −0.487771
\(256\) 1.00000 0.0625000
\(257\) −17.3843 −1.08440 −0.542201 0.840249i \(-0.682409\pi\)
−0.542201 + 0.840249i \(0.682409\pi\)
\(258\) 3.49254 0.217436
\(259\) −10.7961 −0.670839
\(260\) 6.67672 0.414073
\(261\) −13.4392 −0.831868
\(262\) −2.27447 −0.140517
\(263\) −1.69511 −0.104525 −0.0522625 0.998633i \(-0.516643\pi\)
−0.0522625 + 0.998633i \(0.516643\pi\)
\(264\) 2.29529 0.141265
\(265\) −6.47876 −0.397987
\(266\) −16.1036 −0.987376
\(267\) −14.5850 −0.892589
\(268\) 2.27426 0.138923
\(269\) 26.8529 1.63725 0.818626 0.574327i \(-0.194736\pi\)
0.818626 + 0.574327i \(0.194736\pi\)
\(270\) −5.51953 −0.335908
\(271\) 24.6974 1.50026 0.750132 0.661289i \(-0.229990\pi\)
0.750132 + 0.661289i \(0.229990\pi\)
\(272\) 6.33119 0.383885
\(273\) −28.7939 −1.74269
\(274\) 1.03381 0.0624546
\(275\) −1.86568 −0.112505
\(276\) −10.7263 −0.645645
\(277\) −25.3607 −1.52378 −0.761888 0.647708i \(-0.775727\pi\)
−0.761888 + 0.647708i \(0.775727\pi\)
\(278\) 1.19908 0.0719162
\(279\) 12.5949 0.754039
\(280\) 3.50539 0.209487
\(281\) 12.4409 0.742160 0.371080 0.928601i \(-0.378988\pi\)
0.371080 + 0.928601i \(0.378988\pi\)
\(282\) −10.6130 −0.631996
\(283\) −16.5614 −0.984470 −0.492235 0.870462i \(-0.663820\pi\)
−0.492235 + 0.870462i \(0.663820\pi\)
\(284\) −0.782381 −0.0464258
\(285\) −5.65182 −0.334785
\(286\) −12.4566 −0.736575
\(287\) −11.1673 −0.659185
\(288\) 1.48643 0.0875889
\(289\) 23.0840 1.35788
\(290\) 9.04127 0.530922
\(291\) −18.5553 −1.08773
\(292\) −1.86149 −0.108936
\(293\) 3.84987 0.224912 0.112456 0.993657i \(-0.464128\pi\)
0.112456 + 0.993657i \(0.464128\pi\)
\(294\) −6.50537 −0.379401
\(295\) 5.42917 0.316099
\(296\) 3.07987 0.179014
\(297\) 10.2977 0.597531
\(298\) −3.22469 −0.186801
\(299\) 58.2118 3.36647
\(300\) 1.23027 0.0710297
\(301\) −9.95124 −0.573580
\(302\) 8.09195 0.465639
\(303\) 8.88424 0.510386
\(304\) 4.59396 0.263482
\(305\) 4.38698 0.251198
\(306\) 9.41089 0.537985
\(307\) −21.1164 −1.20517 −0.602587 0.798053i \(-0.705863\pi\)
−0.602587 + 0.798053i \(0.705863\pi\)
\(308\) −6.53993 −0.372647
\(309\) −9.47668 −0.539110
\(310\) −8.47326 −0.481249
\(311\) 17.9731 1.01916 0.509581 0.860423i \(-0.329801\pi\)
0.509581 + 0.860423i \(0.329801\pi\)
\(312\) 8.21418 0.465036
\(313\) 26.9382 1.52264 0.761319 0.648377i \(-0.224552\pi\)
0.761319 + 0.648377i \(0.224552\pi\)
\(314\) −9.24673 −0.521823
\(315\) 5.21053 0.293580
\(316\) −8.08705 −0.454932
\(317\) 8.62087 0.484196 0.242098 0.970252i \(-0.422164\pi\)
0.242098 + 0.970252i \(0.422164\pi\)
\(318\) −7.97063 −0.446971
\(319\) −16.8681 −0.944432
\(320\) −1.00000 −0.0559017
\(321\) −0.709702 −0.0396117
\(322\) 30.5621 1.70316
\(323\) 29.0852 1.61835
\(324\) −2.33122 −0.129512
\(325\) −6.67672 −0.370358
\(326\) 3.93017 0.217672
\(327\) −24.7515 −1.36876
\(328\) 3.18575 0.175904
\(329\) 30.2395 1.66716
\(330\) −2.29529 −0.126352
\(331\) −19.3529 −1.06373 −0.531866 0.846828i \(-0.678509\pi\)
−0.531866 + 0.846828i \(0.678509\pi\)
\(332\) −15.8885 −0.871994
\(333\) 4.57802 0.250874
\(334\) −17.6116 −0.963666
\(335\) −2.27426 −0.124256
\(336\) 4.31258 0.235270
\(337\) −22.5312 −1.22735 −0.613675 0.789559i \(-0.710310\pi\)
−0.613675 + 0.789559i \(0.710310\pi\)
\(338\) −31.5786 −1.71765
\(339\) 8.77623 0.476659
\(340\) −6.33119 −0.343357
\(341\) 15.8084 0.856072
\(342\) 6.82861 0.369249
\(343\) −6.00209 −0.324083
\(344\) 2.83884 0.153060
\(345\) 10.7263 0.577482
\(346\) 8.62140 0.463489
\(347\) −8.34036 −0.447734 −0.223867 0.974620i \(-0.571868\pi\)
−0.223867 + 0.974620i \(0.571868\pi\)
\(348\) 11.1232 0.596267
\(349\) 2.91112 0.155828 0.0779142 0.996960i \(-0.475174\pi\)
0.0779142 + 0.996960i \(0.475174\pi\)
\(350\) −3.50539 −0.187371
\(351\) 36.8524 1.96703
\(352\) 1.86568 0.0994410
\(353\) −31.4044 −1.67149 −0.835745 0.549118i \(-0.814964\pi\)
−0.835745 + 0.549118i \(0.814964\pi\)
\(354\) 6.67935 0.355004
\(355\) 0.782381 0.0415245
\(356\) −11.8551 −0.628321
\(357\) 27.3038 1.44507
\(358\) 12.5525 0.663419
\(359\) −15.7995 −0.833865 −0.416933 0.908937i \(-0.636895\pi\)
−0.416933 + 0.908937i \(0.636895\pi\)
\(360\) −1.48643 −0.0783419
\(361\) 2.10448 0.110762
\(362\) −15.6152 −0.820716
\(363\) −9.25071 −0.485536
\(364\) −23.4045 −1.22673
\(365\) 1.86149 0.0974350
\(366\) 5.39718 0.282115
\(367\) −10.9877 −0.573554 −0.286777 0.957997i \(-0.592584\pi\)
−0.286777 + 0.957997i \(0.592584\pi\)
\(368\) −8.71861 −0.454489
\(369\) 4.73541 0.246515
\(370\) −3.07987 −0.160115
\(371\) 22.7106 1.17907
\(372\) −10.4244 −0.540480
\(373\) −11.7560 −0.608702 −0.304351 0.952560i \(-0.598440\pi\)
−0.304351 + 0.952560i \(0.598440\pi\)
\(374\) 11.8120 0.610782
\(375\) −1.23027 −0.0635309
\(376\) −8.62657 −0.444881
\(377\) −60.3661 −3.10901
\(378\) 19.3481 0.995159
\(379\) −8.20803 −0.421618 −0.210809 0.977527i \(-0.567610\pi\)
−0.210809 + 0.977527i \(0.567610\pi\)
\(380\) −4.59396 −0.235665
\(381\) 4.14283 0.212243
\(382\) −13.2113 −0.675951
\(383\) 6.79756 0.347339 0.173670 0.984804i \(-0.444438\pi\)
0.173670 + 0.984804i \(0.444438\pi\)
\(384\) −1.23027 −0.0627820
\(385\) 6.53993 0.333306
\(386\) 21.5214 1.09541
\(387\) 4.21975 0.214502
\(388\) −15.0823 −0.765686
\(389\) −15.0416 −0.762641 −0.381320 0.924443i \(-0.624531\pi\)
−0.381320 + 0.924443i \(0.624531\pi\)
\(390\) −8.21418 −0.415941
\(391\) −55.1992 −2.79154
\(392\) −5.28775 −0.267072
\(393\) 2.79822 0.141152
\(394\) 13.5788 0.684092
\(395\) 8.08705 0.406904
\(396\) 2.77321 0.139359
\(397\) −15.9858 −0.802307 −0.401153 0.916011i \(-0.631391\pi\)
−0.401153 + 0.916011i \(0.631391\pi\)
\(398\) 9.76276 0.489363
\(399\) 19.8118 0.991832
\(400\) 1.00000 0.0500000
\(401\) −1.00000 −0.0499376
\(402\) −2.79796 −0.139550
\(403\) 56.5736 2.81813
\(404\) 7.22136 0.359276
\(405\) 2.33122 0.115839
\(406\) −31.6932 −1.57291
\(407\) 5.74604 0.284821
\(408\) −7.78908 −0.385617
\(409\) 32.7944 1.62158 0.810790 0.585337i \(-0.199038\pi\)
0.810790 + 0.585337i \(0.199038\pi\)
\(410\) −3.18575 −0.157333
\(411\) −1.27186 −0.0627364
\(412\) −7.70292 −0.379496
\(413\) −19.0314 −0.936472
\(414\) −12.9596 −0.636931
\(415\) 15.8885 0.779935
\(416\) 6.67672 0.327353
\(417\) −1.47520 −0.0722407
\(418\) 8.57085 0.419214
\(419\) −20.1649 −0.985122 −0.492561 0.870278i \(-0.663939\pi\)
−0.492561 + 0.870278i \(0.663939\pi\)
\(420\) −4.31258 −0.210432
\(421\) −25.9559 −1.26501 −0.632507 0.774554i \(-0.717974\pi\)
−0.632507 + 0.774554i \(0.717974\pi\)
\(422\) −0.164687 −0.00801682
\(423\) −12.8228 −0.623466
\(424\) −6.47876 −0.314636
\(425\) 6.33119 0.307108
\(426\) 0.962541 0.0466352
\(427\) −15.3781 −0.744198
\(428\) −0.576866 −0.0278839
\(429\) 15.3250 0.739899
\(430\) −2.83884 −0.136901
\(431\) 11.7637 0.566640 0.283320 0.959025i \(-0.408564\pi\)
0.283320 + 0.959025i \(0.408564\pi\)
\(432\) −5.51953 −0.265558
\(433\) −19.7689 −0.950033 −0.475017 0.879977i \(-0.657558\pi\)
−0.475017 + 0.879977i \(0.657558\pi\)
\(434\) 29.7021 1.42575
\(435\) −11.1232 −0.533317
\(436\) −20.1187 −0.963513
\(437\) −40.0530 −1.91599
\(438\) 2.29014 0.109427
\(439\) −1.15129 −0.0549481 −0.0274741 0.999623i \(-0.508746\pi\)
−0.0274741 + 0.999623i \(0.508746\pi\)
\(440\) −1.86568 −0.0889427
\(441\) −7.85989 −0.374280
\(442\) 42.2716 2.01066
\(443\) 24.9362 1.18475 0.592377 0.805661i \(-0.298190\pi\)
0.592377 + 0.805661i \(0.298190\pi\)
\(444\) −3.78907 −0.179821
\(445\) 11.8551 0.561987
\(446\) −22.9746 −1.08788
\(447\) 3.96724 0.187644
\(448\) 3.50539 0.165614
\(449\) 4.63346 0.218666 0.109333 0.994005i \(-0.465128\pi\)
0.109333 + 0.994005i \(0.465128\pi\)
\(450\) 1.48643 0.0700711
\(451\) 5.94359 0.279873
\(452\) 7.13357 0.335535
\(453\) −9.95530 −0.467741
\(454\) 9.13036 0.428509
\(455\) 23.4045 1.09722
\(456\) −5.65182 −0.264671
\(457\) 39.7724 1.86048 0.930238 0.366956i \(-0.119600\pi\)
0.930238 + 0.366956i \(0.119600\pi\)
\(458\) −15.1182 −0.706429
\(459\) −34.9452 −1.63110
\(460\) 8.71861 0.406508
\(461\) 17.5872 0.819117 0.409559 0.912284i \(-0.365683\pi\)
0.409559 + 0.912284i \(0.365683\pi\)
\(462\) 8.04589 0.374329
\(463\) 7.95209 0.369565 0.184783 0.982779i \(-0.440842\pi\)
0.184783 + 0.982779i \(0.440842\pi\)
\(464\) 9.04127 0.419730
\(465\) 10.4244 0.483420
\(466\) 7.18355 0.332772
\(467\) −19.3310 −0.894534 −0.447267 0.894401i \(-0.647603\pi\)
−0.447267 + 0.894401i \(0.647603\pi\)
\(468\) 9.92450 0.458760
\(469\) 7.97217 0.368121
\(470\) 8.62657 0.397914
\(471\) 11.3760 0.524178
\(472\) 5.42917 0.249898
\(473\) 5.29636 0.243527
\(474\) 9.94927 0.456985
\(475\) 4.59396 0.210785
\(476\) 22.1933 1.01723
\(477\) −9.63024 −0.440939
\(478\) −9.40800 −0.430312
\(479\) 23.6652 1.08129 0.540645 0.841251i \(-0.318180\pi\)
0.540645 + 0.841251i \(0.318180\pi\)
\(480\) 1.23027 0.0561539
\(481\) 20.5634 0.937611
\(482\) 18.3916 0.837716
\(483\) −37.5997 −1.71085
\(484\) −7.51924 −0.341784
\(485\) 15.0823 0.684850
\(486\) −13.6906 −0.621016
\(487\) −23.8703 −1.08167 −0.540833 0.841130i \(-0.681891\pi\)
−0.540833 + 0.841130i \(0.681891\pi\)
\(488\) 4.38698 0.198589
\(489\) −4.83517 −0.218654
\(490\) 5.28775 0.238876
\(491\) 0.223451 0.0100842 0.00504209 0.999987i \(-0.498395\pi\)
0.00504209 + 0.999987i \(0.498395\pi\)
\(492\) −3.91934 −0.176697
\(493\) 57.2420 2.57805
\(494\) 30.6726 1.38003
\(495\) −2.77321 −0.124646
\(496\) −8.47326 −0.380461
\(497\) −2.74255 −0.123020
\(498\) 19.5472 0.875929
\(499\) −6.97246 −0.312130 −0.156065 0.987747i \(-0.549881\pi\)
−0.156065 + 0.987747i \(0.549881\pi\)
\(500\) −1.00000 −0.0447214
\(501\) 21.6671 0.968014
\(502\) 0.0298497 0.00133226
\(503\) −38.4956 −1.71644 −0.858218 0.513286i \(-0.828428\pi\)
−0.858218 + 0.513286i \(0.828428\pi\)
\(504\) 5.21053 0.232095
\(505\) −7.22136 −0.321346
\(506\) −16.2661 −0.723118
\(507\) 38.8503 1.72540
\(508\) 3.36741 0.149405
\(509\) 34.8707 1.54562 0.772809 0.634639i \(-0.218851\pi\)
0.772809 + 0.634639i \(0.218851\pi\)
\(510\) 7.78908 0.344906
\(511\) −6.52526 −0.288660
\(512\) −1.00000 −0.0441942
\(513\) −25.3565 −1.11952
\(514\) 17.3843 0.766788
\(515\) 7.70292 0.339431
\(516\) −3.49254 −0.153751
\(517\) −16.0944 −0.707831
\(518\) 10.7961 0.474355
\(519\) −10.6067 −0.465581
\(520\) −6.67672 −0.292794
\(521\) −15.7666 −0.690745 −0.345373 0.938466i \(-0.612248\pi\)
−0.345373 + 0.938466i \(0.612248\pi\)
\(522\) 13.4392 0.588219
\(523\) −35.2794 −1.54266 −0.771331 0.636435i \(-0.780408\pi\)
−0.771331 + 0.636435i \(0.780408\pi\)
\(524\) 2.27447 0.0993609
\(525\) 4.31258 0.188216
\(526\) 1.69511 0.0739103
\(527\) −53.6458 −2.33685
\(528\) −2.29529 −0.0998897
\(529\) 53.0142 2.30497
\(530\) 6.47876 0.281419
\(531\) 8.07010 0.350212
\(532\) 16.1036 0.698181
\(533\) 21.2704 0.921323
\(534\) 14.5850 0.631156
\(535\) 0.576866 0.0249401
\(536\) −2.27426 −0.0982331
\(537\) −15.4429 −0.666412
\(538\) −26.8529 −1.15771
\(539\) −9.86525 −0.424926
\(540\) 5.51953 0.237523
\(541\) 30.9354 1.33001 0.665007 0.746837i \(-0.268428\pi\)
0.665007 + 0.746837i \(0.268428\pi\)
\(542\) −24.6974 −1.06085
\(543\) 19.2109 0.824419
\(544\) −6.33119 −0.271448
\(545\) 20.1187 0.861792
\(546\) 28.7939 1.23227
\(547\) 22.2158 0.949880 0.474940 0.880018i \(-0.342470\pi\)
0.474940 + 0.880018i \(0.342470\pi\)
\(548\) −1.03381 −0.0441621
\(549\) 6.52096 0.278308
\(550\) 1.86568 0.0795528
\(551\) 41.5352 1.76946
\(552\) 10.7263 0.456540
\(553\) −28.3483 −1.20549
\(554\) 25.3607 1.07747
\(555\) 3.78907 0.160837
\(556\) −1.19908 −0.0508524
\(557\) −20.7416 −0.878848 −0.439424 0.898280i \(-0.644818\pi\)
−0.439424 + 0.898280i \(0.644818\pi\)
\(558\) −12.5949 −0.533186
\(559\) 18.9542 0.801675
\(560\) −3.50539 −0.148130
\(561\) −14.5319 −0.613538
\(562\) −12.4409 −0.524787
\(563\) −13.0881 −0.551596 −0.275798 0.961216i \(-0.588942\pi\)
−0.275798 + 0.961216i \(0.588942\pi\)
\(564\) 10.6130 0.446889
\(565\) −7.13357 −0.300112
\(566\) 16.5614 0.696126
\(567\) −8.17183 −0.343185
\(568\) 0.782381 0.0328280
\(569\) 34.4569 1.44451 0.722254 0.691627i \(-0.243106\pi\)
0.722254 + 0.691627i \(0.243106\pi\)
\(570\) 5.65182 0.236729
\(571\) 12.3441 0.516585 0.258292 0.966067i \(-0.416840\pi\)
0.258292 + 0.966067i \(0.416840\pi\)
\(572\) 12.4566 0.520837
\(573\) 16.2535 0.679001
\(574\) 11.1673 0.466114
\(575\) −8.71861 −0.363591
\(576\) −1.48643 −0.0619347
\(577\) 26.1431 1.08835 0.544176 0.838971i \(-0.316842\pi\)
0.544176 + 0.838971i \(0.316842\pi\)
\(578\) −23.0840 −0.960166
\(579\) −26.4772 −1.10035
\(580\) −9.04127 −0.375418
\(581\) −55.6953 −2.31063
\(582\) 18.5553 0.769141
\(583\) −12.0873 −0.500604
\(584\) 1.86149 0.0770291
\(585\) −9.92450 −0.410328
\(586\) −3.84987 −0.159037
\(587\) 14.5314 0.599774 0.299887 0.953975i \(-0.403051\pi\)
0.299887 + 0.953975i \(0.403051\pi\)
\(588\) 6.50537 0.268277
\(589\) −38.9258 −1.60391
\(590\) −5.42917 −0.223515
\(591\) −16.7057 −0.687179
\(592\) −3.07987 −0.126582
\(593\) −6.08413 −0.249845 −0.124923 0.992166i \(-0.539868\pi\)
−0.124923 + 0.992166i \(0.539868\pi\)
\(594\) −10.2977 −0.422518
\(595\) −22.1933 −0.909836
\(596\) 3.22469 0.132088
\(597\) −12.0108 −0.491571
\(598\) −58.2118 −2.38046
\(599\) −1.43166 −0.0584961 −0.0292481 0.999572i \(-0.509311\pi\)
−0.0292481 + 0.999572i \(0.509311\pi\)
\(600\) −1.23027 −0.0502256
\(601\) 41.2129 1.68111 0.840554 0.541728i \(-0.182230\pi\)
0.840554 + 0.541728i \(0.182230\pi\)
\(602\) 9.95124 0.405582
\(603\) −3.38054 −0.137666
\(604\) −8.09195 −0.329257
\(605\) 7.51924 0.305701
\(606\) −8.88424 −0.360897
\(607\) −3.96130 −0.160784 −0.0803921 0.996763i \(-0.525617\pi\)
−0.0803921 + 0.996763i \(0.525617\pi\)
\(608\) −4.59396 −0.186310
\(609\) 38.9912 1.58000
\(610\) −4.38698 −0.177624
\(611\) −57.5972 −2.33013
\(612\) −9.41089 −0.380413
\(613\) −42.6106 −1.72103 −0.860514 0.509427i \(-0.829857\pi\)
−0.860514 + 0.509427i \(0.829857\pi\)
\(614\) 21.1164 0.852187
\(615\) 3.91934 0.158043
\(616\) 6.53993 0.263501
\(617\) 7.67455 0.308966 0.154483 0.987995i \(-0.450629\pi\)
0.154483 + 0.987995i \(0.450629\pi\)
\(618\) 9.47668 0.381208
\(619\) −49.5915 −1.99325 −0.996625 0.0820940i \(-0.973839\pi\)
−0.996625 + 0.0820940i \(0.973839\pi\)
\(620\) 8.47326 0.340294
\(621\) 48.1226 1.93110
\(622\) −17.9731 −0.720656
\(623\) −41.5569 −1.66494
\(624\) −8.21418 −0.328830
\(625\) 1.00000 0.0400000
\(626\) −26.9382 −1.07667
\(627\) −10.5445 −0.421106
\(628\) 9.24673 0.368985
\(629\) −19.4992 −0.777485
\(630\) −5.21053 −0.207592
\(631\) 6.23601 0.248252 0.124126 0.992266i \(-0.460387\pi\)
0.124126 + 0.992266i \(0.460387\pi\)
\(632\) 8.08705 0.321686
\(633\) 0.202609 0.00805300
\(634\) −8.62087 −0.342378
\(635\) −3.36741 −0.133632
\(636\) 7.97063 0.316056
\(637\) −35.3049 −1.39883
\(638\) 16.8681 0.667814
\(639\) 1.16296 0.0460058
\(640\) 1.00000 0.0395285
\(641\) −23.6154 −0.932753 −0.466376 0.884586i \(-0.654441\pi\)
−0.466376 + 0.884586i \(0.654441\pi\)
\(642\) 0.709702 0.0280097
\(643\) 33.9364 1.33832 0.669161 0.743117i \(-0.266654\pi\)
0.669161 + 0.743117i \(0.266654\pi\)
\(644\) −30.5621 −1.20432
\(645\) 3.49254 0.137519
\(646\) −29.0852 −1.14434
\(647\) 23.3364 0.917449 0.458724 0.888579i \(-0.348307\pi\)
0.458724 + 0.888579i \(0.348307\pi\)
\(648\) 2.33122 0.0915790
\(649\) 10.1291 0.397602
\(650\) 6.67672 0.261883
\(651\) −36.5416 −1.43218
\(652\) −3.93017 −0.153917
\(653\) 41.8439 1.63748 0.818739 0.574165i \(-0.194673\pi\)
0.818739 + 0.574165i \(0.194673\pi\)
\(654\) 24.7515 0.967860
\(655\) −2.27447 −0.0888711
\(656\) −3.18575 −0.124383
\(657\) 2.76698 0.107950
\(658\) −30.2395 −1.17886
\(659\) −11.0508 −0.430478 −0.215239 0.976561i \(-0.569053\pi\)
−0.215239 + 0.976561i \(0.569053\pi\)
\(660\) 2.29529 0.0893441
\(661\) −49.4459 −1.92322 −0.961612 0.274412i \(-0.911517\pi\)
−0.961612 + 0.274412i \(0.911517\pi\)
\(662\) 19.3529 0.752173
\(663\) −52.0055 −2.01973
\(664\) 15.8885 0.616593
\(665\) −16.1036 −0.624472
\(666\) −4.57802 −0.177394
\(667\) −78.8273 −3.05221
\(668\) 17.6116 0.681415
\(669\) 28.2650 1.09279
\(670\) 2.27426 0.0878624
\(671\) 8.18470 0.315967
\(672\) −4.31258 −0.166361
\(673\) 35.1239 1.35393 0.676963 0.736017i \(-0.263296\pi\)
0.676963 + 0.736017i \(0.263296\pi\)
\(674\) 22.5312 0.867868
\(675\) −5.51953 −0.212447
\(676\) 31.5786 1.21456
\(677\) 0.724062 0.0278280 0.0139140 0.999903i \(-0.495571\pi\)
0.0139140 + 0.999903i \(0.495571\pi\)
\(678\) −8.77623 −0.337049
\(679\) −52.8692 −2.02893
\(680\) 6.33119 0.242790
\(681\) −11.2328 −0.430443
\(682\) −15.8084 −0.605334
\(683\) −12.9178 −0.494287 −0.247144 0.968979i \(-0.579492\pi\)
−0.247144 + 0.968979i \(0.579492\pi\)
\(684\) −6.82861 −0.261099
\(685\) 1.03381 0.0394998
\(686\) 6.00209 0.229161
\(687\) 18.5995 0.709617
\(688\) −2.83884 −0.108230
\(689\) −43.2569 −1.64796
\(690\) −10.7263 −0.408342
\(691\) 24.6577 0.938022 0.469011 0.883192i \(-0.344610\pi\)
0.469011 + 0.883192i \(0.344610\pi\)
\(692\) −8.62140 −0.327736
\(693\) 9.72116 0.369277
\(694\) 8.34036 0.316596
\(695\) 1.19908 0.0454838
\(696\) −11.1232 −0.421624
\(697\) −20.1696 −0.763978
\(698\) −2.91112 −0.110187
\(699\) −8.83772 −0.334273
\(700\) 3.50539 0.132491
\(701\) 13.8211 0.522017 0.261009 0.965336i \(-0.415945\pi\)
0.261009 + 0.965336i \(0.415945\pi\)
\(702\) −36.8524 −1.39090
\(703\) −14.1488 −0.533632
\(704\) −1.86568 −0.0703154
\(705\) −10.6130 −0.399709
\(706\) 31.4044 1.18192
\(707\) 25.3137 0.952019
\(708\) −6.67935 −0.251025
\(709\) 33.3561 1.25272 0.626358 0.779536i \(-0.284545\pi\)
0.626358 + 0.779536i \(0.284545\pi\)
\(710\) −0.782381 −0.0293622
\(711\) 12.0209 0.450817
\(712\) 11.8551 0.444290
\(713\) 73.8751 2.76664
\(714\) −27.3038 −1.02182
\(715\) −12.4566 −0.465851
\(716\) −12.5525 −0.469108
\(717\) 11.5744 0.432253
\(718\) 15.7995 0.589632
\(719\) 34.6507 1.29225 0.646126 0.763231i \(-0.276388\pi\)
0.646126 + 0.763231i \(0.276388\pi\)
\(720\) 1.48643 0.0553961
\(721\) −27.0017 −1.00560
\(722\) −2.10448 −0.0783205
\(723\) −22.6267 −0.841496
\(724\) 15.6152 0.580334
\(725\) 9.04127 0.335784
\(726\) 9.25071 0.343326
\(727\) 43.9121 1.62861 0.814305 0.580438i \(-0.197118\pi\)
0.814305 + 0.580438i \(0.197118\pi\)
\(728\) 23.4045 0.867429
\(729\) 23.8368 0.882843
\(730\) −1.86149 −0.0688969
\(731\) −17.9732 −0.664764
\(732\) −5.39718 −0.199486
\(733\) −28.7870 −1.06327 −0.531635 0.846973i \(-0.678422\pi\)
−0.531635 + 0.846973i \(0.678422\pi\)
\(734\) 10.9877 0.405564
\(735\) −6.50537 −0.239954
\(736\) 8.71861 0.321372
\(737\) −4.24304 −0.156294
\(738\) −4.73541 −0.174313
\(739\) −27.5448 −1.01325 −0.506626 0.862166i \(-0.669107\pi\)
−0.506626 + 0.862166i \(0.669107\pi\)
\(740\) 3.07987 0.113218
\(741\) −37.7356 −1.38625
\(742\) −22.7106 −0.833732
\(743\) −0.848185 −0.0311169 −0.0155584 0.999879i \(-0.504953\pi\)
−0.0155584 + 0.999879i \(0.504953\pi\)
\(744\) 10.4244 0.382177
\(745\) −3.22469 −0.118144
\(746\) 11.7560 0.430417
\(747\) 23.6172 0.864107
\(748\) −11.8120 −0.431888
\(749\) −2.02214 −0.0738874
\(750\) 1.23027 0.0449232
\(751\) −50.2099 −1.83218 −0.916092 0.400967i \(-0.868674\pi\)
−0.916092 + 0.400967i \(0.868674\pi\)
\(752\) 8.62657 0.314578
\(753\) −0.0367232 −0.00133827
\(754\) 60.3661 2.19840
\(755\) 8.09195 0.294496
\(756\) −19.3481 −0.703683
\(757\) 19.6196 0.713087 0.356544 0.934279i \(-0.383955\pi\)
0.356544 + 0.934279i \(0.383955\pi\)
\(758\) 8.20803 0.298129
\(759\) 20.0118 0.726381
\(760\) 4.59396 0.166640
\(761\) −23.5857 −0.854981 −0.427490 0.904020i \(-0.640602\pi\)
−0.427490 + 0.904020i \(0.640602\pi\)
\(762\) −4.14283 −0.150079
\(763\) −70.5240 −2.55314
\(764\) 13.2113 0.477970
\(765\) 9.41089 0.340251
\(766\) −6.79756 −0.245606
\(767\) 36.2491 1.30888
\(768\) 1.23027 0.0443936
\(769\) 36.8895 1.33027 0.665134 0.746724i \(-0.268374\pi\)
0.665134 + 0.746724i \(0.268374\pi\)
\(770\) −6.53993 −0.235683
\(771\) −21.3874 −0.770248
\(772\) −21.5214 −0.774572
\(773\) −14.4421 −0.519445 −0.259722 0.965683i \(-0.583631\pi\)
−0.259722 + 0.965683i \(0.583631\pi\)
\(774\) −4.21975 −0.151676
\(775\) −8.47326 −0.304369
\(776\) 15.0823 0.541422
\(777\) −13.2822 −0.476495
\(778\) 15.0416 0.539269
\(779\) −14.6352 −0.524361
\(780\) 8.21418 0.294115
\(781\) 1.45967 0.0522311
\(782\) 55.1992 1.97392
\(783\) −49.9035 −1.78341
\(784\) 5.28775 0.188848
\(785\) −9.24673 −0.330030
\(786\) −2.79822 −0.0998092
\(787\) 53.8269 1.91872 0.959360 0.282184i \(-0.0910590\pi\)
0.959360 + 0.282184i \(0.0910590\pi\)
\(788\) −13.5788 −0.483726
\(789\) −2.08544 −0.0742438
\(790\) −8.08705 −0.287724
\(791\) 25.0059 0.889109
\(792\) −2.77321 −0.0985416
\(793\) 29.2907 1.04014
\(794\) 15.9858 0.567317
\(795\) −7.97063 −0.282689
\(796\) −9.76276 −0.346032
\(797\) −27.4417 −0.972036 −0.486018 0.873949i \(-0.661551\pi\)
−0.486018 + 0.873949i \(0.661551\pi\)
\(798\) −19.8118 −0.701331
\(799\) 54.6164 1.93219
\(800\) −1.00000 −0.0353553
\(801\) 17.6219 0.622638
\(802\) 1.00000 0.0353112
\(803\) 3.47295 0.122558
\(804\) 2.79796 0.0986764
\(805\) 30.5621 1.07717
\(806\) −56.5736 −1.99272
\(807\) 33.0364 1.16294
\(808\) −7.22136 −0.254047
\(809\) 52.0779 1.83096 0.915480 0.402363i \(-0.131811\pi\)
0.915480 + 0.402363i \(0.131811\pi\)
\(810\) −2.33122 −0.0819107
\(811\) 54.4632 1.91246 0.956231 0.292611i \(-0.0945242\pi\)
0.956231 + 0.292611i \(0.0945242\pi\)
\(812\) 31.6932 1.11221
\(813\) 30.3846 1.06563
\(814\) −5.74604 −0.201399
\(815\) 3.93017 0.137668
\(816\) 7.78908 0.272672
\(817\) −13.0415 −0.456265
\(818\) −32.7944 −1.14663
\(819\) 34.7892 1.21563
\(820\) 3.18575 0.111251
\(821\) −35.7966 −1.24931 −0.624655 0.780901i \(-0.714760\pi\)
−0.624655 + 0.780901i \(0.714760\pi\)
\(822\) 1.27186 0.0443613
\(823\) 39.5956 1.38022 0.690108 0.723706i \(-0.257563\pi\)
0.690108 + 0.723706i \(0.257563\pi\)
\(824\) 7.70292 0.268344
\(825\) −2.29529 −0.0799118
\(826\) 19.0314 0.662186
\(827\) −44.2405 −1.53839 −0.769197 0.639011i \(-0.779344\pi\)
−0.769197 + 0.639011i \(0.779344\pi\)
\(828\) 12.9596 0.450378
\(829\) −48.5432 −1.68597 −0.842987 0.537934i \(-0.819205\pi\)
−0.842987 + 0.537934i \(0.819205\pi\)
\(830\) −15.8885 −0.551498
\(831\) −31.2005 −1.08233
\(832\) −6.67672 −0.231474
\(833\) 33.4778 1.15994
\(834\) 1.47520 0.0510819
\(835\) −17.6116 −0.609476
\(836\) −8.57085 −0.296429
\(837\) 46.7684 1.61655
\(838\) 20.1649 0.696586
\(839\) −4.76663 −0.164562 −0.0822812 0.996609i \(-0.526221\pi\)
−0.0822812 + 0.996609i \(0.526221\pi\)
\(840\) 4.31258 0.148798
\(841\) 52.7445 1.81878
\(842\) 25.9559 0.894501
\(843\) 15.3056 0.527154
\(844\) 0.164687 0.00566875
\(845\) −31.5786 −1.08634
\(846\) 12.8228 0.440857
\(847\) −26.3579 −0.905667
\(848\) 6.47876 0.222482
\(849\) −20.3750 −0.699267
\(850\) −6.33119 −0.217158
\(851\) 26.8522 0.920481
\(852\) −0.962541 −0.0329761
\(853\) −1.64798 −0.0564258 −0.0282129 0.999602i \(-0.508982\pi\)
−0.0282129 + 0.999602i \(0.508982\pi\)
\(854\) 15.3781 0.526227
\(855\) 6.82861 0.233534
\(856\) 0.576866 0.0197169
\(857\) −2.42222 −0.0827414 −0.0413707 0.999144i \(-0.513172\pi\)
−0.0413707 + 0.999144i \(0.513172\pi\)
\(858\) −15.3250 −0.523188
\(859\) −23.4226 −0.799170 −0.399585 0.916696i \(-0.630846\pi\)
−0.399585 + 0.916696i \(0.630846\pi\)
\(860\) 2.83884 0.0968037
\(861\) −13.7388 −0.468217
\(862\) −11.7637 −0.400675
\(863\) 47.6593 1.62234 0.811171 0.584809i \(-0.198830\pi\)
0.811171 + 0.584809i \(0.198830\pi\)
\(864\) 5.51953 0.187778
\(865\) 8.62140 0.293136
\(866\) 19.7689 0.671775
\(867\) 28.3995 0.964499
\(868\) −29.7021 −1.00815
\(869\) 15.0878 0.511820
\(870\) 11.1232 0.377112
\(871\) −15.1846 −0.514511
\(872\) 20.1187 0.681306
\(873\) 22.4188 0.758760
\(874\) 40.0530 1.35481
\(875\) −3.50539 −0.118504
\(876\) −2.29014 −0.0773767
\(877\) 50.6235 1.70944 0.854718 0.519093i \(-0.173730\pi\)
0.854718 + 0.519093i \(0.173730\pi\)
\(878\) 1.15129 0.0388542
\(879\) 4.73639 0.159754
\(880\) 1.86568 0.0628920
\(881\) −4.73175 −0.159417 −0.0797084 0.996818i \(-0.525399\pi\)
−0.0797084 + 0.996818i \(0.525399\pi\)
\(882\) 7.85989 0.264656
\(883\) −5.98415 −0.201383 −0.100691 0.994918i \(-0.532105\pi\)
−0.100691 + 0.994918i \(0.532105\pi\)
\(884\) −42.2716 −1.42175
\(885\) 6.67935 0.224524
\(886\) −24.9362 −0.837747
\(887\) −33.5805 −1.12752 −0.563762 0.825937i \(-0.690646\pi\)
−0.563762 + 0.825937i \(0.690646\pi\)
\(888\) 3.78907 0.127153
\(889\) 11.8041 0.395896
\(890\) −11.8551 −0.397385
\(891\) 4.34931 0.145707
\(892\) 22.9746 0.769247
\(893\) 39.6301 1.32617
\(894\) −3.96724 −0.132685
\(895\) 12.5525 0.419583
\(896\) −3.50539 −0.117107
\(897\) 71.6163 2.39120
\(898\) −4.63346 −0.154621
\(899\) −76.6090 −2.55505
\(900\) −1.48643 −0.0495478
\(901\) 41.0183 1.36652
\(902\) −5.94359 −0.197900
\(903\) −12.2427 −0.407412
\(904\) −7.13357 −0.237259
\(905\) −15.6152 −0.519066
\(906\) 9.95530 0.330743
\(907\) 12.2532 0.406862 0.203431 0.979089i \(-0.434791\pi\)
0.203431 + 0.979089i \(0.434791\pi\)
\(908\) −9.13036 −0.303002
\(909\) −10.7341 −0.356027
\(910\) −23.4045 −0.775852
\(911\) 53.0914 1.75900 0.879499 0.475901i \(-0.157878\pi\)
0.879499 + 0.475901i \(0.157878\pi\)
\(912\) 5.65182 0.187150
\(913\) 29.6428 0.981034
\(914\) −39.7724 −1.31556
\(915\) 5.39718 0.178425
\(916\) 15.1182 0.499521
\(917\) 7.97292 0.263289
\(918\) 34.9452 1.15336
\(919\) 14.2286 0.469357 0.234678 0.972073i \(-0.424596\pi\)
0.234678 + 0.972073i \(0.424596\pi\)
\(920\) −8.71861 −0.287444
\(921\) −25.9788 −0.856032
\(922\) −17.5872 −0.579203
\(923\) 5.22374 0.171942
\(924\) −8.04589 −0.264690
\(925\) −3.07987 −0.101265
\(926\) −7.95209 −0.261322
\(927\) 11.4499 0.376063
\(928\) −9.04127 −0.296794
\(929\) 31.1373 1.02158 0.510790 0.859705i \(-0.329353\pi\)
0.510790 + 0.859705i \(0.329353\pi\)
\(930\) −10.4244 −0.341830
\(931\) 24.2917 0.796129
\(932\) −7.18355 −0.235305
\(933\) 22.1118 0.723908
\(934\) 19.3310 0.632531
\(935\) 11.8120 0.386293
\(936\) −9.92450 −0.324392
\(937\) 0.167810 0.00548210 0.00274105 0.999996i \(-0.499127\pi\)
0.00274105 + 0.999996i \(0.499127\pi\)
\(938\) −7.97217 −0.260301
\(939\) 33.1413 1.08153
\(940\) −8.62657 −0.281368
\(941\) −0.306413 −0.00998878 −0.00499439 0.999988i \(-0.501590\pi\)
−0.00499439 + 0.999988i \(0.501590\pi\)
\(942\) −11.3760 −0.370650
\(943\) 27.7753 0.904490
\(944\) −5.42917 −0.176704
\(945\) 19.3481 0.629394
\(946\) −5.29636 −0.172200
\(947\) −50.7816 −1.65018 −0.825091 0.565000i \(-0.808876\pi\)
−0.825091 + 0.565000i \(0.808876\pi\)
\(948\) −9.94927 −0.323137
\(949\) 12.4287 0.403452
\(950\) −4.59396 −0.149048
\(951\) 10.6060 0.343923
\(952\) −22.1933 −0.719288
\(953\) 37.2224 1.20575 0.602876 0.797835i \(-0.294021\pi\)
0.602876 + 0.797835i \(0.294021\pi\)
\(954\) 9.63024 0.311791
\(955\) −13.2113 −0.427509
\(956\) 9.40800 0.304276
\(957\) −20.7523 −0.670828
\(958\) −23.6652 −0.764588
\(959\) −3.62390 −0.117022
\(960\) −1.23027 −0.0397068
\(961\) 40.7962 1.31601
\(962\) −20.5634 −0.662991
\(963\) 0.857473 0.0276317
\(964\) −18.3916 −0.592355
\(965\) 21.5214 0.692799
\(966\) 37.5997 1.20975
\(967\) 47.0212 1.51210 0.756050 0.654513i \(-0.227126\pi\)
0.756050 + 0.654513i \(0.227126\pi\)
\(968\) 7.51924 0.241678
\(969\) 35.7827 1.14951
\(970\) −15.0823 −0.484262
\(971\) −12.4900 −0.400824 −0.200412 0.979712i \(-0.564228\pi\)
−0.200412 + 0.979712i \(0.564228\pi\)
\(972\) 13.6906 0.439125
\(973\) −4.20325 −0.134750
\(974\) 23.8703 0.764854
\(975\) −8.21418 −0.263064
\(976\) −4.38698 −0.140424
\(977\) −7.95194 −0.254405 −0.127202 0.991877i \(-0.540600\pi\)
−0.127202 + 0.991877i \(0.540600\pi\)
\(978\) 4.83517 0.154612
\(979\) 22.1179 0.706890
\(980\) −5.28775 −0.168911
\(981\) 29.9051 0.954798
\(982\) −0.223451 −0.00713060
\(983\) 16.9641 0.541071 0.270535 0.962710i \(-0.412799\pi\)
0.270535 + 0.962710i \(0.412799\pi\)
\(984\) 3.91934 0.124944
\(985\) 13.5788 0.432658
\(986\) −57.2420 −1.82296
\(987\) 37.2027 1.18418
\(988\) −30.6726 −0.975826
\(989\) 24.7508 0.787028
\(990\) 2.77321 0.0881383
\(991\) 44.8176 1.42368 0.711839 0.702342i \(-0.247862\pi\)
0.711839 + 0.702342i \(0.247862\pi\)
\(992\) 8.47326 0.269026
\(993\) −23.8093 −0.755567
\(994\) 2.74255 0.0869884
\(995\) 9.76276 0.309500
\(996\) −19.5472 −0.619375
\(997\) −38.1285 −1.20754 −0.603771 0.797158i \(-0.706336\pi\)
−0.603771 + 0.797158i \(0.706336\pi\)
\(998\) 6.97246 0.220709
\(999\) 16.9994 0.537838
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 \(a_p\))