Properties

Label 8015.2.a.l.1.50
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 1.50
Character \(\chi\) = 8015.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.88899 q^{2} +0.0315486 q^{3} +1.56827 q^{4} -1.00000 q^{5} +0.0595948 q^{6} -1.00000 q^{7} -0.815535 q^{8} -2.99900 q^{9} +O(q^{10})\) \(q+1.88899 q^{2} +0.0315486 q^{3} +1.56827 q^{4} -1.00000 q^{5} +0.0595948 q^{6} -1.00000 q^{7} -0.815535 q^{8} -2.99900 q^{9} -1.88899 q^{10} +4.01229 q^{11} +0.0494767 q^{12} +2.50308 q^{13} -1.88899 q^{14} -0.0315486 q^{15} -4.67707 q^{16} -3.17133 q^{17} -5.66508 q^{18} +3.46368 q^{19} -1.56827 q^{20} -0.0315486 q^{21} +7.57915 q^{22} +4.68922 q^{23} -0.0257290 q^{24} +1.00000 q^{25} +4.72827 q^{26} -0.189260 q^{27} -1.56827 q^{28} -1.42042 q^{29} -0.0595948 q^{30} -5.08502 q^{31} -7.20385 q^{32} +0.126582 q^{33} -5.99060 q^{34} +1.00000 q^{35} -4.70324 q^{36} +10.0009 q^{37} +6.54285 q^{38} +0.0789685 q^{39} +0.815535 q^{40} -2.20842 q^{41} -0.0595948 q^{42} -9.76821 q^{43} +6.29234 q^{44} +2.99900 q^{45} +8.85786 q^{46} +11.5894 q^{47} -0.147555 q^{48} +1.00000 q^{49} +1.88899 q^{50} -0.100051 q^{51} +3.92549 q^{52} -6.36751 q^{53} -0.357510 q^{54} -4.01229 q^{55} +0.815535 q^{56} +0.109274 q^{57} -2.68315 q^{58} -6.06626 q^{59} -0.0494767 q^{60} +5.01200 q^{61} -9.60552 q^{62} +2.99900 q^{63} -4.25383 q^{64} -2.50308 q^{65} +0.239112 q^{66} -0.732304 q^{67} -4.97350 q^{68} +0.147938 q^{69} +1.88899 q^{70} +4.73138 q^{71} +2.44579 q^{72} -9.03085 q^{73} +18.8915 q^{74} +0.0315486 q^{75} +5.43199 q^{76} -4.01229 q^{77} +0.149170 q^{78} +8.75647 q^{79} +4.67707 q^{80} +8.99104 q^{81} -4.17167 q^{82} +15.2253 q^{83} -0.0494767 q^{84} +3.17133 q^{85} -18.4520 q^{86} -0.0448122 q^{87} -3.27216 q^{88} -1.80560 q^{89} +5.66508 q^{90} -2.50308 q^{91} +7.35395 q^{92} -0.160425 q^{93} +21.8922 q^{94} -3.46368 q^{95} -0.227271 q^{96} +13.5165 q^{97} +1.88899 q^{98} -12.0329 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} + O(q^{10}) \) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} - 2q^{10} - 13q^{11} + 37q^{12} + 31q^{13} - 2q^{14} - 11q^{15} + 64q^{16} + 30q^{17} + 18q^{18} + 20q^{19} - 64q^{20} - 11q^{21} + 7q^{22} + 29q^{24} + 62q^{25} + 59q^{27} - 64q^{28} - 29q^{29} - 3q^{30} + 20q^{31} + 22q^{32} + 72q^{33} + 13q^{34} + 62q^{35} + 53q^{36} + 35q^{37} + 34q^{38} - 6q^{39} - 15q^{40} + 13q^{41} - 3q^{42} - 4q^{43} - 44q^{44} - 69q^{45} - 19q^{46} + 58q^{47} + 64q^{48} + 62q^{49} + 2q^{50} - 30q^{51} + 82q^{52} + 18q^{53} + 22q^{54} + 13q^{55} - 15q^{56} + 21q^{57} + 18q^{58} - 11q^{59} - 37q^{60} + 24q^{61} + 48q^{62} - 69q^{63} + 65q^{64} - 31q^{65} + 25q^{66} - 6q^{67} + 65q^{68} + 27q^{69} + 2q^{70} - 35q^{71} + 53q^{72} + 116q^{73} - 69q^{74} + 11q^{75} + 65q^{76} + 13q^{77} + 102q^{78} - 83q^{79} - 64q^{80} + 126q^{81} + 71q^{82} + 84q^{83} - 37q^{84} - 30q^{85} + 24q^{86} + 49q^{87} + 20q^{88} - 16q^{89} - 18q^{90} - 31q^{91} + 19q^{92} + 65q^{93} + 54q^{94} - 20q^{95} + 17q^{96} + 155q^{97} + 2q^{98} + 6q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.88899 1.33571 0.667857 0.744289i \(-0.267212\pi\)
0.667857 + 0.744289i \(0.267212\pi\)
\(3\) 0.0315486 0.0182146 0.00910729 0.999959i \(-0.497101\pi\)
0.00910729 + 0.999959i \(0.497101\pi\)
\(4\) 1.56827 0.784134
\(5\) −1.00000 −0.447214
\(6\) 0.0595948 0.0243295
\(7\) −1.00000 −0.377964
\(8\) −0.815535 −0.288335
\(9\) −2.99900 −0.999668
\(10\) −1.88899 −0.597350
\(11\) 4.01229 1.20975 0.604875 0.796320i \(-0.293223\pi\)
0.604875 + 0.796320i \(0.293223\pi\)
\(12\) 0.0494767 0.0142827
\(13\) 2.50308 0.694228 0.347114 0.937823i \(-0.387162\pi\)
0.347114 + 0.937823i \(0.387162\pi\)
\(14\) −1.88899 −0.504853
\(15\) −0.0315486 −0.00814581
\(16\) −4.67707 −1.16927
\(17\) −3.17133 −0.769161 −0.384581 0.923091i \(-0.625654\pi\)
−0.384581 + 0.923091i \(0.625654\pi\)
\(18\) −5.66508 −1.33527
\(19\) 3.46368 0.794624 0.397312 0.917684i \(-0.369943\pi\)
0.397312 + 0.917684i \(0.369943\pi\)
\(20\) −1.56827 −0.350675
\(21\) −0.0315486 −0.00688447
\(22\) 7.57915 1.61588
\(23\) 4.68922 0.977769 0.488885 0.872348i \(-0.337404\pi\)
0.488885 + 0.872348i \(0.337404\pi\)
\(24\) −0.0257290 −0.00525191
\(25\) 1.00000 0.200000
\(26\) 4.72827 0.927291
\(27\) −0.189260 −0.0364231
\(28\) −1.56827 −0.296375
\(29\) −1.42042 −0.263765 −0.131882 0.991265i \(-0.542102\pi\)
−0.131882 + 0.991265i \(0.542102\pi\)
\(30\) −0.0595948 −0.0108805
\(31\) −5.08502 −0.913296 −0.456648 0.889647i \(-0.650950\pi\)
−0.456648 + 0.889647i \(0.650950\pi\)
\(32\) −7.20385 −1.27347
\(33\) 0.126582 0.0220351
\(34\) −5.99060 −1.02738
\(35\) 1.00000 0.169031
\(36\) −4.70324 −0.783874
\(37\) 10.0009 1.64413 0.822065 0.569393i \(-0.192822\pi\)
0.822065 + 0.569393i \(0.192822\pi\)
\(38\) 6.54285 1.06139
\(39\) 0.0789685 0.0126451
\(40\) 0.815535 0.128947
\(41\) −2.20842 −0.344897 −0.172448 0.985019i \(-0.555168\pi\)
−0.172448 + 0.985019i \(0.555168\pi\)
\(42\) −0.0595948 −0.00919568
\(43\) −9.76821 −1.48964 −0.744819 0.667267i \(-0.767464\pi\)
−0.744819 + 0.667267i \(0.767464\pi\)
\(44\) 6.29234 0.948606
\(45\) 2.99900 0.447065
\(46\) 8.85786 1.30602
\(47\) 11.5894 1.69049 0.845245 0.534379i \(-0.179455\pi\)
0.845245 + 0.534379i \(0.179455\pi\)
\(48\) −0.147555 −0.0212977
\(49\) 1.00000 0.142857
\(50\) 1.88899 0.267143
\(51\) −0.100051 −0.0140100
\(52\) 3.92549 0.544368
\(53\) −6.36751 −0.874645 −0.437322 0.899305i \(-0.644073\pi\)
−0.437322 + 0.899305i \(0.644073\pi\)
\(54\) −0.357510 −0.0486509
\(55\) −4.01229 −0.541017
\(56\) 0.815535 0.108980
\(57\) 0.109274 0.0144737
\(58\) −2.68315 −0.352315
\(59\) −6.06626 −0.789760 −0.394880 0.918733i \(-0.629214\pi\)
−0.394880 + 0.918733i \(0.629214\pi\)
\(60\) −0.0494767 −0.00638741
\(61\) 5.01200 0.641721 0.320860 0.947127i \(-0.396028\pi\)
0.320860 + 0.947127i \(0.396028\pi\)
\(62\) −9.60552 −1.21990
\(63\) 2.99900 0.377839
\(64\) −4.25383 −0.531729
\(65\) −2.50308 −0.310468
\(66\) 0.239112 0.0294326
\(67\) −0.732304 −0.0894652 −0.0447326 0.998999i \(-0.514244\pi\)
−0.0447326 + 0.998999i \(0.514244\pi\)
\(68\) −4.97350 −0.603126
\(69\) 0.147938 0.0178097
\(70\) 1.88899 0.225777
\(71\) 4.73138 0.561511 0.280756 0.959779i \(-0.409415\pi\)
0.280756 + 0.959779i \(0.409415\pi\)
\(72\) 2.44579 0.288240
\(73\) −9.03085 −1.05698 −0.528491 0.848939i \(-0.677242\pi\)
−0.528491 + 0.848939i \(0.677242\pi\)
\(74\) 18.8915 2.19609
\(75\) 0.0315486 0.00364292
\(76\) 5.43199 0.623092
\(77\) −4.01229 −0.457243
\(78\) 0.149170 0.0168902
\(79\) 8.75647 0.985179 0.492590 0.870262i \(-0.336050\pi\)
0.492590 + 0.870262i \(0.336050\pi\)
\(80\) 4.67707 0.522912
\(81\) 8.99104 0.999005
\(82\) −4.17167 −0.460684
\(83\) 15.2253 1.67120 0.835598 0.549342i \(-0.185121\pi\)
0.835598 + 0.549342i \(0.185121\pi\)
\(84\) −0.0494767 −0.00539835
\(85\) 3.17133 0.343979
\(86\) −18.4520 −1.98973
\(87\) −0.0448122 −0.00480437
\(88\) −3.27216 −0.348813
\(89\) −1.80560 −0.191393 −0.0956966 0.995411i \(-0.530508\pi\)
−0.0956966 + 0.995411i \(0.530508\pi\)
\(90\) 5.66508 0.597152
\(91\) −2.50308 −0.262394
\(92\) 7.35395 0.766702
\(93\) −0.160425 −0.0166353
\(94\) 21.8922 2.25801
\(95\) −3.46368 −0.355367
\(96\) −0.227271 −0.0231958
\(97\) 13.5165 1.37239 0.686195 0.727417i \(-0.259280\pi\)
0.686195 + 0.727417i \(0.259280\pi\)
\(98\) 1.88899 0.190816
\(99\) −12.0329 −1.20935
\(100\) 1.56827 0.156827
\(101\) 12.7953 1.27318 0.636588 0.771204i \(-0.280345\pi\)
0.636588 + 0.771204i \(0.280345\pi\)
\(102\) −0.188995 −0.0187133
\(103\) 18.4088 1.81387 0.906937 0.421267i \(-0.138414\pi\)
0.906937 + 0.421267i \(0.138414\pi\)
\(104\) −2.04135 −0.200170
\(105\) 0.0315486 0.00307883
\(106\) −12.0281 −1.16828
\(107\) −10.8279 −1.04678 −0.523389 0.852094i \(-0.675332\pi\)
−0.523389 + 0.852094i \(0.675332\pi\)
\(108\) −0.296811 −0.0285606
\(109\) 9.90433 0.948663 0.474331 0.880346i \(-0.342690\pi\)
0.474331 + 0.880346i \(0.342690\pi\)
\(110\) −7.57915 −0.722644
\(111\) 0.315513 0.0299472
\(112\) 4.67707 0.441942
\(113\) −8.72373 −0.820659 −0.410330 0.911937i \(-0.634586\pi\)
−0.410330 + 0.911937i \(0.634586\pi\)
\(114\) 0.206418 0.0193328
\(115\) −4.68922 −0.437272
\(116\) −2.22760 −0.206827
\(117\) −7.50674 −0.693998
\(118\) −11.4591 −1.05489
\(119\) 3.17133 0.290716
\(120\) 0.0257290 0.00234872
\(121\) 5.09844 0.463495
\(122\) 9.46759 0.857156
\(123\) −0.0696725 −0.00628215
\(124\) −7.97467 −0.716147
\(125\) −1.00000 −0.0894427
\(126\) 5.66508 0.504685
\(127\) 5.66591 0.502768 0.251384 0.967887i \(-0.419114\pi\)
0.251384 + 0.967887i \(0.419114\pi\)
\(128\) 6.37227 0.563234
\(129\) −0.308173 −0.0271331
\(130\) −4.72827 −0.414697
\(131\) 19.3345 1.68926 0.844631 0.535349i \(-0.179820\pi\)
0.844631 + 0.535349i \(0.179820\pi\)
\(132\) 0.198515 0.0172785
\(133\) −3.46368 −0.300340
\(134\) −1.38331 −0.119500
\(135\) 0.189260 0.0162889
\(136\) 2.58633 0.221776
\(137\) 17.1644 1.46646 0.733229 0.679982i \(-0.238012\pi\)
0.733229 + 0.679982i \(0.238012\pi\)
\(138\) 0.279453 0.0237886
\(139\) 12.9681 1.09994 0.549970 0.835185i \(-0.314639\pi\)
0.549970 + 0.835185i \(0.314639\pi\)
\(140\) 1.56827 0.132543
\(141\) 0.365630 0.0307916
\(142\) 8.93751 0.750019
\(143\) 10.0431 0.839843
\(144\) 14.0266 1.16888
\(145\) 1.42042 0.117959
\(146\) −17.0592 −1.41183
\(147\) 0.0315486 0.00260208
\(148\) 15.6840 1.28922
\(149\) 6.61572 0.541981 0.270991 0.962582i \(-0.412649\pi\)
0.270991 + 0.962582i \(0.412649\pi\)
\(150\) 0.0595948 0.00486590
\(151\) 15.5005 1.26141 0.630706 0.776022i \(-0.282765\pi\)
0.630706 + 0.776022i \(0.282765\pi\)
\(152\) −2.82476 −0.229118
\(153\) 9.51084 0.768906
\(154\) −7.57915 −0.610746
\(155\) 5.08502 0.408438
\(156\) 0.123844 0.00991544
\(157\) 2.15806 0.172232 0.0861160 0.996285i \(-0.472554\pi\)
0.0861160 + 0.996285i \(0.472554\pi\)
\(158\) 16.5408 1.31592
\(159\) −0.200886 −0.0159313
\(160\) 7.20385 0.569515
\(161\) −4.68922 −0.369562
\(162\) 16.9840 1.33439
\(163\) −12.9903 −1.01748 −0.508739 0.860921i \(-0.669888\pi\)
−0.508739 + 0.860921i \(0.669888\pi\)
\(164\) −3.46339 −0.270445
\(165\) −0.126582 −0.00985439
\(166\) 28.7604 2.23224
\(167\) −18.5483 −1.43531 −0.717655 0.696399i \(-0.754785\pi\)
−0.717655 + 0.696399i \(0.754785\pi\)
\(168\) 0.0257290 0.00198503
\(169\) −6.73461 −0.518047
\(170\) 5.99060 0.459458
\(171\) −10.3876 −0.794360
\(172\) −15.3192 −1.16808
\(173\) 3.65932 0.278213 0.139106 0.990277i \(-0.455577\pi\)
0.139106 + 0.990277i \(0.455577\pi\)
\(174\) −0.0846496 −0.00641727
\(175\) −1.00000 −0.0755929
\(176\) −18.7658 −1.41452
\(177\) −0.191382 −0.0143851
\(178\) −3.41075 −0.255647
\(179\) 21.9680 1.64197 0.820983 0.570953i \(-0.193426\pi\)
0.820983 + 0.570953i \(0.193426\pi\)
\(180\) 4.70324 0.350559
\(181\) −16.9779 −1.26195 −0.630977 0.775801i \(-0.717346\pi\)
−0.630977 + 0.775801i \(0.717346\pi\)
\(182\) −4.72827 −0.350483
\(183\) 0.158121 0.0116887
\(184\) −3.82422 −0.281925
\(185\) −10.0009 −0.735278
\(186\) −0.303041 −0.0222200
\(187\) −12.7243 −0.930493
\(188\) 18.1753 1.32557
\(189\) 0.189260 0.0137666
\(190\) −6.54285 −0.474668
\(191\) 14.9220 1.07972 0.539858 0.841756i \(-0.318478\pi\)
0.539858 + 0.841756i \(0.318478\pi\)
\(192\) −0.134202 −0.00968523
\(193\) −3.99218 −0.287364 −0.143682 0.989624i \(-0.545894\pi\)
−0.143682 + 0.989624i \(0.545894\pi\)
\(194\) 25.5324 1.83312
\(195\) −0.0789685 −0.00565505
\(196\) 1.56827 0.112019
\(197\) 16.7388 1.19259 0.596296 0.802765i \(-0.296639\pi\)
0.596296 + 0.802765i \(0.296639\pi\)
\(198\) −22.7299 −1.61534
\(199\) 0.831093 0.0589146 0.0294573 0.999566i \(-0.490622\pi\)
0.0294573 + 0.999566i \(0.490622\pi\)
\(200\) −0.815535 −0.0576670
\(201\) −0.0231032 −0.00162957
\(202\) 24.1701 1.70060
\(203\) 1.42042 0.0996938
\(204\) −0.156907 −0.0109857
\(205\) 2.20842 0.154243
\(206\) 34.7740 2.42282
\(207\) −14.0630 −0.977445
\(208\) −11.7071 −0.811739
\(209\) 13.8973 0.961296
\(210\) 0.0595948 0.00411244
\(211\) −1.82089 −0.125355 −0.0626775 0.998034i \(-0.519964\pi\)
−0.0626775 + 0.998034i \(0.519964\pi\)
\(212\) −9.98597 −0.685839
\(213\) 0.149268 0.0102277
\(214\) −20.4538 −1.39820
\(215\) 9.76821 0.666186
\(216\) 0.154348 0.0105021
\(217\) 5.08502 0.345193
\(218\) 18.7091 1.26714
\(219\) −0.284911 −0.0192525
\(220\) −6.29234 −0.424230
\(221\) −7.93808 −0.533973
\(222\) 0.596000 0.0400009
\(223\) 20.3774 1.36457 0.682285 0.731086i \(-0.260986\pi\)
0.682285 + 0.731086i \(0.260986\pi\)
\(224\) 7.20385 0.481328
\(225\) −2.99900 −0.199934
\(226\) −16.4790 −1.09617
\(227\) 11.0181 0.731296 0.365648 0.930753i \(-0.380847\pi\)
0.365648 + 0.930753i \(0.380847\pi\)
\(228\) 0.171372 0.0113494
\(229\) 1.00000 0.0660819
\(230\) −8.85786 −0.584070
\(231\) −0.126582 −0.00832848
\(232\) 1.15840 0.0760527
\(233\) −13.7735 −0.902333 −0.451166 0.892440i \(-0.648992\pi\)
−0.451166 + 0.892440i \(0.648992\pi\)
\(234\) −14.1801 −0.926983
\(235\) −11.5894 −0.756010
\(236\) −9.51352 −0.619278
\(237\) 0.276254 0.0179446
\(238\) 5.99060 0.388313
\(239\) −4.00164 −0.258844 −0.129422 0.991590i \(-0.541312\pi\)
−0.129422 + 0.991590i \(0.541312\pi\)
\(240\) 0.147555 0.00952463
\(241\) 4.08531 0.263158 0.131579 0.991306i \(-0.457995\pi\)
0.131579 + 0.991306i \(0.457995\pi\)
\(242\) 9.63089 0.619097
\(243\) 0.851435 0.0546196
\(244\) 7.86016 0.503195
\(245\) −1.00000 −0.0638877
\(246\) −0.131610 −0.00839117
\(247\) 8.66986 0.551650
\(248\) 4.14701 0.263335
\(249\) 0.480337 0.0304401
\(250\) −1.88899 −0.119470
\(251\) −3.77584 −0.238329 −0.119164 0.992875i \(-0.538022\pi\)
−0.119164 + 0.992875i \(0.538022\pi\)
\(252\) 4.70324 0.296277
\(253\) 18.8145 1.18286
\(254\) 10.7028 0.671555
\(255\) 0.100051 0.00626544
\(256\) 20.5448 1.28405
\(257\) −1.13302 −0.0706758 −0.0353379 0.999375i \(-0.511251\pi\)
−0.0353379 + 0.999375i \(0.511251\pi\)
\(258\) −0.582135 −0.0362421
\(259\) −10.0009 −0.621423
\(260\) −3.92549 −0.243449
\(261\) 4.25984 0.263677
\(262\) 36.5226 2.25637
\(263\) −2.19881 −0.135584 −0.0677922 0.997699i \(-0.521595\pi\)
−0.0677922 + 0.997699i \(0.521595\pi\)
\(264\) −0.103232 −0.00635349
\(265\) 6.36751 0.391153
\(266\) −6.54285 −0.401168
\(267\) −0.0569641 −0.00348615
\(268\) −1.14845 −0.0701527
\(269\) −29.0954 −1.77398 −0.886988 0.461793i \(-0.847206\pi\)
−0.886988 + 0.461793i \(0.847206\pi\)
\(270\) 0.357510 0.0217574
\(271\) −2.02262 −0.122865 −0.0614327 0.998111i \(-0.519567\pi\)
−0.0614327 + 0.998111i \(0.519567\pi\)
\(272\) 14.8325 0.899355
\(273\) −0.0789685 −0.00477939
\(274\) 32.4234 1.95877
\(275\) 4.01229 0.241950
\(276\) 0.232007 0.0139652
\(277\) 17.1471 1.03027 0.515134 0.857110i \(-0.327742\pi\)
0.515134 + 0.857110i \(0.327742\pi\)
\(278\) 24.4966 1.46921
\(279\) 15.2500 0.912993
\(280\) −0.815535 −0.0487375
\(281\) −0.385523 −0.0229984 −0.0114992 0.999934i \(-0.503660\pi\)
−0.0114992 + 0.999934i \(0.503660\pi\)
\(282\) 0.690669 0.0411288
\(283\) 7.80331 0.463859 0.231929 0.972733i \(-0.425496\pi\)
0.231929 + 0.972733i \(0.425496\pi\)
\(284\) 7.42007 0.440300
\(285\) −0.109274 −0.00647285
\(286\) 18.9712 1.12179
\(287\) 2.20842 0.130359
\(288\) 21.6044 1.27305
\(289\) −6.94265 −0.408391
\(290\) 2.68315 0.157560
\(291\) 0.426426 0.0249975
\(292\) −14.1628 −0.828815
\(293\) −0.0911613 −0.00532570 −0.00266285 0.999996i \(-0.500848\pi\)
−0.00266285 + 0.999996i \(0.500848\pi\)
\(294\) 0.0595948 0.00347564
\(295\) 6.06626 0.353191
\(296\) −8.15605 −0.474061
\(297\) −0.759366 −0.0440629
\(298\) 12.4970 0.723932
\(299\) 11.7375 0.678795
\(300\) 0.0494767 0.00285654
\(301\) 9.76821 0.563030
\(302\) 29.2802 1.68489
\(303\) 0.403672 0.0231904
\(304\) −16.1999 −0.929128
\(305\) −5.01200 −0.286986
\(306\) 17.9658 1.02704
\(307\) 15.8747 0.906018 0.453009 0.891506i \(-0.350351\pi\)
0.453009 + 0.891506i \(0.350351\pi\)
\(308\) −6.29234 −0.358539
\(309\) 0.580772 0.0330390
\(310\) 9.60552 0.545557
\(311\) −29.8891 −1.69485 −0.847427 0.530912i \(-0.821849\pi\)
−0.847427 + 0.530912i \(0.821849\pi\)
\(312\) −0.0644016 −0.00364602
\(313\) −20.1835 −1.14084 −0.570418 0.821354i \(-0.693219\pi\)
−0.570418 + 0.821354i \(0.693219\pi\)
\(314\) 4.07655 0.230053
\(315\) −2.99900 −0.168975
\(316\) 13.7325 0.772513
\(317\) −35.2914 −1.98216 −0.991082 0.133252i \(-0.957458\pi\)
−0.991082 + 0.133252i \(0.957458\pi\)
\(318\) −0.379471 −0.0212797
\(319\) −5.69912 −0.319090
\(320\) 4.25383 0.237797
\(321\) −0.341607 −0.0190666
\(322\) −8.85786 −0.493629
\(323\) −10.9845 −0.611194
\(324\) 14.1004 0.783354
\(325\) 2.50308 0.138846
\(326\) −24.5385 −1.35906
\(327\) 0.312468 0.0172795
\(328\) 1.80104 0.0994459
\(329\) −11.5894 −0.638945
\(330\) −0.239112 −0.0131627
\(331\) −14.9929 −0.824086 −0.412043 0.911164i \(-0.635185\pi\)
−0.412043 + 0.911164i \(0.635185\pi\)
\(332\) 23.8774 1.31044
\(333\) −29.9926 −1.64359
\(334\) −35.0375 −1.91716
\(335\) 0.732304 0.0400101
\(336\) 0.147555 0.00804979
\(337\) 0.0172887 0.000941773 0 0.000470887 1.00000i \(-0.499850\pi\)
0.000470887 1.00000i \(0.499850\pi\)
\(338\) −12.7216 −0.691963
\(339\) −0.275221 −0.0149480
\(340\) 4.97350 0.269726
\(341\) −20.4025 −1.10486
\(342\) −19.6220 −1.06104
\(343\) −1.00000 −0.0539949
\(344\) 7.96632 0.429515
\(345\) −0.147938 −0.00796472
\(346\) 6.91240 0.371613
\(347\) −9.93796 −0.533498 −0.266749 0.963766i \(-0.585949\pi\)
−0.266749 + 0.963766i \(0.585949\pi\)
\(348\) −0.0702775 −0.00376727
\(349\) −12.5623 −0.672444 −0.336222 0.941783i \(-0.609149\pi\)
−0.336222 + 0.941783i \(0.609149\pi\)
\(350\) −1.88899 −0.100971
\(351\) −0.473732 −0.0252860
\(352\) −28.9039 −1.54058
\(353\) 20.9123 1.11305 0.556526 0.830830i \(-0.312134\pi\)
0.556526 + 0.830830i \(0.312134\pi\)
\(354\) −0.361518 −0.0192145
\(355\) −4.73138 −0.251116
\(356\) −2.83167 −0.150078
\(357\) 0.100051 0.00529526
\(358\) 41.4973 2.19320
\(359\) −18.3259 −0.967202 −0.483601 0.875288i \(-0.660671\pi\)
−0.483601 + 0.875288i \(0.660671\pi\)
\(360\) −2.44579 −0.128905
\(361\) −7.00289 −0.368573
\(362\) −32.0709 −1.68561
\(363\) 0.160849 0.00844237
\(364\) −3.92549 −0.205752
\(365\) 9.03085 0.472696
\(366\) 0.298689 0.0156127
\(367\) 19.2290 1.00375 0.501873 0.864942i \(-0.332645\pi\)
0.501873 + 0.864942i \(0.332645\pi\)
\(368\) −21.9318 −1.14327
\(369\) 6.62305 0.344782
\(370\) −18.8915 −0.982121
\(371\) 6.36751 0.330585
\(372\) −0.251590 −0.0130443
\(373\) −19.4541 −1.00730 −0.503648 0.863909i \(-0.668009\pi\)
−0.503648 + 0.863909i \(0.668009\pi\)
\(374\) −24.0360 −1.24287
\(375\) −0.0315486 −0.00162916
\(376\) −9.45157 −0.487428
\(377\) −3.55541 −0.183113
\(378\) 0.357510 0.0183883
\(379\) −1.78098 −0.0914828 −0.0457414 0.998953i \(-0.514565\pi\)
−0.0457414 + 0.998953i \(0.514565\pi\)
\(380\) −5.43199 −0.278655
\(381\) 0.178751 0.00915771
\(382\) 28.1874 1.44219
\(383\) −9.78680 −0.500082 −0.250041 0.968235i \(-0.580444\pi\)
−0.250041 + 0.968235i \(0.580444\pi\)
\(384\) 0.201036 0.0102591
\(385\) 4.01229 0.204485
\(386\) −7.54118 −0.383836
\(387\) 29.2949 1.48914
\(388\) 21.1975 1.07614
\(389\) 28.2386 1.43175 0.715876 0.698227i \(-0.246027\pi\)
0.715876 + 0.698227i \(0.246027\pi\)
\(390\) −0.149170 −0.00755354
\(391\) −14.8711 −0.752062
\(392\) −0.815535 −0.0411907
\(393\) 0.609976 0.0307692
\(394\) 31.6194 1.59296
\(395\) −8.75647 −0.440586
\(396\) −18.8708 −0.948292
\(397\) 23.2115 1.16495 0.582477 0.812847i \(-0.302084\pi\)
0.582477 + 0.812847i \(0.302084\pi\)
\(398\) 1.56992 0.0786931
\(399\) −0.109274 −0.00547056
\(400\) −4.67707 −0.233854
\(401\) −30.9902 −1.54758 −0.773788 0.633444i \(-0.781641\pi\)
−0.773788 + 0.633444i \(0.781641\pi\)
\(402\) −0.0436416 −0.00217664
\(403\) −12.7282 −0.634036
\(404\) 20.0664 0.998341
\(405\) −8.99104 −0.446769
\(406\) 2.68315 0.133162
\(407\) 40.1263 1.98899
\(408\) 0.0815952 0.00403956
\(409\) −17.2411 −0.852515 −0.426258 0.904602i \(-0.640168\pi\)
−0.426258 + 0.904602i \(0.640168\pi\)
\(410\) 4.17167 0.206024
\(411\) 0.541514 0.0267109
\(412\) 28.8699 1.42232
\(413\) 6.06626 0.298501
\(414\) −26.5648 −1.30559
\(415\) −15.2253 −0.747381
\(416\) −18.0318 −0.884081
\(417\) 0.409125 0.0200349
\(418\) 26.2518 1.28402
\(419\) 18.2138 0.889802 0.444901 0.895580i \(-0.353239\pi\)
0.444901 + 0.895580i \(0.353239\pi\)
\(420\) 0.0494767 0.00241421
\(421\) 33.5234 1.63383 0.816916 0.576756i \(-0.195682\pi\)
0.816916 + 0.576756i \(0.195682\pi\)
\(422\) −3.43963 −0.167439
\(423\) −34.7567 −1.68993
\(424\) 5.19293 0.252191
\(425\) −3.17133 −0.153832
\(426\) 0.281966 0.0136613
\(427\) −5.01200 −0.242548
\(428\) −16.9811 −0.820814
\(429\) 0.316844 0.0152974
\(430\) 18.4520 0.889835
\(431\) 32.0031 1.54154 0.770768 0.637116i \(-0.219873\pi\)
0.770768 + 0.637116i \(0.219873\pi\)
\(432\) 0.885183 0.0425884
\(433\) −33.3052 −1.60055 −0.800273 0.599636i \(-0.795312\pi\)
−0.800273 + 0.599636i \(0.795312\pi\)
\(434\) 9.60552 0.461080
\(435\) 0.0448122 0.00214858
\(436\) 15.5326 0.743879
\(437\) 16.2420 0.776959
\(438\) −0.538192 −0.0257158
\(439\) 17.7760 0.848401 0.424200 0.905568i \(-0.360555\pi\)
0.424200 + 0.905568i \(0.360555\pi\)
\(440\) 3.27216 0.155994
\(441\) −2.99900 −0.142810
\(442\) −14.9949 −0.713236
\(443\) 2.91859 0.138666 0.0693332 0.997594i \(-0.477913\pi\)
0.0693332 + 0.997594i \(0.477913\pi\)
\(444\) 0.494809 0.0234826
\(445\) 1.80560 0.0855936
\(446\) 38.4926 1.82268
\(447\) 0.208717 0.00987196
\(448\) 4.25383 0.200975
\(449\) −2.05565 −0.0970121 −0.0485060 0.998823i \(-0.515446\pi\)
−0.0485060 + 0.998823i \(0.515446\pi\)
\(450\) −5.66508 −0.267054
\(451\) −8.86080 −0.417239
\(452\) −13.6811 −0.643507
\(453\) 0.489019 0.0229761
\(454\) 20.8130 0.976803
\(455\) 2.50308 0.117346
\(456\) −0.0891171 −0.00417329
\(457\) 7.63978 0.357374 0.178687 0.983906i \(-0.442815\pi\)
0.178687 + 0.983906i \(0.442815\pi\)
\(458\) 1.88899 0.0882665
\(459\) 0.600207 0.0280153
\(460\) −7.35395 −0.342880
\(461\) 24.4139 1.13707 0.568535 0.822659i \(-0.307511\pi\)
0.568535 + 0.822659i \(0.307511\pi\)
\(462\) −0.239112 −0.0111245
\(463\) −28.9533 −1.34557 −0.672786 0.739837i \(-0.734903\pi\)
−0.672786 + 0.739837i \(0.734903\pi\)
\(464\) 6.64339 0.308412
\(465\) 0.160425 0.00743954
\(466\) −26.0180 −1.20526
\(467\) −9.13290 −0.422620 −0.211310 0.977419i \(-0.567773\pi\)
−0.211310 + 0.977419i \(0.567773\pi\)
\(468\) −11.7726 −0.544187
\(469\) 0.732304 0.0338147
\(470\) −21.8922 −1.00981
\(471\) 0.0680838 0.00313714
\(472\) 4.94725 0.227715
\(473\) −39.1929 −1.80209
\(474\) 0.521840 0.0239689
\(475\) 3.46368 0.158925
\(476\) 4.97350 0.227960
\(477\) 19.0962 0.874355
\(478\) −7.55904 −0.345742
\(479\) 8.63929 0.394739 0.197370 0.980329i \(-0.436760\pi\)
0.197370 + 0.980329i \(0.436760\pi\)
\(480\) 0.227271 0.0103735
\(481\) 25.0329 1.14140
\(482\) 7.71709 0.351504
\(483\) −0.147938 −0.00673142
\(484\) 7.99573 0.363442
\(485\) −13.5165 −0.613752
\(486\) 1.60835 0.0729562
\(487\) −6.68985 −0.303146 −0.151573 0.988446i \(-0.548434\pi\)
−0.151573 + 0.988446i \(0.548434\pi\)
\(488\) −4.08746 −0.185031
\(489\) −0.409825 −0.0185329
\(490\) −1.88899 −0.0853357
\(491\) −28.6229 −1.29173 −0.645867 0.763450i \(-0.723504\pi\)
−0.645867 + 0.763450i \(0.723504\pi\)
\(492\) −0.109265 −0.00492605
\(493\) 4.50462 0.202878
\(494\) 16.3773 0.736847
\(495\) 12.0329 0.540837
\(496\) 23.7830 1.06789
\(497\) −4.73138 −0.212231
\(498\) 0.907350 0.0406593
\(499\) −31.8613 −1.42631 −0.713155 0.701007i \(-0.752734\pi\)
−0.713155 + 0.701007i \(0.752734\pi\)
\(500\) −1.56827 −0.0701351
\(501\) −0.585173 −0.0261436
\(502\) −7.13251 −0.318339
\(503\) 39.5390 1.76296 0.881479 0.472224i \(-0.156549\pi\)
0.881479 + 0.472224i \(0.156549\pi\)
\(504\) −2.44579 −0.108944
\(505\) −12.7953 −0.569382
\(506\) 35.5403 1.57996
\(507\) −0.212468 −0.00943602
\(508\) 8.88566 0.394238
\(509\) −22.6328 −1.00318 −0.501590 0.865106i \(-0.667251\pi\)
−0.501590 + 0.865106i \(0.667251\pi\)
\(510\) 0.188995 0.00836884
\(511\) 9.03085 0.399501
\(512\) 26.0643 1.15189
\(513\) −0.655537 −0.0289427
\(514\) −2.14026 −0.0944027
\(515\) −18.4088 −0.811189
\(516\) −0.483298 −0.0212760
\(517\) 46.5000 2.04507
\(518\) −18.8915 −0.830044
\(519\) 0.115446 0.00506753
\(520\) 2.04135 0.0895189
\(521\) 31.2907 1.37087 0.685436 0.728133i \(-0.259612\pi\)
0.685436 + 0.728133i \(0.259612\pi\)
\(522\) 8.04678 0.352198
\(523\) 30.4109 1.32977 0.664887 0.746944i \(-0.268480\pi\)
0.664887 + 0.746944i \(0.268480\pi\)
\(524\) 30.3217 1.32461
\(525\) −0.0315486 −0.00137689
\(526\) −4.15352 −0.181102
\(527\) 16.1263 0.702472
\(528\) −0.592033 −0.0257649
\(529\) −1.01126 −0.0439676
\(530\) 12.0281 0.522469
\(531\) 18.1927 0.789498
\(532\) −5.43199 −0.235507
\(533\) −5.52784 −0.239437
\(534\) −0.107604 −0.00465650
\(535\) 10.8279 0.468133
\(536\) 0.597220 0.0257960
\(537\) 0.693060 0.0299077
\(538\) −54.9607 −2.36953
\(539\) 4.01229 0.172821
\(540\) 0.296811 0.0127727
\(541\) −22.3988 −0.963001 −0.481501 0.876446i \(-0.659908\pi\)
−0.481501 + 0.876446i \(0.659908\pi\)
\(542\) −3.82070 −0.164113
\(543\) −0.535628 −0.0229860
\(544\) 22.8458 0.979506
\(545\) −9.90433 −0.424255
\(546\) −0.149170 −0.00638390
\(547\) −19.6316 −0.839387 −0.419694 0.907666i \(-0.637863\pi\)
−0.419694 + 0.907666i \(0.637863\pi\)
\(548\) 26.9185 1.14990
\(549\) −15.0310 −0.641508
\(550\) 7.57915 0.323176
\(551\) −4.91988 −0.209594
\(552\) −0.120649 −0.00513515
\(553\) −8.75647 −0.372363
\(554\) 32.3906 1.37614
\(555\) −0.315513 −0.0133928
\(556\) 20.3375 0.862500
\(557\) −33.4278 −1.41638 −0.708190 0.706022i \(-0.750488\pi\)
−0.708190 + 0.706022i \(0.750488\pi\)
\(558\) 28.8070 1.21950
\(559\) −24.4506 −1.03415
\(560\) −4.67707 −0.197642
\(561\) −0.401434 −0.0169485
\(562\) −0.728247 −0.0307192
\(563\) −0.512607 −0.0216038 −0.0108019 0.999942i \(-0.503438\pi\)
−0.0108019 + 0.999942i \(0.503438\pi\)
\(564\) 0.573405 0.0241447
\(565\) 8.72373 0.367010
\(566\) 14.7403 0.619583
\(567\) −8.99104 −0.377588
\(568\) −3.85861 −0.161903
\(569\) −32.9188 −1.38003 −0.690014 0.723796i \(-0.742396\pi\)
−0.690014 + 0.723796i \(0.742396\pi\)
\(570\) −0.206418 −0.00864589
\(571\) 4.69982 0.196681 0.0983406 0.995153i \(-0.468647\pi\)
0.0983406 + 0.995153i \(0.468647\pi\)
\(572\) 15.7502 0.658549
\(573\) 0.470767 0.0196666
\(574\) 4.17167 0.174122
\(575\) 4.68922 0.195554
\(576\) 12.7573 0.531553
\(577\) 32.6345 1.35859 0.679296 0.733865i \(-0.262285\pi\)
0.679296 + 0.733865i \(0.262285\pi\)
\(578\) −13.1146 −0.545494
\(579\) −0.125948 −0.00523421
\(580\) 2.22760 0.0924959
\(581\) −15.2253 −0.631653
\(582\) 0.805512 0.0333896
\(583\) −25.5483 −1.05810
\(584\) 7.36498 0.304765
\(585\) 7.50674 0.310365
\(586\) −0.172202 −0.00711362
\(587\) 2.03947 0.0841778 0.0420889 0.999114i \(-0.486599\pi\)
0.0420889 + 0.999114i \(0.486599\pi\)
\(588\) 0.0494767 0.00204038
\(589\) −17.6129 −0.725727
\(590\) 11.4591 0.471763
\(591\) 0.528086 0.0217226
\(592\) −46.7747 −1.92243
\(593\) 14.2347 0.584548 0.292274 0.956335i \(-0.405588\pi\)
0.292274 + 0.956335i \(0.405588\pi\)
\(594\) −1.43443 −0.0588554
\(595\) −3.17133 −0.130012
\(596\) 10.3752 0.424986
\(597\) 0.0262198 0.00107311
\(598\) 22.1719 0.906676
\(599\) 29.3609 1.19965 0.599827 0.800130i \(-0.295236\pi\)
0.599827 + 0.800130i \(0.295236\pi\)
\(600\) −0.0257290 −0.00105038
\(601\) −45.8293 −1.86941 −0.934707 0.355418i \(-0.884338\pi\)
−0.934707 + 0.355418i \(0.884338\pi\)
\(602\) 18.4520 0.752048
\(603\) 2.19618 0.0894355
\(604\) 24.3089 0.989117
\(605\) −5.09844 −0.207281
\(606\) 0.762532 0.0309757
\(607\) 22.4559 0.911459 0.455729 0.890118i \(-0.349378\pi\)
0.455729 + 0.890118i \(0.349378\pi\)
\(608\) −24.9519 −1.01193
\(609\) 0.0448122 0.00181588
\(610\) −9.46759 −0.383332
\(611\) 29.0092 1.17359
\(612\) 14.9156 0.602925
\(613\) −13.9880 −0.564972 −0.282486 0.959271i \(-0.591159\pi\)
−0.282486 + 0.959271i \(0.591159\pi\)
\(614\) 29.9871 1.21018
\(615\) 0.0696725 0.00280946
\(616\) 3.27216 0.131839
\(617\) −32.2400 −1.29793 −0.648967 0.760817i \(-0.724799\pi\)
−0.648967 + 0.760817i \(0.724799\pi\)
\(618\) 1.09707 0.0441306
\(619\) 25.7627 1.03549 0.517745 0.855535i \(-0.326772\pi\)
0.517745 + 0.855535i \(0.326772\pi\)
\(620\) 7.97467 0.320270
\(621\) −0.887482 −0.0356134
\(622\) −56.4600 −2.26384
\(623\) 1.80560 0.0723398
\(624\) −0.369341 −0.0147855
\(625\) 1.00000 0.0400000
\(626\) −38.1263 −1.52383
\(627\) 0.438440 0.0175096
\(628\) 3.38442 0.135053
\(629\) −31.7160 −1.26460
\(630\) −5.66508 −0.225702
\(631\) 0.690217 0.0274771 0.0137385 0.999906i \(-0.495627\pi\)
0.0137385 + 0.999906i \(0.495627\pi\)
\(632\) −7.14120 −0.284062
\(633\) −0.0574464 −0.00228329
\(634\) −66.6650 −2.64761
\(635\) −5.66591 −0.224845
\(636\) −0.315043 −0.0124923
\(637\) 2.50308 0.0991755
\(638\) −10.7656 −0.426213
\(639\) −14.1894 −0.561325
\(640\) −6.37227 −0.251886
\(641\) −19.7692 −0.780835 −0.390417 0.920638i \(-0.627669\pi\)
−0.390417 + 0.920638i \(0.627669\pi\)
\(642\) −0.645290 −0.0254676
\(643\) −12.6906 −0.500467 −0.250233 0.968186i \(-0.580507\pi\)
−0.250233 + 0.968186i \(0.580507\pi\)
\(644\) −7.35395 −0.289786
\(645\) 0.308173 0.0121343
\(646\) −20.7496 −0.816380
\(647\) −12.5124 −0.491913 −0.245957 0.969281i \(-0.579102\pi\)
−0.245957 + 0.969281i \(0.579102\pi\)
\(648\) −7.33251 −0.288048
\(649\) −24.3396 −0.955412
\(650\) 4.72827 0.185458
\(651\) 0.160425 0.00628756
\(652\) −20.3723 −0.797840
\(653\) 28.4569 1.11360 0.556802 0.830646i \(-0.312028\pi\)
0.556802 + 0.830646i \(0.312028\pi\)
\(654\) 0.590247 0.0230805
\(655\) −19.3345 −0.755461
\(656\) 10.3289 0.403277
\(657\) 27.0836 1.05663
\(658\) −21.8922 −0.853448
\(659\) −48.2626 −1.88004 −0.940021 0.341116i \(-0.889195\pi\)
−0.940021 + 0.341116i \(0.889195\pi\)
\(660\) −0.198515 −0.00772717
\(661\) 2.26440 0.0880751 0.0440375 0.999030i \(-0.485978\pi\)
0.0440375 + 0.999030i \(0.485978\pi\)
\(662\) −28.3214 −1.10074
\(663\) −0.250435 −0.00972610
\(664\) −12.4168 −0.481864
\(665\) 3.46368 0.134316
\(666\) −56.6556 −2.19536
\(667\) −6.66065 −0.257901
\(668\) −29.0887 −1.12548
\(669\) 0.642877 0.0248551
\(670\) 1.38331 0.0534420
\(671\) 20.1096 0.776321
\(672\) 0.227271 0.00876718
\(673\) 6.02284 0.232164 0.116082 0.993240i \(-0.462967\pi\)
0.116082 + 0.993240i \(0.462967\pi\)
\(674\) 0.0326580 0.00125794
\(675\) −0.189260 −0.00728463
\(676\) −10.5617 −0.406218
\(677\) 1.90815 0.0733362 0.0366681 0.999327i \(-0.488326\pi\)
0.0366681 + 0.999327i \(0.488326\pi\)
\(678\) −0.519889 −0.0199662
\(679\) −13.5165 −0.518715
\(680\) −2.58633 −0.0991813
\(681\) 0.347605 0.0133203
\(682\) −38.5401 −1.47578
\(683\) 4.77522 0.182719 0.0913593 0.995818i \(-0.470879\pi\)
0.0913593 + 0.995818i \(0.470879\pi\)
\(684\) −16.2906 −0.622885
\(685\) −17.1644 −0.655820
\(686\) −1.88899 −0.0721218
\(687\) 0.0315486 0.00120365
\(688\) 45.6866 1.74179
\(689\) −15.9384 −0.607203
\(690\) −0.279453 −0.0106386
\(691\) 46.9873 1.78748 0.893741 0.448583i \(-0.148071\pi\)
0.893741 + 0.448583i \(0.148071\pi\)
\(692\) 5.73879 0.218156
\(693\) 12.0329 0.457091
\(694\) −18.7727 −0.712601
\(695\) −12.9681 −0.491908
\(696\) 0.0365459 0.00138527
\(697\) 7.00363 0.265281
\(698\) −23.7300 −0.898194
\(699\) −0.434535 −0.0164356
\(700\) −1.56827 −0.0592750
\(701\) −6.71717 −0.253704 −0.126852 0.991922i \(-0.540487\pi\)
−0.126852 + 0.991922i \(0.540487\pi\)
\(702\) −0.894874 −0.0337748
\(703\) 34.6398 1.30647
\(704\) −17.0676 −0.643259
\(705\) −0.365630 −0.0137704
\(706\) 39.5031 1.48672
\(707\) −12.7953 −0.481215
\(708\) −0.300138 −0.0112799
\(709\) 40.4078 1.51755 0.758773 0.651355i \(-0.225799\pi\)
0.758773 + 0.651355i \(0.225799\pi\)
\(710\) −8.93751 −0.335419
\(711\) −26.2607 −0.984853
\(712\) 1.47253 0.0551854
\(713\) −23.8447 −0.892992
\(714\) 0.188995 0.00707296
\(715\) −10.0431 −0.375589
\(716\) 34.4517 1.28752
\(717\) −0.126246 −0.00471474
\(718\) −34.6173 −1.29191
\(719\) −36.4578 −1.35965 −0.679824 0.733375i \(-0.737944\pi\)
−0.679824 + 0.733375i \(0.737944\pi\)
\(720\) −14.0266 −0.522739
\(721\) −18.4088 −0.685580
\(722\) −13.2284 −0.492309
\(723\) 0.128886 0.00479331
\(724\) −26.6258 −0.989542
\(725\) −1.42042 −0.0527530
\(726\) 0.303841 0.0112766
\(727\) 28.9177 1.07250 0.536248 0.844060i \(-0.319841\pi\)
0.536248 + 0.844060i \(0.319841\pi\)
\(728\) 2.04135 0.0756573
\(729\) −26.9463 −0.998010
\(730\) 17.0592 0.631388
\(731\) 30.9782 1.14577
\(732\) 0.247977 0.00916549
\(733\) −37.0269 −1.36762 −0.683809 0.729661i \(-0.739678\pi\)
−0.683809 + 0.729661i \(0.739678\pi\)
\(734\) 36.3233 1.34072
\(735\) −0.0315486 −0.00116369
\(736\) −33.7804 −1.24516
\(737\) −2.93821 −0.108231
\(738\) 12.5109 0.460531
\(739\) −37.5752 −1.38223 −0.691113 0.722746i \(-0.742880\pi\)
−0.691113 + 0.722746i \(0.742880\pi\)
\(740\) −15.6840 −0.576556
\(741\) 0.273522 0.0100481
\(742\) 12.0281 0.441567
\(743\) −4.25196 −0.155989 −0.0779947 0.996954i \(-0.524852\pi\)
−0.0779947 + 0.996954i \(0.524852\pi\)
\(744\) 0.130832 0.00479654
\(745\) −6.61572 −0.242381
\(746\) −36.7485 −1.34546
\(747\) −45.6608 −1.67064
\(748\) −19.9551 −0.729631
\(749\) 10.8279 0.395645
\(750\) −0.0595948 −0.00217610
\(751\) 30.0051 1.09490 0.547451 0.836838i \(-0.315598\pi\)
0.547451 + 0.836838i \(0.315598\pi\)
\(752\) −54.2045 −1.97663
\(753\) −0.119122 −0.00434106
\(754\) −6.71613 −0.244587
\(755\) −15.5005 −0.564121
\(756\) 0.296811 0.0107949
\(757\) −2.22302 −0.0807970 −0.0403985 0.999184i \(-0.512863\pi\)
−0.0403985 + 0.999184i \(0.512863\pi\)
\(758\) −3.36425 −0.122195
\(759\) 0.593570 0.0215452
\(760\) 2.82476 0.102465
\(761\) 9.07688 0.329037 0.164518 0.986374i \(-0.447393\pi\)
0.164518 + 0.986374i \(0.447393\pi\)
\(762\) 0.337659 0.0122321
\(763\) −9.90433 −0.358561
\(764\) 23.4017 0.846642
\(765\) −9.51084 −0.343865
\(766\) −18.4871 −0.667967
\(767\) −15.1843 −0.548273
\(768\) 0.648159 0.0233884
\(769\) −1.03985 −0.0374978 −0.0187489 0.999824i \(-0.505968\pi\)
−0.0187489 + 0.999824i \(0.505968\pi\)
\(770\) 7.57915 0.273134
\(771\) −0.0357452 −0.00128733
\(772\) −6.26081 −0.225332
\(773\) −10.5324 −0.378823 −0.189411 0.981898i \(-0.560658\pi\)
−0.189411 + 0.981898i \(0.560658\pi\)
\(774\) 55.3377 1.98907
\(775\) −5.08502 −0.182659
\(776\) −11.0232 −0.395708
\(777\) −0.315513 −0.0113190
\(778\) 53.3423 1.91241
\(779\) −7.64926 −0.274063
\(780\) −0.123844 −0.00443432
\(781\) 18.9836 0.679288
\(782\) −28.0912 −1.00454
\(783\) 0.268828 0.00960715
\(784\) −4.67707 −0.167038
\(785\) −2.15806 −0.0770245
\(786\) 1.15224 0.0410989
\(787\) 38.8606 1.38523 0.692615 0.721307i \(-0.256458\pi\)
0.692615 + 0.721307i \(0.256458\pi\)
\(788\) 26.2510 0.935152
\(789\) −0.0693693 −0.00246961
\(790\) −16.5408 −0.588497
\(791\) 8.72373 0.310180
\(792\) 9.81322 0.348698
\(793\) 12.5454 0.445500
\(794\) 43.8463 1.55605
\(795\) 0.200886 0.00712469
\(796\) 1.30338 0.0461970
\(797\) −7.73964 −0.274152 −0.137076 0.990561i \(-0.543770\pi\)
−0.137076 + 0.990561i \(0.543770\pi\)
\(798\) −0.206418 −0.00730711
\(799\) −36.7539 −1.30026
\(800\) −7.20385 −0.254695
\(801\) 5.41500 0.191330
\(802\) −58.5400 −2.06712
\(803\) −36.2344 −1.27868
\(804\) −0.0362320 −0.00127780
\(805\) 4.68922 0.165273
\(806\) −24.0434 −0.846891
\(807\) −0.917918 −0.0323122
\(808\) −10.4350 −0.367101
\(809\) 9.52161 0.334762 0.167381 0.985892i \(-0.446469\pi\)
0.167381 + 0.985892i \(0.446469\pi\)
\(810\) −16.9840 −0.596755
\(811\) 37.4507 1.31507 0.657535 0.753424i \(-0.271599\pi\)
0.657535 + 0.753424i \(0.271599\pi\)
\(812\) 2.22760 0.0781733
\(813\) −0.0638108 −0.00223794
\(814\) 75.7980 2.65672
\(815\) 12.9903 0.455030
\(816\) 0.467946 0.0163814
\(817\) −33.8340 −1.18370
\(818\) −32.5681 −1.13872
\(819\) 7.50674 0.262307
\(820\) 3.46339 0.120947
\(821\) −4.80751 −0.167783 −0.0838917 0.996475i \(-0.526735\pi\)
−0.0838917 + 0.996475i \(0.526735\pi\)
\(822\) 1.02291 0.0356782
\(823\) −29.3481 −1.02301 −0.511505 0.859280i \(-0.670912\pi\)
−0.511505 + 0.859280i \(0.670912\pi\)
\(824\) −15.0130 −0.523004
\(825\) 0.126582 0.00440702
\(826\) 11.4591 0.398712
\(827\) 57.3984 1.99594 0.997969 0.0636961i \(-0.0202888\pi\)
0.997969 + 0.0636961i \(0.0202888\pi\)
\(828\) −22.0545 −0.766448
\(829\) 23.3854 0.812207 0.406103 0.913827i \(-0.366887\pi\)
0.406103 + 0.913827i \(0.366887\pi\)
\(830\) −28.7604 −0.998288
\(831\) 0.540966 0.0187659
\(832\) −10.6477 −0.369141
\(833\) −3.17133 −0.109880
\(834\) 0.772832 0.0267610
\(835\) 18.5483 0.641890
\(836\) 21.7947 0.753785
\(837\) 0.962391 0.0332651
\(838\) 34.4056 1.18852
\(839\) −40.9060 −1.41223 −0.706116 0.708096i \(-0.749554\pi\)
−0.706116 + 0.708096i \(0.749554\pi\)
\(840\) −0.0257290 −0.000887734 0
\(841\) −26.9824 −0.930428
\(842\) 63.3253 2.18233
\(843\) −0.0121627 −0.000418905 0
\(844\) −2.85564 −0.0982952
\(845\) 6.73461 0.231678
\(846\) −65.6549 −2.25726
\(847\) −5.09844 −0.175185
\(848\) 29.7813 1.02269
\(849\) 0.246183 0.00844899
\(850\) −5.99060 −0.205476
\(851\) 46.8962 1.60758
\(852\) 0.234093 0.00801989
\(853\) 16.1112 0.551637 0.275819 0.961210i \(-0.411051\pi\)
0.275819 + 0.961210i \(0.411051\pi\)
\(854\) −9.46759 −0.323974
\(855\) 10.3876 0.355249
\(856\) 8.83057 0.301823
\(857\) 3.08592 0.105413 0.0527066 0.998610i \(-0.483215\pi\)
0.0527066 + 0.998610i \(0.483215\pi\)
\(858\) 0.598514 0.0204329
\(859\) −34.7741 −1.18648 −0.593238 0.805027i \(-0.702151\pi\)
−0.593238 + 0.805027i \(0.702151\pi\)
\(860\) 15.3192 0.522379
\(861\) 0.0696725 0.00237443
\(862\) 60.4535 2.05905
\(863\) −20.1752 −0.686772 −0.343386 0.939194i \(-0.611574\pi\)
−0.343386 + 0.939194i \(0.611574\pi\)
\(864\) 1.36340 0.0463839
\(865\) −3.65932 −0.124420
\(866\) −62.9131 −2.13787
\(867\) −0.219031 −0.00743868
\(868\) 7.97467 0.270678
\(869\) 35.1335 1.19182
\(870\) 0.0846496 0.00286989
\(871\) −1.83301 −0.0621093
\(872\) −8.07733 −0.273533
\(873\) −40.5360 −1.37194
\(874\) 30.6808 1.03780
\(875\) 1.00000 0.0338062
\(876\) −0.446816 −0.0150965
\(877\) 22.9808 0.776005 0.388003 0.921658i \(-0.373165\pi\)
0.388003 + 0.921658i \(0.373165\pi\)
\(878\) 33.5786 1.13322
\(879\) −0.00287601 −9.70054e−5 0
\(880\) 18.7658 0.632593
\(881\) 31.7615 1.07007 0.535037 0.844829i \(-0.320298\pi\)
0.535037 + 0.844829i \(0.320298\pi\)
\(882\) −5.66508 −0.190753
\(883\) −44.8101 −1.50798 −0.753990 0.656886i \(-0.771873\pi\)
−0.753990 + 0.656886i \(0.771873\pi\)
\(884\) −12.4490 −0.418707
\(885\) 0.191382 0.00643323
\(886\) 5.51318 0.185219
\(887\) 44.6061 1.49773 0.748863 0.662724i \(-0.230600\pi\)
0.748863 + 0.662724i \(0.230600\pi\)
\(888\) −0.257312 −0.00863482
\(889\) −5.66591 −0.190028
\(890\) 3.41075 0.114329
\(891\) 36.0746 1.20855
\(892\) 31.9572 1.07001
\(893\) 40.1421 1.34330
\(894\) 0.394263 0.0131861
\(895\) −21.9680 −0.734310
\(896\) −6.37227 −0.212883
\(897\) 0.370300 0.0123640
\(898\) −3.88309 −0.129581
\(899\) 7.22285 0.240895
\(900\) −4.70324 −0.156775
\(901\) 20.1935 0.672743
\(902\) −16.7379 −0.557312
\(903\) 0.308173 0.0102554
\(904\) 7.11451 0.236625
\(905\) 16.9779 0.564363
\(906\) 0.923750 0.0306895
\(907\) 22.4249 0.744605 0.372303 0.928111i \(-0.378568\pi\)
0.372303 + 0.928111i \(0.378568\pi\)
\(908\) 17.2793 0.573434
\(909\) −38.3730 −1.27275
\(910\) 4.72827 0.156741
\(911\) −31.0064 −1.02729 −0.513644 0.858004i \(-0.671705\pi\)
−0.513644 + 0.858004i \(0.671705\pi\)
\(912\) −0.511084 −0.0169237
\(913\) 61.0883 2.02173
\(914\) 14.4314 0.477350
\(915\) −0.158121 −0.00522733
\(916\) 1.56827 0.0518170
\(917\) −19.3345 −0.638481
\(918\) 1.13378 0.0374204
\(919\) −28.3754 −0.936018 −0.468009 0.883724i \(-0.655029\pi\)
−0.468009 + 0.883724i \(0.655029\pi\)
\(920\) 3.82422 0.126081
\(921\) 0.500825 0.0165027
\(922\) 46.1175 1.51880
\(923\) 11.8430 0.389817
\(924\) −0.198515 −0.00653065
\(925\) 10.0009 0.328826
\(926\) −54.6923 −1.79730
\(927\) −55.2081 −1.81327
\(928\) 10.2325 0.335898
\(929\) −21.8692 −0.717504 −0.358752 0.933433i \(-0.616798\pi\)
−0.358752 + 0.933433i \(0.616798\pi\)
\(930\) 0.303041 0.00993710
\(931\) 3.46368 0.113518
\(932\) −21.6006 −0.707550
\(933\) −0.942958 −0.0308711
\(934\) −17.2519 −0.564500
\(935\) 12.7243 0.416129
\(936\) 6.12201 0.200104
\(937\) 41.5377 1.35698 0.678489 0.734610i \(-0.262635\pi\)
0.678489 + 0.734610i \(0.262635\pi\)
\(938\) 1.38331 0.0451668
\(939\) −0.636759 −0.0207799
\(940\) −18.1753 −0.592813
\(941\) 28.6104 0.932672 0.466336 0.884608i \(-0.345574\pi\)
0.466336 + 0.884608i \(0.345574\pi\)
\(942\) 0.128609 0.00419032
\(943\) −10.3557 −0.337229
\(944\) 28.3723 0.923441
\(945\) −0.189260 −0.00615663
\(946\) −74.0348 −2.40708
\(947\) 60.9523 1.98068 0.990342 0.138645i \(-0.0442747\pi\)
0.990342 + 0.138645i \(0.0442747\pi\)
\(948\) 0.433241 0.0140710
\(949\) −22.6049 −0.733786
\(950\) 6.54285 0.212278
\(951\) −1.11339 −0.0361043
\(952\) −2.58633 −0.0838235
\(953\) −26.0057 −0.842409 −0.421204 0.906966i \(-0.638392\pi\)
−0.421204 + 0.906966i \(0.638392\pi\)
\(954\) 36.0724 1.16789
\(955\) −14.9220 −0.482864
\(956\) −6.27564 −0.202969
\(957\) −0.179799 −0.00581209
\(958\) 16.3195 0.527259
\(959\) −17.1644 −0.554269
\(960\) 0.134202 0.00433137
\(961\) −5.14261 −0.165891
\(962\) 47.2868 1.52459
\(963\) 32.4731 1.04643
\(964\) 6.40686 0.206351
\(965\) 3.99218 0.128513
\(966\) −0.279453 −0.00899126
\(967\) 9.19978 0.295845 0.147923 0.988999i \(-0.452741\pi\)
0.147923 + 0.988999i \(0.452741\pi\)
\(968\) −4.15796 −0.133642
\(969\) −0.346545 −0.0111326
\(970\) −25.5324 −0.819797
\(971\) 41.1393 1.32022 0.660112 0.751167i \(-0.270509\pi\)
0.660112 + 0.751167i \(0.270509\pi\)
\(972\) 1.33528 0.0428291
\(973\) −12.9681 −0.415738
\(974\) −12.6370 −0.404917
\(975\) 0.0789685 0.00252902
\(976\) −23.4415 −0.750343
\(977\) 24.2944 0.777248 0.388624 0.921396i \(-0.372950\pi\)
0.388624 + 0.921396i \(0.372950\pi\)
\(978\) −0.774155 −0.0247547
\(979\) −7.24458 −0.231538
\(980\) −1.56827 −0.0500965
\(981\) −29.7031 −0.948348
\(982\) −54.0683 −1.72539
\(983\) 17.1856 0.548136 0.274068 0.961710i \(-0.411631\pi\)
0.274068 + 0.961710i \(0.411631\pi\)
\(984\) 0.0568203 0.00181137
\(985\) −16.7388 −0.533343
\(986\) 8.50916 0.270987
\(987\) −0.365630 −0.0116381
\(988\) 13.5967 0.432568
\(989\) −45.8052 −1.45652
\(990\) 22.7299 0.722404
\(991\) 1.69894 0.0539687 0.0269844 0.999636i \(-0.491410\pi\)
0.0269844 + 0.999636i \(0.491410\pi\)
\(992\) 36.6317 1.16306
\(993\) −0.473006 −0.0150104
\(994\) −8.93751 −0.283481
\(995\) −0.831093 −0.0263474
\(996\) 0.753298 0.0238692
\(997\) 38.4897 1.21898 0.609491 0.792793i \(-0.291374\pi\)
0.609491 + 0.792793i \(0.291374\pi\)
\(998\) −60.1856 −1.90514
\(999\) −1.89276 −0.0598844
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 \(a_p\))