Properties

Label 4010.2.a.k.1.2
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 1.2
Root \(0.679191\)
Character \(\chi\) = 4010.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -3.00420 q^{3} +1.00000 q^{4} -1.00000 q^{5} +3.00420 q^{6} -4.38135 q^{7} -1.00000 q^{8} +6.02524 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -3.00420 q^{3} +1.00000 q^{4} -1.00000 q^{5} +3.00420 q^{6} -4.38135 q^{7} -1.00000 q^{8} +6.02524 q^{9} +1.00000 q^{10} -3.27120 q^{11} -3.00420 q^{12} -2.26078 q^{13} +4.38135 q^{14} +3.00420 q^{15} +1.00000 q^{16} +0.368220 q^{17} -6.02524 q^{18} -1.86184 q^{19} -1.00000 q^{20} +13.1625 q^{21} +3.27120 q^{22} -0.625538 q^{23} +3.00420 q^{24} +1.00000 q^{25} +2.26078 q^{26} -9.08845 q^{27} -4.38135 q^{28} +0.824083 q^{29} -3.00420 q^{30} +2.48127 q^{31} -1.00000 q^{32} +9.82735 q^{33} -0.368220 q^{34} +4.38135 q^{35} +6.02524 q^{36} -3.19737 q^{37} +1.86184 q^{38} +6.79184 q^{39} +1.00000 q^{40} +4.93053 q^{41} -13.1625 q^{42} +5.23037 q^{43} -3.27120 q^{44} -6.02524 q^{45} +0.625538 q^{46} -1.07028 q^{47} -3.00420 q^{48} +12.1962 q^{49} -1.00000 q^{50} -1.10621 q^{51} -2.26078 q^{52} +0.543690 q^{53} +9.08845 q^{54} +3.27120 q^{55} +4.38135 q^{56} +5.59336 q^{57} -0.824083 q^{58} +1.14090 q^{59} +3.00420 q^{60} -6.83722 q^{61} -2.48127 q^{62} -26.3987 q^{63} +1.00000 q^{64} +2.26078 q^{65} -9.82735 q^{66} -4.96537 q^{67} +0.368220 q^{68} +1.87924 q^{69} -4.38135 q^{70} +5.72963 q^{71} -6.02524 q^{72} +16.8546 q^{73} +3.19737 q^{74} -3.00420 q^{75} -1.86184 q^{76} +14.3323 q^{77} -6.79184 q^{78} +8.03970 q^{79} -1.00000 q^{80} +9.22783 q^{81} -4.93053 q^{82} -14.4168 q^{83} +13.1625 q^{84} -0.368220 q^{85} -5.23037 q^{86} -2.47572 q^{87} +3.27120 q^{88} -0.445164 q^{89} +6.02524 q^{90} +9.90525 q^{91} -0.625538 q^{92} -7.45423 q^{93} +1.07028 q^{94} +1.86184 q^{95} +3.00420 q^{96} +13.9251 q^{97} -12.1962 q^{98} -19.7098 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 15q - 15q^{2} - 6q^{3} + 15q^{4} - 15q^{5} + 6q^{6} - 5q^{7} - 15q^{8} + 19q^{9} + O(q^{10}) \) \( 15q - 15q^{2} - 6q^{3} + 15q^{4} - 15q^{5} + 6q^{6} - 5q^{7} - 15q^{8} + 19q^{9} + 15q^{10} - 2q^{11} - 6q^{12} - 13q^{13} + 5q^{14} + 6q^{15} + 15q^{16} + 11q^{17} - 19q^{18} - 15q^{19} - 15q^{20} - 2q^{21} + 2q^{22} - 3q^{23} + 6q^{24} + 15q^{25} + 13q^{26} - 12q^{27} - 5q^{28} + 28q^{29} - 6q^{30} - 12q^{31} - 15q^{32} - 22q^{33} - 11q^{34} + 5q^{35} + 19q^{36} - 23q^{37} + 15q^{38} - 2q^{39} + 15q^{40} + 24q^{41} + 2q^{42} - 24q^{43} - 2q^{44} - 19q^{45} + 3q^{46} - 3q^{47} - 6q^{48} + 20q^{49} - 15q^{50} - 5q^{51} - 13q^{52} + 10q^{53} + 12q^{54} + 2q^{55} + 5q^{56} - 11q^{57} - 28q^{58} + 2q^{59} + 6q^{60} + 15q^{61} + 12q^{62} - 2q^{63} + 15q^{64} + 13q^{65} + 22q^{66} - 48q^{67} + 11q^{68} + 21q^{69} - 5q^{70} + 15q^{71} - 19q^{72} - 47q^{73} + 23q^{74} - 6q^{75} - 15q^{76} + 7q^{77} + 2q^{78} - 34q^{79} - 15q^{80} + 43q^{81} - 24q^{82} - 32q^{83} - 2q^{84} - 11q^{85} + 24q^{86} + 14q^{87} + 2q^{88} + 25q^{89} + 19q^{90} - 32q^{91} - 3q^{92} - 42q^{93} + 3q^{94} + 15q^{95} + 6q^{96} - 34q^{97} - 20q^{98} + 4q^{99} + O(q^{100}) \)

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
\(3\) −3.00420 −1.73448 −0.867239 0.497892i \(-0.834108\pi\)
−0.867239 + 0.497892i \(0.834108\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) 3.00420 1.22646
\(7\) −4.38135 −1.65599 −0.827997 0.560733i \(-0.810520\pi\)
−0.827997 + 0.560733i \(0.810520\pi\)
\(8\) −1.00000 −0.353553
\(9\) 6.02524 2.00841
\(10\) 1.00000 0.316228
\(11\) −3.27120 −0.986304 −0.493152 0.869943i \(-0.664155\pi\)
−0.493152 + 0.869943i \(0.664155\pi\)
\(12\) −3.00420 −0.867239
\(13\) −2.26078 −0.627027 −0.313513 0.949584i \(-0.601506\pi\)
−0.313513 + 0.949584i \(0.601506\pi\)
\(14\) 4.38135 1.17096
\(15\) 3.00420 0.775682
\(16\) 1.00000 0.250000
\(17\) 0.368220 0.0893064 0.0446532 0.999003i \(-0.485782\pi\)
0.0446532 + 0.999003i \(0.485782\pi\)
\(18\) −6.02524 −1.42016
\(19\) −1.86184 −0.427136 −0.213568 0.976928i \(-0.568509\pi\)
−0.213568 + 0.976928i \(0.568509\pi\)
\(20\) −1.00000 −0.223607
\(21\) 13.1625 2.87229
\(22\) 3.27120 0.697422
\(23\) −0.625538 −0.130434 −0.0652168 0.997871i \(-0.520774\pi\)
−0.0652168 + 0.997871i \(0.520774\pi\)
\(24\) 3.00420 0.613231
\(25\) 1.00000 0.200000
\(26\) 2.26078 0.443375
\(27\) −9.08845 −1.74907
\(28\) −4.38135 −0.827997
\(29\) 0.824083 0.153028 0.0765142 0.997068i \(-0.475621\pi\)
0.0765142 + 0.997068i \(0.475621\pi\)
\(30\) −3.00420 −0.548490
\(31\) 2.48127 0.445649 0.222824 0.974859i \(-0.428472\pi\)
0.222824 + 0.974859i \(0.428472\pi\)
\(32\) −1.00000 −0.176777
\(33\) 9.82735 1.71072
\(34\) −0.368220 −0.0631492
\(35\) 4.38135 0.740583
\(36\) 6.02524 1.00421
\(37\) −3.19737 −0.525644 −0.262822 0.964844i \(-0.584653\pi\)
−0.262822 + 0.964844i \(0.584653\pi\)
\(38\) 1.86184 0.302031
\(39\) 6.79184 1.08756
\(40\) 1.00000 0.158114
\(41\) 4.93053 0.770019 0.385010 0.922913i \(-0.374198\pi\)
0.385010 + 0.922913i \(0.374198\pi\)
\(42\) −13.1625 −2.03101
\(43\) 5.23037 0.797624 0.398812 0.917033i \(-0.369423\pi\)
0.398812 + 0.917033i \(0.369423\pi\)
\(44\) −3.27120 −0.493152
\(45\) −6.02524 −0.898190
\(46\) 0.625538 0.0922305
\(47\) −1.07028 −0.156117 −0.0780585 0.996949i \(-0.524872\pi\)
−0.0780585 + 0.996949i \(0.524872\pi\)
\(48\) −3.00420 −0.433620
\(49\) 12.1962 1.74232
\(50\) −1.00000 −0.141421
\(51\) −1.10621 −0.154900
\(52\) −2.26078 −0.313513
\(53\) 0.543690 0.0746816 0.0373408 0.999303i \(-0.488111\pi\)
0.0373408 + 0.999303i \(0.488111\pi\)
\(54\) 9.08845 1.23678
\(55\) 3.27120 0.441088
\(56\) 4.38135 0.585482
\(57\) 5.59336 0.740859
\(58\) −0.824083 −0.108207
\(59\) 1.14090 0.148532 0.0742660 0.997238i \(-0.476339\pi\)
0.0742660 + 0.997238i \(0.476339\pi\)
\(60\) 3.00420 0.387841
\(61\) −6.83722 −0.875416 −0.437708 0.899117i \(-0.644210\pi\)
−0.437708 + 0.899117i \(0.644210\pi\)
\(62\) −2.48127 −0.315121
\(63\) −26.3987 −3.32592
\(64\) 1.00000 0.125000
\(65\) 2.26078 0.280415
\(66\) −9.82735 −1.20966
\(67\) −4.96537 −0.606616 −0.303308 0.952893i \(-0.598091\pi\)
−0.303308 + 0.952893i \(0.598091\pi\)
\(68\) 0.368220 0.0446532
\(69\) 1.87924 0.226234
\(70\) −4.38135 −0.523671
\(71\) 5.72963 0.679982 0.339991 0.940429i \(-0.389576\pi\)
0.339991 + 0.940429i \(0.389576\pi\)
\(72\) −6.02524 −0.710082
\(73\) 16.8546 1.97268 0.986342 0.164713i \(-0.0526698\pi\)
0.986342 + 0.164713i \(0.0526698\pi\)
\(74\) 3.19737 0.371687
\(75\) −3.00420 −0.346896
\(76\) −1.86184 −0.213568
\(77\) 14.3323 1.63331
\(78\) −6.79184 −0.769024
\(79\) 8.03970 0.904537 0.452269 0.891882i \(-0.350615\pi\)
0.452269 + 0.891882i \(0.350615\pi\)
\(80\) −1.00000 −0.111803
\(81\) 9.22783 1.02531
\(82\) −4.93053 −0.544486
\(83\) −14.4168 −1.58245 −0.791224 0.611526i \(-0.790556\pi\)
−0.791224 + 0.611526i \(0.790556\pi\)
\(84\) 13.1625 1.43614
\(85\) −0.368220 −0.0399391
\(86\) −5.23037 −0.564006
\(87\) −2.47572 −0.265425
\(88\) 3.27120 0.348711
\(89\) −0.445164 −0.0471872 −0.0235936 0.999722i \(-0.507511\pi\)
−0.0235936 + 0.999722i \(0.507511\pi\)
\(90\) 6.02524 0.635116
\(91\) 9.90525 1.03835
\(92\) −0.625538 −0.0652168
\(93\) −7.45423 −0.772968
\(94\) 1.07028 0.110391
\(95\) 1.86184 0.191021
\(96\) 3.00420 0.306615
\(97\) 13.9251 1.41388 0.706939 0.707275i \(-0.250076\pi\)
0.706939 + 0.707275i \(0.250076\pi\)
\(98\) −12.1962 −1.23200
\(99\) −19.7098 −1.98091
\(100\) 1.00000 0.100000
\(101\) 19.3713 1.92752 0.963758 0.266777i \(-0.0859588\pi\)
0.963758 + 0.266777i \(0.0859588\pi\)
\(102\) 1.10621 0.109531
\(103\) 2.38314 0.234818 0.117409 0.993084i \(-0.462541\pi\)
0.117409 + 0.993084i \(0.462541\pi\)
\(104\) 2.26078 0.221687
\(105\) −13.1625 −1.28453
\(106\) −0.543690 −0.0528078
\(107\) 9.76789 0.944298 0.472149 0.881519i \(-0.343478\pi\)
0.472149 + 0.881519i \(0.343478\pi\)
\(108\) −9.08845 −0.874536
\(109\) −0.0384553 −0.00368335 −0.00184167 0.999998i \(-0.500586\pi\)
−0.00184167 + 0.999998i \(0.500586\pi\)
\(110\) −3.27120 −0.311897
\(111\) 9.60555 0.911719
\(112\) −4.38135 −0.413998
\(113\) −3.13526 −0.294940 −0.147470 0.989066i \(-0.547113\pi\)
−0.147470 + 0.989066i \(0.547113\pi\)
\(114\) −5.59336 −0.523866
\(115\) 0.625538 0.0583317
\(116\) 0.824083 0.0765142
\(117\) −13.6217 −1.25933
\(118\) −1.14090 −0.105028
\(119\) −1.61330 −0.147891
\(120\) −3.00420 −0.274245
\(121\) −0.299252 −0.0272047
\(122\) 6.83722 0.619012
\(123\) −14.8123 −1.33558
\(124\) 2.48127 0.222824
\(125\) −1.00000 −0.0894427
\(126\) 26.3987 2.35178
\(127\) −4.70586 −0.417578 −0.208789 0.977961i \(-0.566952\pi\)
−0.208789 + 0.977961i \(0.566952\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −15.7131 −1.38346
\(130\) −2.26078 −0.198283
\(131\) −0.648468 −0.0566569 −0.0283285 0.999599i \(-0.509018\pi\)
−0.0283285 + 0.999599i \(0.509018\pi\)
\(132\) 9.82735 0.855361
\(133\) 8.15739 0.707335
\(134\) 4.96537 0.428943
\(135\) 9.08845 0.782209
\(136\) −0.368220 −0.0315746
\(137\) −4.79646 −0.409789 −0.204894 0.978784i \(-0.565685\pi\)
−0.204894 + 0.978784i \(0.565685\pi\)
\(138\) −1.87924 −0.159972
\(139\) 3.91350 0.331939 0.165969 0.986131i \(-0.446925\pi\)
0.165969 + 0.986131i \(0.446925\pi\)
\(140\) 4.38135 0.370292
\(141\) 3.21535 0.270781
\(142\) −5.72963 −0.480820
\(143\) 7.39545 0.618439
\(144\) 6.02524 0.502104
\(145\) −0.824083 −0.0684364
\(146\) −16.8546 −1.39490
\(147\) −36.6399 −3.02201
\(148\) −3.19737 −0.262822
\(149\) −7.54191 −0.617857 −0.308929 0.951085i \(-0.599970\pi\)
−0.308929 + 0.951085i \(0.599970\pi\)
\(150\) 3.00420 0.245292
\(151\) 3.11492 0.253489 0.126744 0.991935i \(-0.459547\pi\)
0.126744 + 0.991935i \(0.459547\pi\)
\(152\) 1.86184 0.151016
\(153\) 2.21861 0.179364
\(154\) −14.3323 −1.15493
\(155\) −2.48127 −0.199300
\(156\) 6.79184 0.543782
\(157\) 4.02861 0.321518 0.160759 0.986994i \(-0.448606\pi\)
0.160759 + 0.986994i \(0.448606\pi\)
\(158\) −8.03970 −0.639605
\(159\) −1.63336 −0.129534
\(160\) 1.00000 0.0790569
\(161\) 2.74070 0.215997
\(162\) −9.22783 −0.725007
\(163\) −16.9126 −1.32469 −0.662347 0.749197i \(-0.730440\pi\)
−0.662347 + 0.749197i \(0.730440\pi\)
\(164\) 4.93053 0.385010
\(165\) −9.82735 −0.765058
\(166\) 14.4168 1.11896
\(167\) 4.31707 0.334065 0.167033 0.985951i \(-0.446581\pi\)
0.167033 + 0.985951i \(0.446581\pi\)
\(168\) −13.1625 −1.01551
\(169\) −7.88889 −0.606837
\(170\) 0.368220 0.0282412
\(171\) −11.2181 −0.857867
\(172\) 5.23037 0.398812
\(173\) 24.6465 1.87384 0.936920 0.349543i \(-0.113663\pi\)
0.936920 + 0.349543i \(0.113663\pi\)
\(174\) 2.47572 0.187683
\(175\) −4.38135 −0.331199
\(176\) −3.27120 −0.246576
\(177\) −3.42749 −0.257626
\(178\) 0.445164 0.0333664
\(179\) 8.59930 0.642742 0.321371 0.946953i \(-0.395856\pi\)
0.321371 + 0.946953i \(0.395856\pi\)
\(180\) −6.02524 −0.449095
\(181\) 7.47920 0.555924 0.277962 0.960592i \(-0.410341\pi\)
0.277962 + 0.960592i \(0.410341\pi\)
\(182\) −9.90525 −0.734226
\(183\) 20.5404 1.51839
\(184\) 0.625538 0.0461153
\(185\) 3.19737 0.235075
\(186\) 7.45423 0.546571
\(187\) −1.20452 −0.0880833
\(188\) −1.07028 −0.0780585
\(189\) 39.8197 2.89645
\(190\) −1.86184 −0.135072
\(191\) 17.4327 1.26138 0.630692 0.776033i \(-0.282771\pi\)
0.630692 + 0.776033i \(0.282771\pi\)
\(192\) −3.00420 −0.216810
\(193\) 2.95323 0.212578 0.106289 0.994335i \(-0.466103\pi\)
0.106289 + 0.994335i \(0.466103\pi\)
\(194\) −13.9251 −0.999763
\(195\) −6.79184 −0.486374
\(196\) 12.1962 0.871158
\(197\) 4.24292 0.302296 0.151148 0.988511i \(-0.451703\pi\)
0.151148 + 0.988511i \(0.451703\pi\)
\(198\) 19.7098 1.40071
\(199\) −14.8029 −1.04935 −0.524677 0.851302i \(-0.675814\pi\)
−0.524677 + 0.851302i \(0.675814\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 14.9170 1.05216
\(202\) −19.3713 −1.36296
\(203\) −3.61060 −0.253414
\(204\) −1.10621 −0.0774500
\(205\) −4.93053 −0.344363
\(206\) −2.38314 −0.166041
\(207\) −3.76902 −0.261965
\(208\) −2.26078 −0.156757
\(209\) 6.09047 0.421286
\(210\) 13.1625 0.908296
\(211\) −24.5294 −1.68867 −0.844336 0.535814i \(-0.820005\pi\)
−0.844336 + 0.535814i \(0.820005\pi\)
\(212\) 0.543690 0.0373408
\(213\) −17.2130 −1.17941
\(214\) −9.76789 −0.667720
\(215\) −5.23037 −0.356708
\(216\) 9.08845 0.618391
\(217\) −10.8713 −0.737992
\(218\) 0.0384553 0.00260452
\(219\) −50.6347 −3.42158
\(220\) 3.27120 0.220544
\(221\) −0.832463 −0.0559975
\(222\) −9.60555 −0.644682
\(223\) −25.8383 −1.73026 −0.865129 0.501550i \(-0.832763\pi\)
−0.865129 + 0.501550i \(0.832763\pi\)
\(224\) 4.38135 0.292741
\(225\) 6.02524 0.401683
\(226\) 3.13526 0.208554
\(227\) −4.05065 −0.268851 −0.134426 0.990924i \(-0.542919\pi\)
−0.134426 + 0.990924i \(0.542919\pi\)
\(228\) 5.59336 0.370429
\(229\) 14.0087 0.925723 0.462861 0.886431i \(-0.346823\pi\)
0.462861 + 0.886431i \(0.346823\pi\)
\(230\) −0.625538 −0.0412467
\(231\) −43.0571 −2.83295
\(232\) −0.824083 −0.0541037
\(233\) 0.268423 0.0175850 0.00879249 0.999961i \(-0.497201\pi\)
0.00879249 + 0.999961i \(0.497201\pi\)
\(234\) 13.6217 0.890481
\(235\) 1.07028 0.0698176
\(236\) 1.14090 0.0742660
\(237\) −24.1529 −1.56890
\(238\) 1.61330 0.104575
\(239\) 7.07729 0.457792 0.228896 0.973451i \(-0.426488\pi\)
0.228896 + 0.973451i \(0.426488\pi\)
\(240\) 3.00420 0.193921
\(241\) −17.3121 −1.11517 −0.557584 0.830121i \(-0.688271\pi\)
−0.557584 + 0.830121i \(0.688271\pi\)
\(242\) 0.299252 0.0192366
\(243\) −0.456932 −0.0293122
\(244\) −6.83722 −0.437708
\(245\) −12.1962 −0.779187
\(246\) 14.8123 0.944399
\(247\) 4.20922 0.267826
\(248\) −2.48127 −0.157561
\(249\) 43.3110 2.74472
\(250\) 1.00000 0.0632456
\(251\) −14.4545 −0.912360 −0.456180 0.889888i \(-0.650783\pi\)
−0.456180 + 0.889888i \(0.650783\pi\)
\(252\) −26.3987 −1.66296
\(253\) 2.04626 0.128647
\(254\) 4.70586 0.295272
\(255\) 1.10621 0.0692734
\(256\) 1.00000 0.0625000
\(257\) 18.0459 1.12567 0.562836 0.826569i \(-0.309710\pi\)
0.562836 + 0.826569i \(0.309710\pi\)
\(258\) 15.7131 0.978255
\(259\) 14.0088 0.870464
\(260\) 2.26078 0.140207
\(261\) 4.96530 0.307345
\(262\) 0.648468 0.0400625
\(263\) −9.64450 −0.594705 −0.297353 0.954768i \(-0.596104\pi\)
−0.297353 + 0.954768i \(0.596104\pi\)
\(264\) −9.82735 −0.604832
\(265\) −0.543690 −0.0333986
\(266\) −8.15739 −0.500162
\(267\) 1.33736 0.0818452
\(268\) −4.96537 −0.303308
\(269\) 2.99229 0.182443 0.0912215 0.995831i \(-0.470923\pi\)
0.0912215 + 0.995831i \(0.470923\pi\)
\(270\) −9.08845 −0.553105
\(271\) 4.85673 0.295026 0.147513 0.989060i \(-0.452873\pi\)
0.147513 + 0.989060i \(0.452873\pi\)
\(272\) 0.368220 0.0223266
\(273\) −29.7574 −1.80100
\(274\) 4.79646 0.289764
\(275\) −3.27120 −0.197261
\(276\) 1.87924 0.113117
\(277\) 3.53360 0.212313 0.106157 0.994349i \(-0.466145\pi\)
0.106157 + 0.994349i \(0.466145\pi\)
\(278\) −3.91350 −0.234716
\(279\) 14.9502 0.895047
\(280\) −4.38135 −0.261836
\(281\) −28.1683 −1.68038 −0.840188 0.542295i \(-0.817556\pi\)
−0.840188 + 0.542295i \(0.817556\pi\)
\(282\) −3.21535 −0.191471
\(283\) 16.2124 0.963726 0.481863 0.876247i \(-0.339960\pi\)
0.481863 + 0.876247i \(0.339960\pi\)
\(284\) 5.72963 0.339991
\(285\) −5.59336 −0.331322
\(286\) −7.39545 −0.437302
\(287\) −21.6024 −1.27515
\(288\) −6.02524 −0.355041
\(289\) −16.8644 −0.992024
\(290\) 0.824083 0.0483918
\(291\) −41.8338 −2.45234
\(292\) 16.8546 0.986342
\(293\) −13.7452 −0.803004 −0.401502 0.915858i \(-0.631512\pi\)
−0.401502 + 0.915858i \(0.631512\pi\)
\(294\) 36.6399 2.13688
\(295\) −1.14090 −0.0664256
\(296\) 3.19737 0.185843
\(297\) 29.7301 1.72512
\(298\) 7.54191 0.436891
\(299\) 1.41420 0.0817854
\(300\) −3.00420 −0.173448
\(301\) −22.9161 −1.32086
\(302\) −3.11492 −0.179243
\(303\) −58.1953 −3.34324
\(304\) −1.86184 −0.106784
\(305\) 6.83722 0.391498
\(306\) −2.21861 −0.126830
\(307\) −19.0088 −1.08489 −0.542445 0.840091i \(-0.682501\pi\)
−0.542445 + 0.840091i \(0.682501\pi\)
\(308\) 14.3323 0.816657
\(309\) −7.15945 −0.407287
\(310\) 2.48127 0.140927
\(311\) 13.1742 0.747041 0.373520 0.927622i \(-0.378151\pi\)
0.373520 + 0.927622i \(0.378151\pi\)
\(312\) −6.79184 −0.384512
\(313\) 3.86799 0.218632 0.109316 0.994007i \(-0.465134\pi\)
0.109316 + 0.994007i \(0.465134\pi\)
\(314\) −4.02861 −0.227348
\(315\) 26.3987 1.48740
\(316\) 8.03970 0.452269
\(317\) −18.5368 −1.04113 −0.520564 0.853823i \(-0.674278\pi\)
−0.520564 + 0.853823i \(0.674278\pi\)
\(318\) 1.63336 0.0915941
\(319\) −2.69574 −0.150933
\(320\) −1.00000 −0.0559017
\(321\) −29.3448 −1.63786
\(322\) −2.74070 −0.152733
\(323\) −0.685568 −0.0381460
\(324\) 9.22783 0.512657
\(325\) −2.26078 −0.125405
\(326\) 16.9126 0.936700
\(327\) 0.115528 0.00638869
\(328\) −4.93053 −0.272243
\(329\) 4.68929 0.258529
\(330\) 9.82735 0.540978
\(331\) −25.1409 −1.38187 −0.690934 0.722918i \(-0.742800\pi\)
−0.690934 + 0.722918i \(0.742800\pi\)
\(332\) −14.4168 −0.791224
\(333\) −19.2649 −1.05571
\(334\) −4.31707 −0.236220
\(335\) 4.96537 0.271287
\(336\) 13.1625 0.718071
\(337\) 12.4506 0.678228 0.339114 0.940745i \(-0.389873\pi\)
0.339114 + 0.940745i \(0.389873\pi\)
\(338\) 7.88889 0.429099
\(339\) 9.41896 0.511568
\(340\) −0.368220 −0.0199695
\(341\) −8.11672 −0.439545
\(342\) 11.2181 0.606604
\(343\) −22.7664 −1.22927
\(344\) −5.23037 −0.282003
\(345\) −1.87924 −0.101175
\(346\) −24.6465 −1.32501
\(347\) 13.9023 0.746317 0.373159 0.927768i \(-0.378275\pi\)
0.373159 + 0.927768i \(0.378275\pi\)
\(348\) −2.47572 −0.132712
\(349\) −5.12796 −0.274494 −0.137247 0.990537i \(-0.543825\pi\)
−0.137247 + 0.990537i \(0.543825\pi\)
\(350\) 4.38135 0.234193
\(351\) 20.5470 1.09672
\(352\) 3.27120 0.174356
\(353\) −13.7457 −0.731612 −0.365806 0.930691i \(-0.619207\pi\)
−0.365806 + 0.930691i \(0.619207\pi\)
\(354\) 3.42749 0.182169
\(355\) −5.72963 −0.304097
\(356\) −0.445164 −0.0235936
\(357\) 4.84668 0.256514
\(358\) −8.59930 −0.454487
\(359\) −24.2421 −1.27945 −0.639725 0.768604i \(-0.720952\pi\)
−0.639725 + 0.768604i \(0.720952\pi\)
\(360\) 6.02524 0.317558
\(361\) −15.5335 −0.817554
\(362\) −7.47920 −0.393098
\(363\) 0.899013 0.0471859
\(364\) 9.90525 0.519176
\(365\) −16.8546 −0.882211
\(366\) −20.5404 −1.07366
\(367\) −8.27488 −0.431945 −0.215972 0.976399i \(-0.569292\pi\)
−0.215972 + 0.976399i \(0.569292\pi\)
\(368\) −0.625538 −0.0326084
\(369\) 29.7076 1.54652
\(370\) −3.19737 −0.166223
\(371\) −2.38210 −0.123672
\(372\) −7.45423 −0.386484
\(373\) −24.9657 −1.29268 −0.646338 0.763051i \(-0.723701\pi\)
−0.646338 + 0.763051i \(0.723701\pi\)
\(374\) 1.20452 0.0622843
\(375\) 3.00420 0.155136
\(376\) 1.07028 0.0551957
\(377\) −1.86307 −0.0959530
\(378\) −39.8197 −2.04810
\(379\) 5.76871 0.296319 0.148159 0.988963i \(-0.452665\pi\)
0.148159 + 0.988963i \(0.452665\pi\)
\(380\) 1.86184 0.0955106
\(381\) 14.1374 0.724280
\(382\) −17.4327 −0.891934
\(383\) 31.1789 1.59317 0.796584 0.604527i \(-0.206638\pi\)
0.796584 + 0.604527i \(0.206638\pi\)
\(384\) 3.00420 0.153308
\(385\) −14.3323 −0.730440
\(386\) −2.95323 −0.150316
\(387\) 31.5143 1.60196
\(388\) 13.9251 0.706939
\(389\) 15.8001 0.801096 0.400548 0.916276i \(-0.368820\pi\)
0.400548 + 0.916276i \(0.368820\pi\)
\(390\) 6.79184 0.343918
\(391\) −0.230335 −0.0116486
\(392\) −12.1962 −0.616002
\(393\) 1.94813 0.0982702
\(394\) −4.24292 −0.213755
\(395\) −8.03970 −0.404521
\(396\) −19.7098 −0.990453
\(397\) −1.32833 −0.0666672 −0.0333336 0.999444i \(-0.510612\pi\)
−0.0333336 + 0.999444i \(0.510612\pi\)
\(398\) 14.8029 0.742005
\(399\) −24.5065 −1.22686
\(400\) 1.00000 0.0500000
\(401\) −1.00000 −0.0499376
\(402\) −14.9170 −0.743992
\(403\) −5.60959 −0.279434
\(404\) 19.3713 0.963758
\(405\) −9.22783 −0.458534
\(406\) 3.61060 0.179191
\(407\) 10.4592 0.518445
\(408\) 1.10621 0.0547654
\(409\) 8.99084 0.444568 0.222284 0.974982i \(-0.428649\pi\)
0.222284 + 0.974982i \(0.428649\pi\)
\(410\) 4.93053 0.243501
\(411\) 14.4095 0.710770
\(412\) 2.38314 0.117409
\(413\) −4.99867 −0.245968
\(414\) 3.76902 0.185237
\(415\) 14.4168 0.707692
\(416\) 2.26078 0.110844
\(417\) −11.7570 −0.575740
\(418\) −6.09047 −0.297894
\(419\) −17.4387 −0.851936 −0.425968 0.904738i \(-0.640066\pi\)
−0.425968 + 0.904738i \(0.640066\pi\)
\(420\) −13.1625 −0.642263
\(421\) −19.2201 −0.936729 −0.468365 0.883535i \(-0.655157\pi\)
−0.468365 + 0.883535i \(0.655157\pi\)
\(422\) 24.5294 1.19407
\(423\) −6.44872 −0.313547
\(424\) −0.543690 −0.0264039
\(425\) 0.368220 0.0178613
\(426\) 17.2130 0.833971
\(427\) 29.9562 1.44968
\(428\) 9.76789 0.472149
\(429\) −22.2175 −1.07267
\(430\) 5.23037 0.252231
\(431\) 2.69307 0.129720 0.0648602 0.997894i \(-0.479340\pi\)
0.0648602 + 0.997894i \(0.479340\pi\)
\(432\) −9.08845 −0.437268
\(433\) −21.8698 −1.05100 −0.525498 0.850795i \(-0.676121\pi\)
−0.525498 + 0.850795i \(0.676121\pi\)
\(434\) 10.8713 0.521839
\(435\) 2.47572 0.118701
\(436\) −0.0384553 −0.00184167
\(437\) 1.16465 0.0557130
\(438\) 50.6347 2.41942
\(439\) −1.52968 −0.0730075 −0.0365038 0.999334i \(-0.511622\pi\)
−0.0365038 + 0.999334i \(0.511622\pi\)
\(440\) −3.27120 −0.155948
\(441\) 73.4851 3.49929
\(442\) 0.832463 0.0395962
\(443\) −7.30305 −0.346979 −0.173489 0.984836i \(-0.555504\pi\)
−0.173489 + 0.984836i \(0.555504\pi\)
\(444\) 9.60555 0.455859
\(445\) 0.445164 0.0211028
\(446\) 25.8383 1.22348
\(447\) 22.6574 1.07166
\(448\) −4.38135 −0.206999
\(449\) 10.7673 0.508142 0.254071 0.967186i \(-0.418230\pi\)
0.254071 + 0.967186i \(0.418230\pi\)
\(450\) −6.02524 −0.284033
\(451\) −16.1287 −0.759473
\(452\) −3.13526 −0.147470
\(453\) −9.35785 −0.439670
\(454\) 4.05065 0.190107
\(455\) −9.90525 −0.464365
\(456\) −5.59336 −0.261933
\(457\) 27.1707 1.27099 0.635496 0.772104i \(-0.280796\pi\)
0.635496 + 0.772104i \(0.280796\pi\)
\(458\) −14.0087 −0.654585
\(459\) −3.34655 −0.156203
\(460\) 0.625538 0.0291658
\(461\) −9.07414 −0.422625 −0.211312 0.977419i \(-0.567774\pi\)
−0.211312 + 0.977419i \(0.567774\pi\)
\(462\) 43.0571 2.00320
\(463\) −23.5550 −1.09469 −0.547347 0.836906i \(-0.684362\pi\)
−0.547347 + 0.836906i \(0.684362\pi\)
\(464\) 0.824083 0.0382571
\(465\) 7.45423 0.345682
\(466\) −0.268423 −0.0124345
\(467\) 17.4498 0.807482 0.403741 0.914873i \(-0.367710\pi\)
0.403741 + 0.914873i \(0.367710\pi\)
\(468\) −13.6217 −0.629665
\(469\) 21.7550 1.00455
\(470\) −1.07028 −0.0493685
\(471\) −12.1028 −0.557667
\(472\) −1.14090 −0.0525140
\(473\) −17.1096 −0.786700
\(474\) 24.1529 1.10938
\(475\) −1.86184 −0.0854273
\(476\) −1.61330 −0.0739455
\(477\) 3.27587 0.149992
\(478\) −7.07729 −0.323708
\(479\) 9.78078 0.446895 0.223448 0.974716i \(-0.428269\pi\)
0.223448 + 0.974716i \(0.428269\pi\)
\(480\) −3.00420 −0.137123
\(481\) 7.22854 0.329593
\(482\) 17.3121 0.788542
\(483\) −8.23362 −0.374643
\(484\) −0.299252 −0.0136023
\(485\) −13.9251 −0.632305
\(486\) 0.456932 0.0207269
\(487\) 24.3102 1.10160 0.550801 0.834637i \(-0.314322\pi\)
0.550801 + 0.834637i \(0.314322\pi\)
\(488\) 6.83722 0.309506
\(489\) 50.8088 2.29765
\(490\) 12.1962 0.550969
\(491\) −18.0341 −0.813869 −0.406934 0.913457i \(-0.633402\pi\)
−0.406934 + 0.913457i \(0.633402\pi\)
\(492\) −14.8123 −0.667791
\(493\) 0.303444 0.0136664
\(494\) −4.20922 −0.189382
\(495\) 19.7098 0.885889
\(496\) 2.48127 0.111412
\(497\) −25.1035 −1.12605
\(498\) −43.3110 −1.94081
\(499\) 22.4604 1.00547 0.502734 0.864441i \(-0.332328\pi\)
0.502734 + 0.864441i \(0.332328\pi\)
\(500\) −1.00000 −0.0447214
\(501\) −12.9694 −0.579429
\(502\) 14.4545 0.645136
\(503\) 24.7026 1.10144 0.550718 0.834691i \(-0.314354\pi\)
0.550718 + 0.834691i \(0.314354\pi\)
\(504\) 26.3987 1.17589
\(505\) −19.3713 −0.862012
\(506\) −2.04626 −0.0909673
\(507\) 23.6998 1.05255
\(508\) −4.70586 −0.208789
\(509\) 32.9928 1.46238 0.731191 0.682173i \(-0.238965\pi\)
0.731191 + 0.682173i \(0.238965\pi\)
\(510\) −1.10621 −0.0489837
\(511\) −73.8459 −3.26675
\(512\) −1.00000 −0.0441942
\(513\) 16.9213 0.747093
\(514\) −18.0459 −0.795970
\(515\) −2.38314 −0.105014
\(516\) −15.7131 −0.691731
\(517\) 3.50111 0.153979
\(518\) −14.0088 −0.615511
\(519\) −74.0432 −3.25014
\(520\) −2.26078 −0.0991417
\(521\) 25.0471 1.09733 0.548666 0.836042i \(-0.315136\pi\)
0.548666 + 0.836042i \(0.315136\pi\)
\(522\) −4.96530 −0.217325
\(523\) −33.1723 −1.45052 −0.725262 0.688473i \(-0.758281\pi\)
−0.725262 + 0.688473i \(0.758281\pi\)
\(524\) −0.648468 −0.0283285
\(525\) 13.1625 0.574457
\(526\) 9.64450 0.420520
\(527\) 0.913652 0.0397993
\(528\) 9.82735 0.427681
\(529\) −22.6087 −0.982987
\(530\) 0.543690 0.0236164
\(531\) 6.87418 0.298314
\(532\) 8.15739 0.353668
\(533\) −11.1468 −0.482823
\(534\) −1.33736 −0.0578733
\(535\) −9.76789 −0.422303
\(536\) 4.96537 0.214471
\(537\) −25.8341 −1.11482
\(538\) −2.99229 −0.129007
\(539\) −39.8962 −1.71845
\(540\) 9.08845 0.391105
\(541\) −40.0342 −1.72121 −0.860603 0.509276i \(-0.829913\pi\)
−0.860603 + 0.509276i \(0.829913\pi\)
\(542\) −4.85673 −0.208615
\(543\) −22.4690 −0.964239
\(544\) −0.368220 −0.0157873
\(545\) 0.0384553 0.00164724
\(546\) 29.7574 1.27350
\(547\) 35.0640 1.49923 0.749614 0.661876i \(-0.230239\pi\)
0.749614 + 0.661876i \(0.230239\pi\)
\(548\) −4.79646 −0.204894
\(549\) −41.1959 −1.75820
\(550\) 3.27120 0.139484
\(551\) −1.53432 −0.0653640
\(552\) −1.87924 −0.0799859
\(553\) −35.2247 −1.49791
\(554\) −3.53360 −0.150128
\(555\) −9.60555 −0.407733
\(556\) 3.91350 0.165969
\(557\) −42.6982 −1.80918 −0.904591 0.426281i \(-0.859823\pi\)
−0.904591 + 0.426281i \(0.859823\pi\)
\(558\) −14.9502 −0.632894
\(559\) −11.8247 −0.500132
\(560\) 4.38135 0.185146
\(561\) 3.61863 0.152779
\(562\) 28.1683 1.18821
\(563\) 3.47846 0.146600 0.0732998 0.997310i \(-0.476647\pi\)
0.0732998 + 0.997310i \(0.476647\pi\)
\(564\) 3.21535 0.135391
\(565\) 3.13526 0.131901
\(566\) −16.2124 −0.681457
\(567\) −40.4303 −1.69791
\(568\) −5.72963 −0.240410
\(569\) 16.9175 0.709219 0.354610 0.935014i \(-0.384614\pi\)
0.354610 + 0.935014i \(0.384614\pi\)
\(570\) 5.59336 0.234280
\(571\) −3.92420 −0.164223 −0.0821113 0.996623i \(-0.526166\pi\)
−0.0821113 + 0.996623i \(0.526166\pi\)
\(572\) 7.39545 0.309220
\(573\) −52.3713 −2.18784
\(574\) 21.6024 0.901665
\(575\) −0.625538 −0.0260867
\(576\) 6.02524 0.251052
\(577\) 1.47636 0.0614616 0.0307308 0.999528i \(-0.490217\pi\)
0.0307308 + 0.999528i \(0.490217\pi\)
\(578\) 16.8644 0.701467
\(579\) −8.87212 −0.368713
\(580\) −0.824083 −0.0342182
\(581\) 63.1650 2.62052
\(582\) 41.8338 1.73407
\(583\) −1.77852 −0.0736587
\(584\) −16.8546 −0.697449
\(585\) 13.6217 0.563189
\(586\) 13.7452 0.567809
\(587\) −42.4425 −1.75179 −0.875895 0.482501i \(-0.839728\pi\)
−0.875895 + 0.482501i \(0.839728\pi\)
\(588\) −36.6399 −1.51100
\(589\) −4.61973 −0.190353
\(590\) 1.14090 0.0469700
\(591\) −12.7466 −0.524325
\(592\) −3.19737 −0.131411
\(593\) −9.06297 −0.372172 −0.186086 0.982534i \(-0.559580\pi\)
−0.186086 + 0.982534i \(0.559580\pi\)
\(594\) −29.7301 −1.21984
\(595\) 1.61330 0.0661388
\(596\) −7.54191 −0.308929
\(597\) 44.4711 1.82008
\(598\) −1.41420 −0.0578310
\(599\) 24.3541 0.995081 0.497541 0.867441i \(-0.334237\pi\)
0.497541 + 0.867441i \(0.334237\pi\)
\(600\) 3.00420 0.122646
\(601\) −19.8389 −0.809245 −0.404622 0.914484i \(-0.632597\pi\)
−0.404622 + 0.914484i \(0.632597\pi\)
\(602\) 22.9161 0.933990
\(603\) −29.9176 −1.21834
\(604\) 3.11492 0.126744
\(605\) 0.299252 0.0121663
\(606\) 58.1953 2.36402
\(607\) 25.7922 1.04687 0.523437 0.852064i \(-0.324650\pi\)
0.523437 + 0.852064i \(0.324650\pi\)
\(608\) 1.86184 0.0755078
\(609\) 10.8470 0.439541
\(610\) −6.83722 −0.276831
\(611\) 2.41967 0.0978895
\(612\) 2.21861 0.0896822
\(613\) 26.6350 1.07578 0.537889 0.843015i \(-0.319222\pi\)
0.537889 + 0.843015i \(0.319222\pi\)
\(614\) 19.0088 0.767133
\(615\) 14.8123 0.597290
\(616\) −14.3323 −0.577463
\(617\) 18.5084 0.745122 0.372561 0.928008i \(-0.378480\pi\)
0.372561 + 0.928008i \(0.378480\pi\)
\(618\) 7.15945 0.287995
\(619\) 18.1508 0.729540 0.364770 0.931098i \(-0.381148\pi\)
0.364770 + 0.931098i \(0.381148\pi\)
\(620\) −2.48127 −0.0996501
\(621\) 5.68517 0.228138
\(622\) −13.1742 −0.528238
\(623\) 1.95042 0.0781418
\(624\) 6.79184 0.271891
\(625\) 1.00000 0.0400000
\(626\) −3.86799 −0.154596
\(627\) −18.2970 −0.730712
\(628\) 4.02861 0.160759
\(629\) −1.17734 −0.0469434
\(630\) −26.3987 −1.05175
\(631\) −14.9828 −0.596454 −0.298227 0.954495i \(-0.596395\pi\)
−0.298227 + 0.954495i \(0.596395\pi\)
\(632\) −8.03970 −0.319802
\(633\) 73.6913 2.92896
\(634\) 18.5368 0.736189
\(635\) 4.70586 0.186747
\(636\) −1.63336 −0.0647668
\(637\) −27.5729 −1.09248
\(638\) 2.69574 0.106725
\(639\) 34.5224 1.36569
\(640\) 1.00000 0.0395285
\(641\) −14.6679 −0.579346 −0.289673 0.957126i \(-0.593547\pi\)
−0.289673 + 0.957126i \(0.593547\pi\)
\(642\) 29.3448 1.15814
\(643\) 12.6029 0.497009 0.248504 0.968631i \(-0.420061\pi\)
0.248504 + 0.968631i \(0.420061\pi\)
\(644\) 2.74070 0.107999
\(645\) 15.7131 0.618703
\(646\) 0.685568 0.0269733
\(647\) 26.6210 1.04658 0.523291 0.852154i \(-0.324704\pi\)
0.523291 + 0.852154i \(0.324704\pi\)
\(648\) −9.22783 −0.362503
\(649\) −3.73210 −0.146498
\(650\) 2.26078 0.0886750
\(651\) 32.6596 1.28003
\(652\) −16.9126 −0.662347
\(653\) 36.0372 1.41024 0.705122 0.709086i \(-0.250892\pi\)
0.705122 + 0.709086i \(0.250892\pi\)
\(654\) −0.115528 −0.00451748
\(655\) 0.648468 0.0253377
\(656\) 4.93053 0.192505
\(657\) 101.553 3.96197
\(658\) −4.68929 −0.182807
\(659\) 49.0391 1.91029 0.955147 0.296133i \(-0.0956972\pi\)
0.955147 + 0.296133i \(0.0956972\pi\)
\(660\) −9.82735 −0.382529
\(661\) −30.3035 −1.17867 −0.589334 0.807889i \(-0.700610\pi\)
−0.589334 + 0.807889i \(0.700610\pi\)
\(662\) 25.1409 0.977128
\(663\) 2.50089 0.0971265
\(664\) 14.4168 0.559480
\(665\) −8.15739 −0.316330
\(666\) 19.2649 0.746501
\(667\) −0.515495 −0.0199601
\(668\) 4.31707 0.167033
\(669\) 77.6234 3.00109
\(670\) −4.96537 −0.191829
\(671\) 22.3659 0.863426
\(672\) −13.1625 −0.507753
\(673\) −39.8737 −1.53702 −0.768510 0.639838i \(-0.779001\pi\)
−0.768510 + 0.639838i \(0.779001\pi\)
\(674\) −12.4506 −0.479580
\(675\) −9.08845 −0.349815
\(676\) −7.88889 −0.303419
\(677\) 37.1772 1.42884 0.714418 0.699719i \(-0.246691\pi\)
0.714418 + 0.699719i \(0.246691\pi\)
\(678\) −9.41896 −0.361733
\(679\) −61.0106 −2.34137
\(680\) 0.368220 0.0141206
\(681\) 12.1690 0.466317
\(682\) 8.11672 0.310805
\(683\) 13.5008 0.516594 0.258297 0.966066i \(-0.416839\pi\)
0.258297 + 0.966066i \(0.416839\pi\)
\(684\) −11.2181 −0.428933
\(685\) 4.79646 0.183263
\(686\) 22.7664 0.869226
\(687\) −42.0851 −1.60565
\(688\) 5.23037 0.199406
\(689\) −1.22916 −0.0468274
\(690\) 1.87924 0.0715416
\(691\) −15.2582 −0.580450 −0.290225 0.956958i \(-0.593730\pi\)
−0.290225 + 0.956958i \(0.593730\pi\)
\(692\) 24.6465 0.936920
\(693\) 86.3554 3.28037
\(694\) −13.9023 −0.527726
\(695\) −3.91350 −0.148447
\(696\) 2.47572 0.0938417
\(697\) 1.81552 0.0687677
\(698\) 5.12796 0.194096
\(699\) −0.806398 −0.0305008
\(700\) −4.38135 −0.165599
\(701\) −24.7375 −0.934324 −0.467162 0.884172i \(-0.654723\pi\)
−0.467162 + 0.884172i \(0.654723\pi\)
\(702\) −20.5470 −0.775495
\(703\) 5.95301 0.224522
\(704\) −3.27120 −0.123288
\(705\) −3.21535 −0.121097
\(706\) 13.7457 0.517328
\(707\) −84.8724 −3.19196
\(708\) −3.42749 −0.128813
\(709\) 41.9924 1.57706 0.788529 0.614998i \(-0.210843\pi\)
0.788529 + 0.614998i \(0.210843\pi\)
\(710\) 5.72963 0.215029
\(711\) 48.4412 1.81669
\(712\) 0.445164 0.0166832
\(713\) −1.55213 −0.0581276
\(714\) −4.84668 −0.181383
\(715\) −7.39545 −0.276574
\(716\) 8.59930 0.321371
\(717\) −21.2616 −0.794030
\(718\) 24.2421 0.904707
\(719\) 4.68575 0.174749 0.0873744 0.996176i \(-0.472152\pi\)
0.0873744 + 0.996176i \(0.472152\pi\)
\(720\) −6.02524 −0.224548
\(721\) −10.4414 −0.388857
\(722\) 15.5335 0.578098
\(723\) 52.0089 1.93423
\(724\) 7.47920 0.277962
\(725\) 0.824083 0.0306057
\(726\) −0.899013 −0.0333655
\(727\) 27.9141 1.03527 0.517637 0.855600i \(-0.326812\pi\)
0.517637 + 0.855600i \(0.326812\pi\)
\(728\) −9.90525 −0.367113
\(729\) −26.3108 −0.974473
\(730\) 16.8546 0.623817
\(731\) 1.92593 0.0712330
\(732\) 20.5404 0.759195
\(733\) 34.5426 1.27586 0.637930 0.770095i \(-0.279791\pi\)
0.637930 + 0.770095i \(0.279791\pi\)
\(734\) 8.27488 0.305431
\(735\) 36.6399 1.35148
\(736\) 0.625538 0.0230576
\(737\) 16.2427 0.598308
\(738\) −29.7076 −1.09355
\(739\) −18.9705 −0.697840 −0.348920 0.937152i \(-0.613452\pi\)
−0.348920 + 0.937152i \(0.613452\pi\)
\(740\) 3.19737 0.117538
\(741\) −12.6453 −0.464538
\(742\) 2.38210 0.0874495
\(743\) 15.3973 0.564871 0.282436 0.959286i \(-0.408858\pi\)
0.282436 + 0.959286i \(0.408858\pi\)
\(744\) 7.45423 0.273285
\(745\) 7.54191 0.276314
\(746\) 24.9657 0.914061
\(747\) −86.8647 −3.17821
\(748\) −1.20452 −0.0440416
\(749\) −42.7965 −1.56375
\(750\) −3.00420 −0.109698
\(751\) 46.5683 1.69930 0.849651 0.527346i \(-0.176813\pi\)
0.849651 + 0.527346i \(0.176813\pi\)
\(752\) −1.07028 −0.0390292
\(753\) 43.4243 1.58247
\(754\) 1.86307 0.0678490
\(755\) −3.11492 −0.113364
\(756\) 39.8197 1.44823
\(757\) 27.9286 1.01508 0.507540 0.861628i \(-0.330555\pi\)
0.507540 + 0.861628i \(0.330555\pi\)
\(758\) −5.76871 −0.209529
\(759\) −6.14738 −0.223136
\(760\) −1.86184 −0.0675362
\(761\) −25.2055 −0.913700 −0.456850 0.889544i \(-0.651022\pi\)
−0.456850 + 0.889544i \(0.651022\pi\)
\(762\) −14.1374 −0.512143
\(763\) 0.168486 0.00609960
\(764\) 17.4327 0.630692
\(765\) −2.21861 −0.0802142
\(766\) −31.1789 −1.12654
\(767\) −2.57931 −0.0931336
\(768\) −3.00420 −0.108405
\(769\) 35.1757 1.26847 0.634233 0.773142i \(-0.281316\pi\)
0.634233 + 0.773142i \(0.281316\pi\)
\(770\) 14.3323 0.516499
\(771\) −54.2135 −1.95245
\(772\) 2.95323 0.106289
\(773\) 5.98674 0.215328 0.107664 0.994187i \(-0.465663\pi\)
0.107664 + 0.994187i \(0.465663\pi\)
\(774\) −31.5143 −1.13276
\(775\) 2.48127 0.0891298
\(776\) −13.9251 −0.499881
\(777\) −42.0853 −1.50980
\(778\) −15.8001 −0.566461
\(779\) −9.17988 −0.328903
\(780\) −6.79184 −0.243187
\(781\) −18.7428 −0.670669
\(782\) 0.230335 0.00823678
\(783\) −7.48964 −0.267658
\(784\) 12.1962 0.435579
\(785\) −4.02861 −0.143787
\(786\) −1.94813 −0.0694875
\(787\) 0.564328 0.0201161 0.0100581 0.999949i \(-0.496798\pi\)
0.0100581 + 0.999949i \(0.496798\pi\)
\(788\) 4.24292 0.151148
\(789\) 28.9741 1.03150
\(790\) 8.03970 0.286040
\(791\) 13.7367 0.488420
\(792\) 19.7098 0.700356
\(793\) 15.4574 0.548909
\(794\) 1.32833 0.0471408
\(795\) 1.63336 0.0579292
\(796\) −14.8029 −0.524677
\(797\) −5.57121 −0.197342 −0.0986712 0.995120i \(-0.531459\pi\)
−0.0986712 + 0.995120i \(0.531459\pi\)
\(798\) 24.5065 0.867519
\(799\) −0.394100 −0.0139422
\(800\) −1.00000 −0.0353553
\(801\) −2.68222 −0.0947715
\(802\) 1.00000 0.0353112
\(803\) −55.1348 −1.94566
\(804\) 14.9170 0.526081
\(805\) −2.74070 −0.0965969
\(806\) 5.60959 0.197589
\(807\) −8.98944 −0.316443
\(808\) −19.3713 −0.681480
\(809\) 3.85000 0.135359 0.0676795 0.997707i \(-0.478440\pi\)
0.0676795 + 0.997707i \(0.478440\pi\)
\(810\) 9.22783 0.324233
\(811\) −7.46901 −0.262272 −0.131136 0.991364i \(-0.541863\pi\)
−0.131136 + 0.991364i \(0.541863\pi\)
\(812\) −3.61060 −0.126707
\(813\) −14.5906 −0.511715
\(814\) −10.4592 −0.366596
\(815\) 16.9126 0.592421
\(816\) −1.10621 −0.0387250
\(817\) −9.73814 −0.340694
\(818\) −8.99084 −0.314357
\(819\) 59.6816 2.08544
\(820\) −4.93053 −0.172182
\(821\) 18.0808 0.631025 0.315512 0.948921i \(-0.397824\pi\)
0.315512 + 0.948921i \(0.397824\pi\)
\(822\) −14.4095 −0.502590
\(823\) −13.5500 −0.472323 −0.236162 0.971714i \(-0.575889\pi\)
−0.236162 + 0.971714i \(0.575889\pi\)
\(824\) −2.38314 −0.0830207
\(825\) 9.82735 0.342145
\(826\) 4.99867 0.173926
\(827\) 6.20103 0.215631 0.107815 0.994171i \(-0.465614\pi\)
0.107815 + 0.994171i \(0.465614\pi\)
\(828\) −3.76902 −0.130982
\(829\) −21.4092 −0.743572 −0.371786 0.928318i \(-0.621254\pi\)
−0.371786 + 0.928318i \(0.621254\pi\)
\(830\) −14.4168 −0.500414
\(831\) −10.6157 −0.368253
\(832\) −2.26078 −0.0783784
\(833\) 4.49089 0.155600
\(834\) 11.7570 0.407110
\(835\) −4.31707 −0.149398
\(836\) 6.09047 0.210643
\(837\) −22.5509 −0.779472
\(838\) 17.4387 0.602410
\(839\) −45.2264 −1.56139 −0.780695 0.624912i \(-0.785135\pi\)
−0.780695 + 0.624912i \(0.785135\pi\)
\(840\) 13.1625 0.454148
\(841\) −28.3209 −0.976582
\(842\) 19.2201 0.662368
\(843\) 84.6232 2.91458
\(844\) −24.5294 −0.844336
\(845\) 7.88889 0.271386
\(846\) 6.44872 0.221712
\(847\) 1.31113 0.0450508
\(848\) 0.543690 0.0186704
\(849\) −48.7053 −1.67156
\(850\) −0.368220 −0.0126298
\(851\) 2.00008 0.0685617
\(852\) −17.2130 −0.589707
\(853\) 4.77907 0.163632 0.0818160 0.996647i \(-0.473928\pi\)
0.0818160 + 0.996647i \(0.473928\pi\)
\(854\) −29.9562 −1.02508
\(855\) 11.2181 0.383650
\(856\) −9.76789 −0.333860
\(857\) 19.5735 0.668619 0.334310 0.942463i \(-0.391497\pi\)
0.334310 + 0.942463i \(0.391497\pi\)
\(858\) 22.2175 0.758491
\(859\) 28.6355 0.977030 0.488515 0.872555i \(-0.337539\pi\)
0.488515 + 0.872555i \(0.337539\pi\)
\(860\) −5.23037 −0.178354
\(861\) 64.8979 2.21171
\(862\) −2.69307 −0.0917262
\(863\) 45.8524 1.56083 0.780417 0.625259i \(-0.215007\pi\)
0.780417 + 0.625259i \(0.215007\pi\)
\(864\) 9.08845 0.309195
\(865\) −24.6465 −0.838007
\(866\) 21.8698 0.743167
\(867\) 50.6641 1.72064
\(868\) −10.8713 −0.368996
\(869\) −26.2995 −0.892149
\(870\) −2.47572 −0.0839346
\(871\) 11.2256 0.380365
\(872\) 0.0384553 0.00130226
\(873\) 83.9020 2.83965
\(874\) −1.16465 −0.0393950
\(875\) 4.38135 0.148117
\(876\) −50.6347 −1.71079
\(877\) −39.3654 −1.32928 −0.664638 0.747165i \(-0.731414\pi\)
−0.664638 + 0.747165i \(0.731414\pi\)
\(878\) 1.52968 0.0516241
\(879\) 41.2934 1.39279
\(880\) 3.27120 0.110272
\(881\) −9.49150 −0.319777 −0.159888 0.987135i \(-0.551113\pi\)
−0.159888 + 0.987135i \(0.551113\pi\)
\(882\) −73.4851 −2.47437
\(883\) 15.7979 0.531641 0.265821 0.964023i \(-0.414357\pi\)
0.265821 + 0.964023i \(0.414357\pi\)
\(884\) −0.832463 −0.0279988
\(885\) 3.42749 0.115214
\(886\) 7.30305 0.245351
\(887\) 30.2187 1.01464 0.507322 0.861757i \(-0.330636\pi\)
0.507322 + 0.861757i \(0.330636\pi\)
\(888\) −9.60555 −0.322341
\(889\) 20.6180 0.691507
\(890\) −0.445164 −0.0149219
\(891\) −30.1861 −1.01127
\(892\) −25.8383 −0.865129
\(893\) 1.99270 0.0666832
\(894\) −22.6574 −0.757778
\(895\) −8.59930 −0.287443
\(896\) 4.38135 0.146371
\(897\) −4.24855 −0.141855
\(898\) −10.7673 −0.359310
\(899\) 2.04477 0.0681969
\(900\) 6.02524 0.200841
\(901\) 0.200198 0.00666955
\(902\) 16.1287 0.537028
\(903\) 68.8446 2.29100
\(904\) 3.13526 0.104277
\(905\) −7.47920 −0.248617
\(906\) 9.35785 0.310894
\(907\) 29.1017 0.966308 0.483154 0.875535i \(-0.339491\pi\)
0.483154 + 0.875535i \(0.339491\pi\)
\(908\) −4.05065 −0.134426
\(909\) 116.717 3.87125
\(910\) 9.90525 0.328356
\(911\) −45.1221 −1.49496 −0.747481 0.664283i \(-0.768737\pi\)
−0.747481 + 0.664283i \(0.768737\pi\)
\(912\) 5.59336 0.185215
\(913\) 47.1602 1.56077
\(914\) −27.1707 −0.898728
\(915\) −20.5404 −0.679044
\(916\) 14.0087 0.462861
\(917\) 2.84116 0.0938235
\(918\) 3.34655 0.110453
\(919\) 3.90777 0.128905 0.0644527 0.997921i \(-0.479470\pi\)
0.0644527 + 0.997921i \(0.479470\pi\)
\(920\) −0.625538 −0.0206234
\(921\) 57.1063 1.88172
\(922\) 9.07414 0.298841
\(923\) −12.9534 −0.426367
\(924\) −43.0571 −1.41647
\(925\) −3.19737 −0.105129
\(926\) 23.5550 0.774066
\(927\) 14.3590 0.471612
\(928\) −0.824083 −0.0270519
\(929\) 4.84819 0.159064 0.0795319 0.996832i \(-0.474657\pi\)
0.0795319 + 0.996832i \(0.474657\pi\)
\(930\) −7.45423 −0.244434
\(931\) −22.7075 −0.744207
\(932\) 0.268423 0.00879249
\(933\) −39.5780 −1.29573
\(934\) −17.4498 −0.570976
\(935\) 1.20452 0.0393920
\(936\) 13.6217 0.445240
\(937\) −17.0699 −0.557650 −0.278825 0.960342i \(-0.589945\pi\)
−0.278825 + 0.960342i \(0.589945\pi\)
\(938\) −21.7550 −0.710326
\(939\) −11.6202 −0.379212
\(940\) 1.07028 0.0349088
\(941\) 42.5380 1.38670 0.693350 0.720601i \(-0.256134\pi\)
0.693350 + 0.720601i \(0.256134\pi\)
\(942\) 12.1028 0.394330
\(943\) −3.08423 −0.100436
\(944\) 1.14090 0.0371330
\(945\) −39.8197 −1.29533
\(946\) 17.1096 0.556281
\(947\) 9.23495 0.300096 0.150048 0.988679i \(-0.452057\pi\)
0.150048 + 0.988679i \(0.452057\pi\)
\(948\) −24.1529 −0.784450
\(949\) −38.1045 −1.23693
\(950\) 1.86184 0.0604062
\(951\) 55.6882 1.80581
\(952\) 1.61330 0.0522873
\(953\) −23.6660 −0.766617 −0.383309 0.923620i \(-0.625215\pi\)
−0.383309 + 0.923620i \(0.625215\pi\)
\(954\) −3.27587 −0.106060
\(955\) −17.4327 −0.564108
\(956\) 7.07729 0.228896
\(957\) 8.09856 0.261789
\(958\) −9.78078 −0.316003
\(959\) 21.0149 0.678608
\(960\) 3.00420 0.0969603
\(961\) −24.8433 −0.801397
\(962\) −7.22854 −0.233058
\(963\) 58.8539 1.89654
\(964\) −17.3121 −0.557584
\(965\) −2.95323 −0.0950680
\(966\) 8.23362 0.264912
\(967\) 41.3149 1.32860 0.664300 0.747466i \(-0.268730\pi\)
0.664300 + 0.747466i \(0.268730\pi\)
\(968\) 0.299252 0.00961831
\(969\) 2.05959 0.0661635
\(970\) 13.9251 0.447107
\(971\) −50.7255 −1.62786 −0.813929 0.580964i \(-0.802676\pi\)
−0.813929 + 0.580964i \(0.802676\pi\)
\(972\) −0.456932 −0.0146561
\(973\) −17.1464 −0.549688
\(974\) −24.3102 −0.778950
\(975\) 6.79184 0.217513
\(976\) −6.83722 −0.218854
\(977\) 55.0815 1.76221 0.881107 0.472917i \(-0.156799\pi\)
0.881107 + 0.472917i \(0.156799\pi\)
\(978\) −50.8088 −1.62469
\(979\) 1.45622 0.0465410
\(980\) −12.1962 −0.389594
\(981\) −0.231702 −0.00739769
\(982\) 18.0341 0.575492
\(983\) 14.4805 0.461856 0.230928 0.972971i \(-0.425824\pi\)
0.230928 + 0.972971i \(0.425824\pi\)
\(984\) 14.8123 0.472199
\(985\) −4.24292 −0.135191
\(986\) −0.303444 −0.00966362
\(987\) −14.0876 −0.448412
\(988\) 4.20922 0.133913
\(989\) −3.27180 −0.104037
\(990\) −19.7098 −0.626418
\(991\) 52.7667 1.67619 0.838095 0.545524i \(-0.183669\pi\)
0.838095 + 0.545524i \(0.183669\pi\)
\(992\) −2.48127 −0.0787803
\(993\) 75.5283 2.39682
\(994\) 25.1035 0.796235
\(995\) 14.8029 0.469285
\(996\) 43.3110 1.37236
\(997\) −29.4070 −0.931329 −0.465665 0.884961i \(-0.654185\pi\)
−0.465665 + 0.884961i \(0.654185\pi\)
\(998\) −22.4604 −0.710973
\(999\) 29.0591 0.919390
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 \(a_p\))