Properties

Label 4010.2.a.k.1.10
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 1.10
Root \(-1.99921\)
Character \(\chi\) = 4010.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +0.271531 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.271531 q^{6} +1.75980 q^{7} -1.00000 q^{8} -2.92627 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +0.271531 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.271531 q^{6} +1.75980 q^{7} -1.00000 q^{8} -2.92627 q^{9} +1.00000 q^{10} +0.0291242 q^{11} +0.271531 q^{12} +5.25746 q^{13} -1.75980 q^{14} -0.271531 q^{15} +1.00000 q^{16} -3.06941 q^{17} +2.92627 q^{18} -6.99411 q^{19} -1.00000 q^{20} +0.477839 q^{21} -0.0291242 q^{22} +3.94735 q^{23} -0.271531 q^{24} +1.00000 q^{25} -5.25746 q^{26} -1.60916 q^{27} +1.75980 q^{28} +8.01843 q^{29} +0.271531 q^{30} -7.61367 q^{31} -1.00000 q^{32} +0.00790812 q^{33} +3.06941 q^{34} -1.75980 q^{35} -2.92627 q^{36} -3.48546 q^{37} +6.99411 q^{38} +1.42756 q^{39} +1.00000 q^{40} +1.23324 q^{41} -0.477839 q^{42} +3.83856 q^{43} +0.0291242 q^{44} +2.92627 q^{45} -3.94735 q^{46} -11.7435 q^{47} +0.271531 q^{48} -3.90312 q^{49} -1.00000 q^{50} -0.833440 q^{51} +5.25746 q^{52} +13.3734 q^{53} +1.60916 q^{54} -0.0291242 q^{55} -1.75980 q^{56} -1.89912 q^{57} -8.01843 q^{58} +1.28960 q^{59} -0.271531 q^{60} -5.25988 q^{61} +7.61367 q^{62} -5.14964 q^{63} +1.00000 q^{64} -5.25746 q^{65} -0.00790812 q^{66} -2.24766 q^{67} -3.06941 q^{68} +1.07183 q^{69} +1.75980 q^{70} -11.0826 q^{71} +2.92627 q^{72} -15.0109 q^{73} +3.48546 q^{74} +0.271531 q^{75} -6.99411 q^{76} +0.0512527 q^{77} -1.42756 q^{78} -2.43189 q^{79} -1.00000 q^{80} +8.34188 q^{81} -1.23324 q^{82} +8.86540 q^{83} +0.477839 q^{84} +3.06941 q^{85} -3.83856 q^{86} +2.17725 q^{87} -0.0291242 q^{88} +12.0009 q^{89} -2.92627 q^{90} +9.25205 q^{91} +3.94735 q^{92} -2.06734 q^{93} +11.7435 q^{94} +6.99411 q^{95} -0.271531 q^{96} +11.8894 q^{97} +3.90312 q^{98} -0.0852254 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 15q - 15q^{2} - 6q^{3} + 15q^{4} - 15q^{5} + 6q^{6} - 5q^{7} - 15q^{8} + 19q^{9} + O(q^{10}) \) \( 15q - 15q^{2} - 6q^{3} + 15q^{4} - 15q^{5} + 6q^{6} - 5q^{7} - 15q^{8} + 19q^{9} + 15q^{10} - 2q^{11} - 6q^{12} - 13q^{13} + 5q^{14} + 6q^{15} + 15q^{16} + 11q^{17} - 19q^{18} - 15q^{19} - 15q^{20} - 2q^{21} + 2q^{22} - 3q^{23} + 6q^{24} + 15q^{25} + 13q^{26} - 12q^{27} - 5q^{28} + 28q^{29} - 6q^{30} - 12q^{31} - 15q^{32} - 22q^{33} - 11q^{34} + 5q^{35} + 19q^{36} - 23q^{37} + 15q^{38} - 2q^{39} + 15q^{40} + 24q^{41} + 2q^{42} - 24q^{43} - 2q^{44} - 19q^{45} + 3q^{46} - 3q^{47} - 6q^{48} + 20q^{49} - 15q^{50} - 5q^{51} - 13q^{52} + 10q^{53} + 12q^{54} + 2q^{55} + 5q^{56} - 11q^{57} - 28q^{58} + 2q^{59} + 6q^{60} + 15q^{61} + 12q^{62} - 2q^{63} + 15q^{64} + 13q^{65} + 22q^{66} - 48q^{67} + 11q^{68} + 21q^{69} - 5q^{70} + 15q^{71} - 19q^{72} - 47q^{73} + 23q^{74} - 6q^{75} - 15q^{76} + 7q^{77} + 2q^{78} - 34q^{79} - 15q^{80} + 43q^{81} - 24q^{82} - 32q^{83} - 2q^{84} - 11q^{85} + 24q^{86} + 14q^{87} + 2q^{88} + 25q^{89} + 19q^{90} - 32q^{91} - 3q^{92} - 42q^{93} + 3q^{94} + 15q^{95} + 6q^{96} - 34q^{97} - 20q^{98} + 4q^{99} + O(q^{100}) \)

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
\(3\) 0.271531 0.156768 0.0783842 0.996923i \(-0.475024\pi\)
0.0783842 + 0.996923i \(0.475024\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) −0.271531 −0.110852
\(7\) 1.75980 0.665141 0.332570 0.943078i \(-0.392084\pi\)
0.332570 + 0.943078i \(0.392084\pi\)
\(8\) −1.00000 −0.353553
\(9\) −2.92627 −0.975424
\(10\) 1.00000 0.316228
\(11\) 0.0291242 0.00878128 0.00439064 0.999990i \(-0.498602\pi\)
0.00439064 + 0.999990i \(0.498602\pi\)
\(12\) 0.271531 0.0783842
\(13\) 5.25746 1.45816 0.729078 0.684431i \(-0.239949\pi\)
0.729078 + 0.684431i \(0.239949\pi\)
\(14\) −1.75980 −0.470325
\(15\) −0.271531 −0.0701089
\(16\) 1.00000 0.250000
\(17\) −3.06941 −0.744442 −0.372221 0.928144i \(-0.621404\pi\)
−0.372221 + 0.928144i \(0.621404\pi\)
\(18\) 2.92627 0.689729
\(19\) −6.99411 −1.60456 −0.802280 0.596948i \(-0.796380\pi\)
−0.802280 + 0.596948i \(0.796380\pi\)
\(20\) −1.00000 −0.223607
\(21\) 0.477839 0.104273
\(22\) −0.0291242 −0.00620931
\(23\) 3.94735 0.823079 0.411540 0.911392i \(-0.364991\pi\)
0.411540 + 0.911392i \(0.364991\pi\)
\(24\) −0.271531 −0.0554260
\(25\) 1.00000 0.200000
\(26\) −5.25746 −1.03107
\(27\) −1.60916 −0.309684
\(28\) 1.75980 0.332570
\(29\) 8.01843 1.48898 0.744492 0.667631i \(-0.232692\pi\)
0.744492 + 0.667631i \(0.232692\pi\)
\(30\) 0.271531 0.0495745
\(31\) −7.61367 −1.36746 −0.683728 0.729737i \(-0.739642\pi\)
−0.683728 + 0.729737i \(0.739642\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0.00790812 0.00137663
\(34\) 3.06941 0.526400
\(35\) −1.75980 −0.297460
\(36\) −2.92627 −0.487712
\(37\) −3.48546 −0.573006 −0.286503 0.958079i \(-0.592493\pi\)
−0.286503 + 0.958079i \(0.592493\pi\)
\(38\) 6.99411 1.13459
\(39\) 1.42756 0.228593
\(40\) 1.00000 0.158114
\(41\) 1.23324 0.192600 0.0962998 0.995352i \(-0.469299\pi\)
0.0962998 + 0.995352i \(0.469299\pi\)
\(42\) −0.477839 −0.0737321
\(43\) 3.83856 0.585375 0.292687 0.956208i \(-0.405450\pi\)
0.292687 + 0.956208i \(0.405450\pi\)
\(44\) 0.0291242 0.00439064
\(45\) 2.92627 0.436223
\(46\) −3.94735 −0.582005
\(47\) −11.7435 −1.71296 −0.856482 0.516177i \(-0.827355\pi\)
−0.856482 + 0.516177i \(0.827355\pi\)
\(48\) 0.271531 0.0391921
\(49\) −3.90312 −0.557588
\(50\) −1.00000 −0.141421
\(51\) −0.833440 −0.116705
\(52\) 5.25746 0.729078
\(53\) 13.3734 1.83698 0.918492 0.395439i \(-0.129408\pi\)
0.918492 + 0.395439i \(0.129408\pi\)
\(54\) 1.60916 0.218980
\(55\) −0.0291242 −0.00392711
\(56\) −1.75980 −0.235163
\(57\) −1.89912 −0.251544
\(58\) −8.01843 −1.05287
\(59\) 1.28960 0.167892 0.0839460 0.996470i \(-0.473248\pi\)
0.0839460 + 0.996470i \(0.473248\pi\)
\(60\) −0.271531 −0.0350545
\(61\) −5.25988 −0.673459 −0.336729 0.941602i \(-0.609321\pi\)
−0.336729 + 0.941602i \(0.609321\pi\)
\(62\) 7.61367 0.966937
\(63\) −5.14964 −0.648794
\(64\) 1.00000 0.125000
\(65\) −5.25746 −0.652107
\(66\) −0.00790812 −0.000973422 0
\(67\) −2.24766 −0.274595 −0.137298 0.990530i \(-0.543842\pi\)
−0.137298 + 0.990530i \(0.543842\pi\)
\(68\) −3.06941 −0.372221
\(69\) 1.07183 0.129033
\(70\) 1.75980 0.210336
\(71\) −11.0826 −1.31526 −0.657631 0.753340i \(-0.728441\pi\)
−0.657631 + 0.753340i \(0.728441\pi\)
\(72\) 2.92627 0.344864
\(73\) −15.0109 −1.75690 −0.878448 0.477838i \(-0.841421\pi\)
−0.878448 + 0.477838i \(0.841421\pi\)
\(74\) 3.48546 0.405177
\(75\) 0.271531 0.0313537
\(76\) −6.99411 −0.802280
\(77\) 0.0512527 0.00584079
\(78\) −1.42756 −0.161639
\(79\) −2.43189 −0.273609 −0.136805 0.990598i \(-0.543683\pi\)
−0.136805 + 0.990598i \(0.543683\pi\)
\(80\) −1.00000 −0.111803
\(81\) 8.34188 0.926875
\(82\) −1.23324 −0.136189
\(83\) 8.86540 0.973104 0.486552 0.873652i \(-0.338254\pi\)
0.486552 + 0.873652i \(0.338254\pi\)
\(84\) 0.477839 0.0521365
\(85\) 3.06941 0.332925
\(86\) −3.83856 −0.413923
\(87\) 2.17725 0.233426
\(88\) −0.0291242 −0.00310465
\(89\) 12.0009 1.27209 0.636047 0.771651i \(-0.280569\pi\)
0.636047 + 0.771651i \(0.280569\pi\)
\(90\) −2.92627 −0.308456
\(91\) 9.25205 0.969879
\(92\) 3.94735 0.411540
\(93\) −2.06734 −0.214374
\(94\) 11.7435 1.21125
\(95\) 6.99411 0.717581
\(96\) −0.271531 −0.0277130
\(97\) 11.8894 1.20719 0.603593 0.797293i \(-0.293735\pi\)
0.603593 + 0.797293i \(0.293735\pi\)
\(98\) 3.90312 0.394274
\(99\) −0.0852254 −0.00856547
\(100\) 1.00000 0.100000
\(101\) 2.76191 0.274821 0.137410 0.990514i \(-0.456122\pi\)
0.137410 + 0.990514i \(0.456122\pi\)
\(102\) 0.833440 0.0825229
\(103\) −12.0151 −1.18388 −0.591940 0.805982i \(-0.701638\pi\)
−0.591940 + 0.805982i \(0.701638\pi\)
\(104\) −5.25746 −0.515536
\(105\) −0.477839 −0.0466323
\(106\) −13.3734 −1.29894
\(107\) 18.3098 1.77008 0.885038 0.465519i \(-0.154132\pi\)
0.885038 + 0.465519i \(0.154132\pi\)
\(108\) −1.60916 −0.154842
\(109\) −13.5944 −1.30211 −0.651054 0.759031i \(-0.725673\pi\)
−0.651054 + 0.759031i \(0.725673\pi\)
\(110\) 0.0291242 0.00277689
\(111\) −0.946409 −0.0898292
\(112\) 1.75980 0.166285
\(113\) −9.64296 −0.907133 −0.453567 0.891222i \(-0.649849\pi\)
−0.453567 + 0.891222i \(0.649849\pi\)
\(114\) 1.89912 0.177869
\(115\) −3.94735 −0.368092
\(116\) 8.01843 0.744492
\(117\) −15.3847 −1.42232
\(118\) −1.28960 −0.118718
\(119\) −5.40154 −0.495159
\(120\) 0.271531 0.0247872
\(121\) −10.9992 −0.999923
\(122\) 5.25988 0.476207
\(123\) 0.334862 0.0301935
\(124\) −7.61367 −0.683728
\(125\) −1.00000 −0.0894427
\(126\) 5.14964 0.458767
\(127\) −8.79870 −0.780758 −0.390379 0.920654i \(-0.627656\pi\)
−0.390379 + 0.920654i \(0.627656\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 1.04229 0.0917682
\(130\) 5.25746 0.461109
\(131\) −15.1375 −1.32257 −0.661284 0.750136i \(-0.729988\pi\)
−0.661284 + 0.750136i \(0.729988\pi\)
\(132\) 0.00790812 0.000688314 0
\(133\) −12.3082 −1.06726
\(134\) 2.24766 0.194168
\(135\) 1.60916 0.138495
\(136\) 3.06941 0.263200
\(137\) −20.7910 −1.77629 −0.888147 0.459560i \(-0.848007\pi\)
−0.888147 + 0.459560i \(0.848007\pi\)
\(138\) −1.07183 −0.0912399
\(139\) 3.77971 0.320591 0.160295 0.987069i \(-0.448755\pi\)
0.160295 + 0.987069i \(0.448755\pi\)
\(140\) −1.75980 −0.148730
\(141\) −3.18872 −0.268538
\(142\) 11.0826 0.930031
\(143\) 0.153119 0.0128045
\(144\) −2.92627 −0.243856
\(145\) −8.01843 −0.665894
\(146\) 15.0109 1.24231
\(147\) −1.05982 −0.0874121
\(148\) −3.48546 −0.286503
\(149\) 5.04601 0.413385 0.206693 0.978406i \(-0.433730\pi\)
0.206693 + 0.978406i \(0.433730\pi\)
\(150\) −0.271531 −0.0221704
\(151\) −11.7128 −0.953173 −0.476586 0.879128i \(-0.658126\pi\)
−0.476586 + 0.879128i \(0.658126\pi\)
\(152\) 6.99411 0.567297
\(153\) 8.98194 0.726147
\(154\) −0.0512527 −0.00413006
\(155\) 7.61367 0.611545
\(156\) 1.42756 0.114296
\(157\) 0.968067 0.0772601 0.0386301 0.999254i \(-0.487701\pi\)
0.0386301 + 0.999254i \(0.487701\pi\)
\(158\) 2.43189 0.193471
\(159\) 3.63130 0.287981
\(160\) 1.00000 0.0790569
\(161\) 6.94653 0.547463
\(162\) −8.34188 −0.655400
\(163\) −23.9054 −1.87241 −0.936207 0.351450i \(-0.885689\pi\)
−0.936207 + 0.351450i \(0.885689\pi\)
\(164\) 1.23324 0.0962998
\(165\) −0.00790812 −0.000615646 0
\(166\) −8.86540 −0.688088
\(167\) 21.5368 1.66657 0.833286 0.552843i \(-0.186457\pi\)
0.833286 + 0.552843i \(0.186457\pi\)
\(168\) −0.477839 −0.0368661
\(169\) 14.6408 1.12622
\(170\) −3.06941 −0.235413
\(171\) 20.4667 1.56513
\(172\) 3.83856 0.292687
\(173\) −4.48959 −0.341337 −0.170669 0.985328i \(-0.554593\pi\)
−0.170669 + 0.985328i \(0.554593\pi\)
\(174\) −2.17725 −0.165057
\(175\) 1.75980 0.133028
\(176\) 0.0291242 0.00219532
\(177\) 0.350167 0.0263201
\(178\) −12.0009 −0.899506
\(179\) 12.6642 0.946570 0.473285 0.880909i \(-0.343068\pi\)
0.473285 + 0.880909i \(0.343068\pi\)
\(180\) 2.92627 0.218111
\(181\) 11.1385 0.827921 0.413961 0.910295i \(-0.364145\pi\)
0.413961 + 0.910295i \(0.364145\pi\)
\(182\) −9.25205 −0.685808
\(183\) −1.42822 −0.105577
\(184\) −3.94735 −0.291002
\(185\) 3.48546 0.256256
\(186\) 2.06734 0.151585
\(187\) −0.0893943 −0.00653716
\(188\) −11.7435 −0.856482
\(189\) −2.83180 −0.205983
\(190\) −6.99411 −0.507406
\(191\) −15.8182 −1.14457 −0.572284 0.820056i \(-0.693942\pi\)
−0.572284 + 0.820056i \(0.693942\pi\)
\(192\) 0.271531 0.0195960
\(193\) −16.0915 −1.15829 −0.579147 0.815223i \(-0.696614\pi\)
−0.579147 + 0.815223i \(0.696614\pi\)
\(194\) −11.8894 −0.853609
\(195\) −1.42756 −0.102230
\(196\) −3.90312 −0.278794
\(197\) −27.3570 −1.94910 −0.974552 0.224164i \(-0.928035\pi\)
−0.974552 + 0.224164i \(0.928035\pi\)
\(198\) 0.0852254 0.00605670
\(199\) 12.6901 0.899576 0.449788 0.893135i \(-0.351500\pi\)
0.449788 + 0.893135i \(0.351500\pi\)
\(200\) −1.00000 −0.0707107
\(201\) −0.610308 −0.0430478
\(202\) −2.76191 −0.194328
\(203\) 14.1108 0.990384
\(204\) −0.833440 −0.0583525
\(205\) −1.23324 −0.0861332
\(206\) 12.0151 0.837130
\(207\) −11.5510 −0.802851
\(208\) 5.25746 0.364539
\(209\) −0.203698 −0.0140901
\(210\) 0.477839 0.0329740
\(211\) 9.54263 0.656942 0.328471 0.944514i \(-0.393467\pi\)
0.328471 + 0.944514i \(0.393467\pi\)
\(212\) 13.3734 0.918492
\(213\) −3.00927 −0.206191
\(214\) −18.3098 −1.25163
\(215\) −3.83856 −0.261788
\(216\) 1.60916 0.109490
\(217\) −13.3985 −0.909550
\(218\) 13.5944 0.920730
\(219\) −4.07593 −0.275426
\(220\) −0.0291242 −0.00196355
\(221\) −16.1373 −1.08551
\(222\) 0.946409 0.0635188
\(223\) −7.00013 −0.468763 −0.234382 0.972145i \(-0.575307\pi\)
−0.234382 + 0.972145i \(0.575307\pi\)
\(224\) −1.75980 −0.117581
\(225\) −2.92627 −0.195085
\(226\) 9.64296 0.641440
\(227\) −16.3238 −1.08345 −0.541723 0.840557i \(-0.682228\pi\)
−0.541723 + 0.840557i \(0.682228\pi\)
\(228\) −1.89912 −0.125772
\(229\) −7.32344 −0.483947 −0.241973 0.970283i \(-0.577795\pi\)
−0.241973 + 0.970283i \(0.577795\pi\)
\(230\) 3.94735 0.260281
\(231\) 0.0139167 0.000915651 0
\(232\) −8.01843 −0.526435
\(233\) 8.02035 0.525430 0.262715 0.964873i \(-0.415382\pi\)
0.262715 + 0.964873i \(0.415382\pi\)
\(234\) 15.3847 1.00573
\(235\) 11.7435 0.766061
\(236\) 1.28960 0.0839460
\(237\) −0.660333 −0.0428933
\(238\) 5.40154 0.350130
\(239\) −15.5192 −1.00386 −0.501928 0.864910i \(-0.667376\pi\)
−0.501928 + 0.864910i \(0.667376\pi\)
\(240\) −0.271531 −0.0175272
\(241\) −9.21273 −0.593444 −0.296722 0.954964i \(-0.595893\pi\)
−0.296722 + 0.954964i \(0.595893\pi\)
\(242\) 10.9992 0.707052
\(243\) 7.09257 0.454988
\(244\) −5.25988 −0.336729
\(245\) 3.90312 0.249361
\(246\) −0.334862 −0.0213500
\(247\) −36.7712 −2.33970
\(248\) 7.61367 0.483468
\(249\) 2.40723 0.152552
\(250\) 1.00000 0.0632456
\(251\) 9.64811 0.608983 0.304492 0.952515i \(-0.401513\pi\)
0.304492 + 0.952515i \(0.401513\pi\)
\(252\) −5.14964 −0.324397
\(253\) 0.114964 0.00722769
\(254\) 8.79870 0.552079
\(255\) 0.833440 0.0521920
\(256\) 1.00000 0.0625000
\(257\) 23.5815 1.47097 0.735487 0.677539i \(-0.236953\pi\)
0.735487 + 0.677539i \(0.236953\pi\)
\(258\) −1.04229 −0.0648899
\(259\) −6.13370 −0.381130
\(260\) −5.25746 −0.326054
\(261\) −23.4641 −1.45239
\(262\) 15.1375 0.935197
\(263\) 1.06296 0.0655448 0.0327724 0.999463i \(-0.489566\pi\)
0.0327724 + 0.999463i \(0.489566\pi\)
\(264\) −0.00790812 −0.000486711 0
\(265\) −13.3734 −0.821524
\(266\) 12.3082 0.754665
\(267\) 3.25861 0.199424
\(268\) −2.24766 −0.137298
\(269\) 22.1713 1.35181 0.675903 0.736991i \(-0.263754\pi\)
0.675903 + 0.736991i \(0.263754\pi\)
\(270\) −1.60916 −0.0979306
\(271\) −0.657162 −0.0399198 −0.0199599 0.999801i \(-0.506354\pi\)
−0.0199599 + 0.999801i \(0.506354\pi\)
\(272\) −3.06941 −0.186111
\(273\) 2.51222 0.152046
\(274\) 20.7910 1.25603
\(275\) 0.0291242 0.00175626
\(276\) 1.07183 0.0645164
\(277\) 3.29293 0.197853 0.0989264 0.995095i \(-0.468459\pi\)
0.0989264 + 0.995095i \(0.468459\pi\)
\(278\) −3.77971 −0.226692
\(279\) 22.2797 1.33385
\(280\) 1.75980 0.105168
\(281\) 13.6936 0.816892 0.408446 0.912783i \(-0.366071\pi\)
0.408446 + 0.912783i \(0.366071\pi\)
\(282\) 3.18872 0.189885
\(283\) −4.02890 −0.239493 −0.119747 0.992804i \(-0.538208\pi\)
−0.119747 + 0.992804i \(0.538208\pi\)
\(284\) −11.0826 −0.657631
\(285\) 1.89912 0.112494
\(286\) −0.153119 −0.00905414
\(287\) 2.17025 0.128106
\(288\) 2.92627 0.172432
\(289\) −7.57870 −0.445806
\(290\) 8.01843 0.470858
\(291\) 3.22834 0.189248
\(292\) −15.0109 −0.878448
\(293\) −16.4070 −0.958505 −0.479253 0.877677i \(-0.659092\pi\)
−0.479253 + 0.877677i \(0.659092\pi\)
\(294\) 1.05982 0.0618097
\(295\) −1.28960 −0.0750836
\(296\) 3.48546 0.202588
\(297\) −0.0468657 −0.00271942
\(298\) −5.04601 −0.292308
\(299\) 20.7530 1.20018
\(300\) 0.271531 0.0156768
\(301\) 6.75509 0.389357
\(302\) 11.7128 0.673995
\(303\) 0.749945 0.0430832
\(304\) −6.99411 −0.401140
\(305\) 5.25988 0.301180
\(306\) −8.98194 −0.513463
\(307\) −25.3962 −1.44944 −0.724719 0.689045i \(-0.758030\pi\)
−0.724719 + 0.689045i \(0.758030\pi\)
\(308\) 0.0512527 0.00292039
\(309\) −3.26246 −0.185595
\(310\) −7.61367 −0.432427
\(311\) 0.0443761 0.00251634 0.00125817 0.999999i \(-0.499600\pi\)
0.00125817 + 0.999999i \(0.499600\pi\)
\(312\) −1.42756 −0.0808197
\(313\) 6.83705 0.386453 0.193226 0.981154i \(-0.438105\pi\)
0.193226 + 0.981154i \(0.438105\pi\)
\(314\) −0.968067 −0.0546312
\(315\) 5.14964 0.290149
\(316\) −2.43189 −0.136805
\(317\) −30.5804 −1.71756 −0.858782 0.512341i \(-0.828779\pi\)
−0.858782 + 0.512341i \(0.828779\pi\)
\(318\) −3.63130 −0.203633
\(319\) 0.233530 0.0130752
\(320\) −1.00000 −0.0559017
\(321\) 4.97167 0.277492
\(322\) −6.94653 −0.387115
\(323\) 21.4678 1.19450
\(324\) 8.34188 0.463438
\(325\) 5.25746 0.291631
\(326\) 23.9054 1.32400
\(327\) −3.69130 −0.204129
\(328\) −1.23324 −0.0680943
\(329\) −20.6662 −1.13936
\(330\) 0.00790812 0.000435328 0
\(331\) 11.6214 0.638771 0.319385 0.947625i \(-0.396524\pi\)
0.319385 + 0.947625i \(0.396524\pi\)
\(332\) 8.86540 0.486552
\(333\) 10.1994 0.558924
\(334\) −21.5368 −1.17844
\(335\) 2.24766 0.122803
\(336\) 0.477839 0.0260682
\(337\) −14.0702 −0.766454 −0.383227 0.923654i \(-0.625187\pi\)
−0.383227 + 0.923654i \(0.625187\pi\)
\(338\) −14.6408 −0.796357
\(339\) −2.61836 −0.142210
\(340\) 3.06941 0.166462
\(341\) −0.221742 −0.0120080
\(342\) −20.4667 −1.10671
\(343\) −19.1873 −1.03602
\(344\) −3.83856 −0.206961
\(345\) −1.07183 −0.0577052
\(346\) 4.48959 0.241362
\(347\) −22.6695 −1.21696 −0.608482 0.793568i \(-0.708221\pi\)
−0.608482 + 0.793568i \(0.708221\pi\)
\(348\) 2.17725 0.116713
\(349\) 5.47734 0.293195 0.146598 0.989196i \(-0.453168\pi\)
0.146598 + 0.989196i \(0.453168\pi\)
\(350\) −1.75980 −0.0940651
\(351\) −8.46011 −0.451567
\(352\) −0.0291242 −0.00155233
\(353\) −25.5131 −1.35793 −0.678963 0.734173i \(-0.737570\pi\)
−0.678963 + 0.734173i \(0.737570\pi\)
\(354\) −0.350167 −0.0186112
\(355\) 11.0826 0.588203
\(356\) 12.0009 0.636047
\(357\) −1.46669 −0.0776252
\(358\) −12.6642 −0.669326
\(359\) −26.7675 −1.41273 −0.706367 0.707846i \(-0.749667\pi\)
−0.706367 + 0.707846i \(0.749667\pi\)
\(360\) −2.92627 −0.154228
\(361\) 29.9176 1.57461
\(362\) −11.1385 −0.585429
\(363\) −2.98661 −0.156756
\(364\) 9.25205 0.484939
\(365\) 15.0109 0.785708
\(366\) 1.42822 0.0746542
\(367\) 23.4027 1.22161 0.610805 0.791781i \(-0.290846\pi\)
0.610805 + 0.791781i \(0.290846\pi\)
\(368\) 3.94735 0.205770
\(369\) −3.60879 −0.187866
\(370\) −3.48546 −0.181200
\(371\) 23.5346 1.22185
\(372\) −2.06734 −0.107187
\(373\) −20.4967 −1.06128 −0.530639 0.847598i \(-0.678048\pi\)
−0.530639 + 0.847598i \(0.678048\pi\)
\(374\) 0.0893943 0.00462247
\(375\) −0.271531 −0.0140218
\(376\) 11.7435 0.605624
\(377\) 42.1565 2.17117
\(378\) 2.83180 0.145652
\(379\) 2.60987 0.134060 0.0670299 0.997751i \(-0.478648\pi\)
0.0670299 + 0.997751i \(0.478648\pi\)
\(380\) 6.99411 0.358790
\(381\) −2.38912 −0.122398
\(382\) 15.8182 0.809332
\(383\) 9.31699 0.476076 0.238038 0.971256i \(-0.423496\pi\)
0.238038 + 0.971256i \(0.423496\pi\)
\(384\) −0.271531 −0.0138565
\(385\) −0.0512527 −0.00261208
\(386\) 16.0915 0.819037
\(387\) −11.2327 −0.570989
\(388\) 11.8894 0.603593
\(389\) −9.73754 −0.493713 −0.246856 0.969052i \(-0.579398\pi\)
−0.246856 + 0.969052i \(0.579398\pi\)
\(390\) 1.42756 0.0722873
\(391\) −12.1160 −0.612735
\(392\) 3.90312 0.197137
\(393\) −4.11029 −0.207337
\(394\) 27.3570 1.37822
\(395\) 2.43189 0.122362
\(396\) −0.0852254 −0.00428274
\(397\) −32.6545 −1.63888 −0.819441 0.573164i \(-0.805716\pi\)
−0.819441 + 0.573164i \(0.805716\pi\)
\(398\) −12.6901 −0.636096
\(399\) −3.34206 −0.167312
\(400\) 1.00000 0.0500000
\(401\) −1.00000 −0.0499376
\(402\) 0.610308 0.0304394
\(403\) −40.0285 −1.99396
\(404\) 2.76191 0.137410
\(405\) −8.34188 −0.414511
\(406\) −14.1108 −0.700307
\(407\) −0.101511 −0.00503173
\(408\) 0.833440 0.0412614
\(409\) 6.54320 0.323540 0.161770 0.986828i \(-0.448280\pi\)
0.161770 + 0.986828i \(0.448280\pi\)
\(410\) 1.23324 0.0609054
\(411\) −5.64539 −0.278467
\(412\) −12.0151 −0.591940
\(413\) 2.26944 0.111672
\(414\) 11.5510 0.567701
\(415\) −8.86540 −0.435185
\(416\) −5.25746 −0.257768
\(417\) 1.02631 0.0502584
\(418\) 0.203698 0.00996320
\(419\) −31.2137 −1.52489 −0.762445 0.647054i \(-0.776001\pi\)
−0.762445 + 0.647054i \(0.776001\pi\)
\(420\) −0.477839 −0.0233161
\(421\) −7.46544 −0.363843 −0.181922 0.983313i \(-0.558232\pi\)
−0.181922 + 0.983313i \(0.558232\pi\)
\(422\) −9.54263 −0.464528
\(423\) 34.3646 1.67087
\(424\) −13.3734 −0.649472
\(425\) −3.06941 −0.148888
\(426\) 3.00927 0.145799
\(427\) −9.25632 −0.447945
\(428\) 18.3098 0.885038
\(429\) 0.0415766 0.00200734
\(430\) 3.83856 0.185112
\(431\) −16.8501 −0.811639 −0.405819 0.913953i \(-0.633014\pi\)
−0.405819 + 0.913953i \(0.633014\pi\)
\(432\) −1.60916 −0.0774210
\(433\) 36.4196 1.75022 0.875108 0.483928i \(-0.160790\pi\)
0.875108 + 0.483928i \(0.160790\pi\)
\(434\) 13.3985 0.643149
\(435\) −2.17725 −0.104391
\(436\) −13.5944 −0.651054
\(437\) −27.6082 −1.32068
\(438\) 4.07593 0.194755
\(439\) 17.8466 0.851771 0.425886 0.904777i \(-0.359963\pi\)
0.425886 + 0.904777i \(0.359963\pi\)
\(440\) 0.0291242 0.00138844
\(441\) 11.4216 0.543884
\(442\) 16.1373 0.767573
\(443\) −25.6948 −1.22080 −0.610398 0.792095i \(-0.708991\pi\)
−0.610398 + 0.792095i \(0.708991\pi\)
\(444\) −0.946409 −0.0449146
\(445\) −12.0009 −0.568897
\(446\) 7.00013 0.331466
\(447\) 1.37015 0.0648057
\(448\) 1.75980 0.0831426
\(449\) 3.28609 0.155080 0.0775400 0.996989i \(-0.475293\pi\)
0.0775400 + 0.996989i \(0.475293\pi\)
\(450\) 2.92627 0.137946
\(451\) 0.0359171 0.00169127
\(452\) −9.64296 −0.453567
\(453\) −3.18038 −0.149427
\(454\) 16.3238 0.766112
\(455\) −9.25205 −0.433743
\(456\) 1.89912 0.0889343
\(457\) −18.3558 −0.858649 −0.429325 0.903150i \(-0.641248\pi\)
−0.429325 + 0.903150i \(0.641248\pi\)
\(458\) 7.32344 0.342202
\(459\) 4.93919 0.230542
\(460\) −3.94735 −0.184046
\(461\) −7.58525 −0.353280 −0.176640 0.984275i \(-0.556523\pi\)
−0.176640 + 0.984275i \(0.556523\pi\)
\(462\) −0.0139167 −0.000647463 0
\(463\) −35.3015 −1.64060 −0.820300 0.571933i \(-0.806194\pi\)
−0.820300 + 0.571933i \(0.806194\pi\)
\(464\) 8.01843 0.372246
\(465\) 2.06734 0.0958708
\(466\) −8.02035 −0.371535
\(467\) 2.76833 0.128103 0.0640514 0.997947i \(-0.479598\pi\)
0.0640514 + 0.997947i \(0.479598\pi\)
\(468\) −15.3847 −0.711160
\(469\) −3.95542 −0.182645
\(470\) −11.7435 −0.541687
\(471\) 0.262860 0.0121119
\(472\) −1.28960 −0.0593588
\(473\) 0.111795 0.00514034
\(474\) 0.660333 0.0303301
\(475\) −6.99411 −0.320912
\(476\) −5.40154 −0.247579
\(477\) −39.1343 −1.79184
\(478\) 15.5192 0.709833
\(479\) 16.5941 0.758205 0.379103 0.925355i \(-0.376233\pi\)
0.379103 + 0.925355i \(0.376233\pi\)
\(480\) 0.271531 0.0123936
\(481\) −18.3247 −0.835532
\(482\) 9.21273 0.419628
\(483\) 1.88620 0.0858249
\(484\) −10.9992 −0.499961
\(485\) −11.8894 −0.539870
\(486\) −7.09257 −0.321725
\(487\) 12.9950 0.588860 0.294430 0.955673i \(-0.404870\pi\)
0.294430 + 0.955673i \(0.404870\pi\)
\(488\) 5.25988 0.238104
\(489\) −6.49104 −0.293535
\(490\) −3.90312 −0.176325
\(491\) −27.9496 −1.26135 −0.630675 0.776047i \(-0.717222\pi\)
−0.630675 + 0.776047i \(0.717222\pi\)
\(492\) 0.334862 0.0150968
\(493\) −24.6119 −1.10846
\(494\) 36.7712 1.65442
\(495\) 0.0852254 0.00383060
\(496\) −7.61367 −0.341864
\(497\) −19.5031 −0.874835
\(498\) −2.40723 −0.107870
\(499\) 41.1489 1.84208 0.921039 0.389471i \(-0.127342\pi\)
0.921039 + 0.389471i \(0.127342\pi\)
\(500\) −1.00000 −0.0447214
\(501\) 5.84791 0.261266
\(502\) −9.64811 −0.430616
\(503\) 5.70973 0.254584 0.127292 0.991865i \(-0.459371\pi\)
0.127292 + 0.991865i \(0.459371\pi\)
\(504\) 5.14964 0.229383
\(505\) −2.76191 −0.122904
\(506\) −0.114964 −0.00511075
\(507\) 3.97544 0.176555
\(508\) −8.79870 −0.390379
\(509\) −22.6252 −1.00285 −0.501423 0.865202i \(-0.667190\pi\)
−0.501423 + 0.865202i \(0.667190\pi\)
\(510\) −0.833440 −0.0369053
\(511\) −26.4162 −1.16858
\(512\) −1.00000 −0.0441942
\(513\) 11.2547 0.496906
\(514\) −23.5815 −1.04014
\(515\) 12.0151 0.529448
\(516\) 1.04229 0.0458841
\(517\) −0.342020 −0.0150420
\(518\) 6.13370 0.269499
\(519\) −1.21906 −0.0535109
\(520\) 5.25746 0.230555
\(521\) 18.0536 0.790943 0.395471 0.918478i \(-0.370581\pi\)
0.395471 + 0.918478i \(0.370581\pi\)
\(522\) 23.4641 1.02700
\(523\) 13.4196 0.586797 0.293398 0.955990i \(-0.405214\pi\)
0.293398 + 0.955990i \(0.405214\pi\)
\(524\) −15.1375 −0.661284
\(525\) 0.477839 0.0208546
\(526\) −1.06296 −0.0463472
\(527\) 23.3695 1.01799
\(528\) 0.00790812 0.000344157 0
\(529\) −7.41843 −0.322541
\(530\) 13.3734 0.580905
\(531\) −3.77373 −0.163766
\(532\) −12.3082 −0.533629
\(533\) 6.48370 0.280840
\(534\) −3.25861 −0.141014
\(535\) −18.3098 −0.791602
\(536\) 2.24766 0.0970841
\(537\) 3.43873 0.148392
\(538\) −22.1713 −0.955871
\(539\) −0.113675 −0.00489634
\(540\) 1.60916 0.0692474
\(541\) 24.2590 1.04298 0.521489 0.853258i \(-0.325377\pi\)
0.521489 + 0.853258i \(0.325377\pi\)
\(542\) 0.657162 0.0282275
\(543\) 3.02446 0.129792
\(544\) 3.06941 0.131600
\(545\) 13.5944 0.582321
\(546\) −2.51222 −0.107513
\(547\) 9.26995 0.396354 0.198177 0.980166i \(-0.436498\pi\)
0.198177 + 0.980166i \(0.436498\pi\)
\(548\) −20.7910 −0.888147
\(549\) 15.3918 0.656907
\(550\) −0.0291242 −0.00124186
\(551\) −56.0818 −2.38916
\(552\) −1.07183 −0.0456200
\(553\) −4.27964 −0.181989
\(554\) −3.29293 −0.139903
\(555\) 0.946409 0.0401728
\(556\) 3.77971 0.160295
\(557\) 30.9975 1.31341 0.656704 0.754148i \(-0.271950\pi\)
0.656704 + 0.754148i \(0.271950\pi\)
\(558\) −22.2797 −0.943173
\(559\) 20.1811 0.853568
\(560\) −1.75980 −0.0743650
\(561\) −0.0242733 −0.00102482
\(562\) −13.6936 −0.577630
\(563\) −44.3820 −1.87048 −0.935240 0.354015i \(-0.884816\pi\)
−0.935240 + 0.354015i \(0.884816\pi\)
\(564\) −3.18872 −0.134269
\(565\) 9.64296 0.405682
\(566\) 4.02890 0.169347
\(567\) 14.6800 0.616502
\(568\) 11.0826 0.465016
\(569\) 24.8291 1.04089 0.520445 0.853895i \(-0.325766\pi\)
0.520445 + 0.853895i \(0.325766\pi\)
\(570\) −1.89912 −0.0795452
\(571\) −13.6782 −0.572413 −0.286207 0.958168i \(-0.592394\pi\)
−0.286207 + 0.958168i \(0.592394\pi\)
\(572\) 0.153119 0.00640224
\(573\) −4.29514 −0.179432
\(574\) −2.17025 −0.0905845
\(575\) 3.94735 0.164616
\(576\) −2.92627 −0.121928
\(577\) 12.7725 0.531725 0.265862 0.964011i \(-0.414343\pi\)
0.265862 + 0.964011i \(0.414343\pi\)
\(578\) 7.57870 0.315232
\(579\) −4.36934 −0.181584
\(580\) −8.01843 −0.332947
\(581\) 15.6013 0.647251
\(582\) −3.22834 −0.133819
\(583\) 0.389491 0.0161311
\(584\) 15.0109 0.621156
\(585\) 15.3847 0.636081
\(586\) 16.4070 0.677766
\(587\) 6.49999 0.268283 0.134142 0.990962i \(-0.457172\pi\)
0.134142 + 0.990962i \(0.457172\pi\)
\(588\) −1.05982 −0.0437061
\(589\) 53.2508 2.19416
\(590\) 1.28960 0.0530921
\(591\) −7.42825 −0.305558
\(592\) −3.48546 −0.143252
\(593\) 37.6630 1.54664 0.773318 0.634018i \(-0.218596\pi\)
0.773318 + 0.634018i \(0.218596\pi\)
\(594\) 0.0468657 0.00192292
\(595\) 5.40154 0.221442
\(596\) 5.04601 0.206693
\(597\) 3.44575 0.141025
\(598\) −20.7530 −0.848654
\(599\) 5.05231 0.206432 0.103216 0.994659i \(-0.467087\pi\)
0.103216 + 0.994659i \(0.467087\pi\)
\(600\) −0.271531 −0.0110852
\(601\) 12.5379 0.511433 0.255716 0.966752i \(-0.417689\pi\)
0.255716 + 0.966752i \(0.417689\pi\)
\(602\) −6.75509 −0.275317
\(603\) 6.57726 0.267847
\(604\) −11.7128 −0.476586
\(605\) 10.9992 0.447179
\(606\) −0.749945 −0.0304644
\(607\) −3.45440 −0.140210 −0.0701048 0.997540i \(-0.522333\pi\)
−0.0701048 + 0.997540i \(0.522333\pi\)
\(608\) 6.99411 0.283649
\(609\) 3.83151 0.155261
\(610\) −5.25988 −0.212966
\(611\) −61.7409 −2.49777
\(612\) 8.98194 0.363073
\(613\) 7.69344 0.310735 0.155367 0.987857i \(-0.450344\pi\)
0.155367 + 0.987857i \(0.450344\pi\)
\(614\) 25.3962 1.02491
\(615\) −0.334862 −0.0135030
\(616\) −0.0512527 −0.00206503
\(617\) −31.2341 −1.25744 −0.628719 0.777632i \(-0.716420\pi\)
−0.628719 + 0.777632i \(0.716420\pi\)
\(618\) 3.26246 0.131235
\(619\) 14.0250 0.563711 0.281856 0.959457i \(-0.409050\pi\)
0.281856 + 0.959457i \(0.409050\pi\)
\(620\) 7.61367 0.305772
\(621\) −6.35193 −0.254894
\(622\) −0.0443761 −0.00177932
\(623\) 21.1192 0.846121
\(624\) 1.42756 0.0571482
\(625\) 1.00000 0.0400000
\(626\) −6.83705 −0.273263
\(627\) −0.0553103 −0.00220888
\(628\) 0.968067 0.0386301
\(629\) 10.6983 0.426570
\(630\) −5.14964 −0.205167
\(631\) −18.3516 −0.730567 −0.365284 0.930896i \(-0.619028\pi\)
−0.365284 + 0.930896i \(0.619028\pi\)
\(632\) 2.43189 0.0967355
\(633\) 2.59112 0.102988
\(634\) 30.5804 1.21450
\(635\) 8.79870 0.349166
\(636\) 3.63130 0.143990
\(637\) −20.5205 −0.813050
\(638\) −0.233530 −0.00924556
\(639\) 32.4307 1.28294
\(640\) 1.00000 0.0395285
\(641\) −33.3530 −1.31736 −0.658681 0.752422i \(-0.728885\pi\)
−0.658681 + 0.752422i \(0.728885\pi\)
\(642\) −4.97167 −0.196216
\(643\) 27.7008 1.09241 0.546206 0.837651i \(-0.316072\pi\)
0.546206 + 0.837651i \(0.316072\pi\)
\(644\) 6.94653 0.273732
\(645\) −1.04229 −0.0410400
\(646\) −21.4678 −0.844640
\(647\) −19.5184 −0.767347 −0.383673 0.923469i \(-0.625341\pi\)
−0.383673 + 0.923469i \(0.625341\pi\)
\(648\) −8.34188 −0.327700
\(649\) 0.0375587 0.00147431
\(650\) −5.25746 −0.206214
\(651\) −3.63811 −0.142589
\(652\) −23.9054 −0.936207
\(653\) 24.7145 0.967154 0.483577 0.875302i \(-0.339337\pi\)
0.483577 + 0.875302i \(0.339337\pi\)
\(654\) 3.69130 0.144341
\(655\) 15.1375 0.591470
\(656\) 1.23324 0.0481499
\(657\) 43.9260 1.71372
\(658\) 20.6662 0.805650
\(659\) −7.44718 −0.290101 −0.145050 0.989424i \(-0.546334\pi\)
−0.145050 + 0.989424i \(0.546334\pi\)
\(660\) −0.00790812 −0.000307823 0
\(661\) 6.71783 0.261293 0.130647 0.991429i \(-0.458295\pi\)
0.130647 + 0.991429i \(0.458295\pi\)
\(662\) −11.6214 −0.451679
\(663\) −4.38177 −0.170174
\(664\) −8.86540 −0.344044
\(665\) 12.3082 0.477292
\(666\) −10.1994 −0.395219
\(667\) 31.6515 1.22555
\(668\) 21.5368 0.833286
\(669\) −1.90075 −0.0734872
\(670\) −2.24766 −0.0868347
\(671\) −0.153190 −0.00591383
\(672\) −0.477839 −0.0184330
\(673\) 12.8855 0.496701 0.248350 0.968670i \(-0.420112\pi\)
0.248350 + 0.968670i \(0.420112\pi\)
\(674\) 14.0702 0.541965
\(675\) −1.60916 −0.0619368
\(676\) 14.6408 0.563109
\(677\) 12.7159 0.488713 0.244356 0.969686i \(-0.421423\pi\)
0.244356 + 0.969686i \(0.421423\pi\)
\(678\) 2.61836 0.100557
\(679\) 20.9229 0.802948
\(680\) −3.06941 −0.117707
\(681\) −4.43240 −0.169850
\(682\) 0.221742 0.00849095
\(683\) 12.5895 0.481723 0.240862 0.970559i \(-0.422570\pi\)
0.240862 + 0.970559i \(0.422570\pi\)
\(684\) 20.4667 0.782563
\(685\) 20.7910 0.794383
\(686\) 19.1873 0.732573
\(687\) −1.98854 −0.0758675
\(688\) 3.83856 0.146344
\(689\) 70.3103 2.67861
\(690\) 1.07183 0.0408037
\(691\) −14.9825 −0.569960 −0.284980 0.958533i \(-0.591987\pi\)
−0.284980 + 0.958533i \(0.591987\pi\)
\(692\) −4.48959 −0.170669
\(693\) −0.149979 −0.00569724
\(694\) 22.6695 0.860524
\(695\) −3.77971 −0.143372
\(696\) −2.17725 −0.0825284
\(697\) −3.78532 −0.143379
\(698\) −5.47734 −0.207320
\(699\) 2.17777 0.0823708
\(700\) 1.75980 0.0665141
\(701\) −51.2634 −1.93619 −0.968097 0.250577i \(-0.919380\pi\)
−0.968097 + 0.250577i \(0.919380\pi\)
\(702\) 8.46011 0.319306
\(703\) 24.3777 0.919422
\(704\) 0.0291242 0.00109766
\(705\) 3.18872 0.120094
\(706\) 25.5131 0.960198
\(707\) 4.86041 0.182794
\(708\) 0.350167 0.0131601
\(709\) −4.17587 −0.156828 −0.0784140 0.996921i \(-0.524986\pi\)
−0.0784140 + 0.996921i \(0.524986\pi\)
\(710\) −11.0826 −0.415923
\(711\) 7.11638 0.266885
\(712\) −12.0009 −0.449753
\(713\) −30.0538 −1.12552
\(714\) 1.46669 0.0548893
\(715\) −0.153119 −0.00572634
\(716\) 12.6642 0.473285
\(717\) −4.21394 −0.157373
\(718\) 26.7675 0.998953
\(719\) 1.21595 0.0453473 0.0226736 0.999743i \(-0.492782\pi\)
0.0226736 + 0.999743i \(0.492782\pi\)
\(720\) 2.92627 0.109056
\(721\) −21.1441 −0.787447
\(722\) −29.9176 −1.11342
\(723\) −2.50154 −0.0930332
\(724\) 11.1385 0.413961
\(725\) 8.01843 0.297797
\(726\) 2.98661 0.110843
\(727\) −45.3238 −1.68097 −0.840484 0.541837i \(-0.817729\pi\)
−0.840484 + 0.541837i \(0.817729\pi\)
\(728\) −9.25205 −0.342904
\(729\) −23.0998 −0.855547
\(730\) −15.0109 −0.555579
\(731\) −11.7821 −0.435778
\(732\) −1.42822 −0.0527885
\(733\) 14.3936 0.531640 0.265820 0.964023i \(-0.414357\pi\)
0.265820 + 0.964023i \(0.414357\pi\)
\(734\) −23.4027 −0.863808
\(735\) 1.05982 0.0390919
\(736\) −3.94735 −0.145501
\(737\) −0.0654613 −0.00241130
\(738\) 3.60879 0.132842
\(739\) 29.9732 1.10258 0.551290 0.834313i \(-0.314136\pi\)
0.551290 + 0.834313i \(0.314136\pi\)
\(740\) 3.48546 0.128128
\(741\) −9.98452 −0.366790
\(742\) −23.5346 −0.863981
\(743\) −12.3064 −0.451477 −0.225739 0.974188i \(-0.572479\pi\)
−0.225739 + 0.974188i \(0.572479\pi\)
\(744\) 2.06734 0.0757925
\(745\) −5.04601 −0.184872
\(746\) 20.4967 0.750437
\(747\) −25.9426 −0.949189
\(748\) −0.0893943 −0.00326858
\(749\) 32.2215 1.17735
\(750\) 0.271531 0.00991490
\(751\) 15.6235 0.570108 0.285054 0.958511i \(-0.407988\pi\)
0.285054 + 0.958511i \(0.407988\pi\)
\(752\) −11.7435 −0.428241
\(753\) 2.61976 0.0954693
\(754\) −42.1565 −1.53525
\(755\) 11.7128 0.426272
\(756\) −2.83180 −0.102992
\(757\) 7.94228 0.288667 0.144334 0.989529i \(-0.453896\pi\)
0.144334 + 0.989529i \(0.453896\pi\)
\(758\) −2.60987 −0.0947946
\(759\) 0.0312161 0.00113307
\(760\) −6.99411 −0.253703
\(761\) 18.1123 0.656570 0.328285 0.944579i \(-0.393529\pi\)
0.328285 + 0.944579i \(0.393529\pi\)
\(762\) 2.38912 0.0865486
\(763\) −23.9234 −0.866086
\(764\) −15.8182 −0.572284
\(765\) −8.98194 −0.324743
\(766\) −9.31699 −0.336637
\(767\) 6.78003 0.244813
\(768\) 0.271531 0.00979802
\(769\) 49.5322 1.78618 0.893088 0.449883i \(-0.148534\pi\)
0.893088 + 0.449883i \(0.148534\pi\)
\(770\) 0.0512527 0.00184702
\(771\) 6.40310 0.230602
\(772\) −16.0915 −0.579147
\(773\) −1.08752 −0.0391153 −0.0195576 0.999809i \(-0.506226\pi\)
−0.0195576 + 0.999809i \(0.506226\pi\)
\(774\) 11.2327 0.403750
\(775\) −7.61367 −0.273491
\(776\) −11.8894 −0.426805
\(777\) −1.66549 −0.0597491
\(778\) 9.73754 0.349108
\(779\) −8.62542 −0.309038
\(780\) −1.42756 −0.0511149
\(781\) −0.322772 −0.0115497
\(782\) 12.1160 0.433269
\(783\) −12.9030 −0.461114
\(784\) −3.90312 −0.139397
\(785\) −0.968067 −0.0345518
\(786\) 4.11029 0.146609
\(787\) 9.02558 0.321727 0.160864 0.986977i \(-0.448572\pi\)
0.160864 + 0.986977i \(0.448572\pi\)
\(788\) −27.3570 −0.974552
\(789\) 0.288626 0.0102753
\(790\) −2.43189 −0.0865228
\(791\) −16.9696 −0.603371
\(792\) 0.0852254 0.00302835
\(793\) −27.6536 −0.982008
\(794\) 32.6545 1.15886
\(795\) −3.63130 −0.128789
\(796\) 12.6901 0.449788
\(797\) 35.5955 1.26086 0.630429 0.776247i \(-0.282879\pi\)
0.630429 + 0.776247i \(0.282879\pi\)
\(798\) 3.34206 0.118308
\(799\) 36.0456 1.27520
\(800\) −1.00000 −0.0353553
\(801\) −35.1179 −1.24083
\(802\) 1.00000 0.0353112
\(803\) −0.437182 −0.0154278
\(804\) −0.610308 −0.0215239
\(805\) −6.94653 −0.244833
\(806\) 40.0285 1.40994
\(807\) 6.02018 0.211920
\(808\) −2.76191 −0.0971638
\(809\) −38.3573 −1.34857 −0.674286 0.738470i \(-0.735548\pi\)
−0.674286 + 0.738470i \(0.735548\pi\)
\(810\) 8.34188 0.293104
\(811\) 29.6283 1.04039 0.520195 0.854047i \(-0.325859\pi\)
0.520195 + 0.854047i \(0.325859\pi\)
\(812\) 14.1108 0.495192
\(813\) −0.178440 −0.00625815
\(814\) 0.101511 0.00355797
\(815\) 23.9054 0.837369
\(816\) −0.833440 −0.0291762
\(817\) −26.8473 −0.939269
\(818\) −6.54320 −0.228777
\(819\) −27.0740 −0.946043
\(820\) −1.23324 −0.0430666
\(821\) 27.2328 0.950431 0.475216 0.879869i \(-0.342370\pi\)
0.475216 + 0.879869i \(0.342370\pi\)
\(822\) 5.64539 0.196906
\(823\) −15.2644 −0.532083 −0.266042 0.963962i \(-0.585716\pi\)
−0.266042 + 0.963962i \(0.585716\pi\)
\(824\) 12.0151 0.418565
\(825\) 0.00790812 0.000275325 0
\(826\) −2.26944 −0.0789639
\(827\) 30.9897 1.07762 0.538809 0.842428i \(-0.318874\pi\)
0.538809 + 0.842428i \(0.318874\pi\)
\(828\) −11.5510 −0.401426
\(829\) 40.5840 1.40954 0.704771 0.709435i \(-0.251050\pi\)
0.704771 + 0.709435i \(0.251050\pi\)
\(830\) 8.86540 0.307722
\(831\) 0.894131 0.0310170
\(832\) 5.25746 0.182269
\(833\) 11.9803 0.415092
\(834\) −1.02631 −0.0355381
\(835\) −21.5368 −0.745313
\(836\) −0.203698 −0.00704505
\(837\) 12.2516 0.423479
\(838\) 31.2137 1.07826
\(839\) 12.6919 0.438171 0.219086 0.975706i \(-0.429693\pi\)
0.219086 + 0.975706i \(0.429693\pi\)
\(840\) 0.477839 0.0164870
\(841\) 35.2951 1.21707
\(842\) 7.46544 0.257276
\(843\) 3.71823 0.128063
\(844\) 9.54263 0.328471
\(845\) −14.6408 −0.503660
\(846\) −34.3646 −1.18148
\(847\) −19.3563 −0.665089
\(848\) 13.3734 0.459246
\(849\) −1.09397 −0.0375450
\(850\) 3.06941 0.105280
\(851\) −13.7583 −0.471629
\(852\) −3.00927 −0.103096
\(853\) 25.4196 0.870351 0.435175 0.900346i \(-0.356686\pi\)
0.435175 + 0.900346i \(0.356686\pi\)
\(854\) 9.25632 0.316745
\(855\) −20.4667 −0.699945
\(856\) −18.3098 −0.625816
\(857\) −23.8938 −0.816197 −0.408098 0.912938i \(-0.633808\pi\)
−0.408098 + 0.912938i \(0.633808\pi\)
\(858\) −0.0415766 −0.00141940
\(859\) −33.4234 −1.14039 −0.570196 0.821509i \(-0.693133\pi\)
−0.570196 + 0.821509i \(0.693133\pi\)
\(860\) −3.83856 −0.130894
\(861\) 0.589290 0.0200829
\(862\) 16.8501 0.573915
\(863\) 37.2343 1.26747 0.633735 0.773550i \(-0.281521\pi\)
0.633735 + 0.773550i \(0.281521\pi\)
\(864\) 1.60916 0.0547449
\(865\) 4.48959 0.152651
\(866\) −36.4196 −1.23759
\(867\) −2.05785 −0.0698882
\(868\) −13.3985 −0.454775
\(869\) −0.0708270 −0.00240264
\(870\) 2.17725 0.0738156
\(871\) −11.8170 −0.400403
\(872\) 13.5944 0.460365
\(873\) −34.7916 −1.17752
\(874\) 27.6082 0.933861
\(875\) −1.75980 −0.0594920
\(876\) −4.07593 −0.137713
\(877\) −11.6158 −0.392236 −0.196118 0.980580i \(-0.562834\pi\)
−0.196118 + 0.980580i \(0.562834\pi\)
\(878\) −17.8466 −0.602293
\(879\) −4.45500 −0.150263
\(880\) −0.0291242 −0.000981777 0
\(881\) 50.7571 1.71005 0.855025 0.518587i \(-0.173542\pi\)
0.855025 + 0.518587i \(0.173542\pi\)
\(882\) −11.4216 −0.384584
\(883\) −7.00130 −0.235613 −0.117806 0.993037i \(-0.537586\pi\)
−0.117806 + 0.993037i \(0.537586\pi\)
\(884\) −16.1373 −0.542756
\(885\) −0.350167 −0.0117707
\(886\) 25.6948 0.863234
\(887\) 27.4078 0.920264 0.460132 0.887851i \(-0.347802\pi\)
0.460132 + 0.887851i \(0.347802\pi\)
\(888\) 0.946409 0.0317594
\(889\) −15.4839 −0.519314
\(890\) 12.0009 0.402271
\(891\) 0.242951 0.00813915
\(892\) −7.00013 −0.234382
\(893\) 82.1353 2.74855
\(894\) −1.37015 −0.0458246
\(895\) −12.6642 −0.423319
\(896\) −1.75980 −0.0587907
\(897\) 5.63508 0.188150
\(898\) −3.28609 −0.109658
\(899\) −61.0496 −2.03612
\(900\) −2.92627 −0.0975424
\(901\) −41.0486 −1.36753
\(902\) −0.0359171 −0.00119591
\(903\) 1.83421 0.0610388
\(904\) 9.64296 0.320720
\(905\) −11.1385 −0.370258
\(906\) 3.18038 0.105661
\(907\) 34.3599 1.14090 0.570450 0.821332i \(-0.306769\pi\)
0.570450 + 0.821332i \(0.306769\pi\)
\(908\) −16.3238 −0.541723
\(909\) −8.08211 −0.268067
\(910\) 9.25205 0.306703
\(911\) 22.6157 0.749291 0.374646 0.927168i \(-0.377764\pi\)
0.374646 + 0.927168i \(0.377764\pi\)
\(912\) −1.89912 −0.0628860
\(913\) 0.258198 0.00854510
\(914\) 18.3558 0.607157
\(915\) 1.42822 0.0472154
\(916\) −7.32344 −0.241973
\(917\) −26.6389 −0.879694
\(918\) −4.93919 −0.163018
\(919\) 32.5549 1.07389 0.536943 0.843618i \(-0.319579\pi\)
0.536943 + 0.843618i \(0.319579\pi\)
\(920\) 3.94735 0.130140
\(921\) −6.89585 −0.227226
\(922\) 7.58525 0.249807
\(923\) −58.2663 −1.91786
\(924\) 0.0139167 0.000457825 0
\(925\) −3.48546 −0.114601
\(926\) 35.3015 1.16008
\(927\) 35.1594 1.15479
\(928\) −8.01843 −0.263218
\(929\) 31.2694 1.02592 0.512959 0.858413i \(-0.328549\pi\)
0.512959 + 0.858413i \(0.328549\pi\)
\(930\) −2.06734 −0.0677909
\(931\) 27.2988 0.894683
\(932\) 8.02035 0.262715
\(933\) 0.0120495 0.000394482 0
\(934\) −2.76833 −0.0905824
\(935\) 0.0893943 0.00292351
\(936\) 15.3847 0.502866
\(937\) 34.2684 1.11950 0.559749 0.828662i \(-0.310897\pi\)
0.559749 + 0.828662i \(0.310897\pi\)
\(938\) 3.95542 0.129149
\(939\) 1.85647 0.0605835
\(940\) 11.7435 0.383030
\(941\) 36.5540 1.19163 0.595814 0.803122i \(-0.296830\pi\)
0.595814 + 0.803122i \(0.296830\pi\)
\(942\) −0.262860 −0.00856444
\(943\) 4.86803 0.158525
\(944\) 1.28960 0.0419730
\(945\) 2.83180 0.0921185
\(946\) −0.111795 −0.00363477
\(947\) −27.2634 −0.885940 −0.442970 0.896536i \(-0.646075\pi\)
−0.442970 + 0.896536i \(0.646075\pi\)
\(948\) −0.660333 −0.0214466
\(949\) −78.9193 −2.56183
\(950\) 6.99411 0.226919
\(951\) −8.30351 −0.269260
\(952\) 5.40154 0.175065
\(953\) −16.1084 −0.521803 −0.260901 0.965365i \(-0.584020\pi\)
−0.260901 + 0.965365i \(0.584020\pi\)
\(954\) 39.1343 1.26702
\(955\) 15.8182 0.511866
\(956\) −15.5192 −0.501928
\(957\) 0.0634107 0.00204978
\(958\) −16.5941 −0.536132
\(959\) −36.5879 −1.18149
\(960\) −0.271531 −0.00876361
\(961\) 26.9679 0.869934
\(962\) 18.3247 0.590811
\(963\) −53.5795 −1.72657
\(964\) −9.21273 −0.296722
\(965\) 16.0915 0.518005
\(966\) −1.88620 −0.0606874
\(967\) 24.4490 0.786227 0.393113 0.919490i \(-0.371398\pi\)
0.393113 + 0.919490i \(0.371398\pi\)
\(968\) 10.9992 0.353526
\(969\) 5.82917 0.187260
\(970\) 11.8894 0.381746
\(971\) 24.5068 0.786459 0.393230 0.919440i \(-0.371358\pi\)
0.393230 + 0.919440i \(0.371358\pi\)
\(972\) 7.09257 0.227494
\(973\) 6.65152 0.213238
\(974\) −12.9950 −0.416387
\(975\) 1.42756 0.0457185
\(976\) −5.25988 −0.168365
\(977\) 56.8765 1.81964 0.909820 0.415002i \(-0.136219\pi\)
0.909820 + 0.415002i \(0.136219\pi\)
\(978\) 6.49104 0.207561
\(979\) 0.349517 0.0111706
\(980\) 3.90312 0.124680
\(981\) 39.7809 1.27011
\(982\) 27.9496 0.891909
\(983\) −22.2636 −0.710100 −0.355050 0.934847i \(-0.615536\pi\)
−0.355050 + 0.934847i \(0.615536\pi\)
\(984\) −0.334862 −0.0106750
\(985\) 27.3570 0.871665
\(986\) 24.6119 0.783801
\(987\) −5.61149 −0.178616
\(988\) −36.7712 −1.16985
\(989\) 15.1521 0.481810
\(990\) −0.0852254 −0.00270864
\(991\) −41.4677 −1.31727 −0.658633 0.752464i \(-0.728865\pi\)
−0.658633 + 0.752464i \(0.728865\pi\)
\(992\) 7.61367 0.241734
\(993\) 3.15557 0.100139
\(994\) 19.5031 0.618601
\(995\) −12.6901 −0.402303
\(996\) 2.40723 0.0762759
\(997\) 4.39607 0.139225 0.0696124 0.997574i \(-0.477824\pi\)
0.0696124 + 0.997574i \(0.477824\pi\)
\(998\) −41.1489 −1.30255
\(999\) 5.60868 0.177451
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 \(a_p\))