Properties

Label 8041.2.a.g.1.10
Level 8041
Weight 2
Character 8041.1
Self dual Yes
Analytic conductor 64.208
Analytic rank 1
Dimension 69
CM No

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Newspace parameters

Level: \( N \) = \( 8041 = 11 \cdot 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8041.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2077082653\)
Analytic rank: \(1\)
Dimension: \(69\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) = 8041.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.20984 q^{2} +0.750857 q^{3} +2.88340 q^{4} +0.114086 q^{5} -1.65928 q^{6} +4.65666 q^{7} -1.95217 q^{8} -2.43621 q^{9} +O(q^{10})\) \(q-2.20984 q^{2} +0.750857 q^{3} +2.88340 q^{4} +0.114086 q^{5} -1.65928 q^{6} +4.65666 q^{7} -1.95217 q^{8} -2.43621 q^{9} -0.252113 q^{10} -1.00000 q^{11} +2.16502 q^{12} +2.48632 q^{13} -10.2905 q^{14} +0.0856625 q^{15} -1.45281 q^{16} +1.00000 q^{17} +5.38365 q^{18} -2.42814 q^{19} +0.328956 q^{20} +3.49649 q^{21} +2.20984 q^{22} +4.62083 q^{23} -1.46580 q^{24} -4.98698 q^{25} -5.49436 q^{26} -4.08182 q^{27} +13.4270 q^{28} -4.44553 q^{29} -0.189300 q^{30} +4.53728 q^{31} +7.11482 q^{32} -0.750857 q^{33} -2.20984 q^{34} +0.531261 q^{35} -7.02458 q^{36} -4.13773 q^{37} +5.36581 q^{38} +1.86687 q^{39} -0.222716 q^{40} -9.31993 q^{41} -7.72668 q^{42} +1.00000 q^{43} -2.88340 q^{44} -0.277938 q^{45} -10.2113 q^{46} -9.87769 q^{47} -1.09085 q^{48} +14.6845 q^{49} +11.0204 q^{50} +0.750857 q^{51} +7.16904 q^{52} -2.96581 q^{53} +9.02017 q^{54} -0.114086 q^{55} -9.09060 q^{56} -1.82319 q^{57} +9.82391 q^{58} +0.00102671 q^{59} +0.246999 q^{60} +1.83175 q^{61} -10.0267 q^{62} -11.3446 q^{63} -12.8170 q^{64} +0.283654 q^{65} +1.65928 q^{66} -10.9311 q^{67} +2.88340 q^{68} +3.46959 q^{69} -1.17400 q^{70} -8.21270 q^{71} +4.75591 q^{72} +13.0734 q^{73} +9.14373 q^{74} -3.74451 q^{75} -7.00131 q^{76} -4.65666 q^{77} -4.12548 q^{78} +5.13529 q^{79} -0.165745 q^{80} +4.24378 q^{81} +20.5956 q^{82} +7.99483 q^{83} +10.0818 q^{84} +0.114086 q^{85} -2.20984 q^{86} -3.33796 q^{87} +1.95217 q^{88} -14.1732 q^{89} +0.614200 q^{90} +11.5779 q^{91} +13.3237 q^{92} +3.40685 q^{93} +21.8281 q^{94} -0.277018 q^{95} +5.34221 q^{96} -13.1489 q^{97} -32.4503 q^{98} +2.43621 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 69q - 11q^{2} - 3q^{3} + 65q^{4} - 6q^{5} - 10q^{6} - 11q^{7} - 33q^{8} + 56q^{9} + O(q^{10}) \) \( 69q - 11q^{2} - 3q^{3} + 65q^{4} - 6q^{5} - 10q^{6} - 11q^{7} - 33q^{8} + 56q^{9} - q^{10} - 69q^{11} - 3q^{12} - 28q^{13} - 15q^{14} - 45q^{15} + 53q^{16} + 69q^{17} - 17q^{18} - 32q^{19} - 21q^{20} - 38q^{21} + 11q^{22} - 41q^{23} - 11q^{24} + 67q^{25} - 6q^{26} - 3q^{27} - 21q^{28} - 22q^{29} - 22q^{30} - 27q^{31} - 87q^{32} + 3q^{33} - 11q^{34} - 44q^{35} + 59q^{36} + 24q^{37} - 22q^{38} - 59q^{39} + q^{40} - 43q^{41} - 15q^{42} + 69q^{43} - 65q^{44} - 12q^{45} - 21q^{46} - 99q^{47} + 2q^{48} + 64q^{49} - 78q^{50} - 3q^{51} - 57q^{52} - 50q^{53} + 20q^{54} + 6q^{55} - 59q^{56} - 15q^{57} + 22q^{58} - 82q^{59} - 86q^{60} - 24q^{61} + 15q^{62} - 63q^{63} + 63q^{64} - 23q^{65} + 10q^{66} - 54q^{67} + 65q^{68} + 36q^{69} + 9q^{70} - 128q^{71} - 69q^{72} + 2q^{73} - 58q^{74} - 31q^{75} - 76q^{76} + 11q^{77} - 19q^{78} - 43q^{79} - 19q^{80} + 49q^{81} - 2q^{82} - 62q^{83} - 82q^{84} - 6q^{85} - 11q^{86} - 62q^{87} + 33q^{88} - 49q^{89} - 37q^{90} - 2q^{91} - 96q^{92} - 29q^{93} - 75q^{94} - 133q^{95} - 86q^{96} + 5q^{97} - 72q^{98} - 56q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.20984 −1.56259 −0.781297 0.624160i \(-0.785442\pi\)
−0.781297 + 0.624160i \(0.785442\pi\)
\(3\) 0.750857 0.433508 0.216754 0.976226i \(-0.430453\pi\)
0.216754 + 0.976226i \(0.430453\pi\)
\(4\) 2.88340 1.44170
\(5\) 0.114086 0.0510209 0.0255105 0.999675i \(-0.491879\pi\)
0.0255105 + 0.999675i \(0.491879\pi\)
\(6\) −1.65928 −0.677396
\(7\) 4.65666 1.76005 0.880026 0.474926i \(-0.157525\pi\)
0.880026 + 0.474926i \(0.157525\pi\)
\(8\) −1.95217 −0.690197
\(9\) −2.43621 −0.812071
\(10\) −0.252113 −0.0797250
\(11\) −1.00000 −0.301511
\(12\) 2.16502 0.624988
\(13\) 2.48632 0.689580 0.344790 0.938680i \(-0.387950\pi\)
0.344790 + 0.938680i \(0.387950\pi\)
\(14\) −10.2905 −2.75025
\(15\) 0.0856625 0.0221180
\(16\) −1.45281 −0.363202
\(17\) 1.00000 0.242536
\(18\) 5.38365 1.26894
\(19\) −2.42814 −0.557054 −0.278527 0.960428i \(-0.589846\pi\)
−0.278527 + 0.960428i \(0.589846\pi\)
\(20\) 0.328956 0.0735568
\(21\) 3.49649 0.762996
\(22\) 2.20984 0.471140
\(23\) 4.62083 0.963511 0.481755 0.876306i \(-0.339999\pi\)
0.481755 + 0.876306i \(0.339999\pi\)
\(24\) −1.46580 −0.299206
\(25\) −4.98698 −0.997397
\(26\) −5.49436 −1.07753
\(27\) −4.08182 −0.785547
\(28\) 13.4270 2.53747
\(29\) −4.44553 −0.825514 −0.412757 0.910841i \(-0.635434\pi\)
−0.412757 + 0.910841i \(0.635434\pi\)
\(30\) −0.189300 −0.0345614
\(31\) 4.53728 0.814919 0.407460 0.913223i \(-0.366415\pi\)
0.407460 + 0.913223i \(0.366415\pi\)
\(32\) 7.11482 1.25773
\(33\) −0.750857 −0.130707
\(34\) −2.20984 −0.378985
\(35\) 0.531261 0.0897994
\(36\) −7.02458 −1.17076
\(37\) −4.13773 −0.680239 −0.340119 0.940382i \(-0.610467\pi\)
−0.340119 + 0.940382i \(0.610467\pi\)
\(38\) 5.36581 0.870450
\(39\) 1.86687 0.298938
\(40\) −0.222716 −0.0352145
\(41\) −9.31993 −1.45553 −0.727764 0.685827i \(-0.759441\pi\)
−0.727764 + 0.685827i \(0.759441\pi\)
\(42\) −7.72668 −1.19225
\(43\) 1.00000 0.152499
\(44\) −2.88340 −0.434689
\(45\) −0.277938 −0.0414326
\(46\) −10.2113 −1.50558
\(47\) −9.87769 −1.44081 −0.720404 0.693554i \(-0.756044\pi\)
−0.720404 + 0.693554i \(0.756044\pi\)
\(48\) −1.09085 −0.157451
\(49\) 14.6845 2.09778
\(50\) 11.0204 1.55853
\(51\) 0.750857 0.105141
\(52\) 7.16904 0.994167
\(53\) −2.96581 −0.407385 −0.203692 0.979035i \(-0.565294\pi\)
−0.203692 + 0.979035i \(0.565294\pi\)
\(54\) 9.02017 1.22749
\(55\) −0.114086 −0.0153834
\(56\) −9.09060 −1.21478
\(57\) −1.82319 −0.241487
\(58\) 9.82391 1.28994
\(59\) 0.00102671 0.000133666 0 6.68329e−5 1.00000i \(-0.499979\pi\)
6.68329e−5 1.00000i \(0.499979\pi\)
\(60\) 0.246999 0.0318874
\(61\) 1.83175 0.234531 0.117266 0.993101i \(-0.462587\pi\)
0.117266 + 0.993101i \(0.462587\pi\)
\(62\) −10.0267 −1.27339
\(63\) −11.3446 −1.42929
\(64\) −12.8170 −1.60213
\(65\) 0.283654 0.0351830
\(66\) 1.65928 0.204243
\(67\) −10.9311 −1.33545 −0.667725 0.744408i \(-0.732732\pi\)
−0.667725 + 0.744408i \(0.732732\pi\)
\(68\) 2.88340 0.349664
\(69\) 3.46959 0.417689
\(70\) −1.17400 −0.140320
\(71\) −8.21270 −0.974668 −0.487334 0.873216i \(-0.662031\pi\)
−0.487334 + 0.873216i \(0.662031\pi\)
\(72\) 4.75591 0.560489
\(73\) 13.0734 1.53012 0.765062 0.643957i \(-0.222708\pi\)
0.765062 + 0.643957i \(0.222708\pi\)
\(74\) 9.14373 1.06294
\(75\) −3.74451 −0.432379
\(76\) −7.00131 −0.803105
\(77\) −4.65666 −0.530675
\(78\) −4.12548 −0.467119
\(79\) 5.13529 0.577765 0.288882 0.957365i \(-0.406716\pi\)
0.288882 + 0.957365i \(0.406716\pi\)
\(80\) −0.165745 −0.0185309
\(81\) 4.24378 0.471531
\(82\) 20.5956 2.27440
\(83\) 7.99483 0.877547 0.438773 0.898598i \(-0.355413\pi\)
0.438773 + 0.898598i \(0.355413\pi\)
\(84\) 10.0818 1.10001
\(85\) 0.114086 0.0123744
\(86\) −2.20984 −0.238293
\(87\) −3.33796 −0.357867
\(88\) 1.95217 0.208102
\(89\) −14.1732 −1.50235 −0.751176 0.660102i \(-0.770513\pi\)
−0.751176 + 0.660102i \(0.770513\pi\)
\(90\) 0.614200 0.0647424
\(91\) 11.5779 1.21370
\(92\) 13.3237 1.38909
\(93\) 3.40685 0.353274
\(94\) 21.8281 2.25140
\(95\) −0.277018 −0.0284214
\(96\) 5.34221 0.545237
\(97\) −13.1489 −1.33507 −0.667533 0.744580i \(-0.732650\pi\)
−0.667533 + 0.744580i \(0.732650\pi\)
\(98\) −32.4503 −3.27798
\(99\) 2.43621 0.244849
\(100\) −14.3795 −1.43795
\(101\) −4.68091 −0.465768 −0.232884 0.972505i \(-0.574816\pi\)
−0.232884 + 0.972505i \(0.574816\pi\)
\(102\) −1.65928 −0.164293
\(103\) −6.23555 −0.614407 −0.307204 0.951644i \(-0.599393\pi\)
−0.307204 + 0.951644i \(0.599393\pi\)
\(104\) −4.85372 −0.475946
\(105\) 0.398901 0.0389287
\(106\) 6.55396 0.636577
\(107\) 4.26628 0.412437 0.206219 0.978506i \(-0.433884\pi\)
0.206219 + 0.978506i \(0.433884\pi\)
\(108\) −11.7695 −1.13252
\(109\) −11.3114 −1.08344 −0.541718 0.840560i \(-0.682226\pi\)
−0.541718 + 0.840560i \(0.682226\pi\)
\(110\) 0.252113 0.0240380
\(111\) −3.10684 −0.294889
\(112\) −6.76523 −0.639254
\(113\) 7.64233 0.718930 0.359465 0.933159i \(-0.382959\pi\)
0.359465 + 0.933159i \(0.382959\pi\)
\(114\) 4.02896 0.377347
\(115\) 0.527174 0.0491592
\(116\) −12.8182 −1.19014
\(117\) −6.05720 −0.559988
\(118\) −0.00226886 −0.000208865 0
\(119\) 4.65666 0.426875
\(120\) −0.167228 −0.0152657
\(121\) 1.00000 0.0909091
\(122\) −4.04787 −0.366477
\(123\) −6.99794 −0.630983
\(124\) 13.0828 1.17487
\(125\) −1.13938 −0.101909
\(126\) 25.0698 2.23340
\(127\) 0.939159 0.0833369 0.0416685 0.999131i \(-0.486733\pi\)
0.0416685 + 0.999131i \(0.486733\pi\)
\(128\) 14.0939 1.24574
\(129\) 0.750857 0.0661093
\(130\) −0.626831 −0.0549767
\(131\) −14.3213 −1.25126 −0.625629 0.780121i \(-0.715158\pi\)
−0.625629 + 0.780121i \(0.715158\pi\)
\(132\) −2.16502 −0.188441
\(133\) −11.3070 −0.980444
\(134\) 24.1561 2.08677
\(135\) −0.465680 −0.0400793
\(136\) −1.95217 −0.167397
\(137\) −20.7605 −1.77369 −0.886843 0.462072i \(-0.847106\pi\)
−0.886843 + 0.462072i \(0.847106\pi\)
\(138\) −7.66724 −0.652678
\(139\) 1.08117 0.0917036 0.0458518 0.998948i \(-0.485400\pi\)
0.0458518 + 0.998948i \(0.485400\pi\)
\(140\) 1.53184 0.129464
\(141\) −7.41673 −0.624602
\(142\) 18.1488 1.52301
\(143\) −2.48632 −0.207916
\(144\) 3.53935 0.294946
\(145\) −0.507174 −0.0421185
\(146\) −28.8901 −2.39096
\(147\) 11.0259 0.909404
\(148\) −11.9307 −0.980700
\(149\) −1.31801 −0.107976 −0.0539878 0.998542i \(-0.517193\pi\)
−0.0539878 + 0.998542i \(0.517193\pi\)
\(150\) 8.27478 0.675633
\(151\) 7.93258 0.645544 0.322772 0.946477i \(-0.395385\pi\)
0.322772 + 0.946477i \(0.395385\pi\)
\(152\) 4.74015 0.384477
\(153\) −2.43621 −0.196956
\(154\) 10.2905 0.829230
\(155\) 0.517641 0.0415779
\(156\) 5.38293 0.430979
\(157\) −14.1768 −1.13143 −0.565717 0.824599i \(-0.691401\pi\)
−0.565717 + 0.824599i \(0.691401\pi\)
\(158\) −11.3482 −0.902812
\(159\) −2.22690 −0.176604
\(160\) 0.811703 0.0641708
\(161\) 21.5176 1.69583
\(162\) −9.37807 −0.736811
\(163\) −10.3860 −0.813493 −0.406747 0.913541i \(-0.633337\pi\)
−0.406747 + 0.913541i \(0.633337\pi\)
\(164\) −26.8731 −2.09844
\(165\) −0.0856625 −0.00666881
\(166\) −17.6673 −1.37125
\(167\) −11.3738 −0.880127 −0.440064 0.897967i \(-0.645044\pi\)
−0.440064 + 0.897967i \(0.645044\pi\)
\(168\) −6.82574 −0.526617
\(169\) −6.81823 −0.524480
\(170\) −0.252113 −0.0193361
\(171\) 5.91548 0.452368
\(172\) 2.88340 0.219857
\(173\) −1.16678 −0.0887089 −0.0443544 0.999016i \(-0.514123\pi\)
−0.0443544 + 0.999016i \(0.514123\pi\)
\(174\) 7.37636 0.559200
\(175\) −23.2227 −1.75547
\(176\) 1.45281 0.109509
\(177\) 0.000770910 0 5.79451e−5 0
\(178\) 31.3204 2.34757
\(179\) 16.3612 1.22289 0.611446 0.791286i \(-0.290588\pi\)
0.611446 + 0.791286i \(0.290588\pi\)
\(180\) −0.801407 −0.0597334
\(181\) 7.39009 0.549301 0.274651 0.961544i \(-0.411438\pi\)
0.274651 + 0.961544i \(0.411438\pi\)
\(182\) −25.5854 −1.89651
\(183\) 1.37538 0.101671
\(184\) −9.02066 −0.665012
\(185\) −0.472058 −0.0347064
\(186\) −7.52859 −0.552023
\(187\) −1.00000 −0.0731272
\(188\) −28.4813 −2.07721
\(189\) −19.0076 −1.38260
\(190\) 0.612165 0.0444111
\(191\) −6.93051 −0.501474 −0.250737 0.968055i \(-0.580673\pi\)
−0.250737 + 0.968055i \(0.580673\pi\)
\(192\) −9.62374 −0.694534
\(193\) 3.01599 0.217096 0.108548 0.994091i \(-0.465380\pi\)
0.108548 + 0.994091i \(0.465380\pi\)
\(194\) 29.0569 2.08617
\(195\) 0.212984 0.0152521
\(196\) 42.3412 3.02437
\(197\) −19.3333 −1.37744 −0.688719 0.725028i \(-0.741827\pi\)
−0.688719 + 0.725028i \(0.741827\pi\)
\(198\) −5.38365 −0.382599
\(199\) 18.8796 1.33834 0.669170 0.743110i \(-0.266650\pi\)
0.669170 + 0.743110i \(0.266650\pi\)
\(200\) 9.73545 0.688400
\(201\) −8.20772 −0.578928
\(202\) 10.3441 0.727806
\(203\) −20.7013 −1.45295
\(204\) 2.16502 0.151582
\(205\) −1.06328 −0.0742624
\(206\) 13.7796 0.960069
\(207\) −11.2573 −0.782439
\(208\) −3.61214 −0.250457
\(209\) 2.42814 0.167958
\(210\) −0.881508 −0.0608298
\(211\) −0.343098 −0.0236199 −0.0118099 0.999930i \(-0.503759\pi\)
−0.0118099 + 0.999930i \(0.503759\pi\)
\(212\) −8.55161 −0.587327
\(213\) −6.16656 −0.422526
\(214\) −9.42781 −0.644472
\(215\) 0.114086 0.00778062
\(216\) 7.96841 0.542182
\(217\) 21.1286 1.43430
\(218\) 24.9964 1.69297
\(219\) 9.81625 0.663320
\(220\) −0.328956 −0.0221782
\(221\) 2.48632 0.167248
\(222\) 6.86563 0.460791
\(223\) −1.80310 −0.120744 −0.0603721 0.998176i \(-0.519229\pi\)
−0.0603721 + 0.998176i \(0.519229\pi\)
\(224\) 33.1313 2.21368
\(225\) 12.1494 0.809957
\(226\) −16.8883 −1.12340
\(227\) −3.64167 −0.241706 −0.120853 0.992670i \(-0.538563\pi\)
−0.120853 + 0.992670i \(0.538563\pi\)
\(228\) −5.25698 −0.348152
\(229\) 24.0210 1.58735 0.793676 0.608340i \(-0.208164\pi\)
0.793676 + 0.608340i \(0.208164\pi\)
\(230\) −1.16497 −0.0768159
\(231\) −3.49649 −0.230052
\(232\) 8.67844 0.569767
\(233\) −5.24993 −0.343934 −0.171967 0.985103i \(-0.555012\pi\)
−0.171967 + 0.985103i \(0.555012\pi\)
\(234\) 13.3854 0.875034
\(235\) −1.12691 −0.0735114
\(236\) 0.00296041 0.000192706 0
\(237\) 3.85587 0.250466
\(238\) −10.2905 −0.667033
\(239\) 6.73217 0.435468 0.217734 0.976008i \(-0.430134\pi\)
0.217734 + 0.976008i \(0.430134\pi\)
\(240\) −0.124451 −0.00803328
\(241\) −27.5795 −1.77655 −0.888277 0.459308i \(-0.848098\pi\)
−0.888277 + 0.459308i \(0.848098\pi\)
\(242\) −2.20984 −0.142054
\(243\) 15.4319 0.989959
\(244\) 5.28166 0.338123
\(245\) 1.67530 0.107031
\(246\) 15.4643 0.985970
\(247\) −6.03713 −0.384133
\(248\) −8.85755 −0.562455
\(249\) 6.00298 0.380423
\(250\) 2.51784 0.159242
\(251\) 2.95090 0.186259 0.0931297 0.995654i \(-0.470313\pi\)
0.0931297 + 0.995654i \(0.470313\pi\)
\(252\) −32.7111 −2.06060
\(253\) −4.62083 −0.290509
\(254\) −2.07539 −0.130222
\(255\) 0.0856625 0.00536439
\(256\) −5.51130 −0.344456
\(257\) −6.51885 −0.406635 −0.203317 0.979113i \(-0.565172\pi\)
−0.203317 + 0.979113i \(0.565172\pi\)
\(258\) −1.65928 −0.103302
\(259\) −19.2680 −1.19725
\(260\) 0.817889 0.0507233
\(261\) 10.8303 0.670376
\(262\) 31.6478 1.95521
\(263\) −21.6219 −1.33326 −0.666631 0.745388i \(-0.732264\pi\)
−0.666631 + 0.745388i \(0.732264\pi\)
\(264\) 1.46580 0.0902139
\(265\) −0.338358 −0.0207852
\(266\) 24.9868 1.53204
\(267\) −10.6420 −0.651281
\(268\) −31.5188 −1.92532
\(269\) 8.20177 0.500071 0.250035 0.968237i \(-0.419558\pi\)
0.250035 + 0.968237i \(0.419558\pi\)
\(270\) 1.02908 0.0626277
\(271\) 10.2794 0.624427 0.312213 0.950012i \(-0.398930\pi\)
0.312213 + 0.950012i \(0.398930\pi\)
\(272\) −1.45281 −0.0880894
\(273\) 8.69337 0.526146
\(274\) 45.8773 2.77155
\(275\) 4.98698 0.300726
\(276\) 10.0042 0.602182
\(277\) 4.08105 0.245206 0.122603 0.992456i \(-0.460876\pi\)
0.122603 + 0.992456i \(0.460876\pi\)
\(278\) −2.38921 −0.143295
\(279\) −11.0538 −0.661772
\(280\) −1.03711 −0.0619793
\(281\) −17.5969 −1.04974 −0.524871 0.851182i \(-0.675886\pi\)
−0.524871 + 0.851182i \(0.675886\pi\)
\(282\) 16.3898 0.975999
\(283\) −18.5864 −1.10484 −0.552422 0.833564i \(-0.686296\pi\)
−0.552422 + 0.833564i \(0.686296\pi\)
\(284\) −23.6805 −1.40518
\(285\) −0.208001 −0.0123209
\(286\) 5.49436 0.324889
\(287\) −43.3997 −2.56181
\(288\) −17.3332 −1.02137
\(289\) 1.00000 0.0588235
\(290\) 1.12077 0.0658141
\(291\) −9.87293 −0.578762
\(292\) 37.6958 2.20598
\(293\) −12.0587 −0.704478 −0.352239 0.935910i \(-0.614580\pi\)
−0.352239 + 0.935910i \(0.614580\pi\)
\(294\) −24.3656 −1.42103
\(295\) 0.000117133 0 6.81975e−6 0
\(296\) 8.07756 0.469499
\(297\) 4.08182 0.236851
\(298\) 2.91259 0.168722
\(299\) 11.4889 0.664418
\(300\) −10.7969 −0.623361
\(301\) 4.65666 0.268405
\(302\) −17.5297 −1.00872
\(303\) −3.51470 −0.201914
\(304\) 3.52763 0.202323
\(305\) 0.208977 0.0119660
\(306\) 5.38365 0.307763
\(307\) 16.0132 0.913923 0.456962 0.889486i \(-0.348938\pi\)
0.456962 + 0.889486i \(0.348938\pi\)
\(308\) −13.4270 −0.765075
\(309\) −4.68201 −0.266350
\(310\) −1.14390 −0.0649694
\(311\) 5.70637 0.323579 0.161789 0.986825i \(-0.448274\pi\)
0.161789 + 0.986825i \(0.448274\pi\)
\(312\) −3.64445 −0.206326
\(313\) 33.2537 1.87961 0.939806 0.341707i \(-0.111005\pi\)
0.939806 + 0.341707i \(0.111005\pi\)
\(314\) 31.3286 1.76797
\(315\) −1.29426 −0.0729235
\(316\) 14.8071 0.832964
\(317\) 25.1113 1.41039 0.705197 0.709012i \(-0.250859\pi\)
0.705197 + 0.709012i \(0.250859\pi\)
\(318\) 4.92109 0.275961
\(319\) 4.44553 0.248902
\(320\) −1.46224 −0.0817419
\(321\) 3.20337 0.178795
\(322\) −47.5506 −2.64989
\(323\) −2.42814 −0.135106
\(324\) 12.2365 0.679806
\(325\) −12.3992 −0.687785
\(326\) 22.9514 1.27116
\(327\) −8.49325 −0.469678
\(328\) 18.1941 1.00460
\(329\) −45.9970 −2.53590
\(330\) 0.189300 0.0104206
\(331\) 28.9347 1.59039 0.795196 0.606352i \(-0.207368\pi\)
0.795196 + 0.606352i \(0.207368\pi\)
\(332\) 23.0523 1.26516
\(333\) 10.0804 0.552402
\(334\) 25.1342 1.37528
\(335\) −1.24709 −0.0681359
\(336\) −5.07972 −0.277121
\(337\) −13.1526 −0.716470 −0.358235 0.933631i \(-0.616621\pi\)
−0.358235 + 0.933631i \(0.616621\pi\)
\(338\) 15.0672 0.819549
\(339\) 5.73830 0.311661
\(340\) 0.328956 0.0178402
\(341\) −4.53728 −0.245707
\(342\) −13.0723 −0.706867
\(343\) 35.7839 1.93215
\(344\) −1.95217 −0.105254
\(345\) 0.395832 0.0213109
\(346\) 2.57841 0.138616
\(347\) 22.7644 1.22206 0.611029 0.791609i \(-0.290756\pi\)
0.611029 + 0.791609i \(0.290756\pi\)
\(348\) −9.62466 −0.515936
\(349\) 11.6423 0.623200 0.311600 0.950213i \(-0.399135\pi\)
0.311600 + 0.950213i \(0.399135\pi\)
\(350\) 51.3184 2.74309
\(351\) −10.1487 −0.541697
\(352\) −7.11482 −0.379221
\(353\) −11.5931 −0.617039 −0.308519 0.951218i \(-0.599833\pi\)
−0.308519 + 0.951218i \(0.599833\pi\)
\(354\) −0.00170359 −9.05447e−5 0
\(355\) −0.936956 −0.0497285
\(356\) −40.8669 −2.16594
\(357\) 3.49649 0.185054
\(358\) −36.1556 −1.91088
\(359\) 36.7102 1.93749 0.968746 0.248053i \(-0.0797908\pi\)
0.968746 + 0.248053i \(0.0797908\pi\)
\(360\) 0.542584 0.0285967
\(361\) −13.1041 −0.689690
\(362\) −16.3309 −0.858335
\(363\) 0.750857 0.0394098
\(364\) 33.3838 1.74979
\(365\) 1.49149 0.0780683
\(366\) −3.03937 −0.158870
\(367\) 30.9856 1.61744 0.808718 0.588197i \(-0.200162\pi\)
0.808718 + 0.588197i \(0.200162\pi\)
\(368\) −6.71318 −0.349949
\(369\) 22.7053 1.18199
\(370\) 1.04317 0.0542320
\(371\) −13.8108 −0.717019
\(372\) 9.82330 0.509314
\(373\) 15.7210 0.814003 0.407001 0.913427i \(-0.366574\pi\)
0.407001 + 0.913427i \(0.366574\pi\)
\(374\) 2.20984 0.114268
\(375\) −0.855510 −0.0441783
\(376\) 19.2829 0.994442
\(377\) −11.0530 −0.569258
\(378\) 42.0039 2.16045
\(379\) 12.0706 0.620024 0.310012 0.950733i \(-0.399667\pi\)
0.310012 + 0.950733i \(0.399667\pi\)
\(380\) −0.798753 −0.0409752
\(381\) 0.705175 0.0361272
\(382\) 15.3153 0.783600
\(383\) −25.2323 −1.28931 −0.644656 0.764473i \(-0.722999\pi\)
−0.644656 + 0.764473i \(0.722999\pi\)
\(384\) 10.5825 0.540037
\(385\) −0.531261 −0.0270756
\(386\) −6.66486 −0.339233
\(387\) −2.43621 −0.123840
\(388\) −37.9135 −1.92477
\(389\) −14.6318 −0.741863 −0.370932 0.928660i \(-0.620962\pi\)
−0.370932 + 0.928660i \(0.620962\pi\)
\(390\) −0.470661 −0.0238328
\(391\) 4.62083 0.233686
\(392\) −28.6666 −1.44788
\(393\) −10.7533 −0.542430
\(394\) 42.7235 2.15238
\(395\) 0.585866 0.0294781
\(396\) 7.02458 0.352998
\(397\) −2.12611 −0.106707 −0.0533533 0.998576i \(-0.516991\pi\)
−0.0533533 + 0.998576i \(0.516991\pi\)
\(398\) −41.7209 −2.09128
\(399\) −8.48997 −0.425030
\(400\) 7.24513 0.362256
\(401\) 26.1334 1.30504 0.652519 0.757772i \(-0.273712\pi\)
0.652519 + 0.757772i \(0.273712\pi\)
\(402\) 18.1378 0.904629
\(403\) 11.2811 0.561952
\(404\) −13.4969 −0.671498
\(405\) 0.484157 0.0240579
\(406\) 45.7466 2.27037
\(407\) 4.13773 0.205100
\(408\) −1.46580 −0.0725680
\(409\) −3.86768 −0.191244 −0.0956222 0.995418i \(-0.530484\pi\)
−0.0956222 + 0.995418i \(0.530484\pi\)
\(410\) 2.34967 0.116042
\(411\) −15.5881 −0.768906
\(412\) −17.9796 −0.885791
\(413\) 0.00478102 0.000235259 0
\(414\) 24.8769 1.22263
\(415\) 0.912100 0.0447732
\(416\) 17.6897 0.867308
\(417\) 0.811804 0.0397542
\(418\) −5.36581 −0.262450
\(419\) 5.44966 0.266233 0.133117 0.991100i \(-0.457501\pi\)
0.133117 + 0.991100i \(0.457501\pi\)
\(420\) 1.15019 0.0561235
\(421\) −29.5126 −1.43835 −0.719177 0.694827i \(-0.755481\pi\)
−0.719177 + 0.694827i \(0.755481\pi\)
\(422\) 0.758193 0.0369082
\(423\) 24.0642 1.17004
\(424\) 5.78977 0.281176
\(425\) −4.98698 −0.241904
\(426\) 13.6271 0.660237
\(427\) 8.52982 0.412787
\(428\) 12.3014 0.594611
\(429\) −1.86687 −0.0901332
\(430\) −0.252113 −0.0121579
\(431\) −9.21918 −0.444072 −0.222036 0.975038i \(-0.571270\pi\)
−0.222036 + 0.975038i \(0.571270\pi\)
\(432\) 5.93010 0.285312
\(433\) −12.2353 −0.587992 −0.293996 0.955807i \(-0.594985\pi\)
−0.293996 + 0.955807i \(0.594985\pi\)
\(434\) −46.6907 −2.24123
\(435\) −0.380815 −0.0182587
\(436\) −32.6153 −1.56199
\(437\) −11.2200 −0.536728
\(438\) −21.6923 −1.03650
\(439\) 4.24483 0.202595 0.101297 0.994856i \(-0.467701\pi\)
0.101297 + 0.994856i \(0.467701\pi\)
\(440\) 0.222716 0.0106176
\(441\) −35.7745 −1.70355
\(442\) −5.49436 −0.261340
\(443\) −19.6944 −0.935711 −0.467855 0.883805i \(-0.654973\pi\)
−0.467855 + 0.883805i \(0.654973\pi\)
\(444\) −8.95827 −0.425141
\(445\) −1.61696 −0.0766514
\(446\) 3.98456 0.188674
\(447\) −0.989637 −0.0468082
\(448\) −59.6844 −2.81982
\(449\) −21.8415 −1.03076 −0.515382 0.856961i \(-0.672350\pi\)
−0.515382 + 0.856961i \(0.672350\pi\)
\(450\) −26.8482 −1.26563
\(451\) 9.31993 0.438858
\(452\) 22.0359 1.03648
\(453\) 5.95624 0.279848
\(454\) 8.04752 0.377689
\(455\) 1.32088 0.0619239
\(456\) 3.55918 0.166674
\(457\) −4.81329 −0.225156 −0.112578 0.993643i \(-0.535911\pi\)
−0.112578 + 0.993643i \(0.535911\pi\)
\(458\) −53.0826 −2.48039
\(459\) −4.08182 −0.190523
\(460\) 1.52005 0.0708728
\(461\) −5.33600 −0.248522 −0.124261 0.992250i \(-0.539656\pi\)
−0.124261 + 0.992250i \(0.539656\pi\)
\(462\) 7.72668 0.359478
\(463\) 19.4484 0.903842 0.451921 0.892058i \(-0.350739\pi\)
0.451921 + 0.892058i \(0.350739\pi\)
\(464\) 6.45850 0.299828
\(465\) 0.388674 0.0180243
\(466\) 11.6015 0.537430
\(467\) 30.1271 1.39411 0.697057 0.717015i \(-0.254492\pi\)
0.697057 + 0.717015i \(0.254492\pi\)
\(468\) −17.4653 −0.807334
\(469\) −50.9025 −2.35046
\(470\) 2.49029 0.114868
\(471\) −10.6448 −0.490486
\(472\) −0.00200431 −9.22558e−5 0
\(473\) −1.00000 −0.0459800
\(474\) −8.52086 −0.391376
\(475\) 12.1091 0.555604
\(476\) 13.4270 0.615426
\(477\) 7.22534 0.330826
\(478\) −14.8770 −0.680459
\(479\) 6.47622 0.295906 0.147953 0.988994i \(-0.452732\pi\)
0.147953 + 0.988994i \(0.452732\pi\)
\(480\) 0.609473 0.0278185
\(481\) −10.2877 −0.469079
\(482\) 60.9464 2.77603
\(483\) 16.1567 0.735154
\(484\) 2.88340 0.131064
\(485\) −1.50011 −0.0681163
\(486\) −34.1021 −1.54690
\(487\) −11.3463 −0.514152 −0.257076 0.966391i \(-0.582759\pi\)
−0.257076 + 0.966391i \(0.582759\pi\)
\(488\) −3.57588 −0.161873
\(489\) −7.79839 −0.352656
\(490\) −3.70214 −0.167246
\(491\) −24.9536 −1.12614 −0.563069 0.826410i \(-0.690380\pi\)
−0.563069 + 0.826410i \(0.690380\pi\)
\(492\) −20.1778 −0.909688
\(493\) −4.44553 −0.200217
\(494\) 13.3411 0.600245
\(495\) 0.277938 0.0124924
\(496\) −6.59179 −0.295980
\(497\) −38.2437 −1.71547
\(498\) −13.2656 −0.594447
\(499\) −29.8327 −1.33549 −0.667747 0.744388i \(-0.732741\pi\)
−0.667747 + 0.744388i \(0.732741\pi\)
\(500\) −3.28528 −0.146922
\(501\) −8.54006 −0.381542
\(502\) −6.52103 −0.291048
\(503\) −0.682030 −0.0304102 −0.0152051 0.999884i \(-0.504840\pi\)
−0.0152051 + 0.999884i \(0.504840\pi\)
\(504\) 22.1466 0.986490
\(505\) −0.534027 −0.0237639
\(506\) 10.2113 0.453948
\(507\) −5.11952 −0.227366
\(508\) 2.70797 0.120147
\(509\) 19.8110 0.878105 0.439053 0.898461i \(-0.355314\pi\)
0.439053 + 0.898461i \(0.355314\pi\)
\(510\) −0.189300 −0.00838237
\(511\) 60.8783 2.69310
\(512\) −16.0087 −0.707492
\(513\) 9.91124 0.437592
\(514\) 14.4056 0.635405
\(515\) −0.711391 −0.0313476
\(516\) 2.16502 0.0953097
\(517\) 9.87769 0.434420
\(518\) 42.5792 1.87082
\(519\) −0.876087 −0.0384560
\(520\) −0.553742 −0.0242832
\(521\) −29.4872 −1.29186 −0.645928 0.763398i \(-0.723530\pi\)
−0.645928 + 0.763398i \(0.723530\pi\)
\(522\) −23.9331 −1.04753
\(523\) 13.7465 0.601094 0.300547 0.953767i \(-0.402831\pi\)
0.300547 + 0.953767i \(0.402831\pi\)
\(524\) −41.2940 −1.80394
\(525\) −17.4369 −0.761009
\(526\) 47.7809 2.08335
\(527\) 4.53728 0.197647
\(528\) 1.09085 0.0474732
\(529\) −1.64789 −0.0716474
\(530\) 0.747717 0.0324788
\(531\) −0.00250128 −0.000108546 0
\(532\) −32.6027 −1.41351
\(533\) −23.1723 −1.00370
\(534\) 23.5172 1.01769
\(535\) 0.486724 0.0210429
\(536\) 21.3395 0.921724
\(537\) 12.2849 0.530133
\(538\) −18.1246 −0.781407
\(539\) −14.6845 −0.632505
\(540\) −1.34274 −0.0577823
\(541\) 5.59366 0.240490 0.120245 0.992744i \(-0.461632\pi\)
0.120245 + 0.992744i \(0.461632\pi\)
\(542\) −22.7158 −0.975725
\(543\) 5.54890 0.238126
\(544\) 7.11482 0.305045
\(545\) −1.29048 −0.0552779
\(546\) −19.2110 −0.822153
\(547\) −38.5557 −1.64852 −0.824262 0.566208i \(-0.808410\pi\)
−0.824262 + 0.566208i \(0.808410\pi\)
\(548\) −59.8607 −2.55712
\(549\) −4.46252 −0.190456
\(550\) −11.0204 −0.469913
\(551\) 10.7944 0.459856
\(552\) −6.77323 −0.288288
\(553\) 23.9133 1.01690
\(554\) −9.01847 −0.383158
\(555\) −0.354448 −0.0150455
\(556\) 3.11744 0.132209
\(557\) 42.3986 1.79649 0.898244 0.439497i \(-0.144843\pi\)
0.898244 + 0.439497i \(0.144843\pi\)
\(558\) 24.4271 1.03408
\(559\) 2.48632 0.105160
\(560\) −0.771819 −0.0326153
\(561\) −0.750857 −0.0317012
\(562\) 38.8863 1.64032
\(563\) −38.2526 −1.61215 −0.806077 0.591811i \(-0.798413\pi\)
−0.806077 + 0.591811i \(0.798413\pi\)
\(564\) −21.3854 −0.900488
\(565\) 0.871884 0.0366805
\(566\) 41.0729 1.72642
\(567\) 19.7618 0.829918
\(568\) 16.0326 0.672713
\(569\) −27.0419 −1.13365 −0.566827 0.823837i \(-0.691829\pi\)
−0.566827 + 0.823837i \(0.691829\pi\)
\(570\) 0.459649 0.0192526
\(571\) 34.7063 1.45241 0.726206 0.687477i \(-0.241282\pi\)
0.726206 + 0.687477i \(0.241282\pi\)
\(572\) −7.16904 −0.299753
\(573\) −5.20382 −0.217393
\(574\) 95.9065 4.00306
\(575\) −23.0440 −0.961002
\(576\) 31.2250 1.30104
\(577\) 20.8059 0.866160 0.433080 0.901356i \(-0.357427\pi\)
0.433080 + 0.901356i \(0.357427\pi\)
\(578\) −2.20984 −0.0919173
\(579\) 2.26458 0.0941127
\(580\) −1.46238 −0.0607222
\(581\) 37.2292 1.54453
\(582\) 21.8176 0.904369
\(583\) 2.96581 0.122831
\(584\) −25.5215 −1.05609
\(585\) −0.691043 −0.0285711
\(586\) 26.6478 1.10081
\(587\) 29.0898 1.20066 0.600332 0.799751i \(-0.295035\pi\)
0.600332 + 0.799751i \(0.295035\pi\)
\(588\) 31.7922 1.31109
\(589\) −11.0172 −0.453954
\(590\) −0.000258846 0 −1.06565e−5 0
\(591\) −14.5165 −0.597130
\(592\) 6.01133 0.247064
\(593\) −10.7188 −0.440168 −0.220084 0.975481i \(-0.570633\pi\)
−0.220084 + 0.975481i \(0.570633\pi\)
\(594\) −9.02017 −0.370102
\(595\) 0.531261 0.0217796
\(596\) −3.80035 −0.155668
\(597\) 14.1759 0.580180
\(598\) −25.3885 −1.03821
\(599\) 45.2831 1.85022 0.925108 0.379704i \(-0.123974\pi\)
0.925108 + 0.379704i \(0.123974\pi\)
\(600\) 7.30993 0.298427
\(601\) 9.15360 0.373383 0.186692 0.982419i \(-0.440223\pi\)
0.186692 + 0.982419i \(0.440223\pi\)
\(602\) −10.2905 −0.419409
\(603\) 26.6306 1.08448
\(604\) 22.8728 0.930681
\(605\) 0.114086 0.00463827
\(606\) 7.76692 0.315510
\(607\) 36.3496 1.47538 0.737692 0.675138i \(-0.235916\pi\)
0.737692 + 0.675138i \(0.235916\pi\)
\(608\) −17.2758 −0.700626
\(609\) −15.5437 −0.629863
\(610\) −0.461806 −0.0186980
\(611\) −24.5590 −0.993553
\(612\) −7.02458 −0.283952
\(613\) −0.803782 −0.0324645 −0.0162322 0.999868i \(-0.505167\pi\)
−0.0162322 + 0.999868i \(0.505167\pi\)
\(614\) −35.3867 −1.42809
\(615\) −0.798369 −0.0321933
\(616\) 9.09060 0.366271
\(617\) −6.69185 −0.269404 −0.134702 0.990886i \(-0.543008\pi\)
−0.134702 + 0.990886i \(0.543008\pi\)
\(618\) 10.3465 0.416197
\(619\) 16.1139 0.647674 0.323837 0.946113i \(-0.395027\pi\)
0.323837 + 0.946113i \(0.395027\pi\)
\(620\) 1.49257 0.0599429
\(621\) −18.8614 −0.756882
\(622\) −12.6102 −0.505622
\(623\) −65.9995 −2.64422
\(624\) −2.71220 −0.108575
\(625\) 24.8049 0.992197
\(626\) −73.4855 −2.93707
\(627\) 1.82319 0.0728112
\(628\) −40.8775 −1.63119
\(629\) −4.13773 −0.164982
\(630\) 2.86012 0.113950
\(631\) 20.8082 0.828361 0.414180 0.910195i \(-0.364068\pi\)
0.414180 + 0.910195i \(0.364068\pi\)
\(632\) −10.0250 −0.398772
\(633\) −0.257618 −0.0102394
\(634\) −55.4921 −2.20387
\(635\) 0.107145 0.00425193
\(636\) −6.42104 −0.254611
\(637\) 36.5102 1.44659
\(638\) −9.82391 −0.388932
\(639\) 20.0079 0.791500
\(640\) 1.60792 0.0635587
\(641\) −12.9771 −0.512566 −0.256283 0.966602i \(-0.582498\pi\)
−0.256283 + 0.966602i \(0.582498\pi\)
\(642\) −7.07894 −0.279383
\(643\) −7.75787 −0.305941 −0.152970 0.988231i \(-0.548884\pi\)
−0.152970 + 0.988231i \(0.548884\pi\)
\(644\) 62.0440 2.44487
\(645\) 0.0856625 0.00337296
\(646\) 5.36581 0.211115
\(647\) −40.8309 −1.60523 −0.802615 0.596497i \(-0.796559\pi\)
−0.802615 + 0.596497i \(0.796559\pi\)
\(648\) −8.28458 −0.325449
\(649\) −0.00102671 −4.03018e−5 0
\(650\) 27.4003 1.07473
\(651\) 15.8645 0.621780
\(652\) −29.9469 −1.17281
\(653\) 24.3575 0.953183 0.476591 0.879125i \(-0.341872\pi\)
0.476591 + 0.879125i \(0.341872\pi\)
\(654\) 18.7687 0.733916
\(655\) −1.63386 −0.0638403
\(656\) 13.5401 0.528651
\(657\) −31.8496 −1.24257
\(658\) 101.646 3.96258
\(659\) −40.2598 −1.56830 −0.784150 0.620572i \(-0.786901\pi\)
−0.784150 + 0.620572i \(0.786901\pi\)
\(660\) −0.246999 −0.00961443
\(661\) 16.7483 0.651434 0.325717 0.945467i \(-0.394394\pi\)
0.325717 + 0.945467i \(0.394394\pi\)
\(662\) −63.9410 −2.48514
\(663\) 1.86687 0.0725031
\(664\) −15.6073 −0.605680
\(665\) −1.28998 −0.0500232
\(666\) −22.2761 −0.863180
\(667\) −20.5420 −0.795391
\(668\) −32.7951 −1.26888
\(669\) −1.35387 −0.0523435
\(670\) 2.75588 0.106469
\(671\) −1.83175 −0.0707138
\(672\) 24.8769 0.959646
\(673\) −32.6157 −1.25724 −0.628621 0.777712i \(-0.716380\pi\)
−0.628621 + 0.777712i \(0.716380\pi\)
\(674\) 29.0652 1.11955
\(675\) 20.3560 0.783502
\(676\) −19.6597 −0.756142
\(677\) −42.8384 −1.64641 −0.823207 0.567742i \(-0.807817\pi\)
−0.823207 + 0.567742i \(0.807817\pi\)
\(678\) −12.6807 −0.487000
\(679\) −61.2299 −2.34979
\(680\) −0.222716 −0.00854077
\(681\) −2.73438 −0.104782
\(682\) 10.0267 0.383941
\(683\) 22.4783 0.860110 0.430055 0.902803i \(-0.358494\pi\)
0.430055 + 0.902803i \(0.358494\pi\)
\(684\) 17.0567 0.652178
\(685\) −2.36848 −0.0904951
\(686\) −79.0768 −3.01917
\(687\) 18.0363 0.688129
\(688\) −1.45281 −0.0553878
\(689\) −7.37393 −0.280924
\(690\) −0.874726 −0.0333003
\(691\) −39.5969 −1.50634 −0.753168 0.657828i \(-0.771475\pi\)
−0.753168 + 0.657828i \(0.771475\pi\)
\(692\) −3.36430 −0.127892
\(693\) 11.3446 0.430946
\(694\) −50.3057 −1.90958
\(695\) 0.123347 0.00467880
\(696\) 6.51627 0.246998
\(697\) −9.31993 −0.353018
\(698\) −25.7277 −0.973808
\(699\) −3.94195 −0.149098
\(700\) −66.9603 −2.53086
\(701\) 43.3540 1.63746 0.818730 0.574179i \(-0.194679\pi\)
0.818730 + 0.574179i \(0.194679\pi\)
\(702\) 22.4270 0.846453
\(703\) 10.0470 0.378930
\(704\) 12.8170 0.483059
\(705\) −0.846147 −0.0318677
\(706\) 25.6189 0.964181
\(707\) −21.7974 −0.819776
\(708\) 0.00222284 8.35395e−5 0
\(709\) −34.7125 −1.30366 −0.651828 0.758367i \(-0.725998\pi\)
−0.651828 + 0.758367i \(0.725998\pi\)
\(710\) 2.07052 0.0777054
\(711\) −12.5107 −0.469186
\(712\) 27.6684 1.03692
\(713\) 20.9660 0.785183
\(714\) −7.72668 −0.289164
\(715\) −0.283654 −0.0106081
\(716\) 47.1758 1.76304
\(717\) 5.05490 0.188779
\(718\) −81.1238 −3.02751
\(719\) 6.05332 0.225751 0.112875 0.993609i \(-0.463994\pi\)
0.112875 + 0.993609i \(0.463994\pi\)
\(720\) 0.403791 0.0150484
\(721\) −29.0368 −1.08139
\(722\) 28.9580 1.07771
\(723\) −20.7083 −0.770150
\(724\) 21.3086 0.791927
\(725\) 22.1698 0.823365
\(726\) −1.65928 −0.0615815
\(727\) −35.5345 −1.31790 −0.658951 0.752186i \(-0.729000\pi\)
−0.658951 + 0.752186i \(0.729000\pi\)
\(728\) −22.6021 −0.837689
\(729\) −1.14415 −0.0423761
\(730\) −3.29596 −0.121989
\(731\) 1.00000 0.0369863
\(732\) 3.96577 0.146579
\(733\) 14.2633 0.526826 0.263413 0.964683i \(-0.415152\pi\)
0.263413 + 0.964683i \(0.415152\pi\)
\(734\) −68.4733 −2.52740
\(735\) 1.25791 0.0463986
\(736\) 32.8764 1.21184
\(737\) 10.9311 0.402653
\(738\) −50.1752 −1.84698
\(739\) −4.96592 −0.182674 −0.0913371 0.995820i \(-0.529114\pi\)
−0.0913371 + 0.995820i \(0.529114\pi\)
\(740\) −1.36113 −0.0500362
\(741\) −4.53302 −0.166525
\(742\) 30.5196 1.12041
\(743\) −3.69649 −0.135611 −0.0678055 0.997699i \(-0.521600\pi\)
−0.0678055 + 0.997699i \(0.521600\pi\)
\(744\) −6.65075 −0.243828
\(745\) −0.150367 −0.00550901
\(746\) −34.7409 −1.27196
\(747\) −19.4771 −0.712630
\(748\) −2.88340 −0.105428
\(749\) 19.8666 0.725911
\(750\) 1.89054 0.0690328
\(751\) 28.0119 1.02217 0.511084 0.859531i \(-0.329244\pi\)
0.511084 + 0.859531i \(0.329244\pi\)
\(752\) 14.3504 0.523304
\(753\) 2.21571 0.0807448
\(754\) 24.4253 0.889519
\(755\) 0.904998 0.0329363
\(756\) −54.8066 −1.99330
\(757\) −42.8281 −1.55661 −0.778307 0.627883i \(-0.783921\pi\)
−0.778307 + 0.627883i \(0.783921\pi\)
\(758\) −26.6740 −0.968845
\(759\) −3.46959 −0.125938
\(760\) 0.540786 0.0196164
\(761\) −38.7262 −1.40382 −0.701912 0.712264i \(-0.747670\pi\)
−0.701912 + 0.712264i \(0.747670\pi\)
\(762\) −1.55832 −0.0564521
\(763\) −52.6734 −1.90690
\(764\) −19.9834 −0.722975
\(765\) −0.277938 −0.0100489
\(766\) 55.7594 2.01467
\(767\) 0.00255272 9.21733e−5 0
\(768\) −4.13820 −0.149324
\(769\) −20.7572 −0.748525 −0.374263 0.927323i \(-0.622104\pi\)
−0.374263 + 0.927323i \(0.622104\pi\)
\(770\) 1.17400 0.0423081
\(771\) −4.89472 −0.176279
\(772\) 8.69631 0.312987
\(773\) 6.74658 0.242658 0.121329 0.992612i \(-0.461284\pi\)
0.121329 + 0.992612i \(0.461284\pi\)
\(774\) 5.38365 0.193511
\(775\) −22.6273 −0.812798
\(776\) 25.6689 0.921459
\(777\) −14.4675 −0.519019
\(778\) 32.3340 1.15923
\(779\) 22.6301 0.810809
\(780\) 0.614118 0.0219889
\(781\) 8.21270 0.293873
\(782\) −10.2113 −0.365156
\(783\) 18.1458 0.648480
\(784\) −21.3337 −0.761918
\(785\) −1.61738 −0.0577268
\(786\) 23.7630 0.847598
\(787\) 11.2267 0.400188 0.200094 0.979777i \(-0.435875\pi\)
0.200094 + 0.979777i \(0.435875\pi\)
\(788\) −55.7455 −1.98585
\(789\) −16.2349 −0.577979
\(790\) −1.29467 −0.0460623
\(791\) 35.5877 1.26535
\(792\) −4.75591 −0.168994
\(793\) 4.55430 0.161728
\(794\) 4.69837 0.166739
\(795\) −0.254058 −0.00901052
\(796\) 54.4374 1.92948
\(797\) −0.768608 −0.0272255 −0.0136127 0.999907i \(-0.504333\pi\)
−0.0136127 + 0.999907i \(0.504333\pi\)
\(798\) 18.7615 0.664149
\(799\) −9.87769 −0.349447
\(800\) −35.4815 −1.25446
\(801\) 34.5288 1.22002
\(802\) −57.7506 −2.03925
\(803\) −13.0734 −0.461350
\(804\) −23.6661 −0.834640
\(805\) 2.45487 0.0865227
\(806\) −24.9295 −0.878102
\(807\) 6.15836 0.216784
\(808\) 9.13794 0.321472
\(809\) 49.8688 1.75329 0.876646 0.481136i \(-0.159776\pi\)
0.876646 + 0.481136i \(0.159776\pi\)
\(810\) −1.06991 −0.0375928
\(811\) 5.26885 0.185014 0.0925071 0.995712i \(-0.470512\pi\)
0.0925071 + 0.995712i \(0.470512\pi\)
\(812\) −59.6901 −2.09471
\(813\) 7.71833 0.270694
\(814\) −9.14373 −0.320487
\(815\) −1.18490 −0.0415052
\(816\) −1.09085 −0.0381874
\(817\) −2.42814 −0.0849500
\(818\) 8.54695 0.298837
\(819\) −28.2063 −0.985608
\(820\) −3.06585 −0.107064
\(821\) 13.6830 0.477539 0.238770 0.971076i \(-0.423256\pi\)
0.238770 + 0.971076i \(0.423256\pi\)
\(822\) 34.4473 1.20149
\(823\) 7.56635 0.263747 0.131873 0.991267i \(-0.457901\pi\)
0.131873 + 0.991267i \(0.457901\pi\)
\(824\) 12.1729 0.424062
\(825\) 3.74451 0.130367
\(826\) −0.0105653 −0.000367614 0
\(827\) 33.8998 1.17881 0.589406 0.807837i \(-0.299362\pi\)
0.589406 + 0.807837i \(0.299362\pi\)
\(828\) −32.4594 −1.12804
\(829\) 24.3305 0.845032 0.422516 0.906355i \(-0.361147\pi\)
0.422516 + 0.906355i \(0.361147\pi\)
\(830\) −2.01560 −0.0699624
\(831\) 3.06428 0.106299
\(832\) −31.8671 −1.10479
\(833\) 14.6845 0.508787
\(834\) −1.79396 −0.0621197
\(835\) −1.29759 −0.0449049
\(836\) 7.00131 0.242145
\(837\) −18.5203 −0.640157
\(838\) −12.0429 −0.416015
\(839\) 3.38834 0.116979 0.0584893 0.998288i \(-0.481372\pi\)
0.0584893 + 0.998288i \(0.481372\pi\)
\(840\) −0.778723 −0.0268685
\(841\) −9.23728 −0.318527
\(842\) 65.2181 2.24756
\(843\) −13.2127 −0.455071
\(844\) −0.989289 −0.0340527
\(845\) −0.777867 −0.0267594
\(846\) −53.1780 −1.82830
\(847\) 4.65666 0.160005
\(848\) 4.30875 0.147963
\(849\) −13.9557 −0.478959
\(850\) 11.0204 0.377998
\(851\) −19.1198 −0.655417
\(852\) −17.7807 −0.609156
\(853\) −22.2634 −0.762286 −0.381143 0.924516i \(-0.624469\pi\)
−0.381143 + 0.924516i \(0.624469\pi\)
\(854\) −18.8495 −0.645018
\(855\) 0.674874 0.0230802
\(856\) −8.32852 −0.284663
\(857\) −43.1652 −1.47449 −0.737247 0.675623i \(-0.763875\pi\)
−0.737247 + 0.675623i \(0.763875\pi\)
\(858\) 4.12548 0.140842
\(859\) 23.2875 0.794558 0.397279 0.917698i \(-0.369954\pi\)
0.397279 + 0.917698i \(0.369954\pi\)
\(860\) 0.328956 0.0112173
\(861\) −32.5870 −1.11056
\(862\) 20.3729 0.693905
\(863\) 20.5477 0.699453 0.349726 0.936852i \(-0.386275\pi\)
0.349726 + 0.936852i \(0.386275\pi\)
\(864\) −29.0414 −0.988009
\(865\) −0.133114 −0.00452601
\(866\) 27.0381 0.918793
\(867\) 0.750857 0.0255004
\(868\) 60.9220 2.06783
\(869\) −5.13529 −0.174203
\(870\) 0.841541 0.0285309
\(871\) −27.1782 −0.920900
\(872\) 22.0818 0.747785
\(873\) 32.0335 1.08417
\(874\) 24.7945 0.838687
\(875\) −5.30569 −0.179365
\(876\) 28.3042 0.956309
\(877\) 18.8632 0.636966 0.318483 0.947928i \(-0.396827\pi\)
0.318483 + 0.947928i \(0.396827\pi\)
\(878\) −9.38041 −0.316573
\(879\) −9.05437 −0.305396
\(880\) 0.165745 0.00558727
\(881\) −40.9825 −1.38074 −0.690368 0.723459i \(-0.742551\pi\)
−0.690368 + 0.723459i \(0.742551\pi\)
\(882\) 79.0560 2.66195
\(883\) 21.8613 0.735691 0.367846 0.929887i \(-0.380096\pi\)
0.367846 + 0.929887i \(0.380096\pi\)
\(884\) 7.16904 0.241121
\(885\) 8.79502e−5 0 2.95641e−6 0
\(886\) 43.5216 1.46214
\(887\) 2.76245 0.0927540 0.0463770 0.998924i \(-0.485232\pi\)
0.0463770 + 0.998924i \(0.485232\pi\)
\(888\) 6.06509 0.203531
\(889\) 4.37334 0.146677
\(890\) 3.57323 0.119775
\(891\) −4.24378 −0.142172
\(892\) −5.19905 −0.174077
\(893\) 23.9844 0.802609
\(894\) 2.18694 0.0731423
\(895\) 1.86659 0.0623931
\(896\) 65.6305 2.19256
\(897\) 8.62649 0.288030
\(898\) 48.2662 1.61066
\(899\) −20.1706 −0.672727
\(900\) 35.0315 1.16772
\(901\) −2.96581 −0.0988054
\(902\) −20.5956 −0.685758
\(903\) 3.49649 0.116356
\(904\) −14.9191 −0.496203
\(905\) 0.843108 0.0280258
\(906\) −13.1623 −0.437289
\(907\) −27.2878 −0.906076 −0.453038 0.891491i \(-0.649660\pi\)
−0.453038 + 0.891491i \(0.649660\pi\)
\(908\) −10.5004 −0.348468
\(909\) 11.4037 0.378237
\(910\) −2.91894 −0.0967619
\(911\) 20.5703 0.681525 0.340762 0.940149i \(-0.389315\pi\)
0.340762 + 0.940149i \(0.389315\pi\)
\(912\) 2.64874 0.0877086
\(913\) −7.99483 −0.264590
\(914\) 10.6366 0.351828
\(915\) 0.156912 0.00518735
\(916\) 69.2621 2.28849
\(917\) −66.6894 −2.20228
\(918\) 9.02017 0.297710
\(919\) −4.95557 −0.163469 −0.0817346 0.996654i \(-0.526046\pi\)
−0.0817346 + 0.996654i \(0.526046\pi\)
\(920\) −1.02913 −0.0339295
\(921\) 12.0236 0.396193
\(922\) 11.7917 0.388340
\(923\) −20.4194 −0.672112
\(924\) −10.0818 −0.331666
\(925\) 20.6348 0.678468
\(926\) −42.9778 −1.41234
\(927\) 15.1911 0.498943
\(928\) −31.6291 −1.03828
\(929\) −26.1290 −0.857264 −0.428632 0.903479i \(-0.641004\pi\)
−0.428632 + 0.903479i \(0.641004\pi\)
\(930\) −0.858909 −0.0281647
\(931\) −35.6560 −1.16858
\(932\) −15.1376 −0.495850
\(933\) 4.28467 0.140274
\(934\) −66.5761 −2.17844
\(935\) −0.114086 −0.00373102
\(936\) 11.8247 0.386502
\(937\) 54.6458 1.78520 0.892600 0.450849i \(-0.148879\pi\)
0.892600 + 0.450849i \(0.148879\pi\)
\(938\) 112.487 3.67282
\(939\) 24.9688 0.814826
\(940\) −3.24933 −0.105981
\(941\) 3.92662 0.128004 0.0640021 0.997950i \(-0.479614\pi\)
0.0640021 + 0.997950i \(0.479614\pi\)
\(942\) 23.5233 0.766430
\(943\) −43.0659 −1.40242
\(944\) −0.00149161 −4.85477e−5 0
\(945\) −2.16851 −0.0705416
\(946\) 2.20984 0.0718481
\(947\) −58.0611 −1.88673 −0.943366 0.331753i \(-0.892360\pi\)
−0.943366 + 0.331753i \(0.892360\pi\)
\(948\) 11.1180 0.361096
\(949\) 32.5046 1.05514
\(950\) −26.7592 −0.868184
\(951\) 18.8550 0.611416
\(952\) −9.09060 −0.294628
\(953\) −59.4184 −1.92475 −0.962375 0.271726i \(-0.912406\pi\)
−0.962375 + 0.271726i \(0.912406\pi\)
\(954\) −15.9669 −0.516946
\(955\) −0.790675 −0.0255857
\(956\) 19.4115 0.627813
\(957\) 3.33796 0.107901
\(958\) −14.3114 −0.462381
\(959\) −96.6743 −3.12178
\(960\) −1.09794 −0.0354357
\(961\) −10.4131 −0.335907
\(962\) 22.7342 0.732980
\(963\) −10.3936 −0.334928
\(964\) −79.5228 −2.56126
\(965\) 0.344083 0.0110764
\(966\) −35.7037 −1.14875
\(967\) 1.25222 0.0402685 0.0201343 0.999797i \(-0.493591\pi\)
0.0201343 + 0.999797i \(0.493591\pi\)
\(968\) −1.95217 −0.0627452
\(969\) −1.82319 −0.0585693
\(970\) 3.31500 0.106438
\(971\) 32.0937 1.02994 0.514968 0.857210i \(-0.327804\pi\)
0.514968 + 0.857210i \(0.327804\pi\)
\(972\) 44.4964 1.42722
\(973\) 5.03464 0.161403
\(974\) 25.0736 0.803411
\(975\) −9.31004 −0.298160
\(976\) −2.66117 −0.0851821
\(977\) 29.4772 0.943060 0.471530 0.881850i \(-0.343702\pi\)
0.471530 + 0.881850i \(0.343702\pi\)
\(978\) 17.2332 0.551057
\(979\) 14.1732 0.452976
\(980\) 4.83055 0.154306
\(981\) 27.5570 0.879828
\(982\) 55.1434 1.75970
\(983\) −39.7189 −1.26684 −0.633419 0.773809i \(-0.718349\pi\)
−0.633419 + 0.773809i \(0.718349\pi\)
\(984\) 13.6612 0.435503
\(985\) −2.20566 −0.0702782
\(986\) 9.82391 0.312857
\(987\) −34.5372 −1.09933
\(988\) −17.4075 −0.553805
\(989\) 4.62083 0.146934
\(990\) −0.614200 −0.0195206
\(991\) 25.1836 0.799984 0.399992 0.916519i \(-0.369013\pi\)
0.399992 + 0.916519i \(0.369013\pi\)
\(992\) 32.2819 1.02495
\(993\) 21.7258 0.689447
\(994\) 84.5126 2.68058
\(995\) 2.15390 0.0682833
\(996\) 17.3090 0.548456
\(997\) −59.0134 −1.86897 −0.934486 0.355999i \(-0.884141\pi\)
−0.934486 + 0.355999i \(0.884141\pi\)
\(998\) 65.9255 2.08683
\(999\) 16.8895 0.534359
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 \(a_p\))