Properties

Label 4017.2.a.j.1.4
Level 4017
Weight 2
Character 4017.1
Self dual Yes
Analytic conductor 32.076
Analytic rank 0
Dimension 25
CM No

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Newspace parameters

Level: \( N \) = \( 4017 = 3 \cdot 13 \cdot 103 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4017.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0759064919\)
Analytic rank: \(0\)
Dimension: \(25\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) = 4017.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.97968 q^{2} -1.00000 q^{3} +1.91913 q^{4} +2.16016 q^{5} +1.97968 q^{6} +5.12656 q^{7} +0.160099 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.97968 q^{2} -1.00000 q^{3} +1.91913 q^{4} +2.16016 q^{5} +1.97968 q^{6} +5.12656 q^{7} +0.160099 q^{8} +1.00000 q^{9} -4.27642 q^{10} +5.28339 q^{11} -1.91913 q^{12} +1.00000 q^{13} -10.1489 q^{14} -2.16016 q^{15} -4.15520 q^{16} -0.0913774 q^{17} -1.97968 q^{18} -3.04801 q^{19} +4.14562 q^{20} -5.12656 q^{21} -10.4594 q^{22} +0.448356 q^{23} -0.160099 q^{24} -0.333725 q^{25} -1.97968 q^{26} -1.00000 q^{27} +9.83852 q^{28} -2.04909 q^{29} +4.27642 q^{30} +10.1345 q^{31} +7.90577 q^{32} -5.28339 q^{33} +0.180898 q^{34} +11.0742 q^{35} +1.91913 q^{36} +3.51047 q^{37} +6.03409 q^{38} -1.00000 q^{39} +0.345839 q^{40} -5.08046 q^{41} +10.1489 q^{42} -2.08433 q^{43} +10.1395 q^{44} +2.16016 q^{45} -0.887600 q^{46} +2.87315 q^{47} +4.15520 q^{48} +19.2816 q^{49} +0.660668 q^{50} +0.0913774 q^{51} +1.91913 q^{52} +12.1242 q^{53} +1.97968 q^{54} +11.4129 q^{55} +0.820758 q^{56} +3.04801 q^{57} +4.05655 q^{58} -4.87431 q^{59} -4.14562 q^{60} +9.71819 q^{61} -20.0630 q^{62} +5.12656 q^{63} -7.34048 q^{64} +2.16016 q^{65} +10.4594 q^{66} -14.5811 q^{67} -0.175365 q^{68} -0.448356 q^{69} -21.9233 q^{70} +11.2128 q^{71} +0.160099 q^{72} -15.2353 q^{73} -6.94959 q^{74} +0.333725 q^{75} -5.84953 q^{76} +27.0856 q^{77} +1.97968 q^{78} -15.7024 q^{79} -8.97589 q^{80} +1.00000 q^{81} +10.0577 q^{82} +3.47805 q^{83} -9.83852 q^{84} -0.197389 q^{85} +4.12630 q^{86} +2.04909 q^{87} +0.845867 q^{88} +11.6302 q^{89} -4.27642 q^{90} +5.12656 q^{91} +0.860452 q^{92} -10.1345 q^{93} -5.68791 q^{94} -6.58418 q^{95} -7.90577 q^{96} +5.69283 q^{97} -38.1714 q^{98} +5.28339 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 25q + 6q^{2} - 25q^{3} + 28q^{4} + 7q^{5} - 6q^{6} + 17q^{7} + 21q^{8} + 25q^{9} + O(q^{10}) \) \( 25q + 6q^{2} - 25q^{3} + 28q^{4} + 7q^{5} - 6q^{6} + 17q^{7} + 21q^{8} + 25q^{9} - 6q^{10} + 21q^{11} - 28q^{12} + 25q^{13} + 10q^{14} - 7q^{15} + 30q^{16} + 14q^{17} + 6q^{18} + 12q^{19} + 24q^{20} - 17q^{21} + 3q^{22} + 41q^{23} - 21q^{24} + 30q^{25} + 6q^{26} - 25q^{27} + 14q^{28} + 22q^{29} + 6q^{30} + 14q^{31} + 28q^{32} - 21q^{33} - 11q^{34} + 14q^{35} + 28q^{36} - 6q^{37} + 16q^{38} - 25q^{39} - 34q^{40} + 33q^{41} - 10q^{42} + 35q^{43} + 45q^{44} + 7q^{45} + 3q^{46} + 48q^{47} - 30q^{48} - 4q^{49} + 7q^{50} - 14q^{51} + 28q^{52} + 18q^{53} - 6q^{54} + 10q^{55} + 32q^{56} - 12q^{57} + 33q^{58} + 46q^{59} - 24q^{60} - 19q^{61} + 5q^{62} + 17q^{63} + 29q^{64} + 7q^{65} - 3q^{66} + 16q^{67} + 20q^{68} - 41q^{69} - 43q^{70} + 60q^{71} + 21q^{72} - 14q^{73} - 50q^{74} - 30q^{75} + 59q^{77} - 6q^{78} + 7q^{79} + 32q^{80} + 25q^{81} + 18q^{82} + 23q^{83} - 14q^{84} - 9q^{85} - 9q^{86} - 22q^{87} + 23q^{88} + 10q^{89} - 6q^{90} + 17q^{91} + 69q^{92} - 14q^{93} - 30q^{94} + 81q^{95} - 28q^{96} - 10q^{97} + 55q^{98} + 21q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.97968 −1.39984 −0.699922 0.714219i \(-0.746782\pi\)
−0.699922 + 0.714219i \(0.746782\pi\)
\(3\) −1.00000 −0.577350
\(4\) 1.91913 0.959564
\(5\) 2.16016 0.966051 0.483026 0.875606i \(-0.339538\pi\)
0.483026 + 0.875606i \(0.339538\pi\)
\(6\) 1.97968 0.808201
\(7\) 5.12656 1.93766 0.968828 0.247733i \(-0.0796855\pi\)
0.968828 + 0.247733i \(0.0796855\pi\)
\(8\) 0.160099 0.0566036
\(9\) 1.00000 0.333333
\(10\) −4.27642 −1.35232
\(11\) 5.28339 1.59300 0.796501 0.604637i \(-0.206682\pi\)
0.796501 + 0.604637i \(0.206682\pi\)
\(12\) −1.91913 −0.554005
\(13\) 1.00000 0.277350
\(14\) −10.1489 −2.71242
\(15\) −2.16016 −0.557750
\(16\) −4.15520 −1.03880
\(17\) −0.0913774 −0.0221623 −0.0110811 0.999939i \(-0.503527\pi\)
−0.0110811 + 0.999939i \(0.503527\pi\)
\(18\) −1.97968 −0.466615
\(19\) −3.04801 −0.699262 −0.349631 0.936887i \(-0.613693\pi\)
−0.349631 + 0.936887i \(0.613693\pi\)
\(20\) 4.14562 0.926988
\(21\) −5.12656 −1.11871
\(22\) −10.4594 −2.22995
\(23\) 0.448356 0.0934886 0.0467443 0.998907i \(-0.485115\pi\)
0.0467443 + 0.998907i \(0.485115\pi\)
\(24\) −0.160099 −0.0326801
\(25\) −0.333725 −0.0667449
\(26\) −1.97968 −0.388247
\(27\) −1.00000 −0.192450
\(28\) 9.83852 1.85931
\(29\) −2.04909 −0.380507 −0.190254 0.981735i \(-0.560931\pi\)
−0.190254 + 0.981735i \(0.560931\pi\)
\(30\) 4.27642 0.780763
\(31\) 10.1345 1.82020 0.910101 0.414386i \(-0.136004\pi\)
0.910101 + 0.414386i \(0.136004\pi\)
\(32\) 7.90577 1.39756
\(33\) −5.28339 −0.919720
\(34\) 0.180898 0.0310237
\(35\) 11.0742 1.87188
\(36\) 1.91913 0.319855
\(37\) 3.51047 0.577117 0.288558 0.957462i \(-0.406824\pi\)
0.288558 + 0.957462i \(0.406824\pi\)
\(38\) 6.03409 0.978858
\(39\) −1.00000 −0.160128
\(40\) 0.345839 0.0546820
\(41\) −5.08046 −0.793434 −0.396717 0.917941i \(-0.629851\pi\)
−0.396717 + 0.917941i \(0.629851\pi\)
\(42\) 10.1489 1.56602
\(43\) −2.08433 −0.317857 −0.158928 0.987290i \(-0.550804\pi\)
−0.158928 + 0.987290i \(0.550804\pi\)
\(44\) 10.1395 1.52859
\(45\) 2.16016 0.322017
\(46\) −0.887600 −0.130870
\(47\) 2.87315 0.419092 0.209546 0.977799i \(-0.432801\pi\)
0.209546 + 0.977799i \(0.432801\pi\)
\(48\) 4.15520 0.599752
\(49\) 19.2816 2.75451
\(50\) 0.660668 0.0934325
\(51\) 0.0913774 0.0127954
\(52\) 1.91913 0.266135
\(53\) 12.1242 1.66539 0.832694 0.553733i \(-0.186797\pi\)
0.832694 + 0.553733i \(0.186797\pi\)
\(54\) 1.97968 0.269400
\(55\) 11.4129 1.53892
\(56\) 0.820758 0.109678
\(57\) 3.04801 0.403719
\(58\) 4.05655 0.532651
\(59\) −4.87431 −0.634581 −0.317290 0.948328i \(-0.602773\pi\)
−0.317290 + 0.948328i \(0.602773\pi\)
\(60\) −4.14562 −0.535197
\(61\) 9.71819 1.24429 0.622144 0.782903i \(-0.286262\pi\)
0.622144 + 0.782903i \(0.286262\pi\)
\(62\) −20.0630 −2.54800
\(63\) 5.12656 0.645886
\(64\) −7.34048 −0.917560
\(65\) 2.16016 0.267934
\(66\) 10.4594 1.28746
\(67\) −14.5811 −1.78137 −0.890683 0.454625i \(-0.849773\pi\)
−0.890683 + 0.454625i \(0.849773\pi\)
\(68\) −0.175365 −0.0212661
\(69\) −0.448356 −0.0539757
\(70\) −21.9233 −2.62033
\(71\) 11.2128 1.33071 0.665357 0.746525i \(-0.268279\pi\)
0.665357 + 0.746525i \(0.268279\pi\)
\(72\) 0.160099 0.0188679
\(73\) −15.2353 −1.78315 −0.891577 0.452870i \(-0.850400\pi\)
−0.891577 + 0.452870i \(0.850400\pi\)
\(74\) −6.94959 −0.807874
\(75\) 0.333725 0.0385352
\(76\) −5.84953 −0.670987
\(77\) 27.0856 3.08669
\(78\) 1.97968 0.224154
\(79\) −15.7024 −1.76665 −0.883327 0.468757i \(-0.844702\pi\)
−0.883327 + 0.468757i \(0.844702\pi\)
\(80\) −8.97589 −1.00353
\(81\) 1.00000 0.111111
\(82\) 10.0577 1.11068
\(83\) 3.47805 0.381766 0.190883 0.981613i \(-0.438865\pi\)
0.190883 + 0.981613i \(0.438865\pi\)
\(84\) −9.83852 −1.07347
\(85\) −0.197389 −0.0214099
\(86\) 4.12630 0.444950
\(87\) 2.04909 0.219686
\(88\) 0.845867 0.0901697
\(89\) 11.6302 1.23280 0.616400 0.787433i \(-0.288590\pi\)
0.616400 + 0.787433i \(0.288590\pi\)
\(90\) −4.27642 −0.450774
\(91\) 5.12656 0.537409
\(92\) 0.860452 0.0897083
\(93\) −10.1345 −1.05089
\(94\) −5.68791 −0.586663
\(95\) −6.58418 −0.675523
\(96\) −7.90577 −0.806879
\(97\) 5.69283 0.578019 0.289010 0.957326i \(-0.406674\pi\)
0.289010 + 0.957326i \(0.406674\pi\)
\(98\) −38.1714 −3.85589
\(99\) 5.28339 0.531001
\(100\) −0.640461 −0.0640461
\(101\) 7.43844 0.740153 0.370076 0.929001i \(-0.379332\pi\)
0.370076 + 0.929001i \(0.379332\pi\)
\(102\) −0.180898 −0.0179116
\(103\) −1.00000 −0.0985329
\(104\) 0.160099 0.0156990
\(105\) −11.0742 −1.08073
\(106\) −24.0020 −2.33128
\(107\) −7.26779 −0.702604 −0.351302 0.936262i \(-0.614261\pi\)
−0.351302 + 0.936262i \(0.614261\pi\)
\(108\) −1.91913 −0.184668
\(109\) −15.9411 −1.52688 −0.763440 0.645879i \(-0.776491\pi\)
−0.763440 + 0.645879i \(0.776491\pi\)
\(110\) −22.5940 −2.15425
\(111\) −3.51047 −0.333199
\(112\) −21.3019 −2.01284
\(113\) 3.13608 0.295017 0.147509 0.989061i \(-0.452875\pi\)
0.147509 + 0.989061i \(0.452875\pi\)
\(114\) −6.03409 −0.565144
\(115\) 0.968518 0.0903148
\(116\) −3.93248 −0.365121
\(117\) 1.00000 0.0924500
\(118\) 9.64957 0.888314
\(119\) −0.468451 −0.0429429
\(120\) −0.345839 −0.0315707
\(121\) 16.9142 1.53765
\(122\) −19.2389 −1.74181
\(123\) 5.08046 0.458090
\(124\) 19.4493 1.74660
\(125\) −11.5217 −1.03053
\(126\) −10.1489 −0.904139
\(127\) −2.59501 −0.230270 −0.115135 0.993350i \(-0.536730\pi\)
−0.115135 + 0.993350i \(0.536730\pi\)
\(128\) −1.27975 −0.113115
\(129\) 2.08433 0.183515
\(130\) −4.27642 −0.375066
\(131\) 1.84777 0.161441 0.0807203 0.996737i \(-0.474278\pi\)
0.0807203 + 0.996737i \(0.474278\pi\)
\(132\) −10.1395 −0.882531
\(133\) −15.6258 −1.35493
\(134\) 28.8659 2.49363
\(135\) −2.16016 −0.185917
\(136\) −0.0146294 −0.00125446
\(137\) 17.0567 1.45726 0.728628 0.684910i \(-0.240158\pi\)
0.728628 + 0.684910i \(0.240158\pi\)
\(138\) 0.887600 0.0755576
\(139\) −0.625326 −0.0530394 −0.0265197 0.999648i \(-0.508442\pi\)
−0.0265197 + 0.999648i \(0.508442\pi\)
\(140\) 21.2528 1.79619
\(141\) −2.87315 −0.241963
\(142\) −22.1977 −1.86279
\(143\) 5.28339 0.441819
\(144\) −4.15520 −0.346267
\(145\) −4.42636 −0.367590
\(146\) 30.1609 2.49614
\(147\) −19.2816 −1.59032
\(148\) 6.73703 0.553781
\(149\) 8.04548 0.659111 0.329556 0.944136i \(-0.393101\pi\)
0.329556 + 0.944136i \(0.393101\pi\)
\(150\) −0.660668 −0.0539433
\(151\) −7.47406 −0.608230 −0.304115 0.952635i \(-0.598361\pi\)
−0.304115 + 0.952635i \(0.598361\pi\)
\(152\) −0.487984 −0.0395808
\(153\) −0.0913774 −0.00738742
\(154\) −53.6208 −4.32089
\(155\) 21.8920 1.75841
\(156\) −1.91913 −0.153653
\(157\) 12.1690 0.971194 0.485597 0.874183i \(-0.338602\pi\)
0.485597 + 0.874183i \(0.338602\pi\)
\(158\) 31.0856 2.47304
\(159\) −12.1242 −0.961512
\(160\) 17.0777 1.35011
\(161\) 2.29852 0.181149
\(162\) −1.97968 −0.155538
\(163\) −12.7052 −0.995148 −0.497574 0.867422i \(-0.665776\pi\)
−0.497574 + 0.867422i \(0.665776\pi\)
\(164\) −9.75005 −0.761351
\(165\) −11.4129 −0.888497
\(166\) −6.88542 −0.534413
\(167\) −21.3271 −1.65034 −0.825170 0.564885i \(-0.808921\pi\)
−0.825170 + 0.564885i \(0.808921\pi\)
\(168\) −0.820758 −0.0633228
\(169\) 1.00000 0.0769231
\(170\) 0.390768 0.0299705
\(171\) −3.04801 −0.233087
\(172\) −4.00009 −0.305004
\(173\) 10.4525 0.794691 0.397345 0.917669i \(-0.369932\pi\)
0.397345 + 0.917669i \(0.369932\pi\)
\(174\) −4.05655 −0.307526
\(175\) −1.71086 −0.129329
\(176\) −21.9536 −1.65481
\(177\) 4.87431 0.366375
\(178\) −23.0241 −1.72573
\(179\) 6.88247 0.514420 0.257210 0.966356i \(-0.417197\pi\)
0.257210 + 0.966356i \(0.417197\pi\)
\(180\) 4.14562 0.308996
\(181\) −22.4316 −1.66733 −0.833665 0.552271i \(-0.813762\pi\)
−0.833665 + 0.552271i \(0.813762\pi\)
\(182\) −10.1489 −0.752289
\(183\) −9.71819 −0.718390
\(184\) 0.0717814 0.00529179
\(185\) 7.58315 0.557525
\(186\) 20.0630 1.47109
\(187\) −0.482782 −0.0353045
\(188\) 5.51394 0.402146
\(189\) −5.12656 −0.372902
\(190\) 13.0346 0.945627
\(191\) 3.33637 0.241411 0.120706 0.992688i \(-0.461484\pi\)
0.120706 + 0.992688i \(0.461484\pi\)
\(192\) 7.34048 0.529753
\(193\) −4.05623 −0.291974 −0.145987 0.989287i \(-0.546636\pi\)
−0.145987 + 0.989287i \(0.546636\pi\)
\(194\) −11.2700 −0.809137
\(195\) −2.16016 −0.154692
\(196\) 37.0039 2.64313
\(197\) 9.74945 0.694619 0.347310 0.937750i \(-0.387095\pi\)
0.347310 + 0.937750i \(0.387095\pi\)
\(198\) −10.4594 −0.743318
\(199\) 12.2267 0.866730 0.433365 0.901218i \(-0.357326\pi\)
0.433365 + 0.901218i \(0.357326\pi\)
\(200\) −0.0534291 −0.00377800
\(201\) 14.5811 1.02847
\(202\) −14.7257 −1.03610
\(203\) −10.5048 −0.737292
\(204\) 0.175365 0.0122780
\(205\) −10.9746 −0.766498
\(206\) 1.97968 0.137931
\(207\) 0.448356 0.0311629
\(208\) −4.15520 −0.288111
\(209\) −16.1038 −1.11393
\(210\) 21.9233 1.51285
\(211\) −4.52040 −0.311197 −0.155599 0.987820i \(-0.549731\pi\)
−0.155599 + 0.987820i \(0.549731\pi\)
\(212\) 23.2679 1.59805
\(213\) −11.2128 −0.768288
\(214\) 14.3879 0.983536
\(215\) −4.50247 −0.307066
\(216\) −0.160099 −0.0108934
\(217\) 51.9549 3.52693
\(218\) 31.5582 2.13739
\(219\) 15.2353 1.02950
\(220\) 21.9029 1.47669
\(221\) −0.0913774 −0.00614671
\(222\) 6.94959 0.466426
\(223\) 16.1875 1.08399 0.541997 0.840380i \(-0.317668\pi\)
0.541997 + 0.840380i \(0.317668\pi\)
\(224\) 40.5294 2.70798
\(225\) −0.333725 −0.0222483
\(226\) −6.20843 −0.412978
\(227\) 21.7928 1.44644 0.723220 0.690617i \(-0.242661\pi\)
0.723220 + 0.690617i \(0.242661\pi\)
\(228\) 5.84953 0.387394
\(229\) −26.4450 −1.74754 −0.873769 0.486342i \(-0.838331\pi\)
−0.873769 + 0.486342i \(0.838331\pi\)
\(230\) −1.91736 −0.126427
\(231\) −27.0856 −1.78210
\(232\) −0.328058 −0.0215381
\(233\) −15.3338 −1.00455 −0.502274 0.864709i \(-0.667503\pi\)
−0.502274 + 0.864709i \(0.667503\pi\)
\(234\) −1.97968 −0.129416
\(235\) 6.20645 0.404864
\(236\) −9.35442 −0.608921
\(237\) 15.7024 1.01998
\(238\) 0.927383 0.0601133
\(239\) −9.50354 −0.614733 −0.307366 0.951591i \(-0.599448\pi\)
−0.307366 + 0.951591i \(0.599448\pi\)
\(240\) 8.97589 0.579391
\(241\) 8.61404 0.554879 0.277440 0.960743i \(-0.410514\pi\)
0.277440 + 0.960743i \(0.410514\pi\)
\(242\) −33.4847 −2.15248
\(243\) −1.00000 −0.0641500
\(244\) 18.6505 1.19397
\(245\) 41.6513 2.66100
\(246\) −10.0577 −0.641254
\(247\) −3.04801 −0.193940
\(248\) 1.62252 0.103030
\(249\) −3.47805 −0.220413
\(250\) 22.8092 1.44258
\(251\) −6.34058 −0.400214 −0.200107 0.979774i \(-0.564129\pi\)
−0.200107 + 0.979774i \(0.564129\pi\)
\(252\) 9.83852 0.619769
\(253\) 2.36884 0.148928
\(254\) 5.13729 0.322342
\(255\) 0.197389 0.0123610
\(256\) 17.2144 1.07590
\(257\) −11.6725 −0.728111 −0.364056 0.931377i \(-0.618608\pi\)
−0.364056 + 0.931377i \(0.618608\pi\)
\(258\) −4.12630 −0.256892
\(259\) 17.9966 1.11825
\(260\) 4.14562 0.257100
\(261\) −2.04909 −0.126836
\(262\) −3.65800 −0.225992
\(263\) −13.0002 −0.801624 −0.400812 0.916160i \(-0.631272\pi\)
−0.400812 + 0.916160i \(0.631272\pi\)
\(264\) −0.845867 −0.0520595
\(265\) 26.1902 1.60885
\(266\) 30.9341 1.89669
\(267\) −11.6302 −0.711758
\(268\) −27.9830 −1.70934
\(269\) −23.2091 −1.41509 −0.707543 0.706670i \(-0.750196\pi\)
−0.707543 + 0.706670i \(0.750196\pi\)
\(270\) 4.27642 0.260254
\(271\) 12.6090 0.765944 0.382972 0.923760i \(-0.374901\pi\)
0.382972 + 0.923760i \(0.374901\pi\)
\(272\) 0.379691 0.0230222
\(273\) −5.12656 −0.310273
\(274\) −33.7669 −2.03993
\(275\) −1.76320 −0.106325
\(276\) −0.860452 −0.0517931
\(277\) 8.68645 0.521918 0.260959 0.965350i \(-0.415961\pi\)
0.260959 + 0.965350i \(0.415961\pi\)
\(278\) 1.23794 0.0742469
\(279\) 10.1345 0.606734
\(280\) 1.77297 0.105955
\(281\) −16.8805 −1.00701 −0.503503 0.863993i \(-0.667956\pi\)
−0.503503 + 0.863993i \(0.667956\pi\)
\(282\) 5.68791 0.338710
\(283\) 10.4162 0.619177 0.309589 0.950871i \(-0.399809\pi\)
0.309589 + 0.950871i \(0.399809\pi\)
\(284\) 21.5188 1.27691
\(285\) 6.58418 0.390013
\(286\) −10.4594 −0.618478
\(287\) −26.0453 −1.53740
\(288\) 7.90577 0.465852
\(289\) −16.9917 −0.999509
\(290\) 8.76278 0.514568
\(291\) −5.69283 −0.333720
\(292\) −29.2384 −1.71105
\(293\) −28.7560 −1.67995 −0.839973 0.542629i \(-0.817429\pi\)
−0.839973 + 0.542629i \(0.817429\pi\)
\(294\) 38.1714 2.22620
\(295\) −10.5293 −0.613038
\(296\) 0.562023 0.0326669
\(297\) −5.28339 −0.306573
\(298\) −15.9275 −0.922653
\(299\) 0.448356 0.0259291
\(300\) 0.640461 0.0369770
\(301\) −10.6854 −0.615897
\(302\) 14.7962 0.851427
\(303\) −7.43844 −0.427327
\(304\) 12.6651 0.726394
\(305\) 20.9928 1.20205
\(306\) 0.180898 0.0103412
\(307\) −26.0150 −1.48475 −0.742377 0.669983i \(-0.766302\pi\)
−0.742377 + 0.669983i \(0.766302\pi\)
\(308\) 51.9808 2.96188
\(309\) 1.00000 0.0568880
\(310\) −43.3392 −2.46150
\(311\) 27.5881 1.56438 0.782189 0.623041i \(-0.214103\pi\)
0.782189 + 0.623041i \(0.214103\pi\)
\(312\) −0.160099 −0.00906383
\(313\) 2.05595 0.116209 0.0581045 0.998311i \(-0.481494\pi\)
0.0581045 + 0.998311i \(0.481494\pi\)
\(314\) −24.0908 −1.35952
\(315\) 11.0742 0.623959
\(316\) −30.1349 −1.69522
\(317\) 29.8820 1.67834 0.839169 0.543871i \(-0.183042\pi\)
0.839169 + 0.543871i \(0.183042\pi\)
\(318\) 24.0020 1.34597
\(319\) −10.8262 −0.606149
\(320\) −15.8566 −0.886410
\(321\) 7.26779 0.405648
\(322\) −4.55033 −0.253580
\(323\) 0.278519 0.0154972
\(324\) 1.91913 0.106618
\(325\) −0.333725 −0.0185117
\(326\) 25.1522 1.39305
\(327\) 15.9411 0.881544
\(328\) −0.813378 −0.0449113
\(329\) 14.7294 0.812056
\(330\) 22.5940 1.24376
\(331\) −12.4074 −0.681972 −0.340986 0.940068i \(-0.610761\pi\)
−0.340986 + 0.940068i \(0.610761\pi\)
\(332\) 6.67483 0.366329
\(333\) 3.51047 0.192372
\(334\) 42.2208 2.31022
\(335\) −31.4975 −1.72089
\(336\) 21.3019 1.16211
\(337\) −28.0923 −1.53028 −0.765142 0.643862i \(-0.777331\pi\)
−0.765142 + 0.643862i \(0.777331\pi\)
\(338\) −1.97968 −0.107680
\(339\) −3.13608 −0.170328
\(340\) −0.378816 −0.0205442
\(341\) 53.5443 2.89959
\(342\) 6.03409 0.326286
\(343\) 62.9623 3.39965
\(344\) −0.333699 −0.0179918
\(345\) −0.968518 −0.0521433
\(346\) −20.6926 −1.11244
\(347\) 17.8851 0.960121 0.480060 0.877235i \(-0.340615\pi\)
0.480060 + 0.877235i \(0.340615\pi\)
\(348\) 3.93248 0.210803
\(349\) −23.2235 −1.24312 −0.621562 0.783365i \(-0.713501\pi\)
−0.621562 + 0.783365i \(0.713501\pi\)
\(350\) 3.38695 0.181040
\(351\) −1.00000 −0.0533761
\(352\) 41.7693 2.22631
\(353\) 7.43361 0.395651 0.197826 0.980237i \(-0.436612\pi\)
0.197826 + 0.980237i \(0.436612\pi\)
\(354\) −9.64957 −0.512869
\(355\) 24.2214 1.28554
\(356\) 22.3199 1.18295
\(357\) 0.468451 0.0247931
\(358\) −13.6251 −0.720108
\(359\) −20.8797 −1.10199 −0.550995 0.834509i \(-0.685752\pi\)
−0.550995 + 0.834509i \(0.685752\pi\)
\(360\) 0.345839 0.0182273
\(361\) −9.70962 −0.511033
\(362\) 44.4074 2.33400
\(363\) −16.9142 −0.887765
\(364\) 9.83852 0.515679
\(365\) −32.9106 −1.72262
\(366\) 19.2389 1.00563
\(367\) −20.6683 −1.07888 −0.539438 0.842025i \(-0.681363\pi\)
−0.539438 + 0.842025i \(0.681363\pi\)
\(368\) −1.86301 −0.0971160
\(369\) −5.08046 −0.264478
\(370\) −15.0122 −0.780448
\(371\) 62.1555 3.22695
\(372\) −19.4493 −1.00840
\(373\) 2.22158 0.115029 0.0575145 0.998345i \(-0.481682\pi\)
0.0575145 + 0.998345i \(0.481682\pi\)
\(374\) 0.955754 0.0494209
\(375\) 11.5217 0.594977
\(376\) 0.459989 0.0237221
\(377\) −2.04909 −0.105534
\(378\) 10.1489 0.522005
\(379\) 30.4795 1.56563 0.782814 0.622256i \(-0.213784\pi\)
0.782814 + 0.622256i \(0.213784\pi\)
\(380\) −12.6359 −0.648208
\(381\) 2.59501 0.132946
\(382\) −6.60494 −0.337938
\(383\) 25.2787 1.29168 0.645841 0.763472i \(-0.276507\pi\)
0.645841 + 0.763472i \(0.276507\pi\)
\(384\) 1.27975 0.0653068
\(385\) 58.5091 2.98190
\(386\) 8.03003 0.408718
\(387\) −2.08433 −0.105952
\(388\) 10.9253 0.554647
\(389\) −12.7487 −0.646385 −0.323192 0.946333i \(-0.604756\pi\)
−0.323192 + 0.946333i \(0.604756\pi\)
\(390\) 4.27642 0.216545
\(391\) −0.0409696 −0.00207192
\(392\) 3.08697 0.155915
\(393\) −1.84777 −0.0932078
\(394\) −19.3008 −0.972359
\(395\) −33.9196 −1.70668
\(396\) 10.1395 0.509529
\(397\) −6.30062 −0.316219 −0.158109 0.987422i \(-0.550540\pi\)
−0.158109 + 0.987422i \(0.550540\pi\)
\(398\) −24.2050 −1.21329
\(399\) 15.6258 0.782269
\(400\) 1.38669 0.0693347
\(401\) −18.1355 −0.905643 −0.452821 0.891601i \(-0.649583\pi\)
−0.452821 + 0.891601i \(0.649583\pi\)
\(402\) −28.8659 −1.43970
\(403\) 10.1345 0.504833
\(404\) 14.2753 0.710224
\(405\) 2.16016 0.107339
\(406\) 20.7961 1.03209
\(407\) 18.5472 0.919348
\(408\) 0.0146294 0.000724265 0
\(409\) −13.8925 −0.686939 −0.343469 0.939164i \(-0.611602\pi\)
−0.343469 + 0.939164i \(0.611602\pi\)
\(410\) 21.7262 1.07298
\(411\) −17.0567 −0.841347
\(412\) −1.91913 −0.0945487
\(413\) −24.9884 −1.22960
\(414\) −0.887600 −0.0436232
\(415\) 7.51313 0.368805
\(416\) 7.90577 0.387612
\(417\) 0.625326 0.0306223
\(418\) 31.8804 1.55932
\(419\) 3.59714 0.175732 0.0878660 0.996132i \(-0.471995\pi\)
0.0878660 + 0.996132i \(0.471995\pi\)
\(420\) −21.2528 −1.03703
\(421\) 10.9094 0.531690 0.265845 0.964016i \(-0.414349\pi\)
0.265845 + 0.964016i \(0.414349\pi\)
\(422\) 8.94894 0.435628
\(423\) 2.87315 0.139697
\(424\) 1.94108 0.0942670
\(425\) 0.0304949 0.00147922
\(426\) 22.1977 1.07548
\(427\) 49.8209 2.41100
\(428\) −13.9478 −0.674193
\(429\) −5.28339 −0.255084
\(430\) 8.91345 0.429845
\(431\) 9.50082 0.457638 0.228819 0.973469i \(-0.426514\pi\)
0.228819 + 0.973469i \(0.426514\pi\)
\(432\) 4.15520 0.199917
\(433\) 35.4532 1.70377 0.851885 0.523729i \(-0.175460\pi\)
0.851885 + 0.523729i \(0.175460\pi\)
\(434\) −102.854 −4.93715
\(435\) 4.42636 0.212228
\(436\) −30.5930 −1.46514
\(437\) −1.36659 −0.0653730
\(438\) −30.1609 −1.44115
\(439\) 18.9769 0.905716 0.452858 0.891583i \(-0.350404\pi\)
0.452858 + 0.891583i \(0.350404\pi\)
\(440\) 1.82720 0.0871085
\(441\) 19.2816 0.918171
\(442\) 0.180898 0.00860443
\(443\) −13.0402 −0.619559 −0.309779 0.950809i \(-0.600255\pi\)
−0.309779 + 0.950809i \(0.600255\pi\)
\(444\) −6.73703 −0.319726
\(445\) 25.1231 1.19095
\(446\) −32.0460 −1.51742
\(447\) −8.04548 −0.380538
\(448\) −37.6314 −1.77792
\(449\) 24.1258 1.13857 0.569284 0.822141i \(-0.307221\pi\)
0.569284 + 0.822141i \(0.307221\pi\)
\(450\) 0.660668 0.0311442
\(451\) −26.8420 −1.26394
\(452\) 6.01854 0.283088
\(453\) 7.47406 0.351162
\(454\) −43.1428 −2.02479
\(455\) 11.0742 0.519165
\(456\) 0.487984 0.0228520
\(457\) −7.45454 −0.348709 −0.174354 0.984683i \(-0.555784\pi\)
−0.174354 + 0.984683i \(0.555784\pi\)
\(458\) 52.3527 2.44628
\(459\) 0.0913774 0.00426513
\(460\) 1.85871 0.0866629
\(461\) −31.8700 −1.48433 −0.742166 0.670216i \(-0.766201\pi\)
−0.742166 + 0.670216i \(0.766201\pi\)
\(462\) 53.6208 2.49467
\(463\) 39.3231 1.82750 0.913750 0.406277i \(-0.133173\pi\)
0.913750 + 0.406277i \(0.133173\pi\)
\(464\) 8.51440 0.395271
\(465\) −21.8920 −1.01522
\(466\) 30.3559 1.40621
\(467\) 20.9344 0.968726 0.484363 0.874867i \(-0.339051\pi\)
0.484363 + 0.874867i \(0.339051\pi\)
\(468\) 1.91913 0.0887118
\(469\) −74.7509 −3.45168
\(470\) −12.2868 −0.566747
\(471\) −12.1690 −0.560719
\(472\) −0.780373 −0.0359196
\(473\) −11.0123 −0.506346
\(474\) −31.0856 −1.42781
\(475\) 1.01720 0.0466722
\(476\) −0.899018 −0.0412064
\(477\) 12.1242 0.555129
\(478\) 18.8140 0.860530
\(479\) −5.51990 −0.252211 −0.126105 0.992017i \(-0.540248\pi\)
−0.126105 + 0.992017i \(0.540248\pi\)
\(480\) −17.0777 −0.779487
\(481\) 3.51047 0.160063
\(482\) −17.0530 −0.776744
\(483\) −2.29852 −0.104586
\(484\) 32.4605 1.47548
\(485\) 12.2974 0.558396
\(486\) 1.97968 0.0898001
\(487\) −22.9136 −1.03832 −0.519158 0.854678i \(-0.673754\pi\)
−0.519158 + 0.854678i \(0.673754\pi\)
\(488\) 1.55588 0.0704312
\(489\) 12.7052 0.574549
\(490\) −82.4561 −3.72499
\(491\) 30.4097 1.37237 0.686185 0.727427i \(-0.259284\pi\)
0.686185 + 0.727427i \(0.259284\pi\)
\(492\) 9.75005 0.439566
\(493\) 0.187241 0.00843290
\(494\) 6.03409 0.271486
\(495\) 11.4129 0.512974
\(496\) −42.1107 −1.89083
\(497\) 57.4830 2.57847
\(498\) 6.88542 0.308543
\(499\) 26.0427 1.16583 0.582916 0.812532i \(-0.301911\pi\)
0.582916 + 0.812532i \(0.301911\pi\)
\(500\) −22.1116 −0.988860
\(501\) 21.3271 0.952824
\(502\) 12.5523 0.560237
\(503\) 0.894332 0.0398763 0.0199381 0.999801i \(-0.493653\pi\)
0.0199381 + 0.999801i \(0.493653\pi\)
\(504\) 0.820758 0.0365595
\(505\) 16.0682 0.715025
\(506\) −4.68954 −0.208475
\(507\) −1.00000 −0.0444116
\(508\) −4.98016 −0.220959
\(509\) −30.0244 −1.33081 −0.665404 0.746483i \(-0.731741\pi\)
−0.665404 + 0.746483i \(0.731741\pi\)
\(510\) −0.390768 −0.0173035
\(511\) −78.1045 −3.45514
\(512\) −31.5196 −1.39298
\(513\) 3.04801 0.134573
\(514\) 23.1078 1.01924
\(515\) −2.16016 −0.0951879
\(516\) 4.00009 0.176094
\(517\) 15.1800 0.667614
\(518\) −35.6275 −1.56538
\(519\) −10.4525 −0.458815
\(520\) 0.345839 0.0151661
\(521\) 11.5050 0.504042 0.252021 0.967722i \(-0.418905\pi\)
0.252021 + 0.967722i \(0.418905\pi\)
\(522\) 4.05655 0.177550
\(523\) 1.69772 0.0742362 0.0371181 0.999311i \(-0.488182\pi\)
0.0371181 + 0.999311i \(0.488182\pi\)
\(524\) 3.54611 0.154913
\(525\) 1.71086 0.0746680
\(526\) 25.7361 1.12215
\(527\) −0.926060 −0.0403398
\(528\) 21.9536 0.955406
\(529\) −22.7990 −0.991260
\(530\) −51.8482 −2.25214
\(531\) −4.87431 −0.211527
\(532\) −29.9879 −1.30014
\(533\) −5.08046 −0.220059
\(534\) 23.0241 0.996350
\(535\) −15.6996 −0.678751
\(536\) −2.33442 −0.100832
\(537\) −6.88247 −0.297000
\(538\) 45.9466 1.98090
\(539\) 101.872 4.38795
\(540\) −4.14562 −0.178399
\(541\) −35.3643 −1.52043 −0.760216 0.649671i \(-0.774907\pi\)
−0.760216 + 0.649671i \(0.774907\pi\)
\(542\) −24.9618 −1.07220
\(543\) 22.4316 0.962633
\(544\) −0.722408 −0.0309730
\(545\) −34.4352 −1.47504
\(546\) 10.1489 0.434334
\(547\) −18.8060 −0.804087 −0.402044 0.915620i \(-0.631700\pi\)
−0.402044 + 0.915620i \(0.631700\pi\)
\(548\) 32.7341 1.39833
\(549\) 9.71819 0.414762
\(550\) 3.49056 0.148838
\(551\) 6.24566 0.266074
\(552\) −0.0717814 −0.00305522
\(553\) −80.4991 −3.42317
\(554\) −17.1964 −0.730604
\(555\) −7.58315 −0.321887
\(556\) −1.20008 −0.0508947
\(557\) −27.2291 −1.15373 −0.576866 0.816839i \(-0.695725\pi\)
−0.576866 + 0.816839i \(0.695725\pi\)
\(558\) −20.0630 −0.849334
\(559\) −2.08433 −0.0881576
\(560\) −46.0154 −1.94451
\(561\) 0.482782 0.0203831
\(562\) 33.4180 1.40965
\(563\) 17.2386 0.726518 0.363259 0.931688i \(-0.381664\pi\)
0.363259 + 0.931688i \(0.381664\pi\)
\(564\) −5.51394 −0.232179
\(565\) 6.77442 0.285002
\(566\) −20.6207 −0.866752
\(567\) 5.12656 0.215295
\(568\) 1.79516 0.0753232
\(569\) 8.24952 0.345838 0.172919 0.984936i \(-0.444680\pi\)
0.172919 + 0.984936i \(0.444680\pi\)
\(570\) −13.0346 −0.545958
\(571\) 3.32708 0.139234 0.0696169 0.997574i \(-0.477822\pi\)
0.0696169 + 0.997574i \(0.477822\pi\)
\(572\) 10.1395 0.423954
\(573\) −3.33637 −0.139379
\(574\) 51.5613 2.15213
\(575\) −0.149627 −0.00623989
\(576\) −7.34048 −0.305853
\(577\) 19.3393 0.805107 0.402553 0.915396i \(-0.368123\pi\)
0.402553 + 0.915396i \(0.368123\pi\)
\(578\) 33.6380 1.39916
\(579\) 4.05623 0.168571
\(580\) −8.49476 −0.352726
\(581\) 17.8304 0.739731
\(582\) 11.2700 0.467156
\(583\) 64.0569 2.65297
\(584\) −2.43915 −0.100933
\(585\) 2.16016 0.0893115
\(586\) 56.9277 2.35166
\(587\) −17.6941 −0.730314 −0.365157 0.930946i \(-0.618985\pi\)
−0.365157 + 0.930946i \(0.618985\pi\)
\(588\) −37.0039 −1.52601
\(589\) −30.8900 −1.27280
\(590\) 20.8446 0.858157
\(591\) −9.74945 −0.401039
\(592\) −14.5867 −0.599509
\(593\) 35.2011 1.44554 0.722769 0.691090i \(-0.242869\pi\)
0.722769 + 0.691090i \(0.242869\pi\)
\(594\) 10.4594 0.429155
\(595\) −1.01193 −0.0414850
\(596\) 15.4403 0.632459
\(597\) −12.2267 −0.500407
\(598\) −0.887600 −0.0362967
\(599\) −38.6268 −1.57825 −0.789124 0.614234i \(-0.789465\pi\)
−0.789124 + 0.614234i \(0.789465\pi\)
\(600\) 0.0534291 0.00218123
\(601\) −42.2014 −1.72143 −0.860715 0.509088i \(-0.829983\pi\)
−0.860715 + 0.509088i \(0.829983\pi\)
\(602\) 21.1537 0.862160
\(603\) −14.5811 −0.593789
\(604\) −14.3437 −0.583636
\(605\) 36.5373 1.48545
\(606\) 14.7257 0.598192
\(607\) −6.59533 −0.267696 −0.133848 0.991002i \(-0.542733\pi\)
−0.133848 + 0.991002i \(0.542733\pi\)
\(608\) −24.0969 −0.977257
\(609\) 10.5048 0.425676
\(610\) −41.5590 −1.68268
\(611\) 2.87315 0.116235
\(612\) −0.175365 −0.00708871
\(613\) 6.27206 0.253326 0.126663 0.991946i \(-0.459573\pi\)
0.126663 + 0.991946i \(0.459573\pi\)
\(614\) 51.5013 2.07842
\(615\) 10.9746 0.442538
\(616\) 4.33638 0.174718
\(617\) −26.8906 −1.08257 −0.541287 0.840838i \(-0.682063\pi\)
−0.541287 + 0.840838i \(0.682063\pi\)
\(618\) −1.97968 −0.0796344
\(619\) −6.55026 −0.263277 −0.131639 0.991298i \(-0.542024\pi\)
−0.131639 + 0.991298i \(0.542024\pi\)
\(620\) 42.0136 1.68731
\(621\) −0.448356 −0.0179919
\(622\) −54.6156 −2.18989
\(623\) 59.6230 2.38874
\(624\) 4.15520 0.166341
\(625\) −23.2200 −0.928800
\(626\) −4.07012 −0.162675
\(627\) 16.1038 0.643125
\(628\) 23.3539 0.931923
\(629\) −0.320777 −0.0127902
\(630\) −21.9233 −0.873445
\(631\) 28.8500 1.14850 0.574251 0.818679i \(-0.305293\pi\)
0.574251 + 0.818679i \(0.305293\pi\)
\(632\) −2.51394 −0.0999990
\(633\) 4.52040 0.179670
\(634\) −59.1567 −2.34941
\(635\) −5.60563 −0.222453
\(636\) −23.2679 −0.922633
\(637\) 19.2816 0.763965
\(638\) 21.4323 0.848514
\(639\) 11.2128 0.443571
\(640\) −2.76445 −0.109275
\(641\) 4.23827 0.167402 0.0837008 0.996491i \(-0.473326\pi\)
0.0837008 + 0.996491i \(0.473326\pi\)
\(642\) −14.3879 −0.567845
\(643\) 30.9152 1.21918 0.609589 0.792718i \(-0.291334\pi\)
0.609589 + 0.792718i \(0.291334\pi\)
\(644\) 4.41116 0.173824
\(645\) 4.50247 0.177285
\(646\) −0.551379 −0.0216937
\(647\) −34.6658 −1.36285 −0.681427 0.731886i \(-0.738640\pi\)
−0.681427 + 0.731886i \(0.738640\pi\)
\(648\) 0.160099 0.00628929
\(649\) −25.7529 −1.01089
\(650\) 0.660668 0.0259135
\(651\) −51.9549 −2.03627
\(652\) −24.3829 −0.954908
\(653\) 26.2607 1.02766 0.513829 0.857892i \(-0.328226\pi\)
0.513829 + 0.857892i \(0.328226\pi\)
\(654\) −31.5582 −1.23402
\(655\) 3.99148 0.155960
\(656\) 21.1103 0.824220
\(657\) −15.2353 −0.594384
\(658\) −29.1594 −1.13675
\(659\) −22.8862 −0.891519 −0.445760 0.895153i \(-0.647066\pi\)
−0.445760 + 0.895153i \(0.647066\pi\)
\(660\) −21.9029 −0.852570
\(661\) −31.9954 −1.24448 −0.622238 0.782828i \(-0.713776\pi\)
−0.622238 + 0.782828i \(0.713776\pi\)
\(662\) 24.5627 0.954655
\(663\) 0.0913774 0.00354880
\(664\) 0.556833 0.0216093
\(665\) −33.7542 −1.30893
\(666\) −6.94959 −0.269291
\(667\) −0.918723 −0.0355731
\(668\) −40.9294 −1.58361
\(669\) −16.1875 −0.625844
\(670\) 62.3549 2.40898
\(671\) 51.3450 1.98215
\(672\) −40.5294 −1.56345
\(673\) 21.4647 0.827404 0.413702 0.910412i \(-0.364236\pi\)
0.413702 + 0.910412i \(0.364236\pi\)
\(674\) 55.6137 2.14216
\(675\) 0.333725 0.0128451
\(676\) 1.91913 0.0738126
\(677\) −3.70916 −0.142555 −0.0712773 0.997457i \(-0.522708\pi\)
−0.0712773 + 0.997457i \(0.522708\pi\)
\(678\) 6.20843 0.238433
\(679\) 29.1846 1.12000
\(680\) −0.0316019 −0.00121188
\(681\) −21.7928 −0.835103
\(682\) −106.001 −4.05897
\(683\) 26.7177 1.02233 0.511163 0.859484i \(-0.329215\pi\)
0.511163 + 0.859484i \(0.329215\pi\)
\(684\) −5.84953 −0.223662
\(685\) 36.8452 1.40778
\(686\) −124.645 −4.75897
\(687\) 26.4450 1.00894
\(688\) 8.66080 0.330190
\(689\) 12.1242 0.461896
\(690\) 1.91736 0.0729925
\(691\) 8.67769 0.330115 0.165058 0.986284i \(-0.447219\pi\)
0.165058 + 0.986284i \(0.447219\pi\)
\(692\) 20.0597 0.762557
\(693\) 27.0856 1.02890
\(694\) −35.4067 −1.34402
\(695\) −1.35080 −0.0512388
\(696\) 0.328058 0.0124350
\(697\) 0.464239 0.0175843
\(698\) 45.9750 1.74018
\(699\) 15.3338 0.579976
\(700\) −3.28336 −0.124099
\(701\) 29.4582 1.11262 0.556310 0.830975i \(-0.312217\pi\)
0.556310 + 0.830975i \(0.312217\pi\)
\(702\) 1.97968 0.0747182
\(703\) −10.6999 −0.403556
\(704\) −38.7826 −1.46167
\(705\) −6.20645 −0.233749
\(706\) −14.7162 −0.553850
\(707\) 38.1336 1.43416
\(708\) 9.35442 0.351561
\(709\) −20.4843 −0.769302 −0.384651 0.923062i \(-0.625678\pi\)
−0.384651 + 0.923062i \(0.625678\pi\)
\(710\) −47.9506 −1.79955
\(711\) −15.7024 −0.588885
\(712\) 1.86199 0.0697810
\(713\) 4.54384 0.170168
\(714\) −0.927383 −0.0347064
\(715\) 11.4129 0.426820
\(716\) 13.2083 0.493619
\(717\) 9.50354 0.354916
\(718\) 41.3352 1.54261
\(719\) −12.5033 −0.466293 −0.233146 0.972442i \(-0.574902\pi\)
−0.233146 + 0.972442i \(0.574902\pi\)
\(720\) −8.97589 −0.334512
\(721\) −5.12656 −0.190923
\(722\) 19.2219 0.715366
\(723\) −8.61404 −0.320360
\(724\) −43.0492 −1.59991
\(725\) 0.683833 0.0253969
\(726\) 33.4847 1.24273
\(727\) 28.4805 1.05628 0.528141 0.849157i \(-0.322889\pi\)
0.528141 + 0.849157i \(0.322889\pi\)
\(728\) 0.820758 0.0304193
\(729\) 1.00000 0.0370370
\(730\) 65.1523 2.41140
\(731\) 0.190460 0.00704443
\(732\) −18.6505 −0.689341
\(733\) 19.6978 0.727556 0.363778 0.931486i \(-0.381487\pi\)
0.363778 + 0.931486i \(0.381487\pi\)
\(734\) 40.9166 1.51026
\(735\) −41.6513 −1.53633
\(736\) 3.54460 0.130656
\(737\) −77.0377 −2.83772
\(738\) 10.0577 0.370228
\(739\) −1.38039 −0.0507784 −0.0253892 0.999678i \(-0.508083\pi\)
−0.0253892 + 0.999678i \(0.508083\pi\)
\(740\) 14.5530 0.534981
\(741\) 3.04801 0.111972
\(742\) −123.048 −4.51723
\(743\) 0.103395 0.00379320 0.00189660 0.999998i \(-0.499396\pi\)
0.00189660 + 0.999998i \(0.499396\pi\)
\(744\) −1.62252 −0.0594844
\(745\) 17.3795 0.636735
\(746\) −4.39801 −0.161023
\(747\) 3.47805 0.127255
\(748\) −0.926521 −0.0338770
\(749\) −37.2587 −1.36140
\(750\) −22.8092 −0.832875
\(751\) 26.7414 0.975808 0.487904 0.872897i \(-0.337762\pi\)
0.487904 + 0.872897i \(0.337762\pi\)
\(752\) −11.9385 −0.435353
\(753\) 6.34058 0.231064
\(754\) 4.05655 0.147731
\(755\) −16.1451 −0.587581
\(756\) −9.83852 −0.357824
\(757\) 37.8615 1.37610 0.688050 0.725663i \(-0.258467\pi\)
0.688050 + 0.725663i \(0.258467\pi\)
\(758\) −60.3397 −2.19164
\(759\) −2.36884 −0.0859834
\(760\) −1.05412 −0.0382370
\(761\) 19.9429 0.722931 0.361465 0.932386i \(-0.382277\pi\)
0.361465 + 0.932386i \(0.382277\pi\)
\(762\) −5.13729 −0.186104
\(763\) −81.7229 −2.95857
\(764\) 6.40292 0.231650
\(765\) −0.197389 −0.00713663
\(766\) −50.0438 −1.80815
\(767\) −4.87431 −0.176001
\(768\) −17.2144 −0.621173
\(769\) 1.56420 0.0564066 0.0282033 0.999602i \(-0.491021\pi\)
0.0282033 + 0.999602i \(0.491021\pi\)
\(770\) −115.829 −4.17420
\(771\) 11.6725 0.420375
\(772\) −7.78443 −0.280168
\(773\) −45.2344 −1.62697 −0.813484 0.581588i \(-0.802432\pi\)
−0.813484 + 0.581588i \(0.802432\pi\)
\(774\) 4.12630 0.148317
\(775\) −3.38212 −0.121489
\(776\) 0.911418 0.0327180
\(777\) −17.9966 −0.645625
\(778\) 25.2383 0.904838
\(779\) 15.4853 0.554818
\(780\) −4.14562 −0.148437
\(781\) 59.2416 2.11983
\(782\) 0.0811066 0.00290037
\(783\) 2.04909 0.0732287
\(784\) −80.1189 −2.86139
\(785\) 26.2870 0.938223
\(786\) 3.65800 0.130476
\(787\) −26.0429 −0.928329 −0.464164 0.885749i \(-0.653645\pi\)
−0.464164 + 0.885749i \(0.653645\pi\)
\(788\) 18.7104 0.666532
\(789\) 13.0002 0.462818
\(790\) 67.1499 2.38908
\(791\) 16.0773 0.571642
\(792\) 0.845867 0.0300566
\(793\) 9.71819 0.345103
\(794\) 12.4732 0.442657
\(795\) −26.1902 −0.928870
\(796\) 23.4647 0.831684
\(797\) −14.9595 −0.529894 −0.264947 0.964263i \(-0.585355\pi\)
−0.264947 + 0.964263i \(0.585355\pi\)
\(798\) −30.9341 −1.09505
\(799\) −0.262541 −0.00928803
\(800\) −2.63835 −0.0932797
\(801\) 11.6302 0.410933
\(802\) 35.9024 1.26776
\(803\) −80.4938 −2.84057
\(804\) 27.9830 0.986885
\(805\) 4.96517 0.174999
\(806\) −20.0630 −0.706688
\(807\) 23.2091 0.817000
\(808\) 1.19089 0.0418953
\(809\) 23.5806 0.829049 0.414524 0.910038i \(-0.363948\pi\)
0.414524 + 0.910038i \(0.363948\pi\)
\(810\) −4.27642 −0.150258
\(811\) 1.94285 0.0682228 0.0341114 0.999418i \(-0.489140\pi\)
0.0341114 + 0.999418i \(0.489140\pi\)
\(812\) −20.1601 −0.707480
\(813\) −12.6090 −0.442218
\(814\) −36.7174 −1.28694
\(815\) −27.4452 −0.961364
\(816\) −0.379691 −0.0132919
\(817\) 6.35305 0.222265
\(818\) 27.5026 0.961607
\(819\) 5.12656 0.179136
\(820\) −21.0616 −0.735504
\(821\) 8.00173 0.279262 0.139631 0.990204i \(-0.455408\pi\)
0.139631 + 0.990204i \(0.455408\pi\)
\(822\) 33.7669 1.17775
\(823\) 29.6081 1.03207 0.516037 0.856566i \(-0.327407\pi\)
0.516037 + 0.856566i \(0.327407\pi\)
\(824\) −0.160099 −0.00557732
\(825\) 1.76320 0.0613866
\(826\) 49.4691 1.72125
\(827\) 13.0507 0.453817 0.226908 0.973916i \(-0.427138\pi\)
0.226908 + 0.973916i \(0.427138\pi\)
\(828\) 0.860452 0.0299028
\(829\) 7.05072 0.244882 0.122441 0.992476i \(-0.460928\pi\)
0.122441 + 0.992476i \(0.460928\pi\)
\(830\) −14.8736 −0.516270
\(831\) −8.68645 −0.301330
\(832\) −7.34048 −0.254485
\(833\) −1.76190 −0.0610463
\(834\) −1.23794 −0.0428665
\(835\) −46.0699 −1.59431
\(836\) −30.9053 −1.06888
\(837\) −10.1345 −0.350298
\(838\) −7.12119 −0.245997
\(839\) −5.54693 −0.191501 −0.0957506 0.995405i \(-0.530525\pi\)
−0.0957506 + 0.995405i \(0.530525\pi\)
\(840\) −1.77297 −0.0611731
\(841\) −24.8012 −0.855214
\(842\) −21.5970 −0.744283
\(843\) 16.8805 0.581396
\(844\) −8.67523 −0.298614
\(845\) 2.16016 0.0743116
\(846\) −5.68791 −0.195554
\(847\) 86.7116 2.97945
\(848\) −50.3785 −1.73001
\(849\) −10.4162 −0.357482
\(850\) −0.0603701 −0.00207068
\(851\) 1.57394 0.0539539
\(852\) −21.5188 −0.737222
\(853\) 43.2997 1.48255 0.741276 0.671200i \(-0.234221\pi\)
0.741276 + 0.671200i \(0.234221\pi\)
\(854\) −98.6294 −3.37503
\(855\) −6.58418 −0.225174
\(856\) −1.16357 −0.0397699
\(857\) 0.534680 0.0182643 0.00913215 0.999958i \(-0.497093\pi\)
0.00913215 + 0.999958i \(0.497093\pi\)
\(858\) 10.4594 0.357079
\(859\) −34.5674 −1.17942 −0.589712 0.807613i \(-0.700759\pi\)
−0.589712 + 0.807613i \(0.700759\pi\)
\(860\) −8.64082 −0.294650
\(861\) 26.0453 0.887620
\(862\) −18.8086 −0.640622
\(863\) −15.4851 −0.527118 −0.263559 0.964643i \(-0.584896\pi\)
−0.263559 + 0.964643i \(0.584896\pi\)
\(864\) −7.90577 −0.268960
\(865\) 22.5791 0.767712
\(866\) −70.1859 −2.38501
\(867\) 16.9917 0.577067
\(868\) 99.7081 3.38431
\(869\) −82.9617 −2.81428
\(870\) −8.76278 −0.297086
\(871\) −14.5811 −0.494062
\(872\) −2.55216 −0.0864269
\(873\) 5.69283 0.192673
\(874\) 2.70542 0.0915121
\(875\) −59.0666 −1.99681
\(876\) 29.2384 0.987875
\(877\) 24.3046 0.820708 0.410354 0.911926i \(-0.365405\pi\)
0.410354 + 0.911926i \(0.365405\pi\)
\(878\) −37.5681 −1.26786
\(879\) 28.7560 0.969917
\(880\) −47.4231 −1.59863
\(881\) 2.55899 0.0862145 0.0431073 0.999070i \(-0.486274\pi\)
0.0431073 + 0.999070i \(0.486274\pi\)
\(882\) −38.1714 −1.28530
\(883\) −37.2802 −1.25458 −0.627290 0.778786i \(-0.715836\pi\)
−0.627290 + 0.778786i \(0.715836\pi\)
\(884\) −0.175365 −0.00589816
\(885\) 10.5293 0.353937
\(886\) 25.8154 0.867286
\(887\) 49.8625 1.67422 0.837109 0.547036i \(-0.184244\pi\)
0.837109 + 0.547036i \(0.184244\pi\)
\(888\) −0.562023 −0.0188602
\(889\) −13.3035 −0.446184
\(890\) −49.7356 −1.66714
\(891\) 5.28339 0.177000
\(892\) 31.0659 1.04016
\(893\) −8.75739 −0.293055
\(894\) 15.9275 0.532694
\(895\) 14.8672 0.496956
\(896\) −6.56070 −0.219177
\(897\) −0.448356 −0.0149702
\(898\) −47.7613 −1.59382
\(899\) −20.7665 −0.692600
\(900\) −0.640461 −0.0213487
\(901\) −1.10788 −0.0369088
\(902\) 53.1386 1.76932
\(903\) 10.6854 0.355588
\(904\) 0.502084 0.0166991
\(905\) −48.4558 −1.61073
\(906\) −14.7962 −0.491572
\(907\) −3.29256 −0.109328 −0.0546638 0.998505i \(-0.517409\pi\)
−0.0546638 + 0.998505i \(0.517409\pi\)
\(908\) 41.8232 1.38795
\(909\) 7.43844 0.246718
\(910\) −21.9233 −0.726750
\(911\) 13.2275 0.438246 0.219123 0.975697i \(-0.429680\pi\)
0.219123 + 0.975697i \(0.429680\pi\)
\(912\) −12.6651 −0.419384
\(913\) 18.3759 0.608153
\(914\) 14.7576 0.488138
\(915\) −20.9928 −0.694001
\(916\) −50.7514 −1.67687
\(917\) 9.47271 0.312817
\(918\) −0.180898 −0.00597052
\(919\) 26.2911 0.867262 0.433631 0.901090i \(-0.357232\pi\)
0.433631 + 0.901090i \(0.357232\pi\)
\(920\) 0.155059 0.00511214
\(921\) 26.0150 0.857223
\(922\) 63.0923 2.07783
\(923\) 11.2128 0.369074
\(924\) −51.9808 −1.71004
\(925\) −1.17153 −0.0385196
\(926\) −77.8471 −2.55822
\(927\) −1.00000 −0.0328443
\(928\) −16.1997 −0.531780
\(929\) −35.0779 −1.15087 −0.575433 0.817849i \(-0.695167\pi\)
−0.575433 + 0.817849i \(0.695167\pi\)
\(930\) 43.3392 1.42115
\(931\) −58.7705 −1.92613
\(932\) −29.4275 −0.963929
\(933\) −27.5881 −0.903194
\(934\) −41.4433 −1.35607
\(935\) −1.04289 −0.0341060
\(936\) 0.160099 0.00523301
\(937\) 15.9368 0.520631 0.260316 0.965524i \(-0.416173\pi\)
0.260316 + 0.965524i \(0.416173\pi\)
\(938\) 147.983 4.83181
\(939\) −2.05595 −0.0670933
\(940\) 11.9110 0.388493
\(941\) 13.8647 0.451976 0.225988 0.974130i \(-0.427439\pi\)
0.225988 + 0.974130i \(0.427439\pi\)
\(942\) 24.0908 0.784919
\(943\) −2.27785 −0.0741771
\(944\) 20.2537 0.659203
\(945\) −11.0742 −0.360243
\(946\) 21.8008 0.708806
\(947\) 24.3912 0.792608 0.396304 0.918119i \(-0.370293\pi\)
0.396304 + 0.918119i \(0.370293\pi\)
\(948\) 30.1349 0.978735
\(949\) −15.2353 −0.494558
\(950\) −2.01372 −0.0653338
\(951\) −29.8820 −0.968989
\(952\) −0.0749987 −0.00243072
\(953\) 1.89900 0.0615147 0.0307573 0.999527i \(-0.490208\pi\)
0.0307573 + 0.999527i \(0.490208\pi\)
\(954\) −24.0020 −0.777095
\(955\) 7.20708 0.233216
\(956\) −18.2385 −0.589876
\(957\) 10.8262 0.349960
\(958\) 10.9276 0.353056
\(959\) 87.4424 2.82366
\(960\) 15.8566 0.511769
\(961\) 71.7073 2.31314
\(962\) −6.94959 −0.224064
\(963\) −7.26779 −0.234201
\(964\) 16.5315 0.532442
\(965\) −8.76209 −0.282062
\(966\) 4.55033 0.146405
\(967\) −39.1038 −1.25749 −0.628746 0.777610i \(-0.716432\pi\)
−0.628746 + 0.777610i \(0.716432\pi\)
\(968\) 2.70795 0.0870368
\(969\) −0.278519 −0.00894733
\(970\) −24.3449 −0.781668
\(971\) −23.2225 −0.745247 −0.372623 0.927983i \(-0.621542\pi\)
−0.372623 + 0.927983i \(0.621542\pi\)
\(972\) −1.91913 −0.0615561
\(973\) −3.20577 −0.102772
\(974\) 45.3617 1.45348
\(975\) 0.333725 0.0106877
\(976\) −40.3811 −1.29257
\(977\) −21.4840 −0.687333 −0.343667 0.939092i \(-0.611669\pi\)
−0.343667 + 0.939092i \(0.611669\pi\)
\(978\) −25.1522 −0.804279
\(979\) 61.4469 1.96385
\(980\) 79.9341 2.55340
\(981\) −15.9411 −0.508960
\(982\) −60.2014 −1.92110
\(983\) −0.231936 −0.00739761 −0.00369880 0.999993i \(-0.501177\pi\)
−0.00369880 + 0.999993i \(0.501177\pi\)
\(984\) 0.813378 0.0259295
\(985\) 21.0603 0.671038
\(986\) −0.370677 −0.0118048
\(987\) −14.7294 −0.468841
\(988\) −5.84953 −0.186098
\(989\) −0.934520 −0.0297160
\(990\) −22.5940 −0.718084
\(991\) −38.3917 −1.21955 −0.609776 0.792574i \(-0.708741\pi\)
−0.609776 + 0.792574i \(0.708741\pi\)
\(992\) 80.1207 2.54383
\(993\) 12.4074 0.393737
\(994\) −113.798 −3.60945
\(995\) 26.4117 0.837306
\(996\) −6.67483 −0.211500
\(997\) 0.364962 0.0115585 0.00577924 0.999983i \(-0.498160\pi\)
0.00577924 + 0.999983i \(0.498160\pi\)
\(998\) −51.5563 −1.63198
\(999\) −3.51047 −0.111066
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 \(a_p\))