Properties

Label 8021.2.a.a.1.18
Level 8021
Weight 2
Character 8021.1
Self dual Yes
Analytic conductor 64.048
Analytic rank 1
Dimension 134
CM No

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Newspace parameters

Level: \( N \) = \( 8021 = 13 \cdot 617 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8021.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0480074613\)
Analytic rank: \(1\)
Dimension: \(134\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) = 8021.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.20714 q^{2} -0.230793 q^{3} +2.87148 q^{4} -0.451913 q^{5} +0.509393 q^{6} +5.18852 q^{7} -1.92347 q^{8} -2.94673 q^{9} +O(q^{10})\) \(q-2.20714 q^{2} -0.230793 q^{3} +2.87148 q^{4} -0.451913 q^{5} +0.509393 q^{6} +5.18852 q^{7} -1.92347 q^{8} -2.94673 q^{9} +0.997437 q^{10} +2.89647 q^{11} -0.662717 q^{12} +1.00000 q^{13} -11.4518 q^{14} +0.104298 q^{15} -1.49757 q^{16} -6.47981 q^{17} +6.50386 q^{18} -6.93737 q^{19} -1.29766 q^{20} -1.19747 q^{21} -6.39293 q^{22} +0.917653 q^{23} +0.443924 q^{24} -4.79577 q^{25} -2.20714 q^{26} +1.37246 q^{27} +14.8987 q^{28} +9.62541 q^{29} -0.230201 q^{30} +1.11456 q^{31} +7.15231 q^{32} -0.668486 q^{33} +14.3019 q^{34} -2.34476 q^{35} -8.46148 q^{36} +2.16270 q^{37} +15.3118 q^{38} -0.230793 q^{39} +0.869243 q^{40} -6.86239 q^{41} +2.64300 q^{42} -8.50616 q^{43} +8.31715 q^{44} +1.33167 q^{45} -2.02539 q^{46} +4.07184 q^{47} +0.345630 q^{48} +19.9208 q^{49} +10.5850 q^{50} +1.49549 q^{51} +2.87148 q^{52} +9.40538 q^{53} -3.02922 q^{54} -1.30895 q^{55} -9.97999 q^{56} +1.60110 q^{57} -21.2446 q^{58} +2.46817 q^{59} +0.299490 q^{60} +9.03616 q^{61} -2.46000 q^{62} -15.2892 q^{63} -12.7910 q^{64} -0.451913 q^{65} +1.47544 q^{66} -5.94482 q^{67} -18.6066 q^{68} -0.211788 q^{69} +5.17522 q^{70} -9.15770 q^{71} +5.66797 q^{72} -5.61288 q^{73} -4.77338 q^{74} +1.10683 q^{75} -19.9205 q^{76} +15.0284 q^{77} +0.509393 q^{78} -5.60015 q^{79} +0.676774 q^{80} +8.52345 q^{81} +15.1463 q^{82} +9.21822 q^{83} -3.43852 q^{84} +2.92831 q^{85} +18.7743 q^{86} -2.22148 q^{87} -5.57129 q^{88} -5.97374 q^{89} -2.93918 q^{90} +5.18852 q^{91} +2.63502 q^{92} -0.257233 q^{93} -8.98713 q^{94} +3.13509 q^{95} -1.65070 q^{96} -6.15598 q^{97} -43.9680 q^{98} -8.53514 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 134q - 6q^{2} - 33q^{3} + 98q^{4} - 8q^{5} - 16q^{6} - 32q^{7} - 15q^{8} + 101q^{9} + O(q^{10}) \) \( 134q - 6q^{2} - 33q^{3} + 98q^{4} - 8q^{5} - 16q^{6} - 32q^{7} - 15q^{8} + 101q^{9} - 33q^{10} - 47q^{11} - 53q^{12} + 134q^{13} - 28q^{14} - 30q^{15} + 30q^{16} - 17q^{17} - 14q^{18} - 87q^{19} - 12q^{20} - 24q^{21} - 52q^{22} - 44q^{23} - 36q^{24} + 58q^{25} - 6q^{26} - 117q^{27} - 71q^{28} - 42q^{29} - 21q^{30} - 82q^{31} - 31q^{32} + 12q^{33} - 30q^{34} - 54q^{35} + 32q^{36} - 55q^{37} - 12q^{38} - 33q^{39} - 86q^{40} - 16q^{41} + 6q^{42} - 148q^{43} - 54q^{44} - 24q^{45} - 57q^{46} - 21q^{47} - 82q^{48} + 12q^{49} - 17q^{50} - 123q^{51} + 98q^{52} - 17q^{53} - 10q^{54} - 148q^{55} - 47q^{56} - q^{57} - 58q^{58} - 64q^{59} - 16q^{60} - 112q^{61} - 15q^{62} - 58q^{63} - 65q^{64} - 8q^{65} - 20q^{66} - 110q^{67} - 8q^{68} - 57q^{69} - 40q^{70} - 78q^{71} - 28q^{72} - 43q^{73} - 52q^{74} - 150q^{75} - 96q^{76} - 24q^{77} - 16q^{78} - 228q^{79} + 20q^{80} + 54q^{81} - 89q^{82} - 12q^{83} + 6q^{84} - 77q^{85} + 29q^{86} - 77q^{87} - 95q^{88} - 32q^{89} - 46q^{90} - 32q^{91} - 62q^{92} - 9q^{93} - 87q^{94} - 61q^{95} - 54q^{96} - 38q^{97} + 6q^{98} - 193q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.20714 −1.56069 −0.780343 0.625352i \(-0.784955\pi\)
−0.780343 + 0.625352i \(0.784955\pi\)
\(3\) −0.230793 −0.133248 −0.0666242 0.997778i \(-0.521223\pi\)
−0.0666242 + 0.997778i \(0.521223\pi\)
\(4\) 2.87148 1.43574
\(5\) −0.451913 −0.202102 −0.101051 0.994881i \(-0.532220\pi\)
−0.101051 + 0.994881i \(0.532220\pi\)
\(6\) 0.509393 0.207959
\(7\) 5.18852 1.96108 0.980539 0.196326i \(-0.0629010\pi\)
0.980539 + 0.196326i \(0.0629010\pi\)
\(8\) −1.92347 −0.680051
\(9\) −2.94673 −0.982245
\(10\) 0.997437 0.315417
\(11\) 2.89647 0.873319 0.436660 0.899627i \(-0.356161\pi\)
0.436660 + 0.899627i \(0.356161\pi\)
\(12\) −0.662717 −0.191310
\(13\) 1.00000 0.277350
\(14\) −11.4518 −3.06062
\(15\) 0.104298 0.0269297
\(16\) −1.49757 −0.374394
\(17\) −6.47981 −1.57158 −0.785792 0.618491i \(-0.787745\pi\)
−0.785792 + 0.618491i \(0.787745\pi\)
\(18\) 6.50386 1.53298
\(19\) −6.93737 −1.59154 −0.795771 0.605598i \(-0.792934\pi\)
−0.795771 + 0.605598i \(0.792934\pi\)
\(20\) −1.29766 −0.290165
\(21\) −1.19747 −0.261310
\(22\) −6.39293 −1.36298
\(23\) 0.917653 0.191344 0.0956720 0.995413i \(-0.469500\pi\)
0.0956720 + 0.995413i \(0.469500\pi\)
\(24\) 0.443924 0.0906156
\(25\) −4.79577 −0.959155
\(26\) −2.20714 −0.432856
\(27\) 1.37246 0.264131
\(28\) 14.8987 2.81559
\(29\) 9.62541 1.78739 0.893697 0.448671i \(-0.148103\pi\)
0.893697 + 0.448671i \(0.148103\pi\)
\(30\) −0.230201 −0.0420288
\(31\) 1.11456 0.200181 0.100091 0.994978i \(-0.468087\pi\)
0.100091 + 0.994978i \(0.468087\pi\)
\(32\) 7.15231 1.26436
\(33\) −0.668486 −0.116368
\(34\) 14.3019 2.45275
\(35\) −2.34476 −0.396337
\(36\) −8.46148 −1.41025
\(37\) 2.16270 0.355546 0.177773 0.984072i \(-0.443111\pi\)
0.177773 + 0.984072i \(0.443111\pi\)
\(38\) 15.3118 2.48390
\(39\) −0.230793 −0.0369565
\(40\) 0.869243 0.137439
\(41\) −6.86239 −1.07172 −0.535862 0.844305i \(-0.680013\pi\)
−0.535862 + 0.844305i \(0.680013\pi\)
\(42\) 2.64300 0.407823
\(43\) −8.50616 −1.29718 −0.648589 0.761139i \(-0.724640\pi\)
−0.648589 + 0.761139i \(0.724640\pi\)
\(44\) 8.31715 1.25386
\(45\) 1.33167 0.198513
\(46\) −2.02539 −0.298628
\(47\) 4.07184 0.593939 0.296970 0.954887i \(-0.404024\pi\)
0.296970 + 0.954887i \(0.404024\pi\)
\(48\) 0.345630 0.0498874
\(49\) 19.9208 2.84583
\(50\) 10.5850 1.49694
\(51\) 1.49549 0.209411
\(52\) 2.87148 0.398202
\(53\) 9.40538 1.29193 0.645964 0.763367i \(-0.276455\pi\)
0.645964 + 0.763367i \(0.276455\pi\)
\(54\) −3.02922 −0.412225
\(55\) −1.30895 −0.176499
\(56\) −9.97999 −1.33363
\(57\) 1.60110 0.212070
\(58\) −21.2446 −2.78956
\(59\) 2.46817 0.321328 0.160664 0.987009i \(-0.448636\pi\)
0.160664 + 0.987009i \(0.448636\pi\)
\(60\) 0.299490 0.0386640
\(61\) 9.03616 1.15696 0.578481 0.815696i \(-0.303646\pi\)
0.578481 + 0.815696i \(0.303646\pi\)
\(62\) −2.46000 −0.312420
\(63\) −15.2892 −1.92626
\(64\) −12.7910 −1.59888
\(65\) −0.451913 −0.0560529
\(66\) 1.47544 0.181614
\(67\) −5.94482 −0.726275 −0.363137 0.931736i \(-0.618294\pi\)
−0.363137 + 0.931736i \(0.618294\pi\)
\(68\) −18.6066 −2.25638
\(69\) −0.211788 −0.0254963
\(70\) 5.17522 0.618557
\(71\) −9.15770 −1.08682 −0.543410 0.839468i \(-0.682867\pi\)
−0.543410 + 0.839468i \(0.682867\pi\)
\(72\) 5.66797 0.667976
\(73\) −5.61288 −0.656937 −0.328469 0.944515i \(-0.606533\pi\)
−0.328469 + 0.944515i \(0.606533\pi\)
\(74\) −4.77338 −0.554895
\(75\) 1.10683 0.127806
\(76\) −19.9205 −2.28504
\(77\) 15.0284 1.71265
\(78\) 0.509393 0.0576774
\(79\) −5.60015 −0.630067 −0.315033 0.949081i \(-0.602016\pi\)
−0.315033 + 0.949081i \(0.602016\pi\)
\(80\) 0.676774 0.0756656
\(81\) 8.52345 0.947050
\(82\) 15.1463 1.67263
\(83\) 9.21822 1.01183 0.505915 0.862583i \(-0.331155\pi\)
0.505915 + 0.862583i \(0.331155\pi\)
\(84\) −3.43852 −0.375173
\(85\) 2.92831 0.317620
\(86\) 18.7743 2.02449
\(87\) −2.22148 −0.238167
\(88\) −5.57129 −0.593901
\(89\) −5.97374 −0.633215 −0.316608 0.948557i \(-0.602544\pi\)
−0.316608 + 0.948557i \(0.602544\pi\)
\(90\) −2.93918 −0.309817
\(91\) 5.18852 0.543905
\(92\) 2.63502 0.274720
\(93\) −0.257233 −0.0266739
\(94\) −8.98713 −0.926952
\(95\) 3.13509 0.321653
\(96\) −1.65070 −0.168474
\(97\) −6.15598 −0.625045 −0.312523 0.949910i \(-0.601174\pi\)
−0.312523 + 0.949910i \(0.601174\pi\)
\(98\) −43.9680 −4.44144
\(99\) −8.53514 −0.857813
\(100\) −13.7710 −1.37710
\(101\) −11.4666 −1.14097 −0.570486 0.821307i \(-0.693245\pi\)
−0.570486 + 0.821307i \(0.693245\pi\)
\(102\) −3.30077 −0.326825
\(103\) −0.123323 −0.0121513 −0.00607566 0.999982i \(-0.501934\pi\)
−0.00607566 + 0.999982i \(0.501934\pi\)
\(104\) −1.92347 −0.188612
\(105\) 0.541155 0.0528113
\(106\) −20.7590 −2.01629
\(107\) 7.59741 0.734469 0.367235 0.930128i \(-0.380305\pi\)
0.367235 + 0.930128i \(0.380305\pi\)
\(108\) 3.94100 0.379223
\(109\) −14.5547 −1.39409 −0.697043 0.717029i \(-0.745501\pi\)
−0.697043 + 0.717029i \(0.745501\pi\)
\(110\) 2.88905 0.275460
\(111\) −0.499136 −0.0473759
\(112\) −7.77020 −0.734215
\(113\) −7.23308 −0.680431 −0.340216 0.940347i \(-0.610500\pi\)
−0.340216 + 0.940347i \(0.610500\pi\)
\(114\) −3.53385 −0.330975
\(115\) −0.414700 −0.0386709
\(116\) 27.6391 2.56623
\(117\) −2.94673 −0.272426
\(118\) −5.44760 −0.501493
\(119\) −33.6206 −3.08200
\(120\) −0.200615 −0.0183136
\(121\) −2.61045 −0.237313
\(122\) −19.9441 −1.80565
\(123\) 1.58379 0.142806
\(124\) 3.20044 0.287408
\(125\) 4.42684 0.395949
\(126\) 33.7454 3.00628
\(127\) −18.1924 −1.61432 −0.807158 0.590336i \(-0.798995\pi\)
−0.807158 + 0.590336i \(0.798995\pi\)
\(128\) 13.9270 1.23098
\(129\) 1.96316 0.172847
\(130\) 0.997437 0.0874810
\(131\) −10.3108 −0.900855 −0.450428 0.892813i \(-0.648728\pi\)
−0.450428 + 0.892813i \(0.648728\pi\)
\(132\) −1.91954 −0.167075
\(133\) −35.9947 −3.12114
\(134\) 13.1211 1.13349
\(135\) −0.620235 −0.0533813
\(136\) 12.4637 1.06876
\(137\) −22.0323 −1.88235 −0.941173 0.337925i \(-0.890275\pi\)
−0.941173 + 0.337925i \(0.890275\pi\)
\(138\) 0.467446 0.0397917
\(139\) 21.1692 1.79555 0.897775 0.440454i \(-0.145183\pi\)
0.897775 + 0.440454i \(0.145183\pi\)
\(140\) −6.73293 −0.569036
\(141\) −0.939752 −0.0791414
\(142\) 20.2123 1.69618
\(143\) 2.89647 0.242215
\(144\) 4.41295 0.367746
\(145\) −4.34985 −0.361235
\(146\) 12.3884 1.02527
\(147\) −4.59758 −0.379202
\(148\) 6.21014 0.510470
\(149\) 14.0316 1.14952 0.574759 0.818323i \(-0.305096\pi\)
0.574759 + 0.818323i \(0.305096\pi\)
\(150\) −2.44293 −0.199465
\(151\) 8.86436 0.721371 0.360686 0.932687i \(-0.382543\pi\)
0.360686 + 0.932687i \(0.382543\pi\)
\(152\) 13.3438 1.08233
\(153\) 19.0943 1.54368
\(154\) −33.1699 −2.67290
\(155\) −0.503686 −0.0404570
\(156\) −0.662717 −0.0530598
\(157\) −13.8308 −1.10382 −0.551910 0.833904i \(-0.686101\pi\)
−0.551910 + 0.833904i \(0.686101\pi\)
\(158\) 12.3603 0.983336
\(159\) −2.17070 −0.172147
\(160\) −3.23222 −0.255530
\(161\) 4.76127 0.375240
\(162\) −18.8125 −1.47805
\(163\) 0.182995 0.0143333 0.00716666 0.999974i \(-0.497719\pi\)
0.00716666 + 0.999974i \(0.497719\pi\)
\(164\) −19.7052 −1.53872
\(165\) 0.302097 0.0235183
\(166\) −20.3459 −1.57915
\(167\) 20.8957 1.61696 0.808480 0.588524i \(-0.200291\pi\)
0.808480 + 0.588524i \(0.200291\pi\)
\(168\) 2.30331 0.177704
\(169\) 1.00000 0.0769231
\(170\) −6.46320 −0.495705
\(171\) 20.4426 1.56328
\(172\) −24.4252 −1.86241
\(173\) 21.3231 1.62116 0.810582 0.585625i \(-0.199151\pi\)
0.810582 + 0.585625i \(0.199151\pi\)
\(174\) 4.90312 0.371704
\(175\) −24.8830 −1.88098
\(176\) −4.33768 −0.326965
\(177\) −0.569636 −0.0428165
\(178\) 13.1849 0.988250
\(179\) −15.7724 −1.17888 −0.589441 0.807812i \(-0.700652\pi\)
−0.589441 + 0.807812i \(0.700652\pi\)
\(180\) 3.82385 0.285013
\(181\) 8.77353 0.652131 0.326066 0.945347i \(-0.394277\pi\)
0.326066 + 0.945347i \(0.394277\pi\)
\(182\) −11.4518 −0.848865
\(183\) −2.08548 −0.154163
\(184\) −1.76508 −0.130124
\(185\) −0.977352 −0.0718564
\(186\) 0.567751 0.0416295
\(187\) −18.7686 −1.37250
\(188\) 11.6922 0.852741
\(189\) 7.12107 0.517981
\(190\) −6.91959 −0.502000
\(191\) 14.6526 1.06023 0.530113 0.847927i \(-0.322149\pi\)
0.530113 + 0.847927i \(0.322149\pi\)
\(192\) 2.95208 0.213048
\(193\) −23.2228 −1.67162 −0.835808 0.549022i \(-0.815000\pi\)
−0.835808 + 0.549022i \(0.815000\pi\)
\(194\) 13.5871 0.975499
\(195\) 0.104298 0.00746896
\(196\) 57.2020 4.08586
\(197\) 25.3728 1.80774 0.903870 0.427807i \(-0.140714\pi\)
0.903870 + 0.427807i \(0.140714\pi\)
\(198\) 18.8383 1.33878
\(199\) −2.46775 −0.174934 −0.0874670 0.996167i \(-0.527877\pi\)
−0.0874670 + 0.996167i \(0.527877\pi\)
\(200\) 9.22454 0.652274
\(201\) 1.37202 0.0967750
\(202\) 25.3085 1.78070
\(203\) 49.9417 3.50522
\(204\) 4.29428 0.300660
\(205\) 3.10120 0.216597
\(206\) 0.272190 0.0189644
\(207\) −2.70408 −0.187947
\(208\) −1.49757 −0.103838
\(209\) −20.0939 −1.38992
\(210\) −1.19441 −0.0824218
\(211\) 13.7867 0.949114 0.474557 0.880225i \(-0.342608\pi\)
0.474557 + 0.880225i \(0.342608\pi\)
\(212\) 27.0073 1.85487
\(213\) 2.11353 0.144817
\(214\) −16.7686 −1.14628
\(215\) 3.84405 0.262162
\(216\) −2.63990 −0.179622
\(217\) 5.78294 0.392571
\(218\) 32.1243 2.17573
\(219\) 1.29541 0.0875359
\(220\) −3.75863 −0.253407
\(221\) −6.47981 −0.435879
\(222\) 1.10166 0.0739388
\(223\) 5.21306 0.349092 0.174546 0.984649i \(-0.444154\pi\)
0.174546 + 0.984649i \(0.444154\pi\)
\(224\) 37.1099 2.47951
\(225\) 14.1319 0.942125
\(226\) 15.9644 1.06194
\(227\) −23.8489 −1.58291 −0.791455 0.611228i \(-0.790676\pi\)
−0.791455 + 0.611228i \(0.790676\pi\)
\(228\) 4.59751 0.304478
\(229\) −9.31905 −0.615820 −0.307910 0.951415i \(-0.599630\pi\)
−0.307910 + 0.951415i \(0.599630\pi\)
\(230\) 0.915301 0.0603532
\(231\) −3.46845 −0.228207
\(232\) −18.5142 −1.21552
\(233\) −14.2564 −0.933971 −0.466985 0.884265i \(-0.654660\pi\)
−0.466985 + 0.884265i \(0.654660\pi\)
\(234\) 6.50386 0.425171
\(235\) −1.84012 −0.120036
\(236\) 7.08729 0.461344
\(237\) 1.29248 0.0839554
\(238\) 74.2055 4.81003
\(239\) −4.39129 −0.284049 −0.142025 0.989863i \(-0.545361\pi\)
−0.142025 + 0.989863i \(0.545361\pi\)
\(240\) −0.156195 −0.0100823
\(241\) −16.4675 −1.06076 −0.530382 0.847759i \(-0.677952\pi\)
−0.530382 + 0.847759i \(0.677952\pi\)
\(242\) 5.76163 0.370371
\(243\) −6.08455 −0.390324
\(244\) 25.9471 1.66109
\(245\) −9.00246 −0.575146
\(246\) −3.49565 −0.222875
\(247\) −6.93737 −0.441414
\(248\) −2.14383 −0.136133
\(249\) −2.12750 −0.134825
\(250\) −9.77066 −0.617951
\(251\) −23.8218 −1.50362 −0.751811 0.659379i \(-0.770819\pi\)
−0.751811 + 0.659379i \(0.770819\pi\)
\(252\) −43.9026 −2.76560
\(253\) 2.65796 0.167104
\(254\) 40.1532 2.51944
\(255\) −0.675834 −0.0423223
\(256\) −5.15677 −0.322298
\(257\) 6.71002 0.418559 0.209280 0.977856i \(-0.432888\pi\)
0.209280 + 0.977856i \(0.432888\pi\)
\(258\) −4.33298 −0.269760
\(259\) 11.2212 0.697252
\(260\) −1.29766 −0.0804773
\(261\) −28.3635 −1.75566
\(262\) 22.7573 1.40595
\(263\) −17.3872 −1.07214 −0.536069 0.844174i \(-0.680091\pi\)
−0.536069 + 0.844174i \(0.680091\pi\)
\(264\) 1.28581 0.0791364
\(265\) −4.25042 −0.261101
\(266\) 79.4454 4.87111
\(267\) 1.37870 0.0843749
\(268\) −17.0704 −1.04274
\(269\) 31.7981 1.93876 0.969382 0.245558i \(-0.0789712\pi\)
0.969382 + 0.245558i \(0.0789712\pi\)
\(270\) 1.36895 0.0833114
\(271\) −8.95422 −0.543930 −0.271965 0.962307i \(-0.587674\pi\)
−0.271965 + 0.962307i \(0.587674\pi\)
\(272\) 9.70400 0.588391
\(273\) −1.19747 −0.0724745
\(274\) 48.6284 2.93775
\(275\) −13.8908 −0.837649
\(276\) −0.608144 −0.0366060
\(277\) −0.866674 −0.0520734 −0.0260367 0.999661i \(-0.508289\pi\)
−0.0260367 + 0.999661i \(0.508289\pi\)
\(278\) −46.7235 −2.80229
\(279\) −3.28432 −0.196627
\(280\) 4.51009 0.269529
\(281\) −0.757503 −0.0451888 −0.0225944 0.999745i \(-0.507193\pi\)
−0.0225944 + 0.999745i \(0.507193\pi\)
\(282\) 2.07417 0.123515
\(283\) −24.3210 −1.44573 −0.722867 0.690987i \(-0.757176\pi\)
−0.722867 + 0.690987i \(0.757176\pi\)
\(284\) −26.2961 −1.56039
\(285\) −0.723557 −0.0428598
\(286\) −6.39293 −0.378022
\(287\) −35.6057 −2.10174
\(288\) −21.0759 −1.24191
\(289\) 24.9879 1.46988
\(290\) 9.60073 0.563775
\(291\) 1.42076 0.0832863
\(292\) −16.1172 −0.943190
\(293\) −14.5387 −0.849359 −0.424680 0.905344i \(-0.639613\pi\)
−0.424680 + 0.905344i \(0.639613\pi\)
\(294\) 10.1475 0.591814
\(295\) −1.11540 −0.0649410
\(296\) −4.15989 −0.241789
\(297\) 3.97531 0.230671
\(298\) −30.9698 −1.79403
\(299\) 0.917653 0.0530693
\(300\) 3.17824 0.183496
\(301\) −44.1344 −2.54387
\(302\) −19.5649 −1.12583
\(303\) 2.64642 0.152033
\(304\) 10.3892 0.595863
\(305\) −4.08356 −0.233824
\(306\) −42.1438 −2.40920
\(307\) −7.06633 −0.403297 −0.201648 0.979458i \(-0.564630\pi\)
−0.201648 + 0.979458i \(0.564630\pi\)
\(308\) 43.1537 2.45891
\(309\) 0.0284620 0.00161914
\(310\) 1.11171 0.0631407
\(311\) −20.7299 −1.17549 −0.587744 0.809047i \(-0.699984\pi\)
−0.587744 + 0.809047i \(0.699984\pi\)
\(312\) 0.443924 0.0251323
\(313\) −22.6817 −1.28205 −0.641023 0.767522i \(-0.721490\pi\)
−0.641023 + 0.767522i \(0.721490\pi\)
\(314\) 30.5266 1.72272
\(315\) 6.90939 0.389300
\(316\) −16.0807 −0.904611
\(317\) −28.8368 −1.61964 −0.809819 0.586680i \(-0.800435\pi\)
−0.809819 + 0.586680i \(0.800435\pi\)
\(318\) 4.79104 0.268668
\(319\) 27.8797 1.56097
\(320\) 5.78043 0.323136
\(321\) −1.75343 −0.0978668
\(322\) −10.5088 −0.585632
\(323\) 44.9528 2.50124
\(324\) 24.4749 1.35972
\(325\) −4.79577 −0.266022
\(326\) −0.403897 −0.0223698
\(327\) 3.35912 0.185760
\(328\) 13.1996 0.728827
\(329\) 21.1268 1.16476
\(330\) −0.666772 −0.0367046
\(331\) −0.847509 −0.0465833 −0.0232916 0.999729i \(-0.507415\pi\)
−0.0232916 + 0.999729i \(0.507415\pi\)
\(332\) 26.4699 1.45272
\(333\) −6.37290 −0.349233
\(334\) −46.1198 −2.52357
\(335\) 2.68654 0.146781
\(336\) 1.79331 0.0978330
\(337\) 9.44715 0.514619 0.257310 0.966329i \(-0.417164\pi\)
0.257310 + 0.966329i \(0.417164\pi\)
\(338\) −2.20714 −0.120053
\(339\) 1.66935 0.0906664
\(340\) 8.40858 0.456019
\(341\) 3.22830 0.174822
\(342\) −45.1197 −2.43979
\(343\) 67.0397 3.61981
\(344\) 16.3614 0.882146
\(345\) 0.0957098 0.00515284
\(346\) −47.0631 −2.53013
\(347\) 6.58388 0.353441 0.176720 0.984261i \(-0.443451\pi\)
0.176720 + 0.984261i \(0.443451\pi\)
\(348\) −6.37892 −0.341946
\(349\) 11.0286 0.590349 0.295175 0.955443i \(-0.404622\pi\)
0.295175 + 0.955443i \(0.404622\pi\)
\(350\) 54.9203 2.93561
\(351\) 1.37246 0.0732567
\(352\) 20.7165 1.10419
\(353\) −9.01941 −0.480055 −0.240027 0.970766i \(-0.577156\pi\)
−0.240027 + 0.970766i \(0.577156\pi\)
\(354\) 1.25727 0.0668231
\(355\) 4.13849 0.219648
\(356\) −17.1535 −0.909131
\(357\) 7.75941 0.410671
\(358\) 34.8118 1.83986
\(359\) 15.1776 0.801044 0.400522 0.916287i \(-0.368829\pi\)
0.400522 + 0.916287i \(0.368829\pi\)
\(360\) −2.56143 −0.134999
\(361\) 29.1271 1.53301
\(362\) −19.3644 −1.01777
\(363\) 0.602473 0.0316216
\(364\) 14.8987 0.780905
\(365\) 2.53653 0.132768
\(366\) 4.60296 0.240600
\(367\) −13.2199 −0.690074 −0.345037 0.938589i \(-0.612134\pi\)
−0.345037 + 0.938589i \(0.612134\pi\)
\(368\) −1.37425 −0.0716379
\(369\) 20.2216 1.05270
\(370\) 2.15716 0.112145
\(371\) 48.8001 2.53357
\(372\) −0.738640 −0.0382967
\(373\) −22.4884 −1.16441 −0.582203 0.813043i \(-0.697809\pi\)
−0.582203 + 0.813043i \(0.697809\pi\)
\(374\) 41.4249 2.14203
\(375\) −1.02168 −0.0527595
\(376\) −7.83208 −0.403909
\(377\) 9.62541 0.495734
\(378\) −15.7172 −0.808406
\(379\) −21.7511 −1.11728 −0.558640 0.829411i \(-0.688676\pi\)
−0.558640 + 0.829411i \(0.688676\pi\)
\(380\) 9.00234 0.461810
\(381\) 4.19868 0.215105
\(382\) −32.3404 −1.65468
\(383\) 16.6148 0.848977 0.424489 0.905433i \(-0.360454\pi\)
0.424489 + 0.905433i \(0.360454\pi\)
\(384\) −3.21425 −0.164026
\(385\) −6.79154 −0.346129
\(386\) 51.2561 2.60887
\(387\) 25.0654 1.27415
\(388\) −17.6768 −0.897401
\(389\) 21.9478 1.11280 0.556399 0.830915i \(-0.312183\pi\)
0.556399 + 0.830915i \(0.312183\pi\)
\(390\) −0.230201 −0.0116567
\(391\) −5.94622 −0.300713
\(392\) −38.3171 −1.93530
\(393\) 2.37965 0.120037
\(394\) −56.0015 −2.82131
\(395\) 2.53078 0.127338
\(396\) −24.5084 −1.23160
\(397\) −22.1924 −1.11380 −0.556902 0.830578i \(-0.688010\pi\)
−0.556902 + 0.830578i \(0.688010\pi\)
\(398\) 5.44667 0.273017
\(399\) 8.30733 0.415887
\(400\) 7.18203 0.359101
\(401\) −8.91085 −0.444987 −0.222493 0.974934i \(-0.571420\pi\)
−0.222493 + 0.974934i \(0.571420\pi\)
\(402\) −3.02825 −0.151035
\(403\) 1.11456 0.0555203
\(404\) −32.9262 −1.63814
\(405\) −3.85186 −0.191400
\(406\) −110.228 −5.47054
\(407\) 6.26420 0.310505
\(408\) −2.87654 −0.142410
\(409\) −22.3996 −1.10759 −0.553795 0.832653i \(-0.686821\pi\)
−0.553795 + 0.832653i \(0.686821\pi\)
\(410\) −6.84480 −0.338040
\(411\) 5.08490 0.250820
\(412\) −0.354118 −0.0174461
\(413\) 12.8062 0.630150
\(414\) 5.96829 0.293325
\(415\) −4.16583 −0.204493
\(416\) 7.15231 0.350671
\(417\) −4.88571 −0.239254
\(418\) 44.3501 2.16923
\(419\) 29.4001 1.43629 0.718143 0.695895i \(-0.244992\pi\)
0.718143 + 0.695895i \(0.244992\pi\)
\(420\) 1.55391 0.0758232
\(421\) −3.05866 −0.149070 −0.0745350 0.997218i \(-0.523747\pi\)
−0.0745350 + 0.997218i \(0.523747\pi\)
\(422\) −30.4292 −1.48127
\(423\) −11.9986 −0.583394
\(424\) −18.0910 −0.878577
\(425\) 31.0757 1.50739
\(426\) −4.66487 −0.226014
\(427\) 46.8843 2.26889
\(428\) 21.8158 1.05451
\(429\) −0.668486 −0.0322748
\(430\) −8.48436 −0.409152
\(431\) −18.3840 −0.885528 −0.442764 0.896638i \(-0.646002\pi\)
−0.442764 + 0.896638i \(0.646002\pi\)
\(432\) −2.05537 −0.0988889
\(433\) −29.3297 −1.40950 −0.704748 0.709458i \(-0.748940\pi\)
−0.704748 + 0.709458i \(0.748940\pi\)
\(434\) −12.7638 −0.612680
\(435\) 1.00391 0.0481340
\(436\) −41.7934 −2.00154
\(437\) −6.36610 −0.304532
\(438\) −2.85916 −0.136616
\(439\) −8.44414 −0.403017 −0.201508 0.979487i \(-0.564584\pi\)
−0.201508 + 0.979487i \(0.564584\pi\)
\(440\) 2.51774 0.120028
\(441\) −58.7012 −2.79530
\(442\) 14.3019 0.680270
\(443\) −16.3396 −0.776316 −0.388158 0.921593i \(-0.626888\pi\)
−0.388158 + 0.921593i \(0.626888\pi\)
\(444\) −1.43326 −0.0680194
\(445\) 2.69961 0.127974
\(446\) −11.5060 −0.544823
\(447\) −3.23841 −0.153171
\(448\) −66.3664 −3.13552
\(449\) −27.1713 −1.28229 −0.641147 0.767418i \(-0.721541\pi\)
−0.641147 + 0.767418i \(0.721541\pi\)
\(450\) −31.1911 −1.47036
\(451\) −19.8767 −0.935958
\(452\) −20.7696 −0.976921
\(453\) −2.04583 −0.0961216
\(454\) 52.6380 2.47042
\(455\) −2.34476 −0.109924
\(456\) −3.07967 −0.144219
\(457\) −8.60104 −0.402339 −0.201170 0.979556i \(-0.564474\pi\)
−0.201170 + 0.979556i \(0.564474\pi\)
\(458\) 20.5685 0.961102
\(459\) −8.89331 −0.415104
\(460\) −1.19080 −0.0555213
\(461\) −15.7227 −0.732280 −0.366140 0.930560i \(-0.619321\pi\)
−0.366140 + 0.930560i \(0.619321\pi\)
\(462\) 7.65537 0.356160
\(463\) 29.0659 1.35081 0.675403 0.737449i \(-0.263970\pi\)
0.675403 + 0.737449i \(0.263970\pi\)
\(464\) −14.4148 −0.669189
\(465\) 0.116247 0.00539083
\(466\) 31.4660 1.45763
\(467\) 33.0720 1.53039 0.765194 0.643800i \(-0.222643\pi\)
0.765194 + 0.643800i \(0.222643\pi\)
\(468\) −8.46148 −0.391132
\(469\) −30.8448 −1.42428
\(470\) 4.06140 0.187339
\(471\) 3.19206 0.147082
\(472\) −4.74746 −0.218520
\(473\) −24.6379 −1.13285
\(474\) −2.85268 −0.131028
\(475\) 33.2701 1.52654
\(476\) −96.5409 −4.42494
\(477\) −27.7152 −1.26899
\(478\) 9.69221 0.443311
\(479\) 31.9150 1.45823 0.729116 0.684391i \(-0.239932\pi\)
0.729116 + 0.684391i \(0.239932\pi\)
\(480\) 0.745974 0.0340489
\(481\) 2.16270 0.0986106
\(482\) 36.3461 1.65552
\(483\) −1.09887 −0.0500002
\(484\) −7.49584 −0.340720
\(485\) 2.78197 0.126323
\(486\) 13.4295 0.609173
\(487\) 29.8057 1.35063 0.675314 0.737531i \(-0.264008\pi\)
0.675314 + 0.737531i \(0.264008\pi\)
\(488\) −17.3808 −0.786792
\(489\) −0.0422341 −0.00190989
\(490\) 19.8697 0.897622
\(491\) 38.3926 1.73263 0.866317 0.499495i \(-0.166481\pi\)
0.866317 + 0.499495i \(0.166481\pi\)
\(492\) 4.54782 0.205032
\(493\) −62.3708 −2.80904
\(494\) 15.3118 0.688909
\(495\) 3.85714 0.173366
\(496\) −1.66914 −0.0749466
\(497\) −47.5149 −2.13134
\(498\) 4.69569 0.210419
\(499\) −33.2783 −1.48974 −0.744871 0.667209i \(-0.767489\pi\)
−0.744871 + 0.667209i \(0.767489\pi\)
\(500\) 12.7116 0.568479
\(501\) −4.82259 −0.215457
\(502\) 52.5782 2.34668
\(503\) −0.221166 −0.00986131 −0.00493066 0.999988i \(-0.501569\pi\)
−0.00493066 + 0.999988i \(0.501569\pi\)
\(504\) 29.4084 1.30995
\(505\) 5.18192 0.230593
\(506\) −5.86649 −0.260797
\(507\) −0.230793 −0.0102499
\(508\) −52.2391 −2.31774
\(509\) 24.7361 1.09641 0.548205 0.836344i \(-0.315311\pi\)
0.548205 + 0.836344i \(0.315311\pi\)
\(510\) 1.49166 0.0660519
\(511\) −29.1225 −1.28831
\(512\) −16.4722 −0.727975
\(513\) −9.52130 −0.420376
\(514\) −14.8100 −0.653239
\(515\) 0.0557311 0.00245580
\(516\) 5.63718 0.248163
\(517\) 11.7940 0.518698
\(518\) −24.7668 −1.08819
\(519\) −4.92122 −0.216017
\(520\) 0.869243 0.0381188
\(521\) −8.52549 −0.373508 −0.186754 0.982407i \(-0.559797\pi\)
−0.186754 + 0.982407i \(0.559797\pi\)
\(522\) 62.6023 2.74003
\(523\) −14.4011 −0.629714 −0.314857 0.949139i \(-0.601957\pi\)
−0.314857 + 0.949139i \(0.601957\pi\)
\(524\) −29.6071 −1.29339
\(525\) 5.74282 0.250637
\(526\) 38.3760 1.67327
\(527\) −7.22216 −0.314602
\(528\) 1.00111 0.0435676
\(529\) −22.1579 −0.963388
\(530\) 9.38127 0.407497
\(531\) −7.27304 −0.315623
\(532\) −103.358 −4.48114
\(533\) −6.86239 −0.297243
\(534\) −3.04298 −0.131683
\(535\) −3.43337 −0.148437
\(536\) 11.4347 0.493904
\(537\) 3.64015 0.157084
\(538\) −70.1829 −3.02580
\(539\) 57.7000 2.48531
\(540\) −1.78099 −0.0766416
\(541\) 12.9539 0.556931 0.278466 0.960446i \(-0.410174\pi\)
0.278466 + 0.960446i \(0.410174\pi\)
\(542\) 19.7632 0.848904
\(543\) −2.02487 −0.0868954
\(544\) −46.3456 −1.98705
\(545\) 6.57745 0.281747
\(546\) 2.64300 0.113110
\(547\) −9.18558 −0.392747 −0.196374 0.980529i \(-0.562917\pi\)
−0.196374 + 0.980529i \(0.562917\pi\)
\(548\) −63.2652 −2.70256
\(549\) −26.6272 −1.13642
\(550\) 30.6590 1.30731
\(551\) −66.7750 −2.84471
\(552\) 0.407368 0.0173388
\(553\) −29.0565 −1.23561
\(554\) 1.91287 0.0812701
\(555\) 0.225566 0.00957474
\(556\) 60.7869 2.57794
\(557\) 27.3137 1.15732 0.578659 0.815569i \(-0.303576\pi\)
0.578659 + 0.815569i \(0.303576\pi\)
\(558\) 7.24896 0.306873
\(559\) −8.50616 −0.359772
\(560\) 3.51146 0.148386
\(561\) 4.33166 0.182883
\(562\) 1.67192 0.0705255
\(563\) 32.4641 1.36820 0.684100 0.729388i \(-0.260195\pi\)
0.684100 + 0.729388i \(0.260195\pi\)
\(564\) −2.69848 −0.113626
\(565\) 3.26873 0.137516
\(566\) 53.6799 2.25634
\(567\) 44.2241 1.85724
\(568\) 17.6146 0.739092
\(569\) −1.55276 −0.0650950 −0.0325475 0.999470i \(-0.510362\pi\)
−0.0325475 + 0.999470i \(0.510362\pi\)
\(570\) 1.59699 0.0668907
\(571\) −20.4524 −0.855906 −0.427953 0.903801i \(-0.640765\pi\)
−0.427953 + 0.903801i \(0.640765\pi\)
\(572\) 8.31715 0.347758
\(573\) −3.38172 −0.141273
\(574\) 78.5868 3.28015
\(575\) −4.40086 −0.183528
\(576\) 37.6917 1.57049
\(577\) 22.5207 0.937550 0.468775 0.883318i \(-0.344695\pi\)
0.468775 + 0.883318i \(0.344695\pi\)
\(578\) −55.1519 −2.29402
\(579\) 5.35966 0.222740
\(580\) −12.4905 −0.518639
\(581\) 47.8289 1.98428
\(582\) −3.13581 −0.129984
\(583\) 27.2424 1.12827
\(584\) 10.7962 0.446751
\(585\) 1.33167 0.0550577
\(586\) 32.0890 1.32558
\(587\) 20.1048 0.829814 0.414907 0.909864i \(-0.363814\pi\)
0.414907 + 0.909864i \(0.363814\pi\)
\(588\) −13.2018 −0.544434
\(589\) −7.73214 −0.318597
\(590\) 2.46184 0.101352
\(591\) −5.85587 −0.240878
\(592\) −3.23880 −0.133114
\(593\) −15.1131 −0.620620 −0.310310 0.950635i \(-0.600433\pi\)
−0.310310 + 0.950635i \(0.600433\pi\)
\(594\) −8.77407 −0.360004
\(595\) 15.1936 0.622877
\(596\) 40.2916 1.65041
\(597\) 0.569539 0.0233097
\(598\) −2.02539 −0.0828244
\(599\) −41.5753 −1.69872 −0.849360 0.527814i \(-0.823012\pi\)
−0.849360 + 0.527814i \(0.823012\pi\)
\(600\) −2.12896 −0.0869144
\(601\) −12.7449 −0.519874 −0.259937 0.965626i \(-0.583702\pi\)
−0.259937 + 0.965626i \(0.583702\pi\)
\(602\) 97.4109 3.97017
\(603\) 17.5178 0.713380
\(604\) 25.4538 1.03570
\(605\) 1.17969 0.0479614
\(606\) −5.84102 −0.237275
\(607\) −44.9819 −1.82576 −0.912880 0.408228i \(-0.866147\pi\)
−0.912880 + 0.408228i \(0.866147\pi\)
\(608\) −49.6182 −2.01228
\(609\) −11.5262 −0.467065
\(610\) 9.01300 0.364926
\(611\) 4.07184 0.164729
\(612\) 54.8288 2.21632
\(613\) −0.374742 −0.0151357 −0.00756785 0.999971i \(-0.502409\pi\)
−0.00756785 + 0.999971i \(0.502409\pi\)
\(614\) 15.5964 0.629419
\(615\) −0.715736 −0.0288613
\(616\) −28.9068 −1.16469
\(617\) 1.00000 0.0402585
\(618\) −0.0628196 −0.00252698
\(619\) 44.3902 1.78419 0.892096 0.451847i \(-0.149235\pi\)
0.892096 + 0.451847i \(0.149235\pi\)
\(620\) −1.44632 −0.0580857
\(621\) 1.25945 0.0505399
\(622\) 45.7539 1.83457
\(623\) −30.9949 −1.24178
\(624\) 0.345630 0.0138363
\(625\) 21.9783 0.879133
\(626\) 50.0618 2.00087
\(627\) 4.63753 0.185205
\(628\) −39.7149 −1.58480
\(629\) −14.0139 −0.558770
\(630\) −15.2500 −0.607575
\(631\) 5.33695 0.212461 0.106230 0.994342i \(-0.466122\pi\)
0.106230 + 0.994342i \(0.466122\pi\)
\(632\) 10.7717 0.428477
\(633\) −3.18187 −0.126468
\(634\) 63.6470 2.52774
\(635\) 8.22139 0.326256
\(636\) −6.23311 −0.247159
\(637\) 19.9208 0.789290
\(638\) −61.5345 −2.43618
\(639\) 26.9853 1.06752
\(640\) −6.29378 −0.248783
\(641\) −3.28074 −0.129582 −0.0647908 0.997899i \(-0.520638\pi\)
−0.0647908 + 0.997899i \(0.520638\pi\)
\(642\) 3.87007 0.152739
\(643\) 25.8702 1.02022 0.510110 0.860109i \(-0.329605\pi\)
0.510110 + 0.860109i \(0.329605\pi\)
\(644\) 13.6719 0.538747
\(645\) −0.887179 −0.0349326
\(646\) −99.2173 −3.90365
\(647\) 16.5720 0.651512 0.325756 0.945454i \(-0.394381\pi\)
0.325756 + 0.945454i \(0.394381\pi\)
\(648\) −16.3946 −0.644042
\(649\) 7.14899 0.280622
\(650\) 10.5850 0.415176
\(651\) −1.33466 −0.0523095
\(652\) 0.525467 0.0205789
\(653\) −32.8220 −1.28443 −0.642213 0.766526i \(-0.721983\pi\)
−0.642213 + 0.766526i \(0.721983\pi\)
\(654\) −7.41405 −0.289912
\(655\) 4.65957 0.182064
\(656\) 10.2769 0.401247
\(657\) 16.5397 0.645273
\(658\) −46.6299 −1.81782
\(659\) −15.3609 −0.598375 −0.299187 0.954194i \(-0.596716\pi\)
−0.299187 + 0.954194i \(0.596716\pi\)
\(660\) 0.867466 0.0337661
\(661\) 33.2527 1.29338 0.646690 0.762753i \(-0.276153\pi\)
0.646690 + 0.762753i \(0.276153\pi\)
\(662\) 1.87057 0.0727019
\(663\) 1.49549 0.0580802
\(664\) −17.7310 −0.688096
\(665\) 16.2665 0.630787
\(666\) 14.0659 0.545042
\(667\) 8.83279 0.342007
\(668\) 60.0016 2.32153
\(669\) −1.20314 −0.0465160
\(670\) −5.92958 −0.229080
\(671\) 26.1730 1.01040
\(672\) −8.56471 −0.330391
\(673\) 38.5568 1.48626 0.743128 0.669149i \(-0.233341\pi\)
0.743128 + 0.669149i \(0.233341\pi\)
\(674\) −20.8512 −0.803159
\(675\) −6.58203 −0.253343
\(676\) 2.87148 0.110441
\(677\) −35.1867 −1.35234 −0.676168 0.736747i \(-0.736361\pi\)
−0.676168 + 0.736747i \(0.736361\pi\)
\(678\) −3.68448 −0.141502
\(679\) −31.9405 −1.22576
\(680\) −5.63253 −0.215998
\(681\) 5.50417 0.210920
\(682\) −7.12532 −0.272843
\(683\) 12.1155 0.463587 0.231794 0.972765i \(-0.425541\pi\)
0.231794 + 0.972765i \(0.425541\pi\)
\(684\) 58.7004 2.24447
\(685\) 9.95669 0.380425
\(686\) −147.966 −5.64938
\(687\) 2.15077 0.0820571
\(688\) 12.7386 0.485655
\(689\) 9.40538 0.358317
\(690\) −0.211245 −0.00804196
\(691\) −34.5838 −1.31563 −0.657816 0.753179i \(-0.728519\pi\)
−0.657816 + 0.753179i \(0.728519\pi\)
\(692\) 61.2287 2.32757
\(693\) −44.2848 −1.68224
\(694\) −14.5316 −0.551610
\(695\) −9.56665 −0.362884
\(696\) 4.27295 0.161966
\(697\) 44.4670 1.68431
\(698\) −24.3418 −0.921349
\(699\) 3.29029 0.124450
\(700\) −71.4509 −2.70059
\(701\) −50.0941 −1.89203 −0.946015 0.324124i \(-0.894931\pi\)
−0.946015 + 0.324124i \(0.894931\pi\)
\(702\) −3.02922 −0.114331
\(703\) −15.0034 −0.565866
\(704\) −37.0488 −1.39633
\(705\) 0.424686 0.0159946
\(706\) 19.9071 0.749214
\(707\) −59.4949 −2.23754
\(708\) −1.63570 −0.0614733
\(709\) −25.7897 −0.968554 −0.484277 0.874915i \(-0.660917\pi\)
−0.484277 + 0.874915i \(0.660917\pi\)
\(710\) −9.13423 −0.342801
\(711\) 16.5022 0.618880
\(712\) 11.4903 0.430618
\(713\) 1.02278 0.0383035
\(714\) −17.1261 −0.640929
\(715\) −1.30895 −0.0489521
\(716\) −45.2899 −1.69256
\(717\) 1.01348 0.0378491
\(718\) −33.4992 −1.25018
\(719\) −8.31557 −0.310118 −0.155059 0.987905i \(-0.549557\pi\)
−0.155059 + 0.987905i \(0.549557\pi\)
\(720\) −1.99427 −0.0743221
\(721\) −0.639862 −0.0238297
\(722\) −64.2877 −2.39254
\(723\) 3.80058 0.141345
\(724\) 25.1930 0.936290
\(725\) −46.1613 −1.71439
\(726\) −1.32974 −0.0493514
\(727\) 37.2502 1.38153 0.690767 0.723078i \(-0.257273\pi\)
0.690767 + 0.723078i \(0.257273\pi\)
\(728\) −9.97999 −0.369883
\(729\) −24.1661 −0.895040
\(730\) −5.59849 −0.207209
\(731\) 55.1183 2.03862
\(732\) −5.98841 −0.221338
\(733\) −32.0896 −1.18526 −0.592629 0.805476i \(-0.701910\pi\)
−0.592629 + 0.805476i \(0.701910\pi\)
\(734\) 29.1783 1.07699
\(735\) 2.07770 0.0766373
\(736\) 6.56334 0.241928
\(737\) −17.2190 −0.634270
\(738\) −44.6320 −1.64293
\(739\) 1.58107 0.0581605 0.0290802 0.999577i \(-0.490742\pi\)
0.0290802 + 0.999577i \(0.490742\pi\)
\(740\) −2.80644 −0.103167
\(741\) 1.60110 0.0588178
\(742\) −107.709 −3.95411
\(743\) 6.16705 0.226247 0.113124 0.993581i \(-0.463914\pi\)
0.113124 + 0.993581i \(0.463914\pi\)
\(744\) 0.494781 0.0181396
\(745\) −6.34109 −0.232319
\(746\) 49.6351 1.81727
\(747\) −27.1636 −0.993865
\(748\) −53.8936 −1.97054
\(749\) 39.4193 1.44035
\(750\) 2.25500 0.0823410
\(751\) 17.8887 0.652767 0.326384 0.945237i \(-0.394170\pi\)
0.326384 + 0.945237i \(0.394170\pi\)
\(752\) −6.09789 −0.222367
\(753\) 5.49792 0.200355
\(754\) −21.2446 −0.773684
\(755\) −4.00592 −0.145790
\(756\) 20.4480 0.743686
\(757\) −44.5820 −1.62036 −0.810181 0.586180i \(-0.800631\pi\)
−0.810181 + 0.586180i \(0.800631\pi\)
\(758\) 48.0078 1.74372
\(759\) −0.613438 −0.0222664
\(760\) −6.03026 −0.218741
\(761\) −5.35003 −0.193938 −0.0969692 0.995287i \(-0.530915\pi\)
−0.0969692 + 0.995287i \(0.530915\pi\)
\(762\) −9.26709 −0.335711
\(763\) −75.5173 −2.73391
\(764\) 42.0747 1.52221
\(765\) −8.62896 −0.311981
\(766\) −36.6712 −1.32499
\(767\) 2.46817 0.0891205
\(768\) 1.19015 0.0429457
\(769\) 40.4466 1.45854 0.729271 0.684225i \(-0.239859\pi\)
0.729271 + 0.684225i \(0.239859\pi\)
\(770\) 14.9899 0.540198
\(771\) −1.54862 −0.0557724
\(772\) −66.6838 −2.40000
\(773\) −26.3856 −0.949024 −0.474512 0.880249i \(-0.657376\pi\)
−0.474512 + 0.880249i \(0.657376\pi\)
\(774\) −55.3229 −1.98854
\(775\) −5.34519 −0.192005
\(776\) 11.8409 0.425062
\(777\) −2.58978 −0.0929078
\(778\) −48.4419 −1.73673
\(779\) 47.6069 1.70570
\(780\) 0.299490 0.0107235
\(781\) −26.5250 −0.949140
\(782\) 13.1241 0.469319
\(783\) 13.2105 0.472106
\(784\) −29.8328 −1.06546
\(785\) 6.25033 0.223084
\(786\) −5.25223 −0.187341
\(787\) −12.2158 −0.435447 −0.217724 0.976010i \(-0.569863\pi\)
−0.217724 + 0.976010i \(0.569863\pi\)
\(788\) 72.8575 2.59544
\(789\) 4.01284 0.142861
\(790\) −5.58580 −0.198734
\(791\) −37.5290 −1.33438
\(792\) 16.4171 0.583356
\(793\) 9.03616 0.320883
\(794\) 48.9817 1.73830
\(795\) 0.980966 0.0347913
\(796\) −7.08608 −0.251159
\(797\) 6.49392 0.230026 0.115013 0.993364i \(-0.463309\pi\)
0.115013 + 0.993364i \(0.463309\pi\)
\(798\) −18.3355 −0.649068
\(799\) −26.3848 −0.933425
\(800\) −34.3008 −1.21272
\(801\) 17.6030 0.621972
\(802\) 19.6675 0.694484
\(803\) −16.2575 −0.573716
\(804\) 3.93973 0.138944
\(805\) −2.15168 −0.0758367
\(806\) −2.46000 −0.0866498
\(807\) −7.33878 −0.258337
\(808\) 22.0558 0.775919
\(809\) 7.94231 0.279237 0.139618 0.990205i \(-0.455412\pi\)
0.139618 + 0.990205i \(0.455412\pi\)
\(810\) 8.50160 0.298716
\(811\) −39.5023 −1.38711 −0.693557 0.720402i \(-0.743957\pi\)
−0.693557 + 0.720402i \(0.743957\pi\)
\(812\) 143.406 5.03258
\(813\) 2.06657 0.0724779
\(814\) −13.8260 −0.484600
\(815\) −0.0826981 −0.00289679
\(816\) −2.23961 −0.0784022
\(817\) 59.0104 2.06451
\(818\) 49.4391 1.72860
\(819\) −15.2892 −0.534248
\(820\) 8.90503 0.310977
\(821\) −41.8775 −1.46154 −0.730768 0.682626i \(-0.760838\pi\)
−0.730768 + 0.682626i \(0.760838\pi\)
\(822\) −11.2231 −0.391451
\(823\) −9.68439 −0.337576 −0.168788 0.985652i \(-0.553985\pi\)
−0.168788 + 0.985652i \(0.553985\pi\)
\(824\) 0.237208 0.00826352
\(825\) 3.20591 0.111615
\(826\) −28.2650 −0.983466
\(827\) 43.9943 1.52983 0.764916 0.644130i \(-0.222780\pi\)
0.764916 + 0.644130i \(0.222780\pi\)
\(828\) −7.76470 −0.269842
\(829\) −16.6075 −0.576803 −0.288401 0.957510i \(-0.593124\pi\)
−0.288401 + 0.957510i \(0.593124\pi\)
\(830\) 9.19459 0.319149
\(831\) 0.200022 0.00693869
\(832\) −12.7910 −0.443448
\(833\) −129.083 −4.47245
\(834\) 10.7835 0.373400
\(835\) −9.44305 −0.326790
\(836\) −57.6992 −1.99557
\(837\) 1.52970 0.0528741
\(838\) −64.8901 −2.24159
\(839\) −19.6040 −0.676806 −0.338403 0.941001i \(-0.609887\pi\)
−0.338403 + 0.941001i \(0.609887\pi\)
\(840\) −1.04090 −0.0359143
\(841\) 63.6485 2.19478
\(842\) 6.75090 0.232651
\(843\) 0.174826 0.00602134
\(844\) 39.5881 1.36268
\(845\) −0.451913 −0.0155463
\(846\) 26.4827 0.910494
\(847\) −13.5444 −0.465390
\(848\) −14.0853 −0.483690
\(849\) 5.61312 0.192642
\(850\) −68.5885 −2.35257
\(851\) 1.98461 0.0680315
\(852\) 6.06896 0.207919
\(853\) −55.3427 −1.89490 −0.947448 0.319909i \(-0.896348\pi\)
−0.947448 + 0.319909i \(0.896348\pi\)
\(854\) −103.480 −3.54103
\(855\) −9.23828 −0.315942
\(856\) −14.6134 −0.499476
\(857\) −19.3328 −0.660397 −0.330199 0.943912i \(-0.607116\pi\)
−0.330199 + 0.943912i \(0.607116\pi\)
\(858\) 1.47544 0.0503708
\(859\) 8.19201 0.279508 0.139754 0.990186i \(-0.455369\pi\)
0.139754 + 0.990186i \(0.455369\pi\)
\(860\) 11.0381 0.376396
\(861\) 8.21754 0.280053
\(862\) 40.5762 1.38203
\(863\) 10.7047 0.364391 0.182195 0.983262i \(-0.441680\pi\)
0.182195 + 0.983262i \(0.441680\pi\)
\(864\) 9.81629 0.333957
\(865\) −9.63618 −0.327640
\(866\) 64.7348 2.19978
\(867\) −5.76704 −0.195859
\(868\) 16.6056 0.563630
\(869\) −16.2207 −0.550249
\(870\) −2.21578 −0.0751221
\(871\) −5.94482 −0.201432
\(872\) 27.9955 0.948049
\(873\) 18.1400 0.613947
\(874\) 14.0509 0.475278
\(875\) 22.9688 0.776486
\(876\) 3.71975 0.125679
\(877\) 41.1685 1.39016 0.695081 0.718931i \(-0.255369\pi\)
0.695081 + 0.718931i \(0.255369\pi\)
\(878\) 18.6374 0.628982
\(879\) 3.35543 0.113176
\(880\) 1.96026 0.0660802
\(881\) −23.4651 −0.790561 −0.395280 0.918561i \(-0.629353\pi\)
−0.395280 + 0.918561i \(0.629353\pi\)
\(882\) 129.562 4.36258
\(883\) 5.77980 0.194506 0.0972529 0.995260i \(-0.468994\pi\)
0.0972529 + 0.995260i \(0.468994\pi\)
\(884\) −18.6066 −0.625808
\(885\) 0.257426 0.00865329
\(886\) 36.0637 1.21158
\(887\) 29.6720 0.996288 0.498144 0.867094i \(-0.334015\pi\)
0.498144 + 0.867094i \(0.334015\pi\)
\(888\) 0.960074 0.0322180
\(889\) −94.3918 −3.16580
\(890\) −5.95843 −0.199727
\(891\) 24.6879 0.827077
\(892\) 14.9692 0.501205
\(893\) −28.2479 −0.945279
\(894\) 7.14762 0.239052
\(895\) 7.12773 0.238254
\(896\) 72.2604 2.41405
\(897\) −0.211788 −0.00707139
\(898\) 59.9710 2.00126
\(899\) 10.7281 0.357803
\(900\) 40.5794 1.35265
\(901\) −60.9451 −2.03038
\(902\) 43.8707 1.46074
\(903\) 10.1859 0.338966
\(904\) 13.9126 0.462728
\(905\) −3.96487 −0.131797
\(906\) 4.51544 0.150016
\(907\) −8.77916 −0.291507 −0.145754 0.989321i \(-0.546561\pi\)
−0.145754 + 0.989321i \(0.546561\pi\)
\(908\) −68.4817 −2.27264
\(909\) 33.7891 1.12071
\(910\) 5.17522 0.171557
\(911\) −28.1042 −0.931133 −0.465567 0.885013i \(-0.654149\pi\)
−0.465567 + 0.885013i \(0.654149\pi\)
\(912\) −2.39776 −0.0793978
\(913\) 26.7003 0.883651
\(914\) 18.9837 0.627925
\(915\) 0.942457 0.0311567
\(916\) −26.7594 −0.884157
\(917\) −53.4976 −1.76665
\(918\) 19.6288 0.647847
\(919\) 1.25336 0.0413445 0.0206723 0.999786i \(-0.493419\pi\)
0.0206723 + 0.999786i \(0.493419\pi\)
\(920\) 0.797664 0.0262982
\(921\) 1.63086 0.0537386
\(922\) 34.7023 1.14286
\(923\) −9.15770 −0.301429
\(924\) −9.95958 −0.327646
\(925\) −10.3718 −0.341023
\(926\) −64.1525 −2.10818
\(927\) 0.363399 0.0119356
\(928\) 68.8439 2.25991
\(929\) 18.1790 0.596435 0.298218 0.954498i \(-0.403608\pi\)
0.298218 + 0.954498i \(0.403608\pi\)
\(930\) −0.256574 −0.00841339
\(931\) −138.198 −4.52925
\(932\) −40.9371 −1.34094
\(933\) 4.78433 0.156632
\(934\) −72.9945 −2.38845
\(935\) 8.48177 0.277384
\(936\) 5.66797 0.185263
\(937\) 55.9049 1.82633 0.913166 0.407587i \(-0.133630\pi\)
0.913166 + 0.407587i \(0.133630\pi\)
\(938\) 68.0789 2.22285
\(939\) 5.23478 0.170831
\(940\) −5.28386 −0.172340
\(941\) −34.4470 −1.12294 −0.561469 0.827498i \(-0.689764\pi\)
−0.561469 + 0.827498i \(0.689764\pi\)
\(942\) −7.04533 −0.229549
\(943\) −6.29729 −0.205068
\(944\) −3.69627 −0.120303
\(945\) −3.21810 −0.104685
\(946\) 54.3793 1.76802
\(947\) 34.4899 1.12077 0.560385 0.828232i \(-0.310653\pi\)
0.560385 + 0.828232i \(0.310653\pi\)
\(948\) 3.71132 0.120538
\(949\) −5.61288 −0.182202
\(950\) −73.4318 −2.38244
\(951\) 6.65534 0.215814
\(952\) 64.6684 2.09592
\(953\) 27.9044 0.903913 0.451956 0.892040i \(-0.350726\pi\)
0.451956 + 0.892040i \(0.350726\pi\)
\(954\) 61.1713 1.98049
\(955\) −6.62171 −0.214274
\(956\) −12.6095 −0.407820
\(957\) −6.43445 −0.207996
\(958\) −70.4408 −2.27584
\(959\) −114.315 −3.69143
\(960\) −1.33408 −0.0430573
\(961\) −29.7577 −0.959927
\(962\) −4.77338 −0.153900
\(963\) −22.3875 −0.721429
\(964\) −47.2860 −1.52298
\(965\) 10.4947 0.337836
\(966\) 2.42536 0.0780345
\(967\) 27.2711 0.876981 0.438490 0.898736i \(-0.355513\pi\)
0.438490 + 0.898736i \(0.355513\pi\)
\(968\) 5.02112 0.161385
\(969\) −10.3748 −0.333287
\(970\) −6.14020 −0.197150
\(971\) 1.84724 0.0592806 0.0296403 0.999561i \(-0.490564\pi\)
0.0296403 + 0.999561i \(0.490564\pi\)
\(972\) −17.4716 −0.560403
\(973\) 109.837 3.52121
\(974\) −65.7855 −2.10790
\(975\) 1.10683 0.0354470
\(976\) −13.5323 −0.433159
\(977\) 14.7656 0.472393 0.236197 0.971705i \(-0.424099\pi\)
0.236197 + 0.971705i \(0.424099\pi\)
\(978\) 0.0932166 0.00298074
\(979\) −17.3028 −0.552999
\(980\) −25.8504 −0.825759
\(981\) 42.8888 1.36933
\(982\) −84.7379 −2.70410
\(983\) −56.1946 −1.79233 −0.896165 0.443721i \(-0.853658\pi\)
−0.896165 + 0.443721i \(0.853658\pi\)
\(984\) −3.04638 −0.0971150
\(985\) −11.4663 −0.365347
\(986\) 137.661 4.38403
\(987\) −4.87593 −0.155202
\(988\) −19.9205 −0.633756
\(989\) −7.80571 −0.248207
\(990\) −8.51326 −0.270569
\(991\) −5.21079 −0.165526 −0.0827630 0.996569i \(-0.526374\pi\)
−0.0827630 + 0.996569i \(0.526374\pi\)
\(992\) 7.97170 0.253102
\(993\) 0.195599 0.00620715
\(994\) 104.872 3.32635
\(995\) 1.11521 0.0353544
\(996\) −6.10907 −0.193573
\(997\) −11.8446 −0.375123 −0.187561 0.982253i \(-0.560058\pi\)
−0.187561 + 0.982253i \(0.560058\pi\)
\(998\) 73.4499 2.32502
\(999\) 2.96823 0.0939106
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 \(a_p\))