Properties

Label 8041.2.a.g.1.6
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 1.6
Character \(\chi\) = 8041.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.53420 q^{2} -1.82986 q^{3} +4.42217 q^{4} -1.56039 q^{5} +4.63723 q^{6} -0.999486 q^{7} -6.13827 q^{8} +0.348383 q^{9} +O(q^{10})\) \(q-2.53420 q^{2} -1.82986 q^{3} +4.42217 q^{4} -1.56039 q^{5} +4.63723 q^{6} -0.999486 q^{7} -6.13827 q^{8} +0.348383 q^{9} +3.95435 q^{10} -1.00000 q^{11} -8.09195 q^{12} +6.16556 q^{13} +2.53290 q^{14} +2.85530 q^{15} +6.71126 q^{16} +1.00000 q^{17} -0.882871 q^{18} +7.13266 q^{19} -6.90033 q^{20} +1.82892 q^{21} +2.53420 q^{22} -0.590579 q^{23} +11.2322 q^{24} -2.56517 q^{25} -15.6248 q^{26} +4.85209 q^{27} -4.41990 q^{28} -6.99808 q^{29} -7.23591 q^{30} -0.245102 q^{31} -4.73114 q^{32} +1.82986 q^{33} -2.53420 q^{34} +1.55959 q^{35} +1.54061 q^{36} +5.61492 q^{37} -18.0756 q^{38} -11.2821 q^{39} +9.57812 q^{40} +3.92741 q^{41} -4.63485 q^{42} +1.00000 q^{43} -4.42217 q^{44} -0.543614 q^{45} +1.49665 q^{46} -10.9149 q^{47} -12.2807 q^{48} -6.00103 q^{49} +6.50065 q^{50} -1.82986 q^{51} +27.2652 q^{52} -10.7404 q^{53} -12.2962 q^{54} +1.56039 q^{55} +6.13512 q^{56} -13.0518 q^{57} +17.7345 q^{58} -0.228064 q^{59} +12.6266 q^{60} +5.23588 q^{61} +0.621137 q^{62} -0.348204 q^{63} -1.43286 q^{64} -9.62071 q^{65} -4.63723 q^{66} -11.4120 q^{67} +4.42217 q^{68} +1.08068 q^{69} -3.95232 q^{70} -4.95010 q^{71} -2.13847 q^{72} +0.454673 q^{73} -14.2293 q^{74} +4.69390 q^{75} +31.5418 q^{76} +0.999486 q^{77} +28.5911 q^{78} +2.99823 q^{79} -10.4722 q^{80} -9.92378 q^{81} -9.95285 q^{82} +3.32888 q^{83} +8.08779 q^{84} -1.56039 q^{85} -2.53420 q^{86} +12.8055 q^{87} +6.13827 q^{88} +6.66593 q^{89} +1.37763 q^{90} -6.16239 q^{91} -2.61164 q^{92} +0.448502 q^{93} +27.6605 q^{94} -11.1298 q^{95} +8.65732 q^{96} +10.3922 q^{97} +15.2078 q^{98} -0.348383 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 69q - 11q^{2} - 3q^{3} + 65q^{4} - 6q^{5} - 10q^{6} - 11q^{7} - 33q^{8} + 56q^{9} + O(q^{10}) \) \( 69q - 11q^{2} - 3q^{3} + 65q^{4} - 6q^{5} - 10q^{6} - 11q^{7} - 33q^{8} + 56q^{9} - q^{10} - 69q^{11} - 3q^{12} - 28q^{13} - 15q^{14} - 45q^{15} + 53q^{16} + 69q^{17} - 17q^{18} - 32q^{19} - 21q^{20} - 38q^{21} + 11q^{22} - 41q^{23} - 11q^{24} + 67q^{25} - 6q^{26} - 3q^{27} - 21q^{28} - 22q^{29} - 22q^{30} - 27q^{31} - 87q^{32} + 3q^{33} - 11q^{34} - 44q^{35} + 59q^{36} + 24q^{37} - 22q^{38} - 59q^{39} + q^{40} - 43q^{41} - 15q^{42} + 69q^{43} - 65q^{44} - 12q^{45} - 21q^{46} - 99q^{47} + 2q^{48} + 64q^{49} - 78q^{50} - 3q^{51} - 57q^{52} - 50q^{53} + 20q^{54} + 6q^{55} - 59q^{56} - 15q^{57} + 22q^{58} - 82q^{59} - 86q^{60} - 24q^{61} + 15q^{62} - 63q^{63} + 63q^{64} - 23q^{65} + 10q^{66} - 54q^{67} + 65q^{68} + 36q^{69} + 9q^{70} - 128q^{71} - 69q^{72} + 2q^{73} - 58q^{74} - 31q^{75} - 76q^{76} + 11q^{77} - 19q^{78} - 43q^{79} - 19q^{80} + 49q^{81} - 2q^{82} - 62q^{83} - 82q^{84} - 6q^{85} - 11q^{86} - 62q^{87} + 33q^{88} - 49q^{89} - 37q^{90} - 2q^{91} - 96q^{92} - 29q^{93} - 75q^{94} - 133q^{95} - 86q^{96} + 5q^{97} - 72q^{98} - 56q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.53420 −1.79195 −0.895975 0.444104i \(-0.853522\pi\)
−0.895975 + 0.444104i \(0.853522\pi\)
\(3\) −1.82986 −1.05647 −0.528235 0.849098i \(-0.677146\pi\)
−0.528235 + 0.849098i \(0.677146\pi\)
\(4\) 4.42217 2.21109
\(5\) −1.56039 −0.697830 −0.348915 0.937154i \(-0.613450\pi\)
−0.348915 + 0.937154i \(0.613450\pi\)
\(6\) 4.63723 1.89314
\(7\) −0.999486 −0.377770 −0.188885 0.981999i \(-0.560487\pi\)
−0.188885 + 0.981999i \(0.560487\pi\)
\(8\) −6.13827 −2.17021
\(9\) 0.348383 0.116128
\(10\) 3.95435 1.25048
\(11\) −1.00000 −0.301511
\(12\) −8.09195 −2.33594
\(13\) 6.16556 1.71002 0.855010 0.518612i \(-0.173551\pi\)
0.855010 + 0.518612i \(0.173551\pi\)
\(14\) 2.53290 0.676946
\(15\) 2.85530 0.737236
\(16\) 6.71126 1.67781
\(17\) 1.00000 0.242536
\(18\) −0.882871 −0.208095
\(19\) 7.13266 1.63634 0.818172 0.574973i \(-0.194988\pi\)
0.818172 + 0.574973i \(0.194988\pi\)
\(20\) −6.90033 −1.54296
\(21\) 1.82892 0.399103
\(22\) 2.53420 0.540293
\(23\) −0.590579 −0.123144 −0.0615722 0.998103i \(-0.519611\pi\)
−0.0615722 + 0.998103i \(0.519611\pi\)
\(24\) 11.2322 2.29276
\(25\) −2.56517 −0.513034
\(26\) −15.6248 −3.06427
\(27\) 4.85209 0.933784
\(28\) −4.41990 −0.835283
\(29\) −6.99808 −1.29951 −0.649755 0.760143i \(-0.725129\pi\)
−0.649755 + 0.760143i \(0.725129\pi\)
\(30\) −7.23591 −1.32109
\(31\) −0.245102 −0.0440216 −0.0220108 0.999758i \(-0.507007\pi\)
−0.0220108 + 0.999758i \(0.507007\pi\)
\(32\) −4.73114 −0.836355
\(33\) 1.82986 0.318537
\(34\) −2.53420 −0.434612
\(35\) 1.55959 0.263619
\(36\) 1.54061 0.256768
\(37\) 5.61492 0.923088 0.461544 0.887117i \(-0.347296\pi\)
0.461544 + 0.887117i \(0.347296\pi\)
\(38\) −18.0756 −2.93225
\(39\) −11.2821 −1.80658
\(40\) 9.57812 1.51443
\(41\) 3.92741 0.613359 0.306679 0.951813i \(-0.400782\pi\)
0.306679 + 0.951813i \(0.400782\pi\)
\(42\) −4.63485 −0.715172
\(43\) 1.00000 0.152499
\(44\) −4.42217 −0.666667
\(45\) −0.543614 −0.0810372
\(46\) 1.49665 0.220669
\(47\) −10.9149 −1.59210 −0.796049 0.605232i \(-0.793080\pi\)
−0.796049 + 0.605232i \(0.793080\pi\)
\(48\) −12.2807 −1.77256
\(49\) −6.00103 −0.857290
\(50\) 6.50065 0.919331
\(51\) −1.82986 −0.256231
\(52\) 27.2652 3.78100
\(53\) −10.7404 −1.47531 −0.737655 0.675178i \(-0.764067\pi\)
−0.737655 + 0.675178i \(0.764067\pi\)
\(54\) −12.2962 −1.67329
\(55\) 1.56039 0.210404
\(56\) 6.13512 0.819839
\(57\) −13.0518 −1.72875
\(58\) 17.7345 2.32866
\(59\) −0.228064 −0.0296914 −0.0148457 0.999890i \(-0.504726\pi\)
−0.0148457 + 0.999890i \(0.504726\pi\)
\(60\) 12.6266 1.63009
\(61\) 5.23588 0.670385 0.335193 0.942150i \(-0.391199\pi\)
0.335193 + 0.942150i \(0.391199\pi\)
\(62\) 0.621137 0.0788845
\(63\) −0.348204 −0.0438695
\(64\) −1.43286 −0.179108
\(65\) −9.62071 −1.19330
\(66\) −4.63723 −0.570803
\(67\) −11.4120 −1.39420 −0.697100 0.716974i \(-0.745526\pi\)
−0.697100 + 0.716974i \(0.745526\pi\)
\(68\) 4.42217 0.536267
\(69\) 1.08068 0.130098
\(70\) −3.95232 −0.472393
\(71\) −4.95010 −0.587468 −0.293734 0.955887i \(-0.594898\pi\)
−0.293734 + 0.955887i \(0.594898\pi\)
\(72\) −2.13847 −0.252021
\(73\) 0.454673 0.0532154 0.0266077 0.999646i \(-0.491530\pi\)
0.0266077 + 0.999646i \(0.491530\pi\)
\(74\) −14.2293 −1.65413
\(75\) 4.69390 0.542004
\(76\) 31.5418 3.61810
\(77\) 0.999486 0.113902
\(78\) 28.5911 3.23731
\(79\) 2.99823 0.337327 0.168664 0.985674i \(-0.446055\pi\)
0.168664 + 0.985674i \(0.446055\pi\)
\(80\) −10.4722 −1.17083
\(81\) −9.92378 −1.10264
\(82\) −9.95285 −1.09911
\(83\) 3.32888 0.365392 0.182696 0.983169i \(-0.441518\pi\)
0.182696 + 0.983169i \(0.441518\pi\)
\(84\) 8.08779 0.882451
\(85\) −1.56039 −0.169249
\(86\) −2.53420 −0.273270
\(87\) 12.8055 1.37289
\(88\) 6.13827 0.654342
\(89\) 6.66593 0.706587 0.353294 0.935512i \(-0.385062\pi\)
0.353294 + 0.935512i \(0.385062\pi\)
\(90\) 1.37763 0.145215
\(91\) −6.16239 −0.645994
\(92\) −2.61164 −0.272283
\(93\) 0.448502 0.0465075
\(94\) 27.6605 2.85296
\(95\) −11.1298 −1.14189
\(96\) 8.65732 0.883584
\(97\) 10.3922 1.05517 0.527586 0.849502i \(-0.323097\pi\)
0.527586 + 0.849502i \(0.323097\pi\)
\(98\) 15.2078 1.53622
\(99\) −0.348383 −0.0350138
\(100\) −11.3436 −1.13436
\(101\) −8.75457 −0.871112 −0.435556 0.900162i \(-0.643448\pi\)
−0.435556 + 0.900162i \(0.643448\pi\)
\(102\) 4.63723 0.459154
\(103\) −9.30483 −0.916832 −0.458416 0.888738i \(-0.651583\pi\)
−0.458416 + 0.888738i \(0.651583\pi\)
\(104\) −37.8459 −3.71109
\(105\) −2.85384 −0.278506
\(106\) 27.2184 2.64368
\(107\) 8.41358 0.813372 0.406686 0.913568i \(-0.366684\pi\)
0.406686 + 0.913568i \(0.366684\pi\)
\(108\) 21.4568 2.06468
\(109\) 3.87041 0.370718 0.185359 0.982671i \(-0.440655\pi\)
0.185359 + 0.982671i \(0.440655\pi\)
\(110\) −3.95435 −0.377033
\(111\) −10.2745 −0.975214
\(112\) −6.70781 −0.633829
\(113\) 11.1784 1.05158 0.525788 0.850615i \(-0.323770\pi\)
0.525788 + 0.850615i \(0.323770\pi\)
\(114\) 33.0758 3.09783
\(115\) 0.921537 0.0859338
\(116\) −30.9467 −2.87333
\(117\) 2.14797 0.198580
\(118\) 0.577959 0.0532055
\(119\) −0.999486 −0.0916228
\(120\) −17.5266 −1.59995
\(121\) 1.00000 0.0909091
\(122\) −13.2688 −1.20130
\(123\) −7.18661 −0.647995
\(124\) −1.08388 −0.0973355
\(125\) 11.8046 1.05584
\(126\) 0.882418 0.0786120
\(127\) 17.0223 1.51049 0.755244 0.655444i \(-0.227519\pi\)
0.755244 + 0.655444i \(0.227519\pi\)
\(128\) 13.0934 1.15731
\(129\) −1.82986 −0.161110
\(130\) 24.3808 2.13834
\(131\) 5.89092 0.514692 0.257346 0.966319i \(-0.417152\pi\)
0.257346 + 0.966319i \(0.417152\pi\)
\(132\) 8.09195 0.704314
\(133\) −7.12900 −0.618162
\(134\) 28.9203 2.49834
\(135\) −7.57117 −0.651622
\(136\) −6.13827 −0.526352
\(137\) 11.6193 0.992707 0.496354 0.868120i \(-0.334672\pi\)
0.496354 + 0.868120i \(0.334672\pi\)
\(138\) −2.73865 −0.233130
\(139\) −13.8811 −1.17738 −0.588690 0.808359i \(-0.700356\pi\)
−0.588690 + 0.808359i \(0.700356\pi\)
\(140\) 6.89679 0.582885
\(141\) 19.9727 1.68200
\(142\) 12.5445 1.05271
\(143\) −6.16556 −0.515590
\(144\) 2.33809 0.194840
\(145\) 10.9198 0.906837
\(146\) −1.15223 −0.0953594
\(147\) 10.9810 0.905700
\(148\) 24.8302 2.04103
\(149\) −7.74179 −0.634232 −0.317116 0.948387i \(-0.602715\pi\)
−0.317116 + 0.948387i \(0.602715\pi\)
\(150\) −11.8953 −0.971245
\(151\) −2.21864 −0.180550 −0.0902751 0.995917i \(-0.528775\pi\)
−0.0902751 + 0.995917i \(0.528775\pi\)
\(152\) −43.7822 −3.55120
\(153\) 0.348383 0.0281651
\(154\) −2.53290 −0.204107
\(155\) 0.382456 0.0307196
\(156\) −49.8914 −3.99451
\(157\) −22.6023 −1.80386 −0.901929 0.431884i \(-0.857849\pi\)
−0.901929 + 0.431884i \(0.857849\pi\)
\(158\) −7.59812 −0.604474
\(159\) 19.6534 1.55862
\(160\) 7.38245 0.583634
\(161\) 0.590276 0.0465203
\(162\) 25.1488 1.97588
\(163\) 14.6058 1.14401 0.572007 0.820249i \(-0.306165\pi\)
0.572007 + 0.820249i \(0.306165\pi\)
\(164\) 17.3677 1.35619
\(165\) −2.85530 −0.222285
\(166\) −8.43605 −0.654765
\(167\) −6.00698 −0.464834 −0.232417 0.972616i \(-0.574663\pi\)
−0.232417 + 0.972616i \(0.574663\pi\)
\(168\) −11.2264 −0.866135
\(169\) 25.0141 1.92417
\(170\) 3.95435 0.303285
\(171\) 2.48489 0.190025
\(172\) 4.42217 0.337187
\(173\) −24.8736 −1.89110 −0.945551 0.325474i \(-0.894476\pi\)
−0.945551 + 0.325474i \(0.894476\pi\)
\(174\) −32.4517 −2.46016
\(175\) 2.56385 0.193809
\(176\) −6.71126 −0.505880
\(177\) 0.417325 0.0313680
\(178\) −16.8928 −1.26617
\(179\) 14.7713 1.10406 0.552030 0.833824i \(-0.313853\pi\)
0.552030 + 0.833824i \(0.313853\pi\)
\(180\) −2.40396 −0.179180
\(181\) −11.3612 −0.844473 −0.422236 0.906486i \(-0.638755\pi\)
−0.422236 + 0.906486i \(0.638755\pi\)
\(182\) 15.6167 1.15759
\(183\) −9.58092 −0.708242
\(184\) 3.62514 0.267249
\(185\) −8.76150 −0.644158
\(186\) −1.13659 −0.0833391
\(187\) −1.00000 −0.0731272
\(188\) −48.2675 −3.52027
\(189\) −4.84959 −0.352756
\(190\) 28.2051 2.04621
\(191\) 12.9882 0.939792 0.469896 0.882722i \(-0.344291\pi\)
0.469896 + 0.882722i \(0.344291\pi\)
\(192\) 2.62194 0.189222
\(193\) 6.32406 0.455216 0.227608 0.973753i \(-0.426910\pi\)
0.227608 + 0.973753i \(0.426910\pi\)
\(194\) −26.3360 −1.89081
\(195\) 17.6045 1.26069
\(196\) −26.5376 −1.89554
\(197\) −1.03181 −0.0735138 −0.0367569 0.999324i \(-0.511703\pi\)
−0.0367569 + 0.999324i \(0.511703\pi\)
\(198\) 0.882871 0.0627429
\(199\) −22.4072 −1.58840 −0.794201 0.607655i \(-0.792110\pi\)
−0.794201 + 0.607655i \(0.792110\pi\)
\(200\) 15.7457 1.11339
\(201\) 20.8824 1.47293
\(202\) 22.1858 1.56099
\(203\) 6.99449 0.490917
\(204\) −8.09195 −0.566550
\(205\) −6.12831 −0.428020
\(206\) 23.5803 1.64292
\(207\) −0.205748 −0.0143004
\(208\) 41.3787 2.86910
\(209\) −7.13266 −0.493376
\(210\) 7.23219 0.499069
\(211\) −13.5361 −0.931866 −0.465933 0.884820i \(-0.654281\pi\)
−0.465933 + 0.884820i \(0.654281\pi\)
\(212\) −47.4960 −3.26204
\(213\) 9.05797 0.620642
\(214\) −21.3217 −1.45752
\(215\) −1.56039 −0.106418
\(216\) −29.7834 −2.02650
\(217\) 0.244976 0.0166301
\(218\) −9.80840 −0.664308
\(219\) −0.831987 −0.0562205
\(220\) 6.90033 0.465220
\(221\) 6.16556 0.414741
\(222\) 26.0377 1.74754
\(223\) −8.53589 −0.571605 −0.285803 0.958289i \(-0.592260\pi\)
−0.285803 + 0.958289i \(0.592260\pi\)
\(224\) 4.72871 0.315950
\(225\) −0.893660 −0.0595773
\(226\) −28.3283 −1.88437
\(227\) 22.2825 1.47894 0.739469 0.673190i \(-0.235077\pi\)
0.739469 + 0.673190i \(0.235077\pi\)
\(228\) −57.7171 −3.82241
\(229\) −20.4312 −1.35013 −0.675066 0.737757i \(-0.735885\pi\)
−0.675066 + 0.737757i \(0.735885\pi\)
\(230\) −2.33536 −0.153989
\(231\) −1.82892 −0.120334
\(232\) 42.9561 2.82021
\(233\) 15.4588 1.01274 0.506369 0.862317i \(-0.330988\pi\)
0.506369 + 0.862317i \(0.330988\pi\)
\(234\) −5.44340 −0.355846
\(235\) 17.0315 1.11101
\(236\) −1.00854 −0.0656502
\(237\) −5.48634 −0.356376
\(238\) 2.53290 0.164183
\(239\) −7.43154 −0.480707 −0.240353 0.970685i \(-0.577263\pi\)
−0.240353 + 0.970685i \(0.577263\pi\)
\(240\) 19.1627 1.23695
\(241\) 19.8654 1.27965 0.639823 0.768522i \(-0.279008\pi\)
0.639823 + 0.768522i \(0.279008\pi\)
\(242\) −2.53420 −0.162905
\(243\) 3.60285 0.231123
\(244\) 23.1539 1.48228
\(245\) 9.36397 0.598242
\(246\) 18.2123 1.16117
\(247\) 43.9768 2.79818
\(248\) 1.50450 0.0955359
\(249\) −6.09138 −0.386026
\(250\) −29.9153 −1.89201
\(251\) −30.4715 −1.92334 −0.961672 0.274203i \(-0.911586\pi\)
−0.961672 + 0.274203i \(0.911586\pi\)
\(252\) −1.53982 −0.0969993
\(253\) 0.590579 0.0371294
\(254\) −43.1380 −2.70672
\(255\) 2.85530 0.178806
\(256\) −30.3157 −1.89473
\(257\) 21.7124 1.35438 0.677191 0.735807i \(-0.263197\pi\)
0.677191 + 0.735807i \(0.263197\pi\)
\(258\) 4.63723 0.288701
\(259\) −5.61204 −0.348715
\(260\) −42.5444 −2.63849
\(261\) −2.43801 −0.150909
\(262\) −14.9288 −0.922302
\(263\) −18.2135 −1.12309 −0.561545 0.827446i \(-0.689793\pi\)
−0.561545 + 0.827446i \(0.689793\pi\)
\(264\) −11.2322 −0.691292
\(265\) 16.7593 1.02952
\(266\) 18.0663 1.10772
\(267\) −12.1977 −0.746488
\(268\) −50.4659 −3.08269
\(269\) 6.47725 0.394925 0.197462 0.980310i \(-0.436730\pi\)
0.197462 + 0.980310i \(0.436730\pi\)
\(270\) 19.1869 1.16767
\(271\) 22.3713 1.35896 0.679479 0.733695i \(-0.262206\pi\)
0.679479 + 0.733695i \(0.262206\pi\)
\(272\) 6.71126 0.406930
\(273\) 11.2763 0.682473
\(274\) −29.4457 −1.77888
\(275\) 2.56517 0.154685
\(276\) 4.77894 0.287658
\(277\) −25.6123 −1.53889 −0.769447 0.638711i \(-0.779468\pi\)
−0.769447 + 0.638711i \(0.779468\pi\)
\(278\) 35.1775 2.10981
\(279\) −0.0853892 −0.00511212
\(280\) −9.57320 −0.572108
\(281\) −5.90690 −0.352376 −0.176188 0.984357i \(-0.556377\pi\)
−0.176188 + 0.984357i \(0.556377\pi\)
\(282\) −50.6148 −3.01407
\(283\) 19.2251 1.14281 0.571405 0.820668i \(-0.306398\pi\)
0.571405 + 0.820668i \(0.306398\pi\)
\(284\) −21.8902 −1.29894
\(285\) 20.3659 1.20637
\(286\) 15.6248 0.923912
\(287\) −3.92539 −0.231709
\(288\) −1.64825 −0.0971238
\(289\) 1.00000 0.0588235
\(290\) −27.6729 −1.62501
\(291\) −19.0163 −1.11476
\(292\) 2.01064 0.117664
\(293\) 23.8140 1.39123 0.695614 0.718416i \(-0.255133\pi\)
0.695614 + 0.718416i \(0.255133\pi\)
\(294\) −27.8281 −1.62297
\(295\) 0.355870 0.0207195
\(296\) −34.4659 −2.00329
\(297\) −4.85209 −0.281547
\(298\) 19.6193 1.13651
\(299\) −3.64125 −0.210579
\(300\) 20.7572 1.19842
\(301\) −0.999486 −0.0576094
\(302\) 5.62248 0.323537
\(303\) 16.0196 0.920303
\(304\) 47.8691 2.74548
\(305\) −8.17004 −0.467815
\(306\) −0.882871 −0.0504704
\(307\) 19.3343 1.10347 0.551733 0.834021i \(-0.313967\pi\)
0.551733 + 0.834021i \(0.313967\pi\)
\(308\) 4.41990 0.251847
\(309\) 17.0265 0.968605
\(310\) −0.969219 −0.0550480
\(311\) −19.2356 −1.09075 −0.545375 0.838192i \(-0.683613\pi\)
−0.545375 + 0.838192i \(0.683613\pi\)
\(312\) 69.2526 3.92066
\(313\) 11.4858 0.649215 0.324608 0.945849i \(-0.394768\pi\)
0.324608 + 0.945849i \(0.394768\pi\)
\(314\) 57.2787 3.23243
\(315\) 0.543335 0.0306135
\(316\) 13.2587 0.745860
\(317\) −7.51031 −0.421821 −0.210911 0.977505i \(-0.567643\pi\)
−0.210911 + 0.977505i \(0.567643\pi\)
\(318\) −49.8058 −2.79297
\(319\) 6.99808 0.391817
\(320\) 2.23583 0.124987
\(321\) −15.3957 −0.859302
\(322\) −1.49588 −0.0833620
\(323\) 7.13266 0.396872
\(324\) −43.8846 −2.43804
\(325\) −15.8157 −0.877297
\(326\) −37.0140 −2.05001
\(327\) −7.08230 −0.391652
\(328\) −24.1075 −1.33111
\(329\) 10.9093 0.601448
\(330\) 7.23591 0.398324
\(331\) −26.1653 −1.43818 −0.719088 0.694919i \(-0.755440\pi\)
−0.719088 + 0.694919i \(0.755440\pi\)
\(332\) 14.7209 0.807914
\(333\) 1.95614 0.107196
\(334\) 15.2229 0.832960
\(335\) 17.8072 0.972914
\(336\) 12.2743 0.669621
\(337\) 3.45741 0.188337 0.0941685 0.995556i \(-0.469981\pi\)
0.0941685 + 0.995556i \(0.469981\pi\)
\(338\) −63.3909 −3.44801
\(339\) −20.4549 −1.11096
\(340\) −6.90033 −0.374223
\(341\) 0.245102 0.0132730
\(342\) −6.29722 −0.340515
\(343\) 12.9943 0.701629
\(344\) −6.13827 −0.330953
\(345\) −1.68628 −0.0907864
\(346\) 63.0346 3.38876
\(347\) 26.3086 1.41232 0.706161 0.708052i \(-0.250426\pi\)
0.706161 + 0.708052i \(0.250426\pi\)
\(348\) 56.6281 3.03559
\(349\) −12.9494 −0.693164 −0.346582 0.938020i \(-0.612658\pi\)
−0.346582 + 0.938020i \(0.612658\pi\)
\(350\) −6.49731 −0.347296
\(351\) 29.9158 1.59679
\(352\) 4.73114 0.252171
\(353\) 4.51734 0.240434 0.120217 0.992748i \(-0.461641\pi\)
0.120217 + 0.992748i \(0.461641\pi\)
\(354\) −1.05758 −0.0562100
\(355\) 7.72410 0.409953
\(356\) 29.4779 1.56233
\(357\) 1.82892 0.0967966
\(358\) −37.4335 −1.97842
\(359\) 16.3531 0.863082 0.431541 0.902093i \(-0.357970\pi\)
0.431541 + 0.902093i \(0.357970\pi\)
\(360\) 3.33685 0.175867
\(361\) 31.8748 1.67762
\(362\) 28.7916 1.51325
\(363\) −1.82986 −0.0960427
\(364\) −27.2512 −1.42835
\(365\) −0.709469 −0.0371353
\(366\) 24.2800 1.26913
\(367\) 15.8528 0.827508 0.413754 0.910389i \(-0.364217\pi\)
0.413754 + 0.910389i \(0.364217\pi\)
\(368\) −3.96353 −0.206613
\(369\) 1.36824 0.0712278
\(370\) 22.2034 1.15430
\(371\) 10.7349 0.557328
\(372\) 1.98335 0.102832
\(373\) 16.1901 0.838291 0.419146 0.907919i \(-0.362330\pi\)
0.419146 + 0.907919i \(0.362330\pi\)
\(374\) 2.53420 0.131040
\(375\) −21.6008 −1.11546
\(376\) 66.9984 3.45518
\(377\) −43.1471 −2.22219
\(378\) 12.2898 0.632121
\(379\) 24.9685 1.28254 0.641272 0.767313i \(-0.278407\pi\)
0.641272 + 0.767313i \(0.278407\pi\)
\(380\) −49.2177 −2.52482
\(381\) −31.1484 −1.59578
\(382\) −32.9147 −1.68406
\(383\) 16.9048 0.863793 0.431896 0.901923i \(-0.357845\pi\)
0.431896 + 0.901923i \(0.357845\pi\)
\(384\) −23.9591 −1.22266
\(385\) −1.55959 −0.0794842
\(386\) −16.0264 −0.815724
\(387\) 0.348383 0.0177093
\(388\) 45.9562 2.33307
\(389\) 20.3241 1.03047 0.515237 0.857048i \(-0.327704\pi\)
0.515237 + 0.857048i \(0.327704\pi\)
\(390\) −44.6134 −2.25909
\(391\) −0.590579 −0.0298669
\(392\) 36.8359 1.86049
\(393\) −10.7795 −0.543756
\(394\) 2.61483 0.131733
\(395\) −4.67843 −0.235397
\(396\) −1.54061 −0.0774184
\(397\) 31.1292 1.56233 0.781164 0.624326i \(-0.214626\pi\)
0.781164 + 0.624326i \(0.214626\pi\)
\(398\) 56.7842 2.84634
\(399\) 13.0451 0.653069
\(400\) −17.2155 −0.860776
\(401\) 32.6496 1.63045 0.815223 0.579148i \(-0.196615\pi\)
0.815223 + 0.579148i \(0.196615\pi\)
\(402\) −52.9201 −2.63942
\(403\) −1.51119 −0.0752778
\(404\) −38.7142 −1.92610
\(405\) 15.4850 0.769456
\(406\) −17.7254 −0.879698
\(407\) −5.61492 −0.278321
\(408\) 11.2322 0.556075
\(409\) 26.7380 1.32211 0.661055 0.750338i \(-0.270109\pi\)
0.661055 + 0.750338i \(0.270109\pi\)
\(410\) 15.5304 0.766990
\(411\) −21.2618 −1.04876
\(412\) −41.1475 −2.02719
\(413\) 0.227947 0.0112165
\(414\) 0.521406 0.0256257
\(415\) −5.19437 −0.254982
\(416\) −29.1701 −1.43018
\(417\) 25.4005 1.24387
\(418\) 18.0756 0.884106
\(419\) −37.8247 −1.84786 −0.923928 0.382565i \(-0.875041\pi\)
−0.923928 + 0.382565i \(0.875041\pi\)
\(420\) −12.6201 −0.615800
\(421\) −17.2477 −0.840601 −0.420300 0.907385i \(-0.638075\pi\)
−0.420300 + 0.907385i \(0.638075\pi\)
\(422\) 34.3033 1.66986
\(423\) −3.80255 −0.184886
\(424\) 65.9276 3.20173
\(425\) −2.56517 −0.124429
\(426\) −22.9547 −1.11216
\(427\) −5.23319 −0.253252
\(428\) 37.2063 1.79843
\(429\) 11.2821 0.544705
\(430\) 3.95435 0.190696
\(431\) −23.0283 −1.10924 −0.554618 0.832105i \(-0.687136\pi\)
−0.554618 + 0.832105i \(0.687136\pi\)
\(432\) 32.5636 1.56672
\(433\) 20.8049 0.999821 0.499910 0.866077i \(-0.333366\pi\)
0.499910 + 0.866077i \(0.333366\pi\)
\(434\) −0.620818 −0.0298002
\(435\) −19.9816 −0.958046
\(436\) 17.1156 0.819690
\(437\) −4.21240 −0.201507
\(438\) 2.10842 0.100744
\(439\) −14.1932 −0.677406 −0.338703 0.940893i \(-0.609988\pi\)
−0.338703 + 0.940893i \(0.609988\pi\)
\(440\) −9.57812 −0.456619
\(441\) −2.09065 −0.0995549
\(442\) −15.6248 −0.743194
\(443\) 6.66269 0.316554 0.158277 0.987395i \(-0.449406\pi\)
0.158277 + 0.987395i \(0.449406\pi\)
\(444\) −45.4357 −2.15628
\(445\) −10.4015 −0.493078
\(446\) 21.6316 1.02429
\(447\) 14.1664 0.670047
\(448\) 1.43213 0.0676616
\(449\) −40.6818 −1.91989 −0.959946 0.280187i \(-0.909604\pi\)
−0.959946 + 0.280187i \(0.909604\pi\)
\(450\) 2.26471 0.106760
\(451\) −3.92741 −0.184935
\(452\) 49.4329 2.32513
\(453\) 4.05980 0.190746
\(454\) −56.4682 −2.65018
\(455\) 9.61577 0.450794
\(456\) 80.1152 3.75174
\(457\) −25.9993 −1.21620 −0.608098 0.793862i \(-0.708067\pi\)
−0.608098 + 0.793862i \(0.708067\pi\)
\(458\) 51.7768 2.41937
\(459\) 4.85209 0.226476
\(460\) 4.07520 0.190007
\(461\) −29.3223 −1.36568 −0.682838 0.730570i \(-0.739254\pi\)
−0.682838 + 0.730570i \(0.739254\pi\)
\(462\) 4.63485 0.215633
\(463\) 20.1021 0.934222 0.467111 0.884199i \(-0.345295\pi\)
0.467111 + 0.884199i \(0.345295\pi\)
\(464\) −46.9659 −2.18034
\(465\) −0.699840 −0.0324543
\(466\) −39.1756 −1.81477
\(467\) 24.6721 1.14169 0.570845 0.821058i \(-0.306616\pi\)
0.570845 + 0.821058i \(0.306616\pi\)
\(468\) 9.49871 0.439078
\(469\) 11.4062 0.526687
\(470\) −43.1613 −1.99088
\(471\) 41.3590 1.90572
\(472\) 1.39992 0.0644364
\(473\) −1.00000 −0.0459800
\(474\) 13.9035 0.638608
\(475\) −18.2965 −0.839500
\(476\) −4.41990 −0.202586
\(477\) −3.74177 −0.171324
\(478\) 18.8330 0.861402
\(479\) −27.5992 −1.26104 −0.630519 0.776174i \(-0.717158\pi\)
−0.630519 + 0.776174i \(0.717158\pi\)
\(480\) −13.5088 −0.616591
\(481\) 34.6192 1.57850
\(482\) −50.3430 −2.29306
\(483\) −1.08012 −0.0491472
\(484\) 4.42217 0.201008
\(485\) −16.2160 −0.736330
\(486\) −9.13035 −0.414161
\(487\) 5.59841 0.253688 0.126844 0.991923i \(-0.459515\pi\)
0.126844 + 0.991923i \(0.459515\pi\)
\(488\) −32.1392 −1.45487
\(489\) −26.7265 −1.20861
\(490\) −23.7302 −1.07202
\(491\) −4.77195 −0.215355 −0.107678 0.994186i \(-0.534341\pi\)
−0.107678 + 0.994186i \(0.534341\pi\)
\(492\) −31.7804 −1.43277
\(493\) −6.99808 −0.315178
\(494\) −111.446 −5.01420
\(495\) 0.543614 0.0244336
\(496\) −1.64494 −0.0738601
\(497\) 4.94755 0.221928
\(498\) 15.4368 0.691739
\(499\) −14.3057 −0.640413 −0.320206 0.947348i \(-0.603752\pi\)
−0.320206 + 0.947348i \(0.603752\pi\)
\(500\) 52.2022 2.33455
\(501\) 10.9919 0.491083
\(502\) 77.2209 3.44654
\(503\) −0.201806 −0.00899810 −0.00449905 0.999990i \(-0.501432\pi\)
−0.00449905 + 0.999990i \(0.501432\pi\)
\(504\) 2.13737 0.0952059
\(505\) 13.6606 0.607888
\(506\) −1.49665 −0.0665341
\(507\) −45.7724 −2.03282
\(508\) 75.2756 3.33982
\(509\) 21.5438 0.954910 0.477455 0.878656i \(-0.341559\pi\)
0.477455 + 0.878656i \(0.341559\pi\)
\(510\) −7.23591 −0.320411
\(511\) −0.454439 −0.0201032
\(512\) 50.6391 2.23795
\(513\) 34.6083 1.52799
\(514\) −55.0236 −2.42699
\(515\) 14.5192 0.639793
\(516\) −8.09195 −0.356228
\(517\) 10.9149 0.480036
\(518\) 14.2220 0.624880
\(519\) 45.5151 1.99789
\(520\) 59.0545 2.58971
\(521\) 27.2057 1.19190 0.595952 0.803020i \(-0.296775\pi\)
0.595952 + 0.803020i \(0.296775\pi\)
\(522\) 6.17840 0.270421
\(523\) −10.7506 −0.470089 −0.235044 0.971985i \(-0.575524\pi\)
−0.235044 + 0.971985i \(0.575524\pi\)
\(524\) 26.0507 1.13803
\(525\) −4.69148 −0.204753
\(526\) 46.1566 2.01252
\(527\) −0.245102 −0.0106768
\(528\) 12.2807 0.534447
\(529\) −22.6512 −0.984835
\(530\) −42.4714 −1.84484
\(531\) −0.0794535 −0.00344799
\(532\) −31.5256 −1.36681
\(533\) 24.2147 1.04885
\(534\) 30.9114 1.33767
\(535\) −13.1285 −0.567595
\(536\) 70.0500 3.02570
\(537\) −27.0294 −1.16641
\(538\) −16.4146 −0.707685
\(539\) 6.00103 0.258483
\(540\) −33.4810 −1.44079
\(541\) 21.0234 0.903865 0.451933 0.892052i \(-0.350735\pi\)
0.451933 + 0.892052i \(0.350735\pi\)
\(542\) −56.6933 −2.43518
\(543\) 20.7894 0.892159
\(544\) −4.73114 −0.202846
\(545\) −6.03937 −0.258698
\(546\) −28.5764 −1.22296
\(547\) −25.3715 −1.08481 −0.542404 0.840118i \(-0.682486\pi\)
−0.542404 + 0.840118i \(0.682486\pi\)
\(548\) 51.3827 2.19496
\(549\) 1.82409 0.0778502
\(550\) −6.50065 −0.277189
\(551\) −49.9149 −2.12645
\(552\) −6.63349 −0.282340
\(553\) −2.99669 −0.127432
\(554\) 64.9067 2.75762
\(555\) 16.0323 0.680533
\(556\) −61.3847 −2.60329
\(557\) −29.5235 −1.25095 −0.625476 0.780243i \(-0.715095\pi\)
−0.625476 + 0.780243i \(0.715095\pi\)
\(558\) 0.216393 0.00916066
\(559\) 6.16556 0.260775
\(560\) 10.4668 0.442305
\(561\) 1.82986 0.0772567
\(562\) 14.9693 0.631441
\(563\) −24.5612 −1.03513 −0.517565 0.855644i \(-0.673161\pi\)
−0.517565 + 0.855644i \(0.673161\pi\)
\(564\) 88.3226 3.71905
\(565\) −17.4427 −0.733822
\(566\) −48.7201 −2.04786
\(567\) 9.91868 0.416545
\(568\) 30.3850 1.27493
\(569\) 39.2346 1.64480 0.822399 0.568911i \(-0.192635\pi\)
0.822399 + 0.568911i \(0.192635\pi\)
\(570\) −51.6113 −2.16176
\(571\) −11.8389 −0.495444 −0.247722 0.968831i \(-0.579682\pi\)
−0.247722 + 0.968831i \(0.579682\pi\)
\(572\) −27.2652 −1.14001
\(573\) −23.7665 −0.992861
\(574\) 9.94774 0.415210
\(575\) 1.51494 0.0631772
\(576\) −0.499184 −0.0207994
\(577\) −7.16119 −0.298124 −0.149062 0.988828i \(-0.547625\pi\)
−0.149062 + 0.988828i \(0.547625\pi\)
\(578\) −2.53420 −0.105409
\(579\) −11.5721 −0.480921
\(580\) 48.2891 2.00510
\(581\) −3.32717 −0.138034
\(582\) 48.1911 1.99759
\(583\) 10.7404 0.444823
\(584\) −2.79090 −0.115488
\(585\) −3.35169 −0.138575
\(586\) −60.3494 −2.49301
\(587\) −33.1945 −1.37008 −0.685042 0.728504i \(-0.740216\pi\)
−0.685042 + 0.728504i \(0.740216\pi\)
\(588\) 48.5600 2.00258
\(589\) −1.74823 −0.0720345
\(590\) −0.901845 −0.0371284
\(591\) 1.88807 0.0776650
\(592\) 37.6832 1.54877
\(593\) −39.1547 −1.60789 −0.803945 0.594703i \(-0.797270\pi\)
−0.803945 + 0.594703i \(0.797270\pi\)
\(594\) 12.2962 0.504517
\(595\) 1.55959 0.0639371
\(596\) −34.2355 −1.40234
\(597\) 41.0019 1.67810
\(598\) 9.22767 0.377347
\(599\) −21.9570 −0.897137 −0.448568 0.893748i \(-0.648066\pi\)
−0.448568 + 0.893748i \(0.648066\pi\)
\(600\) −28.8124 −1.17626
\(601\) −41.3225 −1.68558 −0.842790 0.538242i \(-0.819089\pi\)
−0.842790 + 0.538242i \(0.819089\pi\)
\(602\) 2.53290 0.103233
\(603\) −3.97575 −0.161905
\(604\) −9.81120 −0.399212
\(605\) −1.56039 −0.0634391
\(606\) −40.5969 −1.64914
\(607\) −5.14936 −0.209006 −0.104503 0.994525i \(-0.533325\pi\)
−0.104503 + 0.994525i \(0.533325\pi\)
\(608\) −33.7456 −1.36857
\(609\) −12.7989 −0.518638
\(610\) 20.7045 0.838301
\(611\) −67.2963 −2.72252
\(612\) 1.54061 0.0622754
\(613\) −13.9140 −0.561981 −0.280991 0.959711i \(-0.590663\pi\)
−0.280991 + 0.959711i \(0.590663\pi\)
\(614\) −48.9969 −1.97735
\(615\) 11.2139 0.452190
\(616\) −6.13512 −0.247191
\(617\) −46.3163 −1.86462 −0.932312 0.361655i \(-0.882212\pi\)
−0.932312 + 0.361655i \(0.882212\pi\)
\(618\) −43.1486 −1.73569
\(619\) 31.7634 1.27668 0.638339 0.769755i \(-0.279622\pi\)
0.638339 + 0.769755i \(0.279622\pi\)
\(620\) 1.69128 0.0679236
\(621\) −2.86554 −0.114990
\(622\) 48.7469 1.95457
\(623\) −6.66251 −0.266928
\(624\) −75.7171 −3.03111
\(625\) −5.59407 −0.223763
\(626\) −29.1073 −1.16336
\(627\) 13.0518 0.521237
\(628\) −99.9512 −3.98849
\(629\) 5.61492 0.223882
\(630\) −1.37692 −0.0548578
\(631\) −42.3794 −1.68710 −0.843550 0.537051i \(-0.819538\pi\)
−0.843550 + 0.537051i \(0.819538\pi\)
\(632\) −18.4040 −0.732070
\(633\) 24.7692 0.984487
\(634\) 19.0326 0.755883
\(635\) −26.5615 −1.05406
\(636\) 86.9109 3.44624
\(637\) −36.9997 −1.46598
\(638\) −17.7345 −0.702117
\(639\) −1.72453 −0.0682212
\(640\) −20.4309 −0.807604
\(641\) −10.5519 −0.416775 −0.208388 0.978046i \(-0.566822\pi\)
−0.208388 + 0.978046i \(0.566822\pi\)
\(642\) 39.0157 1.53983
\(643\) −36.8441 −1.45299 −0.726495 0.687171i \(-0.758852\pi\)
−0.726495 + 0.687171i \(0.758852\pi\)
\(644\) 2.61030 0.102860
\(645\) 2.85530 0.112427
\(646\) −18.0756 −0.711174
\(647\) −48.5244 −1.90769 −0.953845 0.300300i \(-0.902913\pi\)
−0.953845 + 0.300300i \(0.902913\pi\)
\(648\) 60.9148 2.39296
\(649\) 0.228064 0.00895229
\(650\) 40.0802 1.57207
\(651\) −0.448271 −0.0175691
\(652\) 64.5893 2.52951
\(653\) 47.8464 1.87237 0.936187 0.351502i \(-0.114329\pi\)
0.936187 + 0.351502i \(0.114329\pi\)
\(654\) 17.9480 0.701822
\(655\) −9.19216 −0.359167
\(656\) 26.3579 1.02910
\(657\) 0.158400 0.00617977
\(658\) −27.6463 −1.07776
\(659\) −2.81094 −0.109499 −0.0547494 0.998500i \(-0.517436\pi\)
−0.0547494 + 0.998500i \(0.517436\pi\)
\(660\) −12.6266 −0.491491
\(661\) 13.4126 0.521690 0.260845 0.965381i \(-0.415999\pi\)
0.260845 + 0.965381i \(0.415999\pi\)
\(662\) 66.3082 2.57714
\(663\) −11.2821 −0.438161
\(664\) −20.4336 −0.792976
\(665\) 11.1240 0.431372
\(666\) −4.95725 −0.192090
\(667\) 4.13292 0.160027
\(668\) −26.5639 −1.02779
\(669\) 15.6195 0.603883
\(670\) −45.1271 −1.74341
\(671\) −5.23588 −0.202129
\(672\) −8.65287 −0.333792
\(673\) 22.3841 0.862845 0.431423 0.902150i \(-0.358012\pi\)
0.431423 + 0.902150i \(0.358012\pi\)
\(674\) −8.76176 −0.337490
\(675\) −12.4464 −0.479063
\(676\) 110.617 4.25449
\(677\) 30.3551 1.16664 0.583321 0.812242i \(-0.301753\pi\)
0.583321 + 0.812242i \(0.301753\pi\)
\(678\) 51.8369 1.99078
\(679\) −10.3869 −0.398612
\(680\) 9.57812 0.367304
\(681\) −40.7737 −1.56245
\(682\) −0.621137 −0.0237846
\(683\) −9.77309 −0.373957 −0.186978 0.982364i \(-0.559869\pi\)
−0.186978 + 0.982364i \(0.559869\pi\)
\(684\) 10.9886 0.420161
\(685\) −18.1308 −0.692741
\(686\) −32.9303 −1.25728
\(687\) 37.3862 1.42637
\(688\) 6.71126 0.255864
\(689\) −66.2207 −2.52281
\(690\) 4.27338 0.162685
\(691\) −29.9971 −1.14114 −0.570572 0.821248i \(-0.693278\pi\)
−0.570572 + 0.821248i \(0.693278\pi\)
\(692\) −109.995 −4.18139
\(693\) 0.348204 0.0132272
\(694\) −66.6713 −2.53081
\(695\) 21.6600 0.821611
\(696\) −78.6036 −2.97946
\(697\) 3.92741 0.148761
\(698\) 32.8163 1.24212
\(699\) −28.2873 −1.06993
\(700\) 11.3378 0.428528
\(701\) −6.96038 −0.262890 −0.131445 0.991323i \(-0.541962\pi\)
−0.131445 + 0.991323i \(0.541962\pi\)
\(702\) −75.8127 −2.86137
\(703\) 40.0493 1.51049
\(704\) 1.43286 0.0540031
\(705\) −31.1653 −1.17375
\(706\) −11.4478 −0.430845
\(707\) 8.75007 0.329080
\(708\) 1.84548 0.0693574
\(709\) −20.7004 −0.777419 −0.388710 0.921360i \(-0.627079\pi\)
−0.388710 + 0.921360i \(0.627079\pi\)
\(710\) −19.5744 −0.734615
\(711\) 1.04453 0.0391730
\(712\) −40.9173 −1.53344
\(713\) 0.144752 0.00542101
\(714\) −4.63485 −0.173455
\(715\) 9.62071 0.359794
\(716\) 65.3213 2.44117
\(717\) 13.5987 0.507852
\(718\) −41.4420 −1.54660
\(719\) 7.51047 0.280093 0.140047 0.990145i \(-0.455275\pi\)
0.140047 + 0.990145i \(0.455275\pi\)
\(720\) −3.64834 −0.135965
\(721\) 9.30005 0.346352
\(722\) −80.7772 −3.00622
\(723\) −36.3510 −1.35191
\(724\) −50.2413 −1.86720
\(725\) 17.9513 0.666693
\(726\) 4.63723 0.172104
\(727\) −24.7367 −0.917433 −0.458716 0.888583i \(-0.651691\pi\)
−0.458716 + 0.888583i \(0.651691\pi\)
\(728\) 37.8264 1.40194
\(729\) 23.1786 0.858467
\(730\) 1.79794 0.0665446
\(731\) 1.00000 0.0369863
\(732\) −42.3685 −1.56598
\(733\) −19.0462 −0.703488 −0.351744 0.936096i \(-0.614411\pi\)
−0.351744 + 0.936096i \(0.614411\pi\)
\(734\) −40.1741 −1.48285
\(735\) −17.1347 −0.632025
\(736\) 2.79411 0.102992
\(737\) 11.4120 0.420367
\(738\) −3.46740 −0.127637
\(739\) 11.2024 0.412088 0.206044 0.978543i \(-0.433941\pi\)
0.206044 + 0.978543i \(0.433941\pi\)
\(740\) −38.7448 −1.42429
\(741\) −80.4714 −2.95619
\(742\) −27.2044 −0.998705
\(743\) 1.75684 0.0644520 0.0322260 0.999481i \(-0.489740\pi\)
0.0322260 + 0.999481i \(0.489740\pi\)
\(744\) −2.75302 −0.100931
\(745\) 12.0803 0.442586
\(746\) −41.0289 −1.50218
\(747\) 1.15972 0.0424321
\(748\) −4.42217 −0.161691
\(749\) −8.40926 −0.307268
\(750\) 54.7409 1.99885
\(751\) 9.29772 0.339279 0.169639 0.985506i \(-0.445740\pi\)
0.169639 + 0.985506i \(0.445740\pi\)
\(752\) −73.2526 −2.67125
\(753\) 55.7585 2.03195
\(754\) 109.343 3.98205
\(755\) 3.46195 0.125993
\(756\) −21.4457 −0.779974
\(757\) −5.01203 −0.182165 −0.0910826 0.995843i \(-0.529033\pi\)
−0.0910826 + 0.995843i \(0.529033\pi\)
\(758\) −63.2751 −2.29826
\(759\) −1.08068 −0.0392261
\(760\) 68.3175 2.47814
\(761\) −23.9912 −0.869681 −0.434840 0.900508i \(-0.643195\pi\)
−0.434840 + 0.900508i \(0.643195\pi\)
\(762\) 78.9364 2.85956
\(763\) −3.86842 −0.140046
\(764\) 57.4360 2.07796
\(765\) −0.543614 −0.0196544
\(766\) −42.8400 −1.54787
\(767\) −1.40614 −0.0507728
\(768\) 55.4734 2.00172
\(769\) 16.0113 0.577381 0.288690 0.957423i \(-0.406780\pi\)
0.288690 + 0.957423i \(0.406780\pi\)
\(770\) 3.95232 0.142432
\(771\) −39.7306 −1.43086
\(772\) 27.9661 1.00652
\(773\) 20.5736 0.739980 0.369990 0.929036i \(-0.379361\pi\)
0.369990 + 0.929036i \(0.379361\pi\)
\(774\) −0.882871 −0.0317341
\(775\) 0.628727 0.0225846
\(776\) −63.7903 −2.28994
\(777\) 10.2692 0.368407
\(778\) −51.5054 −1.84656
\(779\) 28.0129 1.00367
\(780\) 77.8503 2.78749
\(781\) 4.95010 0.177128
\(782\) 1.49665 0.0535200
\(783\) −33.9553 −1.21346
\(784\) −40.2745 −1.43837
\(785\) 35.2685 1.25879
\(786\) 27.3175 0.974384
\(787\) −4.00865 −0.142893 −0.0714465 0.997444i \(-0.522762\pi\)
−0.0714465 + 0.997444i \(0.522762\pi\)
\(788\) −4.56286 −0.162545
\(789\) 33.3281 1.18651
\(790\) 11.8561 0.421820
\(791\) −11.1727 −0.397255
\(792\) 2.13847 0.0759871
\(793\) 32.2821 1.14637
\(794\) −78.8875 −2.79961
\(795\) −30.6671 −1.08765
\(796\) −99.0883 −3.51209
\(797\) 47.1126 1.66882 0.834408 0.551148i \(-0.185810\pi\)
0.834408 + 0.551148i \(0.185810\pi\)
\(798\) −33.0588 −1.17027
\(799\) −10.9149 −0.386141
\(800\) 12.1362 0.429078
\(801\) 2.32229 0.0820542
\(802\) −82.7407 −2.92168
\(803\) −0.454673 −0.0160450
\(804\) 92.3454 3.25677
\(805\) −0.921064 −0.0324632
\(806\) 3.82966 0.134894
\(807\) −11.8524 −0.417226
\(808\) 53.7379 1.89049
\(809\) −8.95830 −0.314957 −0.157479 0.987522i \(-0.550337\pi\)
−0.157479 + 0.987522i \(0.550337\pi\)
\(810\) −39.2421 −1.37883
\(811\) 10.5605 0.370831 0.185415 0.982660i \(-0.440637\pi\)
0.185415 + 0.982660i \(0.440637\pi\)
\(812\) 30.9308 1.08546
\(813\) −40.9363 −1.43570
\(814\) 14.2293 0.498738
\(815\) −22.7908 −0.798326
\(816\) −12.2807 −0.429909
\(817\) 7.13266 0.249540
\(818\) −67.7595 −2.36915
\(819\) −2.14687 −0.0750177
\(820\) −27.1005 −0.946389
\(821\) −1.28468 −0.0448357 −0.0224178 0.999749i \(-0.507136\pi\)
−0.0224178 + 0.999749i \(0.507136\pi\)
\(822\) 53.8815 1.87933
\(823\) 36.8236 1.28359 0.641795 0.766876i \(-0.278190\pi\)
0.641795 + 0.766876i \(0.278190\pi\)
\(824\) 57.1155 1.98971
\(825\) −4.69390 −0.163420
\(826\) −0.577663 −0.0200995
\(827\) −4.95661 −0.172358 −0.0861791 0.996280i \(-0.527466\pi\)
−0.0861791 + 0.996280i \(0.527466\pi\)
\(828\) −0.909851 −0.0316195
\(829\) −52.0271 −1.80698 −0.903488 0.428613i \(-0.859002\pi\)
−0.903488 + 0.428613i \(0.859002\pi\)
\(830\) 13.1636 0.456914
\(831\) 46.8669 1.62579
\(832\) −8.83440 −0.306278
\(833\) −6.00103 −0.207923
\(834\) −64.3699 −2.22895
\(835\) 9.37327 0.324375
\(836\) −31.5418 −1.09090
\(837\) −1.18926 −0.0411067
\(838\) 95.8553 3.31127
\(839\) −37.4066 −1.29142 −0.645710 0.763583i \(-0.723438\pi\)
−0.645710 + 0.763583i \(0.723438\pi\)
\(840\) 17.5176 0.604415
\(841\) 19.9731 0.688728
\(842\) 43.7091 1.50631
\(843\) 10.8088 0.372275
\(844\) −59.8591 −2.06043
\(845\) −39.0319 −1.34274
\(846\) 9.63643 0.331307
\(847\) −0.999486 −0.0343428
\(848\) −72.0817 −2.47530
\(849\) −35.1791 −1.20734
\(850\) 6.50065 0.222970
\(851\) −3.31606 −0.113673
\(852\) 40.0559 1.37229
\(853\) 11.3056 0.387095 0.193548 0.981091i \(-0.438001\pi\)
0.193548 + 0.981091i \(0.438001\pi\)
\(854\) 13.2619 0.453814
\(855\) −3.87741 −0.132605
\(856\) −51.6448 −1.76518
\(857\) −13.5190 −0.461800 −0.230900 0.972978i \(-0.574167\pi\)
−0.230900 + 0.972978i \(0.574167\pi\)
\(858\) −28.5911 −0.976085
\(859\) −25.9491 −0.885370 −0.442685 0.896677i \(-0.645974\pi\)
−0.442685 + 0.896677i \(0.645974\pi\)
\(860\) −6.90033 −0.235299
\(861\) 7.18292 0.244793
\(862\) 58.3584 1.98770
\(863\) −9.25524 −0.315052 −0.157526 0.987515i \(-0.550352\pi\)
−0.157526 + 0.987515i \(0.550352\pi\)
\(864\) −22.9559 −0.780975
\(865\) 38.8126 1.31967
\(866\) −52.7238 −1.79163
\(867\) −1.82986 −0.0621453
\(868\) 1.08333 0.0367705
\(869\) −2.99823 −0.101708
\(870\) 50.6375 1.71677
\(871\) −70.3615 −2.38411
\(872\) −23.7576 −0.804535
\(873\) 3.62047 0.122534
\(874\) 10.6751 0.361090
\(875\) −11.7986 −0.398865
\(876\) −3.67919 −0.124308
\(877\) −1.10220 −0.0372188 −0.0186094 0.999827i \(-0.505924\pi\)
−0.0186094 + 0.999827i \(0.505924\pi\)
\(878\) 35.9685 1.21388
\(879\) −43.5762 −1.46979
\(880\) 10.4722 0.353018
\(881\) 43.0100 1.44904 0.724521 0.689252i \(-0.242061\pi\)
0.724521 + 0.689252i \(0.242061\pi\)
\(882\) 5.29813 0.178397
\(883\) 28.7762 0.968395 0.484198 0.874959i \(-0.339112\pi\)
0.484198 + 0.874959i \(0.339112\pi\)
\(884\) 27.2652 0.917027
\(885\) −0.651191 −0.0218895
\(886\) −16.8846 −0.567249
\(887\) 42.2820 1.41969 0.709845 0.704358i \(-0.248765\pi\)
0.709845 + 0.704358i \(0.248765\pi\)
\(888\) 63.0677 2.11642
\(889\) −17.0136 −0.570617
\(890\) 26.3594 0.883571
\(891\) 9.92378 0.332459
\(892\) −37.7472 −1.26387
\(893\) −77.8521 −2.60522
\(894\) −35.9005 −1.20069
\(895\) −23.0491 −0.770446
\(896\) −13.0867 −0.437197
\(897\) 6.66298 0.222470
\(898\) 103.096 3.44035
\(899\) 1.71524 0.0572065
\(900\) −3.95192 −0.131731
\(901\) −10.7404 −0.357815
\(902\) 9.95285 0.331394
\(903\) 1.82892 0.0608626
\(904\) −68.6161 −2.28214
\(905\) 17.7280 0.589298
\(906\) −10.2883 −0.341807
\(907\) 46.4361 1.54188 0.770942 0.636905i \(-0.219786\pi\)
0.770942 + 0.636905i \(0.219786\pi\)
\(908\) 98.5368 3.27006
\(909\) −3.04994 −0.101160
\(910\) −24.3683 −0.807801
\(911\) −14.8927 −0.493418 −0.246709 0.969090i \(-0.579349\pi\)
−0.246709 + 0.969090i \(0.579349\pi\)
\(912\) −87.5937 −2.90052
\(913\) −3.32888 −0.110170
\(914\) 65.8875 2.17936
\(915\) 14.9500 0.494232
\(916\) −90.3503 −2.98526
\(917\) −5.88789 −0.194435
\(918\) −12.2962 −0.405834
\(919\) −21.8544 −0.720909 −0.360454 0.932777i \(-0.617378\pi\)
−0.360454 + 0.932777i \(0.617378\pi\)
\(920\) −5.65664 −0.186494
\(921\) −35.3790 −1.16578
\(922\) 74.3086 2.44722
\(923\) −30.5201 −1.00458
\(924\) −8.08779 −0.266069
\(925\) −14.4032 −0.473575
\(926\) −50.9427 −1.67408
\(927\) −3.24164 −0.106469
\(928\) 33.1089 1.08685
\(929\) 26.5534 0.871188 0.435594 0.900143i \(-0.356538\pi\)
0.435594 + 0.900143i \(0.356538\pi\)
\(930\) 1.77353 0.0581565
\(931\) −42.8033 −1.40282
\(932\) 68.3613 2.23925
\(933\) 35.1984 1.15234
\(934\) −62.5241 −2.04585
\(935\) 1.56039 0.0510304
\(936\) −13.1848 −0.430960
\(937\) −48.4100 −1.58149 −0.790743 0.612148i \(-0.790306\pi\)
−0.790743 + 0.612148i \(0.790306\pi\)
\(938\) −28.9055 −0.943797
\(939\) −21.0174 −0.685876
\(940\) 75.3163 2.45655
\(941\) −3.82329 −0.124636 −0.0623178 0.998056i \(-0.519849\pi\)
−0.0623178 + 0.998056i \(0.519849\pi\)
\(942\) −104.812 −3.41496
\(943\) −2.31945 −0.0755316
\(944\) −1.53060 −0.0498166
\(945\) 7.56728 0.246164
\(946\) 2.53420 0.0823940
\(947\) 46.4013 1.50784 0.753920 0.656966i \(-0.228160\pi\)
0.753920 + 0.656966i \(0.228160\pi\)
\(948\) −24.2615 −0.787978
\(949\) 2.80331 0.0909994
\(950\) 46.3669 1.50434
\(951\) 13.7428 0.445641
\(952\) 6.13512 0.198840
\(953\) 11.7784 0.381540 0.190770 0.981635i \(-0.438901\pi\)
0.190770 + 0.981635i \(0.438901\pi\)
\(954\) 9.48241 0.307004
\(955\) −20.2667 −0.655815
\(956\) −32.8636 −1.06288
\(957\) −12.8055 −0.413943
\(958\) 69.9418 2.25972
\(959\) −11.6134 −0.375015
\(960\) −4.09126 −0.132045
\(961\) −30.9399 −0.998062
\(962\) −87.7319 −2.82859
\(963\) 2.93114 0.0944548
\(964\) 87.8484 2.82941
\(965\) −9.86802 −0.317663
\(966\) 2.73725 0.0880694
\(967\) 28.2883 0.909691 0.454846 0.890570i \(-0.349694\pi\)
0.454846 + 0.890570i \(0.349694\pi\)
\(968\) −6.13827 −0.197291
\(969\) −13.0518 −0.419283
\(970\) 41.0946 1.31947
\(971\) 18.6356 0.598044 0.299022 0.954246i \(-0.403340\pi\)
0.299022 + 0.954246i \(0.403340\pi\)
\(972\) 15.9324 0.511033
\(973\) 13.8740 0.444779
\(974\) −14.1875 −0.454597
\(975\) 28.9405 0.926838
\(976\) 35.1393 1.12478
\(977\) −43.2957 −1.38515 −0.692576 0.721345i \(-0.743524\pi\)
−0.692576 + 0.721345i \(0.743524\pi\)
\(978\) 67.7303 2.16578
\(979\) −6.66593 −0.213044
\(980\) 41.4091 1.32276
\(981\) 1.34838 0.0430506
\(982\) 12.0931 0.385906
\(983\) −16.0999 −0.513506 −0.256753 0.966477i \(-0.582653\pi\)
−0.256753 + 0.966477i \(0.582653\pi\)
\(984\) 44.1133 1.40628
\(985\) 1.61004 0.0513001
\(986\) 17.7345 0.564783
\(987\) −19.9624 −0.635411
\(988\) 194.473 6.18702
\(989\) −0.590579 −0.0187793
\(990\) −1.37763 −0.0437839
\(991\) 40.4822 1.28596 0.642980 0.765883i \(-0.277698\pi\)
0.642980 + 0.765883i \(0.277698\pi\)
\(992\) 1.15961 0.0368177
\(993\) 47.8788 1.51939
\(994\) −12.5381 −0.397684
\(995\) 34.9640 1.10843
\(996\) −26.9371 −0.853536
\(997\) 26.2912 0.832649 0.416325 0.909216i \(-0.363318\pi\)
0.416325 + 0.909216i \(0.363318\pi\)
\(998\) 36.2536 1.14759
\(999\) 27.2441 0.861965
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 \(a_p\))