Properties

Label 8041.2.a.i.1.16
Level 8041
Weight 2
Character 8041.1
Self dual Yes
Analytic conductor 64.208
Analytic rank 0
Dimension 78
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: \(0\)
Dimension: \(78\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) = 8041.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.80887 q^{2} +0.743622 q^{3} +1.27201 q^{4} +1.40249 q^{5} -1.34511 q^{6} -0.305829 q^{7} +1.31684 q^{8} -2.44703 q^{9} +O(q^{10})\) \(q-1.80887 q^{2} +0.743622 q^{3} +1.27201 q^{4} +1.40249 q^{5} -1.34511 q^{6} -0.305829 q^{7} +1.31684 q^{8} -2.44703 q^{9} -2.53691 q^{10} +1.00000 q^{11} +0.945892 q^{12} +4.42043 q^{13} +0.553205 q^{14} +1.04292 q^{15} -4.92601 q^{16} -1.00000 q^{17} +4.42635 q^{18} +7.16936 q^{19} +1.78397 q^{20} -0.227421 q^{21} -1.80887 q^{22} -6.56536 q^{23} +0.979235 q^{24} -3.03303 q^{25} -7.99597 q^{26} -4.05053 q^{27} -0.389016 q^{28} +7.88823 q^{29} -1.88650 q^{30} +3.50518 q^{31} +6.27682 q^{32} +0.743622 q^{33} +1.80887 q^{34} -0.428921 q^{35} -3.11263 q^{36} +4.24432 q^{37} -12.9684 q^{38} +3.28713 q^{39} +1.84686 q^{40} +10.7010 q^{41} +0.411375 q^{42} -1.00000 q^{43} +1.27201 q^{44} -3.43192 q^{45} +11.8759 q^{46} -4.24257 q^{47} -3.66309 q^{48} -6.90647 q^{49} +5.48636 q^{50} -0.743622 q^{51} +5.62281 q^{52} -7.25189 q^{53} +7.32688 q^{54} +1.40249 q^{55} -0.402729 q^{56} +5.33130 q^{57} -14.2688 q^{58} +12.2876 q^{59} +1.32660 q^{60} -10.1298 q^{61} -6.34042 q^{62} +0.748372 q^{63} -1.50192 q^{64} +6.19959 q^{65} -1.34511 q^{66} -9.17301 q^{67} -1.27201 q^{68} -4.88215 q^{69} +0.775862 q^{70} +11.7531 q^{71} -3.22235 q^{72} +1.47388 q^{73} -7.67741 q^{74} -2.25543 q^{75} +9.11947 q^{76} -0.305829 q^{77} -5.94598 q^{78} +16.0824 q^{79} -6.90866 q^{80} +4.32902 q^{81} -19.3568 q^{82} -7.13085 q^{83} -0.289281 q^{84} -1.40249 q^{85} +1.80887 q^{86} +5.86586 q^{87} +1.31684 q^{88} -5.01147 q^{89} +6.20789 q^{90} -1.35189 q^{91} -8.35118 q^{92} +2.60653 q^{93} +7.67425 q^{94} +10.0549 q^{95} +4.66758 q^{96} +15.7303 q^{97} +12.4929 q^{98} -2.44703 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 78q + 7q^{2} + 10q^{3} + 91q^{4} + 17q^{5} + 12q^{6} + 11q^{7} + 33q^{8} + 102q^{9} + O(q^{10}) \) \( 78q + 7q^{2} + 10q^{3} + 91q^{4} + 17q^{5} + 12q^{6} + 11q^{7} + 33q^{8} + 102q^{9} + 3q^{10} + 78q^{11} + 31q^{12} - 16q^{13} + 31q^{14} + 38q^{15} + 121q^{16} - 78q^{17} + 11q^{18} + 51q^{20} + 6q^{21} + 7q^{22} + 48q^{23} + 11q^{24} + 101q^{25} + 18q^{26} + 46q^{27} + 27q^{28} + 22q^{29} + 14q^{30} + 56q^{31} + 83q^{32} + 10q^{33} - 7q^{34} + 24q^{35} + 139q^{36} + 53q^{37} + 10q^{38} + 79q^{39} - q^{40} + 23q^{41} + 17q^{42} - 78q^{43} + 91q^{44} + 76q^{45} + 21q^{46} + 57q^{47} + 78q^{48} + 115q^{49} + 58q^{50} - 10q^{51} - 63q^{52} + 22q^{53} - 18q^{54} + 17q^{55} + 111q^{56} - 11q^{57} + 36q^{58} + 71q^{59} + 36q^{60} + 4q^{61} - 5q^{62} + 71q^{63} + 183q^{64} + 47q^{65} + 12q^{66} + 11q^{67} - 91q^{68} + 31q^{69} + 33q^{70} + 159q^{71} + 59q^{72} + 2q^{73} - 4q^{74} + 83q^{75} - 44q^{76} + 11q^{77} + 101q^{78} + 35q^{79} + 85q^{80} + 170q^{81} + 98q^{82} - 32q^{83} + 44q^{84} - 17q^{85} - 7q^{86} - 6q^{87} + 33q^{88} + 50q^{89} - 5q^{90} + 86q^{91} + 106q^{92} + 68q^{93} - q^{94} + 109q^{95} - 50q^{96} + 40q^{97} + 106q^{98} + 102q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.80887 −1.27906 −0.639532 0.768765i \(-0.720872\pi\)
−0.639532 + 0.768765i \(0.720872\pi\)
\(3\) 0.743622 0.429330 0.214665 0.976688i \(-0.431134\pi\)
0.214665 + 0.976688i \(0.431134\pi\)
\(4\) 1.27201 0.636003
\(5\) 1.40249 0.627211 0.313605 0.949553i \(-0.398463\pi\)
0.313605 + 0.949553i \(0.398463\pi\)
\(6\) −1.34511 −0.549141
\(7\) −0.305829 −0.115593 −0.0577963 0.998328i \(-0.518407\pi\)
−0.0577963 + 0.998328i \(0.518407\pi\)
\(8\) 1.31684 0.465575
\(9\) −2.44703 −0.815675
\(10\) −2.53691 −0.802242
\(11\) 1.00000 0.301511
\(12\) 0.945892 0.273055
\(13\) 4.42043 1.22601 0.613003 0.790081i \(-0.289961\pi\)
0.613003 + 0.790081i \(0.289961\pi\)
\(14\) 0.553205 0.147850
\(15\) 1.04292 0.269281
\(16\) −4.92601 −1.23150
\(17\) −1.00000 −0.242536
\(18\) 4.42635 1.04330
\(19\) 7.16936 1.64476 0.822382 0.568935i \(-0.192645\pi\)
0.822382 + 0.568935i \(0.192645\pi\)
\(20\) 1.78397 0.398908
\(21\) −0.227421 −0.0496274
\(22\) −1.80887 −0.385652
\(23\) −6.56536 −1.36897 −0.684486 0.729026i \(-0.739973\pi\)
−0.684486 + 0.729026i \(0.739973\pi\)
\(24\) 0.979235 0.199885
\(25\) −3.03303 −0.606607
\(26\) −7.99597 −1.56814
\(27\) −4.05053 −0.779525
\(28\) −0.389016 −0.0735172
\(29\) 7.88823 1.46481 0.732404 0.680870i \(-0.238398\pi\)
0.732404 + 0.680870i \(0.238398\pi\)
\(30\) −1.88650 −0.344427
\(31\) 3.50518 0.629550 0.314775 0.949166i \(-0.398071\pi\)
0.314775 + 0.949166i \(0.398071\pi\)
\(32\) 6.27682 1.10960
\(33\) 0.743622 0.129448
\(34\) 1.80887 0.310218
\(35\) −0.428921 −0.0725009
\(36\) −3.11263 −0.518772
\(37\) 4.24432 0.697761 0.348881 0.937167i \(-0.386562\pi\)
0.348881 + 0.937167i \(0.386562\pi\)
\(38\) −12.9684 −2.10376
\(39\) 3.28713 0.526362
\(40\) 1.84686 0.292014
\(41\) 10.7010 1.67122 0.835610 0.549323i \(-0.185114\pi\)
0.835610 + 0.549323i \(0.185114\pi\)
\(42\) 0.411375 0.0634766
\(43\) −1.00000 −0.152499
\(44\) 1.27201 0.191762
\(45\) −3.43192 −0.511600
\(46\) 11.8759 1.75100
\(47\) −4.24257 −0.618842 −0.309421 0.950925i \(-0.600135\pi\)
−0.309421 + 0.950925i \(0.600135\pi\)
\(48\) −3.66309 −0.528722
\(49\) −6.90647 −0.986638
\(50\) 5.48636 0.775888
\(51\) −0.743622 −0.104128
\(52\) 5.62281 0.779744
\(53\) −7.25189 −0.996124 −0.498062 0.867142i \(-0.665955\pi\)
−0.498062 + 0.867142i \(0.665955\pi\)
\(54\) 7.32688 0.997061
\(55\) 1.40249 0.189111
\(56\) −0.402729 −0.0538170
\(57\) 5.33130 0.706147
\(58\) −14.2688 −1.87358
\(59\) 12.2876 1.59971 0.799857 0.600191i \(-0.204909\pi\)
0.799857 + 0.600191i \(0.204909\pi\)
\(60\) 1.32660 0.171263
\(61\) −10.1298 −1.29699 −0.648495 0.761219i \(-0.724601\pi\)
−0.648495 + 0.761219i \(0.724601\pi\)
\(62\) −6.34042 −0.805234
\(63\) 0.748372 0.0942860
\(64\) −1.50192 −0.187740
\(65\) 6.19959 0.768964
\(66\) −1.34511 −0.165572
\(67\) −9.17301 −1.12066 −0.560331 0.828269i \(-0.689326\pi\)
−0.560331 + 0.828269i \(0.689326\pi\)
\(68\) −1.27201 −0.154253
\(69\) −4.88215 −0.587742
\(70\) 0.775862 0.0927332
\(71\) 11.7531 1.39484 0.697418 0.716665i \(-0.254332\pi\)
0.697418 + 0.716665i \(0.254332\pi\)
\(72\) −3.22235 −0.379758
\(73\) 1.47388 0.172505 0.0862525 0.996273i \(-0.472511\pi\)
0.0862525 + 0.996273i \(0.472511\pi\)
\(74\) −7.67741 −0.892481
\(75\) −2.25543 −0.260435
\(76\) 9.11947 1.04608
\(77\) −0.305829 −0.0348525
\(78\) −5.94598 −0.673250
\(79\) 16.0824 1.80941 0.904705 0.426039i \(-0.140092\pi\)
0.904705 + 0.426039i \(0.140092\pi\)
\(80\) −6.90866 −0.772412
\(81\) 4.32902 0.481002
\(82\) −19.3568 −2.13760
\(83\) −7.13085 −0.782713 −0.391356 0.920239i \(-0.627994\pi\)
−0.391356 + 0.920239i \(0.627994\pi\)
\(84\) −0.289281 −0.0315632
\(85\) −1.40249 −0.152121
\(86\) 1.80887 0.195055
\(87\) 5.86586 0.628887
\(88\) 1.31684 0.140376
\(89\) −5.01147 −0.531214 −0.265607 0.964081i \(-0.585572\pi\)
−0.265607 + 0.964081i \(0.585572\pi\)
\(90\) 6.20789 0.654369
\(91\) −1.35189 −0.141717
\(92\) −8.35118 −0.870671
\(93\) 2.60653 0.270285
\(94\) 7.67425 0.791539
\(95\) 10.0549 1.03161
\(96\) 4.66758 0.476383
\(97\) 15.7303 1.59717 0.798584 0.601883i \(-0.205583\pi\)
0.798584 + 0.601883i \(0.205583\pi\)
\(98\) 12.4929 1.26197
\(99\) −2.44703 −0.245935
\(100\) −3.85804 −0.385804
\(101\) 13.8189 1.37503 0.687515 0.726170i \(-0.258702\pi\)
0.687515 + 0.726170i \(0.258702\pi\)
\(102\) 1.34511 0.133186
\(103\) 0.963089 0.0948959 0.0474480 0.998874i \(-0.484891\pi\)
0.0474480 + 0.998874i \(0.484891\pi\)
\(104\) 5.82102 0.570798
\(105\) −0.318955 −0.0311268
\(106\) 13.1177 1.27411
\(107\) −2.59418 −0.250789 −0.125394 0.992107i \(-0.540020\pi\)
−0.125394 + 0.992107i \(0.540020\pi\)
\(108\) −5.15230 −0.495780
\(109\) −9.46450 −0.906535 −0.453267 0.891375i \(-0.649742\pi\)
−0.453267 + 0.891375i \(0.649742\pi\)
\(110\) −2.53691 −0.241885
\(111\) 3.15617 0.299570
\(112\) 1.50652 0.142353
\(113\) −1.88070 −0.176922 −0.0884608 0.996080i \(-0.528195\pi\)
−0.0884608 + 0.996080i \(0.528195\pi\)
\(114\) −9.64361 −0.903207
\(115\) −9.20783 −0.858634
\(116\) 10.0339 0.931622
\(117\) −10.8169 −1.00002
\(118\) −22.2267 −2.04614
\(119\) 0.305829 0.0280353
\(120\) 1.37336 0.125370
\(121\) 1.00000 0.0909091
\(122\) 18.3235 1.65893
\(123\) 7.95752 0.717505
\(124\) 4.45862 0.400396
\(125\) −11.2662 −1.00768
\(126\) −1.35371 −0.120598
\(127\) −13.9245 −1.23560 −0.617802 0.786334i \(-0.711977\pi\)
−0.617802 + 0.786334i \(0.711977\pi\)
\(128\) −9.83686 −0.869464
\(129\) −0.743622 −0.0654723
\(130\) −11.2142 −0.983554
\(131\) −4.81722 −0.420883 −0.210441 0.977606i \(-0.567490\pi\)
−0.210441 + 0.977606i \(0.567490\pi\)
\(132\) 0.945892 0.0823293
\(133\) −2.19260 −0.190122
\(134\) 16.5928 1.43340
\(135\) −5.68081 −0.488926
\(136\) −1.31684 −0.112919
\(137\) 11.0248 0.941915 0.470957 0.882156i \(-0.343909\pi\)
0.470957 + 0.882156i \(0.343909\pi\)
\(138\) 8.83117 0.751759
\(139\) 4.88667 0.414482 0.207241 0.978290i \(-0.433552\pi\)
0.207241 + 0.978290i \(0.433552\pi\)
\(140\) −0.545590 −0.0461108
\(141\) −3.15487 −0.265688
\(142\) −21.2598 −1.78408
\(143\) 4.42043 0.369655
\(144\) 12.0541 1.00451
\(145\) 11.0631 0.918743
\(146\) −2.66606 −0.220645
\(147\) −5.13580 −0.423594
\(148\) 5.39880 0.443778
\(149\) −4.66572 −0.382231 −0.191115 0.981568i \(-0.561210\pi\)
−0.191115 + 0.981568i \(0.561210\pi\)
\(150\) 4.07978 0.333112
\(151\) 23.3588 1.90091 0.950455 0.310861i \(-0.100617\pi\)
0.950455 + 0.310861i \(0.100617\pi\)
\(152\) 9.44094 0.765761
\(153\) 2.44703 0.197830
\(154\) 0.553205 0.0445785
\(155\) 4.91597 0.394860
\(156\) 4.18125 0.334768
\(157\) 1.96702 0.156986 0.0784928 0.996915i \(-0.474989\pi\)
0.0784928 + 0.996915i \(0.474989\pi\)
\(158\) −29.0909 −2.31435
\(159\) −5.39266 −0.427666
\(160\) 8.80315 0.695950
\(161\) 2.00788 0.158243
\(162\) −7.83062 −0.615232
\(163\) −7.61558 −0.596499 −0.298249 0.954488i \(-0.596403\pi\)
−0.298249 + 0.954488i \(0.596403\pi\)
\(164\) 13.6118 1.06290
\(165\) 1.04292 0.0811912
\(166\) 12.8988 1.00114
\(167\) −22.7161 −1.75783 −0.878914 0.476981i \(-0.841731\pi\)
−0.878914 + 0.476981i \(0.841731\pi\)
\(168\) −0.299478 −0.0231053
\(169\) 6.54017 0.503090
\(170\) 2.53691 0.194572
\(171\) −17.5436 −1.34159
\(172\) −1.27201 −0.0969896
\(173\) 12.6146 0.959069 0.479535 0.877523i \(-0.340805\pi\)
0.479535 + 0.877523i \(0.340805\pi\)
\(174\) −10.6106 −0.804386
\(175\) 0.927590 0.0701192
\(176\) −4.92601 −0.371312
\(177\) 9.13736 0.686806
\(178\) 9.06509 0.679457
\(179\) 15.2394 1.13904 0.569522 0.821976i \(-0.307128\pi\)
0.569522 + 0.821976i \(0.307128\pi\)
\(180\) −4.36542 −0.325379
\(181\) −12.0926 −0.898834 −0.449417 0.893322i \(-0.648368\pi\)
−0.449417 + 0.893322i \(0.648368\pi\)
\(182\) 2.44540 0.181265
\(183\) −7.53276 −0.556837
\(184\) −8.64556 −0.637359
\(185\) 5.95259 0.437643
\(186\) −4.71487 −0.345711
\(187\) −1.00000 −0.0731272
\(188\) −5.39658 −0.393586
\(189\) 1.23877 0.0901072
\(190\) −18.1880 −1.31950
\(191\) −3.49870 −0.253157 −0.126579 0.991957i \(-0.540400\pi\)
−0.126579 + 0.991957i \(0.540400\pi\)
\(192\) −1.11686 −0.0806025
\(193\) 4.07475 0.293307 0.146653 0.989188i \(-0.453150\pi\)
0.146653 + 0.989188i \(0.453150\pi\)
\(194\) −28.4540 −2.04288
\(195\) 4.61015 0.330140
\(196\) −8.78507 −0.627505
\(197\) −6.94473 −0.494792 −0.247396 0.968915i \(-0.579575\pi\)
−0.247396 + 0.968915i \(0.579575\pi\)
\(198\) 4.42635 0.314567
\(199\) −0.504890 −0.0357907 −0.0178953 0.999840i \(-0.505697\pi\)
−0.0178953 + 0.999840i \(0.505697\pi\)
\(200\) −3.99403 −0.282421
\(201\) −6.82125 −0.481134
\(202\) −24.9965 −1.75875
\(203\) −2.41245 −0.169321
\(204\) −0.945892 −0.0662257
\(205\) 15.0080 1.04821
\(206\) −1.74210 −0.121378
\(207\) 16.0656 1.11664
\(208\) −21.7751 −1.50983
\(209\) 7.16936 0.495915
\(210\) 0.576948 0.0398132
\(211\) −0.556900 −0.0383386 −0.0191693 0.999816i \(-0.506102\pi\)
−0.0191693 + 0.999816i \(0.506102\pi\)
\(212\) −9.22445 −0.633538
\(213\) 8.73986 0.598845
\(214\) 4.69253 0.320775
\(215\) −1.40249 −0.0956487
\(216\) −5.33392 −0.362927
\(217\) −1.07199 −0.0727712
\(218\) 17.1200 1.15952
\(219\) 1.09601 0.0740617
\(220\) 1.78397 0.120275
\(221\) −4.42043 −0.297350
\(222\) −5.70909 −0.383169
\(223\) −11.6748 −0.781806 −0.390903 0.920432i \(-0.627837\pi\)
−0.390903 + 0.920432i \(0.627837\pi\)
\(224\) −1.91963 −0.128261
\(225\) 7.42191 0.494794
\(226\) 3.40194 0.226294
\(227\) 9.52251 0.632031 0.316016 0.948754i \(-0.397655\pi\)
0.316016 + 0.948754i \(0.397655\pi\)
\(228\) 6.78144 0.449112
\(229\) 23.5348 1.55522 0.777610 0.628747i \(-0.216432\pi\)
0.777610 + 0.628747i \(0.216432\pi\)
\(230\) 16.6558 1.09825
\(231\) −0.227421 −0.0149632
\(232\) 10.3876 0.681978
\(233\) −22.9774 −1.50530 −0.752650 0.658421i \(-0.771225\pi\)
−0.752650 + 0.658421i \(0.771225\pi\)
\(234\) 19.5664 1.27909
\(235\) −5.95014 −0.388145
\(236\) 15.6299 1.01742
\(237\) 11.9592 0.776834
\(238\) −0.553205 −0.0358589
\(239\) 21.4075 1.38473 0.692367 0.721545i \(-0.256568\pi\)
0.692367 + 0.721545i \(0.256568\pi\)
\(240\) −5.13743 −0.331620
\(241\) −0.181928 −0.0117190 −0.00585952 0.999983i \(-0.501865\pi\)
−0.00585952 + 0.999983i \(0.501865\pi\)
\(242\) −1.80887 −0.116278
\(243\) 15.3707 0.986033
\(244\) −12.8852 −0.824890
\(245\) −9.68622 −0.618830
\(246\) −14.3941 −0.917735
\(247\) 31.6916 2.01649
\(248\) 4.61578 0.293103
\(249\) −5.30266 −0.336042
\(250\) 20.3791 1.28889
\(251\) −8.50283 −0.536694 −0.268347 0.963322i \(-0.586477\pi\)
−0.268347 + 0.963322i \(0.586477\pi\)
\(252\) 0.951934 0.0599662
\(253\) −6.56536 −0.412761
\(254\) 25.1877 1.58042
\(255\) −1.04292 −0.0653101
\(256\) 20.7974 1.29984
\(257\) 27.5328 1.71745 0.858723 0.512439i \(-0.171258\pi\)
0.858723 + 0.512439i \(0.171258\pi\)
\(258\) 1.34511 0.0837432
\(259\) −1.29804 −0.0806560
\(260\) 7.88591 0.489064
\(261\) −19.3027 −1.19481
\(262\) 8.71372 0.538335
\(263\) 18.1306 1.11798 0.558990 0.829174i \(-0.311189\pi\)
0.558990 + 0.829174i \(0.311189\pi\)
\(264\) 0.979235 0.0602677
\(265\) −10.1707 −0.624779
\(266\) 3.96612 0.243179
\(267\) −3.72664 −0.228066
\(268\) −11.6681 −0.712744
\(269\) 24.7820 1.51099 0.755493 0.655157i \(-0.227397\pi\)
0.755493 + 0.655157i \(0.227397\pi\)
\(270\) 10.2758 0.625368
\(271\) 5.28255 0.320892 0.160446 0.987045i \(-0.448707\pi\)
0.160446 + 0.987045i \(0.448707\pi\)
\(272\) 4.92601 0.298683
\(273\) −1.00530 −0.0608434
\(274\) −19.9425 −1.20477
\(275\) −3.03303 −0.182899
\(276\) −6.21012 −0.373806
\(277\) −2.81766 −0.169297 −0.0846484 0.996411i \(-0.526977\pi\)
−0.0846484 + 0.996411i \(0.526977\pi\)
\(278\) −8.83934 −0.530148
\(279\) −8.57728 −0.513508
\(280\) −0.564822 −0.0337546
\(281\) 3.87575 0.231208 0.115604 0.993295i \(-0.463120\pi\)
0.115604 + 0.993295i \(0.463120\pi\)
\(282\) 5.70674 0.339832
\(283\) 13.9607 0.829879 0.414940 0.909849i \(-0.363803\pi\)
0.414940 + 0.909849i \(0.363803\pi\)
\(284\) 14.9500 0.887120
\(285\) 7.47707 0.442903
\(286\) −7.99597 −0.472812
\(287\) −3.27268 −0.193180
\(288\) −15.3595 −0.905070
\(289\) 1.00000 0.0588235
\(290\) −20.0118 −1.17513
\(291\) 11.6974 0.685713
\(292\) 1.87479 0.109714
\(293\) 12.9446 0.756233 0.378117 0.925758i \(-0.376572\pi\)
0.378117 + 0.925758i \(0.376572\pi\)
\(294\) 9.28999 0.541803
\(295\) 17.2332 1.00336
\(296\) 5.58911 0.324860
\(297\) −4.05053 −0.235036
\(298\) 8.43968 0.488897
\(299\) −29.0217 −1.67837
\(300\) −2.86892 −0.165637
\(301\) 0.305829 0.0176277
\(302\) −42.2530 −2.43139
\(303\) 10.2760 0.590342
\(304\) −35.3164 −2.02553
\(305\) −14.2069 −0.813486
\(306\) −4.42635 −0.253038
\(307\) 19.8089 1.13056 0.565278 0.824900i \(-0.308769\pi\)
0.565278 + 0.824900i \(0.308769\pi\)
\(308\) −0.389016 −0.0221663
\(309\) 0.716174 0.0407417
\(310\) −8.89235 −0.505051
\(311\) 0.680814 0.0386054 0.0193027 0.999814i \(-0.493855\pi\)
0.0193027 + 0.999814i \(0.493855\pi\)
\(312\) 4.32864 0.245061
\(313\) −24.0683 −1.36042 −0.680211 0.733017i \(-0.738112\pi\)
−0.680211 + 0.733017i \(0.738112\pi\)
\(314\) −3.55809 −0.200795
\(315\) 1.04958 0.0591372
\(316\) 20.4569 1.15079
\(317\) 20.0187 1.12436 0.562181 0.827015i \(-0.309963\pi\)
0.562181 + 0.827015i \(0.309963\pi\)
\(318\) 9.75462 0.547012
\(319\) 7.88823 0.441656
\(320\) −2.10642 −0.117753
\(321\) −1.92909 −0.107671
\(322\) −3.63199 −0.202403
\(323\) −7.16936 −0.398914
\(324\) 5.50654 0.305919
\(325\) −13.4073 −0.743703
\(326\) 13.7756 0.762960
\(327\) −7.03801 −0.389203
\(328\) 14.0916 0.778078
\(329\) 1.29750 0.0715335
\(330\) −1.88650 −0.103849
\(331\) −4.40156 −0.241932 −0.120966 0.992657i \(-0.538599\pi\)
−0.120966 + 0.992657i \(0.538599\pi\)
\(332\) −9.07049 −0.497808
\(333\) −10.3860 −0.569147
\(334\) 41.0905 2.24837
\(335\) −12.8650 −0.702891
\(336\) 1.12028 0.0611163
\(337\) −34.2968 −1.86827 −0.934134 0.356924i \(-0.883826\pi\)
−0.934134 + 0.356924i \(0.883826\pi\)
\(338\) −11.8303 −0.643484
\(339\) −1.39853 −0.0759578
\(340\) −1.78397 −0.0967494
\(341\) 3.50518 0.189816
\(342\) 31.7341 1.71598
\(343\) 4.25300 0.229641
\(344\) −1.31684 −0.0709995
\(345\) −6.84714 −0.368638
\(346\) −22.8181 −1.22671
\(347\) −3.69931 −0.198589 −0.0992946 0.995058i \(-0.531659\pi\)
−0.0992946 + 0.995058i \(0.531659\pi\)
\(348\) 7.46141 0.399974
\(349\) −12.9491 −0.693148 −0.346574 0.938023i \(-0.612655\pi\)
−0.346574 + 0.938023i \(0.612655\pi\)
\(350\) −1.67789 −0.0896869
\(351\) −17.9051 −0.955702
\(352\) 6.27682 0.334556
\(353\) −4.74368 −0.252481 −0.126240 0.992000i \(-0.540291\pi\)
−0.126240 + 0.992000i \(0.540291\pi\)
\(354\) −16.5283 −0.878468
\(355\) 16.4835 0.874856
\(356\) −6.37462 −0.337854
\(357\) 0.227421 0.0120364
\(358\) −27.5660 −1.45691
\(359\) 7.15512 0.377633 0.188816 0.982012i \(-0.439535\pi\)
0.188816 + 0.982012i \(0.439535\pi\)
\(360\) −4.51931 −0.238188
\(361\) 32.3998 1.70525
\(362\) 21.8739 1.14967
\(363\) 0.743622 0.0390300
\(364\) −1.71962 −0.0901325
\(365\) 2.06710 0.108197
\(366\) 13.6258 0.712230
\(367\) 32.3582 1.68908 0.844542 0.535490i \(-0.179873\pi\)
0.844542 + 0.535490i \(0.179873\pi\)
\(368\) 32.3411 1.68589
\(369\) −26.1857 −1.36317
\(370\) −10.7675 −0.559774
\(371\) 2.21784 0.115144
\(372\) 3.31553 0.171902
\(373\) −1.07574 −0.0556999 −0.0278499 0.999612i \(-0.508866\pi\)
−0.0278499 + 0.999612i \(0.508866\pi\)
\(374\) 1.80887 0.0935344
\(375\) −8.37781 −0.432628
\(376\) −5.58681 −0.288118
\(377\) 34.8693 1.79586
\(378\) −2.24077 −0.115253
\(379\) 1.69177 0.0869004 0.0434502 0.999056i \(-0.486165\pi\)
0.0434502 + 0.999056i \(0.486165\pi\)
\(380\) 12.7899 0.656110
\(381\) −10.3546 −0.530482
\(382\) 6.32869 0.323804
\(383\) −30.6512 −1.56620 −0.783101 0.621894i \(-0.786363\pi\)
−0.783101 + 0.621894i \(0.786363\pi\)
\(384\) −7.31491 −0.373287
\(385\) −0.428921 −0.0218598
\(386\) −7.37069 −0.375158
\(387\) 2.44703 0.124389
\(388\) 20.0090 1.01580
\(389\) −35.1401 −1.78167 −0.890837 0.454323i \(-0.849881\pi\)
−0.890837 + 0.454323i \(0.849881\pi\)
\(390\) −8.33915 −0.422269
\(391\) 6.56536 0.332025
\(392\) −9.09475 −0.459354
\(393\) −3.58219 −0.180698
\(394\) 12.5621 0.632870
\(395\) 22.5553 1.13488
\(396\) −3.11263 −0.156416
\(397\) −13.1023 −0.657587 −0.328794 0.944402i \(-0.606642\pi\)
−0.328794 + 0.944402i \(0.606642\pi\)
\(398\) 0.913280 0.0457786
\(399\) −1.63046 −0.0816253
\(400\) 14.9408 0.747038
\(401\) 7.83175 0.391099 0.195549 0.980694i \(-0.437351\pi\)
0.195549 + 0.980694i \(0.437351\pi\)
\(402\) 12.3387 0.615401
\(403\) 15.4944 0.771831
\(404\) 17.5777 0.874523
\(405\) 6.07138 0.301690
\(406\) 4.36381 0.216572
\(407\) 4.24432 0.210383
\(408\) −0.979235 −0.0484794
\(409\) 5.67836 0.280777 0.140388 0.990096i \(-0.455165\pi\)
0.140388 + 0.990096i \(0.455165\pi\)
\(410\) −27.1476 −1.34072
\(411\) 8.19831 0.404393
\(412\) 1.22505 0.0603541
\(413\) −3.75792 −0.184915
\(414\) −29.0606 −1.42825
\(415\) −10.0009 −0.490926
\(416\) 27.7462 1.36037
\(417\) 3.63383 0.177950
\(418\) −12.9684 −0.634307
\(419\) −27.8216 −1.35918 −0.679588 0.733594i \(-0.737841\pi\)
−0.679588 + 0.733594i \(0.737841\pi\)
\(420\) −0.405713 −0.0197968
\(421\) 1.76329 0.0859374 0.0429687 0.999076i \(-0.486318\pi\)
0.0429687 + 0.999076i \(0.486318\pi\)
\(422\) 1.00736 0.0490375
\(423\) 10.3817 0.504775
\(424\) −9.54961 −0.463770
\(425\) 3.03303 0.147124
\(426\) −15.8093 −0.765961
\(427\) 3.09799 0.149922
\(428\) −3.29981 −0.159502
\(429\) 3.28713 0.158704
\(430\) 2.53691 0.122341
\(431\) 10.4851 0.505051 0.252525 0.967590i \(-0.418739\pi\)
0.252525 + 0.967590i \(0.418739\pi\)
\(432\) 19.9530 0.959987
\(433\) −28.0288 −1.34698 −0.673488 0.739198i \(-0.735205\pi\)
−0.673488 + 0.739198i \(0.735205\pi\)
\(434\) 1.93908 0.0930790
\(435\) 8.22679 0.394444
\(436\) −12.0389 −0.576559
\(437\) −47.0695 −2.25164
\(438\) −1.98254 −0.0947295
\(439\) −22.6159 −1.07940 −0.539698 0.841858i \(-0.681462\pi\)
−0.539698 + 0.841858i \(0.681462\pi\)
\(440\) 1.84686 0.0880454
\(441\) 16.9003 0.804777
\(442\) 7.99597 0.380330
\(443\) −8.52780 −0.405168 −0.202584 0.979265i \(-0.564934\pi\)
−0.202584 + 0.979265i \(0.564934\pi\)
\(444\) 4.01467 0.190528
\(445\) −7.02851 −0.333183
\(446\) 21.1183 0.999979
\(447\) −3.46953 −0.164103
\(448\) 0.459331 0.0217013
\(449\) −3.76012 −0.177451 −0.0887255 0.996056i \(-0.528279\pi\)
−0.0887255 + 0.996056i \(0.528279\pi\)
\(450\) −13.4253 −0.632873
\(451\) 10.7010 0.503892
\(452\) −2.39226 −0.112523
\(453\) 17.3701 0.816119
\(454\) −17.2250 −0.808408
\(455\) −1.89601 −0.0888865
\(456\) 7.02049 0.328765
\(457\) 8.57980 0.401346 0.200673 0.979658i \(-0.435687\pi\)
0.200673 + 0.979658i \(0.435687\pi\)
\(458\) −42.5713 −1.98923
\(459\) 4.05053 0.189062
\(460\) −11.7124 −0.546094
\(461\) −26.7127 −1.24413 −0.622066 0.782965i \(-0.713707\pi\)
−0.622066 + 0.782965i \(0.713707\pi\)
\(462\) 0.411375 0.0191389
\(463\) 4.35965 0.202610 0.101305 0.994855i \(-0.467698\pi\)
0.101305 + 0.994855i \(0.467698\pi\)
\(464\) −38.8575 −1.80392
\(465\) 3.65562 0.169526
\(466\) 41.5631 1.92537
\(467\) 38.2287 1.76902 0.884508 0.466526i \(-0.154494\pi\)
0.884508 + 0.466526i \(0.154494\pi\)
\(468\) −13.7592 −0.636018
\(469\) 2.80537 0.129540
\(470\) 10.7630 0.496461
\(471\) 1.46272 0.0673987
\(472\) 16.1809 0.744787
\(473\) −1.00000 −0.0459800
\(474\) −21.6326 −0.993620
\(475\) −21.7449 −0.997725
\(476\) 0.389016 0.0178305
\(477\) 17.7456 0.812514
\(478\) −38.7233 −1.77116
\(479\) 18.3274 0.837401 0.418700 0.908124i \(-0.362486\pi\)
0.418700 + 0.908124i \(0.362486\pi\)
\(480\) 6.54622 0.298793
\(481\) 18.7617 0.855460
\(482\) 0.329085 0.0149894
\(483\) 1.49310 0.0679385
\(484\) 1.27201 0.0578185
\(485\) 22.0615 1.00176
\(486\) −27.8036 −1.26120
\(487\) 4.76107 0.215745 0.107872 0.994165i \(-0.465596\pi\)
0.107872 + 0.994165i \(0.465596\pi\)
\(488\) −13.3394 −0.603846
\(489\) −5.66312 −0.256095
\(490\) 17.5211 0.791523
\(491\) 12.0024 0.541661 0.270831 0.962627i \(-0.412702\pi\)
0.270831 + 0.962627i \(0.412702\pi\)
\(492\) 10.1220 0.456336
\(493\) −7.88823 −0.355268
\(494\) −57.3260 −2.57922
\(495\) −3.43192 −0.154253
\(496\) −17.2666 −0.775292
\(497\) −3.59444 −0.161233
\(498\) 9.59181 0.429819
\(499\) −34.8935 −1.56205 −0.781024 0.624501i \(-0.785302\pi\)
−0.781024 + 0.624501i \(0.785302\pi\)
\(500\) −14.3307 −0.640888
\(501\) −16.8922 −0.754689
\(502\) 15.3805 0.686466
\(503\) −33.6210 −1.49908 −0.749542 0.661956i \(-0.769726\pi\)
−0.749542 + 0.661956i \(0.769726\pi\)
\(504\) 0.985489 0.0438972
\(505\) 19.3808 0.862434
\(506\) 11.8759 0.527947
\(507\) 4.86342 0.215992
\(508\) −17.7121 −0.785848
\(509\) −44.7318 −1.98270 −0.991352 0.131229i \(-0.958108\pi\)
−0.991352 + 0.131229i \(0.958108\pi\)
\(510\) 1.88650 0.0835358
\(511\) −0.450756 −0.0199403
\(512\) −17.9461 −0.793113
\(513\) −29.0397 −1.28213
\(514\) −49.8032 −2.19672
\(515\) 1.35072 0.0595197
\(516\) −0.945892 −0.0416406
\(517\) −4.24257 −0.186588
\(518\) 2.34798 0.103164
\(519\) 9.38049 0.411758
\(520\) 8.16389 0.358010
\(521\) 40.1324 1.75823 0.879116 0.476607i \(-0.158134\pi\)
0.879116 + 0.476607i \(0.158134\pi\)
\(522\) 34.9161 1.52823
\(523\) 27.9218 1.22093 0.610467 0.792041i \(-0.290982\pi\)
0.610467 + 0.792041i \(0.290982\pi\)
\(524\) −6.12754 −0.267683
\(525\) 0.689776 0.0301043
\(526\) −32.7959 −1.42997
\(527\) −3.50518 −0.152688
\(528\) −3.66309 −0.159416
\(529\) 20.1040 0.874086
\(530\) 18.3974 0.799132
\(531\) −30.0682 −1.30485
\(532\) −2.78900 −0.120918
\(533\) 47.3031 2.04892
\(534\) 6.74100 0.291711
\(535\) −3.63830 −0.157297
\(536\) −12.0794 −0.521752
\(537\) 11.3323 0.489026
\(538\) −44.8274 −1.93265
\(539\) −6.90647 −0.297483
\(540\) −7.22603 −0.310959
\(541\) −0.779327 −0.0335059 −0.0167529 0.999860i \(-0.505333\pi\)
−0.0167529 + 0.999860i \(0.505333\pi\)
\(542\) −9.55545 −0.410442
\(543\) −8.99230 −0.385897
\(544\) −6.27682 −0.269116
\(545\) −13.2738 −0.568588
\(546\) 1.81845 0.0778226
\(547\) −3.07606 −0.131523 −0.0657615 0.997835i \(-0.520948\pi\)
−0.0657615 + 0.997835i \(0.520948\pi\)
\(548\) 14.0237 0.599061
\(549\) 24.7879 1.05792
\(550\) 5.48636 0.233939
\(551\) 56.5536 2.40926
\(552\) −6.42903 −0.273638
\(553\) −4.91846 −0.209154
\(554\) 5.09678 0.216541
\(555\) 4.42648 0.187894
\(556\) 6.21587 0.263612
\(557\) 15.1346 0.641273 0.320636 0.947202i \(-0.396103\pi\)
0.320636 + 0.947202i \(0.396103\pi\)
\(558\) 15.5152 0.656809
\(559\) −4.42043 −0.186964
\(560\) 2.11287 0.0892850
\(561\) −0.743622 −0.0313957
\(562\) −7.01073 −0.295730
\(563\) 18.5922 0.783566 0.391783 0.920058i \(-0.371858\pi\)
0.391783 + 0.920058i \(0.371858\pi\)
\(564\) −4.01301 −0.168978
\(565\) −2.63766 −0.110967
\(566\) −25.2531 −1.06147
\(567\) −1.32394 −0.0556002
\(568\) 15.4770 0.649401
\(569\) 38.6283 1.61938 0.809691 0.586856i \(-0.199635\pi\)
0.809691 + 0.586856i \(0.199635\pi\)
\(570\) −13.5250 −0.566501
\(571\) −25.9327 −1.08525 −0.542624 0.839976i \(-0.682569\pi\)
−0.542624 + 0.839976i \(0.682569\pi\)
\(572\) 5.62281 0.235102
\(573\) −2.60171 −0.108688
\(574\) 5.91986 0.247090
\(575\) 19.9130 0.830428
\(576\) 3.67524 0.153135
\(577\) −19.6450 −0.817833 −0.408916 0.912572i \(-0.634093\pi\)
−0.408916 + 0.912572i \(0.634093\pi\)
\(578\) −1.80887 −0.0752390
\(579\) 3.03007 0.125926
\(580\) 14.0724 0.584324
\(581\) 2.18082 0.0904757
\(582\) −21.1590 −0.877070
\(583\) −7.25189 −0.300343
\(584\) 1.94088 0.0803140
\(585\) −15.1705 −0.627225
\(586\) −23.4151 −0.967271
\(587\) 31.4803 1.29933 0.649666 0.760220i \(-0.274909\pi\)
0.649666 + 0.760220i \(0.274909\pi\)
\(588\) −6.53277 −0.269407
\(589\) 25.1299 1.03546
\(590\) −31.1727 −1.28336
\(591\) −5.16425 −0.212429
\(592\) −20.9076 −0.859295
\(593\) −4.67485 −0.191973 −0.0959865 0.995383i \(-0.530601\pi\)
−0.0959865 + 0.995383i \(0.530601\pi\)
\(594\) 7.32688 0.300625
\(595\) 0.428921 0.0175840
\(596\) −5.93483 −0.243100
\(597\) −0.375447 −0.0153660
\(598\) 52.4965 2.14674
\(599\) 19.5453 0.798598 0.399299 0.916821i \(-0.369254\pi\)
0.399299 + 0.916821i \(0.369254\pi\)
\(600\) −2.97005 −0.121252
\(601\) 19.6562 0.801791 0.400896 0.916124i \(-0.368699\pi\)
0.400896 + 0.916124i \(0.368699\pi\)
\(602\) −0.553205 −0.0225469
\(603\) 22.4466 0.914096
\(604\) 29.7125 1.20899
\(605\) 1.40249 0.0570192
\(606\) −18.5880 −0.755085
\(607\) 21.7264 0.881849 0.440924 0.897544i \(-0.354651\pi\)
0.440924 + 0.897544i \(0.354651\pi\)
\(608\) 45.0008 1.82502
\(609\) −1.79395 −0.0726946
\(610\) 25.6985 1.04050
\(611\) −18.7540 −0.758704
\(612\) 3.11263 0.125821
\(613\) 0.804862 0.0325081 0.0162540 0.999868i \(-0.494826\pi\)
0.0162540 + 0.999868i \(0.494826\pi\)
\(614\) −35.8318 −1.44605
\(615\) 11.1603 0.450027
\(616\) −0.402729 −0.0162264
\(617\) −17.4886 −0.704063 −0.352031 0.935988i \(-0.614509\pi\)
−0.352031 + 0.935988i \(0.614509\pi\)
\(618\) −1.29546 −0.0521112
\(619\) 23.1821 0.931766 0.465883 0.884846i \(-0.345737\pi\)
0.465883 + 0.884846i \(0.345737\pi\)
\(620\) 6.25315 0.251132
\(621\) 26.5932 1.06715
\(622\) −1.23150 −0.0493788
\(623\) 1.53265 0.0614044
\(624\) −16.1924 −0.648216
\(625\) −0.635539 −0.0254216
\(626\) 43.5364 1.74007
\(627\) 5.33130 0.212911
\(628\) 2.50207 0.0998433
\(629\) −4.24432 −0.169232
\(630\) −1.89855 −0.0756402
\(631\) 29.7771 1.18541 0.592704 0.805420i \(-0.298060\pi\)
0.592704 + 0.805420i \(0.298060\pi\)
\(632\) 21.1780 0.842416
\(633\) −0.414123 −0.0164599
\(634\) −36.2112 −1.43813
\(635\) −19.5290 −0.774984
\(636\) −6.85950 −0.271997
\(637\) −30.5295 −1.20962
\(638\) −14.2688 −0.564906
\(639\) −28.7601 −1.13773
\(640\) −13.7961 −0.545337
\(641\) 8.99717 0.355367 0.177684 0.984088i \(-0.443140\pi\)
0.177684 + 0.984088i \(0.443140\pi\)
\(642\) 3.48947 0.137718
\(643\) 17.4047 0.686373 0.343187 0.939267i \(-0.388494\pi\)
0.343187 + 0.939267i \(0.388494\pi\)
\(644\) 2.55403 0.100643
\(645\) −1.04292 −0.0410649
\(646\) 12.9684 0.510236
\(647\) 35.5134 1.39618 0.698088 0.716012i \(-0.254035\pi\)
0.698088 + 0.716012i \(0.254035\pi\)
\(648\) 5.70064 0.223942
\(649\) 12.2876 0.482332
\(650\) 24.2521 0.951244
\(651\) −0.797153 −0.0312429
\(652\) −9.68707 −0.379375
\(653\) 11.3212 0.443032 0.221516 0.975157i \(-0.428900\pi\)
0.221516 + 0.975157i \(0.428900\pi\)
\(654\) 12.7308 0.497815
\(655\) −6.75608 −0.263982
\(656\) −52.7134 −2.05811
\(657\) −3.60663 −0.140708
\(658\) −2.34701 −0.0914959
\(659\) −36.3856 −1.41738 −0.708691 0.705519i \(-0.750714\pi\)
−0.708691 + 0.705519i \(0.750714\pi\)
\(660\) 1.32660 0.0516378
\(661\) 31.1787 1.21271 0.606355 0.795194i \(-0.292631\pi\)
0.606355 + 0.795194i \(0.292631\pi\)
\(662\) 7.96185 0.309446
\(663\) −3.28713 −0.127661
\(664\) −9.39022 −0.364411
\(665\) −3.07509 −0.119247
\(666\) 18.7868 0.727975
\(667\) −51.7891 −2.00528
\(668\) −28.8951 −1.11798
\(669\) −8.68167 −0.335653
\(670\) 23.2711 0.899042
\(671\) −10.1298 −0.391057
\(672\) −1.42748 −0.0550663
\(673\) 48.9069 1.88522 0.942611 0.333894i \(-0.108363\pi\)
0.942611 + 0.333894i \(0.108363\pi\)
\(674\) 62.0385 2.38963
\(675\) 12.2854 0.472865
\(676\) 8.31914 0.319967
\(677\) 39.8252 1.53061 0.765304 0.643669i \(-0.222589\pi\)
0.765304 + 0.643669i \(0.222589\pi\)
\(678\) 2.52976 0.0971548
\(679\) −4.81078 −0.184621
\(680\) −1.84686 −0.0708237
\(681\) 7.08115 0.271350
\(682\) −6.34042 −0.242787
\(683\) −12.9440 −0.495286 −0.247643 0.968851i \(-0.579656\pi\)
−0.247643 + 0.968851i \(0.579656\pi\)
\(684\) −22.3156 −0.853258
\(685\) 15.4622 0.590779
\(686\) −7.69312 −0.293725
\(687\) 17.5010 0.667703
\(688\) 4.92601 0.187802
\(689\) −32.0564 −1.22125
\(690\) 12.3856 0.471511
\(691\) −14.5793 −0.554622 −0.277311 0.960780i \(-0.589443\pi\)
−0.277311 + 0.960780i \(0.589443\pi\)
\(692\) 16.0458 0.609971
\(693\) 0.748372 0.0284283
\(694\) 6.69156 0.254008
\(695\) 6.85348 0.259967
\(696\) 7.72443 0.292794
\(697\) −10.7010 −0.405330
\(698\) 23.4232 0.886580
\(699\) −17.0865 −0.646271
\(700\) 1.17990 0.0445960
\(701\) 46.0906 1.74082 0.870410 0.492328i \(-0.163854\pi\)
0.870410 + 0.492328i \(0.163854\pi\)
\(702\) 32.3879 1.22240
\(703\) 30.4290 1.14765
\(704\) −1.50192 −0.0566057
\(705\) −4.42466 −0.166642
\(706\) 8.58070 0.322939
\(707\) −4.22621 −0.158943
\(708\) 11.6228 0.436811
\(709\) 3.77523 0.141782 0.0708909 0.997484i \(-0.477416\pi\)
0.0708909 + 0.997484i \(0.477416\pi\)
\(710\) −29.8166 −1.11900
\(711\) −39.3540 −1.47589
\(712\) −6.59932 −0.247320
\(713\) −23.0128 −0.861836
\(714\) −0.411375 −0.0153953
\(715\) 6.19959 0.231851
\(716\) 19.3846 0.724435
\(717\) 15.9191 0.594508
\(718\) −12.9427 −0.483016
\(719\) 30.0074 1.11909 0.559544 0.828801i \(-0.310976\pi\)
0.559544 + 0.828801i \(0.310976\pi\)
\(720\) 16.9057 0.630037
\(721\) −0.294540 −0.0109693
\(722\) −58.6069 −2.18112
\(723\) −0.135286 −0.00503134
\(724\) −15.3818 −0.571661
\(725\) −23.9253 −0.888562
\(726\) −1.34511 −0.0499219
\(727\) −39.5478 −1.46675 −0.733373 0.679827i \(-0.762055\pi\)
−0.733373 + 0.679827i \(0.762055\pi\)
\(728\) −1.78024 −0.0659799
\(729\) −1.55703 −0.0576678
\(730\) −3.73911 −0.138391
\(731\) 1.00000 0.0369863
\(732\) −9.58171 −0.354150
\(733\) 19.3879 0.716108 0.358054 0.933701i \(-0.383440\pi\)
0.358054 + 0.933701i \(0.383440\pi\)
\(734\) −58.5317 −2.16044
\(735\) −7.20289 −0.265683
\(736\) −41.2096 −1.51901
\(737\) −9.17301 −0.337892
\(738\) 47.3665 1.74358
\(739\) 34.8674 1.28262 0.641309 0.767283i \(-0.278392\pi\)
0.641309 + 0.767283i \(0.278392\pi\)
\(740\) 7.57174 0.278343
\(741\) 23.5666 0.865741
\(742\) −4.01178 −0.147277
\(743\) −22.9510 −0.841992 −0.420996 0.907063i \(-0.638319\pi\)
−0.420996 + 0.907063i \(0.638319\pi\)
\(744\) 3.43240 0.125838
\(745\) −6.54361 −0.239739
\(746\) 1.94588 0.0712437
\(747\) 17.4494 0.638439
\(748\) −1.27201 −0.0465092
\(749\) 0.793375 0.0289893
\(750\) 15.1544 0.553359
\(751\) −41.3186 −1.50774 −0.753869 0.657025i \(-0.771815\pi\)
−0.753869 + 0.657025i \(0.771815\pi\)
\(752\) 20.8990 0.762106
\(753\) −6.32289 −0.230419
\(754\) −63.0741 −2.29702
\(755\) 32.7604 1.19227
\(756\) 1.57572 0.0573085
\(757\) 24.0794 0.875182 0.437591 0.899174i \(-0.355832\pi\)
0.437591 + 0.899174i \(0.355832\pi\)
\(758\) −3.06019 −0.111151
\(759\) −4.88215 −0.177211
\(760\) 13.2408 0.480294
\(761\) 31.3933 1.13801 0.569003 0.822335i \(-0.307329\pi\)
0.569003 + 0.822335i \(0.307329\pi\)
\(762\) 18.7301 0.678520
\(763\) 2.89452 0.104789
\(764\) −4.45037 −0.161009
\(765\) 3.43192 0.124081
\(766\) 55.4440 2.00327
\(767\) 54.3166 1.96126
\(768\) 15.4654 0.558061
\(769\) −35.2224 −1.27015 −0.635077 0.772449i \(-0.719032\pi\)
−0.635077 + 0.772449i \(0.719032\pi\)
\(770\) 0.775862 0.0279601
\(771\) 20.4740 0.737352
\(772\) 5.18311 0.186544
\(773\) 6.23078 0.224106 0.112053 0.993702i \(-0.464257\pi\)
0.112053 + 0.993702i \(0.464257\pi\)
\(774\) −4.42635 −0.159102
\(775\) −10.6313 −0.381889
\(776\) 20.7143 0.743601
\(777\) −0.965248 −0.0346281
\(778\) 63.5638 2.27887
\(779\) 76.7195 2.74876
\(780\) 5.86414 0.209970
\(781\) 11.7531 0.420559
\(782\) −11.8759 −0.424681
\(783\) −31.9515 −1.14185
\(784\) 34.0214 1.21505
\(785\) 2.75872 0.0984630
\(786\) 6.47971 0.231124
\(787\) 24.2787 0.865440 0.432720 0.901528i \(-0.357554\pi\)
0.432720 + 0.901528i \(0.357554\pi\)
\(788\) −8.83374 −0.314689
\(789\) 13.4823 0.479983
\(790\) −40.7996 −1.45158
\(791\) 0.575173 0.0204508
\(792\) −3.22235 −0.114501
\(793\) −44.7781 −1.59012
\(794\) 23.7004 0.841096
\(795\) −7.56314 −0.268237
\(796\) −0.642223 −0.0227630
\(797\) 44.8409 1.58835 0.794173 0.607692i \(-0.207905\pi\)
0.794173 + 0.607692i \(0.207905\pi\)
\(798\) 2.94930 0.104404
\(799\) 4.24257 0.150091
\(800\) −19.0378 −0.673088
\(801\) 12.2632 0.433299
\(802\) −14.1666 −0.500240
\(803\) 1.47388 0.0520122
\(804\) −8.67667 −0.306003
\(805\) 2.81602 0.0992517
\(806\) −28.0274 −0.987221
\(807\) 18.4285 0.648712
\(808\) 18.1973 0.640180
\(809\) 45.3872 1.59573 0.797865 0.602836i \(-0.205963\pi\)
0.797865 + 0.602836i \(0.205963\pi\)
\(810\) −10.9823 −0.385880
\(811\) 39.3913 1.38322 0.691608 0.722273i \(-0.256903\pi\)
0.691608 + 0.722273i \(0.256903\pi\)
\(812\) −3.06865 −0.107689
\(813\) 3.92822 0.137769
\(814\) −7.67741 −0.269093
\(815\) −10.6807 −0.374130
\(816\) 3.66309 0.128234
\(817\) −7.16936 −0.250824
\(818\) −10.2714 −0.359132
\(819\) 3.30812 0.115595
\(820\) 19.0903 0.666663
\(821\) 12.5985 0.439692 0.219846 0.975535i \(-0.429445\pi\)
0.219846 + 0.975535i \(0.429445\pi\)
\(822\) −14.8297 −0.517244
\(823\) 19.5740 0.682308 0.341154 0.940007i \(-0.389182\pi\)
0.341154 + 0.940007i \(0.389182\pi\)
\(824\) 1.26824 0.0441812
\(825\) −2.25543 −0.0785240
\(826\) 6.79758 0.236518
\(827\) −3.23953 −0.112650 −0.0563248 0.998412i \(-0.517938\pi\)
−0.0563248 + 0.998412i \(0.517938\pi\)
\(828\) 20.4356 0.710185
\(829\) −17.7198 −0.615434 −0.307717 0.951478i \(-0.599565\pi\)
−0.307717 + 0.951478i \(0.599565\pi\)
\(830\) 18.0903 0.627925
\(831\) −2.09527 −0.0726843
\(832\) −6.63913 −0.230170
\(833\) 6.90647 0.239295
\(834\) −6.57313 −0.227609
\(835\) −31.8591 −1.10253
\(836\) 9.11947 0.315404
\(837\) −14.1978 −0.490749
\(838\) 50.3257 1.73847
\(839\) −38.4235 −1.32653 −0.663263 0.748386i \(-0.730829\pi\)
−0.663263 + 0.748386i \(0.730829\pi\)
\(840\) −0.420014 −0.0144919
\(841\) 33.2242 1.14566
\(842\) −3.18956 −0.109919
\(843\) 2.88209 0.0992646
\(844\) −0.708380 −0.0243835
\(845\) 9.17250 0.315544
\(846\) −18.7791 −0.645639
\(847\) −0.305829 −0.0105084
\(848\) 35.7229 1.22673
\(849\) 10.3815 0.356292
\(850\) −5.48636 −0.188181
\(851\) −27.8655 −0.955216
\(852\) 11.1172 0.380868
\(853\) 4.94254 0.169229 0.0846147 0.996414i \(-0.473034\pi\)
0.0846147 + 0.996414i \(0.473034\pi\)
\(854\) −5.60386 −0.191760
\(855\) −24.6047 −0.841462
\(856\) −3.41613 −0.116761
\(857\) 8.95095 0.305758 0.152879 0.988245i \(-0.451145\pi\)
0.152879 + 0.988245i \(0.451145\pi\)
\(858\) −5.94598 −0.202992
\(859\) 9.57945 0.326847 0.163423 0.986556i \(-0.447746\pi\)
0.163423 + 0.986556i \(0.447746\pi\)
\(860\) −1.78397 −0.0608329
\(861\) −2.43364 −0.0829382
\(862\) −18.9662 −0.645992
\(863\) −7.35886 −0.250498 −0.125249 0.992125i \(-0.539973\pi\)
−0.125249 + 0.992125i \(0.539973\pi\)
\(864\) −25.4244 −0.864957
\(865\) 17.6918 0.601539
\(866\) 50.7003 1.72287
\(867\) 0.743622 0.0252547
\(868\) −1.36357 −0.0462827
\(869\) 16.0824 0.545557
\(870\) −14.8812 −0.504519
\(871\) −40.5486 −1.37394
\(872\) −12.4633 −0.422060
\(873\) −38.4924 −1.30277
\(874\) 85.1425 2.87999
\(875\) 3.44554 0.116480
\(876\) 1.39413 0.0471034
\(877\) 32.5954 1.10067 0.550334 0.834945i \(-0.314500\pi\)
0.550334 + 0.834945i \(0.314500\pi\)
\(878\) 40.9092 1.38062
\(879\) 9.62591 0.324674
\(880\) −6.90866 −0.232891
\(881\) 4.79497 0.161547 0.0807734 0.996732i \(-0.474261\pi\)
0.0807734 + 0.996732i \(0.474261\pi\)
\(882\) −30.5704 −1.02936
\(883\) 27.2051 0.915523 0.457761 0.889075i \(-0.348651\pi\)
0.457761 + 0.889075i \(0.348651\pi\)
\(884\) −5.62281 −0.189116
\(885\) 12.8150 0.430772
\(886\) 15.4257 0.518235
\(887\) −50.3215 −1.68963 −0.844816 0.535058i \(-0.820290\pi\)
−0.844816 + 0.535058i \(0.820290\pi\)
\(888\) 4.15618 0.139472
\(889\) 4.25853 0.142827
\(890\) 12.7137 0.426163
\(891\) 4.32902 0.145028
\(892\) −14.8505 −0.497231
\(893\) −30.4165 −1.01785
\(894\) 6.27593 0.209899
\(895\) 21.3730 0.714420
\(896\) 3.00840 0.100504
\(897\) −21.5812 −0.720575
\(898\) 6.80156 0.226971
\(899\) 27.6497 0.922169
\(900\) 9.44072 0.314691
\(901\) 7.25189 0.241595
\(902\) −19.3568 −0.644509
\(903\) 0.227421 0.00756810
\(904\) −2.47659 −0.0823702
\(905\) −16.9597 −0.563758
\(906\) −31.4202 −1.04387
\(907\) 33.4398 1.11035 0.555176 0.831733i \(-0.312651\pi\)
0.555176 + 0.831733i \(0.312651\pi\)
\(908\) 12.1127 0.401974
\(909\) −33.8152 −1.12158
\(910\) 3.42964 0.113691
\(911\) −2.01929 −0.0669021 −0.0334510 0.999440i \(-0.510650\pi\)
−0.0334510 + 0.999440i \(0.510650\pi\)
\(912\) −26.2620 −0.869623
\(913\) −7.13085 −0.235997
\(914\) −15.5197 −0.513347
\(915\) −10.5646 −0.349254
\(916\) 29.9364 0.989125
\(917\) 1.47325 0.0486509
\(918\) −7.32688 −0.241823
\(919\) −22.5810 −0.744879 −0.372440 0.928056i \(-0.621479\pi\)
−0.372440 + 0.928056i \(0.621479\pi\)
\(920\) −12.1253 −0.399759
\(921\) 14.7304 0.485382
\(922\) 48.3197 1.59132
\(923\) 51.9537 1.71008
\(924\) −0.289281 −0.00951665
\(925\) −12.8732 −0.423267
\(926\) −7.88604 −0.259151
\(927\) −2.35670 −0.0774043
\(928\) 49.5130 1.62534
\(929\) 1.92382 0.0631185 0.0315593 0.999502i \(-0.489953\pi\)
0.0315593 + 0.999502i \(0.489953\pi\)
\(930\) −6.61254 −0.216834
\(931\) −49.5150 −1.62279
\(932\) −29.2274 −0.957375
\(933\) 0.506268 0.0165745
\(934\) −69.1508 −2.26268
\(935\) −1.40249 −0.0458662
\(936\) −14.2442 −0.465586
\(937\) −31.8217 −1.03957 −0.519784 0.854298i \(-0.673988\pi\)
−0.519784 + 0.854298i \(0.673988\pi\)
\(938\) −5.07455 −0.165690
\(939\) −17.8977 −0.584070
\(940\) −7.56862 −0.246861
\(941\) −13.0996 −0.427034 −0.213517 0.976939i \(-0.568492\pi\)
−0.213517 + 0.976939i \(0.568492\pi\)
\(942\) −2.64587 −0.0862072
\(943\) −70.2561 −2.28785
\(944\) −60.5290 −1.97005
\(945\) 1.73736 0.0565162
\(946\) 1.80887 0.0588114
\(947\) 24.7576 0.804515 0.402258 0.915527i \(-0.368226\pi\)
0.402258 + 0.915527i \(0.368226\pi\)
\(948\) 15.2122 0.494069
\(949\) 6.51519 0.211492
\(950\) 39.3337 1.27615
\(951\) 14.8863 0.482722
\(952\) 0.402729 0.0130525
\(953\) 37.1211 1.20247 0.601235 0.799072i \(-0.294676\pi\)
0.601235 + 0.799072i \(0.294676\pi\)
\(954\) −32.0994 −1.03926
\(955\) −4.90688 −0.158783
\(956\) 27.2304 0.880695
\(957\) 5.86586 0.189616
\(958\) −33.1519 −1.07109
\(959\) −3.37171 −0.108878
\(960\) −1.56638 −0.0505547
\(961\) −18.7137 −0.603667
\(962\) −33.9374 −1.09419
\(963\) 6.34803 0.204562
\(964\) −0.231414 −0.00745335
\(965\) 5.71478 0.183965
\(966\) −2.70083 −0.0868977
\(967\) −10.9555 −0.352305 −0.176152 0.984363i \(-0.556365\pi\)
−0.176152 + 0.984363i \(0.556365\pi\)
\(968\) 1.31684 0.0423250
\(969\) −5.33130 −0.171266
\(970\) −39.9064 −1.28132
\(971\) 36.5279 1.17224 0.586119 0.810225i \(-0.300655\pi\)
0.586119 + 0.810225i \(0.300655\pi\)
\(972\) 19.5517 0.627120
\(973\) −1.49448 −0.0479110
\(974\) −8.61214 −0.275951
\(975\) −9.96997 −0.319294
\(976\) 49.8996 1.59725
\(977\) −37.1990 −1.19010 −0.595050 0.803689i \(-0.702868\pi\)
−0.595050 + 0.803689i \(0.702868\pi\)
\(978\) 10.2438 0.327562
\(979\) −5.01147 −0.160167
\(980\) −12.3209 −0.393578
\(981\) 23.1599 0.739438
\(982\) −21.7108 −0.692819
\(983\) 2.74907 0.0876817 0.0438408 0.999039i \(-0.486041\pi\)
0.0438408 + 0.999039i \(0.486041\pi\)
\(984\) 10.4788 0.334053
\(985\) −9.73989 −0.310339
\(986\) 14.2688 0.454410
\(987\) 0.964850 0.0307115
\(988\) 40.3120 1.28249
\(989\) 6.56536 0.208766
\(990\) 6.20789 0.197300
\(991\) 11.9613 0.379962 0.189981 0.981788i \(-0.439157\pi\)
0.189981 + 0.981788i \(0.439157\pi\)
\(992\) 22.0014 0.698545
\(993\) −3.27310 −0.103869
\(994\) 6.50187 0.206227
\(995\) −0.708101 −0.0224483
\(996\) −6.74501 −0.213724
\(997\) 3.84434 0.121751 0.0608757 0.998145i \(-0.480611\pi\)
0.0608757 + 0.998145i \(0.480611\pi\)
\(998\) 63.1178 1.99796
\(999\) −17.1917 −0.543922
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 \(a_p\))