Properties

Label 8021.2.a.a.1.1
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 1.1
Character \(\chi\) = 8021.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.76381 q^{2} -0.591714 q^{3} +5.63866 q^{4} +2.62273 q^{5} +1.63539 q^{6} +1.07036 q^{7} -10.0566 q^{8} -2.64987 q^{9} +O(q^{10})\) \(q-2.76381 q^{2} -0.591714 q^{3} +5.63866 q^{4} +2.62273 q^{5} +1.63539 q^{6} +1.07036 q^{7} -10.0566 q^{8} -2.64987 q^{9} -7.24873 q^{10} -0.657947 q^{11} -3.33648 q^{12} +1.00000 q^{13} -2.95826 q^{14} -1.55191 q^{15} +16.5172 q^{16} -2.81377 q^{17} +7.32376 q^{18} +2.17808 q^{19} +14.7887 q^{20} -0.633345 q^{21} +1.81844 q^{22} -1.05300 q^{23} +5.95062 q^{24} +1.87870 q^{25} -2.76381 q^{26} +3.34311 q^{27} +6.03537 q^{28} +3.46541 q^{29} +4.28918 q^{30} -8.96535 q^{31} -25.5372 q^{32} +0.389317 q^{33} +7.77673 q^{34} +2.80725 q^{35} -14.9417 q^{36} -9.21184 q^{37} -6.01980 q^{38} -0.591714 q^{39} -26.3757 q^{40} +2.58055 q^{41} +1.75045 q^{42} +3.94121 q^{43} -3.70994 q^{44} -6.94990 q^{45} +2.91030 q^{46} +11.5057 q^{47} -9.77345 q^{48} -5.85434 q^{49} -5.19238 q^{50} +1.66495 q^{51} +5.63866 q^{52} +2.79476 q^{53} -9.23973 q^{54} -1.72562 q^{55} -10.7641 q^{56} -1.28880 q^{57} -9.57773 q^{58} +2.89352 q^{59} -8.75067 q^{60} -4.99394 q^{61} +24.7785 q^{62} -2.83631 q^{63} +37.5458 q^{64} +2.62273 q^{65} -1.07600 q^{66} +0.939044 q^{67} -15.8659 q^{68} +0.623077 q^{69} -7.75872 q^{70} +3.82129 q^{71} +26.6487 q^{72} -3.07261 q^{73} +25.4598 q^{74} -1.11166 q^{75} +12.2814 q^{76} -0.704238 q^{77} +1.63539 q^{78} -11.1678 q^{79} +43.3201 q^{80} +5.97146 q^{81} -7.13215 q^{82} +4.05903 q^{83} -3.57122 q^{84} -7.37975 q^{85} -10.8928 q^{86} -2.05053 q^{87} +6.61670 q^{88} +4.43124 q^{89} +19.2082 q^{90} +1.07036 q^{91} -5.93752 q^{92} +5.30493 q^{93} -31.7996 q^{94} +5.71251 q^{95} +15.1107 q^{96} +7.68728 q^{97} +16.1803 q^{98} +1.74348 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 134q - 6q^{2} - 33q^{3} + 98q^{4} - 8q^{5} - 16q^{6} - 32q^{7} - 15q^{8} + 101q^{9} + O(q^{10}) \) \( 134q - 6q^{2} - 33q^{3} + 98q^{4} - 8q^{5} - 16q^{6} - 32q^{7} - 15q^{8} + 101q^{9} - 33q^{10} - 47q^{11} - 53q^{12} + 134q^{13} - 28q^{14} - 30q^{15} + 30q^{16} - 17q^{17} - 14q^{18} - 87q^{19} - 12q^{20} - 24q^{21} - 52q^{22} - 44q^{23} - 36q^{24} + 58q^{25} - 6q^{26} - 117q^{27} - 71q^{28} - 42q^{29} - 21q^{30} - 82q^{31} - 31q^{32} + 12q^{33} - 30q^{34} - 54q^{35} + 32q^{36} - 55q^{37} - 12q^{38} - 33q^{39} - 86q^{40} - 16q^{41} + 6q^{42} - 148q^{43} - 54q^{44} - 24q^{45} - 57q^{46} - 21q^{47} - 82q^{48} + 12q^{49} - 17q^{50} - 123q^{51} + 98q^{52} - 17q^{53} - 10q^{54} - 148q^{55} - 47q^{56} - q^{57} - 58q^{58} - 64q^{59} - 16q^{60} - 112q^{61} - 15q^{62} - 58q^{63} - 65q^{64} - 8q^{65} - 20q^{66} - 110q^{67} - 8q^{68} - 57q^{69} - 40q^{70} - 78q^{71} - 28q^{72} - 43q^{73} - 52q^{74} - 150q^{75} - 96q^{76} - 24q^{77} - 16q^{78} - 228q^{79} + 20q^{80} + 54q^{81} - 89q^{82} - 12q^{83} + 6q^{84} - 77q^{85} + 29q^{86} - 77q^{87} - 95q^{88} - 32q^{89} - 46q^{90} - 32q^{91} - 62q^{92} - 9q^{93} - 87q^{94} - 61q^{95} - 54q^{96} - 38q^{97} + 6q^{98} - 193q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.76381 −1.95431 −0.977155 0.212526i \(-0.931831\pi\)
−0.977155 + 0.212526i \(0.931831\pi\)
\(3\) −0.591714 −0.341626 −0.170813 0.985303i \(-0.554639\pi\)
−0.170813 + 0.985303i \(0.554639\pi\)
\(4\) 5.63866 2.81933
\(5\) 2.62273 1.17292 0.586460 0.809978i \(-0.300521\pi\)
0.586460 + 0.809978i \(0.300521\pi\)
\(6\) 1.63539 0.667644
\(7\) 1.07036 0.404556 0.202278 0.979328i \(-0.435165\pi\)
0.202278 + 0.979328i \(0.435165\pi\)
\(8\) −10.0566 −3.55554
\(9\) −2.64987 −0.883291
\(10\) −7.24873 −2.29225
\(11\) −0.657947 −0.198379 −0.0991893 0.995069i \(-0.531625\pi\)
−0.0991893 + 0.995069i \(0.531625\pi\)
\(12\) −3.33648 −0.963158
\(13\) 1.00000 0.277350
\(14\) −2.95826 −0.790629
\(15\) −1.55191 −0.400700
\(16\) 16.5172 4.12929
\(17\) −2.81377 −0.682439 −0.341220 0.939984i \(-0.610840\pi\)
−0.341220 + 0.939984i \(0.610840\pi\)
\(18\) 7.32376 1.72623
\(19\) 2.17808 0.499686 0.249843 0.968286i \(-0.419621\pi\)
0.249843 + 0.968286i \(0.419621\pi\)
\(20\) 14.7887 3.30685
\(21\) −0.633345 −0.138207
\(22\) 1.81844 0.387693
\(23\) −1.05300 −0.219566 −0.109783 0.993956i \(-0.535016\pi\)
−0.109783 + 0.993956i \(0.535016\pi\)
\(24\) 5.95062 1.21467
\(25\) 1.87870 0.375741
\(26\) −2.76381 −0.542028
\(27\) 3.34311 0.643382
\(28\) 6.03537 1.14058
\(29\) 3.46541 0.643510 0.321755 0.946823i \(-0.395727\pi\)
0.321755 + 0.946823i \(0.395727\pi\)
\(30\) 4.28918 0.783093
\(31\) −8.96535 −1.61022 −0.805112 0.593123i \(-0.797895\pi\)
−0.805112 + 0.593123i \(0.797895\pi\)
\(32\) −25.5372 −4.51439
\(33\) 0.389317 0.0677714
\(34\) 7.77673 1.33370
\(35\) 2.80725 0.474512
\(36\) −14.9417 −2.49029
\(37\) −9.21184 −1.51442 −0.757209 0.653173i \(-0.773438\pi\)
−0.757209 + 0.653173i \(0.773438\pi\)
\(38\) −6.01980 −0.976541
\(39\) −0.591714 −0.0947501
\(40\) −26.3757 −4.17036
\(41\) 2.58055 0.403014 0.201507 0.979487i \(-0.435416\pi\)
0.201507 + 0.979487i \(0.435416\pi\)
\(42\) 1.75045 0.270100
\(43\) 3.94121 0.601029 0.300515 0.953777i \(-0.402842\pi\)
0.300515 + 0.953777i \(0.402842\pi\)
\(44\) −3.70994 −0.559295
\(45\) −6.94990 −1.03603
\(46\) 2.91030 0.429101
\(47\) 11.5057 1.67828 0.839138 0.543918i \(-0.183060\pi\)
0.839138 + 0.543918i \(0.183060\pi\)
\(48\) −9.77345 −1.41068
\(49\) −5.85434 −0.836334
\(50\) −5.19238 −0.734314
\(51\) 1.66495 0.233139
\(52\) 5.63866 0.781942
\(53\) 2.79476 0.383890 0.191945 0.981406i \(-0.438520\pi\)
0.191945 + 0.981406i \(0.438520\pi\)
\(54\) −9.23973 −1.25737
\(55\) −1.72562 −0.232682
\(56\) −10.7641 −1.43842
\(57\) −1.28880 −0.170706
\(58\) −9.57773 −1.25762
\(59\) 2.89352 0.376704 0.188352 0.982102i \(-0.439685\pi\)
0.188352 + 0.982102i \(0.439685\pi\)
\(60\) −8.75067 −1.12971
\(61\) −4.99394 −0.639408 −0.319704 0.947517i \(-0.603584\pi\)
−0.319704 + 0.947517i \(0.603584\pi\)
\(62\) 24.7785 3.14688
\(63\) −2.83631 −0.357341
\(64\) 37.5458 4.69322
\(65\) 2.62273 0.325309
\(66\) −1.07600 −0.132446
\(67\) 0.939044 0.114722 0.0573612 0.998353i \(-0.481731\pi\)
0.0573612 + 0.998353i \(0.481731\pi\)
\(68\) −15.8659 −1.92402
\(69\) 0.623077 0.0750096
\(70\) −7.75872 −0.927344
\(71\) 3.82129 0.453503 0.226752 0.973953i \(-0.427189\pi\)
0.226752 + 0.973953i \(0.427189\pi\)
\(72\) 26.6487 3.14058
\(73\) −3.07261 −0.359622 −0.179811 0.983701i \(-0.557549\pi\)
−0.179811 + 0.983701i \(0.557549\pi\)
\(74\) 25.4598 2.95964
\(75\) −1.11166 −0.128363
\(76\) 12.2814 1.40878
\(77\) −0.704238 −0.0802553
\(78\) 1.63539 0.185171
\(79\) −11.1678 −1.25647 −0.628236 0.778023i \(-0.716223\pi\)
−0.628236 + 0.778023i \(0.716223\pi\)
\(80\) 43.3201 4.84333
\(81\) 5.97146 0.663495
\(82\) −7.13215 −0.787614
\(83\) 4.05903 0.445537 0.222768 0.974871i \(-0.428491\pi\)
0.222768 + 0.974871i \(0.428491\pi\)
\(84\) −3.57122 −0.389652
\(85\) −7.37975 −0.800446
\(86\) −10.8928 −1.17460
\(87\) −2.05053 −0.219840
\(88\) 6.61670 0.705343
\(89\) 4.43124 0.469711 0.234855 0.972030i \(-0.424538\pi\)
0.234855 + 0.972030i \(0.424538\pi\)
\(90\) 19.2082 2.02472
\(91\) 1.07036 0.112204
\(92\) −5.93752 −0.619030
\(93\) 5.30493 0.550095
\(94\) −31.7996 −3.27987
\(95\) 5.71251 0.586091
\(96\) 15.1107 1.54223
\(97\) 7.68728 0.780525 0.390263 0.920704i \(-0.372384\pi\)
0.390263 + 0.920704i \(0.372384\pi\)
\(98\) 16.1803 1.63446
\(99\) 1.74348 0.175226
\(100\) 10.5934 1.05934
\(101\) 6.13759 0.610713 0.305357 0.952238i \(-0.401224\pi\)
0.305357 + 0.952238i \(0.401224\pi\)
\(102\) −4.60160 −0.455627
\(103\) 7.87324 0.775773 0.387886 0.921707i \(-0.373205\pi\)
0.387886 + 0.921707i \(0.373205\pi\)
\(104\) −10.0566 −0.986129
\(105\) −1.66109 −0.162106
\(106\) −7.72420 −0.750241
\(107\) 7.37245 0.712721 0.356361 0.934349i \(-0.384017\pi\)
0.356361 + 0.934349i \(0.384017\pi\)
\(108\) 18.8507 1.81391
\(109\) −9.85633 −0.944065 −0.472033 0.881581i \(-0.656480\pi\)
−0.472033 + 0.881581i \(0.656480\pi\)
\(110\) 4.76928 0.454733
\(111\) 5.45078 0.517365
\(112\) 17.6793 1.67053
\(113\) 16.6941 1.57045 0.785227 0.619209i \(-0.212546\pi\)
0.785227 + 0.619209i \(0.212546\pi\)
\(114\) 3.56200 0.333612
\(115\) −2.76174 −0.257534
\(116\) 19.5403 1.81427
\(117\) −2.64987 −0.244981
\(118\) −7.99715 −0.736198
\(119\) −3.01173 −0.276085
\(120\) 15.6069 1.42471
\(121\) −10.5671 −0.960646
\(122\) 13.8023 1.24960
\(123\) −1.52695 −0.137680
\(124\) −50.5526 −4.53975
\(125\) −8.18631 −0.732206
\(126\) 7.83902 0.698356
\(127\) 1.87527 0.166404 0.0832018 0.996533i \(-0.473485\pi\)
0.0832018 + 0.996533i \(0.473485\pi\)
\(128\) −52.6950 −4.65763
\(129\) −2.33207 −0.205327
\(130\) −7.24873 −0.635756
\(131\) −15.1950 −1.32759 −0.663797 0.747913i \(-0.731056\pi\)
−0.663797 + 0.747913i \(0.731056\pi\)
\(132\) 2.19523 0.191070
\(133\) 2.33132 0.202151
\(134\) −2.59534 −0.224203
\(135\) 8.76807 0.754636
\(136\) 28.2969 2.42644
\(137\) 4.25230 0.363298 0.181649 0.983363i \(-0.441856\pi\)
0.181649 + 0.983363i \(0.441856\pi\)
\(138\) −1.72207 −0.146592
\(139\) −4.19415 −0.355743 −0.177872 0.984054i \(-0.556921\pi\)
−0.177872 + 0.984054i \(0.556921\pi\)
\(140\) 15.8291 1.33781
\(141\) −6.80808 −0.573344
\(142\) −10.5613 −0.886286
\(143\) −0.657947 −0.0550203
\(144\) −43.7684 −3.64737
\(145\) 9.08882 0.754785
\(146\) 8.49213 0.702813
\(147\) 3.46410 0.285714
\(148\) −51.9425 −4.26964
\(149\) −2.17742 −0.178381 −0.0891907 0.996015i \(-0.528428\pi\)
−0.0891907 + 0.996015i \(0.528428\pi\)
\(150\) 3.07241 0.250861
\(151\) 12.2715 0.998641 0.499320 0.866417i \(-0.333583\pi\)
0.499320 + 0.866417i \(0.333583\pi\)
\(152\) −21.9040 −1.77665
\(153\) 7.45613 0.602793
\(154\) 1.94638 0.156844
\(155\) −23.5137 −1.88866
\(156\) −3.33648 −0.267132
\(157\) −21.1098 −1.68475 −0.842373 0.538894i \(-0.818842\pi\)
−0.842373 + 0.538894i \(0.818842\pi\)
\(158\) 30.8656 2.45554
\(159\) −1.65370 −0.131147
\(160\) −66.9772 −5.29501
\(161\) −1.12709 −0.0888269
\(162\) −16.5040 −1.29668
\(163\) −13.2174 −1.03526 −0.517632 0.855604i \(-0.673186\pi\)
−0.517632 + 0.855604i \(0.673186\pi\)
\(164\) 14.5508 1.13623
\(165\) 1.02107 0.0794904
\(166\) −11.2184 −0.870718
\(167\) −16.7542 −1.29648 −0.648239 0.761437i \(-0.724494\pi\)
−0.648239 + 0.761437i \(0.724494\pi\)
\(168\) 6.36928 0.491401
\(169\) 1.00000 0.0769231
\(170\) 20.3962 1.56432
\(171\) −5.77163 −0.441368
\(172\) 22.2232 1.69450
\(173\) 6.70092 0.509462 0.254731 0.967012i \(-0.418013\pi\)
0.254731 + 0.967012i \(0.418013\pi\)
\(174\) 5.66728 0.429636
\(175\) 2.01088 0.152008
\(176\) −10.8674 −0.819164
\(177\) −1.71214 −0.128692
\(178\) −12.2471 −0.917961
\(179\) −10.7996 −0.807198 −0.403599 0.914936i \(-0.632241\pi\)
−0.403599 + 0.914936i \(0.632241\pi\)
\(180\) −39.1881 −2.92091
\(181\) 8.79495 0.653723 0.326862 0.945072i \(-0.394009\pi\)
0.326862 + 0.945072i \(0.394009\pi\)
\(182\) −2.95826 −0.219281
\(183\) 2.95499 0.218439
\(184\) 10.5896 0.780676
\(185\) −24.1602 −1.77629
\(186\) −14.6618 −1.07506
\(187\) 1.85131 0.135381
\(188\) 64.8767 4.73162
\(189\) 3.57832 0.260284
\(190\) −15.7883 −1.14540
\(191\) −10.2555 −0.742062 −0.371031 0.928621i \(-0.620996\pi\)
−0.371031 + 0.928621i \(0.620996\pi\)
\(192\) −22.2164 −1.60333
\(193\) −25.0295 −1.80166 −0.900830 0.434173i \(-0.857041\pi\)
−0.900830 + 0.434173i \(0.857041\pi\)
\(194\) −21.2462 −1.52539
\(195\) −1.55191 −0.111134
\(196\) −33.0106 −2.35790
\(197\) −6.47001 −0.460969 −0.230485 0.973076i \(-0.574031\pi\)
−0.230485 + 0.973076i \(0.574031\pi\)
\(198\) −4.81865 −0.342446
\(199\) −2.16863 −0.153730 −0.0768651 0.997042i \(-0.524491\pi\)
−0.0768651 + 0.997042i \(0.524491\pi\)
\(200\) −18.8933 −1.33596
\(201\) −0.555646 −0.0391922
\(202\) −16.9632 −1.19352
\(203\) 3.70922 0.260336
\(204\) 9.38807 0.657297
\(205\) 6.76807 0.472703
\(206\) −21.7602 −1.51610
\(207\) 2.79032 0.193941
\(208\) 16.5172 1.14526
\(209\) −1.43306 −0.0991269
\(210\) 4.59095 0.316805
\(211\) −17.7708 −1.22339 −0.611695 0.791094i \(-0.709512\pi\)
−0.611695 + 0.791094i \(0.709512\pi\)
\(212\) 15.7587 1.08231
\(213\) −2.26111 −0.154929
\(214\) −20.3761 −1.39288
\(215\) 10.3367 0.704959
\(216\) −33.6203 −2.28757
\(217\) −9.59611 −0.651426
\(218\) 27.2411 1.84500
\(219\) 1.81811 0.122856
\(220\) −9.73017 −0.656008
\(221\) −2.81377 −0.189275
\(222\) −15.0649 −1.01109
\(223\) 6.59973 0.441951 0.220975 0.975279i \(-0.429076\pi\)
0.220975 + 0.975279i \(0.429076\pi\)
\(224\) −27.3339 −1.82632
\(225\) −4.97833 −0.331888
\(226\) −46.1395 −3.06915
\(227\) −4.31146 −0.286161 −0.143081 0.989711i \(-0.545701\pi\)
−0.143081 + 0.989711i \(0.545701\pi\)
\(228\) −7.26711 −0.481276
\(229\) −26.0882 −1.72396 −0.861978 0.506945i \(-0.830775\pi\)
−0.861978 + 0.506945i \(0.830775\pi\)
\(230\) 7.63293 0.503301
\(231\) 0.416708 0.0274173
\(232\) −34.8501 −2.28802
\(233\) 0.0653371 0.00428037 0.00214019 0.999998i \(-0.499319\pi\)
0.00214019 + 0.999998i \(0.499319\pi\)
\(234\) 7.32376 0.478769
\(235\) 30.1763 1.96848
\(236\) 16.3156 1.06205
\(237\) 6.60813 0.429244
\(238\) 8.32387 0.539556
\(239\) −8.00371 −0.517717 −0.258859 0.965915i \(-0.583346\pi\)
−0.258859 + 0.965915i \(0.583346\pi\)
\(240\) −25.6331 −1.65461
\(241\) −3.55639 −0.229087 −0.114544 0.993418i \(-0.536541\pi\)
−0.114544 + 0.993418i \(0.536541\pi\)
\(242\) 29.2055 1.87740
\(243\) −13.5627 −0.870050
\(244\) −28.1591 −1.80270
\(245\) −15.3543 −0.980953
\(246\) 4.22019 0.269070
\(247\) 2.17808 0.138588
\(248\) 90.1607 5.72521
\(249\) −2.40179 −0.152207
\(250\) 22.6254 1.43096
\(251\) −17.7003 −1.11723 −0.558617 0.829426i \(-0.688668\pi\)
−0.558617 + 0.829426i \(0.688668\pi\)
\(252\) −15.9930 −1.00746
\(253\) 0.692820 0.0435572
\(254\) −5.18291 −0.325205
\(255\) 4.36670 0.273454
\(256\) 70.5477 4.40923
\(257\) −16.2614 −1.01436 −0.507179 0.861841i \(-0.669312\pi\)
−0.507179 + 0.861841i \(0.669312\pi\)
\(258\) 6.44541 0.401274
\(259\) −9.85995 −0.612667
\(260\) 14.7887 0.917155
\(261\) −9.18289 −0.568407
\(262\) 41.9962 2.59453
\(263\) 2.64511 0.163104 0.0815522 0.996669i \(-0.474012\pi\)
0.0815522 + 0.996669i \(0.474012\pi\)
\(264\) −3.91520 −0.240964
\(265\) 7.32991 0.450273
\(266\) −6.44333 −0.395066
\(267\) −2.62203 −0.160466
\(268\) 5.29495 0.323441
\(269\) 22.0815 1.34633 0.673166 0.739491i \(-0.264934\pi\)
0.673166 + 0.739491i \(0.264934\pi\)
\(270\) −24.2333 −1.47479
\(271\) 3.29159 0.199950 0.0999750 0.994990i \(-0.468124\pi\)
0.0999750 + 0.994990i \(0.468124\pi\)
\(272\) −46.4755 −2.81799
\(273\) −0.633345 −0.0383318
\(274\) −11.7526 −0.709998
\(275\) −1.23609 −0.0745389
\(276\) 3.51332 0.211477
\(277\) 29.6685 1.78261 0.891303 0.453408i \(-0.149792\pi\)
0.891303 + 0.453408i \(0.149792\pi\)
\(278\) 11.5918 0.695233
\(279\) 23.7570 1.42230
\(280\) −28.2313 −1.68715
\(281\) 5.42150 0.323419 0.161710 0.986838i \(-0.448299\pi\)
0.161710 + 0.986838i \(0.448299\pi\)
\(282\) 18.8163 1.12049
\(283\) 20.6290 1.22627 0.613134 0.789979i \(-0.289908\pi\)
0.613134 + 0.789979i \(0.289908\pi\)
\(284\) 21.5469 1.27858
\(285\) −3.38017 −0.200224
\(286\) 1.81844 0.107527
\(287\) 2.76210 0.163042
\(288\) 67.6705 3.98752
\(289\) −9.08271 −0.534277
\(290\) −25.1198 −1.47508
\(291\) −4.54868 −0.266648
\(292\) −17.3254 −1.01389
\(293\) 15.5022 0.905648 0.452824 0.891600i \(-0.350417\pi\)
0.452824 + 0.891600i \(0.350417\pi\)
\(294\) −9.57411 −0.558374
\(295\) 7.58892 0.441844
\(296\) 92.6396 5.38457
\(297\) −2.19959 −0.127633
\(298\) 6.01799 0.348613
\(299\) −1.05300 −0.0608967
\(300\) −6.26825 −0.361898
\(301\) 4.21850 0.243150
\(302\) −33.9161 −1.95165
\(303\) −3.63170 −0.208636
\(304\) 35.9757 2.06335
\(305\) −13.0977 −0.749975
\(306\) −20.6074 −1.17804
\(307\) −0.326751 −0.0186487 −0.00932434 0.999957i \(-0.502968\pi\)
−0.00932434 + 0.999957i \(0.502968\pi\)
\(308\) −3.97096 −0.226266
\(309\) −4.65871 −0.265025
\(310\) 64.9874 3.69104
\(311\) −32.2087 −1.82639 −0.913195 0.407522i \(-0.866393\pi\)
−0.913195 + 0.407522i \(0.866393\pi\)
\(312\) 5.95062 0.336888
\(313\) −31.5973 −1.78598 −0.892991 0.450074i \(-0.851398\pi\)
−0.892991 + 0.450074i \(0.851398\pi\)
\(314\) 58.3436 3.29252
\(315\) −7.43886 −0.419132
\(316\) −62.9712 −3.54241
\(317\) −24.1963 −1.35900 −0.679501 0.733675i \(-0.737804\pi\)
−0.679501 + 0.733675i \(0.737804\pi\)
\(318\) 4.57052 0.256302
\(319\) −2.28005 −0.127659
\(320\) 98.4724 5.50477
\(321\) −4.36238 −0.243484
\(322\) 3.11506 0.173595
\(323\) −6.12861 −0.341005
\(324\) 33.6710 1.87061
\(325\) 1.87870 0.104212
\(326\) 36.5303 2.02323
\(327\) 5.83213 0.322518
\(328\) −25.9515 −1.43293
\(329\) 12.3152 0.678957
\(330\) −2.82205 −0.155349
\(331\) −8.63363 −0.474547 −0.237274 0.971443i \(-0.576254\pi\)
−0.237274 + 0.971443i \(0.576254\pi\)
\(332\) 22.8875 1.25612
\(333\) 24.4102 1.33767
\(334\) 46.3054 2.53372
\(335\) 2.46286 0.134560
\(336\) −10.4611 −0.570698
\(337\) −13.1776 −0.717829 −0.358915 0.933370i \(-0.616853\pi\)
−0.358915 + 0.933370i \(0.616853\pi\)
\(338\) −2.76381 −0.150332
\(339\) −9.87817 −0.536508
\(340\) −41.6119 −2.25672
\(341\) 5.89873 0.319434
\(342\) 15.9517 0.862570
\(343\) −13.7587 −0.742901
\(344\) −39.6351 −2.13698
\(345\) 1.63416 0.0879803
\(346\) −18.5201 −0.995647
\(347\) 31.7643 1.70519 0.852597 0.522569i \(-0.175026\pi\)
0.852597 + 0.522569i \(0.175026\pi\)
\(348\) −11.5622 −0.619801
\(349\) 12.6312 0.676132 0.338066 0.941122i \(-0.390227\pi\)
0.338066 + 0.941122i \(0.390227\pi\)
\(350\) −5.55770 −0.297071
\(351\) 3.34311 0.178442
\(352\) 16.8022 0.895558
\(353\) 20.2447 1.07752 0.538759 0.842460i \(-0.318893\pi\)
0.538759 + 0.842460i \(0.318893\pi\)
\(354\) 4.73203 0.251505
\(355\) 10.0222 0.531923
\(356\) 24.9863 1.32427
\(357\) 1.78209 0.0943180
\(358\) 29.8480 1.57751
\(359\) −0.273437 −0.0144314 −0.00721572 0.999974i \(-0.502297\pi\)
−0.00721572 + 0.999974i \(0.502297\pi\)
\(360\) 69.8922 3.68364
\(361\) −14.2560 −0.750314
\(362\) −24.3076 −1.27758
\(363\) 6.25271 0.328182
\(364\) 6.03537 0.316339
\(365\) −8.05863 −0.421808
\(366\) −8.16703 −0.426897
\(367\) −2.08904 −0.109047 −0.0545236 0.998512i \(-0.517364\pi\)
−0.0545236 + 0.998512i \(0.517364\pi\)
\(368\) −17.3926 −0.906654
\(369\) −6.83812 −0.355978
\(370\) 66.7742 3.47142
\(371\) 2.99139 0.155305
\(372\) 29.9127 1.55090
\(373\) −5.73885 −0.297147 −0.148573 0.988901i \(-0.547468\pi\)
−0.148573 + 0.988901i \(0.547468\pi\)
\(374\) −5.11668 −0.264577
\(375\) 4.84396 0.250141
\(376\) −115.708 −5.96717
\(377\) 3.46541 0.178477
\(378\) −9.88980 −0.508677
\(379\) 33.1557 1.70309 0.851546 0.524280i \(-0.175665\pi\)
0.851546 + 0.524280i \(0.175665\pi\)
\(380\) 32.2109 1.65238
\(381\) −1.10963 −0.0568479
\(382\) 28.3443 1.45022
\(383\) −28.1923 −1.44056 −0.720279 0.693684i \(-0.755986\pi\)
−0.720279 + 0.693684i \(0.755986\pi\)
\(384\) 31.1804 1.59117
\(385\) −1.84702 −0.0941331
\(386\) 69.1767 3.52100
\(387\) −10.4437 −0.530884
\(388\) 43.3460 2.20056
\(389\) −10.3836 −0.526470 −0.263235 0.964732i \(-0.584789\pi\)
−0.263235 + 0.964732i \(0.584789\pi\)
\(390\) 4.28918 0.217191
\(391\) 2.96291 0.149841
\(392\) 58.8746 2.97362
\(393\) 8.99111 0.453541
\(394\) 17.8819 0.900877
\(395\) −29.2900 −1.47374
\(396\) 9.83088 0.494020
\(397\) 27.3500 1.37266 0.686329 0.727291i \(-0.259221\pi\)
0.686329 + 0.727291i \(0.259221\pi\)
\(398\) 5.99369 0.300437
\(399\) −1.37947 −0.0690601
\(400\) 31.0309 1.55154
\(401\) 25.9508 1.29592 0.647961 0.761673i \(-0.275622\pi\)
0.647961 + 0.761673i \(0.275622\pi\)
\(402\) 1.53570 0.0765938
\(403\) −8.96535 −0.446596
\(404\) 34.6078 1.72180
\(405\) 15.6615 0.778226
\(406\) −10.2516 −0.508777
\(407\) 6.06091 0.300428
\(408\) −16.7437 −0.828935
\(409\) 13.1037 0.647937 0.323969 0.946068i \(-0.394983\pi\)
0.323969 + 0.946068i \(0.394983\pi\)
\(410\) −18.7057 −0.923808
\(411\) −2.51615 −0.124112
\(412\) 44.3945 2.18716
\(413\) 3.09710 0.152398
\(414\) −7.71193 −0.379021
\(415\) 10.6457 0.522579
\(416\) −25.5372 −1.25207
\(417\) 2.48174 0.121531
\(418\) 3.96071 0.193725
\(419\) −25.1347 −1.22791 −0.613955 0.789341i \(-0.710422\pi\)
−0.613955 + 0.789341i \(0.710422\pi\)
\(420\) −9.36633 −0.457030
\(421\) −7.55314 −0.368118 −0.184059 0.982915i \(-0.558924\pi\)
−0.184059 + 0.982915i \(0.558924\pi\)
\(422\) 49.1151 2.39088
\(423\) −30.4886 −1.48241
\(424\) −28.1058 −1.36494
\(425\) −5.28624 −0.256420
\(426\) 6.24928 0.302779
\(427\) −5.34529 −0.258677
\(428\) 41.5707 2.00940
\(429\) 0.389317 0.0187964
\(430\) −28.5688 −1.37771
\(431\) −3.86150 −0.186002 −0.0930010 0.995666i \(-0.529646\pi\)
−0.0930010 + 0.995666i \(0.529646\pi\)
\(432\) 55.2188 2.65671
\(433\) 25.4727 1.22414 0.612069 0.790804i \(-0.290337\pi\)
0.612069 + 0.790804i \(0.290337\pi\)
\(434\) 26.5219 1.27309
\(435\) −5.37798 −0.257855
\(436\) −55.5765 −2.66163
\(437\) −2.29352 −0.109714
\(438\) −5.02491 −0.240100
\(439\) 4.92477 0.235046 0.117523 0.993070i \(-0.462505\pi\)
0.117523 + 0.993070i \(0.462505\pi\)
\(440\) 17.3538 0.827310
\(441\) 15.5133 0.738727
\(442\) 7.77673 0.369901
\(443\) −20.3603 −0.967347 −0.483674 0.875248i \(-0.660698\pi\)
−0.483674 + 0.875248i \(0.660698\pi\)
\(444\) 30.7351 1.45862
\(445\) 11.6219 0.550933
\(446\) −18.2404 −0.863709
\(447\) 1.28841 0.0609398
\(448\) 40.1873 1.89867
\(449\) −29.5154 −1.39292 −0.696459 0.717597i \(-0.745242\pi\)
−0.696459 + 0.717597i \(0.745242\pi\)
\(450\) 13.7592 0.648613
\(451\) −1.69786 −0.0799493
\(452\) 94.1326 4.42763
\(453\) −7.26123 −0.341162
\(454\) 11.9161 0.559248
\(455\) 2.80725 0.131606
\(456\) 12.9609 0.606951
\(457\) −10.5736 −0.494612 −0.247306 0.968937i \(-0.579545\pi\)
−0.247306 + 0.968937i \(0.579545\pi\)
\(458\) 72.1029 3.36915
\(459\) −9.40674 −0.439069
\(460\) −15.5725 −0.726072
\(461\) −15.1162 −0.704030 −0.352015 0.935994i \(-0.614503\pi\)
−0.352015 + 0.935994i \(0.614503\pi\)
\(462\) −1.15170 −0.0535820
\(463\) −18.6858 −0.868404 −0.434202 0.900815i \(-0.642970\pi\)
−0.434202 + 0.900815i \(0.642970\pi\)
\(464\) 57.2387 2.65724
\(465\) 13.9134 0.645217
\(466\) −0.180579 −0.00836518
\(467\) −27.2485 −1.26091 −0.630455 0.776226i \(-0.717132\pi\)
−0.630455 + 0.776226i \(0.717132\pi\)
\(468\) −14.9417 −0.690682
\(469\) 1.00511 0.0464117
\(470\) −83.4016 −3.84703
\(471\) 12.4910 0.575554
\(472\) −29.0989 −1.33939
\(473\) −2.59311 −0.119231
\(474\) −18.2636 −0.838876
\(475\) 4.09196 0.187752
\(476\) −16.9821 −0.778375
\(477\) −7.40577 −0.339087
\(478\) 22.1208 1.01178
\(479\) −9.39706 −0.429362 −0.214681 0.976684i \(-0.568871\pi\)
−0.214681 + 0.976684i \(0.568871\pi\)
\(480\) 39.6314 1.80892
\(481\) −9.21184 −0.420024
\(482\) 9.82920 0.447708
\(483\) 0.666914 0.0303456
\(484\) −59.5843 −2.70838
\(485\) 20.1617 0.915493
\(486\) 37.4848 1.70035
\(487\) 2.73370 0.123876 0.0619378 0.998080i \(-0.480272\pi\)
0.0619378 + 0.998080i \(0.480272\pi\)
\(488\) 50.2219 2.27344
\(489\) 7.82090 0.353673
\(490\) 42.4365 1.91709
\(491\) −7.89944 −0.356497 −0.178248 0.983986i \(-0.557043\pi\)
−0.178248 + 0.983986i \(0.557043\pi\)
\(492\) −8.60993 −0.388166
\(493\) −9.75085 −0.439156
\(494\) −6.01980 −0.270844
\(495\) 4.57267 0.205526
\(496\) −148.082 −6.64909
\(497\) 4.09014 0.183468
\(498\) 6.63809 0.297460
\(499\) 6.51790 0.291781 0.145891 0.989301i \(-0.453395\pi\)
0.145891 + 0.989301i \(0.453395\pi\)
\(500\) −46.1599 −2.06433
\(501\) 9.91369 0.442911
\(502\) 48.9204 2.18342
\(503\) −6.74036 −0.300538 −0.150269 0.988645i \(-0.548014\pi\)
−0.150269 + 0.988645i \(0.548014\pi\)
\(504\) 28.5236 1.27054
\(505\) 16.0972 0.716317
\(506\) −1.91483 −0.0851244
\(507\) −0.591714 −0.0262790
\(508\) 10.5740 0.469147
\(509\) 15.3183 0.678972 0.339486 0.940611i \(-0.389747\pi\)
0.339486 + 0.940611i \(0.389747\pi\)
\(510\) −12.0688 −0.534413
\(511\) −3.28879 −0.145487
\(512\) −89.5904 −3.95938
\(513\) 7.28156 0.321489
\(514\) 44.9435 1.98237
\(515\) 20.6494 0.909919
\(516\) −13.1498 −0.578886
\(517\) −7.57013 −0.332934
\(518\) 27.2511 1.19734
\(519\) −3.96503 −0.174046
\(520\) −26.3757 −1.15665
\(521\) 10.8121 0.473688 0.236844 0.971548i \(-0.423887\pi\)
0.236844 + 0.971548i \(0.423887\pi\)
\(522\) 25.3798 1.11084
\(523\) −0.641001 −0.0280290 −0.0140145 0.999902i \(-0.504461\pi\)
−0.0140145 + 0.999902i \(0.504461\pi\)
\(524\) −85.6795 −3.74293
\(525\) −1.18987 −0.0519300
\(526\) −7.31058 −0.318757
\(527\) 25.2264 1.09888
\(528\) 6.43042 0.279848
\(529\) −21.8912 −0.951791
\(530\) −20.2585 −0.879972
\(531\) −7.66747 −0.332740
\(532\) 13.1455 0.569930
\(533\) 2.58055 0.111776
\(534\) 7.24680 0.313600
\(535\) 19.3359 0.835965
\(536\) −9.44357 −0.407900
\(537\) 6.39026 0.275760
\(538\) −61.0291 −2.63115
\(539\) 3.85185 0.165911
\(540\) 49.4402 2.12757
\(541\) 16.1527 0.694460 0.347230 0.937780i \(-0.387122\pi\)
0.347230 + 0.937780i \(0.387122\pi\)
\(542\) −9.09734 −0.390764
\(543\) −5.20410 −0.223329
\(544\) 71.8559 3.08079
\(545\) −25.8505 −1.10731
\(546\) 1.75045 0.0749122
\(547\) −40.7182 −1.74098 −0.870492 0.492183i \(-0.836199\pi\)
−0.870492 + 0.492183i \(0.836199\pi\)
\(548\) 23.9773 1.02426
\(549\) 13.2333 0.564784
\(550\) 3.41632 0.145672
\(551\) 7.54793 0.321553
\(552\) −6.26602 −0.266700
\(553\) −11.9535 −0.508314
\(554\) −81.9981 −3.48377
\(555\) 14.2959 0.606828
\(556\) −23.6494 −1.00296
\(557\) 5.09376 0.215829 0.107915 0.994160i \(-0.465583\pi\)
0.107915 + 0.994160i \(0.465583\pi\)
\(558\) −65.6600 −2.77961
\(559\) 3.94121 0.166696
\(560\) 46.3679 1.95940
\(561\) −1.09545 −0.0462498
\(562\) −14.9840 −0.632062
\(563\) −30.2989 −1.27695 −0.638473 0.769645i \(-0.720433\pi\)
−0.638473 + 0.769645i \(0.720433\pi\)
\(564\) −38.3884 −1.61645
\(565\) 43.7842 1.84202
\(566\) −57.0148 −2.39651
\(567\) 6.39158 0.268421
\(568\) −38.4291 −1.61245
\(569\) −25.5207 −1.06988 −0.534941 0.844889i \(-0.679666\pi\)
−0.534941 + 0.844889i \(0.679666\pi\)
\(570\) 9.34217 0.391300
\(571\) −28.3537 −1.18656 −0.593282 0.804995i \(-0.702168\pi\)
−0.593282 + 0.804995i \(0.702168\pi\)
\(572\) −3.70994 −0.155120
\(573\) 6.06833 0.253508
\(574\) −7.63393 −0.318634
\(575\) −1.97828 −0.0824999
\(576\) −99.4916 −4.14548
\(577\) −8.84854 −0.368369 −0.184185 0.982892i \(-0.558964\pi\)
−0.184185 + 0.982892i \(0.558964\pi\)
\(578\) 25.1029 1.04414
\(579\) 14.8103 0.615494
\(580\) 51.2488 2.12799
\(581\) 4.34461 0.180245
\(582\) 12.5717 0.521113
\(583\) −1.83881 −0.0761556
\(584\) 30.9000 1.27865
\(585\) −6.94990 −0.287343
\(586\) −42.8452 −1.76992
\(587\) −7.60866 −0.314043 −0.157021 0.987595i \(-0.550189\pi\)
−0.157021 + 0.987595i \(0.550189\pi\)
\(588\) 19.5329 0.805522
\(589\) −19.5272 −0.804606
\(590\) −20.9744 −0.863501
\(591\) 3.82840 0.157479
\(592\) −152.154 −6.25348
\(593\) −26.2359 −1.07738 −0.538689 0.842505i \(-0.681080\pi\)
−0.538689 + 0.842505i \(0.681080\pi\)
\(594\) 6.07926 0.249435
\(595\) −7.89896 −0.323826
\(596\) −12.2777 −0.502916
\(597\) 1.28321 0.0525183
\(598\) 2.91030 0.119011
\(599\) −15.5694 −0.636147 −0.318073 0.948066i \(-0.603036\pi\)
−0.318073 + 0.948066i \(0.603036\pi\)
\(600\) 11.1795 0.456399
\(601\) 31.2521 1.27480 0.637401 0.770532i \(-0.280010\pi\)
0.637401 + 0.770532i \(0.280010\pi\)
\(602\) −11.6591 −0.475191
\(603\) −2.48835 −0.101333
\(604\) 69.1949 2.81550
\(605\) −27.7146 −1.12676
\(606\) 10.0373 0.407739
\(607\) 30.3730 1.23280 0.616401 0.787432i \(-0.288590\pi\)
0.616401 + 0.787432i \(0.288590\pi\)
\(608\) −55.6221 −2.25577
\(609\) −2.19480 −0.0889377
\(610\) 36.1997 1.46568
\(611\) 11.5057 0.465470
\(612\) 42.0426 1.69947
\(613\) 36.2111 1.46255 0.731277 0.682081i \(-0.238925\pi\)
0.731277 + 0.682081i \(0.238925\pi\)
\(614\) 0.903079 0.0364453
\(615\) −4.00476 −0.161488
\(616\) 7.08222 0.285351
\(617\) 1.00000 0.0402585
\(618\) 12.8758 0.517940
\(619\) 9.44032 0.379439 0.189719 0.981838i \(-0.439242\pi\)
0.189719 + 0.981838i \(0.439242\pi\)
\(620\) −132.586 −5.32477
\(621\) −3.52031 −0.141265
\(622\) 89.0189 3.56933
\(623\) 4.74301 0.190025
\(624\) −9.77345 −0.391251
\(625\) −30.8640 −1.23456
\(626\) 87.3289 3.49037
\(627\) 0.847963 0.0338644
\(628\) −119.031 −4.74986
\(629\) 25.9200 1.03350
\(630\) 20.5596 0.819115
\(631\) −26.6434 −1.06066 −0.530328 0.847792i \(-0.677931\pi\)
−0.530328 + 0.847792i \(0.677931\pi\)
\(632\) 112.310 4.46743
\(633\) 10.5152 0.417942
\(634\) 66.8741 2.65591
\(635\) 4.91833 0.195178
\(636\) −9.32466 −0.369747
\(637\) −5.85434 −0.231957
\(638\) 6.30164 0.249485
\(639\) −10.1259 −0.400576
\(640\) −138.205 −5.46302
\(641\) 36.8946 1.45725 0.728624 0.684914i \(-0.240160\pi\)
0.728624 + 0.684914i \(0.240160\pi\)
\(642\) 12.0568 0.475844
\(643\) 41.7028 1.64460 0.822298 0.569057i \(-0.192692\pi\)
0.822298 + 0.569057i \(0.192692\pi\)
\(644\) −6.35526 −0.250432
\(645\) −6.11639 −0.240833
\(646\) 16.9383 0.666430
\(647\) −33.0707 −1.30014 −0.650072 0.759873i \(-0.725261\pi\)
−0.650072 + 0.759873i \(0.725261\pi\)
\(648\) −60.0524 −2.35908
\(649\) −1.90379 −0.0747301
\(650\) −5.19238 −0.203662
\(651\) 5.67816 0.222544
\(652\) −74.5282 −2.91875
\(653\) 41.3500 1.61815 0.809076 0.587704i \(-0.199968\pi\)
0.809076 + 0.587704i \(0.199968\pi\)
\(654\) −16.1189 −0.630300
\(655\) −39.8524 −1.55716
\(656\) 42.6233 1.66416
\(657\) 8.14204 0.317651
\(658\) −34.0368 −1.32689
\(659\) 6.34947 0.247340 0.123670 0.992323i \(-0.460534\pi\)
0.123670 + 0.992323i \(0.460534\pi\)
\(660\) 5.75748 0.224110
\(661\) 23.8071 0.925991 0.462995 0.886361i \(-0.346775\pi\)
0.462995 + 0.886361i \(0.346775\pi\)
\(662\) 23.8617 0.927413
\(663\) 1.66495 0.0646612
\(664\) −40.8200 −1.58412
\(665\) 6.11442 0.237107
\(666\) −67.4653 −2.61423
\(667\) −3.64908 −0.141293
\(668\) −94.4712 −3.65520
\(669\) −3.90516 −0.150982
\(670\) −6.80688 −0.262973
\(671\) 3.28575 0.126845
\(672\) 16.1739 0.623921
\(673\) −11.9508 −0.460670 −0.230335 0.973111i \(-0.573982\pi\)
−0.230335 + 0.973111i \(0.573982\pi\)
\(674\) 36.4204 1.40286
\(675\) 6.28071 0.241745
\(676\) 5.63866 0.216872
\(677\) −0.0527022 −0.00202551 −0.00101276 0.999999i \(-0.500322\pi\)
−0.00101276 + 0.999999i \(0.500322\pi\)
\(678\) 27.3014 1.04850
\(679\) 8.22813 0.315766
\(680\) 74.2150 2.84602
\(681\) 2.55115 0.0977603
\(682\) −16.3030 −0.624273
\(683\) 19.9939 0.765043 0.382522 0.923947i \(-0.375056\pi\)
0.382522 + 0.923947i \(0.375056\pi\)
\(684\) −32.5443 −1.24436
\(685\) 11.1526 0.426120
\(686\) 38.0265 1.45186
\(687\) 15.4368 0.588949
\(688\) 65.0977 2.48183
\(689\) 2.79476 0.106472
\(690\) −4.51651 −0.171941
\(691\) −24.9762 −0.950140 −0.475070 0.879948i \(-0.657577\pi\)
−0.475070 + 0.879948i \(0.657577\pi\)
\(692\) 37.7842 1.43634
\(693\) 1.86614 0.0708888
\(694\) −87.7905 −3.33248
\(695\) −11.0001 −0.417258
\(696\) 20.6213 0.781649
\(697\) −7.26106 −0.275032
\(698\) −34.9103 −1.32137
\(699\) −0.0386609 −0.00146229
\(700\) 11.3387 0.428562
\(701\) −0.758884 −0.0286627 −0.0143313 0.999897i \(-0.504562\pi\)
−0.0143313 + 0.999897i \(0.504562\pi\)
\(702\) −9.23973 −0.348731
\(703\) −20.0641 −0.756733
\(704\) −24.7031 −0.931035
\(705\) −17.8557 −0.672486
\(706\) −55.9527 −2.10581
\(707\) 6.56940 0.247068
\(708\) −9.65417 −0.362826
\(709\) −0.373531 −0.0140282 −0.00701412 0.999975i \(-0.502233\pi\)
−0.00701412 + 0.999975i \(0.502233\pi\)
\(710\) −27.6995 −1.03954
\(711\) 29.5932 1.10983
\(712\) −44.5632 −1.67007
\(713\) 9.44053 0.353551
\(714\) −4.92535 −0.184327
\(715\) −1.72562 −0.0645344
\(716\) −60.8951 −2.27576
\(717\) 4.73591 0.176866
\(718\) 0.755728 0.0282035
\(719\) −30.6445 −1.14285 −0.571423 0.820656i \(-0.693608\pi\)
−0.571423 + 0.820656i \(0.693608\pi\)
\(720\) −114.793 −4.27807
\(721\) 8.42716 0.313844
\(722\) 39.4008 1.46635
\(723\) 2.10437 0.0782622
\(724\) 49.5917 1.84306
\(725\) 6.51047 0.241793
\(726\) −17.2813 −0.641370
\(727\) −11.8581 −0.439792 −0.219896 0.975523i \(-0.570572\pi\)
−0.219896 + 0.975523i \(0.570572\pi\)
\(728\) −10.7641 −0.398945
\(729\) −9.88910 −0.366263
\(730\) 22.2725 0.824344
\(731\) −11.0897 −0.410166
\(732\) 16.6622 0.615851
\(733\) 30.5238 1.12742 0.563712 0.825972i \(-0.309373\pi\)
0.563712 + 0.825972i \(0.309373\pi\)
\(734\) 5.77373 0.213112
\(735\) 9.08538 0.335119
\(736\) 26.8908 0.991207
\(737\) −0.617841 −0.0227585
\(738\) 18.8993 0.695692
\(739\) 26.4789 0.974042 0.487021 0.873390i \(-0.338084\pi\)
0.487021 + 0.873390i \(0.338084\pi\)
\(740\) −136.231 −5.00795
\(741\) −1.28880 −0.0473453
\(742\) −8.26764 −0.303515
\(743\) 17.9438 0.658295 0.329148 0.944279i \(-0.393239\pi\)
0.329148 + 0.944279i \(0.393239\pi\)
\(744\) −53.3494 −1.95588
\(745\) −5.71079 −0.209227
\(746\) 15.8611 0.580717
\(747\) −10.7559 −0.393539
\(748\) 10.4389 0.381685
\(749\) 7.89114 0.288336
\(750\) −13.3878 −0.488853
\(751\) −5.63418 −0.205594 −0.102797 0.994702i \(-0.532779\pi\)
−0.102797 + 0.994702i \(0.532779\pi\)
\(752\) 190.041 6.93010
\(753\) 10.4735 0.381677
\(754\) −9.57773 −0.348800
\(755\) 32.1848 1.17133
\(756\) 20.1769 0.733828
\(757\) −11.7033 −0.425365 −0.212683 0.977121i \(-0.568220\pi\)
−0.212683 + 0.977121i \(0.568220\pi\)
\(758\) −91.6360 −3.32837
\(759\) −0.409952 −0.0148803
\(760\) −57.4483 −2.08387
\(761\) −19.5736 −0.709543 −0.354771 0.934953i \(-0.615441\pi\)
−0.354771 + 0.934953i \(0.615441\pi\)
\(762\) 3.06680 0.111098
\(763\) −10.5498 −0.381928
\(764\) −57.8273 −2.09212
\(765\) 19.5554 0.707027
\(766\) 77.9182 2.81530
\(767\) 2.89352 0.104479
\(768\) −41.7441 −1.50631
\(769\) −45.4659 −1.63954 −0.819771 0.572691i \(-0.805899\pi\)
−0.819771 + 0.572691i \(0.805899\pi\)
\(770\) 5.10483 0.183965
\(771\) 9.62210 0.346532
\(772\) −141.133 −5.07947
\(773\) −46.3230 −1.66612 −0.833062 0.553179i \(-0.813414\pi\)
−0.833062 + 0.553179i \(0.813414\pi\)
\(774\) 28.8645 1.03751
\(775\) −16.8432 −0.605027
\(776\) −77.3078 −2.77519
\(777\) 5.83427 0.209303
\(778\) 28.6983 1.02889
\(779\) 5.62063 0.201380
\(780\) −8.75067 −0.313324
\(781\) −2.51421 −0.0899653
\(782\) −8.18892 −0.292835
\(783\) 11.5852 0.414023
\(784\) −96.6972 −3.45347
\(785\) −55.3653 −1.97607
\(786\) −24.8497 −0.886361
\(787\) 17.6876 0.630495 0.315247 0.949010i \(-0.397912\pi\)
0.315247 + 0.949010i \(0.397912\pi\)
\(788\) −36.4822 −1.29962
\(789\) −1.56515 −0.0557207
\(790\) 80.9521 2.88015
\(791\) 17.8687 0.635337
\(792\) −17.5334 −0.623023
\(793\) −4.99394 −0.177340
\(794\) −75.5903 −2.68260
\(795\) −4.33721 −0.153825
\(796\) −12.2282 −0.433416
\(797\) 25.9172 0.918036 0.459018 0.888427i \(-0.348201\pi\)
0.459018 + 0.888427i \(0.348201\pi\)
\(798\) 3.81261 0.134965
\(799\) −32.3743 −1.14532
\(800\) −47.9769 −1.69624
\(801\) −11.7422 −0.414892
\(802\) −71.7233 −2.53264
\(803\) 2.02162 0.0713413
\(804\) −3.13310 −0.110496
\(805\) −2.95604 −0.104187
\(806\) 24.7785 0.872787
\(807\) −13.0659 −0.459943
\(808\) −61.7232 −2.17141
\(809\) −9.94255 −0.349562 −0.174781 0.984607i \(-0.555922\pi\)
−0.174781 + 0.984607i \(0.555922\pi\)
\(810\) −43.2855 −1.52090
\(811\) 19.9864 0.701819 0.350909 0.936409i \(-0.385872\pi\)
0.350909 + 0.936409i \(0.385872\pi\)
\(812\) 20.9150 0.733973
\(813\) −1.94768 −0.0683082
\(814\) −16.7512 −0.587130
\(815\) −34.6655 −1.21428
\(816\) 27.5002 0.962701
\(817\) 8.58427 0.300326
\(818\) −36.2162 −1.26627
\(819\) −2.83631 −0.0991086
\(820\) 38.1629 1.33270
\(821\) −20.2305 −0.706049 −0.353025 0.935614i \(-0.614847\pi\)
−0.353025 + 0.935614i \(0.614847\pi\)
\(822\) 6.95415 0.242554
\(823\) −37.0117 −1.29015 −0.645074 0.764120i \(-0.723173\pi\)
−0.645074 + 0.764120i \(0.723173\pi\)
\(824\) −79.1778 −2.75829
\(825\) 0.731411 0.0254645
\(826\) −8.55980 −0.297833
\(827\) 11.7570 0.408832 0.204416 0.978884i \(-0.434471\pi\)
0.204416 + 0.978884i \(0.434471\pi\)
\(828\) 15.7337 0.546784
\(829\) −37.4925 −1.30217 −0.651083 0.759006i \(-0.725685\pi\)
−0.651083 + 0.759006i \(0.725685\pi\)
\(830\) −29.4228 −1.02128
\(831\) −17.5553 −0.608985
\(832\) 37.5458 1.30167
\(833\) 16.4728 0.570747
\(834\) −6.85906 −0.237510
\(835\) −43.9417 −1.52066
\(836\) −8.08055 −0.279472
\(837\) −29.9722 −1.03599
\(838\) 69.4675 2.39972
\(839\) 7.71813 0.266459 0.133230 0.991085i \(-0.457465\pi\)
0.133230 + 0.991085i \(0.457465\pi\)
\(840\) 16.7049 0.576374
\(841\) −16.9910 −0.585895
\(842\) 20.8755 0.719416
\(843\) −3.20798 −0.110489
\(844\) −100.203 −3.44914
\(845\) 2.62273 0.0902246
\(846\) 84.2648 2.89708
\(847\) −11.3106 −0.388635
\(848\) 46.1616 1.58520
\(849\) −12.2065 −0.418926
\(850\) 14.6102 0.501125
\(851\) 9.70010 0.332515
\(852\) −12.7496 −0.436795
\(853\) 4.28554 0.146734 0.0733670 0.997305i \(-0.476626\pi\)
0.0733670 + 0.997305i \(0.476626\pi\)
\(854\) 14.7734 0.505535
\(855\) −15.1374 −0.517689
\(856\) −74.1416 −2.53411
\(857\) −3.82734 −0.130739 −0.0653697 0.997861i \(-0.520823\pi\)
−0.0653697 + 0.997861i \(0.520823\pi\)
\(858\) −1.07600 −0.0367340
\(859\) −46.2933 −1.57951 −0.789754 0.613424i \(-0.789792\pi\)
−0.789754 + 0.613424i \(0.789792\pi\)
\(860\) 58.2853 1.98751
\(861\) −1.63438 −0.0556994
\(862\) 10.6725 0.363506
\(863\) 45.4221 1.54619 0.773093 0.634292i \(-0.218708\pi\)
0.773093 + 0.634292i \(0.218708\pi\)
\(864\) −85.3738 −2.90448
\(865\) 17.5747 0.597558
\(866\) −70.4017 −2.39235
\(867\) 5.37437 0.182523
\(868\) −54.1092 −1.83659
\(869\) 7.34780 0.249257
\(870\) 14.8637 0.503928
\(871\) 0.939044 0.0318183
\(872\) 99.1210 3.35666
\(873\) −20.3703 −0.689431
\(874\) 6.33887 0.214415
\(875\) −8.76227 −0.296219
\(876\) 10.2517 0.346373
\(877\) 33.3700 1.12682 0.563412 0.826176i \(-0.309488\pi\)
0.563412 + 0.826176i \(0.309488\pi\)
\(878\) −13.6111 −0.459353
\(879\) −9.17287 −0.309393
\(880\) −28.5023 −0.960813
\(881\) −17.3514 −0.584584 −0.292292 0.956329i \(-0.594418\pi\)
−0.292292 + 0.956329i \(0.594418\pi\)
\(882\) −42.8758 −1.44370
\(883\) 6.25962 0.210653 0.105326 0.994438i \(-0.466411\pi\)
0.105326 + 0.994438i \(0.466411\pi\)
\(884\) −15.8659 −0.533628
\(885\) −4.49047 −0.150946
\(886\) 56.2721 1.89050
\(887\) 14.9361 0.501506 0.250753 0.968051i \(-0.419322\pi\)
0.250753 + 0.968051i \(0.419322\pi\)
\(888\) −54.8162 −1.83951
\(889\) 2.00721 0.0673197
\(890\) −32.1209 −1.07669
\(891\) −3.92890 −0.131623
\(892\) 37.2136 1.24600
\(893\) 25.0603 0.838610
\(894\) −3.56093 −0.119095
\(895\) −28.3243 −0.946778
\(896\) −56.4024 −1.88427
\(897\) 0.623077 0.0208039
\(898\) 81.5750 2.72219
\(899\) −31.0686 −1.03619
\(900\) −28.0711 −0.935703
\(901\) −7.86382 −0.261982
\(902\) 4.69258 0.156246
\(903\) −2.49615 −0.0830665
\(904\) −167.886 −5.58381
\(905\) 23.0668 0.766765
\(906\) 20.0687 0.666737
\(907\) 10.0400 0.333373 0.166686 0.986010i \(-0.446693\pi\)
0.166686 + 0.986010i \(0.446693\pi\)
\(908\) −24.3108 −0.806784
\(909\) −16.2638 −0.539438
\(910\) −7.75872 −0.257199
\(911\) 22.5816 0.748160 0.374080 0.927396i \(-0.377958\pi\)
0.374080 + 0.927396i \(0.377958\pi\)
\(912\) −21.2873 −0.704895
\(913\) −2.67063 −0.0883850
\(914\) 29.2235 0.966626
\(915\) 7.75012 0.256211
\(916\) −147.103 −4.86040
\(917\) −16.2641 −0.537087
\(918\) 25.9985 0.858078
\(919\) −16.4113 −0.541359 −0.270680 0.962669i \(-0.587248\pi\)
−0.270680 + 0.962669i \(0.587248\pi\)
\(920\) 27.7737 0.915670
\(921\) 0.193343 0.00637088
\(922\) 41.7782 1.37589
\(923\) 3.82129 0.125779
\(924\) 2.34967 0.0772986
\(925\) −17.3063 −0.569028
\(926\) 51.6441 1.69713
\(927\) −20.8631 −0.685234
\(928\) −88.4969 −2.90505
\(929\) 9.66178 0.316993 0.158496 0.987360i \(-0.449335\pi\)
0.158496 + 0.987360i \(0.449335\pi\)
\(930\) −38.4540 −1.26096
\(931\) −12.7512 −0.417904
\(932\) 0.368414 0.0120678
\(933\) 19.0584 0.623943
\(934\) 75.3097 2.46421
\(935\) 4.85549 0.158791
\(936\) 26.6487 0.871039
\(937\) 29.8658 0.975672 0.487836 0.872935i \(-0.337786\pi\)
0.487836 + 0.872935i \(0.337786\pi\)
\(938\) −2.77794 −0.0907029
\(939\) 18.6966 0.610139
\(940\) 170.154 5.54981
\(941\) 42.7510 1.39364 0.696822 0.717244i \(-0.254597\pi\)
0.696822 + 0.717244i \(0.254597\pi\)
\(942\) −34.5227 −1.12481
\(943\) −2.71732 −0.0884882
\(944\) 47.7928 1.55552
\(945\) 9.38496 0.305293
\(946\) 7.16687 0.233015
\(947\) 26.4031 0.857986 0.428993 0.903308i \(-0.358868\pi\)
0.428993 + 0.903308i \(0.358868\pi\)
\(948\) 37.2610 1.21018
\(949\) −3.07261 −0.0997412
\(950\) −11.3094 −0.366926
\(951\) 14.3173 0.464271
\(952\) 30.2877 0.981631
\(953\) −2.84048 −0.0920122 −0.0460061 0.998941i \(-0.514649\pi\)
−0.0460061 + 0.998941i \(0.514649\pi\)
\(954\) 20.4682 0.662681
\(955\) −26.8974 −0.870379
\(956\) −45.1302 −1.45962
\(957\) 1.34914 0.0436115
\(958\) 25.9717 0.839108
\(959\) 4.55147 0.146975
\(960\) −58.2675 −1.88058
\(961\) 49.3775 1.59282
\(962\) 25.4598 0.820857
\(963\) −19.5361 −0.629540
\(964\) −20.0533 −0.645873
\(965\) −65.6454 −2.11320
\(966\) −1.84322 −0.0593048
\(967\) −4.16013 −0.133781 −0.0668903 0.997760i \(-0.521308\pi\)
−0.0668903 + 0.997760i \(0.521308\pi\)
\(968\) 106.269 3.41561
\(969\) 3.62639 0.116496
\(970\) −55.7230 −1.78916
\(971\) −8.29182 −0.266097 −0.133049 0.991110i \(-0.542477\pi\)
−0.133049 + 0.991110i \(0.542477\pi\)
\(972\) −76.4756 −2.45296
\(973\) −4.48923 −0.143918
\(974\) −7.55543 −0.242092
\(975\) −1.11166 −0.0356015
\(976\) −82.4858 −2.64031
\(977\) −9.24599 −0.295805 −0.147903 0.989002i \(-0.547252\pi\)
−0.147903 + 0.989002i \(0.547252\pi\)
\(978\) −21.6155 −0.691188
\(979\) −2.91553 −0.0931806
\(980\) −86.5779 −2.76563
\(981\) 26.1180 0.833885
\(982\) 21.8326 0.696706
\(983\) −26.3320 −0.839859 −0.419930 0.907557i \(-0.637945\pi\)
−0.419930 + 0.907557i \(0.637945\pi\)
\(984\) 15.3559 0.489527
\(985\) −16.9691 −0.540680
\(986\) 26.9495 0.858248
\(987\) −7.28706 −0.231950
\(988\) 12.2814 0.390725
\(989\) −4.15011 −0.131966
\(990\) −12.6380 −0.401662
\(991\) −59.9221 −1.90349 −0.951745 0.306891i \(-0.900711\pi\)
−0.951745 + 0.306891i \(0.900711\pi\)
\(992\) 228.950 7.26918
\(993\) 5.10864 0.162118
\(994\) −11.3044 −0.358553
\(995\) −5.68773 −0.180313
\(996\) −13.5429 −0.429122
\(997\) −10.2703 −0.325264 −0.162632 0.986687i \(-0.551998\pi\)
−0.162632 + 0.986687i \(0.551998\pi\)
\(998\) −18.0143 −0.570231
\(999\) −30.7962 −0.974349
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 \(a_p\))