Properties

Label 6047.2.a.a.1.1
Level 6047
Weight 2
Character 6047.1
Self dual Yes
Analytic conductor 48.286
Analytic rank 1
Dimension 217
CM No

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Newspace parameters

Level: \( N \) = \( 6047 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6047.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2855381023\)
Analytic rank: \(1\)
Dimension: \(217\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) = 6047.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.79459 q^{2} -1.21209 q^{3} +5.80974 q^{4} -0.914621 q^{5} +3.38731 q^{6} -4.48023 q^{7} -10.6467 q^{8} -1.53083 q^{9} +O(q^{10})\) \(q-2.79459 q^{2} -1.21209 q^{3} +5.80974 q^{4} -0.914621 q^{5} +3.38731 q^{6} -4.48023 q^{7} -10.6467 q^{8} -1.53083 q^{9} +2.55599 q^{10} -0.426492 q^{11} -7.04195 q^{12} +1.28558 q^{13} +12.5204 q^{14} +1.10861 q^{15} +18.1336 q^{16} +0.227643 q^{17} +4.27803 q^{18} -1.98146 q^{19} -5.31371 q^{20} +5.43046 q^{21} +1.19187 q^{22} +4.20384 q^{23} +12.9048 q^{24} -4.16347 q^{25} -3.59268 q^{26} +5.49179 q^{27} -26.0289 q^{28} +6.36822 q^{29} -3.09810 q^{30} -5.34668 q^{31} -29.3826 q^{32} +0.516949 q^{33} -0.636168 q^{34} +4.09771 q^{35} -8.89370 q^{36} -3.57269 q^{37} +5.53737 q^{38} -1.55825 q^{39} +9.73766 q^{40} -3.75719 q^{41} -15.1759 q^{42} -7.55646 q^{43} -2.47781 q^{44} +1.40013 q^{45} -11.7480 q^{46} -8.56097 q^{47} -21.9796 q^{48} +13.0724 q^{49} +11.6352 q^{50} -0.275924 q^{51} +7.46890 q^{52} -5.56404 q^{53} -15.3473 q^{54} +0.390079 q^{55} +47.6994 q^{56} +2.40172 q^{57} -17.7966 q^{58} +0.103212 q^{59} +6.44072 q^{60} +2.40502 q^{61} +14.9418 q^{62} +6.85845 q^{63} +45.8453 q^{64} -1.17582 q^{65} -1.44466 q^{66} +13.5164 q^{67} +1.32254 q^{68} -5.09545 q^{69} -11.4514 q^{70} +10.0796 q^{71} +16.2982 q^{72} +1.33086 q^{73} +9.98422 q^{74} +5.04652 q^{75} -11.5118 q^{76} +1.91078 q^{77} +4.35467 q^{78} +11.1553 q^{79} -16.5854 q^{80} -2.06409 q^{81} +10.4998 q^{82} -8.22887 q^{83} +31.5495 q^{84} -0.208207 q^{85} +21.1172 q^{86} -7.71888 q^{87} +4.54072 q^{88} +9.10999 q^{89} -3.91278 q^{90} -5.75970 q^{91} +24.4232 q^{92} +6.48068 q^{93} +23.9244 q^{94} +1.81228 q^{95} +35.6145 q^{96} -3.49954 q^{97} -36.5321 q^{98} +0.652885 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 217q - 20q^{2} - 27q^{3} + 184q^{4} - 19q^{5} - 17q^{6} - 48q^{7} - 57q^{8} + 152q^{9} + O(q^{10}) \) \( 217q - 20q^{2} - 27q^{3} + 184q^{4} - 19q^{5} - 17q^{6} - 48q^{7} - 57q^{8} + 152q^{9} - 46q^{10} - 32q^{11} - 72q^{12} - 80q^{13} - 22q^{14} - 43q^{15} + 122q^{16} - 61q^{17} - 88q^{18} - 43q^{19} - 41q^{20} - 61q^{21} - 93q^{22} - 60q^{23} - 41q^{24} + 26q^{25} - 9q^{26} - 93q^{27} - 126q^{28} - 47q^{29} - 36q^{30} - 100q^{31} - 114q^{32} - 133q^{33} - 75q^{34} - 37q^{35} + 75q^{36} - 264q^{37} - 35q^{38} - 47q^{39} - 118q^{40} - 72q^{41} - 64q^{42} - 107q^{43} - 59q^{44} - 69q^{45} - 111q^{46} - 54q^{47} - 135q^{48} + 33q^{49} - 42q^{50} - 26q^{51} - 173q^{52} - 103q^{53} - 28q^{54} - 78q^{55} - 44q^{56} - 205q^{57} - 189q^{58} - 38q^{59} - 105q^{60} - 108q^{61} - 14q^{62} - 116q^{63} + 39q^{64} - 146q^{65} + 5q^{66} - 206q^{67} - 62q^{68} - 55q^{69} - 125q^{70} - 78q^{71} - 225q^{72} - 326q^{73} + 3q^{74} - 95q^{75} - 84q^{76} - 79q^{77} - 86q^{78} - 117q^{79} - 39q^{80} + q^{81} - 96q^{82} - 23q^{83} - 57q^{84} - 224q^{85} - 7q^{86} - 45q^{87} - 250q^{88} - 104q^{89} - 36q^{90} - 96q^{91} - 137q^{92} - 155q^{93} - 48q^{94} - 38q^{95} - 33q^{96} - 447q^{97} - 46q^{98} - 94q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.79459 −1.97607 −0.988037 0.154216i \(-0.950715\pi\)
−0.988037 + 0.154216i \(0.950715\pi\)
\(3\) −1.21209 −0.699803 −0.349902 0.936786i \(-0.613785\pi\)
−0.349902 + 0.936786i \(0.613785\pi\)
\(4\) 5.80974 2.90487
\(5\) −0.914621 −0.409031 −0.204516 0.978863i \(-0.565562\pi\)
−0.204516 + 0.978863i \(0.565562\pi\)
\(6\) 3.38731 1.38286
\(7\) −4.48023 −1.69337 −0.846683 0.532098i \(-0.821404\pi\)
−0.846683 + 0.532098i \(0.821404\pi\)
\(8\) −10.6467 −3.76416
\(9\) −1.53083 −0.510276
\(10\) 2.55599 0.808276
\(11\) −0.426492 −0.128592 −0.0642961 0.997931i \(-0.520480\pi\)
−0.0642961 + 0.997931i \(0.520480\pi\)
\(12\) −7.04195 −2.03284
\(13\) 1.28558 0.356557 0.178278 0.983980i \(-0.442947\pi\)
0.178278 + 0.983980i \(0.442947\pi\)
\(14\) 12.5204 3.34622
\(15\) 1.10861 0.286241
\(16\) 18.1336 4.53340
\(17\) 0.227643 0.0552115 0.0276057 0.999619i \(-0.491212\pi\)
0.0276057 + 0.999619i \(0.491212\pi\)
\(18\) 4.27803 1.00834
\(19\) −1.98146 −0.454578 −0.227289 0.973827i \(-0.572986\pi\)
−0.227289 + 0.973827i \(0.572986\pi\)
\(20\) −5.31371 −1.18818
\(21\) 5.43046 1.18502
\(22\) 1.19187 0.254108
\(23\) 4.20384 0.876560 0.438280 0.898838i \(-0.355588\pi\)
0.438280 + 0.898838i \(0.355588\pi\)
\(24\) 12.9048 2.63417
\(25\) −4.16347 −0.832694
\(26\) −3.59268 −0.704582
\(27\) 5.49179 1.05690
\(28\) −26.0289 −4.91901
\(29\) 6.36822 1.18255 0.591274 0.806471i \(-0.298625\pi\)
0.591274 + 0.806471i \(0.298625\pi\)
\(30\) −3.09810 −0.565634
\(31\) −5.34668 −0.960292 −0.480146 0.877189i \(-0.659416\pi\)
−0.480146 + 0.877189i \(0.659416\pi\)
\(32\) −29.3826 −5.19416
\(33\) 0.516949 0.0899892
\(34\) −0.636168 −0.109102
\(35\) 4.09771 0.692639
\(36\) −8.89370 −1.48228
\(37\) −3.57269 −0.587347 −0.293674 0.955906i \(-0.594878\pi\)
−0.293674 + 0.955906i \(0.594878\pi\)
\(38\) 5.53737 0.898279
\(39\) −1.55825 −0.249519
\(40\) 9.73766 1.53966
\(41\) −3.75719 −0.586775 −0.293387 0.955994i \(-0.594783\pi\)
−0.293387 + 0.955994i \(0.594783\pi\)
\(42\) −15.1759 −2.34169
\(43\) −7.55646 −1.15235 −0.576174 0.817327i \(-0.695455\pi\)
−0.576174 + 0.817327i \(0.695455\pi\)
\(44\) −2.47781 −0.373543
\(45\) 1.40013 0.208719
\(46\) −11.7480 −1.73215
\(47\) −8.56097 −1.24875 −0.624373 0.781126i \(-0.714646\pi\)
−0.624373 + 0.781126i \(0.714646\pi\)
\(48\) −21.9796 −3.17248
\(49\) 13.0724 1.86749
\(50\) 11.6352 1.64546
\(51\) −0.275924 −0.0386372
\(52\) 7.46890 1.03575
\(53\) −5.56404 −0.764280 −0.382140 0.924104i \(-0.624813\pi\)
−0.382140 + 0.924104i \(0.624813\pi\)
\(54\) −15.3473 −2.08850
\(55\) 0.390079 0.0525982
\(56\) 47.6994 6.37411
\(57\) 2.40172 0.318115
\(58\) −17.7966 −2.33680
\(59\) 0.103212 0.0134370 0.00671850 0.999977i \(-0.497861\pi\)
0.00671850 + 0.999977i \(0.497861\pi\)
\(60\) 6.44072 0.831493
\(61\) 2.40502 0.307931 0.153966 0.988076i \(-0.450795\pi\)
0.153966 + 0.988076i \(0.450795\pi\)
\(62\) 14.9418 1.89761
\(63\) 6.85845 0.864083
\(64\) 45.8453 5.73066
\(65\) −1.17582 −0.145843
\(66\) −1.44466 −0.177825
\(67\) 13.5164 1.65129 0.825645 0.564190i \(-0.190812\pi\)
0.825645 + 0.564190i \(0.190812\pi\)
\(68\) 1.32254 0.160382
\(69\) −5.09545 −0.613420
\(70\) −11.4514 −1.36871
\(71\) 10.0796 1.19623 0.598117 0.801409i \(-0.295916\pi\)
0.598117 + 0.801409i \(0.295916\pi\)
\(72\) 16.2982 1.92076
\(73\) 1.33086 0.155765 0.0778825 0.996963i \(-0.475184\pi\)
0.0778825 + 0.996963i \(0.475184\pi\)
\(74\) 9.98422 1.16064
\(75\) 5.04652 0.582722
\(76\) −11.5118 −1.32049
\(77\) 1.91078 0.217754
\(78\) 4.35467 0.493069
\(79\) 11.1553 1.25507 0.627533 0.778590i \(-0.284065\pi\)
0.627533 + 0.778590i \(0.284065\pi\)
\(80\) −16.5854 −1.85430
\(81\) −2.06409 −0.229343
\(82\) 10.4998 1.15951
\(83\) −8.22887 −0.903235 −0.451618 0.892212i \(-0.649153\pi\)
−0.451618 + 0.892212i \(0.649153\pi\)
\(84\) 31.5495 3.44234
\(85\) −0.208207 −0.0225832
\(86\) 21.1172 2.27713
\(87\) −7.71888 −0.827551
\(88\) 4.54072 0.484042
\(89\) 9.10999 0.965657 0.482828 0.875715i \(-0.339609\pi\)
0.482828 + 0.875715i \(0.339609\pi\)
\(90\) −3.91278 −0.412443
\(91\) −5.75970 −0.603781
\(92\) 24.4232 2.54629
\(93\) 6.48068 0.672015
\(94\) 23.9244 2.46762
\(95\) 1.81228 0.185936
\(96\) 35.6145 3.63489
\(97\) −3.49954 −0.355325 −0.177662 0.984092i \(-0.556853\pi\)
−0.177662 + 0.984092i \(0.556853\pi\)
\(98\) −36.5321 −3.69030
\(99\) 0.652885 0.0656174
\(100\) −24.1887 −2.41887
\(101\) 14.2807 1.42098 0.710491 0.703706i \(-0.248473\pi\)
0.710491 + 0.703706i \(0.248473\pi\)
\(102\) 0.771096 0.0763499
\(103\) 8.44198 0.831813 0.415906 0.909407i \(-0.363464\pi\)
0.415906 + 0.909407i \(0.363464\pi\)
\(104\) −13.6872 −1.34214
\(105\) −4.96681 −0.484711
\(106\) 15.5492 1.51027
\(107\) 13.1668 1.27288 0.636442 0.771325i \(-0.280405\pi\)
0.636442 + 0.771325i \(0.280405\pi\)
\(108\) 31.9059 3.07014
\(109\) −19.9674 −1.91253 −0.956266 0.292499i \(-0.905513\pi\)
−0.956266 + 0.292499i \(0.905513\pi\)
\(110\) −1.09011 −0.103938
\(111\) 4.33044 0.411027
\(112\) −81.2425 −7.67670
\(113\) −8.46305 −0.796137 −0.398069 0.917356i \(-0.630319\pi\)
−0.398069 + 0.917356i \(0.630319\pi\)
\(114\) −6.71181 −0.628619
\(115\) −3.84492 −0.358540
\(116\) 36.9977 3.43515
\(117\) −1.96801 −0.181942
\(118\) −0.288434 −0.0265525
\(119\) −1.01989 −0.0934932
\(120\) −11.8030 −1.07746
\(121\) −10.8181 −0.983464
\(122\) −6.72105 −0.608495
\(123\) 4.55407 0.410627
\(124\) −31.0628 −2.78952
\(125\) 8.38110 0.749629
\(126\) −19.1666 −1.70749
\(127\) 3.29113 0.292041 0.146020 0.989282i \(-0.453354\pi\)
0.146020 + 0.989282i \(0.453354\pi\)
\(128\) −69.3535 −6.13004
\(129\) 9.15914 0.806417
\(130\) 3.28594 0.288196
\(131\) 16.5949 1.44990 0.724951 0.688801i \(-0.241863\pi\)
0.724951 + 0.688801i \(0.241863\pi\)
\(132\) 3.00334 0.261407
\(133\) 8.87738 0.769766
\(134\) −37.7728 −3.26307
\(135\) −5.02291 −0.432303
\(136\) −2.42363 −0.207825
\(137\) 12.5911 1.07573 0.537867 0.843030i \(-0.319230\pi\)
0.537867 + 0.843030i \(0.319230\pi\)
\(138\) 14.2397 1.21216
\(139\) 8.71606 0.739286 0.369643 0.929174i \(-0.379480\pi\)
0.369643 + 0.929174i \(0.379480\pi\)
\(140\) 23.8066 2.01203
\(141\) 10.3767 0.873877
\(142\) −28.1685 −2.36385
\(143\) −0.548291 −0.0458504
\(144\) −27.7594 −2.31328
\(145\) −5.82451 −0.483699
\(146\) −3.71920 −0.307803
\(147\) −15.8450 −1.30687
\(148\) −20.7564 −1.70617
\(149\) 5.23431 0.428811 0.214406 0.976745i \(-0.431219\pi\)
0.214406 + 0.976745i \(0.431219\pi\)
\(150\) −14.1030 −1.15150
\(151\) 18.4396 1.50059 0.750295 0.661103i \(-0.229911\pi\)
0.750295 + 0.661103i \(0.229911\pi\)
\(152\) 21.0959 1.71110
\(153\) −0.348482 −0.0281731
\(154\) −5.33985 −0.430297
\(155\) 4.89019 0.392789
\(156\) −9.05302 −0.724821
\(157\) −16.8694 −1.34632 −0.673161 0.739496i \(-0.735064\pi\)
−0.673161 + 0.739496i \(0.735064\pi\)
\(158\) −31.1744 −2.48010
\(159\) 6.74414 0.534845
\(160\) 26.8740 2.12457
\(161\) −18.8341 −1.48434
\(162\) 5.76828 0.453199
\(163\) −8.95554 −0.701452 −0.350726 0.936478i \(-0.614065\pi\)
−0.350726 + 0.936478i \(0.614065\pi\)
\(164\) −21.8283 −1.70450
\(165\) −0.472812 −0.0368084
\(166\) 22.9963 1.78486
\(167\) 15.5230 1.20121 0.600604 0.799547i \(-0.294927\pi\)
0.600604 + 0.799547i \(0.294927\pi\)
\(168\) −57.8162 −4.46062
\(169\) −11.3473 −0.872867
\(170\) 0.581853 0.0446261
\(171\) 3.03327 0.231960
\(172\) −43.9010 −3.34742
\(173\) 21.4978 1.63444 0.817222 0.576323i \(-0.195513\pi\)
0.817222 + 0.576323i \(0.195513\pi\)
\(174\) 21.5711 1.63530
\(175\) 18.6533 1.41005
\(176\) −7.73383 −0.582959
\(177\) −0.125102 −0.00940326
\(178\) −25.4587 −1.90821
\(179\) 22.0751 1.64997 0.824985 0.565155i \(-0.191184\pi\)
0.824985 + 0.565155i \(0.191184\pi\)
\(180\) 8.13437 0.606300
\(181\) −2.76545 −0.205554 −0.102777 0.994704i \(-0.532773\pi\)
−0.102777 + 0.994704i \(0.532773\pi\)
\(182\) 16.0960 1.19312
\(183\) −2.91511 −0.215491
\(184\) −44.7568 −3.29952
\(185\) 3.26766 0.240243
\(186\) −18.1109 −1.32795
\(187\) −0.0970878 −0.00709976
\(188\) −49.7370 −3.62745
\(189\) −24.6045 −1.78971
\(190\) −5.06459 −0.367424
\(191\) −5.13896 −0.371842 −0.185921 0.982565i \(-0.559527\pi\)
−0.185921 + 0.982565i \(0.559527\pi\)
\(192\) −55.5688 −4.01033
\(193\) 10.7492 0.773743 0.386871 0.922134i \(-0.373556\pi\)
0.386871 + 0.922134i \(0.373556\pi\)
\(194\) 9.77979 0.702148
\(195\) 1.42521 0.102061
\(196\) 75.9473 5.42481
\(197\) −9.37150 −0.667692 −0.333846 0.942628i \(-0.608347\pi\)
−0.333846 + 0.942628i \(0.608347\pi\)
\(198\) −1.82455 −0.129665
\(199\) −10.9046 −0.773008 −0.386504 0.922288i \(-0.626317\pi\)
−0.386504 + 0.922288i \(0.626317\pi\)
\(200\) 44.3270 3.13439
\(201\) −16.3831 −1.15558
\(202\) −39.9087 −2.80797
\(203\) −28.5310 −2.00249
\(204\) −1.60305 −0.112236
\(205\) 3.43641 0.240009
\(206\) −23.5919 −1.64372
\(207\) −6.43534 −0.447287
\(208\) 23.3122 1.61641
\(209\) 0.845076 0.0584551
\(210\) 13.8802 0.957825
\(211\) 17.8231 1.22699 0.613496 0.789697i \(-0.289762\pi\)
0.613496 + 0.789697i \(0.289762\pi\)
\(212\) −32.3256 −2.22013
\(213\) −12.2175 −0.837128
\(214\) −36.7959 −2.51531
\(215\) 6.91130 0.471346
\(216\) −58.4692 −3.97833
\(217\) 23.9543 1.62613
\(218\) 55.8008 3.77931
\(219\) −1.61312 −0.109005
\(220\) 2.26625 0.152791
\(221\) 0.292654 0.0196860
\(222\) −12.1018 −0.812221
\(223\) −12.7356 −0.852841 −0.426420 0.904525i \(-0.640226\pi\)
−0.426420 + 0.904525i \(0.640226\pi\)
\(224\) 131.641 8.79562
\(225\) 6.37355 0.424903
\(226\) 23.6508 1.57323
\(227\) 12.2520 0.813193 0.406596 0.913608i \(-0.366716\pi\)
0.406596 + 0.913608i \(0.366716\pi\)
\(228\) 13.9533 0.924082
\(229\) −18.1485 −1.19929 −0.599644 0.800267i \(-0.704691\pi\)
−0.599644 + 0.800267i \(0.704691\pi\)
\(230\) 10.7450 0.708502
\(231\) −2.31605 −0.152385
\(232\) −67.8003 −4.45130
\(233\) 9.03271 0.591753 0.295876 0.955226i \(-0.404388\pi\)
0.295876 + 0.955226i \(0.404388\pi\)
\(234\) 5.49977 0.359531
\(235\) 7.83005 0.510776
\(236\) 0.599632 0.0390327
\(237\) −13.5212 −0.878299
\(238\) 2.85018 0.184750
\(239\) 8.44914 0.546529 0.273265 0.961939i \(-0.411897\pi\)
0.273265 + 0.961939i \(0.411897\pi\)
\(240\) 20.1030 1.29764
\(241\) 2.43983 0.157163 0.0785816 0.996908i \(-0.474961\pi\)
0.0785816 + 0.996908i \(0.474961\pi\)
\(242\) 30.2322 1.94340
\(243\) −13.9735 −0.896400
\(244\) 13.9725 0.894500
\(245\) −11.9563 −0.763861
\(246\) −12.7268 −0.811429
\(247\) −2.54733 −0.162083
\(248\) 56.9243 3.61470
\(249\) 9.97416 0.632087
\(250\) −23.4218 −1.48132
\(251\) 17.0662 1.07721 0.538605 0.842559i \(-0.318952\pi\)
0.538605 + 0.842559i \(0.318952\pi\)
\(252\) 39.8458 2.51005
\(253\) −1.79290 −0.112719
\(254\) −9.19736 −0.577094
\(255\) 0.252366 0.0158038
\(256\) 102.124 6.38276
\(257\) −11.6261 −0.725218 −0.362609 0.931941i \(-0.618114\pi\)
−0.362609 + 0.931941i \(0.618114\pi\)
\(258\) −25.5961 −1.59354
\(259\) 16.0065 0.994594
\(260\) −6.83122 −0.423654
\(261\) −9.74864 −0.603426
\(262\) −46.3759 −2.86511
\(263\) −23.8543 −1.47092 −0.735461 0.677567i \(-0.763034\pi\)
−0.735461 + 0.677567i \(0.763034\pi\)
\(264\) −5.50378 −0.338734
\(265\) 5.08899 0.312614
\(266\) −24.8086 −1.52112
\(267\) −11.0422 −0.675770
\(268\) 78.5267 4.79678
\(269\) −6.57940 −0.401153 −0.200577 0.979678i \(-0.564282\pi\)
−0.200577 + 0.979678i \(0.564282\pi\)
\(270\) 14.0370 0.854263
\(271\) −5.30090 −0.322007 −0.161003 0.986954i \(-0.551473\pi\)
−0.161003 + 0.986954i \(0.551473\pi\)
\(272\) 4.12798 0.250295
\(273\) 6.98130 0.422528
\(274\) −35.1871 −2.12573
\(275\) 1.77569 0.107078
\(276\) −29.6032 −1.78190
\(277\) −0.197680 −0.0118774 −0.00593872 0.999982i \(-0.501890\pi\)
−0.00593872 + 0.999982i \(0.501890\pi\)
\(278\) −24.3578 −1.46088
\(279\) 8.18484 0.490014
\(280\) −43.6269 −2.60721
\(281\) 2.34482 0.139880 0.0699401 0.997551i \(-0.477719\pi\)
0.0699401 + 0.997551i \(0.477719\pi\)
\(282\) −28.9987 −1.72685
\(283\) −11.2977 −0.671581 −0.335791 0.941937i \(-0.609003\pi\)
−0.335791 + 0.941937i \(0.609003\pi\)
\(284\) 58.5601 3.47490
\(285\) −2.19666 −0.130119
\(286\) 1.53225 0.0906038
\(287\) 16.8331 0.993624
\(288\) 44.9797 2.65046
\(289\) −16.9482 −0.996952
\(290\) 16.2771 0.955825
\(291\) 4.24178 0.248657
\(292\) 7.73193 0.452477
\(293\) −4.08951 −0.238912 −0.119456 0.992840i \(-0.538115\pi\)
−0.119456 + 0.992840i \(0.538115\pi\)
\(294\) 44.2803 2.58248
\(295\) −0.0943995 −0.00549615
\(296\) 38.0373 2.21087
\(297\) −2.34220 −0.135908
\(298\) −14.6277 −0.847363
\(299\) 5.40438 0.312543
\(300\) 29.3189 1.69273
\(301\) 33.8546 1.95135
\(302\) −51.5310 −2.96528
\(303\) −17.3096 −0.994408
\(304\) −35.9309 −2.06078
\(305\) −2.19968 −0.125953
\(306\) 0.973863 0.0556721
\(307\) −19.5149 −1.11377 −0.556887 0.830588i \(-0.688005\pi\)
−0.556887 + 0.830588i \(0.688005\pi\)
\(308\) 11.1011 0.632546
\(309\) −10.2325 −0.582105
\(310\) −13.6661 −0.776181
\(311\) 9.29974 0.527340 0.263670 0.964613i \(-0.415067\pi\)
0.263670 + 0.964613i \(0.415067\pi\)
\(312\) 16.5901 0.939232
\(313\) 24.8537 1.40481 0.702406 0.711777i \(-0.252109\pi\)
0.702406 + 0.711777i \(0.252109\pi\)
\(314\) 47.1430 2.66043
\(315\) −6.27288 −0.353437
\(316\) 64.8092 3.64580
\(317\) −15.6566 −0.879361 −0.439680 0.898154i \(-0.644908\pi\)
−0.439680 + 0.898154i \(0.644908\pi\)
\(318\) −18.8471 −1.05689
\(319\) −2.71599 −0.152066
\(320\) −41.9311 −2.34402
\(321\) −15.9594 −0.890768
\(322\) 52.6337 2.93316
\(323\) −0.451065 −0.0250979
\(324\) −11.9918 −0.666212
\(325\) −5.35249 −0.296902
\(326\) 25.0271 1.38612
\(327\) 24.2024 1.33840
\(328\) 40.0015 2.20872
\(329\) 38.3551 2.11458
\(330\) 1.32132 0.0727361
\(331\) −16.7878 −0.922742 −0.461371 0.887207i \(-0.652642\pi\)
−0.461371 + 0.887207i \(0.652642\pi\)
\(332\) −47.8076 −2.62378
\(333\) 5.46917 0.299709
\(334\) −43.3805 −2.37368
\(335\) −12.3624 −0.675429
\(336\) 98.4736 5.37218
\(337\) −11.2959 −0.615327 −0.307663 0.951495i \(-0.599547\pi\)
−0.307663 + 0.951495i \(0.599547\pi\)
\(338\) 31.7110 1.72485
\(339\) 10.2580 0.557139
\(340\) −1.20963 −0.0656013
\(341\) 2.28032 0.123486
\(342\) −8.47675 −0.458370
\(343\) −27.2058 −1.46897
\(344\) 80.4510 4.33763
\(345\) 4.66040 0.250908
\(346\) −60.0774 −3.22978
\(347\) −21.4097 −1.14933 −0.574666 0.818388i \(-0.694868\pi\)
−0.574666 + 0.818388i \(0.694868\pi\)
\(348\) −44.8447 −2.40393
\(349\) 30.0560 1.60886 0.804430 0.594047i \(-0.202471\pi\)
0.804430 + 0.594047i \(0.202471\pi\)
\(350\) −52.1283 −2.78637
\(351\) 7.06015 0.376843
\(352\) 12.5315 0.667929
\(353\) 30.1272 1.60351 0.801754 0.597654i \(-0.203900\pi\)
0.801754 + 0.597654i \(0.203900\pi\)
\(354\) 0.349609 0.0185815
\(355\) −9.21906 −0.489297
\(356\) 52.9267 2.80511
\(357\) 1.23620 0.0654268
\(358\) −61.6909 −3.26046
\(359\) 10.5728 0.558014 0.279007 0.960289i \(-0.409995\pi\)
0.279007 + 0.960289i \(0.409995\pi\)
\(360\) −14.9067 −0.785651
\(361\) −15.0738 −0.793359
\(362\) 7.72829 0.406190
\(363\) 13.1126 0.688231
\(364\) −33.4624 −1.75390
\(365\) −1.21723 −0.0637127
\(366\) 8.14654 0.425827
\(367\) 22.3650 1.16744 0.583722 0.811953i \(-0.301596\pi\)
0.583722 + 0.811953i \(0.301596\pi\)
\(368\) 76.2306 3.97379
\(369\) 5.75161 0.299417
\(370\) −9.13178 −0.474738
\(371\) 24.9282 1.29421
\(372\) 37.6511 1.95212
\(373\) 6.94599 0.359650 0.179825 0.983699i \(-0.442447\pi\)
0.179825 + 0.983699i \(0.442447\pi\)
\(374\) 0.271321 0.0140297
\(375\) −10.1587 −0.524592
\(376\) 91.1458 4.70049
\(377\) 8.18688 0.421646
\(378\) 68.7594 3.53660
\(379\) −9.23700 −0.474473 −0.237236 0.971452i \(-0.576242\pi\)
−0.237236 + 0.971452i \(0.576242\pi\)
\(380\) 10.5289 0.540121
\(381\) −3.98916 −0.204371
\(382\) 14.3613 0.734788
\(383\) 20.9399 1.06998 0.534990 0.844858i \(-0.320315\pi\)
0.534990 + 0.844858i \(0.320315\pi\)
\(384\) 84.0630 4.28982
\(385\) −1.74764 −0.0890680
\(386\) −30.0396 −1.52897
\(387\) 11.5676 0.588016
\(388\) −20.3314 −1.03217
\(389\) −0.0122573 −0.000621468 0 −0.000310734 1.00000i \(-0.500099\pi\)
−0.000310734 1.00000i \(0.500099\pi\)
\(390\) −3.98287 −0.201681
\(391\) 0.956972 0.0483962
\(392\) −139.178 −7.02953
\(393\) −20.1146 −1.01465
\(394\) 26.1895 1.31941
\(395\) −10.2028 −0.513361
\(396\) 3.79309 0.190610
\(397\) −30.7464 −1.54312 −0.771560 0.636157i \(-0.780523\pi\)
−0.771560 + 0.636157i \(0.780523\pi\)
\(398\) 30.4739 1.52752
\(399\) −10.7602 −0.538685
\(400\) −75.4986 −3.77493
\(401\) 2.95771 0.147701 0.0738506 0.997269i \(-0.476471\pi\)
0.0738506 + 0.997269i \(0.476471\pi\)
\(402\) 45.7842 2.28351
\(403\) −6.87360 −0.342399
\(404\) 82.9671 4.12777
\(405\) 1.88786 0.0938085
\(406\) 79.7326 3.95706
\(407\) 1.52372 0.0755282
\(408\) 2.93767 0.145437
\(409\) −14.5776 −0.720815 −0.360407 0.932795i \(-0.617362\pi\)
−0.360407 + 0.932795i \(0.617362\pi\)
\(410\) −9.60335 −0.474276
\(411\) −15.2616 −0.752801
\(412\) 49.0457 2.41631
\(413\) −0.462411 −0.0227538
\(414\) 17.9842 0.883873
\(415\) 7.52630 0.369451
\(416\) −37.7738 −1.85201
\(417\) −10.5647 −0.517355
\(418\) −2.36164 −0.115512
\(419\) −15.6697 −0.765516 −0.382758 0.923849i \(-0.625026\pi\)
−0.382758 + 0.923849i \(0.625026\pi\)
\(420\) −28.8559 −1.40802
\(421\) 3.49158 0.170169 0.0850845 0.996374i \(-0.472884\pi\)
0.0850845 + 0.996374i \(0.472884\pi\)
\(422\) −49.8083 −2.42463
\(423\) 13.1054 0.637205
\(424\) 59.2385 2.87687
\(425\) −0.947783 −0.0459742
\(426\) 34.1429 1.65423
\(427\) −10.7750 −0.521440
\(428\) 76.4958 3.69756
\(429\) 0.664580 0.0320862
\(430\) −19.3142 −0.931416
\(431\) 11.1372 0.536458 0.268229 0.963355i \(-0.413562\pi\)
0.268229 + 0.963355i \(0.413562\pi\)
\(432\) 99.5859 4.79133
\(433\) 16.9007 0.812195 0.406097 0.913830i \(-0.366889\pi\)
0.406097 + 0.913830i \(0.366889\pi\)
\(434\) −66.9426 −3.21335
\(435\) 7.05985 0.338494
\(436\) −116.005 −5.55566
\(437\) −8.32972 −0.398465
\(438\) 4.50802 0.215402
\(439\) 10.5749 0.504712 0.252356 0.967634i \(-0.418795\pi\)
0.252356 + 0.967634i \(0.418795\pi\)
\(440\) −4.15303 −0.197988
\(441\) −20.0116 −0.952934
\(442\) −0.817847 −0.0389010
\(443\) −32.2616 −1.53280 −0.766398 0.642366i \(-0.777953\pi\)
−0.766398 + 0.642366i \(0.777953\pi\)
\(444\) 25.1587 1.19398
\(445\) −8.33219 −0.394984
\(446\) 35.5909 1.68528
\(447\) −6.34447 −0.300083
\(448\) −205.397 −9.70410
\(449\) −29.3845 −1.38674 −0.693370 0.720582i \(-0.743875\pi\)
−0.693370 + 0.720582i \(0.743875\pi\)
\(450\) −17.8115 −0.839640
\(451\) 1.60241 0.0754546
\(452\) −49.1681 −2.31267
\(453\) −22.3505 −1.05012
\(454\) −34.2393 −1.60693
\(455\) 5.26795 0.246965
\(456\) −25.5702 −1.19744
\(457\) 33.0180 1.54452 0.772259 0.635308i \(-0.219127\pi\)
0.772259 + 0.635308i \(0.219127\pi\)
\(458\) 50.7177 2.36988
\(459\) 1.25017 0.0583528
\(460\) −22.3380 −1.04151
\(461\) −23.1621 −1.07877 −0.539383 0.842060i \(-0.681343\pi\)
−0.539383 + 0.842060i \(0.681343\pi\)
\(462\) 6.47240 0.301123
\(463\) −36.2814 −1.68614 −0.843071 0.537803i \(-0.819255\pi\)
−0.843071 + 0.537803i \(0.819255\pi\)
\(464\) 115.479 5.36096
\(465\) −5.92737 −0.274875
\(466\) −25.2427 −1.16935
\(467\) 11.9344 0.552259 0.276129 0.961120i \(-0.410948\pi\)
0.276129 + 0.961120i \(0.410948\pi\)
\(468\) −11.4336 −0.528518
\(469\) −60.5565 −2.79624
\(470\) −21.8818 −1.00933
\(471\) 20.4473 0.942161
\(472\) −1.09886 −0.0505791
\(473\) 3.22277 0.148183
\(474\) 37.7863 1.73558
\(475\) 8.24974 0.378524
\(476\) −5.92530 −0.271586
\(477\) 8.51758 0.389993
\(478\) −23.6119 −1.07998
\(479\) −5.21423 −0.238244 −0.119122 0.992880i \(-0.538008\pi\)
−0.119122 + 0.992880i \(0.538008\pi\)
\(480\) −32.5738 −1.48678
\(481\) −4.59300 −0.209423
\(482\) −6.81832 −0.310566
\(483\) 22.8287 1.03874
\(484\) −62.8504 −2.85683
\(485\) 3.20076 0.145339
\(486\) 39.0502 1.77135
\(487\) 8.81548 0.399467 0.199734 0.979850i \(-0.435992\pi\)
0.199734 + 0.979850i \(0.435992\pi\)
\(488\) −25.6054 −1.15910
\(489\) 10.8550 0.490878
\(490\) 33.4130 1.50945
\(491\) 40.2465 1.81630 0.908150 0.418644i \(-0.137495\pi\)
0.908150 + 0.418644i \(0.137495\pi\)
\(492\) 26.4580 1.19282
\(493\) 1.44968 0.0652902
\(494\) 7.11875 0.320288
\(495\) −0.597143 −0.0268396
\(496\) −96.9545 −4.35339
\(497\) −45.1591 −2.02566
\(498\) −27.8737 −1.24905
\(499\) −39.4831 −1.76751 −0.883753 0.467954i \(-0.844991\pi\)
−0.883753 + 0.467954i \(0.844991\pi\)
\(500\) 48.6920 2.17757
\(501\) −18.8154 −0.840609
\(502\) −47.6931 −2.12865
\(503\) 9.67938 0.431582 0.215791 0.976440i \(-0.430767\pi\)
0.215791 + 0.976440i \(0.430767\pi\)
\(504\) −73.0196 −3.25255
\(505\) −13.0614 −0.581226
\(506\) 5.01043 0.222741
\(507\) 13.7540 0.610835
\(508\) 19.1206 0.848340
\(509\) −9.00561 −0.399167 −0.199583 0.979881i \(-0.563959\pi\)
−0.199583 + 0.979881i \(0.563959\pi\)
\(510\) −0.705261 −0.0312295
\(511\) −5.96254 −0.263767
\(512\) −146.688 −6.48276
\(513\) −10.8818 −0.480441
\(514\) 32.4903 1.43308
\(515\) −7.72121 −0.340237
\(516\) 53.2122 2.34254
\(517\) 3.65119 0.160579
\(518\) −44.7315 −1.96539
\(519\) −26.0573 −1.14379
\(520\) 12.5186 0.548976
\(521\) −31.6804 −1.38794 −0.693972 0.720002i \(-0.744141\pi\)
−0.693972 + 0.720002i \(0.744141\pi\)
\(522\) 27.2435 1.19241
\(523\) −26.6852 −1.16686 −0.583432 0.812162i \(-0.698290\pi\)
−0.583432 + 0.812162i \(0.698290\pi\)
\(524\) 96.4119 4.21177
\(525\) −22.6095 −0.986761
\(526\) 66.6631 2.90665
\(527\) −1.21713 −0.0530191
\(528\) 9.37413 0.407957
\(529\) −5.32777 −0.231642
\(530\) −14.2216 −0.617749
\(531\) −0.157999 −0.00685658
\(532\) 51.5753 2.23607
\(533\) −4.83018 −0.209218
\(534\) 30.8583 1.33537
\(535\) −12.0426 −0.520649
\(536\) −143.904 −6.21572
\(537\) −26.7571 −1.15465
\(538\) 18.3867 0.792708
\(539\) −5.57528 −0.240144
\(540\) −29.1818 −1.25578
\(541\) −30.1681 −1.29703 −0.648513 0.761203i \(-0.724609\pi\)
−0.648513 + 0.761203i \(0.724609\pi\)
\(542\) 14.8138 0.636309
\(543\) 3.35198 0.143847
\(544\) −6.68874 −0.286777
\(545\) 18.2626 0.782285
\(546\) −19.5099 −0.834946
\(547\) 25.7822 1.10237 0.551184 0.834384i \(-0.314176\pi\)
0.551184 + 0.834384i \(0.314176\pi\)
\(548\) 73.1512 3.12486
\(549\) −3.68167 −0.157130
\(550\) −4.96231 −0.211594
\(551\) −12.6184 −0.537560
\(552\) 54.2495 2.30901
\(553\) −49.9781 −2.12529
\(554\) 0.552435 0.0234707
\(555\) −3.96071 −0.168123
\(556\) 50.6380 2.14753
\(557\) 3.17946 0.134718 0.0673589 0.997729i \(-0.478543\pi\)
0.0673589 + 0.997729i \(0.478543\pi\)
\(558\) −22.8733 −0.968303
\(559\) −9.71446 −0.410878
\(560\) 74.3062 3.14001
\(561\) 0.117680 0.00496844
\(562\) −6.55281 −0.276414
\(563\) −23.5743 −0.993536 −0.496768 0.867883i \(-0.665480\pi\)
−0.496768 + 0.867883i \(0.665480\pi\)
\(564\) 60.2860 2.53850
\(565\) 7.74049 0.325645
\(566\) 31.5726 1.32709
\(567\) 9.24758 0.388362
\(568\) −107.315 −4.50282
\(569\) −29.3245 −1.22934 −0.614672 0.788782i \(-0.710712\pi\)
−0.614672 + 0.788782i \(0.710712\pi\)
\(570\) 6.13877 0.257125
\(571\) −25.9696 −1.08679 −0.543397 0.839476i \(-0.682862\pi\)
−0.543397 + 0.839476i \(0.682862\pi\)
\(572\) −3.18543 −0.133189
\(573\) 6.22891 0.260216
\(574\) −47.0415 −1.96348
\(575\) −17.5025 −0.729906
\(576\) −70.1812 −2.92422
\(577\) −10.2125 −0.425153 −0.212577 0.977144i \(-0.568185\pi\)
−0.212577 + 0.977144i \(0.568185\pi\)
\(578\) 47.3632 1.97005
\(579\) −13.0290 −0.541468
\(580\) −33.8389 −1.40508
\(581\) 36.8672 1.52951
\(582\) −11.8540 −0.491365
\(583\) 2.37302 0.0982804
\(584\) −14.1692 −0.586325
\(585\) 1.79998 0.0744200
\(586\) 11.4285 0.472107
\(587\) 15.8686 0.654967 0.327484 0.944857i \(-0.393799\pi\)
0.327484 + 0.944857i \(0.393799\pi\)
\(588\) −92.0553 −3.79630
\(589\) 10.5942 0.436527
\(590\) 0.263808 0.0108608
\(591\) 11.3591 0.467253
\(592\) −64.7857 −2.66268
\(593\) 41.3461 1.69788 0.848940 0.528489i \(-0.177241\pi\)
0.848940 + 0.528489i \(0.177241\pi\)
\(594\) 6.54550 0.268565
\(595\) 0.932814 0.0382416
\(596\) 30.4100 1.24564
\(597\) 13.2174 0.540953
\(598\) −15.1030 −0.617609
\(599\) −13.5022 −0.551683 −0.275842 0.961203i \(-0.588957\pi\)
−0.275842 + 0.961203i \(0.588957\pi\)
\(600\) −53.7286 −2.19346
\(601\) 22.8606 0.932503 0.466252 0.884652i \(-0.345604\pi\)
0.466252 + 0.884652i \(0.345604\pi\)
\(602\) −94.6098 −3.85601
\(603\) −20.6912 −0.842613
\(604\) 107.129 4.35902
\(605\) 9.89447 0.402267
\(606\) 48.3731 1.96502
\(607\) −38.0555 −1.54463 −0.772313 0.635242i \(-0.780900\pi\)
−0.772313 + 0.635242i \(0.780900\pi\)
\(608\) 58.2205 2.36115
\(609\) 34.5823 1.40135
\(610\) 6.14721 0.248893
\(611\) −11.0058 −0.445249
\(612\) −2.02459 −0.0818391
\(613\) 38.4979 1.55491 0.777457 0.628936i \(-0.216509\pi\)
0.777457 + 0.628936i \(0.216509\pi\)
\(614\) 54.5362 2.20090
\(615\) −4.16525 −0.167959
\(616\) −20.3434 −0.819660
\(617\) 27.8232 1.12012 0.560060 0.828452i \(-0.310778\pi\)
0.560060 + 0.828452i \(0.310778\pi\)
\(618\) 28.5956 1.15028
\(619\) 27.6730 1.11227 0.556136 0.831091i \(-0.312283\pi\)
0.556136 + 0.831091i \(0.312283\pi\)
\(620\) 28.4107 1.14100
\(621\) 23.0866 0.926433
\(622\) −25.9890 −1.04206
\(623\) −40.8148 −1.63521
\(624\) −28.2566 −1.13117
\(625\) 13.1518 0.526072
\(626\) −69.4558 −2.77601
\(627\) −1.02431 −0.0409071
\(628\) −98.0067 −3.91089
\(629\) −0.813297 −0.0324283
\(630\) 17.5301 0.698418
\(631\) 0.0369019 0.00146904 0.000734521 1.00000i \(-0.499766\pi\)
0.000734521 1.00000i \(0.499766\pi\)
\(632\) −118.766 −4.72427
\(633\) −21.6033 −0.858653
\(634\) 43.7537 1.73768
\(635\) −3.01014 −0.119454
\(636\) 39.1817 1.55366
\(637\) 16.8057 0.665865
\(638\) 7.59009 0.300495
\(639\) −15.4302 −0.610409
\(640\) 63.4322 2.50738
\(641\) −26.9179 −1.06319 −0.531596 0.846998i \(-0.678408\pi\)
−0.531596 + 0.846998i \(0.678408\pi\)
\(642\) 44.6001 1.76022
\(643\) 30.4760 1.20186 0.600928 0.799303i \(-0.294798\pi\)
0.600928 + 0.799303i \(0.294798\pi\)
\(644\) −109.421 −4.31181
\(645\) −8.37714 −0.329850
\(646\) 1.26054 0.0495953
\(647\) −46.9008 −1.84386 −0.921930 0.387357i \(-0.873388\pi\)
−0.921930 + 0.387357i \(0.873388\pi\)
\(648\) 21.9757 0.863285
\(649\) −0.0440189 −0.00172789
\(650\) 14.9580 0.586701
\(651\) −29.0349 −1.13797
\(652\) −52.0293 −2.03763
\(653\) −31.6870 −1.24001 −0.620005 0.784598i \(-0.712869\pi\)
−0.620005 + 0.784598i \(0.712869\pi\)
\(654\) −67.6358 −2.64477
\(655\) −15.1780 −0.593055
\(656\) −68.1314 −2.66008
\(657\) −2.03731 −0.0794831
\(658\) −107.187 −4.17858
\(659\) −10.7854 −0.420141 −0.210071 0.977686i \(-0.567369\pi\)
−0.210071 + 0.977686i \(0.567369\pi\)
\(660\) −2.74691 −0.106924
\(661\) −3.41140 −0.132688 −0.0663440 0.997797i \(-0.521133\pi\)
−0.0663440 + 0.997797i \(0.521133\pi\)
\(662\) 46.9151 1.82341
\(663\) −0.354724 −0.0137763
\(664\) 87.6100 3.39993
\(665\) −8.11944 −0.314858
\(666\) −15.2841 −0.592247
\(667\) 26.7709 1.03657
\(668\) 90.1848 3.48935
\(669\) 15.4368 0.596821
\(670\) 34.5478 1.33470
\(671\) −1.02572 −0.0395975
\(672\) −159.561 −6.15520
\(673\) −5.59360 −0.215617 −0.107809 0.994172i \(-0.534383\pi\)
−0.107809 + 0.994172i \(0.534383\pi\)
\(674\) 31.5674 1.21593
\(675\) −22.8649 −0.880070
\(676\) −65.9247 −2.53557
\(677\) 21.3254 0.819601 0.409800 0.912175i \(-0.365598\pi\)
0.409800 + 0.912175i \(0.365598\pi\)
\(678\) −28.6670 −1.10095
\(679\) 15.6787 0.601695
\(680\) 2.21671 0.0850069
\(681\) −14.8506 −0.569075
\(682\) −6.37255 −0.244018
\(683\) −34.8788 −1.33460 −0.667299 0.744790i \(-0.732550\pi\)
−0.667299 + 0.744790i \(0.732550\pi\)
\(684\) 17.6225 0.673813
\(685\) −11.5161 −0.440008
\(686\) 76.0291 2.90280
\(687\) 21.9977 0.839265
\(688\) −137.026 −5.22405
\(689\) −7.15304 −0.272509
\(690\) −13.0239 −0.495812
\(691\) 10.0091 0.380764 0.190382 0.981710i \(-0.439027\pi\)
0.190382 + 0.981710i \(0.439027\pi\)
\(692\) 124.896 4.74785
\(693\) −2.92507 −0.111114
\(694\) 59.8313 2.27116
\(695\) −7.97189 −0.302391
\(696\) 82.1803 3.11504
\(697\) −0.855297 −0.0323967
\(698\) −83.9942 −3.17923
\(699\) −10.9485 −0.414110
\(700\) 108.371 4.09603
\(701\) −38.9663 −1.47174 −0.735868 0.677124i \(-0.763226\pi\)
−0.735868 + 0.677124i \(0.763226\pi\)
\(702\) −19.7302 −0.744670
\(703\) 7.07914 0.266995
\(704\) −19.5526 −0.736918
\(705\) −9.49076 −0.357443
\(706\) −84.1932 −3.16865
\(707\) −63.9807 −2.40624
\(708\) −0.726811 −0.0273152
\(709\) −36.8485 −1.38387 −0.691937 0.721958i \(-0.743243\pi\)
−0.691937 + 0.721958i \(0.743243\pi\)
\(710\) 25.7635 0.966887
\(711\) −17.0768 −0.640430
\(712\) −96.9910 −3.63489
\(713\) −22.4766 −0.841754
\(714\) −3.45468 −0.129288
\(715\) 0.501479 0.0187542
\(716\) 128.251 4.79295
\(717\) −10.2412 −0.382463
\(718\) −29.5468 −1.10268
\(719\) −2.88709 −0.107670 −0.0538351 0.998550i \(-0.517145\pi\)
−0.0538351 + 0.998550i \(0.517145\pi\)
\(720\) 25.3893 0.946204
\(721\) −37.8220 −1.40856
\(722\) 42.1252 1.56774
\(723\) −2.95730 −0.109983
\(724\) −16.0665 −0.597108
\(725\) −26.5139 −0.984700
\(726\) −36.6443 −1.36000
\(727\) 17.1855 0.637376 0.318688 0.947860i \(-0.396758\pi\)
0.318688 + 0.947860i \(0.396758\pi\)
\(728\) 61.3216 2.27273
\(729\) 23.1295 0.856647
\(730\) 3.40166 0.125901
\(731\) −1.72017 −0.0636229
\(732\) −16.9360 −0.625974
\(733\) 30.4233 1.12371 0.561856 0.827235i \(-0.310088\pi\)
0.561856 + 0.827235i \(0.310088\pi\)
\(734\) −62.5011 −2.30696
\(735\) 14.4922 0.534552
\(736\) −123.520 −4.55300
\(737\) −5.76463 −0.212343
\(738\) −16.0734 −0.591670
\(739\) 39.9471 1.46948 0.734739 0.678350i \(-0.237305\pi\)
0.734739 + 0.678350i \(0.237305\pi\)
\(740\) 18.9843 0.697875
\(741\) 3.08761 0.113426
\(742\) −69.6640 −2.55745
\(743\) 11.1408 0.408716 0.204358 0.978896i \(-0.434489\pi\)
0.204358 + 0.978896i \(0.434489\pi\)
\(744\) −68.9976 −2.52958
\(745\) −4.78741 −0.175397
\(746\) −19.4112 −0.710694
\(747\) 12.5970 0.460899
\(748\) −0.564055 −0.0206239
\(749\) −58.9903 −2.15546
\(750\) 28.3894 1.03663
\(751\) 21.2368 0.774942 0.387471 0.921882i \(-0.373349\pi\)
0.387471 + 0.921882i \(0.373349\pi\)
\(752\) −155.241 −5.66106
\(753\) −20.6859 −0.753835
\(754\) −22.8790 −0.833203
\(755\) −16.8652 −0.613788
\(756\) −142.945 −5.19888
\(757\) 29.9585 1.08886 0.544429 0.838807i \(-0.316746\pi\)
0.544429 + 0.838807i \(0.316746\pi\)
\(758\) 25.8136 0.937593
\(759\) 2.17317 0.0788809
\(760\) −19.2948 −0.699895
\(761\) −38.3616 −1.39061 −0.695303 0.718717i \(-0.744730\pi\)
−0.695303 + 0.718717i \(0.744730\pi\)
\(762\) 11.1481 0.403852
\(763\) 89.4585 3.23862
\(764\) −29.8560 −1.08015
\(765\) 0.318729 0.0115237
\(766\) −58.5185 −2.11436
\(767\) 0.132687 0.00479105
\(768\) −123.784 −4.46667
\(769\) −16.4140 −0.591902 −0.295951 0.955203i \(-0.595637\pi\)
−0.295951 + 0.955203i \(0.595637\pi\)
\(770\) 4.88394 0.176005
\(771\) 14.0920 0.507510
\(772\) 62.4499 2.24762
\(773\) −42.1091 −1.51456 −0.757280 0.653090i \(-0.773472\pi\)
−0.757280 + 0.653090i \(0.773472\pi\)
\(774\) −32.3268 −1.16196
\(775\) 22.2607 0.799629
\(776\) 37.2584 1.33750
\(777\) −19.4014 −0.696020
\(778\) 0.0342541 0.00122807
\(779\) 7.44472 0.266735
\(780\) 8.28008 0.296475
\(781\) −4.29889 −0.153826
\(782\) −2.67435 −0.0956344
\(783\) 34.9729 1.24983
\(784\) 237.050 8.46606
\(785\) 15.4291 0.550688
\(786\) 56.2120 2.00501
\(787\) −53.9572 −1.92337 −0.961684 0.274161i \(-0.911600\pi\)
−0.961684 + 0.274161i \(0.911600\pi\)
\(788\) −54.4460 −1.93956
\(789\) 28.9137 1.02936
\(790\) 28.5128 1.01444
\(791\) 37.9164 1.34815
\(792\) −6.95105 −0.246995
\(793\) 3.09185 0.109795
\(794\) 85.9237 3.04932
\(795\) −6.16834 −0.218768
\(796\) −63.3530 −2.24549
\(797\) −49.1935 −1.74252 −0.871262 0.490817i \(-0.836698\pi\)
−0.871262 + 0.490817i \(0.836698\pi\)
\(798\) 30.0704 1.06448
\(799\) −1.94884 −0.0689451
\(800\) 122.334 4.32515
\(801\) −13.9458 −0.492751
\(802\) −8.26560 −0.291868
\(803\) −0.567600 −0.0200302
\(804\) −95.1818 −3.35680
\(805\) 17.2261 0.607140
\(806\) 19.2089 0.676605
\(807\) 7.97485 0.280728
\(808\) −152.042 −5.34881
\(809\) 8.87847 0.312151 0.156075 0.987745i \(-0.450116\pi\)
0.156075 + 0.987745i \(0.450116\pi\)
\(810\) −5.27580 −0.185373
\(811\) 1.38301 0.0485642 0.0242821 0.999705i \(-0.492270\pi\)
0.0242821 + 0.999705i \(0.492270\pi\)
\(812\) −165.758 −5.81696
\(813\) 6.42519 0.225341
\(814\) −4.25819 −0.149249
\(815\) 8.19092 0.286916
\(816\) −5.00350 −0.175158
\(817\) 14.9728 0.523832
\(818\) 40.7384 1.42438
\(819\) 8.81711 0.308095
\(820\) 19.9646 0.697195
\(821\) 47.8397 1.66962 0.834809 0.550540i \(-0.185578\pi\)
0.834809 + 0.550540i \(0.185578\pi\)
\(822\) 42.6501 1.48759
\(823\) −11.3481 −0.395570 −0.197785 0.980245i \(-0.563375\pi\)
−0.197785 + 0.980245i \(0.563375\pi\)
\(824\) −89.8789 −3.13108
\(825\) −2.15230 −0.0749334
\(826\) 1.29225 0.0449631
\(827\) 0.795162 0.0276505 0.0138252 0.999904i \(-0.495599\pi\)
0.0138252 + 0.999904i \(0.495599\pi\)
\(828\) −37.3877 −1.29931
\(829\) 25.1587 0.873798 0.436899 0.899511i \(-0.356077\pi\)
0.436899 + 0.899511i \(0.356077\pi\)
\(830\) −21.0329 −0.730063
\(831\) 0.239607 0.00831187
\(832\) 58.9379 2.04330
\(833\) 2.97584 0.103107
\(834\) 29.5240 1.02233
\(835\) −14.1977 −0.491332
\(836\) 4.90967 0.169805
\(837\) −29.3628 −1.01493
\(838\) 43.7905 1.51272
\(839\) 54.2019 1.87126 0.935628 0.352987i \(-0.114834\pi\)
0.935628 + 0.352987i \(0.114834\pi\)
\(840\) 52.8800 1.82453
\(841\) 11.5542 0.398421
\(842\) −9.75752 −0.336267
\(843\) −2.84214 −0.0978885
\(844\) 103.548 3.56425
\(845\) 10.3785 0.357030
\(846\) −36.6241 −1.25916
\(847\) 48.4675 1.66536
\(848\) −100.896 −3.46478
\(849\) 13.6939 0.469975
\(850\) 2.64867 0.0908485
\(851\) −15.0190 −0.514845
\(852\) −70.9804 −2.43175
\(853\) −3.84709 −0.131722 −0.0658609 0.997829i \(-0.520979\pi\)
−0.0658609 + 0.997829i \(0.520979\pi\)
\(854\) 30.1118 1.03040
\(855\) −2.77429 −0.0948788
\(856\) −140.183 −4.79134
\(857\) −11.2926 −0.385748 −0.192874 0.981224i \(-0.561781\pi\)
−0.192874 + 0.981224i \(0.561781\pi\)
\(858\) −1.85723 −0.0634048
\(859\) 7.22184 0.246406 0.123203 0.992381i \(-0.460683\pi\)
0.123203 + 0.992381i \(0.460683\pi\)
\(860\) 40.1528 1.36920
\(861\) −20.4033 −0.695341
\(862\) −31.1238 −1.06008
\(863\) 23.0466 0.784515 0.392257 0.919856i \(-0.371694\pi\)
0.392257 + 0.919856i \(0.371694\pi\)
\(864\) −161.363 −5.48969
\(865\) −19.6623 −0.668538
\(866\) −47.2305 −1.60496
\(867\) 20.5428 0.697670
\(868\) 139.168 4.72368
\(869\) −4.75763 −0.161392
\(870\) −19.7294 −0.668889
\(871\) 17.3764 0.588778
\(872\) 212.586 7.19908
\(873\) 5.35719 0.181314
\(874\) 23.2782 0.787396
\(875\) −37.5492 −1.26940
\(876\) −9.37183 −0.316645
\(877\) 29.6086 0.999810 0.499905 0.866080i \(-0.333368\pi\)
0.499905 + 0.866080i \(0.333368\pi\)
\(878\) −29.5525 −0.997349
\(879\) 4.95687 0.167191
\(880\) 7.07352 0.238448
\(881\) 10.2676 0.345924 0.172962 0.984928i \(-0.444666\pi\)
0.172962 + 0.984928i \(0.444666\pi\)
\(882\) 55.9243 1.88307
\(883\) −5.32155 −0.179084 −0.0895422 0.995983i \(-0.528540\pi\)
−0.0895422 + 0.995983i \(0.528540\pi\)
\(884\) 1.70024 0.0571853
\(885\) 0.114421 0.00384622
\(886\) 90.1580 3.02892
\(887\) −20.6600 −0.693694 −0.346847 0.937922i \(-0.612748\pi\)
−0.346847 + 0.937922i \(0.612748\pi\)
\(888\) −46.1047 −1.54717
\(889\) −14.7450 −0.494532
\(890\) 23.2851 0.780517
\(891\) 0.880317 0.0294917
\(892\) −73.9907 −2.47739
\(893\) 16.9632 0.567652
\(894\) 17.7302 0.592987
\(895\) −20.1904 −0.674889
\(896\) 310.719 10.3804
\(897\) −6.55062 −0.218719
\(898\) 82.1177 2.74030
\(899\) −34.0488 −1.13559
\(900\) 37.0287 1.23429
\(901\) −1.26661 −0.0421970
\(902\) −4.47809 −0.149104
\(903\) −41.0350 −1.36556
\(904\) 90.1033 2.99679
\(905\) 2.52934 0.0840780
\(906\) 62.4605 2.07511
\(907\) −21.9746 −0.729655 −0.364828 0.931075i \(-0.618872\pi\)
−0.364828 + 0.931075i \(0.618872\pi\)
\(908\) 71.1808 2.36222
\(909\) −21.8613 −0.725093
\(910\) −14.7218 −0.488021
\(911\) 24.0125 0.795569 0.397784 0.917479i \(-0.369779\pi\)
0.397784 + 0.917479i \(0.369779\pi\)
\(912\) 43.5517 1.44214
\(913\) 3.50955 0.116149
\(914\) −92.2719 −3.05208
\(915\) 2.66622 0.0881426
\(916\) −105.438 −3.48377
\(917\) −74.3488 −2.45521
\(918\) −3.49370 −0.115309
\(919\) −18.7279 −0.617778 −0.308889 0.951098i \(-0.599957\pi\)
−0.308889 + 0.951098i \(0.599957\pi\)
\(920\) 40.9355 1.34960
\(921\) 23.6539 0.779423
\(922\) 64.7286 2.13172
\(923\) 12.9582 0.426525
\(924\) −13.4556 −0.442657
\(925\) 14.8748 0.489080
\(926\) 101.392 3.33194
\(927\) −12.9232 −0.424454
\(928\) −187.115 −6.14235
\(929\) −1.43056 −0.0469353 −0.0234677 0.999725i \(-0.507471\pi\)
−0.0234677 + 0.999725i \(0.507471\pi\)
\(930\) 16.5646 0.543174
\(931\) −25.9025 −0.848919
\(932\) 52.4777 1.71896
\(933\) −11.2722 −0.369034
\(934\) −33.3518 −1.09130
\(935\) 0.0887985 0.00290402
\(936\) 20.9527 0.684860
\(937\) 0.896442 0.0292855 0.0146427 0.999893i \(-0.495339\pi\)
0.0146427 + 0.999893i \(0.495339\pi\)
\(938\) 169.231 5.52557
\(939\) −30.1250 −0.983092
\(940\) 45.4905 1.48374
\(941\) −20.4367 −0.666217 −0.333108 0.942889i \(-0.608098\pi\)
−0.333108 + 0.942889i \(0.608098\pi\)
\(942\) −57.1418 −1.86178
\(943\) −15.7946 −0.514343
\(944\) 1.87160 0.0609153
\(945\) 22.5038 0.732047
\(946\) −9.00632 −0.292821
\(947\) 9.65097 0.313615 0.156807 0.987629i \(-0.449880\pi\)
0.156807 + 0.987629i \(0.449880\pi\)
\(948\) −78.5549 −2.55134
\(949\) 1.71093 0.0555390
\(950\) −23.0546 −0.747991
\(951\) 18.9772 0.615379
\(952\) 10.8584 0.351924
\(953\) 27.5063 0.891018 0.445509 0.895278i \(-0.353023\pi\)
0.445509 + 0.895278i \(0.353023\pi\)
\(954\) −23.8032 −0.770656
\(955\) 4.70021 0.152095
\(956\) 49.0873 1.58760
\(957\) 3.29204 0.106417
\(958\) 14.5716 0.470789
\(959\) −56.4111 −1.82161
\(960\) 50.8244 1.64035
\(961\) −2.41301 −0.0778389
\(962\) 12.8355 0.413834
\(963\) −20.1561 −0.649522
\(964\) 14.1748 0.456538
\(965\) −9.83143 −0.316485
\(966\) −63.7970 −2.05263
\(967\) −19.8724 −0.639054 −0.319527 0.947577i \(-0.603524\pi\)
−0.319527 + 0.947577i \(0.603524\pi\)
\(968\) 115.177 3.70192
\(969\) 0.546733 0.0175636
\(970\) −8.94480 −0.287200
\(971\) 2.58129 0.0828376 0.0414188 0.999142i \(-0.486812\pi\)
0.0414188 + 0.999142i \(0.486812\pi\)
\(972\) −81.1824 −2.60393
\(973\) −39.0499 −1.25188
\(974\) −24.6357 −0.789377
\(975\) 6.48772 0.207773
\(976\) 43.6116 1.39597
\(977\) 17.6102 0.563399 0.281700 0.959503i \(-0.409102\pi\)
0.281700 + 0.959503i \(0.409102\pi\)
\(978\) −30.3352 −0.970011
\(979\) −3.88534 −0.124176
\(980\) −69.4630 −2.21892
\(981\) 30.5667 0.975918
\(982\) −112.473 −3.58914
\(983\) 45.5776 1.45370 0.726850 0.686796i \(-0.240984\pi\)
0.726850 + 0.686796i \(0.240984\pi\)
\(984\) −48.4857 −1.54567
\(985\) 8.57138 0.273107
\(986\) −4.05126 −0.129018
\(987\) −46.4900 −1.47979
\(988\) −14.7993 −0.470829
\(989\) −31.7661 −1.01010
\(990\) 1.66877 0.0530370
\(991\) 8.83722 0.280723 0.140362 0.990100i \(-0.455173\pi\)
0.140362 + 0.990100i \(0.455173\pi\)
\(992\) 157.100 4.98792
\(993\) 20.3484 0.645737
\(994\) 126.201 4.00286
\(995\) 9.97359 0.316184
\(996\) 57.9473 1.83613
\(997\) −23.2496 −0.736322 −0.368161 0.929762i \(-0.620012\pi\)
−0.368161 + 0.929762i \(0.620012\pi\)
\(998\) 110.339 3.49272
\(999\) −19.6205 −0.620765
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 \(a_p\))