Properties

Label 6023.2.a.b.1.10
Level 6023
Weight 2
Character 6023.1
Self dual Yes
Analytic conductor 48.094
Analytic rank 1
Dimension 99
CM No

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Newspace parameters

Level: \( N \) = \( 6023 = 19 \cdot 317 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6023.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0938971374\)
Analytic rank: \(1\)
Dimension: \(99\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) = 6023.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.31886 q^{2} +2.08746 q^{3} +3.37709 q^{4} -2.67469 q^{5} -4.84053 q^{6} -2.80565 q^{7} -3.19328 q^{8} +1.35751 q^{9} +O(q^{10})\) \(q-2.31886 q^{2} +2.08746 q^{3} +3.37709 q^{4} -2.67469 q^{5} -4.84053 q^{6} -2.80565 q^{7} -3.19328 q^{8} +1.35751 q^{9} +6.20222 q^{10} -0.523568 q^{11} +7.04956 q^{12} -0.617119 q^{13} +6.50589 q^{14} -5.58332 q^{15} +0.650574 q^{16} +1.49554 q^{17} -3.14786 q^{18} -1.00000 q^{19} -9.03268 q^{20} -5.85669 q^{21} +1.21408 q^{22} +2.76755 q^{23} -6.66586 q^{24} +2.15396 q^{25} +1.43101 q^{26} -3.42865 q^{27} -9.47493 q^{28} +0.0305937 q^{29} +12.9469 q^{30} +5.69407 q^{31} +4.87798 q^{32} -1.09293 q^{33} -3.46795 q^{34} +7.50424 q^{35} +4.58442 q^{36} +6.22648 q^{37} +2.31886 q^{38} -1.28821 q^{39} +8.54104 q^{40} +5.91751 q^{41} +13.5808 q^{42} +7.84647 q^{43} -1.76814 q^{44} -3.63091 q^{45} -6.41755 q^{46} +0.916304 q^{47} +1.35805 q^{48} +0.871659 q^{49} -4.99473 q^{50} +3.12189 q^{51} -2.08407 q^{52} -6.24428 q^{53} +7.95054 q^{54} +1.40038 q^{55} +8.95922 q^{56} -2.08746 q^{57} -0.0709423 q^{58} +0.386804 q^{59} -18.8554 q^{60} +7.31561 q^{61} -13.2037 q^{62} -3.80868 q^{63} -12.6125 q^{64} +1.65060 q^{65} +2.53434 q^{66} -7.37904 q^{67} +5.05059 q^{68} +5.77716 q^{69} -17.4012 q^{70} +7.06705 q^{71} -4.33490 q^{72} -14.5270 q^{73} -14.4383 q^{74} +4.49632 q^{75} -3.37709 q^{76} +1.46895 q^{77} +2.98718 q^{78} +0.868280 q^{79} -1.74008 q^{80} -11.2297 q^{81} -13.7219 q^{82} +1.98410 q^{83} -19.7786 q^{84} -4.00012 q^{85} -18.1948 q^{86} +0.0638632 q^{87} +1.67190 q^{88} +14.3097 q^{89} +8.41955 q^{90} +1.73142 q^{91} +9.34627 q^{92} +11.8862 q^{93} -2.12478 q^{94} +2.67469 q^{95} +10.1826 q^{96} +4.63448 q^{97} -2.02125 q^{98} -0.710746 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 99q - 4q^{2} - 3q^{3} + 80q^{4} - 15q^{5} - 12q^{6} - 19q^{7} - 12q^{8} + 58q^{9} + O(q^{10}) \) \( 99q - 4q^{2} - 3q^{3} + 80q^{4} - 15q^{5} - 12q^{6} - 19q^{7} - 12q^{8} + 58q^{9} - 6q^{10} - 9q^{11} - 27q^{12} - 28q^{13} - 13q^{14} - 10q^{15} + 38q^{16} - 36q^{17} - 14q^{18} - 99q^{19} - 34q^{20} - 20q^{21} - 53q^{22} - 38q^{23} - 25q^{24} - 8q^{25} - 3q^{26} - 3q^{27} - 63q^{28} - 34q^{29} - 30q^{30} - 16q^{31} - 43q^{32} - 41q^{33} - 14q^{34} - 25q^{35} - 16q^{36} - 80q^{37} + 4q^{38} - 48q^{39} - 10q^{40} - 32q^{41} - 37q^{42} - 76q^{43} - 21q^{44} - 53q^{45} - 23q^{46} - 31q^{47} - 74q^{48} - 32q^{49} - 29q^{50} - 30q^{51} - 71q^{52} - 35q^{53} - 80q^{54} - 45q^{55} - 33q^{56} + 3q^{57} - 91q^{58} + 12q^{59} - 56q^{60} - 61q^{61} - 46q^{62} - 43q^{63} - 30q^{64} - 46q^{65} - 75q^{66} - 26q^{67} - 55q^{68} - 45q^{69} - 76q^{70} - 41q^{71} - 77q^{72} - 143q^{73} - 64q^{74} - 8q^{75} - 80q^{76} - 58q^{77} - 34q^{78} - 22q^{79} - 36q^{80} - 81q^{81} - 109q^{82} - 7q^{83} - 6q^{84} - 80q^{85} + 32q^{86} - 57q^{87} - 120q^{88} - 28q^{89} - 12q^{90} - 30q^{91} - 107q^{92} - 121q^{93} + 8q^{94} + 15q^{95} + 4q^{96} - 128q^{97} + 54q^{98} - 34q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.31886 −1.63968 −0.819839 0.572593i \(-0.805937\pi\)
−0.819839 + 0.572593i \(0.805937\pi\)
\(3\) 2.08746 1.20520 0.602599 0.798044i \(-0.294132\pi\)
0.602599 + 0.798044i \(0.294132\pi\)
\(4\) 3.37709 1.68855
\(5\) −2.67469 −1.19616 −0.598079 0.801437i \(-0.704069\pi\)
−0.598079 + 0.801437i \(0.704069\pi\)
\(6\) −4.84053 −1.97614
\(7\) −2.80565 −1.06044 −0.530218 0.847862i \(-0.677890\pi\)
−0.530218 + 0.847862i \(0.677890\pi\)
\(8\) −3.19328 −1.12900
\(9\) 1.35751 0.452502
\(10\) 6.20222 1.96131
\(11\) −0.523568 −0.157862 −0.0789308 0.996880i \(-0.525151\pi\)
−0.0789308 + 0.996880i \(0.525151\pi\)
\(12\) 7.04956 2.03503
\(13\) −0.617119 −0.171158 −0.0855791 0.996331i \(-0.527274\pi\)
−0.0855791 + 0.996331i \(0.527274\pi\)
\(14\) 6.50589 1.73877
\(15\) −5.58332 −1.44161
\(16\) 0.650574 0.162643
\(17\) 1.49554 0.362723 0.181361 0.983417i \(-0.441950\pi\)
0.181361 + 0.983417i \(0.441950\pi\)
\(18\) −3.14786 −0.741958
\(19\) −1.00000 −0.229416
\(20\) −9.03268 −2.01977
\(21\) −5.85669 −1.27803
\(22\) 1.21408 0.258842
\(23\) 2.76755 0.577074 0.288537 0.957469i \(-0.406831\pi\)
0.288537 + 0.957469i \(0.406831\pi\)
\(24\) −6.66586 −1.36066
\(25\) 2.15396 0.430792
\(26\) 1.43101 0.280644
\(27\) −3.42865 −0.659843
\(28\) −9.47493 −1.79059
\(29\) 0.0305937 0.00568110 0.00284055 0.999996i \(-0.499096\pi\)
0.00284055 + 0.999996i \(0.499096\pi\)
\(30\) 12.9469 2.36377
\(31\) 5.69407 1.02268 0.511342 0.859377i \(-0.329148\pi\)
0.511342 + 0.859377i \(0.329148\pi\)
\(32\) 4.87798 0.862313
\(33\) −1.09293 −0.190254
\(34\) −3.46795 −0.594749
\(35\) 7.50424 1.26845
\(36\) 4.58442 0.764071
\(37\) 6.22648 1.02363 0.511813 0.859097i \(-0.328974\pi\)
0.511813 + 0.859097i \(0.328974\pi\)
\(38\) 2.31886 0.376168
\(39\) −1.28821 −0.206279
\(40\) 8.54104 1.35046
\(41\) 5.91751 0.924160 0.462080 0.886838i \(-0.347103\pi\)
0.462080 + 0.886838i \(0.347103\pi\)
\(42\) 13.5808 2.09557
\(43\) 7.84647 1.19658 0.598288 0.801281i \(-0.295848\pi\)
0.598288 + 0.801281i \(0.295848\pi\)
\(44\) −1.76814 −0.266557
\(45\) −3.63091 −0.541264
\(46\) −6.41755 −0.946216
\(47\) 0.916304 0.133657 0.0668283 0.997764i \(-0.478712\pi\)
0.0668283 + 0.997764i \(0.478712\pi\)
\(48\) 1.35805 0.196018
\(49\) 0.871659 0.124523
\(50\) −4.99473 −0.706361
\(51\) 3.12189 0.437153
\(52\) −2.08407 −0.289008
\(53\) −6.24428 −0.857718 −0.428859 0.903371i \(-0.641084\pi\)
−0.428859 + 0.903371i \(0.641084\pi\)
\(54\) 7.95054 1.08193
\(55\) 1.40038 0.188827
\(56\) 8.95922 1.19723
\(57\) −2.08746 −0.276491
\(58\) −0.0709423 −0.00931518
\(59\) 0.386804 0.0503576 0.0251788 0.999683i \(-0.491984\pi\)
0.0251788 + 0.999683i \(0.491984\pi\)
\(60\) −18.8554 −2.43422
\(61\) 7.31561 0.936668 0.468334 0.883551i \(-0.344854\pi\)
0.468334 + 0.883551i \(0.344854\pi\)
\(62\) −13.2037 −1.67687
\(63\) −3.80868 −0.479849
\(64\) −12.6125 −1.57656
\(65\) 1.65060 0.204732
\(66\) 2.53434 0.311956
\(67\) −7.37904 −0.901493 −0.450746 0.892652i \(-0.648842\pi\)
−0.450746 + 0.892652i \(0.648842\pi\)
\(68\) 5.05059 0.612474
\(69\) 5.77716 0.695488
\(70\) −17.4012 −2.07985
\(71\) 7.06705 0.838705 0.419352 0.907824i \(-0.362257\pi\)
0.419352 + 0.907824i \(0.362257\pi\)
\(72\) −4.33490 −0.510873
\(73\) −14.5270 −1.70026 −0.850131 0.526571i \(-0.823477\pi\)
−0.850131 + 0.526571i \(0.823477\pi\)
\(74\) −14.4383 −1.67842
\(75\) 4.49632 0.519190
\(76\) −3.37709 −0.387379
\(77\) 1.46895 0.167402
\(78\) 2.98718 0.338232
\(79\) 0.868280 0.0976891 0.0488446 0.998806i \(-0.484446\pi\)
0.0488446 + 0.998806i \(0.484446\pi\)
\(80\) −1.74008 −0.194547
\(81\) −11.2297 −1.24774
\(82\) −13.7219 −1.51533
\(83\) 1.98410 0.217783 0.108891 0.994054i \(-0.465270\pi\)
0.108891 + 0.994054i \(0.465270\pi\)
\(84\) −19.7786 −2.15802
\(85\) −4.00012 −0.433874
\(86\) −18.1948 −1.96200
\(87\) 0.0638632 0.00684685
\(88\) 1.67190 0.178225
\(89\) 14.3097 1.51683 0.758413 0.651774i \(-0.225975\pi\)
0.758413 + 0.651774i \(0.225975\pi\)
\(90\) 8.41955 0.887498
\(91\) 1.73142 0.181502
\(92\) 9.34627 0.974416
\(93\) 11.8862 1.23254
\(94\) −2.12478 −0.219154
\(95\) 2.67469 0.274417
\(96\) 10.1826 1.03926
\(97\) 4.63448 0.470560 0.235280 0.971928i \(-0.424399\pi\)
0.235280 + 0.971928i \(0.424399\pi\)
\(98\) −2.02125 −0.204177
\(99\) −0.710746 −0.0714327
\(100\) 7.27413 0.727413
\(101\) 0.306517 0.0304996 0.0152498 0.999884i \(-0.495146\pi\)
0.0152498 + 0.999884i \(0.495146\pi\)
\(102\) −7.23923 −0.716790
\(103\) −10.6309 −1.04750 −0.523748 0.851873i \(-0.675467\pi\)
−0.523748 + 0.851873i \(0.675467\pi\)
\(104\) 1.97064 0.193237
\(105\) 15.6648 1.52873
\(106\) 14.4796 1.40638
\(107\) −9.36741 −0.905582 −0.452791 0.891617i \(-0.649572\pi\)
−0.452791 + 0.891617i \(0.649572\pi\)
\(108\) −11.5789 −1.11418
\(109\) 6.89495 0.660416 0.330208 0.943908i \(-0.392881\pi\)
0.330208 + 0.943908i \(0.392881\pi\)
\(110\) −3.24728 −0.309616
\(111\) 12.9976 1.23367
\(112\) −1.82528 −0.172473
\(113\) −1.98366 −0.186607 −0.0933036 0.995638i \(-0.529743\pi\)
−0.0933036 + 0.995638i \(0.529743\pi\)
\(114\) 4.84053 0.453357
\(115\) −7.40233 −0.690271
\(116\) 0.103318 0.00959281
\(117\) −0.837743 −0.0774494
\(118\) −0.896944 −0.0825704
\(119\) −4.19597 −0.384644
\(120\) 17.8291 1.62757
\(121\) −10.7259 −0.975080
\(122\) −16.9639 −1.53584
\(123\) 12.3526 1.11380
\(124\) 19.2294 1.72685
\(125\) 7.61227 0.680862
\(126\) 8.83179 0.786798
\(127\) −15.9396 −1.41441 −0.707206 0.707008i \(-0.750044\pi\)
−0.707206 + 0.707008i \(0.750044\pi\)
\(128\) 19.4906 1.72274
\(129\) 16.3792 1.44211
\(130\) −3.82751 −0.335695
\(131\) −1.56198 −0.136471 −0.0682354 0.997669i \(-0.521737\pi\)
−0.0682354 + 0.997669i \(0.521737\pi\)
\(132\) −3.69092 −0.321253
\(133\) 2.80565 0.243281
\(134\) 17.1109 1.47816
\(135\) 9.17057 0.789277
\(136\) −4.77569 −0.409512
\(137\) 13.2396 1.13114 0.565568 0.824702i \(-0.308657\pi\)
0.565568 + 0.824702i \(0.308657\pi\)
\(138\) −13.3964 −1.14038
\(139\) 10.3092 0.874413 0.437207 0.899361i \(-0.355968\pi\)
0.437207 + 0.899361i \(0.355968\pi\)
\(140\) 25.3425 2.14183
\(141\) 1.91275 0.161083
\(142\) −16.3875 −1.37521
\(143\) 0.323104 0.0270193
\(144\) 0.883158 0.0735965
\(145\) −0.0818286 −0.00679549
\(146\) 33.6861 2.78788
\(147\) 1.81956 0.150075
\(148\) 21.0274 1.72844
\(149\) −14.0141 −1.14808 −0.574040 0.818827i \(-0.694625\pi\)
−0.574040 + 0.818827i \(0.694625\pi\)
\(150\) −10.4263 −0.851305
\(151\) −18.5306 −1.50800 −0.753999 0.656875i \(-0.771878\pi\)
−0.753999 + 0.656875i \(0.771878\pi\)
\(152\) 3.19328 0.259009
\(153\) 2.03021 0.164133
\(154\) −3.40627 −0.274485
\(155\) −15.2299 −1.22329
\(156\) −4.35042 −0.348312
\(157\) −21.0577 −1.68058 −0.840292 0.542134i \(-0.817617\pi\)
−0.840292 + 0.542134i \(0.817617\pi\)
\(158\) −2.01342 −0.160179
\(159\) −13.0347 −1.03372
\(160\) −13.0471 −1.03146
\(161\) −7.76477 −0.611949
\(162\) 26.0400 2.04590
\(163\) 15.9279 1.24757 0.623783 0.781597i \(-0.285595\pi\)
0.623783 + 0.781597i \(0.285595\pi\)
\(164\) 19.9840 1.56049
\(165\) 2.92324 0.227574
\(166\) −4.60083 −0.357094
\(167\) 22.1337 1.71276 0.856379 0.516347i \(-0.172709\pi\)
0.856379 + 0.516347i \(0.172709\pi\)
\(168\) 18.7021 1.44290
\(169\) −12.6192 −0.970705
\(170\) 9.27569 0.711413
\(171\) −1.35751 −0.103811
\(172\) 26.4983 2.02047
\(173\) −4.08982 −0.310943 −0.155472 0.987840i \(-0.549690\pi\)
−0.155472 + 0.987840i \(0.549690\pi\)
\(174\) −0.148090 −0.0112266
\(175\) −6.04326 −0.456827
\(176\) −0.340619 −0.0256751
\(177\) 0.807440 0.0606909
\(178\) −33.1822 −2.48711
\(179\) −15.1305 −1.13091 −0.565454 0.824780i \(-0.691299\pi\)
−0.565454 + 0.824780i \(0.691299\pi\)
\(180\) −12.2619 −0.913949
\(181\) −2.69089 −0.200012 −0.100006 0.994987i \(-0.531886\pi\)
−0.100006 + 0.994987i \(0.531886\pi\)
\(182\) −4.01491 −0.297605
\(183\) 15.2711 1.12887
\(184\) −8.83756 −0.651514
\(185\) −16.6539 −1.22442
\(186\) −27.5623 −2.02096
\(187\) −0.783019 −0.0572600
\(188\) 3.09444 0.225685
\(189\) 9.61958 0.699721
\(190\) −6.20222 −0.449956
\(191\) 1.38631 0.100310 0.0501549 0.998741i \(-0.484028\pi\)
0.0501549 + 0.998741i \(0.484028\pi\)
\(192\) −26.3281 −1.90007
\(193\) 4.17797 0.300737 0.150368 0.988630i \(-0.451954\pi\)
0.150368 + 0.988630i \(0.451954\pi\)
\(194\) −10.7467 −0.771567
\(195\) 3.44557 0.246743
\(196\) 2.94368 0.210263
\(197\) −5.62719 −0.400921 −0.200460 0.979702i \(-0.564244\pi\)
−0.200460 + 0.979702i \(0.564244\pi\)
\(198\) 1.64812 0.117127
\(199\) −23.7507 −1.68364 −0.841820 0.539758i \(-0.818516\pi\)
−0.841820 + 0.539758i \(0.818516\pi\)
\(200\) −6.87821 −0.486363
\(201\) −15.4035 −1.08648
\(202\) −0.710770 −0.0500096
\(203\) −0.0858351 −0.00602444
\(204\) 10.5429 0.738153
\(205\) −15.8275 −1.10544
\(206\) 24.6516 1.71756
\(207\) 3.75696 0.261127
\(208\) −0.401482 −0.0278377
\(209\) 0.523568 0.0362159
\(210\) −36.3245 −2.50663
\(211\) −13.0132 −0.895867 −0.447933 0.894067i \(-0.647840\pi\)
−0.447933 + 0.894067i \(0.647840\pi\)
\(212\) −21.0875 −1.44830
\(213\) 14.7522 1.01080
\(214\) 21.7217 1.48486
\(215\) −20.9869 −1.43129
\(216\) 10.9486 0.744960
\(217\) −15.9755 −1.08449
\(218\) −15.9884 −1.08287
\(219\) −30.3247 −2.04915
\(220\) 4.72922 0.318844
\(221\) −0.922929 −0.0620829
\(222\) −30.1395 −2.02283
\(223\) 18.6246 1.24719 0.623597 0.781746i \(-0.285671\pi\)
0.623597 + 0.781746i \(0.285671\pi\)
\(224\) −13.6859 −0.914427
\(225\) 2.92402 0.194934
\(226\) 4.59983 0.305976
\(227\) −20.8972 −1.38700 −0.693498 0.720459i \(-0.743931\pi\)
−0.693498 + 0.720459i \(0.743931\pi\)
\(228\) −7.04956 −0.466869
\(229\) 21.2482 1.40412 0.702059 0.712119i \(-0.252264\pi\)
0.702059 + 0.712119i \(0.252264\pi\)
\(230\) 17.1649 1.13182
\(231\) 3.06637 0.201752
\(232\) −0.0976942 −0.00641394
\(233\) 16.0692 1.05273 0.526365 0.850259i \(-0.323555\pi\)
0.526365 + 0.850259i \(0.323555\pi\)
\(234\) 1.94261 0.126992
\(235\) −2.45083 −0.159874
\(236\) 1.30627 0.0850312
\(237\) 1.81250 0.117735
\(238\) 9.72985 0.630693
\(239\) −6.83459 −0.442093 −0.221046 0.975263i \(-0.570947\pi\)
−0.221046 + 0.975263i \(0.570947\pi\)
\(240\) −3.63236 −0.234468
\(241\) −24.3458 −1.56825 −0.784126 0.620602i \(-0.786888\pi\)
−0.784126 + 0.620602i \(0.786888\pi\)
\(242\) 24.8718 1.59882
\(243\) −13.1556 −0.843935
\(244\) 24.7055 1.58161
\(245\) −2.33142 −0.148949
\(246\) −28.6439 −1.82627
\(247\) 0.617119 0.0392664
\(248\) −18.1828 −1.15461
\(249\) 4.14173 0.262471
\(250\) −17.6517 −1.11639
\(251\) −22.5041 −1.42044 −0.710222 0.703977i \(-0.751406\pi\)
−0.710222 + 0.703977i \(0.751406\pi\)
\(252\) −12.8623 −0.810247
\(253\) −1.44900 −0.0910978
\(254\) 36.9616 2.31918
\(255\) −8.35010 −0.522903
\(256\) −19.9709 −1.24818
\(257\) −22.7200 −1.41723 −0.708617 0.705594i \(-0.750680\pi\)
−0.708617 + 0.705594i \(0.750680\pi\)
\(258\) −37.9811 −2.36460
\(259\) −17.4693 −1.08549
\(260\) 5.57424 0.345700
\(261\) 0.0415311 0.00257071
\(262\) 3.62201 0.223768
\(263\) 15.9402 0.982918 0.491459 0.870901i \(-0.336464\pi\)
0.491459 + 0.870901i \(0.336464\pi\)
\(264\) 3.49003 0.214796
\(265\) 16.7015 1.02597
\(266\) −6.50589 −0.398902
\(267\) 29.8710 1.82808
\(268\) −24.9197 −1.52221
\(269\) −2.03854 −0.124292 −0.0621459 0.998067i \(-0.519794\pi\)
−0.0621459 + 0.998067i \(0.519794\pi\)
\(270\) −21.2652 −1.29416
\(271\) 1.31415 0.0798289 0.0399145 0.999203i \(-0.487291\pi\)
0.0399145 + 0.999203i \(0.487291\pi\)
\(272\) 0.972962 0.0589945
\(273\) 3.61428 0.218746
\(274\) −30.7007 −1.85470
\(275\) −1.12774 −0.0680056
\(276\) 19.5100 1.17436
\(277\) 1.65741 0.0995844 0.0497922 0.998760i \(-0.484144\pi\)
0.0497922 + 0.998760i \(0.484144\pi\)
\(278\) −23.9055 −1.43376
\(279\) 7.72973 0.462767
\(280\) −23.9631 −1.43207
\(281\) −15.6704 −0.934817 −0.467409 0.884041i \(-0.654812\pi\)
−0.467409 + 0.884041i \(0.654812\pi\)
\(282\) −4.43539 −0.264124
\(283\) −0.301582 −0.0179272 −0.00896358 0.999960i \(-0.502853\pi\)
−0.00896358 + 0.999960i \(0.502853\pi\)
\(284\) 23.8661 1.41619
\(285\) 5.58332 0.330727
\(286\) −0.749231 −0.0443030
\(287\) −16.6025 −0.980012
\(288\) 6.62188 0.390198
\(289\) −14.7633 −0.868432
\(290\) 0.189749 0.0111424
\(291\) 9.67430 0.567118
\(292\) −49.0592 −2.87097
\(293\) −8.78123 −0.513005 −0.256502 0.966544i \(-0.582570\pi\)
−0.256502 + 0.966544i \(0.582570\pi\)
\(294\) −4.21929 −0.246074
\(295\) −1.03458 −0.0602357
\(296\) −19.8829 −1.15567
\(297\) 1.79513 0.104164
\(298\) 32.4967 1.88248
\(299\) −1.70791 −0.0987708
\(300\) 15.1845 0.876677
\(301\) −22.0144 −1.26889
\(302\) 42.9698 2.47263
\(303\) 0.639844 0.0367581
\(304\) −0.650574 −0.0373130
\(305\) −19.5670 −1.12040
\(306\) −4.70777 −0.269125
\(307\) −19.5181 −1.11396 −0.556980 0.830526i \(-0.688040\pi\)
−0.556980 + 0.830526i \(0.688040\pi\)
\(308\) 4.96077 0.282666
\(309\) −22.1917 −1.26244
\(310\) 35.3158 2.00580
\(311\) 31.2185 1.77024 0.885118 0.465366i \(-0.154077\pi\)
0.885118 + 0.465366i \(0.154077\pi\)
\(312\) 4.11363 0.232889
\(313\) −12.4909 −0.706028 −0.353014 0.935618i \(-0.614843\pi\)
−0.353014 + 0.935618i \(0.614843\pi\)
\(314\) 48.8297 2.75562
\(315\) 10.1870 0.573975
\(316\) 2.93226 0.164953
\(317\) −1.00000 −0.0561656
\(318\) 30.2256 1.69497
\(319\) −0.0160179 −0.000896828 0
\(320\) 33.7344 1.88581
\(321\) −19.5541 −1.09141
\(322\) 18.0054 1.00340
\(323\) −1.49554 −0.0832143
\(324\) −37.9237 −2.10687
\(325\) −1.32925 −0.0737336
\(326\) −36.9344 −2.04561
\(327\) 14.3930 0.795932
\(328\) −18.8963 −1.04337
\(329\) −2.57083 −0.141734
\(330\) −6.77858 −0.373149
\(331\) −27.4148 −1.50686 −0.753428 0.657531i \(-0.771601\pi\)
−0.753428 + 0.657531i \(0.771601\pi\)
\(332\) 6.70048 0.367737
\(333\) 8.45248 0.463193
\(334\) −51.3249 −2.80837
\(335\) 19.7366 1.07833
\(336\) −3.81021 −0.207864
\(337\) −16.2775 −0.886690 −0.443345 0.896351i \(-0.646208\pi\)
−0.443345 + 0.896351i \(0.646208\pi\)
\(338\) 29.2620 1.59164
\(339\) −4.14082 −0.224899
\(340\) −13.5088 −0.732616
\(341\) −2.98123 −0.161443
\(342\) 3.14786 0.170217
\(343\) 17.1940 0.928387
\(344\) −25.0560 −1.35093
\(345\) −15.4521 −0.831913
\(346\) 9.48371 0.509847
\(347\) 18.7926 1.00884 0.504419 0.863459i \(-0.331707\pi\)
0.504419 + 0.863459i \(0.331707\pi\)
\(348\) 0.215672 0.0115612
\(349\) 20.9810 1.12309 0.561543 0.827448i \(-0.310208\pi\)
0.561543 + 0.827448i \(0.310208\pi\)
\(350\) 14.0134 0.749050
\(351\) 2.11588 0.112938
\(352\) −2.55395 −0.136126
\(353\) −4.12598 −0.219604 −0.109802 0.993953i \(-0.535022\pi\)
−0.109802 + 0.993953i \(0.535022\pi\)
\(354\) −1.87234 −0.0995136
\(355\) −18.9022 −1.00322
\(356\) 48.3252 2.56123
\(357\) −8.75894 −0.463572
\(358\) 35.0855 1.85433
\(359\) −10.1660 −0.536541 −0.268270 0.963344i \(-0.586452\pi\)
−0.268270 + 0.963344i \(0.586452\pi\)
\(360\) 11.5945 0.611084
\(361\) 1.00000 0.0526316
\(362\) 6.23979 0.327956
\(363\) −22.3899 −1.17516
\(364\) 5.84717 0.306475
\(365\) 38.8553 2.03378
\(366\) −35.4114 −1.85099
\(367\) −3.75761 −0.196146 −0.0980728 0.995179i \(-0.531268\pi\)
−0.0980728 + 0.995179i \(0.531268\pi\)
\(368\) 1.80049 0.0938573
\(369\) 8.03306 0.418184
\(370\) 38.6180 2.00765
\(371\) 17.5193 0.909555
\(372\) 40.1407 2.08120
\(373\) −5.65095 −0.292595 −0.146298 0.989241i \(-0.546736\pi\)
−0.146298 + 0.989241i \(0.546736\pi\)
\(374\) 1.81571 0.0938880
\(375\) 15.8903 0.820573
\(376\) −2.92602 −0.150898
\(377\) −0.0188799 −0.000972367 0
\(378\) −22.3064 −1.14732
\(379\) 16.1633 0.830253 0.415127 0.909764i \(-0.363737\pi\)
0.415127 + 0.909764i \(0.363737\pi\)
\(380\) 9.03268 0.463366
\(381\) −33.2733 −1.70465
\(382\) −3.21465 −0.164476
\(383\) −14.5053 −0.741185 −0.370592 0.928796i \(-0.620845\pi\)
−0.370592 + 0.928796i \(0.620845\pi\)
\(384\) 40.6858 2.07624
\(385\) −3.92897 −0.200239
\(386\) −9.68811 −0.493112
\(387\) 10.6516 0.541453
\(388\) 15.6511 0.794562
\(389\) 31.6774 1.60611 0.803053 0.595908i \(-0.203208\pi\)
0.803053 + 0.595908i \(0.203208\pi\)
\(390\) −7.98979 −0.404579
\(391\) 4.13899 0.209318
\(392\) −2.78345 −0.140586
\(393\) −3.26058 −0.164474
\(394\) 13.0486 0.657381
\(395\) −2.32238 −0.116852
\(396\) −2.40026 −0.120617
\(397\) −15.9200 −0.799002 −0.399501 0.916733i \(-0.630817\pi\)
−0.399501 + 0.916733i \(0.630817\pi\)
\(398\) 55.0744 2.76063
\(399\) 5.85669 0.293201
\(400\) 1.40131 0.0700656
\(401\) 24.5378 1.22536 0.612681 0.790331i \(-0.290091\pi\)
0.612681 + 0.790331i \(0.290091\pi\)
\(402\) 35.7184 1.78147
\(403\) −3.51392 −0.175041
\(404\) 1.03514 0.0515000
\(405\) 30.0359 1.49250
\(406\) 0.199039 0.00987815
\(407\) −3.25998 −0.161591
\(408\) −9.96909 −0.493544
\(409\) −9.62036 −0.475696 −0.237848 0.971302i \(-0.576442\pi\)
−0.237848 + 0.971302i \(0.576442\pi\)
\(410\) 36.7017 1.81257
\(411\) 27.6372 1.36324
\(412\) −35.9016 −1.76875
\(413\) −1.08524 −0.0534010
\(414\) −8.71186 −0.428164
\(415\) −5.30684 −0.260503
\(416\) −3.01029 −0.147592
\(417\) 21.5200 1.05384
\(418\) −1.21408 −0.0593825
\(419\) −20.1863 −0.986166 −0.493083 0.869982i \(-0.664130\pi\)
−0.493083 + 0.869982i \(0.664130\pi\)
\(420\) 52.9016 2.58133
\(421\) 7.61530 0.371147 0.185573 0.982630i \(-0.440586\pi\)
0.185573 + 0.982630i \(0.440586\pi\)
\(422\) 30.1758 1.46893
\(423\) 1.24389 0.0604799
\(424\) 19.9398 0.968360
\(425\) 3.22135 0.156258
\(426\) −34.2083 −1.65740
\(427\) −20.5250 −0.993276
\(428\) −31.6346 −1.52912
\(429\) 0.674467 0.0325636
\(430\) 48.6656 2.34686
\(431\) 13.1804 0.634876 0.317438 0.948279i \(-0.397178\pi\)
0.317438 + 0.948279i \(0.397178\pi\)
\(432\) −2.23059 −0.107319
\(433\) −30.0501 −1.44411 −0.722057 0.691833i \(-0.756803\pi\)
−0.722057 + 0.691833i \(0.756803\pi\)
\(434\) 37.0450 1.77822
\(435\) −0.170814 −0.00818991
\(436\) 23.2849 1.11514
\(437\) −2.76755 −0.132390
\(438\) 70.3186 3.35995
\(439\) −8.00880 −0.382239 −0.191120 0.981567i \(-0.561212\pi\)
−0.191120 + 0.981567i \(0.561212\pi\)
\(440\) −4.47181 −0.213185
\(441\) 1.18328 0.0563468
\(442\) 2.14014 0.101796
\(443\) 19.0313 0.904205 0.452103 0.891966i \(-0.350674\pi\)
0.452103 + 0.891966i \(0.350674\pi\)
\(444\) 43.8939 2.08311
\(445\) −38.2740 −1.81436
\(446\) −43.1877 −2.04500
\(447\) −29.2539 −1.38366
\(448\) 35.3862 1.67184
\(449\) 24.9402 1.17700 0.588500 0.808497i \(-0.299718\pi\)
0.588500 + 0.808497i \(0.299718\pi\)
\(450\) −6.78037 −0.319630
\(451\) −3.09822 −0.145889
\(452\) −6.69901 −0.315095
\(453\) −38.6820 −1.81744
\(454\) 48.4576 2.27423
\(455\) −4.63101 −0.217105
\(456\) 6.66586 0.312158
\(457\) 20.8549 0.975549 0.487775 0.872970i \(-0.337809\pi\)
0.487775 + 0.872970i \(0.337809\pi\)
\(458\) −49.2714 −2.30230
\(459\) −5.12769 −0.239340
\(460\) −24.9984 −1.16555
\(461\) −2.42346 −0.112872 −0.0564359 0.998406i \(-0.517974\pi\)
−0.0564359 + 0.998406i \(0.517974\pi\)
\(462\) −7.11048 −0.330809
\(463\) 9.12380 0.424019 0.212009 0.977268i \(-0.431999\pi\)
0.212009 + 0.977268i \(0.431999\pi\)
\(464\) 0.0199034 0.000923994 0
\(465\) −31.7918 −1.47431
\(466\) −37.2622 −1.72614
\(467\) −16.2169 −0.750428 −0.375214 0.926938i \(-0.622431\pi\)
−0.375214 + 0.926938i \(0.622431\pi\)
\(468\) −2.82914 −0.130777
\(469\) 20.7030 0.955975
\(470\) 5.68312 0.262143
\(471\) −43.9571 −2.02544
\(472\) −1.23518 −0.0568536
\(473\) −4.10816 −0.188893
\(474\) −4.20293 −0.193047
\(475\) −2.15396 −0.0988306
\(476\) −14.1702 −0.649489
\(477\) −8.47665 −0.388119
\(478\) 15.8484 0.724890
\(479\) 25.1235 1.14792 0.573960 0.818883i \(-0.305406\pi\)
0.573960 + 0.818883i \(0.305406\pi\)
\(480\) −27.2353 −1.24312
\(481\) −3.84248 −0.175202
\(482\) 56.4544 2.57143
\(483\) −16.2087 −0.737520
\(484\) −36.2223 −1.64647
\(485\) −12.3958 −0.562864
\(486\) 30.5060 1.38378
\(487\) −20.5194 −0.929823 −0.464911 0.885357i \(-0.653914\pi\)
−0.464911 + 0.885357i \(0.653914\pi\)
\(488\) −23.3608 −1.05749
\(489\) 33.2488 1.50356
\(490\) 5.40622 0.244228
\(491\) 16.5837 0.748411 0.374205 0.927346i \(-0.377915\pi\)
0.374205 + 0.927346i \(0.377915\pi\)
\(492\) 41.7159 1.88070
\(493\) 0.0457542 0.00206066
\(494\) −1.43101 −0.0643842
\(495\) 1.90102 0.0854447
\(496\) 3.70441 0.166333
\(497\) −19.8277 −0.889392
\(498\) −9.60407 −0.430369
\(499\) −0.0231070 −0.00103441 −0.000517205 1.00000i \(-0.500165\pi\)
−0.000517205 1.00000i \(0.500165\pi\)
\(500\) 25.7073 1.14967
\(501\) 46.2033 2.06421
\(502\) 52.1837 2.32907
\(503\) −0.700169 −0.0312190 −0.0156095 0.999878i \(-0.504969\pi\)
−0.0156095 + 0.999878i \(0.504969\pi\)
\(504\) 12.1622 0.541747
\(505\) −0.819839 −0.0364823
\(506\) 3.36002 0.149371
\(507\) −26.3420 −1.16989
\(508\) −53.8295 −2.38830
\(509\) 14.0353 0.622102 0.311051 0.950393i \(-0.399319\pi\)
0.311051 + 0.950393i \(0.399319\pi\)
\(510\) 19.3627 0.857394
\(511\) 40.7578 1.80302
\(512\) 7.32841 0.323873
\(513\) 3.42865 0.151378
\(514\) 52.6844 2.32381
\(515\) 28.4344 1.25297
\(516\) 55.3142 2.43507
\(517\) −0.479747 −0.0210992
\(518\) 40.5088 1.77986
\(519\) −8.53736 −0.374748
\(520\) −5.27084 −0.231142
\(521\) −36.6462 −1.60550 −0.802749 0.596316i \(-0.796630\pi\)
−0.802749 + 0.596316i \(0.796630\pi\)
\(522\) −0.0963046 −0.00421514
\(523\) −27.7829 −1.21486 −0.607431 0.794372i \(-0.707800\pi\)
−0.607431 + 0.794372i \(0.707800\pi\)
\(524\) −5.27495 −0.230437
\(525\) −12.6151 −0.550568
\(526\) −36.9631 −1.61167
\(527\) 8.51573 0.370951
\(528\) −0.711031 −0.0309436
\(529\) −15.3407 −0.666986
\(530\) −38.7284 −1.68226
\(531\) 0.525089 0.0227869
\(532\) 9.47493 0.410791
\(533\) −3.65181 −0.158178
\(534\) −69.2665 −2.99746
\(535\) 25.0549 1.08322
\(536\) 23.5633 1.01778
\(537\) −31.5844 −1.36297
\(538\) 4.72707 0.203799
\(539\) −0.456373 −0.0196574
\(540\) 30.9699 1.33273
\(541\) −37.5318 −1.61362 −0.806808 0.590813i \(-0.798807\pi\)
−0.806808 + 0.590813i \(0.798807\pi\)
\(542\) −3.04732 −0.130894
\(543\) −5.61714 −0.241054
\(544\) 7.29523 0.312780
\(545\) −18.4418 −0.789962
\(546\) −8.38099 −0.358673
\(547\) 16.6839 0.713351 0.356675 0.934228i \(-0.383910\pi\)
0.356675 + 0.934228i \(0.383910\pi\)
\(548\) 44.7114 1.90998
\(549\) 9.93099 0.423844
\(550\) 2.61508 0.111507
\(551\) −0.0305937 −0.00130333
\(552\) −18.4481 −0.785203
\(553\) −2.43609 −0.103593
\(554\) −3.84331 −0.163286
\(555\) −34.7644 −1.47567
\(556\) 34.8151 1.47649
\(557\) 30.9867 1.31295 0.656475 0.754348i \(-0.272047\pi\)
0.656475 + 0.754348i \(0.272047\pi\)
\(558\) −17.9241 −0.758789
\(559\) −4.84221 −0.204804
\(560\) 4.88206 0.206305
\(561\) −1.63452 −0.0690096
\(562\) 36.3374 1.53280
\(563\) 16.7628 0.706469 0.353234 0.935535i \(-0.385082\pi\)
0.353234 + 0.935535i \(0.385082\pi\)
\(564\) 6.45954 0.271996
\(565\) 5.30568 0.223212
\(566\) 0.699324 0.0293948
\(567\) 31.5066 1.32315
\(568\) −22.5671 −0.946894
\(569\) 38.3785 1.60891 0.804456 0.594012i \(-0.202457\pi\)
0.804456 + 0.594012i \(0.202457\pi\)
\(570\) −12.9469 −0.542286
\(571\) 38.2492 1.60068 0.800339 0.599548i \(-0.204653\pi\)
0.800339 + 0.599548i \(0.204653\pi\)
\(572\) 1.09115 0.0456233
\(573\) 2.89387 0.120893
\(574\) 38.4987 1.60691
\(575\) 5.96120 0.248599
\(576\) −17.1215 −0.713396
\(577\) 18.4267 0.767112 0.383556 0.923518i \(-0.374699\pi\)
0.383556 + 0.923518i \(0.374699\pi\)
\(578\) 34.2341 1.42395
\(579\) 8.72136 0.362448
\(580\) −0.276343 −0.0114745
\(581\) −5.56668 −0.230945
\(582\) −22.4333 −0.929891
\(583\) 3.26930 0.135401
\(584\) 46.3889 1.91959
\(585\) 2.24070 0.0926416
\(586\) 20.3624 0.841163
\(587\) −5.52862 −0.228191 −0.114095 0.993470i \(-0.536397\pi\)
−0.114095 + 0.993470i \(0.536397\pi\)
\(588\) 6.14482 0.253408
\(589\) −5.69407 −0.234620
\(590\) 2.39905 0.0987672
\(591\) −11.7466 −0.483189
\(592\) 4.05078 0.166486
\(593\) −35.7235 −1.46699 −0.733494 0.679696i \(-0.762112\pi\)
−0.733494 + 0.679696i \(0.762112\pi\)
\(594\) −4.16264 −0.170795
\(595\) 11.2229 0.460095
\(596\) −47.3269 −1.93859
\(597\) −49.5787 −2.02912
\(598\) 3.96039 0.161952
\(599\) −2.95902 −0.120902 −0.0604511 0.998171i \(-0.519254\pi\)
−0.0604511 + 0.998171i \(0.519254\pi\)
\(600\) −14.3580 −0.586163
\(601\) 5.79496 0.236381 0.118191 0.992991i \(-0.462291\pi\)
0.118191 + 0.992991i \(0.462291\pi\)
\(602\) 51.0483 2.08057
\(603\) −10.0171 −0.407927
\(604\) −62.5796 −2.54633
\(605\) 28.6884 1.16635
\(606\) −1.48371 −0.0602714
\(607\) 16.7010 0.677874 0.338937 0.940809i \(-0.389933\pi\)
0.338937 + 0.940809i \(0.389933\pi\)
\(608\) −4.87798 −0.197828
\(609\) −0.179178 −0.00726064
\(610\) 45.3730 1.83710
\(611\) −0.565469 −0.0228764
\(612\) 6.85621 0.277146
\(613\) −31.4572 −1.27054 −0.635272 0.772289i \(-0.719112\pi\)
−0.635272 + 0.772289i \(0.719112\pi\)
\(614\) 45.2598 1.82654
\(615\) −33.0394 −1.33228
\(616\) −4.69076 −0.188996
\(617\) −32.8320 −1.32177 −0.660884 0.750488i \(-0.729818\pi\)
−0.660884 + 0.750488i \(0.729818\pi\)
\(618\) 51.4593 2.07000
\(619\) −5.35451 −0.215216 −0.107608 0.994193i \(-0.534319\pi\)
−0.107608 + 0.994193i \(0.534319\pi\)
\(620\) −51.4326 −2.06558
\(621\) −9.48895 −0.380778
\(622\) −72.3911 −2.90262
\(623\) −40.1480 −1.60850
\(624\) −0.838079 −0.0335500
\(625\) −31.1303 −1.24521
\(626\) 28.9646 1.15766
\(627\) 1.09293 0.0436474
\(628\) −71.1137 −2.83774
\(629\) 9.31198 0.371293
\(630\) −23.6223 −0.941135
\(631\) −38.3929 −1.52840 −0.764198 0.644981i \(-0.776865\pi\)
−0.764198 + 0.644981i \(0.776865\pi\)
\(632\) −2.77266 −0.110291
\(633\) −27.1646 −1.07970
\(634\) 2.31886 0.0920935
\(635\) 42.6335 1.69186
\(636\) −44.0195 −1.74549
\(637\) −0.537918 −0.0213131
\(638\) 0.0371431 0.00147051
\(639\) 9.59356 0.379515
\(640\) −52.1312 −2.06067
\(641\) −6.42111 −0.253619 −0.126809 0.991927i \(-0.540474\pi\)
−0.126809 + 0.991927i \(0.540474\pi\)
\(642\) 45.3432 1.78955
\(643\) −27.1721 −1.07156 −0.535782 0.844356i \(-0.679983\pi\)
−0.535782 + 0.844356i \(0.679983\pi\)
\(644\) −26.2223 −1.03330
\(645\) −43.8094 −1.72499
\(646\) 3.46795 0.136445
\(647\) −21.0942 −0.829297 −0.414648 0.909982i \(-0.636095\pi\)
−0.414648 + 0.909982i \(0.636095\pi\)
\(648\) 35.8596 1.40870
\(649\) −0.202518 −0.00794954
\(650\) 3.08234 0.120899
\(651\) −33.3484 −1.30703
\(652\) 53.7899 2.10657
\(653\) −13.3908 −0.524024 −0.262012 0.965065i \(-0.584386\pi\)
−0.262012 + 0.965065i \(0.584386\pi\)
\(654\) −33.3752 −1.30507
\(655\) 4.17781 0.163241
\(656\) 3.84978 0.150309
\(657\) −19.7205 −0.769372
\(658\) 5.96137 0.232399
\(659\) −0.465637 −0.0181386 −0.00906932 0.999959i \(-0.502887\pi\)
−0.00906932 + 0.999959i \(0.502887\pi\)
\(660\) 9.87207 0.384270
\(661\) −0.692438 −0.0269327 −0.0134664 0.999909i \(-0.504287\pi\)
−0.0134664 + 0.999909i \(0.504287\pi\)
\(662\) 63.5710 2.47076
\(663\) −1.92658 −0.0748222
\(664\) −6.33578 −0.245876
\(665\) −7.50424 −0.291002
\(666\) −19.6001 −0.759488
\(667\) 0.0846695 0.00327841
\(668\) 74.7476 2.89207
\(669\) 38.8781 1.50312
\(670\) −45.7664 −1.76811
\(671\) −3.83022 −0.147864
\(672\) −28.5688 −1.10206
\(673\) 13.2219 0.509667 0.254833 0.966985i \(-0.417979\pi\)
0.254833 + 0.966985i \(0.417979\pi\)
\(674\) 37.7451 1.45389
\(675\) −7.38518 −0.284256
\(676\) −42.6161 −1.63908
\(677\) −6.32435 −0.243065 −0.121532 0.992587i \(-0.538781\pi\)
−0.121532 + 0.992587i \(0.538781\pi\)
\(678\) 9.60197 0.368762
\(679\) −13.0027 −0.498998
\(680\) 12.7735 0.489841
\(681\) −43.6222 −1.67160
\(682\) 6.91304 0.264714
\(683\) 4.02568 0.154038 0.0770192 0.997030i \(-0.475460\pi\)
0.0770192 + 0.997030i \(0.475460\pi\)
\(684\) −4.58442 −0.175290
\(685\) −35.4118 −1.35302
\(686\) −39.8703 −1.52226
\(687\) 44.3548 1.69224
\(688\) 5.10471 0.194615
\(689\) 3.85347 0.146805
\(690\) 35.8312 1.36407
\(691\) 1.08221 0.0411693 0.0205847 0.999788i \(-0.493447\pi\)
0.0205847 + 0.999788i \(0.493447\pi\)
\(692\) −13.8117 −0.525043
\(693\) 1.99410 0.0757497
\(694\) −43.5773 −1.65417
\(695\) −27.5739 −1.04594
\(696\) −0.203933 −0.00773007
\(697\) 8.84990 0.335214
\(698\) −48.6519 −1.84150
\(699\) 33.5439 1.26875
\(700\) −20.4087 −0.771375
\(701\) 34.0524 1.28614 0.643072 0.765806i \(-0.277660\pi\)
0.643072 + 0.765806i \(0.277660\pi\)
\(702\) −4.90643 −0.185181
\(703\) −6.22648 −0.234836
\(704\) 6.60348 0.248878
\(705\) −5.11601 −0.192680
\(706\) 9.56756 0.360080
\(707\) −0.859980 −0.0323429
\(708\) 2.72680 0.102479
\(709\) −30.8739 −1.15949 −0.579746 0.814797i \(-0.696848\pi\)
−0.579746 + 0.814797i \(0.696848\pi\)
\(710\) 43.8314 1.64496
\(711\) 1.17869 0.0442045
\(712\) −45.6949 −1.71249
\(713\) 15.7586 0.590164
\(714\) 20.3107 0.760109
\(715\) −0.864202 −0.0323193
\(716\) −51.0972 −1.90959
\(717\) −14.2670 −0.532809
\(718\) 23.5735 0.879755
\(719\) −25.3908 −0.946918 −0.473459 0.880816i \(-0.656995\pi\)
−0.473459 + 0.880816i \(0.656995\pi\)
\(720\) −2.36217 −0.0880330
\(721\) 29.8266 1.11080
\(722\) −2.31886 −0.0862989
\(723\) −50.8210 −1.89005
\(724\) −9.08739 −0.337730
\(725\) 0.0658976 0.00244738
\(726\) 51.9189 1.92689
\(727\) 6.17281 0.228937 0.114468 0.993427i \(-0.463484\pi\)
0.114468 + 0.993427i \(0.463484\pi\)
\(728\) −5.52891 −0.204915
\(729\) 6.22716 0.230635
\(730\) −90.0999 −3.33475
\(731\) 11.7347 0.434025
\(732\) 51.5719 1.90615
\(733\) −30.7726 −1.13661 −0.568306 0.822817i \(-0.692401\pi\)
−0.568306 + 0.822817i \(0.692401\pi\)
\(734\) 8.71336 0.321616
\(735\) −4.86675 −0.179513
\(736\) 13.5000 0.497618
\(737\) 3.86342 0.142311
\(738\) −18.6275 −0.685688
\(739\) 13.0013 0.478261 0.239131 0.970987i \(-0.423138\pi\)
0.239131 + 0.970987i \(0.423138\pi\)
\(740\) −56.2418 −2.06749
\(741\) 1.28821 0.0473237
\(742\) −40.6247 −1.49138
\(743\) −3.99155 −0.146436 −0.0732180 0.997316i \(-0.523327\pi\)
−0.0732180 + 0.997316i \(0.523327\pi\)
\(744\) −37.9558 −1.39153
\(745\) 37.4834 1.37328
\(746\) 13.1037 0.479762
\(747\) 2.69342 0.0985472
\(748\) −2.64433 −0.0966862
\(749\) 26.2817 0.960311
\(750\) −36.8474 −1.34548
\(751\) −21.3613 −0.779486 −0.389743 0.920924i \(-0.627436\pi\)
−0.389743 + 0.920924i \(0.627436\pi\)
\(752\) 0.596123 0.0217384
\(753\) −46.9764 −1.71192
\(754\) 0.0437799 0.00159437
\(755\) 49.5636 1.80380
\(756\) 32.4862 1.18151
\(757\) 20.6702 0.751271 0.375636 0.926767i \(-0.377424\pi\)
0.375636 + 0.926767i \(0.377424\pi\)
\(758\) −37.4804 −1.36135
\(759\) −3.02473 −0.109791
\(760\) −8.54104 −0.309816
\(761\) −7.49871 −0.271828 −0.135914 0.990721i \(-0.543397\pi\)
−0.135914 + 0.990721i \(0.543397\pi\)
\(762\) 77.1561 2.79507
\(763\) −19.3448 −0.700329
\(764\) 4.68170 0.169378
\(765\) −5.43018 −0.196329
\(766\) 33.6356 1.21531
\(767\) −0.238704 −0.00861912
\(768\) −41.6884 −1.50430
\(769\) −4.57323 −0.164915 −0.0824575 0.996595i \(-0.526277\pi\)
−0.0824575 + 0.996595i \(0.526277\pi\)
\(770\) 9.11073 0.328328
\(771\) −47.4271 −1.70805
\(772\) 14.1094 0.507808
\(773\) −9.17419 −0.329973 −0.164986 0.986296i \(-0.552758\pi\)
−0.164986 + 0.986296i \(0.552758\pi\)
\(774\) −24.6996 −0.887809
\(775\) 12.2648 0.440565
\(776\) −14.7992 −0.531260
\(777\) −36.4666 −1.30823
\(778\) −73.4552 −2.63350
\(779\) −5.91751 −0.212017
\(780\) 11.6360 0.416636
\(781\) −3.70008 −0.132399
\(782\) −9.59773 −0.343214
\(783\) −0.104895 −0.00374864
\(784\) 0.567079 0.0202528
\(785\) 56.3227 2.01024
\(786\) 7.56081 0.269685
\(787\) −46.7401 −1.66610 −0.833052 0.553195i \(-0.813409\pi\)
−0.833052 + 0.553195i \(0.813409\pi\)
\(788\) −19.0035 −0.676973
\(789\) 33.2747 1.18461
\(790\) 5.38526 0.191599
\(791\) 5.56546 0.197885
\(792\) 2.26961 0.0806472
\(793\) −4.51461 −0.160318
\(794\) 36.9162 1.31011
\(795\) 34.8638 1.23649
\(796\) −80.2082 −2.84291
\(797\) −16.6508 −0.589803 −0.294901 0.955528i \(-0.595287\pi\)
−0.294901 + 0.955528i \(0.595287\pi\)
\(798\) −13.5808 −0.480756
\(799\) 1.37037 0.0484803
\(800\) 10.5070 0.371478
\(801\) 19.4255 0.686367
\(802\) −56.8997 −2.00920
\(803\) 7.60589 0.268406
\(804\) −52.0190 −1.83457
\(805\) 20.7683 0.731988
\(806\) 8.14827 0.287011
\(807\) −4.25537 −0.149796
\(808\) −0.978796 −0.0344339
\(809\) −17.2655 −0.607022 −0.303511 0.952828i \(-0.598159\pi\)
−0.303511 + 0.952828i \(0.598159\pi\)
\(810\) −69.6490 −2.44722
\(811\) −6.90694 −0.242535 −0.121268 0.992620i \(-0.538696\pi\)
−0.121268 + 0.992620i \(0.538696\pi\)
\(812\) −0.289873 −0.0101725
\(813\) 2.74324 0.0962096
\(814\) 7.55943 0.264958
\(815\) −42.6021 −1.49229
\(816\) 2.03102 0.0711000
\(817\) −7.84647 −0.274513
\(818\) 22.3082 0.779989
\(819\) 2.35041 0.0821300
\(820\) −53.4510 −1.86659
\(821\) −16.6278 −0.580313 −0.290156 0.956979i \(-0.593707\pi\)
−0.290156 + 0.956979i \(0.593707\pi\)
\(822\) −64.0867 −2.23528
\(823\) −46.9070 −1.63508 −0.817538 0.575875i \(-0.804661\pi\)
−0.817538 + 0.575875i \(0.804661\pi\)
\(824\) 33.9476 1.18262
\(825\) −2.35413 −0.0819602
\(826\) 2.51651 0.0875605
\(827\) −45.2141 −1.57225 −0.786123 0.618070i \(-0.787915\pi\)
−0.786123 + 0.618070i \(0.787915\pi\)
\(828\) 12.6876 0.440925
\(829\) 36.1082 1.25409 0.627045 0.778983i \(-0.284264\pi\)
0.627045 + 0.778983i \(0.284264\pi\)
\(830\) 12.3058 0.427141
\(831\) 3.45979 0.120019
\(832\) 7.78340 0.269841
\(833\) 1.30361 0.0451672
\(834\) −49.9019 −1.72796
\(835\) −59.2008 −2.04873
\(836\) 1.76814 0.0611523
\(837\) −19.5229 −0.674812
\(838\) 46.8092 1.61700
\(839\) 37.9901 1.31156 0.655782 0.754950i \(-0.272339\pi\)
0.655782 + 0.754950i \(0.272339\pi\)
\(840\) −50.0222 −1.72593
\(841\) −28.9991 −0.999968
\(842\) −17.6588 −0.608562
\(843\) −32.7114 −1.12664
\(844\) −43.9469 −1.51271
\(845\) 33.7523 1.16112
\(846\) −2.88440 −0.0991676
\(847\) 30.0930 1.03401
\(848\) −4.06237 −0.139502
\(849\) −0.629541 −0.0216058
\(850\) −7.46984 −0.256213
\(851\) 17.2321 0.590708
\(852\) 49.8196 1.70679
\(853\) 45.2644 1.54983 0.774913 0.632068i \(-0.217794\pi\)
0.774913 + 0.632068i \(0.217794\pi\)
\(854\) 47.5946 1.62865
\(855\) 3.63091 0.124174
\(856\) 29.9128 1.02240
\(857\) 35.1657 1.20124 0.600618 0.799536i \(-0.294921\pi\)
0.600618 + 0.799536i \(0.294921\pi\)
\(858\) −1.56399 −0.0533938
\(859\) 31.1967 1.06442 0.532208 0.846614i \(-0.321362\pi\)
0.532208 + 0.846614i \(0.321362\pi\)
\(860\) −70.8747 −2.41681
\(861\) −34.6570 −1.18111
\(862\) −30.5634 −1.04099
\(863\) −21.3556 −0.726953 −0.363477 0.931603i \(-0.618410\pi\)
−0.363477 + 0.931603i \(0.618410\pi\)
\(864\) −16.7249 −0.568991
\(865\) 10.9390 0.371937
\(866\) 69.6818 2.36788
\(867\) −30.8180 −1.04663
\(868\) −53.9509 −1.83121
\(869\) −0.454603 −0.0154214
\(870\) 0.396093 0.0134288
\(871\) 4.55375 0.154298
\(872\) −22.0175 −0.745607
\(873\) 6.29133 0.212929
\(874\) 6.41755 0.217077
\(875\) −21.3573 −0.722010
\(876\) −102.409 −3.46009
\(877\) −9.98658 −0.337223 −0.168611 0.985683i \(-0.553928\pi\)
−0.168611 + 0.985683i \(0.553928\pi\)
\(878\) 18.5712 0.626749
\(879\) −18.3305 −0.618272
\(880\) 0.911051 0.0307115
\(881\) −14.2030 −0.478512 −0.239256 0.970956i \(-0.576904\pi\)
−0.239256 + 0.970956i \(0.576904\pi\)
\(882\) −2.74386 −0.0923906
\(883\) −11.5078 −0.387268 −0.193634 0.981074i \(-0.562028\pi\)
−0.193634 + 0.981074i \(0.562028\pi\)
\(884\) −3.11682 −0.104830
\(885\) −2.15965 −0.0725959
\(886\) −44.1309 −1.48261
\(887\) −34.0210 −1.14231 −0.571156 0.820841i \(-0.693505\pi\)
−0.571156 + 0.820841i \(0.693505\pi\)
\(888\) −41.5048 −1.39281
\(889\) 44.7209 1.49989
\(890\) 88.7519 2.97497
\(891\) 5.87950 0.196971
\(892\) 62.8970 2.10595
\(893\) −0.916304 −0.0306629
\(894\) 67.8356 2.26876
\(895\) 40.4694 1.35274
\(896\) −54.6836 −1.82685
\(897\) −3.56520 −0.119038
\(898\) −57.8327 −1.92990
\(899\) 0.174202 0.00580997
\(900\) 9.87468 0.329156
\(901\) −9.33860 −0.311114
\(902\) 7.18432 0.239212
\(903\) −45.9544 −1.52927
\(904\) 6.33439 0.210679
\(905\) 7.19730 0.239246
\(906\) 89.6979 2.98001
\(907\) −37.2915 −1.23824 −0.619122 0.785295i \(-0.712512\pi\)
−0.619122 + 0.785295i \(0.712512\pi\)
\(908\) −70.5718 −2.34201
\(909\) 0.416099 0.0138011
\(910\) 10.7386 0.355983
\(911\) −47.5613 −1.57577 −0.787887 0.615819i \(-0.788825\pi\)
−0.787887 + 0.615819i \(0.788825\pi\)
\(912\) −1.35805 −0.0449695
\(913\) −1.03881 −0.0343795
\(914\) −48.3594 −1.59959
\(915\) −40.8454 −1.35031
\(916\) 71.7570 2.37092
\(917\) 4.38236 0.144718
\(918\) 11.8904 0.392441
\(919\) 38.5749 1.27247 0.636234 0.771496i \(-0.280491\pi\)
0.636234 + 0.771496i \(0.280491\pi\)
\(920\) 23.6377 0.779313
\(921\) −40.7434 −1.34254
\(922\) 5.61966 0.185074
\(923\) −4.36121 −0.143551
\(924\) 10.3554 0.340669
\(925\) 13.4116 0.440971
\(926\) −21.1568 −0.695255
\(927\) −14.4315 −0.473994
\(928\) 0.149235 0.00489889
\(929\) −31.2367 −1.02484 −0.512421 0.858734i \(-0.671251\pi\)
−0.512421 + 0.858734i \(0.671251\pi\)
\(930\) 73.7205 2.41739
\(931\) −0.871659 −0.0285675
\(932\) 54.2672 1.77758
\(933\) 65.1674 2.13349
\(934\) 37.6046 1.23046
\(935\) 2.09433 0.0684920
\(936\) 2.67515 0.0874400
\(937\) −24.0447 −0.785505 −0.392753 0.919644i \(-0.628477\pi\)
−0.392753 + 0.919644i \(0.628477\pi\)
\(938\) −48.0072 −1.56749
\(939\) −26.0743 −0.850904
\(940\) −8.27668 −0.269955
\(941\) 26.7481 0.871962 0.435981 0.899956i \(-0.356401\pi\)
0.435981 + 0.899956i \(0.356401\pi\)
\(942\) 101.930 3.32107
\(943\) 16.3770 0.533309
\(944\) 0.251645 0.00819034
\(945\) −25.7294 −0.836977
\(946\) 9.52623 0.309724
\(947\) −9.50520 −0.308878 −0.154439 0.988002i \(-0.549357\pi\)
−0.154439 + 0.988002i \(0.549357\pi\)
\(948\) 6.12099 0.198801
\(949\) 8.96492 0.291014
\(950\) 4.99473 0.162050
\(951\) −2.08746 −0.0676907
\(952\) 13.3989 0.434261
\(953\) −34.4546 −1.11609 −0.558047 0.829809i \(-0.688449\pi\)
−0.558047 + 0.829809i \(0.688449\pi\)
\(954\) 19.6561 0.636391
\(955\) −3.70795 −0.119986
\(956\) −23.0811 −0.746495
\(957\) −0.0334367 −0.00108085
\(958\) −58.2577 −1.88222
\(959\) −37.1457 −1.19950
\(960\) 70.4194 2.27278
\(961\) 1.42238 0.0458831
\(962\) 8.91016 0.287275
\(963\) −12.7163 −0.409778
\(964\) −82.2181 −2.64807
\(965\) −11.1748 −0.359729
\(966\) 37.5856 1.20930
\(967\) 0.946007 0.0304215 0.0152108 0.999884i \(-0.495158\pi\)
0.0152108 + 0.999884i \(0.495158\pi\)
\(968\) 34.2507 1.10086
\(969\) −3.12189 −0.100290
\(970\) 28.7440 0.922916
\(971\) −5.38367 −0.172770 −0.0863852 0.996262i \(-0.527532\pi\)
−0.0863852 + 0.996262i \(0.527532\pi\)
\(972\) −44.4278 −1.42502
\(973\) −28.9239 −0.927259
\(974\) 47.5815 1.52461
\(975\) −2.77477 −0.0888636
\(976\) 4.75935 0.152343
\(977\) 10.3969 0.332625 0.166312 0.986073i \(-0.446814\pi\)
0.166312 + 0.986073i \(0.446814\pi\)
\(978\) −77.0993 −2.46536
\(979\) −7.49210 −0.239449
\(980\) −7.87342 −0.251507
\(981\) 9.35993 0.298840
\(982\) −38.4552 −1.22715
\(983\) −34.9286 −1.11405 −0.557024 0.830496i \(-0.688057\pi\)
−0.557024 + 0.830496i \(0.688057\pi\)
\(984\) −39.4453 −1.25747
\(985\) 15.0510 0.479564
\(986\) −0.106097 −0.00337883
\(987\) −5.36651 −0.170818
\(988\) 2.08407 0.0663031
\(989\) 21.7155 0.690513
\(990\) −4.40820 −0.140102
\(991\) 59.0061 1.87439 0.937195 0.348807i \(-0.113413\pi\)
0.937195 + 0.348807i \(0.113413\pi\)
\(992\) 27.7755 0.881874
\(993\) −57.2275 −1.81606
\(994\) 45.9775 1.45832
\(995\) 63.5257 2.01390
\(996\) 13.9870 0.443195
\(997\) 39.8669 1.26260 0.631299 0.775539i \(-0.282522\pi\)
0.631299 + 0.775539i \(0.282522\pi\)
\(998\) 0.0535817 0.00169610
\(999\) −21.3484 −0.675434
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 \(a_p\))