Properties

Label 8001.2.a.v.1.19
Level 8001
Weight 2
Character 8001.1
Self dual Yes
Analytic conductor 63.888
Analytic rank 0
Dimension 19
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8001 = 3^{2} \cdot 7 \cdot 127 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8001.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.8883066572\)
Analytic rank: \(0\)
Dimension: \(19\)
Coefficient field: \(\mathbb{Q}[x]/(x^{19} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2} \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Root \(-2.69590\)
Character \(\chi\) = 8001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+2.69590 q^{2}\) \(+5.26787 q^{4}\) \(-1.47463 q^{5}\) \(+1.00000 q^{7}\) \(+8.80983 q^{8}\) \(+O(q^{10})\) \(q\)\(+2.69590 q^{2}\) \(+5.26787 q^{4}\) \(-1.47463 q^{5}\) \(+1.00000 q^{7}\) \(+8.80983 q^{8}\) \(-3.97544 q^{10}\) \(+3.56252 q^{11}\) \(+0.225914 q^{13}\) \(+2.69590 q^{14}\) \(+13.2147 q^{16}\) \(-1.78744 q^{17}\) \(+4.11236 q^{19}\) \(-7.76814 q^{20}\) \(+9.60418 q^{22}\) \(+2.13512 q^{23}\) \(-2.82548 q^{25}\) \(+0.609042 q^{26}\) \(+5.26787 q^{28}\) \(+3.51167 q^{29}\) \(-2.58402 q^{31}\) \(+18.0058 q^{32}\) \(-4.81876 q^{34}\) \(-1.47463 q^{35}\) \(+1.05351 q^{37}\) \(+11.0865 q^{38}\) \(-12.9912 q^{40}\) \(-1.46417 q^{41}\) \(+7.65218 q^{43}\) \(+18.7669 q^{44}\) \(+5.75605 q^{46}\) \(-6.34127 q^{47}\) \(+1.00000 q^{49}\) \(-7.61719 q^{50}\) \(+1.19009 q^{52}\) \(-0.703666 q^{53}\) \(-5.25338 q^{55}\) \(+8.80983 q^{56}\) \(+9.46711 q^{58}\) \(-4.82613 q^{59}\) \(+7.39852 q^{61}\) \(-6.96626 q^{62}\) \(+22.1123 q^{64}\) \(-0.333140 q^{65}\) \(+9.46650 q^{67}\) \(-9.41600 q^{68}\) \(-3.97544 q^{70}\) \(-11.6949 q^{71}\) \(+10.0871 q^{73}\) \(+2.84016 q^{74}\) \(+21.6634 q^{76}\) \(+3.56252 q^{77}\) \(+4.56427 q^{79}\) \(-19.4867 q^{80}\) \(-3.94726 q^{82}\) \(+3.07538 q^{83}\) \(+2.63581 q^{85}\) \(+20.6295 q^{86}\) \(+31.3852 q^{88}\) \(+6.29747 q^{89}\) \(+0.225914 q^{91}\) \(+11.2475 q^{92}\) \(-17.0954 q^{94}\) \(-6.06420 q^{95}\) \(-11.5065 q^{97}\) \(+2.69590 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(19q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 22q^{4} \) \(\mathstrut -\mathstrut 5q^{5} \) \(\mathstrut +\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(19q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 22q^{4} \) \(\mathstrut -\mathstrut 5q^{5} \) \(\mathstrut +\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 9q^{11} \) \(\mathstrut +\mathstrut 24q^{13} \) \(\mathstrut -\mathstrut 4q^{14} \) \(\mathstrut +\mathstrut 20q^{16} \) \(\mathstrut -\mathstrut 17q^{17} \) \(\mathstrut +\mathstrut 23q^{19} \) \(\mathstrut -\mathstrut 5q^{20} \) \(\mathstrut -\mathstrut 3q^{22} \) \(\mathstrut +\mathstrut 17q^{23} \) \(\mathstrut +\mathstrut 38q^{25} \) \(\mathstrut -\mathstrut 28q^{26} \) \(\mathstrut +\mathstrut 22q^{28} \) \(\mathstrut -\mathstrut 2q^{29} \) \(\mathstrut +\mathstrut 16q^{31} \) \(\mathstrut -\mathstrut 17q^{32} \) \(\mathstrut +\mathstrut 29q^{34} \) \(\mathstrut -\mathstrut 5q^{35} \) \(\mathstrut +\mathstrut 56q^{37} \) \(\mathstrut -\mathstrut 2q^{38} \) \(\mathstrut -\mathstrut 13q^{40} \) \(\mathstrut +\mathstrut 7q^{41} \) \(\mathstrut +\mathstrut 19q^{43} \) \(\mathstrut +\mathstrut 29q^{44} \) \(\mathstrut +\mathstrut 10q^{46} \) \(\mathstrut -\mathstrut 25q^{47} \) \(\mathstrut +\mathstrut 19q^{49} \) \(\mathstrut +\mathstrut 9q^{50} \) \(\mathstrut +\mathstrut 16q^{52} \) \(\mathstrut -\mathstrut 18q^{53} \) \(\mathstrut +\mathstrut 10q^{55} \) \(\mathstrut -\mathstrut 9q^{56} \) \(\mathstrut +\mathstrut 31q^{58} \) \(\mathstrut -\mathstrut 11q^{59} \) \(\mathstrut +\mathstrut 26q^{61} \) \(\mathstrut -\mathstrut 26q^{62} \) \(\mathstrut +\mathstrut 45q^{64} \) \(\mathstrut -\mathstrut 27q^{65} \) \(\mathstrut +\mathstrut 24q^{67} \) \(\mathstrut -\mathstrut 14q^{68} \) \(\mathstrut +\mathstrut 32q^{71} \) \(\mathstrut +\mathstrut 51q^{73} \) \(\mathstrut +\mathstrut 12q^{76} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut 30q^{79} \) \(\mathstrut +\mathstrut 30q^{80} \) \(\mathstrut -\mathstrut 52q^{82} \) \(\mathstrut -\mathstrut q^{83} \) \(\mathstrut +\mathstrut 44q^{85} \) \(\mathstrut +\mathstrut 24q^{86} \) \(\mathstrut -\mathstrut 30q^{88} \) \(\mathstrut -\mathstrut 5q^{89} \) \(\mathstrut +\mathstrut 24q^{91} \) \(\mathstrut +\mathstrut 88q^{92} \) \(\mathstrut +\mathstrut 7q^{94} \) \(\mathstrut +\mathstrut 24q^{95} \) \(\mathstrut +\mathstrut 5q^{97} \) \(\mathstrut -\mathstrut 4q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.69590 1.90629 0.953144 0.302517i \(-0.0978270\pi\)
0.953144 + 0.302517i \(0.0978270\pi\)
\(3\) 0 0
\(4\) 5.26787 2.63393
\(5\) −1.47463 −0.659473 −0.329737 0.944073i \(-0.606960\pi\)
−0.329737 + 0.944073i \(0.606960\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 8.80983 3.11475
\(9\) 0 0
\(10\) −3.97544 −1.25715
\(11\) 3.56252 1.07414 0.537070 0.843538i \(-0.319531\pi\)
0.537070 + 0.843538i \(0.319531\pi\)
\(12\) 0 0
\(13\) 0.225914 0.0626574 0.0313287 0.999509i \(-0.490026\pi\)
0.0313287 + 0.999509i \(0.490026\pi\)
\(14\) 2.69590 0.720509
\(15\) 0 0
\(16\) 13.2147 3.30367
\(17\) −1.78744 −0.433518 −0.216759 0.976225i \(-0.569549\pi\)
−0.216759 + 0.976225i \(0.569549\pi\)
\(18\) 0 0
\(19\) 4.11236 0.943441 0.471720 0.881748i \(-0.343633\pi\)
0.471720 + 0.881748i \(0.343633\pi\)
\(20\) −7.76814 −1.73701
\(21\) 0 0
\(22\) 9.60418 2.04762
\(23\) 2.13512 0.445202 0.222601 0.974910i \(-0.428545\pi\)
0.222601 + 0.974910i \(0.428545\pi\)
\(24\) 0 0
\(25\) −2.82548 −0.565095
\(26\) 0.609042 0.119443
\(27\) 0 0
\(28\) 5.26787 0.995533
\(29\) 3.51167 0.652101 0.326051 0.945352i \(-0.394282\pi\)
0.326051 + 0.945352i \(0.394282\pi\)
\(30\) 0 0
\(31\) −2.58402 −0.464104 −0.232052 0.972703i \(-0.574544\pi\)
−0.232052 + 0.972703i \(0.574544\pi\)
\(32\) 18.0058 3.18300
\(33\) 0 0
\(34\) −4.81876 −0.826411
\(35\) −1.47463 −0.249257
\(36\) 0 0
\(37\) 1.05351 0.173196 0.0865980 0.996243i \(-0.472400\pi\)
0.0865980 + 0.996243i \(0.472400\pi\)
\(38\) 11.0865 1.79847
\(39\) 0 0
\(40\) −12.9912 −2.05409
\(41\) −1.46417 −0.228665 −0.114333 0.993443i \(-0.536473\pi\)
−0.114333 + 0.993443i \(0.536473\pi\)
\(42\) 0 0
\(43\) 7.65218 1.16695 0.583473 0.812133i \(-0.301693\pi\)
0.583473 + 0.812133i \(0.301693\pi\)
\(44\) 18.7669 2.82921
\(45\) 0 0
\(46\) 5.75605 0.848684
\(47\) −6.34127 −0.924969 −0.462485 0.886627i \(-0.653042\pi\)
−0.462485 + 0.886627i \(0.653042\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) −7.61719 −1.07723
\(51\) 0 0
\(52\) 1.19009 0.165035
\(53\) −0.703666 −0.0966560 −0.0483280 0.998832i \(-0.515389\pi\)
−0.0483280 + 0.998832i \(0.515389\pi\)
\(54\) 0 0
\(55\) −5.25338 −0.708366
\(56\) 8.80983 1.17726
\(57\) 0 0
\(58\) 9.46711 1.24309
\(59\) −4.82613 −0.628309 −0.314154 0.949372i \(-0.601721\pi\)
−0.314154 + 0.949372i \(0.601721\pi\)
\(60\) 0 0
\(61\) 7.39852 0.947283 0.473641 0.880718i \(-0.342939\pi\)
0.473641 + 0.880718i \(0.342939\pi\)
\(62\) −6.96626 −0.884716
\(63\) 0 0
\(64\) 22.1123 2.76404
\(65\) −0.333140 −0.0413209
\(66\) 0 0
\(67\) 9.46650 1.15652 0.578258 0.815854i \(-0.303733\pi\)
0.578258 + 0.815854i \(0.303733\pi\)
\(68\) −9.41600 −1.14186
\(69\) 0 0
\(70\) −3.97544 −0.475156
\(71\) −11.6949 −1.38793 −0.693966 0.720008i \(-0.744138\pi\)
−0.693966 + 0.720008i \(0.744138\pi\)
\(72\) 0 0
\(73\) 10.0871 1.18061 0.590305 0.807181i \(-0.299008\pi\)
0.590305 + 0.807181i \(0.299008\pi\)
\(74\) 2.84016 0.330162
\(75\) 0 0
\(76\) 21.6634 2.48496
\(77\) 3.56252 0.405986
\(78\) 0 0
\(79\) 4.56427 0.513520 0.256760 0.966475i \(-0.417345\pi\)
0.256760 + 0.966475i \(0.417345\pi\)
\(80\) −19.4867 −2.17868
\(81\) 0 0
\(82\) −3.94726 −0.435902
\(83\) 3.07538 0.337566 0.168783 0.985653i \(-0.446016\pi\)
0.168783 + 0.985653i \(0.446016\pi\)
\(84\) 0 0
\(85\) 2.63581 0.285894
\(86\) 20.6295 2.22454
\(87\) 0 0
\(88\) 31.3852 3.34567
\(89\) 6.29747 0.667530 0.333765 0.942656i \(-0.391681\pi\)
0.333765 + 0.942656i \(0.391681\pi\)
\(90\) 0 0
\(91\) 0.225914 0.0236823
\(92\) 11.2475 1.17263
\(93\) 0 0
\(94\) −17.0954 −1.76326
\(95\) −6.06420 −0.622174
\(96\) 0 0
\(97\) −11.5065 −1.16831 −0.584156 0.811641i \(-0.698574\pi\)
−0.584156 + 0.811641i \(0.698574\pi\)
\(98\) 2.69590 0.272327
\(99\) 0 0
\(100\) −14.8842 −1.48842
\(101\) −13.2282 −1.31626 −0.658129 0.752906i \(-0.728652\pi\)
−0.658129 + 0.752906i \(0.728652\pi\)
\(102\) 0 0
\(103\) −0.287794 −0.0283572 −0.0141786 0.999899i \(-0.504513\pi\)
−0.0141786 + 0.999899i \(0.504513\pi\)
\(104\) 1.99027 0.195162
\(105\) 0 0
\(106\) −1.89701 −0.184254
\(107\) 2.14910 0.207761 0.103881 0.994590i \(-0.466874\pi\)
0.103881 + 0.994590i \(0.466874\pi\)
\(108\) 0 0
\(109\) 15.3817 1.47330 0.736648 0.676276i \(-0.236407\pi\)
0.736648 + 0.676276i \(0.236407\pi\)
\(110\) −14.1626 −1.35035
\(111\) 0 0
\(112\) 13.2147 1.24867
\(113\) −15.0444 −1.41525 −0.707627 0.706586i \(-0.750234\pi\)
−0.707627 + 0.706586i \(0.750234\pi\)
\(114\) 0 0
\(115\) −3.14850 −0.293599
\(116\) 18.4990 1.71759
\(117\) 0 0
\(118\) −13.0108 −1.19774
\(119\) −1.78744 −0.163855
\(120\) 0 0
\(121\) 1.69152 0.153775
\(122\) 19.9456 1.80579
\(123\) 0 0
\(124\) −13.6123 −1.22242
\(125\) 11.5397 1.03214
\(126\) 0 0
\(127\) 1.00000 0.0887357
\(128\) 23.6011 2.08606
\(129\) 0 0
\(130\) −0.898110 −0.0787695
\(131\) 8.23090 0.719137 0.359568 0.933119i \(-0.382924\pi\)
0.359568 + 0.933119i \(0.382924\pi\)
\(132\) 0 0
\(133\) 4.11236 0.356587
\(134\) 25.5207 2.20465
\(135\) 0 0
\(136\) −15.7471 −1.35030
\(137\) −12.9097 −1.10295 −0.551476 0.834191i \(-0.685935\pi\)
−0.551476 + 0.834191i \(0.685935\pi\)
\(138\) 0 0
\(139\) 1.60973 0.136536 0.0682678 0.997667i \(-0.478253\pi\)
0.0682678 + 0.997667i \(0.478253\pi\)
\(140\) −7.76814 −0.656527
\(141\) 0 0
\(142\) −31.5283 −2.64580
\(143\) 0.804824 0.0673028
\(144\) 0 0
\(145\) −5.17841 −0.430043
\(146\) 27.1939 2.25058
\(147\) 0 0
\(148\) 5.54975 0.456187
\(149\) 7.63434 0.625430 0.312715 0.949847i \(-0.398762\pi\)
0.312715 + 0.949847i \(0.398762\pi\)
\(150\) 0 0
\(151\) 13.6790 1.11318 0.556592 0.830786i \(-0.312109\pi\)
0.556592 + 0.830786i \(0.312109\pi\)
\(152\) 36.2292 2.93858
\(153\) 0 0
\(154\) 9.60418 0.773927
\(155\) 3.81047 0.306064
\(156\) 0 0
\(157\) 1.96314 0.156676 0.0783378 0.996927i \(-0.475039\pi\)
0.0783378 + 0.996927i \(0.475039\pi\)
\(158\) 12.3048 0.978918
\(159\) 0 0
\(160\) −26.5518 −2.09910
\(161\) 2.13512 0.168271
\(162\) 0 0
\(163\) −13.5412 −1.06063 −0.530313 0.847802i \(-0.677926\pi\)
−0.530313 + 0.847802i \(0.677926\pi\)
\(164\) −7.71306 −0.602289
\(165\) 0 0
\(166\) 8.29090 0.643499
\(167\) −6.38113 −0.493787 −0.246893 0.969043i \(-0.579410\pi\)
−0.246893 + 0.969043i \(0.579410\pi\)
\(168\) 0 0
\(169\) −12.9490 −0.996074
\(170\) 7.10587 0.544996
\(171\) 0 0
\(172\) 40.3106 3.07366
\(173\) −4.05461 −0.308266 −0.154133 0.988050i \(-0.549258\pi\)
−0.154133 + 0.988050i \(0.549258\pi\)
\(174\) 0 0
\(175\) −2.82548 −0.213586
\(176\) 47.0775 3.54860
\(177\) 0 0
\(178\) 16.9773 1.27250
\(179\) 2.72091 0.203370 0.101685 0.994817i \(-0.467577\pi\)
0.101685 + 0.994817i \(0.467577\pi\)
\(180\) 0 0
\(181\) −9.49771 −0.705959 −0.352980 0.935631i \(-0.614832\pi\)
−0.352980 + 0.935631i \(0.614832\pi\)
\(182\) 0.609042 0.0451452
\(183\) 0 0
\(184\) 18.8100 1.38669
\(185\) −1.55353 −0.114218
\(186\) 0 0
\(187\) −6.36779 −0.465659
\(188\) −33.4050 −2.43631
\(189\) 0 0
\(190\) −16.3485 −1.18604
\(191\) 25.9208 1.87556 0.937782 0.347225i \(-0.112876\pi\)
0.937782 + 0.347225i \(0.112876\pi\)
\(192\) 0 0
\(193\) 21.7161 1.56316 0.781581 0.623804i \(-0.214414\pi\)
0.781581 + 0.623804i \(0.214414\pi\)
\(194\) −31.0205 −2.22714
\(195\) 0 0
\(196\) 5.26787 0.376276
\(197\) 2.08379 0.148464 0.0742319 0.997241i \(-0.476349\pi\)
0.0742319 + 0.997241i \(0.476349\pi\)
\(198\) 0 0
\(199\) −27.7717 −1.96868 −0.984340 0.176278i \(-0.943594\pi\)
−0.984340 + 0.176278i \(0.943594\pi\)
\(200\) −24.8920 −1.76013
\(201\) 0 0
\(202\) −35.6619 −2.50917
\(203\) 3.51167 0.246471
\(204\) 0 0
\(205\) 2.15911 0.150799
\(206\) −0.775865 −0.0540570
\(207\) 0 0
\(208\) 2.98539 0.206999
\(209\) 14.6504 1.01339
\(210\) 0 0
\(211\) 9.29244 0.639718 0.319859 0.947465i \(-0.396364\pi\)
0.319859 + 0.947465i \(0.396364\pi\)
\(212\) −3.70682 −0.254585
\(213\) 0 0
\(214\) 5.79376 0.396053
\(215\) −11.2841 −0.769570
\(216\) 0 0
\(217\) −2.58402 −0.175415
\(218\) 41.4674 2.80853
\(219\) 0 0
\(220\) −27.6741 −1.86579
\(221\) −0.403809 −0.0271631
\(222\) 0 0
\(223\) 7.34565 0.491901 0.245950 0.969282i \(-0.420900\pi\)
0.245950 + 0.969282i \(0.420900\pi\)
\(224\) 18.0058 1.20306
\(225\) 0 0
\(226\) −40.5581 −2.69788
\(227\) 4.97373 0.330118 0.165059 0.986284i \(-0.447219\pi\)
0.165059 + 0.986284i \(0.447219\pi\)
\(228\) 0 0
\(229\) 15.3181 1.01225 0.506125 0.862460i \(-0.331078\pi\)
0.506125 + 0.862460i \(0.331078\pi\)
\(230\) −8.48803 −0.559684
\(231\) 0 0
\(232\) 30.9372 2.03113
\(233\) −13.1332 −0.860386 −0.430193 0.902737i \(-0.641554\pi\)
−0.430193 + 0.902737i \(0.641554\pi\)
\(234\) 0 0
\(235\) 9.35101 0.609993
\(236\) −25.4234 −1.65492
\(237\) 0 0
\(238\) −4.81876 −0.312354
\(239\) −1.96196 −0.126909 −0.0634543 0.997985i \(-0.520212\pi\)
−0.0634543 + 0.997985i \(0.520212\pi\)
\(240\) 0 0
\(241\) 5.36551 0.345623 0.172811 0.984955i \(-0.444715\pi\)
0.172811 + 0.984955i \(0.444715\pi\)
\(242\) 4.56018 0.293139
\(243\) 0 0
\(244\) 38.9744 2.49508
\(245\) −1.47463 −0.0942105
\(246\) 0 0
\(247\) 0.929042 0.0591135
\(248\) −22.7648 −1.44557
\(249\) 0 0
\(250\) 31.1097 1.96755
\(251\) 8.17749 0.516159 0.258079 0.966124i \(-0.416910\pi\)
0.258079 + 0.966124i \(0.416910\pi\)
\(252\) 0 0
\(253\) 7.60639 0.478209
\(254\) 2.69590 0.169156
\(255\) 0 0
\(256\) 19.4015 1.21259
\(257\) −16.4034 −1.02322 −0.511609 0.859218i \(-0.670951\pi\)
−0.511609 + 0.859218i \(0.670951\pi\)
\(258\) 0 0
\(259\) 1.05351 0.0654620
\(260\) −1.75493 −0.108836
\(261\) 0 0
\(262\) 22.1897 1.37088
\(263\) −22.1474 −1.36567 −0.682835 0.730573i \(-0.739253\pi\)
−0.682835 + 0.730573i \(0.739253\pi\)
\(264\) 0 0
\(265\) 1.03765 0.0637420
\(266\) 11.0865 0.679758
\(267\) 0 0
\(268\) 49.8683 3.04619
\(269\) 20.8780 1.27296 0.636479 0.771294i \(-0.280390\pi\)
0.636479 + 0.771294i \(0.280390\pi\)
\(270\) 0 0
\(271\) −31.9527 −1.94099 −0.970496 0.241119i \(-0.922486\pi\)
−0.970496 + 0.241119i \(0.922486\pi\)
\(272\) −23.6205 −1.43220
\(273\) 0 0
\(274\) −34.8033 −2.10254
\(275\) −10.0658 −0.606991
\(276\) 0 0
\(277\) 0.338014 0.0203093 0.0101546 0.999948i \(-0.496768\pi\)
0.0101546 + 0.999948i \(0.496768\pi\)
\(278\) 4.33967 0.260276
\(279\) 0 0
\(280\) −12.9912 −0.776374
\(281\) −9.50219 −0.566853 −0.283427 0.958994i \(-0.591471\pi\)
−0.283427 + 0.958994i \(0.591471\pi\)
\(282\) 0 0
\(283\) 8.92113 0.530306 0.265153 0.964206i \(-0.414578\pi\)
0.265153 + 0.964206i \(0.414578\pi\)
\(284\) −61.6073 −3.65572
\(285\) 0 0
\(286\) 2.16972 0.128298
\(287\) −1.46417 −0.0864273
\(288\) 0 0
\(289\) −13.8051 −0.812062
\(290\) −13.9605 −0.819786
\(291\) 0 0
\(292\) 53.1376 3.10965
\(293\) 9.87457 0.576879 0.288439 0.957498i \(-0.406864\pi\)
0.288439 + 0.957498i \(0.406864\pi\)
\(294\) 0 0
\(295\) 7.11674 0.414353
\(296\) 9.28125 0.539462
\(297\) 0 0
\(298\) 20.5814 1.19225
\(299\) 0.482354 0.0278952
\(300\) 0 0
\(301\) 7.65218 0.441064
\(302\) 36.8773 2.12205
\(303\) 0 0
\(304\) 54.3436 3.11682
\(305\) −10.9101 −0.624708
\(306\) 0 0
\(307\) −27.4317 −1.56561 −0.782804 0.622269i \(-0.786211\pi\)
−0.782804 + 0.622269i \(0.786211\pi\)
\(308\) 18.7669 1.06934
\(309\) 0 0
\(310\) 10.2726 0.583447
\(311\) −0.352596 −0.0199939 −0.00999693 0.999950i \(-0.503182\pi\)
−0.00999693 + 0.999950i \(0.503182\pi\)
\(312\) 0 0
\(313\) 7.26435 0.410605 0.205303 0.978699i \(-0.434182\pi\)
0.205303 + 0.978699i \(0.434182\pi\)
\(314\) 5.29242 0.298669
\(315\) 0 0
\(316\) 24.0440 1.35258
\(317\) −12.1028 −0.679764 −0.339882 0.940468i \(-0.610387\pi\)
−0.339882 + 0.940468i \(0.610387\pi\)
\(318\) 0 0
\(319\) 12.5104 0.700447
\(320\) −32.6075 −1.82281
\(321\) 0 0
\(322\) 5.75605 0.320772
\(323\) −7.35061 −0.408999
\(324\) 0 0
\(325\) −0.638316 −0.0354074
\(326\) −36.5056 −2.02186
\(327\) 0 0
\(328\) −12.8991 −0.712234
\(329\) −6.34127 −0.349606
\(330\) 0 0
\(331\) −25.5738 −1.40566 −0.702832 0.711356i \(-0.748081\pi\)
−0.702832 + 0.711356i \(0.748081\pi\)
\(332\) 16.2007 0.889127
\(333\) 0 0
\(334\) −17.2029 −0.941300
\(335\) −13.9596 −0.762692
\(336\) 0 0
\(337\) 11.3205 0.616664 0.308332 0.951279i \(-0.400229\pi\)
0.308332 + 0.951279i \(0.400229\pi\)
\(338\) −34.9091 −1.89880
\(339\) 0 0
\(340\) 13.8851 0.753025
\(341\) −9.20562 −0.498513
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 67.4144 3.63474
\(345\) 0 0
\(346\) −10.9308 −0.587644
\(347\) 0.0553482 0.00297125 0.00148562 0.999999i \(-0.499527\pi\)
0.00148562 + 0.999999i \(0.499527\pi\)
\(348\) 0 0
\(349\) 25.8360 1.38297 0.691484 0.722391i \(-0.256957\pi\)
0.691484 + 0.722391i \(0.256957\pi\)
\(350\) −7.61719 −0.407156
\(351\) 0 0
\(352\) 64.1458 3.41898
\(353\) −7.72286 −0.411046 −0.205523 0.978652i \(-0.565890\pi\)
−0.205523 + 0.978652i \(0.565890\pi\)
\(354\) 0 0
\(355\) 17.2456 0.915304
\(356\) 33.1742 1.75823
\(357\) 0 0
\(358\) 7.33529 0.387682
\(359\) −9.97746 −0.526590 −0.263295 0.964715i \(-0.584809\pi\)
−0.263295 + 0.964715i \(0.584809\pi\)
\(360\) 0 0
\(361\) −2.08847 −0.109919
\(362\) −25.6049 −1.34576
\(363\) 0 0
\(364\) 1.19009 0.0623775
\(365\) −14.8748 −0.778580
\(366\) 0 0
\(367\) 10.8593 0.566849 0.283424 0.958995i \(-0.408529\pi\)
0.283424 + 0.958995i \(0.408529\pi\)
\(368\) 28.2149 1.47080
\(369\) 0 0
\(370\) −4.18817 −0.217733
\(371\) −0.703666 −0.0365325
\(372\) 0 0
\(373\) 3.59117 0.185944 0.0929718 0.995669i \(-0.470363\pi\)
0.0929718 + 0.995669i \(0.470363\pi\)
\(374\) −17.1669 −0.887680
\(375\) 0 0
\(376\) −55.8655 −2.88105
\(377\) 0.793337 0.0408590
\(378\) 0 0
\(379\) −27.5754 −1.41645 −0.708226 0.705986i \(-0.750504\pi\)
−0.708226 + 0.705986i \(0.750504\pi\)
\(380\) −31.9454 −1.63876
\(381\) 0 0
\(382\) 69.8799 3.57536
\(383\) −19.8678 −1.01520 −0.507598 0.861594i \(-0.669466\pi\)
−0.507598 + 0.861594i \(0.669466\pi\)
\(384\) 0 0
\(385\) −5.25338 −0.267737
\(386\) 58.5445 2.97984
\(387\) 0 0
\(388\) −60.6149 −3.07726
\(389\) 15.1334 0.767296 0.383648 0.923479i \(-0.374668\pi\)
0.383648 + 0.923479i \(0.374668\pi\)
\(390\) 0 0
\(391\) −3.81640 −0.193003
\(392\) 8.80983 0.444964
\(393\) 0 0
\(394\) 5.61768 0.283015
\(395\) −6.73059 −0.338653
\(396\) 0 0
\(397\) 1.31022 0.0657578 0.0328789 0.999459i \(-0.489532\pi\)
0.0328789 + 0.999459i \(0.489532\pi\)
\(398\) −74.8696 −3.75287
\(399\) 0 0
\(400\) −37.3378 −1.86689
\(401\) −6.97286 −0.348208 −0.174104 0.984727i \(-0.555703\pi\)
−0.174104 + 0.984727i \(0.555703\pi\)
\(402\) 0 0
\(403\) −0.583768 −0.0290796
\(404\) −69.6845 −3.46693
\(405\) 0 0
\(406\) 9.46711 0.469845
\(407\) 3.75315 0.186037
\(408\) 0 0
\(409\) 7.41016 0.366409 0.183204 0.983075i \(-0.441353\pi\)
0.183204 + 0.983075i \(0.441353\pi\)
\(410\) 5.82073 0.287465
\(411\) 0 0
\(412\) −1.51606 −0.0746911
\(413\) −4.82613 −0.237478
\(414\) 0 0
\(415\) −4.53503 −0.222616
\(416\) 4.06776 0.199438
\(417\) 0 0
\(418\) 39.4959 1.93181
\(419\) −20.9835 −1.02511 −0.512555 0.858655i \(-0.671301\pi\)
−0.512555 + 0.858655i \(0.671301\pi\)
\(420\) 0 0
\(421\) 31.6075 1.54045 0.770227 0.637770i \(-0.220143\pi\)
0.770227 + 0.637770i \(0.220143\pi\)
\(422\) 25.0515 1.21949
\(423\) 0 0
\(424\) −6.19918 −0.301059
\(425\) 5.05037 0.244979
\(426\) 0 0
\(427\) 7.39852 0.358039
\(428\) 11.3212 0.547230
\(429\) 0 0
\(430\) −30.4208 −1.46702
\(431\) −17.7328 −0.854158 −0.427079 0.904214i \(-0.640457\pi\)
−0.427079 + 0.904214i \(0.640457\pi\)
\(432\) 0 0
\(433\) 16.7334 0.804156 0.402078 0.915605i \(-0.368288\pi\)
0.402078 + 0.915605i \(0.368288\pi\)
\(434\) −6.96626 −0.334391
\(435\) 0 0
\(436\) 81.0285 3.88056
\(437\) 8.78037 0.420022
\(438\) 0 0
\(439\) −10.0050 −0.477511 −0.238756 0.971080i \(-0.576739\pi\)
−0.238756 + 0.971080i \(0.576739\pi\)
\(440\) −46.2814 −2.20638
\(441\) 0 0
\(442\) −1.08863 −0.0517807
\(443\) −1.99760 −0.0949089 −0.0474544 0.998873i \(-0.515111\pi\)
−0.0474544 + 0.998873i \(0.515111\pi\)
\(444\) 0 0
\(445\) −9.28641 −0.440218
\(446\) 19.8031 0.937705
\(447\) 0 0
\(448\) 22.1123 1.04471
\(449\) 16.0463 0.757271 0.378636 0.925546i \(-0.376393\pi\)
0.378636 + 0.925546i \(0.376393\pi\)
\(450\) 0 0
\(451\) −5.21613 −0.245618
\(452\) −79.2517 −3.72769
\(453\) 0 0
\(454\) 13.4087 0.629300
\(455\) −0.333140 −0.0156178
\(456\) 0 0
\(457\) −7.98051 −0.373313 −0.186656 0.982425i \(-0.559765\pi\)
−0.186656 + 0.982425i \(0.559765\pi\)
\(458\) 41.2961 1.92964
\(459\) 0 0
\(460\) −16.5859 −0.773320
\(461\) −0.274598 −0.0127893 −0.00639466 0.999980i \(-0.502035\pi\)
−0.00639466 + 0.999980i \(0.502035\pi\)
\(462\) 0 0
\(463\) −13.9300 −0.647384 −0.323692 0.946163i \(-0.604924\pi\)
−0.323692 + 0.946163i \(0.604924\pi\)
\(464\) 46.4056 2.15433
\(465\) 0 0
\(466\) −35.4058 −1.64014
\(467\) 8.85623 0.409818 0.204909 0.978781i \(-0.434310\pi\)
0.204909 + 0.978781i \(0.434310\pi\)
\(468\) 0 0
\(469\) 9.46650 0.437122
\(470\) 25.2094 1.16282
\(471\) 0 0
\(472\) −42.5174 −1.95702
\(473\) 27.2610 1.25346
\(474\) 0 0
\(475\) −11.6194 −0.533134
\(476\) −9.41600 −0.431582
\(477\) 0 0
\(478\) −5.28924 −0.241924
\(479\) −30.7285 −1.40402 −0.702010 0.712168i \(-0.747714\pi\)
−0.702010 + 0.712168i \(0.747714\pi\)
\(480\) 0 0
\(481\) 0.238003 0.0108520
\(482\) 14.4649 0.658856
\(483\) 0 0
\(484\) 8.91072 0.405033
\(485\) 16.9679 0.770471
\(486\) 0 0
\(487\) −8.27967 −0.375188 −0.187594 0.982247i \(-0.560069\pi\)
−0.187594 + 0.982247i \(0.560069\pi\)
\(488\) 65.1797 2.95055
\(489\) 0 0
\(490\) −3.97544 −0.179592
\(491\) 13.2902 0.599778 0.299889 0.953974i \(-0.403050\pi\)
0.299889 + 0.953974i \(0.403050\pi\)
\(492\) 0 0
\(493\) −6.27691 −0.282698
\(494\) 2.50460 0.112687
\(495\) 0 0
\(496\) −34.1470 −1.53325
\(497\) −11.6949 −0.524589
\(498\) 0 0
\(499\) 11.9744 0.536048 0.268024 0.963412i \(-0.413629\pi\)
0.268024 + 0.963412i \(0.413629\pi\)
\(500\) 60.7894 2.71858
\(501\) 0 0
\(502\) 22.0457 0.983947
\(503\) 10.3059 0.459519 0.229759 0.973247i \(-0.426206\pi\)
0.229759 + 0.973247i \(0.426206\pi\)
\(504\) 0 0
\(505\) 19.5067 0.868036
\(506\) 20.5060 0.911605
\(507\) 0 0
\(508\) 5.26787 0.233724
\(509\) −36.4192 −1.61425 −0.807126 0.590379i \(-0.798978\pi\)
−0.807126 + 0.590379i \(0.798978\pi\)
\(510\) 0 0
\(511\) 10.0871 0.446228
\(512\) 5.10215 0.225485
\(513\) 0 0
\(514\) −44.2220 −1.95055
\(515\) 0.424389 0.0187008
\(516\) 0 0
\(517\) −22.5909 −0.993546
\(518\) 2.84016 0.124789
\(519\) 0 0
\(520\) −2.93490 −0.128704
\(521\) −21.2597 −0.931404 −0.465702 0.884942i \(-0.654198\pi\)
−0.465702 + 0.884942i \(0.654198\pi\)
\(522\) 0 0
\(523\) −37.1814 −1.62583 −0.812914 0.582384i \(-0.802120\pi\)
−0.812914 + 0.582384i \(0.802120\pi\)
\(524\) 43.3593 1.89416
\(525\) 0 0
\(526\) −59.7072 −2.60336
\(527\) 4.61879 0.201198
\(528\) 0 0
\(529\) −18.4413 −0.801795
\(530\) 2.79739 0.121511
\(531\) 0 0
\(532\) 21.6634 0.939227
\(533\) −0.330777 −0.0143276
\(534\) 0 0
\(535\) −3.16912 −0.137013
\(536\) 83.3983 3.60226
\(537\) 0 0
\(538\) 56.2851 2.42662
\(539\) 3.56252 0.153448
\(540\) 0 0
\(541\) −44.0566 −1.89414 −0.947071 0.321024i \(-0.895973\pi\)
−0.947071 + 0.321024i \(0.895973\pi\)
\(542\) −86.1414 −3.70009
\(543\) 0 0
\(544\) −32.1843 −1.37989
\(545\) −22.6822 −0.971599
\(546\) 0 0
\(547\) −4.36781 −0.186754 −0.0933770 0.995631i \(-0.529766\pi\)
−0.0933770 + 0.995631i \(0.529766\pi\)
\(548\) −68.0067 −2.90510
\(549\) 0 0
\(550\) −27.1364 −1.15710
\(551\) 14.4413 0.615219
\(552\) 0 0
\(553\) 4.56427 0.194092
\(554\) 0.911251 0.0387154
\(555\) 0 0
\(556\) 8.47984 0.359626
\(557\) −4.46834 −0.189330 −0.0946648 0.995509i \(-0.530178\pi\)
−0.0946648 + 0.995509i \(0.530178\pi\)
\(558\) 0 0
\(559\) 1.72874 0.0731178
\(560\) −19.4867 −0.823464
\(561\) 0 0
\(562\) −25.6169 −1.08058
\(563\) −20.1736 −0.850214 −0.425107 0.905143i \(-0.639764\pi\)
−0.425107 + 0.905143i \(0.639764\pi\)
\(564\) 0 0
\(565\) 22.1848 0.933323
\(566\) 24.0505 1.01092
\(567\) 0 0
\(568\) −103.030 −4.32306
\(569\) −19.9292 −0.835475 −0.417738 0.908568i \(-0.637177\pi\)
−0.417738 + 0.908568i \(0.637177\pi\)
\(570\) 0 0
\(571\) −23.3154 −0.975720 −0.487860 0.872922i \(-0.662222\pi\)
−0.487860 + 0.872922i \(0.662222\pi\)
\(572\) 4.23971 0.177271
\(573\) 0 0
\(574\) −3.94726 −0.164755
\(575\) −6.03272 −0.251582
\(576\) 0 0
\(577\) 3.13955 0.130701 0.0653507 0.997862i \(-0.479183\pi\)
0.0653507 + 0.997862i \(0.479183\pi\)
\(578\) −37.2170 −1.54802
\(579\) 0 0
\(580\) −27.2791 −1.13270
\(581\) 3.07538 0.127588
\(582\) 0 0
\(583\) −2.50682 −0.103822
\(584\) 88.8659 3.67730
\(585\) 0 0
\(586\) 26.6208 1.09970
\(587\) −24.9262 −1.02881 −0.514407 0.857546i \(-0.671988\pi\)
−0.514407 + 0.857546i \(0.671988\pi\)
\(588\) 0 0
\(589\) −10.6264 −0.437855
\(590\) 19.1860 0.789876
\(591\) 0 0
\(592\) 13.9218 0.572183
\(593\) 41.7620 1.71496 0.857480 0.514517i \(-0.172029\pi\)
0.857480 + 0.514517i \(0.172029\pi\)
\(594\) 0 0
\(595\) 2.63581 0.108058
\(596\) 40.2167 1.64734
\(597\) 0 0
\(598\) 1.30038 0.0531763
\(599\) 31.5948 1.29093 0.645465 0.763790i \(-0.276664\pi\)
0.645465 + 0.763790i \(0.276664\pi\)
\(600\) 0 0
\(601\) −43.7000 −1.78256 −0.891279 0.453454i \(-0.850191\pi\)
−0.891279 + 0.453454i \(0.850191\pi\)
\(602\) 20.6295 0.840795
\(603\) 0 0
\(604\) 72.0593 2.93205
\(605\) −2.49437 −0.101410
\(606\) 0 0
\(607\) −40.7124 −1.65246 −0.826232 0.563329i \(-0.809520\pi\)
−0.826232 + 0.563329i \(0.809520\pi\)
\(608\) 74.0462 3.00297
\(609\) 0 0
\(610\) −29.4124 −1.19087
\(611\) −1.43258 −0.0579562
\(612\) 0 0
\(613\) 33.8182 1.36590 0.682952 0.730464i \(-0.260696\pi\)
0.682952 + 0.730464i \(0.260696\pi\)
\(614\) −73.9529 −2.98450
\(615\) 0 0
\(616\) 31.3852 1.26454
\(617\) −10.0308 −0.403824 −0.201912 0.979404i \(-0.564715\pi\)
−0.201912 + 0.979404i \(0.564715\pi\)
\(618\) 0 0
\(619\) −17.0587 −0.685647 −0.342824 0.939400i \(-0.611383\pi\)
−0.342824 + 0.939400i \(0.611383\pi\)
\(620\) 20.0730 0.806153
\(621\) 0 0
\(622\) −0.950562 −0.0381141
\(623\) 6.29747 0.252303
\(624\) 0 0
\(625\) −2.88931 −0.115572
\(626\) 19.5839 0.782731
\(627\) 0 0
\(628\) 10.3416 0.412673
\(629\) −1.88309 −0.0750837
\(630\) 0 0
\(631\) −27.9445 −1.11245 −0.556226 0.831031i \(-0.687751\pi\)
−0.556226 + 0.831031i \(0.687751\pi\)
\(632\) 40.2105 1.59949
\(633\) 0 0
\(634\) −32.6280 −1.29582
\(635\) −1.47463 −0.0585188
\(636\) 0 0
\(637\) 0.225914 0.00895106
\(638\) 33.7267 1.33525
\(639\) 0 0
\(640\) −34.8028 −1.37570
\(641\) −11.6463 −0.460002 −0.230001 0.973190i \(-0.573873\pi\)
−0.230001 + 0.973190i \(0.573873\pi\)
\(642\) 0 0
\(643\) 1.33579 0.0526785 0.0263393 0.999653i \(-0.491615\pi\)
0.0263393 + 0.999653i \(0.491615\pi\)
\(644\) 11.2475 0.443214
\(645\) 0 0
\(646\) −19.8165 −0.779670
\(647\) 18.7574 0.737428 0.368714 0.929543i \(-0.379798\pi\)
0.368714 + 0.929543i \(0.379798\pi\)
\(648\) 0 0
\(649\) −17.1932 −0.674891
\(650\) −1.72083 −0.0674967
\(651\) 0 0
\(652\) −71.3331 −2.79362
\(653\) 22.5480 0.882370 0.441185 0.897416i \(-0.354558\pi\)
0.441185 + 0.897416i \(0.354558\pi\)
\(654\) 0 0
\(655\) −12.1375 −0.474251
\(656\) −19.3486 −0.755434
\(657\) 0 0
\(658\) −17.0954 −0.666449
\(659\) 6.84788 0.266756 0.133378 0.991065i \(-0.457418\pi\)
0.133378 + 0.991065i \(0.457418\pi\)
\(660\) 0 0
\(661\) 29.5627 1.14985 0.574927 0.818205i \(-0.305030\pi\)
0.574927 + 0.818205i \(0.305030\pi\)
\(662\) −68.9444 −2.67960
\(663\) 0 0
\(664\) 27.0936 1.05143
\(665\) −6.06420 −0.235160
\(666\) 0 0
\(667\) 7.49783 0.290317
\(668\) −33.6149 −1.30060
\(669\) 0 0
\(670\) −37.6335 −1.45391
\(671\) 26.3573 1.01751
\(672\) 0 0
\(673\) 14.7263 0.567656 0.283828 0.958875i \(-0.408396\pi\)
0.283828 + 0.958875i \(0.408396\pi\)
\(674\) 30.5188 1.17554
\(675\) 0 0
\(676\) −68.2134 −2.62359
\(677\) 24.8508 0.955095 0.477548 0.878606i \(-0.341526\pi\)
0.477548 + 0.878606i \(0.341526\pi\)
\(678\) 0 0
\(679\) −11.5065 −0.441581
\(680\) 23.2210 0.890487
\(681\) 0 0
\(682\) −24.8174 −0.950308
\(683\) −19.4189 −0.743043 −0.371521 0.928424i \(-0.621164\pi\)
−0.371521 + 0.928424i \(0.621164\pi\)
\(684\) 0 0
\(685\) 19.0370 0.727367
\(686\) 2.69590 0.102930
\(687\) 0 0
\(688\) 101.121 3.85521
\(689\) −0.158968 −0.00605621
\(690\) 0 0
\(691\) 14.1538 0.538435 0.269218 0.963079i \(-0.413235\pi\)
0.269218 + 0.963079i \(0.413235\pi\)
\(692\) −21.3591 −0.811952
\(693\) 0 0
\(694\) 0.149213 0.00566405
\(695\) −2.37375 −0.0900415
\(696\) 0 0
\(697\) 2.61712 0.0991305
\(698\) 69.6512 2.63634
\(699\) 0 0
\(700\) −14.8842 −0.562571
\(701\) 32.1195 1.21314 0.606568 0.795032i \(-0.292546\pi\)
0.606568 + 0.795032i \(0.292546\pi\)
\(702\) 0 0
\(703\) 4.33242 0.163400
\(704\) 78.7756 2.96897
\(705\) 0 0
\(706\) −20.8200 −0.783572
\(707\) −13.2282 −0.497498
\(708\) 0 0
\(709\) 41.5911 1.56199 0.780993 0.624540i \(-0.214713\pi\)
0.780993 + 0.624540i \(0.214713\pi\)
\(710\) 46.4925 1.74483
\(711\) 0 0
\(712\) 55.4796 2.07919
\(713\) −5.51719 −0.206620
\(714\) 0 0
\(715\) −1.18682 −0.0443844
\(716\) 14.3334 0.535664
\(717\) 0 0
\(718\) −26.8982 −1.00383
\(719\) 3.50030 0.130539 0.0652697 0.997868i \(-0.479209\pi\)
0.0652697 + 0.997868i \(0.479209\pi\)
\(720\) 0 0
\(721\) −0.287794 −0.0107180
\(722\) −5.63030 −0.209538
\(723\) 0 0
\(724\) −50.0327 −1.85945
\(725\) −9.92214 −0.368499
\(726\) 0 0
\(727\) 4.18230 0.155113 0.0775565 0.996988i \(-0.475288\pi\)
0.0775565 + 0.996988i \(0.475288\pi\)
\(728\) 1.99027 0.0737643
\(729\) 0 0
\(730\) −40.1008 −1.48420
\(731\) −13.6778 −0.505893
\(732\) 0 0
\(733\) −40.3111 −1.48892 −0.744462 0.667664i \(-0.767294\pi\)
−0.744462 + 0.667664i \(0.767294\pi\)
\(734\) 29.2755 1.08058
\(735\) 0 0
\(736\) 38.4444 1.41708
\(737\) 33.7246 1.24226
\(738\) 0 0
\(739\) 0.374850 0.0137891 0.00689454 0.999976i \(-0.497805\pi\)
0.00689454 + 0.999976i \(0.497805\pi\)
\(740\) −8.18381 −0.300843
\(741\) 0 0
\(742\) −1.89701 −0.0696415
\(743\) −30.0132 −1.10108 −0.550539 0.834809i \(-0.685578\pi\)
−0.550539 + 0.834809i \(0.685578\pi\)
\(744\) 0 0
\(745\) −11.2578 −0.412454
\(746\) 9.68142 0.354462
\(747\) 0 0
\(748\) −33.5447 −1.22651
\(749\) 2.14910 0.0785264
\(750\) 0 0
\(751\) 6.64282 0.242400 0.121200 0.992628i \(-0.461326\pi\)
0.121200 + 0.992628i \(0.461326\pi\)
\(752\) −83.7979 −3.05579
\(753\) 0 0
\(754\) 2.13876 0.0778889
\(755\) −20.1715 −0.734115
\(756\) 0 0
\(757\) 45.9262 1.66922 0.834608 0.550844i \(-0.185694\pi\)
0.834608 + 0.550844i \(0.185694\pi\)
\(758\) −74.3404 −2.70016
\(759\) 0 0
\(760\) −53.4246 −1.93791
\(761\) 16.9692 0.615134 0.307567 0.951526i \(-0.400485\pi\)
0.307567 + 0.951526i \(0.400485\pi\)
\(762\) 0 0
\(763\) 15.3817 0.556854
\(764\) 136.547 4.94011
\(765\) 0 0
\(766\) −53.5615 −1.93526
\(767\) −1.09029 −0.0393682
\(768\) 0 0
\(769\) −17.4485 −0.629211 −0.314605 0.949223i \(-0.601872\pi\)
−0.314605 + 0.949223i \(0.601872\pi\)
\(770\) −14.1626 −0.510384
\(771\) 0 0
\(772\) 114.398 4.11726
\(773\) 24.3032 0.874127 0.437064 0.899431i \(-0.356018\pi\)
0.437064 + 0.899431i \(0.356018\pi\)
\(774\) 0 0
\(775\) 7.30109 0.262263
\(776\) −101.371 −3.63900
\(777\) 0 0
\(778\) 40.7982 1.46269
\(779\) −6.02120 −0.215732
\(780\) 0 0
\(781\) −41.6634 −1.49083
\(782\) −10.2886 −0.367920
\(783\) 0 0
\(784\) 13.2147 0.471953
\(785\) −2.89490 −0.103323
\(786\) 0 0
\(787\) 13.9741 0.498124 0.249062 0.968488i \(-0.419878\pi\)
0.249062 + 0.968488i \(0.419878\pi\)
\(788\) 10.9771 0.391044
\(789\) 0 0
\(790\) −18.1450 −0.645570
\(791\) −15.0444 −0.534916
\(792\) 0 0
\(793\) 1.67143 0.0593543
\(794\) 3.53221 0.125353
\(795\) 0 0
\(796\) −146.297 −5.18537
\(797\) −14.3507 −0.508328 −0.254164 0.967161i \(-0.581800\pi\)
−0.254164 + 0.967161i \(0.581800\pi\)
\(798\) 0 0
\(799\) 11.3347 0.400991
\(800\) −50.8748 −1.79870
\(801\) 0 0
\(802\) −18.7981 −0.663785
\(803\) 35.9356 1.26814
\(804\) 0 0
\(805\) −3.14850 −0.110970
\(806\) −1.57378 −0.0554340
\(807\) 0 0
\(808\) −116.538 −4.09981
\(809\) −40.9336 −1.43915 −0.719575 0.694415i \(-0.755663\pi\)
−0.719575 + 0.694415i \(0.755663\pi\)
\(810\) 0 0
\(811\) 36.9592 1.29781 0.648906 0.760868i \(-0.275227\pi\)
0.648906 + 0.760868i \(0.275227\pi\)
\(812\) 18.4990 0.649188
\(813\) 0 0
\(814\) 10.1181 0.354639
\(815\) 19.9682 0.699455
\(816\) 0 0
\(817\) 31.4685 1.10094
\(818\) 19.9770 0.698480
\(819\) 0 0
\(820\) 11.3739 0.397193
\(821\) −36.5291 −1.27487 −0.637436 0.770503i \(-0.720005\pi\)
−0.637436 + 0.770503i \(0.720005\pi\)
\(822\) 0 0
\(823\) −4.79059 −0.166989 −0.0834947 0.996508i \(-0.526608\pi\)
−0.0834947 + 0.996508i \(0.526608\pi\)
\(824\) −2.53542 −0.0883256
\(825\) 0 0
\(826\) −13.0108 −0.452702
\(827\) −25.5392 −0.888086 −0.444043 0.896005i \(-0.646456\pi\)
−0.444043 + 0.896005i \(0.646456\pi\)
\(828\) 0 0
\(829\) −46.5382 −1.61634 −0.808169 0.588950i \(-0.799541\pi\)
−0.808169 + 0.588950i \(0.799541\pi\)
\(830\) −12.2260 −0.424370
\(831\) 0 0
\(832\) 4.99550 0.173188
\(833\) −1.78744 −0.0619312
\(834\) 0 0
\(835\) 9.40979 0.325639
\(836\) 77.1761 2.66919
\(837\) 0 0
\(838\) −56.5693 −1.95415
\(839\) −9.11328 −0.314625 −0.157313 0.987549i \(-0.550283\pi\)
−0.157313 + 0.987549i \(0.550283\pi\)
\(840\) 0 0
\(841\) −16.6682 −0.574764
\(842\) 85.2105 2.93655
\(843\) 0 0
\(844\) 48.9513 1.68497
\(845\) 19.0949 0.656884
\(846\) 0 0
\(847\) 1.69152 0.0581215
\(848\) −9.29872 −0.319319
\(849\) 0 0
\(850\) 13.6153 0.467001
\(851\) 2.24937 0.0771073
\(852\) 0 0
\(853\) −10.1833 −0.348668 −0.174334 0.984687i \(-0.555777\pi\)
−0.174334 + 0.984687i \(0.555777\pi\)
\(854\) 19.9456 0.682526
\(855\) 0 0
\(856\) 18.9332 0.647124
\(857\) −26.7522 −0.913838 −0.456919 0.889508i \(-0.651047\pi\)
−0.456919 + 0.889508i \(0.651047\pi\)
\(858\) 0 0
\(859\) 49.2129 1.67912 0.839561 0.543266i \(-0.182812\pi\)
0.839561 + 0.543266i \(0.182812\pi\)
\(860\) −59.4432 −2.02700
\(861\) 0 0
\(862\) −47.8058 −1.62827
\(863\) 42.3482 1.44155 0.720775 0.693169i \(-0.243786\pi\)
0.720775 + 0.693169i \(0.243786\pi\)
\(864\) 0 0
\(865\) 5.97903 0.203293
\(866\) 45.1116 1.53295
\(867\) 0 0
\(868\) −13.6123 −0.462031
\(869\) 16.2603 0.551592
\(870\) 0 0
\(871\) 2.13862 0.0724643
\(872\) 135.510 4.58894
\(873\) 0 0
\(874\) 23.6710 0.800683
\(875\) 11.5397 0.390112
\(876\) 0 0
\(877\) −15.5136 −0.523857 −0.261929 0.965087i \(-0.584359\pi\)
−0.261929 + 0.965087i \(0.584359\pi\)
\(878\) −26.9724 −0.910273
\(879\) 0 0
\(880\) −69.4218 −2.34021
\(881\) 8.51738 0.286958 0.143479 0.989653i \(-0.454171\pi\)
0.143479 + 0.989653i \(0.454171\pi\)
\(882\) 0 0
\(883\) −7.04199 −0.236982 −0.118491 0.992955i \(-0.537806\pi\)
−0.118491 + 0.992955i \(0.537806\pi\)
\(884\) −2.12721 −0.0715459
\(885\) 0 0
\(886\) −5.38533 −0.180924
\(887\) −12.0385 −0.404213 −0.202106 0.979364i \(-0.564779\pi\)
−0.202106 + 0.979364i \(0.564779\pi\)
\(888\) 0 0
\(889\) 1.00000 0.0335389
\(890\) −25.0352 −0.839182
\(891\) 0 0
\(892\) 38.6959 1.29563
\(893\) −26.0776 −0.872654
\(894\) 0 0
\(895\) −4.01233 −0.134117
\(896\) 23.6011 0.788457
\(897\) 0 0
\(898\) 43.2592 1.44358
\(899\) −9.07424 −0.302643
\(900\) 0 0
\(901\) 1.25776 0.0419021
\(902\) −14.0622 −0.468219
\(903\) 0 0
\(904\) −132.538 −4.40816
\(905\) 14.0056 0.465561
\(906\) 0 0
\(907\) −34.0032 −1.12906 −0.564529 0.825413i \(-0.690942\pi\)
−0.564529 + 0.825413i \(0.690942\pi\)
\(908\) 26.2009 0.869509
\(909\) 0 0
\(910\) −0.898110 −0.0297721
\(911\) 6.98648 0.231472 0.115736 0.993280i \(-0.463077\pi\)
0.115736 + 0.993280i \(0.463077\pi\)
\(912\) 0 0
\(913\) 10.9561 0.362593
\(914\) −21.5146 −0.711641
\(915\) 0 0
\(916\) 80.6938 2.66620
\(917\) 8.23090 0.271808
\(918\) 0 0
\(919\) −57.1332 −1.88465 −0.942325 0.334699i \(-0.891365\pi\)
−0.942325 + 0.334699i \(0.891365\pi\)
\(920\) −27.7378 −0.914487
\(921\) 0 0
\(922\) −0.740290 −0.0243801
\(923\) −2.64205 −0.0869642
\(924\) 0 0
\(925\) −2.97667 −0.0978722
\(926\) −37.5540 −1.23410
\(927\) 0 0
\(928\) 63.2303 2.07564
\(929\) 13.2551 0.434885 0.217443 0.976073i \(-0.430229\pi\)
0.217443 + 0.976073i \(0.430229\pi\)
\(930\) 0 0
\(931\) 4.11236 0.134777
\(932\) −69.1840 −2.26620
\(933\) 0 0
\(934\) 23.8755 0.781230
\(935\) 9.39012 0.307090
\(936\) 0 0
\(937\) −37.0553 −1.21054 −0.605272 0.796018i \(-0.706936\pi\)
−0.605272 + 0.796018i \(0.706936\pi\)
\(938\) 25.5207 0.833281
\(939\) 0 0
\(940\) 49.2599 1.60668
\(941\) −37.0926 −1.20919 −0.604593 0.796535i \(-0.706664\pi\)
−0.604593 + 0.796535i \(0.706664\pi\)
\(942\) 0 0
\(943\) −3.12618 −0.101802
\(944\) −63.7758 −2.07573
\(945\) 0 0
\(946\) 73.4929 2.38946
\(947\) −34.5410 −1.12243 −0.561216 0.827669i \(-0.689666\pi\)
−0.561216 + 0.827669i \(0.689666\pi\)
\(948\) 0 0
\(949\) 2.27883 0.0739739
\(950\) −31.3247 −1.01631
\(951\) 0 0
\(952\) −15.7471 −0.510365
\(953\) −59.7161 −1.93439 −0.967196 0.254030i \(-0.918244\pi\)
−0.967196 + 0.254030i \(0.918244\pi\)
\(954\) 0 0
\(955\) −38.2235 −1.23688
\(956\) −10.3353 −0.334269
\(957\) 0 0
\(958\) −82.8408 −2.67646
\(959\) −12.9097 −0.416877
\(960\) 0 0
\(961\) −24.3228 −0.784607
\(962\) 0.641633 0.0206871
\(963\) 0 0
\(964\) 28.2648 0.910347
\(965\) −32.0232 −1.03086
\(966\) 0 0
\(967\) 53.0691 1.70659 0.853293 0.521432i \(-0.174602\pi\)
0.853293 + 0.521432i \(0.174602\pi\)
\(968\) 14.9020 0.478970
\(969\) 0 0
\(970\) 45.7436 1.46874
\(971\) −1.31432 −0.0421784 −0.0210892 0.999778i \(-0.506713\pi\)
−0.0210892 + 0.999778i \(0.506713\pi\)
\(972\) 0 0
\(973\) 1.60973 0.0516056
\(974\) −22.3212 −0.715216
\(975\) 0 0
\(976\) 97.7690 3.12951
\(977\) −31.6311 −1.01197 −0.505985 0.862542i \(-0.668871\pi\)
−0.505985 + 0.862542i \(0.668871\pi\)
\(978\) 0 0
\(979\) 22.4348 0.717020
\(980\) −7.76814 −0.248144
\(981\) 0 0
\(982\) 35.8290 1.14335
\(983\) 50.3689 1.60652 0.803260 0.595629i \(-0.203097\pi\)
0.803260 + 0.595629i \(0.203097\pi\)
\(984\) 0 0
\(985\) −3.07281 −0.0979079
\(986\) −16.9219 −0.538903
\(987\) 0 0
\(988\) 4.89407 0.155701
\(989\) 16.3383 0.519527
\(990\) 0 0
\(991\) 11.2592 0.357662 0.178831 0.983880i \(-0.442769\pi\)
0.178831 + 0.983880i \(0.442769\pi\)
\(992\) −46.5273 −1.47724
\(993\) 0 0
\(994\) −31.5283 −1.00002
\(995\) 40.9528 1.29829
\(996\) 0 0
\(997\) 20.9813 0.664485 0.332242 0.943194i \(-0.392195\pi\)
0.332242 + 0.943194i \(0.392195\pi\)
\(998\) 32.2818 1.02186
\(999\) 0 0
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 \(a_p\))