Properties

Label 4028.2.a.d.1.6
Level 4028
Weight 2
Character 4028.1
Self dual Yes
Analytic conductor 32.164
Analytic rank 1
Dimension 19
CM No
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 4028 = 2^{2} \cdot 19 \cdot 53 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4028.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.1637419342\)
Analytic rank: \(1\)
Dimension: \(19\)
Coefficient field: \(\mathbb{Q}[x]/(x^{19} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(1.96979\)
Character \(\chi\) = 4028.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.96979 q^{3} -1.29651 q^{5} -5.21755 q^{7} +0.880060 q^{9} +O(q^{10})\) \(q-1.96979 q^{3} -1.29651 q^{5} -5.21755 q^{7} +0.880060 q^{9} -5.81982 q^{11} +4.89321 q^{13} +2.55386 q^{15} +5.22872 q^{17} -1.00000 q^{19} +10.2775 q^{21} +4.72779 q^{23} -3.31905 q^{25} +4.17583 q^{27} +6.72475 q^{29} +3.44639 q^{31} +11.4638 q^{33} +6.76463 q^{35} +1.61079 q^{37} -9.63857 q^{39} -4.72814 q^{41} -1.03265 q^{43} -1.14101 q^{45} +1.95545 q^{47} +20.2228 q^{49} -10.2995 q^{51} +1.00000 q^{53} +7.54548 q^{55} +1.96979 q^{57} -11.9904 q^{59} +10.5960 q^{61} -4.59175 q^{63} -6.34411 q^{65} -4.14317 q^{67} -9.31274 q^{69} -0.689352 q^{71} -9.72589 q^{73} +6.53782 q^{75} +30.3652 q^{77} +2.39759 q^{79} -10.8657 q^{81} +0.0104429 q^{83} -6.77911 q^{85} -13.2463 q^{87} -8.42399 q^{89} -25.5305 q^{91} -6.78865 q^{93} +1.29651 q^{95} -12.3552 q^{97} -5.12179 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 19q - 4q^{3} - 2q^{5} - 11q^{7} + 19q^{9} + O(q^{10}) \) \( 19q - 4q^{3} - 2q^{5} - 11q^{7} + 19q^{9} - 11q^{11} + q^{13} - 20q^{15} - q^{17} - 19q^{19} - 10q^{21} - 16q^{23} + 21q^{25} - 4q^{27} - 9q^{31} + 7q^{33} - 25q^{37} - 25q^{39} + q^{41} - 41q^{43} - 27q^{45} - 29q^{47} + 14q^{49} - 24q^{51} + 19q^{53} - 28q^{55} + 4q^{57} - 42q^{59} + q^{61} - 41q^{63} + 2q^{65} - 41q^{67} - 25q^{69} - 20q^{73} + 11q^{75} - 19q^{77} - 38q^{79} + 23q^{81} - 36q^{83} - 58q^{85} - 30q^{87} - 25q^{89} - 55q^{91} - 38q^{93} + 2q^{95} - 13q^{97} + q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.96979 −1.13726 −0.568628 0.822594i \(-0.692526\pi\)
−0.568628 + 0.822594i \(0.692526\pi\)
\(4\) 0 0
\(5\) −1.29651 −0.579819 −0.289909 0.957054i \(-0.593625\pi\)
−0.289909 + 0.957054i \(0.593625\pi\)
\(6\) 0 0
\(7\) −5.21755 −1.97205 −0.986024 0.166603i \(-0.946720\pi\)
−0.986024 + 0.166603i \(0.946720\pi\)
\(8\) 0 0
\(9\) 0.880060 0.293353
\(10\) 0 0
\(11\) −5.81982 −1.75474 −0.877372 0.479812i \(-0.840705\pi\)
−0.877372 + 0.479812i \(0.840705\pi\)
\(12\) 0 0
\(13\) 4.89321 1.35713 0.678566 0.734540i \(-0.262602\pi\)
0.678566 + 0.734540i \(0.262602\pi\)
\(14\) 0 0
\(15\) 2.55386 0.659403
\(16\) 0 0
\(17\) 5.22872 1.26815 0.634075 0.773271i \(-0.281381\pi\)
0.634075 + 0.773271i \(0.281381\pi\)
\(18\) 0 0
\(19\) −1.00000 −0.229416
\(20\) 0 0
\(21\) 10.2775 2.24273
\(22\) 0 0
\(23\) 4.72779 0.985812 0.492906 0.870083i \(-0.335935\pi\)
0.492906 + 0.870083i \(0.335935\pi\)
\(24\) 0 0
\(25\) −3.31905 −0.663810
\(26\) 0 0
\(27\) 4.17583 0.803639
\(28\) 0 0
\(29\) 6.72475 1.24876 0.624378 0.781123i \(-0.285353\pi\)
0.624378 + 0.781123i \(0.285353\pi\)
\(30\) 0 0
\(31\) 3.44639 0.618989 0.309495 0.950901i \(-0.399840\pi\)
0.309495 + 0.950901i \(0.399840\pi\)
\(32\) 0 0
\(33\) 11.4638 1.99559
\(34\) 0 0
\(35\) 6.76463 1.14343
\(36\) 0 0
\(37\) 1.61079 0.264812 0.132406 0.991196i \(-0.457730\pi\)
0.132406 + 0.991196i \(0.457730\pi\)
\(38\) 0 0
\(39\) −9.63857 −1.54341
\(40\) 0 0
\(41\) −4.72814 −0.738411 −0.369206 0.929348i \(-0.620370\pi\)
−0.369206 + 0.929348i \(0.620370\pi\)
\(42\) 0 0
\(43\) −1.03265 −0.157477 −0.0787386 0.996895i \(-0.525089\pi\)
−0.0787386 + 0.996895i \(0.525089\pi\)
\(44\) 0 0
\(45\) −1.14101 −0.170092
\(46\) 0 0
\(47\) 1.95545 0.285232 0.142616 0.989778i \(-0.454449\pi\)
0.142616 + 0.989778i \(0.454449\pi\)
\(48\) 0 0
\(49\) 20.2228 2.88897
\(50\) 0 0
\(51\) −10.2995 −1.44221
\(52\) 0 0
\(53\) 1.00000 0.137361
\(54\) 0 0
\(55\) 7.54548 1.01743
\(56\) 0 0
\(57\) 1.96979 0.260905
\(58\) 0 0
\(59\) −11.9904 −1.56102 −0.780510 0.625143i \(-0.785041\pi\)
−0.780510 + 0.625143i \(0.785041\pi\)
\(60\) 0 0
\(61\) 10.5960 1.35668 0.678340 0.734749i \(-0.262700\pi\)
0.678340 + 0.734749i \(0.262700\pi\)
\(62\) 0 0
\(63\) −4.59175 −0.578507
\(64\) 0 0
\(65\) −6.34411 −0.786890
\(66\) 0 0
\(67\) −4.14317 −0.506169 −0.253085 0.967444i \(-0.581445\pi\)
−0.253085 + 0.967444i \(0.581445\pi\)
\(68\) 0 0
\(69\) −9.31274 −1.12112
\(70\) 0 0
\(71\) −0.689352 −0.0818110 −0.0409055 0.999163i \(-0.513024\pi\)
−0.0409055 + 0.999163i \(0.513024\pi\)
\(72\) 0 0
\(73\) −9.72589 −1.13833 −0.569165 0.822224i \(-0.692733\pi\)
−0.569165 + 0.822224i \(0.692733\pi\)
\(74\) 0 0
\(75\) 6.53782 0.754923
\(76\) 0 0
\(77\) 30.3652 3.46044
\(78\) 0 0
\(79\) 2.39759 0.269749 0.134875 0.990863i \(-0.456937\pi\)
0.134875 + 0.990863i \(0.456937\pi\)
\(80\) 0 0
\(81\) −10.8657 −1.20730
\(82\) 0 0
\(83\) 0.0104429 0.00114626 0.000573130 1.00000i \(-0.499818\pi\)
0.000573130 1.00000i \(0.499818\pi\)
\(84\) 0 0
\(85\) −6.77911 −0.735297
\(86\) 0 0
\(87\) −13.2463 −1.42016
\(88\) 0 0
\(89\) −8.42399 −0.892941 −0.446470 0.894798i \(-0.647319\pi\)
−0.446470 + 0.894798i \(0.647319\pi\)
\(90\) 0 0
\(91\) −25.5305 −2.67633
\(92\) 0 0
\(93\) −6.78865 −0.703950
\(94\) 0 0
\(95\) 1.29651 0.133020
\(96\) 0 0
\(97\) −12.3552 −1.25448 −0.627240 0.778826i \(-0.715816\pi\)
−0.627240 + 0.778826i \(0.715816\pi\)
\(98\) 0 0
\(99\) −5.12179 −0.514760
\(100\) 0 0
\(101\) −13.3851 −1.33187 −0.665933 0.746012i \(-0.731966\pi\)
−0.665933 + 0.746012i \(0.731966\pi\)
\(102\) 0 0
\(103\) −6.37542 −0.628188 −0.314094 0.949392i \(-0.601701\pi\)
−0.314094 + 0.949392i \(0.601701\pi\)
\(104\) 0 0
\(105\) −13.3249 −1.30037
\(106\) 0 0
\(107\) 0.657226 0.0635365 0.0317682 0.999495i \(-0.489886\pi\)
0.0317682 + 0.999495i \(0.489886\pi\)
\(108\) 0 0
\(109\) −3.90451 −0.373985 −0.186992 0.982361i \(-0.559874\pi\)
−0.186992 + 0.982361i \(0.559874\pi\)
\(110\) 0 0
\(111\) −3.17291 −0.301159
\(112\) 0 0
\(113\) 12.3708 1.16375 0.581873 0.813280i \(-0.302320\pi\)
0.581873 + 0.813280i \(0.302320\pi\)
\(114\) 0 0
\(115\) −6.12965 −0.571592
\(116\) 0 0
\(117\) 4.30631 0.398119
\(118\) 0 0
\(119\) −27.2811 −2.50085
\(120\) 0 0
\(121\) 22.8704 2.07912
\(122\) 0 0
\(123\) 9.31342 0.839763
\(124\) 0 0
\(125\) 10.7858 0.964708
\(126\) 0 0
\(127\) 13.4231 1.19111 0.595554 0.803316i \(-0.296933\pi\)
0.595554 + 0.803316i \(0.296933\pi\)
\(128\) 0 0
\(129\) 2.03410 0.179092
\(130\) 0 0
\(131\) 13.9258 1.21670 0.608352 0.793667i \(-0.291831\pi\)
0.608352 + 0.793667i \(0.291831\pi\)
\(132\) 0 0
\(133\) 5.21755 0.452419
\(134\) 0 0
\(135\) −5.41402 −0.465965
\(136\) 0 0
\(137\) 6.06657 0.518302 0.259151 0.965837i \(-0.416557\pi\)
0.259151 + 0.965837i \(0.416557\pi\)
\(138\) 0 0
\(139\) 1.40671 0.119315 0.0596576 0.998219i \(-0.480999\pi\)
0.0596576 + 0.998219i \(0.480999\pi\)
\(140\) 0 0
\(141\) −3.85182 −0.324382
\(142\) 0 0
\(143\) −28.4776 −2.38142
\(144\) 0 0
\(145\) −8.71874 −0.724052
\(146\) 0 0
\(147\) −39.8346 −3.28550
\(148\) 0 0
\(149\) −4.00989 −0.328503 −0.164251 0.986419i \(-0.552521\pi\)
−0.164251 + 0.986419i \(0.552521\pi\)
\(150\) 0 0
\(151\) −2.16067 −0.175833 −0.0879164 0.996128i \(-0.528021\pi\)
−0.0879164 + 0.996128i \(0.528021\pi\)
\(152\) 0 0
\(153\) 4.60158 0.372016
\(154\) 0 0
\(155\) −4.46829 −0.358902
\(156\) 0 0
\(157\) −19.5293 −1.55861 −0.779303 0.626647i \(-0.784427\pi\)
−0.779303 + 0.626647i \(0.784427\pi\)
\(158\) 0 0
\(159\) −1.96979 −0.156214
\(160\) 0 0
\(161\) −24.6675 −1.94407
\(162\) 0 0
\(163\) −0.608060 −0.0476269 −0.0238135 0.999716i \(-0.507581\pi\)
−0.0238135 + 0.999716i \(0.507581\pi\)
\(164\) 0 0
\(165\) −14.8630 −1.15708
\(166\) 0 0
\(167\) 19.2419 1.48898 0.744492 0.667632i \(-0.232692\pi\)
0.744492 + 0.667632i \(0.232692\pi\)
\(168\) 0 0
\(169\) 10.9435 0.841805
\(170\) 0 0
\(171\) −0.880060 −0.0672998
\(172\) 0 0
\(173\) −16.1152 −1.22522 −0.612610 0.790386i \(-0.709880\pi\)
−0.612610 + 0.790386i \(0.709880\pi\)
\(174\) 0 0
\(175\) 17.3173 1.30907
\(176\) 0 0
\(177\) 23.6186 1.77528
\(178\) 0 0
\(179\) −2.72804 −0.203903 −0.101952 0.994789i \(-0.532509\pi\)
−0.101952 + 0.994789i \(0.532509\pi\)
\(180\) 0 0
\(181\) 13.5398 1.00640 0.503202 0.864169i \(-0.332155\pi\)
0.503202 + 0.864169i \(0.332155\pi\)
\(182\) 0 0
\(183\) −20.8719 −1.54289
\(184\) 0 0
\(185\) −2.08841 −0.153543
\(186\) 0 0
\(187\) −30.4302 −2.22528
\(188\) 0 0
\(189\) −21.7876 −1.58481
\(190\) 0 0
\(191\) 16.7158 1.20951 0.604757 0.796410i \(-0.293270\pi\)
0.604757 + 0.796410i \(0.293270\pi\)
\(192\) 0 0
\(193\) 21.9979 1.58344 0.791721 0.610883i \(-0.209185\pi\)
0.791721 + 0.610883i \(0.209185\pi\)
\(194\) 0 0
\(195\) 12.4965 0.894896
\(196\) 0 0
\(197\) 17.3672 1.23736 0.618681 0.785642i \(-0.287667\pi\)
0.618681 + 0.785642i \(0.287667\pi\)
\(198\) 0 0
\(199\) 9.55530 0.677357 0.338679 0.940902i \(-0.390020\pi\)
0.338679 + 0.940902i \(0.390020\pi\)
\(200\) 0 0
\(201\) 8.16117 0.575645
\(202\) 0 0
\(203\) −35.0867 −2.46261
\(204\) 0 0
\(205\) 6.13010 0.428145
\(206\) 0 0
\(207\) 4.16074 0.289191
\(208\) 0 0
\(209\) 5.81982 0.402566
\(210\) 0 0
\(211\) −18.2772 −1.25825 −0.629127 0.777302i \(-0.716588\pi\)
−0.629127 + 0.777302i \(0.716588\pi\)
\(212\) 0 0
\(213\) 1.35788 0.0930401
\(214\) 0 0
\(215\) 1.33884 0.0913083
\(216\) 0 0
\(217\) −17.9817 −1.22068
\(218\) 0 0
\(219\) 19.1579 1.29457
\(220\) 0 0
\(221\) 25.5852 1.72105
\(222\) 0 0
\(223\) 17.0794 1.14372 0.571861 0.820351i \(-0.306222\pi\)
0.571861 + 0.820351i \(0.306222\pi\)
\(224\) 0 0
\(225\) −2.92096 −0.194731
\(226\) 0 0
\(227\) 18.7796 1.24645 0.623225 0.782043i \(-0.285822\pi\)
0.623225 + 0.782043i \(0.285822\pi\)
\(228\) 0 0
\(229\) 4.97105 0.328496 0.164248 0.986419i \(-0.447480\pi\)
0.164248 + 0.986419i \(0.447480\pi\)
\(230\) 0 0
\(231\) −59.8130 −3.93541
\(232\) 0 0
\(233\) −24.8924 −1.63076 −0.815379 0.578927i \(-0.803471\pi\)
−0.815379 + 0.578927i \(0.803471\pi\)
\(234\) 0 0
\(235\) −2.53527 −0.165383
\(236\) 0 0
\(237\) −4.72273 −0.306774
\(238\) 0 0
\(239\) 6.31306 0.408358 0.204179 0.978934i \(-0.434548\pi\)
0.204179 + 0.978934i \(0.434548\pi\)
\(240\) 0 0
\(241\) −20.9988 −1.35265 −0.676325 0.736603i \(-0.736429\pi\)
−0.676325 + 0.736603i \(0.736429\pi\)
\(242\) 0 0
\(243\) 8.87557 0.569368
\(244\) 0 0
\(245\) −26.2192 −1.67508
\(246\) 0 0
\(247\) −4.89321 −0.311347
\(248\) 0 0
\(249\) −0.0205704 −0.00130359
\(250\) 0 0
\(251\) 10.2553 0.647308 0.323654 0.946176i \(-0.395089\pi\)
0.323654 + 0.946176i \(0.395089\pi\)
\(252\) 0 0
\(253\) −27.5149 −1.72985
\(254\) 0 0
\(255\) 13.3534 0.836222
\(256\) 0 0
\(257\) −22.7615 −1.41982 −0.709912 0.704290i \(-0.751265\pi\)
−0.709912 + 0.704290i \(0.751265\pi\)
\(258\) 0 0
\(259\) −8.40436 −0.522222
\(260\) 0 0
\(261\) 5.91818 0.366326
\(262\) 0 0
\(263\) −32.4166 −1.99889 −0.999446 0.0332770i \(-0.989406\pi\)
−0.999446 + 0.0332770i \(0.989406\pi\)
\(264\) 0 0
\(265\) −1.29651 −0.0796442
\(266\) 0 0
\(267\) 16.5935 1.01550
\(268\) 0 0
\(269\) −5.64412 −0.344128 −0.172064 0.985086i \(-0.555044\pi\)
−0.172064 + 0.985086i \(0.555044\pi\)
\(270\) 0 0
\(271\) 5.44087 0.330509 0.165255 0.986251i \(-0.447155\pi\)
0.165255 + 0.986251i \(0.447155\pi\)
\(272\) 0 0
\(273\) 50.2897 3.04367
\(274\) 0 0
\(275\) 19.3163 1.16482
\(276\) 0 0
\(277\) 12.7312 0.764941 0.382471 0.923968i \(-0.375073\pi\)
0.382471 + 0.923968i \(0.375073\pi\)
\(278\) 0 0
\(279\) 3.03303 0.181583
\(280\) 0 0
\(281\) 17.6263 1.05150 0.525749 0.850640i \(-0.323785\pi\)
0.525749 + 0.850640i \(0.323785\pi\)
\(282\) 0 0
\(283\) −1.86621 −0.110935 −0.0554674 0.998461i \(-0.517665\pi\)
−0.0554674 + 0.998461i \(0.517665\pi\)
\(284\) 0 0
\(285\) −2.55386 −0.151277
\(286\) 0 0
\(287\) 24.6693 1.45618
\(288\) 0 0
\(289\) 10.3395 0.608205
\(290\) 0 0
\(291\) 24.3371 1.42667
\(292\) 0 0
\(293\) −14.3860 −0.840441 −0.420220 0.907422i \(-0.638047\pi\)
−0.420220 + 0.907422i \(0.638047\pi\)
\(294\) 0 0
\(295\) 15.5458 0.905109
\(296\) 0 0
\(297\) −24.3026 −1.41018
\(298\) 0 0
\(299\) 23.1340 1.33788
\(300\) 0 0
\(301\) 5.38789 0.310553
\(302\) 0 0
\(303\) 26.3658 1.51467
\(304\) 0 0
\(305\) −13.7379 −0.786628
\(306\) 0 0
\(307\) −29.0997 −1.66081 −0.830405 0.557161i \(-0.811891\pi\)
−0.830405 + 0.557161i \(0.811891\pi\)
\(308\) 0 0
\(309\) 12.5582 0.714412
\(310\) 0 0
\(311\) 28.0564 1.59093 0.795467 0.605996i \(-0.207225\pi\)
0.795467 + 0.605996i \(0.207225\pi\)
\(312\) 0 0
\(313\) −9.68353 −0.547345 −0.273673 0.961823i \(-0.588239\pi\)
−0.273673 + 0.961823i \(0.588239\pi\)
\(314\) 0 0
\(315\) 5.95327 0.335429
\(316\) 0 0
\(317\) −14.1958 −0.797313 −0.398656 0.917100i \(-0.630523\pi\)
−0.398656 + 0.917100i \(0.630523\pi\)
\(318\) 0 0
\(319\) −39.1369 −2.19124
\(320\) 0 0
\(321\) −1.29460 −0.0722573
\(322\) 0 0
\(323\) −5.22872 −0.290934
\(324\) 0 0
\(325\) −16.2408 −0.900878
\(326\) 0 0
\(327\) 7.69106 0.425317
\(328\) 0 0
\(329\) −10.2027 −0.562491
\(330\) 0 0
\(331\) 14.3822 0.790516 0.395258 0.918570i \(-0.370655\pi\)
0.395258 + 0.918570i \(0.370655\pi\)
\(332\) 0 0
\(333\) 1.41759 0.0776834
\(334\) 0 0
\(335\) 5.37168 0.293486
\(336\) 0 0
\(337\) −9.30426 −0.506835 −0.253418 0.967357i \(-0.581555\pi\)
−0.253418 + 0.967357i \(0.581555\pi\)
\(338\) 0 0
\(339\) −24.3678 −1.32348
\(340\) 0 0
\(341\) −20.0574 −1.08617
\(342\) 0 0
\(343\) −68.9907 −3.72515
\(344\) 0 0
\(345\) 12.0741 0.650047
\(346\) 0 0
\(347\) 30.1963 1.62102 0.810510 0.585725i \(-0.199190\pi\)
0.810510 + 0.585725i \(0.199190\pi\)
\(348\) 0 0
\(349\) −1.27305 −0.0681450 −0.0340725 0.999419i \(-0.510848\pi\)
−0.0340725 + 0.999419i \(0.510848\pi\)
\(350\) 0 0
\(351\) 20.4332 1.09064
\(352\) 0 0
\(353\) 3.54421 0.188639 0.0943197 0.995542i \(-0.469932\pi\)
0.0943197 + 0.995542i \(0.469932\pi\)
\(354\) 0 0
\(355\) 0.893754 0.0474356
\(356\) 0 0
\(357\) 53.7379 2.84411
\(358\) 0 0
\(359\) −8.41021 −0.443874 −0.221937 0.975061i \(-0.571238\pi\)
−0.221937 + 0.975061i \(0.571238\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) −45.0497 −2.36450
\(364\) 0 0
\(365\) 12.6098 0.660025
\(366\) 0 0
\(367\) −6.39992 −0.334073 −0.167037 0.985951i \(-0.553420\pi\)
−0.167037 + 0.985951i \(0.553420\pi\)
\(368\) 0 0
\(369\) −4.16104 −0.216615
\(370\) 0 0
\(371\) −5.21755 −0.270882
\(372\) 0 0
\(373\) −31.9953 −1.65665 −0.828327 0.560246i \(-0.810707\pi\)
−0.828327 + 0.560246i \(0.810707\pi\)
\(374\) 0 0
\(375\) −21.2457 −1.09712
\(376\) 0 0
\(377\) 32.9056 1.69472
\(378\) 0 0
\(379\) −26.8210 −1.37770 −0.688851 0.724903i \(-0.741885\pi\)
−0.688851 + 0.724903i \(0.741885\pi\)
\(380\) 0 0
\(381\) −26.4406 −1.35459
\(382\) 0 0
\(383\) 0.876156 0.0447695 0.0223847 0.999749i \(-0.492874\pi\)
0.0223847 + 0.999749i \(0.492874\pi\)
\(384\) 0 0
\(385\) −39.3689 −2.00643
\(386\) 0 0
\(387\) −0.908791 −0.0461965
\(388\) 0 0
\(389\) 3.38270 0.171510 0.0857549 0.996316i \(-0.472670\pi\)
0.0857549 + 0.996316i \(0.472670\pi\)
\(390\) 0 0
\(391\) 24.7203 1.25016
\(392\) 0 0
\(393\) −27.4309 −1.38370
\(394\) 0 0
\(395\) −3.10850 −0.156406
\(396\) 0 0
\(397\) −21.4280 −1.07544 −0.537721 0.843123i \(-0.680715\pi\)
−0.537721 + 0.843123i \(0.680715\pi\)
\(398\) 0 0
\(399\) −10.2775 −0.514516
\(400\) 0 0
\(401\) 18.4808 0.922886 0.461443 0.887170i \(-0.347332\pi\)
0.461443 + 0.887170i \(0.347332\pi\)
\(402\) 0 0
\(403\) 16.8639 0.840050
\(404\) 0 0
\(405\) 14.0875 0.700013
\(406\) 0 0
\(407\) −9.37450 −0.464677
\(408\) 0 0
\(409\) −39.1287 −1.93479 −0.967395 0.253271i \(-0.918494\pi\)
−0.967395 + 0.253271i \(0.918494\pi\)
\(410\) 0 0
\(411\) −11.9499 −0.589443
\(412\) 0 0
\(413\) 62.5606 3.07841
\(414\) 0 0
\(415\) −0.0135394 −0.000664624 0
\(416\) 0 0
\(417\) −2.77091 −0.135692
\(418\) 0 0
\(419\) −18.2905 −0.893547 −0.446774 0.894647i \(-0.647427\pi\)
−0.446774 + 0.894647i \(0.647427\pi\)
\(420\) 0 0
\(421\) −21.9161 −1.06812 −0.534062 0.845445i \(-0.679335\pi\)
−0.534062 + 0.845445i \(0.679335\pi\)
\(422\) 0 0
\(423\) 1.72091 0.0836737
\(424\) 0 0
\(425\) −17.3544 −0.841811
\(426\) 0 0
\(427\) −55.2852 −2.67544
\(428\) 0 0
\(429\) 56.0948 2.70828
\(430\) 0 0
\(431\) −28.6450 −1.37978 −0.689891 0.723914i \(-0.742341\pi\)
−0.689891 + 0.723914i \(0.742341\pi\)
\(432\) 0 0
\(433\) 29.2106 1.40377 0.701886 0.712289i \(-0.252341\pi\)
0.701886 + 0.712289i \(0.252341\pi\)
\(434\) 0 0
\(435\) 17.1741 0.823433
\(436\) 0 0
\(437\) −4.72779 −0.226161
\(438\) 0 0
\(439\) −12.5734 −0.600096 −0.300048 0.953924i \(-0.597003\pi\)
−0.300048 + 0.953924i \(0.597003\pi\)
\(440\) 0 0
\(441\) 17.7973 0.847490
\(442\) 0 0
\(443\) 3.00267 0.142661 0.0713306 0.997453i \(-0.477275\pi\)
0.0713306 + 0.997453i \(0.477275\pi\)
\(444\) 0 0
\(445\) 10.9218 0.517744
\(446\) 0 0
\(447\) 7.89862 0.373592
\(448\) 0 0
\(449\) −25.8614 −1.22047 −0.610237 0.792219i \(-0.708926\pi\)
−0.610237 + 0.792219i \(0.708926\pi\)
\(450\) 0 0
\(451\) 27.5169 1.29572
\(452\) 0 0
\(453\) 4.25606 0.199967
\(454\) 0 0
\(455\) 33.1007 1.55178
\(456\) 0 0
\(457\) 24.2264 1.13327 0.566633 0.823971i \(-0.308246\pi\)
0.566633 + 0.823971i \(0.308246\pi\)
\(458\) 0 0
\(459\) 21.8342 1.01913
\(460\) 0 0
\(461\) −19.0271 −0.886180 −0.443090 0.896477i \(-0.646118\pi\)
−0.443090 + 0.896477i \(0.646118\pi\)
\(462\) 0 0
\(463\) 5.91912 0.275085 0.137542 0.990496i \(-0.456080\pi\)
0.137542 + 0.990496i \(0.456080\pi\)
\(464\) 0 0
\(465\) 8.80158 0.408163
\(466\) 0 0
\(467\) −10.5350 −0.487503 −0.243752 0.969838i \(-0.578378\pi\)
−0.243752 + 0.969838i \(0.578378\pi\)
\(468\) 0 0
\(469\) 21.6172 0.998190
\(470\) 0 0
\(471\) 38.4685 1.77254
\(472\) 0 0
\(473\) 6.00983 0.276332
\(474\) 0 0
\(475\) 3.31905 0.152289
\(476\) 0 0
\(477\) 0.880060 0.0402952
\(478\) 0 0
\(479\) 42.0433 1.92101 0.960503 0.278269i \(-0.0897608\pi\)
0.960503 + 0.278269i \(0.0897608\pi\)
\(480\) 0 0
\(481\) 7.88192 0.359384
\(482\) 0 0
\(483\) 48.5897 2.21091
\(484\) 0 0
\(485\) 16.0187 0.727372
\(486\) 0 0
\(487\) −42.2443 −1.91427 −0.957136 0.289640i \(-0.906465\pi\)
−0.957136 + 0.289640i \(0.906465\pi\)
\(488\) 0 0
\(489\) 1.19775 0.0541641
\(490\) 0 0
\(491\) −32.0263 −1.44533 −0.722663 0.691201i \(-0.757082\pi\)
−0.722663 + 0.691201i \(0.757082\pi\)
\(492\) 0 0
\(493\) 35.1618 1.58361
\(494\) 0 0
\(495\) 6.64048 0.298467
\(496\) 0 0
\(497\) 3.59673 0.161335
\(498\) 0 0
\(499\) 32.3743 1.44927 0.724637 0.689131i \(-0.242007\pi\)
0.724637 + 0.689131i \(0.242007\pi\)
\(500\) 0 0
\(501\) −37.9025 −1.69336
\(502\) 0 0
\(503\) −25.3227 −1.12908 −0.564542 0.825404i \(-0.690947\pi\)
−0.564542 + 0.825404i \(0.690947\pi\)
\(504\) 0 0
\(505\) 17.3540 0.772241
\(506\) 0 0
\(507\) −21.5563 −0.957349
\(508\) 0 0
\(509\) 7.74919 0.343477 0.171738 0.985143i \(-0.445062\pi\)
0.171738 + 0.985143i \(0.445062\pi\)
\(510\) 0 0
\(511\) 50.7453 2.24484
\(512\) 0 0
\(513\) −4.17583 −0.184367
\(514\) 0 0
\(515\) 8.26582 0.364235
\(516\) 0 0
\(517\) −11.3804 −0.500509
\(518\) 0 0
\(519\) 31.7436 1.39339
\(520\) 0 0
\(521\) 23.2359 1.01798 0.508991 0.860772i \(-0.330019\pi\)
0.508991 + 0.860772i \(0.330019\pi\)
\(522\) 0 0
\(523\) −14.7581 −0.645324 −0.322662 0.946514i \(-0.604578\pi\)
−0.322662 + 0.946514i \(0.604578\pi\)
\(524\) 0 0
\(525\) −34.1114 −1.48874
\(526\) 0 0
\(527\) 18.0202 0.784972
\(528\) 0 0
\(529\) −0.648008 −0.0281743
\(530\) 0 0
\(531\) −10.5523 −0.457930
\(532\) 0 0
\(533\) −23.1358 −1.00212
\(534\) 0 0
\(535\) −0.852103 −0.0368396
\(536\) 0 0
\(537\) 5.37366 0.231891
\(538\) 0 0
\(539\) −117.693 −5.06941
\(540\) 0 0
\(541\) 2.11018 0.0907238 0.0453619 0.998971i \(-0.485556\pi\)
0.0453619 + 0.998971i \(0.485556\pi\)
\(542\) 0 0
\(543\) −26.6705 −1.14454
\(544\) 0 0
\(545\) 5.06226 0.216843
\(546\) 0 0
\(547\) −9.81048 −0.419466 −0.209733 0.977759i \(-0.567259\pi\)
−0.209733 + 0.977759i \(0.567259\pi\)
\(548\) 0 0
\(549\) 9.32511 0.397986
\(550\) 0 0
\(551\) −6.72475 −0.286484
\(552\) 0 0
\(553\) −12.5095 −0.531959
\(554\) 0 0
\(555\) 4.11372 0.174618
\(556\) 0 0
\(557\) 23.9508 1.01483 0.507414 0.861702i \(-0.330601\pi\)
0.507414 + 0.861702i \(0.330601\pi\)
\(558\) 0 0
\(559\) −5.05296 −0.213717
\(560\) 0 0
\(561\) 59.9410 2.53071
\(562\) 0 0
\(563\) 26.0745 1.09891 0.549455 0.835524i \(-0.314836\pi\)
0.549455 + 0.835524i \(0.314836\pi\)
\(564\) 0 0
\(565\) −16.0389 −0.674762
\(566\) 0 0
\(567\) 56.6922 2.38085
\(568\) 0 0
\(569\) −22.3815 −0.938282 −0.469141 0.883123i \(-0.655436\pi\)
−0.469141 + 0.883123i \(0.655436\pi\)
\(570\) 0 0
\(571\) −7.62134 −0.318943 −0.159472 0.987203i \(-0.550979\pi\)
−0.159472 + 0.987203i \(0.550979\pi\)
\(572\) 0 0
\(573\) −32.9266 −1.37553
\(574\) 0 0
\(575\) −15.6918 −0.654392
\(576\) 0 0
\(577\) 24.6818 1.02751 0.513757 0.857936i \(-0.328253\pi\)
0.513757 + 0.857936i \(0.328253\pi\)
\(578\) 0 0
\(579\) −43.3311 −1.80078
\(580\) 0 0
\(581\) −0.0544865 −0.00226048
\(582\) 0 0
\(583\) −5.81982 −0.241033
\(584\) 0 0
\(585\) −5.58320 −0.230837
\(586\) 0 0
\(587\) −40.6158 −1.67639 −0.838197 0.545368i \(-0.816390\pi\)
−0.838197 + 0.545368i \(0.816390\pi\)
\(588\) 0 0
\(589\) −3.44639 −0.142006
\(590\) 0 0
\(591\) −34.2097 −1.40720
\(592\) 0 0
\(593\) 10.9958 0.451543 0.225772 0.974180i \(-0.427510\pi\)
0.225772 + 0.974180i \(0.427510\pi\)
\(594\) 0 0
\(595\) 35.3703 1.45004
\(596\) 0 0
\(597\) −18.8219 −0.770329
\(598\) 0 0
\(599\) 20.0389 0.818769 0.409384 0.912362i \(-0.365743\pi\)
0.409384 + 0.912362i \(0.365743\pi\)
\(600\) 0 0
\(601\) 34.3763 1.40224 0.701119 0.713044i \(-0.252684\pi\)
0.701119 + 0.713044i \(0.252684\pi\)
\(602\) 0 0
\(603\) −3.64624 −0.148486
\(604\) 0 0
\(605\) −29.6517 −1.20551
\(606\) 0 0
\(607\) 16.6434 0.675536 0.337768 0.941229i \(-0.390328\pi\)
0.337768 + 0.941229i \(0.390328\pi\)
\(608\) 0 0
\(609\) 69.1134 2.80061
\(610\) 0 0
\(611\) 9.56842 0.387097
\(612\) 0 0
\(613\) −40.6343 −1.64120 −0.820602 0.571500i \(-0.806362\pi\)
−0.820602 + 0.571500i \(0.806362\pi\)
\(614\) 0 0
\(615\) −12.0750 −0.486910
\(616\) 0 0
\(617\) −7.51663 −0.302608 −0.151304 0.988487i \(-0.548347\pi\)
−0.151304 + 0.988487i \(0.548347\pi\)
\(618\) 0 0
\(619\) 30.9390 1.24354 0.621771 0.783199i \(-0.286413\pi\)
0.621771 + 0.783199i \(0.286413\pi\)
\(620\) 0 0
\(621\) 19.7424 0.792237
\(622\) 0 0
\(623\) 43.9526 1.76092
\(624\) 0 0
\(625\) 2.61136 0.104454
\(626\) 0 0
\(627\) −11.4638 −0.457821
\(628\) 0 0
\(629\) 8.42235 0.335821
\(630\) 0 0
\(631\) −45.0085 −1.79176 −0.895881 0.444295i \(-0.853454\pi\)
−0.895881 + 0.444295i \(0.853454\pi\)
\(632\) 0 0
\(633\) 36.0022 1.43096
\(634\) 0 0
\(635\) −17.4032 −0.690626
\(636\) 0 0
\(637\) 98.9544 3.92072
\(638\) 0 0
\(639\) −0.606671 −0.0239995
\(640\) 0 0
\(641\) −2.61776 −0.103395 −0.0516976 0.998663i \(-0.516463\pi\)
−0.0516976 + 0.998663i \(0.516463\pi\)
\(642\) 0 0
\(643\) −40.6569 −1.60335 −0.801675 0.597760i \(-0.796058\pi\)
−0.801675 + 0.597760i \(0.796058\pi\)
\(644\) 0 0
\(645\) −2.63723 −0.103841
\(646\) 0 0
\(647\) 17.2443 0.677944 0.338972 0.940796i \(-0.389921\pi\)
0.338972 + 0.940796i \(0.389921\pi\)
\(648\) 0 0
\(649\) 69.7822 2.73919
\(650\) 0 0
\(651\) 35.4201 1.38822
\(652\) 0 0
\(653\) −24.2210 −0.947839 −0.473920 0.880568i \(-0.657161\pi\)
−0.473920 + 0.880568i \(0.657161\pi\)
\(654\) 0 0
\(655\) −18.0550 −0.705468
\(656\) 0 0
\(657\) −8.55936 −0.333932
\(658\) 0 0
\(659\) −0.0140813 −0.000548531 0 −0.000274265 1.00000i \(-0.500087\pi\)
−0.000274265 1.00000i \(0.500087\pi\)
\(660\) 0 0
\(661\) −21.6053 −0.840347 −0.420173 0.907444i \(-0.638031\pi\)
−0.420173 + 0.907444i \(0.638031\pi\)
\(662\) 0 0
\(663\) −50.3974 −1.95727
\(664\) 0 0
\(665\) −6.76463 −0.262321
\(666\) 0 0
\(667\) 31.7932 1.23104
\(668\) 0 0
\(669\) −33.6428 −1.30071
\(670\) 0 0
\(671\) −61.6669 −2.38062
\(672\) 0 0
\(673\) 41.7802 1.61051 0.805254 0.592930i \(-0.202029\pi\)
0.805254 + 0.592930i \(0.202029\pi\)
\(674\) 0 0
\(675\) −13.8598 −0.533464
\(676\) 0 0
\(677\) −0.267033 −0.0102629 −0.00513146 0.999987i \(-0.501633\pi\)
−0.00513146 + 0.999987i \(0.501633\pi\)
\(678\) 0 0
\(679\) 64.4639 2.47390
\(680\) 0 0
\(681\) −36.9919 −1.41753
\(682\) 0 0
\(683\) −22.0413 −0.843388 −0.421694 0.906738i \(-0.638564\pi\)
−0.421694 + 0.906738i \(0.638564\pi\)
\(684\) 0 0
\(685\) −7.86540 −0.300521
\(686\) 0 0
\(687\) −9.79190 −0.373584
\(688\) 0 0
\(689\) 4.89321 0.186416
\(690\) 0 0
\(691\) 17.9762 0.683847 0.341924 0.939728i \(-0.388922\pi\)
0.341924 + 0.939728i \(0.388922\pi\)
\(692\) 0 0
\(693\) 26.7232 1.01513
\(694\) 0 0
\(695\) −1.82381 −0.0691812
\(696\) 0 0
\(697\) −24.7221 −0.936416
\(698\) 0 0
\(699\) 49.0328 1.85459
\(700\) 0 0
\(701\) −36.8121 −1.39037 −0.695187 0.718829i \(-0.744679\pi\)
−0.695187 + 0.718829i \(0.744679\pi\)
\(702\) 0 0
\(703\) −1.61079 −0.0607520
\(704\) 0 0
\(705\) 4.99394 0.188083
\(706\) 0 0
\(707\) 69.8373 2.62650
\(708\) 0 0
\(709\) 2.29726 0.0862754 0.0431377 0.999069i \(-0.486265\pi\)
0.0431377 + 0.999069i \(0.486265\pi\)
\(710\) 0 0
\(711\) 2.11002 0.0791319
\(712\) 0 0
\(713\) 16.2938 0.610207
\(714\) 0 0
\(715\) 36.9216 1.38079
\(716\) 0 0
\(717\) −12.4354 −0.464408
\(718\) 0 0
\(719\) −6.90092 −0.257361 −0.128680 0.991686i \(-0.541074\pi\)
−0.128680 + 0.991686i \(0.541074\pi\)
\(720\) 0 0
\(721\) 33.2640 1.23882
\(722\) 0 0
\(723\) 41.3631 1.53831
\(724\) 0 0
\(725\) −22.3198 −0.828937
\(726\) 0 0
\(727\) −39.1083 −1.45045 −0.725223 0.688514i \(-0.758263\pi\)
−0.725223 + 0.688514i \(0.758263\pi\)
\(728\) 0 0
\(729\) 15.1140 0.559779
\(730\) 0 0
\(731\) −5.39942 −0.199705
\(732\) 0 0
\(733\) −45.5880 −1.68383 −0.841915 0.539610i \(-0.818572\pi\)
−0.841915 + 0.539610i \(0.818572\pi\)
\(734\) 0 0
\(735\) 51.6462 1.90500
\(736\) 0 0
\(737\) 24.1126 0.888197
\(738\) 0 0
\(739\) −12.7034 −0.467302 −0.233651 0.972321i \(-0.575067\pi\)
−0.233651 + 0.972321i \(0.575067\pi\)
\(740\) 0 0
\(741\) 9.63857 0.354082
\(742\) 0 0
\(743\) 28.2085 1.03487 0.517434 0.855723i \(-0.326887\pi\)
0.517434 + 0.855723i \(0.326887\pi\)
\(744\) 0 0
\(745\) 5.19887 0.190472
\(746\) 0 0
\(747\) 0.00919040 0.000336259 0
\(748\) 0 0
\(749\) −3.42911 −0.125297
\(750\) 0 0
\(751\) −5.41814 −0.197711 −0.0988553 0.995102i \(-0.531518\pi\)
−0.0988553 + 0.995102i \(0.531518\pi\)
\(752\) 0 0
\(753\) −20.2007 −0.736155
\(754\) 0 0
\(755\) 2.80134 0.101951
\(756\) 0 0
\(757\) −27.2837 −0.991642 −0.495821 0.868425i \(-0.665133\pi\)
−0.495821 + 0.868425i \(0.665133\pi\)
\(758\) 0 0
\(759\) 54.1985 1.96728
\(760\) 0 0
\(761\) 26.0819 0.945470 0.472735 0.881205i \(-0.343267\pi\)
0.472735 + 0.881205i \(0.343267\pi\)
\(762\) 0 0
\(763\) 20.3720 0.737516
\(764\) 0 0
\(765\) −5.96602 −0.215702
\(766\) 0 0
\(767\) −58.6716 −2.11851
\(768\) 0 0
\(769\) 18.4272 0.664501 0.332250 0.943191i \(-0.392192\pi\)
0.332250 + 0.943191i \(0.392192\pi\)
\(770\) 0 0
\(771\) 44.8353 1.61470
\(772\) 0 0
\(773\) 1.48208 0.0533068 0.0266534 0.999645i \(-0.491515\pi\)
0.0266534 + 0.999645i \(0.491515\pi\)
\(774\) 0 0
\(775\) −11.4387 −0.410892
\(776\) 0 0
\(777\) 16.5548 0.593900
\(778\) 0 0
\(779\) 4.72814 0.169403
\(780\) 0 0
\(781\) 4.01191 0.143557
\(782\) 0 0
\(783\) 28.0814 1.00355
\(784\) 0 0
\(785\) 25.3200 0.903709
\(786\) 0 0
\(787\) −21.8288 −0.778114 −0.389057 0.921214i \(-0.627199\pi\)
−0.389057 + 0.921214i \(0.627199\pi\)
\(788\) 0 0
\(789\) 63.8538 2.27325
\(790\) 0 0
\(791\) −64.5452 −2.29496
\(792\) 0 0
\(793\) 51.8484 1.84119
\(794\) 0 0
\(795\) 2.55386 0.0905759
\(796\) 0 0
\(797\) 12.8962 0.456807 0.228404 0.973567i \(-0.426649\pi\)
0.228404 + 0.973567i \(0.426649\pi\)
\(798\) 0 0
\(799\) 10.2245 0.361717
\(800\) 0 0
\(801\) −7.41361 −0.261947
\(802\) 0 0
\(803\) 56.6030 1.99748
\(804\) 0 0
\(805\) 31.9817 1.12721
\(806\) 0 0
\(807\) 11.1177 0.391362
\(808\) 0 0
\(809\) −52.3210 −1.83951 −0.919754 0.392495i \(-0.871612\pi\)
−0.919754 + 0.392495i \(0.871612\pi\)
\(810\) 0 0
\(811\) 49.3916 1.73437 0.867186 0.497984i \(-0.165926\pi\)
0.867186 + 0.497984i \(0.165926\pi\)
\(812\) 0 0
\(813\) −10.7173 −0.375874
\(814\) 0 0
\(815\) 0.788359 0.0276150
\(816\) 0 0
\(817\) 1.03265 0.0361278
\(818\) 0 0
\(819\) −22.4684 −0.785109
\(820\) 0 0
\(821\) 34.4543 1.20246 0.601231 0.799075i \(-0.294677\pi\)
0.601231 + 0.799075i \(0.294677\pi\)
\(822\) 0 0
\(823\) −51.3415 −1.78965 −0.894827 0.446413i \(-0.852701\pi\)
−0.894827 + 0.446413i \(0.852701\pi\)
\(824\) 0 0
\(825\) −38.0490 −1.32470
\(826\) 0 0
\(827\) −38.2623 −1.33051 −0.665255 0.746617i \(-0.731677\pi\)
−0.665255 + 0.746617i \(0.731677\pi\)
\(828\) 0 0
\(829\) 26.0998 0.906484 0.453242 0.891387i \(-0.350267\pi\)
0.453242 + 0.891387i \(0.350267\pi\)
\(830\) 0 0
\(831\) −25.0777 −0.869935
\(832\) 0 0
\(833\) 105.739 3.66365
\(834\) 0 0
\(835\) −24.9474 −0.863341
\(836\) 0 0
\(837\) 14.3915 0.497444
\(838\) 0 0
\(839\) 51.3229 1.77186 0.885932 0.463815i \(-0.153520\pi\)
0.885932 + 0.463815i \(0.153520\pi\)
\(840\) 0 0
\(841\) 16.2223 0.559390
\(842\) 0 0
\(843\) −34.7201 −1.19582
\(844\) 0 0
\(845\) −14.1884 −0.488094
\(846\) 0 0
\(847\) −119.327 −4.10013
\(848\) 0 0
\(849\) 3.67604 0.126161
\(850\) 0 0
\(851\) 7.61546 0.261055
\(852\) 0 0
\(853\) 48.1042 1.64706 0.823528 0.567276i \(-0.192003\pi\)
0.823528 + 0.567276i \(0.192003\pi\)
\(854\) 0 0
\(855\) 1.14101 0.0390217
\(856\) 0 0
\(857\) 14.9577 0.510944 0.255472 0.966816i \(-0.417769\pi\)
0.255472 + 0.966816i \(0.417769\pi\)
\(858\) 0 0
\(859\) 38.1349 1.30114 0.650572 0.759444i \(-0.274529\pi\)
0.650572 + 0.759444i \(0.274529\pi\)
\(860\) 0 0
\(861\) −48.5932 −1.65605
\(862\) 0 0
\(863\) 17.8644 0.608110 0.304055 0.952655i \(-0.401659\pi\)
0.304055 + 0.952655i \(0.401659\pi\)
\(864\) 0 0
\(865\) 20.8936 0.710405
\(866\) 0 0
\(867\) −20.3666 −0.691685
\(868\) 0 0
\(869\) −13.9535 −0.473341
\(870\) 0 0
\(871\) −20.2734 −0.686938
\(872\) 0 0
\(873\) −10.8733 −0.368006
\(874\) 0 0
\(875\) −56.2753 −1.90245
\(876\) 0 0
\(877\) 4.31446 0.145689 0.0728445 0.997343i \(-0.476792\pi\)
0.0728445 + 0.997343i \(0.476792\pi\)
\(878\) 0 0
\(879\) 28.3374 0.955797
\(880\) 0 0
\(881\) 31.6397 1.06597 0.532985 0.846125i \(-0.321070\pi\)
0.532985 + 0.846125i \(0.321070\pi\)
\(882\) 0 0
\(883\) −36.3038 −1.22172 −0.610861 0.791738i \(-0.709177\pi\)
−0.610861 + 0.791738i \(0.709177\pi\)
\(884\) 0 0
\(885\) −30.6218 −1.02934
\(886\) 0 0
\(887\) 42.6516 1.43210 0.716050 0.698049i \(-0.245948\pi\)
0.716050 + 0.698049i \(0.245948\pi\)
\(888\) 0 0
\(889\) −70.0357 −2.34892
\(890\) 0 0
\(891\) 63.2363 2.11850
\(892\) 0 0
\(893\) −1.95545 −0.0654367
\(894\) 0 0
\(895\) 3.53695 0.118227
\(896\) 0 0
\(897\) −45.5691 −1.52151
\(898\) 0 0
\(899\) 23.1761 0.772966
\(900\) 0 0
\(901\) 5.22872 0.174194
\(902\) 0 0
\(903\) −10.6130 −0.353178
\(904\) 0 0
\(905\) −17.5545 −0.583532
\(906\) 0 0
\(907\) 4.74377 0.157514 0.0787571 0.996894i \(-0.474905\pi\)
0.0787571 + 0.996894i \(0.474905\pi\)
\(908\) 0 0
\(909\) −11.7797 −0.390707
\(910\) 0 0
\(911\) −27.2390 −0.902467 −0.451234 0.892406i \(-0.649016\pi\)
−0.451234 + 0.892406i \(0.649016\pi\)
\(912\) 0 0
\(913\) −0.0607760 −0.00201139
\(914\) 0 0
\(915\) 27.0607 0.894598
\(916\) 0 0
\(917\) −72.6586 −2.39940
\(918\) 0 0
\(919\) −26.2709 −0.866597 −0.433299 0.901250i \(-0.642650\pi\)
−0.433299 + 0.901250i \(0.642650\pi\)
\(920\) 0 0
\(921\) 57.3203 1.88877
\(922\) 0 0
\(923\) −3.37314 −0.111028
\(924\) 0 0
\(925\) −5.34629 −0.175785
\(926\) 0 0
\(927\) −5.61075 −0.184281
\(928\) 0 0
\(929\) 49.4545 1.62255 0.811275 0.584665i \(-0.198774\pi\)
0.811275 + 0.584665i \(0.198774\pi\)
\(930\) 0 0
\(931\) −20.2228 −0.662776
\(932\) 0 0
\(933\) −55.2652 −1.80930
\(934\) 0 0
\(935\) 39.4532 1.29026
\(936\) 0 0
\(937\) −18.2135 −0.595008 −0.297504 0.954721i \(-0.596154\pi\)
−0.297504 + 0.954721i \(0.596154\pi\)
\(938\) 0 0
\(939\) 19.0745 0.622472
\(940\) 0 0
\(941\) 33.0321 1.07682 0.538408 0.842684i \(-0.319026\pi\)
0.538408 + 0.842684i \(0.319026\pi\)
\(942\) 0 0
\(943\) −22.3536 −0.727935
\(944\) 0 0
\(945\) 28.2479 0.918905
\(946\) 0 0
\(947\) −44.3381 −1.44080 −0.720398 0.693561i \(-0.756041\pi\)
−0.720398 + 0.693561i \(0.756041\pi\)
\(948\) 0 0
\(949\) −47.5908 −1.54486
\(950\) 0 0
\(951\) 27.9626 0.906750
\(952\) 0 0
\(953\) 17.3032 0.560506 0.280253 0.959926i \(-0.409582\pi\)
0.280253 + 0.959926i \(0.409582\pi\)
\(954\) 0 0
\(955\) −21.6723 −0.701299
\(956\) 0 0
\(957\) 77.0913 2.49201
\(958\) 0 0
\(959\) −31.6526 −1.02212
\(960\) 0 0
\(961\) −19.1224 −0.616852
\(962\) 0 0
\(963\) 0.578398 0.0186386
\(964\) 0 0
\(965\) −28.5206 −0.918109
\(966\) 0 0
\(967\) −37.7864 −1.21513 −0.607565 0.794270i \(-0.707854\pi\)
−0.607565 + 0.794270i \(0.707854\pi\)
\(968\) 0 0
\(969\) 10.2995 0.330866
\(970\) 0 0
\(971\) 4.19841 0.134733 0.0673666 0.997728i \(-0.478540\pi\)
0.0673666 + 0.997728i \(0.478540\pi\)
\(972\) 0 0
\(973\) −7.33956 −0.235295
\(974\) 0 0
\(975\) 31.9909 1.02453
\(976\) 0 0
\(977\) −5.66411 −0.181211 −0.0906054 0.995887i \(-0.528880\pi\)
−0.0906054 + 0.995887i \(0.528880\pi\)
\(978\) 0 0
\(979\) 49.0261 1.56688
\(980\) 0 0
\(981\) −3.43620 −0.109710
\(982\) 0 0
\(983\) 6.09691 0.194461 0.0972306 0.995262i \(-0.469002\pi\)
0.0972306 + 0.995262i \(0.469002\pi\)
\(984\) 0 0
\(985\) −22.5168 −0.717446
\(986\) 0 0
\(987\) 20.0971 0.639696
\(988\) 0 0
\(989\) −4.88214 −0.155243
\(990\) 0 0
\(991\) 36.9040 1.17229 0.586147 0.810205i \(-0.300644\pi\)
0.586147 + 0.810205i \(0.300644\pi\)
\(992\) 0 0
\(993\) −28.3298 −0.899020
\(994\) 0 0
\(995\) −12.3886 −0.392744
\(996\) 0 0
\(997\) 11.7984 0.373660 0.186830 0.982392i \(-0.440179\pi\)
0.186830 + 0.982392i \(0.440179\pi\)
\(998\) 0 0
\(999\) 6.72638 0.212813
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 \(a_p\))