Properties

Label 4008.2.a.l.1.3
Level 4008
Weight 2
Character 4008.1
Self dual Yes
Analytic conductor 32.004
Analytic rank 0
Dimension 12
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4008 = 2^{3} \cdot 3 \cdot 167 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0040411301\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-2.09997\)
Character \(\chi\) = 4008.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{3}\) \(-2.09997 q^{5}\) \(+2.97416 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{3}\) \(-2.09997 q^{5}\) \(+2.97416 q^{7}\) \(+1.00000 q^{9}\) \(-0.138272 q^{11}\) \(+5.06303 q^{13}\) \(-2.09997 q^{15}\) \(+0.299135 q^{17}\) \(+0.432187 q^{19}\) \(+2.97416 q^{21}\) \(+5.72098 q^{23}\) \(-0.590124 q^{25}\) \(+1.00000 q^{27}\) \(-0.718106 q^{29}\) \(-4.27590 q^{31}\) \(-0.138272 q^{33}\) \(-6.24565 q^{35}\) \(-3.92212 q^{37}\) \(+5.06303 q^{39}\) \(+7.57912 q^{41}\) \(+12.3515 q^{43}\) \(-2.09997 q^{45}\) \(-9.22989 q^{47}\) \(+1.84562 q^{49}\) \(+0.299135 q^{51}\) \(+1.26409 q^{53}\) \(+0.290366 q^{55}\) \(+0.432187 q^{57}\) \(+3.01296 q^{59}\) \(+2.98537 q^{61}\) \(+2.97416 q^{63}\) \(-10.6322 q^{65}\) \(-11.3934 q^{67}\) \(+5.72098 q^{69}\) \(-7.07665 q^{71}\) \(+14.5486 q^{73}\) \(-0.590124 q^{75}\) \(-0.411242 q^{77}\) \(+13.7670 q^{79}\) \(+1.00000 q^{81}\) \(-15.7764 q^{83}\) \(-0.628175 q^{85}\) \(-0.718106 q^{87}\) \(-12.4982 q^{89}\) \(+15.0583 q^{91}\) \(-4.27590 q^{93}\) \(-0.907580 q^{95}\) \(+7.54510 q^{97}\) \(-0.138272 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(12q \) \(\mathstrut +\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 4q^{5} \) \(\mathstrut +\mathstrut 11q^{7} \) \(\mathstrut +\mathstrut 12q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(12q \) \(\mathstrut +\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 4q^{5} \) \(\mathstrut +\mathstrut 11q^{7} \) \(\mathstrut +\mathstrut 12q^{9} \) \(\mathstrut +\mathstrut q^{11} \) \(\mathstrut +\mathstrut 8q^{13} \) \(\mathstrut +\mathstrut 4q^{15} \) \(\mathstrut +\mathstrut 3q^{17} \) \(\mathstrut +\mathstrut 12q^{19} \) \(\mathstrut +\mathstrut 11q^{21} \) \(\mathstrut +\mathstrut 7q^{23} \) \(\mathstrut +\mathstrut 18q^{25} \) \(\mathstrut +\mathstrut 12q^{27} \) \(\mathstrut +\mathstrut 5q^{29} \) \(\mathstrut +\mathstrut 33q^{31} \) \(\mathstrut +\mathstrut q^{33} \) \(\mathstrut +\mathstrut 15q^{35} \) \(\mathstrut +\mathstrut 8q^{37} \) \(\mathstrut +\mathstrut 8q^{39} \) \(\mathstrut -\mathstrut 6q^{41} \) \(\mathstrut +\mathstrut 16q^{43} \) \(\mathstrut +\mathstrut 4q^{45} \) \(\mathstrut +\mathstrut 18q^{47} \) \(\mathstrut +\mathstrut 25q^{49} \) \(\mathstrut +\mathstrut 3q^{51} \) \(\mathstrut +\mathstrut 20q^{53} \) \(\mathstrut +\mathstrut 39q^{55} \) \(\mathstrut +\mathstrut 12q^{57} \) \(\mathstrut +\mathstrut 4q^{59} \) \(\mathstrut +\mathstrut 10q^{61} \) \(\mathstrut +\mathstrut 11q^{63} \) \(\mathstrut +\mathstrut 9q^{67} \) \(\mathstrut +\mathstrut 7q^{69} \) \(\mathstrut +\mathstrut 11q^{71} \) \(\mathstrut +\mathstrut 22q^{73} \) \(\mathstrut +\mathstrut 18q^{75} \) \(\mathstrut +\mathstrut 24q^{77} \) \(\mathstrut +\mathstrut 56q^{79} \) \(\mathstrut +\mathstrut 12q^{81} \) \(\mathstrut +\mathstrut 26q^{83} \) \(\mathstrut +\mathstrut 15q^{85} \) \(\mathstrut +\mathstrut 5q^{87} \) \(\mathstrut -\mathstrut 15q^{89} \) \(\mathstrut +\mathstrut 11q^{91} \) \(\mathstrut +\mathstrut 33q^{93} \) \(\mathstrut +\mathstrut 3q^{95} \) \(\mathstrut +\mathstrut 8q^{97} \) \(\mathstrut +\mathstrut q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.00000 0.577350
\(4\) 0 0
\(5\) −2.09997 −0.939135 −0.469568 0.882896i \(-0.655590\pi\)
−0.469568 + 0.882896i \(0.655590\pi\)
\(6\) 0 0
\(7\) 2.97416 1.12413 0.562063 0.827094i \(-0.310008\pi\)
0.562063 + 0.827094i \(0.310008\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −0.138272 −0.0416905 −0.0208452 0.999783i \(-0.506636\pi\)
−0.0208452 + 0.999783i \(0.506636\pi\)
\(12\) 0 0
\(13\) 5.06303 1.40423 0.702116 0.712063i \(-0.252239\pi\)
0.702116 + 0.712063i \(0.252239\pi\)
\(14\) 0 0
\(15\) −2.09997 −0.542210
\(16\) 0 0
\(17\) 0.299135 0.0725509 0.0362755 0.999342i \(-0.488451\pi\)
0.0362755 + 0.999342i \(0.488451\pi\)
\(18\) 0 0
\(19\) 0.432187 0.0991505 0.0495753 0.998770i \(-0.484213\pi\)
0.0495753 + 0.998770i \(0.484213\pi\)
\(20\) 0 0
\(21\) 2.97416 0.649015
\(22\) 0 0
\(23\) 5.72098 1.19291 0.596454 0.802647i \(-0.296576\pi\)
0.596454 + 0.802647i \(0.296576\pi\)
\(24\) 0 0
\(25\) −0.590124 −0.118025
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −0.718106 −0.133349 −0.0666745 0.997775i \(-0.521239\pi\)
−0.0666745 + 0.997775i \(0.521239\pi\)
\(30\) 0 0
\(31\) −4.27590 −0.767974 −0.383987 0.923339i \(-0.625449\pi\)
−0.383987 + 0.923339i \(0.625449\pi\)
\(32\) 0 0
\(33\) −0.138272 −0.0240700
\(34\) 0 0
\(35\) −6.24565 −1.05571
\(36\) 0 0
\(37\) −3.92212 −0.644792 −0.322396 0.946605i \(-0.604488\pi\)
−0.322396 + 0.946605i \(0.604488\pi\)
\(38\) 0 0
\(39\) 5.06303 0.810733
\(40\) 0 0
\(41\) 7.57912 1.18366 0.591830 0.806063i \(-0.298406\pi\)
0.591830 + 0.806063i \(0.298406\pi\)
\(42\) 0 0
\(43\) 12.3515 1.88359 0.941797 0.336183i \(-0.109136\pi\)
0.941797 + 0.336183i \(0.109136\pi\)
\(44\) 0 0
\(45\) −2.09997 −0.313045
\(46\) 0 0
\(47\) −9.22989 −1.34632 −0.673159 0.739498i \(-0.735063\pi\)
−0.673159 + 0.739498i \(0.735063\pi\)
\(48\) 0 0
\(49\) 1.84562 0.263660
\(50\) 0 0
\(51\) 0.299135 0.0418873
\(52\) 0 0
\(53\) 1.26409 0.173636 0.0868178 0.996224i \(-0.472330\pi\)
0.0868178 + 0.996224i \(0.472330\pi\)
\(54\) 0 0
\(55\) 0.290366 0.0391530
\(56\) 0 0
\(57\) 0.432187 0.0572446
\(58\) 0 0
\(59\) 3.01296 0.392253 0.196127 0.980579i \(-0.437164\pi\)
0.196127 + 0.980579i \(0.437164\pi\)
\(60\) 0 0
\(61\) 2.98537 0.382237 0.191118 0.981567i \(-0.438789\pi\)
0.191118 + 0.981567i \(0.438789\pi\)
\(62\) 0 0
\(63\) 2.97416 0.374709
\(64\) 0 0
\(65\) −10.6322 −1.31876
\(66\) 0 0
\(67\) −11.3934 −1.39193 −0.695964 0.718076i \(-0.745023\pi\)
−0.695964 + 0.718076i \(0.745023\pi\)
\(68\) 0 0
\(69\) 5.72098 0.688726
\(70\) 0 0
\(71\) −7.07665 −0.839844 −0.419922 0.907560i \(-0.637943\pi\)
−0.419922 + 0.907560i \(0.637943\pi\)
\(72\) 0 0
\(73\) 14.5486 1.70278 0.851392 0.524531i \(-0.175759\pi\)
0.851392 + 0.524531i \(0.175759\pi\)
\(74\) 0 0
\(75\) −0.590124 −0.0681417
\(76\) 0 0
\(77\) −0.411242 −0.0468654
\(78\) 0 0
\(79\) 13.7670 1.54891 0.774454 0.632630i \(-0.218025\pi\)
0.774454 + 0.632630i \(0.218025\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −15.7764 −1.73168 −0.865840 0.500321i \(-0.833215\pi\)
−0.865840 + 0.500321i \(0.833215\pi\)
\(84\) 0 0
\(85\) −0.628175 −0.0681351
\(86\) 0 0
\(87\) −0.718106 −0.0769891
\(88\) 0 0
\(89\) −12.4982 −1.32481 −0.662404 0.749147i \(-0.730464\pi\)
−0.662404 + 0.749147i \(0.730464\pi\)
\(90\) 0 0
\(91\) 15.0583 1.57853
\(92\) 0 0
\(93\) −4.27590 −0.443390
\(94\) 0 0
\(95\) −0.907580 −0.0931157
\(96\) 0 0
\(97\) 7.54510 0.766089 0.383044 0.923730i \(-0.374876\pi\)
0.383044 + 0.923730i \(0.374876\pi\)
\(98\) 0 0
\(99\) −0.138272 −0.0138968
\(100\) 0 0
\(101\) 10.4322 1.03804 0.519021 0.854761i \(-0.326296\pi\)
0.519021 + 0.854761i \(0.326296\pi\)
\(102\) 0 0
\(103\) 12.4671 1.22842 0.614211 0.789142i \(-0.289475\pi\)
0.614211 + 0.789142i \(0.289475\pi\)
\(104\) 0 0
\(105\) −6.24565 −0.609513
\(106\) 0 0
\(107\) −5.84644 −0.565196 −0.282598 0.959238i \(-0.591196\pi\)
−0.282598 + 0.959238i \(0.591196\pi\)
\(108\) 0 0
\(109\) 11.4163 1.09348 0.546742 0.837301i \(-0.315868\pi\)
0.546742 + 0.837301i \(0.315868\pi\)
\(110\) 0 0
\(111\) −3.92212 −0.372271
\(112\) 0 0
\(113\) 17.7140 1.66640 0.833198 0.552975i \(-0.186508\pi\)
0.833198 + 0.552975i \(0.186508\pi\)
\(114\) 0 0
\(115\) −12.0139 −1.12030
\(116\) 0 0
\(117\) 5.06303 0.468077
\(118\) 0 0
\(119\) 0.889675 0.0815564
\(120\) 0 0
\(121\) −10.9809 −0.998262
\(122\) 0 0
\(123\) 7.57912 0.683387
\(124\) 0 0
\(125\) 11.7391 1.04998
\(126\) 0 0
\(127\) 8.49463 0.753776 0.376888 0.926259i \(-0.376994\pi\)
0.376888 + 0.926259i \(0.376994\pi\)
\(128\) 0 0
\(129\) 12.3515 1.08749
\(130\) 0 0
\(131\) −2.85564 −0.249499 −0.124749 0.992188i \(-0.539813\pi\)
−0.124749 + 0.992188i \(0.539813\pi\)
\(132\) 0 0
\(133\) 1.28539 0.111458
\(134\) 0 0
\(135\) −2.09997 −0.180737
\(136\) 0 0
\(137\) 1.64533 0.140570 0.0702850 0.997527i \(-0.477609\pi\)
0.0702850 + 0.997527i \(0.477609\pi\)
\(138\) 0 0
\(139\) 12.1666 1.03196 0.515978 0.856602i \(-0.327429\pi\)
0.515978 + 0.856602i \(0.327429\pi\)
\(140\) 0 0
\(141\) −9.22989 −0.777297
\(142\) 0 0
\(143\) −0.700073 −0.0585431
\(144\) 0 0
\(145\) 1.50800 0.125233
\(146\) 0 0
\(147\) 1.84562 0.152224
\(148\) 0 0
\(149\) −12.9793 −1.06331 −0.531653 0.846962i \(-0.678429\pi\)
−0.531653 + 0.846962i \(0.678429\pi\)
\(150\) 0 0
\(151\) −20.5738 −1.67427 −0.837135 0.546997i \(-0.815771\pi\)
−0.837135 + 0.546997i \(0.815771\pi\)
\(152\) 0 0
\(153\) 0.299135 0.0241836
\(154\) 0 0
\(155\) 8.97925 0.721231
\(156\) 0 0
\(157\) 3.76196 0.300237 0.150119 0.988668i \(-0.452034\pi\)
0.150119 + 0.988668i \(0.452034\pi\)
\(158\) 0 0
\(159\) 1.26409 0.100249
\(160\) 0 0
\(161\) 17.0151 1.34098
\(162\) 0 0
\(163\) 18.3629 1.43829 0.719147 0.694858i \(-0.244533\pi\)
0.719147 + 0.694858i \(0.244533\pi\)
\(164\) 0 0
\(165\) 0.290366 0.0226050
\(166\) 0 0
\(167\) 1.00000 0.0773823
\(168\) 0 0
\(169\) 12.6343 0.971866
\(170\) 0 0
\(171\) 0.432187 0.0330502
\(172\) 0 0
\(173\) −24.3625 −1.85225 −0.926125 0.377217i \(-0.876881\pi\)
−0.926125 + 0.377217i \(0.876881\pi\)
\(174\) 0 0
\(175\) −1.75512 −0.132675
\(176\) 0 0
\(177\) 3.01296 0.226468
\(178\) 0 0
\(179\) −0.719729 −0.0537951 −0.0268975 0.999638i \(-0.508563\pi\)
−0.0268975 + 0.999638i \(0.508563\pi\)
\(180\) 0 0
\(181\) −3.81586 −0.283630 −0.141815 0.989893i \(-0.545294\pi\)
−0.141815 + 0.989893i \(0.545294\pi\)
\(182\) 0 0
\(183\) 2.98537 0.220685
\(184\) 0 0
\(185\) 8.23633 0.605547
\(186\) 0 0
\(187\) −0.0413619 −0.00302468
\(188\) 0 0
\(189\) 2.97416 0.216338
\(190\) 0 0
\(191\) 17.9273 1.29717 0.648585 0.761142i \(-0.275361\pi\)
0.648585 + 0.761142i \(0.275361\pi\)
\(192\) 0 0
\(193\) −6.31831 −0.454802 −0.227401 0.973801i \(-0.573023\pi\)
−0.227401 + 0.973801i \(0.573023\pi\)
\(194\) 0 0
\(195\) −10.6322 −0.761388
\(196\) 0 0
\(197\) −2.17097 −0.154675 −0.0773375 0.997005i \(-0.524642\pi\)
−0.0773375 + 0.997005i \(0.524642\pi\)
\(198\) 0 0
\(199\) 12.0022 0.850816 0.425408 0.905002i \(-0.360131\pi\)
0.425408 + 0.905002i \(0.360131\pi\)
\(200\) 0 0
\(201\) −11.3934 −0.803630
\(202\) 0 0
\(203\) −2.13576 −0.149901
\(204\) 0 0
\(205\) −15.9159 −1.11162
\(206\) 0 0
\(207\) 5.72098 0.397636
\(208\) 0 0
\(209\) −0.0597592 −0.00413363
\(210\) 0 0
\(211\) 12.4126 0.854521 0.427260 0.904129i \(-0.359479\pi\)
0.427260 + 0.904129i \(0.359479\pi\)
\(212\) 0 0
\(213\) −7.07665 −0.484884
\(214\) 0 0
\(215\) −25.9379 −1.76895
\(216\) 0 0
\(217\) −12.7172 −0.863299
\(218\) 0 0
\(219\) 14.5486 0.983102
\(220\) 0 0
\(221\) 1.51453 0.101878
\(222\) 0 0
\(223\) 16.6831 1.11719 0.558593 0.829442i \(-0.311341\pi\)
0.558593 + 0.829442i \(0.311341\pi\)
\(224\) 0 0
\(225\) −0.590124 −0.0393416
\(226\) 0 0
\(227\) −7.20014 −0.477890 −0.238945 0.971033i \(-0.576802\pi\)
−0.238945 + 0.971033i \(0.576802\pi\)
\(228\) 0 0
\(229\) 16.3304 1.07914 0.539572 0.841939i \(-0.318586\pi\)
0.539572 + 0.841939i \(0.318586\pi\)
\(230\) 0 0
\(231\) −0.411242 −0.0270577
\(232\) 0 0
\(233\) 16.8678 1.10504 0.552522 0.833498i \(-0.313666\pi\)
0.552522 + 0.833498i \(0.313666\pi\)
\(234\) 0 0
\(235\) 19.3825 1.26437
\(236\) 0 0
\(237\) 13.7670 0.894262
\(238\) 0 0
\(239\) 24.1014 1.55899 0.779494 0.626410i \(-0.215476\pi\)
0.779494 + 0.626410i \(0.215476\pi\)
\(240\) 0 0
\(241\) −1.37146 −0.0883434 −0.0441717 0.999024i \(-0.514065\pi\)
−0.0441717 + 0.999024i \(0.514065\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) −3.87575 −0.247613
\(246\) 0 0
\(247\) 2.18818 0.139230
\(248\) 0 0
\(249\) −15.7764 −0.999786
\(250\) 0 0
\(251\) 2.57248 0.162374 0.0811868 0.996699i \(-0.474129\pi\)
0.0811868 + 0.996699i \(0.474129\pi\)
\(252\) 0 0
\(253\) −0.791050 −0.0497329
\(254\) 0 0
\(255\) −0.628175 −0.0393378
\(256\) 0 0
\(257\) 6.87895 0.429097 0.214549 0.976713i \(-0.431172\pi\)
0.214549 + 0.976713i \(0.431172\pi\)
\(258\) 0 0
\(259\) −11.6650 −0.724828
\(260\) 0 0
\(261\) −0.718106 −0.0444497
\(262\) 0 0
\(263\) 30.1737 1.86059 0.930296 0.366810i \(-0.119550\pi\)
0.930296 + 0.366810i \(0.119550\pi\)
\(264\) 0 0
\(265\) −2.65454 −0.163067
\(266\) 0 0
\(267\) −12.4982 −0.764878
\(268\) 0 0
\(269\) 8.26235 0.503764 0.251882 0.967758i \(-0.418950\pi\)
0.251882 + 0.967758i \(0.418950\pi\)
\(270\) 0 0
\(271\) 23.3323 1.41734 0.708669 0.705541i \(-0.249296\pi\)
0.708669 + 0.705541i \(0.249296\pi\)
\(272\) 0 0
\(273\) 15.0583 0.911367
\(274\) 0 0
\(275\) 0.0815975 0.00492051
\(276\) 0 0
\(277\) −2.10722 −0.126610 −0.0633052 0.997994i \(-0.520164\pi\)
−0.0633052 + 0.997994i \(0.520164\pi\)
\(278\) 0 0
\(279\) −4.27590 −0.255991
\(280\) 0 0
\(281\) −7.06113 −0.421232 −0.210616 0.977569i \(-0.567547\pi\)
−0.210616 + 0.977569i \(0.567547\pi\)
\(282\) 0 0
\(283\) −10.3953 −0.617937 −0.308969 0.951072i \(-0.599984\pi\)
−0.308969 + 0.951072i \(0.599984\pi\)
\(284\) 0 0
\(285\) −0.907580 −0.0537604
\(286\) 0 0
\(287\) 22.5415 1.33058
\(288\) 0 0
\(289\) −16.9105 −0.994736
\(290\) 0 0
\(291\) 7.54510 0.442302
\(292\) 0 0
\(293\) −24.7202 −1.44417 −0.722086 0.691803i \(-0.756817\pi\)
−0.722086 + 0.691803i \(0.756817\pi\)
\(294\) 0 0
\(295\) −6.32712 −0.368379
\(296\) 0 0
\(297\) −0.138272 −0.00802334
\(298\) 0 0
\(299\) 28.9655 1.67512
\(300\) 0 0
\(301\) 36.7355 2.11740
\(302\) 0 0
\(303\) 10.4322 0.599314
\(304\) 0 0
\(305\) −6.26918 −0.358972
\(306\) 0 0
\(307\) −31.2025 −1.78082 −0.890410 0.455159i \(-0.849582\pi\)
−0.890410 + 0.455159i \(0.849582\pi\)
\(308\) 0 0
\(309\) 12.4671 0.709229
\(310\) 0 0
\(311\) 33.4235 1.89527 0.947636 0.319353i \(-0.103466\pi\)
0.947636 + 0.319353i \(0.103466\pi\)
\(312\) 0 0
\(313\) −18.4281 −1.04162 −0.520808 0.853674i \(-0.674369\pi\)
−0.520808 + 0.853674i \(0.674369\pi\)
\(314\) 0 0
\(315\) −6.24565 −0.351902
\(316\) 0 0
\(317\) −23.6150 −1.32635 −0.663176 0.748463i \(-0.730792\pi\)
−0.663176 + 0.748463i \(0.730792\pi\)
\(318\) 0 0
\(319\) 0.0992938 0.00555938
\(320\) 0 0
\(321\) −5.84644 −0.326316
\(322\) 0 0
\(323\) 0.129282 0.00719346
\(324\) 0 0
\(325\) −2.98782 −0.165734
\(326\) 0 0
\(327\) 11.4163 0.631323
\(328\) 0 0
\(329\) −27.4512 −1.51343
\(330\) 0 0
\(331\) 0.822383 0.0452023 0.0226011 0.999745i \(-0.492805\pi\)
0.0226011 + 0.999745i \(0.492805\pi\)
\(332\) 0 0
\(333\) −3.92212 −0.214931
\(334\) 0 0
\(335\) 23.9259 1.30721
\(336\) 0 0
\(337\) −14.7926 −0.805805 −0.402902 0.915243i \(-0.631999\pi\)
−0.402902 + 0.915243i \(0.631999\pi\)
\(338\) 0 0
\(339\) 17.7140 0.962094
\(340\) 0 0
\(341\) 0.591235 0.0320172
\(342\) 0 0
\(343\) −15.3299 −0.827739
\(344\) 0 0
\(345\) −12.0139 −0.646807
\(346\) 0 0
\(347\) −23.3182 −1.25179 −0.625894 0.779908i \(-0.715266\pi\)
−0.625894 + 0.779908i \(0.715266\pi\)
\(348\) 0 0
\(349\) −23.5530 −1.26076 −0.630382 0.776285i \(-0.717102\pi\)
−0.630382 + 0.776285i \(0.717102\pi\)
\(350\) 0 0
\(351\) 5.06303 0.270244
\(352\) 0 0
\(353\) −22.7213 −1.20933 −0.604666 0.796479i \(-0.706693\pi\)
−0.604666 + 0.796479i \(0.706693\pi\)
\(354\) 0 0
\(355\) 14.8608 0.788727
\(356\) 0 0
\(357\) 0.889675 0.0470866
\(358\) 0 0
\(359\) −4.45309 −0.235025 −0.117513 0.993071i \(-0.537492\pi\)
−0.117513 + 0.993071i \(0.537492\pi\)
\(360\) 0 0
\(361\) −18.8132 −0.990169
\(362\) 0 0
\(363\) −10.9809 −0.576347
\(364\) 0 0
\(365\) −30.5516 −1.59914
\(366\) 0 0
\(367\) 31.0004 1.61821 0.809103 0.587667i \(-0.199953\pi\)
0.809103 + 0.587667i \(0.199953\pi\)
\(368\) 0 0
\(369\) 7.57912 0.394553
\(370\) 0 0
\(371\) 3.75960 0.195188
\(372\) 0 0
\(373\) −14.5252 −0.752089 −0.376044 0.926602i \(-0.622716\pi\)
−0.376044 + 0.926602i \(0.622716\pi\)
\(374\) 0 0
\(375\) 11.7391 0.606204
\(376\) 0 0
\(377\) −3.63579 −0.187253
\(378\) 0 0
\(379\) −5.36141 −0.275397 −0.137698 0.990474i \(-0.543970\pi\)
−0.137698 + 0.990474i \(0.543970\pi\)
\(380\) 0 0
\(381\) 8.49463 0.435193
\(382\) 0 0
\(383\) −35.4614 −1.81200 −0.905998 0.423283i \(-0.860878\pi\)
−0.905998 + 0.423283i \(0.860878\pi\)
\(384\) 0 0
\(385\) 0.863596 0.0440129
\(386\) 0 0
\(387\) 12.3515 0.627865
\(388\) 0 0
\(389\) −11.3561 −0.575777 −0.287889 0.957664i \(-0.592953\pi\)
−0.287889 + 0.957664i \(0.592953\pi\)
\(390\) 0 0
\(391\) 1.71135 0.0865466
\(392\) 0 0
\(393\) −2.85564 −0.144048
\(394\) 0 0
\(395\) −28.9103 −1.45463
\(396\) 0 0
\(397\) 29.2022 1.46562 0.732808 0.680436i \(-0.238210\pi\)
0.732808 + 0.680436i \(0.238210\pi\)
\(398\) 0 0
\(399\) 1.28539 0.0643501
\(400\) 0 0
\(401\) −20.5988 −1.02866 −0.514328 0.857594i \(-0.671959\pi\)
−0.514328 + 0.857594i \(0.671959\pi\)
\(402\) 0 0
\(403\) −21.6490 −1.07841
\(404\) 0 0
\(405\) −2.09997 −0.104348
\(406\) 0 0
\(407\) 0.542318 0.0268817
\(408\) 0 0
\(409\) −6.71740 −0.332154 −0.166077 0.986113i \(-0.553110\pi\)
−0.166077 + 0.986113i \(0.553110\pi\)
\(410\) 0 0
\(411\) 1.64533 0.0811581
\(412\) 0 0
\(413\) 8.96101 0.440942
\(414\) 0 0
\(415\) 33.1299 1.62628
\(416\) 0 0
\(417\) 12.1666 0.595800
\(418\) 0 0
\(419\) −2.90625 −0.141980 −0.0709898 0.997477i \(-0.522616\pi\)
−0.0709898 + 0.997477i \(0.522616\pi\)
\(420\) 0 0
\(421\) −11.0417 −0.538140 −0.269070 0.963121i \(-0.586716\pi\)
−0.269070 + 0.963121i \(0.586716\pi\)
\(422\) 0 0
\(423\) −9.22989 −0.448772
\(424\) 0 0
\(425\) −0.176527 −0.00856281
\(426\) 0 0
\(427\) 8.87895 0.429683
\(428\) 0 0
\(429\) −0.700073 −0.0337999
\(430\) 0 0
\(431\) −17.6903 −0.852110 −0.426055 0.904697i \(-0.640097\pi\)
−0.426055 + 0.904697i \(0.640097\pi\)
\(432\) 0 0
\(433\) −17.4174 −0.837025 −0.418513 0.908211i \(-0.637448\pi\)
−0.418513 + 0.908211i \(0.637448\pi\)
\(434\) 0 0
\(435\) 1.50800 0.0723032
\(436\) 0 0
\(437\) 2.47254 0.118277
\(438\) 0 0
\(439\) 16.5212 0.788512 0.394256 0.919001i \(-0.371002\pi\)
0.394256 + 0.919001i \(0.371002\pi\)
\(440\) 0 0
\(441\) 1.84562 0.0878867
\(442\) 0 0
\(443\) −21.4189 −1.01764 −0.508822 0.860871i \(-0.669919\pi\)
−0.508822 + 0.860871i \(0.669919\pi\)
\(444\) 0 0
\(445\) 26.2459 1.24417
\(446\) 0 0
\(447\) −12.9793 −0.613900
\(448\) 0 0
\(449\) 31.1123 1.46828 0.734141 0.678998i \(-0.237585\pi\)
0.734141 + 0.678998i \(0.237585\pi\)
\(450\) 0 0
\(451\) −1.04798 −0.0493474
\(452\) 0 0
\(453\) −20.5738 −0.966640
\(454\) 0 0
\(455\) −31.6219 −1.48246
\(456\) 0 0
\(457\) 11.2728 0.527321 0.263660 0.964616i \(-0.415070\pi\)
0.263660 + 0.964616i \(0.415070\pi\)
\(458\) 0 0
\(459\) 0.299135 0.0139624
\(460\) 0 0
\(461\) 25.0888 1.16850 0.584251 0.811573i \(-0.301388\pi\)
0.584251 + 0.811573i \(0.301388\pi\)
\(462\) 0 0
\(463\) 29.9933 1.39391 0.696954 0.717116i \(-0.254538\pi\)
0.696954 + 0.717116i \(0.254538\pi\)
\(464\) 0 0
\(465\) 8.97925 0.416403
\(466\) 0 0
\(467\) −26.6386 −1.23269 −0.616343 0.787478i \(-0.711386\pi\)
−0.616343 + 0.787478i \(0.711386\pi\)
\(468\) 0 0
\(469\) −33.8859 −1.56470
\(470\) 0 0
\(471\) 3.76196 0.173342
\(472\) 0 0
\(473\) −1.70787 −0.0785279
\(474\) 0 0
\(475\) −0.255044 −0.0117022
\(476\) 0 0
\(477\) 1.26409 0.0578786
\(478\) 0 0
\(479\) 34.6774 1.58445 0.792225 0.610229i \(-0.208922\pi\)
0.792225 + 0.610229i \(0.208922\pi\)
\(480\) 0 0
\(481\) −19.8578 −0.905437
\(482\) 0 0
\(483\) 17.0151 0.774215
\(484\) 0 0
\(485\) −15.8445 −0.719461
\(486\) 0 0
\(487\) −15.7054 −0.711678 −0.355839 0.934547i \(-0.615805\pi\)
−0.355839 + 0.934547i \(0.615805\pi\)
\(488\) 0 0
\(489\) 18.3629 0.830399
\(490\) 0 0
\(491\) 16.0372 0.723751 0.361875 0.932226i \(-0.382137\pi\)
0.361875 + 0.932226i \(0.382137\pi\)
\(492\) 0 0
\(493\) −0.214811 −0.00967459
\(494\) 0 0
\(495\) 0.290366 0.0130510
\(496\) 0 0
\(497\) −21.0471 −0.944090
\(498\) 0 0
\(499\) −12.7331 −0.570011 −0.285005 0.958526i \(-0.591995\pi\)
−0.285005 + 0.958526i \(0.591995\pi\)
\(500\) 0 0
\(501\) 1.00000 0.0446767
\(502\) 0 0
\(503\) 3.14474 0.140217 0.0701086 0.997539i \(-0.477665\pi\)
0.0701086 + 0.997539i \(0.477665\pi\)
\(504\) 0 0
\(505\) −21.9073 −0.974863
\(506\) 0 0
\(507\) 12.6343 0.561107
\(508\) 0 0
\(509\) −4.63793 −0.205572 −0.102786 0.994703i \(-0.532776\pi\)
−0.102786 + 0.994703i \(0.532776\pi\)
\(510\) 0 0
\(511\) 43.2698 1.91414
\(512\) 0 0
\(513\) 0.432187 0.0190815
\(514\) 0 0
\(515\) −26.1806 −1.15365
\(516\) 0 0
\(517\) 1.27623 0.0561286
\(518\) 0 0
\(519\) −24.3625 −1.06940
\(520\) 0 0
\(521\) 37.2557 1.63220 0.816102 0.577908i \(-0.196131\pi\)
0.816102 + 0.577908i \(0.196131\pi\)
\(522\) 0 0
\(523\) −27.9630 −1.22274 −0.611369 0.791346i \(-0.709381\pi\)
−0.611369 + 0.791346i \(0.709381\pi\)
\(524\) 0 0
\(525\) −1.75512 −0.0765999
\(526\) 0 0
\(527\) −1.27907 −0.0557172
\(528\) 0 0
\(529\) 9.72967 0.423029
\(530\) 0 0
\(531\) 3.01296 0.130751
\(532\) 0 0
\(533\) 38.3733 1.66213
\(534\) 0 0
\(535\) 12.2773 0.530796
\(536\) 0 0
\(537\) −0.719729 −0.0310586
\(538\) 0 0
\(539\) −0.255197 −0.0109921
\(540\) 0 0
\(541\) −22.7551 −0.978316 −0.489158 0.872195i \(-0.662696\pi\)
−0.489158 + 0.872195i \(0.662696\pi\)
\(542\) 0 0
\(543\) −3.81586 −0.163754
\(544\) 0 0
\(545\) −23.9739 −1.02693
\(546\) 0 0
\(547\) 6.58788 0.281677 0.140839 0.990033i \(-0.455020\pi\)
0.140839 + 0.990033i \(0.455020\pi\)
\(548\) 0 0
\(549\) 2.98537 0.127412
\(550\) 0 0
\(551\) −0.310356 −0.0132216
\(552\) 0 0
\(553\) 40.9452 1.74117
\(554\) 0 0
\(555\) 8.23633 0.349613
\(556\) 0 0
\(557\) 16.1334 0.683594 0.341797 0.939774i \(-0.388964\pi\)
0.341797 + 0.939774i \(0.388964\pi\)
\(558\) 0 0
\(559\) 62.5362 2.64500
\(560\) 0 0
\(561\) −0.0413619 −0.00174630
\(562\) 0 0
\(563\) 11.2526 0.474240 0.237120 0.971480i \(-0.423797\pi\)
0.237120 + 0.971480i \(0.423797\pi\)
\(564\) 0 0
\(565\) −37.1989 −1.56497
\(566\) 0 0
\(567\) 2.97416 0.124903
\(568\) 0 0
\(569\) 19.1087 0.801079 0.400539 0.916280i \(-0.368823\pi\)
0.400539 + 0.916280i \(0.368823\pi\)
\(570\) 0 0
\(571\) −26.7499 −1.11945 −0.559725 0.828679i \(-0.689093\pi\)
−0.559725 + 0.828679i \(0.689093\pi\)
\(572\) 0 0
\(573\) 17.9273 0.748922
\(574\) 0 0
\(575\) −3.37609 −0.140793
\(576\) 0 0
\(577\) 2.62594 0.109319 0.0546596 0.998505i \(-0.482593\pi\)
0.0546596 + 0.998505i \(0.482593\pi\)
\(578\) 0 0
\(579\) −6.31831 −0.262580
\(580\) 0 0
\(581\) −46.9214 −1.94663
\(582\) 0 0
\(583\) −0.174787 −0.00723895
\(584\) 0 0
\(585\) −10.6322 −0.439588
\(586\) 0 0
\(587\) −24.6288 −1.01654 −0.508269 0.861198i \(-0.669714\pi\)
−0.508269 + 0.861198i \(0.669714\pi\)
\(588\) 0 0
\(589\) −1.84799 −0.0761450
\(590\) 0 0
\(591\) −2.17097 −0.0893016
\(592\) 0 0
\(593\) 12.2107 0.501433 0.250716 0.968061i \(-0.419334\pi\)
0.250716 + 0.968061i \(0.419334\pi\)
\(594\) 0 0
\(595\) −1.86829 −0.0765925
\(596\) 0 0
\(597\) 12.0022 0.491219
\(598\) 0 0
\(599\) −21.7233 −0.887591 −0.443796 0.896128i \(-0.646368\pi\)
−0.443796 + 0.896128i \(0.646368\pi\)
\(600\) 0 0
\(601\) −28.7575 −1.17304 −0.586521 0.809934i \(-0.699503\pi\)
−0.586521 + 0.809934i \(0.699503\pi\)
\(602\) 0 0
\(603\) −11.3934 −0.463976
\(604\) 0 0
\(605\) 23.0595 0.937503
\(606\) 0 0
\(607\) −22.9370 −0.930985 −0.465493 0.885052i \(-0.654123\pi\)
−0.465493 + 0.885052i \(0.654123\pi\)
\(608\) 0 0
\(609\) −2.13576 −0.0865455
\(610\) 0 0
\(611\) −46.7312 −1.89054
\(612\) 0 0
\(613\) −39.7699 −1.60629 −0.803145 0.595784i \(-0.796842\pi\)
−0.803145 + 0.595784i \(0.796842\pi\)
\(614\) 0 0
\(615\) −15.9159 −0.641792
\(616\) 0 0
\(617\) −16.6341 −0.669663 −0.334832 0.942278i \(-0.608679\pi\)
−0.334832 + 0.942278i \(0.608679\pi\)
\(618\) 0 0
\(619\) −20.5361 −0.825416 −0.412708 0.910863i \(-0.635417\pi\)
−0.412708 + 0.910863i \(0.635417\pi\)
\(620\) 0 0
\(621\) 5.72098 0.229575
\(622\) 0 0
\(623\) −37.1717 −1.48925
\(624\) 0 0
\(625\) −21.7011 −0.868045
\(626\) 0 0
\(627\) −0.0597592 −0.00238655
\(628\) 0 0
\(629\) −1.17324 −0.0467802
\(630\) 0 0
\(631\) 26.0602 1.03744 0.518721 0.854944i \(-0.326408\pi\)
0.518721 + 0.854944i \(0.326408\pi\)
\(632\) 0 0
\(633\) 12.4126 0.493358
\(634\) 0 0
\(635\) −17.8385 −0.707898
\(636\) 0 0
\(637\) 9.34443 0.370240
\(638\) 0 0
\(639\) −7.07665 −0.279948
\(640\) 0 0
\(641\) −17.1851 −0.678771 −0.339386 0.940647i \(-0.610219\pi\)
−0.339386 + 0.940647i \(0.610219\pi\)
\(642\) 0 0
\(643\) −39.0699 −1.54077 −0.770383 0.637582i \(-0.779935\pi\)
−0.770383 + 0.637582i \(0.779935\pi\)
\(644\) 0 0
\(645\) −25.9379 −1.02130
\(646\) 0 0
\(647\) −1.31198 −0.0515794 −0.0257897 0.999667i \(-0.508210\pi\)
−0.0257897 + 0.999667i \(0.508210\pi\)
\(648\) 0 0
\(649\) −0.416606 −0.0163532
\(650\) 0 0
\(651\) −12.7172 −0.498426
\(652\) 0 0
\(653\) 36.2903 1.42015 0.710074 0.704127i \(-0.248661\pi\)
0.710074 + 0.704127i \(0.248661\pi\)
\(654\) 0 0
\(655\) 5.99676 0.234313
\(656\) 0 0
\(657\) 14.5486 0.567594
\(658\) 0 0
\(659\) 7.04958 0.274613 0.137306 0.990529i \(-0.456156\pi\)
0.137306 + 0.990529i \(0.456156\pi\)
\(660\) 0 0
\(661\) 21.4844 0.835648 0.417824 0.908528i \(-0.362793\pi\)
0.417824 + 0.908528i \(0.362793\pi\)
\(662\) 0 0
\(663\) 1.51453 0.0588194
\(664\) 0 0
\(665\) −2.69929 −0.104674
\(666\) 0 0
\(667\) −4.10827 −0.159073
\(668\) 0 0
\(669\) 16.6831 0.645008
\(670\) 0 0
\(671\) −0.412792 −0.0159356
\(672\) 0 0
\(673\) −6.31641 −0.243480 −0.121740 0.992562i \(-0.538847\pi\)
−0.121740 + 0.992562i \(0.538847\pi\)
\(674\) 0 0
\(675\) −0.590124 −0.0227139
\(676\) 0 0
\(677\) 21.2225 0.815648 0.407824 0.913061i \(-0.366288\pi\)
0.407824 + 0.913061i \(0.366288\pi\)
\(678\) 0 0
\(679\) 22.4403 0.861181
\(680\) 0 0
\(681\) −7.20014 −0.275910
\(682\) 0 0
\(683\) 40.0609 1.53289 0.766443 0.642312i \(-0.222025\pi\)
0.766443 + 0.642312i \(0.222025\pi\)
\(684\) 0 0
\(685\) −3.45514 −0.132014
\(686\) 0 0
\(687\) 16.3304 0.623044
\(688\) 0 0
\(689\) 6.40011 0.243825
\(690\) 0 0
\(691\) 41.3269 1.57215 0.786075 0.618131i \(-0.212110\pi\)
0.786075 + 0.618131i \(0.212110\pi\)
\(692\) 0 0
\(693\) −0.411242 −0.0156218
\(694\) 0 0
\(695\) −25.5494 −0.969146
\(696\) 0 0
\(697\) 2.26718 0.0858756
\(698\) 0 0
\(699\) 16.8678 0.637997
\(700\) 0 0
\(701\) −26.1035 −0.985916 −0.492958 0.870053i \(-0.664084\pi\)
−0.492958 + 0.870053i \(0.664084\pi\)
\(702\) 0 0
\(703\) −1.69509 −0.0639314
\(704\) 0 0
\(705\) 19.3825 0.729987
\(706\) 0 0
\(707\) 31.0270 1.16689
\(708\) 0 0
\(709\) −0.259309 −0.00973854 −0.00486927 0.999988i \(-0.501550\pi\)
−0.00486927 + 0.999988i \(0.501550\pi\)
\(710\) 0 0
\(711\) 13.7670 0.516303
\(712\) 0 0
\(713\) −24.4623 −0.916122
\(714\) 0 0
\(715\) 1.47013 0.0549799
\(716\) 0 0
\(717\) 24.1014 0.900082
\(718\) 0 0
\(719\) −44.6788 −1.66624 −0.833120 0.553093i \(-0.813447\pi\)
−0.833120 + 0.553093i \(0.813447\pi\)
\(720\) 0 0
\(721\) 37.0792 1.38090
\(722\) 0 0
\(723\) −1.37146 −0.0510051
\(724\) 0 0
\(725\) 0.423772 0.0157385
\(726\) 0 0
\(727\) 11.9819 0.444384 0.222192 0.975003i \(-0.428679\pi\)
0.222192 + 0.975003i \(0.428679\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 3.69478 0.136656
\(732\) 0 0
\(733\) −18.2924 −0.675645 −0.337822 0.941210i \(-0.609690\pi\)
−0.337822 + 0.941210i \(0.609690\pi\)
\(734\) 0 0
\(735\) −3.87575 −0.142959
\(736\) 0 0
\(737\) 1.57539 0.0580302
\(738\) 0 0
\(739\) −11.5860 −0.426197 −0.213099 0.977031i \(-0.568356\pi\)
−0.213099 + 0.977031i \(0.568356\pi\)
\(740\) 0 0
\(741\) 2.18818 0.0803846
\(742\) 0 0
\(743\) −14.2882 −0.524183 −0.262092 0.965043i \(-0.584412\pi\)
−0.262092 + 0.965043i \(0.584412\pi\)
\(744\) 0 0
\(745\) 27.2562 0.998589
\(746\) 0 0
\(747\) −15.7764 −0.577226
\(748\) 0 0
\(749\) −17.3882 −0.635352
\(750\) 0 0
\(751\) 1.28638 0.0469407 0.0234703 0.999725i \(-0.492528\pi\)
0.0234703 + 0.999725i \(0.492528\pi\)
\(752\) 0 0
\(753\) 2.57248 0.0937465
\(754\) 0 0
\(755\) 43.2043 1.57237
\(756\) 0 0
\(757\) 15.5228 0.564185 0.282092 0.959387i \(-0.408972\pi\)
0.282092 + 0.959387i \(0.408972\pi\)
\(758\) 0 0
\(759\) −0.791050 −0.0287133
\(760\) 0 0
\(761\) −1.55417 −0.0563385 −0.0281693 0.999603i \(-0.508968\pi\)
−0.0281693 + 0.999603i \(0.508968\pi\)
\(762\) 0 0
\(763\) 33.9539 1.22921
\(764\) 0 0
\(765\) −0.628175 −0.0227117
\(766\) 0 0
\(767\) 15.2547 0.550815
\(768\) 0 0
\(769\) −45.1817 −1.62929 −0.814647 0.579957i \(-0.803069\pi\)
−0.814647 + 0.579957i \(0.803069\pi\)
\(770\) 0 0
\(771\) 6.87895 0.247739
\(772\) 0 0
\(773\) −53.9167 −1.93925 −0.969625 0.244597i \(-0.921344\pi\)
−0.969625 + 0.244597i \(0.921344\pi\)
\(774\) 0 0
\(775\) 2.52331 0.0906399
\(776\) 0 0
\(777\) −11.6650 −0.418479
\(778\) 0 0
\(779\) 3.27560 0.117361
\(780\) 0 0
\(781\) 0.978500 0.0350135
\(782\) 0 0
\(783\) −0.718106 −0.0256630
\(784\) 0 0
\(785\) −7.90001 −0.281963
\(786\) 0 0
\(787\) 8.43062 0.300519 0.150260 0.988647i \(-0.451989\pi\)
0.150260 + 0.988647i \(0.451989\pi\)
\(788\) 0 0
\(789\) 30.1737 1.07421
\(790\) 0 0
\(791\) 52.6843 1.87324
\(792\) 0 0
\(793\) 15.1150 0.536749
\(794\) 0 0
\(795\) −2.65454 −0.0941470
\(796\) 0 0
\(797\) 24.7547 0.876856 0.438428 0.898766i \(-0.355535\pi\)
0.438428 + 0.898766i \(0.355535\pi\)
\(798\) 0 0
\(799\) −2.76098 −0.0976766
\(800\) 0 0
\(801\) −12.4982 −0.441603
\(802\) 0 0
\(803\) −2.01166 −0.0709899
\(804\) 0 0
\(805\) −35.7312 −1.25936
\(806\) 0 0
\(807\) 8.26235 0.290849
\(808\) 0 0
\(809\) −27.3604 −0.961941 −0.480970 0.876737i \(-0.659716\pi\)
−0.480970 + 0.876737i \(0.659716\pi\)
\(810\) 0 0
\(811\) −2.45887 −0.0863426 −0.0431713 0.999068i \(-0.513746\pi\)
−0.0431713 + 0.999068i \(0.513746\pi\)
\(812\) 0 0
\(813\) 23.3323 0.818300
\(814\) 0 0
\(815\) −38.5616 −1.35075
\(816\) 0 0
\(817\) 5.33818 0.186759
\(818\) 0 0
\(819\) 15.0583 0.526178
\(820\) 0 0
\(821\) 6.86656 0.239645 0.119822 0.992795i \(-0.461768\pi\)
0.119822 + 0.992795i \(0.461768\pi\)
\(822\) 0 0
\(823\) 19.4606 0.678355 0.339178 0.940722i \(-0.389851\pi\)
0.339178 + 0.940722i \(0.389851\pi\)
\(824\) 0 0
\(825\) 0.0815975 0.00284086
\(826\) 0 0
\(827\) 8.19257 0.284884 0.142442 0.989803i \(-0.454505\pi\)
0.142442 + 0.989803i \(0.454505\pi\)
\(828\) 0 0
\(829\) −46.2894 −1.60770 −0.803849 0.594833i \(-0.797218\pi\)
−0.803849 + 0.594833i \(0.797218\pi\)
\(830\) 0 0
\(831\) −2.10722 −0.0730986
\(832\) 0 0
\(833\) 0.552090 0.0191288
\(834\) 0 0
\(835\) −2.09997 −0.0726725
\(836\) 0 0
\(837\) −4.27590 −0.147797
\(838\) 0 0
\(839\) 4.64299 0.160294 0.0801468 0.996783i \(-0.474461\pi\)
0.0801468 + 0.996783i \(0.474461\pi\)
\(840\) 0 0
\(841\) −28.4843 −0.982218
\(842\) 0 0
\(843\) −7.06113 −0.243198
\(844\) 0 0
\(845\) −26.5316 −0.912713
\(846\) 0 0
\(847\) −32.6589 −1.12217
\(848\) 0 0
\(849\) −10.3953 −0.356766
\(850\) 0 0
\(851\) −22.4384 −0.769177
\(852\) 0 0
\(853\) 9.12150 0.312314 0.156157 0.987732i \(-0.450089\pi\)
0.156157 + 0.987732i \(0.450089\pi\)
\(854\) 0 0
\(855\) −0.907580 −0.0310386
\(856\) 0 0
\(857\) −7.34645 −0.250950 −0.125475 0.992097i \(-0.540046\pi\)
−0.125475 + 0.992097i \(0.540046\pi\)
\(858\) 0 0
\(859\) −37.2638 −1.27142 −0.635712 0.771927i \(-0.719293\pi\)
−0.635712 + 0.771927i \(0.719293\pi\)
\(860\) 0 0
\(861\) 22.5415 0.768213
\(862\) 0 0
\(863\) −17.3469 −0.590496 −0.295248 0.955421i \(-0.595402\pi\)
−0.295248 + 0.955421i \(0.595402\pi\)
\(864\) 0 0
\(865\) 51.1606 1.73951
\(866\) 0 0
\(867\) −16.9105 −0.574311
\(868\) 0 0
\(869\) −1.90359 −0.0645747
\(870\) 0 0
\(871\) −57.6852 −1.95459
\(872\) 0 0
\(873\) 7.54510 0.255363
\(874\) 0 0
\(875\) 34.9139 1.18031
\(876\) 0 0
\(877\) 9.09836 0.307230 0.153615 0.988131i \(-0.450908\pi\)
0.153615 + 0.988131i \(0.450908\pi\)
\(878\) 0 0
\(879\) −24.7202 −0.833793
\(880\) 0 0
\(881\) −26.1065 −0.879550 −0.439775 0.898108i \(-0.644942\pi\)
−0.439775 + 0.898108i \(0.644942\pi\)
\(882\) 0 0
\(883\) 22.3088 0.750750 0.375375 0.926873i \(-0.377514\pi\)
0.375375 + 0.926873i \(0.377514\pi\)
\(884\) 0 0
\(885\) −6.32712 −0.212684
\(886\) 0 0
\(887\) −34.3987 −1.15500 −0.577498 0.816392i \(-0.695971\pi\)
−0.577498 + 0.816392i \(0.695971\pi\)
\(888\) 0 0
\(889\) 25.2644 0.847340
\(890\) 0 0
\(891\) −0.138272 −0.00463228
\(892\) 0 0
\(893\) −3.98904 −0.133488
\(894\) 0 0
\(895\) 1.51141 0.0505208
\(896\) 0 0
\(897\) 28.9655 0.967130
\(898\) 0 0
\(899\) 3.07055 0.102408
\(900\) 0 0
\(901\) 0.378133 0.0125974
\(902\) 0 0
\(903\) 36.7355 1.22248
\(904\) 0 0
\(905\) 8.01318 0.266367
\(906\) 0 0
\(907\) 18.7791 0.623551 0.311776 0.950156i \(-0.399076\pi\)
0.311776 + 0.950156i \(0.399076\pi\)
\(908\) 0 0
\(909\) 10.4322 0.346014
\(910\) 0 0
\(911\) 42.3954 1.40462 0.702311 0.711870i \(-0.252151\pi\)
0.702311 + 0.711870i \(0.252151\pi\)
\(912\) 0 0
\(913\) 2.18142 0.0721945
\(914\) 0 0
\(915\) −6.26918 −0.207253
\(916\) 0 0
\(917\) −8.49313 −0.280468
\(918\) 0 0
\(919\) 21.3230 0.703379 0.351690 0.936117i \(-0.385607\pi\)
0.351690 + 0.936117i \(0.385607\pi\)
\(920\) 0 0
\(921\) −31.2025 −1.02816
\(922\) 0 0
\(923\) −35.8293 −1.17933
\(924\) 0 0
\(925\) 2.31454 0.0761015
\(926\) 0 0
\(927\) 12.4671 0.409474
\(928\) 0 0
\(929\) 44.9861 1.47595 0.737973 0.674830i \(-0.235783\pi\)
0.737973 + 0.674830i \(0.235783\pi\)
\(930\) 0 0
\(931\) 0.797654 0.0261420
\(932\) 0 0
\(933\) 33.4235 1.09424
\(934\) 0 0
\(935\) 0.0868588 0.00284059
\(936\) 0 0
\(937\) −34.2610 −1.11926 −0.559629 0.828743i \(-0.689056\pi\)
−0.559629 + 0.828743i \(0.689056\pi\)
\(938\) 0 0
\(939\) −18.4281 −0.601377
\(940\) 0 0
\(941\) −18.7215 −0.610303 −0.305152 0.952304i \(-0.598707\pi\)
−0.305152 + 0.952304i \(0.598707\pi\)
\(942\) 0 0
\(943\) 43.3600 1.41200
\(944\) 0 0
\(945\) −6.24565 −0.203171
\(946\) 0 0
\(947\) 33.2088 1.07914 0.539570 0.841941i \(-0.318587\pi\)
0.539570 + 0.841941i \(0.318587\pi\)
\(948\) 0 0
\(949\) 73.6599 2.39110
\(950\) 0 0
\(951\) −23.6150 −0.765770
\(952\) 0 0
\(953\) −29.9705 −0.970838 −0.485419 0.874282i \(-0.661333\pi\)
−0.485419 + 0.874282i \(0.661333\pi\)
\(954\) 0 0
\(955\) −37.6467 −1.21822
\(956\) 0 0
\(957\) 0.0992938 0.00320971
\(958\) 0 0
\(959\) 4.89347 0.158018
\(960\) 0 0
\(961\) −12.7167 −0.410217
\(962\) 0 0
\(963\) −5.84644 −0.188399
\(964\) 0 0
\(965\) 13.2683 0.427121
\(966\) 0 0
\(967\) −14.7207 −0.473387 −0.236693 0.971584i \(-0.576064\pi\)
−0.236693 + 0.971584i \(0.576064\pi\)
\(968\) 0 0
\(969\) 0.129282 0.00415315
\(970\) 0 0
\(971\) 11.0754 0.355428 0.177714 0.984082i \(-0.443130\pi\)
0.177714 + 0.984082i \(0.443130\pi\)
\(972\) 0 0
\(973\) 36.1853 1.16005
\(974\) 0 0
\(975\) −2.98782 −0.0956867
\(976\) 0 0
\(977\) −24.1829 −0.773681 −0.386840 0.922147i \(-0.626434\pi\)
−0.386840 + 0.922147i \(0.626434\pi\)
\(978\) 0 0
\(979\) 1.72815 0.0552319
\(980\) 0 0
\(981\) 11.4163 0.364494
\(982\) 0 0
\(983\) −21.5383 −0.686964 −0.343482 0.939159i \(-0.611607\pi\)
−0.343482 + 0.939159i \(0.611607\pi\)
\(984\) 0 0
\(985\) 4.55897 0.145261
\(986\) 0 0
\(987\) −27.4512 −0.873780
\(988\) 0 0
\(989\) 70.6630 2.24695
\(990\) 0 0
\(991\) 31.2346 0.992199 0.496099 0.868266i \(-0.334765\pi\)
0.496099 + 0.868266i \(0.334765\pi\)
\(992\) 0 0
\(993\) 0.822383 0.0260975
\(994\) 0 0
\(995\) −25.2043 −0.799032
\(996\) 0 0
\(997\) 50.4341 1.59726 0.798632 0.601820i \(-0.205557\pi\)
0.798632 + 0.601820i \(0.205557\pi\)
\(998\) 0 0
\(999\) −3.92212 −0.124090
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 \(a_p\))