Properties

Label 6040.2.a.p.1.11
Level 6040
Weight 2
Character 6040.1
Self dual Yes
Analytic conductor 48.230
Analytic rank 1
Dimension 19
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6040 = 2^{3} \cdot 5 \cdot 151 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6040.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2296428209\)
Analytic rank: \(1\)
Dimension: \(19\)
Coefficient field: \(\mathbb{Q}[x]/(x^{19} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{7} \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Root \(-0.435585\)
Character \(\chi\) = 6040.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+0.435585 q^{3}\) \(+1.00000 q^{5}\) \(-2.87898 q^{7}\) \(-2.81027 q^{9}\) \(+O(q^{10})\) \(q\)\(+0.435585 q^{3}\) \(+1.00000 q^{5}\) \(-2.87898 q^{7}\) \(-2.81027 q^{9}\) \(-2.29647 q^{11}\) \(-0.0953190 q^{13}\) \(+0.435585 q^{15}\) \(+3.92440 q^{17}\) \(+6.59133 q^{19}\) \(-1.25404 q^{21}\) \(-0.150319 q^{23}\) \(+1.00000 q^{25}\) \(-2.53086 q^{27}\) \(+2.49904 q^{29}\) \(-0.535578 q^{31}\) \(-1.00031 q^{33}\) \(-2.87898 q^{35}\) \(-11.7988 q^{37}\) \(-0.0415195 q^{39}\) \(+9.05597 q^{41}\) \(+8.32623 q^{43}\) \(-2.81027 q^{45}\) \(-1.88440 q^{47}\) \(+1.28851 q^{49}\) \(+1.70941 q^{51}\) \(+10.4032 q^{53}\) \(-2.29647 q^{55}\) \(+2.87108 q^{57}\) \(-2.46632 q^{59}\) \(-13.0317 q^{61}\) \(+8.09069 q^{63}\) \(-0.0953190 q^{65}\) \(-4.05767 q^{67}\) \(-0.0654768 q^{69}\) \(-14.0463 q^{71}\) \(+5.10385 q^{73}\) \(+0.435585 q^{75}\) \(+6.61150 q^{77}\) \(-17.1799 q^{79}\) \(+7.32839 q^{81}\) \(-8.49380 q^{83}\) \(+3.92440 q^{85}\) \(+1.08855 q^{87}\) \(-7.92067 q^{89}\) \(+0.274421 q^{91}\) \(-0.233289 q^{93}\) \(+6.59133 q^{95}\) \(+10.3248 q^{97}\) \(+6.45371 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(19q \) \(\mathstrut -\mathstrut 5q^{3} \) \(\mathstrut +\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(19q \) \(\mathstrut -\mathstrut 5q^{3} \) \(\mathstrut +\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut -\mathstrut 18q^{11} \) \(\mathstrut +\mathstrut 5q^{13} \) \(\mathstrut -\mathstrut 5q^{15} \) \(\mathstrut -\mathstrut 4q^{17} \) \(\mathstrut -\mathstrut 27q^{19} \) \(\mathstrut -\mathstrut 18q^{21} \) \(\mathstrut -\mathstrut 25q^{23} \) \(\mathstrut +\mathstrut 19q^{25} \) \(\mathstrut -\mathstrut 35q^{27} \) \(\mathstrut -\mathstrut 35q^{29} \) \(\mathstrut -\mathstrut 26q^{31} \) \(\mathstrut -\mathstrut 8q^{35} \) \(\mathstrut -\mathstrut 10q^{37} \) \(\mathstrut -\mathstrut 48q^{39} \) \(\mathstrut -\mathstrut 14q^{41} \) \(\mathstrut -\mathstrut 21q^{43} \) \(\mathstrut +\mathstrut 26q^{45} \) \(\mathstrut -\mathstrut 40q^{47} \) \(\mathstrut +\mathstrut 23q^{49} \) \(\mathstrut -\mathstrut 32q^{51} \) \(\mathstrut -\mathstrut 3q^{53} \) \(\mathstrut -\mathstrut 18q^{55} \) \(\mathstrut -\mathstrut 13q^{57} \) \(\mathstrut -\mathstrut 28q^{59} \) \(\mathstrut -\mathstrut 46q^{61} \) \(\mathstrut -\mathstrut 53q^{63} \) \(\mathstrut +\mathstrut 5q^{65} \) \(\mathstrut -\mathstrut 42q^{67} \) \(\mathstrut -\mathstrut 31q^{69} \) \(\mathstrut -\mathstrut 46q^{71} \) \(\mathstrut +\mathstrut 31q^{73} \) \(\mathstrut -\mathstrut 5q^{75} \) \(\mathstrut +\mathstrut 15q^{77} \) \(\mathstrut -\mathstrut 56q^{79} \) \(\mathstrut +\mathstrut 31q^{81} \) \(\mathstrut -\mathstrut 25q^{83} \) \(\mathstrut -\mathstrut 4q^{85} \) \(\mathstrut -\mathstrut 20q^{87} \) \(\mathstrut -\mathstrut 7q^{89} \) \(\mathstrut -\mathstrut 61q^{91} \) \(\mathstrut +\mathstrut 29q^{93} \) \(\mathstrut -\mathstrut 27q^{95} \) \(\mathstrut +\mathstrut 39q^{97} \) \(\mathstrut -\mathstrut 52q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 0.435585 0.251485 0.125742 0.992063i \(-0.459869\pi\)
0.125742 + 0.992063i \(0.459869\pi\)
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) −2.87898 −1.08815 −0.544076 0.839036i \(-0.683120\pi\)
−0.544076 + 0.839036i \(0.683120\pi\)
\(8\) 0 0
\(9\) −2.81027 −0.936755
\(10\) 0 0
\(11\) −2.29647 −0.692413 −0.346207 0.938158i \(-0.612530\pi\)
−0.346207 + 0.938158i \(0.612530\pi\)
\(12\) 0 0
\(13\) −0.0953190 −0.0264367 −0.0132184 0.999913i \(-0.504208\pi\)
−0.0132184 + 0.999913i \(0.504208\pi\)
\(14\) 0 0
\(15\) 0.435585 0.112467
\(16\) 0 0
\(17\) 3.92440 0.951808 0.475904 0.879497i \(-0.342121\pi\)
0.475904 + 0.879497i \(0.342121\pi\)
\(18\) 0 0
\(19\) 6.59133 1.51216 0.756078 0.654482i \(-0.227113\pi\)
0.756078 + 0.654482i \(0.227113\pi\)
\(20\) 0 0
\(21\) −1.25404 −0.273654
\(22\) 0 0
\(23\) −0.150319 −0.0313438 −0.0156719 0.999877i \(-0.504989\pi\)
−0.0156719 + 0.999877i \(0.504989\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −2.53086 −0.487065
\(28\) 0 0
\(29\) 2.49904 0.464061 0.232030 0.972709i \(-0.425463\pi\)
0.232030 + 0.972709i \(0.425463\pi\)
\(30\) 0 0
\(31\) −0.535578 −0.0961926 −0.0480963 0.998843i \(-0.515315\pi\)
−0.0480963 + 0.998843i \(0.515315\pi\)
\(32\) 0 0
\(33\) −1.00031 −0.174132
\(34\) 0 0
\(35\) −2.87898 −0.486636
\(36\) 0 0
\(37\) −11.7988 −1.93971 −0.969853 0.243691i \(-0.921642\pi\)
−0.969853 + 0.243691i \(0.921642\pi\)
\(38\) 0 0
\(39\) −0.0415195 −0.00664844
\(40\) 0 0
\(41\) 9.05597 1.41430 0.707152 0.707061i \(-0.249980\pi\)
0.707152 + 0.707061i \(0.249980\pi\)
\(42\) 0 0
\(43\) 8.32623 1.26974 0.634869 0.772619i \(-0.281054\pi\)
0.634869 + 0.772619i \(0.281054\pi\)
\(44\) 0 0
\(45\) −2.81027 −0.418930
\(46\) 0 0
\(47\) −1.88440 −0.274869 −0.137434 0.990511i \(-0.543886\pi\)
−0.137434 + 0.990511i \(0.543886\pi\)
\(48\) 0 0
\(49\) 1.28851 0.184073
\(50\) 0 0
\(51\) 1.70941 0.239365
\(52\) 0 0
\(53\) 10.4032 1.42899 0.714495 0.699641i \(-0.246656\pi\)
0.714495 + 0.699641i \(0.246656\pi\)
\(54\) 0 0
\(55\) −2.29647 −0.309657
\(56\) 0 0
\(57\) 2.87108 0.380284
\(58\) 0 0
\(59\) −2.46632 −0.321088 −0.160544 0.987029i \(-0.551325\pi\)
−0.160544 + 0.987029i \(0.551325\pi\)
\(60\) 0 0
\(61\) −13.0317 −1.66854 −0.834272 0.551353i \(-0.814112\pi\)
−0.834272 + 0.551353i \(0.814112\pi\)
\(62\) 0 0
\(63\) 8.09069 1.01933
\(64\) 0 0
\(65\) −0.0953190 −0.0118229
\(66\) 0 0
\(67\) −4.05767 −0.495723 −0.247862 0.968795i \(-0.579728\pi\)
−0.247862 + 0.968795i \(0.579728\pi\)
\(68\) 0 0
\(69\) −0.0654768 −0.00788248
\(70\) 0 0
\(71\) −14.0463 −1.66699 −0.833496 0.552526i \(-0.813664\pi\)
−0.833496 + 0.552526i \(0.813664\pi\)
\(72\) 0 0
\(73\) 5.10385 0.597360 0.298680 0.954353i \(-0.403454\pi\)
0.298680 + 0.954353i \(0.403454\pi\)
\(74\) 0 0
\(75\) 0.435585 0.0502970
\(76\) 0 0
\(77\) 6.61150 0.753450
\(78\) 0 0
\(79\) −17.1799 −1.93290 −0.966448 0.256864i \(-0.917311\pi\)
−0.966448 + 0.256864i \(0.917311\pi\)
\(80\) 0 0
\(81\) 7.32839 0.814266
\(82\) 0 0
\(83\) −8.49380 −0.932316 −0.466158 0.884702i \(-0.654362\pi\)
−0.466158 + 0.884702i \(0.654362\pi\)
\(84\) 0 0
\(85\) 3.92440 0.425661
\(86\) 0 0
\(87\) 1.08855 0.116704
\(88\) 0 0
\(89\) −7.92067 −0.839590 −0.419795 0.907619i \(-0.637898\pi\)
−0.419795 + 0.907619i \(0.637898\pi\)
\(90\) 0 0
\(91\) 0.274421 0.0287672
\(92\) 0 0
\(93\) −0.233289 −0.0241910
\(94\) 0 0
\(95\) 6.59133 0.676256
\(96\) 0 0
\(97\) 10.3248 1.04833 0.524164 0.851617i \(-0.324378\pi\)
0.524164 + 0.851617i \(0.324378\pi\)
\(98\) 0 0
\(99\) 6.45371 0.648622
\(100\) 0 0
\(101\) 12.8058 1.27422 0.637111 0.770772i \(-0.280129\pi\)
0.637111 + 0.770772i \(0.280129\pi\)
\(102\) 0 0
\(103\) −9.53362 −0.939375 −0.469688 0.882833i \(-0.655633\pi\)
−0.469688 + 0.882833i \(0.655633\pi\)
\(104\) 0 0
\(105\) −1.25404 −0.122382
\(106\) 0 0
\(107\) −8.03299 −0.776578 −0.388289 0.921538i \(-0.626934\pi\)
−0.388289 + 0.921538i \(0.626934\pi\)
\(108\) 0 0
\(109\) −16.2799 −1.55934 −0.779668 0.626194i \(-0.784612\pi\)
−0.779668 + 0.626194i \(0.784612\pi\)
\(110\) 0 0
\(111\) −5.13936 −0.487807
\(112\) 0 0
\(113\) −11.2119 −1.05473 −0.527365 0.849639i \(-0.676820\pi\)
−0.527365 + 0.849639i \(0.676820\pi\)
\(114\) 0 0
\(115\) −0.150319 −0.0140174
\(116\) 0 0
\(117\) 0.267872 0.0247647
\(118\) 0 0
\(119\) −11.2983 −1.03571
\(120\) 0 0
\(121\) −5.72620 −0.520564
\(122\) 0 0
\(123\) 3.94464 0.355676
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 13.5298 1.20058 0.600288 0.799784i \(-0.295053\pi\)
0.600288 + 0.799784i \(0.295053\pi\)
\(128\) 0 0
\(129\) 3.62678 0.319320
\(130\) 0 0
\(131\) −13.9965 −1.22288 −0.611440 0.791291i \(-0.709410\pi\)
−0.611440 + 0.791291i \(0.709410\pi\)
\(132\) 0 0
\(133\) −18.9763 −1.64545
\(134\) 0 0
\(135\) −2.53086 −0.217822
\(136\) 0 0
\(137\) −13.6311 −1.16458 −0.582290 0.812981i \(-0.697843\pi\)
−0.582290 + 0.812981i \(0.697843\pi\)
\(138\) 0 0
\(139\) 5.05697 0.428927 0.214463 0.976732i \(-0.431200\pi\)
0.214463 + 0.976732i \(0.431200\pi\)
\(140\) 0 0
\(141\) −0.820818 −0.0691253
\(142\) 0 0
\(143\) 0.218898 0.0183051
\(144\) 0 0
\(145\) 2.49904 0.207534
\(146\) 0 0
\(147\) 0.561256 0.0462916
\(148\) 0 0
\(149\) 10.7804 0.883163 0.441582 0.897221i \(-0.354418\pi\)
0.441582 + 0.897221i \(0.354418\pi\)
\(150\) 0 0
\(151\) 1.00000 0.0813788
\(152\) 0 0
\(153\) −11.0286 −0.891611
\(154\) 0 0
\(155\) −0.535578 −0.0430186
\(156\) 0 0
\(157\) −6.79705 −0.542464 −0.271232 0.962514i \(-0.587431\pi\)
−0.271232 + 0.962514i \(0.587431\pi\)
\(158\) 0 0
\(159\) 4.53148 0.359370
\(160\) 0 0
\(161\) 0.432766 0.0341068
\(162\) 0 0
\(163\) −10.9477 −0.857490 −0.428745 0.903426i \(-0.641044\pi\)
−0.428745 + 0.903426i \(0.641044\pi\)
\(164\) 0 0
\(165\) −1.00031 −0.0778740
\(166\) 0 0
\(167\) −18.1080 −1.40124 −0.700619 0.713536i \(-0.747093\pi\)
−0.700619 + 0.713536i \(0.747093\pi\)
\(168\) 0 0
\(169\) −12.9909 −0.999301
\(170\) 0 0
\(171\) −18.5234 −1.41652
\(172\) 0 0
\(173\) −10.0264 −0.762293 −0.381147 0.924515i \(-0.624471\pi\)
−0.381147 + 0.924515i \(0.624471\pi\)
\(174\) 0 0
\(175\) −2.87898 −0.217630
\(176\) 0 0
\(177\) −1.07429 −0.0807488
\(178\) 0 0
\(179\) −6.55432 −0.489893 −0.244946 0.969537i \(-0.578770\pi\)
−0.244946 + 0.969537i \(0.578770\pi\)
\(180\) 0 0
\(181\) −1.98392 −0.147464 −0.0737319 0.997278i \(-0.523491\pi\)
−0.0737319 + 0.997278i \(0.523491\pi\)
\(182\) 0 0
\(183\) −5.67643 −0.419614
\(184\) 0 0
\(185\) −11.7988 −0.867463
\(186\) 0 0
\(187\) −9.01229 −0.659044
\(188\) 0 0
\(189\) 7.28630 0.530000
\(190\) 0 0
\(191\) −23.2637 −1.68331 −0.841653 0.540019i \(-0.818417\pi\)
−0.841653 + 0.540019i \(0.818417\pi\)
\(192\) 0 0
\(193\) −6.70918 −0.482937 −0.241469 0.970409i \(-0.577629\pi\)
−0.241469 + 0.970409i \(0.577629\pi\)
\(194\) 0 0
\(195\) −0.0415195 −0.00297327
\(196\) 0 0
\(197\) 11.4808 0.817973 0.408987 0.912540i \(-0.365882\pi\)
0.408987 + 0.912540i \(0.365882\pi\)
\(198\) 0 0
\(199\) −0.798470 −0.0566021 −0.0283010 0.999599i \(-0.509010\pi\)
−0.0283010 + 0.999599i \(0.509010\pi\)
\(200\) 0 0
\(201\) −1.76746 −0.124667
\(202\) 0 0
\(203\) −7.19469 −0.504968
\(204\) 0 0
\(205\) 9.05597 0.632496
\(206\) 0 0
\(207\) 0.422438 0.0293614
\(208\) 0 0
\(209\) −15.1368 −1.04704
\(210\) 0 0
\(211\) −1.44453 −0.0994458 −0.0497229 0.998763i \(-0.515834\pi\)
−0.0497229 + 0.998763i \(0.515834\pi\)
\(212\) 0 0
\(213\) −6.11836 −0.419223
\(214\) 0 0
\(215\) 8.32623 0.567844
\(216\) 0 0
\(217\) 1.54192 0.104672
\(218\) 0 0
\(219\) 2.22316 0.150227
\(220\) 0 0
\(221\) −0.374070 −0.0251627
\(222\) 0 0
\(223\) −26.8447 −1.79766 −0.898829 0.438300i \(-0.855581\pi\)
−0.898829 + 0.438300i \(0.855581\pi\)
\(224\) 0 0
\(225\) −2.81027 −0.187351
\(226\) 0 0
\(227\) −20.8675 −1.38503 −0.692514 0.721404i \(-0.743497\pi\)
−0.692514 + 0.721404i \(0.743497\pi\)
\(228\) 0 0
\(229\) 17.3475 1.14635 0.573177 0.819431i \(-0.305711\pi\)
0.573177 + 0.819431i \(0.305711\pi\)
\(230\) 0 0
\(231\) 2.87987 0.189481
\(232\) 0 0
\(233\) 13.6111 0.891695 0.445848 0.895109i \(-0.352902\pi\)
0.445848 + 0.895109i \(0.352902\pi\)
\(234\) 0 0
\(235\) −1.88440 −0.122925
\(236\) 0 0
\(237\) −7.48332 −0.486094
\(238\) 0 0
\(239\) 14.8966 0.963583 0.481792 0.876286i \(-0.339986\pi\)
0.481792 + 0.876286i \(0.339986\pi\)
\(240\) 0 0
\(241\) 22.0346 1.41937 0.709687 0.704517i \(-0.248836\pi\)
0.709687 + 0.704517i \(0.248836\pi\)
\(242\) 0 0
\(243\) 10.7847 0.691840
\(244\) 0 0
\(245\) 1.28851 0.0823200
\(246\) 0 0
\(247\) −0.628279 −0.0399764
\(248\) 0 0
\(249\) −3.69977 −0.234463
\(250\) 0 0
\(251\) 10.9392 0.690474 0.345237 0.938515i \(-0.387798\pi\)
0.345237 + 0.938515i \(0.387798\pi\)
\(252\) 0 0
\(253\) 0.345205 0.0217028
\(254\) 0 0
\(255\) 1.70941 0.107047
\(256\) 0 0
\(257\) −12.7485 −0.795229 −0.397615 0.917553i \(-0.630162\pi\)
−0.397615 + 0.917553i \(0.630162\pi\)
\(258\) 0 0
\(259\) 33.9684 2.11069
\(260\) 0 0
\(261\) −7.02298 −0.434711
\(262\) 0 0
\(263\) 23.7818 1.46645 0.733226 0.679986i \(-0.238014\pi\)
0.733226 + 0.679986i \(0.238014\pi\)
\(264\) 0 0
\(265\) 10.4032 0.639064
\(266\) 0 0
\(267\) −3.45012 −0.211144
\(268\) 0 0
\(269\) 21.5279 1.31258 0.656289 0.754509i \(-0.272125\pi\)
0.656289 + 0.754509i \(0.272125\pi\)
\(270\) 0 0
\(271\) −15.8224 −0.961142 −0.480571 0.876956i \(-0.659571\pi\)
−0.480571 + 0.876956i \(0.659571\pi\)
\(272\) 0 0
\(273\) 0.119534 0.00723451
\(274\) 0 0
\(275\) −2.29647 −0.138483
\(276\) 0 0
\(277\) 15.7192 0.944473 0.472236 0.881472i \(-0.343447\pi\)
0.472236 + 0.881472i \(0.343447\pi\)
\(278\) 0 0
\(279\) 1.50512 0.0901089
\(280\) 0 0
\(281\) 25.2396 1.50567 0.752836 0.658209i \(-0.228686\pi\)
0.752836 + 0.658209i \(0.228686\pi\)
\(282\) 0 0
\(283\) 20.2312 1.20262 0.601309 0.799017i \(-0.294646\pi\)
0.601309 + 0.799017i \(0.294646\pi\)
\(284\) 0 0
\(285\) 2.87108 0.170068
\(286\) 0 0
\(287\) −26.0719 −1.53898
\(288\) 0 0
\(289\) −1.59906 −0.0940621
\(290\) 0 0
\(291\) 4.49734 0.263639
\(292\) 0 0
\(293\) 1.18611 0.0692935 0.0346467 0.999400i \(-0.488969\pi\)
0.0346467 + 0.999400i \(0.488969\pi\)
\(294\) 0 0
\(295\) −2.46632 −0.143595
\(296\) 0 0
\(297\) 5.81206 0.337250
\(298\) 0 0
\(299\) 0.0143283 0.000828627 0
\(300\) 0 0
\(301\) −23.9710 −1.38167
\(302\) 0 0
\(303\) 5.57800 0.320448
\(304\) 0 0
\(305\) −13.0317 −0.746195
\(306\) 0 0
\(307\) 16.8285 0.960452 0.480226 0.877145i \(-0.340555\pi\)
0.480226 + 0.877145i \(0.340555\pi\)
\(308\) 0 0
\(309\) −4.15270 −0.236239
\(310\) 0 0
\(311\) −24.3198 −1.37905 −0.689524 0.724263i \(-0.742180\pi\)
−0.689524 + 0.724263i \(0.742180\pi\)
\(312\) 0 0
\(313\) −11.3054 −0.639018 −0.319509 0.947583i \(-0.603518\pi\)
−0.319509 + 0.947583i \(0.603518\pi\)
\(314\) 0 0
\(315\) 8.09069 0.455859
\(316\) 0 0
\(317\) −11.1520 −0.626358 −0.313179 0.949694i \(-0.601394\pi\)
−0.313179 + 0.949694i \(0.601394\pi\)
\(318\) 0 0
\(319\) −5.73899 −0.321322
\(320\) 0 0
\(321\) −3.49905 −0.195298
\(322\) 0 0
\(323\) 25.8670 1.43928
\(324\) 0 0
\(325\) −0.0953190 −0.00528735
\(326\) 0 0
\(327\) −7.09129 −0.392149
\(328\) 0 0
\(329\) 5.42516 0.299099
\(330\) 0 0
\(331\) −30.4711 −1.67484 −0.837421 0.546558i \(-0.815938\pi\)
−0.837421 + 0.546558i \(0.815938\pi\)
\(332\) 0 0
\(333\) 33.1577 1.81703
\(334\) 0 0
\(335\) −4.05767 −0.221694
\(336\) 0 0
\(337\) −7.12539 −0.388145 −0.194072 0.980987i \(-0.562170\pi\)
−0.194072 + 0.980987i \(0.562170\pi\)
\(338\) 0 0
\(339\) −4.88375 −0.265249
\(340\) 0 0
\(341\) 1.22994 0.0666050
\(342\) 0 0
\(343\) 16.4432 0.887852
\(344\) 0 0
\(345\) −0.0654768 −0.00352515
\(346\) 0 0
\(347\) 16.6155 0.891968 0.445984 0.895041i \(-0.352854\pi\)
0.445984 + 0.895041i \(0.352854\pi\)
\(348\) 0 0
\(349\) −2.03464 −0.108912 −0.0544560 0.998516i \(-0.517342\pi\)
−0.0544560 + 0.998516i \(0.517342\pi\)
\(350\) 0 0
\(351\) 0.241239 0.0128764
\(352\) 0 0
\(353\) −5.89772 −0.313904 −0.156952 0.987606i \(-0.550167\pi\)
−0.156952 + 0.987606i \(0.550167\pi\)
\(354\) 0 0
\(355\) −14.0463 −0.745501
\(356\) 0 0
\(357\) −4.92135 −0.260466
\(358\) 0 0
\(359\) 34.5127 1.82151 0.910755 0.412947i \(-0.135501\pi\)
0.910755 + 0.412947i \(0.135501\pi\)
\(360\) 0 0
\(361\) 24.4456 1.28661
\(362\) 0 0
\(363\) −2.49425 −0.130914
\(364\) 0 0
\(365\) 5.10385 0.267148
\(366\) 0 0
\(367\) 28.4303 1.48405 0.742026 0.670372i \(-0.233865\pi\)
0.742026 + 0.670372i \(0.233865\pi\)
\(368\) 0 0
\(369\) −25.4497 −1.32486
\(370\) 0 0
\(371\) −29.9506 −1.55496
\(372\) 0 0
\(373\) 1.71457 0.0887769 0.0443884 0.999014i \(-0.485866\pi\)
0.0443884 + 0.999014i \(0.485866\pi\)
\(374\) 0 0
\(375\) 0.435585 0.0224935
\(376\) 0 0
\(377\) −0.238206 −0.0122682
\(378\) 0 0
\(379\) 12.4490 0.639462 0.319731 0.947508i \(-0.396407\pi\)
0.319731 + 0.947508i \(0.396407\pi\)
\(380\) 0 0
\(381\) 5.89338 0.301927
\(382\) 0 0
\(383\) 5.31980 0.271829 0.135915 0.990721i \(-0.456603\pi\)
0.135915 + 0.990721i \(0.456603\pi\)
\(384\) 0 0
\(385\) 6.61150 0.336953
\(386\) 0 0
\(387\) −23.3989 −1.18943
\(388\) 0 0
\(389\) 31.9844 1.62167 0.810837 0.585272i \(-0.199012\pi\)
0.810837 + 0.585272i \(0.199012\pi\)
\(390\) 0 0
\(391\) −0.589914 −0.0298332
\(392\) 0 0
\(393\) −6.09666 −0.307536
\(394\) 0 0
\(395\) −17.1799 −0.864417
\(396\) 0 0
\(397\) 9.29137 0.466320 0.233160 0.972438i \(-0.425093\pi\)
0.233160 + 0.972438i \(0.425093\pi\)
\(398\) 0 0
\(399\) −8.26578 −0.413807
\(400\) 0 0
\(401\) −37.7900 −1.88714 −0.943571 0.331170i \(-0.892557\pi\)
−0.943571 + 0.331170i \(0.892557\pi\)
\(402\) 0 0
\(403\) 0.0510507 0.00254302
\(404\) 0 0
\(405\) 7.32839 0.364151
\(406\) 0 0
\(407\) 27.0956 1.34308
\(408\) 0 0
\(409\) −2.84897 −0.140873 −0.0704363 0.997516i \(-0.522439\pi\)
−0.0704363 + 0.997516i \(0.522439\pi\)
\(410\) 0 0
\(411\) −5.93748 −0.292874
\(412\) 0 0
\(413\) 7.10049 0.349392
\(414\) 0 0
\(415\) −8.49380 −0.416944
\(416\) 0 0
\(417\) 2.20274 0.107869
\(418\) 0 0
\(419\) −3.33413 −0.162883 −0.0814413 0.996678i \(-0.525952\pi\)
−0.0814413 + 0.996678i \(0.525952\pi\)
\(420\) 0 0
\(421\) −30.6477 −1.49368 −0.746838 0.665006i \(-0.768429\pi\)
−0.746838 + 0.665006i \(0.768429\pi\)
\(422\) 0 0
\(423\) 5.29568 0.257485
\(424\) 0 0
\(425\) 3.92440 0.190362
\(426\) 0 0
\(427\) 37.5181 1.81563
\(428\) 0 0
\(429\) 0.0953485 0.00460347
\(430\) 0 0
\(431\) −33.7009 −1.62332 −0.811658 0.584133i \(-0.801435\pi\)
−0.811658 + 0.584133i \(0.801435\pi\)
\(432\) 0 0
\(433\) −5.02391 −0.241434 −0.120717 0.992687i \(-0.538519\pi\)
−0.120717 + 0.992687i \(0.538519\pi\)
\(434\) 0 0
\(435\) 1.08855 0.0521918
\(436\) 0 0
\(437\) −0.990805 −0.0473966
\(438\) 0 0
\(439\) −33.1409 −1.58173 −0.790864 0.611992i \(-0.790368\pi\)
−0.790864 + 0.611992i \(0.790368\pi\)
\(440\) 0 0
\(441\) −3.62106 −0.172431
\(442\) 0 0
\(443\) 18.3387 0.871298 0.435649 0.900117i \(-0.356519\pi\)
0.435649 + 0.900117i \(0.356519\pi\)
\(444\) 0 0
\(445\) −7.92067 −0.375476
\(446\) 0 0
\(447\) 4.69577 0.222102
\(448\) 0 0
\(449\) 32.2443 1.52170 0.760852 0.648925i \(-0.224781\pi\)
0.760852 + 0.648925i \(0.224781\pi\)
\(450\) 0 0
\(451\) −20.7968 −0.979283
\(452\) 0 0
\(453\) 0.435585 0.0204656
\(454\) 0 0
\(455\) 0.274421 0.0128651
\(456\) 0 0
\(457\) 33.3685 1.56091 0.780457 0.625210i \(-0.214987\pi\)
0.780457 + 0.625210i \(0.214987\pi\)
\(458\) 0 0
\(459\) −9.93213 −0.463592
\(460\) 0 0
\(461\) −18.8368 −0.877317 −0.438659 0.898654i \(-0.644546\pi\)
−0.438659 + 0.898654i \(0.644546\pi\)
\(462\) 0 0
\(463\) −30.5919 −1.42173 −0.710863 0.703330i \(-0.751695\pi\)
−0.710863 + 0.703330i \(0.751695\pi\)
\(464\) 0 0
\(465\) −0.233289 −0.0108185
\(466\) 0 0
\(467\) −4.66251 −0.215755 −0.107878 0.994164i \(-0.534405\pi\)
−0.107878 + 0.994164i \(0.534405\pi\)
\(468\) 0 0
\(469\) 11.6819 0.539422
\(470\) 0 0
\(471\) −2.96069 −0.136421
\(472\) 0 0
\(473\) −19.1210 −0.879184
\(474\) 0 0
\(475\) 6.59133 0.302431
\(476\) 0 0
\(477\) −29.2358 −1.33861
\(478\) 0 0
\(479\) 33.7934 1.54406 0.772030 0.635586i \(-0.219241\pi\)
0.772030 + 0.635586i \(0.219241\pi\)
\(480\) 0 0
\(481\) 1.12465 0.0512795
\(482\) 0 0
\(483\) 0.188506 0.00857734
\(484\) 0 0
\(485\) 10.3248 0.468826
\(486\) 0 0
\(487\) −24.3168 −1.10190 −0.550950 0.834538i \(-0.685734\pi\)
−0.550950 + 0.834538i \(0.685734\pi\)
\(488\) 0 0
\(489\) −4.76865 −0.215646
\(490\) 0 0
\(491\) 17.9100 0.808268 0.404134 0.914700i \(-0.367573\pi\)
0.404134 + 0.914700i \(0.367573\pi\)
\(492\) 0 0
\(493\) 9.80726 0.441697
\(494\) 0 0
\(495\) 6.45371 0.290072
\(496\) 0 0
\(497\) 40.4390 1.81394
\(498\) 0 0
\(499\) 4.95485 0.221809 0.110905 0.993831i \(-0.464625\pi\)
0.110905 + 0.993831i \(0.464625\pi\)
\(500\) 0 0
\(501\) −7.88756 −0.352390
\(502\) 0 0
\(503\) −15.5787 −0.694621 −0.347311 0.937750i \(-0.612905\pi\)
−0.347311 + 0.937750i \(0.612905\pi\)
\(504\) 0 0
\(505\) 12.8058 0.569850
\(506\) 0 0
\(507\) −5.65864 −0.251309
\(508\) 0 0
\(509\) −40.7094 −1.80441 −0.902207 0.431304i \(-0.858054\pi\)
−0.902207 + 0.431304i \(0.858054\pi\)
\(510\) 0 0
\(511\) −14.6939 −0.650018
\(512\) 0 0
\(513\) −16.6818 −0.736518
\(514\) 0 0
\(515\) −9.53362 −0.420101
\(516\) 0 0
\(517\) 4.32749 0.190323
\(518\) 0 0
\(519\) −4.36735 −0.191705
\(520\) 0 0
\(521\) 26.4160 1.15731 0.578654 0.815573i \(-0.303578\pi\)
0.578654 + 0.815573i \(0.303578\pi\)
\(522\) 0 0
\(523\) 19.6940 0.861157 0.430578 0.902553i \(-0.358310\pi\)
0.430578 + 0.902553i \(0.358310\pi\)
\(524\) 0 0
\(525\) −1.25404 −0.0547307
\(526\) 0 0
\(527\) −2.10182 −0.0915568
\(528\) 0 0
\(529\) −22.9774 −0.999018
\(530\) 0 0
\(531\) 6.93102 0.300781
\(532\) 0 0
\(533\) −0.863206 −0.0373896
\(534\) 0 0
\(535\) −8.03299 −0.347296
\(536\) 0 0
\(537\) −2.85496 −0.123201
\(538\) 0 0
\(539\) −2.95903 −0.127455
\(540\) 0 0
\(541\) −25.9581 −1.11603 −0.558013 0.829832i \(-0.688436\pi\)
−0.558013 + 0.829832i \(0.688436\pi\)
\(542\) 0 0
\(543\) −0.864166 −0.0370849
\(544\) 0 0
\(545\) −16.2799 −0.697356
\(546\) 0 0
\(547\) 16.0398 0.685811 0.342905 0.939370i \(-0.388589\pi\)
0.342905 + 0.939370i \(0.388589\pi\)
\(548\) 0 0
\(549\) 36.6227 1.56302
\(550\) 0 0
\(551\) 16.4720 0.701732
\(552\) 0 0
\(553\) 49.4607 2.10328
\(554\) 0 0
\(555\) −5.13936 −0.218154
\(556\) 0 0
\(557\) −3.91035 −0.165687 −0.0828435 0.996563i \(-0.526400\pi\)
−0.0828435 + 0.996563i \(0.526400\pi\)
\(558\) 0 0
\(559\) −0.793648 −0.0335677
\(560\) 0 0
\(561\) −3.92562 −0.165740
\(562\) 0 0
\(563\) −20.3282 −0.856729 −0.428365 0.903606i \(-0.640910\pi\)
−0.428365 + 0.903606i \(0.640910\pi\)
\(564\) 0 0
\(565\) −11.2119 −0.471690
\(566\) 0 0
\(567\) −21.0983 −0.886044
\(568\) 0 0
\(569\) −35.2925 −1.47954 −0.739768 0.672862i \(-0.765065\pi\)
−0.739768 + 0.672862i \(0.765065\pi\)
\(570\) 0 0
\(571\) −38.6754 −1.61852 −0.809259 0.587453i \(-0.800131\pi\)
−0.809259 + 0.587453i \(0.800131\pi\)
\(572\) 0 0
\(573\) −10.1333 −0.423326
\(574\) 0 0
\(575\) −0.150319 −0.00626875
\(576\) 0 0
\(577\) 19.4030 0.807756 0.403878 0.914813i \(-0.367662\pi\)
0.403878 + 0.914813i \(0.367662\pi\)
\(578\) 0 0
\(579\) −2.92242 −0.121451
\(580\) 0 0
\(581\) 24.4535 1.01450
\(582\) 0 0
\(583\) −23.8907 −0.989452
\(584\) 0 0
\(585\) 0.267872 0.0110751
\(586\) 0 0
\(587\) 5.30229 0.218849 0.109424 0.993995i \(-0.465099\pi\)
0.109424 + 0.993995i \(0.465099\pi\)
\(588\) 0 0
\(589\) −3.53017 −0.145458
\(590\) 0 0
\(591\) 5.00086 0.205708
\(592\) 0 0
\(593\) 33.1485 1.36125 0.680623 0.732634i \(-0.261709\pi\)
0.680623 + 0.732634i \(0.261709\pi\)
\(594\) 0 0
\(595\) −11.2983 −0.463184
\(596\) 0 0
\(597\) −0.347801 −0.0142346
\(598\) 0 0
\(599\) −1.07126 −0.0437704 −0.0218852 0.999760i \(-0.506967\pi\)
−0.0218852 + 0.999760i \(0.506967\pi\)
\(600\) 0 0
\(601\) −45.9381 −1.87386 −0.936928 0.349524i \(-0.886343\pi\)
−0.936928 + 0.349524i \(0.886343\pi\)
\(602\) 0 0
\(603\) 11.4031 0.464371
\(604\) 0 0
\(605\) −5.72620 −0.232803
\(606\) 0 0
\(607\) 35.3792 1.43600 0.717999 0.696044i \(-0.245058\pi\)
0.717999 + 0.696044i \(0.245058\pi\)
\(608\) 0 0
\(609\) −3.13390 −0.126992
\(610\) 0 0
\(611\) 0.179619 0.00726663
\(612\) 0 0
\(613\) 9.71728 0.392477 0.196239 0.980556i \(-0.437127\pi\)
0.196239 + 0.980556i \(0.437127\pi\)
\(614\) 0 0
\(615\) 3.94464 0.159063
\(616\) 0 0
\(617\) 26.5619 1.06934 0.534670 0.845061i \(-0.320436\pi\)
0.534670 + 0.845061i \(0.320436\pi\)
\(618\) 0 0
\(619\) −30.6930 −1.23366 −0.616828 0.787098i \(-0.711583\pi\)
−0.616828 + 0.787098i \(0.711583\pi\)
\(620\) 0 0
\(621\) 0.380438 0.0152664
\(622\) 0 0
\(623\) 22.8034 0.913601
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −6.59337 −0.263314
\(628\) 0 0
\(629\) −46.3031 −1.84623
\(630\) 0 0
\(631\) −10.9175 −0.434618 −0.217309 0.976103i \(-0.569728\pi\)
−0.217309 + 0.976103i \(0.569728\pi\)
\(632\) 0 0
\(633\) −0.629216 −0.0250091
\(634\) 0 0
\(635\) 13.5298 0.536914
\(636\) 0 0
\(637\) −0.122820 −0.00486629
\(638\) 0 0
\(639\) 39.4739 1.56156
\(640\) 0 0
\(641\) −13.0137 −0.514011 −0.257005 0.966410i \(-0.582736\pi\)
−0.257005 + 0.966410i \(0.582736\pi\)
\(642\) 0 0
\(643\) −37.1789 −1.46619 −0.733096 0.680125i \(-0.761925\pi\)
−0.733096 + 0.680125i \(0.761925\pi\)
\(644\) 0 0
\(645\) 3.62678 0.142804
\(646\) 0 0
\(647\) −40.7533 −1.60218 −0.801088 0.598547i \(-0.795745\pi\)
−0.801088 + 0.598547i \(0.795745\pi\)
\(648\) 0 0
\(649\) 5.66385 0.222326
\(650\) 0 0
\(651\) 0.671635 0.0263234
\(652\) 0 0
\(653\) 9.45694 0.370079 0.185039 0.982731i \(-0.440759\pi\)
0.185039 + 0.982731i \(0.440759\pi\)
\(654\) 0 0
\(655\) −13.9965 −0.546889
\(656\) 0 0
\(657\) −14.3432 −0.559580
\(658\) 0 0
\(659\) −19.9956 −0.778917 −0.389458 0.921044i \(-0.627338\pi\)
−0.389458 + 0.921044i \(0.627338\pi\)
\(660\) 0 0
\(661\) 30.6198 1.19097 0.595486 0.803366i \(-0.296959\pi\)
0.595486 + 0.803366i \(0.296959\pi\)
\(662\) 0 0
\(663\) −0.162939 −0.00632804
\(664\) 0 0
\(665\) −18.9763 −0.735869
\(666\) 0 0
\(667\) −0.375655 −0.0145454
\(668\) 0 0
\(669\) −11.6932 −0.452084
\(670\) 0 0
\(671\) 29.9271 1.15532
\(672\) 0 0
\(673\) 18.4372 0.710700 0.355350 0.934733i \(-0.384362\pi\)
0.355350 + 0.934733i \(0.384362\pi\)
\(674\) 0 0
\(675\) −2.53086 −0.0974130
\(676\) 0 0
\(677\) −31.2683 −1.20174 −0.600870 0.799347i \(-0.705179\pi\)
−0.600870 + 0.799347i \(0.705179\pi\)
\(678\) 0 0
\(679\) −29.7250 −1.14074
\(680\) 0 0
\(681\) −9.08959 −0.348314
\(682\) 0 0
\(683\) −20.9300 −0.800866 −0.400433 0.916326i \(-0.631140\pi\)
−0.400433 + 0.916326i \(0.631140\pi\)
\(684\) 0 0
\(685\) −13.6311 −0.520816
\(686\) 0 0
\(687\) 7.55630 0.288291
\(688\) 0 0
\(689\) −0.991623 −0.0377778
\(690\) 0 0
\(691\) 25.0385 0.952510 0.476255 0.879307i \(-0.341994\pi\)
0.476255 + 0.879307i \(0.341994\pi\)
\(692\) 0 0
\(693\) −18.5801 −0.705799
\(694\) 0 0
\(695\) 5.05697 0.191822
\(696\) 0 0
\(697\) 35.5393 1.34615
\(698\) 0 0
\(699\) 5.92880 0.224248
\(700\) 0 0
\(701\) 12.6976 0.479583 0.239792 0.970824i \(-0.422921\pi\)
0.239792 + 0.970824i \(0.422921\pi\)
\(702\) 0 0
\(703\) −77.7696 −2.93314
\(704\) 0 0
\(705\) −0.820818 −0.0309138
\(706\) 0 0
\(707\) −36.8676 −1.38655
\(708\) 0 0
\(709\) 35.3293 1.32682 0.663410 0.748256i \(-0.269109\pi\)
0.663410 + 0.748256i \(0.269109\pi\)
\(710\) 0 0
\(711\) 48.2802 1.81065
\(712\) 0 0
\(713\) 0.0805077 0.00301504
\(714\) 0 0
\(715\) 0.218898 0.00818631
\(716\) 0 0
\(717\) 6.48875 0.242327
\(718\) 0 0
\(719\) 6.63766 0.247543 0.123771 0.992311i \(-0.460501\pi\)
0.123771 + 0.992311i \(0.460501\pi\)
\(720\) 0 0
\(721\) 27.4471 1.02218
\(722\) 0 0
\(723\) 9.59794 0.356951
\(724\) 0 0
\(725\) 2.49904 0.0928122
\(726\) 0 0
\(727\) −35.6453 −1.32201 −0.661005 0.750381i \(-0.729870\pi\)
−0.661005 + 0.750381i \(0.729870\pi\)
\(728\) 0 0
\(729\) −17.2875 −0.640278
\(730\) 0 0
\(731\) 32.6755 1.20855
\(732\) 0 0
\(733\) 27.7386 1.02455 0.512275 0.858821i \(-0.328803\pi\)
0.512275 + 0.858821i \(0.328803\pi\)
\(734\) 0 0
\(735\) 0.561256 0.0207022
\(736\) 0 0
\(737\) 9.31834 0.343245
\(738\) 0 0
\(739\) −27.7731 −1.02165 −0.510825 0.859685i \(-0.670660\pi\)
−0.510825 + 0.859685i \(0.670660\pi\)
\(740\) 0 0
\(741\) −0.273669 −0.0100535
\(742\) 0 0
\(743\) −33.2912 −1.22133 −0.610667 0.791887i \(-0.709099\pi\)
−0.610667 + 0.791887i \(0.709099\pi\)
\(744\) 0 0
\(745\) 10.7804 0.394963
\(746\) 0 0
\(747\) 23.8698 0.873352
\(748\) 0 0
\(749\) 23.1268 0.845035
\(750\) 0 0
\(751\) −19.1238 −0.697839 −0.348919 0.937153i \(-0.613451\pi\)
−0.348919 + 0.937153i \(0.613451\pi\)
\(752\) 0 0
\(753\) 4.76494 0.173644
\(754\) 0 0
\(755\) 1.00000 0.0363937
\(756\) 0 0
\(757\) 38.8844 1.41328 0.706639 0.707574i \(-0.250210\pi\)
0.706639 + 0.707574i \(0.250210\pi\)
\(758\) 0 0
\(759\) 0.150366 0.00545794
\(760\) 0 0
\(761\) 28.6053 1.03694 0.518471 0.855095i \(-0.326501\pi\)
0.518471 + 0.855095i \(0.326501\pi\)
\(762\) 0 0
\(763\) 46.8696 1.69679
\(764\) 0 0
\(765\) −11.0286 −0.398741
\(766\) 0 0
\(767\) 0.235087 0.00848851
\(768\) 0 0
\(769\) −1.10018 −0.0396735 −0.0198368 0.999803i \(-0.506315\pi\)
−0.0198368 + 0.999803i \(0.506315\pi\)
\(770\) 0 0
\(771\) −5.55305 −0.199988
\(772\) 0 0
\(773\) −20.1611 −0.725146 −0.362573 0.931955i \(-0.618102\pi\)
−0.362573 + 0.931955i \(0.618102\pi\)
\(774\) 0 0
\(775\) −0.535578 −0.0192385
\(776\) 0 0
\(777\) 14.7961 0.530808
\(778\) 0 0
\(779\) 59.6909 2.13865
\(780\) 0 0
\(781\) 32.2570 1.15425
\(782\) 0 0
\(783\) −6.32474 −0.226028
\(784\) 0 0
\(785\) −6.79705 −0.242597
\(786\) 0 0
\(787\) −36.1630 −1.28907 −0.644537 0.764573i \(-0.722950\pi\)
−0.644537 + 0.764573i \(0.722950\pi\)
\(788\) 0 0
\(789\) 10.3590 0.368790
\(790\) 0 0
\(791\) 32.2789 1.14771
\(792\) 0 0
\(793\) 1.24217 0.0441108
\(794\) 0 0
\(795\) 4.53148 0.160715
\(796\) 0 0
\(797\) −0.711463 −0.0252013 −0.0126007 0.999921i \(-0.504011\pi\)
−0.0126007 + 0.999921i \(0.504011\pi\)
\(798\) 0 0
\(799\) −7.39516 −0.261622
\(800\) 0 0
\(801\) 22.2592 0.786490
\(802\) 0 0
\(803\) −11.7209 −0.413620
\(804\) 0 0
\(805\) 0.432766 0.0152530
\(806\) 0 0
\(807\) 9.37722 0.330094
\(808\) 0 0
\(809\) 33.0952 1.16357 0.581783 0.813344i \(-0.302355\pi\)
0.581783 + 0.813344i \(0.302355\pi\)
\(810\) 0 0
\(811\) −16.9967 −0.596835 −0.298418 0.954435i \(-0.596459\pi\)
−0.298418 + 0.954435i \(0.596459\pi\)
\(812\) 0 0
\(813\) −6.89199 −0.241713
\(814\) 0 0
\(815\) −10.9477 −0.383481
\(816\) 0 0
\(817\) 54.8810 1.92004
\(818\) 0 0
\(819\) −0.771197 −0.0269478
\(820\) 0 0
\(821\) −40.8714 −1.42642 −0.713211 0.700949i \(-0.752760\pi\)
−0.713211 + 0.700949i \(0.752760\pi\)
\(822\) 0 0
\(823\) 13.8495 0.482763 0.241382 0.970430i \(-0.422399\pi\)
0.241382 + 0.970430i \(0.422399\pi\)
\(824\) 0 0
\(825\) −1.00031 −0.0348263
\(826\) 0 0
\(827\) −4.02260 −0.139879 −0.0699397 0.997551i \(-0.522281\pi\)
−0.0699397 + 0.997551i \(0.522281\pi\)
\(828\) 0 0
\(829\) −57.0302 −1.98074 −0.990371 0.138439i \(-0.955791\pi\)
−0.990371 + 0.138439i \(0.955791\pi\)
\(830\) 0 0
\(831\) 6.84703 0.237521
\(832\) 0 0
\(833\) 5.05664 0.175202
\(834\) 0 0
\(835\) −18.1080 −0.626652
\(836\) 0 0
\(837\) 1.35547 0.0468520
\(838\) 0 0
\(839\) −37.4269 −1.29212 −0.646060 0.763286i \(-0.723585\pi\)
−0.646060 + 0.763286i \(0.723585\pi\)
\(840\) 0 0
\(841\) −22.7548 −0.784648
\(842\) 0 0
\(843\) 10.9940 0.378654
\(844\) 0 0
\(845\) −12.9909 −0.446901
\(846\) 0 0
\(847\) 16.4856 0.566452
\(848\) 0 0
\(849\) 8.81238 0.302440
\(850\) 0 0
\(851\) 1.77358 0.0607977
\(852\) 0 0
\(853\) −8.50988 −0.291373 −0.145686 0.989331i \(-0.546539\pi\)
−0.145686 + 0.989331i \(0.546539\pi\)
\(854\) 0 0
\(855\) −18.5234 −0.633487
\(856\) 0 0
\(857\) −7.12565 −0.243407 −0.121704 0.992566i \(-0.538836\pi\)
−0.121704 + 0.992566i \(0.538836\pi\)
\(858\) 0 0
\(859\) 22.1830 0.756873 0.378437 0.925627i \(-0.376462\pi\)
0.378437 + 0.925627i \(0.376462\pi\)
\(860\) 0 0
\(861\) −11.3565 −0.387030
\(862\) 0 0
\(863\) 27.3622 0.931420 0.465710 0.884937i \(-0.345799\pi\)
0.465710 + 0.884937i \(0.345799\pi\)
\(864\) 0 0
\(865\) −10.0264 −0.340908
\(866\) 0 0
\(867\) −0.696524 −0.0236552
\(868\) 0 0
\(869\) 39.4533 1.33836
\(870\) 0 0
\(871\) 0.386773 0.0131053
\(872\) 0 0
\(873\) −29.0155 −0.982027
\(874\) 0 0
\(875\) −2.87898 −0.0973272
\(876\) 0 0
\(877\) 27.6885 0.934973 0.467487 0.884000i \(-0.345160\pi\)
0.467487 + 0.884000i \(0.345160\pi\)
\(878\) 0 0
\(879\) 0.516653 0.0174263
\(880\) 0 0
\(881\) −34.6743 −1.16821 −0.584103 0.811679i \(-0.698554\pi\)
−0.584103 + 0.811679i \(0.698554\pi\)
\(882\) 0 0
\(883\) 51.3340 1.72753 0.863763 0.503898i \(-0.168101\pi\)
0.863763 + 0.503898i \(0.168101\pi\)
\(884\) 0 0
\(885\) −1.07429 −0.0361120
\(886\) 0 0
\(887\) −1.81524 −0.0609498 −0.0304749 0.999536i \(-0.509702\pi\)
−0.0304749 + 0.999536i \(0.509702\pi\)
\(888\) 0 0
\(889\) −38.9520 −1.30641
\(890\) 0 0
\(891\) −16.8295 −0.563808
\(892\) 0 0
\(893\) −12.4207 −0.415644
\(894\) 0 0
\(895\) −6.55432 −0.219087
\(896\) 0 0
\(897\) 0.00624119 0.000208387 0
\(898\) 0 0
\(899\) −1.33843 −0.0446392
\(900\) 0 0
\(901\) 40.8264 1.36012
\(902\) 0 0
\(903\) −10.4414 −0.347469
\(904\) 0 0
\(905\) −1.98392 −0.0659478
\(906\) 0 0
\(907\) 4.41840 0.146711 0.0733553 0.997306i \(-0.476629\pi\)
0.0733553 + 0.997306i \(0.476629\pi\)
\(908\) 0 0
\(909\) −35.9876 −1.19363
\(910\) 0 0
\(911\) 4.72012 0.156385 0.0781923 0.996938i \(-0.475085\pi\)
0.0781923 + 0.996938i \(0.475085\pi\)
\(912\) 0 0
\(913\) 19.5058 0.645548
\(914\) 0 0
\(915\) −5.67643 −0.187657
\(916\) 0 0
\(917\) 40.2956 1.33068
\(918\) 0 0
\(919\) 34.5048 1.13821 0.569105 0.822265i \(-0.307290\pi\)
0.569105 + 0.822265i \(0.307290\pi\)
\(920\) 0 0
\(921\) 7.33023 0.241539
\(922\) 0 0
\(923\) 1.33888 0.0440698
\(924\) 0 0
\(925\) −11.7988 −0.387941
\(926\) 0 0
\(927\) 26.7920 0.879965
\(928\) 0 0
\(929\) 20.8723 0.684799 0.342399 0.939555i \(-0.388760\pi\)
0.342399 + 0.939555i \(0.388760\pi\)
\(930\) 0 0
\(931\) 8.49301 0.278347
\(932\) 0 0
\(933\) −10.5933 −0.346810
\(934\) 0 0
\(935\) −9.01229 −0.294734
\(936\) 0 0
\(937\) −22.2913 −0.728226 −0.364113 0.931355i \(-0.618628\pi\)
−0.364113 + 0.931355i \(0.618628\pi\)
\(938\) 0 0
\(939\) −4.92445 −0.160703
\(940\) 0 0
\(941\) −52.8416 −1.72259 −0.861293 0.508109i \(-0.830345\pi\)
−0.861293 + 0.508109i \(0.830345\pi\)
\(942\) 0 0
\(943\) −1.36129 −0.0443296
\(944\) 0 0
\(945\) 7.28630 0.237023
\(946\) 0 0
\(947\) 16.6008 0.539454 0.269727 0.962937i \(-0.413067\pi\)
0.269727 + 0.962937i \(0.413067\pi\)
\(948\) 0 0
\(949\) −0.486494 −0.0157923
\(950\) 0 0
\(951\) −4.85763 −0.157520
\(952\) 0 0
\(953\) 54.7708 1.77420 0.887100 0.461577i \(-0.152716\pi\)
0.887100 + 0.461577i \(0.152716\pi\)
\(954\) 0 0
\(955\) −23.2637 −0.752797
\(956\) 0 0
\(957\) −2.49982 −0.0808076
\(958\) 0 0
\(959\) 39.2435 1.26724
\(960\) 0 0
\(961\) −30.7132 −0.990747
\(962\) 0 0
\(963\) 22.5748 0.727464
\(964\) 0 0
\(965\) −6.70918 −0.215976
\(966\) 0 0
\(967\) −2.82755 −0.0909277 −0.0454639 0.998966i \(-0.514477\pi\)
−0.0454639 + 0.998966i \(0.514477\pi\)
\(968\) 0 0
\(969\) 11.2673 0.361957
\(970\) 0 0
\(971\) −32.4830 −1.04243 −0.521215 0.853425i \(-0.674521\pi\)
−0.521215 + 0.853425i \(0.674521\pi\)
\(972\) 0 0
\(973\) −14.5589 −0.466737
\(974\) 0 0
\(975\) −0.0415195 −0.00132969
\(976\) 0 0
\(977\) 16.9936 0.543673 0.271837 0.962343i \(-0.412369\pi\)
0.271837 + 0.962343i \(0.412369\pi\)
\(978\) 0 0
\(979\) 18.1896 0.581343
\(980\) 0 0
\(981\) 45.7510 1.46072
\(982\) 0 0
\(983\) −36.9257 −1.17775 −0.588874 0.808225i \(-0.700429\pi\)
−0.588874 + 0.808225i \(0.700429\pi\)
\(984\) 0 0
\(985\) 11.4808 0.365809
\(986\) 0 0
\(987\) 2.36312 0.0752188
\(988\) 0 0
\(989\) −1.25159 −0.0397984
\(990\) 0 0
\(991\) 29.2820 0.930172 0.465086 0.885265i \(-0.346023\pi\)
0.465086 + 0.885265i \(0.346023\pi\)
\(992\) 0 0
\(993\) −13.2727 −0.421198
\(994\) 0 0
\(995\) −0.798470 −0.0253132
\(996\) 0 0
\(997\) 52.3315 1.65736 0.828678 0.559726i \(-0.189094\pi\)
0.828678 + 0.559726i \(0.189094\pi\)
\(998\) 0 0
\(999\) 29.8611 0.944763
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 \(a_p\))