Properties

Label 4012.2.a.g.1.8
Level 4012
Weight 2
Character 4012.1
Self dual Yes
Analytic conductor 32.036
Analytic rank 1
Dimension 12
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4012 = 2^{2} \cdot 17 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4012.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0359812909\)
Analytic rank: \(1\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Root \(-0.692763\)
Character \(\chi\) = 4012.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+0.692763 q^{3}\) \(-3.58411 q^{5}\) \(+3.81064 q^{7}\) \(-2.52008 q^{9}\) \(+O(q^{10})\) \(q\)\(+0.692763 q^{3}\) \(-3.58411 q^{5}\) \(+3.81064 q^{7}\) \(-2.52008 q^{9}\) \(-3.20083 q^{11}\) \(+3.92337 q^{13}\) \(-2.48294 q^{15}\) \(-1.00000 q^{17}\) \(+0.300487 q^{19}\) \(+2.63987 q^{21}\) \(-1.11886 q^{23}\) \(+7.84587 q^{25}\) \(-3.82410 q^{27}\) \(+7.45432 q^{29}\) \(+0.368034 q^{31}\) \(-2.21742 q^{33}\) \(-13.6578 q^{35}\) \(-5.36832 q^{37}\) \(+2.71796 q^{39}\) \(+0.470342 q^{41}\) \(+8.69365 q^{43}\) \(+9.03225 q^{45}\) \(-8.28528 q^{47}\) \(+7.52094 q^{49}\) \(-0.692763 q^{51}\) \(-14.2904 q^{53}\) \(+11.4721 q^{55}\) \(+0.208166 q^{57}\) \(+1.00000 q^{59}\) \(-2.58276 q^{61}\) \(-9.60311 q^{63}\) \(-14.0618 q^{65}\) \(-6.13324 q^{67}\) \(-0.775108 q^{69}\) \(-5.69456 q^{71}\) \(+0.352353 q^{73}\) \(+5.43533 q^{75}\) \(-12.1972 q^{77}\) \(+0.179372 q^{79}\) \(+4.91104 q^{81}\) \(+11.2386 q^{83}\) \(+3.58411 q^{85}\) \(+5.16408 q^{87}\) \(-16.2719 q^{89}\) \(+14.9505 q^{91}\) \(+0.254960 q^{93}\) \(-1.07698 q^{95}\) \(-13.6598 q^{97}\) \(+8.06635 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(12q \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 6q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(12q \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 6q^{9} \) \(\mathstrut -\mathstrut 5q^{11} \) \(\mathstrut +\mathstrut 9q^{13} \) \(\mathstrut -\mathstrut 16q^{15} \) \(\mathstrut -\mathstrut 12q^{17} \) \(\mathstrut -\mathstrut 15q^{19} \) \(\mathstrut +\mathstrut 5q^{21} \) \(\mathstrut -\mathstrut 22q^{23} \) \(\mathstrut +\mathstrut 5q^{25} \) \(\mathstrut -\mathstrut 16q^{27} \) \(\mathstrut -\mathstrut 17q^{29} \) \(\mathstrut +\mathstrut 5q^{31} \) \(\mathstrut -\mathstrut 33q^{33} \) \(\mathstrut -\mathstrut 9q^{35} \) \(\mathstrut -\mathstrut 2q^{37} \) \(\mathstrut -\mathstrut 24q^{39} \) \(\mathstrut -\mathstrut 18q^{41} \) \(\mathstrut -\mathstrut 16q^{43} \) \(\mathstrut +\mathstrut 30q^{45} \) \(\mathstrut -\mathstrut 60q^{47} \) \(\mathstrut +\mathstrut 10q^{49} \) \(\mathstrut +\mathstrut 4q^{51} \) \(\mathstrut -\mathstrut 24q^{53} \) \(\mathstrut -\mathstrut q^{55} \) \(\mathstrut +\mathstrut 41q^{57} \) \(\mathstrut +\mathstrut 12q^{59} \) \(\mathstrut -\mathstrut 17q^{61} \) \(\mathstrut -\mathstrut 23q^{63} \) \(\mathstrut +\mathstrut 2q^{65} \) \(\mathstrut -\mathstrut 22q^{67} \) \(\mathstrut +\mathstrut 6q^{69} \) \(\mathstrut -\mathstrut 10q^{71} \) \(\mathstrut +\mathstrut 4q^{73} \) \(\mathstrut -\mathstrut 62q^{75} \) \(\mathstrut -\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut 48q^{79} \) \(\mathstrut +\mathstrut 4q^{81} \) \(\mathstrut -\mathstrut 20q^{83} \) \(\mathstrut -\mathstrut 3q^{85} \) \(\mathstrut +\mathstrut 13q^{87} \) \(\mathstrut -\mathstrut 29q^{89} \) \(\mathstrut -\mathstrut 28q^{91} \) \(\mathstrut -\mathstrut 31q^{93} \) \(\mathstrut -\mathstrut 48q^{95} \) \(\mathstrut -\mathstrut 26q^{97} \) \(\mathstrut -\mathstrut 3q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 0.692763 0.399967 0.199983 0.979799i \(-0.435911\pi\)
0.199983 + 0.979799i \(0.435911\pi\)
\(4\) 0 0
\(5\) −3.58411 −1.60286 −0.801432 0.598086i \(-0.795928\pi\)
−0.801432 + 0.598086i \(0.795928\pi\)
\(6\) 0 0
\(7\) 3.81064 1.44028 0.720142 0.693826i \(-0.244076\pi\)
0.720142 + 0.693826i \(0.244076\pi\)
\(8\) 0 0
\(9\) −2.52008 −0.840027
\(10\) 0 0
\(11\) −3.20083 −0.965087 −0.482543 0.875872i \(-0.660287\pi\)
−0.482543 + 0.875872i \(0.660287\pi\)
\(12\) 0 0
\(13\) 3.92337 1.08815 0.544073 0.839038i \(-0.316881\pi\)
0.544073 + 0.839038i \(0.316881\pi\)
\(14\) 0 0
\(15\) −2.48294 −0.641092
\(16\) 0 0
\(17\) −1.00000 −0.242536
\(18\) 0 0
\(19\) 0.300487 0.0689364 0.0344682 0.999406i \(-0.489026\pi\)
0.0344682 + 0.999406i \(0.489026\pi\)
\(20\) 0 0
\(21\) 2.63987 0.576066
\(22\) 0 0
\(23\) −1.11886 −0.233299 −0.116650 0.993173i \(-0.537215\pi\)
−0.116650 + 0.993173i \(0.537215\pi\)
\(24\) 0 0
\(25\) 7.84587 1.56917
\(26\) 0 0
\(27\) −3.82410 −0.735949
\(28\) 0 0
\(29\) 7.45432 1.38423 0.692117 0.721786i \(-0.256678\pi\)
0.692117 + 0.721786i \(0.256678\pi\)
\(30\) 0 0
\(31\) 0.368034 0.0661009 0.0330504 0.999454i \(-0.489478\pi\)
0.0330504 + 0.999454i \(0.489478\pi\)
\(32\) 0 0
\(33\) −2.21742 −0.386002
\(34\) 0 0
\(35\) −13.6578 −2.30858
\(36\) 0 0
\(37\) −5.36832 −0.882547 −0.441273 0.897373i \(-0.645473\pi\)
−0.441273 + 0.897373i \(0.645473\pi\)
\(38\) 0 0
\(39\) 2.71796 0.435222
\(40\) 0 0
\(41\) 0.470342 0.0734552 0.0367276 0.999325i \(-0.488307\pi\)
0.0367276 + 0.999325i \(0.488307\pi\)
\(42\) 0 0
\(43\) 8.69365 1.32577 0.662884 0.748722i \(-0.269332\pi\)
0.662884 + 0.748722i \(0.269332\pi\)
\(44\) 0 0
\(45\) 9.03225 1.34645
\(46\) 0 0
\(47\) −8.28528 −1.20853 −0.604266 0.796783i \(-0.706534\pi\)
−0.604266 + 0.796783i \(0.706534\pi\)
\(48\) 0 0
\(49\) 7.52094 1.07442
\(50\) 0 0
\(51\) −0.692763 −0.0970062
\(52\) 0 0
\(53\) −14.2904 −1.96294 −0.981469 0.191621i \(-0.938625\pi\)
−0.981469 + 0.191621i \(0.938625\pi\)
\(54\) 0 0
\(55\) 11.4721 1.54690
\(56\) 0 0
\(57\) 0.208166 0.0275723
\(58\) 0 0
\(59\) 1.00000 0.130189
\(60\) 0 0
\(61\) −2.58276 −0.330689 −0.165344 0.986236i \(-0.552874\pi\)
−0.165344 + 0.986236i \(0.552874\pi\)
\(62\) 0 0
\(63\) −9.60311 −1.20988
\(64\) 0 0
\(65\) −14.0618 −1.74415
\(66\) 0 0
\(67\) −6.13324 −0.749294 −0.374647 0.927167i \(-0.622236\pi\)
−0.374647 + 0.927167i \(0.622236\pi\)
\(68\) 0 0
\(69\) −0.775108 −0.0933120
\(70\) 0 0
\(71\) −5.69456 −0.675820 −0.337910 0.941178i \(-0.609720\pi\)
−0.337910 + 0.941178i \(0.609720\pi\)
\(72\) 0 0
\(73\) 0.352353 0.0412398 0.0206199 0.999787i \(-0.493436\pi\)
0.0206199 + 0.999787i \(0.493436\pi\)
\(74\) 0 0
\(75\) 5.43533 0.627617
\(76\) 0 0
\(77\) −12.1972 −1.39000
\(78\) 0 0
\(79\) 0.179372 0.0201809 0.0100905 0.999949i \(-0.496788\pi\)
0.0100905 + 0.999949i \(0.496788\pi\)
\(80\) 0 0
\(81\) 4.91104 0.545671
\(82\) 0 0
\(83\) 11.2386 1.23360 0.616798 0.787121i \(-0.288429\pi\)
0.616798 + 0.787121i \(0.288429\pi\)
\(84\) 0 0
\(85\) 3.58411 0.388752
\(86\) 0 0
\(87\) 5.16408 0.553647
\(88\) 0 0
\(89\) −16.2719 −1.72482 −0.862409 0.506211i \(-0.831046\pi\)
−0.862409 + 0.506211i \(0.831046\pi\)
\(90\) 0 0
\(91\) 14.9505 1.56724
\(92\) 0 0
\(93\) 0.254960 0.0264382
\(94\) 0 0
\(95\) −1.07698 −0.110496
\(96\) 0 0
\(97\) −13.6598 −1.38694 −0.693472 0.720484i \(-0.743920\pi\)
−0.693472 + 0.720484i \(0.743920\pi\)
\(98\) 0 0
\(99\) 8.06635 0.810698
\(100\) 0 0
\(101\) −8.66079 −0.861781 −0.430890 0.902404i \(-0.641800\pi\)
−0.430890 + 0.902404i \(0.641800\pi\)
\(102\) 0 0
\(103\) −14.1870 −1.39789 −0.698943 0.715177i \(-0.746346\pi\)
−0.698943 + 0.715177i \(0.746346\pi\)
\(104\) 0 0
\(105\) −9.46158 −0.923356
\(106\) 0 0
\(107\) 8.38089 0.810211 0.405105 0.914270i \(-0.367235\pi\)
0.405105 + 0.914270i \(0.367235\pi\)
\(108\) 0 0
\(109\) −8.81795 −0.844606 −0.422303 0.906455i \(-0.638778\pi\)
−0.422303 + 0.906455i \(0.638778\pi\)
\(110\) 0 0
\(111\) −3.71897 −0.352989
\(112\) 0 0
\(113\) 0.435370 0.0409562 0.0204781 0.999790i \(-0.493481\pi\)
0.0204781 + 0.999790i \(0.493481\pi\)
\(114\) 0 0
\(115\) 4.01014 0.373947
\(116\) 0 0
\(117\) −9.88721 −0.914072
\(118\) 0 0
\(119\) −3.81064 −0.349320
\(120\) 0 0
\(121\) −0.754687 −0.0686079
\(122\) 0 0
\(123\) 0.325836 0.0293796
\(124\) 0 0
\(125\) −10.1999 −0.912309
\(126\) 0 0
\(127\) −9.07527 −0.805300 −0.402650 0.915354i \(-0.631911\pi\)
−0.402650 + 0.915354i \(0.631911\pi\)
\(128\) 0 0
\(129\) 6.02263 0.530263
\(130\) 0 0
\(131\) 14.0044 1.22357 0.611787 0.791023i \(-0.290451\pi\)
0.611787 + 0.791023i \(0.290451\pi\)
\(132\) 0 0
\(133\) 1.14505 0.0992881
\(134\) 0 0
\(135\) 13.7060 1.17963
\(136\) 0 0
\(137\) −9.00200 −0.769093 −0.384546 0.923106i \(-0.625642\pi\)
−0.384546 + 0.923106i \(0.625642\pi\)
\(138\) 0 0
\(139\) −12.9014 −1.09428 −0.547141 0.837040i \(-0.684284\pi\)
−0.547141 + 0.837040i \(0.684284\pi\)
\(140\) 0 0
\(141\) −5.73973 −0.483373
\(142\) 0 0
\(143\) −12.5580 −1.05016
\(144\) 0 0
\(145\) −26.7171 −2.21874
\(146\) 0 0
\(147\) 5.21023 0.429732
\(148\) 0 0
\(149\) −3.80897 −0.312043 −0.156022 0.987754i \(-0.549867\pi\)
−0.156022 + 0.987754i \(0.549867\pi\)
\(150\) 0 0
\(151\) 12.1450 0.988348 0.494174 0.869363i \(-0.335471\pi\)
0.494174 + 0.869363i \(0.335471\pi\)
\(152\) 0 0
\(153\) 2.52008 0.203736
\(154\) 0 0
\(155\) −1.31908 −0.105951
\(156\) 0 0
\(157\) 18.5153 1.47768 0.738840 0.673881i \(-0.235374\pi\)
0.738840 + 0.673881i \(0.235374\pi\)
\(158\) 0 0
\(159\) −9.89986 −0.785110
\(160\) 0 0
\(161\) −4.26359 −0.336018
\(162\) 0 0
\(163\) −6.75710 −0.529257 −0.264629 0.964350i \(-0.585249\pi\)
−0.264629 + 0.964350i \(0.585249\pi\)
\(164\) 0 0
\(165\) 7.94747 0.618710
\(166\) 0 0
\(167\) −10.4916 −0.811861 −0.405930 0.913904i \(-0.633052\pi\)
−0.405930 + 0.913904i \(0.633052\pi\)
\(168\) 0 0
\(169\) 2.39283 0.184064
\(170\) 0 0
\(171\) −0.757251 −0.0579084
\(172\) 0 0
\(173\) 19.7242 1.49961 0.749803 0.661662i \(-0.230148\pi\)
0.749803 + 0.661662i \(0.230148\pi\)
\(174\) 0 0
\(175\) 29.8978 2.26006
\(176\) 0 0
\(177\) 0.692763 0.0520712
\(178\) 0 0
\(179\) 4.76708 0.356308 0.178154 0.984003i \(-0.442987\pi\)
0.178154 + 0.984003i \(0.442987\pi\)
\(180\) 0 0
\(181\) −13.0646 −0.971084 −0.485542 0.874213i \(-0.661378\pi\)
−0.485542 + 0.874213i \(0.661378\pi\)
\(182\) 0 0
\(183\) −1.78924 −0.132265
\(184\) 0 0
\(185\) 19.2407 1.41460
\(186\) 0 0
\(187\) 3.20083 0.234068
\(188\) 0 0
\(189\) −14.5723 −1.05998
\(190\) 0 0
\(191\) −5.78852 −0.418842 −0.209421 0.977826i \(-0.567158\pi\)
−0.209421 + 0.977826i \(0.567158\pi\)
\(192\) 0 0
\(193\) 7.30748 0.526004 0.263002 0.964795i \(-0.415287\pi\)
0.263002 + 0.964795i \(0.415287\pi\)
\(194\) 0 0
\(195\) −9.74149 −0.697603
\(196\) 0 0
\(197\) −13.6653 −0.973611 −0.486805 0.873511i \(-0.661838\pi\)
−0.486805 + 0.873511i \(0.661838\pi\)
\(198\) 0 0
\(199\) 20.1075 1.42538 0.712692 0.701477i \(-0.247476\pi\)
0.712692 + 0.701477i \(0.247476\pi\)
\(200\) 0 0
\(201\) −4.24888 −0.299693
\(202\) 0 0
\(203\) 28.4057 1.99369
\(204\) 0 0
\(205\) −1.68576 −0.117739
\(206\) 0 0
\(207\) 2.81963 0.195978
\(208\) 0 0
\(209\) −0.961808 −0.0665296
\(210\) 0 0
\(211\) −6.34017 −0.436475 −0.218238 0.975896i \(-0.570031\pi\)
−0.218238 + 0.975896i \(0.570031\pi\)
\(212\) 0 0
\(213\) −3.94498 −0.270305
\(214\) 0 0
\(215\) −31.1590 −2.12503
\(216\) 0 0
\(217\) 1.40244 0.0952041
\(218\) 0 0
\(219\) 0.244097 0.0164945
\(220\) 0 0
\(221\) −3.92337 −0.263914
\(222\) 0 0
\(223\) −24.9219 −1.66890 −0.834448 0.551087i \(-0.814213\pi\)
−0.834448 + 0.551087i \(0.814213\pi\)
\(224\) 0 0
\(225\) −19.7722 −1.31815
\(226\) 0 0
\(227\) −1.19663 −0.0794232 −0.0397116 0.999211i \(-0.512644\pi\)
−0.0397116 + 0.999211i \(0.512644\pi\)
\(228\) 0 0
\(229\) −12.2340 −0.808443 −0.404222 0.914661i \(-0.632458\pi\)
−0.404222 + 0.914661i \(0.632458\pi\)
\(230\) 0 0
\(231\) −8.44976 −0.555954
\(232\) 0 0
\(233\) −26.1054 −1.71022 −0.855112 0.518443i \(-0.826512\pi\)
−0.855112 + 0.518443i \(0.826512\pi\)
\(234\) 0 0
\(235\) 29.6954 1.93711
\(236\) 0 0
\(237\) 0.124262 0.00807169
\(238\) 0 0
\(239\) −25.8474 −1.67193 −0.835964 0.548784i \(-0.815091\pi\)
−0.835964 + 0.548784i \(0.815091\pi\)
\(240\) 0 0
\(241\) −15.0375 −0.968650 −0.484325 0.874888i \(-0.660935\pi\)
−0.484325 + 0.874888i \(0.660935\pi\)
\(242\) 0 0
\(243\) 14.8745 0.954200
\(244\) 0 0
\(245\) −26.9559 −1.72215
\(246\) 0 0
\(247\) 1.17892 0.0750130
\(248\) 0 0
\(249\) 7.78568 0.493397
\(250\) 0 0
\(251\) −20.8418 −1.31552 −0.657762 0.753226i \(-0.728497\pi\)
−0.657762 + 0.753226i \(0.728497\pi\)
\(252\) 0 0
\(253\) 3.58130 0.225154
\(254\) 0 0
\(255\) 2.48294 0.155488
\(256\) 0 0
\(257\) −13.4010 −0.835934 −0.417967 0.908462i \(-0.637257\pi\)
−0.417967 + 0.908462i \(0.637257\pi\)
\(258\) 0 0
\(259\) −20.4567 −1.27112
\(260\) 0 0
\(261\) −18.7855 −1.16279
\(262\) 0 0
\(263\) −8.41728 −0.519032 −0.259516 0.965739i \(-0.583563\pi\)
−0.259516 + 0.965739i \(0.583563\pi\)
\(264\) 0 0
\(265\) 51.2184 3.14632
\(266\) 0 0
\(267\) −11.2726 −0.689870
\(268\) 0 0
\(269\) −4.89470 −0.298435 −0.149218 0.988804i \(-0.547676\pi\)
−0.149218 + 0.988804i \(0.547676\pi\)
\(270\) 0 0
\(271\) 14.9323 0.907072 0.453536 0.891238i \(-0.350162\pi\)
0.453536 + 0.891238i \(0.350162\pi\)
\(272\) 0 0
\(273\) 10.3572 0.626844
\(274\) 0 0
\(275\) −25.1133 −1.51439
\(276\) 0 0
\(277\) 6.76980 0.406758 0.203379 0.979100i \(-0.434808\pi\)
0.203379 + 0.979100i \(0.434808\pi\)
\(278\) 0 0
\(279\) −0.927476 −0.0555265
\(280\) 0 0
\(281\) 12.2942 0.733411 0.366705 0.930337i \(-0.380486\pi\)
0.366705 + 0.930337i \(0.380486\pi\)
\(282\) 0 0
\(283\) 3.09484 0.183969 0.0919846 0.995760i \(-0.470679\pi\)
0.0919846 + 0.995760i \(0.470679\pi\)
\(284\) 0 0
\(285\) −0.746091 −0.0441946
\(286\) 0 0
\(287\) 1.79230 0.105796
\(288\) 0 0
\(289\) 1.00000 0.0588235
\(290\) 0 0
\(291\) −9.46300 −0.554731
\(292\) 0 0
\(293\) 18.8018 1.09841 0.549207 0.835686i \(-0.314930\pi\)
0.549207 + 0.835686i \(0.314930\pi\)
\(294\) 0 0
\(295\) −3.58411 −0.208675
\(296\) 0 0
\(297\) 12.2403 0.710255
\(298\) 0 0
\(299\) −4.38972 −0.253864
\(300\) 0 0
\(301\) 33.1283 1.90948
\(302\) 0 0
\(303\) −5.99987 −0.344684
\(304\) 0 0
\(305\) 9.25692 0.530049
\(306\) 0 0
\(307\) −2.82586 −0.161280 −0.0806402 0.996743i \(-0.525696\pi\)
−0.0806402 + 0.996743i \(0.525696\pi\)
\(308\) 0 0
\(309\) −9.82822 −0.559108
\(310\) 0 0
\(311\) 22.9631 1.30212 0.651058 0.759028i \(-0.274325\pi\)
0.651058 + 0.759028i \(0.274325\pi\)
\(312\) 0 0
\(313\) −17.5078 −0.989599 −0.494799 0.869007i \(-0.664758\pi\)
−0.494799 + 0.869007i \(0.664758\pi\)
\(314\) 0 0
\(315\) 34.4186 1.93927
\(316\) 0 0
\(317\) −4.53591 −0.254762 −0.127381 0.991854i \(-0.540657\pi\)
−0.127381 + 0.991854i \(0.540657\pi\)
\(318\) 0 0
\(319\) −23.8600 −1.33591
\(320\) 0 0
\(321\) 5.80596 0.324057
\(322\) 0 0
\(323\) −0.300487 −0.0167195
\(324\) 0 0
\(325\) 30.7823 1.70749
\(326\) 0 0
\(327\) −6.10874 −0.337814
\(328\) 0 0
\(329\) −31.5722 −1.74063
\(330\) 0 0
\(331\) −35.8706 −1.97163 −0.985813 0.167849i \(-0.946318\pi\)
−0.985813 + 0.167849i \(0.946318\pi\)
\(332\) 0 0
\(333\) 13.5286 0.741363
\(334\) 0 0
\(335\) 21.9822 1.20102
\(336\) 0 0
\(337\) 20.6893 1.12702 0.563509 0.826110i \(-0.309451\pi\)
0.563509 + 0.826110i \(0.309451\pi\)
\(338\) 0 0
\(339\) 0.301608 0.0163811
\(340\) 0 0
\(341\) −1.17801 −0.0637931
\(342\) 0 0
\(343\) 1.98513 0.107187
\(344\) 0 0
\(345\) 2.77807 0.149566
\(346\) 0 0
\(347\) 7.48174 0.401641 0.200820 0.979628i \(-0.435639\pi\)
0.200820 + 0.979628i \(0.435639\pi\)
\(348\) 0 0
\(349\) 13.7804 0.737647 0.368823 0.929500i \(-0.379761\pi\)
0.368823 + 0.929500i \(0.379761\pi\)
\(350\) 0 0
\(351\) −15.0034 −0.800821
\(352\) 0 0
\(353\) −35.9004 −1.91079 −0.955394 0.295336i \(-0.904569\pi\)
−0.955394 + 0.295336i \(0.904569\pi\)
\(354\) 0 0
\(355\) 20.4099 1.08325
\(356\) 0 0
\(357\) −2.63987 −0.139717
\(358\) 0 0
\(359\) 24.4040 1.28800 0.643998 0.765027i \(-0.277275\pi\)
0.643998 + 0.765027i \(0.277275\pi\)
\(360\) 0 0
\(361\) −18.9097 −0.995248
\(362\) 0 0
\(363\) −0.522819 −0.0274409
\(364\) 0 0
\(365\) −1.26287 −0.0661018
\(366\) 0 0
\(367\) 21.6956 1.13250 0.566251 0.824233i \(-0.308393\pi\)
0.566251 + 0.824233i \(0.308393\pi\)
\(368\) 0 0
\(369\) −1.18530 −0.0617043
\(370\) 0 0
\(371\) −54.4555 −2.82719
\(372\) 0 0
\(373\) 14.9830 0.775789 0.387894 0.921704i \(-0.373203\pi\)
0.387894 + 0.921704i \(0.373203\pi\)
\(374\) 0 0
\(375\) −7.06613 −0.364893
\(376\) 0 0
\(377\) 29.2461 1.50625
\(378\) 0 0
\(379\) 11.1479 0.572631 0.286315 0.958135i \(-0.407570\pi\)
0.286315 + 0.958135i \(0.407570\pi\)
\(380\) 0 0
\(381\) −6.28701 −0.322093
\(382\) 0 0
\(383\) −3.15935 −0.161435 −0.0807177 0.996737i \(-0.525721\pi\)
−0.0807177 + 0.996737i \(0.525721\pi\)
\(384\) 0 0
\(385\) 43.7161 2.22798
\(386\) 0 0
\(387\) −21.9087 −1.11368
\(388\) 0 0
\(389\) 13.2268 0.670627 0.335313 0.942107i \(-0.391158\pi\)
0.335313 + 0.942107i \(0.391158\pi\)
\(390\) 0 0
\(391\) 1.11886 0.0565834
\(392\) 0 0
\(393\) 9.70175 0.489389
\(394\) 0 0
\(395\) −0.642889 −0.0323473
\(396\) 0 0
\(397\) 19.7146 0.989446 0.494723 0.869051i \(-0.335270\pi\)
0.494723 + 0.869051i \(0.335270\pi\)
\(398\) 0 0
\(399\) 0.793245 0.0397119
\(400\) 0 0
\(401\) 7.86494 0.392756 0.196378 0.980528i \(-0.437082\pi\)
0.196378 + 0.980528i \(0.437082\pi\)
\(402\) 0 0
\(403\) 1.44393 0.0719275
\(404\) 0 0
\(405\) −17.6017 −0.874637
\(406\) 0 0
\(407\) 17.1831 0.851734
\(408\) 0 0
\(409\) 1.23480 0.0610570 0.0305285 0.999534i \(-0.490281\pi\)
0.0305285 + 0.999534i \(0.490281\pi\)
\(410\) 0 0
\(411\) −6.23625 −0.307611
\(412\) 0 0
\(413\) 3.81064 0.187509
\(414\) 0 0
\(415\) −40.2804 −1.97729
\(416\) 0 0
\(417\) −8.93761 −0.437676
\(418\) 0 0
\(419\) −23.6080 −1.15333 −0.576664 0.816982i \(-0.695646\pi\)
−0.576664 + 0.816982i \(0.695646\pi\)
\(420\) 0 0
\(421\) −13.6336 −0.664463 −0.332231 0.943198i \(-0.607801\pi\)
−0.332231 + 0.943198i \(0.607801\pi\)
\(422\) 0 0
\(423\) 20.8796 1.01520
\(424\) 0 0
\(425\) −7.84587 −0.380581
\(426\) 0 0
\(427\) −9.84197 −0.476286
\(428\) 0 0
\(429\) −8.69974 −0.420027
\(430\) 0 0
\(431\) 9.74132 0.469223 0.234611 0.972089i \(-0.424618\pi\)
0.234611 + 0.972089i \(0.424618\pi\)
\(432\) 0 0
\(433\) 26.3878 1.26812 0.634060 0.773284i \(-0.281387\pi\)
0.634060 + 0.773284i \(0.281387\pi\)
\(434\) 0 0
\(435\) −18.5086 −0.887421
\(436\) 0 0
\(437\) −0.336204 −0.0160828
\(438\) 0 0
\(439\) 25.7372 1.22837 0.614184 0.789163i \(-0.289485\pi\)
0.614184 + 0.789163i \(0.289485\pi\)
\(440\) 0 0
\(441\) −18.9534 −0.902542
\(442\) 0 0
\(443\) −0.988469 −0.0469636 −0.0234818 0.999724i \(-0.507475\pi\)
−0.0234818 + 0.999724i \(0.507475\pi\)
\(444\) 0 0
\(445\) 58.3204 2.76465
\(446\) 0 0
\(447\) −2.63871 −0.124807
\(448\) 0 0
\(449\) 2.09037 0.0986507 0.0493253 0.998783i \(-0.484293\pi\)
0.0493253 + 0.998783i \(0.484293\pi\)
\(450\) 0 0
\(451\) −1.50549 −0.0708906
\(452\) 0 0
\(453\) 8.41362 0.395306
\(454\) 0 0
\(455\) −53.5844 −2.51208
\(456\) 0 0
\(457\) 10.9053 0.510129 0.255065 0.966924i \(-0.417903\pi\)
0.255065 + 0.966924i \(0.417903\pi\)
\(458\) 0 0
\(459\) 3.82410 0.178494
\(460\) 0 0
\(461\) −13.5249 −0.629917 −0.314959 0.949105i \(-0.601991\pi\)
−0.314959 + 0.949105i \(0.601991\pi\)
\(462\) 0 0
\(463\) −26.0581 −1.21102 −0.605510 0.795837i \(-0.707031\pi\)
−0.605510 + 0.795837i \(0.707031\pi\)
\(464\) 0 0
\(465\) −0.913807 −0.0423768
\(466\) 0 0
\(467\) 4.03898 0.186902 0.0934509 0.995624i \(-0.470210\pi\)
0.0934509 + 0.995624i \(0.470210\pi\)
\(468\) 0 0
\(469\) −23.3715 −1.07920
\(470\) 0 0
\(471\) 12.8267 0.591022
\(472\) 0 0
\(473\) −27.8269 −1.27948
\(474\) 0 0
\(475\) 2.35758 0.108173
\(476\) 0 0
\(477\) 36.0130 1.64892
\(478\) 0 0
\(479\) −2.89988 −0.132499 −0.0662494 0.997803i \(-0.521103\pi\)
−0.0662494 + 0.997803i \(0.521103\pi\)
\(480\) 0 0
\(481\) −21.0619 −0.960341
\(482\) 0 0
\(483\) −2.95365 −0.134396
\(484\) 0 0
\(485\) 48.9583 2.22308
\(486\) 0 0
\(487\) 17.2211 0.780362 0.390181 0.920738i \(-0.372412\pi\)
0.390181 + 0.920738i \(0.372412\pi\)
\(488\) 0 0
\(489\) −4.68107 −0.211685
\(490\) 0 0
\(491\) 36.3473 1.64033 0.820165 0.572127i \(-0.193881\pi\)
0.820165 + 0.572127i \(0.193881\pi\)
\(492\) 0 0
\(493\) −7.45432 −0.335726
\(494\) 0 0
\(495\) −28.9107 −1.29944
\(496\) 0 0
\(497\) −21.6999 −0.973373
\(498\) 0 0
\(499\) −9.02762 −0.404132 −0.202066 0.979372i \(-0.564765\pi\)
−0.202066 + 0.979372i \(0.564765\pi\)
\(500\) 0 0
\(501\) −7.26816 −0.324717
\(502\) 0 0
\(503\) 7.88686 0.351658 0.175829 0.984421i \(-0.443739\pi\)
0.175829 + 0.984421i \(0.443739\pi\)
\(504\) 0 0
\(505\) 31.0413 1.38132
\(506\) 0 0
\(507\) 1.65766 0.0736194
\(508\) 0 0
\(509\) 38.5727 1.70970 0.854852 0.518873i \(-0.173648\pi\)
0.854852 + 0.518873i \(0.173648\pi\)
\(510\) 0 0
\(511\) 1.34269 0.0593971
\(512\) 0 0
\(513\) −1.14909 −0.0507337
\(514\) 0 0
\(515\) 50.8478 2.24062
\(516\) 0 0
\(517\) 26.5198 1.16634
\(518\) 0 0
\(519\) 13.6642 0.599792
\(520\) 0 0
\(521\) −29.7094 −1.30159 −0.650797 0.759252i \(-0.725565\pi\)
−0.650797 + 0.759252i \(0.725565\pi\)
\(522\) 0 0
\(523\) −28.4939 −1.24595 −0.622975 0.782242i \(-0.714076\pi\)
−0.622975 + 0.782242i \(0.714076\pi\)
\(524\) 0 0
\(525\) 20.7120 0.903948
\(526\) 0 0
\(527\) −0.368034 −0.0160318
\(528\) 0 0
\(529\) −21.7481 −0.945571
\(530\) 0 0
\(531\) −2.52008 −0.109362
\(532\) 0 0
\(533\) 1.84533 0.0799300
\(534\) 0 0
\(535\) −30.0381 −1.29866
\(536\) 0 0
\(537\) 3.30246 0.142511
\(538\) 0 0
\(539\) −24.0733 −1.03691
\(540\) 0 0
\(541\) −43.5547 −1.87256 −0.936282 0.351250i \(-0.885757\pi\)
−0.936282 + 0.351250i \(0.885757\pi\)
\(542\) 0 0
\(543\) −9.05067 −0.388401
\(544\) 0 0
\(545\) 31.6045 1.35379
\(546\) 0 0
\(547\) 19.7898 0.846149 0.423075 0.906095i \(-0.360951\pi\)
0.423075 + 0.906095i \(0.360951\pi\)
\(548\) 0 0
\(549\) 6.50877 0.277788
\(550\) 0 0
\(551\) 2.23993 0.0954241
\(552\) 0 0
\(553\) 0.683521 0.0290663
\(554\) 0 0
\(555\) 13.3292 0.565794
\(556\) 0 0
\(557\) 39.6368 1.67947 0.839734 0.542999i \(-0.182711\pi\)
0.839734 + 0.542999i \(0.182711\pi\)
\(558\) 0 0
\(559\) 34.1084 1.44263
\(560\) 0 0
\(561\) 2.21742 0.0936193
\(562\) 0 0
\(563\) 11.4248 0.481496 0.240748 0.970588i \(-0.422607\pi\)
0.240748 + 0.970588i \(0.422607\pi\)
\(564\) 0 0
\(565\) −1.56042 −0.0656472
\(566\) 0 0
\(567\) 18.7142 0.785922
\(568\) 0 0
\(569\) 45.1045 1.89088 0.945440 0.325797i \(-0.105633\pi\)
0.945440 + 0.325797i \(0.105633\pi\)
\(570\) 0 0
\(571\) 2.36082 0.0987974 0.0493987 0.998779i \(-0.484269\pi\)
0.0493987 + 0.998779i \(0.484269\pi\)
\(572\) 0 0
\(573\) −4.01007 −0.167523
\(574\) 0 0
\(575\) −8.77847 −0.366088
\(576\) 0 0
\(577\) −0.880750 −0.0366661 −0.0183330 0.999832i \(-0.505836\pi\)
−0.0183330 + 0.999832i \(0.505836\pi\)
\(578\) 0 0
\(579\) 5.06235 0.210384
\(580\) 0 0
\(581\) 42.8262 1.77673
\(582\) 0 0
\(583\) 45.7412 1.89440
\(584\) 0 0
\(585\) 35.4369 1.46513
\(586\) 0 0
\(587\) −22.6217 −0.933699 −0.466849 0.884337i \(-0.654611\pi\)
−0.466849 + 0.884337i \(0.654611\pi\)
\(588\) 0 0
\(589\) 0.110589 0.00455676
\(590\) 0 0
\(591\) −9.46679 −0.389412
\(592\) 0 0
\(593\) 22.7829 0.935580 0.467790 0.883840i \(-0.345050\pi\)
0.467790 + 0.883840i \(0.345050\pi\)
\(594\) 0 0
\(595\) 13.6578 0.559913
\(596\) 0 0
\(597\) 13.9297 0.570106
\(598\) 0 0
\(599\) −44.6684 −1.82510 −0.912550 0.408966i \(-0.865890\pi\)
−0.912550 + 0.408966i \(0.865890\pi\)
\(600\) 0 0
\(601\) −20.7217 −0.845257 −0.422628 0.906303i \(-0.638892\pi\)
−0.422628 + 0.906303i \(0.638892\pi\)
\(602\) 0 0
\(603\) 15.4562 0.629427
\(604\) 0 0
\(605\) 2.70488 0.109969
\(606\) 0 0
\(607\) −34.9290 −1.41772 −0.708862 0.705347i \(-0.750791\pi\)
−0.708862 + 0.705347i \(0.750791\pi\)
\(608\) 0 0
\(609\) 19.6784 0.797410
\(610\) 0 0
\(611\) −32.5062 −1.31506
\(612\) 0 0
\(613\) −2.34421 −0.0946819 −0.0473410 0.998879i \(-0.515075\pi\)
−0.0473410 + 0.998879i \(0.515075\pi\)
\(614\) 0 0
\(615\) −1.16783 −0.0470915
\(616\) 0 0
\(617\) 45.1366 1.81713 0.908566 0.417741i \(-0.137178\pi\)
0.908566 + 0.417741i \(0.137178\pi\)
\(618\) 0 0
\(619\) 38.4049 1.54362 0.771811 0.635852i \(-0.219351\pi\)
0.771811 + 0.635852i \(0.219351\pi\)
\(620\) 0 0
\(621\) 4.27866 0.171697
\(622\) 0 0
\(623\) −62.0063 −2.48423
\(624\) 0 0
\(625\) −2.67166 −0.106866
\(626\) 0 0
\(627\) −0.666304 −0.0266096
\(628\) 0 0
\(629\) 5.36832 0.214049
\(630\) 0 0
\(631\) 6.61255 0.263241 0.131621 0.991300i \(-0.457982\pi\)
0.131621 + 0.991300i \(0.457982\pi\)
\(632\) 0 0
\(633\) −4.39223 −0.174575
\(634\) 0 0
\(635\) 32.5268 1.29079
\(636\) 0 0
\(637\) 29.5074 1.16913
\(638\) 0 0
\(639\) 14.3507 0.567707
\(640\) 0 0
\(641\) −1.06934 −0.0422365 −0.0211182 0.999777i \(-0.506723\pi\)
−0.0211182 + 0.999777i \(0.506723\pi\)
\(642\) 0 0
\(643\) 40.6006 1.60113 0.800566 0.599245i \(-0.204532\pi\)
0.800566 + 0.599245i \(0.204532\pi\)
\(644\) 0 0
\(645\) −21.5858 −0.849940
\(646\) 0 0
\(647\) 1.55716 0.0612183 0.0306091 0.999531i \(-0.490255\pi\)
0.0306091 + 0.999531i \(0.490255\pi\)
\(648\) 0 0
\(649\) −3.20083 −0.125644
\(650\) 0 0
\(651\) 0.971561 0.0380785
\(652\) 0 0
\(653\) −13.1250 −0.513620 −0.256810 0.966462i \(-0.582671\pi\)
−0.256810 + 0.966462i \(0.582671\pi\)
\(654\) 0 0
\(655\) −50.1935 −1.96122
\(656\) 0 0
\(657\) −0.887958 −0.0346425
\(658\) 0 0
\(659\) −8.17999 −0.318647 −0.159324 0.987226i \(-0.550931\pi\)
−0.159324 + 0.987226i \(0.550931\pi\)
\(660\) 0 0
\(661\) −14.7286 −0.572878 −0.286439 0.958099i \(-0.592472\pi\)
−0.286439 + 0.958099i \(0.592472\pi\)
\(662\) 0 0
\(663\) −2.71796 −0.105557
\(664\) 0 0
\(665\) −4.10398 −0.159145
\(666\) 0 0
\(667\) −8.34038 −0.322941
\(668\) 0 0
\(669\) −17.2650 −0.667503
\(670\) 0 0
\(671\) 8.26699 0.319143
\(672\) 0 0
\(673\) 13.5275 0.521445 0.260723 0.965414i \(-0.416039\pi\)
0.260723 + 0.965414i \(0.416039\pi\)
\(674\) 0 0
\(675\) −30.0034 −1.15483
\(676\) 0 0
\(677\) 25.7809 0.990839 0.495420 0.868654i \(-0.335014\pi\)
0.495420 + 0.868654i \(0.335014\pi\)
\(678\) 0 0
\(679\) −52.0525 −1.99759
\(680\) 0 0
\(681\) −0.828981 −0.0317666
\(682\) 0 0
\(683\) −24.9326 −0.954020 −0.477010 0.878898i \(-0.658279\pi\)
−0.477010 + 0.878898i \(0.658279\pi\)
\(684\) 0 0
\(685\) 32.2642 1.23275
\(686\) 0 0
\(687\) −8.47524 −0.323350
\(688\) 0 0
\(689\) −56.0665 −2.13596
\(690\) 0 0
\(691\) −16.3247 −0.621022 −0.310511 0.950570i \(-0.600500\pi\)
−0.310511 + 0.950570i \(0.600500\pi\)
\(692\) 0 0
\(693\) 30.7379 1.16764
\(694\) 0 0
\(695\) 46.2401 1.75399
\(696\) 0 0
\(697\) −0.470342 −0.0178155
\(698\) 0 0
\(699\) −18.0849 −0.684033
\(700\) 0 0
\(701\) −5.69946 −0.215266 −0.107633 0.994191i \(-0.534327\pi\)
−0.107633 + 0.994191i \(0.534327\pi\)
\(702\) 0 0
\(703\) −1.61311 −0.0608396
\(704\) 0 0
\(705\) 20.5719 0.774781
\(706\) 0 0
\(707\) −33.0031 −1.24121
\(708\) 0 0
\(709\) 12.3714 0.464619 0.232309 0.972642i \(-0.425372\pi\)
0.232309 + 0.972642i \(0.425372\pi\)
\(710\) 0 0
\(711\) −0.452032 −0.0169525
\(712\) 0 0
\(713\) −0.411781 −0.0154213
\(714\) 0 0
\(715\) 45.0094 1.68326
\(716\) 0 0
\(717\) −17.9061 −0.668716
\(718\) 0 0
\(719\) −52.0627 −1.94161 −0.970805 0.239869i \(-0.922895\pi\)
−0.970805 + 0.239869i \(0.922895\pi\)
\(720\) 0 0
\(721\) −54.0615 −2.01336
\(722\) 0 0
\(723\) −10.4174 −0.387428
\(724\) 0 0
\(725\) 58.4857 2.17210
\(726\) 0 0
\(727\) −33.8084 −1.25389 −0.626943 0.779065i \(-0.715694\pi\)
−0.626943 + 0.779065i \(0.715694\pi\)
\(728\) 0 0
\(729\) −4.42863 −0.164023
\(730\) 0 0
\(731\) −8.69365 −0.321546
\(732\) 0 0
\(733\) 7.37380 0.272358 0.136179 0.990684i \(-0.456518\pi\)
0.136179 + 0.990684i \(0.456518\pi\)
\(734\) 0 0
\(735\) −18.6741 −0.688803
\(736\) 0 0
\(737\) 19.6314 0.723134
\(738\) 0 0
\(739\) 0.110613 0.00406896 0.00203448 0.999998i \(-0.499352\pi\)
0.00203448 + 0.999998i \(0.499352\pi\)
\(740\) 0 0
\(741\) 0.816713 0.0300027
\(742\) 0 0
\(743\) 22.2344 0.815702 0.407851 0.913049i \(-0.366278\pi\)
0.407851 + 0.913049i \(0.366278\pi\)
\(744\) 0 0
\(745\) 13.6518 0.500163
\(746\) 0 0
\(747\) −28.3222 −1.03625
\(748\) 0 0
\(749\) 31.9365 1.16693
\(750\) 0 0
\(751\) 28.1473 1.02711 0.513554 0.858057i \(-0.328328\pi\)
0.513554 + 0.858057i \(0.328328\pi\)
\(752\) 0 0
\(753\) −14.4384 −0.526165
\(754\) 0 0
\(755\) −43.5291 −1.58419
\(756\) 0 0
\(757\) 11.2648 0.409426 0.204713 0.978822i \(-0.434374\pi\)
0.204713 + 0.978822i \(0.434374\pi\)
\(758\) 0 0
\(759\) 2.48099 0.0900542
\(760\) 0 0
\(761\) −23.5576 −0.853962 −0.426981 0.904261i \(-0.640423\pi\)
−0.426981 + 0.904261i \(0.640423\pi\)
\(762\) 0 0
\(763\) −33.6020 −1.21647
\(764\) 0 0
\(765\) −9.03225 −0.326562
\(766\) 0 0
\(767\) 3.92337 0.141665
\(768\) 0 0
\(769\) −12.5349 −0.452021 −0.226011 0.974125i \(-0.572568\pi\)
−0.226011 + 0.974125i \(0.572568\pi\)
\(770\) 0 0
\(771\) −9.28374 −0.334346
\(772\) 0 0
\(773\) 54.3872 1.95617 0.978085 0.208205i \(-0.0667620\pi\)
0.978085 + 0.208205i \(0.0667620\pi\)
\(774\) 0 0
\(775\) 2.88755 0.103724
\(776\) 0 0
\(777\) −14.1717 −0.508405
\(778\) 0 0
\(779\) 0.141332 0.00506374
\(780\) 0 0
\(781\) 18.2273 0.652225
\(782\) 0 0
\(783\) −28.5061 −1.01873
\(784\) 0 0
\(785\) −66.3608 −2.36852
\(786\) 0 0
\(787\) −9.50206 −0.338712 −0.169356 0.985555i \(-0.554169\pi\)
−0.169356 + 0.985555i \(0.554169\pi\)
\(788\) 0 0
\(789\) −5.83118 −0.207595
\(790\) 0 0
\(791\) 1.65904 0.0589886
\(792\) 0 0
\(793\) −10.1331 −0.359838
\(794\) 0 0
\(795\) 35.4822 1.25842
\(796\) 0 0
\(797\) 42.6128 1.50942 0.754711 0.656058i \(-0.227777\pi\)
0.754711 + 0.656058i \(0.227777\pi\)
\(798\) 0 0
\(799\) 8.28528 0.293112
\(800\) 0 0
\(801\) 41.0065 1.44889
\(802\) 0 0
\(803\) −1.12782 −0.0398000
\(804\) 0 0
\(805\) 15.2812 0.538591
\(806\) 0 0
\(807\) −3.39087 −0.119364
\(808\) 0 0
\(809\) −22.8115 −0.802011 −0.401006 0.916076i \(-0.631339\pi\)
−0.401006 + 0.916076i \(0.631339\pi\)
\(810\) 0 0
\(811\) −2.69462 −0.0946209 −0.0473105 0.998880i \(-0.515065\pi\)
−0.0473105 + 0.998880i \(0.515065\pi\)
\(812\) 0 0
\(813\) 10.3445 0.362799
\(814\) 0 0
\(815\) 24.2182 0.848327
\(816\) 0 0
\(817\) 2.61233 0.0913938
\(818\) 0 0
\(819\) −37.6765 −1.31652
\(820\) 0 0
\(821\) 5.74454 0.200486 0.100243 0.994963i \(-0.468038\pi\)
0.100243 + 0.994963i \(0.468038\pi\)
\(822\) 0 0
\(823\) 17.8613 0.622605 0.311302 0.950311i \(-0.399235\pi\)
0.311302 + 0.950311i \(0.399235\pi\)
\(824\) 0 0
\(825\) −17.3976 −0.605705
\(826\) 0 0
\(827\) 32.3309 1.12425 0.562127 0.827051i \(-0.309983\pi\)
0.562127 + 0.827051i \(0.309983\pi\)
\(828\) 0 0
\(829\) 0.458180 0.0159132 0.00795662 0.999968i \(-0.497467\pi\)
0.00795662 + 0.999968i \(0.497467\pi\)
\(830\) 0 0
\(831\) 4.68986 0.162689
\(832\) 0 0
\(833\) −7.52094 −0.260585
\(834\) 0 0
\(835\) 37.6029 1.30130
\(836\) 0 0
\(837\) −1.40740 −0.0486469
\(838\) 0 0
\(839\) −14.6189 −0.504701 −0.252350 0.967636i \(-0.581204\pi\)
−0.252350 + 0.967636i \(0.581204\pi\)
\(840\) 0 0
\(841\) 26.5670 0.916102
\(842\) 0 0
\(843\) 8.51697 0.293340
\(844\) 0 0
\(845\) −8.57617 −0.295029
\(846\) 0 0
\(847\) −2.87584 −0.0988149
\(848\) 0 0
\(849\) 2.14399 0.0735816
\(850\) 0 0
\(851\) 6.00643 0.205898
\(852\) 0 0
\(853\) −11.5233 −0.394549 −0.197274 0.980348i \(-0.563209\pi\)
−0.197274 + 0.980348i \(0.563209\pi\)
\(854\) 0 0
\(855\) 2.71407 0.0928194
\(856\) 0 0
\(857\) 49.2779 1.68330 0.841651 0.540022i \(-0.181584\pi\)
0.841651 + 0.540022i \(0.181584\pi\)
\(858\) 0 0
\(859\) 14.3279 0.488863 0.244431 0.969667i \(-0.421399\pi\)
0.244431 + 0.969667i \(0.421399\pi\)
\(860\) 0 0
\(861\) 1.24164 0.0423150
\(862\) 0 0
\(863\) −15.8495 −0.539524 −0.269762 0.962927i \(-0.586945\pi\)
−0.269762 + 0.962927i \(0.586945\pi\)
\(864\) 0 0
\(865\) −70.6939 −2.40366
\(866\) 0 0
\(867\) 0.692763 0.0235275
\(868\) 0 0
\(869\) −0.574139 −0.0194763
\(870\) 0 0
\(871\) −24.0630 −0.815342
\(872\) 0 0
\(873\) 34.4238 1.16507
\(874\) 0 0
\(875\) −38.8682 −1.31399
\(876\) 0 0
\(877\) −50.8841 −1.71823 −0.859116 0.511780i \(-0.828986\pi\)
−0.859116 + 0.511780i \(0.828986\pi\)
\(878\) 0 0
\(879\) 13.0252 0.439329
\(880\) 0 0
\(881\) −39.7076 −1.33778 −0.668892 0.743359i \(-0.733231\pi\)
−0.668892 + 0.743359i \(0.733231\pi\)
\(882\) 0 0
\(883\) −19.0582 −0.641358 −0.320679 0.947188i \(-0.603911\pi\)
−0.320679 + 0.947188i \(0.603911\pi\)
\(884\) 0 0
\(885\) −2.48294 −0.0834631
\(886\) 0 0
\(887\) 27.3854 0.919512 0.459756 0.888045i \(-0.347937\pi\)
0.459756 + 0.888045i \(0.347937\pi\)
\(888\) 0 0
\(889\) −34.5826 −1.15986
\(890\) 0 0
\(891\) −15.7194 −0.526620
\(892\) 0 0
\(893\) −2.48962 −0.0833119
\(894\) 0 0
\(895\) −17.0858 −0.571114
\(896\) 0 0
\(897\) −3.04103 −0.101537
\(898\) 0 0
\(899\) 2.74345 0.0914991
\(900\) 0 0
\(901\) 14.2904 0.476082
\(902\) 0 0
\(903\) 22.9501 0.763730
\(904\) 0 0
\(905\) 46.8250 1.55652
\(906\) 0 0
\(907\) 17.9406 0.595709 0.297855 0.954611i \(-0.403729\pi\)
0.297855 + 0.954611i \(0.403729\pi\)
\(908\) 0 0
\(909\) 21.8259 0.723919
\(910\) 0 0
\(911\) 31.3761 1.03954 0.519769 0.854307i \(-0.326018\pi\)
0.519769 + 0.854307i \(0.326018\pi\)
\(912\) 0 0
\(913\) −35.9728 −1.19053
\(914\) 0 0
\(915\) 6.41285 0.212002
\(916\) 0 0
\(917\) 53.3658 1.76229
\(918\) 0 0
\(919\) −16.9055 −0.557660 −0.278830 0.960340i \(-0.589947\pi\)
−0.278830 + 0.960340i \(0.589947\pi\)
\(920\) 0 0
\(921\) −1.95765 −0.0645068
\(922\) 0 0
\(923\) −22.3419 −0.735391
\(924\) 0 0
\(925\) −42.1192 −1.38487
\(926\) 0 0
\(927\) 35.7524 1.17426
\(928\) 0 0
\(929\) 21.8038 0.715358 0.357679 0.933845i \(-0.383568\pi\)
0.357679 + 0.933845i \(0.383568\pi\)
\(930\) 0 0
\(931\) 2.25995 0.0740667
\(932\) 0 0
\(933\) 15.9080 0.520803
\(934\) 0 0
\(935\) −11.4721 −0.375179
\(936\) 0 0
\(937\) −34.3037 −1.12065 −0.560326 0.828272i \(-0.689324\pi\)
−0.560326 + 0.828272i \(0.689324\pi\)
\(938\) 0 0
\(939\) −12.1287 −0.395807
\(940\) 0 0
\(941\) 12.7394 0.415293 0.207647 0.978204i \(-0.433420\pi\)
0.207647 + 0.978204i \(0.433420\pi\)
\(942\) 0 0
\(943\) −0.526250 −0.0171370
\(944\) 0 0
\(945\) 52.2287 1.69900
\(946\) 0 0
\(947\) −44.6263 −1.45016 −0.725081 0.688664i \(-0.758197\pi\)
−0.725081 + 0.688664i \(0.758197\pi\)
\(948\) 0 0
\(949\) 1.38241 0.0448750
\(950\) 0 0
\(951\) −3.14231 −0.101896
\(952\) 0 0
\(953\) 15.3491 0.497206 0.248603 0.968605i \(-0.420028\pi\)
0.248603 + 0.968605i \(0.420028\pi\)
\(954\) 0 0
\(955\) 20.7467 0.671348
\(956\) 0 0
\(957\) −16.5293 −0.534317
\(958\) 0 0
\(959\) −34.3033 −1.10771
\(960\) 0 0
\(961\) −30.8646 −0.995631
\(962\) 0 0
\(963\) −21.1205 −0.680599
\(964\) 0 0
\(965\) −26.1908 −0.843113
\(966\) 0 0
\(967\) −0.432866 −0.0139200 −0.00696002 0.999976i \(-0.502215\pi\)
−0.00696002 + 0.999976i \(0.502215\pi\)
\(968\) 0 0
\(969\) −0.208166 −0.00668726
\(970\) 0 0
\(971\) −31.1896 −1.00092 −0.500462 0.865759i \(-0.666836\pi\)
−0.500462 + 0.865759i \(0.666836\pi\)
\(972\) 0 0
\(973\) −49.1625 −1.57608
\(974\) 0 0
\(975\) 21.3248 0.682940
\(976\) 0 0
\(977\) −15.5044 −0.496029 −0.248015 0.968756i \(-0.579778\pi\)
−0.248015 + 0.968756i \(0.579778\pi\)
\(978\) 0 0
\(979\) 52.0836 1.66460
\(980\) 0 0
\(981\) 22.2219 0.709492
\(982\) 0 0
\(983\) −6.89845 −0.220026 −0.110013 0.993930i \(-0.535089\pi\)
−0.110013 + 0.993930i \(0.535089\pi\)
\(984\) 0 0
\(985\) 48.9779 1.56057
\(986\) 0 0
\(987\) −21.8720 −0.696194
\(988\) 0 0
\(989\) −9.72702 −0.309301
\(990\) 0 0
\(991\) −1.14244 −0.0362907 −0.0181453 0.999835i \(-0.505776\pi\)
−0.0181453 + 0.999835i \(0.505776\pi\)
\(992\) 0 0
\(993\) −24.8498 −0.788584
\(994\) 0 0
\(995\) −72.0676 −2.28470
\(996\) 0 0
\(997\) −2.05148 −0.0649710 −0.0324855 0.999472i \(-0.510342\pi\)
−0.0324855 + 0.999472i \(0.510342\pi\)
\(998\) 0 0
\(999\) 20.5290 0.649510
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 \(a_p\))